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The Project Gutenberg eBook of The Phase Rule and Its
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Title: The Phase Rule and Its Applications
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E-text prepared by Juliet Sutherland, Keith Edkins,
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Applications
This eBook is for the use of anyone anywhere in the United States and
most other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms
of the Project Gutenberg License included with this eBook or online at
www.gutenberg.org. If you are not located in the United States, you
will have to check the laws of the country where you are located
before using this eBook.
Title: The Phase Rule and Its Applications
Author: Alexander Findlay
Release date: November 27, 2010 [eBook #34457]
Language: English
Other information and formats: www.gutenberg.org/ebooks/34457
Credits: E-text prepared by Juliet Sutherland, Keith Edkins, and the
Online Distributed Proofreading Team
*** START OF THE PROJECT GUTENBERG EBOOK THE PHASE
RULE AND ITS APPLICATIONS ***
E-text prepared by Juliet Sutherland, Keith Edkins,
and the Online Distributed Proofreading Team
(http://www.pgdp.net)
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TEXT-BOOKS of PHYSICAL CHEMISTRY.
Edited by SIR WILLIAM RAMSAY, K.C.B., F.R.S., D.Sc.
STOICHIOMETRY. By Sydney Young, D.Sc., F.R.S., Professor of
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Page 6
LONGMANS, GREEN, AND CO.
39 PATERNOSTER ROW, LONDON
NEW YORK, BOMBAY, AND CALCUTTA
THE PHASE RULE
AND ITS APPLICATIONS
BY
ALEX. FINDLAY, M.A., Ph.D., D.Sc.
LECTURER ON PHYSICAL CHEMISTRY, UNIVERSITY OF
BIRMINGHAM
WITH ONE HUNDRED AND THIRTY-FOUR FIGURES
IN THE TEXT
THIRD IMPRESSION
LONGMANS, GREEN, AND CO.
39 PATERNOSTER ROW, LONDON
NEW YORK, BOMBAY, AND CALCUTTA
1908
All rights reserved
39 PATERNOSTER ROW, LONDON
NEW YORK, BOMBAY, AND CALCUTTA
THE PHASE RULE
AND ITS APPLICATIONS
BY
ALEX. FINDLAY, M.A., Ph.D., D.Sc.
LECTURER ON PHYSICAL CHEMISTRY, UNIVERSITY OF
BIRMINGHAM
WITH ONE HUNDRED AND THIRTY-FOUR FIGURES
IN THE TEXT
THIRD IMPRESSION
LONGMANS, GREEN, AND CO.
39 PATERNOSTER ROW, LONDON
NEW YORK, BOMBAY, AND CALCUTTA
1908
All rights reserved
Page 7
DEDICATED
TO
FRANCIS ROBERT JAPP, LL.D., F.R.S.
PROFESSOR OF CHEMISTRY, UNIVERSITY OF ABERDEEN,
IN GRATITUDE FOR EARLY TRAINING
AND ADVICE
PREFACE TO THE SECOND EDITION.
During the two years which have elapsed since the first edition of this book
appeared, the study of chemical equilibria has been prosecuted with
considerable activity, and valuable additions have been made to our
knowledge in several departments of this subject. In view of the scope of
the present work, it has been, of course, impossible to incorporate all that
has been done; but several new sections have been inserted, notably those
on the study of basic salts; the interpretation of cooling curves, and the
determination of the composition of solid phases without analysis; the
equilibria between iron, carbon monoxide, and carbon dioxide, which are of
importance in connection with the processes occurring in the blast furnace;
and the Phase Rule study of the ammonia-soda process. I have also
incorporated a short section on the reciprocal salt-pair barium carbonate—
potassium sulphate, which had been written for the German edition of this
book by the late Professor W. Meyerhoffer. The section on the iron-carbon
alloys, which in the first edition was somewhat unsatisfactory, has been
rewritten.
A. F.
September, 1906.
TO
FRANCIS ROBERT JAPP, LL.D., F.R.S.
PROFESSOR OF CHEMISTRY, UNIVERSITY OF ABERDEEN,
IN GRATITUDE FOR EARLY TRAINING
AND ADVICE
PREFACE TO THE SECOND EDITION.
During the two years which have elapsed since the first edition of this book
appeared, the study of chemical equilibria has been prosecuted with
considerable activity, and valuable additions have been made to our
knowledge in several departments of this subject. In view of the scope of
the present work, it has been, of course, impossible to incorporate all that
has been done; but several new sections have been inserted, notably those
on the study of basic salts; the interpretation of cooling curves, and the
determination of the composition of solid phases without analysis; the
equilibria between iron, carbon monoxide, and carbon dioxide, which are of
importance in connection with the processes occurring in the blast furnace;
and the Phase Rule study of the ammonia-soda process. I have also
incorporated a short section on the reciprocal salt-pair barium carbonate—
potassium sulphate, which had been written for the German edition of this
book by the late Professor W. Meyerhoffer. The section on the iron-carbon
alloys, which in the first edition was somewhat unsatisfactory, has been
rewritten.
A. F.
September, 1906.
Page 8
PREFACE
Although we are indebted to the late Professor Willard Gibbs for the first
enunciation of the Phase Rule, it was not till 1887 that its practical
applicability to the study of Chemical Equilibria was made apparent. In that
year Roozeboom disclosed the great generalization, which for upwards of
ten years had remained hidden and unknown save to a very few, by
stripping from it the garb of abstract Mathematics in which it had been
clothed by its first discoverer. The Phase Rule was thus made generally
accessible; and its adoption by Roozeboom as the basis of classification of
the different cases of chemical equilibrium then known established its
value, not only as a means of co-ordinating the large number of isolated
cases of equilibrium and of giving a deeper insight into the relationships
existing between the different systems, but also as a guide in the
investigation of unknown systems.
While the revelation of the principle embedded in the Phase Rule is
primarily due to Roozeboom, it should not be forgotten that, some years
previously, van't Hoff, in ignorance of the work of Willard Gibbs, had
enunciated his "law of the incompatibility of condensed systems," which in
some respects coincides with the Phase Rule; and it is only owing to the
more general applicability of the latter that the very important
generalization of van't Hoff has been somewhat lost sight of.
The exposition of the Phase Rule and its applications given in the following
pages has been made entirely non-mathematical, the desire having been to
explain as clearly as possible the principles underlying the Phase Rule, and
to illustrate their application to the classification and investigation of
equilibria, by means of a number of cases actually studied. While it has
been sought to make the treatment sufficiently elementary to be understood
by the student just commencing the study of chemical equilibria, an attempt
has been made to advance his knowledge to such a stage as to enable him to
study with profit the larger works on the subject, and to follow with
intelligence the course of investigation in this department of Physical
Chemistry. It is also hoped that the volume may be of use, not only to the
Although we are indebted to the late Professor Willard Gibbs for the first
enunciation of the Phase Rule, it was not till 1887 that its practical
applicability to the study of Chemical Equilibria was made apparent. In that
year Roozeboom disclosed the great generalization, which for upwards of
ten years had remained hidden and unknown save to a very few, by
stripping from it the garb of abstract Mathematics in which it had been
clothed by its first discoverer. The Phase Rule was thus made generally
accessible; and its adoption by Roozeboom as the basis of classification of
the different cases of chemical equilibrium then known established its
value, not only as a means of co-ordinating the large number of isolated
cases of equilibrium and of giving a deeper insight into the relationships
existing between the different systems, but also as a guide in the
investigation of unknown systems.
While the revelation of the principle embedded in the Phase Rule is
primarily due to Roozeboom, it should not be forgotten that, some years
previously, van't Hoff, in ignorance of the work of Willard Gibbs, had
enunciated his "law of the incompatibility of condensed systems," which in
some respects coincides with the Phase Rule; and it is only owing to the
more general applicability of the latter that the very important
generalization of van't Hoff has been somewhat lost sight of.
The exposition of the Phase Rule and its applications given in the following
pages has been made entirely non-mathematical, the desire having been to
explain as clearly as possible the principles underlying the Phase Rule, and
to illustrate their application to the classification and investigation of
equilibria, by means of a number of cases actually studied. While it has
been sought to make the treatment sufficiently elementary to be understood
by the student just commencing the study of chemical equilibria, an attempt
has been made to advance his knowledge to such a stage as to enable him to
study with profit the larger works on the subject, and to follow with
intelligence the course of investigation in this department of Physical
Chemistry. It is also hoped that the volume may be of use, not only to the
Page 9
student of Physical Chemistry, or of the other branches of that science, but
also to the student of Metallurgy and of Geology, for whom an acquaintance
with at least the principles of the Phase Rule is becoming increasingly
important.
In writing the following account of the Phase Rule, it is scarcely necessary
to say that I have been greatly indebted to the larger works on Chemical
Equilibria by Ostwald ("Lehrbuch"), Roozeboom ("Die Heterogenen
Gleichgewichte"), and Bancroft ("The Phase Rule"); and in the case of the
first-named, to the inspiration also of personal teaching. My indebtedness to
these and other authors I have indicated in the following pages.
In conclusion, I would express my thanks to Sir William Ramsay, whose
guidance and counsel have been constantly at my disposal; and to my
colleagues, Dr. T. Slater Price and Dr. A. McKenzie, for their friendly
criticism and advice. To Messrs. J. N. Friend, M.Sc., and W. E. S. Turner,
B.Sc., I am also indebted for their assistance in reading the proof-sheets.
A. F.
November, 1903.
CONTENTS
PAGE
CHAPTER I
Introduction 1
General, I. Homogeneous and heterogeneous equilibrium, 5.
Real and apparent equilibrium, 5.
CHAPTER II
The Phase Rule 7
also to the student of Metallurgy and of Geology, for whom an acquaintance
with at least the principles of the Phase Rule is becoming increasingly
important.
In writing the following account of the Phase Rule, it is scarcely necessary
to say that I have been greatly indebted to the larger works on Chemical
Equilibria by Ostwald ("Lehrbuch"), Roozeboom ("Die Heterogenen
Gleichgewichte"), and Bancroft ("The Phase Rule"); and in the case of the
first-named, to the inspiration also of personal teaching. My indebtedness to
these and other authors I have indicated in the following pages.
In conclusion, I would express my thanks to Sir William Ramsay, whose
guidance and counsel have been constantly at my disposal; and to my
colleagues, Dr. T. Slater Price and Dr. A. McKenzie, for their friendly
criticism and advice. To Messrs. J. N. Friend, M.Sc., and W. E. S. Turner,
B.Sc., I am also indebted for their assistance in reading the proof-sheets.
A. F.
November, 1903.
CONTENTS
PAGE
CHAPTER I
Introduction 1
General, I. Homogeneous and heterogeneous equilibrium, 5.
Real and apparent equilibrium, 5.
CHAPTER II
The Phase Rule 7
Page 10
Phases, 8. Components, 10. Degree of freedom. Variability of a
system, 14. The Phase Rule, 16. Classification of systems
according to the Phase Rule, 17. Deduction of the Phase Rule,
18.
CHAPTER III
Typical Systems of One Component 21
A. Water. Equilibrium between liquid and vapour. Vaporization
curve, 21. Upper limit of vaporization curve, 23. Sublimation
curve of ice, 24. Equilibrium between ice and water. Curve of
fusion, 25. Equilibrium between ice, water, and vapour. The
triple point, 27. Bivariant systems of water, 29. Supercooled
water. Metastable state, 30. Other systems of the substance
water, 32. B. Sulphur, 33. Polymorphism, 33. Sulphur, 34.
Triple point—Rhombic and monoclinic sulphur and vapour.
Transition point, 34. Condensed systems, 36. Suspended
transformation, 37. Transition curve—Rhombic and monoclinic
sulphur, 37. Triple point—Monoclinic sulphur, liquid, and
vapour. Melting point of monoclinic sulphur, 38. Triple point—
Rhombic and monoclinic sulphur and liquid, 38. Triple point—
Rhombic sulphur, liquid, and vapour. Metastable triple point,
38. Fusion curve of rhombic sulphur, 39. Bivariant systems, 39.
C. Tin, 41. Transition point, 41. Enantiotropy and monotropy,
44. D. Phosphorus, 46. Enantiotropy combined with monotropy,
51. E. Liquid Crystals, 51. Phenomena observed, 51. Nature of
liquid crystals, 52. Equilibrium relations in the case of liquid
crystals, 53.
CHAPTER IV
General Summary 55
Triple point, 55. Theorems of van't Hoff and of Le Chatelier, 57.
Changes at the triple point, 58. Triple point solid—solid—
vapour, 62. Sublimation and vaporization curves, 63. Fusion
curve—Transition curve, 66. Suspended transformation.
Metastable equilibria, 69. Velocity of transformation, 70. Law of
successive reactions, 73.
system, 14. The Phase Rule, 16. Classification of systems
according to the Phase Rule, 17. Deduction of the Phase Rule,
18.
CHAPTER III
Typical Systems of One Component 21
A. Water. Equilibrium between liquid and vapour. Vaporization
curve, 21. Upper limit of vaporization curve, 23. Sublimation
curve of ice, 24. Equilibrium between ice and water. Curve of
fusion, 25. Equilibrium between ice, water, and vapour. The
triple point, 27. Bivariant systems of water, 29. Supercooled
water. Metastable state, 30. Other systems of the substance
water, 32. B. Sulphur, 33. Polymorphism, 33. Sulphur, 34.
Triple point—Rhombic and monoclinic sulphur and vapour.
Transition point, 34. Condensed systems, 36. Suspended
transformation, 37. Transition curve—Rhombic and monoclinic
sulphur, 37. Triple point—Monoclinic sulphur, liquid, and
vapour. Melting point of monoclinic sulphur, 38. Triple point—
Rhombic and monoclinic sulphur and liquid, 38. Triple point—
Rhombic sulphur, liquid, and vapour. Metastable triple point,
38. Fusion curve of rhombic sulphur, 39. Bivariant systems, 39.
C. Tin, 41. Transition point, 41. Enantiotropy and monotropy,
44. D. Phosphorus, 46. Enantiotropy combined with monotropy,
51. E. Liquid Crystals, 51. Phenomena observed, 51. Nature of
liquid crystals, 52. Equilibrium relations in the case of liquid
crystals, 53.
CHAPTER IV
General Summary 55
Triple point, 55. Theorems of van't Hoff and of Le Chatelier, 57.
Changes at the triple point, 58. Triple point solid—solid—
vapour, 62. Sublimation and vaporization curves, 63. Fusion
curve—Transition curve, 66. Suspended transformation.
Metastable equilibria, 69. Velocity of transformation, 70. Law of
successive reactions, 73.
Page 11
CHAPTER V
Systems of Two Components—Phenomena of Dissociation 76
Different systems of two components, 77. Phenomena of
Dissociation. Bivariant systems, 79. Univariant systems, 80.
Ammonia compounds of metal chlorides, 82. Salts with water of
crystallization, 85. Efflorescence, 86. Indefiniteness of the
vapour pressure of a hydrate, 87. Suspended transformation, 89.
Range of existence of hydrates, 90. Constancy of vapour
pressure and the formation of compounds, 90. Measurement of
the vapour pressure of hydrates, 91.
CHAPTER VI
Solutions 92
Definition, 92. Solutions of Gases in Liquids, 93. Solutions of
Liquids in Liquids, 95. Partial or limited miscibility, 96. Phenol
and water, 97. Methylethylketone and water, 100. Triethylamine
and water, 101. General form of concentration-temperature
curve, 101. Pressure-concentration diagram, 102. Complete
miscibility, 104. Pressure-concentration diagram, 104.
CHAPTER VII
Solutions of Solids in Liquids, only One of the Components being
106
Volatile
General, 106. The saturated solution, 108. Form of the solubility
curve, 108. A. Anhydrous Salt and Water. The solubility
curve, 111. Suspended transformation and supersaturation, 113.
Solubility curve at higher temperatures, 114. (1) Complete
miscibility of the fused components. Ice as solid phase, 116.
Cryohydrates, 117. Changes at the quadruple point, 119.
Freezing mixtures, 120. (2) Partial miscibility of the fused
components. Supersaturation, 124. Pressure-temperature
diagram, 126. Vapour pressure of solid—solution—vapour, 126.
Other univariant systems, 127. Bivariant systems, 129.
Deliquescence, 130. Separation of salt on evaporation, 130.
General summary, 131.
Systems of Two Components—Phenomena of Dissociation 76
Different systems of two components, 77. Phenomena of
Dissociation. Bivariant systems, 79. Univariant systems, 80.
Ammonia compounds of metal chlorides, 82. Salts with water of
crystallization, 85. Efflorescence, 86. Indefiniteness of the
vapour pressure of a hydrate, 87. Suspended transformation, 89.
Range of existence of hydrates, 90. Constancy of vapour
pressure and the formation of compounds, 90. Measurement of
the vapour pressure of hydrates, 91.
CHAPTER VI
Solutions 92
Definition, 92. Solutions of Gases in Liquids, 93. Solutions of
Liquids in Liquids, 95. Partial or limited miscibility, 96. Phenol
and water, 97. Methylethylketone and water, 100. Triethylamine
and water, 101. General form of concentration-temperature
curve, 101. Pressure-concentration diagram, 102. Complete
miscibility, 104. Pressure-concentration diagram, 104.
CHAPTER VII
Solutions of Solids in Liquids, only One of the Components being
106
Volatile
General, 106. The saturated solution, 108. Form of the solubility
curve, 108. A. Anhydrous Salt and Water. The solubility
curve, 111. Suspended transformation and supersaturation, 113.
Solubility curve at higher temperatures, 114. (1) Complete
miscibility of the fused components. Ice as solid phase, 116.
Cryohydrates, 117. Changes at the quadruple point, 119.
Freezing mixtures, 120. (2) Partial miscibility of the fused
components. Supersaturation, 124. Pressure-temperature
diagram, 126. Vapour pressure of solid—solution—vapour, 126.
Other univariant systems, 127. Bivariant systems, 129.
Deliquescence, 130. Separation of salt on evaporation, 130.
General summary, 131.
Page 12
CHAPTER VIII
Solutions of Solids in Liquids, only One of the Components being
133
Volatile
B. Hydrated Salt and Water, (1) The compounds formed do
not have a definite melting point. Concentration-temperature
diagram, 133. Sodium sulphate and water, 134. Suspended
transformation, 137. Dehydration by means of anhydrous
sodium sulphate, 138. Pressure-temperature diagram, 138. (2)
The compounds formed have a definite melting point. Solubility
curve of calcium chloride hexahydrate, 145. Pressure-
temperature diagram, 149. The indifferent point, 150. The
hydrates of ferric chloride, 151. Suspended transformation, 155.
Evaporation of solutions at constant temperature, 155.
Inevaporable solutions, 157. Illustration, 158.
CHAPTER IX
Equilibria between Two Volatile Components 161
General, 161. Iodine and chlorine, 161. Concentration-
temperature diagram, 162. Pressure-temperature diagram, 165.
Bivariant systems, 167. Sulphur dioxide and water, 169.
Pressure-temperature diagram, 170. Bivariant systems, 173.
CHAPTER X
Solid Solutions. Mixed Crystals 175
General, 175. Solution of gases in solids, 176. Palladium and
hydrogen, 178. Solutions of solids in solids. Mixed crystals,
180. Formation of mixed crystals of isomorphous substances,
182. I. The two components can form an unbroken series of
mixed crystals. (a) The freezing points of all mixtures lie
between the freezing points of the pure components. Examples,
183. Melting-point curve, 183. (b) The freezing-point curve
passes through a maximum. Example, 186. (c) The freezing-
point curve passes through a minimum. Example, 188.
Fractional crystallization of mixed crystals, 188. II. The two
components do not form a continuous series of mixed crystals.
(a) The freezing-point curve exhibits a transition point, 190.
Solutions of Solids in Liquids, only One of the Components being
133
Volatile
B. Hydrated Salt and Water, (1) The compounds formed do
not have a definite melting point. Concentration-temperature
diagram, 133. Sodium sulphate and water, 134. Suspended
transformation, 137. Dehydration by means of anhydrous
sodium sulphate, 138. Pressure-temperature diagram, 138. (2)
The compounds formed have a definite melting point. Solubility
curve of calcium chloride hexahydrate, 145. Pressure-
temperature diagram, 149. The indifferent point, 150. The
hydrates of ferric chloride, 151. Suspended transformation, 155.
Evaporation of solutions at constant temperature, 155.
Inevaporable solutions, 157. Illustration, 158.
CHAPTER IX
Equilibria between Two Volatile Components 161
General, 161. Iodine and chlorine, 161. Concentration-
temperature diagram, 162. Pressure-temperature diagram, 165.
Bivariant systems, 167. Sulphur dioxide and water, 169.
Pressure-temperature diagram, 170. Bivariant systems, 173.
CHAPTER X
Solid Solutions. Mixed Crystals 175
General, 175. Solution of gases in solids, 176. Palladium and
hydrogen, 178. Solutions of solids in solids. Mixed crystals,
180. Formation of mixed crystals of isomorphous substances,
182. I. The two components can form an unbroken series of
mixed crystals. (a) The freezing points of all mixtures lie
between the freezing points of the pure components. Examples,
183. Melting-point curve, 183. (b) The freezing-point curve
passes through a maximum. Example, 186. (c) The freezing-
point curve passes through a minimum. Example, 188.
Fractional crystallization of mixed crystals, 188. II. The two
components do not form a continuous series of mixed crystals.
(a) The freezing-point curve exhibits a transition point, 190.
Page 13
Example, 190. (b) The freezing-point curve exhibits a eutectic
point, 191. Examples, 192. Changes in mixed crystals with the
temperature, 192.
CHAPTER XI
Equilibrium between Dynamic Isomerides 195
Temperature-concentration diagram, 196. Transformation of the
unstable into the stable form, 201. Examples, 203.
Benzaldoximes, 203. Acetaldehyde and paraldehyde, 204.
CHAPTER XII
Summary.—Application of the Phase Rule to the Study of Systems
207
of Two Components
Summary of the different systems of two components, 208. (1)
Organic compounds, 212. (2) Optically active substances, 213.
Examples, 216. Transformations, 217. (3) Alloys, 220. Iron—
carbon alloys, 223. Determination of the composition of
compounds without analysis, 228. Formation of minerals, 232.
CHAPTER XIII
Systems of Three Components 234
General, 234. Graphic representation, 235.
CHAPTER XIV
Solutions of Liquids in Liquids 240
1. The three components form only one pair of partially miscible
liquids, 240. Retrograde solubility, 245. The influence of
temperature, 247. 2. The three components can form two pairs
of partially miscible liquids, 249. 3. The three components form
three pairs of partially miscible liquids, 251.
CHAPTER XV
Presence of Solid Phases 253
A. The ternary eutectic point, 253. Formation of compounds,
255. B. Equilibria at higher temperatures. Formation of double
salts, 258. Transition point, 258. Vapour pressure. Quintuple
point, 261. Solubility curves at the transition point, 264.
point, 191. Examples, 192. Changes in mixed crystals with the
temperature, 192.
CHAPTER XI
Equilibrium between Dynamic Isomerides 195
Temperature-concentration diagram, 196. Transformation of the
unstable into the stable form, 201. Examples, 203.
Benzaldoximes, 203. Acetaldehyde and paraldehyde, 204.
CHAPTER XII
Summary.—Application of the Phase Rule to the Study of Systems
207
of Two Components
Summary of the different systems of two components, 208. (1)
Organic compounds, 212. (2) Optically active substances, 213.
Examples, 216. Transformations, 217. (3) Alloys, 220. Iron—
carbon alloys, 223. Determination of the composition of
compounds without analysis, 228. Formation of minerals, 232.
CHAPTER XIII
Systems of Three Components 234
General, 234. Graphic representation, 235.
CHAPTER XIV
Solutions of Liquids in Liquids 240
1. The three components form only one pair of partially miscible
liquids, 240. Retrograde solubility, 245. The influence of
temperature, 247. 2. The three components can form two pairs
of partially miscible liquids, 249. 3. The three components form
three pairs of partially miscible liquids, 251.
CHAPTER XV
Presence of Solid Phases 253
A. The ternary eutectic point, 253. Formation of compounds,
255. B. Equilibria at higher temperatures. Formation of double
salts, 258. Transition point, 258. Vapour pressure. Quintuple
point, 261. Solubility curves at the transition point, 264.
Page 14
Decomposition of the double salt by water, 267. Transition
interval, 270. Summary, 271.
CHAPTER XVI
Isothermal Curves and the Space Model 272
Non-formation of double salts, 272. Formation of double salt,
273. Transition interval, 277. Isothermal evaporation, 278.
Crystallization of double salt from solutions containing excess
of one component, 280. Formation of mixed crystals, 281.
Application to the characterization of racemates, 282.
Representation in space. Space model for carnallite, 284.
Summary and numerical data, 287. Ferric chloride—hydrogen
chloride—water, 290. Ternary systems, 291. The isothermal
curves, 294. Basic Salts, 296. Bi2O3—N2O5—H2O, 298. Basic
mercury salts, 301. Indirect determination of the composition of
the solid phase, 302.
CHAPTER XVII
Absence of Liquid Phase 305
Iron, carbon monoxide, carbon dioxide, 305.
CHAPTER XVIII
Systems of Four Components 312
Reciprocal salt-pairs. Choice of components, 313. Transition
point, 314. Formation of double salts, 315. Transition interval,
315. Graphic representation, 316. Example, 317. Ammonia-soda
process, 320. Preparation of barium nitrite, 327. Barium
carbonate and potassium sulphate, 328.
APPENDIX
Experimental Determination of the Transition Point 331
I. The dilatometric method, 331. II. Measurement of the vapour
pressure, 334. III. Solubility measurements, 335. IV.
Thermometric method, 337. V. Optical method, 338. VI.
Electrical methods, 338.
interval, 270. Summary, 271.
CHAPTER XVI
Isothermal Curves and the Space Model 272
Non-formation of double salts, 272. Formation of double salt,
273. Transition interval, 277. Isothermal evaporation, 278.
Crystallization of double salt from solutions containing excess
of one component, 280. Formation of mixed crystals, 281.
Application to the characterization of racemates, 282.
Representation in space. Space model for carnallite, 284.
Summary and numerical data, 287. Ferric chloride—hydrogen
chloride—water, 290. Ternary systems, 291. The isothermal
curves, 294. Basic Salts, 296. Bi2O3—N2O5—H2O, 298. Basic
mercury salts, 301. Indirect determination of the composition of
the solid phase, 302.
CHAPTER XVII
Absence of Liquid Phase 305
Iron, carbon monoxide, carbon dioxide, 305.
CHAPTER XVIII
Systems of Four Components 312
Reciprocal salt-pairs. Choice of components, 313. Transition
point, 314. Formation of double salts, 315. Transition interval,
315. Graphic representation, 316. Example, 317. Ammonia-soda
process, 320. Preparation of barium nitrite, 327. Barium
carbonate and potassium sulphate, 328.
APPENDIX
Experimental Determination of the Transition Point 331
I. The dilatometric method, 331. II. Measurement of the vapour
pressure, 334. III. Solubility measurements, 335. IV.
Thermometric method, 337. V. Optical method, 338. VI.
Electrical methods, 338.
Page 15
Name Index 341
Subject Index 345
Subject Index 345
Page 16
THE PHASE RULE
CHAPTER I
INTRODUCTION
General.—Before proceeding to the more systematic treatment of the
Phase Rule, it may, perhaps, be not amiss to give first a brief forecast of the
nature of the subject we are about to study, in order that we may gain some
idea of what the Phase Rule is, of the kind of problem which it enables us to
solve, and of the scope of its application.
It has long been known that if water is placed in a closed, exhausted space,
vapour is given off and a certain pressure is created in the enclosing vessel.
Thus, when water is placed in the Torricellian vacuum of the barometer, the
mercury is depressed, and the amount of depression increases as the
temperature is raised. But, although the pressure of the vapour increases as
the temperature rises, its value at any given temperature is constant, no
matter whether the amount of water present or the volume of the vapour is
great or small; if the pressure on the vapour is altered while the temperature
is maintained constant, either the water or the vapour will ultimately
disappear; the former by evaporation, the latter by condensation. At any
given temperature within certain limits, therefore, water and vapour can
exist permanently in contact with one another—or, as it is said, be in
equilibrium with one another—only when the pressure has a certain definite
value. The same law of constancy of vapour pressure at a given
temperature, quite irrespective of the volumes of liquid and vapour,[1] holds
good also in the case of alcohol, ether, benzene, and other pure liquids. It is,
therefore, not unnatural to ask the question, Does it hold good for all
liquids? Is it valid, for example, in the case of solutions?
We can find the answer to these questions by studying the behaviour of a
solution—say, a solution of common salt in water—when placed in the
Torricellian vacuum. In this case, also, it is observed that the pressure of the
vapour increases as the temperature is raised, but the pressure is no longer
CHAPTER I
INTRODUCTION
General.—Before proceeding to the more systematic treatment of the
Phase Rule, it may, perhaps, be not amiss to give first a brief forecast of the
nature of the subject we are about to study, in order that we may gain some
idea of what the Phase Rule is, of the kind of problem which it enables us to
solve, and of the scope of its application.
It has long been known that if water is placed in a closed, exhausted space,
vapour is given off and a certain pressure is created in the enclosing vessel.
Thus, when water is placed in the Torricellian vacuum of the barometer, the
mercury is depressed, and the amount of depression increases as the
temperature is raised. But, although the pressure of the vapour increases as
the temperature rises, its value at any given temperature is constant, no
matter whether the amount of water present or the volume of the vapour is
great or small; if the pressure on the vapour is altered while the temperature
is maintained constant, either the water or the vapour will ultimately
disappear; the former by evaporation, the latter by condensation. At any
given temperature within certain limits, therefore, water and vapour can
exist permanently in contact with one another—or, as it is said, be in
equilibrium with one another—only when the pressure has a certain definite
value. The same law of constancy of vapour pressure at a given
temperature, quite irrespective of the volumes of liquid and vapour,[1] holds
good also in the case of alcohol, ether, benzene, and other pure liquids. It is,
therefore, not unnatural to ask the question, Does it hold good for all
liquids? Is it valid, for example, in the case of solutions?
We can find the answer to these questions by studying the behaviour of a
solution—say, a solution of common salt in water—when placed in the
Torricellian vacuum. In this case, also, it is observed that the pressure of the
vapour increases as the temperature is raised, but the pressure is no longer
Page 17
independent of the volume; as the volume increases, the pressure slowly
diminishes. If, however, solid salt is present in contact with the solution,
then the pressure again becomes constant at constant temperature, even
when the volume of the vapour is altered. As we see, therefore, solutions do
not behave in the same way as pure liquids.
Moreover, on lowering the temperature of water, a point is reached at which
ice begins to separate out; and if heat be now added to the system or
withdrawn from it, no change will take place in the temperature or vapour
pressure of the latter until either the ice or the water has disappeared.[2] Ice,
water, and vapour, therefore, can be in equilibrium with one another only at
one definite temperature and one definite pressure.
In the case of a solution of common salt, however, we may have ice in
contact with the solution at different temperatures and pressures. Further, it
is possible to have a solution in equilibrium not only with anhydrous salt
(NaCl), but also with the hydrated salt (NaCl, 2H2O), as well as with ice,
and the question, therefore, arises: Is it possible to state in a general manner
the conditions under which such different systems can exist in equilibrium;
or to obtain some insight into the relations which exist between pure liquids
and solutions? As we shall learn, the Phase Rule enables us to give an
answer to this question.
The preceding examples belong to the class of so-called "physical"
equilibria, or equilibria depending on changes in the physical state. More
than a hundred years ago, however, it was shown by Wenzel and Berthollet
that "chemical" equilibria can also exist; that chemical reactions do not
always take place completely in one direction as indicated by the usual
chemical equation, but that before the reacting substances are all used up
the reaction ceases, and there is a condition of equilibrium between the
reacting substances and the products of reaction. As an example of this,
there may be taken the process of lime-burning, which depends on the fact
that when calcium carbonate is heated, carbon dioxide is given off and
quicklime is produced. If the carbonate is heated in a closed vessel it will be
found, however, not to undergo entire decomposition. When the pressure of
the carbon dioxide reaches a certain value (which is found to depend on the
temperature), decomposition ceases, and calcium carbonate exists side by
side with calcium oxide and carbon dioxide. Moreover, at any given
diminishes. If, however, solid salt is present in contact with the solution,
then the pressure again becomes constant at constant temperature, even
when the volume of the vapour is altered. As we see, therefore, solutions do
not behave in the same way as pure liquids.
Moreover, on lowering the temperature of water, a point is reached at which
ice begins to separate out; and if heat be now added to the system or
withdrawn from it, no change will take place in the temperature or vapour
pressure of the latter until either the ice or the water has disappeared.[2] Ice,
water, and vapour, therefore, can be in equilibrium with one another only at
one definite temperature and one definite pressure.
In the case of a solution of common salt, however, we may have ice in
contact with the solution at different temperatures and pressures. Further, it
is possible to have a solution in equilibrium not only with anhydrous salt
(NaCl), but also with the hydrated salt (NaCl, 2H2O), as well as with ice,
and the question, therefore, arises: Is it possible to state in a general manner
the conditions under which such different systems can exist in equilibrium;
or to obtain some insight into the relations which exist between pure liquids
and solutions? As we shall learn, the Phase Rule enables us to give an
answer to this question.
The preceding examples belong to the class of so-called "physical"
equilibria, or equilibria depending on changes in the physical state. More
than a hundred years ago, however, it was shown by Wenzel and Berthollet
that "chemical" equilibria can also exist; that chemical reactions do not
always take place completely in one direction as indicated by the usual
chemical equation, but that before the reacting substances are all used up
the reaction ceases, and there is a condition of equilibrium between the
reacting substances and the products of reaction. As an example of this,
there may be taken the process of lime-burning, which depends on the fact
that when calcium carbonate is heated, carbon dioxide is given off and
quicklime is produced. If the carbonate is heated in a closed vessel it will be
found, however, not to undergo entire decomposition. When the pressure of
the carbon dioxide reaches a certain value (which is found to depend on the
temperature), decomposition ceases, and calcium carbonate exists side by
side with calcium oxide and carbon dioxide. Moreover, at any given
Page 18
temperature the pressure is constant and independent of the amount of
carbonate or oxide present, or of the volume of the gas; nor does the
addition of either of the products of dissociation, carbon dioxide or calcium
oxide, cause any change in the equilibrium. Here, then, we see that,
although there are three different substances present, and although the
equilibrium is no longer due to physical, but to chemical change, it
nevertheless obeys the same law as the vapour pressure of a pure volatile
liquid, such as water.
It might be supposed, now, that this behaviour would be shown by other
dissociating substances, e.g. ammonium chloride. When this substance is
heated it dissociates into ammonia and hydrogen chloride, and at any given
temperature the pressure of these gases is constant,[3] and is independent of
the amounts of solid and gas present. So far, therefore, ammonium chloride
behaves like calcium carbonate. If, however, one of the products of
dissociation be added to the system, it is found that the pressure is no longer
constant at a given temperature, but varies with the amount of gas,
ammonia or hydrogen chloride, which is added. In the case of certain
dissociating substances, therefore, addition of one of the products of
dissociation alters the equilibrium, while in other cases it does not. With the
help of the Phase Rule, however, a general interpretation of this difference
of behaviour can be given—an interpretation which can be applied not only
to the two cases cited, but to all cases of dissociation.
Again, it is well known that sulphur exists in two different crystalline
forms, octahedral and prismatic, each of which melts at a different
temperature. The problem here is, therefore, more complicated than in the
case of ice, for there is now a possibility not only of one solid form, but of
two different forms of the same substance existing in contact with liquid.
What are the conditions under which these two forms can exist in contact
with liquid, either singly or together, and under what conditions can the two
solid forms exist together without the presence of liquid sulphur? To these
questions an answer can also be given with the help of the Phase Rule.
These cases are, however, comparatively simple; but when we come, for
instance, to study the conditions under which solutions are formed, and
especially when we inquire into the solubility relations of salts capable of
forming, perhaps, a series of crystalline hydrates; and when we seek to
carbonate or oxide present, or of the volume of the gas; nor does the
addition of either of the products of dissociation, carbon dioxide or calcium
oxide, cause any change in the equilibrium. Here, then, we see that,
although there are three different substances present, and although the
equilibrium is no longer due to physical, but to chemical change, it
nevertheless obeys the same law as the vapour pressure of a pure volatile
liquid, such as water.
It might be supposed, now, that this behaviour would be shown by other
dissociating substances, e.g. ammonium chloride. When this substance is
heated it dissociates into ammonia and hydrogen chloride, and at any given
temperature the pressure of these gases is constant,[3] and is independent of
the amounts of solid and gas present. So far, therefore, ammonium chloride
behaves like calcium carbonate. If, however, one of the products of
dissociation be added to the system, it is found that the pressure is no longer
constant at a given temperature, but varies with the amount of gas,
ammonia or hydrogen chloride, which is added. In the case of certain
dissociating substances, therefore, addition of one of the products of
dissociation alters the equilibrium, while in other cases it does not. With the
help of the Phase Rule, however, a general interpretation of this difference
of behaviour can be given—an interpretation which can be applied not only
to the two cases cited, but to all cases of dissociation.
Again, it is well known that sulphur exists in two different crystalline
forms, octahedral and prismatic, each of which melts at a different
temperature. The problem here is, therefore, more complicated than in the
case of ice, for there is now a possibility not only of one solid form, but of
two different forms of the same substance existing in contact with liquid.
What are the conditions under which these two forms can exist in contact
with liquid, either singly or together, and under what conditions can the two
solid forms exist together without the presence of liquid sulphur? To these
questions an answer can also be given with the help of the Phase Rule.
These cases are, however, comparatively simple; but when we come, for
instance, to study the conditions under which solutions are formed, and
especially when we inquire into the solubility relations of salts capable of
forming, perhaps, a series of crystalline hydrates; and when we seek to
Page 19
determine the conditions under which these different forms can exist in
contact with the solution, the problem becomes more complicated, and the
necessity of some general guide to the elucidation of the behaviour of these
different systems becomes more urgent.
It is, now, to the study of such physical and chemical equilibria as those
above-mentioned that the Phase Rule finds application; to the study, also, of
the conditions regulating, for example, the formation of alloys from
mixtures of the fused metals, or of the various salts of the Stassfurt
deposits; the behaviour of iron and carbon in the formation of steel and the
separation of different minerals from a fused rock-mass.[4] With the help of
the Phase Rule we can group together into classes the large number of
different isolated cases of systems in equilibrium; with its aid we are able to
state, in a general manner at least, the conditions under which a system can
be in equilibrium, and by its means we can gain some insight into the
relations existing between different kinds of systems.
Homogeneous and Heterogeneous Equilibrium.—Before passing to the
consideration of this generalization, it will be well to first make mention of
certain restrictions which must be placed on its treatment, and also of the
limitations to which it is subject. If a system is uniform throughout its
whole extent, and possesses in every part identical physical properties and
chemical composition, it is called homogeneous. Such is, for example, a
solution of sodium chloride in water. An equilibrium occurring in such a
homogeneous system (such as the equilibrium occurring in the formation of
an ester in alcoholic solution) is called homogeneous equilibrium. If,
however, the system consists of parts which have different physical
properties, perhaps also different chemical properties, and which are
marked off and separated from one another by bounding surfaces, the
system is said to be heterogeneous. Such a system is formed by ice, water,
and vapour, in which the three portions, each in itself homogeneous, can be
mechanically separated from one another. When equilibrium exists between
different, physically distinct parts, it is known as heterogeneous
equilibrium. It is, now, with heterogeneous equilibria, with the conditions
under which a heterogeneous system can exist, that we shall deal here.
Further, we shall not take into account changes of equilibrium due to the
action of electrical, magnetic, or capillary forces, or of gravity; but shall
contact with the solution, the problem becomes more complicated, and the
necessity of some general guide to the elucidation of the behaviour of these
different systems becomes more urgent.
It is, now, to the study of such physical and chemical equilibria as those
above-mentioned that the Phase Rule finds application; to the study, also, of
the conditions regulating, for example, the formation of alloys from
mixtures of the fused metals, or of the various salts of the Stassfurt
deposits; the behaviour of iron and carbon in the formation of steel and the
separation of different minerals from a fused rock-mass.[4] With the help of
the Phase Rule we can group together into classes the large number of
different isolated cases of systems in equilibrium; with its aid we are able to
state, in a general manner at least, the conditions under which a system can
be in equilibrium, and by its means we can gain some insight into the
relations existing between different kinds of systems.
Homogeneous and Heterogeneous Equilibrium.—Before passing to the
consideration of this generalization, it will be well to first make mention of
certain restrictions which must be placed on its treatment, and also of the
limitations to which it is subject. If a system is uniform throughout its
whole extent, and possesses in every part identical physical properties and
chemical composition, it is called homogeneous. Such is, for example, a
solution of sodium chloride in water. An equilibrium occurring in such a
homogeneous system (such as the equilibrium occurring in the formation of
an ester in alcoholic solution) is called homogeneous equilibrium. If,
however, the system consists of parts which have different physical
properties, perhaps also different chemical properties, and which are
marked off and separated from one another by bounding surfaces, the
system is said to be heterogeneous. Such a system is formed by ice, water,
and vapour, in which the three portions, each in itself homogeneous, can be
mechanically separated from one another. When equilibrium exists between
different, physically distinct parts, it is known as heterogeneous
equilibrium. It is, now, with heterogeneous equilibria, with the conditions
under which a heterogeneous system can exist, that we shall deal here.
Further, we shall not take into account changes of equilibrium due to the
action of electrical, magnetic, or capillary forces, or of gravity; but shall
Page 20
discuss only those which are due to changes of pressure, temperature, and
volume (or concentration).
Real and Apparent Equilibrium.—In discussing equilibria, also, a
distinction must be drawn between real and apparent equilibria. In the
former case there is a state of rest which undergoes continuous change with
change of the conditions (e.g. change of temperature or of pressure), and for
which the chief criterion is that the same condition of equilibrium is
reached from whichever side it is approached. Thus in the case of a
solution, if the temperature is maintained constant, the same concentration
will be obtained, no matter whether we start with an unsaturated solution to
which we add more solid, or with a supersaturated solution from which we
allow solid to crystallize out; or, in the case of water in contact with vapour,
the same vapour pressure will be obtained, no matter whether we heat the
water up to the given temperature or cool it down from a higher
temperature. In this case, water and vapour are in real equilibrium. On the
other hand, water in contact with hydrogen and oxygen at the ordinary
temperature is a case only of apparent equilibrium; on changing the
pressure and temperature continuously within certain limits there is no
continuous change observed in the relative amounts of the two gases. On
heating beyond these limits there is a sudden and not a continuous change,
and the system no longer regains its former condition on being cooled to the
ordinary temperature. In all such cases the system may be regarded as
undergoing change and as tending towards a state of true or real
equilibrium, but with such slowness that no change is observed.
Although the case of water in contact with hydrogen and oxygen is an
extreme one, it must be borne in mind that the condition of true equilibrium
may not be reached instantaneously or even with measurable velocity, and
in all cases it is necessary to be on one's guard against mistaking apparent
(or false) for real (or true) equilibrium. The importance of this will be fully
illustrated in the sequel.
CHAPTER II
volume (or concentration).
Real and Apparent Equilibrium.—In discussing equilibria, also, a
distinction must be drawn between real and apparent equilibria. In the
former case there is a state of rest which undergoes continuous change with
change of the conditions (e.g. change of temperature or of pressure), and for
which the chief criterion is that the same condition of equilibrium is
reached from whichever side it is approached. Thus in the case of a
solution, if the temperature is maintained constant, the same concentration
will be obtained, no matter whether we start with an unsaturated solution to
which we add more solid, or with a supersaturated solution from which we
allow solid to crystallize out; or, in the case of water in contact with vapour,
the same vapour pressure will be obtained, no matter whether we heat the
water up to the given temperature or cool it down from a higher
temperature. In this case, water and vapour are in real equilibrium. On the
other hand, water in contact with hydrogen and oxygen at the ordinary
temperature is a case only of apparent equilibrium; on changing the
pressure and temperature continuously within certain limits there is no
continuous change observed in the relative amounts of the two gases. On
heating beyond these limits there is a sudden and not a continuous change,
and the system no longer regains its former condition on being cooled to the
ordinary temperature. In all such cases the system may be regarded as
undergoing change and as tending towards a state of true or real
equilibrium, but with such slowness that no change is observed.
Although the case of water in contact with hydrogen and oxygen is an
extreme one, it must be borne in mind that the condition of true equilibrium
may not be reached instantaneously or even with measurable velocity, and
in all cases it is necessary to be on one's guard against mistaking apparent
(or false) for real (or true) equilibrium. The importance of this will be fully
illustrated in the sequel.
CHAPTER II
Page 21
THE PHASE RULE
Although the fact that chemical reactions do not take place completely in
one direction, but proceed only to a certain point and there make a halt, was
known in the last quarter of the eighteenth century (Wenzel, 1777;
Berthollet, 1799); and although the opening and subsequent decades of the
following century brought many further examples of such equilibria to our
knowledge, it was not until the last quarter of the nineteenth century that a
theorem, general in its application and with foundations weakened by no
hypothetical assumptions as to the nature or constitution of matter, was put
forward by Willard Gibbs;[5] a generalization which serves at once as a
golden rule by which the condition of equilibrium of a system can be tested,
and as a guide to the similarities and dissimilarities existing in different
systems.
Before that time, certainly, attempts had been made to bring the different
known cases of equilibria—chemical and physical—under general laws.
From the very first, both Wenzel[6] and Berthollet[7] recognized the
influence exercised by the mass of the substances on the equilibrium of the
system. It was reserved, however, for Guldberg and Waage, by their more
general statement and mathematical treatment of the Law of Mass Action,[8]
to inaugurate the period of quantitative study of equilibria. The law which
these investigators enunciated served satisfactorily to summarize the
conditions of equilibrium in many cases both of homogeneous and, with the
help of certain assumptions and additions, of heterogeneous equilibrium. By
reason, however, of the fact that it was developed on the basis of the kinetic
and molecular theories, and involved, therefore, certain hypothetical
assumptions as to the nature and condition of the substances taking part in
the equilibrium, the law of mass action failed, as it necessarily must, when
applied to those systems in which neither the number of different molecular
aggregates nor the degree of their molecular complexity was known.
Ten years after the law of mass action was propounded by Guldberg and
Waage, Willard Gibbs,[9] Professor of Physics in Yale University, showed
how, in a perfectly general manner, free from all hypothetical assumptions
as to the molecular condition of the participating substances, all cases of
equilibrium could be surveyed and grouped into classes, and how
Although the fact that chemical reactions do not take place completely in
one direction, but proceed only to a certain point and there make a halt, was
known in the last quarter of the eighteenth century (Wenzel, 1777;
Berthollet, 1799); and although the opening and subsequent decades of the
following century brought many further examples of such equilibria to our
knowledge, it was not until the last quarter of the nineteenth century that a
theorem, general in its application and with foundations weakened by no
hypothetical assumptions as to the nature or constitution of matter, was put
forward by Willard Gibbs;[5] a generalization which serves at once as a
golden rule by which the condition of equilibrium of a system can be tested,
and as a guide to the similarities and dissimilarities existing in different
systems.
Before that time, certainly, attempts had been made to bring the different
known cases of equilibria—chemical and physical—under general laws.
From the very first, both Wenzel[6] and Berthollet[7] recognized the
influence exercised by the mass of the substances on the equilibrium of the
system. It was reserved, however, for Guldberg and Waage, by their more
general statement and mathematical treatment of the Law of Mass Action,[8]
to inaugurate the period of quantitative study of equilibria. The law which
these investigators enunciated served satisfactorily to summarize the
conditions of equilibrium in many cases both of homogeneous and, with the
help of certain assumptions and additions, of heterogeneous equilibrium. By
reason, however, of the fact that it was developed on the basis of the kinetic
and molecular theories, and involved, therefore, certain hypothetical
assumptions as to the nature and condition of the substances taking part in
the equilibrium, the law of mass action failed, as it necessarily must, when
applied to those systems in which neither the number of different molecular
aggregates nor the degree of their molecular complexity was known.
Ten years after the law of mass action was propounded by Guldberg and
Waage, Willard Gibbs,[9] Professor of Physics in Yale University, showed
how, in a perfectly general manner, free from all hypothetical assumptions
as to the molecular condition of the participating substances, all cases of
equilibrium could be surveyed and grouped into classes, and how
Page 22
similarities in the behaviour of apparently different kinds of systems, and
differences in apparently similar systems, could be explained.
As the basis of his theory of equilibria, Gibbs adopted the laws of
thermodynamics,[10] a method of treatment which had first been employed
by Horstmann.[11] In deducing the law of equilibrium, Gibbs regarded a
system as possessing only three independently variable factors[12]—
temperature, pressure, and the concentration of the components of the
system—and he enunciated the general theorem now usually known as the
Phase Rule, by which he defined the conditions of equilibrium as a
relationship between the number of what are called the phases and the
components of the system.
Phases.—Before proceeding farther we shall first consider what exactly is
meant by the terms phase and component. We have already seen (p. 5) that
a heterogeneous system is made up of different portions, each in itself
homogeneous, but marked off in space and separated from the other
portions by bounding surfaces. These homogeneous, physically distinct and
mechanically separable portions are called phases. Thus ice, water, and
vapour, are three phases of the same chemical substance—water. A phase,
however, whilst it must be physically and chemically homogeneous, need
not necessarily be chemically simple. Thus, a gaseous mixture or a solution
may form a phase; but a heterogeneous mixture of solid substances
constitutes as many phases as there are substances present. Thus when
calcium carbonate dissociates under the influence of heat, calcium oxide
and carbon dioxide are formed. There are then two solid phases present, viz.
calcium carbonate and oxide, and one gas phase, carbon dioxide.
The number of phases which can exist side by side may vary greatly in
different systems. In all cases, however, there can be but one gas or vapour
phase on the account of the fact that all gases are miscible with one another
in all proportions. In the case of liquid and solid phases the number is
indefinite, since the above property does not apply to them. The number of
phases which can be formed by any given substance or group of substances
also differs greatly, and in general increases with the number of
participating substances. Even in the case of a single substance, however,
the number may be considerable; in the case of sulphur, for example, at
least eight different solid phases are known (v. Chap. III.).
differences in apparently similar systems, could be explained.
As the basis of his theory of equilibria, Gibbs adopted the laws of
thermodynamics,[10] a method of treatment which had first been employed
by Horstmann.[11] In deducing the law of equilibrium, Gibbs regarded a
system as possessing only three independently variable factors[12]—
temperature, pressure, and the concentration of the components of the
system—and he enunciated the general theorem now usually known as the
Phase Rule, by which he defined the conditions of equilibrium as a
relationship between the number of what are called the phases and the
components of the system.
Phases.—Before proceeding farther we shall first consider what exactly is
meant by the terms phase and component. We have already seen (p. 5) that
a heterogeneous system is made up of different portions, each in itself
homogeneous, but marked off in space and separated from the other
portions by bounding surfaces. These homogeneous, physically distinct and
mechanically separable portions are called phases. Thus ice, water, and
vapour, are three phases of the same chemical substance—water. A phase,
however, whilst it must be physically and chemically homogeneous, need
not necessarily be chemically simple. Thus, a gaseous mixture or a solution
may form a phase; but a heterogeneous mixture of solid substances
constitutes as many phases as there are substances present. Thus when
calcium carbonate dissociates under the influence of heat, calcium oxide
and carbon dioxide are formed. There are then two solid phases present, viz.
calcium carbonate and oxide, and one gas phase, carbon dioxide.
The number of phases which can exist side by side may vary greatly in
different systems. In all cases, however, there can be but one gas or vapour
phase on the account of the fact that all gases are miscible with one another
in all proportions. In the case of liquid and solid phases the number is
indefinite, since the above property does not apply to them. The number of
phases which can be formed by any given substance or group of substances
also differs greatly, and in general increases with the number of
participating substances. Even in the case of a single substance, however,
the number may be considerable; in the case of sulphur, for example, at
least eight different solid phases are known (v. Chap. III.).
Page 23
It is of importance to bear in mind that equilibrium is independent of the
amounts of the phases present.[13] Thus it is a familiar fact that the pressure
of a vapour in contact with a liquid (i.e. the pressure of the saturated
vapour) is unaffected by the amounts, whether relative or absolute, of the
liquid and vapour; also the amount of a substance dissolved by a liquid is
independent of the amount of solid in contact with the solution. It is true
that deviations from this general law occur when the amount of liquid or the
size of the solid particles is reduced beyond a certain point,[14] owing to the
influence of surface energy; but we have already (p. 5) excluded such cases
from consideration.
Components.—Although the conception of phases is one which is readily
understood, somewhat greater difficulty is experienced when we come to
consider what is meant by the term component; for the components of a
system are not synonymous with the chemical elements or compounds
present, i.e. with the constituents of the system, although both elements and
compounds may be components. By the latter term there are meant only
those constituents the concentration of which can undergo independent
variation in the different phases, and it is only with these that we are
concerned here.[15]
To understand the meaning of this term we shall consider briefly some cases
with which the reader will be familiar, and at the outset it must be
emphasized that the Phase Rule is concerned merely with those constituents
which take part in the state of real equilibrium (p. 5); for it is only to the
final state, not to the processes by which that state is reached, that the Phase
Rule applies.
Consider now the case of the system water—vapour or ice—water—
vapour. The number of constituents taking part in the equilibrium here is
only one, viz. the chemical substance, water. Hydrogen and oxygen, the
constituents of water, are not to be regarded as components, because, in the
first place, they are not present in the system in a state of real equilibrium
(p. 6); in the second place, they are combined in definite proportions to
form water, and their amounts, therefore, cannot be varied independently. A
variation in the amount of hydrogen necessitates a definite variation in the
amount of oxygen.
amounts of the phases present.[13] Thus it is a familiar fact that the pressure
of a vapour in contact with a liquid (i.e. the pressure of the saturated
vapour) is unaffected by the amounts, whether relative or absolute, of the
liquid and vapour; also the amount of a substance dissolved by a liquid is
independent of the amount of solid in contact with the solution. It is true
that deviations from this general law occur when the amount of liquid or the
size of the solid particles is reduced beyond a certain point,[14] owing to the
influence of surface energy; but we have already (p. 5) excluded such cases
from consideration.
Components.—Although the conception of phases is one which is readily
understood, somewhat greater difficulty is experienced when we come to
consider what is meant by the term component; for the components of a
system are not synonymous with the chemical elements or compounds
present, i.e. with the constituents of the system, although both elements and
compounds may be components. By the latter term there are meant only
those constituents the concentration of which can undergo independent
variation in the different phases, and it is only with these that we are
concerned here.[15]
To understand the meaning of this term we shall consider briefly some cases
with which the reader will be familiar, and at the outset it must be
emphasized that the Phase Rule is concerned merely with those constituents
which take part in the state of real equilibrium (p. 5); for it is only to the
final state, not to the processes by which that state is reached, that the Phase
Rule applies.
Consider now the case of the system water—vapour or ice—water—
vapour. The number of constituents taking part in the equilibrium here is
only one, viz. the chemical substance, water. Hydrogen and oxygen, the
constituents of water, are not to be regarded as components, because, in the
first place, they are not present in the system in a state of real equilibrium
(p. 6); in the second place, they are combined in definite proportions to
form water, and their amounts, therefore, cannot be varied independently. A
variation in the amount of hydrogen necessitates a definite variation in the
amount of oxygen.
Page 24
In the case, already referred to, in which hydrogen and oxygen are present
along with water at the ordinary temperature, we are not dealing with a
condition of true equilibrium. If, however, the temperature is raised to a
certain point, a state of true equilibrium between hydrogen, oxygen, and
water-vapour will be possible. In this case hydrogen and oxygen will be
components, because now they do take part in the equilibrium; also, they
need no longer be present in definite proportions, but excess of one or the
other may be added. Of course, if the restriction be arbitrarily made that the
free hydrogen and oxygen shall be present always and only in the
proportions in which they are combined to form water, there will be, as
before, only one component, water. From this, then, we see that a change in
the conditions of the experiment (in the present case a rise of temperature)
may necessitate a change in the number of the components.
It is, however, only in the case of systems of more than one component that
any difficulty will be found; for only in this case will a choice of
components be possible. Take, for instance, the dissociation of calcium
carbonate into calcium oxide and carbon dioxide. At each temperature, as
we have seen, there is a definite state of equilibrium. When equilibrium has
been established, there are three different substances present—calcium
carbonate, calcium oxide, and carbon dioxide; and these are the constituents
of the system between which equilibrium exists. Now, although these
constituents take part in the equilibrium, they are not all to be regarded as
components, for they are not mutually independent. On the contrary, the
different phases are related to one another, and if two of these are taken, the
composition of the third is defined by the equation
CaCO3 = CaO + CO2
Now, in deciding the number of components in any given system, not only
must the constituents chosen be capable of independent variation, but a
further restriction is imposed, and we obtain the following rule: As the
components of a system there are to be chosen the smallest number of
independently variable constituents by means of which the composition of
each phase participating in the state of equilibrium can be expressed in the
form of a chemical equation.
along with water at the ordinary temperature, we are not dealing with a
condition of true equilibrium. If, however, the temperature is raised to a
certain point, a state of true equilibrium between hydrogen, oxygen, and
water-vapour will be possible. In this case hydrogen and oxygen will be
components, because now they do take part in the equilibrium; also, they
need no longer be present in definite proportions, but excess of one or the
other may be added. Of course, if the restriction be arbitrarily made that the
free hydrogen and oxygen shall be present always and only in the
proportions in which they are combined to form water, there will be, as
before, only one component, water. From this, then, we see that a change in
the conditions of the experiment (in the present case a rise of temperature)
may necessitate a change in the number of the components.
It is, however, only in the case of systems of more than one component that
any difficulty will be found; for only in this case will a choice of
components be possible. Take, for instance, the dissociation of calcium
carbonate into calcium oxide and carbon dioxide. At each temperature, as
we have seen, there is a definite state of equilibrium. When equilibrium has
been established, there are three different substances present—calcium
carbonate, calcium oxide, and carbon dioxide; and these are the constituents
of the system between which equilibrium exists. Now, although these
constituents take part in the equilibrium, they are not all to be regarded as
components, for they are not mutually independent. On the contrary, the
different phases are related to one another, and if two of these are taken, the
composition of the third is defined by the equation
CaCO3 = CaO + CO2
Now, in deciding the number of components in any given system, not only
must the constituents chosen be capable of independent variation, but a
further restriction is imposed, and we obtain the following rule: As the
components of a system there are to be chosen the smallest number of
independently variable constituents by means of which the composition of
each phase participating in the state of equilibrium can be expressed in the
form of a chemical equation.
Page 25
Applying this rule to the case under consideration, we see that of the three
constituents present when the system is in a state of equilibrium, only two,
as already stated, are independently variable. It will further be seen that in
order to express the composition of each phase present, two of these
constituents are necessary. The system is, therefore, one of two components,
or a system of the second order.
When, now, we proceed to the actual choice of components, it is evident
that any two of the constituents can be selected. Thus, if we choose as
components CaCO3 and CaO, the composition of each phase can be
expressed by the following equations:—
CaCO3 = CaCO3 + 0CaO
CaO = CaO + 0CaCO3
CO2 = CaCO3 - CaO
As we see, then, both zero and negative quantities of the components have
been introduced; and similar expressions would be obtained if CaCO3 and
CO2 were chosen as components. The matter can, however, be simplified
and the use of negative quantities avoided if CaO and CO2 are chosen; and
it is, therefore, customary to select these as the components.
While it is possible in the case of systems of the second order to choose the
two components in such a way that the composition of each phase can be
expressed by positive quantities of these, such a choice is not always
possible when dealing with systems of a higher order (containing three or
four components).
From the example which has just been discussed, it might appear as if the
choice of the components was rather arbitrary. On examining the point,
however, it will be seen that the arbitrariness affects only the nature, not the
number, of the components; a choice could be made with respect to which,
not to how many, constituents were to be regarded as components. As we
shall see presently, however, it is only the number, not the nature of the
components that is of importance.
After the discussion of the conditions which the substances chosen as
components must satisfy, another method may be given by which the
constituents present when the system is in a state of equilibrium, only two,
as already stated, are independently variable. It will further be seen that in
order to express the composition of each phase present, two of these
constituents are necessary. The system is, therefore, one of two components,
or a system of the second order.
When, now, we proceed to the actual choice of components, it is evident
that any two of the constituents can be selected. Thus, if we choose as
components CaCO3 and CaO, the composition of each phase can be
expressed by the following equations:—
CaCO3 = CaCO3 + 0CaO
CaO = CaO + 0CaCO3
CO2 = CaCO3 - CaO
As we see, then, both zero and negative quantities of the components have
been introduced; and similar expressions would be obtained if CaCO3 and
CO2 were chosen as components. The matter can, however, be simplified
and the use of negative quantities avoided if CaO and CO2 are chosen; and
it is, therefore, customary to select these as the components.
While it is possible in the case of systems of the second order to choose the
two components in such a way that the composition of each phase can be
expressed by positive quantities of these, such a choice is not always
possible when dealing with systems of a higher order (containing three or
four components).
From the example which has just been discussed, it might appear as if the
choice of the components was rather arbitrary. On examining the point,
however, it will be seen that the arbitrariness affects only the nature, not the
number, of the components; a choice could be made with respect to which,
not to how many, constituents were to be regarded as components. As we
shall see presently, however, it is only the number, not the nature of the
components that is of importance.
After the discussion of the conditions which the substances chosen as
components must satisfy, another method may be given by which the
Page 26
number of components present in a system can be determined. Suppose a
system consisting of several phases in equilibrium, and the composition of
each phase determined by analysis. If each phase present, regarded as a
whole, has the same composition, the system contains only one component,
or is of the first order. If two phases must be mixed in suitable quantities in
order that the composition of a third phase may be obtained, the system is
one of two components or of the second order; and if three phases are
necessary to give the composition of a fourth coexisting phase, the system
is one of three components, or of the third order.[16]
Although the examples to be considered in the sequel will afford sufficient
illustration of the application of the rules given above, one case may
perhaps be discussed to show the application of the method just given for
determining the number of components.
Consider the system consisting of Glauber's salt in equilibrium with
solution and vapour. If these three phases are analyzed, the composition of
the solid will be expressed by Na2SO4, 10H2O; that of the solution by
Na2SO4 + xH2O, while the vapour phase will be H2O. The system evidently
cannot be a one-component system, for the phases have not all the same
composition. By varying the amounts of two phases, however (e.g. Na2SO4,
10H2O and H2O), the composition of the third phase—the solution—can be
obtained. The system is, therefore, one of two components.
But sodium sulphate can also exist in the anhydrous form and as the hydrate
Na2SO4, 7H2O. In these cases there may be chosen as components Na2SO4
and H2O, and Na2SO4, 7H2O and H2O respectively. In both cases,
therefore, there are two components. But the two systems (Na2SO4, 10H2O
—H2O, and Na2SO4, 7H2O—H2O) can be regarded as special cases of the
system Na2SO4—H2O, and these two components will apply to all systems
made up of sodium sulphate and water, no matter whether the solid phase is
anhydrous salt or one of the hydrates. In all three cases, of course, the
number of components is the same; but by choosing Na2SO4 and H2O as
components, the possible occurrence of negative quantities of components
in expressing the composition of the phases is avoided; and, further, these
components apply over a much larger range of experimental conditions.
system consisting of several phases in equilibrium, and the composition of
each phase determined by analysis. If each phase present, regarded as a
whole, has the same composition, the system contains only one component,
or is of the first order. If two phases must be mixed in suitable quantities in
order that the composition of a third phase may be obtained, the system is
one of two components or of the second order; and if three phases are
necessary to give the composition of a fourth coexisting phase, the system
is one of three components, or of the third order.[16]
Although the examples to be considered in the sequel will afford sufficient
illustration of the application of the rules given above, one case may
perhaps be discussed to show the application of the method just given for
determining the number of components.
Consider the system consisting of Glauber's salt in equilibrium with
solution and vapour. If these three phases are analyzed, the composition of
the solid will be expressed by Na2SO4, 10H2O; that of the solution by
Na2SO4 + xH2O, while the vapour phase will be H2O. The system evidently
cannot be a one-component system, for the phases have not all the same
composition. By varying the amounts of two phases, however (e.g. Na2SO4,
10H2O and H2O), the composition of the third phase—the solution—can be
obtained. The system is, therefore, one of two components.
But sodium sulphate can also exist in the anhydrous form and as the hydrate
Na2SO4, 7H2O. In these cases there may be chosen as components Na2SO4
and H2O, and Na2SO4, 7H2O and H2O respectively. In both cases,
therefore, there are two components. But the two systems (Na2SO4, 10H2O
—H2O, and Na2SO4, 7H2O—H2O) can be regarded as special cases of the
system Na2SO4—H2O, and these two components will apply to all systems
made up of sodium sulphate and water, no matter whether the solid phase is
anhydrous salt or one of the hydrates. In all three cases, of course, the
number of components is the same; but by choosing Na2SO4 and H2O as
components, the possible occurrence of negative quantities of components
in expressing the composition of the phases is avoided; and, further, these
components apply over a much larger range of experimental conditions.
Page 27
Again, therefore, we see that, although the number of the components of a
system is definite, a certain amount of liberty is allowed in the choice of the
substances; and we also see that the choice will be influenced by the
conditions of experiment.
Summing up, now, we may say—
(1) The components are to be chosen from among the constituents which
are present when the system is in a state of true equilibrium, and which take
part in that equilibrium.
(2) As components are to be chosen the smallest number of such
constituents necessary to express the composition of each phase
participating in the equilibrium, zero and negative quantities of the
components being permissible.
(3) In any given system the number of the components is definite, but may
alter with alteration of the conditions of experiment. A certain freedom of
choice, however, is allowed in the (qualitative, not quantitative) selection of
the components, the choice being influenced by considerations of
simplicity, suitability, or generality of application.[17]
Degree of Freedom. Variability of a System.—It is well known that in
dealing with a certain mass of gas or vapour, e.g. water vapour, if only one
of the independently variable factors—temperature, pressure, and
concentration (or volume)—is fixed, the state of the gas or vapour is
undefined; while occupying the same volume (the concentration, therefore,
remaining unchanged), the temperature and the pressure may be altered; at
a given temperature, a gas can exist under different pressures and occupy
different volumes, and under any given pressure the temperature and
volume may vary. If, however, two of the factors are arbitrarily fixed, then
the third factor can only have a certain definite value; at any given values of
temperature and pressure a given mass of gas can occupy only a definite
volume.
Suppose, however, that the system consists of water in contact with vapour.
The condition of the system then becomes perfectly defined on arbitrarily
giving one of the variables a certain value. If the temperature is fixed, the
pressure under which water and water vapour can coexist is also
system is definite, a certain amount of liberty is allowed in the choice of the
substances; and we also see that the choice will be influenced by the
conditions of experiment.
Summing up, now, we may say—
(1) The components are to be chosen from among the constituents which
are present when the system is in a state of true equilibrium, and which take
part in that equilibrium.
(2) As components are to be chosen the smallest number of such
constituents necessary to express the composition of each phase
participating in the equilibrium, zero and negative quantities of the
components being permissible.
(3) In any given system the number of the components is definite, but may
alter with alteration of the conditions of experiment. A certain freedom of
choice, however, is allowed in the (qualitative, not quantitative) selection of
the components, the choice being influenced by considerations of
simplicity, suitability, or generality of application.[17]
Degree of Freedom. Variability of a System.—It is well known that in
dealing with a certain mass of gas or vapour, e.g. water vapour, if only one
of the independently variable factors—temperature, pressure, and
concentration (or volume)—is fixed, the state of the gas or vapour is
undefined; while occupying the same volume (the concentration, therefore,
remaining unchanged), the temperature and the pressure may be altered; at
a given temperature, a gas can exist under different pressures and occupy
different volumes, and under any given pressure the temperature and
volume may vary. If, however, two of the factors are arbitrarily fixed, then
the third factor can only have a certain definite value; at any given values of
temperature and pressure a given mass of gas can occupy only a definite
volume.
Suppose, however, that the system consists of water in contact with vapour.
The condition of the system then becomes perfectly defined on arbitrarily
giving one of the variables a certain value. If the temperature is fixed, the
pressure under which water and water vapour can coexist is also
Page 28
determined; and conversely, if a definite pressure is chosen, the temperature
is also defined. Water and vapour can coexist under a given pressure only at
a definite temperature.
Finally, let the water and vapour be cooled down until ice begins to separate
out. So soon as the third phase, ice, appears, the state of the system as
regards temperature and pressure of the vapour is perfectly defined, and
none of the variables can be arbitrarily changed without causing the
disappearance of one of the phases, ice, water, or vapour.
We see, therefore, that in the case of some systems two, in other cases, only
one of the independent variables (temperature, pressure, concentration) can
be altered without destroying the nature of the system; while in other
systems, again, these variables have all fixed and definite values. We shall
therefore define the number of degrees of freedom[18] of a system as the
number of the variable factors, temperature, pressure, and concentration of
the components, which must be arbitrarily fixed in order that the condition
of the system may be perfectly defined. From what has been said, therefore,
we shall describe a gas or vapour as having two degrees of freedom; the
system water—vapour as having only one; and the system ice—water—
vapour as having no degrees of freedom. We may also speak of the
variability or variance of a system, and describe a system as being
invariant, univariant, bivariant, multivariant,[19] according as the number of
degrees of freedom is nought, one, two, or more than two.
A knowledge of its variability is, therefore, of essential importance in
studying the condition and behaviour of a system, and it is the great merit of
the Phase Rule that the state of a system is defined entirely by the relation
existing between the number of the components and the phases present, no
account being taken of the molecular complexity of the participating
substances, nor any assumption made with regard to the constitution of
matter. It is, further, as we see, quite immaterial whether we are dealing
with "physical" or "chemical" equilibrium; in principle, indeed, no
distinction need be drawn between the two classes, although it is
nevertheless often convenient to make use of the terms, in spite of a certain
amount of indefiniteness which attaches to them—an indefiniteness, indeed,
which attaches equally to the terms "physical" and "chemical" process.[20]
is also defined. Water and vapour can coexist under a given pressure only at
a definite temperature.
Finally, let the water and vapour be cooled down until ice begins to separate
out. So soon as the third phase, ice, appears, the state of the system as
regards temperature and pressure of the vapour is perfectly defined, and
none of the variables can be arbitrarily changed without causing the
disappearance of one of the phases, ice, water, or vapour.
We see, therefore, that in the case of some systems two, in other cases, only
one of the independent variables (temperature, pressure, concentration) can
be altered without destroying the nature of the system; while in other
systems, again, these variables have all fixed and definite values. We shall
therefore define the number of degrees of freedom[18] of a system as the
number of the variable factors, temperature, pressure, and concentration of
the components, which must be arbitrarily fixed in order that the condition
of the system may be perfectly defined. From what has been said, therefore,
we shall describe a gas or vapour as having two degrees of freedom; the
system water—vapour as having only one; and the system ice—water—
vapour as having no degrees of freedom. We may also speak of the
variability or variance of a system, and describe a system as being
invariant, univariant, bivariant, multivariant,[19] according as the number of
degrees of freedom is nought, one, two, or more than two.
A knowledge of its variability is, therefore, of essential importance in
studying the condition and behaviour of a system, and it is the great merit of
the Phase Rule that the state of a system is defined entirely by the relation
existing between the number of the components and the phases present, no
account being taken of the molecular complexity of the participating
substances, nor any assumption made with regard to the constitution of
matter. It is, further, as we see, quite immaterial whether we are dealing
with "physical" or "chemical" equilibrium; in principle, indeed, no
distinction need be drawn between the two classes, although it is
nevertheless often convenient to make use of the terms, in spite of a certain
amount of indefiniteness which attaches to them—an indefiniteness, indeed,
which attaches equally to the terms "physical" and "chemical" process.[20]
Page 29
The Phase Rule.—The Phase Rule of Gibbs, which defines the condition
of equilibrium by the relation between the number of coexisting phases and
the components, may be stated as follows: A system consisting of n
components can exist in n + 2 phases only when the temperature, pressure,
and concentration have fixed and definite values; if there are n components
in n + 1 phases, equilibrium can exist while one of the factors varies, and if
there are only n phases, two of the varying factors may be arbitrarily fixed.
This rule, the application of which, it is hoped, will become clear in the
sequel, may be very concisely and conveniently summarized in the form of
the equation—
P + F = C + 2, or F = C + 2 - P
where P denotes the number of the phases, F the degrees of freedom, and C
the number of components. From the second form of the equation it can be
readily seen that the greater the number of the phases, the fewer are the
degrees of freedom. With increase in the number of the phases, therefore,
the condition of the system becomes more and more defined, or less and
less variable.
Classification of Systems according to the Phase Rule.—We have
already learned in the introductory chapter that systems which are
apparently quite different in character may behave in a very similar manner.
Thus it was stated that the laws which govern the equilibrium between
water and its vapour are quite analogous to those which are obeyed by the
dissociation of calcium carbonate into carbon dioxide and calcium oxide; in
each case a certain temperature is associated with a definite pressure, no
matter what the relative or absolute amounts of the respective substances
are. And other examples were given of systems which were apparently
similar in character, but which nevertheless behaved in a different manner.
The relations between the various systems, however, become perfectly clear
and intelligible in the light of the Phase Rule. In the case first mentioned,
that of water in equilibrium with its vapour, we have one component—
water—present in two phases, i.e. in two physically distinct forms, viz.
liquid and vapour. According to the Phase Rule, therefore, since C = 1, and
P = 2, the degree of freedom F is equal to 1 + 2 - 2 = 1; the system
possesses one degree of freedom, as has already been stated. But in the case
of the second system mentioned above there are two components, viz.
of equilibrium by the relation between the number of coexisting phases and
the components, may be stated as follows: A system consisting of n
components can exist in n + 2 phases only when the temperature, pressure,
and concentration have fixed and definite values; if there are n components
in n + 1 phases, equilibrium can exist while one of the factors varies, and if
there are only n phases, two of the varying factors may be arbitrarily fixed.
This rule, the application of which, it is hoped, will become clear in the
sequel, may be very concisely and conveniently summarized in the form of
the equation—
P + F = C + 2, or F = C + 2 - P
where P denotes the number of the phases, F the degrees of freedom, and C
the number of components. From the second form of the equation it can be
readily seen that the greater the number of the phases, the fewer are the
degrees of freedom. With increase in the number of the phases, therefore,
the condition of the system becomes more and more defined, or less and
less variable.
Classification of Systems according to the Phase Rule.—We have
already learned in the introductory chapter that systems which are
apparently quite different in character may behave in a very similar manner.
Thus it was stated that the laws which govern the equilibrium between
water and its vapour are quite analogous to those which are obeyed by the
dissociation of calcium carbonate into carbon dioxide and calcium oxide; in
each case a certain temperature is associated with a definite pressure, no
matter what the relative or absolute amounts of the respective substances
are. And other examples were given of systems which were apparently
similar in character, but which nevertheless behaved in a different manner.
The relations between the various systems, however, become perfectly clear
and intelligible in the light of the Phase Rule. In the case first mentioned,
that of water in equilibrium with its vapour, we have one component—
water—present in two phases, i.e. in two physically distinct forms, viz.
liquid and vapour. According to the Phase Rule, therefore, since C = 1, and
P = 2, the degree of freedom F is equal to 1 + 2 - 2 = 1; the system
possesses one degree of freedom, as has already been stated. But in the case
of the second system mentioned above there are two components, viz.
Page 30
calcium oxide and carbon dioxide (p. 12), and three phases, viz. two solid
phases, CaO and CaCO3, and the gaseous phase, CO2. The number of
degrees of freedom of the system, therefore, is 2 + 2 - 3 = 1; this system,
therefore, also possesses one degree of freedom. We can now understand
why these two systems behave in a similar manner; both are univariant, or
possess only one degree of freedom. We shall therefore expect a similar
behaviour in the case of all univariant systems, no matter how dissimilar the
systems may outwardly appear. Similarly, all bivariant systems will exhibit
analogous behaviour; and generally, systems possessing the same degree of
freedom will show a like behaviour. In accordance with the Phase Rule,
therefore, we may classify the different systems which may be found into
invariant, univariant, bivariant, multivariant, according to the relation which
obtains between the number of the components and the number of
coexisting phases; and we shall expect that in each case the members of any
particular group will exhibit a uniform behaviour. By this means we are
enabled to obtain an insight into the general behaviour of any system, so
soon as we have determined the number of the components and the number
of the coexisting phases.
The adoption of the Phase Rule for the purposes of classification has been
of great importance in studying changes in the equilibrium existing between
different substances; for not only does it render possible the grouping
together of a large number of isolated phenomena, but the guidance it
affords has led to the discovery of new substances, has given the clue to the
conditions under which these substances can exist, and has led to the
recognition of otherwise unobserved resemblances existing between
different systems.
Deduction of the Phase Rule.—In the preceding pages we have restricted
ourselves to the statement of the Phase Rule, without giving any indication
of how it has been deduced. At the close of this chapter, therefore, the
mathematical deduction of the generalization will be given, but in brief
outline only, the reader being referred to works on Thermodynamics for a
fuller treatment of the subject.[21]
All forms of energy can be resolved into two factors, the capacity factor and
the intensity factor; but for the production of equilibrium, only the intensity
factor is of importance. Thus, if two bodies having the same temperature are
phases, CaO and CaCO3, and the gaseous phase, CO2. The number of
degrees of freedom of the system, therefore, is 2 + 2 - 3 = 1; this system,
therefore, also possesses one degree of freedom. We can now understand
why these two systems behave in a similar manner; both are univariant, or
possess only one degree of freedom. We shall therefore expect a similar
behaviour in the case of all univariant systems, no matter how dissimilar the
systems may outwardly appear. Similarly, all bivariant systems will exhibit
analogous behaviour; and generally, systems possessing the same degree of
freedom will show a like behaviour. In accordance with the Phase Rule,
therefore, we may classify the different systems which may be found into
invariant, univariant, bivariant, multivariant, according to the relation which
obtains between the number of the components and the number of
coexisting phases; and we shall expect that in each case the members of any
particular group will exhibit a uniform behaviour. By this means we are
enabled to obtain an insight into the general behaviour of any system, so
soon as we have determined the number of the components and the number
of the coexisting phases.
The adoption of the Phase Rule for the purposes of classification has been
of great importance in studying changes in the equilibrium existing between
different substances; for not only does it render possible the grouping
together of a large number of isolated phenomena, but the guidance it
affords has led to the discovery of new substances, has given the clue to the
conditions under which these substances can exist, and has led to the
recognition of otherwise unobserved resemblances existing between
different systems.
Deduction of the Phase Rule.—In the preceding pages we have restricted
ourselves to the statement of the Phase Rule, without giving any indication
of how it has been deduced. At the close of this chapter, therefore, the
mathematical deduction of the generalization will be given, but in brief
outline only, the reader being referred to works on Thermodynamics for a
fuller treatment of the subject.[21]
All forms of energy can be resolved into two factors, the capacity factor and
the intensity factor; but for the production of equilibrium, only the intensity
factor is of importance. Thus, if two bodies having the same temperature are
Page 31
brought in contact with each other, they will be in equilibrium as regards
heat energy, no matter what may be the amounts of heat (capacity factor)
contained in either, because the intensity factor—the temperature—is the
same. But if the temperature of the two bodies is different, i.e. if the
intensity factor of heat energy is different, the two bodies will no longer be
in equilibrium; but heat will pass from the hotter to the colder until both
have the same temperature.
As with heat energy, so with chemical energy. If we have a substance
existing in two different states, or in two different phases of a system,
equilibrium can occur only when the intensity factor of chemical energy is
the same. This intensity factor may be called the chemical potential; and we
can therefore say that a system will be in equilibrium when the chemical
potential of each component is the same in all the phases in which the
component occurs. Thus, for example, ice, water, and vapour have, at the
triple point, the same chemical potential.
The potential of a component in any phase depends not only on the
composition of the phase, but also on the temperature and the pressure (or
volume). If, therefore, we have a system of C components existing in P
phases, then, in order to fix the composition of unit mass of each phase, it is
necessary to know the masses of (C - 1) components in each of the phases.
As regards the composition, therefore, each phase possesses (C - 1)
variables. Since there are P phases, it follows that, as regards composition,
the whole system possesses P(C - 1) variables. Besides these there are,
however, two other variables, viz. temperature and pressure, so that
altogether a system of C components in P phases possesses P(C - 1) + 2
variables.
In order to define the state of the system completely, it will be necessary to
have as many equations as there are variables. If, therefore, there are fewer
equations than there are variables, then, according to the deficiency in the
number of the equations, one or more of the variables will have an
undefined value; and values must be assigned to these variables before the
system is entirely defined. The number of these undefined values gives us
the variability or the degree of freedom of the system.
heat energy, no matter what may be the amounts of heat (capacity factor)
contained in either, because the intensity factor—the temperature—is the
same. But if the temperature of the two bodies is different, i.e. if the
intensity factor of heat energy is different, the two bodies will no longer be
in equilibrium; but heat will pass from the hotter to the colder until both
have the same temperature.
As with heat energy, so with chemical energy. If we have a substance
existing in two different states, or in two different phases of a system,
equilibrium can occur only when the intensity factor of chemical energy is
the same. This intensity factor may be called the chemical potential; and we
can therefore say that a system will be in equilibrium when the chemical
potential of each component is the same in all the phases in which the
component occurs. Thus, for example, ice, water, and vapour have, at the
triple point, the same chemical potential.
The potential of a component in any phase depends not only on the
composition of the phase, but also on the temperature and the pressure (or
volume). If, therefore, we have a system of C components existing in P
phases, then, in order to fix the composition of unit mass of each phase, it is
necessary to know the masses of (C - 1) components in each of the phases.
As regards the composition, therefore, each phase possesses (C - 1)
variables. Since there are P phases, it follows that, as regards composition,
the whole system possesses P(C - 1) variables. Besides these there are,
however, two other variables, viz. temperature and pressure, so that
altogether a system of C components in P phases possesses P(C - 1) + 2
variables.
In order to define the state of the system completely, it will be necessary to
have as many equations as there are variables. If, therefore, there are fewer
equations than there are variables, then, according to the deficiency in the
number of the equations, one or more of the variables will have an
undefined value; and values must be assigned to these variables before the
system is entirely defined. The number of these undefined values gives us
the variability or the degree of freedom of the system.
Page 32
The equations by which the system is to be defined are obtained from the
relationship between the potential of a component and the composition of
the phase, the temperature and the pressure. Further, as has already been
stated, equilibrium occurs when the potential of each component is the
same in the different phases in which it is present. If, therefore, we choose
as standard one of the phases in which all the components occur, then in any
other phase in equilibrium with it, the potential of each component must be
the same as in the standard phase. For each phase in equilibrium with the
standard phase, therefore, there will be a definite equation of state for each
component in the phase; so that, if there are P phases, we obtain for each
component (P - 1) equations; and for C components, therefore, we obtain
C(P - 1) equations.
But we have seen above that there are P(C - 1) + 2 variables, and as we
have only C(P - 1) equations, there must be P(C - 1) + 2 - C(P - 1) = C + 2 -
P variables undefined. That is to say, the degree of freedom (F) of a system
consisting of C components in P phases is—
F=C+2-P
CHAPTER III
TYPICAL SYSTEMS OF ONE COMPONENT
A. Water.
For the sake of rendering the Phase Rule more readily intelligible, and at
the same time also for the purpose of obtaining examples by which we may
illustrate the general behaviour of systems, we shall in this chapter examine
in detail the behaviour of several well-known systems consisting of only
one component.
The most familiar examples of equilibria in a one-component system are
those furnished by the three phases of water, viz. ice, water, water vapour.
The system consists of one component, because all three phases have the
same chemical composition, represented by the formula H2O. As the
relationship between the potential of a component and the composition of
the phase, the temperature and the pressure. Further, as has already been
stated, equilibrium occurs when the potential of each component is the
same in the different phases in which it is present. If, therefore, we choose
as standard one of the phases in which all the components occur, then in any
other phase in equilibrium with it, the potential of each component must be
the same as in the standard phase. For each phase in equilibrium with the
standard phase, therefore, there will be a definite equation of state for each
component in the phase; so that, if there are P phases, we obtain for each
component (P - 1) equations; and for C components, therefore, we obtain
C(P - 1) equations.
But we have seen above that there are P(C - 1) + 2 variables, and as we
have only C(P - 1) equations, there must be P(C - 1) + 2 - C(P - 1) = C + 2 -
P variables undefined. That is to say, the degree of freedom (F) of a system
consisting of C components in P phases is—
F=C+2-P
CHAPTER III
TYPICAL SYSTEMS OF ONE COMPONENT
A. Water.
For the sake of rendering the Phase Rule more readily intelligible, and at
the same time also for the purpose of obtaining examples by which we may
illustrate the general behaviour of systems, we shall in this chapter examine
in detail the behaviour of several well-known systems consisting of only
one component.
The most familiar examples of equilibria in a one-component system are
those furnished by the three phases of water, viz. ice, water, water vapour.
The system consists of one component, because all three phases have the
same chemical composition, represented by the formula H2O. As the
Page 33
criterion of equilibrium we shall choose a definite pressure, and shall study
the variation of the pressure with the temperature; and for the purpose of
representing the relationships which we obtain we shall employ a
temperature-pressure diagram, in which the temperatures are measured as
abscissæ and the pressures as ordinates. In such a diagram invariant systems
will be represented by points; univariant systems by lines, and bivariant
systems by areas.
Equilibrium between Liquid and Vapour. Vaporization Curve.—
Consider in the first place the conditions for the coexistence of liquid and
vapour. According to the Phase Rule (p. 16), a system consisting of one
component in two phases has one degree of freedom, or is univariant. We
should therefore expect that it will be possible for liquid water to coexist
with water vapour at different values of temperature and pressure, but that if
we arbitrarily fix one of the variable factors, pressure, temperature, or
volume (in the case of a given mass of substance), the state of the system
will then be defined. If we fix, say, the temperature, then the pressure will
have a definite value; or if we adopt a certain pressure, the liquid and
vapour can coexist only at a certain definite temperature. Each temperature,
therefore, will correspond to a definite pressure; and if in our diagram we
join by a continuous line all the points indicating the values of the pressure
corresponding to the different temperatures, we shall obtain a curve (Fig. 1)
representing the variation of the pressure with the temperature. This is the
curve of vapour pressure, or the vaporization curve of water.
Fig. 1.
Now, the results of experiment are quite in agreement with the requirements
of the Phase Rule, and at any given temperature the system water—vapour
can exist in equilibrium only under a definite pressure.
the variation of the pressure with the temperature; and for the purpose of
representing the relationships which we obtain we shall employ a
temperature-pressure diagram, in which the temperatures are measured as
abscissæ and the pressures as ordinates. In such a diagram invariant systems
will be represented by points; univariant systems by lines, and bivariant
systems by areas.
Equilibrium between Liquid and Vapour. Vaporization Curve.—
Consider in the first place the conditions for the coexistence of liquid and
vapour. According to the Phase Rule (p. 16), a system consisting of one
component in two phases has one degree of freedom, or is univariant. We
should therefore expect that it will be possible for liquid water to coexist
with water vapour at different values of temperature and pressure, but that if
we arbitrarily fix one of the variable factors, pressure, temperature, or
volume (in the case of a given mass of substance), the state of the system
will then be defined. If we fix, say, the temperature, then the pressure will
have a definite value; or if we adopt a certain pressure, the liquid and
vapour can coexist only at a certain definite temperature. Each temperature,
therefore, will correspond to a definite pressure; and if in our diagram we
join by a continuous line all the points indicating the values of the pressure
corresponding to the different temperatures, we shall obtain a curve (Fig. 1)
representing the variation of the pressure with the temperature. This is the
curve of vapour pressure, or the vaporization curve of water.
Fig. 1.
Now, the results of experiment are quite in agreement with the requirements
of the Phase Rule, and at any given temperature the system water—vapour
can exist in equilibrium only under a definite pressure.
Page 34
The vapour pressure of water at different temperatures has been subjected
to careful measurement by Magnus,[22] Regnault,[23] Ramsay and Young,[24]
Juhlin,[25] Thiesen and Scheel,[26] and others. In the following table the
values of the vapour pressure from -10° to +100° are those calculated from
the measurements of Regnault, corrected by the measurements of Wiebe
and Thiesen and Scheel;[27] those from 120° to 270° were determined by
Ramsay and Young, while the values of the critical pressure and
temperature are those determined by Battelli.[28]
Vapour Pressure of Water.
Pressure in
Pressure in cm.
Temperature. cm. Temperature.
mercury.
mercury.
-10° 0.213 120° 148.4
0° 0.458[29] 130° 201.9
+20° 1.752 150° 356.8
40° 5.516 200° 1162.5
60° 14.932 250° 2973.4
80° 35.54 270° 4110.1
100° 76.00 364.3° 14790.4 (194.6
(critical atm.)
temperature) (critical pressure).
The pressure is, of course, independent of the relative or absolute volumes
of the liquid and vapour; on increasing the volume at constant temperature,
a certain amount of the liquid will pass into vapour, and the pressure will
regain its former value. If, however, the pressure be permanently
maintained at a value different from that corresponding to the temperature
employed, then either all the liquid will pass into vapour, or all the vapour
will pass into liquid, and we shall have either vapour alone or liquid alone.
Upper Limit of Vaporization Curve.—On continuing to add heat to water
contained in a closed vessel, the pressure of the vapour will gradually
increase. Since with increase of pressure the density of the vapour must
increase, and since with rise of temperature the density of the liquid must
decrease, a point will be reached at which the density of liquid and vapour
to careful measurement by Magnus,[22] Regnault,[23] Ramsay and Young,[24]
Juhlin,[25] Thiesen and Scheel,[26] and others. In the following table the
values of the vapour pressure from -10° to +100° are those calculated from
the measurements of Regnault, corrected by the measurements of Wiebe
and Thiesen and Scheel;[27] those from 120° to 270° were determined by
Ramsay and Young, while the values of the critical pressure and
temperature are those determined by Battelli.[28]
Vapour Pressure of Water.
Pressure in
Pressure in cm.
Temperature. cm. Temperature.
mercury.
mercury.
-10° 0.213 120° 148.4
0° 0.458[29] 130° 201.9
+20° 1.752 150° 356.8
40° 5.516 200° 1162.5
60° 14.932 250° 2973.4
80° 35.54 270° 4110.1
100° 76.00 364.3° 14790.4 (194.6
(critical atm.)
temperature) (critical pressure).
The pressure is, of course, independent of the relative or absolute volumes
of the liquid and vapour; on increasing the volume at constant temperature,
a certain amount of the liquid will pass into vapour, and the pressure will
regain its former value. If, however, the pressure be permanently
maintained at a value different from that corresponding to the temperature
employed, then either all the liquid will pass into vapour, or all the vapour
will pass into liquid, and we shall have either vapour alone or liquid alone.
Upper Limit of Vaporization Curve.—On continuing to add heat to water
contained in a closed vessel, the pressure of the vapour will gradually
increase. Since with increase of pressure the density of the vapour must
increase, and since with rise of temperature the density of the liquid must
decrease, a point will be reached at which the density of liquid and vapour
Page 35
become identical; the system ceases to be heterogeneous, and passes into
one homogeneous phase. The temperature at which this occurs is called the
critical temperature. To this temperature there will, of course, correspond a
certain definite pressure, called the critical pressure. The curve representing
the equilibrium between liquid and vapour must, therefore, end abruptly at
the critical point. At temperatures above this point no pressure, however
great, can cause the formation of the liquid phase; at temperatures above the
critical point the vapour becomes a gas. In the case of water, the critical
temperature is 364.3°, and the critical pressure 194.6 atm.; at the point
representing these conditions the vapour-pressure curve of water must
cease.
Sublimation Curve of Ice.—Vapour is given off not only by liquid water,
but also by solid water, or ice. That this is so is familiar to every one
through the fact that ice or snow, even at temperatures below the melting
point, gradually disappears in the form of vapour. Even at temperatures
considerably lower than 0°, the vapour pressure of ice, although small, is
quite appreciable; and it is possible, therefore, to have ice and vapour
coexisting in equilibrium. When we inquire into the conditions under which
such a system can exist, we see again that we are dealing with a univariant
system—one component existing in two phases—and that, therefore, just as
in the case of the system water and vapour, there will be for each
temperature a certain definite pressure of the vapour, and this pressure will
be independent of the relative or absolute amounts of the solid or vapour
present, and will depend solely on the temperature. Further, just as in the
case of the vapour pressure of water, the condition of equilibrium between
ice and water vapour will be represented by a line or curve showing the
change of pressure with the temperature. Such a curve, representing the
conditions of equilibrium between a solid and its vapour, is called a
sublimation curve. At temperatures represented by any point on this curve,
the solid (ice) will sublime or pass into vapour without previously fusing.
Since ice melts at 0° (vide infra), the sublimation curve must end at that
temperature.
The following are the values of the vapour pressure of ice between 0° and
-50°.[30]
Vapour Pressure of Ice.
one homogeneous phase. The temperature at which this occurs is called the
critical temperature. To this temperature there will, of course, correspond a
certain definite pressure, called the critical pressure. The curve representing
the equilibrium between liquid and vapour must, therefore, end abruptly at
the critical point. At temperatures above this point no pressure, however
great, can cause the formation of the liquid phase; at temperatures above the
critical point the vapour becomes a gas. In the case of water, the critical
temperature is 364.3°, and the critical pressure 194.6 atm.; at the point
representing these conditions the vapour-pressure curve of water must
cease.
Sublimation Curve of Ice.—Vapour is given off not only by liquid water,
but also by solid water, or ice. That this is so is familiar to every one
through the fact that ice or snow, even at temperatures below the melting
point, gradually disappears in the form of vapour. Even at temperatures
considerably lower than 0°, the vapour pressure of ice, although small, is
quite appreciable; and it is possible, therefore, to have ice and vapour
coexisting in equilibrium. When we inquire into the conditions under which
such a system can exist, we see again that we are dealing with a univariant
system—one component existing in two phases—and that, therefore, just as
in the case of the system water and vapour, there will be for each
temperature a certain definite pressure of the vapour, and this pressure will
be independent of the relative or absolute amounts of the solid or vapour
present, and will depend solely on the temperature. Further, just as in the
case of the vapour pressure of water, the condition of equilibrium between
ice and water vapour will be represented by a line or curve showing the
change of pressure with the temperature. Such a curve, representing the
conditions of equilibrium between a solid and its vapour, is called a
sublimation curve. At temperatures represented by any point on this curve,
the solid (ice) will sublime or pass into vapour without previously fusing.
Since ice melts at 0° (vide infra), the sublimation curve must end at that
temperature.
The following are the values of the vapour pressure of ice between 0° and
-50°.[30]
Vapour Pressure of Ice.
Page 36
Pressure in mm. Pressure in mm.
Temperature. Temperature.
mercury. mercury.
-50° 0.050 -8° 2.379
-40° 0.121 -6° 2.821
-30° 0.312 -4° 3.334
-20° 0.806 -2° 3.925
-15° 1.279 0° 4.602
-10° 1.999
Equilibrium between Ice and Water. Curve of Fusion.—There is still
another univariant system of the one component water, the existence of
which, at definite values of temperature and pressure, the Phase Rule allows
us to predict. This is the system solid—liquid. Ice on being heated to a
certain temperature melts and passes into the liquid state; and since this
system solid—liquid is univariant, there will be for each temperature a
certain definite pressure at which ice and water can coexist or be in
equilibrium, independently of the amounts of the two phases present. Since
now the temperature at which the solid phase is in equilibrium with the
liquid phase is known as the melting point or point of fusion of the solid,
the curve representing the temperatures and pressures at which the solid and
liquid are in equilibrium will represent the change of the melting point with
the pressure. Such a curve is called the curve of fusion, or the melting-point
curve.
It was not until the middle of the nineteenth century that this connection
between the pressure and the melting point, or the change of the melting
point with the pressure, was observed. The first to recognize the existence
of such a relationship was James Thomson,[31] who in 1849 showed that
from theoretical considerations such a relationship must exist, and predicted
that in the case of ice the melting point would be lowered by pressure. This
prediction was fully confirmed by his brother, W. Thomson[32] (Lord
Kelvin), who found that under a pressure of 8.1 atm. the melting point of
ice was -0.059°; under a pressure of 16.8 atm. the melting point was
-0.129°.
The experiments which were first made in this connection were more of a
qualitative nature, but in recent years careful measurements of the influence
Temperature. Temperature.
mercury. mercury.
-50° 0.050 -8° 2.379
-40° 0.121 -6° 2.821
-30° 0.312 -4° 3.334
-20° 0.806 -2° 3.925
-15° 1.279 0° 4.602
-10° 1.999
Equilibrium between Ice and Water. Curve of Fusion.—There is still
another univariant system of the one component water, the existence of
which, at definite values of temperature and pressure, the Phase Rule allows
us to predict. This is the system solid—liquid. Ice on being heated to a
certain temperature melts and passes into the liquid state; and since this
system solid—liquid is univariant, there will be for each temperature a
certain definite pressure at which ice and water can coexist or be in
equilibrium, independently of the amounts of the two phases present. Since
now the temperature at which the solid phase is in equilibrium with the
liquid phase is known as the melting point or point of fusion of the solid,
the curve representing the temperatures and pressures at which the solid and
liquid are in equilibrium will represent the change of the melting point with
the pressure. Such a curve is called the curve of fusion, or the melting-point
curve.
It was not until the middle of the nineteenth century that this connection
between the pressure and the melting point, or the change of the melting
point with the pressure, was observed. The first to recognize the existence
of such a relationship was James Thomson,[31] who in 1849 showed that
from theoretical considerations such a relationship must exist, and predicted
that in the case of ice the melting point would be lowered by pressure. This
prediction was fully confirmed by his brother, W. Thomson[32] (Lord
Kelvin), who found that under a pressure of 8.1 atm. the melting point of
ice was -0.059°; under a pressure of 16.8 atm. the melting point was
-0.129°.
The experiments which were first made in this connection were more of a
qualitative nature, but in recent years careful measurements of the influence
Page 37
of pressure on the melting point of ice have been made more especially by
Tammann,[33] and the results obtained by him are given in the following
table and represented graphically in Fig. 2.
Fusion Pressure of Ice.
Pressure in kilogms. per Change of melting point for an
Temperature. increase of pressure of
sq. cm.[34]
1 kilogm. per sq. cm.
-0° 1
0.0074°
-2.5° 336
0.0090°
-5° 615
0.0091°
-7.5° 890
0.0094°
-10.0° 1155
0.0100°
-12.5° 1410
0.0116°
-15.0° 1625
0.0119°
-17.5° 1835
0.0121°
-20.0° 2042
0.0133°
-22.1° 2200
From the numbers in the table and from the figure we see that as the
pressure is increased the melting point of ice is lowered; but we also
observe that a very large change of pressure is required in order to produce
a very small change in the melting point. The curve, therefore, is very steep.
Increase of pressure by one atmosphere lowers the melting point by only
0.0076°,[35] or an increase of pressure of 135 atm. is required to produce a
lowering of the melting point of 1°. We see further that the fusion curve
bends slightly as the pressure is increased, which signifies that the variation
of the melting point with the pressure changes; at -15°, when the pressure is
1625 kilogm. per sq. cm., increase of pressure by 1 kilogm. per sq. cm.
lowers the melting point by 0.012°. This curvature of the fusion curve we
shall later (Chap. IV.) see to be an almost universal phenomenon.
Tammann,[33] and the results obtained by him are given in the following
table and represented graphically in Fig. 2.
Fusion Pressure of Ice.
Pressure in kilogms. per Change of melting point for an
Temperature. increase of pressure of
sq. cm.[34]
1 kilogm. per sq. cm.
-0° 1
0.0074°
-2.5° 336
0.0090°
-5° 615
0.0091°
-7.5° 890
0.0094°
-10.0° 1155
0.0100°
-12.5° 1410
0.0116°
-15.0° 1625
0.0119°
-17.5° 1835
0.0121°
-20.0° 2042
0.0133°
-22.1° 2200
From the numbers in the table and from the figure we see that as the
pressure is increased the melting point of ice is lowered; but we also
observe that a very large change of pressure is required in order to produce
a very small change in the melting point. The curve, therefore, is very steep.
Increase of pressure by one atmosphere lowers the melting point by only
0.0076°,[35] or an increase of pressure of 135 atm. is required to produce a
lowering of the melting point of 1°. We see further that the fusion curve
bends slightly as the pressure is increased, which signifies that the variation
of the melting point with the pressure changes; at -15°, when the pressure is
1625 kilogm. per sq. cm., increase of pressure by 1 kilogm. per sq. cm.
lowers the melting point by 0.012°. This curvature of the fusion curve we
shall later (Chap. IV.) see to be an almost universal phenomenon.
Page 38
Fig. 2.
Equilibrium between Ice, Water, and Vapour. The
Triple Point.—On examining the vapour-pressure
curves of ice and water (Fig. 3), we see that at a
temperature of about 0° and under a pressure of about
4.6 mm. mercury, the two curves cut. At this point
liquid water and solid ice are each in equilibrium with
vapour at the same pressure. Since this is so, they must, Fig. 3.
of course, be in equilibrium with one another, as
experiment also shows. At this point, therefore, ice, water, and vapour can
be in equilibrium, and as there are three phases present, the point is called a
triple point.[36]
The triple point, however, does not lie exactly at 0° C., for this temperature
is defined as the melting point of ice under atmospheric pressure. At the
triple point, however, the pressure is equal to the vapour pressure of ice and
water, and this pressure, as we see from the tables on pp. 21 and 23, is very
nearly 4.6 mm., or almost 1 atm. less than in the previous case. Now, we
have just seen that a change of pressure of 1 atm. corresponds to a change
of the melting point of 0.0076°; the melting point of ice, therefore, when
under the pressure of its own vapour, will be very nearly +0.0076°, and the
pressure of the vapour will be very slightly greater than 4.579 mm., which
is the pressure at 0° (p. 21). The difference is, however, slight, and may be
neglected here. At the temperature, then, of +0.0076°, and under a pressure
of 4.6 mm. of mercury, ice, water, and vapour will be in equilibrium; the
Equilibrium between Ice, Water, and Vapour. The
Triple Point.—On examining the vapour-pressure
curves of ice and water (Fig. 3), we see that at a
temperature of about 0° and under a pressure of about
4.6 mm. mercury, the two curves cut. At this point
liquid water and solid ice are each in equilibrium with
vapour at the same pressure. Since this is so, they must, Fig. 3.
of course, be in equilibrium with one another, as
experiment also shows. At this point, therefore, ice, water, and vapour can
be in equilibrium, and as there are three phases present, the point is called a
triple point.[36]
The triple point, however, does not lie exactly at 0° C., for this temperature
is defined as the melting point of ice under atmospheric pressure. At the
triple point, however, the pressure is equal to the vapour pressure of ice and
water, and this pressure, as we see from the tables on pp. 21 and 23, is very
nearly 4.6 mm., or almost 1 atm. less than in the previous case. Now, we
have just seen that a change of pressure of 1 atm. corresponds to a change
of the melting point of 0.0076°; the melting point of ice, therefore, when
under the pressure of its own vapour, will be very nearly +0.0076°, and the
pressure of the vapour will be very slightly greater than 4.579 mm., which
is the pressure at 0° (p. 21). The difference is, however, slight, and may be
neglected here. At the temperature, then, of +0.0076°, and under a pressure
of 4.6 mm. of mercury, ice, water, and vapour will be in equilibrium; the
Page 39
point in our diagram representing this particular temperature and pressure
is, therefore, the triple point of the system ice—water—vapour.
Since at the triple point we have three phases of one component, the system
at this point is invariant—it possesses no degrees of freedom. If the
temperature is changed, the system will undergo alteration in such a way
that one of the phases will disappear, and a univariant system will result; if
heat be added, ice will melt, and we shall have left water and vapour; if heat
be abstracted, water will freeze, and we shall have left ice and vapour; if,
when the temperature is altered, the pressure is kept constant, then we shall
ultimately obtain only one phase (see Chap. IV.).
The triple point is not only the point of intersection of the vaporization and
sublimation curves, but it is also the end-point of the fusion curve. The
fusion curve, as we have seen, is the curve of equilibrium between ice and
water; and since at the triple point ice and water are each in equilibrium
with vapour of the same pressure, they must, of course, also be in
equilibrium with one another.
Fig. 4.
Bivariant Systems of Water.—If we examine Fig. 4, we see that the curves
OA, OB, OC, which represent diagrammatically the conditions under which
water and vapour, ice and vapour, and water and ice are in equilibrium,
form the boundaries of three "fields," or areas, I., II., III. These areas, now,
represent the conditions for the existence of the single phases, solid, liquid,
and vapour respectively. At temperatures and pressures represented by any
point in the field I., solid only can exist as a stable phase. Since we have
here one component in only one phase, the system is bivariant, and at any
given temperature, therefore, ice can exist under a series of pressures; and
under any given pressure, at a series of temperatures, these pressures and
is, therefore, the triple point of the system ice—water—vapour.
Since at the triple point we have three phases of one component, the system
at this point is invariant—it possesses no degrees of freedom. If the
temperature is changed, the system will undergo alteration in such a way
that one of the phases will disappear, and a univariant system will result; if
heat be added, ice will melt, and we shall have left water and vapour; if heat
be abstracted, water will freeze, and we shall have left ice and vapour; if,
when the temperature is altered, the pressure is kept constant, then we shall
ultimately obtain only one phase (see Chap. IV.).
The triple point is not only the point of intersection of the vaporization and
sublimation curves, but it is also the end-point of the fusion curve. The
fusion curve, as we have seen, is the curve of equilibrium between ice and
water; and since at the triple point ice and water are each in equilibrium
with vapour of the same pressure, they must, of course, also be in
equilibrium with one another.
Fig. 4.
Bivariant Systems of Water.—If we examine Fig. 4, we see that the curves
OA, OB, OC, which represent diagrammatically the conditions under which
water and vapour, ice and vapour, and water and ice are in equilibrium,
form the boundaries of three "fields," or areas, I., II., III. These areas, now,
represent the conditions for the existence of the single phases, solid, liquid,
and vapour respectively. At temperatures and pressures represented by any
point in the field I., solid only can exist as a stable phase. Since we have
here one component in only one phase, the system is bivariant, and at any
given temperature, therefore, ice can exist under a series of pressures; and
under any given pressure, at a series of temperatures, these pressures and
Page 40
temperatures being limited only by the curves OB, OC. Similarly also with
the areas II. and III.
We see, further, that the different areas are the regions of stability of the
phase common to the two curves by which the area is enclosed.[37] Thus,
the phase common to the two systems represented by BO (ice and vapour),
and OA (water and vapour) is the vapour phase; and the area BOA is
therefore the area of the vapour phase. Similarly, BOC is the area of the ice
phase, and COA the area of the water phase.
Supercooled Water. Metastable State.—When heated under the ordinary
atmospheric pressure, ice melts when the temperature reaches 0°, and it has
so far not been found possible to raise the temperature of ice above this
point without liquefaction taking place. On the other hand, it has long been
known that water can be cooled below zero without solidification occurring.
This was first discovered in 1724 by Fahrenheit,[38] who found that water
could be exposed to a temperature of -9.4° without solidifying; so soon,
however, as a small particle of ice was brought in contact with the water,
crystallization commenced. Superfused or supercooled water—i.e. water
cooled below 0°—is unstable only in respect of the solid phase; so long as
the presence of the solid phase is carefully avoided, the water can be kept
for any length of time without solidifying, and the system supercooled
water and vapour behaves in every way like a stable system. A system, now,
which in itself is stable, and which becomes instable only in contact with a
particular phase, is said to be metastable, and the region throughout which
this condition exists is called the metastable region. Supercooled water,
therefore, is in a metastable condition. If the supercooling be carried below
a certain temperature, solidification takes place spontaneously without the
addition of the solid phase; the system then ceases to be metastable, and
becomes instable.
Not only has water been cooled to temperatures considerably below the
melting point of ice, but the vapour pressure of the supercooled water has
been measured. It is of interest and importance, now, to see what
relationship exists between the vapour pressure of ice and that of
supercooled water at the same temperature. This relationship is clearly
shown by the numbers in the following table,[39] and is represented in Fig.
3, p. 27., and diagrammatically in Fig. 4, the vapour pressures of
the areas II. and III.
We see, further, that the different areas are the regions of stability of the
phase common to the two curves by which the area is enclosed.[37] Thus,
the phase common to the two systems represented by BO (ice and vapour),
and OA (water and vapour) is the vapour phase; and the area BOA is
therefore the area of the vapour phase. Similarly, BOC is the area of the ice
phase, and COA the area of the water phase.
Supercooled Water. Metastable State.—When heated under the ordinary
atmospheric pressure, ice melts when the temperature reaches 0°, and it has
so far not been found possible to raise the temperature of ice above this
point without liquefaction taking place. On the other hand, it has long been
known that water can be cooled below zero without solidification occurring.
This was first discovered in 1724 by Fahrenheit,[38] who found that water
could be exposed to a temperature of -9.4° without solidifying; so soon,
however, as a small particle of ice was brought in contact with the water,
crystallization commenced. Superfused or supercooled water—i.e. water
cooled below 0°—is unstable only in respect of the solid phase; so long as
the presence of the solid phase is carefully avoided, the water can be kept
for any length of time without solidifying, and the system supercooled
water and vapour behaves in every way like a stable system. A system, now,
which in itself is stable, and which becomes instable only in contact with a
particular phase, is said to be metastable, and the region throughout which
this condition exists is called the metastable region. Supercooled water,
therefore, is in a metastable condition. If the supercooling be carried below
a certain temperature, solidification takes place spontaneously without the
addition of the solid phase; the system then ceases to be metastable, and
becomes instable.
Not only has water been cooled to temperatures considerably below the
melting point of ice, but the vapour pressure of the supercooled water has
been measured. It is of interest and importance, now, to see what
relationship exists between the vapour pressure of ice and that of
supercooled water at the same temperature. This relationship is clearly
shown by the numbers in the following table,[39] and is represented in Fig.
3, p. 27., and diagrammatically in Fig. 4, the vapour pressures of
Page 41
supercooled water being represented by the curve OA′, which is the
unbroken continuation of AO.
Vapour Pressure of Ice and of Supercooled Water.
Pressure in mm. mercury.
Temperature.
Water. Ice. Difference.
0° 4.618 4.602 0.016[40]
-2° 3.995 3.925 0.070
-4° 3.450 3.334 0.116
-8° 2.558 2.379 0.179
-10° 2.197 1.999 0.198
-15° 1.492 1.279 0.213
-20° 1.005 0.806 0.199
At all temperatures below 0° (more correctly +0.0076°), at which
temperature water and ice have the same vapour pressure, the vapour
pressure of supercooled water is greater than that of ice at the same
temperature.
From the relative positions of the curves OB and OA (Fig. 4) we see that at
all temperatures above 0°, the (metastable) sublimation curve of ice, if it
could be obtained, would be higher than the vaporization curve of water.
This shows, therefore, that at 0° a "break" must occur in the curve of states,
and that in the neighbourhood of this break the curve above that point must
ascend less rapidly than the curve below the break. Since, however, the
differences in the vapour pressures of supercooled water and of ice are very
small, the change in the direction of the vapour-pressure curve on passing
from ice to water was at first not observed, and Regnault regarded the
sublimation curve as passing continuously into the vaporization curve. The
existence of a break was, however, shown by James Thomson[41] and by
Kirchhoff[42] to be demanded by thermo-dynamical considerations, and the
prediction of theory was afterwards realized experimentally by Ramsay and
Young in their determinations of the vapour pressure of water and ice, as
well as in the case of other substances.[43]
unbroken continuation of AO.
Vapour Pressure of Ice and of Supercooled Water.
Pressure in mm. mercury.
Temperature.
Water. Ice. Difference.
0° 4.618 4.602 0.016[40]
-2° 3.995 3.925 0.070
-4° 3.450 3.334 0.116
-8° 2.558 2.379 0.179
-10° 2.197 1.999 0.198
-15° 1.492 1.279 0.213
-20° 1.005 0.806 0.199
At all temperatures below 0° (more correctly +0.0076°), at which
temperature water and ice have the same vapour pressure, the vapour
pressure of supercooled water is greater than that of ice at the same
temperature.
From the relative positions of the curves OB and OA (Fig. 4) we see that at
all temperatures above 0°, the (metastable) sublimation curve of ice, if it
could be obtained, would be higher than the vaporization curve of water.
This shows, therefore, that at 0° a "break" must occur in the curve of states,
and that in the neighbourhood of this break the curve above that point must
ascend less rapidly than the curve below the break. Since, however, the
differences in the vapour pressures of supercooled water and of ice are very
small, the change in the direction of the vapour-pressure curve on passing
from ice to water was at first not observed, and Regnault regarded the
sublimation curve as passing continuously into the vaporization curve. The
existence of a break was, however, shown by James Thomson[41] and by
Kirchhoff[42] to be demanded by thermo-dynamical considerations, and the
prediction of theory was afterwards realized experimentally by Ramsay and
Young in their determinations of the vapour pressure of water and ice, as
well as in the case of other substances.[43]
Page 42
From what has just been said, we can readily understand why ice and water
cannot exist in equilibrium below 0°. For, suppose we have ice and water in
the same closed space, but not in contact with one another, then since the
vapour pressure of the supercooled water is higher than that of ice, the
vapour of the former must be supersaturated in contact with the latter;
vapour must, therefore, condense on the ice; and in this way there will be a
slow distillation from the water to the ice, until at last all the water will
have disappeared, and only ice and vapour remain.[44]
Other Systems of the Substance Water.—We have thus far discussed only
those systems which are constituted by the three phases—ice, water, and
water vapour. It has, however, been recently found that at a low temperature
and under a high pressure ordinary ice can pass into two other crystalline
varieties, called by Tammann[45] ice II. and ice III., ordinary ice being ice I.
According to the Phase Rule, now, since each of these solid forms
constitutes a separate phase (p. 9), it will be possible to have the following
(and more) systems of water, in addition to those already studied, viz. water,
ice I., ice II.; water, ice I., ice III.; water, ice II., ice III., forming invariant
systems and existing in equilibrium only at a definite triple point; further,
water, ice II.; water, ice III.; ice I., ice II.; ice I., ice III.; ice II., ice III.,
forming univariant systems, existing, therefore, at definite corresponding
values of temperature and pressure; and lastly, the bivariant systems, ice II.
and ice III. Several of these systems have been investigated by Tammann.
The triple point for water, ice I., ice III., lies at -22°, and a pressure of 2200
kilogms. per sq. cm. (2130 atm.), as indicated in Fig. 2, p. 27.[46] In contrast
with the behaviour of ordinary ice, the temperature of equilibrium in the
case of water—ice II., and water—ice III., is raised by increase of pressure.
B. Sulphur.
Polymorphism.—Reference has just been made to the fact that ice can
exist not only in the ordinary form, but in at least two other crystalline
varieties. This phenomenon, the existence of a substance in two or more
different crystalline forms, is called polymorphism. Polymorphism was first
observed by Mitscherlich[47] in the case of sodium phosphate, and later in
the case of sulphur. To these two cases others were soon added, at first of
inorganic, and later of organic substances, so that polymorphism is now
cannot exist in equilibrium below 0°. For, suppose we have ice and water in
the same closed space, but not in contact with one another, then since the
vapour pressure of the supercooled water is higher than that of ice, the
vapour of the former must be supersaturated in contact with the latter;
vapour must, therefore, condense on the ice; and in this way there will be a
slow distillation from the water to the ice, until at last all the water will
have disappeared, and only ice and vapour remain.[44]
Other Systems of the Substance Water.—We have thus far discussed only
those systems which are constituted by the three phases—ice, water, and
water vapour. It has, however, been recently found that at a low temperature
and under a high pressure ordinary ice can pass into two other crystalline
varieties, called by Tammann[45] ice II. and ice III., ordinary ice being ice I.
According to the Phase Rule, now, since each of these solid forms
constitutes a separate phase (p. 9), it will be possible to have the following
(and more) systems of water, in addition to those already studied, viz. water,
ice I., ice II.; water, ice I., ice III.; water, ice II., ice III., forming invariant
systems and existing in equilibrium only at a definite triple point; further,
water, ice II.; water, ice III.; ice I., ice II.; ice I., ice III.; ice II., ice III.,
forming univariant systems, existing, therefore, at definite corresponding
values of temperature and pressure; and lastly, the bivariant systems, ice II.
and ice III. Several of these systems have been investigated by Tammann.
The triple point for water, ice I., ice III., lies at -22°, and a pressure of 2200
kilogms. per sq. cm. (2130 atm.), as indicated in Fig. 2, p. 27.[46] In contrast
with the behaviour of ordinary ice, the temperature of equilibrium in the
case of water—ice II., and water—ice III., is raised by increase of pressure.
B. Sulphur.
Polymorphism.—Reference has just been made to the fact that ice can
exist not only in the ordinary form, but in at least two other crystalline
varieties. This phenomenon, the existence of a substance in two or more
different crystalline forms, is called polymorphism. Polymorphism was first
observed by Mitscherlich[47] in the case of sodium phosphate, and later in
the case of sulphur. To these two cases others were soon added, at first of
inorganic, and later of organic substances, so that polymorphism is now
Page 43
recognized as of very frequent occurrence indeed.[48] These various forms
of a substance differ not only in crystalline shape, but also in melting point,
specific gravity, and other physical properties. In the liquid state, however,
the differences do not exist.
According to our definition of phases (p. 9), each of these polymorphic
forms constitutes a separate phase of the particular substance. As is readily
apparent, the number of possible systems formed of one component may be
considerably increased when that component is capable of existing in
different crystalline forms. We have, therefore, to inquire what are the
conditions under which different polymorphic forms can coexist, either
alone or in presence of the liquid and vapour phase. For the purpose of
illustrating the general behaviour of such systems, we shall study the
systems formed by the different crystalline forms of sulphur, tin, and
benzophenone.
Sulphur exists in two well-known crystalline forms—rhombic, or
octahedral, and monoclinic, or prismatic sulphur. Of these, the former melts
at 114.5°; the latter at 120°.[49] Further, at the ordinary temperature,
rhombic sulphur can exist unchanged, whereas, on being heated to
temperatures somewhat below the melting point, it passes into the prismatic
variety. On the other hand, at temperatures above 96°, prismatic sulphur can
remain unchanged, whereas at the ordinary temperature it passes slowly
into the rhombic form.
If, now, we examine the case of sulphur with the help of the Phase Rule, we
see that the following systems are theoretically possible:—
I. Bivariant Systems: One component in one phase.
(a) Rhombic sulphur.
(b) Monoclinic sulphur.
(c) Sulphur vapour.
(d) Liquid sulphur.
II. Univariant Systems: One component in two phases.
(a) Rhombic sulphur and vapour.
(b) Monoclinic sulphur and vapour.
(c) Rhombic sulphur and liquid.
of a substance differ not only in crystalline shape, but also in melting point,
specific gravity, and other physical properties. In the liquid state, however,
the differences do not exist.
According to our definition of phases (p. 9), each of these polymorphic
forms constitutes a separate phase of the particular substance. As is readily
apparent, the number of possible systems formed of one component may be
considerably increased when that component is capable of existing in
different crystalline forms. We have, therefore, to inquire what are the
conditions under which different polymorphic forms can coexist, either
alone or in presence of the liquid and vapour phase. For the purpose of
illustrating the general behaviour of such systems, we shall study the
systems formed by the different crystalline forms of sulphur, tin, and
benzophenone.
Sulphur exists in two well-known crystalline forms—rhombic, or
octahedral, and monoclinic, or prismatic sulphur. Of these, the former melts
at 114.5°; the latter at 120°.[49] Further, at the ordinary temperature,
rhombic sulphur can exist unchanged, whereas, on being heated to
temperatures somewhat below the melting point, it passes into the prismatic
variety. On the other hand, at temperatures above 96°, prismatic sulphur can
remain unchanged, whereas at the ordinary temperature it passes slowly
into the rhombic form.
If, now, we examine the case of sulphur with the help of the Phase Rule, we
see that the following systems are theoretically possible:—
I. Bivariant Systems: One component in one phase.
(a) Rhombic sulphur.
(b) Monoclinic sulphur.
(c) Sulphur vapour.
(d) Liquid sulphur.
II. Univariant Systems: One component in two phases.
(a) Rhombic sulphur and vapour.
(b) Monoclinic sulphur and vapour.
(c) Rhombic sulphur and liquid.
Page 44
(d) Monoclinic sulphur and liquid.
(e) Rhombic and monoclinic sulphur.
(f) Liquid and vapour.
III. Invariant Systems: One component in three phases.
(a) Rhombic and monoclinic sulphur and vapour.
(b) Rhombic sulphur, liquid and vapour.
(c) Monoclinic sulphur, liquid and vapour.
(d) Rhombic and monoclinic sulphur and liquid.
Triple Point—Rhombic and Monoclinic
Sulphur and Vapour. Transition Point.—In
the case of ice, water and vapour, we saw that at
the triple point the vapour pressures of ice and
water are equal; below this point, ice is stable;
above this point, water is stable. We saw, further,
that below 0° the vapour pressure of the stable
system is lower than that of the metastable, and
therefore that at the triple point there is a break
in the vapour pressure curve of such a kind that Fig. 5.
above the triple point the vapour-pressure curve
ascends more slowly than below it. Now, although the vapour pressure of
solid sulphur has not been determined, we can nevertheless consider that it
does possess a certain, even if very small, vapour pressure,[50] and that at
the temperature at which the vapour pressures of rhombic and monoclinic
sulphur become equal, we can have these two solid forms existing in
equilibrium with the vapour. Below that point only one form, that with the
lower vapour pressure, will be stable; above that point only the other form
will be stable. On passing through the triple point, therefore, there will be a
change of the one form into the other. This point is represented in our
diagram (Fig. 5) by the point O, the two curves AO and OB representing
diagrammatically the vapour pressures of rhombic and monoclinic sulphur
respectively. If the vapour phase is absent and the system maintained under
a constant pressure, e.g. atmospheric pressure, there will also be a definite
temperature at which the two solid forms are in equilibrium, and on passing
through which complete and reversible transformation of one form into the
other occurs. This temperature, which refers to equilibrium in absence of
(e) Rhombic and monoclinic sulphur.
(f) Liquid and vapour.
III. Invariant Systems: One component in three phases.
(a) Rhombic and monoclinic sulphur and vapour.
(b) Rhombic sulphur, liquid and vapour.
(c) Monoclinic sulphur, liquid and vapour.
(d) Rhombic and monoclinic sulphur and liquid.
Triple Point—Rhombic and Monoclinic
Sulphur and Vapour. Transition Point.—In
the case of ice, water and vapour, we saw that at
the triple point the vapour pressures of ice and
water are equal; below this point, ice is stable;
above this point, water is stable. We saw, further,
that below 0° the vapour pressure of the stable
system is lower than that of the metastable, and
therefore that at the triple point there is a break
in the vapour pressure curve of such a kind that Fig. 5.
above the triple point the vapour-pressure curve
ascends more slowly than below it. Now, although the vapour pressure of
solid sulphur has not been determined, we can nevertheless consider that it
does possess a certain, even if very small, vapour pressure,[50] and that at
the temperature at which the vapour pressures of rhombic and monoclinic
sulphur become equal, we can have these two solid forms existing in
equilibrium with the vapour. Below that point only one form, that with the
lower vapour pressure, will be stable; above that point only the other form
will be stable. On passing through the triple point, therefore, there will be a
change of the one form into the other. This point is represented in our
diagram (Fig. 5) by the point O, the two curves AO and OB representing
diagrammatically the vapour pressures of rhombic and monoclinic sulphur
respectively. If the vapour phase is absent and the system maintained under
a constant pressure, e.g. atmospheric pressure, there will also be a definite
temperature at which the two solid forms are in equilibrium, and on passing
through which complete and reversible transformation of one form into the
other occurs. This temperature, which refers to equilibrium in absence of
Page 45
the vapour phase, is known as the transition temperature or inversion
temperature.
Were we dependent on measurements of pressure and temperature, the
determination of the transition point might be a matter of great difficulty.
When we consider, however, that the other physical properties of the solid
phases, e.g. the density, undergo an abrupt change on passing through the
transition point, owing to the transformation of one form into the other, then
any method by which this abrupt change in the physical properties can be
detected may be employed for determining the transition point. A
considerable number of such methods have been devised, and a description
of the most important of these is given in the Appendix.
In the case of sulphur, the transition point of rhombic into monoclinic
sulphur was found by Reicher[51] to lie at 95.5°. Below this temperature the
octahedral, above it the monoclinic, is the stable form.
Condensed Systems.—We have already seen that in the change of the
melting point of water with the pressure, a very great increase of the latter
was necessary in order to produce a comparatively small change in the
temperature of equilibrium. This is a characteristic of all systems from
which the vapour phase is absent, and which are composed only of solid
and liquid phases. Such systems are called condensed systems,[52] and in
determining the temperature of equilibrium of such systems, practically the
same point will be obtained whether the measurements are carried out under
atmospheric pressure or under the pressure of the vapour of the solid or
liquid phases. The transition point, therefore, as determined in open vessels
at atmospheric pressure, will differ only by a very slight amount from the
triple point, or point at which the two solid or liquid phases are in
equilibrium under the pressure of their vapour. The determination of the
transition point is thereby greatly simplified.
Suspended Transformation.—In many respects the transition point of two
solid phases is analogous to the melting point of a solid, or point at which
the solid passes into a liquid. In both cases the change of phase is associated
with a definite temperature and pressure in such a way that below the point
the one phase, above the point the other phase, is stable. The transition
point, however, differs in so far from a point of fusion, that while it is
temperature.
Were we dependent on measurements of pressure and temperature, the
determination of the transition point might be a matter of great difficulty.
When we consider, however, that the other physical properties of the solid
phases, e.g. the density, undergo an abrupt change on passing through the
transition point, owing to the transformation of one form into the other, then
any method by which this abrupt change in the physical properties can be
detected may be employed for determining the transition point. A
considerable number of such methods have been devised, and a description
of the most important of these is given in the Appendix.
In the case of sulphur, the transition point of rhombic into monoclinic
sulphur was found by Reicher[51] to lie at 95.5°. Below this temperature the
octahedral, above it the monoclinic, is the stable form.
Condensed Systems.—We have already seen that in the change of the
melting point of water with the pressure, a very great increase of the latter
was necessary in order to produce a comparatively small change in the
temperature of equilibrium. This is a characteristic of all systems from
which the vapour phase is absent, and which are composed only of solid
and liquid phases. Such systems are called condensed systems,[52] and in
determining the temperature of equilibrium of such systems, practically the
same point will be obtained whether the measurements are carried out under
atmospheric pressure or under the pressure of the vapour of the solid or
liquid phases. The transition point, therefore, as determined in open vessels
at atmospheric pressure, will differ only by a very slight amount from the
triple point, or point at which the two solid or liquid phases are in
equilibrium under the pressure of their vapour. The determination of the
transition point is thereby greatly simplified.
Suspended Transformation.—In many respects the transition point of two
solid phases is analogous to the melting point of a solid, or point at which
the solid passes into a liquid. In both cases the change of phase is associated
with a definite temperature and pressure in such a way that below the point
the one phase, above the point the other phase, is stable. The transition
point, however, differs in so far from a point of fusion, that while it is
Page 46
possible to supercool a liquid, no definite case is known where the solid has
been heated above the triple point without passing into the liquid state.
Transformation, therefore, is suspended only on one side of the melting
point. In the case of two solid phases, however, the transition point can be
overstepped in both directions, so that each phase can be obtained in the
metastable condition. In the case of supercooled water, further, we saw that
the introduction of the stable, solid phase caused the speedy transformation
of the metastable to the stable condition of equilibrium; but in the case of
two solid phases the change from the metastable to the stable modification
may occur with great slowness, even in presence of the stable form. This
tardiness with which the stable condition of equilibrium is reached greatly
increases in many cases the difficulty of accurately determining the
transition point. The phenomena of suspended transformation will,
however, receive a fuller discussion later (p. 68).
Transition Curve—Rhombic and Monoclinic Sulphur.—Just as we
found the melting point of ice to vary with the pressure, so also do we find
that change of pressure causes an alteration in the transition point. In the
case of the transition point of rhombic into monoclinic sulphur, increase of
pressure by 1 atm. raises the transition point by 0.04°-0.05°.[53] The
transition curve, or curve representing the change of the transition point
with pressure, will therefore slope to the right away from the pressure axis.
This is curve OC (Fig. 5).
Triple Point—Monoclinic Sulphur, Liquid, and Vapour. Melting Point
of Monoclinic Sulphur.—Above 95.5°, monoclinic sulphur is, as we have
seen, the stable form. On being heated to 120°, under atmospheric pressure,
it melts. This temperature is, therefore, the point of equilibrium between
monoclinic sulphur and liquid sulphur under atmospheric pressure. Since
we are dealing with a condensed system, this temperature may be regarded
as very nearly that at which the solid and liquid are in equilibrium with their
vapour, i.e. the triple point, solid (monoclinic)—liquid—vapour. This point
is represented in the diagram by B.
Triple Point—Rhombic and Monoclinic Sulphur and Liquid.—In
contrast with that of ice, the fusion point of monoclinic sulphur is raised by
increase of pressure, and the fusion curve, therefore, slopes to the right. The
transition curve of rhombic and monoclinic sulphur, as we have seen, also
been heated above the triple point without passing into the liquid state.
Transformation, therefore, is suspended only on one side of the melting
point. In the case of two solid phases, however, the transition point can be
overstepped in both directions, so that each phase can be obtained in the
metastable condition. In the case of supercooled water, further, we saw that
the introduction of the stable, solid phase caused the speedy transformation
of the metastable to the stable condition of equilibrium; but in the case of
two solid phases the change from the metastable to the stable modification
may occur with great slowness, even in presence of the stable form. This
tardiness with which the stable condition of equilibrium is reached greatly
increases in many cases the difficulty of accurately determining the
transition point. The phenomena of suspended transformation will,
however, receive a fuller discussion later (p. 68).
Transition Curve—Rhombic and Monoclinic Sulphur.—Just as we
found the melting point of ice to vary with the pressure, so also do we find
that change of pressure causes an alteration in the transition point. In the
case of the transition point of rhombic into monoclinic sulphur, increase of
pressure by 1 atm. raises the transition point by 0.04°-0.05°.[53] The
transition curve, or curve representing the change of the transition point
with pressure, will therefore slope to the right away from the pressure axis.
This is curve OC (Fig. 5).
Triple Point—Monoclinic Sulphur, Liquid, and Vapour. Melting Point
of Monoclinic Sulphur.—Above 95.5°, monoclinic sulphur is, as we have
seen, the stable form. On being heated to 120°, under atmospheric pressure,
it melts. This temperature is, therefore, the point of equilibrium between
monoclinic sulphur and liquid sulphur under atmospheric pressure. Since
we are dealing with a condensed system, this temperature may be regarded
as very nearly that at which the solid and liquid are in equilibrium with their
vapour, i.e. the triple point, solid (monoclinic)—liquid—vapour. This point
is represented in the diagram by B.
Triple Point—Rhombic and Monoclinic Sulphur and Liquid.—In
contrast with that of ice, the fusion point of monoclinic sulphur is raised by
increase of pressure, and the fusion curve, therefore, slopes to the right. The
transition curve of rhombic and monoclinic sulphur, as we have seen, also
Page 47
slopes to the right, and more so than the fusion curve of monoclinic sulphur.
There will, therefore, be a certain pressure and temperature at which the
two curves will cut. This point lies at 151°, and a pressure of 1320 kilogm.
per sq. cm., or about 1288 atm.[54] It, therefore, forms another triple point,
the existence of which had been predicted by Roozeboom,[55] at which
rhombic and monoclinic sulphur are in equilibrium with liquid sulphur. It is
represented in our diagram by the point C. Beyond this point monoclinic
sulphur ceases to exist in a stable condition. At temperatures and pressures
above this triple point, rhombic sulphur will be the stable modification, and
this fact is of mineralogical interest, because it explains the occurrence in
nature of well-formed rhombic crystals. Under ordinary conditions,
prismatic sulphur separates out on cooling fused sulphur, but at
temperatures above 151° and under pressures greater than 1288 atm., the
rhombic form would be produced.[56]
Triple Point—Rhombic Sulphur, Liquid, and Vapour. Metastable
Triple Point.—On account of the slowness with which transformation of
one form into the other takes place on passing the transition point, it has
been found possible to heat rhombic sulphur up to its melting point
(114.5°). At this temperature, not only is rhombic sulphur in a metastable
condition, but the liquid is also metastable, its vapour pressure being greater
than that of solid monoclinic sulphur. This point is represented in our
diagram by the point b.
From the relative positions of the metastable melting point of rhombic
sulphur and the stable melting point of monoclinic sulphur at 120°, we see
that, of the two forms, the metastable form has the lower melting point.
This, of course, is valid only for the relative stability in the neighbourhood
of the melting point; for we have already learned that at lower temperatures
rhombic sulphur is the stable, monoclinic sulphur the metastable (or
unstable) form.
Fusion Curve of Rhombic Sulphur.—Like any other melting point, that of
rhombic sulphur will be displaced by increase of pressure; increase of
pressure raises the melting point, and we can therefore obtain a metastable
fusion curve representing the conditions under which rhombic sulphur is in
equilibrium with liquid sulphur. This metastable fusion curve must pass
through the triple point for rhombic sulphur—monoclinic sulphur—liquid
There will, therefore, be a certain pressure and temperature at which the
two curves will cut. This point lies at 151°, and a pressure of 1320 kilogm.
per sq. cm., or about 1288 atm.[54] It, therefore, forms another triple point,
the existence of which had been predicted by Roozeboom,[55] at which
rhombic and monoclinic sulphur are in equilibrium with liquid sulphur. It is
represented in our diagram by the point C. Beyond this point monoclinic
sulphur ceases to exist in a stable condition. At temperatures and pressures
above this triple point, rhombic sulphur will be the stable modification, and
this fact is of mineralogical interest, because it explains the occurrence in
nature of well-formed rhombic crystals. Under ordinary conditions,
prismatic sulphur separates out on cooling fused sulphur, but at
temperatures above 151° and under pressures greater than 1288 atm., the
rhombic form would be produced.[56]
Triple Point—Rhombic Sulphur, Liquid, and Vapour. Metastable
Triple Point.—On account of the slowness with which transformation of
one form into the other takes place on passing the transition point, it has
been found possible to heat rhombic sulphur up to its melting point
(114.5°). At this temperature, not only is rhombic sulphur in a metastable
condition, but the liquid is also metastable, its vapour pressure being greater
than that of solid monoclinic sulphur. This point is represented in our
diagram by the point b.
From the relative positions of the metastable melting point of rhombic
sulphur and the stable melting point of monoclinic sulphur at 120°, we see
that, of the two forms, the metastable form has the lower melting point.
This, of course, is valid only for the relative stability in the neighbourhood
of the melting point; for we have already learned that at lower temperatures
rhombic sulphur is the stable, monoclinic sulphur the metastable (or
unstable) form.
Fusion Curve of Rhombic Sulphur.—Like any other melting point, that of
rhombic sulphur will be displaced by increase of pressure; increase of
pressure raises the melting point, and we can therefore obtain a metastable
fusion curve representing the conditions under which rhombic sulphur is in
equilibrium with liquid sulphur. This metastable fusion curve must pass
through the triple point for rhombic sulphur—monoclinic sulphur—liquid
Page 48
sulphur, and on passing this point it becomes a stable fusion curve. The
continuation of this curve, therefore, above 151° forms the stable fusion
curve of rhombic sulphur (curve CD).
These curves have been investigated at high pressures by Tammann, and the
results are represented according to scale in Fig. 6,[57] a being the curve for
monoclinic sulphur and liquid; b, that for rhombic sulphur and liquid; and c,
that for rhombic and monoclinic sulphur.
Bivariant Systems.—Just as in the case of the diagram of states of water,
the areas in Fig. 5 represent the conditions for the stable existence of the
single phases: rhombic sulphur in the area to the left of AOCD; monoclinic
sulphur in the area OBC; liquid sulphur in the area EBCD; sulphur vapour
below the curves AOBE. As can be seen from the diagram, the existence of
monoclinic sulphur is limited on all sides, its area being bounded by the
curves OB, OC, BC. At any point outside this area, monoclinic sulphur can
exist only in a metastable condition.
continuation of this curve, therefore, above 151° forms the stable fusion
curve of rhombic sulphur (curve CD).
These curves have been investigated at high pressures by Tammann, and the
results are represented according to scale in Fig. 6,[57] a being the curve for
monoclinic sulphur and liquid; b, that for rhombic sulphur and liquid; and c,
that for rhombic and monoclinic sulphur.
Bivariant Systems.—Just as in the case of the diagram of states of water,
the areas in Fig. 5 represent the conditions for the stable existence of the
single phases: rhombic sulphur in the area to the left of AOCD; monoclinic
sulphur in the area OBC; liquid sulphur in the area EBCD; sulphur vapour
below the curves AOBE. As can be seen from the diagram, the existence of
monoclinic sulphur is limited on all sides, its area being bounded by the
curves OB, OC, BC. At any point outside this area, monoclinic sulphur can
exist only in a metastable condition.
Page 49
Fig. 6.
Other crystalline forms of sulphur have been obtained,[58] so that the existence of other
systems of the one-component sulphur besides those already described is possible.
Reference will be made to these later (p. 51).
C. Tin.
Another substance capable of existing in more than one crystalline form, is the metal tin,
and although the general behaviour, so far as studied, is analogous to that of sulphur, a
short account of the two varieties of tin may be given here, not only on account of their
metallurgical interest, but also on account of the importance which the phenomena
possess for the employment of this metal in everyday life.
After a winter of extreme severity in Russia (1867-1868), the somewhat unpleasant
discovery was made that a number of blocks of tin, which had been stored in the Customs
House at St. Petersburg, had undergone disintegration and crumbled to a grey powder.[59]
That tin undergoes change on exposure to extreme cold was known, however, before that
time, even as far back as the time of Aristotle, who spoke of the tin as "melting."[60]
Ludicrous as that term may now appear, Aristotle nevertheless unconsciously employed a
strikingly accurate analogy, for the conditions under which ordinary white tin passes into
the grey modification are, in many ways, quite analogous to those under which a
substance passes from the solid to the liquid state. The knowledge of this was, however,
beyond the wisdom of the Greek philosopher.
For many years there existed considerable confusion both as to the conditions under
which the transformation of white tin into its allotropic modification occurs, and to the
reason of the change. Under the guidance of the Phase Rule, however, the confusion
Other crystalline forms of sulphur have been obtained,[58] so that the existence of other
systems of the one-component sulphur besides those already described is possible.
Reference will be made to these later (p. 51).
C. Tin.
Another substance capable of existing in more than one crystalline form, is the metal tin,
and although the general behaviour, so far as studied, is analogous to that of sulphur, a
short account of the two varieties of tin may be given here, not only on account of their
metallurgical interest, but also on account of the importance which the phenomena
possess for the employment of this metal in everyday life.
After a winter of extreme severity in Russia (1867-1868), the somewhat unpleasant
discovery was made that a number of blocks of tin, which had been stored in the Customs
House at St. Petersburg, had undergone disintegration and crumbled to a grey powder.[59]
That tin undergoes change on exposure to extreme cold was known, however, before that
time, even as far back as the time of Aristotle, who spoke of the tin as "melting."[60]
Ludicrous as that term may now appear, Aristotle nevertheless unconsciously employed a
strikingly accurate analogy, for the conditions under which ordinary white tin passes into
the grey modification are, in many ways, quite analogous to those under which a
substance passes from the solid to the liquid state. The knowledge of this was, however,
beyond the wisdom of the Greek philosopher.
For many years there existed considerable confusion both as to the conditions under
which the transformation of white tin into its allotropic modification occurs, and to the
reason of the change. Under the guidance of the Phase Rule, however, the confusion
Page 50
which obtained has been cleared away, and the "mysterious" behaviour of tin brought into
accord with other phenomena of transformation.[61]
Transition Point.—Just as in the case of sulphur, so also in the case of tin, there is a
transition point above which the one form, ordinary white tin, and below which the other
form, grey tin, is the stable variety. In the case of this metal, the transition point was
found by Cohen and van Eyk, who employed both the dilatometric and the electrical
methods (Appendix) to be 20°. Below this temperature, grey tin is the stable form. But, as
we have seen in the case of sulphur, the change of the metastable into the stable solid
phase occurs with considerable slowness, and this behaviour is found also in the case of
tin. Were it not so, we should not be able to use this metal for the many purposes to which
it is applied in everyday life; for, with the exception of a comparatively small number of
days in the year, the temperature of our climate is below 20°, and white tin is, therefore,
at the ordinary temperature, in a metastable condition. The change, however, into the
stable form at the ordinary temperature, although slow, nevertheless takes place, as is
shown by the partial or entire conversion of articles of tin which have lain buried for
several hundreds of years.
On lowering the temperature, the velocity with which the transformation of the tin occurs
is increased, and Cohen and van Eyk found that the temperature of maximum velocity is
about -50°. Contact with the stable form will, of course, facilitate the transformation.
The change of white tin into grey takes place also with increased velocity in presence of a
solution of tin ammonium chloride (pink salt), which is able to dissolve small quantities
of tin. In presence of such a solution also, it was found that the temperature at which the
velocity of transformation was greatest was raised to 0°. At this temperature, white tin in
contact with a solution of tin ammonium chloride, and the grey modification, undergoes
transformation to an appreciable extent in the course of a few days.
Fig. 7 is a photograph of a piece of white tin undergoing transformation into the grey
variety.[62] The bright surface of the tin becomes covered with a number of warty masses,
formed of the less dense grey form, and the number and size of these continue to grow
until the whole of the white tin has passed into a grey powder. On account of the
appearance which is here seen, this transformation of tin has been called by Cohen the
"tin plague."
accord with other phenomena of transformation.[61]
Transition Point.—Just as in the case of sulphur, so also in the case of tin, there is a
transition point above which the one form, ordinary white tin, and below which the other
form, grey tin, is the stable variety. In the case of this metal, the transition point was
found by Cohen and van Eyk, who employed both the dilatometric and the electrical
methods (Appendix) to be 20°. Below this temperature, grey tin is the stable form. But, as
we have seen in the case of sulphur, the change of the metastable into the stable solid
phase occurs with considerable slowness, and this behaviour is found also in the case of
tin. Were it not so, we should not be able to use this metal for the many purposes to which
it is applied in everyday life; for, with the exception of a comparatively small number of
days in the year, the temperature of our climate is below 20°, and white tin is, therefore,
at the ordinary temperature, in a metastable condition. The change, however, into the
stable form at the ordinary temperature, although slow, nevertheless takes place, as is
shown by the partial or entire conversion of articles of tin which have lain buried for
several hundreds of years.
On lowering the temperature, the velocity with which the transformation of the tin occurs
is increased, and Cohen and van Eyk found that the temperature of maximum velocity is
about -50°. Contact with the stable form will, of course, facilitate the transformation.
The change of white tin into grey takes place also with increased velocity in presence of a
solution of tin ammonium chloride (pink salt), which is able to dissolve small quantities
of tin. In presence of such a solution also, it was found that the temperature at which the
velocity of transformation was greatest was raised to 0°. At this temperature, white tin in
contact with a solution of tin ammonium chloride, and the grey modification, undergoes
transformation to an appreciable extent in the course of a few days.
Fig. 7 is a photograph of a piece of white tin undergoing transformation into the grey
variety.[62] The bright surface of the tin becomes covered with a number of warty masses,
formed of the less dense grey form, and the number and size of these continue to grow
until the whole of the white tin has passed into a grey powder. On account of the
appearance which is here seen, this transformation of tin has been called by Cohen the
"tin plague."
Page 51
Fig. 7.
Enantiotropy and Monotropy.—In the case of sulphur and tin, we have met with two
substances existing in polymorphic forms, and we have also learned that these forms
exhibit a definite transition point at which their relative stability is reversed. Each form,
therefore, possesses a definite range of stable existence, and is capable of undergoing
transformation into the other, at temperatures above or below that of the transition point.
Another class of dimorphous substances is, however, met with as, for instance, in the case
of the well-known compounds iodine monochloride and benzophenone. Each crystalline
form has its own melting point, the dimorphous forms of iodine monochloride melting at
13.9° and 27.2°,[63] and those of benzophenone at 26° and 48°.[64] This class of substance
differs from that which we have already studied (e.g. sulphur and tin), in that at all
temperatures up to the melting point, only one of the forms is stable, the other being
metastable. There is, therefore, no transition point, and transformation of the crystalline
forms can be observed only in one direction. These two classes of phenomena are
distinguished by the names enantiotropy and monotropy; enantiotropic substances being
such that the change of one form into the other is a reversible process (e.g. rhombic
sulphur into monoclinic, and monoclinic sulphur into rhombic), and monotropic
substances, those in which the transformation of the crystalline forms is irreversible.
These differences in the behaviour can be
explained very well in many cases by
supposing that in the case of enantiotropic
substances the transition point lies below the
melting point, while in the case of monotropic
substances, it lies above the melting point.[65]
These conditions would be represented by the Fig. 8.
Figs. 8 and 9. Fig. 9.
Enantiotropy and Monotropy.—In the case of sulphur and tin, we have met with two
substances existing in polymorphic forms, and we have also learned that these forms
exhibit a definite transition point at which their relative stability is reversed. Each form,
therefore, possesses a definite range of stable existence, and is capable of undergoing
transformation into the other, at temperatures above or below that of the transition point.
Another class of dimorphous substances is, however, met with as, for instance, in the case
of the well-known compounds iodine monochloride and benzophenone. Each crystalline
form has its own melting point, the dimorphous forms of iodine monochloride melting at
13.9° and 27.2°,[63] and those of benzophenone at 26° and 48°.[64] This class of substance
differs from that which we have already studied (e.g. sulphur and tin), in that at all
temperatures up to the melting point, only one of the forms is stable, the other being
metastable. There is, therefore, no transition point, and transformation of the crystalline
forms can be observed only in one direction. These two classes of phenomena are
distinguished by the names enantiotropy and monotropy; enantiotropic substances being
such that the change of one form into the other is a reversible process (e.g. rhombic
sulphur into monoclinic, and monoclinic sulphur into rhombic), and monotropic
substances, those in which the transformation of the crystalline forms is irreversible.
These differences in the behaviour can be
explained very well in many cases by
supposing that in the case of enantiotropic
substances the transition point lies below the
melting point, while in the case of monotropic
substances, it lies above the melting point.[65]
These conditions would be represented by the Fig. 8.
Figs. 8 and 9. Fig. 9.
Page 52
In these two figures, O3 is the transition point, O1 and O2 the melting points of the
metastable and stable forms respectively. From Fig. 9 we see that the crystalline form I. at
all temperatures up to its melting point is metastable with respect to the form II. In such
cases the transition point could be reached only at higher pressures.
Although, as already stated, this explanation suffices for many cases, it does not prove
that in all cases of monotropy the transition point is above the melting point of the two
forms. It is also quite possible that the transition point may lie below the melting points;
[66] in this case we have what is known as pseudomonotropy. It is possible that graphite
and diamond,[67] perhaps also the two forms of phosphorus, stand in the relation of
pseudomonotropy (v. p. 49).
The disposition of the curves in Figs. 8 and 9 also explains the phenomenon sometimes
met with, especially in organic chemistry, that the substance first melts, then solidifies,
and remelts at a higher temperature. On again determining the melting point after re-
solidification, only the higher melting point is obtained.
The explanation of such a behaviour is, that if the determination of the melting point is
carried out rapidly, the point O1, the melting point of the metastable solid form, may be
realized. At this temperature, however, the liquid is metastable with respect to the stable
solid form, and if the temperature is not allowed to rise above the melting point of the
latter, the liquid may solidify. The stable solid modification thus obtained will melt only
at a higher temperature.
D. Phosphorus.
An interesting case of a monotropic dimorphous substance is found in phosphorus, which
occurs in two crystalline forms; white phosphorus belonging to the regular system, and
red phosphorus belonging to the hexagonal system. From determinations of the vapour
pressures of liquid white phosphorus, and of solid red phosphorus,[68] it was found that
the vapour pressure of red phosphorus was considerably lower than that of liquid white
phosphorus at the same temperature, the values obtained being given in the following
table.
Vapour Pressures of White and Red Phosphorus.
Vapour pressure of red
Vapour pressure of liquid white phosphorus.
phosphorus.
Pressure Pressure Pressure
Temperature. Temperature. Temperature.
in cm. in atm. in atm.
165° 12 360° 3.2 360° 0.1
180° 20.4 440° 7.5 440°
1.75
200° 26.6 494° 18.0 487° 6.8
metastable and stable forms respectively. From Fig. 9 we see that the crystalline form I. at
all temperatures up to its melting point is metastable with respect to the form II. In such
cases the transition point could be reached only at higher pressures.
Although, as already stated, this explanation suffices for many cases, it does not prove
that in all cases of monotropy the transition point is above the melting point of the two
forms. It is also quite possible that the transition point may lie below the melting points;
[66] in this case we have what is known as pseudomonotropy. It is possible that graphite
and diamond,[67] perhaps also the two forms of phosphorus, stand in the relation of
pseudomonotropy (v. p. 49).
The disposition of the curves in Figs. 8 and 9 also explains the phenomenon sometimes
met with, especially in organic chemistry, that the substance first melts, then solidifies,
and remelts at a higher temperature. On again determining the melting point after re-
solidification, only the higher melting point is obtained.
The explanation of such a behaviour is, that if the determination of the melting point is
carried out rapidly, the point O1, the melting point of the metastable solid form, may be
realized. At this temperature, however, the liquid is metastable with respect to the stable
solid form, and if the temperature is not allowed to rise above the melting point of the
latter, the liquid may solidify. The stable solid modification thus obtained will melt only
at a higher temperature.
D. Phosphorus.
An interesting case of a monotropic dimorphous substance is found in phosphorus, which
occurs in two crystalline forms; white phosphorus belonging to the regular system, and
red phosphorus belonging to the hexagonal system. From determinations of the vapour
pressures of liquid white phosphorus, and of solid red phosphorus,[68] it was found that
the vapour pressure of red phosphorus was considerably lower than that of liquid white
phosphorus at the same temperature, the values obtained being given in the following
table.
Vapour Pressures of White and Red Phosphorus.
Vapour pressure of red
Vapour pressure of liquid white phosphorus.
phosphorus.
Pressure Pressure Pressure
Temperature. Temperature. Temperature.
in cm. in atm. in atm.
165° 12 360° 3.2 360° 0.1
180° 20.4 440° 7.5 440°
1.75
200° 26.6 494° 18.0 487° 6.8
Page 53
219° 35.9 503° 21.9 510° 10.8
230° 51.4 511° 26.2 531° 16.0
290° 76.0 — — 550° 31.0
— — — — 577° 56.0
These values are also represented graphically in Fig. 10.
At all temperatures above about 260°, transformation of the white
into the red modification takes place with appreciable velocity, and
this velocity increases as the temperature is raised. Even at lower
temperatures, e.g. at the ordinary temperature, the velocity of
transformation is increased under the influence of light,[69] or by
the presence of certain substances, e.g. iodine,[70] just as the
velocity of transformation of white tin into the grey modification
was increased by the presence of a solution of tin ammonium Fig. 10.
chloride (p. 40). At the ordinary temperature, therefore, white
phosphorus must be considered as the less stable (metastable) form, for although it can
exist in contact with red phosphorus for a long period, its vapour pressure, as we have
seen, is greater than that of the red modification, and also, its solubility in different
solvents is greater[71] than that of the red modification; as we shall find later, the
solubility of the metastable form is always greater than that of the stable.
The relationships which are met with in the case of phosphorus can be best represented
by the diagram, Fig. 11.[72]
In this figure, BO1 represents the conditions of equilibrium of the univariant system red
phosphorus and vapour, which ends at O1, the melting point of red phosphorus. By
heating in capillary tubes of hard glass, Chapman[73] found that red phosphorus melts at
the melting point of potassium iodide, i.e. about 630°,[74] but the pressure at this
temperature is unknown.
At O1, then, we have the triple point, red phosphorus, liquid, and vapour, and starting
from it, we should have the vaporization curve of liquid phosphorus, O1A, and the fusion
curve of red phosphorus, O1F. Although these have not been determined, the latter curve
must, from theoretical considerations (v. p. 58), slope slightly to the right; i.e. increase of
pressure raises the melting point of red phosphorus.
230° 51.4 511° 26.2 531° 16.0
290° 76.0 — — 550° 31.0
— — — — 577° 56.0
These values are also represented graphically in Fig. 10.
At all temperatures above about 260°, transformation of the white
into the red modification takes place with appreciable velocity, and
this velocity increases as the temperature is raised. Even at lower
temperatures, e.g. at the ordinary temperature, the velocity of
transformation is increased under the influence of light,[69] or by
the presence of certain substances, e.g. iodine,[70] just as the
velocity of transformation of white tin into the grey modification
was increased by the presence of a solution of tin ammonium Fig. 10.
chloride (p. 40). At the ordinary temperature, therefore, white
phosphorus must be considered as the less stable (metastable) form, for although it can
exist in contact with red phosphorus for a long period, its vapour pressure, as we have
seen, is greater than that of the red modification, and also, its solubility in different
solvents is greater[71] than that of the red modification; as we shall find later, the
solubility of the metastable form is always greater than that of the stable.
The relationships which are met with in the case of phosphorus can be best represented
by the diagram, Fig. 11.[72]
In this figure, BO1 represents the conditions of equilibrium of the univariant system red
phosphorus and vapour, which ends at O1, the melting point of red phosphorus. By
heating in capillary tubes of hard glass, Chapman[73] found that red phosphorus melts at
the melting point of potassium iodide, i.e. about 630°,[74] but the pressure at this
temperature is unknown.
At O1, then, we have the triple point, red phosphorus, liquid, and vapour, and starting
from it, we should have the vaporization curve of liquid phosphorus, O1A, and the fusion
curve of red phosphorus, O1F. Although these have not been determined, the latter curve
must, from theoretical considerations (v. p. 58), slope slightly to the right; i.e. increase of
pressure raises the melting point of red phosphorus.
Page 54
Fig. 11.
When white phosphorus is heated to 44°, it melts. At this point, therefore, we shall have
another triple point, white phosphorus—liquid—vapour; the pressure at this point has
been calculated to be 3 mm.[75] This point is the intersection of three curves, viz.
sublimation curve, vaporization curve, and the fusion curve of white phosphorus. The
fusion curve, O2E, has been determined by Tammann[76] and by G. A. Hulett,[77] and it
was found that increase of pressure by 1 atm. raises the melting point by 0.029°. The
sublimation curve of white phosphorus has not yet been determined.
As can be seen from the table of vapour pressures (p. 46), the vapour pressure of white
phosphorus has been determined up to 500°; at temperatures above this, however, the
velocity with which transformation into red phosphorus takes place is so great as to
render the determination of the vapour pressure at higher temperatures impossible. Since,
however, the difference between white phosphorus and red phosphorus disappears in the
liquid state, the vapour pressure curve of white phosphorus must pass through the point
O1, the melting point of red phosphorus, and must be continuous with the curve O1A, the
vapour pressure curve of liquid phosphorus (vide infra). Since, as Fig. 10 shows, the
vapour pressure curve of white phosphorus ascends very rapidly at higher temperatures,
the "break" between BO1 and O1A must be very slight.
As compared with monotropic substances like benzophenone, phosphorus exhibits the
peculiarity that transformation of the metastable into the stable modification takes place
with great slowness; and further, the time required for the production of equilibrium
between red phosphorus and phosphorus vapour is great compared with that required for
establishing the same equilibrium in the case of white phosphorus. This behaviour can be
best explained by the assumption that change in the molecular complexity
(polymerization) occurs in the conversion of white into red phosphorus, and when red
phosphorus passes into vapour (depolymerization).[78]
This is borne out by the fact that measurements of the vapour density of phosphorus
vapour at temperatures of 500° and more, show it to have the molecular weight
represented by P4,[79] and the same molecular weight has been found for phosphorus in
solution.[80] On the other hand, it has recently been shown by R. Schenck,[81] that the
molecular weight of red phosphorus is at least P8, and very possibly higher.
When white phosphorus is heated to 44°, it melts. At this point, therefore, we shall have
another triple point, white phosphorus—liquid—vapour; the pressure at this point has
been calculated to be 3 mm.[75] This point is the intersection of three curves, viz.
sublimation curve, vaporization curve, and the fusion curve of white phosphorus. The
fusion curve, O2E, has been determined by Tammann[76] and by G. A. Hulett,[77] and it
was found that increase of pressure by 1 atm. raises the melting point by 0.029°. The
sublimation curve of white phosphorus has not yet been determined.
As can be seen from the table of vapour pressures (p. 46), the vapour pressure of white
phosphorus has been determined up to 500°; at temperatures above this, however, the
velocity with which transformation into red phosphorus takes place is so great as to
render the determination of the vapour pressure at higher temperatures impossible. Since,
however, the difference between white phosphorus and red phosphorus disappears in the
liquid state, the vapour pressure curve of white phosphorus must pass through the point
O1, the melting point of red phosphorus, and must be continuous with the curve O1A, the
vapour pressure curve of liquid phosphorus (vide infra). Since, as Fig. 10 shows, the
vapour pressure curve of white phosphorus ascends very rapidly at higher temperatures,
the "break" between BO1 and O1A must be very slight.
As compared with monotropic substances like benzophenone, phosphorus exhibits the
peculiarity that transformation of the metastable into the stable modification takes place
with great slowness; and further, the time required for the production of equilibrium
between red phosphorus and phosphorus vapour is great compared with that required for
establishing the same equilibrium in the case of white phosphorus. This behaviour can be
best explained by the assumption that change in the molecular complexity
(polymerization) occurs in the conversion of white into red phosphorus, and when red
phosphorus passes into vapour (depolymerization).[78]
This is borne out by the fact that measurements of the vapour density of phosphorus
vapour at temperatures of 500° and more, show it to have the molecular weight
represented by P4,[79] and the same molecular weight has been found for phosphorus in
solution.[80] On the other hand, it has recently been shown by R. Schenck,[81] that the
molecular weight of red phosphorus is at least P8, and very possibly higher.
Page 55
In the case of phosphorus, therefore, it is more than possible that we are dealing, not
simply with two polymorphic forms of the same substance, but with polymeric forms,
and that there is no transition point at temperatures above the absolute zero, unless we
assume the molecular complexity of the two forms to become the same. The curve for red
phosphorus would therefore lie below that of white phosphorus, for the vapour pressure
of the polymeric form, if produced from the simpler form with evolution of heat, must be
lower than that of the latter. A transition point would, of course, become possible if the
sign of the heat effect in the transformation of the one modification into the other should
change. If, further, the liquid which is produced by the fusion of red phosphorus at 630°
under high pressure also exists in a polymeric form, greater than P4, then the metastable
vaporization curve of white phosphorus would not pass through the melting point of red
phosphorus, as was assumed above.[82]
We have already seen in the case of water (p. 31) that the vapour pressure of supercooled
water is greater than that of ice, and that therefore it is possible, theoretically at least, by a
process of distillation, to transfer the water from one end of a closed tube to the other, and
to there condense it as ice. On account of the very small difference between the vapour
pressure of supercooled water and ice, this distillation process has not been
experimentally realized. In the case of phosphorus, however, where the difference in the
vapour pressures is comparatively great, it has been found possible to distil white
phosphorus from one part of a closed tube to another, and to there condense it as red
phosphorus; and since the vapour pressure of red phosphorus at 350° is less than the
vapour pressure of white phosphorus at 200°, it is possible to carry out the distillation
from a colder part of the tube to a hotter, by having white phosphorus at the former and
red phosphorus at the latter. Such a process of distillation has been carried out by Troost
and Hautefeuille between 324° and 350°.[83]
Relationships similar to those found in the case of phosphorus are also met with in the
case of cyanogen and paracyanogen, which have been studied by Chappuis,[84] Troost and
Hautefeuille,[85] and Dewar,[86] and also in the case of other organic substances.
Enantiotropy combined with Monotropy.—Not only can polymorphic substances
exhibit enantiotropy or monotropy, but, if the substance is capable of existing in more
than two crystalline forms, both relationships may be found, so that some of the forms
may be enantiotropic to one another, while the other forms exhibit only monotropy. This
behaviour is seen in the case of sulphur, which can exist in as many as eight different
crystalline varieties. Of these only monoclinic and rhombic sulphur exhibit the
relationship of enantiotropy, i.e. they possess a definite transition point, while the other
forms are all metastable with respect to rhombic and monoclinic sulphur, and remain so
up to the melting point; that is to say, they are monotropic modifications.[87]
E. Liquid Crystals.
simply with two polymorphic forms of the same substance, but with polymeric forms,
and that there is no transition point at temperatures above the absolute zero, unless we
assume the molecular complexity of the two forms to become the same. The curve for red
phosphorus would therefore lie below that of white phosphorus, for the vapour pressure
of the polymeric form, if produced from the simpler form with evolution of heat, must be
lower than that of the latter. A transition point would, of course, become possible if the
sign of the heat effect in the transformation of the one modification into the other should
change. If, further, the liquid which is produced by the fusion of red phosphorus at 630°
under high pressure also exists in a polymeric form, greater than P4, then the metastable
vaporization curve of white phosphorus would not pass through the melting point of red
phosphorus, as was assumed above.[82]
We have already seen in the case of water (p. 31) that the vapour pressure of supercooled
water is greater than that of ice, and that therefore it is possible, theoretically at least, by a
process of distillation, to transfer the water from one end of a closed tube to the other, and
to there condense it as ice. On account of the very small difference between the vapour
pressure of supercooled water and ice, this distillation process has not been
experimentally realized. In the case of phosphorus, however, where the difference in the
vapour pressures is comparatively great, it has been found possible to distil white
phosphorus from one part of a closed tube to another, and to there condense it as red
phosphorus; and since the vapour pressure of red phosphorus at 350° is less than the
vapour pressure of white phosphorus at 200°, it is possible to carry out the distillation
from a colder part of the tube to a hotter, by having white phosphorus at the former and
red phosphorus at the latter. Such a process of distillation has been carried out by Troost
and Hautefeuille between 324° and 350°.[83]
Relationships similar to those found in the case of phosphorus are also met with in the
case of cyanogen and paracyanogen, which have been studied by Chappuis,[84] Troost and
Hautefeuille,[85] and Dewar,[86] and also in the case of other organic substances.
Enantiotropy combined with Monotropy.—Not only can polymorphic substances
exhibit enantiotropy or monotropy, but, if the substance is capable of existing in more
than two crystalline forms, both relationships may be found, so that some of the forms
may be enantiotropic to one another, while the other forms exhibit only monotropy. This
behaviour is seen in the case of sulphur, which can exist in as many as eight different
crystalline varieties. Of these only monoclinic and rhombic sulphur exhibit the
relationship of enantiotropy, i.e. they possess a definite transition point, while the other
forms are all metastable with respect to rhombic and monoclinic sulphur, and remain so
up to the melting point; that is to say, they are monotropic modifications.[87]
E. Liquid Crystals.
Page 56
Phenomena observed.—In 1888 it was discovered by Reinitzer[88] that the two
substances, cholesteryl acetate and cholesteryl benzoate, possess the peculiar property of
melting sharply at a definite temperature to milky liquids; and that the latter, on being
further heated, suddenly become clear, also at a definite temperature. Other substances,
more especially p-azoxyanisole and p-azoxyphenetole, were, later, found to possess the
same property of having apparently a double melting point.[89] On cooling the clear
liquids, the reverse series of changes occurred.
The turbid liquids which were thus obtained were found to possess not only the usual
properties of liquids (such as the property of flowing and of assuming a perfectly
spherical shape when suspended in a liquid of the same density), but also those properties
which had hitherto been observed only in the case of solid crystalline substances, viz. the
property of double refraction and of giving interference colours when examined by
polarized light; the turbid liquids are anisotropic. To such liquids, the optical properties of
which were discovered by O. Lehmann,[90] the name liquid crystals, or crystalline liquids,
was given.
Nature of Liquid Crystals.—During the past ten years the question as to the nature of
liquid crystals has been discussed by a number of investigators, several of whom have
contended strongly against the idea of the term "liquid" being applied to the crystalline
condition; and various attempts have been made to prove that the turbid liquids are in
reality heterogeneous and are to be classed along with emulsions.[91] This view was no
doubt largely suggested by the fact that the anisotropic liquids were turbid, whereas the
"solid" crystals were clear. Lehmann found, however, that, when examined under the
microscope, the "simple" liquid crystals were also clear,[92] the apparent turbidity being
due to the aggregation of a number of differently oriented crystals, in the same way as a
piece of marble does not appear transparent although composed of transparent crystals.
[93]
Further, no proof of the heterogeneity of liquid crystals has yet been obtained, but rather
all chemical and physical investigations indicate that they are homogeneous.[94] No
separation of a solid substance from the milky, anisotropic liquids has been effected; the
anisotropic liquid is in some cases less viscous than the isotropic liquid formed at a
higher temperature; and the temperature of liquefaction is constant, and is affected by
pressure and admixture with foreign substances exactly as in the case of a pure substance.
[95]
substances, cholesteryl acetate and cholesteryl benzoate, possess the peculiar property of
melting sharply at a definite temperature to milky liquids; and that the latter, on being
further heated, suddenly become clear, also at a definite temperature. Other substances,
more especially p-azoxyanisole and p-azoxyphenetole, were, later, found to possess the
same property of having apparently a double melting point.[89] On cooling the clear
liquids, the reverse series of changes occurred.
The turbid liquids which were thus obtained were found to possess not only the usual
properties of liquids (such as the property of flowing and of assuming a perfectly
spherical shape when suspended in a liquid of the same density), but also those properties
which had hitherto been observed only in the case of solid crystalline substances, viz. the
property of double refraction and of giving interference colours when examined by
polarized light; the turbid liquids are anisotropic. To such liquids, the optical properties of
which were discovered by O. Lehmann,[90] the name liquid crystals, or crystalline liquids,
was given.
Nature of Liquid Crystals.—During the past ten years the question as to the nature of
liquid crystals has been discussed by a number of investigators, several of whom have
contended strongly against the idea of the term "liquid" being applied to the crystalline
condition; and various attempts have been made to prove that the turbid liquids are in
reality heterogeneous and are to be classed along with emulsions.[91] This view was no
doubt largely suggested by the fact that the anisotropic liquids were turbid, whereas the
"solid" crystals were clear. Lehmann found, however, that, when examined under the
microscope, the "simple" liquid crystals were also clear,[92] the apparent turbidity being
due to the aggregation of a number of differently oriented crystals, in the same way as a
piece of marble does not appear transparent although composed of transparent crystals.
[93]
Further, no proof of the heterogeneity of liquid crystals has yet been obtained, but rather
all chemical and physical investigations indicate that they are homogeneous.[94] No
separation of a solid substance from the milky, anisotropic liquids has been effected; the
anisotropic liquid is in some cases less viscous than the isotropic liquid formed at a
higher temperature; and the temperature of liquefaction is constant, and is affected by
pressure and admixture with foreign substances exactly as in the case of a pure substance.
[95]
Page 57
Fig. 12.
Equilibrium Relations in the Case of Liquid Crystals.—Since, now, we have seen that
we are dealing here with substances in two crystalline forms (which we may call the solid
and liquid[96] crystalline form), which possess a definite transition point, at which,
transformation of the one form into the other occurs in both directions, we can represent
the conditions of equilibrium by a diagram in all respects similar to that employed in the
case of other enantiotropic substances, e.g. sulphur (p. 35).
In Fig. 12 there is given a diagrammatic representation of the relationships found in the
case of p-azoxyanisole.[97]
Although the vapour pressure of the substance in the solid, or liquid state, has not been
determined, it will be understood from what we have already learned, that the curves AO,
OB, BC, representing the vapour pressure of solid crystals, liquid crystals, isotropic
liquid, must have the relative positions shown in the diagram. Point O, the transition point
of the solid into the liquid crystals, lies at 118.27°, and the change of the transition point
with the pressure is +0.032° pro 1 atm. The transition curve OE slopes, therefore, slightly
to the right. The point B, the melting point of the liquid crystals, lies at 135.85°, and the
melting point is raised 0.0485° pro 1 atm. The curve BD, therefore, also slopes to the
right, and more so than the transition curve. In this respect azoxyanisole is different from
sulphur.
The areas bounded by the curves represent the conditions for the stable existence of the
four single phases, solid crystals, liquid crystals, isotropic liquid and vapour.
The most important substances hitherto found to form liquid crystals are[98]:—
Transition Melting
Substance.
point. point.
Cholesteryl benzoate 145.5° 178.5°
Azoxyanisole 118.3° 135.9°
Azoxyphenetole 134.5° 168.1°
Condensation product from benzaldehyde
and benzidine 234° 260°
Azine of p-oxyethylbenzaldehyde 172° 196°
Equilibrium Relations in the Case of Liquid Crystals.—Since, now, we have seen that
we are dealing here with substances in two crystalline forms (which we may call the solid
and liquid[96] crystalline form), which possess a definite transition point, at which,
transformation of the one form into the other occurs in both directions, we can represent
the conditions of equilibrium by a diagram in all respects similar to that employed in the
case of other enantiotropic substances, e.g. sulphur (p. 35).
In Fig. 12 there is given a diagrammatic representation of the relationships found in the
case of p-azoxyanisole.[97]
Although the vapour pressure of the substance in the solid, or liquid state, has not been
determined, it will be understood from what we have already learned, that the curves AO,
OB, BC, representing the vapour pressure of solid crystals, liquid crystals, isotropic
liquid, must have the relative positions shown in the diagram. Point O, the transition point
of the solid into the liquid crystals, lies at 118.27°, and the change of the transition point
with the pressure is +0.032° pro 1 atm. The transition curve OE slopes, therefore, slightly
to the right. The point B, the melting point of the liquid crystals, lies at 135.85°, and the
melting point is raised 0.0485° pro 1 atm. The curve BD, therefore, also slopes to the
right, and more so than the transition curve. In this respect azoxyanisole is different from
sulphur.
The areas bounded by the curves represent the conditions for the stable existence of the
four single phases, solid crystals, liquid crystals, isotropic liquid and vapour.
The most important substances hitherto found to form liquid crystals are[98]:—
Transition Melting
Substance.
point. point.
Cholesteryl benzoate 145.5° 178.5°
Azoxyanisole 118.3° 135.9°
Azoxyphenetole 134.5° 168.1°
Condensation product from benzaldehyde
and benzidine 234° 260°
Azine of p-oxyethylbenzaldehyde 172° 196°
Page 58
Condensation product from p-tolylaldehyde
and benzidine 231° —
p-Methoxycinnamic acid 169° 185°
CHAPTER IV
GENERAL SUMMARY
In the preceding pages we have learned how the principles of the Phase Rule can be
applied to the elucidation of various systems consisting of one component. In the present
chapter it is proposed to give a short summary of the relationships we have met with, and
also to discuss more generally how the Phase Rule applies to other one-component
systems. On account of the fact that beginners are sometimes inclined to expect too much
of the Phase Rule; to expect, for example, that it will inform them as to the exact
behaviour of a substance, it may here be emphasized that the Phase Rule is a general rule;
it informs us only as to the general conditions of equilibrium, and leaves the
determination of the definite, numerical data to experiment.
Triple Point.—We have already (p. 28) defined a triple point in a one-component system,
as being that pressure and temperature at which three phases coexist in equilibrium; it
represents, therefore, an invariant system (p. 16). At the triple point also, three curves cut,
viz. the curves representing the conditions of equilibrium of the three univariant systems
formed by the combination of the three phases in pairs. The most common triple point of
a one-component system is, of course, the triple point, solid, liquid, vapour (S-L-V), but
other triple points[99] are also possible when, as in the case of sulphur or benzophenone,
polymorphic forms occur. Whether or not all the triple points can be experimentally
realized will, of course, depend on circumstances. We shall, in the first place, consider
only the triple point S-L-V.
As to the general arrangement of the three univariant curves around the triple point, the
following rules may be given. (1) The prolongation of each of the curves beyond the
triple point must lie between the other two curves. (2) The middle position at one and the
same temperature in the neighbourhood of the triple point is taken by that curve (or its
metastable prolongation) which represents the two phases of most widely differing
specific volume.[100] That is to say, if a line of constant temperature is drawn immediately
above or below the triple point so as to cut the three curves—two stable curves and the
metastable prolongation of the third—the position of the curves at that temperature will
be such that the middle position is occupied by that curve (or its metastable prolongation)
which represents the two phases of most widely differing specific volume.
Now, although these rules admit of a considerable variety of possible arrangements of
curves around the triple point,[101] only two of these have been experimentally obtained
and benzidine 231° —
p-Methoxycinnamic acid 169° 185°
CHAPTER IV
GENERAL SUMMARY
In the preceding pages we have learned how the principles of the Phase Rule can be
applied to the elucidation of various systems consisting of one component. In the present
chapter it is proposed to give a short summary of the relationships we have met with, and
also to discuss more generally how the Phase Rule applies to other one-component
systems. On account of the fact that beginners are sometimes inclined to expect too much
of the Phase Rule; to expect, for example, that it will inform them as to the exact
behaviour of a substance, it may here be emphasized that the Phase Rule is a general rule;
it informs us only as to the general conditions of equilibrium, and leaves the
determination of the definite, numerical data to experiment.
Triple Point.—We have already (p. 28) defined a triple point in a one-component system,
as being that pressure and temperature at which three phases coexist in equilibrium; it
represents, therefore, an invariant system (p. 16). At the triple point also, three curves cut,
viz. the curves representing the conditions of equilibrium of the three univariant systems
formed by the combination of the three phases in pairs. The most common triple point of
a one-component system is, of course, the triple point, solid, liquid, vapour (S-L-V), but
other triple points[99] are also possible when, as in the case of sulphur or benzophenone,
polymorphic forms occur. Whether or not all the triple points can be experimentally
realized will, of course, depend on circumstances. We shall, in the first place, consider
only the triple point S-L-V.
As to the general arrangement of the three univariant curves around the triple point, the
following rules may be given. (1) The prolongation of each of the curves beyond the
triple point must lie between the other two curves. (2) The middle position at one and the
same temperature in the neighbourhood of the triple point is taken by that curve (or its
metastable prolongation) which represents the two phases of most widely differing
specific volume.[100] That is to say, if a line of constant temperature is drawn immediately
above or below the triple point so as to cut the three curves—two stable curves and the
metastable prolongation of the third—the position of the curves at that temperature will
be such that the middle position is occupied by that curve (or its metastable prolongation)
which represents the two phases of most widely differing specific volume.
Now, although these rules admit of a considerable variety of possible arrangements of
curves around the triple point,[101] only two of these have been experimentally obtained
Page 59
in the case of the triple point solid—liquid—vapour. At present, therefore, we shall
consider only these two cases (Figs. 13 and 14).
An examination of these two figures shows
that they satisfy the rules laid down. Each of
the curves on being prolonged passes between
the other two curves. In the case of substances
of the first type (Fig. 13), the specific volume
of the solid is greater than that of the liquid
(the substance contracts on fusion); the
difference of specific volume will, therefore, Fig. 13. Fig. 14.
be greatest between liquid and vapour. The
curve, therefore, for liquid and vapour (or its prolongation) must lie between the other
two curves; this is seen from the figure to be the case. Similarly, the rule is satisfied by
the arrangement of curves in Fig. 14, where the difference of specific volumes is greatest
between the solid and vapour. In this case the curve S-V occupies the intermediate
position.
As we see, the two figures differ from one another only in that the fusion curve OC in one
case slopes to the right away from the pressure axis, thus indicating that the melting point
is raised by increase of pressure; in the other case, to the left, indicating a lowering of the
melting point with the pressure. These conditions are found exemplified in the case of
sulphur and ice (pp. 29 and 35). We see further from the two figures, that O in Fig. 13
gives the highest temperature at which the solid can exist, for the curve for solid—liquid
slopes back to regions of lower temperature; in Fig. 14, O gives the lowest temperature at
which the liquid phase can exist as stable phase.[102]
Theorems of van't Hoff and of Le Chatelier.—So far we have studied only the
conditions under which various systems exist in equilibrium; and we now pass to a
consideration of the changes which take place in a system when the external conditions of
temperature and pressure are altered. For all such changes there exist two theorems, based
on the laws of thermodynamics, by means of which the alterations in a system can be
qualitatively predicted.[103] The first of these, usually known as van't Hoff's law of
movable equilibrium,[104] states: When the temperature of a system in equilibrium is
raised, that reaction takes place which is accompanied by absorption of heat; and,
conversely, when the temperature is lowered, that reaction occurs which is accompanied
by an evolution of heat.
The second of the two theorems refers to the effect of change of pressure, and states:[105]
When the pressure on a system in equilibrium is increased, that reaction takes place
which is accompanied by a diminution of volume; and when the pressure is diminished, a
reaction ensues which is accompanied by an increase of volume.
The demonstration of the universal applicability of these two theorems is due chiefly to
Le Chatelier, who showed that they may be regarded as consequences of the general law
consider only these two cases (Figs. 13 and 14).
An examination of these two figures shows
that they satisfy the rules laid down. Each of
the curves on being prolonged passes between
the other two curves. In the case of substances
of the first type (Fig. 13), the specific volume
of the solid is greater than that of the liquid
(the substance contracts on fusion); the
difference of specific volume will, therefore, Fig. 13. Fig. 14.
be greatest between liquid and vapour. The
curve, therefore, for liquid and vapour (or its prolongation) must lie between the other
two curves; this is seen from the figure to be the case. Similarly, the rule is satisfied by
the arrangement of curves in Fig. 14, where the difference of specific volumes is greatest
between the solid and vapour. In this case the curve S-V occupies the intermediate
position.
As we see, the two figures differ from one another only in that the fusion curve OC in one
case slopes to the right away from the pressure axis, thus indicating that the melting point
is raised by increase of pressure; in the other case, to the left, indicating a lowering of the
melting point with the pressure. These conditions are found exemplified in the case of
sulphur and ice (pp. 29 and 35). We see further from the two figures, that O in Fig. 13
gives the highest temperature at which the solid can exist, for the curve for solid—liquid
slopes back to regions of lower temperature; in Fig. 14, O gives the lowest temperature at
which the liquid phase can exist as stable phase.[102]
Theorems of van't Hoff and of Le Chatelier.—So far we have studied only the
conditions under which various systems exist in equilibrium; and we now pass to a
consideration of the changes which take place in a system when the external conditions of
temperature and pressure are altered. For all such changes there exist two theorems, based
on the laws of thermodynamics, by means of which the alterations in a system can be
qualitatively predicted.[103] The first of these, usually known as van't Hoff's law of
movable equilibrium,[104] states: When the temperature of a system in equilibrium is
raised, that reaction takes place which is accompanied by absorption of heat; and,
conversely, when the temperature is lowered, that reaction occurs which is accompanied
by an evolution of heat.
The second of the two theorems refers to the effect of change of pressure, and states:[105]
When the pressure on a system in equilibrium is increased, that reaction takes place
which is accompanied by a diminution of volume; and when the pressure is diminished, a
reaction ensues which is accompanied by an increase of volume.
The demonstration of the universal applicability of these two theorems is due chiefly to
Le Chatelier, who showed that they may be regarded as consequences of the general law
Page 60
of action and reaction. For this reason they are generally regarded as special cases of the
more general law, known as the theorem of Le Chatelier, which may be stated in the
words of Ostwald, as follows:[106] If a system in equilibrium is subjected to a constraint
by which the equilibrium is shifted, a reaction takes place which opposes the constraint,
i.e. one by which its effect is partially destroyed.
This theorem of Le Chatelier is of very great importance, for it applies to all systems and
changes of the condition of equilibrium, whether physical or chemical; to vaporization
and fusion; to solution and chemical action. In all cases, whenever changes in the external
condition of a system in equilibrium are produced, processes also occur within the system
which tend to counteract the effect of the external changes.
Changes at the Triple Point.—If now we apply this theorem to equilibria at the triple
point S-L-V, and ask what changes will occur in such a system when the external
conditions of pressure and temperature are altered, the general answer to the question will
be: So long as the three phases are present, no change in the temperature or pressure of
the system can occur, but only changes in the relative amounts of the phases; that is to
say, the effect on the system of change in the external conditions is opposed by the
reactions or changes which take place within the system (according to the theorems of
van't Hoff and Le Chatelier). We now proceed to discuss what these changes are, and
shall consider first the effect of alteration of the temperature at constant volume and
constant pressure, and then the effect of alteration of the pressure both when the
temperature remains constant and when it varies.
When the volume is kept constant, the effect of the addition of heat to a system at the
triple point S-L-V differs somewhat according as there is an increase or diminution of
volume when the solid passes into the liquid state. In the former and most general case
(Fig. 14), addition of heat will cause a certain amount of the solid phase to melt, whereby
the heat which is added becomes latent; the temperature of the system therefore does not
rise. Since, however, the melting of the solid is accompanied by an increase of volume,
whereby an increase of pressure would result, a certain portion of the vapour must
condense to liquid, in order that the pressure may remain constant. The total effect of
addition of heat, therefore, is to cause both solid and vapour to pass into liquid, i.e. there
occurs the change S + V L. It will, therefore, depend on the relative quantities of
solid and vapour, which will disappear first. If the solid disappears first, then we shall
pass to the system L-V; if vapour disappears first, we shall obtain the system S-L.
Withdrawal of heat causes the reverse change, L S + V; at all temperatures below the
triple point the liquid is unstable or metastable (p. 30).
When fusion is accompanied by a diminution of volume (e.g. ice, Fig. 13), then, since the
melting of the solid phase would decrease the total volume, i.e. would lower the pressure,
a certain quantity of the solid must also pass into vapour in order that the pressure may be
maintained constant. On addition of heat, therefore, there occurs the reaction S L+
V; withdrawal of heat causes the reverse change L + V S. Above the temperature of
the triple point the solid cannot exist; below the triple point both systems, S-L and S-V,
more general law, known as the theorem of Le Chatelier, which may be stated in the
words of Ostwald, as follows:[106] If a system in equilibrium is subjected to a constraint
by which the equilibrium is shifted, a reaction takes place which opposes the constraint,
i.e. one by which its effect is partially destroyed.
This theorem of Le Chatelier is of very great importance, for it applies to all systems and
changes of the condition of equilibrium, whether physical or chemical; to vaporization
and fusion; to solution and chemical action. In all cases, whenever changes in the external
condition of a system in equilibrium are produced, processes also occur within the system
which tend to counteract the effect of the external changes.
Changes at the Triple Point.—If now we apply this theorem to equilibria at the triple
point S-L-V, and ask what changes will occur in such a system when the external
conditions of pressure and temperature are altered, the general answer to the question will
be: So long as the three phases are present, no change in the temperature or pressure of
the system can occur, but only changes in the relative amounts of the phases; that is to
say, the effect on the system of change in the external conditions is opposed by the
reactions or changes which take place within the system (according to the theorems of
van't Hoff and Le Chatelier). We now proceed to discuss what these changes are, and
shall consider first the effect of alteration of the temperature at constant volume and
constant pressure, and then the effect of alteration of the pressure both when the
temperature remains constant and when it varies.
When the volume is kept constant, the effect of the addition of heat to a system at the
triple point S-L-V differs somewhat according as there is an increase or diminution of
volume when the solid passes into the liquid state. In the former and most general case
(Fig. 14), addition of heat will cause a certain amount of the solid phase to melt, whereby
the heat which is added becomes latent; the temperature of the system therefore does not
rise. Since, however, the melting of the solid is accompanied by an increase of volume,
whereby an increase of pressure would result, a certain portion of the vapour must
condense to liquid, in order that the pressure may remain constant. The total effect of
addition of heat, therefore, is to cause both solid and vapour to pass into liquid, i.e. there
occurs the change S + V L. It will, therefore, depend on the relative quantities of
solid and vapour, which will disappear first. If the solid disappears first, then we shall
pass to the system L-V; if vapour disappears first, we shall obtain the system S-L.
Withdrawal of heat causes the reverse change, L S + V; at all temperatures below the
triple point the liquid is unstable or metastable (p. 30).
When fusion is accompanied by a diminution of volume (e.g. ice, Fig. 13), then, since the
melting of the solid phase would decrease the total volume, i.e. would lower the pressure,
a certain quantity of the solid must also pass into vapour in order that the pressure may be
maintained constant. On addition of heat, therefore, there occurs the reaction S L+
V; withdrawal of heat causes the reverse change L + V S. Above the temperature of
the triple point the solid cannot exist; below the triple point both systems, S-L and S-V,
Page 61
can exist, and it will therefore depend on the relative amounts of liquid and vapour which
of these two systems is obtained on withdrawing heat from the system at constant
volume.
The same changes in the phases occur when heat is added or withdrawn at constant
pressure, so long as the three phases are present. Continued addition of heat, however, at
constant pressure will ultimately cause the formation of the bivariant system vapour
alone; continued withdrawal of heat will ultimately cause the formation of solid alone.
This will be readily understood from Fig. 15. The dotted line D′OD is a line of constant
pressure; on adding heat, the system passes along the line OD into the region of vapour;
on heat being withdrawn, the system passes along OD′ into the area of solid.
Fig. 15.
Similar changes are produced when the volume of the system is altered. Alteration of
volume may take place either while transference of heat to or from the system is cut off
(adiabatic change), or while such transference may occur (isothermal change). In the
latter case, the temperature of the system will remain constant; in the former case, since at
the triple point the pressure must be constant so long as the three phases are present,
increase of volume must be compensated by the evaporation of liquid. This, however,
would cause the temperature to fall (since communication of heat from the outside is
supposed to be cut off), and a portion of the liquid must therefore freeze. In this way the
latent heat of evaporation is counterbalanced by the latent heat of fusion. As the result of
increase of volume, therefore, the process occurs L S + V. Diminution of volume,
without transference of heat, will bring about the opposite change, S + V L. In the
former case there is ultimately obtained the univariant system S-V; in the latter case there
will be obtained either S-L or L-V according as the vapour or solid phase disappears first.
This argument holds good for both types of triple point shown in Figs. 13 and 14 (p. 57).
A glance at these figures will show that increase of volume (diminution of pressure) will
lead ultimately to the system S-V, for at pressures lower than that of the triple point, the
liquid phase cannot exist. Decrease of volume (increase of pressure), on the other hand,
will lead either to the system S-L or L-V, because these systems can exist at pressures
higher than that of the triple point. If the vapour phase disappears and we pass to the
curve S-L, continued diminution of volume will be accompanied by a fall in temperature
in the case of systems of the first type (Fig. 13), and by a rise in temperature in the case
of systems of the second type (Fig. 14).
of these two systems is obtained on withdrawing heat from the system at constant
volume.
The same changes in the phases occur when heat is added or withdrawn at constant
pressure, so long as the three phases are present. Continued addition of heat, however, at
constant pressure will ultimately cause the formation of the bivariant system vapour
alone; continued withdrawal of heat will ultimately cause the formation of solid alone.
This will be readily understood from Fig. 15. The dotted line D′OD is a line of constant
pressure; on adding heat, the system passes along the line OD into the region of vapour;
on heat being withdrawn, the system passes along OD′ into the area of solid.
Fig. 15.
Similar changes are produced when the volume of the system is altered. Alteration of
volume may take place either while transference of heat to or from the system is cut off
(adiabatic change), or while such transference may occur (isothermal change). In the
latter case, the temperature of the system will remain constant; in the former case, since at
the triple point the pressure must be constant so long as the three phases are present,
increase of volume must be compensated by the evaporation of liquid. This, however,
would cause the temperature to fall (since communication of heat from the outside is
supposed to be cut off), and a portion of the liquid must therefore freeze. In this way the
latent heat of evaporation is counterbalanced by the latent heat of fusion. As the result of
increase of volume, therefore, the process occurs L S + V. Diminution of volume,
without transference of heat, will bring about the opposite change, S + V L. In the
former case there is ultimately obtained the univariant system S-V; in the latter case there
will be obtained either S-L or L-V according as the vapour or solid phase disappears first.
This argument holds good for both types of triple point shown in Figs. 13 and 14 (p. 57).
A glance at these figures will show that increase of volume (diminution of pressure) will
lead ultimately to the system S-V, for at pressures lower than that of the triple point, the
liquid phase cannot exist. Decrease of volume (increase of pressure), on the other hand,
will lead either to the system S-L or L-V, because these systems can exist at pressures
higher than that of the triple point. If the vapour phase disappears and we pass to the
curve S-L, continued diminution of volume will be accompanied by a fall in temperature
in the case of systems of the first type (Fig. 13), and by a rise in temperature in the case
of systems of the second type (Fig. 14).
Page 62
Lastly, if the temperature is maintained
constant, i.e. if heat can pass into or out of
the system, then on changing the volume the
same changes in the phases will take place as
described above until one of the phases has
disappeared. Continued increase of volume
(decrease of pressure) will then cause the
disappearance of a second phase, the system Fig. 16. Fig. 17.
passing along the dotted line OE′ (Figs. 16,
17), so that ultimately there remains only the vapour phase. Conversely, diminution of
volume (increase of pressure) will ultimately lead either to solid (Fig. 16) or to liquid
alone (Fig. 17), the system passing along the dotted line OE.
In discussing the alterations which may take place at the triple point with change of
temperature and pressure, we have considered only the triple point S-L-V. The same
reasoning, however, applies, mutatis mutandis, to all other triple points, so that if the
specific volumes of the phases are known, and the sign of the heat effects which
accompany the transformation of one phase into the other, it is possible to predict (by
means of the theorem of Le Chatelier) the changes which will be produced in the system
by alteration of the pressure and temperature.
In all cases of transformation at the triple point, it should be noted that all three phases
are involved in the change,[107] and not two only; the fact that in the case, say, of the
transformation from solid to liquid, or liquid to solid, at the melting point with change of
temperature, only these two phases appear to be affected, is due to there generally being a
large excess of the vapour phase present and to the prior disappearance therefore of the
solid or liquid phase.
In the case of triple points at which two solid phases are in equilibrium with liquid, other
arrangements of the curves around the triple point are found. It is, however, unnecessary
to give a general treatment of these here, since the principles which have been applied to
the triple point S-L-V can also be applied to the other triple points.[108]
Triple Point Solid—Solid—Vapour.—The triple point solid—solid—vapour is one
which is of considerable importance. Examples of such a triple point have already been
given in sulphur and tin, and a list of other substances capable of yielding two solid
phases is given below. The triple point S-S-V is not precisely the same as the transition
point, but is very nearly so. The transition point is the temperature at which the relative
stability of the two solid phases undergoes change, when the vapour phase is absent and
the pressure is 1 atm.; whereas at the triple point the pressure is that of the system itself.
The transition point, therefore, bears the same relation to the triple point S-S-V as the
melting point to the triple point S-L-V.
In the following table is given a list of the most important polymorphous substances, and
the temperatures of the transition point.[109]
constant, i.e. if heat can pass into or out of
the system, then on changing the volume the
same changes in the phases will take place as
described above until one of the phases has
disappeared. Continued increase of volume
(decrease of pressure) will then cause the
disappearance of a second phase, the system Fig. 16. Fig. 17.
passing along the dotted line OE′ (Figs. 16,
17), so that ultimately there remains only the vapour phase. Conversely, diminution of
volume (increase of pressure) will ultimately lead either to solid (Fig. 16) or to liquid
alone (Fig. 17), the system passing along the dotted line OE.
In discussing the alterations which may take place at the triple point with change of
temperature and pressure, we have considered only the triple point S-L-V. The same
reasoning, however, applies, mutatis mutandis, to all other triple points, so that if the
specific volumes of the phases are known, and the sign of the heat effects which
accompany the transformation of one phase into the other, it is possible to predict (by
means of the theorem of Le Chatelier) the changes which will be produced in the system
by alteration of the pressure and temperature.
In all cases of transformation at the triple point, it should be noted that all three phases
are involved in the change,[107] and not two only; the fact that in the case, say, of the
transformation from solid to liquid, or liquid to solid, at the melting point with change of
temperature, only these two phases appear to be affected, is due to there generally being a
large excess of the vapour phase present and to the prior disappearance therefore of the
solid or liquid phase.
In the case of triple points at which two solid phases are in equilibrium with liquid, other
arrangements of the curves around the triple point are found. It is, however, unnecessary
to give a general treatment of these here, since the principles which have been applied to
the triple point S-L-V can also be applied to the other triple points.[108]
Triple Point Solid—Solid—Vapour.—The triple point solid—solid—vapour is one
which is of considerable importance. Examples of such a triple point have already been
given in sulphur and tin, and a list of other substances capable of yielding two solid
phases is given below. The triple point S-S-V is not precisely the same as the transition
point, but is very nearly so. The transition point is the temperature at which the relative
stability of the two solid phases undergoes change, when the vapour phase is absent and
the pressure is 1 atm.; whereas at the triple point the pressure is that of the system itself.
The transition point, therefore, bears the same relation to the triple point S-S-V as the
melting point to the triple point S-L-V.
In the following table is given a list of the most important polymorphous substances, and
the temperatures of the transition point.[109]
Page 63
Transition
Substance.
temperature.
Ammonium nitrate—
β-rhombic α-rhombic 35°
α-rhombic rhombohedral 83°
Rhombohedral regular 125°
Mercuric iodide 126°
Potassium nitrate 129°
Silver iodide 145°
Silver nitrate 160°
Sulphur 95.5°
Tetrabrommethane 46.8°
Thallium nitrate—
Rhombic rhombohedral 80°
Rhombohedral regular 142.5°
Thallium picrate 46°
Tin 20°
Sublimation and Vaporization Curves.—We have already seen, in the case of ice and
liquid water, that the vapour pressure increases as the temperature rises, the increase of
pressure per degree being greater the higher the temperature. The sublimation and
vaporization curves, therefore, are not straight lines, but are bent, the convex side of the
curve being towards the temperature axis in the ordinary pt-diagram.
In the case of sulphur and of tin, we assumed vapour to be given off by the solid
substance, although the pressure of the vapour has not hitherto been measured. The
assumption, however, is entirely justified, not only on theoretical grounds, but also
because the existence of a vapour pressure has been observed in the case of many solid
substances at temperatures much below the melting point,[110] and in some cases, e.g.
camphor,[111] the vapour pressure is considerable.
As the result of a large number of determinations, it has been found that all vapour
pressure curves have the same general form alluded to above. Attempts have also been
made to obtain a general expression for the quantitative changes in the vapour pressure
with change of temperature, but without success. Nevertheless, the qualitative changes, or
the general direction of the curves, can be predicted by means of the theorem of Le
Chatelier.
As we have already learned (p. 16), the Phase Rule takes no account of the molecular
complexity of the substances participating in an equilibrium. A dissociating substance,
therefore, in contact with its vaporous products of dissociation (e.g. ammonium chloride
in contact with ammonia and hydrogen chloride), will likewise constitute a univariant
system of one component, provided the composition of the vapour phase as a whole is the
Substance.
temperature.
Ammonium nitrate—
β-rhombic α-rhombic 35°
α-rhombic rhombohedral 83°
Rhombohedral regular 125°
Mercuric iodide 126°
Potassium nitrate 129°
Silver iodide 145°
Silver nitrate 160°
Sulphur 95.5°
Tetrabrommethane 46.8°
Thallium nitrate—
Rhombic rhombohedral 80°
Rhombohedral regular 142.5°
Thallium picrate 46°
Tin 20°
Sublimation and Vaporization Curves.—We have already seen, in the case of ice and
liquid water, that the vapour pressure increases as the temperature rises, the increase of
pressure per degree being greater the higher the temperature. The sublimation and
vaporization curves, therefore, are not straight lines, but are bent, the convex side of the
curve being towards the temperature axis in the ordinary pt-diagram.
In the case of sulphur and of tin, we assumed vapour to be given off by the solid
substance, although the pressure of the vapour has not hitherto been measured. The
assumption, however, is entirely justified, not only on theoretical grounds, but also
because the existence of a vapour pressure has been observed in the case of many solid
substances at temperatures much below the melting point,[110] and in some cases, e.g.
camphor,[111] the vapour pressure is considerable.
As the result of a large number of determinations, it has been found that all vapour
pressure curves have the same general form alluded to above. Attempts have also been
made to obtain a general expression for the quantitative changes in the vapour pressure
with change of temperature, but without success. Nevertheless, the qualitative changes, or
the general direction of the curves, can be predicted by means of the theorem of Le
Chatelier.
As we have already learned (p. 16), the Phase Rule takes no account of the molecular
complexity of the substances participating in an equilibrium. A dissociating substance,
therefore, in contact with its vaporous products of dissociation (e.g. ammonium chloride
in contact with ammonia and hydrogen chloride), will likewise constitute a univariant
system of one component, provided the composition of the vapour phase as a whole is the
Page 64
same as that of the solid or liquid phase (p. 13). For all such substances, therefore, the
conditions of equilibrium will be represented by a curve of the same general form as the
vapour pressure curve of a non-dissociating substance.[112] The same behaviour is also
found in the case of substances which polymerize on passing into the solid or liquid state
(e.g. red phosphorus). Where such changes in the molecular state occur, however, the
time required for equilibrium to be established is, as a rule, greater than when the
molecular state is the same in both phases.
From an examination of Figs. 13 and 14, it will be easy to predict the effect of change of
pressure and temperature on the univariant systems S-V or L-V. If the volume is kept
constant, addition of heat will cause an increase of pressure, the system S-V moving
along the curve AO until at the triple point the liquid phase is formed, and the system L-V
moving along the curve OB; so long as two phases are present, the condition of the
system must be represented by these two curves. Conversely, withdrawal of heat will
cause condensation of vapour, and therefore diminution of pressure; the system will
therefore move along the vaporization or sublimation curve to lower temperatures and
pressures, so long as the system remains univariant.
If transference of heat to or from the system is prevented, increase of volume (diminution
of pressure) will cause the system L-V to pass along the curve BO; liquid will pass into
vapour and the temperature will fall.[113] At O solid may appear, and the temperature of
the system will then remain constant until the liquid phase has disappeared (p. 57); the
system will then follow the curve OA until the solid phase disappears, and we are
ultimately left with vapour. On the other hand, diminution of volume (increase of
pressure) will cause condensation of vapour, and the system S-V will pass along the curve
AO to higher temperatures and pressures; at O the solid will melt, and the system will
ultimately pass to the curve OB or to OC (p. 57).
Addition or withdrawal of heat at constant pressure, and increase or diminution of the
pressure at constant temperature, will cause the system to pass along lines parallel to the
temperature and the pressure axis respectively; the working out of these changes may be
left to the reader, guided by what has been said on pp. 60 and 61.
The sublimation curve of all substances, so far as yet found, has its upper limit at the
melting point (triple point), although the possibility of the existence of a superheated
solid is not excluded. The lower limit is, theoretically at least, at the absolute zero,
provided no new phase, e.g. a different crystalline modification, is formed. If the
sublimation pressure of a substance is greater than the atmospheric pressure at any
temperature below the point of fusion, then the substance will sublime without melting
when heated in an open vessel; and fusion will be possible only at a pressure higher than
the atmospheric. This is found, for example, in the case of red phosphorus (p. 47). If,
however, the sublimation pressure of a substance at its triple point S-L-V is less than one
atmosphere, then the substance will melt when heated in an open vessel.
conditions of equilibrium will be represented by a curve of the same general form as the
vapour pressure curve of a non-dissociating substance.[112] The same behaviour is also
found in the case of substances which polymerize on passing into the solid or liquid state
(e.g. red phosphorus). Where such changes in the molecular state occur, however, the
time required for equilibrium to be established is, as a rule, greater than when the
molecular state is the same in both phases.
From an examination of Figs. 13 and 14, it will be easy to predict the effect of change of
pressure and temperature on the univariant systems S-V or L-V. If the volume is kept
constant, addition of heat will cause an increase of pressure, the system S-V moving
along the curve AO until at the triple point the liquid phase is formed, and the system L-V
moving along the curve OB; so long as two phases are present, the condition of the
system must be represented by these two curves. Conversely, withdrawal of heat will
cause condensation of vapour, and therefore diminution of pressure; the system will
therefore move along the vaporization or sublimation curve to lower temperatures and
pressures, so long as the system remains univariant.
If transference of heat to or from the system is prevented, increase of volume (diminution
of pressure) will cause the system L-V to pass along the curve BO; liquid will pass into
vapour and the temperature will fall.[113] At O solid may appear, and the temperature of
the system will then remain constant until the liquid phase has disappeared (p. 57); the
system will then follow the curve OA until the solid phase disappears, and we are
ultimately left with vapour. On the other hand, diminution of volume (increase of
pressure) will cause condensation of vapour, and the system S-V will pass along the curve
AO to higher temperatures and pressures; at O the solid will melt, and the system will
ultimately pass to the curve OB or to OC (p. 57).
Addition or withdrawal of heat at constant pressure, and increase or diminution of the
pressure at constant temperature, will cause the system to pass along lines parallel to the
temperature and the pressure axis respectively; the working out of these changes may be
left to the reader, guided by what has been said on pp. 60 and 61.
The sublimation curve of all substances, so far as yet found, has its upper limit at the
melting point (triple point), although the possibility of the existence of a superheated
solid is not excluded. The lower limit is, theoretically at least, at the absolute zero,
provided no new phase, e.g. a different crystalline modification, is formed. If the
sublimation pressure of a substance is greater than the atmospheric pressure at any
temperature below the point of fusion, then the substance will sublime without melting
when heated in an open vessel; and fusion will be possible only at a pressure higher than
the atmospheric. This is found, for example, in the case of red phosphorus (p. 47). If,
however, the sublimation pressure of a substance at its triple point S-L-V is less than one
atmosphere, then the substance will melt when heated in an open vessel.
Page 65
In the case of the vaporization curve, the upper limit lies at the critical point where the
liquid ceases to exist;[114] the lower limit is determined by the range of the metastable
state of the supercooled liquid.
The interpolation and extrapolation of vapour-pressure curves is rendered very easy by
means of a relationship which Ramsay and Young[115] found to exist between the vapour-
pressure curves of different substances. It was observed that in the case of closely related
substances, the ratio of the absolute temperatures corresponding to equal vapour
pressures is constant, i.e. T1/T′1 = T2/T′2. When the two substances are not closely
related, it was found that the relationship could be expressed by the equation T1/T′1 =
T2/T′2 + c(t′ - t) where c is a constant having a small positive or negative value, and t′ and
t are the temperatures at which one of the substances has the two values of the vapour
pressure in question. By means of this equation, if the vapour-pressure curve of one
substance is known, the vapour-pressure curve of any other substance can be calculated
from the values at any two temperatures of the vapour pressure of that substance.
Fusion Curve—Transition Curve.—The fusion curve represents the conditions of
equilibrium between the solid and liquid phase; it shows the change of the melting point
of a substance with change of pressure.
As shown in Figs. 13 and 14, the fusion curve is inclined either towards the pressure axis
or away from it; that is, increase of pressure can either lower or raise the melting point. It
is easy to predict in a qualitative manner the different effect of pressure on the melting
point in the two cases mentioned, if we consider the matter in the light of the theorem of
Le Chatelier (p. 58). Water, on passing into ice, expands; therefore, if the pressure on the
system ice—water be increased, a reaction will take place which is accompanied by a
diminution in volume, i.e. the ice will melt. Consequently, a lower temperature will be
required in order to counteract the effect of increase of pressure; or, in other words, the
melting point will be lowered by pressure.[116] In the second case, the passage of the
liquid to the solid state is accompanied by a diminution of volume; the effect of increase
of pressure will therefore be the reverse of that in the previous case.
If the value of the heat of fusion and the alteration of volume accompanying the change
of state are known, it is possible to calculate quantitatively the effect of pressure.[117]
We have already seen (p. 25) that the effect of pressure on the melting point of a
substance was predicted as the result of theoretical considerations, and was first proved
experimentally in the case of ice. Soon after, Bunsen[118] showed that the melting point of
other substances is also affected by pressure; and in more recent years, ample
experimental proof of the change of the melting point with the pressure has been
obtained. The change of the melting point is, however, small; as a rule, increase of
pressure by 1 atm. changes the melting point by about 0.03°, but in the case of water the
change is much less (0.0076°), and in the case of camphor much more (0.13°). In other
liquid ceases to exist;[114] the lower limit is determined by the range of the metastable
state of the supercooled liquid.
The interpolation and extrapolation of vapour-pressure curves is rendered very easy by
means of a relationship which Ramsay and Young[115] found to exist between the vapour-
pressure curves of different substances. It was observed that in the case of closely related
substances, the ratio of the absolute temperatures corresponding to equal vapour
pressures is constant, i.e. T1/T′1 = T2/T′2. When the two substances are not closely
related, it was found that the relationship could be expressed by the equation T1/T′1 =
T2/T′2 + c(t′ - t) where c is a constant having a small positive or negative value, and t′ and
t are the temperatures at which one of the substances has the two values of the vapour
pressure in question. By means of this equation, if the vapour-pressure curve of one
substance is known, the vapour-pressure curve of any other substance can be calculated
from the values at any two temperatures of the vapour pressure of that substance.
Fusion Curve—Transition Curve.—The fusion curve represents the conditions of
equilibrium between the solid and liquid phase; it shows the change of the melting point
of a substance with change of pressure.
As shown in Figs. 13 and 14, the fusion curve is inclined either towards the pressure axis
or away from it; that is, increase of pressure can either lower or raise the melting point. It
is easy to predict in a qualitative manner the different effect of pressure on the melting
point in the two cases mentioned, if we consider the matter in the light of the theorem of
Le Chatelier (p. 58). Water, on passing into ice, expands; therefore, if the pressure on the
system ice—water be increased, a reaction will take place which is accompanied by a
diminution in volume, i.e. the ice will melt. Consequently, a lower temperature will be
required in order to counteract the effect of increase of pressure; or, in other words, the
melting point will be lowered by pressure.[116] In the second case, the passage of the
liquid to the solid state is accompanied by a diminution of volume; the effect of increase
of pressure will therefore be the reverse of that in the previous case.
If the value of the heat of fusion and the alteration of volume accompanying the change
of state are known, it is possible to calculate quantitatively the effect of pressure.[117]
We have already seen (p. 25) that the effect of pressure on the melting point of a
substance was predicted as the result of theoretical considerations, and was first proved
experimentally in the case of ice. Soon after, Bunsen[118] showed that the melting point of
other substances is also affected by pressure; and in more recent years, ample
experimental proof of the change of the melting point with the pressure has been
obtained. The change of the melting point is, however, small; as a rule, increase of
pressure by 1 atm. changes the melting point by about 0.03°, but in the case of water the
change is much less (0.0076°), and in the case of camphor much more (0.13°). In other
Page 66
words, if we take the mean case, an increase of pressure of more than 30 atm. is required
to produce a change in the melting point of 1°.
Investigations which were made of the influence of pressure on the melting-point,
showed that up to pressures of several hundred atmospheres the fusion curve is a straight
line.[119] Tammann[120] has, however, found that on increasing the pressure the fusion
curve no longer remains straight, but bends towards the pressure axis, so that, on
sufficiently increasing the pressure, a maximum temperature might at length be reached.
This maximum has, so far, however, not been attained, although the melting point curves
of various substances have been studied up to pressures of 4500 atm. This is to be
accounted for partly by the fact that the probable maximum temperature in the case of
most substances lies at very great pressures, and also by the fact that other solid phases
make their appearance, as, for example, in the case of ice (p. 32).
As to the upper limit of the fusion curve, the view has been expressed[121] that just as in
the case of liquid and vapour, so also in the case of solid and liquid, there exists a critical
point at which the solid and the liquid phase become identical. Experimental evidence,
however, does not appear to favour this view.[122]
The transition point, like the melting point, is also influenced by the pressure, and in this
case also it is found that pressure may either raise or lower the transition point, so that the
transition curve may be inclined either away from or towards the pressure axis. The
direction of the transition curve can also be predicted if the change of volume
accompanying the passage of one form into the other is known. In the case of sulphur, we
saw that the transition point is raised by increase of pressure; in the case of the transition
of rhombohedral into α-rhombic form of ammonium nitrate, however, the transition point
is lowered by pressure, as shown by the following table.[123]
Temperature. Pressure.
85.85° 1 atm.
84.38° 100 "
83.03° 200 "
82.29° 250 "
So far as investigations have been carried out, it appears that in most cases the transition
curve is practically a straight line.
It has, however, been found in the case of Glauber's salt, that with increase of pressure the
transition curve passes through a point of maximum temperature, and exhibits, therefore,
a form similar to that assumed by Tammann for the fusion curve.[124]
Suspended Transformation. Metastable Equilibria.—Hitherto we have considered
only systems in stable equilibrium. We have, however, already seen, in the case of water,
that on cooling the liquid down to the triple point, solidification did not necessarily take
place, although the conditions were such as to allow of its formation. Similarly, we saw
to produce a change in the melting point of 1°.
Investigations which were made of the influence of pressure on the melting-point,
showed that up to pressures of several hundred atmospheres the fusion curve is a straight
line.[119] Tammann[120] has, however, found that on increasing the pressure the fusion
curve no longer remains straight, but bends towards the pressure axis, so that, on
sufficiently increasing the pressure, a maximum temperature might at length be reached.
This maximum has, so far, however, not been attained, although the melting point curves
of various substances have been studied up to pressures of 4500 atm. This is to be
accounted for partly by the fact that the probable maximum temperature in the case of
most substances lies at very great pressures, and also by the fact that other solid phases
make their appearance, as, for example, in the case of ice (p. 32).
As to the upper limit of the fusion curve, the view has been expressed[121] that just as in
the case of liquid and vapour, so also in the case of solid and liquid, there exists a critical
point at which the solid and the liquid phase become identical. Experimental evidence,
however, does not appear to favour this view.[122]
The transition point, like the melting point, is also influenced by the pressure, and in this
case also it is found that pressure may either raise or lower the transition point, so that the
transition curve may be inclined either away from or towards the pressure axis. The
direction of the transition curve can also be predicted if the change of volume
accompanying the passage of one form into the other is known. In the case of sulphur, we
saw that the transition point is raised by increase of pressure; in the case of the transition
of rhombohedral into α-rhombic form of ammonium nitrate, however, the transition point
is lowered by pressure, as shown by the following table.[123]
Temperature. Pressure.
85.85° 1 atm.
84.38° 100 "
83.03° 200 "
82.29° 250 "
So far as investigations have been carried out, it appears that in most cases the transition
curve is practically a straight line.
It has, however, been found in the case of Glauber's salt, that with increase of pressure the
transition curve passes through a point of maximum temperature, and exhibits, therefore,
a form similar to that assumed by Tammann for the fusion curve.[124]
Suspended Transformation. Metastable Equilibria.—Hitherto we have considered
only systems in stable equilibrium. We have, however, already seen, in the case of water,
that on cooling the liquid down to the triple point, solidification did not necessarily take
place, although the conditions were such as to allow of its formation. Similarly, we saw
Page 67
that rhombic sulphur can be heated above the transition point, and monoclinic sulphur
can be obtained at temperatures below the transition point, although in both cases
transformation into a more stable form is possible; the system becomes metastable.
The same reluctance to form a new phase is observed also in the phenomena of
superheating of liquids, and in the "hanging" of mercury in barometers, in which case the
vapour phase is not formed. In general, then, we may say that a new phase will not
necessarily be formed immediately the system passes into such a condition that the
existence of that phase is possible; but rather, instead of the system undergoing
transformation so as to pass into the most stable condition under the existing pressure and
temperature, this transformation will be "suspended" or delayed, and the system will
become metastable. Only in the case of the formation of the liquid from the solid phase,
in a one-component system, has this reluctance to form a new phase not been observed.
To ensure the formation of the new phase, it is necessary to have that phase present. The
presence of the solid phase will prevent the supercooling of the liquid; and the presence
of the vapour phase will prevent the superheating of the liquid. However, even in the
presence of the more stable phase, transformation of the metastable phase occurs with
very varying velocity; in some cases so quickly as to appear almost instantaneous; while
in other cases, the change takes place so slowly as to require hundreds of years for its
achievement. It is this slow rate of transformation that renders the existence of metastable
forms possible, when in contact with the more stable phase. Thus, for example, although
calcite is the most stable form of calcium carbonate at the ordinary temperature,[125] the
less stable modification, aragonite, nevertheless exists under the ordinary conditions in an
apparently very stable state.
As to the amount of the new phase required to bring about the transformation of the
metastable phase, quantitative measurements have been carried out only in the case of the
initiation of crystallization in a supercooled liquid.[126] As the result of these
investigations, it was found that, in the case of superfused salol, the very small amount of
1 × 10-7 gm. of the solid phase was sufficient to induce crystallization. Crystallization of
a supercooled liquid, however, can be initiated only by a "nucleus" of the same substance
in the solid state, or, as has also been found, by a nucleus of an isomorphous solid phase;
it is not brought about by the presence of any chance solid.
Velocity of Transformation.—Attention has already been drawn to the sluggishness with
which reciprocal transformation of the polymorphic forms of a substance may occur. In
the case of tin, for example, it was found that the white modification, although apparently
possessing permanence, is in reality in a metastable state, under the ordinary conditions
of temperature and pressure. This great degree of stability is due to the tardiness with
which transformation into the grey form occurs.
What was found in the case of tin, is met with also in the case of all transformations in
the solid state, but the velocity of the change is less in some cases than in others, and
appears to decrease with increase of the valency of the element.[127] To this fact van't
can be obtained at temperatures below the transition point, although in both cases
transformation into a more stable form is possible; the system becomes metastable.
The same reluctance to form a new phase is observed also in the phenomena of
superheating of liquids, and in the "hanging" of mercury in barometers, in which case the
vapour phase is not formed. In general, then, we may say that a new phase will not
necessarily be formed immediately the system passes into such a condition that the
existence of that phase is possible; but rather, instead of the system undergoing
transformation so as to pass into the most stable condition under the existing pressure and
temperature, this transformation will be "suspended" or delayed, and the system will
become metastable. Only in the case of the formation of the liquid from the solid phase,
in a one-component system, has this reluctance to form a new phase not been observed.
To ensure the formation of the new phase, it is necessary to have that phase present. The
presence of the solid phase will prevent the supercooling of the liquid; and the presence
of the vapour phase will prevent the superheating of the liquid. However, even in the
presence of the more stable phase, transformation of the metastable phase occurs with
very varying velocity; in some cases so quickly as to appear almost instantaneous; while
in other cases, the change takes place so slowly as to require hundreds of years for its
achievement. It is this slow rate of transformation that renders the existence of metastable
forms possible, when in contact with the more stable phase. Thus, for example, although
calcite is the most stable form of calcium carbonate at the ordinary temperature,[125] the
less stable modification, aragonite, nevertheless exists under the ordinary conditions in an
apparently very stable state.
As to the amount of the new phase required to bring about the transformation of the
metastable phase, quantitative measurements have been carried out only in the case of the
initiation of crystallization in a supercooled liquid.[126] As the result of these
investigations, it was found that, in the case of superfused salol, the very small amount of
1 × 10-7 gm. of the solid phase was sufficient to induce crystallization. Crystallization of
a supercooled liquid, however, can be initiated only by a "nucleus" of the same substance
in the solid state, or, as has also been found, by a nucleus of an isomorphous solid phase;
it is not brought about by the presence of any chance solid.
Velocity of Transformation.—Attention has already been drawn to the sluggishness with
which reciprocal transformation of the polymorphic forms of a substance may occur. In
the case of tin, for example, it was found that the white modification, although apparently
possessing permanence, is in reality in a metastable state, under the ordinary conditions
of temperature and pressure. This great degree of stability is due to the tardiness with
which transformation into the grey form occurs.
What was found in the case of tin, is met with also in the case of all transformations in
the solid state, but the velocity of the change is less in some cases than in others, and
appears to decrease with increase of the valency of the element.[127] To this fact van't
Page 68
Hoff attributes the great permanence of many really unstable (or metastable) carbon
compounds.
Reference has been made to the fact that the velocity of transformation can be accelerated
by various means. One of the most important of these is the employment of a liquid
which has a solvent action on the solid phases. Just as we have seen that at any given
temperature the less stable form has the higher vapour pressure, but that at the transition
point the vapour pressure of both forms becomes identical, so also it can be proved
theoretically, and be shown experimentally, that at a given temperature the solubility of
the less stable form is greater than that of the more stable, but that at the transition point
the solubility of the two forms becomes identical.[128]
If, then, the two solid phases are brought into contact with a solvent, the less stable phase
will dissolve more abundantly than the more stable; the solution will therefore become
supersaturated with respect to the latter, which will be deposited. A gradual change of the
less stable form, therefore, takes place through the medium of the solvent. In this way the
more rapid conversion of white tin into grey in presence of a solution of tin ammonium
chloride (p. 42) is to be explained. Although, as a rule, solvents accelerate the
transformation of one solid phase into the other, they may also have a retarding influence
on the velocity of transformation, as was found by Reinders in the case of mercuric
iodide.[129]
The velocity of inversion, also, is variously affected by different solvents, and in some
cases, at least, it appears to be slower the more viscous the solvent;[130] indeed, Kastle
and Reed state that yellow crystals of mercuric iodide, which, ordinarily, change with
considerable velocity into the red modification, have been preserved for more than a year
under vaseline.
Temperature, also, has a very considerable influence on the velocity of transformation.
The higher the temperature, and the farther it is removed from the equilibrium point
(transition point), the greater is the velocity of change. Above the transition point, these
two factors act in the same direction, and the velocity of transformation will therefore go
on increasing indefinitely the higher the temperature is raised. Below the transition point,
however, the two factors act in opposite directions, and the more the temperature is
lowered, the more is the effect of removal from the equilibrium point counteracted. A
point will therefore be reached at which the velocity is a maximum. Reduction of the
temperature below this point causes a rapid falling off in the velocity of change. The
point of maximum velocity, however, is not definite, but may be altered by various
causes. Thus, Cohen found that in the case of tin, the point of maximum velocity was
altered if the metal had already undergone transformation; and also by the presence of
different liquids.[131]
Lastly, the presence of small quantities of different substances—catalytic agents or
catalyzers—has a great influence on the velocity of transformation. Thus, e.g., the
conversion of white to red phosphorus is accelerated by the presence of iodine (p. 47).
compounds.
Reference has been made to the fact that the velocity of transformation can be accelerated
by various means. One of the most important of these is the employment of a liquid
which has a solvent action on the solid phases. Just as we have seen that at any given
temperature the less stable form has the higher vapour pressure, but that at the transition
point the vapour pressure of both forms becomes identical, so also it can be proved
theoretically, and be shown experimentally, that at a given temperature the solubility of
the less stable form is greater than that of the more stable, but that at the transition point
the solubility of the two forms becomes identical.[128]
If, then, the two solid phases are brought into contact with a solvent, the less stable phase
will dissolve more abundantly than the more stable; the solution will therefore become
supersaturated with respect to the latter, which will be deposited. A gradual change of the
less stable form, therefore, takes place through the medium of the solvent. In this way the
more rapid conversion of white tin into grey in presence of a solution of tin ammonium
chloride (p. 42) is to be explained. Although, as a rule, solvents accelerate the
transformation of one solid phase into the other, they may also have a retarding influence
on the velocity of transformation, as was found by Reinders in the case of mercuric
iodide.[129]
The velocity of inversion, also, is variously affected by different solvents, and in some
cases, at least, it appears to be slower the more viscous the solvent;[130] indeed, Kastle
and Reed state that yellow crystals of mercuric iodide, which, ordinarily, change with
considerable velocity into the red modification, have been preserved for more than a year
under vaseline.
Temperature, also, has a very considerable influence on the velocity of transformation.
The higher the temperature, and the farther it is removed from the equilibrium point
(transition point), the greater is the velocity of change. Above the transition point, these
two factors act in the same direction, and the velocity of transformation will therefore go
on increasing indefinitely the higher the temperature is raised. Below the transition point,
however, the two factors act in opposite directions, and the more the temperature is
lowered, the more is the effect of removal from the equilibrium point counteracted. A
point will therefore be reached at which the velocity is a maximum. Reduction of the
temperature below this point causes a rapid falling off in the velocity of change. The
point of maximum velocity, however, is not definite, but may be altered by various
causes. Thus, Cohen found that in the case of tin, the point of maximum velocity was
altered if the metal had already undergone transformation; and also by the presence of
different liquids.[131]
Lastly, the presence of small quantities of different substances—catalytic agents or
catalyzers—has a great influence on the velocity of transformation. Thus, e.g., the
conversion of white to red phosphorus is accelerated by the presence of iodine (p. 47).
Page 69
Greater attention, however, has been paid to the study of the velocity of crystallization of
a supercooled liquid, the first experiments in this direction having been made by
Gernez[132] on the velocity of crystallization of phosphorus and sulphur. Since that time,
the velocity of crystallization of other supercooled liquids has been investigated; such as
acetic acid and phenol by Moore;[133] supercooled water by Tumlirz;[134] and a number of
organic substances by Tammann,[135] Friedländer and Tammann,[136] and by
Bogojawlenski.[137]
In measuring the velocity of crystallization, the supercooled liquids were contained in
narrow glass tubes, and the time required for the crystallization to advance along a certain
length of the tube was determined, the velocity being expressed in millimetres per
minute. The results which have so far been obtained may be summarized as follows. For
any given degree of supercooling of a substance, the velocity of crystallization is
constant. As the degree of supercooling increases, the velocity of crystallization also
increases, until a certain point is reached at which the velocity is a maximum, which has a
definite characteristic value for each substance. This maximum velocity remains constant
over a certain range of temperature; thereafter, the velocity diminishes fairly rapidly, and,
with sufficient supercooling, may become zero. The liquid then passes into a glassy mass,
which will remain (practically) permanent even in contact with the crystalline solid.
In ordinary glass we have a familiar example of a liquid which has been cooled to a
temperature at which crystallization takes place with very great slowness. If, however,
glass is heated, a temperature is reached, much below the melting point of the glass, at
which crystallization occurs with appreciable velocity, and we observe the phenomenon
of devitrification.[138]
When the velocity of crystallization is studied at temperatures above the maximum point,
it is found that the velocity is diminished by the addition of foreign substances; and in
many cases, indeed, it has been found that the diminution is the same for equimolecular
quantities of different substances. It would hence appear possible to utilize this behaviour
as a method for determining molecular weights.[139] The rule is, however, by no means a
universal one. Thus it has been found by F. Dreyer,[140] in studying the velocity of
crystallization of formanilide, that the diminution in the velocity produced by equivalent
amounts of different substances is not the same, but that the foreign substances exercise a
specific influence. Further, von Pickardt's rule does not hold when the foreign substance
forms mixed crystals (Chap. X.) with the crystallizing substance.[141]
Law of Successive Reactions.—When sulphur vapour is cooled at the ordinary
temperature, it first of all condenses to drops of liquid, which solidify in an amorphous
form, and only after some time undergo crystallization; or, when phosphorus vapour is
condensed, white phosphorus is first formed, and not the more stable form—red
phosphorus. It has also been observed that even at the ordinary temperature (therefore
much below the transition point) sulphur may crystallize out from solution in benzene,
alcohol, carbon disulphide, and other solvents, in the prismatic form, the less stable
a supercooled liquid, the first experiments in this direction having been made by
Gernez[132] on the velocity of crystallization of phosphorus and sulphur. Since that time,
the velocity of crystallization of other supercooled liquids has been investigated; such as
acetic acid and phenol by Moore;[133] supercooled water by Tumlirz;[134] and a number of
organic substances by Tammann,[135] Friedländer and Tammann,[136] and by
Bogojawlenski.[137]
In measuring the velocity of crystallization, the supercooled liquids were contained in
narrow glass tubes, and the time required for the crystallization to advance along a certain
length of the tube was determined, the velocity being expressed in millimetres per
minute. The results which have so far been obtained may be summarized as follows. For
any given degree of supercooling of a substance, the velocity of crystallization is
constant. As the degree of supercooling increases, the velocity of crystallization also
increases, until a certain point is reached at which the velocity is a maximum, which has a
definite characteristic value for each substance. This maximum velocity remains constant
over a certain range of temperature; thereafter, the velocity diminishes fairly rapidly, and,
with sufficient supercooling, may become zero. The liquid then passes into a glassy mass,
which will remain (practically) permanent even in contact with the crystalline solid.
In ordinary glass we have a familiar example of a liquid which has been cooled to a
temperature at which crystallization takes place with very great slowness. If, however,
glass is heated, a temperature is reached, much below the melting point of the glass, at
which crystallization occurs with appreciable velocity, and we observe the phenomenon
of devitrification.[138]
When the velocity of crystallization is studied at temperatures above the maximum point,
it is found that the velocity is diminished by the addition of foreign substances; and in
many cases, indeed, it has been found that the diminution is the same for equimolecular
quantities of different substances. It would hence appear possible to utilize this behaviour
as a method for determining molecular weights.[139] The rule is, however, by no means a
universal one. Thus it has been found by F. Dreyer,[140] in studying the velocity of
crystallization of formanilide, that the diminution in the velocity produced by equivalent
amounts of different substances is not the same, but that the foreign substances exercise a
specific influence. Further, von Pickardt's rule does not hold when the foreign substance
forms mixed crystals (Chap. X.) with the crystallizing substance.[141]
Law of Successive Reactions.—When sulphur vapour is cooled at the ordinary
temperature, it first of all condenses to drops of liquid, which solidify in an amorphous
form, and only after some time undergo crystallization; or, when phosphorus vapour is
condensed, white phosphorus is first formed, and not the more stable form—red
phosphorus. It has also been observed that even at the ordinary temperature (therefore
much below the transition point) sulphur may crystallize out from solution in benzene,
alcohol, carbon disulphide, and other solvents, in the prismatic form, the less stable
Page 70
prismatic crystals then undergoing transformation into the rhombic form;[142] a similar
behaviour has also been observed in the transformation of the monotropic crystalline
forms of sulphur.[143]
Many other examples might be given. In organic chemistry, for instance, it is often found
that when a substance is thrown out of solution, it is first deposited as a liquid, which
passes later into the more stable crystalline form. In analysis, also, rapid precipitation
from concentrated solution often causes the separation of a less stable and more soluble
amorphous form.
On account of the great frequency with which the prior formation of the less stable form
occurs, Ostwald[144] has put forward the law of successive reactions, which states that
when a system passes from a less stable condition it does not pass directly into the most
stable of the possible states; but into the next more stable, and so step by step into the
most stable. This law explains the formation of the metastable forms of monotropic
substances, which would otherwise not be obtainable. Although it is not always possible
to observe the formation of the least stable form, it should be remembered that that may
quite conceivably be due to the great velocity of transformation of the less stable into the
more stable form. From what we have learned about the velocity of transformation of
metastable phases, we can understand that rapid cooling to a low temperature will tend to
preserve the less stable form; and, on account of the influence of temperature in
increasing the velocity of change, it can be seen that the formation of the less stable form
will be more difficult to observe in superheated than in supercooled systems. The factors,
however, which affect the readiness with which the less stable modification is produced,
appear to be rather various.[145]
Although a number of at least apparent exceptions to Ostwald's law have been found, it
may nevertheless be accepted as a very useful generalization which sums up very
frequently observed phenomena.
CHAPTER V
SYSTEMS OF TWO COMPONENTS—PHENOMENA OF DISSOCIATION
In the preceding pages we have studied the behaviour of systems consisting of only one
component, or systems in which all the phases, whether solid, liquid, or vapour, had the
same chemical composition (p. 13). In some cases, as, for example, in the case of
phosphorus and sulphur, the component was an elementary substance; in other cases,
however, e.g. water, the component was a compound. The systems which we now
proceed to study are characterized by the fact that the different phases have no longer all
the same chemical composition, and cannot, therefore, according to definition, be
considered as one-component systems.
behaviour has also been observed in the transformation of the monotropic crystalline
forms of sulphur.[143]
Many other examples might be given. In organic chemistry, for instance, it is often found
that when a substance is thrown out of solution, it is first deposited as a liquid, which
passes later into the more stable crystalline form. In analysis, also, rapid precipitation
from concentrated solution often causes the separation of a less stable and more soluble
amorphous form.
On account of the great frequency with which the prior formation of the less stable form
occurs, Ostwald[144] has put forward the law of successive reactions, which states that
when a system passes from a less stable condition it does not pass directly into the most
stable of the possible states; but into the next more stable, and so step by step into the
most stable. This law explains the formation of the metastable forms of monotropic
substances, which would otherwise not be obtainable. Although it is not always possible
to observe the formation of the least stable form, it should be remembered that that may
quite conceivably be due to the great velocity of transformation of the less stable into the
more stable form. From what we have learned about the velocity of transformation of
metastable phases, we can understand that rapid cooling to a low temperature will tend to
preserve the less stable form; and, on account of the influence of temperature in
increasing the velocity of change, it can be seen that the formation of the less stable form
will be more difficult to observe in superheated than in supercooled systems. The factors,
however, which affect the readiness with which the less stable modification is produced,
appear to be rather various.[145]
Although a number of at least apparent exceptions to Ostwald's law have been found, it
may nevertheless be accepted as a very useful generalization which sums up very
frequently observed phenomena.
CHAPTER V
SYSTEMS OF TWO COMPONENTS—PHENOMENA OF DISSOCIATION
In the preceding pages we have studied the behaviour of systems consisting of only one
component, or systems in which all the phases, whether solid, liquid, or vapour, had the
same chemical composition (p. 13). In some cases, as, for example, in the case of
phosphorus and sulphur, the component was an elementary substance; in other cases,
however, e.g. water, the component was a compound. The systems which we now
proceed to study are characterized by the fact that the different phases have no longer all
the same chemical composition, and cannot, therefore, according to definition, be
considered as one-component systems.
Page 71
In most cases, little or no difficulty will be experienced in deciding as to the number of
the components, if the rules given on pp. 12 and 13 are borne in mind. If the composition
of all the phases, each regarded as a whole, is the same, the system is to be regarded as of
the first order, or a one-component system; if the composition of the different phases
varies, the system must contain more than one component. If, in order to express the
composition of all the phases present when the system is in equilibrium, two of the
constituents participating in the equilibrium are necessary and sufficient, the system is
one of two components. Which two of the possible substances are to be regarded as
components will, however, be to a certain extent a matter of arbitrary choice.
The principles affecting the choice of components will best be learned by a study of the
examples to be discussed in the sequel.
Different Systems of Two Components.—Applying the Phase Rule
P+F=C+2
to systems of two components, we see that in order that the system may be invariant,
there must be four phases in equilibrium together; two components in three phases
constitute a univariant, two components in two phases a bivariant system. In the case of
systems of one component, the highest degree of variability found was two (one
component in one phase); but, as is evident from the formula, there is a higher degree of
freedom possible in the case of two-component systems. Two components existing in
only one phase constitute a tervariant system, or a system with three degrees of freedom.
In addition to the pressure and temperature, therefore, a third variable factor must be
chosen, and as such there is taken the concentration of the components. In systems of two
components, therefore, not only may there be change of pressure and temperature, as in
the case of one-component systems, but the concentration of the components in the
different phases may also alter; a variation which did not require to be considered in the
case of one-component systems.
Fig. 18.
Since a two-component system may undergo three possible independent variations, we
should require for the graphic representation of all the possible conditions of equilibrium
a system of three co-ordinates in space, three axes being chosen, say, at right angles to
one another, and representing the three variables—pressure, temperature, and
the components, if the rules given on pp. 12 and 13 are borne in mind. If the composition
of all the phases, each regarded as a whole, is the same, the system is to be regarded as of
the first order, or a one-component system; if the composition of the different phases
varies, the system must contain more than one component. If, in order to express the
composition of all the phases present when the system is in equilibrium, two of the
constituents participating in the equilibrium are necessary and sufficient, the system is
one of two components. Which two of the possible substances are to be regarded as
components will, however, be to a certain extent a matter of arbitrary choice.
The principles affecting the choice of components will best be learned by a study of the
examples to be discussed in the sequel.
Different Systems of Two Components.—Applying the Phase Rule
P+F=C+2
to systems of two components, we see that in order that the system may be invariant,
there must be four phases in equilibrium together; two components in three phases
constitute a univariant, two components in two phases a bivariant system. In the case of
systems of one component, the highest degree of variability found was two (one
component in one phase); but, as is evident from the formula, there is a higher degree of
freedom possible in the case of two-component systems. Two components existing in
only one phase constitute a tervariant system, or a system with three degrees of freedom.
In addition to the pressure and temperature, therefore, a third variable factor must be
chosen, and as such there is taken the concentration of the components. In systems of two
components, therefore, not only may there be change of pressure and temperature, as in
the case of one-component systems, but the concentration of the components in the
different phases may also alter; a variation which did not require to be considered in the
case of one-component systems.
Fig. 18.
Since a two-component system may undergo three possible independent variations, we
should require for the graphic representation of all the possible conditions of equilibrium
a system of three co-ordinates in space, three axes being chosen, say, at right angles to
one another, and representing the three variables—pressure, temperature, and
Page 72
concentration of components (Fig. 18). A curve (e.g. AB) in the plane containing the
pressure and temperature axes would then represent the change of pressure with the
temperature, the concentration remaining unaltered (pt-diagram); one in the plane
containing the pressure and concentration axes (e.g. AF or DF), the change of pressure
with the concentration, the temperature remaining constant (pc-diagram), while in the
plane containing the concentration and the temperature axes, the simultaneous change of
these two factors at constant pressure would be represented (tc-diagram). If the points on
these three curves are joined together, a surface, ABDE, will be formed, and any line on
that surface (e.g. FG, or GH, or GI) would represent the simultaneous variation of the
three factors—pressure, temperature, concentration. Although we shall at a later point
make some use of these solid figures, we shall for the present employ the more readily
intelligible plane diagram.
The number of different systems which can be formed from two components, as well as
the number of the different phenomena which can there be observed, is much greater than
in the case of one component. In the case of no two substances, however, have all the
possible relationships been studied; so that for the purpose of gaining an insight into the
very varied behaviour of two-component systems, a number of different examples will be
discussed, each of which will serve to give a picture of some of the relationships.
Although the strict classification of the different systems according to the Phase Rule
would be based on the variability of the systems, the study of the many different
phenomena, and the correlation of the comparatively large number of different systems,
will probably be rendered easiest by grouping these different phenomena into classes,
each of these classes being studied with the help of one or more typical examples. The
order of treatment adopted here is, of course, quite arbitrary; but has been selected from
considerations of simplicity and clearness.
Phenomena of Dissociation.
Bivariant Systems.—As the first examples of the equilibria between a substance and its
products of dissociation, we shall consider very briefly those cases in which there is one
solid phase in equilibrium with vapour. Reference has already been made to such systems
in the case of ammonium chloride. On being heated, ammonium chloride dissociates into
ammonia and hydrogen chloride. Since, however, in that case the vapour phase has the
same total composition as the solid phase, viz. NH3 + HCl = NH4Cl, the system consists
of only one component existing in two phases; it is therefore univariant, and to each
temperature there will correspond a definite vapour pressure (dissociation pressure).[146]
If, however, excess of one of the products of dissociation be added, the system becomes
one of two components.
In the first place, analysis of each of the two phases yields as the composition of each,
solid: NH4Cl (= NH3 + HCl); vapour: mNH3 + nHCl. Obviously the smallest number of
substances by which the composition of the two phases can be expressed is two; that is,
pressure and temperature axes would then represent the change of pressure with the
temperature, the concentration remaining unaltered (pt-diagram); one in the plane
containing the pressure and concentration axes (e.g. AF or DF), the change of pressure
with the concentration, the temperature remaining constant (pc-diagram), while in the
plane containing the concentration and the temperature axes, the simultaneous change of
these two factors at constant pressure would be represented (tc-diagram). If the points on
these three curves are joined together, a surface, ABDE, will be formed, and any line on
that surface (e.g. FG, or GH, or GI) would represent the simultaneous variation of the
three factors—pressure, temperature, concentration. Although we shall at a later point
make some use of these solid figures, we shall for the present employ the more readily
intelligible plane diagram.
The number of different systems which can be formed from two components, as well as
the number of the different phenomena which can there be observed, is much greater than
in the case of one component. In the case of no two substances, however, have all the
possible relationships been studied; so that for the purpose of gaining an insight into the
very varied behaviour of two-component systems, a number of different examples will be
discussed, each of which will serve to give a picture of some of the relationships.
Although the strict classification of the different systems according to the Phase Rule
would be based on the variability of the systems, the study of the many different
phenomena, and the correlation of the comparatively large number of different systems,
will probably be rendered easiest by grouping these different phenomena into classes,
each of these classes being studied with the help of one or more typical examples. The
order of treatment adopted here is, of course, quite arbitrary; but has been selected from
considerations of simplicity and clearness.
Phenomena of Dissociation.
Bivariant Systems.—As the first examples of the equilibria between a substance and its
products of dissociation, we shall consider very briefly those cases in which there is one
solid phase in equilibrium with vapour. Reference has already been made to such systems
in the case of ammonium chloride. On being heated, ammonium chloride dissociates into
ammonia and hydrogen chloride. Since, however, in that case the vapour phase has the
same total composition as the solid phase, viz. NH3 + HCl = NH4Cl, the system consists
of only one component existing in two phases; it is therefore univariant, and to each
temperature there will correspond a definite vapour pressure (dissociation pressure).[146]
If, however, excess of one of the products of dissociation be added, the system becomes
one of two components.
In the first place, analysis of each of the two phases yields as the composition of each,
solid: NH4Cl (= NH3 + HCl); vapour: mNH3 + nHCl. Obviously the smallest number of
substances by which the composition of the two phases can be expressed is two; that is,
Page 73
the number of components is two. What, then, are the components? The choice lies
between NH3 + HCl, NH4Cl + NH3, and NH4Cl + HCl; for the three substances,
ammonium chloride, ammonia, hydrogen chloride, are the only ones taking part in the
equilibrium of the system.
Of these three pairs of components, we should obviously choose as the most simple NH3
and HCl, for we can then represent the composition of the two phases as the sum of the
two components. If one of the other two possible pairs of components be chosen, we
should have to introduce negative quantities of one of the components, in order to
represent the composition of the vapour phase. Although it must be allowed that the
introduction of negative quantities of a component in such cases is quite permissible, still
it will be better to adopt the simpler and more direct choice, whereby the composition of
each of the phases is represented as a sum of two components in varying proportions
(p. 12).
If, therefore, we have a solid substance, such as ammonium chloride, which dissociates
on volatilization, and if the products of dissociation are added in varying amounts to the
system, we shall have, in the sense of the Phase Rule, a two-component system existing in
two phases. Such a system will possess two degrees of freedom. At any given
temperature, not only the pressure, but also the composition, of the vapour-phase, i.e. the
concentration of the components, can vary. Only after one of these independent variables,
pressure or composition, has been arbitrarily fixed does the system become univariant,
and exhibit a definite, constant pressure at a given temperature.
Now, although the Phase Rule informs us that at a given temperature change of
composition of the vapour phase will be accompanied by change of pressure, it does not
cast any light on the relation between these two variables. This relationship, however, can
be calculated theoretically by means of the Law of Mass Action.[147] From this we learn
that in the case of a substance which dissociates into equivalent quantities of two gases,
the product of the partial pressures of the gases is constant at a given temperature.
This has been proved experimentally in the case of ammonium hydrosulphide,
ammonium cyanide, phosphonium bromide, and other substances.[148]
Univariant Systems.—In order that a system of two components shall possess only one
degree of freedom, three phases must be present. Of such systems, there are seven
possible, viz. S-S-S, S-S-L, S-S-V, L-L-L, S-L-L, L-L-V, S-L-V; S denoting solid, L
liquid, and V vapour. In the present chapter we shall consider only the systems S-S-V, i.e.
those systems in which there are two solid phases and a vapour phase present.
As an example of this, we may first consider the well-known case of the dissociation of
calcium carbonate. This substance on being heated dissociates into calcium oxide, or
quick-lime, and carbon dioxide, as shown by the equation CaCO3 CaO + CO2. In
accordance with our definition (p. 9), we have here two solid phases, the carbonate and
the quick-lime, and one vapour phase; the system is therefore univariant. To each
between NH3 + HCl, NH4Cl + NH3, and NH4Cl + HCl; for the three substances,
ammonium chloride, ammonia, hydrogen chloride, are the only ones taking part in the
equilibrium of the system.
Of these three pairs of components, we should obviously choose as the most simple NH3
and HCl, for we can then represent the composition of the two phases as the sum of the
two components. If one of the other two possible pairs of components be chosen, we
should have to introduce negative quantities of one of the components, in order to
represent the composition of the vapour phase. Although it must be allowed that the
introduction of negative quantities of a component in such cases is quite permissible, still
it will be better to adopt the simpler and more direct choice, whereby the composition of
each of the phases is represented as a sum of two components in varying proportions
(p. 12).
If, therefore, we have a solid substance, such as ammonium chloride, which dissociates
on volatilization, and if the products of dissociation are added in varying amounts to the
system, we shall have, in the sense of the Phase Rule, a two-component system existing in
two phases. Such a system will possess two degrees of freedom. At any given
temperature, not only the pressure, but also the composition, of the vapour-phase, i.e. the
concentration of the components, can vary. Only after one of these independent variables,
pressure or composition, has been arbitrarily fixed does the system become univariant,
and exhibit a definite, constant pressure at a given temperature.
Now, although the Phase Rule informs us that at a given temperature change of
composition of the vapour phase will be accompanied by change of pressure, it does not
cast any light on the relation between these two variables. This relationship, however, can
be calculated theoretically by means of the Law of Mass Action.[147] From this we learn
that in the case of a substance which dissociates into equivalent quantities of two gases,
the product of the partial pressures of the gases is constant at a given temperature.
This has been proved experimentally in the case of ammonium hydrosulphide,
ammonium cyanide, phosphonium bromide, and other substances.[148]
Univariant Systems.—In order that a system of two components shall possess only one
degree of freedom, three phases must be present. Of such systems, there are seven
possible, viz. S-S-S, S-S-L, S-S-V, L-L-L, S-L-L, L-L-V, S-L-V; S denoting solid, L
liquid, and V vapour. In the present chapter we shall consider only the systems S-S-V, i.e.
those systems in which there are two solid phases and a vapour phase present.
As an example of this, we may first consider the well-known case of the dissociation of
calcium carbonate. This substance on being heated dissociates into calcium oxide, or
quick-lime, and carbon dioxide, as shown by the equation CaCO3 CaO + CO2. In
accordance with our definition (p. 9), we have here two solid phases, the carbonate and
the quick-lime, and one vapour phase; the system is therefore univariant. To each
Page 74
temperature, therefore, there will correspond a certain, definite maximum pressure of
carbon dioxide (dissociation pressure), and this will follow the same law as the vapour
pressure of a pure liquid (p. 21). More particularly, it will be independent of the relative
or absolute amounts of the two solid phases, and of the volume of the vapour phase. If the
temperature is maintained constant, increase of volume will cause the dissociation of a
further amount of the carbonate until the pressure again reaches its maximum value
corresponding to the given temperature. Diminution of volume, on the other hand, will
bring about the combination of a certain quantity of the carbon dioxide with the calcium
oxide until the pressure again reaches its original value.
The dissociation pressure of calcium carbonate was first studied by Debray,[149] but more
exact measurements have been made by Le Chatelier,[150] who found the following
corresponding values of temperature and pressure:—
Temperature. Pressure in cm. mercury.
547° 2.7
610° 4.6
625° 5.6
740° 25.5
745° 28.9
810° 67.8
812° 76.3
865° 133.3
From this table we see that it is only at a temperature of about 812° that the pressure of
the carbon dioxide becomes equal to atmospheric pressure. In a vessel open to the air,
therefore, the complete decomposition of the calcium carbonate would not take place
below this temperature by the mere heating of the carbonate. If, however, the carbon
dioxide is removed as quickly as it is formed, say by a current of air, then the entire
decomposition can be made to take place at a much lower temperature. For the
dissociation equilibrium of the carbonate depends only on the partial pressure of the
carbon dioxide, and if this is kept small, then the decomposition can proceed, even at a
temperature below that at which the pressure of the carbon dioxide is less than
atmospheric pressure.
Ammonia Compounds of Metal Chlorides.—Ammonia possesses the property of
combining with various substances, chiefly the halides of metals, to form compounds
which again yield up the ammonia on being heated. Thus, for example, on passing
ammonia over silver chloride, absorption of the gas takes place with formation of the
substances AgCl,3NH3 and 2AgCl,3NH3, according to the conditions of the experiment.
These were the first known substances belonging to this class, and were employed by
Faraday in his experiments on the liquefaction of ammonia. Similar compounds have also
been obtained by the action of ammonia on silver bromide, iodide, cyanide, and nitrate;
and with the halogen compounds of calcium, zinc, and magnesium, as well as with other
carbon dioxide (dissociation pressure), and this will follow the same law as the vapour
pressure of a pure liquid (p. 21). More particularly, it will be independent of the relative
or absolute amounts of the two solid phases, and of the volume of the vapour phase. If the
temperature is maintained constant, increase of volume will cause the dissociation of a
further amount of the carbonate until the pressure again reaches its maximum value
corresponding to the given temperature. Diminution of volume, on the other hand, will
bring about the combination of a certain quantity of the carbon dioxide with the calcium
oxide until the pressure again reaches its original value.
The dissociation pressure of calcium carbonate was first studied by Debray,[149] but more
exact measurements have been made by Le Chatelier,[150] who found the following
corresponding values of temperature and pressure:—
Temperature. Pressure in cm. mercury.
547° 2.7
610° 4.6
625° 5.6
740° 25.5
745° 28.9
810° 67.8
812° 76.3
865° 133.3
From this table we see that it is only at a temperature of about 812° that the pressure of
the carbon dioxide becomes equal to atmospheric pressure. In a vessel open to the air,
therefore, the complete decomposition of the calcium carbonate would not take place
below this temperature by the mere heating of the carbonate. If, however, the carbon
dioxide is removed as quickly as it is formed, say by a current of air, then the entire
decomposition can be made to take place at a much lower temperature. For the
dissociation equilibrium of the carbonate depends only on the partial pressure of the
carbon dioxide, and if this is kept small, then the decomposition can proceed, even at a
temperature below that at which the pressure of the carbon dioxide is less than
atmospheric pressure.
Ammonia Compounds of Metal Chlorides.—Ammonia possesses the property of
combining with various substances, chiefly the halides of metals, to form compounds
which again yield up the ammonia on being heated. Thus, for example, on passing
ammonia over silver chloride, absorption of the gas takes place with formation of the
substances AgCl,3NH3 and 2AgCl,3NH3, according to the conditions of the experiment.
These were the first known substances belonging to this class, and were employed by
Faraday in his experiments on the liquefaction of ammonia. Similar compounds have also
been obtained by the action of ammonia on silver bromide, iodide, cyanide, and nitrate;
and with the halogen compounds of calcium, zinc, and magnesium, as well as with other
Page 75
salts. The behaviour of the ammonia compounds of silver chloride is typical for the
compounds of this class, and may be briefly considered here.
It was found by Isambert[151] that at temperatures below 15°, silver chloride combined
with ammonia to form the compound AgCl,3NH3, while at temperatures above 20° the
compound 2AgCl,3NH3 was produced. On heating these substances, ammonia was
evolved, and the pressure of this gas was found in the case of both compounds to be
constant at a given temperature, but was greater in the case of the former than in the case
of the latter substance; the pressure, further, was independent of the amount decomposed.
The behaviour of these two substances is, therefore, exactly analogous to that shown by
calcium carbonate, and the explanation is also similar.
Regarded from the point of view of the Phase Rule, we see that we are here dealing with
two components, AgCl and NH3. On being heated, the compounds decompose according
to the equations:—
2(AgCl,3NH3) 2AgCl,3NH3 + 3NH3.
2AgCl,3NH3 2AgCl + 3NH3.
There are, therefore, three phases, viz. AgCl,3NH3; 2AgCl,3NH3, and NH3, in the one
case; and 2AgCl,3NH3; AgCl, and NH3 in the other. These two systems are therefore
univariant, and to each temperature there must correspond a definite pressure of
dissociation, quite irrespective of the amounts of the phases present. Similarly, if, at
constant temperature, the volume is increased (or if the ammonia which is evolved is
pumped off), the pressure will remain constant so long as two solid phases, AgCl,3NH3
and 2AgCl,3NH3, are present, i.e. until the compound richer in ammonia is completely
decomposed, when there will be a sudden fall in the pressure to the value corresponding
to the system 2AgCl,3NH3—AgCl—NH3. The pressure will again remain constant at
constant temperature, until all the ammonia has been pumped off, when there will again
be a sudden fall in the pressure to that of the system formed by solid silver chloride in
contact with its vapour.
The reverse changes take place when the pressure of the ammonia is gradually increased.
If the volume is continuously diminished, the pressure will first increase until it has
reached a certain value; the compound 2AgCl,3NH3 can then be formed, and the pressure
will now remain constant until all the silver chloride has disappeared. The pressure will
again rise, until it has reached the value at which the compound AgCl,3NH3 can be
formed, when it will again remain constant until the complete disappearance of the lower
compound. There is no gradual change of pressure on passing from one system to
another; but the changes are abrupt, as is demanded by the Phase Rule, and as experiment
has conclusively proved.[152]
compounds of this class, and may be briefly considered here.
It was found by Isambert[151] that at temperatures below 15°, silver chloride combined
with ammonia to form the compound AgCl,3NH3, while at temperatures above 20° the
compound 2AgCl,3NH3 was produced. On heating these substances, ammonia was
evolved, and the pressure of this gas was found in the case of both compounds to be
constant at a given temperature, but was greater in the case of the former than in the case
of the latter substance; the pressure, further, was independent of the amount decomposed.
The behaviour of these two substances is, therefore, exactly analogous to that shown by
calcium carbonate, and the explanation is also similar.
Regarded from the point of view of the Phase Rule, we see that we are here dealing with
two components, AgCl and NH3. On being heated, the compounds decompose according
to the equations:—
2(AgCl,3NH3) 2AgCl,3NH3 + 3NH3.
2AgCl,3NH3 2AgCl + 3NH3.
There are, therefore, three phases, viz. AgCl,3NH3; 2AgCl,3NH3, and NH3, in the one
case; and 2AgCl,3NH3; AgCl, and NH3 in the other. These two systems are therefore
univariant, and to each temperature there must correspond a definite pressure of
dissociation, quite irrespective of the amounts of the phases present. Similarly, if, at
constant temperature, the volume is increased (or if the ammonia which is evolved is
pumped off), the pressure will remain constant so long as two solid phases, AgCl,3NH3
and 2AgCl,3NH3, are present, i.e. until the compound richer in ammonia is completely
decomposed, when there will be a sudden fall in the pressure to the value corresponding
to the system 2AgCl,3NH3—AgCl—NH3. The pressure will again remain constant at
constant temperature, until all the ammonia has been pumped off, when there will again
be a sudden fall in the pressure to that of the system formed by solid silver chloride in
contact with its vapour.
The reverse changes take place when the pressure of the ammonia is gradually increased.
If the volume is continuously diminished, the pressure will first increase until it has
reached a certain value; the compound 2AgCl,3NH3 can then be formed, and the pressure
will now remain constant until all the silver chloride has disappeared. The pressure will
again rise, until it has reached the value at which the compound AgCl,3NH3 can be
formed, when it will again remain constant until the complete disappearance of the lower
compound. There is no gradual change of pressure on passing from one system to
another; but the changes are abrupt, as is demanded by the Phase Rule, and as experiment
has conclusively proved.[152]
Page 76
The dissociation pressures of the two compounds of silver chloride and ammonia, as
determined by Isambert,[153] are given in the following table:—
AgCl,3NH3. 2AgCl,3NH3.
Temperature. Pressure. Temperature. Pressure.
0° 29.3 cm. 20.0° 9.3 cm.
10.6° 50.5 ,, 31.0° 12.5 ,,
17.5° 65.5 ,, 47.0° 26.8 ,,
24.0° 93.7 ,, 58.5° 52.8 ,,
28.0° 135.5 ,, 69.0° 78.6 ,,
34.2° 171.3 ,, 71.5° 94.6 ,,
48.5° 241.4 ,, 77.5° 119.8 ,,
51.5° 413.2 ,, 83.5° 159.3 ,,
54.0° 464.1 ,, 86.1° 181.3 ,,
88.5° 201.3 ,,
The conditions for the formation of these two compounds, by passing ammonia over
silver chloride, to which reference has already been made, will be readily understood
from the above tables. In the case of the triammonia mono-chloride, the dissociation
pressure becomes equal to atmospheric pressure at a temperature of about 20°; above this
temperature, therefore, it cannot be formed by the action of ammonia at atmospheric
pressure on silver chloride. The triammonia dichloride can, however, be formed, for its
dissociation pressure at this temperature amounts to only 9 cm., and becomes equal to the
atmospheric pressure only at a temperature of about 68°; and this temperature, therefore,
constitutes the limit above which no combination can take place between silver chloride
and ammonia under atmospheric pressure.
Attention may be here drawn to the fact, to which reference will also be made later, that
two solid phases are necessary in order that the dissociation pressure at a given
temperature shall be definite; and for the exact definition of this pressure it is necessary
to know, not merely what is the substance undergoing dissociation, but also what is the
solid product of dissociation formed. For the definition of the equilibrium, the latter is as
important as the former. We shall presently find proof of this in the case of an analogous
class of phenomena, viz. the dissociation of salt hydrates.
Salts with Water of Crystallization.—In the case of the dehydration of crystalline salts
containing water of crystallization, we meet with phenomena which are in all respects
similar to those just studied. A salt hydrate on being heated dissociates into a lower
hydrate (or anhydrous salt) and water vapour. Since we are dealing with two components
—salt and water[154]—in three phases, viz. hydrate a, hydrate b (or anhydrous salt), and
vapour, the system is univariant, and to each temperature there will correspond a certain,
definite vapour pressure (the dissociation pressure), which will be independent of the
determined by Isambert,[153] are given in the following table:—
AgCl,3NH3. 2AgCl,3NH3.
Temperature. Pressure. Temperature. Pressure.
0° 29.3 cm. 20.0° 9.3 cm.
10.6° 50.5 ,, 31.0° 12.5 ,,
17.5° 65.5 ,, 47.0° 26.8 ,,
24.0° 93.7 ,, 58.5° 52.8 ,,
28.0° 135.5 ,, 69.0° 78.6 ,,
34.2° 171.3 ,, 71.5° 94.6 ,,
48.5° 241.4 ,, 77.5° 119.8 ,,
51.5° 413.2 ,, 83.5° 159.3 ,,
54.0° 464.1 ,, 86.1° 181.3 ,,
88.5° 201.3 ,,
The conditions for the formation of these two compounds, by passing ammonia over
silver chloride, to which reference has already been made, will be readily understood
from the above tables. In the case of the triammonia mono-chloride, the dissociation
pressure becomes equal to atmospheric pressure at a temperature of about 20°; above this
temperature, therefore, it cannot be formed by the action of ammonia at atmospheric
pressure on silver chloride. The triammonia dichloride can, however, be formed, for its
dissociation pressure at this temperature amounts to only 9 cm., and becomes equal to the
atmospheric pressure only at a temperature of about 68°; and this temperature, therefore,
constitutes the limit above which no combination can take place between silver chloride
and ammonia under atmospheric pressure.
Attention may be here drawn to the fact, to which reference will also be made later, that
two solid phases are necessary in order that the dissociation pressure at a given
temperature shall be definite; and for the exact definition of this pressure it is necessary
to know, not merely what is the substance undergoing dissociation, but also what is the
solid product of dissociation formed. For the definition of the equilibrium, the latter is as
important as the former. We shall presently find proof of this in the case of an analogous
class of phenomena, viz. the dissociation of salt hydrates.
Salts with Water of Crystallization.—In the case of the dehydration of crystalline salts
containing water of crystallization, we meet with phenomena which are in all respects
similar to those just studied. A salt hydrate on being heated dissociates into a lower
hydrate (or anhydrous salt) and water vapour. Since we are dealing with two components
—salt and water[154]—in three phases, viz. hydrate a, hydrate b (or anhydrous salt), and
vapour, the system is univariant, and to each temperature there will correspond a certain,
definite vapour pressure (the dissociation pressure), which will be independent of the
Page 77
relative or absolute amounts of the phases, i.e. of the amount of hydrate which has
already undergone dissociation or dehydration.
Fig. 19.
The constancy of the dissociation pressure had been proved experimentally by several
investigators[155] a number of years before the theoretical basis for its necessity had been
given. In the case of salts capable of forming more than one hydrate, we should obtain a
series of dissociation curves (pt-curves), as in the case of the different hydrates of copper
sulphate. In Fig. 19 there are represented diagrammatically the vapour-pressure curves of
the following univariant systems of copper sulphate and water:—
Curve OA: CuSO4,5H2O CuSO4,3H2O + 2H2O.
Curve OB: CuSO4,3H2O CuSO4,H2O + 2H2O.
Curve OC: CuSO4,H2O CuSO4 + H2O.
Let us now follow the changes which take place on increasing the pressure of the aqueous
vapour in contact with anhydrous copper sulphate, the temperature being meanwhile
maintained constant. If, starting from the point D, we slowly add water vapour to the
system, the pressure will gradually rise, without formation of hydrate taking place; for at
pressures below the curve OC only the anhydrous salt can exist. At E, however, the
hydrate CuSO4,H2O will be formed, and as there are now three phases present, viz.
CuSO4, CuSO4,H2O, and vapour, the system becomes univariant; and since the
temperature is constant, the pressure must also be constant. Continued addition of vapour
will result merely in an increase in the amount of the hydrate, and a decrease in the
amount of the anhydrous salt. When the latter has entirely disappeared, i.e. has passed
into hydrated salt, the system again becomes bivariant, and passes along the line EF; the
pressure gradually increases, therefore, until at F the hydrate 3H2O is formed, and the
system again becomes univariant; the three phases present are CuSO4,H2O,
CuSO4,3H2O, vapour. The pressure will remain constant, therefore, until the hydrate
1H2O has disappeared, when it will again increase till G is reached; here the hydrate
5H2O is formed, and the pressure once more remains constant until the complete
disappearance of the hydrate 3H2O has taken place.
already undergone dissociation or dehydration.
Fig. 19.
The constancy of the dissociation pressure had been proved experimentally by several
investigators[155] a number of years before the theoretical basis for its necessity had been
given. In the case of salts capable of forming more than one hydrate, we should obtain a
series of dissociation curves (pt-curves), as in the case of the different hydrates of copper
sulphate. In Fig. 19 there are represented diagrammatically the vapour-pressure curves of
the following univariant systems of copper sulphate and water:—
Curve OA: CuSO4,5H2O CuSO4,3H2O + 2H2O.
Curve OB: CuSO4,3H2O CuSO4,H2O + 2H2O.
Curve OC: CuSO4,H2O CuSO4 + H2O.
Let us now follow the changes which take place on increasing the pressure of the aqueous
vapour in contact with anhydrous copper sulphate, the temperature being meanwhile
maintained constant. If, starting from the point D, we slowly add water vapour to the
system, the pressure will gradually rise, without formation of hydrate taking place; for at
pressures below the curve OC only the anhydrous salt can exist. At E, however, the
hydrate CuSO4,H2O will be formed, and as there are now three phases present, viz.
CuSO4, CuSO4,H2O, and vapour, the system becomes univariant; and since the
temperature is constant, the pressure must also be constant. Continued addition of vapour
will result merely in an increase in the amount of the hydrate, and a decrease in the
amount of the anhydrous salt. When the latter has entirely disappeared, i.e. has passed
into hydrated salt, the system again becomes bivariant, and passes along the line EF; the
pressure gradually increases, therefore, until at F the hydrate 3H2O is formed, and the
system again becomes univariant; the three phases present are CuSO4,H2O,
CuSO4,3H2O, vapour. The pressure will remain constant, therefore, until the hydrate
1H2O has disappeared, when it will again increase till G is reached; here the hydrate
5H2O is formed, and the pressure once more remains constant until the complete
disappearance of the hydrate 3H2O has taken place.
Page 78
Conversely, on dehydrating CuSO4,5H2O at constant temperature, we should find that the
pressure would maintain the value corresponding to the dissociation pressure of the
system CuSO4,5H2O—CuSO4,3H2O—vapour, until all the hydrate 5H2O had
disappeared; further removal of water would then cause the pressure to fall abruptly to
the pressure of the system CuSO4,3H2O—CuSO4,H2O—vapour, at which value it would
again remain constant until the tri-hydrate had passed into the monohydrate, when a
further sudden diminution of the pressure would occur. This behaviour is represented
diagrammatically in Fig. 20, the values of the pressure being those at 50°.
Efflorescence.—From Fig. 19 we are enabled to predict the conditions under which a
given hydrated salt will effloresce when exposed to the air. We have just learned that
copper sulphate pentahydrate, for example, will not be formed unless the pressure of the
aqueous vapour reaches a certain value; and that conversely, if the vapour pressure falls
below the dissociation pressure of the pentahydrate, this salt will undergo dehydration.
From this, then, it is evident that a crystalline salt hydrate will effloresce when exposed to
the air, if the partial pressure of the water vapour in the air is lower than the dissociation
pressure of the hydrate. At the ordinary temperature the dissociation pressure of copper
sulphate is less than the pressure of water vapour in the air, and therefore copper sulphate
does not effloresce. In the case of sodium sulphate decahydrate, however, the dissociation
pressure is greater than the normal vapour pressure in a room, and this salt therefore
effloresces.
Fig. 20.
Indefiniteness of the Vapour Pressure of a Hydrate.—Reference has already been
made (p. 84), in the case of the ammonia compounds of the metal chlorides, to the
importance of the solid product of dissociation for the definition of the dissociation
pressure. Similarly also in the case of a hydrated salt. A salt hydrate in contact with
vapour constitutes only a bivariant system, and can exist therefore at different values of
temperature and pressure of vapour, as is seen from the diagram, Fig. 19. Anhydrous
copper sulphate can exist in contact with water vapour at all values of temperature and
pressure lying in the field below the curve OC; and the hydrate CuSO4,H2O can exist in
contact with vapour at all values of temperature and pressure in the field BOC. Similarly,
each of the other hydrates can exist in contact with vapour at different values of
temperature and pressure.
pressure would maintain the value corresponding to the dissociation pressure of the
system CuSO4,5H2O—CuSO4,3H2O—vapour, until all the hydrate 5H2O had
disappeared; further removal of water would then cause the pressure to fall abruptly to
the pressure of the system CuSO4,3H2O—CuSO4,H2O—vapour, at which value it would
again remain constant until the tri-hydrate had passed into the monohydrate, when a
further sudden diminution of the pressure would occur. This behaviour is represented
diagrammatically in Fig. 20, the values of the pressure being those at 50°.
Efflorescence.—From Fig. 19 we are enabled to predict the conditions under which a
given hydrated salt will effloresce when exposed to the air. We have just learned that
copper sulphate pentahydrate, for example, will not be formed unless the pressure of the
aqueous vapour reaches a certain value; and that conversely, if the vapour pressure falls
below the dissociation pressure of the pentahydrate, this salt will undergo dehydration.
From this, then, it is evident that a crystalline salt hydrate will effloresce when exposed to
the air, if the partial pressure of the water vapour in the air is lower than the dissociation
pressure of the hydrate. At the ordinary temperature the dissociation pressure of copper
sulphate is less than the pressure of water vapour in the air, and therefore copper sulphate
does not effloresce. In the case of sodium sulphate decahydrate, however, the dissociation
pressure is greater than the normal vapour pressure in a room, and this salt therefore
effloresces.
Fig. 20.
Indefiniteness of the Vapour Pressure of a Hydrate.—Reference has already been
made (p. 84), in the case of the ammonia compounds of the metal chlorides, to the
importance of the solid product of dissociation for the definition of the dissociation
pressure. Similarly also in the case of a hydrated salt. A salt hydrate in contact with
vapour constitutes only a bivariant system, and can exist therefore at different values of
temperature and pressure of vapour, as is seen from the diagram, Fig. 19. Anhydrous
copper sulphate can exist in contact with water vapour at all values of temperature and
pressure lying in the field below the curve OC; and the hydrate CuSO4,H2O can exist in
contact with vapour at all values of temperature and pressure in the field BOC. Similarly,
each of the other hydrates can exist in contact with vapour at different values of
temperature and pressure.
Page 79
From the Phase Rule, however, we learn that, in order that at a given temperature the
pressure of a two-component system may be constant, there must be three phases present.
Strictly, therefore, we can speak only of the vapour pressure of a system; and since, in the
cases under discussion, the hydrates dissociate into a solid and a vapour, any statement as
to the vapour pressure of a hydrate has a definite meaning only when the second solid
phase produced by the dissociation is given. The everyday custom of speaking of the
vapour pressure of a hydrated salt acquires a meaning only through the assumption,
tacitly made, that the second solid phase, or the solid produced by the dehydration of the
hydrate, is the next lower hydrate, where more hydrates than one exist. That a hydrate
always dissociates in such a way that the next lower hydrate is formed is, however, by no
means certain; indeed, cases have been met with where apparently the anhydrous salt, and
not the lower hydrate (the existence of which was possible), was produced by the
dissociation of the higher hydrate.[156]
That a salt hydrate can exhibit different vapour pressures according to the solid product of
dissociation, can not only be proved theoretically, but it has also been shown
experimentally to be a fact. Thus CaCl2,6H2O can dissociate into water vapour and either
of two lower hydrates, each containing four molecules of water of crystallization, and
designated respectively as CaCl2,4H2Oα, and CaCl2,4H2Oβ. Roozeboom[157] has shown
that the vapour pressure which is obtained differs according to which of these two
hydrates is formed, as can be seen from the following figures:—
Pressure of System.
Temperature. CaCl2,6H2O; CaCl2, CaCl2,6H2O; CaCl2,
4H2Oα; vapour. 4H2Oβ; vapour.
-15° 0.027 cm. 0.022 cm.
0 0.092 ,, 0.076 ,,
+10 0.192 ,, 0.162 ,,
20 0.378 ,, 0.315 ,,
25 0.508 ,, 0.432 ,,
29.2 — 0.567 ,,
29.8 0.680 ,, —
By reason of the non-recognition of the importance of the solid dissociation product for
the definition of the dissociation pressure of a salt hydrate, many of the older
determinations lose much of their value.
Suspended Transformation.—Just as in systems of one component we found that a new
phase was not necessarily formed when the conditions for its existence were established,
so also we find that even when the vapour pressure is lowered below the dissociation
pressure of a system, dissociation does not necessarily occur. This is well known in the
case of Glauber's salt, first observed by Faraday. Undamaged crystals of Na2SO4,10H2O
could be kept unchanged in the open air, although the vapour pressure of the system
pressure of a two-component system may be constant, there must be three phases present.
Strictly, therefore, we can speak only of the vapour pressure of a system; and since, in the
cases under discussion, the hydrates dissociate into a solid and a vapour, any statement as
to the vapour pressure of a hydrate has a definite meaning only when the second solid
phase produced by the dissociation is given. The everyday custom of speaking of the
vapour pressure of a hydrated salt acquires a meaning only through the assumption,
tacitly made, that the second solid phase, or the solid produced by the dehydration of the
hydrate, is the next lower hydrate, where more hydrates than one exist. That a hydrate
always dissociates in such a way that the next lower hydrate is formed is, however, by no
means certain; indeed, cases have been met with where apparently the anhydrous salt, and
not the lower hydrate (the existence of which was possible), was produced by the
dissociation of the higher hydrate.[156]
That a salt hydrate can exhibit different vapour pressures according to the solid product of
dissociation, can not only be proved theoretically, but it has also been shown
experimentally to be a fact. Thus CaCl2,6H2O can dissociate into water vapour and either
of two lower hydrates, each containing four molecules of water of crystallization, and
designated respectively as CaCl2,4H2Oα, and CaCl2,4H2Oβ. Roozeboom[157] has shown
that the vapour pressure which is obtained differs according to which of these two
hydrates is formed, as can be seen from the following figures:—
Pressure of System.
Temperature. CaCl2,6H2O; CaCl2, CaCl2,6H2O; CaCl2,
4H2Oα; vapour. 4H2Oβ; vapour.
-15° 0.027 cm. 0.022 cm.
0 0.092 ,, 0.076 ,,
+10 0.192 ,, 0.162 ,,
20 0.378 ,, 0.315 ,,
25 0.508 ,, 0.432 ,,
29.2 — 0.567 ,,
29.8 0.680 ,, —
By reason of the non-recognition of the importance of the solid dissociation product for
the definition of the dissociation pressure of a salt hydrate, many of the older
determinations lose much of their value.
Suspended Transformation.—Just as in systems of one component we found that a new
phase was not necessarily formed when the conditions for its existence were established,
so also we find that even when the vapour pressure is lowered below the dissociation
pressure of a system, dissociation does not necessarily occur. This is well known in the
case of Glauber's salt, first observed by Faraday. Undamaged crystals of Na2SO4,10H2O
could be kept unchanged in the open air, although the vapour pressure of the system
Page 80
Na2SO4,10H2O—Na2SO4—vapour is greater than the ordinary pressure of aqueous
vapour in the air. That is to say, the possibility of the formation of the new phase Na2SO4
was given; nevertheless this new phase did not appear, and the system therefore became
metastable, or unstable with respect to the anhydrous salt. When, however, a trace of the
new phase—the anhydrous salt—was brought in contact with the hydrate, transformation
occurred; the hydrate effloresced.
The possibility of suspended transformation or the non-formation of the new phases must
also be granted in the case where the vapour pressure is raised above that corresponding
to the system hydrate—anhydrous salt (or lower hydrate)—vapour; in this case the
formation of the higher hydrate becomes a possibility, but not a certainty. Although there
is no example of this known in the case of hydrated salts, the suspension of the
transformation has been observed in the case of the compounds of ammonia with the
metal chlorides (p. 82). Horstmann,[158] for example, found that the pressure of ammonia
in contact with 2AgCl,3NH3 could be raised to a value higher than the dissociation
pressure of AgCl,3NH3 without this compound being formed. We see, therefore, that even
when the existence of the higher compound in contact with the lower became possible,
the higher compound was not immediately formed.
Range of Existence of Hydrates.—In Fig. 19 the vapour pressure curves of the different
hydrates of copper sulphate are represented as maintaining their relative positions
throughout the whole range of temperatures. But this is not necessarily the case. It is
possible that at some temperature the vapour pressure curve of a lower hydrate may cut
that of a higher hydrate. At temperatures above the point of intersection, the lower
hydrate would have a higher vapour pressure than the higher hydrate, and would
therefore be metastable with respect to the latter. The range of stable existence of the
lower hydrate would therefore end at the point of intersection. This appears to be the case
with the two hydrates of sodium sulphate, to which reference will be made later.[159]
Constancy of Vapour Pressure and the Formation of Compounds.—We have seen in
the case of the salt hydrates that the continued addition of the vapour phase to the system
caused an increase in the pressure until at a definite value of the pressure a hydrate is
formed; the pressure then becomes constant, and remains so, until one of the solid phases
has disappeared. Conversely, on withdrawing the vapour phase, the pressure remained
constant so long as any of the dissociating compound was present, independently of the
degree of the decomposition (p. 86). This behaviour, now, has been employed for the
purpose of determining whether or not definite chemical compounds are formed. Should
compounds be formed between the vapour phase and the solid, then, on continued
addition or withdrawal of the vapour phase, it will be found that the vapour pressure
remains constant for a certain time, and will then suddenly assume a new value, at which
it will again remain constant. By this method, Ramsay[160] found that no definite hydrates
were formed in the case of ferric and aluminium oxides, but that two are formed in the
case of lead oxide, viz. 2PbO,H2O and 3PbO,H2O.
vapour in the air. That is to say, the possibility of the formation of the new phase Na2SO4
was given; nevertheless this new phase did not appear, and the system therefore became
metastable, or unstable with respect to the anhydrous salt. When, however, a trace of the
new phase—the anhydrous salt—was brought in contact with the hydrate, transformation
occurred; the hydrate effloresced.
The possibility of suspended transformation or the non-formation of the new phases must
also be granted in the case where the vapour pressure is raised above that corresponding
to the system hydrate—anhydrous salt (or lower hydrate)—vapour; in this case the
formation of the higher hydrate becomes a possibility, but not a certainty. Although there
is no example of this known in the case of hydrated salts, the suspension of the
transformation has been observed in the case of the compounds of ammonia with the
metal chlorides (p. 82). Horstmann,[158] for example, found that the pressure of ammonia
in contact with 2AgCl,3NH3 could be raised to a value higher than the dissociation
pressure of AgCl,3NH3 without this compound being formed. We see, therefore, that even
when the existence of the higher compound in contact with the lower became possible,
the higher compound was not immediately formed.
Range of Existence of Hydrates.—In Fig. 19 the vapour pressure curves of the different
hydrates of copper sulphate are represented as maintaining their relative positions
throughout the whole range of temperatures. But this is not necessarily the case. It is
possible that at some temperature the vapour pressure curve of a lower hydrate may cut
that of a higher hydrate. At temperatures above the point of intersection, the lower
hydrate would have a higher vapour pressure than the higher hydrate, and would
therefore be metastable with respect to the latter. The range of stable existence of the
lower hydrate would therefore end at the point of intersection. This appears to be the case
with the two hydrates of sodium sulphate, to which reference will be made later.[159]
Constancy of Vapour Pressure and the Formation of Compounds.—We have seen in
the case of the salt hydrates that the continued addition of the vapour phase to the system
caused an increase in the pressure until at a definite value of the pressure a hydrate is
formed; the pressure then becomes constant, and remains so, until one of the solid phases
has disappeared. Conversely, on withdrawing the vapour phase, the pressure remained
constant so long as any of the dissociating compound was present, independently of the
degree of the decomposition (p. 86). This behaviour, now, has been employed for the
purpose of determining whether or not definite chemical compounds are formed. Should
compounds be formed between the vapour phase and the solid, then, on continued
addition or withdrawal of the vapour phase, it will be found that the vapour pressure
remains constant for a certain time, and will then suddenly assume a new value, at which
it will again remain constant. By this method, Ramsay[160] found that no definite hydrates
were formed in the case of ferric and aluminium oxides, but that two are formed in the
case of lead oxide, viz. 2PbO,H2O and 3PbO,H2O.
Page 81
The method has also been applied to the investigation of the so-called palladium hydride,
[161] and the results obtained appear to show that no compound is formed. Reference will,
however, be made to this case later (Chap. X.).
Measurement of the Vapour Pressure of Hydrates.—For the purpose of measuring the
small pressures exerted by the vapour of salt hydrates, use is very generally made of a
differential manometer called the Bremer-Frowein tensimeter.[162]
This apparatus has the form shown in Fig. 21. It consists of a U-tube, the limbs of which
are bent close together, and placed in front of a millimetre scale. The bend of the tube is
filled with oil or other suitable liquid, e.g. bromonaphthalene. If it is desired to measure
the dissociation pressure of, say, a salt hydrate, concentrated sulphuric acid is placed in
the flask e, and a quantity of the hydrate, well dried and powdered,[163] in the bulb d. The
necks of the bulbs d and e are then sealed off. Since, as we have learned, suspended
transformation may occur, it is advisable to first partially dehydrate the salt, in order to
ensure the presence of the second solid product of dissociation; the value of the
dissociation pressure being independent of the degree of dissociation of the hydrate
(p. 86). The small bulbs d and e having been filled, the apparatus is placed on its side, so
as to allow the liquid to run from the bend of the tube into the bulbs a and b; it is then
exhausted through f by means of a mercury pump, and sealed off. The apparatus is now
placed in a perpendicular position in a thermostat, and kept at constant temperature until
equilibrium is established. Since the vapour pressure on the side containing the sulphuric
acid may be regarded as zero, the difference in level of the two surfaces of liquid in the
U-tube gives directly the dissociation pressure of the hydrate in terms of the particular
liquid employed; if the density of the latter is known, the pressure can then be calculated
to cm. of mercury.
[161] and the results obtained appear to show that no compound is formed. Reference will,
however, be made to this case later (Chap. X.).
Measurement of the Vapour Pressure of Hydrates.—For the purpose of measuring the
small pressures exerted by the vapour of salt hydrates, use is very generally made of a
differential manometer called the Bremer-Frowein tensimeter.[162]
This apparatus has the form shown in Fig. 21. It consists of a U-tube, the limbs of which
are bent close together, and placed in front of a millimetre scale. The bend of the tube is
filled with oil or other suitable liquid, e.g. bromonaphthalene. If it is desired to measure
the dissociation pressure of, say, a salt hydrate, concentrated sulphuric acid is placed in
the flask e, and a quantity of the hydrate, well dried and powdered,[163] in the bulb d. The
necks of the bulbs d and e are then sealed off. Since, as we have learned, suspended
transformation may occur, it is advisable to first partially dehydrate the salt, in order to
ensure the presence of the second solid product of dissociation; the value of the
dissociation pressure being independent of the degree of dissociation of the hydrate
(p. 86). The small bulbs d and e having been filled, the apparatus is placed on its side, so
as to allow the liquid to run from the bend of the tube into the bulbs a and b; it is then
exhausted through f by means of a mercury pump, and sealed off. The apparatus is now
placed in a perpendicular position in a thermostat, and kept at constant temperature until
equilibrium is established. Since the vapour pressure on the side containing the sulphuric
acid may be regarded as zero, the difference in level of the two surfaces of liquid in the
U-tube gives directly the dissociation pressure of the hydrate in terms of the particular
liquid employed; if the density of the latter is known, the pressure can then be calculated
to cm. of mercury.
Page 82
Fig. 21.
CHAPTER VI
SOLUTIONS
Definition.—In all the cases which have been considered in the preceding
pages, the different phases—with the exception of the vapour phase—
consisted of a single substance of definite composition, or were definite
chemical individuals.[164] But this invariability of the composition is by no
means imposed by the Phase Rule; on the contrary, we shall find in the
examples which we now proceed to study, that the participation of phases of
variable composition in the equilibrium of a system is in no way excluded.
To such phases of variable composition there is applied the term solution. A
solution, therefore, is to be defined as a homogeneous mixture, the
composition of which can undergo continuous variation within certain
limits; the limits, namely, of its existence.[165]
From this definition we see that the term solution is not restricted to any
particular physical state of substances, but includes within its range not only
the liquid, but also the gaseous and solid states. We may therefore have
solutions of gases in liquids, and of gases in solids; of liquids in liquids or
CHAPTER VI
SOLUTIONS
Definition.—In all the cases which have been considered in the preceding
pages, the different phases—with the exception of the vapour phase—
consisted of a single substance of definite composition, or were definite
chemical individuals.[164] But this invariability of the composition is by no
means imposed by the Phase Rule; on the contrary, we shall find in the
examples which we now proceed to study, that the participation of phases of
variable composition in the equilibrium of a system is in no way excluded.
To such phases of variable composition there is applied the term solution. A
solution, therefore, is to be defined as a homogeneous mixture, the
composition of which can undergo continuous variation within certain
limits; the limits, namely, of its existence.[165]
From this definition we see that the term solution is not restricted to any
particular physical state of substances, but includes within its range not only
the liquid, but also the gaseous and solid states. We may therefore have
solutions of gases in liquids, and of gases in solids; of liquids in liquids or
Page 83
in solids; of solids in liquids, or of solids in solids. Solutions of gases in
gases are, of course, also possible; since, however, gas solutions never give
rise to more than one phase, their treatment does not come within the scope
of the Phase Rule, which deals with heterogeneous equilibria.
It should also be emphasized that the definition of solution given above,
neither creates nor recognizes any distinction between solvent and dissolved
substance (solute); and, indeed, a too persistent use of these terms and the
attempt to permanently label the one or other of two components as the
solvent or the solute, can only obscure the true relationships and aggravate
the difficulty of their interpretation. In all cases it should be remembered
that we are dealing with equilibria between two components (we confine
our attention in the first instance to such), the solution being constituted of
these components in variable and varying amounts. The change from the
case where the one component is in great excess (ordinarily called the
solvent) to that in which the other component predominates, may be quite
gradual, so that it is difficult or impossible to say at what point the one
component ceases to be the solvent and becomes the solute. The adoption of
this standpoint need not, however, preclude one from employing the
conventional terms solvent and solute in ordinary language, especially
when reference is made only to some particular condition of equilibrium of
the system, when the concentration of the two components in the solution is
widely different.
Solutions of Gases in Liquids.
As the first class of solutions to which we shall turn our attention, there may
be chosen the solutions of gases in liquids, or the equilibria between a
liquid and a gas. These equilibria really constitute a part of the equilibria to
be studied more fully in Chapter VIII.; but since the two-phase systems
formed by the solutions of gases in liquids are among the best-known of the
two-component systems, a short section may be here allotted to their
treatment.
When a gas is passed into a liquid, absorption takes place to a greater or
less extent, and a point is at length reached when the liquid absorbs no more
of the gas; a condition of equilibrium is attained, and the liquid is said to be
saturated with the gas. In the light of the Phase Rule, now, such a system is
gases are, of course, also possible; since, however, gas solutions never give
rise to more than one phase, their treatment does not come within the scope
of the Phase Rule, which deals with heterogeneous equilibria.
It should also be emphasized that the definition of solution given above,
neither creates nor recognizes any distinction between solvent and dissolved
substance (solute); and, indeed, a too persistent use of these terms and the
attempt to permanently label the one or other of two components as the
solvent or the solute, can only obscure the true relationships and aggravate
the difficulty of their interpretation. In all cases it should be remembered
that we are dealing with equilibria between two components (we confine
our attention in the first instance to such), the solution being constituted of
these components in variable and varying amounts. The change from the
case where the one component is in great excess (ordinarily called the
solvent) to that in which the other component predominates, may be quite
gradual, so that it is difficult or impossible to say at what point the one
component ceases to be the solvent and becomes the solute. The adoption of
this standpoint need not, however, preclude one from employing the
conventional terms solvent and solute in ordinary language, especially
when reference is made only to some particular condition of equilibrium of
the system, when the concentration of the two components in the solution is
widely different.
Solutions of Gases in Liquids.
As the first class of solutions to which we shall turn our attention, there may
be chosen the solutions of gases in liquids, or the equilibria between a
liquid and a gas. These equilibria really constitute a part of the equilibria to
be studied more fully in Chapter VIII.; but since the two-phase systems
formed by the solutions of gases in liquids are among the best-known of the
two-component systems, a short section may be here allotted to their
treatment.
When a gas is passed into a liquid, absorption takes place to a greater or
less extent, and a point is at length reached when the liquid absorbs no more
of the gas; a condition of equilibrium is attained, and the liquid is said to be
saturated with the gas. In the light of the Phase Rule, now, such a system is
Page 84
bivariant (two components in two phases); and two of the variable factors,
pressure, temperature, and concentration of the components, must therefore
be chosen in order that the condition of the system may be defined. If the
concentration and the temperature are fixed, then the pressure is also
defined; or under given conditions of temperature and pressure, the
concentration of the gas in the solution must have a definite value. If,
however, the temperature alone is fixed, the concentration and the pressure
can alter; a fact so well known that it does not require to be further insisted
on.
As to the way in which the solubility of a gas in a liquid varies with the
pressure, the Phase Rule of course does not state; but guidance on this point
is again yielded by the theorem of van't Hoff and Le Chatelier. Since the
absorption of a gas is in all cases accompanied by a diminution of the total
volume, this process must take place with increase of pressure. This,
indeed, is stated in a quantitative manner in the law of Henry, according to
which the amount of a gas absorbed is proportional to the pressure. But this
law must be modified in the case of gases which are very readily absorbed;
the direction of change of concentration with the pressure will, however,
still be in accordance with the theorem of Le Chatelier.
If, on the other hand, the pressure is fixed, then the concentration will vary
with the temperature; and since the absorption of gases is in all cases
accompanied by the evolution of heat, the solubility is found, in accordance
with the theorem of Le Chatelier, to diminish with rise of temperature.
In considering the changes of pressure accompanying changes of
concentration and temperature, a distinction must be drawn between the
total pressure and the partial pressure of the dissolved gas, in cases where
the solvent is volatile. In these cases, the law of Henry applies not to the
total pressure of the vapour, but only to the partial pressure of the dissolved
gas.
Solutions of Liquids in Liquids.
When mercury and water are brought together, the two liquids remain side
by side without mixing. Strictly speaking, mercury undoubtedly dissolves to
a certain extent in the water, and water no doubt dissolves, although to a
less extent, in the mercury; the amount of substance passing into solution is,
pressure, temperature, and concentration of the components, must therefore
be chosen in order that the condition of the system may be defined. If the
concentration and the temperature are fixed, then the pressure is also
defined; or under given conditions of temperature and pressure, the
concentration of the gas in the solution must have a definite value. If,
however, the temperature alone is fixed, the concentration and the pressure
can alter; a fact so well known that it does not require to be further insisted
on.
As to the way in which the solubility of a gas in a liquid varies with the
pressure, the Phase Rule of course does not state; but guidance on this point
is again yielded by the theorem of van't Hoff and Le Chatelier. Since the
absorption of a gas is in all cases accompanied by a diminution of the total
volume, this process must take place with increase of pressure. This,
indeed, is stated in a quantitative manner in the law of Henry, according to
which the amount of a gas absorbed is proportional to the pressure. But this
law must be modified in the case of gases which are very readily absorbed;
the direction of change of concentration with the pressure will, however,
still be in accordance with the theorem of Le Chatelier.
If, on the other hand, the pressure is fixed, then the concentration will vary
with the temperature; and since the absorption of gases is in all cases
accompanied by the evolution of heat, the solubility is found, in accordance
with the theorem of Le Chatelier, to diminish with rise of temperature.
In considering the changes of pressure accompanying changes of
concentration and temperature, a distinction must be drawn between the
total pressure and the partial pressure of the dissolved gas, in cases where
the solvent is volatile. In these cases, the law of Henry applies not to the
total pressure of the vapour, but only to the partial pressure of the dissolved
gas.
Solutions of Liquids in Liquids.
When mercury and water are brought together, the two liquids remain side
by side without mixing. Strictly speaking, mercury undoubtedly dissolves to
a certain extent in the water, and water no doubt dissolves, although to a
less extent, in the mercury; the amount of substance passing into solution is,
Page 85
however, so minute, that it may, for all practical purposes, be left out of
account, so long as the temperature does not rise much above the ordinary.
[166] On the other hand, if alcohol and water be brought together, complete
miscibility takes place, and one homogeneous solution is obtained. Whether
water be added in increasing quantities to pure alcohol, or pure alcohol be
added in increasing amount to water, at no point, at no degree of
concentration, is a system obtained containing more than one liquid phase.
At the ordinary temperature, water and alcohol can form only two phases,
liquid and vapour. If, however, water be added to ether, or if ether be added
to water, solution will not occur to an indefinite extent; but a point will be
reached when the water or the ether will no longer dissolve more of the
other component, and a further addition of water on the one hand, or ether
on the other, will cause the formation of two liquid layers, one containing
excess of water, the other excess of ether. We shall, therefore, expect to find
all grades of miscibility, from almost perfect immiscibility to perfect
miscibility, or miscibility in all proportions. In cases of perfect
immiscibility, the components do not affect one another, and the system
therefore remains unchanged. Such cases do not call for treatment here. We
have to concern ourselves here only with the second and third cases, viz.
with cases of complete and of partial miscibility. There is no essential
difference between the two classes, for, as we shall see, the one passes into
the other with change of temperature. The formal separation into two
groups is based on the miscibility relations at ordinary temperatures.
Partial or Limited Miscibility.—In accordance with the Phase Rule, a pure
liquid in contact with its vapour constitutes a univariant system. If,
however, a small quantity of a second substance is added, which is capable
of dissolving in the first, a bivariant system will be obtained; for there are
now two components and, as before, only two phases—the homogeneous
liquid solution and the vapour. At constant temperature, therefore, both the
composition of the solution and the pressure of the vapour can undergo
change; or, if the composition of the solution remains unchanged, the
pressure and the temperature can alter. If the second (liquid) component is
added in increasing amount, the liquid will at first remain homogeneous,
and its composition and pressure will undergo a continuous change; when,
however, the concentration has reached a definite value, solution no longer
takes place; two liquid phases are produced. Since there are now three
account, so long as the temperature does not rise much above the ordinary.
[166] On the other hand, if alcohol and water be brought together, complete
miscibility takes place, and one homogeneous solution is obtained. Whether
water be added in increasing quantities to pure alcohol, or pure alcohol be
added in increasing amount to water, at no point, at no degree of
concentration, is a system obtained containing more than one liquid phase.
At the ordinary temperature, water and alcohol can form only two phases,
liquid and vapour. If, however, water be added to ether, or if ether be added
to water, solution will not occur to an indefinite extent; but a point will be
reached when the water or the ether will no longer dissolve more of the
other component, and a further addition of water on the one hand, or ether
on the other, will cause the formation of two liquid layers, one containing
excess of water, the other excess of ether. We shall, therefore, expect to find
all grades of miscibility, from almost perfect immiscibility to perfect
miscibility, or miscibility in all proportions. In cases of perfect
immiscibility, the components do not affect one another, and the system
therefore remains unchanged. Such cases do not call for treatment here. We
have to concern ourselves here only with the second and third cases, viz.
with cases of complete and of partial miscibility. There is no essential
difference between the two classes, for, as we shall see, the one passes into
the other with change of temperature. The formal separation into two
groups is based on the miscibility relations at ordinary temperatures.
Partial or Limited Miscibility.—In accordance with the Phase Rule, a pure
liquid in contact with its vapour constitutes a univariant system. If,
however, a small quantity of a second substance is added, which is capable
of dissolving in the first, a bivariant system will be obtained; for there are
now two components and, as before, only two phases—the homogeneous
liquid solution and the vapour. At constant temperature, therefore, both the
composition of the solution and the pressure of the vapour can undergo
change; or, if the composition of the solution remains unchanged, the
pressure and the temperature can alter. If the second (liquid) component is
added in increasing amount, the liquid will at first remain homogeneous,
and its composition and pressure will undergo a continuous change; when,
however, the concentration has reached a definite value, solution no longer
takes place; two liquid phases are produced. Since there are now three
Page 86
phases present, two liquids and vapour, the system is univariant; at a given
temperature, therefore, the concentration of the components in the two
liquid phases, as well as the vapour pressure, must have definite values.
Addition of one of the components, therefore, cannot alter the
concentrations or the pressure, but can only cause a change in the relative
amounts of the phases.
The two liquid phases can be regarded, the one as a solution of the
component I. in component II., the other as a solution of component II. in
component I. If the pressure is maintained constant, then to each
temperature there will correspond a definite concentration of the
components in the two liquid phases; and addition of excess of one will
merely alter the relative amounts of the two solutions. As the temperature
changes, the composition of the two solutions will change, and there will
therefore be obtained two solubility curves, one showing the solubility of
component I. in component II., the other showing the solubility of
component II. in component I. Since heat may be either evolved or
absorbed when one liquid dissolves in another, the solubility may diminish
or increase with rise of temperature. The two solutions which at a given
temperature correspond to one another are known as conjugate solutions.
The solubility relations of partially miscible liquids have been studied by
Guthrie,[167] and more especially by Alexejeff[168] and by Rothmund.[169] A
considerable variety of curves have been obtained, and we shall therefore
discuss only a few of the different cases which may be taken as typical of
the rest.
Phenol and Water.—When phenol is added to water at the ordinary
temperature, solution takes place, and a homogeneous liquid is produced.
When, however, the concentration of the phenol in the solution has risen to
about 8 per cent., phenol ceases to be dissolved; and a further addition of it
causes the formation of a second liquid phase, which consists of excess of
phenol and a small quantity of water. In ordinary language it may be called
a solution of water in phenol. If now the temperature is raised, this second
liquid phase will disappear, and a further amount of phenol must be added
in order to produce a separation of the liquid into two layers. In this way, by
increasing the amount of phenol and noting the temperature at which the
two layers disappear, the so-called solubility curve of phenol in water can
temperature, therefore, the concentration of the components in the two
liquid phases, as well as the vapour pressure, must have definite values.
Addition of one of the components, therefore, cannot alter the
concentrations or the pressure, but can only cause a change in the relative
amounts of the phases.
The two liquid phases can be regarded, the one as a solution of the
component I. in component II., the other as a solution of component II. in
component I. If the pressure is maintained constant, then to each
temperature there will correspond a definite concentration of the
components in the two liquid phases; and addition of excess of one will
merely alter the relative amounts of the two solutions. As the temperature
changes, the composition of the two solutions will change, and there will
therefore be obtained two solubility curves, one showing the solubility of
component I. in component II., the other showing the solubility of
component II. in component I. Since heat may be either evolved or
absorbed when one liquid dissolves in another, the solubility may diminish
or increase with rise of temperature. The two solutions which at a given
temperature correspond to one another are known as conjugate solutions.
The solubility relations of partially miscible liquids have been studied by
Guthrie,[167] and more especially by Alexejeff[168] and by Rothmund.[169] A
considerable variety of curves have been obtained, and we shall therefore
discuss only a few of the different cases which may be taken as typical of
the rest.
Phenol and Water.—When phenol is added to water at the ordinary
temperature, solution takes place, and a homogeneous liquid is produced.
When, however, the concentration of the phenol in the solution has risen to
about 8 per cent., phenol ceases to be dissolved; and a further addition of it
causes the formation of a second liquid phase, which consists of excess of
phenol and a small quantity of water. In ordinary language it may be called
a solution of water in phenol. If now the temperature is raised, this second
liquid phase will disappear, and a further amount of phenol must be added
in order to produce a separation of the liquid into two layers. In this way, by
increasing the amount of phenol and noting the temperature at which the
two layers disappear, the so-called solubility curve of phenol in water can
Page 87
be obtained. By noting the change of the solubility with the temperature in
this manner, it is found that at all temperatures below 68.4°, the addition of
more than a certain amount of phenol causes the formation of two layers; at
temperatures above this, however, two layers cannot be formed, no matter
how much phenol is added. At temperatures above 68.4°, therefore, water
and phenol are miscible in all proportions.
On the other hand, if water is added to phenol at the ordinary temperature, a
liquid is produced which consists chiefly of phenol, and on increasing the
amount of water beyond a certain point, two layers are formed. On raising
the temperature these two layers disappear, and a homogeneous solution is
again obtained. The phenomena are exactly analogous to those already
described. Since, now, in the second case the concentration of the phenol in
the solution gradually decreases, while in the former case it gradually
increases, a point must at length be reached at which the composition of the
two solutions becomes the same. On mixing the two solutions, therefore,
one homogeneous liquid will be obtained. But the point at which two
phases become identical is called a critical point, so that, in accordance with
this definition, the temperature at which the two solutions of phenol and
water become identical may be called the critical solution temperature, and
the concentration at this point may be called the critical concentration.
Fig. 22.
From what has been said above, it will be seen that at any temperature
below the critical solution temperature, two conjugate solutions containing
water and phenol in different concentration can exist together, one
containing excess of water, the other excess of phenol. The following table
gives the composition of the two layers, and the values are represented
graphically in Fig. 22.[170]
Phenol and Water.
this manner, it is found that at all temperatures below 68.4°, the addition of
more than a certain amount of phenol causes the formation of two layers; at
temperatures above this, however, two layers cannot be formed, no matter
how much phenol is added. At temperatures above 68.4°, therefore, water
and phenol are miscible in all proportions.
On the other hand, if water is added to phenol at the ordinary temperature, a
liquid is produced which consists chiefly of phenol, and on increasing the
amount of water beyond a certain point, two layers are formed. On raising
the temperature these two layers disappear, and a homogeneous solution is
again obtained. The phenomena are exactly analogous to those already
described. Since, now, in the second case the concentration of the phenol in
the solution gradually decreases, while in the former case it gradually
increases, a point must at length be reached at which the composition of the
two solutions becomes the same. On mixing the two solutions, therefore,
one homogeneous liquid will be obtained. But the point at which two
phases become identical is called a critical point, so that, in accordance with
this definition, the temperature at which the two solutions of phenol and
water become identical may be called the critical solution temperature, and
the concentration at this point may be called the critical concentration.
Fig. 22.
From what has been said above, it will be seen that at any temperature
below the critical solution temperature, two conjugate solutions containing
water and phenol in different concentration can exist together, one
containing excess of water, the other excess of phenol. The following table
gives the composition of the two layers, and the values are represented
graphically in Fig. 22.[170]
Phenol and Water.
Page 88
C1 is the percentage amount of phenol in the first layer.
C2 ,, ,, ,, second layer.
Temperature. C 1. C 2.
20° 8.5 72.2
30° 8.7 69.9
40° 9.7 66.8
50° 12.0 62.7
55° 14.2 60.0
60° 17.5 56.2
65° 22.7 49.7
68.4° 36.1 36.1
The critical solution temperature for phenol and water is 68.4°, the critical
concentration 36.1 per cent. of phenol. At all temperatures above 68.4°,
only homogeneous solutions of phenol and water can be obtained; water
and phenol are then miscible in all proportions.
At the critical solution point the system exists in only two phases—liquid
and vapour. It ought, therefore, to possess two degrees of freedom. The
restriction is, however, imposed that the composition of the two liquid
phases, coexisting at a point infinitely near to the critical point, becomes the
same, and this disposes of one of the degrees of freedom. The system is
therefore univariant; and at a given temperature the pressure will have a
definite value. Conversely, if the pressure is fixed (as is the case when the
system is under the pressure of its own vapour), then the temperature will
also be fixed; that is, the critical solution temperature has a definite value
depending only on the substances. If the vapour phase is omitted, the
temperature will alter with the pressure; in this case, however, as in the case
of other condensed systems, the effect of pressure is slight.
From Fig. 22 it is easy to predict the effect of bringing together water and
phenol in any given quantities at any temperature. Start with a solution of
phenol and water having the composition represented by the point x. If to
this solution phenol is added at constant temperature, it will dissolve, and
the composition of the solution will gradually change, as shown by the
dotted line xy. When, however, the concentration has reached the value
C2 ,, ,, ,, second layer.
Temperature. C 1. C 2.
20° 8.5 72.2
30° 8.7 69.9
40° 9.7 66.8
50° 12.0 62.7
55° 14.2 60.0
60° 17.5 56.2
65° 22.7 49.7
68.4° 36.1 36.1
The critical solution temperature for phenol and water is 68.4°, the critical
concentration 36.1 per cent. of phenol. At all temperatures above 68.4°,
only homogeneous solutions of phenol and water can be obtained; water
and phenol are then miscible in all proportions.
At the critical solution point the system exists in only two phases—liquid
and vapour. It ought, therefore, to possess two degrees of freedom. The
restriction is, however, imposed that the composition of the two liquid
phases, coexisting at a point infinitely near to the critical point, becomes the
same, and this disposes of one of the degrees of freedom. The system is
therefore univariant; and at a given temperature the pressure will have a
definite value. Conversely, if the pressure is fixed (as is the case when the
system is under the pressure of its own vapour), then the temperature will
also be fixed; that is, the critical solution temperature has a definite value
depending only on the substances. If the vapour phase is omitted, the
temperature will alter with the pressure; in this case, however, as in the case
of other condensed systems, the effect of pressure is slight.
From Fig. 22 it is easy to predict the effect of bringing together water and
phenol in any given quantities at any temperature. Start with a solution of
phenol and water having the composition represented by the point x. If to
this solution phenol is added at constant temperature, it will dissolve, and
the composition of the solution will gradually change, as shown by the
dotted line xy. When, however, the concentration has reached the value
Page 89
represented by the point y, two liquid layers will be formed, the one
solution having the composition represented by y, the other that represented
by y′. The system is now univariant, and on further addition of phenol, the
composition of the two liquid phases will remain unchanged, but their
relative amounts will alter. The phase richer in phenol will increase in
amount; that richer in water will decrease, and ultimately disappear, and
there will remain the solution y′. Continued addition of phenol will then
lead to the point x′, there being now only one liquid phase present.
Since the critical solution point represents the highest temperature at which
two liquid phases consisting of phenol and water can exist together, these
two substances can be brought together in any amount whatever at
temperatures higher than 68.4°, without the formation of two layers. It will
therefore be possible to pass from a system represented by x to one
represented by x′, without at any time two liquid phases appearing. Starting
with x, the temperature is first raised above the critical solution
temperature; phenol is then added until the concentration reaches the point
x2. On allowing the temperature to fall, the system will then pass into the
condition represented by x′.
Fig. 23.
Methylethylketone and Water.—In the case just described, the solubility
of each component in the other increased continuously with the
temperature. There are, however, cases where a maximum or minimum of
solubility is found, e.g. methylethylketone and water. The curve which
represents the equilibria between these two substances is given in Fig. 23,
the concentration values being contained in the following table:[171]—
Methylethylketone and Water.
solution having the composition represented by y, the other that represented
by y′. The system is now univariant, and on further addition of phenol, the
composition of the two liquid phases will remain unchanged, but their
relative amounts will alter. The phase richer in phenol will increase in
amount; that richer in water will decrease, and ultimately disappear, and
there will remain the solution y′. Continued addition of phenol will then
lead to the point x′, there being now only one liquid phase present.
Since the critical solution point represents the highest temperature at which
two liquid phases consisting of phenol and water can exist together, these
two substances can be brought together in any amount whatever at
temperatures higher than 68.4°, without the formation of two layers. It will
therefore be possible to pass from a system represented by x to one
represented by x′, without at any time two liquid phases appearing. Starting
with x, the temperature is first raised above the critical solution
temperature; phenol is then added until the concentration reaches the point
x2. On allowing the temperature to fall, the system will then pass into the
condition represented by x′.
Fig. 23.
Methylethylketone and Water.—In the case just described, the solubility
of each component in the other increased continuously with the
temperature. There are, however, cases where a maximum or minimum of
solubility is found, e.g. methylethylketone and water. The curve which
represents the equilibria between these two substances is given in Fig. 23,
the concentration values being contained in the following table:[171]—
Methylethylketone and Water.
Page 90
Temperature. C1 per cent. C2 per cent.
-10° 34.5 89.7
+10° 26.1 90.0
30° 21.9 89.9
50° 17.5 89.0
70° 16.2 85.7
90° 16.1 84.8
110° 17.7 80.0
130° 21.8 71.9
140° 26.0 64.0
151.8° 44.2 44.2
These numbers and Fig. 23 show clearly the occurrence of a minimum in
the solubility of the ketone in water, and also a minimum (at about 10°) in
the solubility of water in methylethylketone. Minima of solubility have also
been found in other cases.
Fig. 24.
Triethylamine and Water.—Although in most of the cases studied the
solubility of one liquid in another increases with rise of temperature, this is
not so in all cases. Thus, at temperatures below 18°, triethylamine and water
mix together in all proportions; but, on raising the temperature, the
homogeneous solution becomes turbid and separates into two layers. In this
case, therefore, the critical solution temperature is found in the direction of
lower temperature, not in the direction of higher.[172] This behaviour is
clearly shown by the graphic representation in Fig. 24, and also by the
numbers in the following table:—
-10° 34.5 89.7
+10° 26.1 90.0
30° 21.9 89.9
50° 17.5 89.0
70° 16.2 85.7
90° 16.1 84.8
110° 17.7 80.0
130° 21.8 71.9
140° 26.0 64.0
151.8° 44.2 44.2
These numbers and Fig. 23 show clearly the occurrence of a minimum in
the solubility of the ketone in water, and also a minimum (at about 10°) in
the solubility of water in methylethylketone. Minima of solubility have also
been found in other cases.
Fig. 24.
Triethylamine and Water.—Although in most of the cases studied the
solubility of one liquid in another increases with rise of temperature, this is
not so in all cases. Thus, at temperatures below 18°, triethylamine and water
mix together in all proportions; but, on raising the temperature, the
homogeneous solution becomes turbid and separates into two layers. In this
case, therefore, the critical solution temperature is found in the direction of
lower temperature, not in the direction of higher.[172] This behaviour is
clearly shown by the graphic representation in Fig. 24, and also by the
numbers in the following table:—
Page 91
Triethylamine and Water.
Temperature. C1 per cent. C2 per cent.
70° 1.6 —
50° 2.9 —
30° 5.6 96
25° 7.3 95.5
20° 15.5 73
±18.5° ±30 ±30
General Form of Concentration-Temperature Curve.—From the
preceding figures it will be seen that the general form of the solubility curve
is somewhat parabolic in shape; in the case of triethylamine and water, the
closed end of the curve is very flat. Since for all liquids there is a point
(critical point) at which the liquid and gaseous states become identical, and
since all gases are miscible in all proportions, it follows that there must be
some temperature at which the liquids become perfectly miscible. In the
case of triethylamine and water, which has just been considered, there must
therefore be an upper critical solution temperature, so that the complete
solubility relations would be represented by a closed curve of an ellipsoidal
aspect. An example of such a curve is furnished by nicotine and water. At
temperatures below 60° and above 210°, nicotine and water mix in all
proportions.[173] Although it is possible that this is the general form of the
curve for all pairs of liquids, there are as yet insufficient data to prove it.
With regard to the closed end of the curve it may be said that it is
continuous; the critical solution point is not the intersection of two curves,
for such a break in the continuity of the curve could occur only if there were
some discontinuity in one of the phases. No such discontinuity exists. The
curve is, therefore, not to be considered as two solubility curves cutting at a
point; it is a curve of equilibrium between two components, and so long as
the phases undergo continuous change, the curve representing the
equilibrium must also be continuous. As has already been emphasized, a
distinction between solvent and solute is merely conventional (p. 93).
Pressure-Concentration Diagram.—In considering the pressure-
concentration diagram of a system of two liquid components, a distinction
Temperature. C1 per cent. C2 per cent.
70° 1.6 —
50° 2.9 —
30° 5.6 96
25° 7.3 95.5
20° 15.5 73
±18.5° ±30 ±30
General Form of Concentration-Temperature Curve.—From the
preceding figures it will be seen that the general form of the solubility curve
is somewhat parabolic in shape; in the case of triethylamine and water, the
closed end of the curve is very flat. Since for all liquids there is a point
(critical point) at which the liquid and gaseous states become identical, and
since all gases are miscible in all proportions, it follows that there must be
some temperature at which the liquids become perfectly miscible. In the
case of triethylamine and water, which has just been considered, there must
therefore be an upper critical solution temperature, so that the complete
solubility relations would be represented by a closed curve of an ellipsoidal
aspect. An example of such a curve is furnished by nicotine and water. At
temperatures below 60° and above 210°, nicotine and water mix in all
proportions.[173] Although it is possible that this is the general form of the
curve for all pairs of liquids, there are as yet insufficient data to prove it.
With regard to the closed end of the curve it may be said that it is
continuous; the critical solution point is not the intersection of two curves,
for such a break in the continuity of the curve could occur only if there were
some discontinuity in one of the phases. No such discontinuity exists. The
curve is, therefore, not to be considered as two solubility curves cutting at a
point; it is a curve of equilibrium between two components, and so long as
the phases undergo continuous change, the curve representing the
equilibrium must also be continuous. As has already been emphasized, a
distinction between solvent and solute is merely conventional (p. 93).
Pressure-Concentration Diagram.—In considering the pressure-
concentration diagram of a system of two liquid components, a distinction
Page 92
must be drawn between the total pressure of the system and the partial
pressures of the components. On studying the total pressure of a system, it
is found that two cases can be obtained.[174]
So long as there is only one liquid phase, the system is bivariant. The
pressure therefore can change with the concentration and the temperature. If
the temperature is maintained constant, the pressure will vary only with the
concentration, and this variation can therefore be represented by a curve. If,
however, two liquid phases are formed, the system becomes univariant: and
if one of the variables, say the temperature, is arbitrarily fixed, the system
no longer possesses any degree of freedom. When two liquid phases are
formed, therefore, the concentrations and the vapour pressure have definite
values, which are maintained so long as the two liquid phases are present;
the temperature being supposed constant.
In Fig. 25 is given a diagrammatic representation of the two kinds of
pressure-concentration curves which have so far been obtained. In the one
case, the vapour pressure of the invariant system (at constant temperature)
lies higher than the vapour pressure of either of the pure components; a
phenomenon which is very generally found in the case of partially miscible
liquids, e.g. ether and water.[175] Accordingly, by the addition of water to
ether, or of ether to water, there is an increase in the total vapour pressure of
the system.
Fig. 25.
With regard to the second type, the vapour pressure of the systems with two
liquid phases lies between that of the two single components. An example
of this is found in sulphur dioxide and water.[176] On adding sulphur dioxide
to water there is an increase of the total vapour pressure; but on adding
water to liquid sulphur dioxide, the total vapour pressure is diminished.
pressures of the components. On studying the total pressure of a system, it
is found that two cases can be obtained.[174]
So long as there is only one liquid phase, the system is bivariant. The
pressure therefore can change with the concentration and the temperature. If
the temperature is maintained constant, the pressure will vary only with the
concentration, and this variation can therefore be represented by a curve. If,
however, two liquid phases are formed, the system becomes univariant: and
if one of the variables, say the temperature, is arbitrarily fixed, the system
no longer possesses any degree of freedom. When two liquid phases are
formed, therefore, the concentrations and the vapour pressure have definite
values, which are maintained so long as the two liquid phases are present;
the temperature being supposed constant.
In Fig. 25 is given a diagrammatic representation of the two kinds of
pressure-concentration curves which have so far been obtained. In the one
case, the vapour pressure of the invariant system (at constant temperature)
lies higher than the vapour pressure of either of the pure components; a
phenomenon which is very generally found in the case of partially miscible
liquids, e.g. ether and water.[175] Accordingly, by the addition of water to
ether, or of ether to water, there is an increase in the total vapour pressure of
the system.
Fig. 25.
With regard to the second type, the vapour pressure of the systems with two
liquid phases lies between that of the two single components. An example
of this is found in sulphur dioxide and water.[176] On adding sulphur dioxide
to water there is an increase of the total vapour pressure; but on adding
water to liquid sulphur dioxide, the total vapour pressure is diminished.
Page 93
The case that the vapour pressure of the system with two liquid phases is
less than that of each of the components is not possible.
With regard to the partial pressure of the components, the behaviour is
more uniform. The partial pressure of one component is in all cases lowered
by the addition of the other component, the diminution being approximately
proportional to the amount added. If two liquid phases are present, the
partial pressure of the components, as well as the total pressure, is constant,
and is the same for both phases. That is to say, in the case of the two liquids,
saturated solution of water in ether, and of ether in water, the partial
pressure of the ether in the vapour in contact with the one solution is the
same as that in the vapour over the other solution.[177]
Complete Miscibility.—Although the phenomena of complete miscibility
are here treated under a separate heading, it must not be thought that there is
any essential difference between those cases where the liquids exhibit
limited miscibility and those in which only one homogeneous solution is
formed. As has been already pointed out, the solubility relations alter with
the temperature; and liquids which at one temperature can dissolve in one
another only to a limited extent, are found at some other temperature to
possess the property of complete miscibility. Conversely, we may expect
that liquids which at one temperature, say at the ordinary temperature, are
miscible in all proportions, will be found at some other temperature to be
only partially miscible. Thus, for example, it was found by Guthrie that
ethyl alcohol and carbon disulphide, which are miscible in all proportions at
the ordinary temperature, possess only limited miscibility at temperatures
below -14.4°.[178] Nevertheless, it is doubtful if the critical solution
temperature is in all cases experimentally realizable.
Pressure-Concentration Diagram.—Since, in the cases of complete
miscibility of two liquid components, there are never more than two phases
present, the system must always be bivariant; and two of the variables
pressure, temperature or concentration of the components, must be
arbitrarily chosen before the system becomes defined. For this reason the
Phase Rule affords only a slight guidance in the study of such equilibria;
and we shall therefore not enter in detail into the behaviour of these
homogeneous mixtures. All that the Phase Rule can tell us in connection
with these solutions, is that at constant temperature the vapour pressure of
less than that of each of the components is not possible.
With regard to the partial pressure of the components, the behaviour is
more uniform. The partial pressure of one component is in all cases lowered
by the addition of the other component, the diminution being approximately
proportional to the amount added. If two liquid phases are present, the
partial pressure of the components, as well as the total pressure, is constant,
and is the same for both phases. That is to say, in the case of the two liquids,
saturated solution of water in ether, and of ether in water, the partial
pressure of the ether in the vapour in contact with the one solution is the
same as that in the vapour over the other solution.[177]
Complete Miscibility.—Although the phenomena of complete miscibility
are here treated under a separate heading, it must not be thought that there is
any essential difference between those cases where the liquids exhibit
limited miscibility and those in which only one homogeneous solution is
formed. As has been already pointed out, the solubility relations alter with
the temperature; and liquids which at one temperature can dissolve in one
another only to a limited extent, are found at some other temperature to
possess the property of complete miscibility. Conversely, we may expect
that liquids which at one temperature, say at the ordinary temperature, are
miscible in all proportions, will be found at some other temperature to be
only partially miscible. Thus, for example, it was found by Guthrie that
ethyl alcohol and carbon disulphide, which are miscible in all proportions at
the ordinary temperature, possess only limited miscibility at temperatures
below -14.4°.[178] Nevertheless, it is doubtful if the critical solution
temperature is in all cases experimentally realizable.
Pressure-Concentration Diagram.—Since, in the cases of complete
miscibility of two liquid components, there are never more than two phases
present, the system must always be bivariant; and two of the variables
pressure, temperature or concentration of the components, must be
arbitrarily chosen before the system becomes defined. For this reason the
Phase Rule affords only a slight guidance in the study of such equilibria;
and we shall therefore not enter in detail into the behaviour of these
homogeneous mixtures. All that the Phase Rule can tell us in connection
with these solutions, is that at constant temperature the vapour pressure of
Page 94
the solution varies with the composition of the liquid phase; and if the
composition of the liquid phase remains unchanged, the pressure also must
remain unchanged. This constancy of composition is exhibited not only by
pure liquids, but also by liquid solutions in all cases where the vapour
pressure of the solution reaches a maximum or minimum value. This is the
case, for example, with mixtures of constant boiling point.[179]
CHAPTER VII
SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE
COMPONENTS BEING VOLATILE
General.—When a solid is brought into contact with a liquid in which it
can dissolve, a certain amount of it passes into solution; and the process
continues until the concentration reaches a definite value independent of the
amount of solid present. A condition of equilibrium is established between
the solid and the solution; the solution becomes saturated. Since the
number of components is two, and the number of phases three, viz. solid,
liquid solution, vapour, the system is univariant. If, therefore, one of the
factors, pressure, temperature, or concentration of the components (in the
solution[180]), is arbitrarily fixed, the state of the system becomes perfectly
defined. Thus, at any given temperature, the vapour pressure of the system
and the concentration of the components have a definite value. If the
temperature is altered, the vapour pressure and also, in general, the
concentration will undergo change. Likewise, if the pressure varies, while
the system is isolated so that no heat can pass between it and its
surroundings, the concentration and the temperature must also undergo
variation until they attain values corresponding to the particular pressure.
That the temperature has an influence, sometimes a very considerable
influence, on the amount of substance passing into solution, is sufficiently
well known; the effect of pressure, although less apparent, is no less certain.
If at any given temperature the volume of the vapour phase is diminished,
vapour will condense to liquid, in order that the pressure may remain
constant, and so much of the solid will pass into solution that the
composition of the liquid phase remains unchanged, the pressure also must
remain unchanged. This constancy of composition is exhibited not only by
pure liquids, but also by liquid solutions in all cases where the vapour
pressure of the solution reaches a maximum or minimum value. This is the
case, for example, with mixtures of constant boiling point.[179]
CHAPTER VII
SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE
COMPONENTS BEING VOLATILE
General.—When a solid is brought into contact with a liquid in which it
can dissolve, a certain amount of it passes into solution; and the process
continues until the concentration reaches a definite value independent of the
amount of solid present. A condition of equilibrium is established between
the solid and the solution; the solution becomes saturated. Since the
number of components is two, and the number of phases three, viz. solid,
liquid solution, vapour, the system is univariant. If, therefore, one of the
factors, pressure, temperature, or concentration of the components (in the
solution[180]), is arbitrarily fixed, the state of the system becomes perfectly
defined. Thus, at any given temperature, the vapour pressure of the system
and the concentration of the components have a definite value. If the
temperature is altered, the vapour pressure and also, in general, the
concentration will undergo change. Likewise, if the pressure varies, while
the system is isolated so that no heat can pass between it and its
surroundings, the concentration and the temperature must also undergo
variation until they attain values corresponding to the particular pressure.
That the temperature has an influence, sometimes a very considerable
influence, on the amount of substance passing into solution, is sufficiently
well known; the effect of pressure, although less apparent, is no less certain.
If at any given temperature the volume of the vapour phase is diminished,
vapour will condense to liquid, in order that the pressure may remain
constant, and so much of the solid will pass into solution that the
Page 95
concentration may remain unchanged; for, so long as the three phases are
present, the state of the system cannot alter. If, however, one of the phases,
e.g. the vapour phase, disappears, the system becomes bivariant; at any
given temperature, therefore, there may be different values of concentration
and pressure.
The direction in which change of concentration will occur with change of
pressure can be predicted by means of the theorem of Le Chatelier, if it is
known whether solution is accompanied by increase or diminution of the
total volume. If diminution of the total volume of the system occurs on
solution, increase of pressure will increase the solubility; in the reverse
case, increase of pressure will diminish the solubility.
This conclusion has also been verified by experiment, as is shown by the
following figures.[181]
Change of
Solubility (at 18°) (grams salt
volume by
in
dissolving 1
1 gram of solution).
Salt. gm.
of salt in the
saturated Pressure Pressure
solution. = 1 atm. = 500 atm.
Sodium chloride -0.07 0.264 0.270
Ammonium
+0.10 0.272 0.258
chloride
Alum -0.067 0.115 0.142
(p = 400 atm.)
As can be seen, a large increase of the pressure brings about a no more than
appreciable alteration of the solubility; a result which is due, as in the case
of the alteration of the fusion point with the pressure, to the small change in
volume accompanying solution or increase of pressure. For all practical
purposes, therefore, the solubility as determined under atmospheric pressure
may be taken as equal to the true solubility, that is, the solubility when the
system is under the pressure of its own vapour.
present, the state of the system cannot alter. If, however, one of the phases,
e.g. the vapour phase, disappears, the system becomes bivariant; at any
given temperature, therefore, there may be different values of concentration
and pressure.
The direction in which change of concentration will occur with change of
pressure can be predicted by means of the theorem of Le Chatelier, if it is
known whether solution is accompanied by increase or diminution of the
total volume. If diminution of the total volume of the system occurs on
solution, increase of pressure will increase the solubility; in the reverse
case, increase of pressure will diminish the solubility.
This conclusion has also been verified by experiment, as is shown by the
following figures.[181]
Change of
Solubility (at 18°) (grams salt
volume by
in
dissolving 1
1 gram of solution).
Salt. gm.
of salt in the
saturated Pressure Pressure
solution. = 1 atm. = 500 atm.
Sodium chloride -0.07 0.264 0.270
Ammonium
+0.10 0.272 0.258
chloride
Alum -0.067 0.115 0.142
(p = 400 atm.)
As can be seen, a large increase of the pressure brings about a no more than
appreciable alteration of the solubility; a result which is due, as in the case
of the alteration of the fusion point with the pressure, to the small change in
volume accompanying solution or increase of pressure. For all practical
purposes, therefore, the solubility as determined under atmospheric pressure
may be taken as equal to the true solubility, that is, the solubility when the
system is under the pressure of its own vapour.
Page 96
The Saturated Solution.—From what has been said above, it will be seen
that the condition of saturation of a solution can be defined only with
respect to a certain solid phase; if no solid is present, the system is
undefined, for it then consists of only two phases, and is therefore bivariant.
Under such circumstances not only can there be at one given temperature
solutions of different concentration, all containing less of one of the
components than when that component is present in the solid form, but
there can also exist solutions containing more of that component than
corresponds to the equilibrium when the solid is present. In the former case
the solutions are unsaturated, in the latter case they are supersaturated with
respect to a certain solid phase; in themselves, the solutions are stable, and
are neither unsaturated nor supersaturated. Further, if the solid substance
can exist in different allotropic modifications, the particular form of the
substance which is in equilibrium with the solution must be known, in order
that the statement of the solubility may be definite; for each form has its
own solubility, and, as we shall see presently, the less stable form has the
greater solubility (cf. p. 47). In all determinations of the solubility,
therefore, not only must the concentration of the components in the solution
be determined, but equal importance should be attached to the
characterisation of the solid phase present.
In this connection, also, one other point may be emphasised. For the
production of the equilibrium between a solid and a liquid, time is
necessary, and this time not only varies with the state of division of the
solid and the efficiency of the stirring, but is also dependent on the nature of
the substance.[182] Considerable care must therefore be taken that sufficient
time is allowed for equilibrium to be established. Such care is more
especially needful when changes may occur in the solid phase, and neglect
of it has greatly diminished the value of many of the older determinations of
solubility.
Form of the Solubility Curve.—The solubility curve—that is, the curve
representing the change of concentration of the components in the solution
with the temperature—differs markedly from the curve of vapour pressure
(p. 63), in that it possesses no general form, but may vary in the most
diverse manner. Not only may the curve have an almost straight and
horizontal course, or slope or curve upwards at varying angles; but it may
even slope downwards, corresponding to a decrease in the solubility with
that the condition of saturation of a solution can be defined only with
respect to a certain solid phase; if no solid is present, the system is
undefined, for it then consists of only two phases, and is therefore bivariant.
Under such circumstances not only can there be at one given temperature
solutions of different concentration, all containing less of one of the
components than when that component is present in the solid form, but
there can also exist solutions containing more of that component than
corresponds to the equilibrium when the solid is present. In the former case
the solutions are unsaturated, in the latter case they are supersaturated with
respect to a certain solid phase; in themselves, the solutions are stable, and
are neither unsaturated nor supersaturated. Further, if the solid substance
can exist in different allotropic modifications, the particular form of the
substance which is in equilibrium with the solution must be known, in order
that the statement of the solubility may be definite; for each form has its
own solubility, and, as we shall see presently, the less stable form has the
greater solubility (cf. p. 47). In all determinations of the solubility,
therefore, not only must the concentration of the components in the solution
be determined, but equal importance should be attached to the
characterisation of the solid phase present.
In this connection, also, one other point may be emphasised. For the
production of the equilibrium between a solid and a liquid, time is
necessary, and this time not only varies with the state of division of the
solid and the efficiency of the stirring, but is also dependent on the nature of
the substance.[182] Considerable care must therefore be taken that sufficient
time is allowed for equilibrium to be established. Such care is more
especially needful when changes may occur in the solid phase, and neglect
of it has greatly diminished the value of many of the older determinations of
solubility.
Form of the Solubility Curve.—The solubility curve—that is, the curve
representing the change of concentration of the components in the solution
with the temperature—differs markedly from the curve of vapour pressure
(p. 63), in that it possesses no general form, but may vary in the most
diverse manner. Not only may the curve have an almost straight and
horizontal course, or slope or curve upwards at varying angles; but it may
even slope downwards, corresponding to a decrease in the solubility with
Page 97
rise of temperature; may exhibit maxima or minima of solubility, or may, as
in the case of some hydrated salts, pass through a point of maximum
temperature. In the latter case the salt may possess two values of solubility
at the same temperature. We shall consider these cases in the following
chapter.
Fig. 26.
The great variety of form shown by solubility curves is at once apparent
from Fig. 26, in which the solubility curves of various substances (not,
however, drawn to scale) are reproduced.[183]
Varied as is the form of the solubility curve, its direction, nevertheless, can
be predicted by means of the theorem of van't Hoff and Le Chatelier; for in
accordance with that theorem (p. 57) increase of solubility with the
temperature must occur in those cases where the process of solution is
accompanied by an absorption of heat; and a decrease in the solubility with
rise of temperature will be found in cases where solution occurs with
evolution of heat. Where there is no heat effect accompanying solution,
change of temperature will be without influence on the solubility; and if the
sign of the heat of solution changes, the direction of the solubility curve
must also change, i.e. must show a maximum or minimum point. This has
in all cases been verified by experiment.[184]
In applying the theorem of Le Chatelier to the course of the solubility
curve, it should be noted that by heat of solution there is meant, not the heat
effect produced on dissolving the salt in a large amount of solvent (which is
the usual signification of the expression), but the heat which is absorbed or
evolved when the salt is dissolved in the almost saturated solution (the so-
called last heat of solution). Not only does the heat effect in the two cases
in the case of some hydrated salts, pass through a point of maximum
temperature. In the latter case the salt may possess two values of solubility
at the same temperature. We shall consider these cases in the following
chapter.
Fig. 26.
The great variety of form shown by solubility curves is at once apparent
from Fig. 26, in which the solubility curves of various substances (not,
however, drawn to scale) are reproduced.[183]
Varied as is the form of the solubility curve, its direction, nevertheless, can
be predicted by means of the theorem of van't Hoff and Le Chatelier; for in
accordance with that theorem (p. 57) increase of solubility with the
temperature must occur in those cases where the process of solution is
accompanied by an absorption of heat; and a decrease in the solubility with
rise of temperature will be found in cases where solution occurs with
evolution of heat. Where there is no heat effect accompanying solution,
change of temperature will be without influence on the solubility; and if the
sign of the heat of solution changes, the direction of the solubility curve
must also change, i.e. must show a maximum or minimum point. This has
in all cases been verified by experiment.[184]
In applying the theorem of Le Chatelier to the course of the solubility
curve, it should be noted that by heat of solution there is meant, not the heat
effect produced on dissolving the salt in a large amount of solvent (which is
the usual signification of the expression), but the heat which is absorbed or
evolved when the salt is dissolved in the almost saturated solution (the so-
called last heat of solution). Not only does the heat effect in the two cases
Page 98
have a different value, but it may even have a different sign. A striking
example of this is afforded by cupric chloride, as the following figures
show:[185]—
Number of gram-molecules of
CuCl2, 2H2O dissolved in 198 Heat effect.
gram-molecules of water.
1 +37 K
2.02 +66 ,,
4.15 +105 ,,
7.07 +117 ,,
9.95 +117 ,,
11 +91 ,,
18.8 -10 ,,
19.6 -31 ,,
24.75 -198 ,,
In the above table the positive sign indicates evolution of heat, the negative
sign, absorption of heat; and the values of the heat effect are expressed in
centuple calories. Judging from the heat effect produced on dissolving
cupric chloride in a large bulk of water, we should predict that the solubility
of that salt would diminish with rise of temperature; as a matter of fact, it
increases. This is in accordance with the fact that the last heat of solution is
negative (as expressed above), i.e. solution of the salt in the almost
saturated solution is accompanied by absorption of heat. We are led to
expect this from the fact that the heat of solution changes sign from positive
to negative as the concentration increases; experiment also showed it to be
the case.
Despite its many forms, it should be particularly noted that the solubility
curve of any substance is continuous, so long as the solid phase, or solid
substance in contact with the solution, remains unchanged. If any "break" or
discontinuous change in the direction of the curve occurs, it is a sign that
the solid phase has undergone alteration. Conversely, if it is known that a
change takes place in the solid phase, a break in the solubility curve can be
predicted. We shall presently meet with examples of this.[186]
example of this is afforded by cupric chloride, as the following figures
show:[185]—
Number of gram-molecules of
CuCl2, 2H2O dissolved in 198 Heat effect.
gram-molecules of water.
1 +37 K
2.02 +66 ,,
4.15 +105 ,,
7.07 +117 ,,
9.95 +117 ,,
11 +91 ,,
18.8 -10 ,,
19.6 -31 ,,
24.75 -198 ,,
In the above table the positive sign indicates evolution of heat, the negative
sign, absorption of heat; and the values of the heat effect are expressed in
centuple calories. Judging from the heat effect produced on dissolving
cupric chloride in a large bulk of water, we should predict that the solubility
of that salt would diminish with rise of temperature; as a matter of fact, it
increases. This is in accordance with the fact that the last heat of solution is
negative (as expressed above), i.e. solution of the salt in the almost
saturated solution is accompanied by absorption of heat. We are led to
expect this from the fact that the heat of solution changes sign from positive
to negative as the concentration increases; experiment also showed it to be
the case.
Despite its many forms, it should be particularly noted that the solubility
curve of any substance is continuous, so long as the solid phase, or solid
substance in contact with the solution, remains unchanged. If any "break" or
discontinuous change in the direction of the curve occurs, it is a sign that
the solid phase has undergone alteration. Conversely, if it is known that a
change takes place in the solid phase, a break in the solubility curve can be
predicted. We shall presently meet with examples of this.[186]
Page 99
A.—Anhydrous Salt and Water.
The Solubility Curve.—In studying the equilibria in those systems of two
components in which the liquid phase is a solution or phase of varying
composition, we shall in the present chapter limit the discussion to those
cases where no compounds are formed, but where the components
crystallise out in the pure state. Since some of the best-known examples of
such systems are yielded by the solutions of anhydrous salts in water, we
shall first of all briefly consider some of the results which have been
obtained with them.
For the most part the solubility curves have been studied only at
temperatures lying between 0° and 100°, the solid phase in contact with the
solution being the anhydrous salt. For the representation of these equilibria,
the concentration-temperature diagram is employed, the concentration
being expressed as the number of grams of the salt dissolved in 100 grams
of water, or as the number of gram-molecules of salt in 100 gram-molecules
of water. The curves thus obtained exhibit the different forms to which
reference has already been made. So long as the salt remains unchanged the
curve will be continuous, but if the salt alters its form, then the solubility
curve will show a break.
Fig. 27.
Now, we have already seen in Chapter III. that certain substances are
capable of existing in various crystalline forms, and these forms are so
related to one another that at a given temperature the relative stability of
each pair of polymorphic forms undergoes change. Since each crystalline
variety of a substance must have its own solubility, there must be a break in
the solubility curve at the temperature of transition of the two enantiotropic
forms. At this point the two solubility curves must cut, for since the two
The Solubility Curve.—In studying the equilibria in those systems of two
components in which the liquid phase is a solution or phase of varying
composition, we shall in the present chapter limit the discussion to those
cases where no compounds are formed, but where the components
crystallise out in the pure state. Since some of the best-known examples of
such systems are yielded by the solutions of anhydrous salts in water, we
shall first of all briefly consider some of the results which have been
obtained with them.
For the most part the solubility curves have been studied only at
temperatures lying between 0° and 100°, the solid phase in contact with the
solution being the anhydrous salt. For the representation of these equilibria,
the concentration-temperature diagram is employed, the concentration
being expressed as the number of grams of the salt dissolved in 100 grams
of water, or as the number of gram-molecules of salt in 100 gram-molecules
of water. The curves thus obtained exhibit the different forms to which
reference has already been made. So long as the salt remains unchanged the
curve will be continuous, but if the salt alters its form, then the solubility
curve will show a break.
Fig. 27.
Now, we have already seen in Chapter III. that certain substances are
capable of existing in various crystalline forms, and these forms are so
related to one another that at a given temperature the relative stability of
each pair of polymorphic forms undergoes change. Since each crystalline
variety of a substance must have its own solubility, there must be a break in
the solubility curve at the temperature of transition of the two enantiotropic
forms. At this point the two solubility curves must cut, for since the two
Page 100
forms are in equilibrium with respect to their vapour, they must also be in
equilibrium with respect to their solutions. From the table on p. 63 it is seen
that potassium nitrate, ammonium nitrate, silver nitrate, thallium nitrate,
thallium picrate, are capable of existing in two or more different
enantiotropic crystalline forms, the range of stability of these forms being
limited by definite temperatures (transition temperature). Since the
transition point is not altered by a solvent (provided the latter is not
absorbed by the solid phase), we should find on studying the solubility of
these substances in water that the solubility curve would exhibit a change in
direction at the temperature of transition. As a matter of fact this has been
verified, more especially in the case of ammonium nitrate[187] and thallium
picrate.[188] The following table contains the values of the solubility of
ammonium nitrate obtained by Müller and Kaufmann, the solubility being
expressed in gram-molecules NH4NO3 in 100 gram-molecules of water. In
Fig. 27 these results are represented graphically. The equilibrium point was
approached both from the side of unsaturation and of supersaturation, and
the condition of equilibrium was controlled by determinations of the density
of the solution.
Solubility of Ammonium Nitrate.
Temperature. Solubility. Temperature. Solubility.
12.2° 34.50 32.7° 57.90
20.2° 43.30 34.0° 58.89
25.05° 48.19 35.0° 59.80
28.0° 51.86 36.0° 61.00
30.0° 54.40 37.5° 62.90
30.2° 54.61 38.0° 63.60
31.9° 57.20 39.0° 65.09
32.1° 57.60 40.0° 66.80
From the graphic representation of the solubility given in Fig. 27, there is
seen to be a distinct change in the direction of the curve at a temperature of
32°; and this break in the curve corresponds to the transition of the β-
rhombic into the α-rhombic form of ammonium nitrate (p. 63).
equilibrium with respect to their solutions. From the table on p. 63 it is seen
that potassium nitrate, ammonium nitrate, silver nitrate, thallium nitrate,
thallium picrate, are capable of existing in two or more different
enantiotropic crystalline forms, the range of stability of these forms being
limited by definite temperatures (transition temperature). Since the
transition point is not altered by a solvent (provided the latter is not
absorbed by the solid phase), we should find on studying the solubility of
these substances in water that the solubility curve would exhibit a change in
direction at the temperature of transition. As a matter of fact this has been
verified, more especially in the case of ammonium nitrate[187] and thallium
picrate.[188] The following table contains the values of the solubility of
ammonium nitrate obtained by Müller and Kaufmann, the solubility being
expressed in gram-molecules NH4NO3 in 100 gram-molecules of water. In
Fig. 27 these results are represented graphically. The equilibrium point was
approached both from the side of unsaturation and of supersaturation, and
the condition of equilibrium was controlled by determinations of the density
of the solution.
Solubility of Ammonium Nitrate.
Temperature. Solubility. Temperature. Solubility.
12.2° 34.50 32.7° 57.90
20.2° 43.30 34.0° 58.89
25.05° 48.19 35.0° 59.80
28.0° 51.86 36.0° 61.00
30.0° 54.40 37.5° 62.90
30.2° 54.61 38.0° 63.60
31.9° 57.20 39.0° 65.09
32.1° 57.60 40.0° 66.80
From the graphic representation of the solubility given in Fig. 27, there is
seen to be a distinct change in the direction of the curve at a temperature of
32°; and this break in the curve corresponds to the transition of the β-
rhombic into the α-rhombic form of ammonium nitrate (p. 63).
Page 101
Suspended Transformation and Supersaturation.—As has already been
learned, the transformation of the one crystalline form into the other does
not necessarily take place immediately the transition point has been passed;
and it has therefore been found possible in a number of cases to follow the
solubility curve of a given crystalline form beyond the point at which it
ceases to be the most stable modification. Now, it will be readily seen from
Fig. 27 that if the two solubility curves be prolonged beyond the point of
intersection, the solubility of the less stable form is greater than that of the
more stable. A solution, therefore, which is saturated with respect to the less
stable form, i.e. which is in equilibrium with that form, is supersaturated
with respect to the more stable modification. If, therefore, a small quantity
of the more stable form is introduced into the solution, the latter must
deposit such an amount of the more stable form that the concentration of the
solution corresponds to the solubility of the stable form at the particular
temperature. Since, however, the solution is now unsaturated with respect
to the less stable variety, the latter, if present, must pass into solution; and
the two processes, deposition of the stable and solution of the metastable
form, must go on until the latter form has entirely disappeared and a
saturated solution of the stable form is obtained. There will thus be a
conversion, through the medium of the solvent, of the less stable into the
more stable modification. This behaviour is of practical importance in the
determination of transition points (v. Appendix).
From the above discussion it will be seen how important is the statement of
the solid phase for the definition of saturation and supersaturation.[189]
Solubility Curve at Higher Temperatures.—On passing to the
consideration of the solubility curves at higher temperatures, two chief
cases must be distinguished.
(1) The two components in the fused state can mix in all proportions.
(2) The two components in the fused state cannot mix in all
proportions.
1. Complete Miscibility of the Fused Components.
learned, the transformation of the one crystalline form into the other does
not necessarily take place immediately the transition point has been passed;
and it has therefore been found possible in a number of cases to follow the
solubility curve of a given crystalline form beyond the point at which it
ceases to be the most stable modification. Now, it will be readily seen from
Fig. 27 that if the two solubility curves be prolonged beyond the point of
intersection, the solubility of the less stable form is greater than that of the
more stable. A solution, therefore, which is saturated with respect to the less
stable form, i.e. which is in equilibrium with that form, is supersaturated
with respect to the more stable modification. If, therefore, a small quantity
of the more stable form is introduced into the solution, the latter must
deposit such an amount of the more stable form that the concentration of the
solution corresponds to the solubility of the stable form at the particular
temperature. Since, however, the solution is now unsaturated with respect
to the less stable variety, the latter, if present, must pass into solution; and
the two processes, deposition of the stable and solution of the metastable
form, must go on until the latter form has entirely disappeared and a
saturated solution of the stable form is obtained. There will thus be a
conversion, through the medium of the solvent, of the less stable into the
more stable modification. This behaviour is of practical importance in the
determination of transition points (v. Appendix).
From the above discussion it will be seen how important is the statement of
the solid phase for the definition of saturation and supersaturation.[189]
Solubility Curve at Higher Temperatures.—On passing to the
consideration of the solubility curves at higher temperatures, two chief
cases must be distinguished.
(1) The two components in the fused state can mix in all proportions.
(2) The two components in the fused state cannot mix in all
proportions.
1. Complete Miscibility of the Fused Components.
Page 102
Fig. 28.
The best example of this which has been studied, so far as anhydrous salts
and water are concerned, is that of silver nitrate and water. The solubility of
this salt at temperatures above 100° has been studied chiefly by Etard[190]
and by Tilden and Shenstone.[191] The values obtained by Etard are given in
the following table, and represented graphically in Fig. 28.
Solubility of Silver Nitrate.
Parts of dry salt in 100 parts
Temperature.
of solution.
-7° 46.2
-1° 52.1
+5° 56.3
10° 61.2
20° 67.8
40.5° 76.8
73° 84.0
135° 92.8
182° 96.9
In this figure the composition of the solution is expressed in parts of silver
nitrate in 100 parts by weight of the solution, so that 100 per cent.
represents pure silver nitrate. As can be seen, the solubility increases with
the temperature. At a temperature of about 160° there should be a break in
the curve due to change of crystalline form (p. 63). Such a change in the
direction of the solubility curve, however, does not in any way alter the
essential nature of the relationships discussed here, and may for the present
be left out of account. On following the solubility curve of silver nitrate to
higher temperatures, therefore, the concentration of silver nitrate in the
solution gradually increases, until at last, at a temperature of 208°,[192] the
melting point of pure silver nitrate is reached, and the concentration of the
The best example of this which has been studied, so far as anhydrous salts
and water are concerned, is that of silver nitrate and water. The solubility of
this salt at temperatures above 100° has been studied chiefly by Etard[190]
and by Tilden and Shenstone.[191] The values obtained by Etard are given in
the following table, and represented graphically in Fig. 28.
Solubility of Silver Nitrate.
Parts of dry salt in 100 parts
Temperature.
of solution.
-7° 46.2
-1° 52.1
+5° 56.3
10° 61.2
20° 67.8
40.5° 76.8
73° 84.0
135° 92.8
182° 96.9
In this figure the composition of the solution is expressed in parts of silver
nitrate in 100 parts by weight of the solution, so that 100 per cent.
represents pure silver nitrate. As can be seen, the solubility increases with
the temperature. At a temperature of about 160° there should be a break in
the curve due to change of crystalline form (p. 63). Such a change in the
direction of the solubility curve, however, does not in any way alter the
essential nature of the relationships discussed here, and may for the present
be left out of account. On following the solubility curve of silver nitrate to
higher temperatures, therefore, the concentration of silver nitrate in the
solution gradually increases, until at last, at a temperature of 208°,[192] the
melting point of pure silver nitrate is reached, and the concentration of the
Page 103
water has become zero. The curve throughout its whole extent represents
the equilibrium between silver nitrate, solution, and vapour. Conversely,
starting with pure silver nitrate in contact with the fused salt, addition of
water will lower the melting point, i.e. will lower the temperature at which
the solid salt can exist in contact with the liquid; and the depression will be
all the greater the larger the amount of water added. As the concentration of
the water in the liquid phase is increased, therefore, the system will pass
back along the curve from higher to lower temperatures, and from greater to
smaller concentrations of silver nitrate in the liquid phase. The curve in Fig.
28 may, therefore, be regarded either as the solubility curve of silver nitrate
in water, or as the freezing point curve for silver nitrate in contact with a
solution consisting of that salt and water.
As the temperature of the saturated solution falls, silver nitrate is deposited,
and on lowering the temperature sufficiently a point will at last be reached
at which ice also begins to separate out. Since there are now four phases co-
existing, viz. silver nitrate, ice, solution, vapour, the system is invariant, and
the point is a quadruple point. This quadruple point, therefore, forms the
lower limit of the solubility curve of silver nitrate. Below this point the
solution becomes metastable.
Ice as Solid Phase.—Ice melts or is in equilibrium with water at a
temperature of 0°. The melting point, will, however, be lowered by the
solution of silver nitrate in the water; and the greater the concentration of
the salt in the solution the greater will be the depression of the temperature
of equilibrium. On continuing the addition of silver nitrate, a point will at
length be reached at which the salt is no longer dissolved, but remains in the
solid form along with the ice. We again obtain, therefore, the invariant
system ice—salt—solution—vapour. The temperature at which this
invariant system can exist has been found by Middelberg[193] to be -7.3°,
the solution at this point containing 47.1 per cent. of silver nitrate.
The same general behaviour will be found in the case of all other systems of
two components belonging to this class; that is, in the case of systems from
which the components crystallise out in the pure state, and in which the
fused components are miscible in all proportions. In all such cases,
therefore, the solubility curves (curves of equilibrium) can be represented
diagrammatically as in Fig. 29. In this figure OA represents the solubility
the equilibrium between silver nitrate, solution, and vapour. Conversely,
starting with pure silver nitrate in contact with the fused salt, addition of
water will lower the melting point, i.e. will lower the temperature at which
the solid salt can exist in contact with the liquid; and the depression will be
all the greater the larger the amount of water added. As the concentration of
the water in the liquid phase is increased, therefore, the system will pass
back along the curve from higher to lower temperatures, and from greater to
smaller concentrations of silver nitrate in the liquid phase. The curve in Fig.
28 may, therefore, be regarded either as the solubility curve of silver nitrate
in water, or as the freezing point curve for silver nitrate in contact with a
solution consisting of that salt and water.
As the temperature of the saturated solution falls, silver nitrate is deposited,
and on lowering the temperature sufficiently a point will at last be reached
at which ice also begins to separate out. Since there are now four phases co-
existing, viz. silver nitrate, ice, solution, vapour, the system is invariant, and
the point is a quadruple point. This quadruple point, therefore, forms the
lower limit of the solubility curve of silver nitrate. Below this point the
solution becomes metastable.
Ice as Solid Phase.—Ice melts or is in equilibrium with water at a
temperature of 0°. The melting point, will, however, be lowered by the
solution of silver nitrate in the water; and the greater the concentration of
the salt in the solution the greater will be the depression of the temperature
of equilibrium. On continuing the addition of silver nitrate, a point will at
length be reached at which the salt is no longer dissolved, but remains in the
solid form along with the ice. We again obtain, therefore, the invariant
system ice—salt—solution—vapour. The temperature at which this
invariant system can exist has been found by Middelberg[193] to be -7.3°,
the solution at this point containing 47.1 per cent. of silver nitrate.
The same general behaviour will be found in the case of all other systems of
two components belonging to this class; that is, in the case of systems from
which the components crystallise out in the pure state, and in which the
fused components are miscible in all proportions. In all such cases,
therefore, the solubility curves (curves of equilibrium) can be represented
diagrammatically as in Fig. 29. In this figure OA represents the solubility
Page 104
curve of the salt, and OB the freezing point curve of ice. O is the quadruple
point at which the invariant system exists, and may be regarded as the point
of intersection of the solubility curve with the freezing-point curve. Since
this point is fixed, the condition of the system as regards temperature,
vapour pressure, and concentration of the components (or composition of
the solution), is perfectly definite. From the way, also, in which the
condition is attained, it is evident that the quadruple point is the lowest
temperature that can be obtained with mixtures of the two components in
presence of vapour. It is known as the cryohydric point, or, generally, the
eutectic point.[194]
Fig. 29.
Cryohydrates.[195]—On cooling a solution of common salt in water to a
temperature of -3°, Guthrie observed that the hydrate NaCl,2H2O separated
out. This salt continued to be deposited until at a temperature of -22°
opaque crystals made their appearance, and the liquid passed into the solid
state without change of temperature. A similar behaviour was found by
Guthrie in the case of a large number of other salts, a temperature below
that of the melting point of ice being reached at which on continued
withdrawal of heat, the solution solidified at a constant temperature. When
the system had attained this minimum temperature, it was found that the
composition of the solid and the liquid phases was the same, and remained
unchanged throughout the period of solidification. This is shown by the
following figures, which give the composition of different samples of the
solid phase deposited from the solution at constant temperature.[196]
Temperature of NaCl.
No.
solidification. Per cent.
1 -21° to -22° 23.72
2 -22° 23.66
point at which the invariant system exists, and may be regarded as the point
of intersection of the solubility curve with the freezing-point curve. Since
this point is fixed, the condition of the system as regards temperature,
vapour pressure, and concentration of the components (or composition of
the solution), is perfectly definite. From the way, also, in which the
condition is attained, it is evident that the quadruple point is the lowest
temperature that can be obtained with mixtures of the two components in
presence of vapour. It is known as the cryohydric point, or, generally, the
eutectic point.[194]
Fig. 29.
Cryohydrates.[195]—On cooling a solution of common salt in water to a
temperature of -3°, Guthrie observed that the hydrate NaCl,2H2O separated
out. This salt continued to be deposited until at a temperature of -22°
opaque crystals made their appearance, and the liquid passed into the solid
state without change of temperature. A similar behaviour was found by
Guthrie in the case of a large number of other salts, a temperature below
that of the melting point of ice being reached at which on continued
withdrawal of heat, the solution solidified at a constant temperature. When
the system had attained this minimum temperature, it was found that the
composition of the solid and the liquid phases was the same, and remained
unchanged throughout the period of solidification. This is shown by the
following figures, which give the composition of different samples of the
solid phase deposited from the solution at constant temperature.[196]
Temperature of NaCl.
No.
solidification. Per cent.
1 -21° to -22° 23.72
2 -22° 23.66
Page 105
3 -22° 23.73
4 -23° 23.82
5 -23° 23.34
6 -23° 23.35
Mean 23.6
Conversely, a mixture of ice and salt containing 23.6 per cent. of sodium
chloride will melt at a definite and constant temperature, and exhibit,
therefore, a behaviour supposed to be characteristic of a pure chemical
compound. This, then, combined with the fact that the solid which was
deposited was crystalline, and that the same constant temperature was
attained, no matter with what proportions of water and salt one started, led
Guthrie to the belief that the solids which thus separated at constant
temperature were definite chemical compounds, to which he gave the
general name cryohydrate. A large number of such cryohydrates were
prepared and analysed by Guthrie, and a few of these are given in the
following table, together with the temperature of the cryohydric point:[197]
—
Cryohydrates.
Percentage of anhydrous
Salt. Cryohydric point.
salt in the cryohydrate.
Sodium bromide -24° 41.33
Sodium chloride -22° 23.60
Potassium iodide -22° 52.07
Sodium nitrate -17.5° 40.80
Ammonium sulphate -17° 41.70
Ammonium chloride -15° 19.27
Sodium iodide -15° 59.45
Potassium bromide -13° 32.15
Potassium chloride -11.4° 20.03
Magnesium sulphate - 5° 21.86
Potassium nitrate -2.6° 11.20
Sodium sulphate -0.7° 4.55
4 -23° 23.82
5 -23° 23.34
6 -23° 23.35
Mean 23.6
Conversely, a mixture of ice and salt containing 23.6 per cent. of sodium
chloride will melt at a definite and constant temperature, and exhibit,
therefore, a behaviour supposed to be characteristic of a pure chemical
compound. This, then, combined with the fact that the solid which was
deposited was crystalline, and that the same constant temperature was
attained, no matter with what proportions of water and salt one started, led
Guthrie to the belief that the solids which thus separated at constant
temperature were definite chemical compounds, to which he gave the
general name cryohydrate. A large number of such cryohydrates were
prepared and analysed by Guthrie, and a few of these are given in the
following table, together with the temperature of the cryohydric point:[197]
—
Cryohydrates.
Percentage of anhydrous
Salt. Cryohydric point.
salt in the cryohydrate.
Sodium bromide -24° 41.33
Sodium chloride -22° 23.60
Potassium iodide -22° 52.07
Sodium nitrate -17.5° 40.80
Ammonium sulphate -17° 41.70
Ammonium chloride -15° 19.27
Sodium iodide -15° 59.45
Potassium bromide -13° 32.15
Potassium chloride -11.4° 20.03
Magnesium sulphate - 5° 21.86
Potassium nitrate -2.6° 11.20
Sodium sulphate -0.7° 4.55
Page 106
The chemical individuality of these cryohydrates was, however, called in
question by Pfaundler,[198] and disproved by Offer,[199] who showed that in
spite of the constancy of the melting point, the cryohydrates had the
properties, not of definite chemical compounds, but of mixtures; the
arguments given being that the heat of solution and the specific volume are
the same for the cryohydrate as for a mixture of ice and salt of the same
composition; and it was further shown that the cryohydrate had not a
definite crystalline form, but separated out as an opaque mass containing
the two components in close juxtaposition. The heterogeneous nature of
cryohydrates can also be shown by a microscopical examination.
At the cryohydric point, therefore, we are not dealing with a single solid
phase, but with two solid phases, ice and salt; the cryohydric point,
therefore, as already stated, is a quadruple point and represents an invariant
system.
Although on cooling a solution to the cryohydric point, separation of ice
may occur, it will not necessarily take place; the system may become
metastable. Similarly, separation of salt may not take place immediately the
cryohydric point is reached. It will, therefore, be possible to follow the
curves BO and AO beyond the quadruple point,[200] which is thereby clearly
seen to be the point of intersection of the solubility curve of the salt and the
freezing-point curve of ice. At this point, also, the curves of the univariant
systems ice—salt—vapour and ice—salt—solution intersect.
Changes at the Quadruple Point.—Since the invariant system ice—salt—
solution—vapour can exist only at a definite temperature, addition or
withdrawal of heat must cause the disappearance of one of the phases,
whereby the system will become univariant. So long as all four phases are
present the temperature, pressure, and concentration of the components in
the solution must remain constant. When, therefore, heat is added to or
withdrawn from the system, mutually compensatory changes will take place
within the system whereby the condition of the latter is preserved. These
changes can in all cases be foreseen with the help of the theorem of van't
Hoff and Le Chatelier; and, after what was said in Chap. IV., need only be
briefly referred to here. In the first place, addition of heat will cause ice to
melt, and the concentration of the solution will be thereby altered; salt must
therefore dissolve until the original concentration is reached, and the heat of
question by Pfaundler,[198] and disproved by Offer,[199] who showed that in
spite of the constancy of the melting point, the cryohydrates had the
properties, not of definite chemical compounds, but of mixtures; the
arguments given being that the heat of solution and the specific volume are
the same for the cryohydrate as for a mixture of ice and salt of the same
composition; and it was further shown that the cryohydrate had not a
definite crystalline form, but separated out as an opaque mass containing
the two components in close juxtaposition. The heterogeneous nature of
cryohydrates can also be shown by a microscopical examination.
At the cryohydric point, therefore, we are not dealing with a single solid
phase, but with two solid phases, ice and salt; the cryohydric point,
therefore, as already stated, is a quadruple point and represents an invariant
system.
Although on cooling a solution to the cryohydric point, separation of ice
may occur, it will not necessarily take place; the system may become
metastable. Similarly, separation of salt may not take place immediately the
cryohydric point is reached. It will, therefore, be possible to follow the
curves BO and AO beyond the quadruple point,[200] which is thereby clearly
seen to be the point of intersection of the solubility curve of the salt and the
freezing-point curve of ice. At this point, also, the curves of the univariant
systems ice—salt—vapour and ice—salt—solution intersect.
Changes at the Quadruple Point.—Since the invariant system ice—salt—
solution—vapour can exist only at a definite temperature, addition or
withdrawal of heat must cause the disappearance of one of the phases,
whereby the system will become univariant. So long as all four phases are
present the temperature, pressure, and concentration of the components in
the solution must remain constant. When, therefore, heat is added to or
withdrawn from the system, mutually compensatory changes will take place
within the system whereby the condition of the latter is preserved. These
changes can in all cases be foreseen with the help of the theorem of van't
Hoff and Le Chatelier; and, after what was said in Chap. IV., need only be
briefly referred to here. In the first place, addition of heat will cause ice to
melt, and the concentration of the solution will be thereby altered; salt must
therefore dissolve until the original concentration is reached, and the heat of
Page 107
fusion of ice will be counteracted by the heat of solution of the salt.
Changes of volume of the solid and liquid phases must also be taken into
account; an alteration in the volume of these phases being compensated by
condensation or evaporation. All four phases will therefore be involved in
the change, and the final state of the system will be dependent on the
amounts of the different phases present; the ultimate result of addition or
withdrawal of heat or of change of pressure at the quadruple point will be
one of the four univariant systems: ice—solution—vapour; salt—solution—
vapour; ice—salt—vapour; ice—salt—solution. If the vapour phase
disappear, there will be left the univariant system ice—salt—solution, and
the temperature at which this system can exist will alter with the pressure.
Since in this case the influence of pressure is comparatively slight, the
temperature of the quadruple point will differ only slightly from that of the
cryohydric point as determined under atmospheric pressure.
Freezing Mixtures.—Not only will the composition of a univariant system
undergo change when the temperature is varied, but, conversely, if the
composition of the system is caused to change, corresponding changes of
temperature must ensue. Thus, if ice is added to the univariant system salt—
solution—vapour, the ice must melt and the temperature fall; and if
sufficient ice is added, the temperature of the cryohydric point must be at
length reached, for it is only at this temperature that the four phases ice—
salt—solution—vapour can coexist. Or, on the other hand, if salt is added to
the system ice—solution—vapour, the concentration of the solution will
increase, ice must melt, and the temperature must thereby fall; and this
process also will go on until the cryohydric point is reached. In both cases
ice melts and there is a change in the composition of the solution; in the
former case, salt will be deposited[201] because the solubility diminishes as
the temperature falls; in the latter, salt will pass into solution. This process
may be accompanied either by an evolution or, more generally, by
absorption of heat; in the former case the effect of the addition of ice will be
partially counteracted; in the latter case it will be augmented.
These principles are made use of in the preparation of freezing mixtures.
The lowest temperature which can be reached by means of these (under
atmospheric pressure) is the cryohydric point. This temperature-minimum
is, however, not always attained in the preparation of a freezing mixture,
and that for various reasons. The chief of these are radiation and the heat
Changes of volume of the solid and liquid phases must also be taken into
account; an alteration in the volume of these phases being compensated by
condensation or evaporation. All four phases will therefore be involved in
the change, and the final state of the system will be dependent on the
amounts of the different phases present; the ultimate result of addition or
withdrawal of heat or of change of pressure at the quadruple point will be
one of the four univariant systems: ice—solution—vapour; salt—solution—
vapour; ice—salt—vapour; ice—salt—solution. If the vapour phase
disappear, there will be left the univariant system ice—salt—solution, and
the temperature at which this system can exist will alter with the pressure.
Since in this case the influence of pressure is comparatively slight, the
temperature of the quadruple point will differ only slightly from that of the
cryohydric point as determined under atmospheric pressure.
Freezing Mixtures.—Not only will the composition of a univariant system
undergo change when the temperature is varied, but, conversely, if the
composition of the system is caused to change, corresponding changes of
temperature must ensue. Thus, if ice is added to the univariant system salt—
solution—vapour, the ice must melt and the temperature fall; and if
sufficient ice is added, the temperature of the cryohydric point must be at
length reached, for it is only at this temperature that the four phases ice—
salt—solution—vapour can coexist. Or, on the other hand, if salt is added to
the system ice—solution—vapour, the concentration of the solution will
increase, ice must melt, and the temperature must thereby fall; and this
process also will go on until the cryohydric point is reached. In both cases
ice melts and there is a change in the composition of the solution; in the
former case, salt will be deposited[201] because the solubility diminishes as
the temperature falls; in the latter, salt will pass into solution. This process
may be accompanied either by an evolution or, more generally, by
absorption of heat; in the former case the effect of the addition of ice will be
partially counteracted; in the latter case it will be augmented.
These principles are made use of in the preparation of freezing mixtures.
The lowest temperature which can be reached by means of these (under
atmospheric pressure) is the cryohydric point. This temperature-minimum
is, however, not always attained in the preparation of a freezing mixture,
and that for various reasons. The chief of these are radiation and the heat
Page 108
absorbed in cooling the solution produced. The lower the temperature falls,
the more rapid does the radiation become; and the rate at which the
temperature sinks decreases as the amount of solution increases. Both these
factors counteract the effect of the latent heat of fusion and the heat of
solution, so that a point is reached (which may lie considerably above the
cryohydric point) at which the two opposing influences balance. The
absorption of heat by the solution can be diminished by allowing the
solution to drain off as fast as it is produced; and the effect of radiation can
be partially annulled by increasing the rate of cooling. This can be done by
the more intimate mixing of the components. Since, under atmospheric
pressure, the temperature of the cryohydric point is constant, the
cryohydrates are very valuable for the production of baths of constant low
temperature.
2. Partial Miscibility of the Fused Components.
On passing to the study of the second class of systems of two components
belonging to this group, namely, those in which the fused components are
not miscible in all proportions, we find that the relationships are not quite
so simple as in the case of silver nitrate and water. In the latter case, only
one liquid phase was possible; in the cases now to be studied, two liquid
phases can be formed, and there is a marked discontinuity in the solubility
curve on passing from the cryohydric point to the melting point of the
second (non-volatile) component.
Paratoluidine dissolves in water, and the solubility increases as the
temperature rises.[202] At 44.2°, however, paratoluidine in contact with
water melts, and two liquid phases are formed, viz. a solution of water in
fused paratoluidine and a solution of fused paratoluidine in water. We have,
therefore, the phenomenon of melting under the solvent. This melting point
will, of course, be lower than the melting point of the pure substance,
because the solid is now in contact with a solution, and, as we have already
seen, addition of a foreign substance lowers the melting point. Such cases
of melting under the solvent are by no means rare, and a review of the
relationships met with may, therefore, be undertaken here. As an example,
there may be chosen the equilibrium between succinic nitrile, C2H4(CN)2
and water, which has been fully studied by Schreinemakers.[203]
the more rapid does the radiation become; and the rate at which the
temperature sinks decreases as the amount of solution increases. Both these
factors counteract the effect of the latent heat of fusion and the heat of
solution, so that a point is reached (which may lie considerably above the
cryohydric point) at which the two opposing influences balance. The
absorption of heat by the solution can be diminished by allowing the
solution to drain off as fast as it is produced; and the effect of radiation can
be partially annulled by increasing the rate of cooling. This can be done by
the more intimate mixing of the components. Since, under atmospheric
pressure, the temperature of the cryohydric point is constant, the
cryohydrates are very valuable for the production of baths of constant low
temperature.
2. Partial Miscibility of the Fused Components.
On passing to the study of the second class of systems of two components
belonging to this group, namely, those in which the fused components are
not miscible in all proportions, we find that the relationships are not quite
so simple as in the case of silver nitrate and water. In the latter case, only
one liquid phase was possible; in the cases now to be studied, two liquid
phases can be formed, and there is a marked discontinuity in the solubility
curve on passing from the cryohydric point to the melting point of the
second (non-volatile) component.
Paratoluidine dissolves in water, and the solubility increases as the
temperature rises.[202] At 44.2°, however, paratoluidine in contact with
water melts, and two liquid phases are formed, viz. a solution of water in
fused paratoluidine and a solution of fused paratoluidine in water. We have,
therefore, the phenomenon of melting under the solvent. This melting point
will, of course, be lower than the melting point of the pure substance,
because the solid is now in contact with a solution, and, as we have already
seen, addition of a foreign substance lowers the melting point. Such cases
of melting under the solvent are by no means rare, and a review of the
relationships met with may, therefore, be undertaken here. As an example,
there may be chosen the equilibrium between succinic nitrile, C2H4(CN)2
and water, which has been fully studied by Schreinemakers.[203]
Page 109
Fig. 30.
If to the system ice—water at 0° succinic nitrile is added, the temperature
will fall; and continued addition of the nitrile will lead at last to the
cryohydric point b (Fig. 30), at which solid nitrile, ice, solution, and vapour
can coexist. The temperature of the cryohydric point is -1.2°, and the
composition of the solution is 1.29 mol. of nitrile in 100 mol. of solution.
From a to b the solid phase in contact with the solution is ice. If the
temperature be now raised so as to cause the disappearance of the ice, and
the addition of nitrile be continued, the concentration of the nitrile in the
solution will increase as represented by the curve bc. At the point c (18.5°),
when the concentration of the nitrile in the solution has increased to 2.5
molecules per cent., the nitrile melts and two liquid phases are formed; the
concentration of the nitrile in these two phases is given by the points c and
c′. As there are now four phases present, viz. solid nitrile, solution of fused
nitrile in water, solution of water in fused nitrile, and vapour, the system is
invariant. Since at this point the concentration, temperature, and pressure
are completely defined, addition or withdrawal of heat can only cause a
change in the relative amounts of the phases, but no variation of the
concentrations of the respective phases. As a matter of fact, continued
addition of nitrile and addition of heat will cause an increase in the amount
of the liquid phase containing excess of nitrile (i.e. the solution of water in
fused nitrile), whereas the other liquid phase, the solution of fused nitrile in
water, will gradually disappear. When it has completely disappeared, the
system will be represented by the point c′, where the molecular
concentration of nitrile is now 75 per cent., and again becomes univariant,
the three phases being solid nitrile, liquid phase containing excess of nitrile,
and vapour; and as the amount of the water is diminished the temperature of
equilibrium rises, until at 54° the melting point of the pure nitrile is reached.
Return now to the point c. At this point there exists the invariant system
solid nitrile, two liquid phases, vapour. If heat be added, the solid nitrile
will disappear, and there will be left the univariant system, consisting of
If to the system ice—water at 0° succinic nitrile is added, the temperature
will fall; and continued addition of the nitrile will lead at last to the
cryohydric point b (Fig. 30), at which solid nitrile, ice, solution, and vapour
can coexist. The temperature of the cryohydric point is -1.2°, and the
composition of the solution is 1.29 mol. of nitrile in 100 mol. of solution.
From a to b the solid phase in contact with the solution is ice. If the
temperature be now raised so as to cause the disappearance of the ice, and
the addition of nitrile be continued, the concentration of the nitrile in the
solution will increase as represented by the curve bc. At the point c (18.5°),
when the concentration of the nitrile in the solution has increased to 2.5
molecules per cent., the nitrile melts and two liquid phases are formed; the
concentration of the nitrile in these two phases is given by the points c and
c′. As there are now four phases present, viz. solid nitrile, solution of fused
nitrile in water, solution of water in fused nitrile, and vapour, the system is
invariant. Since at this point the concentration, temperature, and pressure
are completely defined, addition or withdrawal of heat can only cause a
change in the relative amounts of the phases, but no variation of the
concentrations of the respective phases. As a matter of fact, continued
addition of nitrile and addition of heat will cause an increase in the amount
of the liquid phase containing excess of nitrile (i.e. the solution of water in
fused nitrile), whereas the other liquid phase, the solution of fused nitrile in
water, will gradually disappear. When it has completely disappeared, the
system will be represented by the point c′, where the molecular
concentration of nitrile is now 75 per cent., and again becomes univariant,
the three phases being solid nitrile, liquid phase containing excess of nitrile,
and vapour; and as the amount of the water is diminished the temperature of
equilibrium rises, until at 54° the melting point of the pure nitrile is reached.
Return now to the point c. At this point there exists the invariant system
solid nitrile, two liquid phases, vapour. If heat be added, the solid nitrile
will disappear, and there will be left the univariant system, consisting of
Page 110
two liquid phases and vapour.[204] Such a system will exhibit relationships
similar to those already studied in the previous chapter. As the temperature
rises, the mutual solubility of the two fused components becomes greater,
until at d (55.5°) the critical solution temperature is reached, and the fused
components become miscible in all proportions.
At all temperatures and concentrations lying to the right of the curve
abcdc′e there can be only one liquid phase; in the field cdc′ there are two
liquid phases.
From the figure it will be easy to see what will be the result of bringing
together succinic nitrile and water at different temperatures and in different
amounts. Since b is the lowest temperature at which liquid can exist in
stable equilibrium with solid, ice and succinic nitrile can be mixed in any
proportions at temperatures below b without undergoing change. Between b
and c succinic nitrile will be dissolved until the concentration reaches the
value on the curve bc, corresponding to the given temperature. On adding
the nitrile to water at temperatures between c and d, it will dissolve until a
concentration lying on the curve cd is attained; at this point two liquid
phases will be formed, and further addition of nitrile will cause the one
liquid phase (that containing excess of nitrile) to increase, while the other
liquid phase will decrease, until it finally disappears and there is only one
liquid phase left, that containing excess of nitrile. This can dissolve further
quantities of the nitrile, and the concentration will increase until the curve
c′e is reached, when the concentration will remain unchanged, and addition
of solid will merely increase the amount of the solid phase.
If a solution represented by any point in the field lying below the curve bcd
is heated to a temperature above d, the critical solution temperature, then
the concentration of the nitrile can be increased to any desired amount
without at any time two liquid phases making their appearance; the system
can then be cooled down to a temperature represented by any point between
the curves dc′e. In this way it is possible to pass continuously from a
solution containing excess of one component to solutions containing excess
of the other, as represented by the dotted line xxxx (v. p. 100). At no point is
there formation of two liquid phases.
similar to those already studied in the previous chapter. As the temperature
rises, the mutual solubility of the two fused components becomes greater,
until at d (55.5°) the critical solution temperature is reached, and the fused
components become miscible in all proportions.
At all temperatures and concentrations lying to the right of the curve
abcdc′e there can be only one liquid phase; in the field cdc′ there are two
liquid phases.
From the figure it will be easy to see what will be the result of bringing
together succinic nitrile and water at different temperatures and in different
amounts. Since b is the lowest temperature at which liquid can exist in
stable equilibrium with solid, ice and succinic nitrile can be mixed in any
proportions at temperatures below b without undergoing change. Between b
and c succinic nitrile will be dissolved until the concentration reaches the
value on the curve bc, corresponding to the given temperature. On adding
the nitrile to water at temperatures between c and d, it will dissolve until a
concentration lying on the curve cd is attained; at this point two liquid
phases will be formed, and further addition of nitrile will cause the one
liquid phase (that containing excess of nitrile) to increase, while the other
liquid phase will decrease, until it finally disappears and there is only one
liquid phase left, that containing excess of nitrile. This can dissolve further
quantities of the nitrile, and the concentration will increase until the curve
c′e is reached, when the concentration will remain unchanged, and addition
of solid will merely increase the amount of the solid phase.
If a solution represented by any point in the field lying below the curve bcd
is heated to a temperature above d, the critical solution temperature, then
the concentration of the nitrile can be increased to any desired amount
without at any time two liquid phases making their appearance; the system
can then be cooled down to a temperature represented by any point between
the curves dc′e. In this way it is possible to pass continuously from a
solution containing excess of one component to solutions containing excess
of the other, as represented by the dotted line xxxx (v. p. 100). At no point is
there formation of two liquid phases.
Page 111
Supersaturation.—Just as suspended transformation is rarely met with in
the passage from the solid to the liquid state, so also it is found in the case
of the melting of substances under the solvent that suspended fusion does
not occur; but that when the temperature of the invariant point is reached at
which, therefore, the formation of two liquid layers is possible, these two
liquid layers, as a matter of fact, make their appearance. Suspended
transformation can, however, take place from the side of the liquid phase,
just as water or other liquid can be cooled below the normal freezing point
without solidification occurring. The question, therefore, arises as to the
relative solubilities of the solid and the supercooled liquid at the same
temperature.
Fig. 31.
The answer to this question can at once be given from what we have
already learned (p. 113), if we recollect that at temperatures below the point
of fusion under the solvent, the solid form, at temperatures above that point,
the liquid form, is the more stable; at this temperature, therefore, the
relative stability of the solid and liquid forms changes. Since, as we have
already seen, the less stable form has the greater solubility, it follows that
the supercooled liquid, being the less stable form, must have the greater
solubility. This was first proved experimentally by Alexejeff[205] in the case
of benzoic acid and water, the solubility curves for which are given in Fig.
31. As can be seen from the figure, the prolongation of the curve for liquid
—liquid, which represents the solubility of the supercooled liquid benzoic
acid, lies above that for the solubility of the solid benzoic acid in water; the
solution saturated with respect to the supercooled liquid is therefore
supersaturated with respect to the solid form. A similar behaviour has been
found in the case of other substances.[206]
the passage from the solid to the liquid state, so also it is found in the case
of the melting of substances under the solvent that suspended fusion does
not occur; but that when the temperature of the invariant point is reached at
which, therefore, the formation of two liquid layers is possible, these two
liquid layers, as a matter of fact, make their appearance. Suspended
transformation can, however, take place from the side of the liquid phase,
just as water or other liquid can be cooled below the normal freezing point
without solidification occurring. The question, therefore, arises as to the
relative solubilities of the solid and the supercooled liquid at the same
temperature.
Fig. 31.
The answer to this question can at once be given from what we have
already learned (p. 113), if we recollect that at temperatures below the point
of fusion under the solvent, the solid form, at temperatures above that point,
the liquid form, is the more stable; at this temperature, therefore, the
relative stability of the solid and liquid forms changes. Since, as we have
already seen, the less stable form has the greater solubility, it follows that
the supercooled liquid, being the less stable form, must have the greater
solubility. This was first proved experimentally by Alexejeff[205] in the case
of benzoic acid and water, the solubility curves for which are given in Fig.
31. As can be seen from the figure, the prolongation of the curve for liquid
—liquid, which represents the solubility of the supercooled liquid benzoic
acid, lies above that for the solubility of the solid benzoic acid in water; the
solution saturated with respect to the supercooled liquid is therefore
supersaturated with respect to the solid form. A similar behaviour has been
found in the case of other substances.[206]
Page 112
Pressure-Temperature Diagram.—Having considered the changes which
occur in the concentration of the components in a solution with the
temperature, we may conclude the discussion of the equilibrium between a
salt and water by studying the variation of the vapour pressure.
Since in systems of two components the two phases, solution and vapour,
constitute a bivariant system, the vapour pressure is undefined, and may
have different values at the same temperature, depending on the
concentration. In order that there may be for each temperature a definite
corresponding pressure of the vapour, a third phase must be present. This
condition is satisfied by the system solid—liquid (solution)—vapour; that
is, by the saturated solution (p. 108). In the case of a saturated solution,
therefore, the pressure of the vapour at any given temperature is constant.
Vapour Pressure of Solid—Solution—Vapour.—It has long been known
that the addition of a non-volatile solid to a liquid in which it is soluble
lowers the vapour pressure of the solvent; and the diminution of the
pressure is approximately proportional to the amount of substance dissolved
(Law of Babo). The vapour-pressure curve, therefore, of a solution of a salt
in water must lie below that for pure water. Further, in the case of a pure
liquid, the vaporization curve is a function only of the temperature (p. 63),
whereas, in the case of a solution, the pressure varies both with the
temperature and the concentration. These two factors, however, act in
opposite directions; for although the vapour pressure in all cases increases
as the temperature rises, increase of concentration, as we have seen, lowers
the vapour pressure. Again, since the concentration itself varies with the
temperature, two cases have to be considered, viz. where the concentration
increases with rise of temperature, and where the concentration diminishes
with rise of temperature.
The relations which are found here will be best understood with the help of
Fig. 32.[207] In this figure, OB represents the sublimation curve of ice, and
BC the vaporization curve of water; the curve for the solution must lie
below this, and must cut the sublimation curve of ice at some temperature
below the melting point. The point of intersection A is the cryohydric point.
If the solubility increases with rise of temperature, the increase of the
vapour pressure due to the latter will be partially annulled. Since at first the
effect of increase of temperature more than counteracts the depressing
occur in the concentration of the components in a solution with the
temperature, we may conclude the discussion of the equilibrium between a
salt and water by studying the variation of the vapour pressure.
Since in systems of two components the two phases, solution and vapour,
constitute a bivariant system, the vapour pressure is undefined, and may
have different values at the same temperature, depending on the
concentration. In order that there may be for each temperature a definite
corresponding pressure of the vapour, a third phase must be present. This
condition is satisfied by the system solid—liquid (solution)—vapour; that
is, by the saturated solution (p. 108). In the case of a saturated solution,
therefore, the pressure of the vapour at any given temperature is constant.
Vapour Pressure of Solid—Solution—Vapour.—It has long been known
that the addition of a non-volatile solid to a liquid in which it is soluble
lowers the vapour pressure of the solvent; and the diminution of the
pressure is approximately proportional to the amount of substance dissolved
(Law of Babo). The vapour-pressure curve, therefore, of a solution of a salt
in water must lie below that for pure water. Further, in the case of a pure
liquid, the vaporization curve is a function only of the temperature (p. 63),
whereas, in the case of a solution, the pressure varies both with the
temperature and the concentration. These two factors, however, act in
opposite directions; for although the vapour pressure in all cases increases
as the temperature rises, increase of concentration, as we have seen, lowers
the vapour pressure. Again, since the concentration itself varies with the
temperature, two cases have to be considered, viz. where the concentration
increases with rise of temperature, and where the concentration diminishes
with rise of temperature.
The relations which are found here will be best understood with the help of
Fig. 32.[207] In this figure, OB represents the sublimation curve of ice, and
BC the vaporization curve of water; the curve for the solution must lie
below this, and must cut the sublimation curve of ice at some temperature
below the melting point. The point of intersection A is the cryohydric point.
If the solubility increases with rise of temperature, the increase of the
vapour pressure due to the latter will be partially annulled. Since at first the
effect of increase of temperature more than counteracts the depressing
Page 113
action of increase of concentration, the vapour pressure will increase on
raising the temperature above the cryohydric point. If the elevation of
temperature is continued, however, to the melting point of the salt, the
effect of increasing concentration makes itself more and more felt, so that
the vapour-pressure curve of the solution falls more and more below that of
the pure liquid, and the pressure will ultimately become equal to that of the
pure salt; that is to say, practically equal to zero. The curve will therefore be
of the general form AMF shown in Fig. 32. If the solubility should diminish
with rise of temperature, the two factors, temperature and concentration,
will act in the same direction, and the vapour-pressure curve will rise
relatively more rapid than that of the pure liquid; since, however, the pure
salt is ultimately obtained, the vapour-pressure curve must in this case also
finally approach the value zero.
Fig. 32.
Other Univariant Systems.—Besides the univariant system salt—solution
—vapour already considered, three others are possible, viz. ice—solution—
vapour, ice—salt—solution, and ice—salt—vapour.
The fusion point of a substance is lowered, as we have seen, by the addition
of a foreign substance, and the depression is all the greater the larger the
quantity of substance added. The vapour pressure of the water, also, is
lowered by the solution in it of other substances, so that the vapour pressure
of the system ice—solution—vapour must decrease as the temperature falls
from the fusion point of ice to the cryohydric point. This curve is
represented by BA (Fig. 32), and is coincident with the sublimation curve of
ice.
This, at first sight, strange fact will be readily understood when we consider
that since ice and solution are together in equilibrium with the same vapour,
raising the temperature above the cryohydric point. If the elevation of
temperature is continued, however, to the melting point of the salt, the
effect of increasing concentration makes itself more and more felt, so that
the vapour-pressure curve of the solution falls more and more below that of
the pure liquid, and the pressure will ultimately become equal to that of the
pure salt; that is to say, practically equal to zero. The curve will therefore be
of the general form AMF shown in Fig. 32. If the solubility should diminish
with rise of temperature, the two factors, temperature and concentration,
will act in the same direction, and the vapour-pressure curve will rise
relatively more rapid than that of the pure liquid; since, however, the pure
salt is ultimately obtained, the vapour-pressure curve must in this case also
finally approach the value zero.
Fig. 32.
Other Univariant Systems.—Besides the univariant system salt—solution
—vapour already considered, three others are possible, viz. ice—solution—
vapour, ice—salt—solution, and ice—salt—vapour.
The fusion point of a substance is lowered, as we have seen, by the addition
of a foreign substance, and the depression is all the greater the larger the
quantity of substance added. The vapour pressure of the water, also, is
lowered by the solution in it of other substances, so that the vapour pressure
of the system ice—solution—vapour must decrease as the temperature falls
from the fusion point of ice to the cryohydric point. This curve is
represented by BA (Fig. 32), and is coincident with the sublimation curve of
ice.
This, at first sight, strange fact will be readily understood when we consider
that since ice and solution are together in equilibrium with the same vapour,
Page 114
they must have the same vapour pressure. For suppose at any given
temperature equilibrium to have been established in the system ice—
solution—vapour, removal of the ice will not alter this equilibrium.
Suppose, now, the ice and the solution placed under a bell-jar so that they
have a common vapour, but are not themselves in contact; then, if they do
not have the same vapour pressure, distillation must take place and the
solution will become more dilute or more concentrated. Since, at the
completion of this process, the ice and solution are now in equilibrium
when they are not in contact, they must also be in equilibrium when they
are in contact (p. 32). But if distillation has taken place the concentration of
the solution must have altered, so that the ice will now be in equilibrium
with a solution of a different concentration from before. But according to
the Phase Rule ice cannot at one and the same temperature be in
equilibrium with two solutions of different concentration, for the system ice
—solution—vapour is univariant, and at any given temperature, therefore,
not only the pressure but also the concentration of the components in the
solution must be constant. Distillation could not, therefore, take place from
the ice to the solution or vice versâ; that is to say, the solution and the ice
must have the same vapour pressure—the sublimation pressure of ice. The
reason of the coincidence is the non-volatility of the salt: had the salt a
measurable vapour pressure itself, the sublimation curve of ice and the
curve for ice—solution—vapour would no longer fall together.
The curve AO represents the pressures of the system ice—salt—vapour.
This curve will also be coincident with the sublimation curve of ice, on
account of the non-volatility of the salt.
The equilibria of the fourth univariant system ice—salt—solution are
represented by AE. Since this is a condensed system, the effect of a small
change of temperature will be to cause a large change of pressure, as in the
case of the fusion point of a pure substance. The direction of this curve will
depend on whether there is an increase or diminution of volume on
solidification; but the effect in any given case can be predicted with the help
of the theorem of Le Chatelier.
Since the cryohydric point is a quadruple point in a two-component system,
it represents an invariant system. The condition of the system is, therefore,
completely defined; the four phases, ice, salt, solution, vapour, can co-exist
temperature equilibrium to have been established in the system ice—
solution—vapour, removal of the ice will not alter this equilibrium.
Suppose, now, the ice and the solution placed under a bell-jar so that they
have a common vapour, but are not themselves in contact; then, if they do
not have the same vapour pressure, distillation must take place and the
solution will become more dilute or more concentrated. Since, at the
completion of this process, the ice and solution are now in equilibrium
when they are not in contact, they must also be in equilibrium when they
are in contact (p. 32). But if distillation has taken place the concentration of
the solution must have altered, so that the ice will now be in equilibrium
with a solution of a different concentration from before. But according to
the Phase Rule ice cannot at one and the same temperature be in
equilibrium with two solutions of different concentration, for the system ice
—solution—vapour is univariant, and at any given temperature, therefore,
not only the pressure but also the concentration of the components in the
solution must be constant. Distillation could not, therefore, take place from
the ice to the solution or vice versâ; that is to say, the solution and the ice
must have the same vapour pressure—the sublimation pressure of ice. The
reason of the coincidence is the non-volatility of the salt: had the salt a
measurable vapour pressure itself, the sublimation curve of ice and the
curve for ice—solution—vapour would no longer fall together.
The curve AO represents the pressures of the system ice—salt—vapour.
This curve will also be coincident with the sublimation curve of ice, on
account of the non-volatility of the salt.
The equilibria of the fourth univariant system ice—salt—solution are
represented by AE. Since this is a condensed system, the effect of a small
change of temperature will be to cause a large change of pressure, as in the
case of the fusion point of a pure substance. The direction of this curve will
depend on whether there is an increase or diminution of volume on
solidification; but the effect in any given case can be predicted with the help
of the theorem of Le Chatelier.
Since the cryohydric point is a quadruple point in a two-component system,
it represents an invariant system. The condition of the system is, therefore,
completely defined; the four phases, ice, salt, solution, vapour, can co-exist
Page 115
only when the temperature, pressure, and concentration of the solution have
constant and definite values. Addition or withdrawal of heat, therefore, can
cause no alteration of the condition of the system except a variation of the
relative amounts of the phases. Addition of heat at constant volume will
ultimately lead to the system salt—solution—vapour or the system ice—
solution—vapour, according as ice or salt disappears first. This is readily
apparent from the diagram (Fig. 32), for the systems ice—salt—solution
and ice—salt—vapour can exist only at temperatures below the cryohydric
point (provided the curve for ice—salt—solution slopes towards the
pressure axis).
Bivariant Systems.—Besides the univariant systems already discussed,
various bivariant systems are possible, the conditions for the existence of
which are represented by the different areas of Fig. 32. They are as follows:
—
Area. System.
OAMF Salt—vapour.
CBAMF Solution—vapour; salt—solution.
EABD Salt—solution; ice—solution.
EAO Ice—salt.
Deliquescence.—As is evident from Fig. 32, salt can exist in contact with
water vapour at pressures under those represented by OAMF. If, however,
the pressure of the vapour is increased until it reaches a value lying on this
curve at temperatures above the cryohydric point, solution will be formed;
for the curve AMF represents the equilibria between salt—solution—
vapour. From this, therefore, it is clear that if the pressure of the aqueous
vapour in the atmosphere is greater than that of the saturated solution of a
salt, that salt will, on being placed in the air, form a solution; it will
deliquesce.
Separation of Salt on Evaporation.—With the help of Fig. 32 it is
possible to state in a general manner whether or not salt will be deposited
when a solution is evaporated under a constant pressure.[208]
The curve AMF (Fig. 32) is the vapour-pressure curve of the saturated
solutions of the salt, i.e. it represents, as we have seen, the maximum
constant and definite values. Addition or withdrawal of heat, therefore, can
cause no alteration of the condition of the system except a variation of the
relative amounts of the phases. Addition of heat at constant volume will
ultimately lead to the system salt—solution—vapour or the system ice—
solution—vapour, according as ice or salt disappears first. This is readily
apparent from the diagram (Fig. 32), for the systems ice—salt—solution
and ice—salt—vapour can exist only at temperatures below the cryohydric
point (provided the curve for ice—salt—solution slopes towards the
pressure axis).
Bivariant Systems.—Besides the univariant systems already discussed,
various bivariant systems are possible, the conditions for the existence of
which are represented by the different areas of Fig. 32. They are as follows:
—
Area. System.
OAMF Salt—vapour.
CBAMF Solution—vapour; salt—solution.
EABD Salt—solution; ice—solution.
EAO Ice—salt.
Deliquescence.—As is evident from Fig. 32, salt can exist in contact with
water vapour at pressures under those represented by OAMF. If, however,
the pressure of the vapour is increased until it reaches a value lying on this
curve at temperatures above the cryohydric point, solution will be formed;
for the curve AMF represents the equilibria between salt—solution—
vapour. From this, therefore, it is clear that if the pressure of the aqueous
vapour in the atmosphere is greater than that of the saturated solution of a
salt, that salt will, on being placed in the air, form a solution; it will
deliquesce.
Separation of Salt on Evaporation.—With the help of Fig. 32 it is
possible to state in a general manner whether or not salt will be deposited
when a solution is evaporated under a constant pressure.[208]
The curve AMF (Fig. 32) is the vapour-pressure curve of the saturated
solutions of the salt, i.e. it represents, as we have seen, the maximum
Page 116
vapour pressure at which salt can exist in contact with solution and vapour.
The dotted line aa represents atmospheric pressure. If, now, an unsaturated
solution, the composition of which is represented by the point x, is heated in
an open vessel, the temperature will rise, and the vapour pressure of the
solution will increase. The system will, therefore, pass along a line
represented diagrammatically by xx′. At the point x′ the vapour pressure of
the system becomes equal to 1 atm.; and as the vessel is open to the air, the
pressure cannot further rise; the solution boils. If the heating is continued,
water passes off, the concentration increases, and the boiling point rises.
The system will therefore pass along the line x′m, until at the point m solid
salt separates out (provided supersaturation is excluded). The system is now
univariant, and continued heating will no longer cause an alteration of the
concentration; as water passes off, solid salt will be deposited, and the
solution will evaporate to dryness.
If, however, the atmospheric pressure is represented not by aa but by bb,
then, as Fig. 32 shows, the maximum vapour pressure of the system salt—
solution—vapour never reaches the pressure of 1 atm. Further, since the
curve bb lies in the area of the bivariant system solution—vapour there can
at no point be a separation of the solid form; for the system solid—solution
—vapour can exist only along the curve AMF.
On evaporating the solution of a salt in an open vessel, therefore, salt can be
deposited only if at some temperature the pressure of the saturated solution
is equal to the atmospheric pressure. This is found to be the case with most
salts. In the case of aqueous solutions of sodium and potassium hydroxide,
however, the vapour pressure of the saturated solution never reaches the
value of 1 atm., and on evaporating these solutions, therefore, in an open
vessel, there is no separation of the solid. Only a homogeneous fused mass
is obtained. If, however, the evaporation be carried out under a pressure
which is lower than the maximum pressure of the saturated solution,
separation of the solid substance will be possible.
General Summary.—The systems which have been discussed in the
present chapter contained water as one of their components, and an
anhydrous salt as the other. It will, however, be clear that the relationships
which were found in the case of these will be found also in other cases
where it is a question of the equilibria between two components, which
The dotted line aa represents atmospheric pressure. If, now, an unsaturated
solution, the composition of which is represented by the point x, is heated in
an open vessel, the temperature will rise, and the vapour pressure of the
solution will increase. The system will, therefore, pass along a line
represented diagrammatically by xx′. At the point x′ the vapour pressure of
the system becomes equal to 1 atm.; and as the vessel is open to the air, the
pressure cannot further rise; the solution boils. If the heating is continued,
water passes off, the concentration increases, and the boiling point rises.
The system will therefore pass along the line x′m, until at the point m solid
salt separates out (provided supersaturation is excluded). The system is now
univariant, and continued heating will no longer cause an alteration of the
concentration; as water passes off, solid salt will be deposited, and the
solution will evaporate to dryness.
If, however, the atmospheric pressure is represented not by aa but by bb,
then, as Fig. 32 shows, the maximum vapour pressure of the system salt—
solution—vapour never reaches the pressure of 1 atm. Further, since the
curve bb lies in the area of the bivariant system solution—vapour there can
at no point be a separation of the solid form; for the system solid—solution
—vapour can exist only along the curve AMF.
On evaporating the solution of a salt in an open vessel, therefore, salt can be
deposited only if at some temperature the pressure of the saturated solution
is equal to the atmospheric pressure. This is found to be the case with most
salts. In the case of aqueous solutions of sodium and potassium hydroxide,
however, the vapour pressure of the saturated solution never reaches the
value of 1 atm., and on evaporating these solutions, therefore, in an open
vessel, there is no separation of the solid. Only a homogeneous fused mass
is obtained. If, however, the evaporation be carried out under a pressure
which is lower than the maximum pressure of the saturated solution,
separation of the solid substance will be possible.
General Summary.—The systems which have been discussed in the
present chapter contained water as one of their components, and an
anhydrous salt as the other. It will, however, be clear that the relationships
which were found in the case of these will be found also in other cases
where it is a question of the equilibria between two components, which
Page 117
crystallize out in the pure state, and only one of which possesses a
measurable vapour pressure. A similar behaviour will, for example, be
found in the case of many pairs of organic substances; and in all cases the
equilibria will be represented by a diagram of the general appearance of
Fig. 29 or Fig. 30. That is to say: Starting from the fusion point of
component I., the system will pass, by progressive addition of component
II., to regions of lower temperature, until at last the cryohydric or eutectic
point is reached. On further addition of component II., the system will pass
to regions of higher temperature, the solid phase now being component II.
If the fused components are miscible with one another in all proportions a
continuous curve will be obtained leading up to the point of fusion of
component II. Slight changes of direction, it is true, due to changes in the
crystalline form, may be found along this curve, but throughout its whole
course there will be but one liquid phase. If, on the other hand, the fused
components are not miscible in all proportions, then the second curve will
exhibit a marked discontinuity, and two liquid phases will make their
appearance.
CHAPTER VIII
SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE
COMPONENTS BEING VOLATILE
B.—Hydrated Salt and Water.
In the preceding chapter we discussed the behaviour of systems formed of
two components, only one of which was volatile, in those cases where the
two components separated from solution in the pure state. In the present
chapter we shall consider those systems in which combination between the
components can occur with the formation of definite compounds; such as
are found in the case of crystalline salt hydrates. Since a not inconsiderable
amount of study has been devoted to the systems formed by hydrated salts
and water, systems which are of great chemical interest and importance, the
behaviour of these will first call for discussion in some detail, and it will be
measurable vapour pressure. A similar behaviour will, for example, be
found in the case of many pairs of organic substances; and in all cases the
equilibria will be represented by a diagram of the general appearance of
Fig. 29 or Fig. 30. That is to say: Starting from the fusion point of
component I., the system will pass, by progressive addition of component
II., to regions of lower temperature, until at last the cryohydric or eutectic
point is reached. On further addition of component II., the system will pass
to regions of higher temperature, the solid phase now being component II.
If the fused components are miscible with one another in all proportions a
continuous curve will be obtained leading up to the point of fusion of
component II. Slight changes of direction, it is true, due to changes in the
crystalline form, may be found along this curve, but throughout its whole
course there will be but one liquid phase. If, on the other hand, the fused
components are not miscible in all proportions, then the second curve will
exhibit a marked discontinuity, and two liquid phases will make their
appearance.
CHAPTER VIII
SOLUTIONS OF SOLIDS IN LIQUIDS, ONLY ONE OF THE
COMPONENTS BEING VOLATILE
B.—Hydrated Salt and Water.
In the preceding chapter we discussed the behaviour of systems formed of
two components, only one of which was volatile, in those cases where the
two components separated from solution in the pure state. In the present
chapter we shall consider those systems in which combination between the
components can occur with the formation of definite compounds; such as
are found in the case of crystalline salt hydrates. Since a not inconsiderable
amount of study has been devoted to the systems formed by hydrated salts
and water, systems which are of great chemical interest and importance, the
behaviour of these will first call for discussion in some detail, and it will be
Page 118
found later that the relationships which exist in such systems appear also in
a large number of other two-component systems.
The systems belonging to this group may be divided into two classes
according as the compounds formed possess a definite melting point, i.e.
form a liquid phase of the same composition, or do not do so. We shall
consider the latter first.
1. The Compounds formed do not have a Definite Melting Point.
Concentration-Temperature Diagram.—In the case of salts which can
form crystalline hydrates, the temperature-concentration diagram,
representing the equilibria of the different possible systems, must
necessarily be somewhat more complicated than where no such
combination of the components occurs. For, as has already been pointed
out, each substance has its own solubility curve; and there will therefore be
as many solubility curves as there are solid phases possible, the curve for
each particular solid phase being continuous so long as it remains
unchanged in contact with the solution. As an example of the relationships
met with in such cases, we shall first of all consider the systems formed of
sodium sulphate and water.
Fig. 33.
Sodium Sulphate and Water.—At the ordinary temperatures, sodium
sulphate crystallises from water with ten molecules of water of
crystallisation, forming Glauber's salt. On determining the solubility of this
salt in water, it is found that the solubility increases as the temperature rises,
the values of the solubility, represented graphically by the curve AC (Fig.
33), being given in the following table.[209] The numbers denote grams of
sodium sulphate, calculated as anhydrous salt, dissolved by 100 grams of
water.
a large number of other two-component systems.
The systems belonging to this group may be divided into two classes
according as the compounds formed possess a definite melting point, i.e.
form a liquid phase of the same composition, or do not do so. We shall
consider the latter first.
1. The Compounds formed do not have a Definite Melting Point.
Concentration-Temperature Diagram.—In the case of salts which can
form crystalline hydrates, the temperature-concentration diagram,
representing the equilibria of the different possible systems, must
necessarily be somewhat more complicated than where no such
combination of the components occurs. For, as has already been pointed
out, each substance has its own solubility curve; and there will therefore be
as many solubility curves as there are solid phases possible, the curve for
each particular solid phase being continuous so long as it remains
unchanged in contact with the solution. As an example of the relationships
met with in such cases, we shall first of all consider the systems formed of
sodium sulphate and water.
Fig. 33.
Sodium Sulphate and Water.—At the ordinary temperatures, sodium
sulphate crystallises from water with ten molecules of water of
crystallisation, forming Glauber's salt. On determining the solubility of this
salt in water, it is found that the solubility increases as the temperature rises,
the values of the solubility, represented graphically by the curve AC (Fig.
33), being given in the following table.[209] The numbers denote grams of
sodium sulphate, calculated as anhydrous salt, dissolved by 100 grams of
water.
Page 119
Solubility of Na2SO4,10H2O.
Temperature. Solubility.
0° 5.02
10° 9.00
15° 13.20
18° 16.80
20° 19.40
25° 28.00
30° 40.00
33° 50.76
34° 55.00
On continuing the investigation at higher temperatures, it was found that the
solubility no longer increased, but decreased with rise of temperature. At
the same time, it was observed that the solid phase was now different from
that in contact with the solution at temperatures below 33°; for whereas in
the latter case the solid phase was sodium sulphate decahydrate, at
temperatures above 33° the solid phase was the anhydrous salt. The course
of the solubility curve of anhydrous sodium sulphate is shown by BD, and
the values of the solubility are given in the following table:—[210]
Solubility of Anhydrous Sodium Sulphate.
Temperature. Solubility.
18° 53.25
20° 52.76
25° 51.53
30° 50.37
33° 49.71
34° 49.53
36° 49.27
40.15° 48.78
50.40° 46.82
Temperature. Solubility.
0° 5.02
10° 9.00
15° 13.20
18° 16.80
20° 19.40
25° 28.00
30° 40.00
33° 50.76
34° 55.00
On continuing the investigation at higher temperatures, it was found that the
solubility no longer increased, but decreased with rise of temperature. At
the same time, it was observed that the solid phase was now different from
that in contact with the solution at temperatures below 33°; for whereas in
the latter case the solid phase was sodium sulphate decahydrate, at
temperatures above 33° the solid phase was the anhydrous salt. The course
of the solubility curve of anhydrous sodium sulphate is shown by BD, and
the values of the solubility are given in the following table:—[210]
Solubility of Anhydrous Sodium Sulphate.
Temperature. Solubility.
18° 53.25
20° 52.76
25° 51.53
30° 50.37
33° 49.71
34° 49.53
36° 49.27
40.15° 48.78
50.40° 46.82
Page 120
As is evident from the figure, the solubility curve which is obtained when
anhydrous sodium sulphate is present as the solid phase, cuts the curve
representing the solubility of the decahydrate, at a temperature of about 33°.
If a solution of sodium sulphate which has been saturated at a temperature
of about 34° be cooled down to a temperature below 17°, while care is
taken that the solution is protected against access of particles of Glauber's
salt, crystals of a second hydrate of sodium sulphate, having the
composition Na2SO4,7H2O, separate out. On determining the composition
of the solutions in equilibrium with this hydrate at different temperatures,
the following values were obtained, these values being represented by the
curve FE (Fig. 33):—
Solubility of Na2SO4,7H2O.
Temperature. Solubility.
0° 19.62
10° 30.49
15° 37.43
18° 41.63
20° 44.73
25° 52.94
26° 54.97
Since, as has already been stated, each solid substance has its own solubility
curve, there are three separate curves to be considered in the case of sodium
sulphate and water. Where two curves cut, the solution must be saturated
with respect to two solid phases; at the point B, therefore, the point of
intersection of the solubility curve of anhydrous sodium sulphate with that
of the decahydrate, the solution must be saturated with respect to these two
solid substances. But a system of two components existing in four phases,
anhydrous salt—hydrated salt—solution—vapour, is invariant; and this
invariability will remain even if only three phases are present, provided that
one of the factors, pressure, temperature, or concentration of components
retains a constant value. This is the case when solubilities are determined in
open vessels; the pressure is then equal to atmospheric pressure. Under
these circumstances, then, the system, anhydrous sodium sulphate—
anhydrous sodium sulphate is present as the solid phase, cuts the curve
representing the solubility of the decahydrate, at a temperature of about 33°.
If a solution of sodium sulphate which has been saturated at a temperature
of about 34° be cooled down to a temperature below 17°, while care is
taken that the solution is protected against access of particles of Glauber's
salt, crystals of a second hydrate of sodium sulphate, having the
composition Na2SO4,7H2O, separate out. On determining the composition
of the solutions in equilibrium with this hydrate at different temperatures,
the following values were obtained, these values being represented by the
curve FE (Fig. 33):—
Solubility of Na2SO4,7H2O.
Temperature. Solubility.
0° 19.62
10° 30.49
15° 37.43
18° 41.63
20° 44.73
25° 52.94
26° 54.97
Since, as has already been stated, each solid substance has its own solubility
curve, there are three separate curves to be considered in the case of sodium
sulphate and water. Where two curves cut, the solution must be saturated
with respect to two solid phases; at the point B, therefore, the point of
intersection of the solubility curve of anhydrous sodium sulphate with that
of the decahydrate, the solution must be saturated with respect to these two
solid substances. But a system of two components existing in four phases,
anhydrous salt—hydrated salt—solution—vapour, is invariant; and this
invariability will remain even if only three phases are present, provided that
one of the factors, pressure, temperature, or concentration of components
retains a constant value. This is the case when solubilities are determined in
open vessels; the pressure is then equal to atmospheric pressure. Under
these circumstances, then, the system, anhydrous sodium sulphate—
Page 121
decahydrate—solution, will possess no degree of freedom, and can exist,
therefore, only at one definite temperature and when the solution has a
certain definite composition. The temperature of this point is 32.482° on a
mercury thermometer, or 32.379° on the hydrogen thermometer.[211]
Suspended Transformation.—Although it is possible for the anhydrous
salt to make its appearance at the temperature of the quadruple point, it will
not necessarily do so; and it is therefore possible to follow the solubility
curve of sodium sulphate decahydrate to a higher temperature. Since,
however, the solubility of the decahydrate at temperatures above the
quadruple point is greater than that of the anhydrous salt, the solution which
is saturated with respect to the former will be supersaturated with respect
to the latter. On bringing a small quantity of the anhydrous salt in contact
with the solution, therefore, anhydrous salt will be deposited; and all the
hydrated salt present will ultimately undergo conversion into the anhydrous
salt, through the medium of the solution. In this case, as in all cases, the
solid phase, which is the most stable at the temperature of the experiment,
has at that temperature the least solubility.
Similarly, the solubility curve of anhydrous sodium sulphate has been
followed to temperatures below 32.5°. Below this temperature, however,
the solubility of this salt is greater than that of the decahydrate, and the
saturated solution of the anhydrous salt will therefore be supersaturated for
the decahydrate, and will deposit this salt if a "nucleus" is added to the
solution. From this we see that at temperatures above 32.5° the anhydrous
salt is the stable form, while the decahydrate is unstable (or metastable); at
temperatures below 32.5° the decahydrate is stable. This temperature,
therefore, is the transition temperature for decahydrate and anhydrous salt.
From Fig. 33 we see further that the solubility curve of the anhydrous salt
(which at all temperatures below 32.5° is metastable) is cut by the solubility
curve of the heptahydrate; and this point of intersection (at a temperature of
24.2°) must be the transition point for heptahydrate and anhydrous salt.
Since at all temperatures the solubility of the heptahydrate is greater than
that of the decahydrate, the former hydrate must be metastable with respect
to the latter; so that throughout its whole course the solubility curve of the
heptahydrate represents only metastable equilibria. Sodium sulphate,
therefore, forms only one stable hydrate, the decahydrate.
therefore, only at one definite temperature and when the solution has a
certain definite composition. The temperature of this point is 32.482° on a
mercury thermometer, or 32.379° on the hydrogen thermometer.[211]
Suspended Transformation.—Although it is possible for the anhydrous
salt to make its appearance at the temperature of the quadruple point, it will
not necessarily do so; and it is therefore possible to follow the solubility
curve of sodium sulphate decahydrate to a higher temperature. Since,
however, the solubility of the decahydrate at temperatures above the
quadruple point is greater than that of the anhydrous salt, the solution which
is saturated with respect to the former will be supersaturated with respect
to the latter. On bringing a small quantity of the anhydrous salt in contact
with the solution, therefore, anhydrous salt will be deposited; and all the
hydrated salt present will ultimately undergo conversion into the anhydrous
salt, through the medium of the solution. In this case, as in all cases, the
solid phase, which is the most stable at the temperature of the experiment,
has at that temperature the least solubility.
Similarly, the solubility curve of anhydrous sodium sulphate has been
followed to temperatures below 32.5°. Below this temperature, however,
the solubility of this salt is greater than that of the decahydrate, and the
saturated solution of the anhydrous salt will therefore be supersaturated for
the decahydrate, and will deposit this salt if a "nucleus" is added to the
solution. From this we see that at temperatures above 32.5° the anhydrous
salt is the stable form, while the decahydrate is unstable (or metastable); at
temperatures below 32.5° the decahydrate is stable. This temperature,
therefore, is the transition temperature for decahydrate and anhydrous salt.
From Fig. 33 we see further that the solubility curve of the anhydrous salt
(which at all temperatures below 32.5° is metastable) is cut by the solubility
curve of the heptahydrate; and this point of intersection (at a temperature of
24.2°) must be the transition point for heptahydrate and anhydrous salt.
Since at all temperatures the solubility of the heptahydrate is greater than
that of the decahydrate, the former hydrate must be metastable with respect
to the latter; so that throughout its whole course the solubility curve of the
heptahydrate represents only metastable equilibria. Sodium sulphate,
therefore, forms only one stable hydrate, the decahydrate.
Page 122
The solubility relations of sodium sulphate illustrate very clearly the
importance of the solid phase for the definition of saturation and
supersaturation. Since the solubility curve of the anhydrous salt has been
followed backwards to a temperature of about 18°, it is readily seen, from
Fig. 33, that at a temperature of, say, 20° three different saturated solutions
of sodium sulphate are possible, according as the anhydrous salt, the
heptahydrate or the decahydrate, is present as the solid phase. Two of these
solutions, however, would be metastable and supersaturated with respect to
the decahydrate.
Further, the behaviour of sodium sulphate and water furnishes a very good
example of the fact that a "break" in the solubility curve occurs when, and
only when, the solid phase undergoes change. So long as the decahydrate,
for example, remained unaltered in contact with the solution, the solubility
curve was continuous; but when the anhydrous salt appeared in the solid
phase, a distinct change in the direction of the solubility curve was
observed.
Dehydration by Means of Anhydrous Sodium Sulphate.—The change in
the relative stability of sodium sulphate decahydrate and anhydrous salt in
presence of water at a temperature of 32.5° explains why the latter salt
cannot be employed for dehydration purposes at temperatures above the
transition point. The dehydrating action of the anhydrous salt depends on
the formation of the decahydrate; but since at temperatures above 33° the
latter is unstable, and cannot be formed in presence of the anhydrous salt,
this salt cannot, of course, effect a dehydration above that temperature.
Pressure-Temperature Diagram.—The consideration of the pressure-
temperature relations of the two components, sodium sulphate and water,
must include not only the vapour pressure of the saturated solutions, but
also that of the crystalline hydrates. The vapour pressures of salt hydrates
have already been treated in a general manner (Chap. V.), so that it is only
necessary here to point out the connection between the two classes of
systems.
In most cases the vapour pressure of a salt hydrate, i.e. the vapour pressure
of the system hydrate—anhydrous salt (or lower hydrate)—vapour, is at all
temperatures lower than that of the system anhydrous salt (or lower
importance of the solid phase for the definition of saturation and
supersaturation. Since the solubility curve of the anhydrous salt has been
followed backwards to a temperature of about 18°, it is readily seen, from
Fig. 33, that at a temperature of, say, 20° three different saturated solutions
of sodium sulphate are possible, according as the anhydrous salt, the
heptahydrate or the decahydrate, is present as the solid phase. Two of these
solutions, however, would be metastable and supersaturated with respect to
the decahydrate.
Further, the behaviour of sodium sulphate and water furnishes a very good
example of the fact that a "break" in the solubility curve occurs when, and
only when, the solid phase undergoes change. So long as the decahydrate,
for example, remained unaltered in contact with the solution, the solubility
curve was continuous; but when the anhydrous salt appeared in the solid
phase, a distinct change in the direction of the solubility curve was
observed.
Dehydration by Means of Anhydrous Sodium Sulphate.—The change in
the relative stability of sodium sulphate decahydrate and anhydrous salt in
presence of water at a temperature of 32.5° explains why the latter salt
cannot be employed for dehydration purposes at temperatures above the
transition point. The dehydrating action of the anhydrous salt depends on
the formation of the decahydrate; but since at temperatures above 33° the
latter is unstable, and cannot be formed in presence of the anhydrous salt,
this salt cannot, of course, effect a dehydration above that temperature.
Pressure-Temperature Diagram.—The consideration of the pressure-
temperature relations of the two components, sodium sulphate and water,
must include not only the vapour pressure of the saturated solutions, but
also that of the crystalline hydrates. The vapour pressures of salt hydrates
have already been treated in a general manner (Chap. V.), so that it is only
necessary here to point out the connection between the two classes of
systems.
In most cases the vapour pressure of a salt hydrate, i.e. the vapour pressure
of the system hydrate—anhydrous salt (or lower hydrate)—vapour, is at all
temperatures lower than that of the system anhydrous salt (or lower
Page 123
hydrate)—solution—vapour. This, however, is not a necessity; and cases
are known where the vapour pressure of the former system is, under certain
circumstances, equal to or higher than that of the latter. An example of this
is found in sodium sulphate decahydrate.
On heating Na2SO4,10H2O, a point is reached at which the dissociation
pressure into anhydrous salt and water vapour becomes equal to the vapour
pressure of the saturated solution of the anhydrous salt, as is apparent from
the following measurements;[212] the differences in pressure being
expressed in millimetres of a particular oil.
Temperature: 29.0° 30.83° 31.79° 32.09° 32.35° 32.6°
Difference of
23.8 10.8 5.6 3.6 1.6 0
pressure:
At 32.6°, therefore, the vapour pressures of the two systems
Na2SO4,10H2O—Na2SO4—vapour
Na2SO4—solution—vapour
are equal; at this temperature the four phases, Na2SO4,10H2O; Na2SO4;
solution; vapour, can coexist. From this it is evident that when sodium
sulphate decahydrate is heated to 32.6°, the two new phases anhydrous salt
and solution will be formed (suspended transformation being supposed
excluded), and the hydrate will appear to undergo partial fusion; and during
the process of "melting" the vapour pressure and temperature will remain
constant.[213] This is, however, not a true but a so-called incongruent
melting point; for the composition of the liquid phase is not the same as that
of the solid. As has already been pointed out (p. 137), we are dealing here
with the transition point of the decahydrate and anhydrous salt, i.e. with the
reaction Na2SO4,10H2O Na2SO4 + 10H2O.
Since at the point of partial fusion of the decahydrate four phases can
coexist, the point is a quadruple point in a two-component system, and the
system at this point is therefore invariant. The temperature of this point is
therefore perfectly definite, and on this account the proposal has been made
to adopt this as a fixed point in thermometry.[214] The temperature is, of
are known where the vapour pressure of the former system is, under certain
circumstances, equal to or higher than that of the latter. An example of this
is found in sodium sulphate decahydrate.
On heating Na2SO4,10H2O, a point is reached at which the dissociation
pressure into anhydrous salt and water vapour becomes equal to the vapour
pressure of the saturated solution of the anhydrous salt, as is apparent from
the following measurements;[212] the differences in pressure being
expressed in millimetres of a particular oil.
Temperature: 29.0° 30.83° 31.79° 32.09° 32.35° 32.6°
Difference of
23.8 10.8 5.6 3.6 1.6 0
pressure:
At 32.6°, therefore, the vapour pressures of the two systems
Na2SO4,10H2O—Na2SO4—vapour
Na2SO4—solution—vapour
are equal; at this temperature the four phases, Na2SO4,10H2O; Na2SO4;
solution; vapour, can coexist. From this it is evident that when sodium
sulphate decahydrate is heated to 32.6°, the two new phases anhydrous salt
and solution will be formed (suspended transformation being supposed
excluded), and the hydrate will appear to undergo partial fusion; and during
the process of "melting" the vapour pressure and temperature will remain
constant.[213] This is, however, not a true but a so-called incongruent
melting point; for the composition of the liquid phase is not the same as that
of the solid. As has already been pointed out (p. 137), we are dealing here
with the transition point of the decahydrate and anhydrous salt, i.e. with the
reaction Na2SO4,10H2O Na2SO4 + 10H2O.
Since at the point of partial fusion of the decahydrate four phases can
coexist, the point is a quadruple point in a two-component system, and the
system at this point is therefore invariant. The temperature of this point is
therefore perfectly definite, and on this account the proposal has been made
to adopt this as a fixed point in thermometry.[214] The temperature is, of
Page 124
course, practically the same as that at which the two solubility curves
intersect (p. 112). If, however, the vapour phase disappears, the system
becomes univariant, and the equilibrium temperature undergoes change
with change of pressure. The transition curve has been determined by
Tammann,[215] and shown to pass through a point of maximum temperature.
Fig. 34.
The vapour pressure of the different systems of sodium sulphate and water
can best be studied with the help of the diagram in Fig. 34.[216] The curve
ABCD represents the vapour-pressure curve of the saturated solution of
anhydrous sodium sulphate. GC is the pressure curve of decahydrate +
anhydrous salt, which, as we have seen, cuts the curve ABCD at the
transition temperature, 32.6°. Since at this point the solution is saturated
with respect to both the anhydrous salt and the decahydrate, the vapour-
pressure curve of the saturated solution of the latter must also pass through
the point C.[217] As at temperatures below this point the solubility of the
decahydrate is less than that of the anhydrous salt, the vapour pressure of
the solution will, in accordance with Babo's law (p. 126), be higher than
that of the solution of the anhydrous salt; which was also found
experimentally to be the case (curve HC).
In connection with the vapour pressure of the saturated solutions of the
anhydrous salt and the decahydrate, attention must be drawn to a
conspicuous deviation from what was found to hold in the case of one-
component systems in which a vapour phase was present (p. 31). There, it
was seen that the vapour pressure of the more stable system was always
lower than that of the less stable; in the present case, however, we find that
this is no longer so. We have already learned that at temperatures below
32.5° the system decahydrate—solution—vapour is more stable than the
system anhydrous salt—solution—vapour; but the vapour pressure of the
intersect (p. 112). If, however, the vapour phase disappears, the system
becomes univariant, and the equilibrium temperature undergoes change
with change of pressure. The transition curve has been determined by
Tammann,[215] and shown to pass through a point of maximum temperature.
Fig. 34.
The vapour pressure of the different systems of sodium sulphate and water
can best be studied with the help of the diagram in Fig. 34.[216] The curve
ABCD represents the vapour-pressure curve of the saturated solution of
anhydrous sodium sulphate. GC is the pressure curve of decahydrate +
anhydrous salt, which, as we have seen, cuts the curve ABCD at the
transition temperature, 32.6°. Since at this point the solution is saturated
with respect to both the anhydrous salt and the decahydrate, the vapour-
pressure curve of the saturated solution of the latter must also pass through
the point C.[217] As at temperatures below this point the solubility of the
decahydrate is less than that of the anhydrous salt, the vapour pressure of
the solution will, in accordance with Babo's law (p. 126), be higher than
that of the solution of the anhydrous salt; which was also found
experimentally to be the case (curve HC).
In connection with the vapour pressure of the saturated solutions of the
anhydrous salt and the decahydrate, attention must be drawn to a
conspicuous deviation from what was found to hold in the case of one-
component systems in which a vapour phase was present (p. 31). There, it
was seen that the vapour pressure of the more stable system was always
lower than that of the less stable; in the present case, however, we find that
this is no longer so. We have already learned that at temperatures below
32.5° the system decahydrate—solution—vapour is more stable than the
system anhydrous salt—solution—vapour; but the vapour pressure of the
Page 125
latter system is, as has just been stated, lower than that of the former. At
temperatures above the transition point the vapour pressure of the saturated
solution of the decahydrate will be lower than that of the saturated solution
of the anhydrous salt.
This behaviour depends on the fact that the less stable form is the more
soluble, and that the diminution of the vapour pressure increases with the
amount of salt dissolved.
With regard to sodium sulphate heptahydrate the same considerations will
hold as in the case of the decahydrate. Since at 24° the four phases
heptahydrate, anhydrous salt, solution, vapour can coexist, the vapour-
pressure curves of the systems hydrate—anhydrous salt—vapour (curve
EB) and hydrate—solution—vapour (curve FB) must cut the pressure curve
of the saturated solution of the anhydrous salt at the above temperature, as
represented in Fig. 34 by the point B. This constitutes, therefore, a second
quadruple point, which is, however, metastable.
From the diagram it is also evident that the dissociation pressure of the
heptahydrate is higher than that of the decahydrate, although it contains less
water of crystallization. The system heptahydrate—anhydrous salt—vapour
must be metastable with respect to the system decahydrate—anhydrous salt
—vapour, and will pass into the latter.[218] Whether or not there is a
temperature at which the vapour-pressure curves of the two systems
intersect, and below which the heptahydrate becomes the more stable form,
is not known.
In the case of sodium sulphate there is only one stable hydrate. Other salts
are known which exhibit a similar behaviour; and we shall therefore expect
that the solubility relationships will be represented by a diagram similar to
that for sodium sulphate. A considerable number of such cases have, indeed,
been found,[219] and in some cases there is more than one metastable
hydrate. This is found, for example, in the case of nickel iodate,[220] the
solubility curves for which are given in Fig. 35. As can be seen from the
figure, suspended transformation occurs, the solubility curves having in
some cases been followed to a considerable distance beyond the transition
point. One of the most brilliant examples, however, of suspended
transformation in the case of salt hydrates, and the sluggish transition from
temperatures above the transition point the vapour pressure of the saturated
solution of the decahydrate will be lower than that of the saturated solution
of the anhydrous salt.
This behaviour depends on the fact that the less stable form is the more
soluble, and that the diminution of the vapour pressure increases with the
amount of salt dissolved.
With regard to sodium sulphate heptahydrate the same considerations will
hold as in the case of the decahydrate. Since at 24° the four phases
heptahydrate, anhydrous salt, solution, vapour can coexist, the vapour-
pressure curves of the systems hydrate—anhydrous salt—vapour (curve
EB) and hydrate—solution—vapour (curve FB) must cut the pressure curve
of the saturated solution of the anhydrous salt at the above temperature, as
represented in Fig. 34 by the point B. This constitutes, therefore, a second
quadruple point, which is, however, metastable.
From the diagram it is also evident that the dissociation pressure of the
heptahydrate is higher than that of the decahydrate, although it contains less
water of crystallization. The system heptahydrate—anhydrous salt—vapour
must be metastable with respect to the system decahydrate—anhydrous salt
—vapour, and will pass into the latter.[218] Whether or not there is a
temperature at which the vapour-pressure curves of the two systems
intersect, and below which the heptahydrate becomes the more stable form,
is not known.
In the case of sodium sulphate there is only one stable hydrate. Other salts
are known which exhibit a similar behaviour; and we shall therefore expect
that the solubility relationships will be represented by a diagram similar to
that for sodium sulphate. A considerable number of such cases have, indeed,
been found,[219] and in some cases there is more than one metastable
hydrate. This is found, for example, in the case of nickel iodate,[220] the
solubility curves for which are given in Fig. 35. As can be seen from the
figure, suspended transformation occurs, the solubility curves having in
some cases been followed to a considerable distance beyond the transition
point. One of the most brilliant examples, however, of suspended
transformation in the case of salt hydrates, and the sluggish transition from
Page 126
the less stable to the more stable form, is found in the case of the hydrates
of calcium chromate.[221]
Fig. 35.
In the preceding cases, the dissociation-pressure curve of the hydrated salt
cuts the vapour-pressure curve of the saturated solution of the anhydrous
salt. It can, however, happen that the dissociation-pressure curve of one
hydrate cuts the solubility curve, not of the anhydrous salt, but of a lower
hydrate; in this case there will be more than one stable hydrate, each having
a stable solubility curve; and these curves will intersect at the temperature
of the transition point. Various examples of this behaviour are known, and
we choose for illustration the solubility relationships of barium acetate and
its hydrates[222] (Fig. 36).
Fig. 36.
At temperatures above 0°, barium acetate can form two stable hydrates, a
trihydrate and a monohydrate. The solubility of the trihydrate increases very
rapidly with rise of temperature, and has been determined up to 26.1°. At
temperatures above 24.7°, however, the trihydrate is metastable with respect
to the monohydrate; for at this temperature the solubility curve of the latter
hydrate cuts that of the former. This is, therefore, the transition temperature
of calcium chromate.[221]
Fig. 35.
In the preceding cases, the dissociation-pressure curve of the hydrated salt
cuts the vapour-pressure curve of the saturated solution of the anhydrous
salt. It can, however, happen that the dissociation-pressure curve of one
hydrate cuts the solubility curve, not of the anhydrous salt, but of a lower
hydrate; in this case there will be more than one stable hydrate, each having
a stable solubility curve; and these curves will intersect at the temperature
of the transition point. Various examples of this behaviour are known, and
we choose for illustration the solubility relationships of barium acetate and
its hydrates[222] (Fig. 36).
Fig. 36.
At temperatures above 0°, barium acetate can form two stable hydrates, a
trihydrate and a monohydrate. The solubility of the trihydrate increases very
rapidly with rise of temperature, and has been determined up to 26.1°. At
temperatures above 24.7°, however, the trihydrate is metastable with respect
to the monohydrate; for at this temperature the solubility curve of the latter
hydrate cuts that of the former. This is, therefore, the transition temperature
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for the trihydrate and monohydrate. The solubility curve of the
monohydrate succeeds that of the trihydrate, and exhibits a conspicuous
point of minimum solubility at about 30°. Below 24.7° the monohydrate is
the less stable hydrate, but its solubility has been determined to a
temperature of 22°. At 41° the solubility curve of the monohydrate
intersects that of the anhydrous salt, and this is therefore the transition
temperature for the monohydrate and anhydrous salt. Above this
temperature the anhydrous salt is the stable solid phase. Its solubility curve
also passes through a minimum.
The diagram of solubilities of barium acetate not only illustrates the way in
which the solubility curves of the different stable hydrates of a salt succeed
one another, but it has also an interest and importance from another point of
view. In Fig. 36 there is also shown a faintly drawn curve which is
continuous throughout its whole course. This curve represents the solubility
of barium acetate as determined by Krasnicki.[223] Since, however, three
different solid phases can exist under the conditions of experiment, it is
evident, from what has already been stated (p. 111), that the different
equilibria between barium acetate and water could not be represented by
one continuous curve.
Another point which these experiments illustrate and which it is of the
highest importance to bear in mind is, that in making determinations of the
solubility of salts which are capable of forming hydrates, it is not only
necessary to determine the composition of the solution, but it is of equal
importance to determine the composition of the solid phase in contact with
it. In view of the fact, also, that the solution equilibrium is in many cases
established with comparative slowness, it is necessary to confirm the point
of equilibrium, either by approaching it from higher as well as from lower
temperatures, or by actually determining the rate with which the condition
of equilibrium is attained. This can be accomplished by actual weighing of
the dissolved salt or by determinations of the density of the solution, as well
as by other methods.
2. The Compounds formed have a Definite Melting Point.
In the cases which have just been considered we saw that the salt hydrates
on being heated did not undergo complete fusion, but that a solid was
monohydrate succeeds that of the trihydrate, and exhibits a conspicuous
point of minimum solubility at about 30°. Below 24.7° the monohydrate is
the less stable hydrate, but its solubility has been determined to a
temperature of 22°. At 41° the solubility curve of the monohydrate
intersects that of the anhydrous salt, and this is therefore the transition
temperature for the monohydrate and anhydrous salt. Above this
temperature the anhydrous salt is the stable solid phase. Its solubility curve
also passes through a minimum.
The diagram of solubilities of barium acetate not only illustrates the way in
which the solubility curves of the different stable hydrates of a salt succeed
one another, but it has also an interest and importance from another point of
view. In Fig. 36 there is also shown a faintly drawn curve which is
continuous throughout its whole course. This curve represents the solubility
of barium acetate as determined by Krasnicki.[223] Since, however, three
different solid phases can exist under the conditions of experiment, it is
evident, from what has already been stated (p. 111), that the different
equilibria between barium acetate and water could not be represented by
one continuous curve.
Another point which these experiments illustrate and which it is of the
highest importance to bear in mind is, that in making determinations of the
solubility of salts which are capable of forming hydrates, it is not only
necessary to determine the composition of the solution, but it is of equal
importance to determine the composition of the solid phase in contact with
it. In view of the fact, also, that the solution equilibrium is in many cases
established with comparative slowness, it is necessary to confirm the point
of equilibrium, either by approaching it from higher as well as from lower
temperatures, or by actually determining the rate with which the condition
of equilibrium is attained. This can be accomplished by actual weighing of
the dissolved salt or by determinations of the density of the solution, as well
as by other methods.
2. The Compounds formed have a Definite Melting Point.
In the cases which have just been considered we saw that the salt hydrates
on being heated did not undergo complete fusion, but that a solid was
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deposited consisting of a lower hydrate or of the anhydrous salt. It has,
however, been long known that certain crystalline salt hydrates (e.g. sodium
thiosulphate, Na2S2O3,5H2O, sodium acetate, NaC2H3O2,3H2O) melt
completely in their water of crystallization, and yield a liquid of the same
composition as the crystalline salt. In the case of sodium thiosulphate
pentahydrate the temperature of liquefaction is 56°; in the case of sodium
acetate trihydrate, 58°. These two salts, therefore, have a definite melting
point. For the purpose of studying the behaviour of such salt hydrates, we
shall choose not the cases which have just been mentioned, but two others
which have been more fully studied, viz. the hydrates of calcium chloride
and of ferric chloride.
Solubility Curve of Calcium Chloride Hexahydrate.[224]—Although
calcium chloride forms several hydrates, each of which possesses its own
solubility, it is nevertheless the solubility curve of the hexahydrate which
will chiefly interest us at present, and we shall therefore first discuss that
curve by itself.
however, been long known that certain crystalline salt hydrates (e.g. sodium
thiosulphate, Na2S2O3,5H2O, sodium acetate, NaC2H3O2,3H2O) melt
completely in their water of crystallization, and yield a liquid of the same
composition as the crystalline salt. In the case of sodium thiosulphate
pentahydrate the temperature of liquefaction is 56°; in the case of sodium
acetate trihydrate, 58°. These two salts, therefore, have a definite melting
point. For the purpose of studying the behaviour of such salt hydrates, we
shall choose not the cases which have just been mentioned, but two others
which have been more fully studied, viz. the hydrates of calcium chloride
and of ferric chloride.
Solubility Curve of Calcium Chloride Hexahydrate.[224]—Although
calcium chloride forms several hydrates, each of which possesses its own
solubility, it is nevertheless the solubility curve of the hexahydrate which
will chiefly interest us at present, and we shall therefore first discuss that
curve by itself.
Page 129
Fig. 37.
The solubility of this salt has been determined from the cryohydric point,
which lies at about -55°, up to the melting point of the salt.[225] The solubility
increases with rise of temperature, as is shown by the figures in the following
table, and by the (diagrammatic) curve AB in Fig. 37. In the table, the numbers
under the heading "solubility" denote the number of grams of CaCl2 dissolved
in 100 grams of water; those under the heading "composition," the number of
gram-molecules of water in the solution to one gram-molecule of CaCl2.
Solubility of Calcium Chloride Hexahydrate.
Temperature. Solubility. Composition.
-55° 42.5 14.5
-25° 50.0 12.3
-10° 55.0 11.2
0° 59.5 10.37
10° 65.0 9.49
20° 74.5 8.28
25° 82.0 7.52
28.5° 90.5 6.81
29.5° 95.5 6.46
30.2° 102.7 6.00
29.6° 109.0 5.70
29.2° 112.8 5.41
So far as the first portion of the curve is concerned, it resembles the most
general type of solubility curve. In the present case the solubility is so great
and increases so rapidly with rise of temperature, that a point is reached at
which the water of crystallization of the salt is sufficient for its complete
solution. This temperature is 30.2°; and since the composition of the solution is
the same as that of the solid salt, viz. 1 mol. of CaCl2 to 6 mols. of water, this
The solubility of this salt has been determined from the cryohydric point,
which lies at about -55°, up to the melting point of the salt.[225] The solubility
increases with rise of temperature, as is shown by the figures in the following
table, and by the (diagrammatic) curve AB in Fig. 37. In the table, the numbers
under the heading "solubility" denote the number of grams of CaCl2 dissolved
in 100 grams of water; those under the heading "composition," the number of
gram-molecules of water in the solution to one gram-molecule of CaCl2.
Solubility of Calcium Chloride Hexahydrate.
Temperature. Solubility. Composition.
-55° 42.5 14.5
-25° 50.0 12.3
-10° 55.0 11.2
0° 59.5 10.37
10° 65.0 9.49
20° 74.5 8.28
25° 82.0 7.52
28.5° 90.5 6.81
29.5° 95.5 6.46
30.2° 102.7 6.00
29.6° 109.0 5.70
29.2° 112.8 5.41
So far as the first portion of the curve is concerned, it resembles the most
general type of solubility curve. In the present case the solubility is so great
and increases so rapidly with rise of temperature, that a point is reached at
which the water of crystallization of the salt is sufficient for its complete
solution. This temperature is 30.2°; and since the composition of the solution is
the same as that of the solid salt, viz. 1 mol. of CaCl2 to 6 mols. of water, this
Page 130
temperature must be the melting point of the hexahydrate. At this point the
hydrate will fuse or the solution will solidify without change of temperature
and without change of composition. Such a melting point is called a congruent
melting point.
But the solubility curve of calcium chloride hexahydrate differs markedly from
the other solubility curves hitherto considered in that it possesses a retroflex
portion, represented in the figure by BC. As is evident from the figure,
therefore, calcium chloride hexahydrate exhibits the peculiar and, as it was at
first thought, impossible behaviour that it can be in equilibrium at one and the
same temperature with two different solutions, one of which contains more, the
other less, water than the solid hydrate; for it must be remembered that
throughout the whole course of the curve ABC the solid phase present in
equilibrium with the solution is the hexahydrate.
Such a behaviour, however, on the part of calcium chloride hexahydrate will
appear less strange if one reflects that the melting point of the hydrate will,
like the melting point of other substances, be lowered by the addition of a
second substance. If, therefore, water is added to the hydrate at its melting
point, the temperature at which the solid hydrate will be in equilibrium with
the liquid phase (solution) will be lowered; or if, on the other hand, anhydrous
calcium chloride is added to the hydrate at its melting point (or what is the
same thing, if water is removed from the solution), the temperature at which
the hydrate will be in equilibrium with the liquid will also be lowered; i.e. the
hydrate will melt at a lower temperature. In the former case we have the
hydrate in equilibrium with a solution containing more water, in the latter case
with a solution containing less water than is contained in the hydrate itself.
It has already been stated (p. 109) that the solubility curve (in general, the
equilibrium curve) is continuous so long as the solid phase remains
unchanged; and we shall therefore expect that the curve ABC will be
continuous. Formerly, however, it was considered by some that the curve was
not continuous, but that the melting point is the point of intersection of two
curves, a solubility curve and a fusion curve. Although the earlier solubility
determinations were insufficient to decide this point conclusively, more recent
investigation has proved beyond doubt that the curve is continuous and
exhibits no break.[226]
Although in taking up the discussion of the equilibria between calcium
chloride and water, it was desired especially to call attention to the form of the
hydrate will fuse or the solution will solidify without change of temperature
and without change of composition. Such a melting point is called a congruent
melting point.
But the solubility curve of calcium chloride hexahydrate differs markedly from
the other solubility curves hitherto considered in that it possesses a retroflex
portion, represented in the figure by BC. As is evident from the figure,
therefore, calcium chloride hexahydrate exhibits the peculiar and, as it was at
first thought, impossible behaviour that it can be in equilibrium at one and the
same temperature with two different solutions, one of which contains more, the
other less, water than the solid hydrate; for it must be remembered that
throughout the whole course of the curve ABC the solid phase present in
equilibrium with the solution is the hexahydrate.
Such a behaviour, however, on the part of calcium chloride hexahydrate will
appear less strange if one reflects that the melting point of the hydrate will,
like the melting point of other substances, be lowered by the addition of a
second substance. If, therefore, water is added to the hydrate at its melting
point, the temperature at which the solid hydrate will be in equilibrium with
the liquid phase (solution) will be lowered; or if, on the other hand, anhydrous
calcium chloride is added to the hydrate at its melting point (or what is the
same thing, if water is removed from the solution), the temperature at which
the hydrate will be in equilibrium with the liquid will also be lowered; i.e. the
hydrate will melt at a lower temperature. In the former case we have the
hydrate in equilibrium with a solution containing more water, in the latter case
with a solution containing less water than is contained in the hydrate itself.
It has already been stated (p. 109) that the solubility curve (in general, the
equilibrium curve) is continuous so long as the solid phase remains
unchanged; and we shall therefore expect that the curve ABC will be
continuous. Formerly, however, it was considered by some that the curve was
not continuous, but that the melting point is the point of intersection of two
curves, a solubility curve and a fusion curve. Although the earlier solubility
determinations were insufficient to decide this point conclusively, more recent
investigation has proved beyond doubt that the curve is continuous and
exhibits no break.[226]
Although in taking up the discussion of the equilibria between calcium
chloride and water, it was desired especially to call attention to the form of the
Page 131
solubility curve in the case of salt hydrates possessing a definite melting point,
nevertheless, for the sake of completeness, brief mention may be made of the
other systems which these two components can form.
Fig. 38.
Besides the hexahydrate, the solubility curve of which has already been
described, calcium chloride can also crystallize in two different forms, each of
which contains four molecules of water of crystallization; these are
distinguished as α-tetrahydrate, and β-tetrahydrate. Two other hydrates are
also known, viz. a dihydrate and a monohydrate. The solubility curves of these
different hydrates are given in Fig. 38.
On following the solubility curve of the hexahydrate from the ordinary
temperature upwards, it is seen that at a temperature of 29.8° represented by
the point H, it cuts the solubility curve of the α-tetrahydrate. This point is
therefore a quadruple point at which the four phases hexahydrate, α-
tetrahydrate, solution, and vapour can coexist. It is also the transition point for
these two hydrates. Since, at temperatures above 29.8°, the α-tetrahydrate is
the stable form, it is evident from the data given before (p. 146), as also from
Fig. 38, that the portion of the solubility curve of the hexahydrate lying above
this temperature represents metastable equilibria. The realization of the
metastable melting point of the hexahydrate is, therefore, due to suspended
nevertheless, for the sake of completeness, brief mention may be made of the
other systems which these two components can form.
Fig. 38.
Besides the hexahydrate, the solubility curve of which has already been
described, calcium chloride can also crystallize in two different forms, each of
which contains four molecules of water of crystallization; these are
distinguished as α-tetrahydrate, and β-tetrahydrate. Two other hydrates are
also known, viz. a dihydrate and a monohydrate. The solubility curves of these
different hydrates are given in Fig. 38.
On following the solubility curve of the hexahydrate from the ordinary
temperature upwards, it is seen that at a temperature of 29.8° represented by
the point H, it cuts the solubility curve of the α-tetrahydrate. This point is
therefore a quadruple point at which the four phases hexahydrate, α-
tetrahydrate, solution, and vapour can coexist. It is also the transition point for
these two hydrates. Since, at temperatures above 29.8°, the α-tetrahydrate is
the stable form, it is evident from the data given before (p. 146), as also from
Fig. 38, that the portion of the solubility curve of the hexahydrate lying above
this temperature represents metastable equilibria. The realization of the
metastable melting point of the hexahydrate is, therefore, due to suspended
Page 132
transformation. At the transition point, 29.8°, the solubility of the hexahydrate
and α-tetrahydrate is 100.6 parts of CaCl2 in 100 parts of water.
The retroflex portion of the solubility curve of the hexahydrate extends to only
1° below the melting point of the hydrate. At 29.2° crystals of a new hydrate,
β-tetrahydrate, separate out, and the solution, which now contains 112.8 parts
of CaCl2 to 100 parts of water, is saturated with respect to the two hydrates.
Throughout its whole extent the solubility curve EDF of the β-tetrahydrate
represents metastable equilibria. The upper limit of the solubility curve of β-
tetrahydrate is reached at 38.4° (F), the point of intersection with the curve for
the dihydrate.
Above 29.8° the stable hydrate is the α-tetrahydrate; and its solubility curve
extends to 45.3° (K), at which temperature it cuts the solubility curve of the
dihydrate. The curve of the latter hydrate extends to 175.5° (L), and is then
succeeded by the curve for the monohydrate. The solubility curve of the
anhydrous salt does not begin until a temperature of about 260°. The whole
diagram, therefore, shows a succession of stable hydrates, a metastable
hydrate, a metastable melting point and retroflex solubility curve.
Pressure-Temperature Diagram.—The complete study of the equilibria
between the two components calcium chloride and water would require the
discussion of the vapour pressure of the different systems, and its variation
with the temperature. For our present purpose, however, such a discussion
would not be of great value, and will therefore be omitted here; in general, the
same relationships would be found as in the case of sodium sulphate (p. 138),
except that the rounded portion of the solubility curve of the hexahydrate
would be represented by a similar rounded portion in the pressure curve.[227]
As in the case of sodium sulphate, the transition points of the different
hydrates would be indicated by breaks in the curve of pressures. Finally,
mention may again be made of the difference of the pressure of dissociation of
the hexahydrate according as it becomes dehydrated to the α- or the β-
tetrahydrate (p. 88).
The Indifferent Point.—We have already seen that at 30.2° calcium chloride
hexahydrate melts congruently, and that, provided the pressure is maintained
constant, addition or withdrawal of heat will cause the complete liquefaction or
solidification, without the temperature of the system undergoing change. This
behaviour, therefore, is similar to, but is not quite the same as the fusion of a
and α-tetrahydrate is 100.6 parts of CaCl2 in 100 parts of water.
The retroflex portion of the solubility curve of the hexahydrate extends to only
1° below the melting point of the hydrate. At 29.2° crystals of a new hydrate,
β-tetrahydrate, separate out, and the solution, which now contains 112.8 parts
of CaCl2 to 100 parts of water, is saturated with respect to the two hydrates.
Throughout its whole extent the solubility curve EDF of the β-tetrahydrate
represents metastable equilibria. The upper limit of the solubility curve of β-
tetrahydrate is reached at 38.4° (F), the point of intersection with the curve for
the dihydrate.
Above 29.8° the stable hydrate is the α-tetrahydrate; and its solubility curve
extends to 45.3° (K), at which temperature it cuts the solubility curve of the
dihydrate. The curve of the latter hydrate extends to 175.5° (L), and is then
succeeded by the curve for the monohydrate. The solubility curve of the
anhydrous salt does not begin until a temperature of about 260°. The whole
diagram, therefore, shows a succession of stable hydrates, a metastable
hydrate, a metastable melting point and retroflex solubility curve.
Pressure-Temperature Diagram.—The complete study of the equilibria
between the two components calcium chloride and water would require the
discussion of the vapour pressure of the different systems, and its variation
with the temperature. For our present purpose, however, such a discussion
would not be of great value, and will therefore be omitted here; in general, the
same relationships would be found as in the case of sodium sulphate (p. 138),
except that the rounded portion of the solubility curve of the hexahydrate
would be represented by a similar rounded portion in the pressure curve.[227]
As in the case of sodium sulphate, the transition points of the different
hydrates would be indicated by breaks in the curve of pressures. Finally,
mention may again be made of the difference of the pressure of dissociation of
the hexahydrate according as it becomes dehydrated to the α- or the β-
tetrahydrate (p. 88).
The Indifferent Point.—We have already seen that at 30.2° calcium chloride
hexahydrate melts congruently, and that, provided the pressure is maintained
constant, addition or withdrawal of heat will cause the complete liquefaction or
solidification, without the temperature of the system undergoing change. This
behaviour, therefore, is similar to, but is not quite the same as the fusion of a
Page 133
simple substance such as ice; and the difference is due to the fact that in the
case of the hexahydrate the emission of vapour by the liquid phase causes an
alteration in the composition of the latter, owing to the non-volatility of the
calcium chloride; whereas in the case of ice this is, of course, not so.
Consider, however, for the present that the vapour phase is absent, and that we
are dealing with the two-phase system solid—solution. Then, since there are
two components, the system is bivariant. For any given value of the pressure,
therefore, we should expect that the system could exist at different
temperatures; which, indeed, is the case. It has, however, already been noted
that when the composition of the liquid phase becomes the same as that of the
solid, the system then behaves as a univariant system; for, at a given pressure,
the system solid—solution can exist only at one temperature, change of
temperature producing complete transformation in one or other direction. The
variability of the system has therefore been diminished.
This behaviour will perhaps be more clearly understood when one reflects that
since the composition of the two phases is the same, the system may be
regarded as being formed of one component, just as the system NH4Cl NH3
+ HCl was regarded as being composed of one component when the vapour
had the same total composition as the solid (p. 13). One component in two
phases, however, constitutes a univariant system, and we can therefore see that
calcium chloride hexahydrate in contact with solution of the same composition
will constitute a univariant system. The temperature of equilibrium will,
however, vary with the pressure;[228] if the latter is constant, the temperature
will also be constant.
A point such as has just been referred to, which represents the special
behaviour of a system of two (or more) components, in which the composition
of two phases becomes identical, is known as an indifferent point,[229] and it
has been shown[230] that at a given pressure the temperature in the indifferent
point is the maximum or minimum temperature possible at the particular
pressure[231] (cf. critical solution temperature). At such a point a system loses
one degree of freedom, or behaves like a system of the next lower order.
The Hydrates of Ferric Chloride.—A better illustration of the formation of
compounds possessing a definite melting point, and of the existence of
retroflex solubility curves, is afforded by the hydrates of ferric chloride, which
case of the hexahydrate the emission of vapour by the liquid phase causes an
alteration in the composition of the latter, owing to the non-volatility of the
calcium chloride; whereas in the case of ice this is, of course, not so.
Consider, however, for the present that the vapour phase is absent, and that we
are dealing with the two-phase system solid—solution. Then, since there are
two components, the system is bivariant. For any given value of the pressure,
therefore, we should expect that the system could exist at different
temperatures; which, indeed, is the case. It has, however, already been noted
that when the composition of the liquid phase becomes the same as that of the
solid, the system then behaves as a univariant system; for, at a given pressure,
the system solid—solution can exist only at one temperature, change of
temperature producing complete transformation in one or other direction. The
variability of the system has therefore been diminished.
This behaviour will perhaps be more clearly understood when one reflects that
since the composition of the two phases is the same, the system may be
regarded as being formed of one component, just as the system NH4Cl NH3
+ HCl was regarded as being composed of one component when the vapour
had the same total composition as the solid (p. 13). One component in two
phases, however, constitutes a univariant system, and we can therefore see that
calcium chloride hexahydrate in contact with solution of the same composition
will constitute a univariant system. The temperature of equilibrium will,
however, vary with the pressure;[228] if the latter is constant, the temperature
will also be constant.
A point such as has just been referred to, which represents the special
behaviour of a system of two (or more) components, in which the composition
of two phases becomes identical, is known as an indifferent point,[229] and it
has been shown[230] that at a given pressure the temperature in the indifferent
point is the maximum or minimum temperature possible at the particular
pressure[231] (cf. critical solution temperature). At such a point a system loses
one degree of freedom, or behaves like a system of the next lower order.
The Hydrates of Ferric Chloride.—A better illustration of the formation of
compounds possessing a definite melting point, and of the existence of
retroflex solubility curves, is afforded by the hydrates of ferric chloride, which
Page 134
not only possess definite points of fusion, but these melting points are stable. A
very brief description of the relations met with will suffice.[232]
Ferric chloride can form no less than four stable hydrates, viz. Fe2Cl6,12H2O,
Fe2Cl6,7H2O, Fe2Cl6,5H2O, and Fe2Cl6,4H2O, and each of these hydrates
possesses a definite, stable melting point. On analogy with the behaviour of
calcium chloride, therefore, we shall expect that the solubility curves of these
different hydrates will exhibit a series of temperature maxima; the points of
maximum temperature representing systems in which the composition of the
solid and liquid phases is the same. A graphical representation of the solubility
relations is given in Fig. 39, and the composition of the different saturated
solutions which can be formed is given in the following tables, the
composition being expressed in molecules of Fe2Cl6 to 100 molecules of
water. The figures printed in thick type refer to transition and melting points.
Fig. 39.
Composition of the Saturated Solutions of Ferric Chloride and its
Hydrates.
(The name placed at the head of each table is the solid phase.)
Ice.
Temperature. Composition.
±-55° ±2.75
-40° 2.37
-27.5° 1.90
-20.5° 1.64
very brief description of the relations met with will suffice.[232]
Ferric chloride can form no less than four stable hydrates, viz. Fe2Cl6,12H2O,
Fe2Cl6,7H2O, Fe2Cl6,5H2O, and Fe2Cl6,4H2O, and each of these hydrates
possesses a definite, stable melting point. On analogy with the behaviour of
calcium chloride, therefore, we shall expect that the solubility curves of these
different hydrates will exhibit a series of temperature maxima; the points of
maximum temperature representing systems in which the composition of the
solid and liquid phases is the same. A graphical representation of the solubility
relations is given in Fig. 39, and the composition of the different saturated
solutions which can be formed is given in the following tables, the
composition being expressed in molecules of Fe2Cl6 to 100 molecules of
water. The figures printed in thick type refer to transition and melting points.
Fig. 39.
Composition of the Saturated Solutions of Ferric Chloride and its
Hydrates.
(The name placed at the head of each table is the solid phase.)
Ice.
Temperature. Composition.
±-55° ±2.75
-40° 2.37
-27.5° 1.90
-20.5° 1.64
Page 135
-10° 1.00
0° 0
Fe2Cl6,12H2O.
Temperature. Composition.
-55° ±2.75
-41° 2.81
-27° 2.98
0° 4.13
10° 4.54
20° 5.10
30° 5.93
35° 6.78
36.5° 7.93
37° 8.33
36° 9.29
33° 10.45
30° 11.20
27·4° 12.15
20° 12.83
10° 13.20
8° 13.70
Fe2Cl6,7H2O.
Temperature. Composition.
20° 11.35
27·4° 12.15
32° 13.55
32.5° 14.29
30° 15.12
25° 15.54
Fe2Cl6,5H2O.
Temperature. Composition.
12° 12.87
0° 0
Fe2Cl6,12H2O.
Temperature. Composition.
-55° ±2.75
-41° 2.81
-27° 2.98
0° 4.13
10° 4.54
20° 5.10
30° 5.93
35° 6.78
36.5° 7.93
37° 8.33
36° 9.29
33° 10.45
30° 11.20
27·4° 12.15
20° 12.83
10° 13.20
8° 13.70
Fe2Cl6,7H2O.
Temperature. Composition.
20° 11.35
27·4° 12.15
32° 13.55
32.5° 14.29
30° 15.12
25° 15.54
Fe2Cl6,5H2O.
Temperature. Composition.
12° 12.87
Page 136
20° 13.95
27° 14.85
30° 15.12
35° 15.64
50° 17.50
55° 19.15
56° 20.00
55° 20.32
Fe2Cl6,4H2O
Temperature. Composition.
50° 19.96
55° 20.32
60° 20.70
69° 21.53
72.5° 23.35
73.5° 25.00
72.5° 26.15
70° 27.90
66° 29.20
Fe2Cl6 (ANHYDROUS).
Temperature. Composition.
66° 29.20
70° 29.42
75° 28.92
80° 29.20
100° 29.75
The lowest portion of the curve, AB, represents the equilibria between ice and
solutions containing ferric chloride. It represents, in other words, the lowering
of the fusion point of ice by addition of ferric chloride. At the point B (-55°),
the cryohydric point (p. 117) is reached, at which the solution is in equilibrium
with ice and ferric chloride dodecahydrate. As has already been shown, such a
point represents an invariant system; and the liquid phase will, therefore,
solidify to a mixture of ice and hydrate without change of temperature. If heat
27° 14.85
30° 15.12
35° 15.64
50° 17.50
55° 19.15
56° 20.00
55° 20.32
Fe2Cl6,4H2O
Temperature. Composition.
50° 19.96
55° 20.32
60° 20.70
69° 21.53
72.5° 23.35
73.5° 25.00
72.5° 26.15
70° 27.90
66° 29.20
Fe2Cl6 (ANHYDROUS).
Temperature. Composition.
66° 29.20
70° 29.42
75° 28.92
80° 29.20
100° 29.75
The lowest portion of the curve, AB, represents the equilibria between ice and
solutions containing ferric chloride. It represents, in other words, the lowering
of the fusion point of ice by addition of ferric chloride. At the point B (-55°),
the cryohydric point (p. 117) is reached, at which the solution is in equilibrium
with ice and ferric chloride dodecahydrate. As has already been shown, such a
point represents an invariant system; and the liquid phase will, therefore,
solidify to a mixture of ice and hydrate without change of temperature. If heat
Page 137
is added, ice will melt and the system will pass to the curve BCDN, which is
the solubility curve of the dodecahydrate. At C (37°), the point of maximum
temperature, the hydrate melts completely. The retroflex portion of this curve
can be followed backwards to a temperature of 8°, but below 27.4° (D), the
solutions are supersaturated with respect to the heptahydrate; point D is the
eutectic point for dodecahydrate and heptahydrate. The curve DEF is the
solubility curve of the heptahydrate, E being the melting point, 32.5°. On
further increasing the quantity of ferric chloride, the temperature of
equilibrium is lowered until at F (30°) another eutectic point is reached, at
which the heptahydrate and pentahydrate can co-exist with solution. Then
follow the solubility curves for the pentahydrate, the tetrahydrate, and the
anhydrous salt; G (56°) is the melting point of the former hydrate, J (73.5°) the
melting point of the latter. H and K, the points at which the curves intersect,
represent eutectic points; the temperature of the former is 55°, that of the latter
66°. The dotted portions of the curves represent metastable equilibria.
As is seen from the diagram, a remarkable series of solubility curves is
obtained, each passing through a point of maximum temperature, the whole
series of curves forming an undulating "festoon." To the right of the series of
curves the diagram represents unsaturated solutions; to the left, supersaturated.
If an unsaturated solution, the composition of which is represented by a point
in the field to the right of the solubility curves, is cooled down, the result
obtained will differ according as the composition of the solution is the same as
that of a cryohydric point, or of a melting point, or has an intermediate value.
Thus, if a solution represented by x1 is cooled down, the composition will
remain unchanged as indicated by the horizontal dotted line, until the point D
is reached. At this point, dodecahydrate and heptahydrate will separate out, and
the liquid will ultimately solidify completely to a mixture or "conglomerate" of
these two hydrates; the temperature of the system remaining constant until
complete solidification has taken place. If, on the other hand, a solution of the
composition x3 is cooled down, ferric chloride dodecahydrate will be formed
when the temperature has fallen to that represented by C, and the solution will
completely solidify, without alteration of temperature, with formation of this
hydrate. In both these cases, therefore, a point is reached at which complete
solidification occurs without change of temperature.
Somewhat different, however, is the result when the solution has an
intermediate composition, as represented by x2 or x4. In the former case the
the solubility curve of the dodecahydrate. At C (37°), the point of maximum
temperature, the hydrate melts completely. The retroflex portion of this curve
can be followed backwards to a temperature of 8°, but below 27.4° (D), the
solutions are supersaturated with respect to the heptahydrate; point D is the
eutectic point for dodecahydrate and heptahydrate. The curve DEF is the
solubility curve of the heptahydrate, E being the melting point, 32.5°. On
further increasing the quantity of ferric chloride, the temperature of
equilibrium is lowered until at F (30°) another eutectic point is reached, at
which the heptahydrate and pentahydrate can co-exist with solution. Then
follow the solubility curves for the pentahydrate, the tetrahydrate, and the
anhydrous salt; G (56°) is the melting point of the former hydrate, J (73.5°) the
melting point of the latter. H and K, the points at which the curves intersect,
represent eutectic points; the temperature of the former is 55°, that of the latter
66°. The dotted portions of the curves represent metastable equilibria.
As is seen from the diagram, a remarkable series of solubility curves is
obtained, each passing through a point of maximum temperature, the whole
series of curves forming an undulating "festoon." To the right of the series of
curves the diagram represents unsaturated solutions; to the left, supersaturated.
If an unsaturated solution, the composition of which is represented by a point
in the field to the right of the solubility curves, is cooled down, the result
obtained will differ according as the composition of the solution is the same as
that of a cryohydric point, or of a melting point, or has an intermediate value.
Thus, if a solution represented by x1 is cooled down, the composition will
remain unchanged as indicated by the horizontal dotted line, until the point D
is reached. At this point, dodecahydrate and heptahydrate will separate out, and
the liquid will ultimately solidify completely to a mixture or "conglomerate" of
these two hydrates; the temperature of the system remaining constant until
complete solidification has taken place. If, on the other hand, a solution of the
composition x3 is cooled down, ferric chloride dodecahydrate will be formed
when the temperature has fallen to that represented by C, and the solution will
completely solidify, without alteration of temperature, with formation of this
hydrate. In both these cases, therefore, a point is reached at which complete
solidification occurs without change of temperature.
Somewhat different, however, is the result when the solution has an
intermediate composition, as represented by x2 or x4. In the former case the
Page 138
dodecahydrate will first of all separate out, but on further withdrawal of heat
the temperature will fall, the solution will become relatively richer in ferric
chloride, owing to separation of the hydrate, and ultimately the eutectic point
D will be reached, at which complete solidification will occur. Similarly with
the second solution. Ferric chloride dodecahydrate will first be formed, and the
temperature will gradually fall, the composition of the solution following the
curve CB until the cryohydric point B is reached, when the whole will solidify
to a conglomerate of ice and dodecahydrate.
Suspended Transformation.—Not only can the upper branch of the solubility
curve of the dodecahydrate be followed backwards to a temperature of 8°, or
about 19° below the temperature of transition to the heptahydrate; but
suspended transformation has also been observed in the case of the
heptahydrate and the pentahydrate. To such an extent is this the case that the
solubility curve of the latter hydrate has been followed downwards to its point
of intersection with the curve for the dodecahydrate. This point of intersection,
represented in Fig. 39 by M, lies at a temperature of about 15°; and at this
temperature, therefore, it is possible for the two solid phases dodecahydrate
and pentahydrate to coexist, so that M is a eutectic point for the dodecahydrate
and the pentahydrate. It is, however, a metastable eutectic point, for it lies in
the region of supersaturation with respect to the heptahydrate; and it can be
realized only because of the fact that the latter hydrate is not readily formed.
Evaporation of Solutions at Constant Temperature.—On evaporating dilute
solutions of ferric chloride at constant temperature, a remarkable series of
changes is observed, which, however, will be understood with the help of Fig.
40. Suppose an unsaturated solution, the composition of which is represented
by the point x1, is evaporated at a temperature of about 17° - 18°. As water
passes off, the composition of the solution will follow the dotted line of
constant temperature, until at the point where it cuts the curve BC the solid
hydrate Fe2Cl6,12H2O separates out. As water continues to be removed, the
hydrate must be deposited (in order that the solution shall remain saturated),
until finally the solution dries up to the hydrate. As dehydration proceeds, the
heptahydrate can be formed, and the dodecahydrate will finally pass into the
heptahydrate; and this, in turn, into the pentahydrate.
the temperature will fall, the solution will become relatively richer in ferric
chloride, owing to separation of the hydrate, and ultimately the eutectic point
D will be reached, at which complete solidification will occur. Similarly with
the second solution. Ferric chloride dodecahydrate will first be formed, and the
temperature will gradually fall, the composition of the solution following the
curve CB until the cryohydric point B is reached, when the whole will solidify
to a conglomerate of ice and dodecahydrate.
Suspended Transformation.—Not only can the upper branch of the solubility
curve of the dodecahydrate be followed backwards to a temperature of 8°, or
about 19° below the temperature of transition to the heptahydrate; but
suspended transformation has also been observed in the case of the
heptahydrate and the pentahydrate. To such an extent is this the case that the
solubility curve of the latter hydrate has been followed downwards to its point
of intersection with the curve for the dodecahydrate. This point of intersection,
represented in Fig. 39 by M, lies at a temperature of about 15°; and at this
temperature, therefore, it is possible for the two solid phases dodecahydrate
and pentahydrate to coexist, so that M is a eutectic point for the dodecahydrate
and the pentahydrate. It is, however, a metastable eutectic point, for it lies in
the region of supersaturation with respect to the heptahydrate; and it can be
realized only because of the fact that the latter hydrate is not readily formed.
Evaporation of Solutions at Constant Temperature.—On evaporating dilute
solutions of ferric chloride at constant temperature, a remarkable series of
changes is observed, which, however, will be understood with the help of Fig.
40. Suppose an unsaturated solution, the composition of which is represented
by the point x1, is evaporated at a temperature of about 17° - 18°. As water
passes off, the composition of the solution will follow the dotted line of
constant temperature, until at the point where it cuts the curve BC the solid
hydrate Fe2Cl6,12H2O separates out. As water continues to be removed, the
hydrate must be deposited (in order that the solution shall remain saturated),
until finally the solution dries up to the hydrate. As dehydration proceeds, the
heptahydrate can be formed, and the dodecahydrate will finally pass into the
heptahydrate; and this, in turn, into the pentahydrate.
Page 139
Fig. 40.
But the heptahydrate is not always formed by the dehydration of the
dodecahydrate, and the behaviour on evaporation is therefore somewhat
perplexing at first sight. After the solution has dried to the dodecahydrate, as
explained above, further removal of water causes liquefaction, and the system
is now represented by the point of intersection at a; at this point the solid
hydrate is in equilibrium with a solution containing relatively more ferric
chloride. If, therefore, evaporation is continued, the solid hydrate must pass
into solution in order that the composition of the latter may remain unchanged,
so that ultimately a liquid will again be obtained. A very slight further
dehydration will bring the solution into the state represented by b, at which the
pentahydrate is formed, and the solution will at last disappear and leave this
hydrate alone.
Without the information to be obtained from the curves in Figs. 39 and 40, the
phenomena which would be observed on carrying out the evaporation at a
temperature of about 31 - 32° would be still more bewildering. The
composition of the different solutions formed will be represented by the
perpendicular line x212345. Evaporation will first cause the separation of the
dodecahydrate, and then total disappearance of the liquid phase. Then
liquefaction will occur, and the system will now be represented by the point 2,
in which condition it will remain until the solid hydrate has disappeared.
Following this there will be deposition of the heptahydrate (point 3), with
subsequent disappearance of the liquid phase. Further dehydration will again
cause liquefaction, when the concentration of the solution will be represented
by the point 4; the heptahydrate will ultimately disappear, and then will ensue
the deposition of the pentahydrate, and complete solidification will result. On
evaporating a solution, therefore, of the composition x2, the following series of
phenomena will be observed: solidification to dodecahydrate; liquefaction;
solidification to heptahydrate; liquefaction; solidification to pentahydrate.[233]
But the heptahydrate is not always formed by the dehydration of the
dodecahydrate, and the behaviour on evaporation is therefore somewhat
perplexing at first sight. After the solution has dried to the dodecahydrate, as
explained above, further removal of water causes liquefaction, and the system
is now represented by the point of intersection at a; at this point the solid
hydrate is in equilibrium with a solution containing relatively more ferric
chloride. If, therefore, evaporation is continued, the solid hydrate must pass
into solution in order that the composition of the latter may remain unchanged,
so that ultimately a liquid will again be obtained. A very slight further
dehydration will bring the solution into the state represented by b, at which the
pentahydrate is formed, and the solution will at last disappear and leave this
hydrate alone.
Without the information to be obtained from the curves in Figs. 39 and 40, the
phenomena which would be observed on carrying out the evaporation at a
temperature of about 31 - 32° would be still more bewildering. The
composition of the different solutions formed will be represented by the
perpendicular line x212345. Evaporation will first cause the separation of the
dodecahydrate, and then total disappearance of the liquid phase. Then
liquefaction will occur, and the system will now be represented by the point 2,
in which condition it will remain until the solid hydrate has disappeared.
Following this there will be deposition of the heptahydrate (point 3), with
subsequent disappearance of the liquid phase. Further dehydration will again
cause liquefaction, when the concentration of the solution will be represented
by the point 4; the heptahydrate will ultimately disappear, and then will ensue
the deposition of the pentahydrate, and complete solidification will result. On
evaporating a solution, therefore, of the composition x2, the following series of
phenomena will be observed: solidification to dodecahydrate; liquefaction;
solidification to heptahydrate; liquefaction; solidification to pentahydrate.[233]
Page 140
Although ferric chloride and water form the largest and best-studied series of
hydrates possessing definite melting points, examples of similar hydrates are
not few in number; and more careful investigation is constantly adding to the
list.[234] In all these cases the solubility curve will show a point of maximum
temperature, at which the hydrate melts, and will end, above and below, in a
cryohydric point. Conversely, if such a curve is found in a system of two
components, we can argue that a definite compound of the components
possessing a definite melting point is formed.
Inevaporable Solutions.—If a saturated solution in contact with two hydrates,
or with a hydrate and anhydrous salt is heated, the temperature and
composition of the solution will, of course, remain unchanged so long as the
two solid phases are present, for such a system is invariant. In addition to this,
however, the quantity of the solution will also remain unchanged, the water
which evaporates being supplied by the higher hydrate. The same phenomenon
is also observed in the case of cryohydric points when ice is a solid phase; so
long as the latter is present, evaporation will be accompanied by fusion of the
ice, and the quantity of solution will remain constant. Such solutions are called
inevaporable.[235]
Fig. 41.
Illustration.—In order to illustrate the application of the principles of the
Phase Rule to the study of systems formed by a volatile and a non-volatile
component, a brief description may be given of the behaviour of sulphur
dioxide and potassium iodide, which has formed the subject of a recent
investigation. After it had been found[236] that liquid sulphur dioxide has the
property of dissolving potassium iodide, and that the solutions thus obtained
present certain peculiarities of behaviour, the question arose as to whether or
not compounds are formed between the sulphur dioxide and the potassium
iodide, and if so, what these compounds are. To find an answer to this
question, Walden and Centnerszwer[237] made a complete investigation of the
solubility curves (equilibrium curves) of these two components, the
investigation extending from the freezing point to the critical point of sulphur
hydrates possessing definite melting points, examples of similar hydrates are
not few in number; and more careful investigation is constantly adding to the
list.[234] In all these cases the solubility curve will show a point of maximum
temperature, at which the hydrate melts, and will end, above and below, in a
cryohydric point. Conversely, if such a curve is found in a system of two
components, we can argue that a definite compound of the components
possessing a definite melting point is formed.
Inevaporable Solutions.—If a saturated solution in contact with two hydrates,
or with a hydrate and anhydrous salt is heated, the temperature and
composition of the solution will, of course, remain unchanged so long as the
two solid phases are present, for such a system is invariant. In addition to this,
however, the quantity of the solution will also remain unchanged, the water
which evaporates being supplied by the higher hydrate. The same phenomenon
is also observed in the case of cryohydric points when ice is a solid phase; so
long as the latter is present, evaporation will be accompanied by fusion of the
ice, and the quantity of solution will remain constant. Such solutions are called
inevaporable.[235]
Fig. 41.
Illustration.—In order to illustrate the application of the principles of the
Phase Rule to the study of systems formed by a volatile and a non-volatile
component, a brief description may be given of the behaviour of sulphur
dioxide and potassium iodide, which has formed the subject of a recent
investigation. After it had been found[236] that liquid sulphur dioxide has the
property of dissolving potassium iodide, and that the solutions thus obtained
present certain peculiarities of behaviour, the question arose as to whether or
not compounds are formed between the sulphur dioxide and the potassium
iodide, and if so, what these compounds are. To find an answer to this
question, Walden and Centnerszwer[237] made a complete investigation of the
solubility curves (equilibrium curves) of these two components, the
investigation extending from the freezing point to the critical point of sulphur
Page 141
dioxide. For convenience of reference, the results which they obtained are
represented diagrammatically in Fig. 41. The freezing point (A) of pure
sulphur dioxide was found to be -72.7°. Addition of potassium iodide lowered
the freezing point, but the maximum depression obtained was very small, and
was reached when the concentration of the potassium iodide in the solution
was only 0.336 mols. per cent. Beyond this point, an increase in the
concentration of the iodide was accompanied by an elevation of the freezing
point, the change of the freezing point with the concentration being
represented by the curve BC. The solid which separated from the solutions
represented by BC was a bright yellow crystalline substance. At the point C
(-23.4°) a temperature-maximum was reached; and as the concentration of the
potassium iodide was continuously increased, the temperature of equilibrium
first fell and then slowly rose, until at +0.26° (E) a second temperature-
maximum was registered. On passing the point D, the solid which was
deposited from the solution was a red crystalline substance. On withdrawing
sulphur dioxide from the system, the solution became turbid, and the
temperature remained constant. The investigation was not pursued farther at
this point, the attention being then directed to the equilibria at higher
temperatures.
When a solution of potassium iodide in liquid sulphur dioxide containing 1.49
per cent. of potassium iodide was heated, solid (potassium iodide) was
deposited at a temperature of 96.4°. Solutions containing more than about 3
per cent. of the iodide separated, on being heated, into two layers, and the
temperature at which the liquid became heterogeneous fell as the concentration
was increased; a temperature-minimum being obtained with solutions
containing 12 per cent. of potassium iodide. On the other hand, solutions
containing 30.9 per cent. of the iodide, on being heated, deposited potassium
iodide; while a solution containing 24.5 per cent. of the salt first separated into
two layers at 89.3°, and then, on cooling, solid was deposited and one of the
liquid layers disappeared.
Such are, in brief, the results of experiment; their interpretation in the light of
the Phase Rule is the following:—
The curve AB is the freezing-point curve of solid sulphur dioxide in contact
with solutions of potassium iodide. BCD is the solubility curve of the yellow
crystalline solid which is deposited from the solutions. C, the temperature-
maximum, is the melting point of this yellow solid, and the composition of the
latter must be the same as that of the solution at this point (p. 145), which was
represented diagrammatically in Fig. 41. The freezing point (A) of pure
sulphur dioxide was found to be -72.7°. Addition of potassium iodide lowered
the freezing point, but the maximum depression obtained was very small, and
was reached when the concentration of the potassium iodide in the solution
was only 0.336 mols. per cent. Beyond this point, an increase in the
concentration of the iodide was accompanied by an elevation of the freezing
point, the change of the freezing point with the concentration being
represented by the curve BC. The solid which separated from the solutions
represented by BC was a bright yellow crystalline substance. At the point C
(-23.4°) a temperature-maximum was reached; and as the concentration of the
potassium iodide was continuously increased, the temperature of equilibrium
first fell and then slowly rose, until at +0.26° (E) a second temperature-
maximum was registered. On passing the point D, the solid which was
deposited from the solution was a red crystalline substance. On withdrawing
sulphur dioxide from the system, the solution became turbid, and the
temperature remained constant. The investigation was not pursued farther at
this point, the attention being then directed to the equilibria at higher
temperatures.
When a solution of potassium iodide in liquid sulphur dioxide containing 1.49
per cent. of potassium iodide was heated, solid (potassium iodide) was
deposited at a temperature of 96.4°. Solutions containing more than about 3
per cent. of the iodide separated, on being heated, into two layers, and the
temperature at which the liquid became heterogeneous fell as the concentration
was increased; a temperature-minimum being obtained with solutions
containing 12 per cent. of potassium iodide. On the other hand, solutions
containing 30.9 per cent. of the iodide, on being heated, deposited potassium
iodide; while a solution containing 24.5 per cent. of the salt first separated into
two layers at 89.3°, and then, on cooling, solid was deposited and one of the
liquid layers disappeared.
Such are, in brief, the results of experiment; their interpretation in the light of
the Phase Rule is the following:—
The curve AB is the freezing-point curve of solid sulphur dioxide in contact
with solutions of potassium iodide. BCD is the solubility curve of the yellow
crystalline solid which is deposited from the solutions. C, the temperature-
maximum, is the melting point of this yellow solid, and the composition of the
latter must be the same as that of the solution at this point (p. 145), which was
Page 142
found to be that represented by the formula KI,14SO2. B is therefore the
eutectic point, at which solid sulphur dioxide and the compound KI,14SO2 can
exist together in equilibrium with solution and vapour. The curve DE is the
solubility curve of the red crystalline solid, and the point E, at which the
composition of solution and solid is the same, is the melting point of the solid.
The composition of this substance was found to be KI,4SO2.[238] D is,
therefore, the eutectic point at which the compounds KI,14SO2 and KI,4SO2
can coexist in equilibrium with solution and vapour. The curve DE does not
exhibit a retroflex portion; on the contrary, on attempting to obtain more
concentrated solutions in equilibrium with the compound KI,4SO2, a new solid
phase (probably potassium iodide) was formed. Since at this point there are
four phases in equilibrium, viz. the compound KI,4SO2, potassium iodide,
solution, and vapour, the system is invariant. E is, therefore, the transition
point for KI,4SO2 and KI.
Passing to higher temperatures, FG is the solubility curve of potassium iodide
in sulphur dioxide; at G two liquid phases are formed, and the system therefore
becomes invariant (cf. p. 121). The curve GHK is the solubility curve for two
partially miscible liquids; and since complete miscibility occurs on lowering
the temperature, the curve is similar to that obtained with triethylamine and
water (p. 101). K is also an invariant point at which potassium iodide is in
equilibrium with two liquid phases and vapour.
The complete investigation of the equilibria between sulphur dioxide and
potassium iodide, therefore, shows that these two components form the
compounds KI,14SO2 and KI,4SO2; and that when solutions having a
concentration between those represented by the points G and K are heated,
separation into two layers occurs. The temperatures and concentrations of the
different characteristic points are as follows:—
Composition of
Point. Temperature. the solution
per cent. KI.
A (m.p. of SO2) -72.7° —
B (eutectic point) — 0.86
C (m.p. of KI,14SO2) -23.4° 17.63
E (m.p. of KI,4SO2) +0.26° 39.33
eutectic point, at which solid sulphur dioxide and the compound KI,14SO2 can
exist together in equilibrium with solution and vapour. The curve DE is the
solubility curve of the red crystalline solid, and the point E, at which the
composition of solution and solid is the same, is the melting point of the solid.
The composition of this substance was found to be KI,4SO2.[238] D is,
therefore, the eutectic point at which the compounds KI,14SO2 and KI,4SO2
can coexist in equilibrium with solution and vapour. The curve DE does not
exhibit a retroflex portion; on the contrary, on attempting to obtain more
concentrated solutions in equilibrium with the compound KI,4SO2, a new solid
phase (probably potassium iodide) was formed. Since at this point there are
four phases in equilibrium, viz. the compound KI,4SO2, potassium iodide,
solution, and vapour, the system is invariant. E is, therefore, the transition
point for KI,4SO2 and KI.
Passing to higher temperatures, FG is the solubility curve of potassium iodide
in sulphur dioxide; at G two liquid phases are formed, and the system therefore
becomes invariant (cf. p. 121). The curve GHK is the solubility curve for two
partially miscible liquids; and since complete miscibility occurs on lowering
the temperature, the curve is similar to that obtained with triethylamine and
water (p. 101). K is also an invariant point at which potassium iodide is in
equilibrium with two liquid phases and vapour.
The complete investigation of the equilibria between sulphur dioxide and
potassium iodide, therefore, shows that these two components form the
compounds KI,14SO2 and KI,4SO2; and that when solutions having a
concentration between those represented by the points G and K are heated,
separation into two layers occurs. The temperatures and concentrations of the
different characteristic points are as follows:—
Composition of
Point. Temperature. the solution
per cent. KI.
A (m.p. of SO2) -72.7° —
B (eutectic point) — 0.86
C (m.p. of KI,14SO2) -23.4° 17.63
E (m.p. of KI,4SO2) +0.26° 39.33
Page 143
G (KI + two liquid phases) (about) 88° 24.0
H (critical solution point) 77.3° 12
K (KI + two liquid phases) (about) 88° 2.7
CHAPTER IX
EQUILIBRIA BETWEEN TWO VOLATILE COMPONENTS
General.—In the two preceding chapters certain restrictions were imposed on
the discussion of the equilibria between two components; but in the present
chapter the restriction that only one of the components is volatile will be
allowed to fall, and the general behaviour of two volatile[239] components,
each of which is capable of forming a liquid solution with the other, will be
studied. As we shall see, however, the removal of the previous restriction
produces no alteration in the general aspect of the equilibrium curves for
concentration and temperature, but changes to some extent the appearance of
the pressure-temperature diagram. The latter would become still more
complicated if account were taken not only of the total pressure but also of the
partial pressures of the two components in the vapour phase; this complication,
however, will not be introduced in the present discussion.[240] In this chapter
we shall consider the systems formed by the two components iodine and
chlorine, and sulphur dioxide and water.
Iodine and Chlorine.—The different systems furnished by iodine and
chlorine, rendered classical by the studies of Stortenbeker,[241] form a very
complete example of equilibria in a two-component system. We shall first of
all consider the relations between concentration and temperature, with the help
of the accompanying diagram, Fig. 42.
H (critical solution point) 77.3° 12
K (KI + two liquid phases) (about) 88° 2.7
CHAPTER IX
EQUILIBRIA BETWEEN TWO VOLATILE COMPONENTS
General.—In the two preceding chapters certain restrictions were imposed on
the discussion of the equilibria between two components; but in the present
chapter the restriction that only one of the components is volatile will be
allowed to fall, and the general behaviour of two volatile[239] components,
each of which is capable of forming a liquid solution with the other, will be
studied. As we shall see, however, the removal of the previous restriction
produces no alteration in the general aspect of the equilibrium curves for
concentration and temperature, but changes to some extent the appearance of
the pressure-temperature diagram. The latter would become still more
complicated if account were taken not only of the total pressure but also of the
partial pressures of the two components in the vapour phase; this complication,
however, will not be introduced in the present discussion.[240] In this chapter
we shall consider the systems formed by the two components iodine and
chlorine, and sulphur dioxide and water.
Iodine and Chlorine.—The different systems furnished by iodine and
chlorine, rendered classical by the studies of Stortenbeker,[241] form a very
complete example of equilibria in a two-component system. We shall first of
all consider the relations between concentration and temperature, with the help
of the accompanying diagram, Fig. 42.
Page 144
Fig. 42.
Concentration-Temperature Diagram.—In this diagram the temperatures
are taken as the abscissæ, and the composition of the solution, expressed in
atoms of chlorine to one atom of iodine,[242] is represented by the ordinates. In
the diagram, A represents the melting point of pure iodine, 114°. If chlorine is
added to the system, a solution of chlorine in liquid iodine is obtained, and the
temperature at which solid iodine is in equilibrium with the liquid solution will
be all the lower the greater the concentration of the chlorine. We therefore
obtain the curve ABF, which represents the composition of the solution with
which solid iodine is in equilibrium at different temperatures. This curve can
be followed down to 0°, but at temperatures below 7.9° (B) it represents
metastable equilibria. At B iodine monochloride can be formed, and if present
the system becomes invariant; B is therefore a quadruple point at which the
four phases, iodine, iodine monochloride, solution, and vapour, can coexist.
Continued withdrawal of heat at this point will therefore lead to the complete
solidification of the solution to a mixture or conglomerate of iodine and iodine
monochloride, while the temperature remains constant during the process. B is
the eutectic point for iodine and iodine monochloride.
Just as we found in the case of aqueous salt solutions that at temperatures
above the cryohydric or eutectic point, two different solutions could exist, one
in equilibrium with ice, the other in equilibrium with the salt (or salt hydrate),
so in the case of iodine and chlorine there can be two solutions above the
eutectic point B, one containing a lower proportion of chlorine in equilibrium
with iodine, the other containing a higher proportion of chlorine in equilibrium
with iodine monochloride. The composition of the latter solution is represented
by the curve BCD. As the concentration of chlorine is increased, the
Concentration-Temperature Diagram.—In this diagram the temperatures
are taken as the abscissæ, and the composition of the solution, expressed in
atoms of chlorine to one atom of iodine,[242] is represented by the ordinates. In
the diagram, A represents the melting point of pure iodine, 114°. If chlorine is
added to the system, a solution of chlorine in liquid iodine is obtained, and the
temperature at which solid iodine is in equilibrium with the liquid solution will
be all the lower the greater the concentration of the chlorine. We therefore
obtain the curve ABF, which represents the composition of the solution with
which solid iodine is in equilibrium at different temperatures. This curve can
be followed down to 0°, but at temperatures below 7.9° (B) it represents
metastable equilibria. At B iodine monochloride can be formed, and if present
the system becomes invariant; B is therefore a quadruple point at which the
four phases, iodine, iodine monochloride, solution, and vapour, can coexist.
Continued withdrawal of heat at this point will therefore lead to the complete
solidification of the solution to a mixture or conglomerate of iodine and iodine
monochloride, while the temperature remains constant during the process. B is
the eutectic point for iodine and iodine monochloride.
Just as we found in the case of aqueous salt solutions that at temperatures
above the cryohydric or eutectic point, two different solutions could exist, one
in equilibrium with ice, the other in equilibrium with the salt (or salt hydrate),
so in the case of iodine and chlorine there can be two solutions above the
eutectic point B, one containing a lower proportion of chlorine in equilibrium
with iodine, the other containing a higher proportion of chlorine in equilibrium
with iodine monochloride. The composition of the latter solution is represented
by the curve BCD. As the concentration of chlorine is increased, the
Page 145
temperature at which there is equilibrium between iodine monochloride and
solution rises until a point is reached at which the composition of the solution
is the same as that of the solid. At this point (C), iodine monochloride melts.
Addition of one of the components will lower the temperature of fusion, and a
continuous curve,[243] exhibiting a retroflex portion as in the case of
CaCl2,6H2O, will be obtained. At temperatures below its melting point,
therefore, iodine monochloride can be in equilibrium with two different
solutions.
The upper portion of this curve, CD, can be followed downwards to a
temperature of 22.7°. At this temperature iodine trichloride can separate out,
and a second quadruple point (D) is obtained. This is the eutectic point for
iodine monochloride and iodine trichloride.
By addition of heat and increase in the amount of chlorine, the iodine
monochloride disappears, and the system passes along the curve DE, which
represents the composition of the solutions in equilibrium with solid iodine
trichloride. The concentration of chlorine in the solution increases as the
temperature is raised, until at the point E, where the solution has the same
composition as the solid, the maximum temperature is reached; the iodine
trichloride melts. On increasing still further the concentration of chlorine in the
solution, the temperature of equilibrium falls, and a continuous curve, similar
to that for the monochloride, is obtained. The upper branch of this curve has
been followed down to a temperature of 30°, the solution at this point
containing 99.6 per cent. of chlorine.[244] The very rounded form of the curve
is due to the trichloride being largely dissociated in the liquid state.
One curve still remains to be considered. As has already been mentioned,
iodine monochloride can exist in two crystalline forms, only one of which,
however, is stable at temperatures below the melting point; the two forms are
monotropic (p. 44). The stable form which melts at 27.2°, is called the α-form,
while the less stable variety, melting at 13.9°, is known as the β-form. If, now,
the presence of α-ICl is excluded, it is possible to obtain the β-form, and to
study the conditions of equilibrium between it and solutions of iodine and
chlorine, from the eutectic point F to the melting point G. As the β-ICl
becomes less stable in presence of excess of chlorine, it has not been possible
to study the retroflex portion of the curve represented by the dotted
continuation of FG.
solution rises until a point is reached at which the composition of the solution
is the same as that of the solid. At this point (C), iodine monochloride melts.
Addition of one of the components will lower the temperature of fusion, and a
continuous curve,[243] exhibiting a retroflex portion as in the case of
CaCl2,6H2O, will be obtained. At temperatures below its melting point,
therefore, iodine monochloride can be in equilibrium with two different
solutions.
The upper portion of this curve, CD, can be followed downwards to a
temperature of 22.7°. At this temperature iodine trichloride can separate out,
and a second quadruple point (D) is obtained. This is the eutectic point for
iodine monochloride and iodine trichloride.
By addition of heat and increase in the amount of chlorine, the iodine
monochloride disappears, and the system passes along the curve DE, which
represents the composition of the solutions in equilibrium with solid iodine
trichloride. The concentration of chlorine in the solution increases as the
temperature is raised, until at the point E, where the solution has the same
composition as the solid, the maximum temperature is reached; the iodine
trichloride melts. On increasing still further the concentration of chlorine in the
solution, the temperature of equilibrium falls, and a continuous curve, similar
to that for the monochloride, is obtained. The upper branch of this curve has
been followed down to a temperature of 30°, the solution at this point
containing 99.6 per cent. of chlorine.[244] The very rounded form of the curve
is due to the trichloride being largely dissociated in the liquid state.
One curve still remains to be considered. As has already been mentioned,
iodine monochloride can exist in two crystalline forms, only one of which,
however, is stable at temperatures below the melting point; the two forms are
monotropic (p. 44). The stable form which melts at 27.2°, is called the α-form,
while the less stable variety, melting at 13.9°, is known as the β-form. If, now,
the presence of α-ICl is excluded, it is possible to obtain the β-form, and to
study the conditions of equilibrium between it and solutions of iodine and
chlorine, from the eutectic point F to the melting point G. As the β-ICl
becomes less stable in presence of excess of chlorine, it has not been possible
to study the retroflex portion of the curve represented by the dotted
continuation of FG.
Page 146
The following table gives some of the numerical data from which Fig. 42 was
constructed.[245]
Iodine and Chlorine.
I. Invariant systems.
Phases present.
Temperature. Pressure.
Solid. Liquid. Vapour.
I
11 I+
7.9° I2,α-ICl
mm. Cl0.92
Cl0.66
I
0.9° — I2,β-ICl —
Cl0.72
I
42 α- I+
22.7° ICl,ICl3 Cl1.75
mm.
Cl1.19
I
<1 I+
[-102° ICl3,Cl2
atm. Cln]
Clm
II. Melting points.
A. Iodine,[246] 114.15° (pressure 89.8 mm.).
C. α-Iodine monochloride, 27.2° (pressure 37
mm.).
E. Iodine trichloride, 101° (pressure 16 atm.).
G. β-Iodine monochloride, 13.9°.
Since the vapour pressure at the melting point of iodine trichloride amounts to
16 atm., the experiments must of course be carried out in closed vessels. At
63.7° the vapour pressure of the system trichloride—solution—vapour is equal
to 1 atm.
Pressure-Temperature Diagram.—In this diagram there are represented the
values of the vapour pressure of the saturated solutions of chlorine and iodine.
To give a complete picture of the relations between pressure, temperature, and
constructed.[245]
Iodine and Chlorine.
I. Invariant systems.
Phases present.
Temperature. Pressure.
Solid. Liquid. Vapour.
I
11 I+
7.9° I2,α-ICl
mm. Cl0.92
Cl0.66
I
0.9° — I2,β-ICl —
Cl0.72
I
42 α- I+
22.7° ICl,ICl3 Cl1.75
mm.
Cl1.19
I
<1 I+
[-102° ICl3,Cl2
atm. Cln]
Clm
II. Melting points.
A. Iodine,[246] 114.15° (pressure 89.8 mm.).
C. α-Iodine monochloride, 27.2° (pressure 37
mm.).
E. Iodine trichloride, 101° (pressure 16 atm.).
G. β-Iodine monochloride, 13.9°.
Since the vapour pressure at the melting point of iodine trichloride amounts to
16 atm., the experiments must of course be carried out in closed vessels. At
63.7° the vapour pressure of the system trichloride—solution—vapour is equal
to 1 atm.
Pressure-Temperature Diagram.—In this diagram there are represented the
values of the vapour pressure of the saturated solutions of chlorine and iodine.
To give a complete picture of the relations between pressure, temperature, and
Page 147
concentration, a solid model would be required, with three axes at right angles
to one another along which could be measured the values of pressure,
temperature, and concentration of the components in the solution. Instead of
this, however, there may be employed the accompanying projection figure[247]
(Fig. 43), the lower portion of which shows the projection of the equilibrium
curve on the surface containing the concentration and temperature axes, while
the upper portion is the projection on the plane containing the pressure and
temperature axes. The lower portion is therefore a concentration-temperature
diagram; the upper portion, a pressure-temperature diagram. The
corresponding points of the two diagrams are joined by dotted lines.
Fig. 43.
Corresponding to the point C, the melting point of pure iodine, there is the
point C1, which represents the vapour pressure of iodine at its melting point. At
this point three curves cut: 1, the sublimation curve of iodine; 2, the
vaporization curve of fused iodine; 3, C1B1, the vapour-pressure curve of the
saturated solutions in equilibrium with solid iodine. Starting, therefore, with
the system solid iodine—liquid iodine, addition of chlorine will cause the
temperature of equilibrium to fall continuously, while the vapour pressure will
first increase, pass through a maximum and then fall continuously until the
eutectic point, B (B1), is reached.[248] At this point the system is invariant, and
the pressure will therefore remain constant until all the iodine has disappeared.
As the concentration of the chlorine increases in the manner represented by the
curve BfH, the pressure of the vapour also increases as represented by the
to one another along which could be measured the values of pressure,
temperature, and concentration of the components in the solution. Instead of
this, however, there may be employed the accompanying projection figure[247]
(Fig. 43), the lower portion of which shows the projection of the equilibrium
curve on the surface containing the concentration and temperature axes, while
the upper portion is the projection on the plane containing the pressure and
temperature axes. The lower portion is therefore a concentration-temperature
diagram; the upper portion, a pressure-temperature diagram. The
corresponding points of the two diagrams are joined by dotted lines.
Fig. 43.
Corresponding to the point C, the melting point of pure iodine, there is the
point C1, which represents the vapour pressure of iodine at its melting point. At
this point three curves cut: 1, the sublimation curve of iodine; 2, the
vaporization curve of fused iodine; 3, C1B1, the vapour-pressure curve of the
saturated solutions in equilibrium with solid iodine. Starting, therefore, with
the system solid iodine—liquid iodine, addition of chlorine will cause the
temperature of equilibrium to fall continuously, while the vapour pressure will
first increase, pass through a maximum and then fall continuously until the
eutectic point, B (B1), is reached.[248] At this point the system is invariant, and
the pressure will therefore remain constant until all the iodine has disappeared.
As the concentration of the chlorine increases in the manner represented by the
curve BfH, the pressure of the vapour also increases as represented by the
Page 148
curve B1f1H1. At H1, the eutectic point for iodine monochloride and iodine
trichloride, the pressure again remains constant until all the monochloride has
disappeared. As the concentration of the solution passes along the curve HF,
the pressure of the vapour increases as represented by the curve H1F1; F1
represents the pressure of the vapour at the melting point of iodine trichloride.
If the concentration of the chlorine in the solution is continuously increased
from this point, the vapour pressure first increases and then decreases, until the
eutectic point for iodine trichloride and solid chlorine is reached (D1). Curves
Cl2 solid and Cl2 liquid represent the sublimation and vaporization curves of
chlorine, the melting point of chlorine being -102°.
Although complete measurements of the vapour pressure of the different
systems of pure iodine to pure chlorine have not been made, the experimental
data are nevertheless sufficient to allow of the general form of the curves being
indicated with certainty.
Bivariant Systems.—To these, only a brief reference need be made. Since
there are two components, two phases will form a bivariant system. The fields
in which these systems can exist are shown in Fig. 43 and Fig. 44, which is a
more diagrammatic representation of a portion of Fig. 43.
I. Iodine—vapour.
II. Solution—vapour.
III. Iodine trichloride—vapour.
IV. Iodine monochloride—vapour.
Fig. 44.
The conditions for the existence of these systems will probably be best
understood from Fig. 44. Since the curve B′A′ represents the pressures under
which the system iodine—solution—vapour can exist, increase of volume
trichloride, the pressure again remains constant until all the monochloride has
disappeared. As the concentration of the solution passes along the curve HF,
the pressure of the vapour increases as represented by the curve H1F1; F1
represents the pressure of the vapour at the melting point of iodine trichloride.
If the concentration of the chlorine in the solution is continuously increased
from this point, the vapour pressure first increases and then decreases, until the
eutectic point for iodine trichloride and solid chlorine is reached (D1). Curves
Cl2 solid and Cl2 liquid represent the sublimation and vaporization curves of
chlorine, the melting point of chlorine being -102°.
Although complete measurements of the vapour pressure of the different
systems of pure iodine to pure chlorine have not been made, the experimental
data are nevertheless sufficient to allow of the general form of the curves being
indicated with certainty.
Bivariant Systems.—To these, only a brief reference need be made. Since
there are two components, two phases will form a bivariant system. The fields
in which these systems can exist are shown in Fig. 43 and Fig. 44, which is a
more diagrammatic representation of a portion of Fig. 43.
I. Iodine—vapour.
II. Solution—vapour.
III. Iodine trichloride—vapour.
IV. Iodine monochloride—vapour.
Fig. 44.
The conditions for the existence of these systems will probably be best
understood from Fig. 44. Since the curve B′A′ represents the pressures under
which the system iodine—solution—vapour can exist, increase of volume
Page 149
(diminution of pressure) will cause the volatilization of the solution, and the
system iodine—vapour will remain. If, therefore, we start with a system
represented by a, diminution of pressure at constant temperature will lead to
the condition represented by x. On the other hand, increase of pressure at a will
lead to the condensation of a portion of the vapour phase. Since, now, the
concentration of chlorine in the vapour is greater than in the solution,
condensation of vapour would increase the concentration of chlorine in the
solution; a certain amount of iodine must therefore pass into solution in order
that the composition of the latter shall remain unchanged.[249] If, therefore, the
volume of vapour be sufficiently great, continued diminution of volume will
ultimately lead to the disappearance of all the iodine, and there will remain
only solution and vapour (field II.). As the diminution of volume is continued,
the vapour pressure and the concentration of the chlorine in the solution will
increase, until when the pressure has reached the value b, iodine monochloride
can separate out. The system, therefore, again becomes univariant, and at
constant temperature the pressure and composition of the phases must remain
unchanged. Diminution of volume will therefore not effect an increase of
pressure, but a condensation of the vapour; and since this is richer in chlorine
than the solution, solid iodine monochloride must separate out in order that the
concentration of the solution remain unchanged.[250] As the result, therefore,
we obtain the bivariant system iodine monochloride—vapour.
A detailed discussion of the effect of a continued increase of pressure will not
be necessary. From what has already been said and with the help of Fig. 44, it
will readily be understood that this will lead successively to the univariant
system (c), iodine monochloride—solution—vapour; the bivariant system
solution—vapour (field II.); the univariant system (d), iodine trichloride—
solution—vapour; and the bivariant system x′, iodine trichloride—vapour. If
the temperature of the experiment is above the melting point of the
monochloride, then the systems in which this compound occurs will not be
formed.
Sulphur Dioxide and Water.—In the case just studied we have seen that the
components can combine to form definite compounds possessing stable
melting points. The curves of equilibrium, therefore, resemble in their general
aspect those of calcium chloride and water, or of ferric chloride and water. In
the case of sulphur dioxide and water, however, the melting point of the
compound formed cannot be realized, because transition to another system
occurs; retroflex concentration-temperature curves are therefore not found
system iodine—vapour will remain. If, therefore, we start with a system
represented by a, diminution of pressure at constant temperature will lead to
the condition represented by x. On the other hand, increase of pressure at a will
lead to the condensation of a portion of the vapour phase. Since, now, the
concentration of chlorine in the vapour is greater than in the solution,
condensation of vapour would increase the concentration of chlorine in the
solution; a certain amount of iodine must therefore pass into solution in order
that the composition of the latter shall remain unchanged.[249] If, therefore, the
volume of vapour be sufficiently great, continued diminution of volume will
ultimately lead to the disappearance of all the iodine, and there will remain
only solution and vapour (field II.). As the diminution of volume is continued,
the vapour pressure and the concentration of the chlorine in the solution will
increase, until when the pressure has reached the value b, iodine monochloride
can separate out. The system, therefore, again becomes univariant, and at
constant temperature the pressure and composition of the phases must remain
unchanged. Diminution of volume will therefore not effect an increase of
pressure, but a condensation of the vapour; and since this is richer in chlorine
than the solution, solid iodine monochloride must separate out in order that the
concentration of the solution remain unchanged.[250] As the result, therefore,
we obtain the bivariant system iodine monochloride—vapour.
A detailed discussion of the effect of a continued increase of pressure will not
be necessary. From what has already been said and with the help of Fig. 44, it
will readily be understood that this will lead successively to the univariant
system (c), iodine monochloride—solution—vapour; the bivariant system
solution—vapour (field II.); the univariant system (d), iodine trichloride—
solution—vapour; and the bivariant system x′, iodine trichloride—vapour. If
the temperature of the experiment is above the melting point of the
monochloride, then the systems in which this compound occurs will not be
formed.
Sulphur Dioxide and Water.—In the case just studied we have seen that the
components can combine to form definite compounds possessing stable
melting points. The curves of equilibrium, therefore, resemble in their general
aspect those of calcium chloride and water, or of ferric chloride and water. In
the case of sulphur dioxide and water, however, the melting point of the
compound formed cannot be realized, because transition to another system
occurs; retroflex concentration-temperature curves are therefore not found
Page 150
here, but the curves exhibit breaks or sudden changes in direction at the
transition points, as in the case of the systems formed by sodium sulphate and
water. The case of sulphur dioxide and water is also of interest from the fact
that two liquid phases can be formed.
The phases which occur are—Solid: ice, sulphur dioxide hydrate, SO2,7H2O.
Liquid: two solutions, the one containing excess of sulphur dioxide, the other
excess of water, and represented by the symbols SO2 xH2O (solution I.),
and H2O ySO2 (solution II.). Vapour: a mixture of sulphur dioxide and
water vapour in varying proportions. Since there are two components, sulphur
dioxide and water, the number of possible systems is considerable. Only the
following, however, have been studied:—
I. Invariant Systems: Four co-existing phases.
(a) Ice, hydrate, solution, vapour.
(b) Hydrate, solution I., solution II., vapour.
II. Univariant Systems: Three co-existing phases.
(a) Hydrate, solution I., vapour.
(b) Hydrate, solution II., vapour.
(c) Solution I., solution II., vapour.
(d) Hydrate, solution I., solution II.
(e) Hydrate, ice, vapour.
(f) Ice, solution II., vapour.
(g) Ice, hydrate, solution II.
III. Bivariant Systems: Two co-existing phases.
(a) Hydrate, solution I.
(b) Hydrate, solution II.
(c) Hydrate, vapour.
(d) Hydrate, ice.
(e) Solution I., solution II.
(f) Solution I., vapour.
(g) Solution I., ice.
(h) Solution II., vapour.
(i) Solution II., ice.
(j) Ice, vapour.
transition points, as in the case of the systems formed by sodium sulphate and
water. The case of sulphur dioxide and water is also of interest from the fact
that two liquid phases can be formed.
The phases which occur are—Solid: ice, sulphur dioxide hydrate, SO2,7H2O.
Liquid: two solutions, the one containing excess of sulphur dioxide, the other
excess of water, and represented by the symbols SO2 xH2O (solution I.),
and H2O ySO2 (solution II.). Vapour: a mixture of sulphur dioxide and
water vapour in varying proportions. Since there are two components, sulphur
dioxide and water, the number of possible systems is considerable. Only the
following, however, have been studied:—
I. Invariant Systems: Four co-existing phases.
(a) Ice, hydrate, solution, vapour.
(b) Hydrate, solution I., solution II., vapour.
II. Univariant Systems: Three co-existing phases.
(a) Hydrate, solution I., vapour.
(b) Hydrate, solution II., vapour.
(c) Solution I., solution II., vapour.
(d) Hydrate, solution I., solution II.
(e) Hydrate, ice, vapour.
(f) Ice, solution II., vapour.
(g) Ice, hydrate, solution II.
III. Bivariant Systems: Two co-existing phases.
(a) Hydrate, solution I.
(b) Hydrate, solution II.
(c) Hydrate, vapour.
(d) Hydrate, ice.
(e) Solution I., solution II.
(f) Solution I., vapour.
(g) Solution I., ice.
(h) Solution II., vapour.
(i) Solution II., ice.
(j) Ice, vapour.
Page 151
Pressure-Temperature Diagram.[251]—If
sulphur dioxide is passed into water at 0°, a
solution will be formed and the temperature at
which ice can exist in equilibrium with this
solution will fall more and more as the
concentration of the sulphur dioxide increases.
At -2.6°, however, a cryohydric point is reached
at which solid hydrate separates out, and the
system becomes invariant. The curve AB (Fig.
45) therefore represents the pressure of the Fig. 45.
system ice—solution II.—vapour, and B
represents the temperature and pressure at which the invariant system ice—
hydrate—solution II.—vapour can exist. At this point the temperature is -2.6°,
and the pressure 21.1 cm. If heat is withdrawn from this system, the solution
will ultimately solidify to a mixture of ice and hydrate, and there will be
obtained the univariant system ice—hydrate—vapour. The vapour pressure of
this system has been determined down to a temperature of -9.5°, at which
temperature the pressure amounts to 15 cm. The pressures for this system are
represented by the curve BC. If at the point B the volume is diminished, the
pressure must remain constant, but the relative amounts of the different phases
will undergo change. If suitable quantities of these are present, diminution of
volume will ultimately lead to the total condensation of the vapour phase, and
there will remain the univariant system ice—hydrate—solution. The
temperature of equilibrium of this system will alter with the pressure, but, as in
the case of the melting point of a simple substance, great differences of
pressure will cause only comparatively small changes in the temperature of
equilibrium. The change of the cryohydric point with the pressure is
represented by the line BE; the actual values have not been determined, but the
curve must slope towards the pressure axis because fusion is accompanied by
diminution of volume, as in the case of pure ice.
A fourth univariant system can be formed at B. This is the system hydrate—
solution II.—vapour. The conditions for the existence of this system are
represented by the curve BF, which may therefore be regarded as the vapour-
pressure curve of the saturated solution of sulphur dioxide heptahydrate in
water. Unlike the curve for iodine trichloride—solution—vapour, this curve
cannot be followed to the melting point of the hydrate. Before this point is
reached, a second liquid phase appears, and an invariant system consisting of
hydrate—solution I.—solution II.—vapour is formed. We have here, therefore,
sulphur dioxide is passed into water at 0°, a
solution will be formed and the temperature at
which ice can exist in equilibrium with this
solution will fall more and more as the
concentration of the sulphur dioxide increases.
At -2.6°, however, a cryohydric point is reached
at which solid hydrate separates out, and the
system becomes invariant. The curve AB (Fig.
45) therefore represents the pressure of the Fig. 45.
system ice—solution II.—vapour, and B
represents the temperature and pressure at which the invariant system ice—
hydrate—solution II.—vapour can exist. At this point the temperature is -2.6°,
and the pressure 21.1 cm. If heat is withdrawn from this system, the solution
will ultimately solidify to a mixture of ice and hydrate, and there will be
obtained the univariant system ice—hydrate—vapour. The vapour pressure of
this system has been determined down to a temperature of -9.5°, at which
temperature the pressure amounts to 15 cm. The pressures for this system are
represented by the curve BC. If at the point B the volume is diminished, the
pressure must remain constant, but the relative amounts of the different phases
will undergo change. If suitable quantities of these are present, diminution of
volume will ultimately lead to the total condensation of the vapour phase, and
there will remain the univariant system ice—hydrate—solution. The
temperature of equilibrium of this system will alter with the pressure, but, as in
the case of the melting point of a simple substance, great differences of
pressure will cause only comparatively small changes in the temperature of
equilibrium. The change of the cryohydric point with the pressure is
represented by the line BE; the actual values have not been determined, but the
curve must slope towards the pressure axis because fusion is accompanied by
diminution of volume, as in the case of pure ice.
A fourth univariant system can be formed at B. This is the system hydrate—
solution II.—vapour. The conditions for the existence of this system are
represented by the curve BF, which may therefore be regarded as the vapour-
pressure curve of the saturated solution of sulphur dioxide heptahydrate in
water. Unlike the curve for iodine trichloride—solution—vapour, this curve
cannot be followed to the melting point of the hydrate. Before this point is
reached, a second liquid phase appears, and an invariant system consisting of
hydrate—solution I.—solution II.—vapour is formed. We have here, therefore,
Page 152
the phenomenon of melting under the solution as in the case of succinic nitrile
and water (p. 122). This point is represented in the diagram by F; the
temperature at this point is 12.1°, and the pressure 177.3 cm. The range of
stable existence of the hydrate is therefore from -2.6° to 12.1°; nevertheless,
the curve FB has been followed down to a temperature of -6°, at which point
ice formed spontaneously.
So long as the four phases hydrate, two liquid phases, and vapour are present,
the condition of the system is perfectly defined. By altering the conditions,
however, one of the phases can be made to disappear, and a univariant system
will then be obtained. Thus, if the vapour phase is made to disappear, the
univariant system solution I.—solution II.—hydrate, will be left, and the
temperature at which this system is in equilibrium will vary with the pressure.
This is represented by the curve FI; under a pressure of 225 atm. the
temperature of equilibrium is 17.1°. Increase of pressure, therefore, raises the
temperature at which the three phases can coexist.
Again, addition of heat to the invariant system at F will cause the
disappearance of the solid phase, and there will be formed the univariant
system solution I.—solution II.—vapour. In the case of this system the vapour
pressure increases as the temperature rises, as represented by the curve FG.
Such a system is analogous to the case of ether and water, or other two
partially miscible liquids (p. 103). As the temperature changes, the
composition of the two liquid phases will undergo change; but this system has
not been studied fully.
The fourth curve, which ends at the quadruple point F, is that representing the
vapour pressure of the system hydrate—solution I.—vapour (FH). This curve
has been followed to a temperature of 0°, the pressure at this point being 113
cm. The metastable prolongation of GF has also been determined. Although,
theoretically, this curve must lie below FH, it was found that the difference in
the pressure for the two curves was within the error of experiment.
Bivariant Systems.—The different bivariant systems, consisting of two
phases, which can exist within the range of temperature and pressure included
in Fig. 45, were given on p. 170. The conditions under which these systems
can exist are represented by the areas in the diagram, and the fields of the
different bivariant systems are indicated by letters, corresponding to the letters
on p. 170. Just as in the case of one-component systems (p. 29), we found that
the field lying between any two curves gave the conditions of existence of that
and water (p. 122). This point is represented in the diagram by F; the
temperature at this point is 12.1°, and the pressure 177.3 cm. The range of
stable existence of the hydrate is therefore from -2.6° to 12.1°; nevertheless,
the curve FB has been followed down to a temperature of -6°, at which point
ice formed spontaneously.
So long as the four phases hydrate, two liquid phases, and vapour are present,
the condition of the system is perfectly defined. By altering the conditions,
however, one of the phases can be made to disappear, and a univariant system
will then be obtained. Thus, if the vapour phase is made to disappear, the
univariant system solution I.—solution II.—hydrate, will be left, and the
temperature at which this system is in equilibrium will vary with the pressure.
This is represented by the curve FI; under a pressure of 225 atm. the
temperature of equilibrium is 17.1°. Increase of pressure, therefore, raises the
temperature at which the three phases can coexist.
Again, addition of heat to the invariant system at F will cause the
disappearance of the solid phase, and there will be formed the univariant
system solution I.—solution II.—vapour. In the case of this system the vapour
pressure increases as the temperature rises, as represented by the curve FG.
Such a system is analogous to the case of ether and water, or other two
partially miscible liquids (p. 103). As the temperature changes, the
composition of the two liquid phases will undergo change; but this system has
not been studied fully.
The fourth curve, which ends at the quadruple point F, is that representing the
vapour pressure of the system hydrate—solution I.—vapour (FH). This curve
has been followed to a temperature of 0°, the pressure at this point being 113
cm. The metastable prolongation of GF has also been determined. Although,
theoretically, this curve must lie below FH, it was found that the difference in
the pressure for the two curves was within the error of experiment.
Bivariant Systems.—The different bivariant systems, consisting of two
phases, which can exist within the range of temperature and pressure included
in Fig. 45, were given on p. 170. The conditions under which these systems
can exist are represented by the areas in the diagram, and the fields of the
different bivariant systems are indicated by letters, corresponding to the letters
on p. 170. Just as in the case of one-component systems (p. 29), we found that
the field lying between any two curves gave the conditions of existence of that
Page 153
phase which was common to the two curves, so also in the case of two-
component systems, a bivariant two-phase system occurs in the field
enclosed[252] by the two curves to which the two phases are common. As can
be seen, the same bivariant system can occur in more than one field.
As is evident from Fig. 45, three different bivariant systems are capable of
existing in the area HFI; which of these will be obtained will depend on the
relative masses of the different phases in the univariant or invariant system.
Thus, starting with a system represented by a point on the curve HF,
diminution of volume at constant temperature will cause the condensation of a
portion of the vapour, which is rich in sulphur dioxide; since this would
increase the concentration of sulphur dioxide in the solution, it must be
counteracted by the passage of a portion of the hydrate (which is relatively
poor in sulphur dioxide) into the solution. If, therefore, the amount of hydrate
present is relatively very small, the final result of the compression will be the
production of the system f, solution I.—vapour. On the other hand, if the
vapour is present in relatively small amount, it will be the first phase to
disappear, and the bivariant system a, hydrate—solution I., will be obtained.
Finally, if we start with the invariant system at F, compression will cause the
condensation of vapour, while the composition of the two solutions will remain
unchanged. When all the vapour has disappeared, the univariant system
hydrate—solution I.—solution II. will be left. If, now, the pressure is still
further increased, while the temperature is kept below 12°, more and more
hydrate must be formed at the expense of the two liquid phases (because 12° is
the lower limit for the coexistence of the two liquid phases), and if the amount
of the solution I. (containing excess of sulphur dioxide) is relatively small, it
will disappear before solution II., and there will be obtained the bivariant
system hydrate—solution II. (bivariant system b).
In a similar manner, account can be taken of the formation of the other
bivariant systems.
A behaviour similar to that of sulphur dioxide and water is shown by chlorine
and water and by bromine and water, although these have not been so fully
studied.[253] In the case of hydrogen bromide and water, and of hydrogen
chloride and water, a hydrate, viz. HBr,2H2O and HCl,2H2O, is formed which
possesses a definite melting point, as in the case of iodine trichloride. In these
cases, therefore, a retroflex curve is obtained. Further, just as in the case of the
chlorides of iodine the upper branch of the retroflex curve ended in a eutectic
component systems, a bivariant two-phase system occurs in the field
enclosed[252] by the two curves to which the two phases are common. As can
be seen, the same bivariant system can occur in more than one field.
As is evident from Fig. 45, three different bivariant systems are capable of
existing in the area HFI; which of these will be obtained will depend on the
relative masses of the different phases in the univariant or invariant system.
Thus, starting with a system represented by a point on the curve HF,
diminution of volume at constant temperature will cause the condensation of a
portion of the vapour, which is rich in sulphur dioxide; since this would
increase the concentration of sulphur dioxide in the solution, it must be
counteracted by the passage of a portion of the hydrate (which is relatively
poor in sulphur dioxide) into the solution. If, therefore, the amount of hydrate
present is relatively very small, the final result of the compression will be the
production of the system f, solution I.—vapour. On the other hand, if the
vapour is present in relatively small amount, it will be the first phase to
disappear, and the bivariant system a, hydrate—solution I., will be obtained.
Finally, if we start with the invariant system at F, compression will cause the
condensation of vapour, while the composition of the two solutions will remain
unchanged. When all the vapour has disappeared, the univariant system
hydrate—solution I.—solution II. will be left. If, now, the pressure is still
further increased, while the temperature is kept below 12°, more and more
hydrate must be formed at the expense of the two liquid phases (because 12° is
the lower limit for the coexistence of the two liquid phases), and if the amount
of the solution I. (containing excess of sulphur dioxide) is relatively small, it
will disappear before solution II., and there will be obtained the bivariant
system hydrate—solution II. (bivariant system b).
In a similar manner, account can be taken of the formation of the other
bivariant systems.
A behaviour similar to that of sulphur dioxide and water is shown by chlorine
and water and by bromine and water, although these have not been so fully
studied.[253] In the case of hydrogen bromide and water, and of hydrogen
chloride and water, a hydrate, viz. HBr,2H2O and HCl,2H2O, is formed which
possesses a definite melting point, as in the case of iodine trichloride. In these
cases, therefore, a retroflex curve is obtained. Further, just as in the case of the
chlorides of iodine the upper branch of the retroflex curve ended in a eutectic
Page 154
point, so also in the case of the hydrate HBr,2H2O the upper branch of the
curve ends in a eutectic point at which the system dihydrate—monohydrate—
solution—vapour can exist. Before the melting point of the monohydrate is
reached, two liquid phases are formed, as in the case of sulphur dioxide and
water.
CHAPTER X
SOLID SOLUTIONS. MIXED CRYSTALS
General.—With the conception of gaseous and liquid solutions, every one is
familiar. Gases can mix in all proportions to form homogeneous solutions.
Gases can dissolve in or be "absorbed" by liquids; and solids, also, when
brought in contact with liquids, "pass into solution" and yield a homogeneous
liquid phase. On the other hand, the conception of a solid solution is one which
in many cases is found more difficult to appreciate; and the existence and
behaviour of solid solutions, in spite of their not uncommon occurrence and
importance, are in general comparatively little known.
The reason of this is to be found, to some extent, no doubt, in the fact that the
term "solid solution" was introduced at a comparatively recent date,[254] but it
is probably also due in some measure to a somewhat hazy comprehension of
the definition of the term "solution" itself. As has already been said (p. 92), a
solution is a homogeneous phase, the composition of which can vary
continuously within certain limits; the definition involves, therefore, no
condition as to the physical state of the substances. Accordingly, solid
solutions are homogeneous solid phases, the composition of which can
undergo continuous variation within certain limits. Just as we saw that the
range of variation of composition is more limited in the case of liquids than in
the case of gases, so also we find that the limits of miscibility are in general
still more restricted in the case of solids. Examples of complete miscibility are,
however, not unknown even in the case of solid substances.
Solid solutions have long been known, although, of course, they were not
defined as such. Thus, the phenomena of "occlusion" of gases by metals and
other substances (occlusion of hydrogen by palladium; occlusion of hydrogen
by iron) are due to the formation of solid solutions. The same is probably also
curve ends in a eutectic point at which the system dihydrate—monohydrate—
solution—vapour can exist. Before the melting point of the monohydrate is
reached, two liquid phases are formed, as in the case of sulphur dioxide and
water.
CHAPTER X
SOLID SOLUTIONS. MIXED CRYSTALS
General.—With the conception of gaseous and liquid solutions, every one is
familiar. Gases can mix in all proportions to form homogeneous solutions.
Gases can dissolve in or be "absorbed" by liquids; and solids, also, when
brought in contact with liquids, "pass into solution" and yield a homogeneous
liquid phase. On the other hand, the conception of a solid solution is one which
in many cases is found more difficult to appreciate; and the existence and
behaviour of solid solutions, in spite of their not uncommon occurrence and
importance, are in general comparatively little known.
The reason of this is to be found, to some extent, no doubt, in the fact that the
term "solid solution" was introduced at a comparatively recent date,[254] but it
is probably also due in some measure to a somewhat hazy comprehension of
the definition of the term "solution" itself. As has already been said (p. 92), a
solution is a homogeneous phase, the composition of which can vary
continuously within certain limits; the definition involves, therefore, no
condition as to the physical state of the substances. Accordingly, solid
solutions are homogeneous solid phases, the composition of which can
undergo continuous variation within certain limits. Just as we saw that the
range of variation of composition is more limited in the case of liquids than in
the case of gases, so also we find that the limits of miscibility are in general
still more restricted in the case of solids. Examples of complete miscibility are,
however, not unknown even in the case of solid substances.
Solid solutions have long been known, although, of course, they were not
defined as such. Thus, the phenomena of "occlusion" of gases by metals and
other substances (occlusion of hydrogen by palladium; occlusion of hydrogen
by iron) are due to the formation of solid solutions. The same is probably also
Page 155
true of the phenomena of "adsorption," as in the removal of organic colouring
matter by charcoal, although, in this case, surface tension no doubt plays a
considerable part.[255]
As examples of the solution of gases in solids there may be cited (in addition
to the phenomena of occlusion already mentioned), the hydrated silicates and
the zeolites. During dehydration these crystalline substances remain clear and
transparent, and the pressure of the water vapour which they emit varies with
the degree of hydration or the concentration of water in the mineral.[256] As
examples of the solution of solids in solids we have the cementation of iron by
charcoal, the formation of glass, and the crystallization together of
isomorphous substances.
Although we have here spoken of the glasses as "solid solutions," it should be
mentioned that the term "solid" is used in its popular sense. Strictly speaking,
the glasses are to be regarded as supercooled liquids (see also p. 53, footnote).
In discussing the equilibria in systems containing a solid solution, it is of
essential importance to remember that a solid solution constitutes only one
phase, a phase of varying composition, as in the case of liquid solutions.
Solution of Gases in Solids.—Comparatively little work has been done in this
connection, the investigations being limited chiefly to the phenomena of
occlusion or adsorption of gases by charcoal.[257] We shall, therefore, indicate
only briefly and in a general manner, the behaviour which the Phase Rule
enables us to foresee.[258]
In dealing with the systems formed by the two phases gas—solid, three chief
cases call for mention:—
I. The gas is not absorbed by the solid, but when the pressure reaches a certain
value, combination of the two components can result.
The graphic representation of such a system is shown in
Fig. 46, the ordinates being the pressures of the gas, and the
abscissæ the concentrations of the gaseous component in
the solid phase. Since there is no formation of a solid
solution, the concentration of gas in the solid phase remains
zero until the pressure has increased to the point A. At this Fig. 46.
point combination can take place. There will now be three
matter by charcoal, although, in this case, surface tension no doubt plays a
considerable part.[255]
As examples of the solution of gases in solids there may be cited (in addition
to the phenomena of occlusion already mentioned), the hydrated silicates and
the zeolites. During dehydration these crystalline substances remain clear and
transparent, and the pressure of the water vapour which they emit varies with
the degree of hydration or the concentration of water in the mineral.[256] As
examples of the solution of solids in solids we have the cementation of iron by
charcoal, the formation of glass, and the crystallization together of
isomorphous substances.
Although we have here spoken of the glasses as "solid solutions," it should be
mentioned that the term "solid" is used in its popular sense. Strictly speaking,
the glasses are to be regarded as supercooled liquids (see also p. 53, footnote).
In discussing the equilibria in systems containing a solid solution, it is of
essential importance to remember that a solid solution constitutes only one
phase, a phase of varying composition, as in the case of liquid solutions.
Solution of Gases in Solids.—Comparatively little work has been done in this
connection, the investigations being limited chiefly to the phenomena of
occlusion or adsorption of gases by charcoal.[257] We shall, therefore, indicate
only briefly and in a general manner, the behaviour which the Phase Rule
enables us to foresee.[258]
In dealing with the systems formed by the two phases gas—solid, three chief
cases call for mention:—
I. The gas is not absorbed by the solid, but when the pressure reaches a certain
value, combination of the two components can result.
The graphic representation of such a system is shown in
Fig. 46, the ordinates being the pressures of the gas, and the
abscissæ the concentrations of the gaseous component in
the solid phase. Since there is no formation of a solid
solution, the concentration of gas in the solid phase remains
zero until the pressure has increased to the point A. At this Fig. 46.
point combination can take place. There will now be three
Page 156
phases present, viz. solid component, compound, and vapour. The system is
therefore univariant, and if the temperature is maintained constant, the vapour
pressure will be constant, irrespective of the amount of compound formed, i.e.
irrespective of the relative amounts of gas and solid. This is indicated by the
line AB. When the solid component has entirely disappeared, the system
ceases to be univariant, and if no absorption occurs, the pressure will increase
again, as shown by BC. If a second compound can be formed, then a second
pc-line will be obtained, similar to the preceding. To this group belong the salt
hydrates (Chap. VII.).
II. The gas may be absorbed and may also form a compound.
If absorption of gas occurs with formation of a solid solution, then, as the
system consists of two phases, solution—vapour, it is bivariant. At constant
temperature, therefore, the pressure will still vary with the concentration of the
gaseous component in the solid phase. This is represented by the curve AB in
Fig. 47. When, however, the pressure has reached a certain value, combination
can take place; and since there are now three phases present, the system is
univariant, and at constant temperature the pressure is constant, as shown by
the line BC.
III. Absorption of gas occurs, but at a certain concentration the solid solution
can separate into two immiscible solid solutions.
We have seen, in Chapter VI., that two liquids can form two immiscible
solutions, and the same has also been found true of solid solutions, as we shall
presently learn more fully. If, now, two immiscible solutions are formed, then
the system will become univariant, and at constant temperature the pc-curve
will be a straight line, as in the case of the formation of a compound (cf. p. 86).
The behaviour of this system will, therefore, also be represented
diagrammatically by Fig. 47.
Fig. 47.
Palladium and Hydrogen.—The phenomenon of the absorption of hydrogen
by palladium, to which Graham gave the name "occlusion," is one that has
therefore univariant, and if the temperature is maintained constant, the vapour
pressure will be constant, irrespective of the amount of compound formed, i.e.
irrespective of the relative amounts of gas and solid. This is indicated by the
line AB. When the solid component has entirely disappeared, the system
ceases to be univariant, and if no absorption occurs, the pressure will increase
again, as shown by BC. If a second compound can be formed, then a second
pc-line will be obtained, similar to the preceding. To this group belong the salt
hydrates (Chap. VII.).
II. The gas may be absorbed and may also form a compound.
If absorption of gas occurs with formation of a solid solution, then, as the
system consists of two phases, solution—vapour, it is bivariant. At constant
temperature, therefore, the pressure will still vary with the concentration of the
gaseous component in the solid phase. This is represented by the curve AB in
Fig. 47. When, however, the pressure has reached a certain value, combination
can take place; and since there are now three phases present, the system is
univariant, and at constant temperature the pressure is constant, as shown by
the line BC.
III. Absorption of gas occurs, but at a certain concentration the solid solution
can separate into two immiscible solid solutions.
We have seen, in Chapter VI., that two liquids can form two immiscible
solutions, and the same has also been found true of solid solutions, as we shall
presently learn more fully. If, now, two immiscible solutions are formed, then
the system will become univariant, and at constant temperature the pc-curve
will be a straight line, as in the case of the formation of a compound (cf. p. 86).
The behaviour of this system will, therefore, also be represented
diagrammatically by Fig. 47.
Fig. 47.
Palladium and Hydrogen.—The phenomenon of the absorption of hydrogen
by palladium, to which Graham gave the name "occlusion," is one that has
Page 157
claimed the attention of several investigators. Although Graham was not of
opinion that a compound is formed, but rather that the gas undergoes very
great condensation, acts as a quasi-metal (to which he gave the name
hydrogenium), and forms a homogeneous alloy with the palladium, later
investigations, especially those of Troost and Hautefeuille,[259] pointed to the
formation of a definite chemical compound, having the formula Pd2H. This
conclusion has, however, not been confirmed by subsequent investigation.[260]
Roozeboom and Hoitsema[261] sought to arrive at a final decision as to the
nature of the phenomenon by an investigation of the equilibrium between
hydrogen and palladium on the basis of the Phase Rule classification given
above. If a compound is formed, diminution of volume would cause no
increase of pressure, but only an increase in the amount of the compound.
As this is the only case of gas absorption which has been accurately studied
from this point of view, a brief account of the results obtained will be given
here, although these are not so clear and free from ambiguity as one would
desire.
The scientists just mentioned investigated the variation of the pressure of
hydrogen with the amount absorbed by the metal at different temperatures, and
a few of their results, typical of all, are represented graphically in Fig. 48; the
curves indicating the variation of the gas pressure with the concentration of the
hydrogen in the palladium at the temperatures 120°, 170°, and 200°. As can be
seen, the curve consists of three parts, an ascending portion which passes
gradually and continuously into an almost horizontal but slightly ascending
middle part, which in turn passes without break into a second rapidly
ascending curve. This, as Fig. 48 indicates, is the general form of the curve;
but the length of the middle portion varies with the temperature, being shorter
at higher than at lower temperatures.
opinion that a compound is formed, but rather that the gas undergoes very
great condensation, acts as a quasi-metal (to which he gave the name
hydrogenium), and forms a homogeneous alloy with the palladium, later
investigations, especially those of Troost and Hautefeuille,[259] pointed to the
formation of a definite chemical compound, having the formula Pd2H. This
conclusion has, however, not been confirmed by subsequent investigation.[260]
Roozeboom and Hoitsema[261] sought to arrive at a final decision as to the
nature of the phenomenon by an investigation of the equilibrium between
hydrogen and palladium on the basis of the Phase Rule classification given
above. If a compound is formed, diminution of volume would cause no
increase of pressure, but only an increase in the amount of the compound.
As this is the only case of gas absorption which has been accurately studied
from this point of view, a brief account of the results obtained will be given
here, although these are not so clear and free from ambiguity as one would
desire.
The scientists just mentioned investigated the variation of the pressure of
hydrogen with the amount absorbed by the metal at different temperatures, and
a few of their results, typical of all, are represented graphically in Fig. 48; the
curves indicating the variation of the gas pressure with the concentration of the
hydrogen in the palladium at the temperatures 120°, 170°, and 200°. As can be
seen, the curve consists of three parts, an ascending portion which passes
gradually and continuously into an almost horizontal but slightly ascending
middle part, which in turn passes without break into a second rapidly
ascending curve. This, as Fig. 48 indicates, is the general form of the curve;
but the length of the middle portion varies with the temperature, being shorter
at higher than at lower temperatures.
Page 158
Fig. 48.
What is the interpretation to be put on these curves? With regard to the two
end portions, these represent bivariant, two-phase systems, consisting of a
solid solution and gas. They correspond, therefore, to curve AB in Fig. 47. If
the middle portion were horizontal, it would indicate either the formation of a
compound or of two immiscible solid solutions. If a compound Pd2H were
formed, then the middle portion would at all temperatures end at the same
value of the concentration, viz. that corresponding to 0.5 atoms of hydrogen to
1 atom of palladium. As the figure shows, however, this is not the case; the
higher the temperature, the lower is the concentration at which the middle
passes into the terminal portion of the curve. Such a behaviour would,
however, agree with the assumption of the formation of two solid solutions, the
"miscibility" of which increases with the temperature, as in the case of the
liquid solutions of phenol and water (p. 97). Nevertheless, although the
assumption of the formation of two solid solutions is more satisfactory than
that of the formation of a compound, it does not entirely explain the facts. If
two solid solutions are formed, the pressure curve should be horizontal, but
this is not the case; and the deviation from the horizontal does not appear to be
due to impurities either in the gas or in the metal, but is apparently a
peculiarity of the system. Further, the gradual instead of abrupt passage of the
three portions of the curve into one another remains unexplained. Hoitsema
has expressed the opinion that the occlusion of hydrogen by palladium is a
process of continuous absorption, the peculiar form of the curve—the flat
middle portion—being possibly due to a condensation of the gas, even at
temperatures far above the critical temperature of liquid hydrogen.
While, therefore, the occlusion of hydrogen by palladium still presents some
unexplained phenomena, the behaviour found by Hoitsema would appear to
disprove conclusively the formation of a definite chemical compound.[262]
Solution of Solids in Solids. Mixed Crystals.
The introduction by van't Hoff of the term "solid solution" resulted from the
discovery of a number of deviations from the Raoult-van't Hoff law for the
depression of the freezing point by dissolved substances. In all cases, the
depression was too small; in some instances, indeed, the freezing point may be
raised. To explain these irregularities, van't Hoff assumed that the dissolved
substance crystallized out along with the solid solvent; and he showed how this
What is the interpretation to be put on these curves? With regard to the two
end portions, these represent bivariant, two-phase systems, consisting of a
solid solution and gas. They correspond, therefore, to curve AB in Fig. 47. If
the middle portion were horizontal, it would indicate either the formation of a
compound or of two immiscible solid solutions. If a compound Pd2H were
formed, then the middle portion would at all temperatures end at the same
value of the concentration, viz. that corresponding to 0.5 atoms of hydrogen to
1 atom of palladium. As the figure shows, however, this is not the case; the
higher the temperature, the lower is the concentration at which the middle
passes into the terminal portion of the curve. Such a behaviour would,
however, agree with the assumption of the formation of two solid solutions, the
"miscibility" of which increases with the temperature, as in the case of the
liquid solutions of phenol and water (p. 97). Nevertheless, although the
assumption of the formation of two solid solutions is more satisfactory than
that of the formation of a compound, it does not entirely explain the facts. If
two solid solutions are formed, the pressure curve should be horizontal, but
this is not the case; and the deviation from the horizontal does not appear to be
due to impurities either in the gas or in the metal, but is apparently a
peculiarity of the system. Further, the gradual instead of abrupt passage of the
three portions of the curve into one another remains unexplained. Hoitsema
has expressed the opinion that the occlusion of hydrogen by palladium is a
process of continuous absorption, the peculiar form of the curve—the flat
middle portion—being possibly due to a condensation of the gas, even at
temperatures far above the critical temperature of liquid hydrogen.
While, therefore, the occlusion of hydrogen by palladium still presents some
unexplained phenomena, the behaviour found by Hoitsema would appear to
disprove conclusively the formation of a definite chemical compound.[262]
Solution of Solids in Solids. Mixed Crystals.
The introduction by van't Hoff of the term "solid solution" resulted from the
discovery of a number of deviations from the Raoult-van't Hoff law for the
depression of the freezing point by dissolved substances. In all cases, the
depression was too small; in some instances, indeed, the freezing point may be
raised. To explain these irregularities, van't Hoff assumed that the dissolved
substance crystallized out along with the solid solvent; and he showed how this
Page 159
would account for the deviations from the law of the depression of the freezing
point, which had been developed on the assumption that only the pure solvent
crystallized out from the solution.[263]
The "mixed crystals" which were thus obtained, and which van't Hoff called
dilute solid solutions, showed great resemblance in their behaviour to ordinary
liquid solutions, and obeyed the laws applicable to these. These laws, however,
can no longer be applied in the case of the concentrated solid solutions formed
by the crystallization together of isomorphous substances, and known as
isomorphous mixtures. Indeed, it has been contended[264] that these
isomorphous mixtures should not be considered as solid solutions at all,
although no sharp line of demarcation can be drawn between the two classes.
The differences, however, in the behaviour of the two groups are of a
quantitative rather than a qualitative nature; and since we are concerned at
present only with the qualitative behaviour, we shall make no distinction
between the crystalline solid solutions and the isomorphous mixtures, but shall
study the behaviour of the two classes under the head of "mixed crystals."
Mixed crystals can be formed either by sublimation[265] or from a liquid phase;
and in the latter case the mixed crystals can be deposited either from solution
in a common solvent or from a mixture of the fused components. In this
method of formation, which alone will be discussed in the present chapter, we
are dealing with the fusion curves of two substances, where, however, the
liquid solution is in equilibrium not with one of the pure components, but with
a solid solution or mixed crystal. The simple scheme (Fig. 29, p. 117) which
was obtained in the case of two components which crystallize out in the pure
state, is no longer sufficient in the case of the formation of mixed crystals.
With the help of the Phase Rule, however, the different possible systems can
be classified; and examples of the different cases predicted by the Phase Rule
have also been obtained by experiment.
We shall now consider briefly the formation of mixed crystals by isomorphous
substances; the consideration of the formation of mixed crystals of
isodimorphous substances will, on account of the complexity of the
relationships, not be undertaken here.[266]
Formation of Mixed Crystals of Isomorphous Substances.
point, which had been developed on the assumption that only the pure solvent
crystallized out from the solution.[263]
The "mixed crystals" which were thus obtained, and which van't Hoff called
dilute solid solutions, showed great resemblance in their behaviour to ordinary
liquid solutions, and obeyed the laws applicable to these. These laws, however,
can no longer be applied in the case of the concentrated solid solutions formed
by the crystallization together of isomorphous substances, and known as
isomorphous mixtures. Indeed, it has been contended[264] that these
isomorphous mixtures should not be considered as solid solutions at all,
although no sharp line of demarcation can be drawn between the two classes.
The differences, however, in the behaviour of the two groups are of a
quantitative rather than a qualitative nature; and since we are concerned at
present only with the qualitative behaviour, we shall make no distinction
between the crystalline solid solutions and the isomorphous mixtures, but shall
study the behaviour of the two classes under the head of "mixed crystals."
Mixed crystals can be formed either by sublimation[265] or from a liquid phase;
and in the latter case the mixed crystals can be deposited either from solution
in a common solvent or from a mixture of the fused components. In this
method of formation, which alone will be discussed in the present chapter, we
are dealing with the fusion curves of two substances, where, however, the
liquid solution is in equilibrium not with one of the pure components, but with
a solid solution or mixed crystal. The simple scheme (Fig. 29, p. 117) which
was obtained in the case of two components which crystallize out in the pure
state, is no longer sufficient in the case of the formation of mixed crystals.
With the help of the Phase Rule, however, the different possible systems can
be classified; and examples of the different cases predicted by the Phase Rule
have also been obtained by experiment.
We shall now consider briefly the formation of mixed crystals by isomorphous
substances; the consideration of the formation of mixed crystals of
isodimorphous substances will, on account of the complexity of the
relationships, not be undertaken here.[266]
Formation of Mixed Crystals of Isomorphous Substances.
Page 160
For the purpose of representing the relationships found here we shall employ a
temperature-concentration diagram,[267] in which the ordinates represent the
temperature and the abscissæ the concentration of the components. Since there
are two solutions, the liquid and the solid, and since the concentration of the
components in these two phases is not, in general, the same, two curves will be
required for each system, one relating to the liquid phase, the other relating to
the solid. The temperature at which solid begins to be deposited from the
liquid solution will be called the freezing point of the mixture, and the
temperature at which the solid solution just begins to liquefy will be called the
melting point of the solid solution. The temperature-concentration curve for the
liquid phase will therefore be the freezing-point curve; that for the solid
solution, the melting-point curve. The latter will be represented by a dotted
line.[268]
I.—The Two Components can form an Unbroken Series of Mixed Crystals.
Since, as has already been pointed out (p. 176), a mixed crystal (solid solution)
constitutes only one phase, it is evident that if the two components are miscible
with one another in all proportions in the solid state, there can never be more
than one solid phase present, viz. the solid solution or mixed crystal. If the
components are completely miscible in the solid state, they will also be
completely miscible in the liquid state, and there can therefore be only one
liquid phase. The system can at no point become invariant, because there can
never be more than three phases present. When, therefore, the two components
form a continuous series of mixed crystals, the equilibrium curve must also be
continuous. Of these systems three types are found.
Fig. 49.
(a) The freezing points of all mixtures lie between the freezing points of the
pure components (Curve I., Fig. 49).
temperature-concentration diagram,[267] in which the ordinates represent the
temperature and the abscissæ the concentration of the components. Since there
are two solutions, the liquid and the solid, and since the concentration of the
components in these two phases is not, in general, the same, two curves will be
required for each system, one relating to the liquid phase, the other relating to
the solid. The temperature at which solid begins to be deposited from the
liquid solution will be called the freezing point of the mixture, and the
temperature at which the solid solution just begins to liquefy will be called the
melting point of the solid solution. The temperature-concentration curve for the
liquid phase will therefore be the freezing-point curve; that for the solid
solution, the melting-point curve. The latter will be represented by a dotted
line.[268]
I.—The Two Components can form an Unbroken Series of Mixed Crystals.
Since, as has already been pointed out (p. 176), a mixed crystal (solid solution)
constitutes only one phase, it is evident that if the two components are miscible
with one another in all proportions in the solid state, there can never be more
than one solid phase present, viz. the solid solution or mixed crystal. If the
components are completely miscible in the solid state, they will also be
completely miscible in the liquid state, and there can therefore be only one
liquid phase. The system can at no point become invariant, because there can
never be more than three phases present. When, therefore, the two components
form a continuous series of mixed crystals, the equilibrium curve must also be
continuous. Of these systems three types are found.
Fig. 49.
(a) The freezing points of all mixtures lie between the freezing points of the
pure components (Curve I., Fig. 49).
Page 161
Examples.—This type of curve is represented by the mixed crystals of
naphthalene and β-naphthol.[269] The addition of β-naphthol to naphthalene
raises the freezing point of the latter, and the rise is directly proportional to the
amount of naphthol added. The freezing point curve is therefore a straight line
joining the melting points of the two components. This behaviour, however, is
rather exceptional, the freezing-point curve lying generally above, sometimes
also below, the straight line joining the melting points of the pure components.
Thus the freezing-point curve of mixtures of α-monochlorocinnamic aldehyde
and α-monobromocinnamic aldehyde[270] lies above the straight line joining
the melting points of the pure components (31.22° and 69.56°), as is evident
from the following table:—
Molecules of bromo-
Deviation from straight
cinnamic aldehyde in Freezing point.
line.
100 mols. of mixture.
0.00 31.22° —
10.48 37.28° 2.04°
21.91 43.12° 3.50°
30.07 46.80° 4.05°
45.04 52.94° 4.45°
62.16 58.82° 3.77°
82.98 65.07° 2.03°
93.50 67.91° 0.84°
100.00 69.56° —
Melting-point Curve.—This curve, like the freezing-point curve, must also be
continuous, and the melting points of the different solid solutions will lie
between the melting points of the pure components. This is represented by the
dotted line in Fig. 49, I. The relative position of the two curves, which can be
deduced with the help of thermodynamics and also by experimental
determination, is found in all cases to be in accordance with the following rule:
At any given temperature, the concentration of that component by the addition
of which the freezing point is depressed, is greater in the liquid than in the
solid phase; or, conversely, the concentration of that component by the
addition of which the freezing point is raised, is greater in the solid than in the
liquid phase. An illustration of this rule is afforded by the two substances
chloro- and bromo-cinnamic aldehyde already mentioned. As can be seen from
the above table, the addition of chlorocinnamic aldehyde lowers the melting
naphthalene and β-naphthol.[269] The addition of β-naphthol to naphthalene
raises the freezing point of the latter, and the rise is directly proportional to the
amount of naphthol added. The freezing point curve is therefore a straight line
joining the melting points of the two components. This behaviour, however, is
rather exceptional, the freezing-point curve lying generally above, sometimes
also below, the straight line joining the melting points of the pure components.
Thus the freezing-point curve of mixtures of α-monochlorocinnamic aldehyde
and α-monobromocinnamic aldehyde[270] lies above the straight line joining
the melting points of the pure components (31.22° and 69.56°), as is evident
from the following table:—
Molecules of bromo-
Deviation from straight
cinnamic aldehyde in Freezing point.
line.
100 mols. of mixture.
0.00 31.22° —
10.48 37.28° 2.04°
21.91 43.12° 3.50°
30.07 46.80° 4.05°
45.04 52.94° 4.45°
62.16 58.82° 3.77°
82.98 65.07° 2.03°
93.50 67.91° 0.84°
100.00 69.56° —
Melting-point Curve.—This curve, like the freezing-point curve, must also be
continuous, and the melting points of the different solid solutions will lie
between the melting points of the pure components. This is represented by the
dotted line in Fig. 49, I. The relative position of the two curves, which can be
deduced with the help of thermodynamics and also by experimental
determination, is found in all cases to be in accordance with the following rule:
At any given temperature, the concentration of that component by the addition
of which the freezing point is depressed, is greater in the liquid than in the
solid phase; or, conversely, the concentration of that component by the
addition of which the freezing point is raised, is greater in the solid than in the
liquid phase. An illustration of this rule is afforded by the two substances
chloro- and bromo-cinnamic aldehyde already mentioned. As can be seen from
the above table, the addition of chlorocinnamic aldehyde lowers the melting
Page 162
point of the bromo-compound. In accordance with the rule, therefore, the
concentration of the chloro-compound in the liquid phase must be greater than
in the solid phase; and this was found experimentally. At a temperature of
49.44°, the liquid contained 58.52 per cent., the solid only 52.57 per cent. of
the chlorocinnamic aldehyde.
From this it will also be clear that on cooling a fused mixture of two
substances capable of forming mixed crystals, the temperature of solidification
will not remain constant during the separation of the solid; nor, on the other
hand, will the temperature of liquefaction of the solid solution be constant.
Thus, for example, if a liquid solution of two components, A and B, having the
composition represented by the point x (Fig. 50), is allowed to cool, the system
will pass along the line xx′. At the temperature of the point a, mixed crystals
will be deposited, the composition of which will be that represented by b. As
the temperature continues to fall, more and more solid will be deposited; and
since the solid phase is relatively rich in the component B, the liquid will
become relatively poorer in this. The composition of the liquid solution will
therefore pass along the curve ad, the composition of the solid solution at the
same time passing along the curve bc; at the point c the liquid will solidify
completely.[271]
Fig. 50.
Conversely, if mixed crystals of the composition and at the temperature x′ are
heated, liquefaction will begin at the temperature c, yielding a liquid of the
composition d. On continuing to add heat, the temperature of the mass will
rise, more of the solid will melt, and the composition of the two phases will
change as represented by the curves da and cb. When the temperature has risen
to a, complete liquefaction will have occurred. The process of solidification or
of liquefaction is therefore extended over a temperature interval ac.
concentration of the chloro-compound in the liquid phase must be greater than
in the solid phase; and this was found experimentally. At a temperature of
49.44°, the liquid contained 58.52 per cent., the solid only 52.57 per cent. of
the chlorocinnamic aldehyde.
From this it will also be clear that on cooling a fused mixture of two
substances capable of forming mixed crystals, the temperature of solidification
will not remain constant during the separation of the solid; nor, on the other
hand, will the temperature of liquefaction of the solid solution be constant.
Thus, for example, if a liquid solution of two components, A and B, having the
composition represented by the point x (Fig. 50), is allowed to cool, the system
will pass along the line xx′. At the temperature of the point a, mixed crystals
will be deposited, the composition of which will be that represented by b. As
the temperature continues to fall, more and more solid will be deposited; and
since the solid phase is relatively rich in the component B, the liquid will
become relatively poorer in this. The composition of the liquid solution will
therefore pass along the curve ad, the composition of the solid solution at the
same time passing along the curve bc; at the point c the liquid will solidify
completely.[271]
Fig. 50.
Conversely, if mixed crystals of the composition and at the temperature x′ are
heated, liquefaction will begin at the temperature c, yielding a liquid of the
composition d. On continuing to add heat, the temperature of the mass will
rise, more of the solid will melt, and the composition of the two phases will
change as represented by the curves da and cb. When the temperature has risen
to a, complete liquefaction will have occurred. The process of solidification or
of liquefaction is therefore extended over a temperature interval ac.
Page 163
Even when the freezing-point curve is a straight line joining the melting points
of the pure components, the melting-point curve will not necessarily coincide
with the freezing-point curve, although it may approach very near to it;
complete coincidence can take place only when the melting points of the two
components are identical. An example of this will be given later (Chap. XII.).
(b) The freezing-point curve passes through a maximum (Curve II., Fig. 49).
Fig. 51.
This curve exhibits the greatest degree of contrast to the freezing-point curve
which is obtained when the pure components crystallize out. For, since the
curve passes through a maximum, it is evident that the freezing point of each
of the components must be raised by the addition of the other component.
Example.—Very few cases belonging to this type are known. The best
example is found in the freezing-point curve of mixtures of d- and l-
carvoxime[272] (C10H14N.OH). The freezing points and melting points of the
different mixtures of d- and l-carvoxime are given in the following table, and
represented graphically in Fig. 51:—
Per cent. of Per cent. of
Freezing point. Melting point.
d-carvoxime. l-carvoxime.
100 0 72.0° 72.0°
99 1 72.4° —
98 2 73.0° —
95 5 75.4° 73.0°
90 10 79.0° 75.0°
80 20 84.6° 80.0°
70 30 88.2° 85.0°
60 40 90.4° —
50 50 91.4° 91.4°
of the pure components, the melting-point curve will not necessarily coincide
with the freezing-point curve, although it may approach very near to it;
complete coincidence can take place only when the melting points of the two
components are identical. An example of this will be given later (Chap. XII.).
(b) The freezing-point curve passes through a maximum (Curve II., Fig. 49).
Fig. 51.
This curve exhibits the greatest degree of contrast to the freezing-point curve
which is obtained when the pure components crystallize out. For, since the
curve passes through a maximum, it is evident that the freezing point of each
of the components must be raised by the addition of the other component.
Example.—Very few cases belonging to this type are known. The best
example is found in the freezing-point curve of mixtures of d- and l-
carvoxime[272] (C10H14N.OH). The freezing points and melting points of the
different mixtures of d- and l-carvoxime are given in the following table, and
represented graphically in Fig. 51:—
Per cent. of Per cent. of
Freezing point. Melting point.
d-carvoxime. l-carvoxime.
100 0 72.0° 72.0°
99 1 72.4° —
98 2 73.0° —
95 5 75.4° 73.0°
90 10 79.0° 75.0°
80 20 84.6° 80.0°
70 30 88.2° 85.0°
60 40 90.4° —
50 50 91.4° 91.4°
Page 164
25 75 86.4° 82.0°
8 92 77.4° —
1 99 72.4° —
0 100 72.0° 72.0°
In this figure, the melting-point curve, i.e. the temperature-concentration curve
for the mixed crystals, is represented by the lower curve. Since the addition of
the lævo-form to the dextro-form raises the melting point of the latter, the
concentration of the lævo-form (on the right-hand branch of the curve) must,
in accordance with the rule given, be greater in the solid phase than in the
liquid. Similarly, since addition of the dextro-form raises the melting point of
the lævo-form, the solid phase (on the left-hand branch of the curve) must be
richer in dextro- than in lævo-carvoxime. At the maximum point, the melting-
point and freezing-point curves touch; at this point, therefore, the composition
of the solid and liquid phases must be identical. It is evident, therefore, that at
the maximum point the liquid will solidify, or the solid will liquefy completely
without change of temperature; and, accordingly, mixed crystals of the
composition represented by the maximum point will exhibit a definite melting
point, and will in this respect behave like a simple substance.
(c) The freezing-point curve passes through a minimum (Curve III., Fig. 49).
In this case, as in the case of those systems where the pure components are
deposited, a minimum freezing point is obtained. In the latter case, however,
there are two freezing-point curves which intersect at a eutectic point; in the
case where mixed crystals are formed there is only one continuous curve. On
one side of the minimum point the liquid phase contains relatively more, on
the other side relatively less, of the one component than does the solid phase;
while at the minimum point the composition of the two phases is the same. At
this point, therefore, complete solidification or complete liquefaction will
occur without change of temperature, and the mixed crystals will accordingly
exhibit a definite melting point.
8 92 77.4° —
1 99 72.4° —
0 100 72.0° 72.0°
In this figure, the melting-point curve, i.e. the temperature-concentration curve
for the mixed crystals, is represented by the lower curve. Since the addition of
the lævo-form to the dextro-form raises the melting point of the latter, the
concentration of the lævo-form (on the right-hand branch of the curve) must,
in accordance with the rule given, be greater in the solid phase than in the
liquid. Similarly, since addition of the dextro-form raises the melting point of
the lævo-form, the solid phase (on the left-hand branch of the curve) must be
richer in dextro- than in lævo-carvoxime. At the maximum point, the melting-
point and freezing-point curves touch; at this point, therefore, the composition
of the solid and liquid phases must be identical. It is evident, therefore, that at
the maximum point the liquid will solidify, or the solid will liquefy completely
without change of temperature; and, accordingly, mixed crystals of the
composition represented by the maximum point will exhibit a definite melting
point, and will in this respect behave like a simple substance.
(c) The freezing-point curve passes through a minimum (Curve III., Fig. 49).
In this case, as in the case of those systems where the pure components are
deposited, a minimum freezing point is obtained. In the latter case, however,
there are two freezing-point curves which intersect at a eutectic point; in the
case where mixed crystals are formed there is only one continuous curve. On
one side of the minimum point the liquid phase contains relatively more, on
the other side relatively less, of the one component than does the solid phase;
while at the minimum point the composition of the two phases is the same. At
this point, therefore, complete solidification or complete liquefaction will
occur without change of temperature, and the mixed crystals will accordingly
exhibit a definite melting point.
Page 165
Fig. 52.
Example.—As an example of this there may be taken the mixed crystals of
mercuric bromide and iodide.[273] Mercuric bromide melts at 236.5°, and
mercuric iodide at 255.4°. The mixed crystal of definite constant melting point
(minimum point) contains 59 mols. per cent. of mercuric bromide, the melting
point being 216.1°.
The numerical data are contained in the following table, and represented
graphically in Fig. 52:—
Mols. per cent. of
Freezing point. Melting point.
HgBr2.
100 236.5° 236°
90 228.8° 226°
80 222.2° 219°
70 217.8° 217°
65 216.6° 216°
60 216.1° 215.5°
55 216.3° 216°
50 217.3° 216°
40 221.1° 218°
30 227.8° 223°
20 236.2° 231°
10 245.5° 242°
0 255.4° 254°
Fractional Crystallization of Mixed Crystals.—With
the help of the diagrams already given it will be possible
to predict what will be the result of the fractional
crystallization of a fused mixture of two substances
which can form mixed crystals. Suppose, for example, a
fused mixture of the composition x (Fig. 53) is cooled Fig. 53.
down; then, as we have already seen, when the
temperature has fallen to a, mixed crystals of composition, b, are deposited. If
the temperature is allowed to fall to x′, and the solid then separated from the
liquid, the mixed crystals so obtained will have the composition represented by
e. If, now, the mixed crystals e are completely fused and the fused mass
Example.—As an example of this there may be taken the mixed crystals of
mercuric bromide and iodide.[273] Mercuric bromide melts at 236.5°, and
mercuric iodide at 255.4°. The mixed crystal of definite constant melting point
(minimum point) contains 59 mols. per cent. of mercuric bromide, the melting
point being 216.1°.
The numerical data are contained in the following table, and represented
graphically in Fig. 52:—
Mols. per cent. of
Freezing point. Melting point.
HgBr2.
100 236.5° 236°
90 228.8° 226°
80 222.2° 219°
70 217.8° 217°
65 216.6° 216°
60 216.1° 215.5°
55 216.3° 216°
50 217.3° 216°
40 221.1° 218°
30 227.8° 223°
20 236.2° 231°
10 245.5° 242°
0 255.4° 254°
Fractional Crystallization of Mixed Crystals.—With
the help of the diagrams already given it will be possible
to predict what will be the result of the fractional
crystallization of a fused mixture of two substances
which can form mixed crystals. Suppose, for example, a
fused mixture of the composition x (Fig. 53) is cooled Fig. 53.
down; then, as we have already seen, when the
temperature has fallen to a, mixed crystals of composition, b, are deposited. If
the temperature is allowed to fall to x′, and the solid then separated from the
liquid, the mixed crystals so obtained will have the composition represented by
e. If, now, the mixed crystals e are completely fused and the fused mass
Page 166
allowed to cool, separation of solid will occur when the temperature has fallen
to the point f. The mixed crystals which are deposited have now the
composition represented by g, i.e. they are richer in B than the original mixed
crystals. By repeating this process, the composition of the successive crops of
mixed crystals which are obtained approximates more and more to that of the
pure component B, while, on the other hand, the composition of the liquid
phase produced tends to that of pure A. By a systematic and methodical
repetition of the process of fractional crystallization, therefore, a practically
complete separation of the components can be effected; a perfect separation is
theoretically impossible.
From this it will be readily understood that in the case of substances the
freezing point of which passes through a maximum, fractional crystallization
will ultimately lead to mixed crystals having the composition of the maximum
point, while the liquid phase will more and more assume the composition of
either pure A or pure B, according as the initial composition was on the A side
or the B side of the maximum point. In those cases, however, where the curves
exhibit a minimum, the solid phase which separates out will ultimately be one
of the pure components, while a liquid phase will finally be obtained which
has the composition of the minimum point.
II.—The Two Components do not form a Continuous Series of Mixed
Crystals.
This case corresponds to that of the partial miscibility of liquids. The solid
component A can "dissolve" the component B until the concentration of the
latter in the mixed crystal has reached a certain value. Addition of a further
amount of B will not alter the composition of the mixed crystal, but there will
be formed a second solid phase consisting of a solution of A in B. At this point
the four phases, mixed crystals containing excess of A, mixed crystals
containing excess of B, liquid solution, vapour, can coexist; this will therefore
be an invariant point. The temperature-concentration curves will therefore no
longer be continuous, but will exhibit a break or discontinuity at the point at
which the invariant system is formed.
(a) The freezing-point curve exhibits a transition point (Curve I., Fig. 54).
As is evident from the figure, addition of B raises the melting point of A, and,
in accordance with the rule previously given, the concentration of B in the
mixed crystals will be greater than in the solution. This is represented in the
to the point f. The mixed crystals which are deposited have now the
composition represented by g, i.e. they are richer in B than the original mixed
crystals. By repeating this process, the composition of the successive crops of
mixed crystals which are obtained approximates more and more to that of the
pure component B, while, on the other hand, the composition of the liquid
phase produced tends to that of pure A. By a systematic and methodical
repetition of the process of fractional crystallization, therefore, a practically
complete separation of the components can be effected; a perfect separation is
theoretically impossible.
From this it will be readily understood that in the case of substances the
freezing point of which passes through a maximum, fractional crystallization
will ultimately lead to mixed crystals having the composition of the maximum
point, while the liquid phase will more and more assume the composition of
either pure A or pure B, according as the initial composition was on the A side
or the B side of the maximum point. In those cases, however, where the curves
exhibit a minimum, the solid phase which separates out will ultimately be one
of the pure components, while a liquid phase will finally be obtained which
has the composition of the minimum point.
II.—The Two Components do not form a Continuous Series of Mixed
Crystals.
This case corresponds to that of the partial miscibility of liquids. The solid
component A can "dissolve" the component B until the concentration of the
latter in the mixed crystal has reached a certain value. Addition of a further
amount of B will not alter the composition of the mixed crystal, but there will
be formed a second solid phase consisting of a solution of A in B. At this point
the four phases, mixed crystals containing excess of A, mixed crystals
containing excess of B, liquid solution, vapour, can coexist; this will therefore
be an invariant point. The temperature-concentration curves will therefore no
longer be continuous, but will exhibit a break or discontinuity at the point at
which the invariant system is formed.
(a) The freezing-point curve exhibits a transition point (Curve I., Fig. 54).
As is evident from the figure, addition of B raises the melting point of A, and,
in accordance with the rule previously given, the concentration of B in the
mixed crystals will be greater than in the solution. This is represented in the
Page 167
figure by the dotted curve AD. On the other hand, addition of A lowers the
melting point of B, and the two curves BC and BE are obtained for the liquid
and solid phases respectively. At the temperature of the line CDE the liquid
solution of the composition represented by C is in equilibrium with the two
different mixed crystals represented by D and E. At this temperature, therefore,
the tc-curve for the solid phase exhibits a discontinuity; and, since the solid
phase undergoes change at this point, the freezing-point curve must show a
break (p. 111).
Fig. 54.
Example.—Curves of the form given in Fig. 54 I. have been found
experimentally in the case of silver nitrate and sodium nitrate.[274] The
following table contains the numerical data, which are also represented
graphically in Fig. 55:—
Molecules NaNO3
Freezing point. Melting point.
per cent.
0 208.6° 208.6°
8 211.4° 210°
15.06 215° 212°
19.46 217.2° 214.8°
21.9 222° 215°
26 228.4° 216.5°
29.7 234.8° 217.5°
36.2 244.4° 217.5°
47.3 259.4° 237.6°
58.9 272° 257°
72 284° 274°
100 308° 308°
melting point of B, and the two curves BC and BE are obtained for the liquid
and solid phases respectively. At the temperature of the line CDE the liquid
solution of the composition represented by C is in equilibrium with the two
different mixed crystals represented by D and E. At this temperature, therefore,
the tc-curve for the solid phase exhibits a discontinuity; and, since the solid
phase undergoes change at this point, the freezing-point curve must show a
break (p. 111).
Fig. 54.
Example.—Curves of the form given in Fig. 54 I. have been found
experimentally in the case of silver nitrate and sodium nitrate.[274] The
following table contains the numerical data, which are also represented
graphically in Fig. 55:—
Molecules NaNO3
Freezing point. Melting point.
per cent.
0 208.6° 208.6°
8 211.4° 210°
15.06 215° 212°
19.46 217.2° 214.8°
21.9 222° 215°
26 228.4° 216.5°
29.7 234.8° 217.5°
36.2 244.4° 217.5°
47.3 259.4° 237.6°
58.9 272° 257°
72 284° 274°
100 308° 308°
Page 168
The temperature of the transition point is 217.5°; at this point the liquid
contains 19.5, and the two conjugate solid solutions 26 and 38 molecules of
sodium nitrate per cent. respectively.
Fig. 55.
Fig. 56.
(b) The freezing-point curve exhibits a eutectic point (Curve II., Fig. 54).
In this case the freezing point of each of the components is lowered by the
addition of the other, until at last a point is reached at which the liquid solution
solidifies to a mixture or conglomerate of two mixed crystals.
Examples.—Curves belonging to this class have been obtained in the case of
potassium and thallium nitrates[275] and of naphthalene and monochloracetic
acid.[276] The data for the latter are given in the following table and
represented in Fig. 56:—
Liquid solution. Solid solution.
Temperature. Per cent. Per cent. Per cent. Per cent.
naphthalene. acid. naphthalene. acid.
62° — 100 — 100
contains 19.5, and the two conjugate solid solutions 26 and 38 molecules of
sodium nitrate per cent. respectively.
Fig. 55.
Fig. 56.
(b) The freezing-point curve exhibits a eutectic point (Curve II., Fig. 54).
In this case the freezing point of each of the components is lowered by the
addition of the other, until at last a point is reached at which the liquid solution
solidifies to a mixture or conglomerate of two mixed crystals.
Examples.—Curves belonging to this class have been obtained in the case of
potassium and thallium nitrates[275] and of naphthalene and monochloracetic
acid.[276] The data for the latter are given in the following table and
represented in Fig. 56:—
Liquid solution. Solid solution.
Temperature. Per cent. Per cent. Per cent. Per cent.
naphthalene. acid. naphthalene. acid.
62° — 100 — 100
Page 169
60° 4.0 96.0 1.7 98.3
55° 21.0 79.0 2.1 97.9
53.5° 29.4 70.0 — —
55° 31.3 68.7 59.6 40.4
60° 42.4 57.6 80.3 19.7
65° 53.3 46.7 89.2 10.8
70° 69.7 32.3 95.4 4.6
75° 84.4 15.6 96.6 3.4
100 100
79.9° — —
At the eutectic point the liquid solution is in equilibrium with two different
mixed crystals the composition of which is represented by D and E
respectively. If, therefore, a fused mixture containing the two components A
and B in the proportions represented by C is cooled down, it will, when the
temperature has reached the point C, solidify completely to a conglomerate of
mixed crystals, D and E.
Fig. 58.
55° 21.0 79.0 2.1 97.9
53.5° 29.4 70.0 — —
55° 31.3 68.7 59.6 40.4
60° 42.4 57.6 80.3 19.7
65° 53.3 46.7 89.2 10.8
70° 69.7 32.3 95.4 4.6
75° 84.4 15.6 96.6 3.4
100 100
79.9° — —
At the eutectic point the liquid solution is in equilibrium with two different
mixed crystals the composition of which is represented by D and E
respectively. If, therefore, a fused mixture containing the two components A
and B in the proportions represented by C is cooled down, it will, when the
temperature has reached the point C, solidify completely to a conglomerate of
mixed crystals, D and E.
Fig. 58.
Page 170
Changes in Mixed Crystals with the Temperature.—In the case
of the different types of systems represented in Fig. 49, a
homogeneous liquid solution of the two components will exist at
temperatures above the freezing-point curve, a homogeneous
mixed crystal at temperatures below the melting-point curve, while
at any point between the freezing-point and melting-point curves
the mixture will separate into a solid phase and a liquid phase. In
the case, however, of the two types shown in Fig. 54 the
relationships are somewhat more complicated. As before, the area
Fig. 57.
above the freezing-point curve gives the conditions under which
homogeneous liquid solutions can exist; but below the melting-
point curve two different mixed crystals can coexist. This will be best understood from
Figs. 57 and 58. D and E represent, as we have seen, the composition of two mixed crystals
which are in equilibrium with the liquid solution at the temperature of the point C. These
two mixed crystals represent, in the one case, a saturated solution of B in A (point D), and
the other a saturated solution of A in B (point E). Just as we saw that the mutual solubility
of two liquids varied with the temperature, so also in the case of two solids; as the
temperature alters, the solubility of the two solid components in one another will change.
This alteration is indicated diagrammatically in Figs. 57 and 58 by the dotted curve similar
to the solubility curves for two mutually soluble liquids (p. 101).
Suppose, now, that a mixed crystal of the composition x is cooled down, it will remain
unchanged until, when the temperature has fallen to t′, the homogeneous mixed crystal
breaks up into a conglomerate of two mixed crystals the composition of which is
represented by x′ and x″ respectively. From this, then, it can be seen that in the case of
substances which form two solid solutions, the mixed crystals which are desposited from
the liquid fused mass need not remain unchanged in the solid state, but may at some lower
temperature lose their homogeneity. This fact is of considerable importance for the
formation of alloys.[277]
A good example of this will soon be met with in the case of the iron and carbon alloys. The
alloys of copper and tin also furnish examples of the great changes which may take place in
the alloy between the temperature at which it separates out from the fused mass and the
ordinary temperature. Thus, for example, one of the alloys of copper and tin which
separates out from the liquid as a solid solution breaks up, on cooling, into the compound
Cu3Sn and liquid:[278] a striking example of a solid substance partially liquefying on being
cooled.
CHAPTER XI
EQUILIBRIUM BETWEEN DYNAMIC ISOMERIDES
of the different types of systems represented in Fig. 49, a
homogeneous liquid solution of the two components will exist at
temperatures above the freezing-point curve, a homogeneous
mixed crystal at temperatures below the melting-point curve, while
at any point between the freezing-point and melting-point curves
the mixture will separate into a solid phase and a liquid phase. In
the case, however, of the two types shown in Fig. 54 the
relationships are somewhat more complicated. As before, the area
Fig. 57.
above the freezing-point curve gives the conditions under which
homogeneous liquid solutions can exist; but below the melting-
point curve two different mixed crystals can coexist. This will be best understood from
Figs. 57 and 58. D and E represent, as we have seen, the composition of two mixed crystals
which are in equilibrium with the liquid solution at the temperature of the point C. These
two mixed crystals represent, in the one case, a saturated solution of B in A (point D), and
the other a saturated solution of A in B (point E). Just as we saw that the mutual solubility
of two liquids varied with the temperature, so also in the case of two solids; as the
temperature alters, the solubility of the two solid components in one another will change.
This alteration is indicated diagrammatically in Figs. 57 and 58 by the dotted curve similar
to the solubility curves for two mutually soluble liquids (p. 101).
Suppose, now, that a mixed crystal of the composition x is cooled down, it will remain
unchanged until, when the temperature has fallen to t′, the homogeneous mixed crystal
breaks up into a conglomerate of two mixed crystals the composition of which is
represented by x′ and x″ respectively. From this, then, it can be seen that in the case of
substances which form two solid solutions, the mixed crystals which are desposited from
the liquid fused mass need not remain unchanged in the solid state, but may at some lower
temperature lose their homogeneity. This fact is of considerable importance for the
formation of alloys.[277]
A good example of this will soon be met with in the case of the iron and carbon alloys. The
alloys of copper and tin also furnish examples of the great changes which may take place in
the alloy between the temperature at which it separates out from the fused mass and the
ordinary temperature. Thus, for example, one of the alloys of copper and tin which
separates out from the liquid as a solid solution breaks up, on cooling, into the compound
Cu3Sn and liquid:[278] a striking example of a solid substance partially liquefying on being
cooled.
CHAPTER XI
EQUILIBRIUM BETWEEN DYNAMIC ISOMERIDES
Page 171
It has long been known that certain substances, e.g. acetoacetic ester, are capable when in
solution or in the fused state, of reacting as if they possessed two different constitutions;
and in order to explain this behaviour the view was advanced (by Laar) that in such cases a
hydrogen atom oscillated between two positions in the molecule, being at one time
attached to oxygen, at another time to carbon, as represented by the formula—
When the hydrogen is in one position, the substance will act as an hydroxy-compound;
with hydrogen in the other position, as a ketone. Substances possessing this double
function are called tautomeric.
Doubt, however, arose as to the validity of the above explanation, and this doubt was
confirmed by the isolation of the two isomerides in the solid state, and also by the fact that
the velocity of change of the one isomeride into the other could in some cases be
quantitatively measured. These and other observations then led to the view, in harmony
with the laws of chemical dynamics, that tautomeric substances in the dissolved or fused
state represent a mixture of two isomeric forms, and that equilibrium is established not by
intra- but by inter-molecular change, as expressed by the equation—
CH3.CO.CH2.CO2C2H5 CH3.C(OH):CH.CO2C2H5
In the solid state, the one or other of the isomerides represents the stable form; but in the
liquid state (solution or fusion) the stable condition is an equilibrium between the two
forms.
A similar behaviour is also found in the case of other isomeric substances where the
isomerism is due to difference of structure, i.e. structure isomerism (e.g. in the case of the
oximes and , or to difference in configuration, i.e. stereoisomerism
(e.g. optically active substances), or to polymerism (e.g. acetaldehyde and paraldehyde). In
all such cases, although the different solid forms correspond to a single definite
constitution, in the liquid state a condition of equilibrium between the two modifications is
established. As a general name for these different classes of substances, the term "dynamic
isomerides" has been introduced; and the different kinds of isomerism are classed together
under the title "dynamic isomerism."[279]
By reason of the importance of these phenomena in the study more especially of Organic
Chemistry, a brief account of the equilibrium relations exhibited by systems composed of
dynamic isomerides may be given here.[280]
In studying the fusion and solidification of those substances which exhibit the relationships
of dynamic isomerism, the phenomena observed will vary somewhat according as the
reversible transformation of the one form into the other takes place with measurable
velocity at temperatures in the neighbourhood of the melting points, or only at some higher
solution or in the fused state, of reacting as if they possessed two different constitutions;
and in order to explain this behaviour the view was advanced (by Laar) that in such cases a
hydrogen atom oscillated between two positions in the molecule, being at one time
attached to oxygen, at another time to carbon, as represented by the formula—
When the hydrogen is in one position, the substance will act as an hydroxy-compound;
with hydrogen in the other position, as a ketone. Substances possessing this double
function are called tautomeric.
Doubt, however, arose as to the validity of the above explanation, and this doubt was
confirmed by the isolation of the two isomerides in the solid state, and also by the fact that
the velocity of change of the one isomeride into the other could in some cases be
quantitatively measured. These and other observations then led to the view, in harmony
with the laws of chemical dynamics, that tautomeric substances in the dissolved or fused
state represent a mixture of two isomeric forms, and that equilibrium is established not by
intra- but by inter-molecular change, as expressed by the equation—
CH3.CO.CH2.CO2C2H5 CH3.C(OH):CH.CO2C2H5
In the solid state, the one or other of the isomerides represents the stable form; but in the
liquid state (solution or fusion) the stable condition is an equilibrium between the two
forms.
A similar behaviour is also found in the case of other isomeric substances where the
isomerism is due to difference of structure, i.e. structure isomerism (e.g. in the case of the
oximes and , or to difference in configuration, i.e. stereoisomerism
(e.g. optically active substances), or to polymerism (e.g. acetaldehyde and paraldehyde). In
all such cases, although the different solid forms correspond to a single definite
constitution, in the liquid state a condition of equilibrium between the two modifications is
established. As a general name for these different classes of substances, the term "dynamic
isomerides" has been introduced; and the different kinds of isomerism are classed together
under the title "dynamic isomerism."[279]
By reason of the importance of these phenomena in the study more especially of Organic
Chemistry, a brief account of the equilibrium relations exhibited by systems composed of
dynamic isomerides may be given here.[280]
In studying the fusion and solidification of those substances which exhibit the relationships
of dynamic isomerism, the phenomena observed will vary somewhat according as the
reversible transformation of the one form into the other takes place with measurable
velocity at temperatures in the neighbourhood of the melting points, or only at some higher
Page 172
temperature. If the transformation is very rapid, the system will behave like a one-
component system, but if the isomeric change is comparatively slow, the behaviour will be
that of a two-component system.
Temperature-Concentration Diagram.—The relationships which are met with here will
be most readily understood with the help of Fig. 59. Suppose, in the first instance, that
isomeric transformation does not take place at the temperature of the melting point, then
the freezing point curve will have the simple form ACB; the formation of compounds being
for the present excluded. This is the simplest type of curve, and gives the composition of
the solutions in equilibrium with the one modification (α modification) at different
temperatures (curve AC); and of the solutions in equilibrium with the other modification (β
modification) at different temperatures (curve BC). C is the eutectic point at which the two
solid isomerides can exist side by side in contact with the solution.
Fig. 59.
Now, suppose that isomeric transformation takes place with measurable velocity. If the
pure α-modification is heated to a temperature t′ above its melting point, and the liquid
maintained at that temperature until equilibrium has been established, a certain amount of
the β-form will be present in the liquid, the composition of which will be represented by
the point x′. The same condition of equilibrium will also be reached by starting with pure β.
Similarly, if the temperature of the liquid is maintained at the temperature t″, equilibrium
will be reached, we shall suppose, when the solution has the composition x″. The curve
DE, therefore, which passes through all the different values of x corresponding to different
values of t, will represent the change of equilibrium with the temperature. It will slope to
the right (as in the figure) if the transformation of α into β is accompanied by absorption of
heat; to the left if the transformation is accompanied by evolution of heat, in accordance
with van't Hoff's Law of movable equilibrium. If transformation occurs without heat effect,
the equilibrium will be independent of the temperature, and the equilibrium curve DE will
therefore be perpendicular and parallel to the temperature axis.
We must now find the meaning of the point D. Suppose the pure α- or pure β-form heated
to the temperature t′, and the temperature maintained constant until the liquid has the
composition x′ corresponding to the equilibrium at that temperature. If the temperature is
now allowed to fall sufficiently slowly so that the condition of equilibrium is continually
readjusted as the temperature changes, the composition of the solution will gradually alter
as represented by the curve x′D. Since D is on the freezing point curve of pure α, this form
will be deposited on cooling; and since D is also on the equilibrium curve of the liquid, D
component system, but if the isomeric change is comparatively slow, the behaviour will be
that of a two-component system.
Temperature-Concentration Diagram.—The relationships which are met with here will
be most readily understood with the help of Fig. 59. Suppose, in the first instance, that
isomeric transformation does not take place at the temperature of the melting point, then
the freezing point curve will have the simple form ACB; the formation of compounds being
for the present excluded. This is the simplest type of curve, and gives the composition of
the solutions in equilibrium with the one modification (α modification) at different
temperatures (curve AC); and of the solutions in equilibrium with the other modification (β
modification) at different temperatures (curve BC). C is the eutectic point at which the two
solid isomerides can exist side by side in contact with the solution.
Fig. 59.
Now, suppose that isomeric transformation takes place with measurable velocity. If the
pure α-modification is heated to a temperature t′ above its melting point, and the liquid
maintained at that temperature until equilibrium has been established, a certain amount of
the β-form will be present in the liquid, the composition of which will be represented by
the point x′. The same condition of equilibrium will also be reached by starting with pure β.
Similarly, if the temperature of the liquid is maintained at the temperature t″, equilibrium
will be reached, we shall suppose, when the solution has the composition x″. The curve
DE, therefore, which passes through all the different values of x corresponding to different
values of t, will represent the change of equilibrium with the temperature. It will slope to
the right (as in the figure) if the transformation of α into β is accompanied by absorption of
heat; to the left if the transformation is accompanied by evolution of heat, in accordance
with van't Hoff's Law of movable equilibrium. If transformation occurs without heat effect,
the equilibrium will be independent of the temperature, and the equilibrium curve DE will
therefore be perpendicular and parallel to the temperature axis.
We must now find the meaning of the point D. Suppose the pure α- or pure β-form heated
to the temperature t′, and the temperature maintained constant until the liquid has the
composition x′ corresponding to the equilibrium at that temperature. If the temperature is
now allowed to fall sufficiently slowly so that the condition of equilibrium is continually
readjusted as the temperature changes, the composition of the solution will gradually alter
as represented by the curve x′D. Since D is on the freezing point curve of pure α, this form
will be deposited on cooling; and since D is also on the equilibrium curve of the liquid, D
Page 173
is the only point at which solid can exist in stable equilibrium with the liquid phase. (The
vapour phase may be omitted from consideration, as we shall suppose the experiments
carried out in open vessels.) All systems consisting of the two hylotropic[281] isomeric
substances α and β will, therefore, ultimately freeze at the point D, which is called the
"natural" freezing point[282] of the system; provided, of course, that sufficient time is
allowed for equilibrium to be established. From this it is apparent that the stable
modification at temperatures in the neighbourhood of the melting point is that which is in
equilibrium with the liquid phase at the natural freezing point.
From what has been said, it will be easy to predict what will be the behaviour of the system
under different conditions. If pure α is heated, a temperature will be reached at which it
will melt, but this melting point will be sharp only if the velocity of isomeric
transformation is comparatively slow; i.e. slow in comparison with the determination of the
melting point. If the substance be maintained in the fused condition for some time, a certain
amount of the β modification will be formed, and on lowering the temperature the pure α
form will be deposited, not at the temperature of the melting point, but at some lower
temperature depending on the concentration of the β modification in the liquid phase. If
isomeric transformation takes place slowly in comparison with the rate at which deposition
of the solid occurs, the liquid will become increasingly rich in the β modification, and the
freezing point will, therefore, sink continuously. At the eutectic point, however, the β
modification will also be deposited, and the temperature will remain constant until all has
become solid. If, on the other hand, the velocity of transformation is sufficiently rapid, then
as quickly as the α modification is deposited, the equilibrium between the two isomeric
forms in the liquid phase will continuously readjust itself, and the end-point of
solidification will be the natural freezing point.
Similarly, starting with the pure β modification, the freezing point after fusion will
gradually fall owing to the formation of the α modification; and the composition of the
liquid phase will pass along the curve BC. If, now, the rate of cooling is not too great, or if
the velocity of isomeric transformation is sufficiently rapid, complete solidification will not
occur at the eutectic point; for at this temperature solid and liquid are not in stable
equilibrium with one another. On the contrary, a further quantity of the β modification will
undergo isomeric change, the liquid phase will become richer in the α form, and the
freezing point will rise; the solid phase in contact with the liquid being now the α
modification. The freezing point will continue to rise until the point D is reached, at which
complete solidification will take place without further change of temperature.
The diagram also allows us to predict what will be the result of rapidly cooling a fused
mixture of the two isomerides. Suppose that either the α or the β modification has been
maintained in the fused state at the temperature t′ sufficiently long for equilibrium to be
established. The composition of the liquid phase will be represented by x′. If the liquid is
now rapidly cooled, the composition will remain unchanged as represented by the dotted
line x′G. At the temperature of the point G solid α modification will be deposited. If the
cooling is not carried below the point G, so as to cause complete solidification, the freezing
point will be found to rise with time, owing to the conversion of some of the β form into
vapour phase may be omitted from consideration, as we shall suppose the experiments
carried out in open vessels.) All systems consisting of the two hylotropic[281] isomeric
substances α and β will, therefore, ultimately freeze at the point D, which is called the
"natural" freezing point[282] of the system; provided, of course, that sufficient time is
allowed for equilibrium to be established. From this it is apparent that the stable
modification at temperatures in the neighbourhood of the melting point is that which is in
equilibrium with the liquid phase at the natural freezing point.
From what has been said, it will be easy to predict what will be the behaviour of the system
under different conditions. If pure α is heated, a temperature will be reached at which it
will melt, but this melting point will be sharp only if the velocity of isomeric
transformation is comparatively slow; i.e. slow in comparison with the determination of the
melting point. If the substance be maintained in the fused condition for some time, a certain
amount of the β modification will be formed, and on lowering the temperature the pure α
form will be deposited, not at the temperature of the melting point, but at some lower
temperature depending on the concentration of the β modification in the liquid phase. If
isomeric transformation takes place slowly in comparison with the rate at which deposition
of the solid occurs, the liquid will become increasingly rich in the β modification, and the
freezing point will, therefore, sink continuously. At the eutectic point, however, the β
modification will also be deposited, and the temperature will remain constant until all has
become solid. If, on the other hand, the velocity of transformation is sufficiently rapid, then
as quickly as the α modification is deposited, the equilibrium between the two isomeric
forms in the liquid phase will continuously readjust itself, and the end-point of
solidification will be the natural freezing point.
Similarly, starting with the pure β modification, the freezing point after fusion will
gradually fall owing to the formation of the α modification; and the composition of the
liquid phase will pass along the curve BC. If, now, the rate of cooling is not too great, or if
the velocity of isomeric transformation is sufficiently rapid, complete solidification will not
occur at the eutectic point; for at this temperature solid and liquid are not in stable
equilibrium with one another. On the contrary, a further quantity of the β modification will
undergo isomeric change, the liquid phase will become richer in the α form, and the
freezing point will rise; the solid phase in contact with the liquid being now the α
modification. The freezing point will continue to rise until the point D is reached, at which
complete solidification will take place without further change of temperature.
The diagram also allows us to predict what will be the result of rapidly cooling a fused
mixture of the two isomerides. Suppose that either the α or the β modification has been
maintained in the fused state at the temperature t′ sufficiently long for equilibrium to be
established. The composition of the liquid phase will be represented by x′. If the liquid is
now rapidly cooled, the composition will remain unchanged as represented by the dotted
line x′G. At the temperature of the point G solid α modification will be deposited. If the
cooling is not carried below the point G, so as to cause complete solidification, the freezing
point will be found to rise with time, owing to the conversion of some of the β form into
Page 174
the α form in the liquid phase; and this will continue until the composition of the liquid has
reached the point D. From what has just been said, it can also be seen that if the freezing
point curves can be obtained by actual determination of the freezing points of different
synthetic mixtures of the two isomerides, it will be possible to determine the condition of
equilibrium in the fused state at any given temperature without having recourse to analysis.
All that is necessary is to rapidly cool the fused mass, after equilibrium has been
established, and find the freezing point at which solid is deposited; that is, find the point at
which the line of constant temperature cuts the freezing point curve. The composition
corresponding to this temperature gives the composition of the equilibrium mixture at the
given temperature.
It will be evident, from what has gone before, that the degree of completeness with which
the different curves can be realised will depend on the velocity with which isomeric change
takes place, and on the rapidity with which the determinations of the freezing point can be
carried out. As the two extremes we have, on the one hand, practically instantaneous
transformation, and on the other, practically infinite slowness of transformation. In the
former case, only one melting and freezing point will be found, viz. the natural freezing
point; in the latter case, the two isomerides will behave as two perfectly independent
components, and the equilibrium curve DE will not be realised.
The diagram which is obtained when isomeric transformation does not occur within
measurable time at the temperature of the melting point is somewhat different from that
already given in Fig. 59. In this case, the two freezing point curves AC and BC (Fig. 60)
can be readily realized, as no isomeric change occurs in the liquid phase. Suppose,
however, that at a higher temperature, t′, reversible isomeric transformation can take place,
the composition of the liquid phase will alter until at the point x′ a condition of equilibrium
is reached; and the composition of the liquid at higher temperatures will be represented by
the curve x′F. Below the temperature t′ the position of the equilibrium curve is
hypothetical; but as the temperature falls the velocity of transformation diminishes, and at
last becomes practically zero. The equilibrium curve can therefore be regarded as dividing
into two branches x′G and x′H. At temperatures between G and t′ the α modification can
undergo isomeric change leading to a point on the curve Gx′; and the β modification can
undergo change leading to a point on the curve Hx′. The same condition of equilibrium is
therefore not reached from each side, and we are therefore dealing not with true but with
false equilibrium (p. 5). Below the temperatures G and H, isomeric transformation does not
occur in measurable time. We shall not, however, enter into a detailed discussion of the
equilibria in such systems, more especially as they are not systems in true equilibrium, and
as the temperature at which true equilibrium can be established with appreciable velocity
alters under the influence of catalytic agents.[283] Examples of such systems will no doubt
be found in the case of optically active substances, where both isomerides are apparently
quite stable at the melting point. In the case of such substances, also, the action of catalytic
agents in producing isomeric transformation (racemisation) is well known.
reached the point D. From what has just been said, it can also be seen that if the freezing
point curves can be obtained by actual determination of the freezing points of different
synthetic mixtures of the two isomerides, it will be possible to determine the condition of
equilibrium in the fused state at any given temperature without having recourse to analysis.
All that is necessary is to rapidly cool the fused mass, after equilibrium has been
established, and find the freezing point at which solid is deposited; that is, find the point at
which the line of constant temperature cuts the freezing point curve. The composition
corresponding to this temperature gives the composition of the equilibrium mixture at the
given temperature.
It will be evident, from what has gone before, that the degree of completeness with which
the different curves can be realised will depend on the velocity with which isomeric change
takes place, and on the rapidity with which the determinations of the freezing point can be
carried out. As the two extremes we have, on the one hand, practically instantaneous
transformation, and on the other, practically infinite slowness of transformation. In the
former case, only one melting and freezing point will be found, viz. the natural freezing
point; in the latter case, the two isomerides will behave as two perfectly independent
components, and the equilibrium curve DE will not be realised.
The diagram which is obtained when isomeric transformation does not occur within
measurable time at the temperature of the melting point is somewhat different from that
already given in Fig. 59. In this case, the two freezing point curves AC and BC (Fig. 60)
can be readily realized, as no isomeric change occurs in the liquid phase. Suppose,
however, that at a higher temperature, t′, reversible isomeric transformation can take place,
the composition of the liquid phase will alter until at the point x′ a condition of equilibrium
is reached; and the composition of the liquid at higher temperatures will be represented by
the curve x′F. Below the temperature t′ the position of the equilibrium curve is
hypothetical; but as the temperature falls the velocity of transformation diminishes, and at
last becomes practically zero. The equilibrium curve can therefore be regarded as dividing
into two branches x′G and x′H. At temperatures between G and t′ the α modification can
undergo isomeric change leading to a point on the curve Gx′; and the β modification can
undergo change leading to a point on the curve Hx′. The same condition of equilibrium is
therefore not reached from each side, and we are therefore dealing not with true but with
false equilibrium (p. 5). Below the temperatures G and H, isomeric transformation does not
occur in measurable time. We shall not, however, enter into a detailed discussion of the
equilibria in such systems, more especially as they are not systems in true equilibrium, and
as the temperature at which true equilibrium can be established with appreciable velocity
alters under the influence of catalytic agents.[283] Examples of such systems will no doubt
be found in the case of optically active substances, where both isomerides are apparently
quite stable at the melting point. In the case of such substances, also, the action of catalytic
agents in producing isomeric transformation (racemisation) is well known.
Page 175
Fig. 60.
Transformation of the Unstable into the Stable Form.—As has already been stated, the
stable modification in the neighbourhood of the melting point is that one which is in
equilibrium with the liquid phase at the natural freezing point. In the case of polymorphic
substances, we have seen (p. 39) that that form which is stable in the neighbourhood of the
melting point melts at the higher temperature. That was a consequence of the fact that the
two polymorphic forms on melting gave identical liquid phases. In the present case,
however, the above rule does not apply, for the simple reason that the liquid phase obtained
by the fusion of the one modification is not identical with that obtained by the fusion of the
other. In the case of isomeric substances, therefore, the form of lower melting point may be
the more stable; and where this behaviour is found it is a sign that the two forms are
isomeric (or polymeric) and not polymorphic.[284] An example of this is found in the case
of the isomeric benzaldoximes (p. 203).
Since in Fig. 59 the α modification has been represented as the stable form, the
transformation of the β into the α form will be possible at all temperatures down to the
transition point. At temperatures below the eutectic point, transformation will occur
without formation of a liquid phase; but at temperatures above the eutectic point
liquefaction can take place. This will be more readily understood by drawing a line of
constant temperature, HK, at some point between C and B. Then if the β modification is
maintained for a sufficiently long time at that temperature, a certain amount of the α
modification will be formed; and when the composition of the mixture has reached the
point H, fusion will occur. If the temperature is maintained constant, isomeric
transformation will continue to take place in the liquid phase until the equilibrium point for
that temperature is reached. If this temperature is higher than the natural melting point, the
mixture will remain liquid all the time; but if it is below the natural melting point, then the
α modification will be deposited when the system reaches the condition represented by the
point on the curve AC corresponding to the particular temperature. As isomeric
transformation continues, the freezing point of the system will rise until it reaches the
natural freezing point D. Similarly, if the α modification is maintained at a temperature
above that of the point D, liquefaction will ultimately occur, and the system will again
reach the final state represented by D.[285]
Transformation of the Unstable into the Stable Form.—As has already been stated, the
stable modification in the neighbourhood of the melting point is that one which is in
equilibrium with the liquid phase at the natural freezing point. In the case of polymorphic
substances, we have seen (p. 39) that that form which is stable in the neighbourhood of the
melting point melts at the higher temperature. That was a consequence of the fact that the
two polymorphic forms on melting gave identical liquid phases. In the present case,
however, the above rule does not apply, for the simple reason that the liquid phase obtained
by the fusion of the one modification is not identical with that obtained by the fusion of the
other. In the case of isomeric substances, therefore, the form of lower melting point may be
the more stable; and where this behaviour is found it is a sign that the two forms are
isomeric (or polymeric) and not polymorphic.[284] An example of this is found in the case
of the isomeric benzaldoximes (p. 203).
Since in Fig. 59 the α modification has been represented as the stable form, the
transformation of the β into the α form will be possible at all temperatures down to the
transition point. At temperatures below the eutectic point, transformation will occur
without formation of a liquid phase; but at temperatures above the eutectic point
liquefaction can take place. This will be more readily understood by drawing a line of
constant temperature, HK, at some point between C and B. Then if the β modification is
maintained for a sufficiently long time at that temperature, a certain amount of the α
modification will be formed; and when the composition of the mixture has reached the
point H, fusion will occur. If the temperature is maintained constant, isomeric
transformation will continue to take place in the liquid phase until the equilibrium point for
that temperature is reached. If this temperature is higher than the natural melting point, the
mixture will remain liquid all the time; but if it is below the natural melting point, then the
α modification will be deposited when the system reaches the condition represented by the
point on the curve AC corresponding to the particular temperature. As isomeric
transformation continues, the freezing point of the system will rise until it reaches the
natural freezing point D. Similarly, if the α modification is maintained at a temperature
above that of the point D, liquefaction will ultimately occur, and the system will again
reach the final state represented by D.[285]
Page 176
Examples.—Benzaldoximes. The relationships which have just been discussed from the
theoretical point of view will be rendered clearer by a brief description of cases which have
been experimentally investigated. The first we shall consider is that of the two isomeric
benzaldoximes:[286]—
Benzantialdoxime (α-modification). Benzsynaldoxime (β-modification).
Fig. 61 gives a graphic representation of the results obtained.
The melting point of the α modification is 34-35°; the melting point of the unstable β-
modification being 130°. The freezing curves AC and BC were obtained by determining
the freezing points of different mixtures of known composition, and the numbers so
obtained are given in the following table.
Grams of the α modification
Freezing point.
in 100 gm. of mixture.
26.2 101°
49.2 79°
73.7 46°
91.7 26.2°
95.0 28.6°
96.0 30.0°
The eutectic point C was found to lie at 25-26°, and the natural
freezing point D was found to be 27.7°. The equilibrium curve DE
was determined by heating the liquid mixtures at different
temperatures until equilibrium was attained, and then rapidly
cooling the liquid. In all cases the freezing point was practically
that of the point D. From this it is seen that the equilibrium curve
must be a straight line parallel to the temperature axis; and,
therefore, isomeric transformation in the case of the two
benzaldoximes is not accompanied by any heat effect (p. 197). This
behaviour has also been found in the case of acetaldoxime.[287] Fig. 61.
The isomeric benzaldoximes are also of interest from the fact that
the stable modification has the lower melting point (v. p. 202).
Acetaldehyde and Paraldehyde.—As a second example of the equilibria between two
isomerides, we shall take the two isomeric (polymeric) forms of acetaldehyde, which have
recently been exhaustively studied.[288]
In the case of these two substances the reaction
3CH3.CHO (CH3.CHO)3
theoretical point of view will be rendered clearer by a brief description of cases which have
been experimentally investigated. The first we shall consider is that of the two isomeric
benzaldoximes:[286]—
Benzantialdoxime (α-modification). Benzsynaldoxime (β-modification).
Fig. 61 gives a graphic representation of the results obtained.
The melting point of the α modification is 34-35°; the melting point of the unstable β-
modification being 130°. The freezing curves AC and BC were obtained by determining
the freezing points of different mixtures of known composition, and the numbers so
obtained are given in the following table.
Grams of the α modification
Freezing point.
in 100 gm. of mixture.
26.2 101°
49.2 79°
73.7 46°
91.7 26.2°
95.0 28.6°
96.0 30.0°
The eutectic point C was found to lie at 25-26°, and the natural
freezing point D was found to be 27.7°. The equilibrium curve DE
was determined by heating the liquid mixtures at different
temperatures until equilibrium was attained, and then rapidly
cooling the liquid. In all cases the freezing point was practically
that of the point D. From this it is seen that the equilibrium curve
must be a straight line parallel to the temperature axis; and,
therefore, isomeric transformation in the case of the two
benzaldoximes is not accompanied by any heat effect (p. 197). This
behaviour has also been found in the case of acetaldoxime.[287] Fig. 61.
The isomeric benzaldoximes are also of interest from the fact that
the stable modification has the lower melting point (v. p. 202).
Acetaldehyde and Paraldehyde.—As a second example of the equilibria between two
isomerides, we shall take the two isomeric (polymeric) forms of acetaldehyde, which have
recently been exhaustively studied.[288]
In the case of these two substances the reaction
3CH3.CHO (CH3.CHO)3
Page 177
takes place at the ordinary temperature with very great slowness. For this reason it is
possible to determine the freezing point curves of acetaldehyde and paraldehyde. The three
chief points on these curves, represented graphically in Fig. 62, are:—
m.p. of acetaldehyde - 118.45°
m.p. of paraldehyde + 12.55°
eutectic point - 119.9°
In order to determine the position of the natural melting point, it
was necessary, on account of the slowness of transformation, to
employ a catalytic agent in order to increase the velocity with
which the equilibrium was established. A drop of concentrated
sulphuric acid served the purpose. In presence of a trace of this
substance, isomeric transformation very speedily occurs, and leads
to the condition of equilibrium. Starting in the one case with fused
paraldehyde, and in the other case with acetaldehyde, the same
freezing point, viz. 6.75°, was obtained, the solid phase being
paraldehyde. This temperature, 6.75°, is therefore the natural Fig. 62.
freezing point, and paraldehyde, the solid in equilibrium with the
liquid phase at this point, is the stable form.
With regard to the change of equilibrium with the temperature, it was found that whereas
the liquid phase contained 11.7 molecules per cent. of acetaldehyde at the natural freezing
point, the liquid at the temperature of 41.6° contains 46.6 molecules per cent. of
acetaldehyde. As the temperature rises, therefore, there is increased formation of
acetaldehyde, or a decreasing amount of polymerisation. This is in harmony with the fact
that the polymerisation of acetaldehyde is accompanied by evolution of heat.
While speaking of these isomerides, it may be mentioned that at the temperature 41.6° the
equilibrium mixture has a vapour pressure equal to the atmospheric pressure. At this
temperature, therefore, the equilibrium mixture (obtained quickly with the help of a trace of
sulphuric acid) boils.[289]
CHAPTER XII
SUMMARY.—APPLICATION OF THE PHASE RULE TO THE STUDY OF SYSTEMS
OF TWO COMPONENTS
In this concluding chapter on two-component systems, it is proposed to indicate briefly
how the Phase Rule has been applied to the elucidation of a number of problems connected
with the equilibria between two components, and how it has been employed for the
interpretation of the data obtained by experiment. It is hoped that the practical value of the
possible to determine the freezing point curves of acetaldehyde and paraldehyde. The three
chief points on these curves, represented graphically in Fig. 62, are:—
m.p. of acetaldehyde - 118.45°
m.p. of paraldehyde + 12.55°
eutectic point - 119.9°
In order to determine the position of the natural melting point, it
was necessary, on account of the slowness of transformation, to
employ a catalytic agent in order to increase the velocity with
which the equilibrium was established. A drop of concentrated
sulphuric acid served the purpose. In presence of a trace of this
substance, isomeric transformation very speedily occurs, and leads
to the condition of equilibrium. Starting in the one case with fused
paraldehyde, and in the other case with acetaldehyde, the same
freezing point, viz. 6.75°, was obtained, the solid phase being
paraldehyde. This temperature, 6.75°, is therefore the natural Fig. 62.
freezing point, and paraldehyde, the solid in equilibrium with the
liquid phase at this point, is the stable form.
With regard to the change of equilibrium with the temperature, it was found that whereas
the liquid phase contained 11.7 molecules per cent. of acetaldehyde at the natural freezing
point, the liquid at the temperature of 41.6° contains 46.6 molecules per cent. of
acetaldehyde. As the temperature rises, therefore, there is increased formation of
acetaldehyde, or a decreasing amount of polymerisation. This is in harmony with the fact
that the polymerisation of acetaldehyde is accompanied by evolution of heat.
While speaking of these isomerides, it may be mentioned that at the temperature 41.6° the
equilibrium mixture has a vapour pressure equal to the atmospheric pressure. At this
temperature, therefore, the equilibrium mixture (obtained quickly with the help of a trace of
sulphuric acid) boils.[289]
CHAPTER XII
SUMMARY.—APPLICATION OF THE PHASE RULE TO THE STUDY OF SYSTEMS
OF TWO COMPONENTS
In this concluding chapter on two-component systems, it is proposed to indicate briefly
how the Phase Rule has been applied to the elucidation of a number of problems connected
with the equilibria between two components, and how it has been employed for the
interpretation of the data obtained by experiment. It is hoped that the practical value of the
Page 178
Phase Rule may thereby become more apparent, and its application to other cases be
rendered easier.
The interest and importance of investigations into the conditions of equilibrium between
two substances, lie in the determination not only of the conditions for the stable existence
of the participating substances, but also of whether or not chemical action takes place
between these two components; and if combination occurs, in the determination of the
nature of the compounds formed and the range of their existence. In all such investigations,
the Phase Rule becomes of conspicuous value on account of the fact that its principles
afford, as it were, a touchstone by which the character of the system can be determined,
and that from the form of the equilibrium curves obtained, conclusions can be drawn as to
the nature of the interaction between the two substances. In order to exemplify the
application of the principles of the Phase Rule more fully than has already been done,
illustrations will be drawn from investigations on the interaction of organic compounds; on
the equilibria between optically active compounds; and on alloys.
Summary of the Different Systems of Two Components.—Before passing to the
consideration of the application of the Phase Rule to the investigation of particular
problems, it will be well to collect together the different types of equilibrium curves with
which we are already acquainted; to compare them with one another, in order that we may
then employ these characteristic curves for the interpretation of the curves obtained as the
result of experiment.
In investigating the equilibria between two components, three chief classes of curves will
be obtained according as—
I. No combination takes place between the two components.
II. The components can form definite compounds.
III. The components separate out in the form of mixed crystals.
The different types of curves which are obtained in these three cases are represented in
Figs. 63, 64, 65. These different diagrams represent the whole series of equilibria, from the
melting point of the one component (A) to that of the other component (B). The curves
represent, in all cases, the composition of the solution, or phase of variable composition;
the temperature being measured along one axis, and the composition along the other.
We shall now recapitulate very briefly the characteristics of the different curves.
If no compound is formed between the two components, the general form of the
equilibrium curve will be that of curve I. or II., Fig. 63. Type I. is the simplest form of
curve found, and consists, as the diagram shows, of only two branches, AC and BC,
meeting at the point C, which lies below the melting point of either component. The solid
phase which is in equilibrium with the solutions AC is pure A; that in equilibrium with BC,
pure B. C is the eutectic point. Although at the eutectic point the solution solidifies entirely
without change of temperature, the solid which is deposited is not a homogeneous solid
rendered easier.
The interest and importance of investigations into the conditions of equilibrium between
two substances, lie in the determination not only of the conditions for the stable existence
of the participating substances, but also of whether or not chemical action takes place
between these two components; and if combination occurs, in the determination of the
nature of the compounds formed and the range of their existence. In all such investigations,
the Phase Rule becomes of conspicuous value on account of the fact that its principles
afford, as it were, a touchstone by which the character of the system can be determined,
and that from the form of the equilibrium curves obtained, conclusions can be drawn as to
the nature of the interaction between the two substances. In order to exemplify the
application of the principles of the Phase Rule more fully than has already been done,
illustrations will be drawn from investigations on the interaction of organic compounds; on
the equilibria between optically active compounds; and on alloys.
Summary of the Different Systems of Two Components.—Before passing to the
consideration of the application of the Phase Rule to the investigation of particular
problems, it will be well to collect together the different types of equilibrium curves with
which we are already acquainted; to compare them with one another, in order that we may
then employ these characteristic curves for the interpretation of the curves obtained as the
result of experiment.
In investigating the equilibria between two components, three chief classes of curves will
be obtained according as—
I. No combination takes place between the two components.
II. The components can form definite compounds.
III. The components separate out in the form of mixed crystals.
The different types of curves which are obtained in these three cases are represented in
Figs. 63, 64, 65. These different diagrams represent the whole series of equilibria, from the
melting point of the one component (A) to that of the other component (B). The curves
represent, in all cases, the composition of the solution, or phase of variable composition;
the temperature being measured along one axis, and the composition along the other.
We shall now recapitulate very briefly the characteristics of the different curves.
If no compound is formed between the two components, the general form of the
equilibrium curve will be that of curve I. or II., Fig. 63. Type I. is the simplest form of
curve found, and consists, as the diagram shows, of only two branches, AC and BC,
meeting at the point C, which lies below the melting point of either component. The solid
phase which is in equilibrium with the solutions AC is pure A; that in equilibrium with BC,
pure B. C is the eutectic point. Although at the eutectic point the solution solidifies entirely
without change of temperature, the solid which is deposited is not a homogeneous solid
Page 179
phase, but a mixture, or conglomerate of the two
components. The eutectic point, therefore, represents
the melting or freezing point, not of a compound, but of
a mixture (p. 119).
Curve II., Fig. 63, is obtained when two liquid phases
are formed. C is an eutectic point, D and F are
transition points at which there can co-exist the four
phases—solid, two liquid phases, vapour. DEF Fig. 63.
represents the change in the composition of the two
liquid phases with rise of temperature; the curve might also have the reversed form with the
critical solution point below the transition points D and F.
In the second class of systems (Fig. 64), that in which combination
between the components occurs, there are again two types
according as the compound formed has a definite melting point (i.e.
can exist in equilibrium with a solution of the same composition),
or undergoes only partial fusion; that is, exhibits a transition point.
If a compound possessing a definite melting point is formed, the
equilibrium curve will have the general form shown by curve I.,
Fig. 64. A, B, and D are the melting points of pure A, pure B, and
of the compound AxBy respectively. AC is the freezing point curve
of A in presence of B; BE that of B in presence of A; and DC and Fig. 64.
DE the freezing point curves of the compound in presence of a
solution containing excess of one of the components. C and E are eutectic points at which
mixtures of A and AxBy, or B and AxBy can co-exist in contact with solution. The curve
CDE may be large or small, and the melting point of the compound, D, may lie above or
below that of each of the components, or may have an intermediate position. If more than
one compound can be formed, a series of curves similar to CDE will be obtained (cf.
p. 152).
On the other hand, if the compound undergoes transition to another solid phase at a
temperature below its melting point, a curve of the form II., Fig. 64, will be found. This
corresponds to the case where a compound can exist only in contact with solutions
containing excess of one of the components. The metastable continuation of the
equilibrium curve for the compound is indicated by the dotted line, the summit of which
would be the melting point of the compound. Before this temperature is reached, however,
the solid compound ceases to be able to exist in contact with solution, and transition to a
different solid phase occurs at the point E (cf. p. 134). This point, therefore, represents the
limit of the existence of the compound AB. If a series of compounds can be formed none of
which possess a definite melting point, then a series of curves will be obtained which do
not exhibit a temperature-maximum, and there will be only one eutectic point. The limits of
existence of each compound will be marked by a break in the curve (cf. p. 143).
components. The eutectic point, therefore, represents
the melting or freezing point, not of a compound, but of
a mixture (p. 119).
Curve II., Fig. 63, is obtained when two liquid phases
are formed. C is an eutectic point, D and F are
transition points at which there can co-exist the four
phases—solid, two liquid phases, vapour. DEF Fig. 63.
represents the change in the composition of the two
liquid phases with rise of temperature; the curve might also have the reversed form with the
critical solution point below the transition points D and F.
In the second class of systems (Fig. 64), that in which combination
between the components occurs, there are again two types
according as the compound formed has a definite melting point (i.e.
can exist in equilibrium with a solution of the same composition),
or undergoes only partial fusion; that is, exhibits a transition point.
If a compound possessing a definite melting point is formed, the
equilibrium curve will have the general form shown by curve I.,
Fig. 64. A, B, and D are the melting points of pure A, pure B, and
of the compound AxBy respectively. AC is the freezing point curve
of A in presence of B; BE that of B in presence of A; and DC and Fig. 64.
DE the freezing point curves of the compound in presence of a
solution containing excess of one of the components. C and E are eutectic points at which
mixtures of A and AxBy, or B and AxBy can co-exist in contact with solution. The curve
CDE may be large or small, and the melting point of the compound, D, may lie above or
below that of each of the components, or may have an intermediate position. If more than
one compound can be formed, a series of curves similar to CDE will be obtained (cf.
p. 152).
On the other hand, if the compound undergoes transition to another solid phase at a
temperature below its melting point, a curve of the form II., Fig. 64, will be found. This
corresponds to the case where a compound can exist only in contact with solutions
containing excess of one of the components. The metastable continuation of the
equilibrium curve for the compound is indicated by the dotted line, the summit of which
would be the melting point of the compound. Before this temperature is reached, however,
the solid compound ceases to be able to exist in contact with solution, and transition to a
different solid phase occurs at the point E (cf. p. 134). This point, therefore, represents the
limit of the existence of the compound AB. If a series of compounds can be formed none of
which possess a definite melting point, then a series of curves will be obtained which do
not exhibit a temperature-maximum, and there will be only one eutectic point. The limits of
existence of each compound will be marked by a break in the curve (cf. p. 143).
Page 180
Turning, lastly, to the third class of systems, in which formation of
mixed crystals can occur, five different types of curves can be
obtained, as shown in Fig. 65. With regard to the first three types,
curves I., II., and III., these differ entirely from those of the previous
classes, in that they are continuous; they exhibit no eutectic point, and
no transition point. Curve II. bears some resemblance to the melting-
point curve of a compound (e.g. CDE, Fig. 64, I.), but differs markedly
from it in not ending in eutectic points.
Further, in the case of the formation of a compound, the composition
of the solid phase remains unchanged throughout the whole curve Fig. 65.
between the eutectic points; whereas, when mixed crystals are
produced, the composition of the solid phase varies with the composition of the liquid
solution. On passing through the maximum, the relative proportions of A and B in the solid
and the liquid phase undergo change; on the one side of the maximum, the solid phase
contains relatively more A, and on the other side of the maximum, relatively more B than
the liquid phase. Lastly, when mixed crystals are formed, the temperature at which
complete solidification occurs changes as the composition of the solution changes, whereas
in the case of the formation of compounds, the temperature of complete solidification for
all solutions is a eutectic point.
The third type of curve, Fig. 65, can be distinguished in a similar manner from the ordinary
eutectic curve, Fig. 63, I., to which it bears a certain resemblance. Whereas in the case of
the latter, the eutectic point is the temperature of complete solidification of all solutions,
the point of minimum temperature in the case of the formation of mixed crystals, is the
solidification point only of solutions having one particular composition; that, namely, of
the minimum point. For all other solutions, the temperature of complete solidification is
different. Whereas, also, in the case of the simple eutectic curve, the solid which separates
out from the solutions represented by either curve remains the same throughout the whole
extent of that curve, the composition of the mixed crystal varies with variation of the
composition of the liquid phase, and the relative proportions of the two components in the
solid and the liquid phase are reversed on passing through the minimum.[290]
In a similar manner, type IV., Fig. 65, can be distinguished from type II., Fig. 64, by the
fact that it does not exhibit a eutectic point, and that the composition of the solid phase
undergoes continuous variation with variation of the liquid phase on either side of the
transition point. Lastly, type V., which does exhibit a eutectic point, differs from the
eutectic curve of Fig. 63, in that the eutectic point does not constitute the point of complete
solidification for all solutions, and that the composition of the solid phase varies with the
composition of the liquid phase.
Such, then, are the chief general types of equilibrium curves for two-components; they are
the pattern curves with which other curves, experimentally determined, can be compared;
and from the comparison it will be possible to draw conclusions as to the nature of the
equilibria between the two components under investigation.
mixed crystals can occur, five different types of curves can be
obtained, as shown in Fig. 65. With regard to the first three types,
curves I., II., and III., these differ entirely from those of the previous
classes, in that they are continuous; they exhibit no eutectic point, and
no transition point. Curve II. bears some resemblance to the melting-
point curve of a compound (e.g. CDE, Fig. 64, I.), but differs markedly
from it in not ending in eutectic points.
Further, in the case of the formation of a compound, the composition
of the solid phase remains unchanged throughout the whole curve Fig. 65.
between the eutectic points; whereas, when mixed crystals are
produced, the composition of the solid phase varies with the composition of the liquid
solution. On passing through the maximum, the relative proportions of A and B in the solid
and the liquid phase undergo change; on the one side of the maximum, the solid phase
contains relatively more A, and on the other side of the maximum, relatively more B than
the liquid phase. Lastly, when mixed crystals are formed, the temperature at which
complete solidification occurs changes as the composition of the solution changes, whereas
in the case of the formation of compounds, the temperature of complete solidification for
all solutions is a eutectic point.
The third type of curve, Fig. 65, can be distinguished in a similar manner from the ordinary
eutectic curve, Fig. 63, I., to which it bears a certain resemblance. Whereas in the case of
the latter, the eutectic point is the temperature of complete solidification of all solutions,
the point of minimum temperature in the case of the formation of mixed crystals, is the
solidification point only of solutions having one particular composition; that, namely, of
the minimum point. For all other solutions, the temperature of complete solidification is
different. Whereas, also, in the case of the simple eutectic curve, the solid which separates
out from the solutions represented by either curve remains the same throughout the whole
extent of that curve, the composition of the mixed crystal varies with variation of the
composition of the liquid phase, and the relative proportions of the two components in the
solid and the liquid phase are reversed on passing through the minimum.[290]
In a similar manner, type IV., Fig. 65, can be distinguished from type II., Fig. 64, by the
fact that it does not exhibit a eutectic point, and that the composition of the solid phase
undergoes continuous variation with variation of the liquid phase on either side of the
transition point. Lastly, type V., which does exhibit a eutectic point, differs from the
eutectic curve of Fig. 63, in that the eutectic point does not constitute the point of complete
solidification for all solutions, and that the composition of the solid phase varies with the
composition of the liquid phase.
Such, then, are the chief general types of equilibrium curves for two-components; they are
the pattern curves with which other curves, experimentally determined, can be compared;
and from the comparison it will be possible to draw conclusions as to the nature of the
equilibria between the two components under investigation.
Page 181
1. Organic Compounds.
Fig. 66.
The principles of the Phase Rule have been applied to the investigation of the equilibria
between organic compounds, and Figs. 66-69 reproduce some of the results which have
been obtained.[291]
Fig. 66, the freezing point curve (curve of equilibrium) for o-nitrophenol and p-toluidine,
shows a curve of the simplest type[292] (type I., Fig. 63), in which two branches meet at an
eutectic point. The solid phase in equilibrium with solutions represented by the left-hand
branch of the curve was o-nitrophenol (m.p. 44.1°); that in equilibrium with the solutions
represented by the right-hand branch, was p-toluidine (m.p. 43.3°). At the eutectic point
(15.6°), these two solid phases could co-exist with the liquid phase. This equilibrium curve,
therefore, shows that o-nitrophenol and p-toluidine do not combine with one another.
In connection with this curve, attention may be called to the interesting fact that although
the solid produced by cooling the liquid phase at the eutectic point has a composition
approximating to that of a compound of equimolecular proportions of the phenol and
toluidine, and a constant melting point, it is nevertheless a mixture. Although, as a rule, the
constituents of the eutectic mixture are not present in simple molecular proportions, there is
no reason why they should not be so; and it is therefore necessary to beware of assuming
the formation of compounds in such cases.[293]
Fig. 67, on the other hand, indicates with perfect certainty the formation of a compound
between phenol and α-naphthylamine.[294] (Cf. curve I., Fig. 64.)
Phenol freezes at 40.4°, but the addition of α-naphthylamine lowers the freezing point as
represented by the curve AC. At C (16.0°) the compound C6H5OH,C10H7NH2 is formed,
and the system becomes invariant. On increasing the amount of the amine, the temperature
of equilibrium rises, the solid phase now being the compound. At D, the curve passes
through a maximum (28.8°), at which the solid and liquid phases have the same
composition. This is the melting point of the compound. Further addition of the amine
lowers the temperature of equilibrium, until at E solid α-naphthylamine separates out, and
a second eutectic point (24.0°) is obtained. BE is the freezing-point curve of α-
naphthylamine in presence of phenol, the freezing point of the pure amine being 48.3°.
Fig. 66.
The principles of the Phase Rule have been applied to the investigation of the equilibria
between organic compounds, and Figs. 66-69 reproduce some of the results which have
been obtained.[291]
Fig. 66, the freezing point curve (curve of equilibrium) for o-nitrophenol and p-toluidine,
shows a curve of the simplest type[292] (type I., Fig. 63), in which two branches meet at an
eutectic point. The solid phase in equilibrium with solutions represented by the left-hand
branch of the curve was o-nitrophenol (m.p. 44.1°); that in equilibrium with the solutions
represented by the right-hand branch, was p-toluidine (m.p. 43.3°). At the eutectic point
(15.6°), these two solid phases could co-exist with the liquid phase. This equilibrium curve,
therefore, shows that o-nitrophenol and p-toluidine do not combine with one another.
In connection with this curve, attention may be called to the interesting fact that although
the solid produced by cooling the liquid phase at the eutectic point has a composition
approximating to that of a compound of equimolecular proportions of the phenol and
toluidine, and a constant melting point, it is nevertheless a mixture. Although, as a rule, the
constituents of the eutectic mixture are not present in simple molecular proportions, there is
no reason why they should not be so; and it is therefore necessary to beware of assuming
the formation of compounds in such cases.[293]
Fig. 67, on the other hand, indicates with perfect certainty the formation of a compound
between phenol and α-naphthylamine.[294] (Cf. curve I., Fig. 64.)
Phenol freezes at 40.4°, but the addition of α-naphthylamine lowers the freezing point as
represented by the curve AC. At C (16.0°) the compound C6H5OH,C10H7NH2 is formed,
and the system becomes invariant. On increasing the amount of the amine, the temperature
of equilibrium rises, the solid phase now being the compound. At D, the curve passes
through a maximum (28.8°), at which the solid and liquid phases have the same
composition. This is the melting point of the compound. Further addition of the amine
lowers the temperature of equilibrium, until at E solid α-naphthylamine separates out, and
a second eutectic point (24.0°) is obtained. BE is the freezing-point curve of α-
naphthylamine in presence of phenol, the freezing point of the pure amine being 48.3°.
Page 182
On account of the great sluggishness with which the compound of phenol and α-
naphthylamine crystallizes, it was found possible to follow the freezing point curves of
phenol and the amine to temperatures considerably below the eutectic points, as shown by
the curves CF and EG.
Fig. 67.
Phenol can also combine with p-toluidine in equimolecular proportions; and this compound
is of interest, from the fact that it exists in two crystalline forms melting at 28.5° and 30°.
Each of these forms now must have its own equilibrium curve, and it was found that the
intermediate portion of the freezing point curve was duplicated, as shown in Fig. 68.[295]
Fig. 68.
naphthylamine crystallizes, it was found possible to follow the freezing point curves of
phenol and the amine to temperatures considerably below the eutectic points, as shown by
the curves CF and EG.
Fig. 67.
Phenol can also combine with p-toluidine in equimolecular proportions; and this compound
is of interest, from the fact that it exists in two crystalline forms melting at 28.5° and 30°.
Each of these forms now must have its own equilibrium curve, and it was found that the
intermediate portion of the freezing point curve was duplicated, as shown in Fig. 68.[295]
Fig. 68.
Page 183
Fig. 69.
Lastly, a curve is given, Fig. 69,[296] which corresponds with curve II., Fig. 64. Picric acid
and benzene can form a compound, which, however, can exist only in contact with
solutions containing excess of benzene. When the temperature is raised, a point (K) is
reached at which the compound melts with separation of solid picric acid. The point, K, is,
therefore, a transition point; analysis, however, showed that the composition of the solution
at this point is very nearly that of the compound C6H2(NO2)3OH,C6H6, so that the melting
point of the compound can almost be reached. The fusion of the compound of benzene and
picric acid with separation of the latter is analogous to the (partial) fusion of Glauber's salt
with separation of anhydrous sodium sulphate.
2. Optically Active Substances.
The question as to whether a resolvable inactive body is a mixture of the two oppositely
active constituents (a dl-mixture), or a racemic compound, is one which has given rise to
considerable discussion during the past decade; and several investigators have endeavoured
to establish general rules by which the question could be decided. In the case of inactive
liquids it is a matter of great difficulty to arrive at a certain conclusion as to whether one is
dealing with a mixture or a compound, for in this case the usual physical methods give but
a dubious answer; and although the existence of a racemate in the liquid state (in the case
of conine) has been asserted,[297] most chemists incline to the belief that such a thing is
improbable.
Even in the case of crystalline substances, where the differences between the various forms
is greater, it was not always easy to discriminate between the dl-mixture and the racemic
compound. The occurrence of hemihedral faces was considered by Pasteur to be a
sufficient criterion for an optically active substance. It has, however, been found that
hemihedry in crystals, although a frequent accompaniment of optical activity, is by no
means a necessary or constant expression of this property. Other rules, also, which were
given, although in some cases reliable, were in other cases insufficient; and all were in so
far unsatisfactory that they lacked a theoretical basis.
Lastly, a curve is given, Fig. 69,[296] which corresponds with curve II., Fig. 64. Picric acid
and benzene can form a compound, which, however, can exist only in contact with
solutions containing excess of benzene. When the temperature is raised, a point (K) is
reached at which the compound melts with separation of solid picric acid. The point, K, is,
therefore, a transition point; analysis, however, showed that the composition of the solution
at this point is very nearly that of the compound C6H2(NO2)3OH,C6H6, so that the melting
point of the compound can almost be reached. The fusion of the compound of benzene and
picric acid with separation of the latter is analogous to the (partial) fusion of Glauber's salt
with separation of anhydrous sodium sulphate.
2. Optically Active Substances.
The question as to whether a resolvable inactive body is a mixture of the two oppositely
active constituents (a dl-mixture), or a racemic compound, is one which has given rise to
considerable discussion during the past decade; and several investigators have endeavoured
to establish general rules by which the question could be decided. In the case of inactive
liquids it is a matter of great difficulty to arrive at a certain conclusion as to whether one is
dealing with a mixture or a compound, for in this case the usual physical methods give but
a dubious answer; and although the existence of a racemate in the liquid state (in the case
of conine) has been asserted,[297] most chemists incline to the belief that such a thing is
improbable.
Even in the case of crystalline substances, where the differences between the various forms
is greater, it was not always easy to discriminate between the dl-mixture and the racemic
compound. The occurrence of hemihedral faces was considered by Pasteur to be a
sufficient criterion for an optically active substance. It has, however, been found that
hemihedry in crystals, although a frequent accompaniment of optical activity, is by no
means a necessary or constant expression of this property. Other rules, also, which were
given, although in some cases reliable, were in other cases insufficient; and all were in so
far unsatisfactory that they lacked a theoretical basis.
Page 184
With the help of the Phase Rule, however, it is possible from a study of the solubility or
fusion curves of the optically active and inactive substances, to decide the nature of the
inactive substance, at least under certain conditions. On account of the interest and
importance which these compounds possess, a brief description of the application of the
Phase Rule to the study of such substances will be given here;[298] the two optical
antipodes being regarded as the two components.
In the present chapter we shall consider only the fusion curves, the solubility curves being
discussed in the next section on three-component systems. The rules which are hereby
obtained, have reference only to the nature of the inactive substance in the neighbourhood
of the melting points.
I. The inactive substance is a dl-mixture.
In this case the fusion curves will have the simple form shown in type I, Fig. 63. A and B
are the melting points of the two optical isomerides, and C the eutectic point at which the
inactive mixture consisting of equal amounts of d- and l-form melts. Owing to the similar
effect of the one form on the freezing point of the other, the figure is symmetrical. No
example of this simple case has been investigated.
II. The two components form a racemic compound.
In this case there will be three melting point curves as in Fig. 64, type I. In this case also
the figure must be symmetrical.
Examples.—As examples of this, may be taken dimethyl tartrate and mandelic acid, the
freezing point curves of which are given in Figs. 70 and 71.[299] As can be seen, the curve
for the racemic tartrate occupies a large part of the diagram, while that for racemic
mandelic acid is much smaller. In the case of dimethyldiacetyl tartrate, this middle portion
is still less.
Fig. 70. Fig. 71.
Fig. 72.
Active dimethyl tartrate melts at 43.3°; racemic dimethyl tartrate at 89.4°. Active mandelic
acid melts at 132.8°; the racemic acid at 118.0°. In the one case, therefore, the racemic
fusion curves of the optically active and inactive substances, to decide the nature of the
inactive substance, at least under certain conditions. On account of the interest and
importance which these compounds possess, a brief description of the application of the
Phase Rule to the study of such substances will be given here;[298] the two optical
antipodes being regarded as the two components.
In the present chapter we shall consider only the fusion curves, the solubility curves being
discussed in the next section on three-component systems. The rules which are hereby
obtained, have reference only to the nature of the inactive substance in the neighbourhood
of the melting points.
I. The inactive substance is a dl-mixture.
In this case the fusion curves will have the simple form shown in type I, Fig. 63. A and B
are the melting points of the two optical isomerides, and C the eutectic point at which the
inactive mixture consisting of equal amounts of d- and l-form melts. Owing to the similar
effect of the one form on the freezing point of the other, the figure is symmetrical. No
example of this simple case has been investigated.
II. The two components form a racemic compound.
In this case there will be three melting point curves as in Fig. 64, type I. In this case also
the figure must be symmetrical.
Examples.—As examples of this, may be taken dimethyl tartrate and mandelic acid, the
freezing point curves of which are given in Figs. 70 and 71.[299] As can be seen, the curve
for the racemic tartrate occupies a large part of the diagram, while that for racemic
mandelic acid is much smaller. In the case of dimethyldiacetyl tartrate, this middle portion
is still less.
Fig. 70. Fig. 71.
Fig. 72.
Active dimethyl tartrate melts at 43.3°; racemic dimethyl tartrate at 89.4°. Active mandelic
acid melts at 132.8°; the racemic acid at 118.0°. In the one case, therefore, the racemic
Page 185
compound has a higher, in the other a lower melting point than the active forms.
In the case of partially racemic compounds (i.e. the compound of a racemate with an
optically active substance) the type of curve will be the same, but the figure will no longer
be symmetrical. Such a curve has been found in the case of the l-menthyl esters of d- and l-
mandelic acid (Fig. 72).[300] The freezing point of l-menthyl d-mandelate is 97.2°, of l-
menthyl l-mandelate 77.6°, and of l-menthyl r-mandelate 83.7.° It will be observed that the
summit of the curve for the partially racemic mandelate is very flat, indicating that the
compound is largely dissociated into its components at the temperature of fusion.
III. The inactive substance is a pseudo-racemic mixed crystal.
In cases where the active components can form mixed crystals, the freezing-point curve
will exhibit one of the forms given in Fig. 65. The inactive mixed crystal containing 50 per
cent. of the dextro and laevo compound, is known as a pseudo-racemic mixed crystal.[301]
So far, only curves of the types I. and II. have been obtained.
Examples.—The two active camphor oximes are of interest from the fact that they form a
continuous series of mixed crystals, all of which have the same melting point. The curve
which is obtained in this case is, therefore, a straight line joining the melting points of the
pure active components; the melting point of the active isomerides and of the whole series
of mixed crystals being 118.8°.
Fig. 73.
In the case of the carvoximes mixed crystals are also formed, but the equilibrium curve in
this case exhibits a maximum (Fig. 73). At this maximum point the composition of the
solid and of the liquid solution is the same. Since the curve must be symmetrical, this
maximum point must occur in the case of the solution containing 50 per cent. of each
component, which will therefore be inactive. Further, this inactive mixed crystal will melt
and solidify at the same temperature, and behave, therefore, like a chemical compound
(p. 187). The melting point of the active compounds is 72°; that of the inactive pseudo-
racemic mixed crystal is 91.4°·
Transformations.—As has already been remarked, the conclusions which can be drawn
from the fusion curves regarding the nature of the inactive substances formed hold only for
temperatures in the neighbourhood of the melting points. At temperatures below the
melting point transformation may occur; e.g. a racemate may break up into a dl-mixture, or
a pseudo-racemic mixed crystal may form a racemic compound. We shall at a later point
In the case of partially racemic compounds (i.e. the compound of a racemate with an
optically active substance) the type of curve will be the same, but the figure will no longer
be symmetrical. Such a curve has been found in the case of the l-menthyl esters of d- and l-
mandelic acid (Fig. 72).[300] The freezing point of l-menthyl d-mandelate is 97.2°, of l-
menthyl l-mandelate 77.6°, and of l-menthyl r-mandelate 83.7.° It will be observed that the
summit of the curve for the partially racemic mandelate is very flat, indicating that the
compound is largely dissociated into its components at the temperature of fusion.
III. The inactive substance is a pseudo-racemic mixed crystal.
In cases where the active components can form mixed crystals, the freezing-point curve
will exhibit one of the forms given in Fig. 65. The inactive mixed crystal containing 50 per
cent. of the dextro and laevo compound, is known as a pseudo-racemic mixed crystal.[301]
So far, only curves of the types I. and II. have been obtained.
Examples.—The two active camphor oximes are of interest from the fact that they form a
continuous series of mixed crystals, all of which have the same melting point. The curve
which is obtained in this case is, therefore, a straight line joining the melting points of the
pure active components; the melting point of the active isomerides and of the whole series
of mixed crystals being 118.8°.
Fig. 73.
In the case of the carvoximes mixed crystals are also formed, but the equilibrium curve in
this case exhibits a maximum (Fig. 73). At this maximum point the composition of the
solid and of the liquid solution is the same. Since the curve must be symmetrical, this
maximum point must occur in the case of the solution containing 50 per cent. of each
component, which will therefore be inactive. Further, this inactive mixed crystal will melt
and solidify at the same temperature, and behave, therefore, like a chemical compound
(p. 187). The melting point of the active compounds is 72°; that of the inactive pseudo-
racemic mixed crystal is 91.4°·
Transformations.—As has already been remarked, the conclusions which can be drawn
from the fusion curves regarding the nature of the inactive substances formed hold only for
temperatures in the neighbourhood of the melting points. At temperatures below the
melting point transformation may occur; e.g. a racemate may break up into a dl-mixture, or
a pseudo-racemic mixed crystal may form a racemic compound. We shall at a later point
Page 186
meet with examples of a racemic compound changing into a dl-mixture at a definite
transition point; and the pseudo-racemic mixed crystal of camphoroxime is an example of
the second transformation. Although at temperatures in the neighbourhood of the melting
point the two active camphoroximes form only mixed crystals but no compound, a racemic
compound is formed at temperatures below 103°. At this temperature the inactive pseudo-
racemic mixed crystal changes into a racemic compound; and in the case of the other
mixed crystals transformation to racemate and (excess of) active component also occurs,
although at a lower temperature than in the case of the inactive mixed crystal. Although
this behaviour is one of considerable importance, this brief reference to it must suffice
here.[302]
3. Alloys.
One of the most important classes of substances in the study of which the Phase Rule has
been of very considerable importance, is that formed by the mixtures or compounds of
metals with one another known as alloys. Although in the investigation of the nature of
these bodies various methods are employed, one of the most important is the determination
of the character of the freezing-point curve; for from the form of this, valuable information
can, as we have already learned, be obtained regarding the nature of the solid substances
which separate out from the molten mixture.
Although it is impossible here to discuss fully the experimental results and the oftentimes
very complicated relationships which the study of the alloys has brought to light, a brief
reference to these bodies will be advisable on account both of the scientific interest and of
the industrial importance attaching to them.[303]
We have already seen that there are three chief types of freezing-point curves in systems of
two components, viz. those obtained when (1) the pure components crystallize out from the
molten mass; (2) the components form one or more compounds; (3) the components form
mixed crystals. In the case of the metals, representatives of these three classes are also
found.
1. The components separate out in the pure state.
In this case the freezing-point curve is of the simple type, Fig. 63, I. Such curves have been
obtained in the case of a number of pairs of metals, e.g. zinc—cadmium, zinc—aluminium,
copper—silver (Heycock and Neville), tin—zinc, bismuth—lead (Gautier), and in other
cases. From molten mixtures represented by one branch of the freezing-point curve one of
the metals will be deposited; while from mixtures represented by the other branch, the
other metal will separate out. At the eutectic point the molten mass will solidify to a
heterogeneous mixture of the two metals, forming what is known as the eutectic alloy.
Such an alloy, therefore, will melt at a definite temperature lower than the melting point of
either of the pure metals.
In the following table are given the temperature and the composition of the liquid at the
eutectic point, for three pairs of metals:—
transition point; and the pseudo-racemic mixed crystal of camphoroxime is an example of
the second transformation. Although at temperatures in the neighbourhood of the melting
point the two active camphoroximes form only mixed crystals but no compound, a racemic
compound is formed at temperatures below 103°. At this temperature the inactive pseudo-
racemic mixed crystal changes into a racemic compound; and in the case of the other
mixed crystals transformation to racemate and (excess of) active component also occurs,
although at a lower temperature than in the case of the inactive mixed crystal. Although
this behaviour is one of considerable importance, this brief reference to it must suffice
here.[302]
3. Alloys.
One of the most important classes of substances in the study of which the Phase Rule has
been of very considerable importance, is that formed by the mixtures or compounds of
metals with one another known as alloys. Although in the investigation of the nature of
these bodies various methods are employed, one of the most important is the determination
of the character of the freezing-point curve; for from the form of this, valuable information
can, as we have already learned, be obtained regarding the nature of the solid substances
which separate out from the molten mixture.
Although it is impossible here to discuss fully the experimental results and the oftentimes
very complicated relationships which the study of the alloys has brought to light, a brief
reference to these bodies will be advisable on account both of the scientific interest and of
the industrial importance attaching to them.[303]
We have already seen that there are three chief types of freezing-point curves in systems of
two components, viz. those obtained when (1) the pure components crystallize out from the
molten mass; (2) the components form one or more compounds; (3) the components form
mixed crystals. In the case of the metals, representatives of these three classes are also
found.
1. The components separate out in the pure state.
In this case the freezing-point curve is of the simple type, Fig. 63, I. Such curves have been
obtained in the case of a number of pairs of metals, e.g. zinc—cadmium, zinc—aluminium,
copper—silver (Heycock and Neville), tin—zinc, bismuth—lead (Gautier), and in other
cases. From molten mixtures represented by one branch of the freezing-point curve one of
the metals will be deposited; while from mixtures represented by the other branch, the
other metal will separate out. At the eutectic point the molten mass will solidify to a
heterogeneous mixture of the two metals, forming what is known as the eutectic alloy.
Such an alloy, therefore, will melt at a definite temperature lower than the melting point of
either of the pure metals.
In the following table are given the temperature and the composition of the liquid at the
eutectic point, for three pairs of metals:—
Page 187
Temperature. Composition of liquid.
Zinc—cadmium 264.5° 73.5 atoms per cent. of cadmium.
Zinc—aluminium 380.5° 11 ,, ,, aluminium.
Copper—silver 778° 40 ,, ,, copper.
The melting points of the pure metals are, zinc, 419°; cadmium, 322°; silver, 960°; copper,
1081°; aluminium, 650°.
2. The two metals can form one or more compounds.
In this case there will be obtained not only the freezing-point curves of the pure metals, but
each compound formed will have its own freezing-point curve, exhibiting a point of
maximum temperature, and ending on either side in an eutectic point. The simplest curve
of this type will be obtained when only one compound is formed, as is the case with
mercury and thallium.[304] This curve is represented in Fig. 74, where the summit of the
intermediate curve corresponds with a composition TlHg2. Similar curves are also given by
nickel and tin, by aluminium and silver, and by other metals, the formation of definite
compounds between these pairs of metals being thereby indicated.[305]
Fig. 74.
A curve belonging to the same type, but more complicated, is obtained with gold and
aluminium;[306] in this case, several compounds are formed, some of which have a definite
melting point, while others exhibit only a transition point. The chief compound is AuAl2,
which has practically the same melting point as pure gold.
3. The two metals form mixed crystals (solid solutions).
The simplest case in which the metals crystallize out together is found in silver and gold.
[307] The freezing-point curve in this case is an almost straight line joining the freezing
points of the pure metals (cf. curve I., Fig. 65, p. 210). These two metals, therefore, can
form an unbroken series of mixed crystals.
Zinc—cadmium 264.5° 73.5 atoms per cent. of cadmium.
Zinc—aluminium 380.5° 11 ,, ,, aluminium.
Copper—silver 778° 40 ,, ,, copper.
The melting points of the pure metals are, zinc, 419°; cadmium, 322°; silver, 960°; copper,
1081°; aluminium, 650°.
2. The two metals can form one or more compounds.
In this case there will be obtained not only the freezing-point curves of the pure metals, but
each compound formed will have its own freezing-point curve, exhibiting a point of
maximum temperature, and ending on either side in an eutectic point. The simplest curve
of this type will be obtained when only one compound is formed, as is the case with
mercury and thallium.[304] This curve is represented in Fig. 74, where the summit of the
intermediate curve corresponds with a composition TlHg2. Similar curves are also given by
nickel and tin, by aluminium and silver, and by other metals, the formation of definite
compounds between these pairs of metals being thereby indicated.[305]
Fig. 74.
A curve belonging to the same type, but more complicated, is obtained with gold and
aluminium;[306] in this case, several compounds are formed, some of which have a definite
melting point, while others exhibit only a transition point. The chief compound is AuAl2,
which has practically the same melting point as pure gold.
3. The two metals form mixed crystals (solid solutions).
The simplest case in which the metals crystallize out together is found in silver and gold.
[307] The freezing-point curve in this case is an almost straight line joining the freezing
points of the pure metals (cf. curve I., Fig. 65, p. 210). These two metals, therefore, can
form an unbroken series of mixed crystals.
Page 188
In some cases, however, the two metals do not form an unbroken series of mixed crystals.
In the case of zinc and silver,[308] for example, the addition of silver raises the freezing
point of the mixture, until a transition point is reached. This corresponds with curve IV.,
Fig. 65. Silver and copper, and gold and copper, on the other hand, do not form unbroken
series of mixed crystals, but the freezing-point curve exhibits an eutectic point, as in curve
V., Fig. 65.
Not only may there be these three different types of curves, but there may also be
combinations of these. Thus the two metals may not only form compounds, but one of the
metals may not separate out in the pure state at all, but form mixed crystals. In this case the
freezing point may rise (as in the case of silver and zinc), and one of the eutectic points will
be absent.
Iron-Carbon Alloys.—Of all the different binary alloys, probably the most important are
those formed by iron and carbon: alloys consisting not of two metals, but of a metal and a
non-metal. On account of the importance of these alloys, an attempt will be made to
describe in brief some of the most important relationships met with.
Before proceeding to discuss the applications of the Phase Rule to the study of the iron-
carbon alloys, however, the main facts with which we have to deal may be stated very
briefly. With regard to the metal itself, it is known to exist in three different allotropic
modifications, called α-, β-, and γ-ferrite respectively. Like the two modifications of
sulphur and of tin, these different forms exhibit transition points at which the relative
stability of the forms changes. Thus the transition point for α- and β-ferrite is about 780°;
and below this temperature the α- form, above it the β- form is stable. For β- and γ-ferrite,
the transition point is about 870°, the γ- form being the stable modification above this
temperature.
The different modifications of iron also possess different properties. Thus, α-ferrite is
magnetic, but does not possess the power of dissolving carbon; β-ferrite is non-magnetic,
and likewise does not dissolve carbon; γ-ferrite is also non-magnetic, but possesses the
power of dissolving carbon, and of thus giving rise to solid solutions of carbon in iron.
Various alloys of iron and carbon, also, have to be distinguished. First of all, there is hard
steel, which contains varying amounts of carbon up to 2 per cent. Microscopic examination
shows that these mixtures are all homogeneous; and they are therefore to be regarded as
solid solutions of carbon in iron (γ-ferrite). To these solutions the name martensite has
been given. Pearlite contains about 0.8 per cent. of carbon, and, on microscopic
examination, is found to be a heterogeneous mixture. If heated above 670°, pearlite
becomes homogeneous, and forms martensite. Lastly, there is a definite compound of iron
and carbon, iron carbide or cementite, having the formula Fe3C.
A short description may now be given of the application of the Phase Rule to the two-
component system iron—carbon; and of the diagram showing how the different systems
are related, and with the help of which the behaviour of the different mixtures under given
conditions can be predicted. Although, with regard to the main features of this diagram, the
In the case of zinc and silver,[308] for example, the addition of silver raises the freezing
point of the mixture, until a transition point is reached. This corresponds with curve IV.,
Fig. 65. Silver and copper, and gold and copper, on the other hand, do not form unbroken
series of mixed crystals, but the freezing-point curve exhibits an eutectic point, as in curve
V., Fig. 65.
Not only may there be these three different types of curves, but there may also be
combinations of these. Thus the two metals may not only form compounds, but one of the
metals may not separate out in the pure state at all, but form mixed crystals. In this case the
freezing point may rise (as in the case of silver and zinc), and one of the eutectic points will
be absent.
Iron-Carbon Alloys.—Of all the different binary alloys, probably the most important are
those formed by iron and carbon: alloys consisting not of two metals, but of a metal and a
non-metal. On account of the importance of these alloys, an attempt will be made to
describe in brief some of the most important relationships met with.
Before proceeding to discuss the applications of the Phase Rule to the study of the iron-
carbon alloys, however, the main facts with which we have to deal may be stated very
briefly. With regard to the metal itself, it is known to exist in three different allotropic
modifications, called α-, β-, and γ-ferrite respectively. Like the two modifications of
sulphur and of tin, these different forms exhibit transition points at which the relative
stability of the forms changes. Thus the transition point for α- and β-ferrite is about 780°;
and below this temperature the α- form, above it the β- form is stable. For β- and γ-ferrite,
the transition point is about 870°, the γ- form being the stable modification above this
temperature.
The different modifications of iron also possess different properties. Thus, α-ferrite is
magnetic, but does not possess the power of dissolving carbon; β-ferrite is non-magnetic,
and likewise does not dissolve carbon; γ-ferrite is also non-magnetic, but possesses the
power of dissolving carbon, and of thus giving rise to solid solutions of carbon in iron.
Various alloys of iron and carbon, also, have to be distinguished. First of all, there is hard
steel, which contains varying amounts of carbon up to 2 per cent. Microscopic examination
shows that these mixtures are all homogeneous; and they are therefore to be regarded as
solid solutions of carbon in iron (γ-ferrite). To these solutions the name martensite has
been given. Pearlite contains about 0.8 per cent. of carbon, and, on microscopic
examination, is found to be a heterogeneous mixture. If heated above 670°, pearlite
becomes homogeneous, and forms martensite. Lastly, there is a definite compound of iron
and carbon, iron carbide or cementite, having the formula Fe3C.
A short description may now be given of the application of the Phase Rule to the two-
component system iron—carbon; and of the diagram showing how the different systems
are related, and with the help of which the behaviour of the different mixtures under given
conditions can be predicted. Although, with regard to the main features of this diagram, the
Page 189
different areas to be mapped and the position of the frontier lines, there is general
agreement; a final decision has not yet been reached with regard to the interpretation to be
put on all the curves.
Fig. 75.
The chief relationships met with in the case of the iron-carbon alloys are represented
graphically in Fig. 75.[309] The curve AC is the freezing-point curve for iron,[310] BC the
unknown freezing-point curve for graphite. C is an eutectic point. Suppose, now, that we
start with a mixture of iron and carbon, represented by the point x. On lowering the
temperature, a point, y, will be reached at which solid begins to separate out. This solid
phase, however, is not pure iron, but a solid solution of carbon in iron, having the
composition represented by y′ (cf. p. 185). As the temperature continues to fall, the
composition of the liquid phase changes in the direction of yC, while the composition of
the solid which separates out changes in the direction y′D; and, finally, when the
composition of the molten mass is that of the point C (4.3 per cent. of carbon), the whole
mass solidifies to a heterogeneous mixture of two solid solutions, one of which is
represented by D (containing 2 per cent. of carbon), while the other will consist practically
of pure graphite, and is not shown in the figure. The temperature of the eutectic point is
1130°.
Even below the solidification point, however, changes can take place. As has been said, the
solid phase which finally separates out from the molten mass is a solid solution represented
by the point D; and the curve DE represents the change in the composition of this solid
solution with the temperature. As indicated in the figure, DE forms a part of a curve
representing the mutual solubility of graphite in iron and iron in graphite; the latter
solutions, however, not being shown, as they would lie far outside the diagram. As the
temperature falls below 1130°, more and more graphite separates out, until at E, when the
temperature is 1000°, the solid solution contains only 1.8 per cent. of carbon. At this
temperature cementite also begins to be formed, so that as the temperature continues to fall,
separation of cementite (represented by the line E′F′) occurs, and the composition of the
solid solution undergoes alteration, as represented by the curve EF. Below the temperature
of the point F (670°) the martensite becomes heterogeneous, and forms pearlite.
agreement; a final decision has not yet been reached with regard to the interpretation to be
put on all the curves.
Fig. 75.
The chief relationships met with in the case of the iron-carbon alloys are represented
graphically in Fig. 75.[309] The curve AC is the freezing-point curve for iron,[310] BC the
unknown freezing-point curve for graphite. C is an eutectic point. Suppose, now, that we
start with a mixture of iron and carbon, represented by the point x. On lowering the
temperature, a point, y, will be reached at which solid begins to separate out. This solid
phase, however, is not pure iron, but a solid solution of carbon in iron, having the
composition represented by y′ (cf. p. 185). As the temperature continues to fall, the
composition of the liquid phase changes in the direction of yC, while the composition of
the solid which separates out changes in the direction y′D; and, finally, when the
composition of the molten mass is that of the point C (4.3 per cent. of carbon), the whole
mass solidifies to a heterogeneous mixture of two solid solutions, one of which is
represented by D (containing 2 per cent. of carbon), while the other will consist practically
of pure graphite, and is not shown in the figure. The temperature of the eutectic point is
1130°.
Even below the solidification point, however, changes can take place. As has been said, the
solid phase which finally separates out from the molten mass is a solid solution represented
by the point D; and the curve DE represents the change in the composition of this solid
solution with the temperature. As indicated in the figure, DE forms a part of a curve
representing the mutual solubility of graphite in iron and iron in graphite; the latter
solutions, however, not being shown, as they would lie far outside the diagram. As the
temperature falls below 1130°, more and more graphite separates out, until at E, when the
temperature is 1000°, the solid solution contains only 1.8 per cent. of carbon. At this
temperature cementite also begins to be formed, so that as the temperature continues to fall,
separation of cementite (represented by the line E′F′) occurs, and the composition of the
solid solution undergoes alteration, as represented by the curve EF. Below the temperature
of the point F (670°) the martensite becomes heterogeneous, and forms pearlite.
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From the above description, therefore, it follows that if we start with a molten mixture of
iron and carbon, the composition of which is represented by any point between D and C
(from 2 to 4.3 per cent. of carbon), we shall obtain, on cooling the mass, first of all solid
solutions, the composition of which will be represented by points on the line AD; that then,
after the mass has completely solidified at 1130°, further cooling will lead to a separation
of graphite and a change in the composition of the martensite (from 2 to 1.8 per cent. of
carbon). On cooling below 1000°, however, the martensite and graphite will give rise to
cementite and solid solutions containing less carbon than before, until, at temperatures
below 670°, we are left with a mixture of pearlite and cementite.
We have already said that iron consists in three allotropic modifications, the regions of
stability of which are separated by definite transition points. The transition point for α- and
β-ferrite (780°) is represented in Fig. 75 by the point H; and the transition point for β- and
γ-ferrite (870°) by the point I. Since neither the α- nor the β-ferrite dissolves carbon, the
transition point will be unaffected by addition of carbon, and we therefore obtain the
horizontal transition curve HG. In the case of the β- and γ-ferrite, however, the latter
dissolves carbon, and the transition point is consequently affected by the amount of carbon
present. This is shown by the line IG.
If a martensite containing less carbon than that represented by the point G is cooled down
from a temperature of, say, 900°, then when the temperature has fallen to that, represented
by a point on the curve IG, β-ferrite will separate out, and, as the temperature falls, the
composition of the solid solution will alter as represented by IG. On passing below the
temperature of HG, the β-ferrite will be converted into α-ferrite, and, as the temperature
falls, the latter will separate out more and more, while the composition of the solid solution
alters in the direction GF. On passing to still lower temperatures, the solid solution at F (0.8
per cent. of carbon) breaks up into pearlite. If the percentage of carbon in the original solid
solution was between that represented by the points G and F, then, on cooling down, no β-
ferrite, but only α-ferrite would separate out.
We see, therefore, that when martensite is allowed to cool slowly, it yields a heterogeneous
mixture either of ferrite and pearlite (when the original mixture contained up to 0.8 per
cent. of carbon), or pearlite and cementite (when the original mixture contained between
0.8 and 2 per cent. of carbon). These heterogeneous mixtures constitute soft steels, or,
when the carbon content is low, wrought iron.
The case, however, is different if the solid solution of carbon in iron is rapidly cooled
(quenched) from a temperature above the curve IGFE to a temperature below this curve. In
this case, the rapid cooling does not allow time for the various changes which have been
described to take place; so that the homogeneous solid solution, on being rapidly cooled,
remains homogeneous. In this way hard steel is obtained. By varying the rapidity of
cooling, as is done in the tempering of steel, varying degrees of hardness can be obtained.
The interpretation of the curves given above is that due essentially to Roozeboom, who
concluded from the experimental data that at temperatures below 1000° the stable systems
are martensite and cementite, or ferrite and cementite, graphite being labile. It has,
iron and carbon, the composition of which is represented by any point between D and C
(from 2 to 4.3 per cent. of carbon), we shall obtain, on cooling the mass, first of all solid
solutions, the composition of which will be represented by points on the line AD; that then,
after the mass has completely solidified at 1130°, further cooling will lead to a separation
of graphite and a change in the composition of the martensite (from 2 to 1.8 per cent. of
carbon). On cooling below 1000°, however, the martensite and graphite will give rise to
cementite and solid solutions containing less carbon than before, until, at temperatures
below 670°, we are left with a mixture of pearlite and cementite.
We have already said that iron consists in three allotropic modifications, the regions of
stability of which are separated by definite transition points. The transition point for α- and
β-ferrite (780°) is represented in Fig. 75 by the point H; and the transition point for β- and
γ-ferrite (870°) by the point I. Since neither the α- nor the β-ferrite dissolves carbon, the
transition point will be unaffected by addition of carbon, and we therefore obtain the
horizontal transition curve HG. In the case of the β- and γ-ferrite, however, the latter
dissolves carbon, and the transition point is consequently affected by the amount of carbon
present. This is shown by the line IG.
If a martensite containing less carbon than that represented by the point G is cooled down
from a temperature of, say, 900°, then when the temperature has fallen to that, represented
by a point on the curve IG, β-ferrite will separate out, and, as the temperature falls, the
composition of the solid solution will alter as represented by IG. On passing below the
temperature of HG, the β-ferrite will be converted into α-ferrite, and, as the temperature
falls, the latter will separate out more and more, while the composition of the solid solution
alters in the direction GF. On passing to still lower temperatures, the solid solution at F (0.8
per cent. of carbon) breaks up into pearlite. If the percentage of carbon in the original solid
solution was between that represented by the points G and F, then, on cooling down, no β-
ferrite, but only α-ferrite would separate out.
We see, therefore, that when martensite is allowed to cool slowly, it yields a heterogeneous
mixture either of ferrite and pearlite (when the original mixture contained up to 0.8 per
cent. of carbon), or pearlite and cementite (when the original mixture contained between
0.8 and 2 per cent. of carbon). These heterogeneous mixtures constitute soft steels, or,
when the carbon content is low, wrought iron.
The case, however, is different if the solid solution of carbon in iron is rapidly cooled
(quenched) from a temperature above the curve IGFE to a temperature below this curve. In
this case, the rapid cooling does not allow time for the various changes which have been
described to take place; so that the homogeneous solid solution, on being rapidly cooled,
remains homogeneous. In this way hard steel is obtained. By varying the rapidity of
cooling, as is done in the tempering of steel, varying degrees of hardness can be obtained.
The interpretation of the curves given above is that due essentially to Roozeboom, who
concluded from the experimental data that at temperatures below 1000° the stable systems
are martensite and cementite, or ferrite and cementite, graphite being labile. It has,
Page 191
however, been pointed out, more especially by E. Heyn,[311] that this is not in harmony
with the facts of metallurgy, which show that graphite is undoubtedly formed on slow
cooling, and more especially when small quantities of silicon are present in the iron.[312]
While, therefore, the relationships represented by Fig. 75 are obtained under certain
conditions (especially when manganese is present), Heyn considers that all the curves in
that figure, except ACB, represent metastable systems—systems, therefore, akin to
supercooled liquids. Rapid cooling will favour the production of the metastable systems
containing cementite, and therefore give rise to relationships represented by Fig. 75;
whereas slow cooling will lead to the stable system ferrite and graphite. Presence of silicon
tends to prevent, presence of manganese tends to assist, the production of the metastable
systems.
Although this view put forward by Heyn has not been conclusively proved, it must be said
that there is much evidence in its favour. Further investigation is, however, required before
a final decision as to the interpretation of the curves can be reached.
Determination of the Composition of Compounds, without Analysis.—Since the
equilibrium between a solid and a liquid phase depends not only on the composition of the
liquid (solution) but also on that of the solid, it is necessary to determine the composition
of the latter. In some cases this is easily effected by separating the solid from the liquid
phase and analyzing it. In other cases, however, this method is inapplicable, or is
accompanied by difficulties, due either to the fact that the solid phase undergoes
decomposition (e.g. when it contains a volatile constituent), or to the difficulty of
completely separating the mother liquor; as, for example, in the case of alloys. In all such
cases, therefore, recourse must be had to other methods.
In the first place, synthetic methods may be employed.[313] In this case we start with a
solution of the two components, to which a third substance is added, which, however, does
not enter into the solid phase.[314] We will assume that the initial solution contains x gm. of
A and y gm. of B to 1 gm. of C. After the solution has been cooled down to such a
temperature that solid substance separates out, a portion of the liquid phase is removed
with a pipette and analyzed. If, now, the composition of the solution is such that there are x′
gm. of A and y′ gm. of B to 1 gm. of C., then the composition of the solid phase is x - x′
gm. of A and y - y′ gm. of B. When x = x′, the solid phase is pure B; when y = y′, the solid
phase is pure A.
We have assumed here that there is only one solid phase present, containing A and B. To
make sure that the solid phase is not a solid solution in which A and B are present in the
same ratio as in the liquid solution, a second determination of the composition must be
made, with different initial and end concentrations. If the solid phase is a solid solution, the
composition will now be found different from that found previously.
The composition of the solid phase can, however, be determined in another manner, viz. by
studying the fusion curve and the curve of cooling. From the form of the fusion curve
alone, it is possible to decide whether the two components form a compound or not; and if
with the facts of metallurgy, which show that graphite is undoubtedly formed on slow
cooling, and more especially when small quantities of silicon are present in the iron.[312]
While, therefore, the relationships represented by Fig. 75 are obtained under certain
conditions (especially when manganese is present), Heyn considers that all the curves in
that figure, except ACB, represent metastable systems—systems, therefore, akin to
supercooled liquids. Rapid cooling will favour the production of the metastable systems
containing cementite, and therefore give rise to relationships represented by Fig. 75;
whereas slow cooling will lead to the stable system ferrite and graphite. Presence of silicon
tends to prevent, presence of manganese tends to assist, the production of the metastable
systems.
Although this view put forward by Heyn has not been conclusively proved, it must be said
that there is much evidence in its favour. Further investigation is, however, required before
a final decision as to the interpretation of the curves can be reached.
Determination of the Composition of Compounds, without Analysis.—Since the
equilibrium between a solid and a liquid phase depends not only on the composition of the
liquid (solution) but also on that of the solid, it is necessary to determine the composition
of the latter. In some cases this is easily effected by separating the solid from the liquid
phase and analyzing it. In other cases, however, this method is inapplicable, or is
accompanied by difficulties, due either to the fact that the solid phase undergoes
decomposition (e.g. when it contains a volatile constituent), or to the difficulty of
completely separating the mother liquor; as, for example, in the case of alloys. In all such
cases, therefore, recourse must be had to other methods.
In the first place, synthetic methods may be employed.[313] In this case we start with a
solution of the two components, to which a third substance is added, which, however, does
not enter into the solid phase.[314] We will assume that the initial solution contains x gm. of
A and y gm. of B to 1 gm. of C. After the solution has been cooled down to such a
temperature that solid substance separates out, a portion of the liquid phase is removed
with a pipette and analyzed. If, now, the composition of the solution is such that there are x′
gm. of A and y′ gm. of B to 1 gm. of C., then the composition of the solid phase is x - x′
gm. of A and y - y′ gm. of B. When x = x′, the solid phase is pure B; when y = y′, the solid
phase is pure A.
We have assumed here that there is only one solid phase present, containing A and B. To
make sure that the solid phase is not a solid solution in which A and B are present in the
same ratio as in the liquid solution, a second determination of the composition must be
made, with different initial and end concentrations. If the solid phase is a solid solution, the
composition will now be found different from that found previously.
The composition of the solid phase can, however, be determined in another manner, viz. by
studying the fusion curve and the curve of cooling. From the form of the fusion curve
alone, it is possible to decide whether the two components form a compound or not; and if
Page 192
the compounds which may be formed have a definite melting point, the position of the
latter gives at once the composition of the compounds (cf. p. 231).
This method, however, cannot be applied when the compounds undergo decomposition
before the melting point is reached. In such cases, however, the form of the cooling curve
enables one to decide the composition of the solid phase.[315] If a solution is allowed to
cool slowly, and the temperature noted at definite times, the graphic representation of the
rate of cooling will give a continuous curve; e.g. ab in Fig. 76. So soon, however, as a solid
phase begins to be formed, the rate of cooling alters abruptly, and the cooling curve then
exhibits a break, or change in direction (point b). When the eutectic point is reached, the
temperature remains constant, until all the liquid has solidified. This is represented by the
line cd. When complete solidification has occurred, the fall of temperature again becomes
uniform (de).
Fig. 76.
The length of time during which the temperature
remains constant at the point c, depends, of course,
on the eutectic solution. If, therefore, we take equal
amounts of solution having a different initial
composition, the period of constant temperature in
the cooling curve will evidently be greatest in the Fig. 77. Fig. 78.
case of the solution having the composition of the
eutectic point; and the period will become less and less as we increase the amount of one of
the components. The relationship between initial composition of solution and the duration
of constant temperature at the eutectic point is represented by the curve a′c′b′ (Fig. 77).
When a compound possessing a definite melting point is formed, it behaves as a pure
substance. If, therefore, the initial composition of the solution is the same as that of the
compound, no eutectic solution will be obtained; and therefore no line of constant
temperature, such as cd (Fig. 76). In such a case, if we represent graphically the relation
between the initial composition of the solution and the duration of constant temperature, a
diagram is obtained such as shown in Fig. 78. The two maxima on the time-composition
curve represent eutectic points, and the minima, a′, b′, e′, pure substances. The position of
e′ gives the composition of the compound. When a series of compounds is formed, then for
each compound a minimum is found on the time-composition curve.
If the compound formed has no definite melting point, the diagram obtained is like that
shown in Fig. 79. If we start with a solution, the composition of which is represented by a
point between d and b, then, on cooling, b will separate out first, and the temperature will
latter gives at once the composition of the compounds (cf. p. 231).
This method, however, cannot be applied when the compounds undergo decomposition
before the melting point is reached. In such cases, however, the form of the cooling curve
enables one to decide the composition of the solid phase.[315] If a solution is allowed to
cool slowly, and the temperature noted at definite times, the graphic representation of the
rate of cooling will give a continuous curve; e.g. ab in Fig. 76. So soon, however, as a solid
phase begins to be formed, the rate of cooling alters abruptly, and the cooling curve then
exhibits a break, or change in direction (point b). When the eutectic point is reached, the
temperature remains constant, until all the liquid has solidified. This is represented by the
line cd. When complete solidification has occurred, the fall of temperature again becomes
uniform (de).
Fig. 76.
The length of time during which the temperature
remains constant at the point c, depends, of course,
on the eutectic solution. If, therefore, we take equal
amounts of solution having a different initial
composition, the period of constant temperature in
the cooling curve will evidently be greatest in the Fig. 77. Fig. 78.
case of the solution having the composition of the
eutectic point; and the period will become less and less as we increase the amount of one of
the components. The relationship between initial composition of solution and the duration
of constant temperature at the eutectic point is represented by the curve a′c′b′ (Fig. 77).
When a compound possessing a definite melting point is formed, it behaves as a pure
substance. If, therefore, the initial composition of the solution is the same as that of the
compound, no eutectic solution will be obtained; and therefore no line of constant
temperature, such as cd (Fig. 76). In such a case, if we represent graphically the relation
between the initial composition of the solution and the duration of constant temperature, a
diagram is obtained such as shown in Fig. 78. The two maxima on the time-composition
curve represent eutectic points, and the minima, a′, b′, e′, pure substances. The position of
e′ gives the composition of the compound. When a series of compounds is formed, then for
each compound a minimum is found on the time-composition curve.
If the compound formed has no definite melting point, the diagram obtained is like that
shown in Fig. 79. If we start with a solution, the composition of which is represented by a
point between d and b, then, on cooling, b will separate out first, and the temperature will
Page 193
fall until the point d is reached. The temperature then remains constant
until the component b, which has separated out, is converted into the
compound. After this the temperature again falls, until it again remains
constant at the eutectic point c. In the case of the first halt, the period of
constant temperature is greatest when the initial composition of the
solution is the same as that of the compound; and it becomes shorter
Fig. 79.
and shorter with increase in the amount of either component. In this
way we obtain the time-composition curve b′e″d′, of which the
maximum point e″ gives the composition of the compound.
On the other hand, the period of constant temperature for the eutectic point c is greatest in
the case of solutions having the same initial composition as that corresponding with the
eutectic point; and it decreases the more the initial composition approaches that of the pure
component a or the component e. In this way we obtain the time-composition curve a′c′e′.
Here also the point e′ represents the composition of the compound. We see, therefore, that
from the graphic representation of the freezing-point curve, and from the duration of the
temperature-arrests on the cooling curve, for solutions of different initial composition, it is
possible, without having recourse to analysis, to decide what solid phases are formed, and
what is their composition.
Formation of Minerals.—Important and interesting as is the application of the Phase Rule
to the study of alloys, its application to the study of the conditions regulating the formation
of minerals is no less so; and although we do not propose to consider different cases in
detail here, still attention must be drawn to certain points connected with this interesting
subject.
In the first place, it will be evident from what has already been said, that that mineral which
first crystallizes out from a molten magma is not necessarily the one with the highest
melting point. The composition of the fused mass must be taken into account. When the
system consists of two components which do not form a compound, one or other of these
will separate out in a pure state, according as the composition of the molten mass lies on
one or other side of the eutectic composition; and the separation of the one component will
continue until the composition of the eutectic point is reached. Further cooling will then
lead to the simultaneous separation of the two components.
If, however, the two components form a stable compound (e.g. orthoclase, from a fused
mixture of silica and potassium aluminate), then the freezing-point curve will resemble that
shown in Fig. 64; i.e. there will be a middle curve possessing a dystectic point, and ending
on either side at a eutectic point. This curve would represent the conditions under which
orthoclase is in equilibrium with the molten magma. If the initial composition of the
magma is represented by a point between the two eutectic points, orthoclase will separate
first. The composition of the magma will thereby change, and the mass will finally solidify
to a mixture of orthoclase and silica, or orthoclase and potassium aluminate, according to
the initial composition.
until the component b, which has separated out, is converted into the
compound. After this the temperature again falls, until it again remains
constant at the eutectic point c. In the case of the first halt, the period of
constant temperature is greatest when the initial composition of the
solution is the same as that of the compound; and it becomes shorter
Fig. 79.
and shorter with increase in the amount of either component. In this
way we obtain the time-composition curve b′e″d′, of which the
maximum point e″ gives the composition of the compound.
On the other hand, the period of constant temperature for the eutectic point c is greatest in
the case of solutions having the same initial composition as that corresponding with the
eutectic point; and it decreases the more the initial composition approaches that of the pure
component a or the component e. In this way we obtain the time-composition curve a′c′e′.
Here also the point e′ represents the composition of the compound. We see, therefore, that
from the graphic representation of the freezing-point curve, and from the duration of the
temperature-arrests on the cooling curve, for solutions of different initial composition, it is
possible, without having recourse to analysis, to decide what solid phases are formed, and
what is their composition.
Formation of Minerals.—Important and interesting as is the application of the Phase Rule
to the study of alloys, its application to the study of the conditions regulating the formation
of minerals is no less so; and although we do not propose to consider different cases in
detail here, still attention must be drawn to certain points connected with this interesting
subject.
In the first place, it will be evident from what has already been said, that that mineral which
first crystallizes out from a molten magma is not necessarily the one with the highest
melting point. The composition of the fused mass must be taken into account. When the
system consists of two components which do not form a compound, one or other of these
will separate out in a pure state, according as the composition of the molten mass lies on
one or other side of the eutectic composition; and the separation of the one component will
continue until the composition of the eutectic point is reached. Further cooling will then
lead to the simultaneous separation of the two components.
If, however, the two components form a stable compound (e.g. orthoclase, from a fused
mixture of silica and potassium aluminate), then the freezing-point curve will resemble that
shown in Fig. 64; i.e. there will be a middle curve possessing a dystectic point, and ending
on either side at a eutectic point. This curve would represent the conditions under which
orthoclase is in equilibrium with the molten magma. If the initial composition of the
magma is represented by a point between the two eutectic points, orthoclase will separate
first. The composition of the magma will thereby change, and the mass will finally solidify
to a mixture of orthoclase and silica, or orthoclase and potassium aluminate, according to
the initial composition.
Page 194
What has just been said holds, however, only for stable equilibria, and it must not be
forgotten that complications can arise owing to suspended transformation (when, for
example, the magma is rapidly cooled) and the production of metastable equilibria. These
conditions occur very frequently in nature.
The study of the formation of minerals from the point of view of the Phase Rule is still in
its initial stages, but the results which have already been obtained give promise of a rich
harvest in the future.[316]
CHAPTER XIII
SYSTEMS OF THREE COMPONENTS
General.—It has already been made evident that an increase in the number of the
components from one to two gives rise to a considerable increase in the possible number of
systems, and introduces not a few complications into the equilibrium relations of these. No
less is this the case when the number of components increases from two to three; and
although examples of all the possible types of systems of three components have not been
investigated, nor, indeed, any one type fully, nevertheless, among the systems which have
been studied experimentally, cases occur which not only possess a high scientific interest,
but are also of great industrial importance. On account not only of the number, but more
especially of the complexity of the systems constituted of three components, no attempt
will be made to give a full account, or, indeed, even a survey of all the cases which have
been subjected to a more or less complete experimental investigation; on the contrary, only
a few of the more important classes will be selected, and the most important points in
connection with the behaviour of these described.
On applying the Phase Rule
P+F=C+2
to the systems of three components, we see that in order that the system shall be invariant,
no fewer than five phases must be present together, and an invariant system will therefore
exist at a quintuple point. Since the number of liquid phases can never exceed the number
of the components, and since there can be only one vapour phase, it is evident that in this
case, as in others, there must always be at least one solid phase present at the quintuple
point. As the number of phases diminishes, the variability of the system can increase from
one to four, so that in the last case the condition of the system will not be completely
defined until not only the temperature and the total pressure of the system, but also the
concentrations of two of the components have been fixed. Or, instead of the concentrations,
the partial pressures of the components may also be taken as independent variables.
Graphic Representation.—Hitherto the concentrations of the components have been
represented by means of rectangular co-ordinates, although the numerical relationships
forgotten that complications can arise owing to suspended transformation (when, for
example, the magma is rapidly cooled) and the production of metastable equilibria. These
conditions occur very frequently in nature.
The study of the formation of minerals from the point of view of the Phase Rule is still in
its initial stages, but the results which have already been obtained give promise of a rich
harvest in the future.[316]
CHAPTER XIII
SYSTEMS OF THREE COMPONENTS
General.—It has already been made evident that an increase in the number of the
components from one to two gives rise to a considerable increase in the possible number of
systems, and introduces not a few complications into the equilibrium relations of these. No
less is this the case when the number of components increases from two to three; and
although examples of all the possible types of systems of three components have not been
investigated, nor, indeed, any one type fully, nevertheless, among the systems which have
been studied experimentally, cases occur which not only possess a high scientific interest,
but are also of great industrial importance. On account not only of the number, but more
especially of the complexity of the systems constituted of three components, no attempt
will be made to give a full account, or, indeed, even a survey of all the cases which have
been subjected to a more or less complete experimental investigation; on the contrary, only
a few of the more important classes will be selected, and the most important points in
connection with the behaviour of these described.
On applying the Phase Rule
P+F=C+2
to the systems of three components, we see that in order that the system shall be invariant,
no fewer than five phases must be present together, and an invariant system will therefore
exist at a quintuple point. Since the number of liquid phases can never exceed the number
of the components, and since there can be only one vapour phase, it is evident that in this
case, as in others, there must always be at least one solid phase present at the quintuple
point. As the number of phases diminishes, the variability of the system can increase from
one to four, so that in the last case the condition of the system will not be completely
defined until not only the temperature and the total pressure of the system, but also the
concentrations of two of the components have been fixed. Or, instead of the concentrations,
the partial pressures of the components may also be taken as independent variables.
Graphic Representation.—Hitherto the concentrations of the components have been
represented by means of rectangular co-ordinates, although the numerical relationships
Page 195
have been expressed in two different ways. In the one case, the concentration of the one
component was expressed in terms of a fixed amount of the other component. Thus, the
solubility of a salt was expressed by the number of grams of salt dissolved by 100 grams of
water or other solvent; and the numbers so obtained were measured along one of the co-
ordinates. The second co-ordinate was then employed to indicate the change of another
independent variable, e.g. temperature. In the other case, the combined weights of the two
components A and B were put equal to unity, and the concentration of the one expressed as
a fraction of the whole amount. This method allows of the representation of the complete
series of concentrations, from pure A to pure B, and was employed, for example, in the
graphic representation of the freezing point curves.
Even in the case of three components rectangular co-ordinates can also be employed, and,
indeed, are the most convenient in those cases where the behaviour of two of the
components to one another is very different from their behaviour to the third component;
as, for example, in the case of two salts and water. In these cases, the composition of the
system can be represented by measuring the amounts of each of the two components in a
given weight of the third, along two co-ordinates at right angles to one another; and the
change of the system with the temperature can then be represented by a third axis at right
angles to the first two. In those cases, however, where the three components behave in
much the same manner towards one another, the rectangular co-ordinates are not at all
suitable, and instead of these a triangular diagram is employed. Various methods have
been proposed for the graphic representation of systems of three components by means of a
triangle, but only two of these have been employed to any considerable extent; and a short
description of these two methods will therefore suffice.[317]
Fig. 80.
In the method proposed by Gibbs an equilateral triangle of unit height is used (Fig 80).[318]
The quantities of the different components are expressed as fractional parts of the whole,
and the sum of their concentrations is therefore equal to unity, and can be represented by
the height of the triangle. The corners of the triangle represent the pure substances A, B,
and C respectively. A point on one of the sides of the triangle will give the composition of a
mixture in which only two components are present, while a point within the triangle will
component was expressed in terms of a fixed amount of the other component. Thus, the
solubility of a salt was expressed by the number of grams of salt dissolved by 100 grams of
water or other solvent; and the numbers so obtained were measured along one of the co-
ordinates. The second co-ordinate was then employed to indicate the change of another
independent variable, e.g. temperature. In the other case, the combined weights of the two
components A and B were put equal to unity, and the concentration of the one expressed as
a fraction of the whole amount. This method allows of the representation of the complete
series of concentrations, from pure A to pure B, and was employed, for example, in the
graphic representation of the freezing point curves.
Even in the case of three components rectangular co-ordinates can also be employed, and,
indeed, are the most convenient in those cases where the behaviour of two of the
components to one another is very different from their behaviour to the third component;
as, for example, in the case of two salts and water. In these cases, the composition of the
system can be represented by measuring the amounts of each of the two components in a
given weight of the third, along two co-ordinates at right angles to one another; and the
change of the system with the temperature can then be represented by a third axis at right
angles to the first two. In those cases, however, where the three components behave in
much the same manner towards one another, the rectangular co-ordinates are not at all
suitable, and instead of these a triangular diagram is employed. Various methods have
been proposed for the graphic representation of systems of three components by means of a
triangle, but only two of these have been employed to any considerable extent; and a short
description of these two methods will therefore suffice.[317]
Fig. 80.
In the method proposed by Gibbs an equilateral triangle of unit height is used (Fig 80).[318]
The quantities of the different components are expressed as fractional parts of the whole,
and the sum of their concentrations is therefore equal to unity, and can be represented by
the height of the triangle. The corners of the triangle represent the pure substances A, B,
and C respectively. A point on one of the sides of the triangle will give the composition of a
mixture in which only two components are present, while a point within the triangle will
Page 196
represent the composition of a ternary mixture. Since every point within the triangle has the
property that the sum of the perpendiculars from that point on the sides of the triangle is
equal to unity (the height of the triangle), it is evident that the composition of a ternary
mixture can be represented by fixing a point within the triangle such that the lengths of the
perpendiculars from the point to the sides of the triangle are equal respectively to the
fractional amounts of the three components present; the fractional amount of A, B, or C
being represented by the perpendicular distance from the side of the triangle opposite the
corners A, B, and C respectively.
The location of this point is simplified by dividing the normals from each of the corners on
the opposite side into ten or one hundred parts, and drawing through these divisions lines at
right angles to the normal and parallel to the side of the triangle. A network of
rhombohedra is thus obtained, and the position of any point can be read off in practically
the same manner as in the case of rectangular co-ordinates. Thus the point P in Fig. 80
represents a ternary mixture of the composition A = 0.5, B = 0.3, C = 0.2; the
perpendiculars Pa, Pb, and Pc being equal respectively to 0.5, 0.2, and 0.3 of the height of
the triangle.
Another method of representation, due to Roozeboom, consists in employing an equilateral
triangle, the length of whose side is made equal to unity, or one hundred; the sum of the
fractional or percentage amounts of the three components being represented therefore by a
side of the triangle. In this case the composition of a ternary mixture is obtained by
determining, not the perpendicular distance of a point P from the three sides of the triangle,
but the distance in a direction parallel to the sides of the triangle (Fig. 81). Conversely, in
order to represent a mixture consisting of a, b, and c parts of the components A, B, and C
respectively, one side of the triangle, say AB, is first of all divided into ten or one hundred
parts; a portion, Bx = a, is then measured off, and represents the amount of A present.
Similarly, a portion, Ax′ = b, is measured off and represents the fractional amount of B,
while the remainder, xx′ = c, represents the amount of C. From x and x′ lines are drawn
parallel to the sides of the triangle, and the point of intersection, P, represents the
composition of the ternary mixture of given composition; for, as is evident from the figure,
the distance of the point P from the three sides of the triangle, when measured in directions
parallel to the sides, is equal to a, b, and c respectively. From the division marks on the
side AB, it is seen that the point P in this figure also represents a mixture of 0.5 parts of A,
0.2 parts of B, and 0.3 parts of C. This gives exactly the same result as the previous
method. The employment of a right-angled isosceles triangle has also been suggested,[319]
but is not in general use.
property that the sum of the perpendiculars from that point on the sides of the triangle is
equal to unity (the height of the triangle), it is evident that the composition of a ternary
mixture can be represented by fixing a point within the triangle such that the lengths of the
perpendiculars from the point to the sides of the triangle are equal respectively to the
fractional amounts of the three components present; the fractional amount of A, B, or C
being represented by the perpendicular distance from the side of the triangle opposite the
corners A, B, and C respectively.
The location of this point is simplified by dividing the normals from each of the corners on
the opposite side into ten or one hundred parts, and drawing through these divisions lines at
right angles to the normal and parallel to the side of the triangle. A network of
rhombohedra is thus obtained, and the position of any point can be read off in practically
the same manner as in the case of rectangular co-ordinates. Thus the point P in Fig. 80
represents a ternary mixture of the composition A = 0.5, B = 0.3, C = 0.2; the
perpendiculars Pa, Pb, and Pc being equal respectively to 0.5, 0.2, and 0.3 of the height of
the triangle.
Another method of representation, due to Roozeboom, consists in employing an equilateral
triangle, the length of whose side is made equal to unity, or one hundred; the sum of the
fractional or percentage amounts of the three components being represented therefore by a
side of the triangle. In this case the composition of a ternary mixture is obtained by
determining, not the perpendicular distance of a point P from the three sides of the triangle,
but the distance in a direction parallel to the sides of the triangle (Fig. 81). Conversely, in
order to represent a mixture consisting of a, b, and c parts of the components A, B, and C
respectively, one side of the triangle, say AB, is first of all divided into ten or one hundred
parts; a portion, Bx = a, is then measured off, and represents the amount of A present.
Similarly, a portion, Ax′ = b, is measured off and represents the fractional amount of B,
while the remainder, xx′ = c, represents the amount of C. From x and x′ lines are drawn
parallel to the sides of the triangle, and the point of intersection, P, represents the
composition of the ternary mixture of given composition; for, as is evident from the figure,
the distance of the point P from the three sides of the triangle, when measured in directions
parallel to the sides, is equal to a, b, and c respectively. From the division marks on the
side AB, it is seen that the point P in this figure also represents a mixture of 0.5 parts of A,
0.2 parts of B, and 0.3 parts of C. This gives exactly the same result as the previous
method. The employment of a right-angled isosceles triangle has also been suggested,[319]
but is not in general use.
Page 197
Fig. 81.
In employing the triangular diagram, it will be of use to note a property of the equilateral
triangle. A line drawn from one corner of the triangle to the opposite side, represents the
composition of all mixtures in which the relative amounts of two of the components remain
unchanged. Thus, as Fig. 82 shows, if the component C is added to a mixture x, in which A
and B are present in the proportions of a : b, a mixture x′, which is thereby obtained, also
contains A and B in the ratio a : b. For the two triangles ACx and BCx are similar to the
two triangles HCx′ and KCx′; and, therefore, Ax : Bx = Hx′ : Kx′. But Ax = Dx and Bx = Ex;
further Hx′ = Fx′ and Kx′ = Gx′. Therefore, Dx : Ex = Fx′ : Gx′ = b : a. At all points on the
line Cx, therefore, the ratio of A to B is the same.
Fig. 82.
Fig. 83.
If it is desired to represent at the same time the change of another independent variable, e.g.
temperature, this can be done by measuring the latter along axes drawn perpendicular to the
corners of the triangle. In this way a right prism (Fig. 83) is obtained, and each section of
this cut parallel to the base represents therefore an isothermal surface.
In employing the triangular diagram, it will be of use to note a property of the equilateral
triangle. A line drawn from one corner of the triangle to the opposite side, represents the
composition of all mixtures in which the relative amounts of two of the components remain
unchanged. Thus, as Fig. 82 shows, if the component C is added to a mixture x, in which A
and B are present in the proportions of a : b, a mixture x′, which is thereby obtained, also
contains A and B in the ratio a : b. For the two triangles ACx and BCx are similar to the
two triangles HCx′ and KCx′; and, therefore, Ax : Bx = Hx′ : Kx′. But Ax = Dx and Bx = Ex;
further Hx′ = Fx′ and Kx′ = Gx′. Therefore, Dx : Ex = Fx′ : Gx′ = b : a. At all points on the
line Cx, therefore, the ratio of A to B is the same.
Fig. 82.
Fig. 83.
If it is desired to represent at the same time the change of another independent variable, e.g.
temperature, this can be done by measuring the latter along axes drawn perpendicular to the
corners of the triangle. In this way a right prism (Fig. 83) is obtained, and each section of
this cut parallel to the base represents therefore an isothermal surface.
Page 198
CHAPTER XIV
SOLUTIONS OF LIQUIDS IN LIQUIDS
We have already seen (p. 95) that when two liquids are brought together, they may mix in
all proportions and form one homogeneous liquid phase; or, only partial miscibility may
occur, and two phases be formed consisting of two mutually saturated solutions. In the
latter case, the concentration of the components in either phase and also the vapour
pressure of the system had, at a given temperature, perfectly definite values. In the case of
three liquid components, a similar behaviour may be found, although complete miscibility
of three components with the formation of only one liquid phase is of much rarer
occurrence than in the case of two components. When only partial miscibility occurs,
various cases are met with according as the three components form one, two, or three pairs
of partially miscible liquids. Further, when two of the components are only partially
miscible, the addition of the third may cause either an increase or a diminution in the
mutual solubility of these. An increase in the mutual solubility is generally found when the
third component dissolves readily in each of the other two; but when the third component
dissolves only sparingly in the other two, its addition diminishes the mutual solubility of
the latter.
We shall consider here only a few examples illustrating the three chief cases which can
occur, viz. (1) A and B, and also B and C are miscible in all proportions, while A and C are
only partially miscible. (2) A and B are miscible in all proportions, but A and C and B and
C are only partially miscible. (3) A and B, B and C, and A and C are only partially
miscible. A, B, and C here represent the three components.
1.—The three components form only one pair of partially miscible liquids.
An example of this is found in the three substances: chloroform, water, and acetic acid.[320]
Chloroform and acetic acid, and water and acetic acid, are miscible with one another in all
proportions, but chloroform and water are only partially miscible with one another. If,
therefore, chloroform is shaken with a larger quantity of water than it can dissolve, two
layers will be formed consisting one of a saturated solution of water in chloroform, the
other of a saturated solution of chloroform in water. The composition of these two solutions
at a temperature of about 18°, will be represented by the points a and b in Fig. 84; a
representing a solution of the composition: chloroform, 99 per cent.; water, 1 per cent.; and
b a solution of the composition: chloroform, 0.8 per cent.; water, 99.2 per cent. When
acetic acid is added, it distributes itself between the two liquid layers, and two conjugate
ternary solutions, consisting of chloroform, water, and acetic acid are thereby produced
which are in equilibrium with one another, and the composition of which will be
represented by two points inside the triangle. In this way a series of pairs of ternary
solutions will be obtained by the addition of acetic acid to the mixture of chloroform and
water. By this addition, also, not only do the two liquid phases become increasingly rich in
SOLUTIONS OF LIQUIDS IN LIQUIDS
We have already seen (p. 95) that when two liquids are brought together, they may mix in
all proportions and form one homogeneous liquid phase; or, only partial miscibility may
occur, and two phases be formed consisting of two mutually saturated solutions. In the
latter case, the concentration of the components in either phase and also the vapour
pressure of the system had, at a given temperature, perfectly definite values. In the case of
three liquid components, a similar behaviour may be found, although complete miscibility
of three components with the formation of only one liquid phase is of much rarer
occurrence than in the case of two components. When only partial miscibility occurs,
various cases are met with according as the three components form one, two, or three pairs
of partially miscible liquids. Further, when two of the components are only partially
miscible, the addition of the third may cause either an increase or a diminution in the
mutual solubility of these. An increase in the mutual solubility is generally found when the
third component dissolves readily in each of the other two; but when the third component
dissolves only sparingly in the other two, its addition diminishes the mutual solubility of
the latter.
We shall consider here only a few examples illustrating the three chief cases which can
occur, viz. (1) A and B, and also B and C are miscible in all proportions, while A and C are
only partially miscible. (2) A and B are miscible in all proportions, but A and C and B and
C are only partially miscible. (3) A and B, B and C, and A and C are only partially
miscible. A, B, and C here represent the three components.
1.—The three components form only one pair of partially miscible liquids.
An example of this is found in the three substances: chloroform, water, and acetic acid.[320]
Chloroform and acetic acid, and water and acetic acid, are miscible with one another in all
proportions, but chloroform and water are only partially miscible with one another. If,
therefore, chloroform is shaken with a larger quantity of water than it can dissolve, two
layers will be formed consisting one of a saturated solution of water in chloroform, the
other of a saturated solution of chloroform in water. The composition of these two solutions
at a temperature of about 18°, will be represented by the points a and b in Fig. 84; a
representing a solution of the composition: chloroform, 99 per cent.; water, 1 per cent.; and
b a solution of the composition: chloroform, 0.8 per cent.; water, 99.2 per cent. When
acetic acid is added, it distributes itself between the two liquid layers, and two conjugate
ternary solutions, consisting of chloroform, water, and acetic acid are thereby produced
which are in equilibrium with one another, and the composition of which will be
represented by two points inside the triangle. In this way a series of pairs of ternary
solutions will be obtained by the addition of acetic acid to the mixture of chloroform and
water. By this addition, also, not only do the two liquid phases become increasingly rich in
Page 199
acetic acid, but the mutual solubility of the chloroform and water increases; so that the
layer a becomes relatively richer in water, and layer b relatively richer in chloroform. This
is seen from the following table, which gives the percentage composition of different
conjugate ternary solutions at 18°.
Heavier layer. Lighter layer.
Chloroform. Water. Acetic acid. Chloroform. Water. Acetic acid.
99.01 0.99 0 0.84 99.16 0
91.85 1.38 6.77 1.21 73.69 25.10
80.00 2.28 17.72 7.30 48.58 44.12
70.13 4.12 25.75 15.11 34.71 50.18
67.15 5.20 27.65 18.33 31.11 50.56
59.99 7.93 32.08 25.20 25.39 49.41
55.81 9.58 34.61 28.85 23.28 47.87
By the continued addition of acetic acid, the composition of the successive conjugate
solutions in equilibrium with one another becomes, as the table shows, more nearly the
same, and a point is at length reached at which the two solutions become identical. This
will therefore be a critical point (p. 98). Increased addition of acetic acid beyond this point
will lead to a single homogeneous solution.
These relationships are represented graphically by the curve aKb, Fig. 84. The points on
the branch aK represent the composition of the solutions relatively rich in chloroform
(heavier layer), those on the curve bK the composition of solutions relatively rich in water
(lighter layer); and the points on these two branches representing conjugate solutions are
joined together by "tie-lines." Thus, the points a′b′ represent conjugate solutions, and the
line a′b′ is a tie-line.
Fig. 84.
Since, now, acetic acid when added to a heterogeneous mixture of chloroform and water
does not enter in equal amounts into the two layers, but in amounts depending on its
coefficient of distribution between chloroform and water,[321] the tie-lines will not be
parallel to AB, but will be inclined at an angle. As the solutions become more nearly the
same, the tie-lines diminish in length, and at last, when the conjugate solutions become
layer a becomes relatively richer in water, and layer b relatively richer in chloroform. This
is seen from the following table, which gives the percentage composition of different
conjugate ternary solutions at 18°.
Heavier layer. Lighter layer.
Chloroform. Water. Acetic acid. Chloroform. Water. Acetic acid.
99.01 0.99 0 0.84 99.16 0
91.85 1.38 6.77 1.21 73.69 25.10
80.00 2.28 17.72 7.30 48.58 44.12
70.13 4.12 25.75 15.11 34.71 50.18
67.15 5.20 27.65 18.33 31.11 50.56
59.99 7.93 32.08 25.20 25.39 49.41
55.81 9.58 34.61 28.85 23.28 47.87
By the continued addition of acetic acid, the composition of the successive conjugate
solutions in equilibrium with one another becomes, as the table shows, more nearly the
same, and a point is at length reached at which the two solutions become identical. This
will therefore be a critical point (p. 98). Increased addition of acetic acid beyond this point
will lead to a single homogeneous solution.
These relationships are represented graphically by the curve aKb, Fig. 84. The points on
the branch aK represent the composition of the solutions relatively rich in chloroform
(heavier layer), those on the curve bK the composition of solutions relatively rich in water
(lighter layer); and the points on these two branches representing conjugate solutions are
joined together by "tie-lines." Thus, the points a′b′ represent conjugate solutions, and the
line a′b′ is a tie-line.
Fig. 84.
Since, now, acetic acid when added to a heterogeneous mixture of chloroform and water
does not enter in equal amounts into the two layers, but in amounts depending on its
coefficient of distribution between chloroform and water,[321] the tie-lines will not be
parallel to AB, but will be inclined at an angle. As the solutions become more nearly the
same, the tie-lines diminish in length, and at last, when the conjugate solutions become
Page 200
identical, shrink to a point. For the reason that the tie-lines are, in general, not parallel to
the side of the triangle, the critical point at which the tie-line vanishes will not be at the
summit of the curve, but somewhere below this, as represented by the point K.
The curve aKb, further, forms the boundary between the heterogeneous and homogeneous
systems. A mixture of chloroform, water, and acetic acid represented by any point outside
the curve aKb, will form only one homogeneous phase; while any mixture represented by a
point within the curve, will separate into two layers having the composition represented by
the ends of the tie-line passing through that point. Thus, a mixture of the total composition
x, will separate into two layers having the composition a′ and b′ respectively.
Since three components existing in three phases (two liquid and a vapour phase) constitute
a bivariant system, the final result, i.e. the composition of the two layers and the total
vapour pressure, will not depend merely on the temperature, as in the case of two-
component systems (p. 102), but also on the composition of the mixture with which we
start. At constant temperature, however, all mixtures, the composition of which is
represented by a point on one and the same tie-line, will separate into the same two liquid
phases, although the relative amounts of the two phases will vary. If we omit the vapour
phase, the condition of the system will depend on the pressure as well as on the
temperature and composition of the initial mixture. By keeping the pressure constant, e.g.
at atmospheric pressure (by working with open vessels), the system again becomes
bivariant. We see, therefore, that the position of the curve aKb, or, in other words, the
composition of the different conjugate ternary solutions, will vary with the temperature,
and only with the temperature, if we assume either constancy of pressure or the presence of
the vapour phase. Since at the critical point the condition is imposed that the two liquid
phases become identical, one degree of freedom is thereby lost, and therefore only one
degree of freedom remains. The critical point, therefore, depends on the temperature, and
only on the temperature; always on the assumption, of course, that the pressure is constant,
or that a vapour phase is present. Fig. 84, therefore, represents an isothermal (p. 239).
It is of importance to note that the composition of the different ternary solutions obtained
by the addition of acetic acid to a heterogeneous mixture of chloroform and water, will
depend not only on the amount of acetic acid added, but also on the relative amounts of
chloroform and water at the commencement. Suppose, for example, that we start with
chloroform and water in the proportions represented by the point c′ (Fig. 84). On mixing
these, two liquid layers having the composition a and b respectively will be formed. Since
by the addition of acetic acid the relative amounts of these two substances in the system as
a whole cannot undergo alteration, the total composition of the different ternary systems
which will be obtained must be represented by a point on the line Cc′ (p. 238). Thus, for
example, by the addition of acetic acid a system may be obtained, the total composition of
which is represented by the point c″. Such a system, however, will separate into two
conjugate ternary solutions, the composition of which will be represented by the ends of
the tie-line passing through the point c″. So long as the total composition of the system lies
below the point S, i.e. the point of intersection of the line Cc′ with the boundary curve, two
liquid layers will be formed; while all systems having a total composition represented by a
point on the line Cc′, above S, will form only one homogeneous solution.
the side of the triangle, the critical point at which the tie-line vanishes will not be at the
summit of the curve, but somewhere below this, as represented by the point K.
The curve aKb, further, forms the boundary between the heterogeneous and homogeneous
systems. A mixture of chloroform, water, and acetic acid represented by any point outside
the curve aKb, will form only one homogeneous phase; while any mixture represented by a
point within the curve, will separate into two layers having the composition represented by
the ends of the tie-line passing through that point. Thus, a mixture of the total composition
x, will separate into two layers having the composition a′ and b′ respectively.
Since three components existing in three phases (two liquid and a vapour phase) constitute
a bivariant system, the final result, i.e. the composition of the two layers and the total
vapour pressure, will not depend merely on the temperature, as in the case of two-
component systems (p. 102), but also on the composition of the mixture with which we
start. At constant temperature, however, all mixtures, the composition of which is
represented by a point on one and the same tie-line, will separate into the same two liquid
phases, although the relative amounts of the two phases will vary. If we omit the vapour
phase, the condition of the system will depend on the pressure as well as on the
temperature and composition of the initial mixture. By keeping the pressure constant, e.g.
at atmospheric pressure (by working with open vessels), the system again becomes
bivariant. We see, therefore, that the position of the curve aKb, or, in other words, the
composition of the different conjugate ternary solutions, will vary with the temperature,
and only with the temperature, if we assume either constancy of pressure or the presence of
the vapour phase. Since at the critical point the condition is imposed that the two liquid
phases become identical, one degree of freedom is thereby lost, and therefore only one
degree of freedom remains. The critical point, therefore, depends on the temperature, and
only on the temperature; always on the assumption, of course, that the pressure is constant,
or that a vapour phase is present. Fig. 84, therefore, represents an isothermal (p. 239).
It is of importance to note that the composition of the different ternary solutions obtained
by the addition of acetic acid to a heterogeneous mixture of chloroform and water, will
depend not only on the amount of acetic acid added, but also on the relative amounts of
chloroform and water at the commencement. Suppose, for example, that we start with
chloroform and water in the proportions represented by the point c′ (Fig. 84). On mixing
these, two liquid layers having the composition a and b respectively will be formed. Since
by the addition of acetic acid the relative amounts of these two substances in the system as
a whole cannot undergo alteration, the total composition of the different ternary systems
which will be obtained must be represented by a point on the line Cc′ (p. 238). Thus, for
example, by the addition of acetic acid a system may be obtained, the total composition of
which is represented by the point c″. Such a system, however, will separate into two
conjugate ternary solutions, the composition of which will be represented by the ends of
the tie-line passing through the point c″. So long as the total composition of the system lies
below the point S, i.e. the point of intersection of the line Cc′ with the boundary curve, two
liquid layers will be formed; while all systems having a total composition represented by a
point on the line Cc′, above S, will form only one homogeneous solution.
Page 201
From the figure, also, it is evident that as the amount of acetic acid is increased, the relative
amounts of the two liquid layers formed differ more and more until at S a limiting position
is reached, when the amount of the one liquid layer dwindles to nought, and only one
solution remains.
The same reasoning can be carried through for different initial amounts of chloroform and
water, but it would be fruitless to discuss all the different systems which can be obtained.
The reason for the preceding discussion was to show that although the addition of acetic
acid to a mixture of chloroform and water will, in all cases, lead ultimately to a limiting
system, beyond which homogeneity occurs, that point is not necessarily the critical point.
On the contrary, in order that addition of acetic acid shall lead to the critical mixture, it is
necessary to start with a binary mixture of chloroform and water in the proportions
represented by the point c′. In this case, addition of acetic acid will give rise to a series of
conjugate ternary solutions, the composition of which will gradually approach to one
another, and at last become identical.
From the foregoing it will be evident that the amount of acetic acid required to produce a
homogenous solution, will depend on the relative amounts of chloroform and water from
which we start, and can be ascertained by joining the corner C with the point on the line
AB representing the total composition of the initial binary system. The point where this
line intersects the boundary curve aKb will indicate the minimum amount of acetic acid
which, under these particular conditions, is necessary to give one homogeneous solution.
Retrograde Solubility.—As a consequence of the fact that acetic acid distributes itself
unequally between chloroform and water, and the critical point K, therefore, does not lie at
the summit of the curve, it is possible to start with a homogeneous solution in which the
percentage amount of acetic acid is greater than at the critical point, and to pass from this
first to a heterogenous and then again to a homogenous system merely by altering the
relative amounts of chloroform and water. This phenomenon, to which the term retrograde
solubility is applied, will be observed not only in the case of chloroform, water, and acetic
acid, but in all other systems in which the critical point lies below the highest point of the
boundary curve for heterogeneous systems. This will be seen from the diagram, Fig. 85.
Starting with the homogeneous system represented by x, in which, therefore, the
concentration of C is greater than in the critical mixture (K), if the relative amounts of A
and B are altered in the direction xx′, while the amount of C is maintained constant, the
system will become heterogeneous when the composition reaches the point y, and will
remain heterogeneous with changing composition until the point y′ is passed, when it will
again become homogeneous. If the relative concentration of C is increased above that
represented by the line SS, this phenomenon will, of course, no longer be observed.
amounts of the two liquid layers formed differ more and more until at S a limiting position
is reached, when the amount of the one liquid layer dwindles to nought, and only one
solution remains.
The same reasoning can be carried through for different initial amounts of chloroform and
water, but it would be fruitless to discuss all the different systems which can be obtained.
The reason for the preceding discussion was to show that although the addition of acetic
acid to a mixture of chloroform and water will, in all cases, lead ultimately to a limiting
system, beyond which homogeneity occurs, that point is not necessarily the critical point.
On the contrary, in order that addition of acetic acid shall lead to the critical mixture, it is
necessary to start with a binary mixture of chloroform and water in the proportions
represented by the point c′. In this case, addition of acetic acid will give rise to a series of
conjugate ternary solutions, the composition of which will gradually approach to one
another, and at last become identical.
From the foregoing it will be evident that the amount of acetic acid required to produce a
homogenous solution, will depend on the relative amounts of chloroform and water from
which we start, and can be ascertained by joining the corner C with the point on the line
AB representing the total composition of the initial binary system. The point where this
line intersects the boundary curve aKb will indicate the minimum amount of acetic acid
which, under these particular conditions, is necessary to give one homogeneous solution.
Retrograde Solubility.—As a consequence of the fact that acetic acid distributes itself
unequally between chloroform and water, and the critical point K, therefore, does not lie at
the summit of the curve, it is possible to start with a homogeneous solution in which the
percentage amount of acetic acid is greater than at the critical point, and to pass from this
first to a heterogenous and then again to a homogenous system merely by altering the
relative amounts of chloroform and water. This phenomenon, to which the term retrograde
solubility is applied, will be observed not only in the case of chloroform, water, and acetic
acid, but in all other systems in which the critical point lies below the highest point of the
boundary curve for heterogeneous systems. This will be seen from the diagram, Fig. 85.
Starting with the homogeneous system represented by x, in which, therefore, the
concentration of C is greater than in the critical mixture (K), if the relative amounts of A
and B are altered in the direction xx′, while the amount of C is maintained constant, the
system will become heterogeneous when the composition reaches the point y, and will
remain heterogeneous with changing composition until the point y′ is passed, when it will
again become homogeneous. If the relative concentration of C is increased above that
represented by the line SS, this phenomenon will, of course, no longer be observed.
Page 202
Fig. 85.
Relationships similar to those described for chloroform, water, and acetic acid are also
found in the case of a number of other trios, e.g. ether, water, and alcohol; chloroform,
water, and alcohol.[322] They have also been observed in the case of a considerable number
of molten metals.[323] Thus, molten lead and silver, as well as molten zinc and silver, mix
in all proportions; but molten lead and zinc are only partially miscible with one another.
When melted together, therefore, the last two metals will separate into two liquid layers,
one rich in lead, the other rich in zinc. If silver is now added, and the temperature
maintained above the freezing point of the mixture, the silver passes for the most part, in
accordance with the law of distribution, into the upper layer, which is rich in zinc; silver
being more soluble in molten zinc than in molten lead. This is clearly shown by the
following figures:—[324]
Heavier alloy. Lighter alloy.
Percentage amount of Percentage amount of
Silver. Lead. Zinc. Silver. Lead. Zinc.
1.25 96.69 2.06 38.91 3.12 57.97
1.71 96.43 1.86 45.01 3.37 51.62
5.55 93.16 1.29 54.93 4.21 40.86
The numbers in the same horizontal row give the composition of the conjugate alloys, and
it is evident that the upper layer consists almost entirely of silver and zinc. On allowing the
mixture to cool slightly, the upper layer solidifies first, and can be separated from the still
molten lead layer. It is on this behaviour of silver towards a mixture of molten lead and
zinc that the Parkes's method for the desilverization of lead depends.[325] If aluminium is
also added, a still larger proportion of silver passes into the lighter layer, and the
desilverization of the lead is more complete.[326]
The Influence of Temperature.—As has already been said, a ternary system existing in
three phases possesses two degrees of freedom; and the state of the system is therefore
dependent not only on the relative concentration of the components, but also on the
temperature. As the temperature changes, therefore, the boundary curve of the
heterogeneous system will also alter; and in order to represent this alteration we shall make
use of the right prism, in which the temperature is measured upwards. In this way the
boundary curve passes into a boundary surface (called a dineric surface), as shown in Fig.
Relationships similar to those described for chloroform, water, and acetic acid are also
found in the case of a number of other trios, e.g. ether, water, and alcohol; chloroform,
water, and alcohol.[322] They have also been observed in the case of a considerable number
of molten metals.[323] Thus, molten lead and silver, as well as molten zinc and silver, mix
in all proportions; but molten lead and zinc are only partially miscible with one another.
When melted together, therefore, the last two metals will separate into two liquid layers,
one rich in lead, the other rich in zinc. If silver is now added, and the temperature
maintained above the freezing point of the mixture, the silver passes for the most part, in
accordance with the law of distribution, into the upper layer, which is rich in zinc; silver
being more soluble in molten zinc than in molten lead. This is clearly shown by the
following figures:—[324]
Heavier alloy. Lighter alloy.
Percentage amount of Percentage amount of
Silver. Lead. Zinc. Silver. Lead. Zinc.
1.25 96.69 2.06 38.91 3.12 57.97
1.71 96.43 1.86 45.01 3.37 51.62
5.55 93.16 1.29 54.93 4.21 40.86
The numbers in the same horizontal row give the composition of the conjugate alloys, and
it is evident that the upper layer consists almost entirely of silver and zinc. On allowing the
mixture to cool slightly, the upper layer solidifies first, and can be separated from the still
molten lead layer. It is on this behaviour of silver towards a mixture of molten lead and
zinc that the Parkes's method for the desilverization of lead depends.[325] If aluminium is
also added, a still larger proportion of silver passes into the lighter layer, and the
desilverization of the lead is more complete.[326]
The Influence of Temperature.—As has already been said, a ternary system existing in
three phases possesses two degrees of freedom; and the state of the system is therefore
dependent not only on the relative concentration of the components, but also on the
temperature. As the temperature changes, therefore, the boundary curve of the
heterogeneous system will also alter; and in order to represent this alteration we shall make
use of the right prism, in which the temperature is measured upwards. In this way the
boundary curve passes into a boundary surface (called a dineric surface), as shown in Fig.
Page 203
86. In this figure the curve akb is the isothermal for the
ternary system; the curve aKb shows the change in the
binary system AB with the temperature, with a critical
point at K. This curve has the same meaning as those
given in Chapter VI. The curve kK is a critical curve
joining together the critical points of the different
isothermals. In such a case as is shown in Fig. 86, there
does not exist any real critical temperature for the Fig. 86. Fig. 87.
ternary system, for as the temperature is raised, the
amount of C in the "critical" solution becomes less and less, and at K only two
components, A and B, are present. In the case, however, represented in Fig. 87, a real
ternary critical point is found. In this figure ak′b is an isothermal, ak″ is the curve for the
binary system, and K is the ternary critical point. All points outside the helmet-shaped
boundary surface represent homogeneous ternary solutions, while all points within the
surface belong to heterogeneous systems. Above the temperature of the point K, the three
components are miscible in all proportions. An example of a ternary system yielding such a
boundary surface is that consisting of phenol, water, and acetone.[327] In this case the
critical temperature K is 92°, and the composition at this ternary critical point is—
Water 59 per cent.
Acetone 12 ,,
Phenol 29 ,,
Fig. 88.
The difference between the two classes of systems just mentioned, is seen very clearly by a
glance at the Figs. 88 and 89, which show the projection of the isothermals on the base of
the prism. In Fig. 88, the projections yield paraboloid curves, the two branches of which
are cut by one side of the triangle; and the critical point is represented by a point on this
side. In the second case (Fig. 89), however, the projections of the isothermals form
ellipsoidal curves surrounding the supreme critical point, which now lies inside the
triangle. At lower temperatures, these isothermal boundary curves are cut by a side of the
triangle; at the critical temperature, k″, of the binary system AB, the boundary curve
touches the side AB, while at still higher temperatures the boundary curve comes to lie
entirely within the triangle. At any given temperature, therefore, between the critical point
of the binary system (k″), and the supreme critical point of the ternary system (K), each
pair of the three components are miscible with one another in all proportions; for the region
of heterogeneous systems is now bounded by a closed curve lying entirely within the
ternary system; the curve aKb shows the change in the
binary system AB with the temperature, with a critical
point at K. This curve has the same meaning as those
given in Chapter VI. The curve kK is a critical curve
joining together the critical points of the different
isothermals. In such a case as is shown in Fig. 86, there
does not exist any real critical temperature for the Fig. 86. Fig. 87.
ternary system, for as the temperature is raised, the
amount of C in the "critical" solution becomes less and less, and at K only two
components, A and B, are present. In the case, however, represented in Fig. 87, a real
ternary critical point is found. In this figure ak′b is an isothermal, ak″ is the curve for the
binary system, and K is the ternary critical point. All points outside the helmet-shaped
boundary surface represent homogeneous ternary solutions, while all points within the
surface belong to heterogeneous systems. Above the temperature of the point K, the three
components are miscible in all proportions. An example of a ternary system yielding such a
boundary surface is that consisting of phenol, water, and acetone.[327] In this case the
critical temperature K is 92°, and the composition at this ternary critical point is—
Water 59 per cent.
Acetone 12 ,,
Phenol 29 ,,
Fig. 88.
The difference between the two classes of systems just mentioned, is seen very clearly by a
glance at the Figs. 88 and 89, which show the projection of the isothermals on the base of
the prism. In Fig. 88, the projections yield paraboloid curves, the two branches of which
are cut by one side of the triangle; and the critical point is represented by a point on this
side. In the second case (Fig. 89), however, the projections of the isothermals form
ellipsoidal curves surrounding the supreme critical point, which now lies inside the
triangle. At lower temperatures, these isothermal boundary curves are cut by a side of the
triangle; at the critical temperature, k″, of the binary system AB, the boundary curve
touches the side AB, while at still higher temperatures the boundary curve comes to lie
entirely within the triangle. At any given temperature, therefore, between the critical point
of the binary system (k″), and the supreme critical point of the ternary system (K), each
pair of the three components are miscible with one another in all proportions; for the region
of heterogeneous systems is now bounded by a closed curve lying entirely within the
Page 204
triangle. Outside this curve only homogeneous systems are found. Binary mixtures,
therefore, represented by any point on one of the sides of the triangle must be
homogeneous, for they all lie outside the boundary curve for heterogeneous states.
Fig. 89.
2. The three components can form two pairs of partially miscible liquids.
In the case of the three components water, alcohol, and succinic nitrile, water and alcohol
are miscible in all proportions, but not so water and succinic nitrile, or alcohol and succinic
nitrile.
As we have already seen (p. 122), water and
succinic nitrile can form two liquid layers
between the temperatures 18.5° and 55.5°;
while alcohol and nitrile can form two liquid
layers between 13° and 31°. If, then, between
these two temperature limits, alcohol is
added to a heterogeneous mixture of water
and nitrile, or water is added to a mixture of Fig. 90. Fig. 91.
alcohol and nitrile, two heterogeneous
ternary systems will be formed, and two boundary curves will be obtained in the triangular
diagram, as shown in Fig. 90.[328] On changing the temperature, the boundary curves will
also undergo alteration, in a manner similar to that just discussed. As the temperature falls,
the two curves will spread out more and more into the centre of the triangle, and might at
last meet one another; while at still lower temperatures we may imagine the curves still
further expanding so that the two heterogeneous regions flow into one another and form a
band on the triangular diagram (Fig. 91). This, certainly, has not been realized in the case
of the three components mentioned, because at a temperature higher than that at which the
two heterogeneous regions could fuse together, solid separates out.
Fig. 92.
therefore, represented by any point on one of the sides of the triangle must be
homogeneous, for they all lie outside the boundary curve for heterogeneous states.
Fig. 89.
2. The three components can form two pairs of partially miscible liquids.
In the case of the three components water, alcohol, and succinic nitrile, water and alcohol
are miscible in all proportions, but not so water and succinic nitrile, or alcohol and succinic
nitrile.
As we have already seen (p. 122), water and
succinic nitrile can form two liquid layers
between the temperatures 18.5° and 55.5°;
while alcohol and nitrile can form two liquid
layers between 13° and 31°. If, then, between
these two temperature limits, alcohol is
added to a heterogeneous mixture of water
and nitrile, or water is added to a mixture of Fig. 90. Fig. 91.
alcohol and nitrile, two heterogeneous
ternary systems will be formed, and two boundary curves will be obtained in the triangular
diagram, as shown in Fig. 90.[328] On changing the temperature, the boundary curves will
also undergo alteration, in a manner similar to that just discussed. As the temperature falls,
the two curves will spread out more and more into the centre of the triangle, and might at
last meet one another; while at still lower temperatures we may imagine the curves still
further expanding so that the two heterogeneous regions flow into one another and form a
band on the triangular diagram (Fig. 91). This, certainly, has not been realized in the case
of the three components mentioned, because at a temperature higher than that at which the
two heterogeneous regions could fuse together, solid separates out.
Fig. 92.
Page 205
The gradual expansion of a paraboloid into a band-like area of heterogeneous ternary
systems, has, however, been observed in the case of water, phenol, and aniline.[329] In Fig.
92 are shown three isothermals, viz. those for 148°, 95°, and 50°. At 148°, water and
aniline form two layers having the composition—
Water, 83.5 per cent. water, 20 per cent.
and
Aniline, 16.5 ,, aniline, 80 ,,
and the critical point k′ has the composition—
Water, 65; phenol, 13.2; aniline, 21.8 per cent.
At 95°, the composition of the two binary solutions is—
Water, 93 per cent. water, 8 per cent.
and
Aniline, 7 ,, aniline, 92 ,,
while the point k″ has the composition
Water, 69.9; phenol, 26.6; aniline, 3.5 per cent.
At 50°, the region of heterogeneous states now forms a band, and the two layers formed by
water and aniline have the composition—
Water, 96.5 per cent. water, 5.5 per cent.
and
Aniline, 3.5 ,, aniline, 94.5 ,,
while the two layers formed by water and phenol have the composition—
Water, 89 per cent. water, 20 per cent.
and
Phenol, 11 ,, phenol, 80 ,,
All mixtures of water, phenol, and aniline, therefore, the composition of which is
represented by any point within the band abcd, will form two ternary solutions; while if the
composition is represented by a point outside the band, only one homogeneous solution
will be produced.
3. The three components form three pairs of partially miscible liquids.
systems, has, however, been observed in the case of water, phenol, and aniline.[329] In Fig.
92 are shown three isothermals, viz. those for 148°, 95°, and 50°. At 148°, water and
aniline form two layers having the composition—
Water, 83.5 per cent. water, 20 per cent.
and
Aniline, 16.5 ,, aniline, 80 ,,
and the critical point k′ has the composition—
Water, 65; phenol, 13.2; aniline, 21.8 per cent.
At 95°, the composition of the two binary solutions is—
Water, 93 per cent. water, 8 per cent.
and
Aniline, 7 ,, aniline, 92 ,,
while the point k″ has the composition
Water, 69.9; phenol, 26.6; aniline, 3.5 per cent.
At 50°, the region of heterogeneous states now forms a band, and the two layers formed by
water and aniline have the composition—
Water, 96.5 per cent. water, 5.5 per cent.
and
Aniline, 3.5 ,, aniline, 94.5 ,,
while the two layers formed by water and phenol have the composition—
Water, 89 per cent. water, 20 per cent.
and
Phenol, 11 ,, phenol, 80 ,,
All mixtures of water, phenol, and aniline, therefore, the composition of which is
represented by any point within the band abcd, will form two ternary solutions; while if the
composition is represented by a point outside the band, only one homogeneous solution
will be produced.
3. The three components form three pairs of partially miscible liquids.
Page 206
Fig. 93.
The third chief case which can occur is that no two of the components are
completely miscible with one another. In this case, therefore, we shall
obtain three paraboloid boundary curves, as shown in Fig. 93. If, now, we
imagine these three curves to expand in towards the centre of the triangle,
as might happen, for example, by lowering the temperature, a point will be
reached at which the curves partly overlap, and we shall get the appearance
shown in Fig. 94.
The points a, b, and c represent the points where the three curves cut, and
the triangle abc is a region where the curves overlap. From this diagram we
can see that any mixture having a composition represented by a point in one
of the clear spaces at the corners of the larger triangle, will form a
homogeneous solution; if the composition corresponds to any point lying in
one of the quadrilateral regions x1, x2 or x3, two ternary solutions will be
formed; while, if the composition is represented by any point in the inner
triangle, separation into three layers will occur.
Fig. 94.
Since in the clear regions at the corners of the triangle we have three
components in two phases, liquid and vapour, the systems have three
degrees of freedom. At constant temperature, therefore, the condition of the
The third chief case which can occur is that no two of the components are
completely miscible with one another. In this case, therefore, we shall
obtain three paraboloid boundary curves, as shown in Fig. 93. If, now, we
imagine these three curves to expand in towards the centre of the triangle,
as might happen, for example, by lowering the temperature, a point will be
reached at which the curves partly overlap, and we shall get the appearance
shown in Fig. 94.
The points a, b, and c represent the points where the three curves cut, and
the triangle abc is a region where the curves overlap. From this diagram we
can see that any mixture having a composition represented by a point in one
of the clear spaces at the corners of the larger triangle, will form a
homogeneous solution; if the composition corresponds to any point lying in
one of the quadrilateral regions x1, x2 or x3, two ternary solutions will be
formed; while, if the composition is represented by any point in the inner
triangle, separation into three layers will occur.
Fig. 94.
Since in the clear regions at the corners of the triangle we have three
components in two phases, liquid and vapour, the systems have three
degrees of freedom. At constant temperature, therefore, the condition of the
Page 207
system is not defined until the concentrations of two of the components are
fixed. A system belonging to one of the quadrilateral spaces has, as we have
seen, two degrees of freedom; besides the temperature, one concentration
must be fixed. Lastly, a system the composition of which falls within the
inner triangle abc, will form three layers, and will therefore possess only
one degree of freedom. If the temperature is fixed, the composition of the
three layers is also determined, viz. that of the points a, b, and c
respectively; and a change in the composition of the original mixture can
lead only to a difference in the relative amounts of the three layers, not to a
difference in their composition.
An example of a system which can form three liquid phases is found in
water, ether, and succinic nitrile.[330]
CHAPTER XV
PRESENCE OF SOLID PHASES
A. The Ternary Eutectic Point.—In passing to the consideration of those
ternary systems in which one or more solid phases can exist together with
one liquid phase, we shall first discuss not the solubility curves, as in the
case of two-component systems, but the simpler relationships met with at
the freezing point. That is, we shall first of all examine the freezing point
curves of ternary systems.
Since it is necessary to take into account not only the
changing composition of the liquid phase, but also the
variation of the temperature, we shall employ the right
prism for the graphic representation of the systems, as
shown in Fig. 95. A, B, and C in this figure, therefore,
denote the melting points of the pure components. If we
start with the component A at its melting point, and add
B, which is capable of dissolving in liquid A, the freezing Fig. 95.
point of A will be lowered; and, similarly, the freezing
point of B by addition of A. In this way we get the freezing point curve
fixed. A system belonging to one of the quadrilateral spaces has, as we have
seen, two degrees of freedom; besides the temperature, one concentration
must be fixed. Lastly, a system the composition of which falls within the
inner triangle abc, will form three layers, and will therefore possess only
one degree of freedom. If the temperature is fixed, the composition of the
three layers is also determined, viz. that of the points a, b, and c
respectively; and a change in the composition of the original mixture can
lead only to a difference in the relative amounts of the three layers, not to a
difference in their composition.
An example of a system which can form three liquid phases is found in
water, ether, and succinic nitrile.[330]
CHAPTER XV
PRESENCE OF SOLID PHASES
A. The Ternary Eutectic Point.—In passing to the consideration of those
ternary systems in which one or more solid phases can exist together with
one liquid phase, we shall first discuss not the solubility curves, as in the
case of two-component systems, but the simpler relationships met with at
the freezing point. That is, we shall first of all examine the freezing point
curves of ternary systems.
Since it is necessary to take into account not only the
changing composition of the liquid phase, but also the
variation of the temperature, we shall employ the right
prism for the graphic representation of the systems, as
shown in Fig. 95. A, B, and C in this figure, therefore,
denote the melting points of the pure components. If we
start with the component A at its melting point, and add
B, which is capable of dissolving in liquid A, the freezing Fig. 95.
point of A will be lowered; and, similarly, the freezing
point of B by addition of A. In this way we get the freezing point curve
Page 208
Ak1B for the binary system; k1; being an eutectic point. This curve will of
course lie in the plane formed by one face of the prism. In a similar manner
we obtain the freezing point curves Ak2C and Bk3C. These curves give the
composition of the binary liquid phases in equilibrium with one of the pure
components, or at the eutectic points, with a mixture of two solid
components. If, now, to the system represented say by the point k1, a small
quantity of the third component, C, is added, the temperature at which the
two solid phases A and B can exist in equilibrium with the liquid phase is
lowered; and this depression of the eutectic point is all the greater the larger
the addition of C. In this way we obtain the curve k1K, which slopes
inwards and downwards, and indicates the varying composition of the
ternary liquid phase with which a mixture of solid A and B are in
equilibrium. Similarly, the curves k2K and k3K are the corresponding
eutectic curves for A and C, and B and C in equilibrium with ternary
solutions. At the point K, the three solid components are in equilibrium with
the liquid phase; and this point, therefore, represents the lowest temperature
attainable with the three components given. Each of the ternary eutectic
curves, as they may be called, is produced by the intersection of two
surfaces, while at the ternary eutectic point, three surfaces, viz. Ak1Kk2,
Bk1Kk3, and Ck1Kk3 intersect. Any point on one of these surfaces represents
a ternary solution in equilibrium with only one component in the solid state;
the lines or curves of intersection of these represent equilibria with two
solid phases, while at the point K, the ternary eutectic point, there are three
solid phases in equilibrium with a liquid and a vapour phase. The surfaces
just mentioned represent bivariant systems. One component in the solid
state can exist in equilibrium with a ternary liquid phase under varying
conditions of temperature and concentration of the components in the
solution; and before the state of the system is defined, these two variables,
temperature and composition of the liquid phase, must be fixed. On the
other hand, the curves formed by the intersection of these planes represent
univariant systems; at a given temperature two solid phases can exist in
equilibrium with a ternary solution, only when the latter has a definite
composition. Lastly, the ternary eutectic point, K, represents an invariant
system; three solid phases can exist in equilibrium with a ternary solution,
only when the latter has one fixed composition and when the temperature
course lie in the plane formed by one face of the prism. In a similar manner
we obtain the freezing point curves Ak2C and Bk3C. These curves give the
composition of the binary liquid phases in equilibrium with one of the pure
components, or at the eutectic points, with a mixture of two solid
components. If, now, to the system represented say by the point k1, a small
quantity of the third component, C, is added, the temperature at which the
two solid phases A and B can exist in equilibrium with the liquid phase is
lowered; and this depression of the eutectic point is all the greater the larger
the addition of C. In this way we obtain the curve k1K, which slopes
inwards and downwards, and indicates the varying composition of the
ternary liquid phase with which a mixture of solid A and B are in
equilibrium. Similarly, the curves k2K and k3K are the corresponding
eutectic curves for A and C, and B and C in equilibrium with ternary
solutions. At the point K, the three solid components are in equilibrium with
the liquid phase; and this point, therefore, represents the lowest temperature
attainable with the three components given. Each of the ternary eutectic
curves, as they may be called, is produced by the intersection of two
surfaces, while at the ternary eutectic point, three surfaces, viz. Ak1Kk2,
Bk1Kk3, and Ck1Kk3 intersect. Any point on one of these surfaces represents
a ternary solution in equilibrium with only one component in the solid state;
the lines or curves of intersection of these represent equilibria with two
solid phases, while at the point K, the ternary eutectic point, there are three
solid phases in equilibrium with a liquid and a vapour phase. The surfaces
just mentioned represent bivariant systems. One component in the solid
state can exist in equilibrium with a ternary liquid phase under varying
conditions of temperature and concentration of the components in the
solution; and before the state of the system is defined, these two variables,
temperature and composition of the liquid phase, must be fixed. On the
other hand, the curves formed by the intersection of these planes represent
univariant systems; at a given temperature two solid phases can exist in
equilibrium with a ternary solution, only when the latter has a definite
composition. Lastly, the ternary eutectic point, K, represents an invariant
system; three solid phases can exist in equilibrium with a ternary solution,
only when the latter has one fixed composition and when the temperature
Page 209
has a definite value. This eutectic point, therefore, has a perfectly definite
position, depending only on the nature of the three components.
Instead of employing the prism, the change in the composition of the
ternary solutions can also be indicated by means of the projections of the
curves k1K, k2K, and k3K on the base of the prism, the particular
temperature being written beside the different eutectic points and curves.
This is shown in Fig. 96.
Fig. 96.
The numbers which are given in this diagram refer to the eutectic points for
the system bismuth—lead—tin, the data for which are as follows:—[331]
Melting point of Percentage composition of Temperature of binary
pure metal. binary eutectic mixture. eutectic point.
Bi Pb Sn
Bismuth, 268° 55 45 — Bi—Pb, 127°
Lead, 325° 58 — 42 Bi—Sn, 133°
Tin, 232° — 37 63 Pb—Sn, 182°
Percentage composition of Temperature of ternary
ternary eutectic mixture. eutectic point.
Bi Pb Sn
52 32 16 96°
Formation of Compounds.—In the case just discussed, the components
crystallized out from solution in the pure state. If, however, combination
can take place between two of the components, the relationships will be
somewhat different; the curves which are obtained in such a case being
position, depending only on the nature of the three components.
Instead of employing the prism, the change in the composition of the
ternary solutions can also be indicated by means of the projections of the
curves k1K, k2K, and k3K on the base of the prism, the particular
temperature being written beside the different eutectic points and curves.
This is shown in Fig. 96.
Fig. 96.
The numbers which are given in this diagram refer to the eutectic points for
the system bismuth—lead—tin, the data for which are as follows:—[331]
Melting point of Percentage composition of Temperature of binary
pure metal. binary eutectic mixture. eutectic point.
Bi Pb Sn
Bismuth, 268° 55 45 — Bi—Pb, 127°
Lead, 325° 58 — 42 Bi—Sn, 133°
Tin, 232° — 37 63 Pb—Sn, 182°
Percentage composition of Temperature of ternary
ternary eutectic mixture. eutectic point.
Bi Pb Sn
52 32 16 96°
Formation of Compounds.—In the case just discussed, the components
crystallized out from solution in the pure state. If, however, combination
can take place between two of the components, the relationships will be
somewhat different; the curves which are obtained in such a case being
Page 210
represented in Fig. 97. From the figure, we see that the two components B
and C form a compound, and the freezing point curve of the binary system
has therefore the form shown in Fig. 64 (p. 209). Further, there are two
ternary eutectic points, K1 and K2, the solid phases present being A, B, and
compound, and A, C, and compound respectively.
Fig. 97.
The particular point, now, to which it is desired to draw attention is this.
Suppose the ternary eutectic curves projected on a plane parallel to the face
of the prism containing B and C, i.e. suppose the concentrations of the two
components B and C, between which interaction can occur, expressed in
terms of a constant amount of the third component A,[332] curves will then
be obtained which are in every respect analogous to the freezing point
curves of binary systems. Thus, suppose the eutectic curves k1K and k2K in
Fig. 95 projected on the face BC of the prism, then evidently a curve will be
obtained consisting of two branches meeting in an eutectic point. On the
other hand, the projection of the ternary eutectic curves in Fig. 97 on the
face BC of the prism, will give a curve consisting of three portions, as
shown by the outline k1K1K2k2 in Fig. 97.
Various examples of this have been studied, and the following table
contains some of the data for the system ethylene bromide (A), picric acid
(B), and β-naphthol (C), obtained by Bruni.[333]
Temperature. Solid phases present.
Point k1 9.41° Ethylene bromide, picric acid.
Curve k1K1 — ,, ,,
and C form a compound, and the freezing point curve of the binary system
has therefore the form shown in Fig. 64 (p. 209). Further, there are two
ternary eutectic points, K1 and K2, the solid phases present being A, B, and
compound, and A, C, and compound respectively.
Fig. 97.
The particular point, now, to which it is desired to draw attention is this.
Suppose the ternary eutectic curves projected on a plane parallel to the face
of the prism containing B and C, i.e. suppose the concentrations of the two
components B and C, between which interaction can occur, expressed in
terms of a constant amount of the third component A,[332] curves will then
be obtained which are in every respect analogous to the freezing point
curves of binary systems. Thus, suppose the eutectic curves k1K and k2K in
Fig. 95 projected on the face BC of the prism, then evidently a curve will be
obtained consisting of two branches meeting in an eutectic point. On the
other hand, the projection of the ternary eutectic curves in Fig. 97 on the
face BC of the prism, will give a curve consisting of three portions, as
shown by the outline k1K1K2k2 in Fig. 97.
Various examples of this have been studied, and the following table
contains some of the data for the system ethylene bromide (A), picric acid
(B), and β-naphthol (C), obtained by Bruni.[333]
Temperature. Solid phases present.
Point k1 9.41° Ethylene bromide, picric acid.
Curve k1K1 — ,, ,,
Page 211
Point K1 Ethylene bromide, picric acid, and β-
9.32°
naphthol picrate.
Curve
K1D′K2 — Ethylene bromide, β-naphthol picrate.
Point D′ 9.75° ,, ,, ,, ,,
Point K2 8.89° ,, ,, β-naphthol, and picrate.
Curve K2k2 — ,, ,, β-naphthol.
Point k2 9.04° ,, ,, ,,
From what has been said, it will be apparent that if the ternary eutectic
curve of a three-component system (in which one of the components is
present in constant amount) is determined, it will be possible to state, from
the form of curve obtained, whether or not the two components present in
varying amount crystallize out pure or combine with one another to form a
compound. It may be left to the reader to work out the curves for the other
possible systems; but it will be apparent, that the projections of the ternary
eutectic curves in the manner given will yield a series of curves alike in all
points to the binary curves given in Figs. 63-65, pp. 208-210.
Since, from the method of investigation, the temperatures of the eutectic
curves will depend on the melting point of the third component (A), it is
possible, by employing substances with widely differing melting points, to
investigate the interaction of the two components (e.g. two optical
antipodes) B and C over a range of temperature; and thus determine the
range of stability of the compound, if one is formed. Since, in some cases,
two substances which at one temperature form mixed crystals combine at
another temperature to form a definite compound, the relationships which
have just been described can be employed, and indeed, have been
employed, to determine the temperature at which this change occurs.[334]
By means of this method, Adriani found that below 103° i-camphoroxime
exists as a racemic compound, while above that temperature it occurs as a
racemic mixed crystal[335] (cf. p. 219).
B. Equilibria at Higher Temperatures. Formation of Double Salts.—
After having studied the relationships which are found in the
neighbourhood of the freezing points of the components, we now pass to
the discussion of the equilibria which are met with at higher temperatures.
9.32°
naphthol picrate.
Curve
K1D′K2 — Ethylene bromide, β-naphthol picrate.
Point D′ 9.75° ,, ,, ,, ,,
Point K2 8.89° ,, ,, β-naphthol, and picrate.
Curve K2k2 — ,, ,, β-naphthol.
Point k2 9.04° ,, ,, ,,
From what has been said, it will be apparent that if the ternary eutectic
curve of a three-component system (in which one of the components is
present in constant amount) is determined, it will be possible to state, from
the form of curve obtained, whether or not the two components present in
varying amount crystallize out pure or combine with one another to form a
compound. It may be left to the reader to work out the curves for the other
possible systems; but it will be apparent, that the projections of the ternary
eutectic curves in the manner given will yield a series of curves alike in all
points to the binary curves given in Figs. 63-65, pp. 208-210.
Since, from the method of investigation, the temperatures of the eutectic
curves will depend on the melting point of the third component (A), it is
possible, by employing substances with widely differing melting points, to
investigate the interaction of the two components (e.g. two optical
antipodes) B and C over a range of temperature; and thus determine the
range of stability of the compound, if one is formed. Since, in some cases,
two substances which at one temperature form mixed crystals combine at
another temperature to form a definite compound, the relationships which
have just been described can be employed, and indeed, have been
employed, to determine the temperature at which this change occurs.[334]
By means of this method, Adriani found that below 103° i-camphoroxime
exists as a racemic compound, while above that temperature it occurs as a
racemic mixed crystal[335] (cf. p. 219).
B. Equilibria at Higher Temperatures. Formation of Double Salts.—
After having studied the relationships which are found in the
neighbourhood of the freezing points of the components, we now pass to
the discussion of the equilibria which are met with at higher temperatures.
Page 212
In this connection we shall confine the discussion entirely to the systems
formed of two salts and water, dealing more particularly with those cases in
which the water is present in relatively large amount and acts as solvent.
Further, in studying these systems, one restriction must be made, viz. that
the single salts are salts either of the same base or of the same acid; or are,
in other words, capable of yielding a common ion in solution. Such a
restriction is necessary, because otherwise the system would be one not of
three but of four components.[336]
Transition Point.—As is very well known, there exist a number of
hydrated salts which, on being heated, undergo apparent partial fusion; and
in Chapter V. the behaviour of such hydrates was more fully studied in the
light of the Phase Rule. Glauber's salt, or sodium sulphate decahydrate, for
example, on being heated to a temperature of about 32.5°, partially
liquefies, owing to the fact that the water of crystallization is split off and
anhydrous sodium sulphate formed, as shown by the equation—
Na2SO4,10H2O = Na2SO4 + 10H2O
The temperature of 32.5°, it was learned, constituted a transition point for
the decahydrate and anhydrous salt plus water; decomposition of the
hydrated salt occurring above this temperature, combination of the
anhydrous salt and water below it.
Analogous phenomena are met with in systems constituted of two salts and
water in which the formation of double salts can take place. Thus, for
example, if d-sodium potassium tartrate is heated to above 55°, apparent
partial fusion occurs, and the two single salts, d-sodium tartrate and d-
potassium tartrate, are deposited, the change which occurs being
represented by the equation—
4NaKC4O6H4,4H2O = 2Na2C4O6H4,2H2O + 2K2C4O6H4,½H2O + 11H2O
On the other hand, if sodium and potassium tartrates are mixed with water
in the proportions shown on the right side of the equation, the system will
remain partially liquid so long as the temperature is maintained above 55°
(in a closed vessel to prevent loss of water), but on allowing the
temperature to fall below this point, complete solidification will ensue,
formed of two salts and water, dealing more particularly with those cases in
which the water is present in relatively large amount and acts as solvent.
Further, in studying these systems, one restriction must be made, viz. that
the single salts are salts either of the same base or of the same acid; or are,
in other words, capable of yielding a common ion in solution. Such a
restriction is necessary, because otherwise the system would be one not of
three but of four components.[336]
Transition Point.—As is very well known, there exist a number of
hydrated salts which, on being heated, undergo apparent partial fusion; and
in Chapter V. the behaviour of such hydrates was more fully studied in the
light of the Phase Rule. Glauber's salt, or sodium sulphate decahydrate, for
example, on being heated to a temperature of about 32.5°, partially
liquefies, owing to the fact that the water of crystallization is split off and
anhydrous sodium sulphate formed, as shown by the equation—
Na2SO4,10H2O = Na2SO4 + 10H2O
The temperature of 32.5°, it was learned, constituted a transition point for
the decahydrate and anhydrous salt plus water; decomposition of the
hydrated salt occurring above this temperature, combination of the
anhydrous salt and water below it.
Analogous phenomena are met with in systems constituted of two salts and
water in which the formation of double salts can take place. Thus, for
example, if d-sodium potassium tartrate is heated to above 55°, apparent
partial fusion occurs, and the two single salts, d-sodium tartrate and d-
potassium tartrate, are deposited, the change which occurs being
represented by the equation—
4NaKC4O6H4,4H2O = 2Na2C4O6H4,2H2O + 2K2C4O6H4,½H2O + 11H2O
On the other hand, if sodium and potassium tartrates are mixed with water
in the proportions shown on the right side of the equation, the system will
remain partially liquid so long as the temperature is maintained above 55°
(in a closed vessel to prevent loss of water), but on allowing the
temperature to fall below this point, complete solidification will ensue,
Page 213
owing to the formation of the hydrated double salt. Below 55°, therefore,
the hydrated double salt is the stable system, while above this temperature
the two single salts plus saturated solution are stable.[337]
A similar behaviour is found in the case of the double salt copper
dipotassium chloride (CuCl2,2KCl,2H2O or CuK2Cl4,2H2O).[338] When this
salt is heated to 92°, partial liquefaction occurs, and the original blue plate-
shaped crystals give place to brown crystalline needles and white cubes;
while on allowing the temperature to fall, re-formation of the blue double
salt ensues. The temperature 92° is, therefore, a transition point at which the
reversible reaction—
CuK2Cl4,2H2O CuKCl3 + KCl + 2H2O
takes place.
The decomposition of sodium potassium tartrate, or of copper dipotassium
chloride, differs in so far from that of Glauber's salt that two new solid
phases are formed; and in the case of copper dipotassium chloride, one of
the decomposition products is itself a double salt.
In the two examples of double salt decomposition which have just been
mentioned, sufficient water was yielded to cause a partial liquefaction; but
other cases are known where this is not so. Thus, when copper calcium
acetate is heated to a temperature of 75°, although decomposition of the
double salt into the two single salts occurs as represented by the
equation[339]—
CuCa(C2H3O2)4,8H2O = Cu(C2H3O2)2,H2O + Ca(C2H3O2)2,H2O + 6H2O
the amount of water split off is insufficient to give the appearance of partial
fusion, and, therefore, only a change in the crystals is observed.
The preceding examples, in which decomposition of the double salt was
effected by a rise of temperature, were chosen for first consideration as
being more analogous to the case of Glauber's salt; but not a few examples
are known where the reverse change takes place, formation of the double
salt occurring above the transition point, and decomposition into the
constituent salts below it. Instances of this behaviour are found in the case
the hydrated double salt is the stable system, while above this temperature
the two single salts plus saturated solution are stable.[337]
A similar behaviour is found in the case of the double salt copper
dipotassium chloride (CuCl2,2KCl,2H2O or CuK2Cl4,2H2O).[338] When this
salt is heated to 92°, partial liquefaction occurs, and the original blue plate-
shaped crystals give place to brown crystalline needles and white cubes;
while on allowing the temperature to fall, re-formation of the blue double
salt ensues. The temperature 92° is, therefore, a transition point at which the
reversible reaction—
CuK2Cl4,2H2O CuKCl3 + KCl + 2H2O
takes place.
The decomposition of sodium potassium tartrate, or of copper dipotassium
chloride, differs in so far from that of Glauber's salt that two new solid
phases are formed; and in the case of copper dipotassium chloride, one of
the decomposition products is itself a double salt.
In the two examples of double salt decomposition which have just been
mentioned, sufficient water was yielded to cause a partial liquefaction; but
other cases are known where this is not so. Thus, when copper calcium
acetate is heated to a temperature of 75°, although decomposition of the
double salt into the two single salts occurs as represented by the
equation[339]—
CuCa(C2H3O2)4,8H2O = Cu(C2H3O2)2,H2O + Ca(C2H3O2)2,H2O + 6H2O
the amount of water split off is insufficient to give the appearance of partial
fusion, and, therefore, only a change in the crystals is observed.
The preceding examples, in which decomposition of the double salt was
effected by a rise of temperature, were chosen for first consideration as
being more analogous to the case of Glauber's salt; but not a few examples
are known where the reverse change takes place, formation of the double
salt occurring above the transition point, and decomposition into the
constituent salts below it. Instances of this behaviour are found in the case
Page 214
of the formation of astracanite from sodium and magnesium sulphates, and
of sodium ammonium racemate from the two sodium ammonium tartrates,
to which reference will be made later. Between these various systems,
however, there is no essential difference; and whether decomposition or
formation of the double salt occurs at temperatures above the transition
point, will of course depend on the heat of change at that point. For, in
accordance with van't Hoff's law of movable equilibrium (p. 58), that
change will take place at the higher temperature which is accompanied by
an absorption of heat. If, therefore, the formation of the double salt from the
single salts is accompanied by an absorption of heat, the double salt will be
formed from the single salts on raising the temperature; but if the reverse is
the case, then the double salt on being heated will decompose into the
constituent salts.[340]
In those cases, now, which have so far been studied, the change at the
transition point is accompanied by a taking up or a splitting off of water;
and in such cases the general rule can be given, that if the water of
crystallization of the two constituent salts together is greater than that of
the double salt, the latter will be produced from the former on raising the
temperature (e.g. astracanite from sodium and magnesium sulphates); but if
the double salt contains more water of crystallization than the two single
salts, increase of temperature will effect the decomposition of the double
salt. When we seek for the connection between this rule and the law of van't
Hoff, it is found in the fact that the heat effect involved in the hydration or
dehydration of the salts is much greater than that of the other changes which
occur, and determines, therefore, the sign of the total heat effect.[341]
Vapour Pressure. Quintuple Point.—In the case of Glauber's salt, we saw
that at a certain temperature the vapour pressure curve of the hydrated salt
cut that of the saturated solution of anhydrous sodium sulphate. That point,
it will be remembered, was a quadruple point at which the four phases
sodium sulphate decahydrate, anhydrous sodium sulphate, solution, and
vapour, could co-exist; and was also the point of intersection of the curves
for four univariant systems. In the case of the formation of double salts,
similar relationships are met with; and also certain differences, due to the
fact that we are now dealing with systems of three components. Two cases
will be chosen here for brief description, one in which formation, the other
in which decomposition of the double salt occurs with rise of temperature.
of sodium ammonium racemate from the two sodium ammonium tartrates,
to which reference will be made later. Between these various systems,
however, there is no essential difference; and whether decomposition or
formation of the double salt occurs at temperatures above the transition
point, will of course depend on the heat of change at that point. For, in
accordance with van't Hoff's law of movable equilibrium (p. 58), that
change will take place at the higher temperature which is accompanied by
an absorption of heat. If, therefore, the formation of the double salt from the
single salts is accompanied by an absorption of heat, the double salt will be
formed from the single salts on raising the temperature; but if the reverse is
the case, then the double salt on being heated will decompose into the
constituent salts.[340]
In those cases, now, which have so far been studied, the change at the
transition point is accompanied by a taking up or a splitting off of water;
and in such cases the general rule can be given, that if the water of
crystallization of the two constituent salts together is greater than that of
the double salt, the latter will be produced from the former on raising the
temperature (e.g. astracanite from sodium and magnesium sulphates); but if
the double salt contains more water of crystallization than the two single
salts, increase of temperature will effect the decomposition of the double
salt. When we seek for the connection between this rule and the law of van't
Hoff, it is found in the fact that the heat effect involved in the hydration or
dehydration of the salts is much greater than that of the other changes which
occur, and determines, therefore, the sign of the total heat effect.[341]
Vapour Pressure. Quintuple Point.—In the case of Glauber's salt, we saw
that at a certain temperature the vapour pressure curve of the hydrated salt
cut that of the saturated solution of anhydrous sodium sulphate. That point,
it will be remembered, was a quadruple point at which the four phases
sodium sulphate decahydrate, anhydrous sodium sulphate, solution, and
vapour, could co-exist; and was also the point of intersection of the curves
for four univariant systems. In the case of the formation of double salts,
similar relationships are met with; and also certain differences, due to the
fact that we are now dealing with systems of three components. Two cases
will be chosen here for brief description, one in which formation, the other
in which decomposition of the double salt occurs with rise of temperature.
Page 215
On heating a mixture of sodium sulphate decahydrate and magnesium
sulphate heptahydrate, it is found that at 22° partial liquefaction occurs with
formation of astracanite. At this temperature, therefore, there can coexist the
five phases—
Na2SO4,10H2O; MgSO4,7H2O; Na2Mg(SO4)2,4H2O; solution; vapour.
This constitutes, therefore, a quintuple point; and since there are three
components present in five phases, the system is invariant. This point, also,
will be the point of intersection of curves for five univariant systems,
which, in this case, must each be composed of four phases. These systems
are—
I. Na2SO4,10H2O; MgSO4,7H2O; Na2Mg(SO4)2,4H2O; vapour.
II. Na2SO4,10H2O; MgSO4,7H2O; solution; vapour.
III. MgSO4,7H2O; Na2Mg(SO4)2,4H2O; solution; vapour.
IV. Na2SO4,10H2O; Na2Mg(SO4)2,4H2O; solution; vapour.
V. Na2SO4,10H2O; MgSO4,7H2O; Na2Mg(SO4)2,4H2O; solution.
Fig. 98.
On representing the vapour pressures of these different systems graphically,
a diagram is obtained such as is shown in Fig. 98,[342] the curves being
numbered in accordance with the above list. When the system I. is heated,
the vapour pressure increases until at the quintuple point the liquid phase
(solution) is formed, and it will then depend on the relative amounts of the
different phases whether on further heating there is formed system III., IV.,
or V. If either of the first two is produced, we shall obtain the vapour
sulphate heptahydrate, it is found that at 22° partial liquefaction occurs with
formation of astracanite. At this temperature, therefore, there can coexist the
five phases—
Na2SO4,10H2O; MgSO4,7H2O; Na2Mg(SO4)2,4H2O; solution; vapour.
This constitutes, therefore, a quintuple point; and since there are three
components present in five phases, the system is invariant. This point, also,
will be the point of intersection of curves for five univariant systems,
which, in this case, must each be composed of four phases. These systems
are—
I. Na2SO4,10H2O; MgSO4,7H2O; Na2Mg(SO4)2,4H2O; vapour.
II. Na2SO4,10H2O; MgSO4,7H2O; solution; vapour.
III. MgSO4,7H2O; Na2Mg(SO4)2,4H2O; solution; vapour.
IV. Na2SO4,10H2O; Na2Mg(SO4)2,4H2O; solution; vapour.
V. Na2SO4,10H2O; MgSO4,7H2O; Na2Mg(SO4)2,4H2O; solution.
Fig. 98.
On representing the vapour pressures of these different systems graphically,
a diagram is obtained such as is shown in Fig. 98,[342] the curves being
numbered in accordance with the above list. When the system I. is heated,
the vapour pressure increases until at the quintuple point the liquid phase
(solution) is formed, and it will then depend on the relative amounts of the
different phases whether on further heating there is formed system III., IV.,
or V. If either of the first two is produced, we shall obtain the vapour
Page 216
pressure of the solutions saturated with respect to both double salt and one
of the single salts; while if the vapour phase disappears, there will be
obtained the pressure of the condensed systems formed of double salt, two
single salts and solution. This curve, therefore, indicates the change of the
transition point with pressure; and since in the ordinary determinations of
the transition point in open vessels, we are in reality dealing with condensed
systems under the pressure of 1 atm., it will be evident that the transition
point does not accurately coincide with the quintuple point (at which the
system is under the pressure of its own vapour). As in the case of other
condensed systems, however, pressure has only a slight influence on the
temperature of the transition point. Whether or not pressure raises or lowers
the transition point will depend on whether transformation is accompanied
by an increase or diminution of volume (theorem of Le Chatelier, p. 58). In
the case of the formation of astracanite, expansion occurs, and the transition
point will therefore be raised by increase of pressure. Although
measurements have not been made in the case of this system, the existence
of such a curve has been experimentally verified in the case of copper and
calcium acetates and water (v. infra).[343]
Fig. 99.
The vapour pressure diagram in the case of copper calcium acetate and
water (Fig. 99), is almost the reverse of that already discussed. In this case,
the double salt decomposes on heating, and the decomposition is
accompanied by a contraction. Curve I. is the vapour pressure curve for
double salt, two single salts (p. 260), and vapour; curves II. and III. give the
vapour pressures of solutions saturated with respect to double salt and one
of the single salts; curve IV. is the curve of pressures for the solutions
saturated with respect to the two single salts; while curve V. again
represents the change of the transition point with pressure. On examining
this diagram, it is seen that whereas astracanite could exist both above and
of the single salts; while if the vapour phase disappears, there will be
obtained the pressure of the condensed systems formed of double salt, two
single salts and solution. This curve, therefore, indicates the change of the
transition point with pressure; and since in the ordinary determinations of
the transition point in open vessels, we are in reality dealing with condensed
systems under the pressure of 1 atm., it will be evident that the transition
point does not accurately coincide with the quintuple point (at which the
system is under the pressure of its own vapour). As in the case of other
condensed systems, however, pressure has only a slight influence on the
temperature of the transition point. Whether or not pressure raises or lowers
the transition point will depend on whether transformation is accompanied
by an increase or diminution of volume (theorem of Le Chatelier, p. 58). In
the case of the formation of astracanite, expansion occurs, and the transition
point will therefore be raised by increase of pressure. Although
measurements have not been made in the case of this system, the existence
of such a curve has been experimentally verified in the case of copper and
calcium acetates and water (v. infra).[343]
Fig. 99.
The vapour pressure diagram in the case of copper calcium acetate and
water (Fig. 99), is almost the reverse of that already discussed. In this case,
the double salt decomposes on heating, and the decomposition is
accompanied by a contraction. Curve I. is the vapour pressure curve for
double salt, two single salts (p. 260), and vapour; curves II. and III. give the
vapour pressures of solutions saturated with respect to double salt and one
of the single salts; curve IV. is the curve of pressures for the solutions
saturated with respect to the two single salts; while curve V. again
represents the change of the transition point with pressure. On examining
this diagram, it is seen that whereas astracanite could exist both above and
Page 217
below the quintuple point, copper calcium acetate can exist only below the
quintuple point. This behaviour is found only in those cases in which the
double salt is decomposed by rise of temperature, and where the
decomposition is accompanied by a diminution of volume.[344]
As already mentioned, the decomposition of copper calcium acetate into the
single salts and saturated solution is accompanied by a contraction, and it
was therefore to be expected that increase of pressure would lower the
transition point. This expectation of theory was confirmed by experiment,
for van't Hoff and Spring found that although the transition point under
atmospheric pressure is about 75°, decomposition of the double salt took
place even at the ordinary temperature when the pressure was increased to
6000 atm.[345]
Solubility Curves at the Transition Point.—At the transition point, as has
already been shown, the double salt and the two constituent salts can exist
in equilibrium with the same solution. The transition point, therefore, must
be the point of intersection of two solubility curves; the solubility curve of
the double salt and the solubility curve of the mixtures of the two
constituent salts. It should be noted here that we are not dealing with the
solubility curves of the single salts separately, for since the systems are
composed of three components, a single solid phase can, at a given
temperature, be in equilibrium with solutions of different composition, and
two solid phases in contact with solution (and vapour) are therefore
necessary to give an univariant system. The same applies, of course, to the
solubility of the double salt; for a double salt also constitutes a single phase,
and can therefore exist in equilibrium with solutions of varying
composition. If, however, we make the restriction (which we do for the
present) that the double salt is not decomposed by water, then the solution
will contain the constituent salts in the same relative proportions as they are
contained in the double salt, and the system may therefore be regarded as
one of two components, viz. double salt and water. In this case one solid
phase is sufficient, with solution and vapour, to give an univariant system;
and at a given temperature, therefore, the solubility will have a perfectly
definite value.
Since in almost all cases the solubility is determined in open vessels, we
shall in the following discussion consider that the vapour phase is absent,
quintuple point. This behaviour is found only in those cases in which the
double salt is decomposed by rise of temperature, and where the
decomposition is accompanied by a diminution of volume.[344]
As already mentioned, the decomposition of copper calcium acetate into the
single salts and saturated solution is accompanied by a contraction, and it
was therefore to be expected that increase of pressure would lower the
transition point. This expectation of theory was confirmed by experiment,
for van't Hoff and Spring found that although the transition point under
atmospheric pressure is about 75°, decomposition of the double salt took
place even at the ordinary temperature when the pressure was increased to
6000 atm.[345]
Solubility Curves at the Transition Point.—At the transition point, as has
already been shown, the double salt and the two constituent salts can exist
in equilibrium with the same solution. The transition point, therefore, must
be the point of intersection of two solubility curves; the solubility curve of
the double salt and the solubility curve of the mixtures of the two
constituent salts. It should be noted here that we are not dealing with the
solubility curves of the single salts separately, for since the systems are
composed of three components, a single solid phase can, at a given
temperature, be in equilibrium with solutions of different composition, and
two solid phases in contact with solution (and vapour) are therefore
necessary to give an univariant system. The same applies, of course, to the
solubility of the double salt; for a double salt also constitutes a single phase,
and can therefore exist in equilibrium with solutions of varying
composition. If, however, we make the restriction (which we do for the
present) that the double salt is not decomposed by water, then the solution
will contain the constituent salts in the same relative proportions as they are
contained in the double salt, and the system may therefore be regarded as
one of two components, viz. double salt and water. In this case one solid
phase is sufficient, with solution and vapour, to give an univariant system;
and at a given temperature, therefore, the solubility will have a perfectly
definite value.
Since in almost all cases the solubility is determined in open vessels, we
shall in the following discussion consider that the vapour phase is absent,
Page 218
and that the system is under a constant pressure, that of the atmosphere.
With this restriction, therefore, four phases will constitute an invariant
system, three phases an univariant, and two phases a bivariant system.
It has already been learned that in the case of sodium sulphate and water,
the solubility curve of the salt undergoes a sudden change in direction at the
transition point, and that this is accompanied by a change in the solid phase
in equilibrium with the solution. The same behaviour is also found in the
case of double salts. To illustrate this, we shall briefly discuss the solubility
relations of a few double salts, beginning with one of the simplest cases,
that of the formation of rubidium racemate from rubidium d- and l-tartrates.
The solubilities are represented diagrammatically in Fig. 100, the numerical
data being contained in the following table, in which the solubility is
expressed as the number of gram-molecules Rb2C4H4O6 in 100 gm.-
molecules of water.[346]
Solubility of tartrate
Temperature. Solubility of racemate.
mixture.
25° 13.03 10.91
35° — 12.63
40.4° — 13.48
40.7° 13.46 —
54° 13.83 —
In Fig. 100 the curve AB represents the solubility of the racemate, while
A′BC represents the solubility of the mixed tartrates. Below the transition
point, therefore, the solubility of the racemate is less than that of the mixed
tartrates. The solution, saturated with respect to the latter, will be
supersaturated with respect to the racemate; and if a nucleus of this is
present, racemate will be deposited, and the mixed tartrates, if present in
equimolecular amounts, will ultimately entirely disappear, and only
racemate will be left as solid phase. The solution will then have the
composition represented by a point on the curve AB. Conversely, above the
transition point, the saturated solution of the racemate would be
supersaturated with respect to the two tartrates, and transformation into the
latter would ensue. If, therefore, a solution of equimolecular proportions of
rubidium d- and l-tartrates is allowed to evaporate at a temperature above
With this restriction, therefore, four phases will constitute an invariant
system, three phases an univariant, and two phases a bivariant system.
It has already been learned that in the case of sodium sulphate and water,
the solubility curve of the salt undergoes a sudden change in direction at the
transition point, and that this is accompanied by a change in the solid phase
in equilibrium with the solution. The same behaviour is also found in the
case of double salts. To illustrate this, we shall briefly discuss the solubility
relations of a few double salts, beginning with one of the simplest cases,
that of the formation of rubidium racemate from rubidium d- and l-tartrates.
The solubilities are represented diagrammatically in Fig. 100, the numerical
data being contained in the following table, in which the solubility is
expressed as the number of gram-molecules Rb2C4H4O6 in 100 gm.-
molecules of water.[346]
Solubility of tartrate
Temperature. Solubility of racemate.
mixture.
25° 13.03 10.91
35° — 12.63
40.4° — 13.48
40.7° 13.46 —
54° 13.83 —
In Fig. 100 the curve AB represents the solubility of the racemate, while
A′BC represents the solubility of the mixed tartrates. Below the transition
point, therefore, the solubility of the racemate is less than that of the mixed
tartrates. The solution, saturated with respect to the latter, will be
supersaturated with respect to the racemate; and if a nucleus of this is
present, racemate will be deposited, and the mixed tartrates, if present in
equimolecular amounts, will ultimately entirely disappear, and only
racemate will be left as solid phase. The solution will then have the
composition represented by a point on the curve AB. Conversely, above the
transition point, the saturated solution of the racemate would be
supersaturated with respect to the two tartrates, and transformation into the
latter would ensue. If, therefore, a solution of equimolecular proportions of
rubidium d- and l-tartrates is allowed to evaporate at a temperature above
Page 219
40°, a mixture of the two tartrates will be deposited; while at temperatures
below 40° the racemate will separate out.
Fig. 100.
Similar relationships are met with in the case of sodium ammonium d- and
l-tartrate and sodium ammonium racemate; but in this case the racemate is
the stable form in contact with solution above the transition point (27°).[347]
Below the transition point, therefore, the solubility curve of the mixed
tartrates will lie below the solubility curve of the racemate. Below the
transition point, therefore, sodium ammonium racemate will break up in
contact with solution into a mixture of sodium ammonium d- and l-tartrates.
At a higher temperature, 35°, sodium ammonium racemate undergoes
decomposition into sodium racemate and ammonium racemate.[348]
The behaviour of sodium ammonium racemate is of interest from the fact
that it was the first racemic substance to be resolved into its optically active
forms by a process of crystallization. On neutralizing a solution of racemic
tartaric acid, half with soda and half with ammonia, and allowing the
solution to evaporate, Pasteur[349] obtained a mixture of sodium ammonium
d- and l-tartrates. Since Pasteur was unaware of the existence of a transition
point, the success of his experiment was due to the happy chance that he
allowed the solution to evaporate at a temperature below 27°; for had he
employed a temperature above this, separation of the racemate into the two
enantiomorphous forms would not have occurred. For this reason the
attempt of Staedel to perform the same resolution met only with failure.[350]
Decomposition of the Double Salt by Water.—In the two cases just
described, the solubility relationships at the transition point are of a simpler
character than in the case of most double salts. If, at a temperature above
the transition point, a mixture of rubidium d- and l-tartrates in
below 40° the racemate will separate out.
Fig. 100.
Similar relationships are met with in the case of sodium ammonium d- and
l-tartrate and sodium ammonium racemate; but in this case the racemate is
the stable form in contact with solution above the transition point (27°).[347]
Below the transition point, therefore, the solubility curve of the mixed
tartrates will lie below the solubility curve of the racemate. Below the
transition point, therefore, sodium ammonium racemate will break up in
contact with solution into a mixture of sodium ammonium d- and l-tartrates.
At a higher temperature, 35°, sodium ammonium racemate undergoes
decomposition into sodium racemate and ammonium racemate.[348]
The behaviour of sodium ammonium racemate is of interest from the fact
that it was the first racemic substance to be resolved into its optically active
forms by a process of crystallization. On neutralizing a solution of racemic
tartaric acid, half with soda and half with ammonia, and allowing the
solution to evaporate, Pasteur[349] obtained a mixture of sodium ammonium
d- and l-tartrates. Since Pasteur was unaware of the existence of a transition
point, the success of his experiment was due to the happy chance that he
allowed the solution to evaporate at a temperature below 27°; for had he
employed a temperature above this, separation of the racemate into the two
enantiomorphous forms would not have occurred. For this reason the
attempt of Staedel to perform the same resolution met only with failure.[350]
Decomposition of the Double Salt by Water.—In the two cases just
described, the solubility relationships at the transition point are of a simpler
character than in the case of most double salts. If, at a temperature above
the transition point, a mixture of rubidium d- and l-tartrates in
Page 220
equimolecular proportions is brought in contact with water a solution will
be obtained, which is saturated with respect to both enantiomorphous
forms; and since the solubility of the two optical antipodes is identical, and
the effect of one on the solubility of the other also the same, the solution
will contain equimolecular amounts of the d- and l-salt. If, now, the solution
is cooled down in contact with the solid salts to just below the transition
point, it becomes supersaturated with respect to the racemate, and this will
be deposited. The solution thereby becomes unsaturated with respect to the
mixture of the active salts, and these must therefore pass into solution. As
the latter are equally soluble, equal amounts of each will dissolve, and a
further quantity of the racemate will be deposited. These processes of
solution and deposition will continue until the single tartrates have
completely disappeared, and only racemate is left as solid phase. As a
consequence of the identical solubility of the two tartrates, therefore, no
excess of either form will be left on passing through the transition point.
From this it will be evident that the racemate can exist as single solid phase
in contact with its saturated solution at the transition point; or, in other
words, the racemate is not decomposed by water at the transition point. The
same behaviour will evidently be exhibited by sodium ammonium racemate
at 27°, for the two enantiomorphous sodium ammonium tartrates have also
identical solubility.
Very different, however, is the behaviour of, say, astracanite, or of the
majority of double salts; for the solubility of the constituent salts is now no
longer the same. If, for example, excess of a mixture of sodium sulphate
and magnesium sulphate, in equimolecular proportions, is brought in
contact with water below the transition point (22°), more magnesium
sulphate than sodium sulphate will dissolve, the solubility of these two salts
in a common solution being given by the following figures, which express
number of molecules of the salt in 100 molecules of water.[351]
Composition of Solutions saturated with respect to Na2SO4,10H2O and
MgSO4,7H2O.
Temperature. Na2SO4. MgSO4.
18.5° 2.16 4.57
24.5° 3.43 4.68
be obtained, which is saturated with respect to both enantiomorphous
forms; and since the solubility of the two optical antipodes is identical, and
the effect of one on the solubility of the other also the same, the solution
will contain equimolecular amounts of the d- and l-salt. If, now, the solution
is cooled down in contact with the solid salts to just below the transition
point, it becomes supersaturated with respect to the racemate, and this will
be deposited. The solution thereby becomes unsaturated with respect to the
mixture of the active salts, and these must therefore pass into solution. As
the latter are equally soluble, equal amounts of each will dissolve, and a
further quantity of the racemate will be deposited. These processes of
solution and deposition will continue until the single tartrates have
completely disappeared, and only racemate is left as solid phase. As a
consequence of the identical solubility of the two tartrates, therefore, no
excess of either form will be left on passing through the transition point.
From this it will be evident that the racemate can exist as single solid phase
in contact with its saturated solution at the transition point; or, in other
words, the racemate is not decomposed by water at the transition point. The
same behaviour will evidently be exhibited by sodium ammonium racemate
at 27°, for the two enantiomorphous sodium ammonium tartrates have also
identical solubility.
Very different, however, is the behaviour of, say, astracanite, or of the
majority of double salts; for the solubility of the constituent salts is now no
longer the same. If, for example, excess of a mixture of sodium sulphate
and magnesium sulphate, in equimolecular proportions, is brought in
contact with water below the transition point (22°), more magnesium
sulphate than sodium sulphate will dissolve, the solubility of these two salts
in a common solution being given by the following figures, which express
number of molecules of the salt in 100 molecules of water.[351]
Composition of Solutions saturated with respect to Na2SO4,10H2O and
MgSO4,7H2O.
Temperature. Na2SO4. MgSO4.
18.5° 2.16 4.57
24.5° 3.43 4.68
Page 221
At the transition point, then, it is evident that the solution contains more
magnesium sulphate than sodium sulphate: and this must still be the case
when astracanite, which contains sodium sulphate and magnesium sulphate
in equimolecular proportions, separates out. If, therefore, the temperature is
raised slightly above the transition point, magnesium sulphate and sodium
sulphate will pass into solution, the former, however, in larger quantities
than the latter, and astracanite will be deposited; and this will go on until all
the magnesium sulphate has disappeared, and a mixture of astracanite and
sodium sulphate decahydrate is left as solid phases. Since there are now
three phases present, the system is univariant (by reason of the restriction
previously made that the vapour phase is absent), and at a given
temperature the solution will have a definite composition; as given in the
following table:—
Composition of Solutions saturated with respect to Na2Mg(SO4)2,4H2O
and Na2SO4,10H2O.
Temperature. Na2SO4. MgSO4.
22° 2.95 4.70
24.5° 3.45 3.62
From the above figures, therefore, it will be seen that at a temperature just
above the transition point a solution in contact with the two solid phases,
astracanite and Glauber's salt, contains a relatively smaller amount of
sodium sulphate than a pure solution of astracanite would; for in this case
there would be equal molecular amounts of Na2SO4 and MgSO4. A solution
which is saturated with respect to astracanite alone, will contain more
sodium sulphate than the solution saturated with respect to astracanite plus
Glauber's salt, and the latter will therefore be deposited. From this,
therefore, it is clear that if astracanite is brought in contact with water at
about the transition point, it will undergo decomposition with separation of
Glauber's salt (supersaturation being excluded).
magnesium sulphate than sodium sulphate: and this must still be the case
when astracanite, which contains sodium sulphate and magnesium sulphate
in equimolecular proportions, separates out. If, therefore, the temperature is
raised slightly above the transition point, magnesium sulphate and sodium
sulphate will pass into solution, the former, however, in larger quantities
than the latter, and astracanite will be deposited; and this will go on until all
the magnesium sulphate has disappeared, and a mixture of astracanite and
sodium sulphate decahydrate is left as solid phases. Since there are now
three phases present, the system is univariant (by reason of the restriction
previously made that the vapour phase is absent), and at a given
temperature the solution will have a definite composition; as given in the
following table:—
Composition of Solutions saturated with respect to Na2Mg(SO4)2,4H2O
and Na2SO4,10H2O.
Temperature. Na2SO4. MgSO4.
22° 2.95 4.70
24.5° 3.45 3.62
From the above figures, therefore, it will be seen that at a temperature just
above the transition point a solution in contact with the two solid phases,
astracanite and Glauber's salt, contains a relatively smaller amount of
sodium sulphate than a pure solution of astracanite would; for in this case
there would be equal molecular amounts of Na2SO4 and MgSO4. A solution
which is saturated with respect to astracanite alone, will contain more
sodium sulphate than the solution saturated with respect to astracanite plus
Glauber's salt, and the latter will therefore be deposited. From this,
therefore, it is clear that if astracanite is brought in contact with water at
about the transition point, it will undergo decomposition with separation of
Glauber's salt (supersaturation being excluded).
Page 222
Fig. 101.
This will perhaps be made clearer by considering Fig. 101. In this diagram
the ordinates represent the ratio of sodium sulphate to magnesium sulphate
in the solutions, and the abscissæ represent the temperatures. The line AB
represents solutions saturated with respect to a mixture of the single salts
(p. 268); BC refers to solutions in equilibrium with astracanite and
magnesium sulphate; while BX represents the composition of solutions in
contact with the solid phases astracanite and Glauber's salt. The values of
the solubility are contained in the following table, and in that on p. 268, and
are, as before, expressed in gm.-molecules of salt in 100 gm.-molecules of
water.[352]
Astracanite + sodium Astracanite + magnesium
Temperature. sulphate. sulphate.
Na2SO4. MgSO4. Na2SO4. MgSO4.
18.5° — — 3.41 4.27
22° 2.95 4.70 2.85 4.63
24.5° 3.45 3.62 2.68 4.76
30° 4.58 2.91 2.30 5.31
35° 4.30 2.76 1.73 5.88
At the transition point the ratio of sodium sulphate to magnesium sulphate
is approximately 1 : 1.6. In the case of solutions saturated with respect to
both astracanite and Glauber's salt, the relative amount of sodium sulphate
increases as the temperature rises, while in the solutions saturated for
astracanite and magnesium sulphate, the ratio of sodium sulphate to
magnesium sulphate decreases.
If, now, we consider only the temperatures above the transition point, we
see from the figure that solutions represented by points above the line BX
This will perhaps be made clearer by considering Fig. 101. In this diagram
the ordinates represent the ratio of sodium sulphate to magnesium sulphate
in the solutions, and the abscissæ represent the temperatures. The line AB
represents solutions saturated with respect to a mixture of the single salts
(p. 268); BC refers to solutions in equilibrium with astracanite and
magnesium sulphate; while BX represents the composition of solutions in
contact with the solid phases astracanite and Glauber's salt. The values of
the solubility are contained in the following table, and in that on p. 268, and
are, as before, expressed in gm.-molecules of salt in 100 gm.-molecules of
water.[352]
Astracanite + sodium Astracanite + magnesium
Temperature. sulphate. sulphate.
Na2SO4. MgSO4. Na2SO4. MgSO4.
18.5° — — 3.41 4.27
22° 2.95 4.70 2.85 4.63
24.5° 3.45 3.62 2.68 4.76
30° 4.58 2.91 2.30 5.31
35° 4.30 2.76 1.73 5.88
At the transition point the ratio of sodium sulphate to magnesium sulphate
is approximately 1 : 1.6. In the case of solutions saturated with respect to
both astracanite and Glauber's salt, the relative amount of sodium sulphate
increases as the temperature rises, while in the solutions saturated for
astracanite and magnesium sulphate, the ratio of sodium sulphate to
magnesium sulphate decreases.
If, now, we consider only the temperatures above the transition point, we
see from the figure that solutions represented by points above the line BX
Page 223
contain relatively more sodium sulphate than solutions in contact with
astracanite and Glauber's salt; and solutions lying below the line BC contain
relatively more magnesium sulphate than solutions saturated with this salt
and astracanite. These solutions will therefore not be stable, but will deposit
in the one case, astracanite and Glauber's salt, and in the other case,
astracanite and magnesium sulphate, until a point on BX or BC is reached.
All solutions, however, lying to the right of CBX, will be unsaturated with
respect to these two pairs of salts, and only the solutions represented by the
line XY (and which contain equimolecular amounts of sodium and
magnesium sulphates) will be saturated with respect to the pure double salt.
Transition Interval.—Fig. 101 will also render intelligible a point of great
importance in connection with astracanite, and of double salts generally. At
temperatures between those represented by the points B and X, the double
salt when brought in contact with water will be decomposed with separation
of sodium sulphate. Above the temperature of the point X, however, the
solution of the pure double salt is stable, because it can still take up a little
of either of the components. At temperatures, then, above that at which the
solution in contact with the double salt and the less soluble single salt,
contains the single salts in the ratio in which they are present in the double
salt, solution of the latter will take place without decomposition. The range
of temperature between that at which double salt can begin to be formed
(the transition point) and that at which it ceases to be decomposed by water
is called the transition interval.[353] If the two single salts have identical
solubility at the transition point, the transition interval diminishes to nought.
In those cases where the double salt is the stable form below the transition
point, the transition interval will extend downwards to a lower temperature.
Fig. 101 will then have the reverse form.
Summary.—With regard to double salts we have learned that their
formation from and their decomposition into the single salts, is connected
with a definite temperature, the transition temperature. At this transition
temperature two vapour pressure curves cut, viz. a curve of dehydration of a
mixture of the single salts and the solubility curve of the double salt; or the
dehydration curve of the double salt and the solubility curve of the mixed
single salts. The solubility curves, also, of these two systems intersect at the
transition point, but although the formation of the double salt commences at
astracanite and Glauber's salt; and solutions lying below the line BC contain
relatively more magnesium sulphate than solutions saturated with this salt
and astracanite. These solutions will therefore not be stable, but will deposit
in the one case, astracanite and Glauber's salt, and in the other case,
astracanite and magnesium sulphate, until a point on BX or BC is reached.
All solutions, however, lying to the right of CBX, will be unsaturated with
respect to these two pairs of salts, and only the solutions represented by the
line XY (and which contain equimolecular amounts of sodium and
magnesium sulphates) will be saturated with respect to the pure double salt.
Transition Interval.—Fig. 101 will also render intelligible a point of great
importance in connection with astracanite, and of double salts generally. At
temperatures between those represented by the points B and X, the double
salt when brought in contact with water will be decomposed with separation
of sodium sulphate. Above the temperature of the point X, however, the
solution of the pure double salt is stable, because it can still take up a little
of either of the components. At temperatures, then, above that at which the
solution in contact with the double salt and the less soluble single salt,
contains the single salts in the ratio in which they are present in the double
salt, solution of the latter will take place without decomposition. The range
of temperature between that at which double salt can begin to be formed
(the transition point) and that at which it ceases to be decomposed by water
is called the transition interval.[353] If the two single salts have identical
solubility at the transition point, the transition interval diminishes to nought.
In those cases where the double salt is the stable form below the transition
point, the transition interval will extend downwards to a lower temperature.
Fig. 101 will then have the reverse form.
Summary.—With regard to double salts we have learned that their
formation from and their decomposition into the single salts, is connected
with a definite temperature, the transition temperature. At this transition
temperature two vapour pressure curves cut, viz. a curve of dehydration of a
mixture of the single salts and the solubility curve of the double salt; or the
dehydration curve of the double salt and the solubility curve of the mixed
single salts. The solubility curves, also, of these two systems intersect at the
transition point, but although the formation of the double salt commences at
Page 224
the transition point, complete stability in contact with water may not be
attained till some temperature above (or below) that point. Only when the
temperature is beyond the transition interval, will a double salt dissolve in
water without decomposition (e.g. the alums).
CHAPTER XVI
ISOTHERMAL CURVES AND THE SPACE MODEL
In the preceding chapter we considered the changes in the solubility of
double salts and of mixtures of their constituent salts with the temperature;
noting, more especially, the relationships between the two systems at the
transition point. It is now proposed to conclude the study of the three-
component systems by discussing very briefly the solubility relations at
constant temperature, or the isothermal solubility curves. In this way fresh
light will be thrown on the change in the solubility of one component by the
addition of another component, and also on the conditions of formation and
stable existence of double salts in solution. With the help of these
isothermal curves, also, the phenomena of crystallization at constant
temperature—phenomena which have not only a scientific interest but also
an important bearing on the industrial preparation of double salts—will be
more clearly understood.[354]
A brief description will also be given of the method of representing the
variation of the concentration of the two salts in the solution with the
temperature.
Non-formation of Double Salts.—In Fig. 102 are shown the solubility
curves of two salts, A and B, which at the given temperature do not form a
double salt.[355] The ordinates represent the amount of A, the abscissæ the
amount of B in a constant amount of the third component, the solvent. The
point A, therefore, represents the solubility of the salt A at the given
temperature; and similarly, point B represents the solubility of B. Since we
are dealing with a three-component system, one solid phase in contact with
solution will constitute a bivariant system (in the absence of the vapour
attained till some temperature above (or below) that point. Only when the
temperature is beyond the transition interval, will a double salt dissolve in
water without decomposition (e.g. the alums).
CHAPTER XVI
ISOTHERMAL CURVES AND THE SPACE MODEL
In the preceding chapter we considered the changes in the solubility of
double salts and of mixtures of their constituent salts with the temperature;
noting, more especially, the relationships between the two systems at the
transition point. It is now proposed to conclude the study of the three-
component systems by discussing very briefly the solubility relations at
constant temperature, or the isothermal solubility curves. In this way fresh
light will be thrown on the change in the solubility of one component by the
addition of another component, and also on the conditions of formation and
stable existence of double salts in solution. With the help of these
isothermal curves, also, the phenomena of crystallization at constant
temperature—phenomena which have not only a scientific interest but also
an important bearing on the industrial preparation of double salts—will be
more clearly understood.[354]
A brief description will also be given of the method of representing the
variation of the concentration of the two salts in the solution with the
temperature.
Non-formation of Double Salts.—In Fig. 102 are shown the solubility
curves of two salts, A and B, which at the given temperature do not form a
double salt.[355] The ordinates represent the amount of A, the abscissæ the
amount of B in a constant amount of the third component, the solvent. The
point A, therefore, represents the solubility of the salt A at the given
temperature; and similarly, point B represents the solubility of B. Since we
are dealing with a three-component system, one solid phase in contact with
solution will constitute a bivariant system (in the absence of the vapour
Page 225
phase and under a constant pressure). At any given temperature, therefore,
the concentration of the solution in equilibrium with the solid can undergo
change. If, now, to a pure solution of A a small quantity of B is added, the
solubility of A will in general be altered; as a rule it is diminished, but
sometimes it is increased.[356] The curve AC represents the varying
composition of the solution in equilibrium with the solid component A.
Similarly, the curve BC represents the composition of the solutions in
contact with pure B as solid phase. At the point, C, where these two curves
intersect, there are two solid phases, viz. pure A and pure B, in equilibrium
with solution, and the system becomes invariant. At this point the solution
is saturated with respect to both A and B, and at a given temperature must
have a perfectly definite composition. To take an example, if we suppose A
to represent sodium sulphate decahydrate, and B, magnesium sulphate
heptahydrate, and the temperature to be 18.5° (i.e. below the transition
point), the point C would represent a solution containing 2.16 gm.-
molecules Na2SO4 and 4.57 gm.-molecules MgSO4 per 100 gm.-molecules
of water (p. 268). The curve ACB is the boundary curve for saturated
solutions; solutions lying outside this curve are supersaturated, those lying
within the area ACBO, are unsaturated.
Fig. 102.
Formation of Double Salt.—We
have already learned in the preceding
chapter that if the temperature is
outside[357] the transition interval, it
is possible to prepare a pure
saturated solution of the double salt. Fig. 103.
Fig. 104.
If, now, we suppose the double salt
to contain the two constituent salts in equimolecular proportions, its
saturated solution must be represented by a point lying on the line which
bisects the angle AOB; e.g. point D, Fig. 103. But a double salt constitutes
the concentration of the solution in equilibrium with the solid can undergo
change. If, now, to a pure solution of A a small quantity of B is added, the
solubility of A will in general be altered; as a rule it is diminished, but
sometimes it is increased.[356] The curve AC represents the varying
composition of the solution in equilibrium with the solid component A.
Similarly, the curve BC represents the composition of the solutions in
contact with pure B as solid phase. At the point, C, where these two curves
intersect, there are two solid phases, viz. pure A and pure B, in equilibrium
with solution, and the system becomes invariant. At this point the solution
is saturated with respect to both A and B, and at a given temperature must
have a perfectly definite composition. To take an example, if we suppose A
to represent sodium sulphate decahydrate, and B, magnesium sulphate
heptahydrate, and the temperature to be 18.5° (i.e. below the transition
point), the point C would represent a solution containing 2.16 gm.-
molecules Na2SO4 and 4.57 gm.-molecules MgSO4 per 100 gm.-molecules
of water (p. 268). The curve ACB is the boundary curve for saturated
solutions; solutions lying outside this curve are supersaturated, those lying
within the area ACBO, are unsaturated.
Fig. 102.
Formation of Double Salt.—We
have already learned in the preceding
chapter that if the temperature is
outside[357] the transition interval, it
is possible to prepare a pure
saturated solution of the double salt. Fig. 103.
Fig. 104.
If, now, we suppose the double salt
to contain the two constituent salts in equimolecular proportions, its
saturated solution must be represented by a point lying on the line which
bisects the angle AOB; e.g. point D, Fig. 103. But a double salt constitutes
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only a single phase, and can exist, therefore, in contact with solutions of
varying concentration, as represented by EDF.
Let us compare, now, the relations between the solubility curve for the
double salt, and those for the two constituent salts. We shall suppose that
the double salt is formed from the single salts when the temperature is
raised above a certain point (as in the formation of astracanite). At a
temperature below the transition point, as we have already seen, the
solubility of the double salt is greater than that of a mixture of the single
salts. The curve EDF, therefore, must lie above the point C, in the region
representing solutions supersaturated with respect to the single salts (Fig.
104). Such a solution, however, would be metastable, and on being brought
in contact with the single salts would deposit these and yield a solution
represented by the point C. At this particular temperature, therefore, the
isothermal solubility curve will consist of only two branches.
Suppose, now, that the temperature is that of the transition
point. At this point, the double salt can exist together with
the single salts in contact with solution. The solubility
curve of the double salt must, therefore, pass through the
point C, as shown in Fig. 105.
From this figure, now, it is seen that a solution saturated Fig. 105.
with respect to double salt alone (point D), is
supersaturated with respect to the component A. If, then, at the temperature
of the transition point, excess of the double salt is brought in contact with
water,[358] and if supersaturation is excluded, the double salt will undergo
decomposition and the component A will be deposited. The relative
concentration of the component B in the solution will, therefore, increase,
and the composition of the solution will be thereby altered in the direction
DC. When the solution has the composition of C, the single salt ceases to be
deposited, for at this point the solution is saturated for both double and
single salt; and the system becomes invariant.
This diagram explains very clearly the phenomenon of the decomposition
of a double salt at the transition point. As is evident, this decomposition will
occur when the solution which is saturated at the temperature of the
transition point, with respect to the two single salts (point C), does not
varying concentration, as represented by EDF.
Let us compare, now, the relations between the solubility curve for the
double salt, and those for the two constituent salts. We shall suppose that
the double salt is formed from the single salts when the temperature is
raised above a certain point (as in the formation of astracanite). At a
temperature below the transition point, as we have already seen, the
solubility of the double salt is greater than that of a mixture of the single
salts. The curve EDF, therefore, must lie above the point C, in the region
representing solutions supersaturated with respect to the single salts (Fig.
104). Such a solution, however, would be metastable, and on being brought
in contact with the single salts would deposit these and yield a solution
represented by the point C. At this particular temperature, therefore, the
isothermal solubility curve will consist of only two branches.
Suppose, now, that the temperature is that of the transition
point. At this point, the double salt can exist together with
the single salts in contact with solution. The solubility
curve of the double salt must, therefore, pass through the
point C, as shown in Fig. 105.
From this figure, now, it is seen that a solution saturated Fig. 105.
with respect to double salt alone (point D), is
supersaturated with respect to the component A. If, then, at the temperature
of the transition point, excess of the double salt is brought in contact with
water,[358] and if supersaturation is excluded, the double salt will undergo
decomposition and the component A will be deposited. The relative
concentration of the component B in the solution will, therefore, increase,
and the composition of the solution will be thereby altered in the direction
DC. When the solution has the composition of C, the single salt ceases to be
deposited, for at this point the solution is saturated for both double and
single salt; and the system becomes invariant.
This diagram explains very clearly the phenomenon of the decomposition
of a double salt at the transition point. As is evident, this decomposition will
occur when the solution which is saturated at the temperature of the
transition point, with respect to the two single salts (point C), does not
Page 227
contain these salts in the same ratio in which they are present in the double
salt. If point C lay on the dotted line bisecting the right angle, then the pure
saturated solution of the double salt would not be supersaturated with
respect to either of the single salts, and the double salt would, therefore, not
be decomposed by water. As has already been mentioned, this behaviour is
found in the case of optically active isomerides, the solubilities of which are
identical.
At the transition point, therefore, the isothermal curve also consists of two
branches; but the point of intersection of the two branches now represents a
solution which is saturated not only with respect to the single salts, but also
for the double salt in presence of the single salts.
We have just seen that by a change of temperature the two solubility curves,
that for the two single salts and that for the double salt, were made to
approach one another (cf. Figs. 104 and 105). In the previous chapter,
however, we found that on passing the transition point to the region of
stability for the double salt, the solution which is saturated for a mixture of
the two constituent salts, is supersaturated for the double salt. In this case,
therefore, point C must lie above the solubility curve of the pure double salt
(Fig. 106), and a solution of the composition C, if brought in contact with
double salt, will deposit the latter. If the single salts were also present, then
as the double salt separated out, the single salts would pass into solution,
because so long as the two single salts are present, the composition of the
solution must remain unaltered. If one of the single salts disappear before
the other, there will be left double salt plus A or double salt plus B,
according to which was in excess; and the composition of the solution will
be either that represented by D (saturated for double salt plus A), or that of
the point F (saturated for double salt plus B).
Fig. 106.
salt. If point C lay on the dotted line bisecting the right angle, then the pure
saturated solution of the double salt would not be supersaturated with
respect to either of the single salts, and the double salt would, therefore, not
be decomposed by water. As has already been mentioned, this behaviour is
found in the case of optically active isomerides, the solubilities of which are
identical.
At the transition point, therefore, the isothermal curve also consists of two
branches; but the point of intersection of the two branches now represents a
solution which is saturated not only with respect to the single salts, but also
for the double salt in presence of the single salts.
We have just seen that by a change of temperature the two solubility curves,
that for the two single salts and that for the double salt, were made to
approach one another (cf. Figs. 104 and 105). In the previous chapter,
however, we found that on passing the transition point to the region of
stability for the double salt, the solution which is saturated for a mixture of
the two constituent salts, is supersaturated for the double salt. In this case,
therefore, point C must lie above the solubility curve of the pure double salt
(Fig. 106), and a solution of the composition C, if brought in contact with
double salt, will deposit the latter. If the single salts were also present, then
as the double salt separated out, the single salts would pass into solution,
because so long as the two single salts are present, the composition of the
solution must remain unaltered. If one of the single salts disappear before
the other, there will be left double salt plus A or double salt plus B,
according to which was in excess; and the composition of the solution will
be either that represented by D (saturated for double salt plus A), or that of
the point F (saturated for double salt plus B).
Fig. 106.
Page 228
In connection with the isothermal represented in Fig. 106, it should be
noted that at this particular temperature a solution saturated with respect to
the pure double salt is no longer supersaturated for one of the single salts
(point D); so that at the temperature of this isothermal the double salt is not
decomposed by water. At this temperature, further, the boundary curve
consists of three branches AD, DF, and FB, which give the composition of
the solutions in equilibrium with pure A, double salt, and pure B
respectively; while the points D and F represent solutions saturated for
double salt plus A and double salt plus B.
On continuing to alter the temperature in the same direction as before, the
relative shifting of the solubility curves becomes more marked, as shown in
Fig. 107. At the temperature of this isothermal, the solution saturated for the
double salt now lies in a region of distinct unsaturation with respect to the
single salts; and the double salt can now exist as solid phase in contact with
solutions containing both relatively more of A (curve ED), and relatively
more of B (curve DF), than is contained in the double salt itself.
Fig. 107.
Transition Interval.—From what has been said, and from an examination
of the isothermal diagrams, Figs. 104-107, it will be seen that by a variation
of the temperature we can pass from a condition where the double salt is
quite incapable of existing in contact with solution (supersaturation being
excluded), to a condition where the existence of the double salt in presence
of solution becomes possible; only in the presence, however, of one of the
single salts (transition point, Fig. 105). A further change of temperature
leads to a condition where the stable existence of the pure double salt in
contact with solution just becomes possible (Fig. 106); and from this point
onwards, pure saturated solutions of the double salt can be obtained (Fig.
107). At any temperature, therefore, between that represented by Fig. 105,
and that represented by Fig. 106, the double salt undergoes partial
noted that at this particular temperature a solution saturated with respect to
the pure double salt is no longer supersaturated for one of the single salts
(point D); so that at the temperature of this isothermal the double salt is not
decomposed by water. At this temperature, further, the boundary curve
consists of three branches AD, DF, and FB, which give the composition of
the solutions in equilibrium with pure A, double salt, and pure B
respectively; while the points D and F represent solutions saturated for
double salt plus A and double salt plus B.
On continuing to alter the temperature in the same direction as before, the
relative shifting of the solubility curves becomes more marked, as shown in
Fig. 107. At the temperature of this isothermal, the solution saturated for the
double salt now lies in a region of distinct unsaturation with respect to the
single salts; and the double salt can now exist as solid phase in contact with
solutions containing both relatively more of A (curve ED), and relatively
more of B (curve DF), than is contained in the double salt itself.
Fig. 107.
Transition Interval.—From what has been said, and from an examination
of the isothermal diagrams, Figs. 104-107, it will be seen that by a variation
of the temperature we can pass from a condition where the double salt is
quite incapable of existing in contact with solution (supersaturation being
excluded), to a condition where the existence of the double salt in presence
of solution becomes possible; only in the presence, however, of one of the
single salts (transition point, Fig. 105). A further change of temperature
leads to a condition where the stable existence of the pure double salt in
contact with solution just becomes possible (Fig. 106); and from this point
onwards, pure saturated solutions of the double salt can be obtained (Fig.
107). At any temperature, therefore, between that represented by Fig. 105,
and that represented by Fig. 106, the double salt undergoes partial
Page 229
decomposition, with deposition of one of the constituent salts. The
temperature range between the transition point and the temperature at which
a stable saturated solution of the pure double salt just begins to be possible,
is known as the transition interval (p. 270). As the figures show, the
transition interval is limited on the one side by the transition temperature,
and on the other by the temperature at which the solution saturated for
double salt and the less soluble of the single salts, contains the component
salts in the same ratio as they are present in the double salt. The greater the
difference in the solubility of the single salts, the larger will be the
transition interval.
Isothermal Evaporation.—The isothermal solubility curves are of great
importance for obtaining an insight into the behaviour of a solution when
subjected to isothermal evaporation. To simplify the discussion of the
relationships found here, we shall still suppose that the double salt contains
the single salts in equimolecular proportions; and we shall, in the first
instance, suppose that the unsaturated solution with which we commence,
also contains the single salts in the same ratio. The composition of the
solution must, therefore, be represented by some point lying on the line OD,
the bisectrix of the right angle.
From what has been said, it is evident that when the formation of a double
salt can occur, three temperature intervals can be distinguished, viz. the
single-salt interval, the transition interval, and the double-salt interval.[359]
When the temperature lies in the first interval, evaporation leads first of all
to the crystallization of one of the single salts, and then to the separation of
both the single salts together. In the second temperature interval,
evaporation again leads, in the first place, to the deposition of one of the
single salts, and afterwards to the crystallization of the double salt. In the
third temperature interval, only the double salt crystallizes out. This will
become clearer from what follows.
If an unsaturated solution of the two
single salts in equimolecular proportion
(e.g. point x, Fig. 108) is evaporated at a
temperature at which the formation of
double salt is impossible, the
component A, the solubility curve of
temperature range between the transition point and the temperature at which
a stable saturated solution of the pure double salt just begins to be possible,
is known as the transition interval (p. 270). As the figures show, the
transition interval is limited on the one side by the transition temperature,
and on the other by the temperature at which the solution saturated for
double salt and the less soluble of the single salts, contains the component
salts in the same ratio as they are present in the double salt. The greater the
difference in the solubility of the single salts, the larger will be the
transition interval.
Isothermal Evaporation.—The isothermal solubility curves are of great
importance for obtaining an insight into the behaviour of a solution when
subjected to isothermal evaporation. To simplify the discussion of the
relationships found here, we shall still suppose that the double salt contains
the single salts in equimolecular proportions; and we shall, in the first
instance, suppose that the unsaturated solution with which we commence,
also contains the single salts in the same ratio. The composition of the
solution must, therefore, be represented by some point lying on the line OD,
the bisectrix of the right angle.
From what has been said, it is evident that when the formation of a double
salt can occur, three temperature intervals can be distinguished, viz. the
single-salt interval, the transition interval, and the double-salt interval.[359]
When the temperature lies in the first interval, evaporation leads first of all
to the crystallization of one of the single salts, and then to the separation of
both the single salts together. In the second temperature interval,
evaporation again leads, in the first place, to the deposition of one of the
single salts, and afterwards to the crystallization of the double salt. In the
third temperature interval, only the double salt crystallizes out. This will
become clearer from what follows.
If an unsaturated solution of the two
single salts in equimolecular proportion
(e.g. point x, Fig. 108) is evaporated at a
temperature at which the formation of
double salt is impossible, the
component A, the solubility curve of
Page 230
which is cut by the line OD, will first Fig. 108. Fig. 109.
separate out; the solution will thereby
become richer in B. On continued evaporation, more A will be deposited,
and the composition of the solution will change until it attains the
composition represented by the point C, when both A and B will be
deposited, and the composition of the solution will remain unchanged. The
result of evaporation will therefore be a mixture of the two components.
If the formation of double salt is possible, but if the temperature lies within
the transition interval, the relations will be represented by a diagram like
Fig. 109. Isothermal evaporation of the solution X will lead to the
deposition of the component A, and the composition of the solution will
alter in the direction DE; at the latter point the double salt will be formed,
and the composition of the solution will remain unchanged so long as the
two solid phases are present. As can be seen from the diagram, however, the
solution in E contains less of component A than is contained in the double
salt. Deposition of the double salt at E, therefore, would lead to a relative
decrease in the concentration of A in the solution, and to counterbalance
this, the salt which separated out at the commencement must redissolve.
Since the salts were originally present in equimolecular proportions, the
final result of evaporation will be the pure double salt. If when the solution
has reached the point E the salt A which had separated out is removed,
double salt only will be left as solid phase. At a given temperature,
however, a single solid phase can exist in equilibrium with solutions of
different composition. If, therefore, isothermal evaporation is continued
after the removal of the salt A, double salt will be deposited, and the
composition of the solution will change in the direction EF. At the point F
the salt B will separate out, and on evaporation both double salt and the salt
B will be deposited. In the former case (when the salt A disappears on
evaporation) we are dealing with an incongruently saturated solution; but in
the latter case, where both solid phases continue to be deposited, the
solution is said to be congruently saturated.[360]
A "congruently saturated solution" is one from which the solid phases are
continuously deposited during isothermal evaporation to dryness, whereas
in the case of "incongruently saturated solutions," at least one of the solid
phases disappears during the process of evaporation.
separate out; the solution will thereby
become richer in B. On continued evaporation, more A will be deposited,
and the composition of the solution will change until it attains the
composition represented by the point C, when both A and B will be
deposited, and the composition of the solution will remain unchanged. The
result of evaporation will therefore be a mixture of the two components.
If the formation of double salt is possible, but if the temperature lies within
the transition interval, the relations will be represented by a diagram like
Fig. 109. Isothermal evaporation of the solution X will lead to the
deposition of the component A, and the composition of the solution will
alter in the direction DE; at the latter point the double salt will be formed,
and the composition of the solution will remain unchanged so long as the
two solid phases are present. As can be seen from the diagram, however, the
solution in E contains less of component A than is contained in the double
salt. Deposition of the double salt at E, therefore, would lead to a relative
decrease in the concentration of A in the solution, and to counterbalance
this, the salt which separated out at the commencement must redissolve.
Since the salts were originally present in equimolecular proportions, the
final result of evaporation will be the pure double salt. If when the solution
has reached the point E the salt A which had separated out is removed,
double salt only will be left as solid phase. At a given temperature,
however, a single solid phase can exist in equilibrium with solutions of
different composition. If, therefore, isothermal evaporation is continued
after the removal of the salt A, double salt will be deposited, and the
composition of the solution will change in the direction EF. At the point F
the salt B will separate out, and on evaporation both double salt and the salt
B will be deposited. In the former case (when the salt A disappears on
evaporation) we are dealing with an incongruently saturated solution; but in
the latter case, where both solid phases continue to be deposited, the
solution is said to be congruently saturated.[360]
A "congruently saturated solution" is one from which the solid phases are
continuously deposited during isothermal evaporation to dryness, whereas
in the case of "incongruently saturated solutions," at least one of the solid
phases disappears during the process of evaporation.
Page 231
Fig. 110.
Lastly, if the temperature lies outside the transition interval, isothermal
evaporation of an unsaturated solution of the composition X (Fig. 110) will
lead to the deposition of pure double salt from beginning to end. If a
solution of the composition Y is evaporated, the component A will first be
deposited and the composition of the solution will alter in the direction of
E, at which point double salt will separate out. Since the solution at this
point contains relatively more of A than is present in the double salt, both
the double salt and the single salt A will be deposited on continued
evaporation, in order that the composition of the solution shall remain
unchanged. In the case of solution Z, first component B and afterwards the
double salt will be deposited. The result will, therefore, be a mixture of
double salt and the salt B (congruently saturated solutions),
It may be stated here that the same relationships as have been explained
above for double salts are also found in the resolution of racemic
compounds by means of optically active substances (third method of
Pasteur). In this case the single salts are doubly active substances (e.g.
strychnine-d-tartrate and strychnine-l-tartrate), and the double salt is a
partially racemic compound.[361]
Crystallization of Double Salt from Solutions containing Excess of One
Component.—One more case of isothermal crystallization may be
discussed. It is well known that a double salt which is decomposed by pure
water can nevertheless be obtained pure by crystallization from a solution
containing excess of one of the single salts (e.g. in the case of carnallite).
Since the double salt is partially decomposed by water, the temperature of
the experiment must be within the transition interval, and the relations will,
therefore, be represented by a diagram like Fig. 109. If, now, instead of
starting with an unsaturated solution containing the single salts in
equimolecular proportions, we commence with one in which excess of one
of the salts is present, as represented by the point Y, isothermal evaporation
Lastly, if the temperature lies outside the transition interval, isothermal
evaporation of an unsaturated solution of the composition X (Fig. 110) will
lead to the deposition of pure double salt from beginning to end. If a
solution of the composition Y is evaporated, the component A will first be
deposited and the composition of the solution will alter in the direction of
E, at which point double salt will separate out. Since the solution at this
point contains relatively more of A than is present in the double salt, both
the double salt and the single salt A will be deposited on continued
evaporation, in order that the composition of the solution shall remain
unchanged. In the case of solution Z, first component B and afterwards the
double salt will be deposited. The result will, therefore, be a mixture of
double salt and the salt B (congruently saturated solutions),
It may be stated here that the same relationships as have been explained
above for double salts are also found in the resolution of racemic
compounds by means of optically active substances (third method of
Pasteur). In this case the single salts are doubly active substances (e.g.
strychnine-d-tartrate and strychnine-l-tartrate), and the double salt is a
partially racemic compound.[361]
Crystallization of Double Salt from Solutions containing Excess of One
Component.—One more case of isothermal crystallization may be
discussed. It is well known that a double salt which is decomposed by pure
water can nevertheless be obtained pure by crystallization from a solution
containing excess of one of the single salts (e.g. in the case of carnallite).
Since the double salt is partially decomposed by water, the temperature of
the experiment must be within the transition interval, and the relations will,
therefore, be represented by a diagram like Fig. 109. If, now, instead of
starting with an unsaturated solution containing the single salts in
equimolecular proportions, we commence with one in which excess of one
of the salts is present, as represented by the point Y, isothermal evaporation
Page 232
will cause the composition to alter in the direction YD′, the relative amounts
of the single salts remaining the same throughout. When the composition of
the solution reaches the point D′, pure double salt will be deposited. The
separation of double salt will, however, cause a relative decrease in the
concentration of the salt A, and the composition of the solution will,
therefore, alter in the direction D′F. If the evaporation is discontinued
before the solution has attained the composition F, only double salt will
have separated out. Even within the transition interval, therefore, pure
double salt can be obtained by crystallization, provided the original solution
has a composition represented by a point lying between the two lines OE
and OF. Since, as already shown, the composition of the solution alters on
evaporation in the direction EF, it will be best to employ a solution having a
composition near to the line OE.
Formation of Mixed Crystals.—If the two single salts A and B do not
crystallize out pure from solution, but form an unbroken series of mixed
crystals, it is evident that an invariant system cannot be produced. The
solubility curve will therefore be continuous from A to B; the liquid
solutions of varying composition being in equilibrium with solid solutions
also of varying composition. If, however, the series of mixed crystals is not
continuous, there will be a break in the solubility curve at which two solid
solutions of different composition will be in equilibrium with liquid
solution. This, of course, will constitute an invariant system, and the point
will correspond to the point C in Fig. 108. A full discussion of these
systems would, however, lead us too far, and the above indication of the
behaviour must suffice.[362]
Application to the Characterization of Racemates.—The form of the
isothermal solubility curves is also of great value for determining whether
an inactive substance is a racemic compound or a conglomerate of equal
proportions of the optical antipodes.[363]
As has already been pointed out, the formation of racemic compounds from
the two enantiomorphous isomerides, is analogous to the formation of
double salts. The isothermal solubility curves, also, have a similar form. In
the case of the latter, indeed, the relationships are simplified by the fact that
the two enantiomorphous forms have identical solubility, and the solubility
curves are therefore symmetrical to the line bisecting the angle of the co-
of the single salts remaining the same throughout. When the composition of
the solution reaches the point D′, pure double salt will be deposited. The
separation of double salt will, however, cause a relative decrease in the
concentration of the salt A, and the composition of the solution will,
therefore, alter in the direction D′F. If the evaporation is discontinued
before the solution has attained the composition F, only double salt will
have separated out. Even within the transition interval, therefore, pure
double salt can be obtained by crystallization, provided the original solution
has a composition represented by a point lying between the two lines OE
and OF. Since, as already shown, the composition of the solution alters on
evaporation in the direction EF, it will be best to employ a solution having a
composition near to the line OE.
Formation of Mixed Crystals.—If the two single salts A and B do not
crystallize out pure from solution, but form an unbroken series of mixed
crystals, it is evident that an invariant system cannot be produced. The
solubility curve will therefore be continuous from A to B; the liquid
solutions of varying composition being in equilibrium with solid solutions
also of varying composition. If, however, the series of mixed crystals is not
continuous, there will be a break in the solubility curve at which two solid
solutions of different composition will be in equilibrium with liquid
solution. This, of course, will constitute an invariant system, and the point
will correspond to the point C in Fig. 108. A full discussion of these
systems would, however, lead us too far, and the above indication of the
behaviour must suffice.[362]
Application to the Characterization of Racemates.—The form of the
isothermal solubility curves is also of great value for determining whether
an inactive substance is a racemic compound or a conglomerate of equal
proportions of the optical antipodes.[363]
As has already been pointed out, the formation of racemic compounds from
the two enantiomorphous isomerides, is analogous to the formation of
double salts. The isothermal solubility curves, also, have a similar form. In
the case of the latter, indeed, the relationships are simplified by the fact that
the two enantiomorphous forms have identical solubility, and the solubility
curves are therefore symmetrical to the line bisecting the angle of the co-
Page 233
ordinates. Further, with the exception of the partially racemic compounds to
be mentioned later, there is no transition interval.
In Fig. 111, are given diagrammatically two isothermal solubility curves for
optically active substances. From what has been said in the immediately
preceding pages, the figure ought really to explain itself. The upper
isothermal acb represents the solubility relations when the formation of a
racemic compound is excluded, as, e.g. in the case of rubidium d- and l-
tartrates above the transition point (p. 265). The solution at the point c is, of
course, inactive, and is unaffected by addition of either the d- or l- form.
The lower isothermal, on the other hand, would be obtained at a
temperature at which the racemic compound could be formed. The curve a′e
is the solubility curve for the l- form; b′f, that for the d- form; and edf, that
for the racemic compound in presence of solutions of varying
concentration. The point d corresponds to saturation for the pure racemic
compound.
Fig. 111.
From these curves now, it will be evident that it will be possible, in any
given case, to decide whether or not an inactive body is a mixture or a
racemic compound. For this purpose, two solubility determinations are
made, first with the inactive material alone (in excess), and then with the
inactive material plus excess of one of the optically active forms. If we are
dealing with a mixture, the two solutions thus obtained will be identical;
both will have the composition corresponding to the point c, and will be
inactive. If, however, the inactive material is a racemic compound, then two
different solutions will be obtained; namely, an inactive solution
corresponding to the point d (Fig. 111), and an active solution
corresponding either to e or to f, according to which enantiomorphous form
was added.
be mentioned later, there is no transition interval.
In Fig. 111, are given diagrammatically two isothermal solubility curves for
optically active substances. From what has been said in the immediately
preceding pages, the figure ought really to explain itself. The upper
isothermal acb represents the solubility relations when the formation of a
racemic compound is excluded, as, e.g. in the case of rubidium d- and l-
tartrates above the transition point (p. 265). The solution at the point c is, of
course, inactive, and is unaffected by addition of either the d- or l- form.
The lower isothermal, on the other hand, would be obtained at a
temperature at which the racemic compound could be formed. The curve a′e
is the solubility curve for the l- form; b′f, that for the d- form; and edf, that
for the racemic compound in presence of solutions of varying
concentration. The point d corresponds to saturation for the pure racemic
compound.
Fig. 111.
From these curves now, it will be evident that it will be possible, in any
given case, to decide whether or not an inactive body is a mixture or a
racemic compound. For this purpose, two solubility determinations are
made, first with the inactive material alone (in excess), and then with the
inactive material plus excess of one of the optically active forms. If we are
dealing with a mixture, the two solutions thus obtained will be identical;
both will have the composition corresponding to the point c, and will be
inactive. If, however, the inactive material is a racemic compound, then two
different solutions will be obtained; namely, an inactive solution
corresponding to the point d (Fig. 111), and an active solution
corresponding either to e or to f, according to which enantiomorphous form
was added.
Page 234
Partially racemic compounds.[364] In this case we are no longer dealing
with enantiomorphous forms, and the solubility of the two oppositely active
isomerides is no longer the same. The symmetry of the solubility curves
therefore disappears, and a figure is obtained which is identical in its
general form with that found in the case of ordinary double salts (Fig. 112).
In this case there is a transition interval.
Fig. 112.
The curves acb belong to a temperature at which the partially racemic
compound cannot be formed; a′dfb′, to the temperature at which the
compound just begins to be stable in contact with water, and a″ed′f′b″
belongs to a temperature at which the partially racemic compound is quite
stable in contact with water. Suppose now solubility determinations, made
in the first case with the original material alone, and then with the original
body plus each of the two compounds, formed from the enantiomorphous
substances separately, then if the original body was a mixture, identical
solutions will be obtained in all three cases (point c); if it was a partially
racemic compound, three different solutions (e, d′, and f′) will be obtained if
the temperature was outside the transition interval, and two solutions, d and
f, if the temperature belonged to the transition interval.
Representation in Space.
Space Model for Carnallite.—Interesting and important as the isothermal
solubility curves are, they are insufficient for the purpose of obtaining a
clear insight into the complete behaviour of the systems of two salts and
water. A short description will, therefore, be given here of the representation
in space of the solubility relations of potassium and magnesium chlorides,
and of the double salt which they form, carnallite.[365]
with enantiomorphous forms, and the solubility of the two oppositely active
isomerides is no longer the same. The symmetry of the solubility curves
therefore disappears, and a figure is obtained which is identical in its
general form with that found in the case of ordinary double salts (Fig. 112).
In this case there is a transition interval.
Fig. 112.
The curves acb belong to a temperature at which the partially racemic
compound cannot be formed; a′dfb′, to the temperature at which the
compound just begins to be stable in contact with water, and a″ed′f′b″
belongs to a temperature at which the partially racemic compound is quite
stable in contact with water. Suppose now solubility determinations, made
in the first case with the original material alone, and then with the original
body plus each of the two compounds, formed from the enantiomorphous
substances separately, then if the original body was a mixture, identical
solutions will be obtained in all three cases (point c); if it was a partially
racemic compound, three different solutions (e, d′, and f′) will be obtained if
the temperature was outside the transition interval, and two solutions, d and
f, if the temperature belonged to the transition interval.
Representation in Space.
Space Model for Carnallite.—Interesting and important as the isothermal
solubility curves are, they are insufficient for the purpose of obtaining a
clear insight into the complete behaviour of the systems of two salts and
water. A short description will, therefore, be given here of the representation
in space of the solubility relations of potassium and magnesium chlorides,
and of the double salt which they form, carnallite.[365]
Page 235
Fig. 113.
Fig. 113 is a diagrammatic sketch of the model for carnallite looked at
sideways from above. Along the X-axis is measured the concentration of
magnesium chloride in the solution; along the Y-axis, the concentration of
potassium chloride; while along the T-axis is measured the temperature. The
three axes are at right angles to one another. The XT-plane, therefore,
contains the solubility curve of magnesium chloride; the YT-plane, the
solubility curve of potassium chloride, and in the space between the two
planes, there are represented the composition of solutions containing both
magnesium and potassium chlorides. Any surface between the two planes
will represent the various solutions in equilibrium with only one solid
phase, and will therefore indicate the area or field of existence of bivariant
ternary systems. A line or curve formed by the intersection of two surfaces
will represent solutions in equilibrium with two solid phases (viz. those
belonging to the intersecting surfaces), and will show the conditions for the
existence of univariant systems. Lastly, points formed by the intersection of
three surfaces will represent invariant systems, in which a solution can exist
in equilibrium with three solid phases (viz. those belonging to the three
surfaces).
We shall first consider the solubility relations of the single salts. The
complete equilibrium curve for magnesium chloride and water is
represented in Fig. 113 by the series of curves ABF1 G1 H1 J1 L1 N1. AB is
the freezing-point curve of ice in contact with solutions containing
Fig. 113 is a diagrammatic sketch of the model for carnallite looked at
sideways from above. Along the X-axis is measured the concentration of
magnesium chloride in the solution; along the Y-axis, the concentration of
potassium chloride; while along the T-axis is measured the temperature. The
three axes are at right angles to one another. The XT-plane, therefore,
contains the solubility curve of magnesium chloride; the YT-plane, the
solubility curve of potassium chloride, and in the space between the two
planes, there are represented the composition of solutions containing both
magnesium and potassium chlorides. Any surface between the two planes
will represent the various solutions in equilibrium with only one solid
phase, and will therefore indicate the area or field of existence of bivariant
ternary systems. A line or curve formed by the intersection of two surfaces
will represent solutions in equilibrium with two solid phases (viz. those
belonging to the intersecting surfaces), and will show the conditions for the
existence of univariant systems. Lastly, points formed by the intersection of
three surfaces will represent invariant systems, in which a solution can exist
in equilibrium with three solid phases (viz. those belonging to the three
surfaces).
We shall first consider the solubility relations of the single salts. The
complete equilibrium curve for magnesium chloride and water is
represented in Fig. 113 by the series of curves ABF1 G1 H1 J1 L1 N1. AB is
the freezing-point curve of ice in contact with solutions containing
Page 236
magnesium chloride, and B is the cryohydric point at which the solid phases
ice and MgCl2,12H2O can co-exist with solution. BFG is the solubility
curve of magnesium chloride dodecahydrate. This curve shows a point of
maximum temperature at F1, and a retroflex portion F1G1. The curve is
therefore of the form exhibited by calcium chloride hexahydrate, or the
hydrates of ferric chloride (Chapter VIII.). G1 is a transition point at which
the solid phase changes from dodecahydrate to octahydrate, the solubility of
which is represented by the curve G1H1. At H1 the octahydrate gives place
to the hexahydrate, which is the solid phase in equilibrium with the
solutions represented by the curve H1J1. J1 and L1 are also transition points
at which the solid phase undergoes change, in the former case from
hexahydrate to tetrahydrate; and in the latter case, from tetrahydrate to
dihydrate. The complete curve of equilibrium for magnesium chloride and
water is, therefore, somewhat complicated, and is a good example of the
solubility curves obtained with salts capable of forming several hydrates.
The solubility curve of potassium chloride is of the simplest form,
consisting only of the two branches AC, the freezing-point curve of ice, and
CO, the solubility curve of the salt. C is the cryohydric point. This point and
the two curves lie in the YT-plane.
On passing to the ternary systems, the composition of the solutions must be
represented by points or curves situated between the two planes. We shall
now turn to the consideration of these. BD and CD are ternary eutectic
curves (p. 284). They give the composition of solutions in equilibrium with
ice and magnesium chloride dodecahydrate (BD), and with ice and
potassium chloride (CD). D is a ternary cryohydric point. If the temperature
is raised and the ice allowed to disappear, we shall pass to the solubility
curve for MgCl2,12H2O + KCl (curve DE). At E carnallite is formed and
the potassium chloride disappears; EFG is then the solubility curve for
MgCl2,12H2O + carnallite (KMgCl3,6H2O). This curve also shows a point
of maximum temperature (F) and a retroflex portion. GH and HJ represent
the solubility curves of carnallite + MgCl2,8H2O and carnallite +
MgCl2,6H2O, G and H being transition points. JK is the solubility curve for
carnallite + MgCl2,4H2O. At the point K we have the highest temperature
at which carnallite can exist with magnesium chloride in contact with
ice and MgCl2,12H2O can co-exist with solution. BFG is the solubility
curve of magnesium chloride dodecahydrate. This curve shows a point of
maximum temperature at F1, and a retroflex portion F1G1. The curve is
therefore of the form exhibited by calcium chloride hexahydrate, or the
hydrates of ferric chloride (Chapter VIII.). G1 is a transition point at which
the solid phase changes from dodecahydrate to octahydrate, the solubility of
which is represented by the curve G1H1. At H1 the octahydrate gives place
to the hexahydrate, which is the solid phase in equilibrium with the
solutions represented by the curve H1J1. J1 and L1 are also transition points
at which the solid phase undergoes change, in the former case from
hexahydrate to tetrahydrate; and in the latter case, from tetrahydrate to
dihydrate. The complete curve of equilibrium for magnesium chloride and
water is, therefore, somewhat complicated, and is a good example of the
solubility curves obtained with salts capable of forming several hydrates.
The solubility curve of potassium chloride is of the simplest form,
consisting only of the two branches AC, the freezing-point curve of ice, and
CO, the solubility curve of the salt. C is the cryohydric point. This point and
the two curves lie in the YT-plane.
On passing to the ternary systems, the composition of the solutions must be
represented by points or curves situated between the two planes. We shall
now turn to the consideration of these. BD and CD are ternary eutectic
curves (p. 284). They give the composition of solutions in equilibrium with
ice and magnesium chloride dodecahydrate (BD), and with ice and
potassium chloride (CD). D is a ternary cryohydric point. If the temperature
is raised and the ice allowed to disappear, we shall pass to the solubility
curve for MgCl2,12H2O + KCl (curve DE). At E carnallite is formed and
the potassium chloride disappears; EFG is then the solubility curve for
MgCl2,12H2O + carnallite (KMgCl3,6H2O). This curve also shows a point
of maximum temperature (F) and a retroflex portion. GH and HJ represent
the solubility curves of carnallite + MgCl2,8H2O and carnallite +
MgCl2,6H2O, G and H being transition points. JK is the solubility curve for
carnallite + MgCl2,4H2O. At the point K we have the highest temperature
at which carnallite can exist with magnesium chloride in contact with
Page 237
solution. Above this temperature decomposition takes place and potassium
chloride separates out.
If at the point E, at which the two single salts and the double salt are
present, excess of potassium chloride is added, the magnesium chloride will
all disappear owing to the formation of carnallite, and there will be left
carnallite and potassium chloride. The solubility curve for a mixture of
these two salts is represented by EMK; a simple curve exhibiting, however,
a temperature maximum at M. This maximum point corresponds with the
fact that dry carnallite melts at this temperature with separation of
potassium chloride. At all temperatures above this point, the formation of
double salt is impossible. The retroflex portion of the curve represents
solutions in equilibrium with carnallite and potassium chloride, but in
which the ratio MgCl2 : KCl is greater than in the double salt.
Throughout its whole course, the curve EMK represents solutions in which
the ratio of MgCl2 : KCl is greater than in the double salt. As this is a point
of some importance, it will be well, perhaps, to make it clearer by giving
one of the isothermal curves, e.g. the curve for 10°, which is represented
diagrammatically in Fig. 114. E and F here represent solutions saturated for
carnallite plus magnesium chloride hydrate, and for carnallite plus
potassium chloride. As is evident, the point F lies above the line
representing equimolecular proportions of the salts (OD).
Fig. 114.
Summary and Numerical Data.—We may now sum up the different
systems which can be formed, and give the numerical data from which the
model is constructed.[366]
I. Bivariant Systems.
chloride separates out.
If at the point E, at which the two single salts and the double salt are
present, excess of potassium chloride is added, the magnesium chloride will
all disappear owing to the formation of carnallite, and there will be left
carnallite and potassium chloride. The solubility curve for a mixture of
these two salts is represented by EMK; a simple curve exhibiting, however,
a temperature maximum at M. This maximum point corresponds with the
fact that dry carnallite melts at this temperature with separation of
potassium chloride. At all temperatures above this point, the formation of
double salt is impossible. The retroflex portion of the curve represents
solutions in equilibrium with carnallite and potassium chloride, but in
which the ratio MgCl2 : KCl is greater than in the double salt.
Throughout its whole course, the curve EMK represents solutions in which
the ratio of MgCl2 : KCl is greater than in the double salt. As this is a point
of some importance, it will be well, perhaps, to make it clearer by giving
one of the isothermal curves, e.g. the curve for 10°, which is represented
diagrammatically in Fig. 114. E and F here represent solutions saturated for
carnallite plus magnesium chloride hydrate, and for carnallite plus
potassium chloride. As is evident, the point F lies above the line
representing equimolecular proportions of the salts (OD).
Fig. 114.
Summary and Numerical Data.—We may now sum up the different
systems which can be formed, and give the numerical data from which the
model is constructed.[366]
I. Bivariant Systems.
Page 238
Solid phase. Area of existence.
Ice ABDC
KCl CDEMKLNO
Carnallite EFGHJKM
MgCl2,12H2O BF1G1GFED
MgCl2,8H2O G1H1HG
MgCl2,6H2O H1I1IH
MgCl2,4H2O I1L1LKI
MgCl2,2H2O L1N1NL
II. Univariant Systems.—The different univariant systems have already
been described. The course of the curves will be sufficiently indicated if the
temperature and composition of the solutions for the different invariant
systems are given.
III.—Invariant Systems—Binary and Ternary.
Composition of solution.
Gram-
Point. Solid Phases. Temperature. molecules of salt per
1000 gram-
mol. water.
A Ice 0° —
B Ice; MgCl2,12H2O -33.6° 49.2 MgCl2
C Ice; KCl -11.1° 59.4 KCl
Ice; MgCl2,12H2O;
D -34.3° 43 MgCl2; 3 KCl
KCl
MgCl2,12H2O;
E KCl; -21° 66.1 MgCl2; 4.9 KCl
carnallite
F1 MgCl2,12H2O -16.4° 83.33 MgCl2
Almost same as F1;
MgCl2,12H2O;
F -16.6° contains
carnallite
small amount of KCl
Ice ABDC
KCl CDEMKLNO
Carnallite EFGHJKM
MgCl2,12H2O BF1G1GFED
MgCl2,8H2O G1H1HG
MgCl2,6H2O H1I1IH
MgCl2,4H2O I1L1LKI
MgCl2,2H2O L1N1NL
II. Univariant Systems.—The different univariant systems have already
been described. The course of the curves will be sufficiently indicated if the
temperature and composition of the solutions for the different invariant
systems are given.
III.—Invariant Systems—Binary and Ternary.
Composition of solution.
Gram-
Point. Solid Phases. Temperature. molecules of salt per
1000 gram-
mol. water.
A Ice 0° —
B Ice; MgCl2,12H2O -33.6° 49.2 MgCl2
C Ice; KCl -11.1° 59.4 KCl
Ice; MgCl2,12H2O;
D -34.3° 43 MgCl2; 3 KCl
KCl
MgCl2,12H2O;
E KCl; -21° 66.1 MgCl2; 4.9 KCl
carnallite
F1 MgCl2,12H2O -16.4° 83.33 MgCl2
Almost same as F1;
MgCl2,12H2O;
F -16.6° contains
carnallite
small amount of KCl
Page 239
MgCl2,12H2O;
G1 -16.8° 87.5 MgCl2
MgCl2,8H2O
MgCl2,12H2O; Almost same as G1, but
G MgCl2,8H2O; -16.9° contains small quantity
carnallite of KCl
MgCl2,8H2O;
H1 -3.4° 99 MgCl2
MgCl2,6H2O
MgCl2,8H2O; Almost same as H1, but
H MgCl2,6H2O; ca. -3.4° contains small amount of
carnallite KCl
MgCl2,6H2O;
J1 116.67° 161.8 MgCl2
MgCl2,4H2O
MgCl2,6H2O;
J MgCl2,4H2O; 115.7° 162 MgCl2; 4 KCl
carnallite
MgCl2,4H2O; KCl;
K 152.5° 200 MgCl2; 24 KCl
carnallite
MgCl2,4H2O;
L1 181° 238.1 MgCl2
MgCl2,2H2O
MgCl2,4H2O;
L 176° 240 MgCl2; 41 KCl
MgCl2,2H2O; KCl
M Carnallite; KCl 167.5° 166.7 MgCl2; 41.7 KCl
[N1 MgCl2,2H2O 186° ca. 241 MgCl2]
N MgCl2,2H2O; KCl 186° 240 MgCl2; 63 KCl
[O KCl 186° 195.6 KCl]
With the help of the data in the preceding table and of the solid model it
will be possible to state in any given case what will be the behaviour of a
system composed of magnesium chloride, potassium chloride and water.
One or two different cases will be very briefly described; and the reader
should have no difficulty in working out the behaviour under other
conditions with the help of the model and the numerical data just given.
G1 -16.8° 87.5 MgCl2
MgCl2,8H2O
MgCl2,12H2O; Almost same as G1, but
G MgCl2,8H2O; -16.9° contains small quantity
carnallite of KCl
MgCl2,8H2O;
H1 -3.4° 99 MgCl2
MgCl2,6H2O
MgCl2,8H2O; Almost same as H1, but
H MgCl2,6H2O; ca. -3.4° contains small amount of
carnallite KCl
MgCl2,6H2O;
J1 116.67° 161.8 MgCl2
MgCl2,4H2O
MgCl2,6H2O;
J MgCl2,4H2O; 115.7° 162 MgCl2; 4 KCl
carnallite
MgCl2,4H2O; KCl;
K 152.5° 200 MgCl2; 24 KCl
carnallite
MgCl2,4H2O;
L1 181° 238.1 MgCl2
MgCl2,2H2O
MgCl2,4H2O;
L 176° 240 MgCl2; 41 KCl
MgCl2,2H2O; KCl
M Carnallite; KCl 167.5° 166.7 MgCl2; 41.7 KCl
[N1 MgCl2,2H2O 186° ca. 241 MgCl2]
N MgCl2,2H2O; KCl 186° 240 MgCl2; 63 KCl
[O KCl 186° 195.6 KCl]
With the help of the data in the preceding table and of the solid model it
will be possible to state in any given case what will be the behaviour of a
system composed of magnesium chloride, potassium chloride and water.
One or two different cases will be very briefly described; and the reader
should have no difficulty in working out the behaviour under other
conditions with the help of the model and the numerical data just given.
Page 240
In the first place it may be again noted that at a temperature above 167.5°
(point M) carnallite cannot exist. If, therefore, a solution of magnesium and
potassium chlorides is evaporated at a temperature above this point, the
result will be a mixture of potassium chloride and either magnesium
chloride tetrahydrate or magnesium chloride dihydrate, according as the
temperature is below or above 176°. The isothermal curve here consists of
only two branches.
Further, reference has already been made to the fact that all points of the
carnallite area correspond to solutions in equilibrium with carnallite, but in
which the ratio of MgCl2 to KCl is greater than in the double salt. A
solution which is saturated with respect to double salt alone will be
supersaturated with respect to potassium chloride. At all temperatures,
therefore, carnallite is decomposed by water with separation of potassium
chloride; hence all solutions obtained by adding excess of carnallite to
water will lie on the curve EM. A pure saturated solution of carnallite
cannot be obtained.
If an unsaturated solution of the two salts in equimolecular amounts is
evaporated, potassium chloride will first be deposited, because the plane
bisecting the right angle formed by the X and Y axes cuts the area for that
salt. Deposition of potassium chloride will lead to a relative increase in the
concentration of magnesium chloride in the solution; and on continued
evaporation a point (on the curve EM) will be reached at which carnallite
will separate out. So long as the two solid phases are present, the
composition of the solution must remain unchanged. Since the separation of
carnallite causes a decrease in the relative concentration of the potassium
chloride in the solution, the portion of this salt which was deposited at the
commencement must redissolve, and carnallite will be left on evaporating
to dryness. (Incongruently saturated solution.)
Although carnallite is decomposed by pure water, it will be possible to
crystallize it from a solution having a composition represented by any point
in the carnallite area. Since during the separation of the double salt the
relative amount of magnesium chloride increases, it is most advantageous to
commence with a solution the composition of which is represented by a
point lying just above the curve EM (cf. p. 281).
(point M) carnallite cannot exist. If, therefore, a solution of magnesium and
potassium chlorides is evaporated at a temperature above this point, the
result will be a mixture of potassium chloride and either magnesium
chloride tetrahydrate or magnesium chloride dihydrate, according as the
temperature is below or above 176°. The isothermal curve here consists of
only two branches.
Further, reference has already been made to the fact that all points of the
carnallite area correspond to solutions in equilibrium with carnallite, but in
which the ratio of MgCl2 to KCl is greater than in the double salt. A
solution which is saturated with respect to double salt alone will be
supersaturated with respect to potassium chloride. At all temperatures,
therefore, carnallite is decomposed by water with separation of potassium
chloride; hence all solutions obtained by adding excess of carnallite to
water will lie on the curve EM. A pure saturated solution of carnallite
cannot be obtained.
If an unsaturated solution of the two salts in equimolecular amounts is
evaporated, potassium chloride will first be deposited, because the plane
bisecting the right angle formed by the X and Y axes cuts the area for that
salt. Deposition of potassium chloride will lead to a relative increase in the
concentration of magnesium chloride in the solution; and on continued
evaporation a point (on the curve EM) will be reached at which carnallite
will separate out. So long as the two solid phases are present, the
composition of the solution must remain unchanged. Since the separation of
carnallite causes a decrease in the relative concentration of the potassium
chloride in the solution, the portion of this salt which was deposited at the
commencement must redissolve, and carnallite will be left on evaporating
to dryness. (Incongruently saturated solution.)
Although carnallite is decomposed by pure water, it will be possible to
crystallize it from a solution having a composition represented by any point
in the carnallite area. Since during the separation of the double salt the
relative amount of magnesium chloride increases, it is most advantageous to
commence with a solution the composition of which is represented by a
point lying just above the curve EM (cf. p. 281).
Page 241
From the above description of the behaviour of carnallite in solution, the
processes usually employed for obtaining potassium chloride will be readily
intelligible.[367]
Ferric Chloride—Hydrogen Chloride—Water.—In the case of another
system of three components which we shall now describe, the relationships
are considerably more complicated than in those already discussed. They
deserve discussion, however, on account of the fact that they exhibit a
number of new phenomena.
In the system formed by the three components, ferric chloride, hydrogen
chloride, and water, not only can various compounds of ferric chloride and
water (p. 152), and of hydrogen chloride and water be formed, each of
which possesses a definite melting point, but various ternary compounds are
also known. Thus we have the following solid phases:—
2FeCl3,12H2O HCl,3H2O 2FeCl3,2HCl,12H2O
2FeCl3,7H2O HCl,2H2O 2FeCl3,2HCl,8H2O
2FeCl3,5H2O HCl,H2O 2FeCl3,2HCl,4H2O
2FeCl3,4H2O
FeCl3
From this it will be readily understood that the complete study of the
conditions of temperature and concentration under which solutions can
exist, either with one solid phase or with two or three solid phases, are
exceedingly complicated; and, as a matter of fact, only a few of the possible
equilibria have been investigated. We shall attempt here only a brief
description of the most important of these.[368]
If we again employ rectangular co-ordinates for the graphic representation
of the results, we have the two planes XOT and YOT (Fig. 115): the
concentration of ferric chloride being measured along the X-axis, the
concentration of hydrogen chloride along the Y-axis, and the temperature
along the T-axis. The curve ABCDEFGHJK is, therefore, the solubility
curve of ferric chloride in water (p. 152), and the curve A′B′C′D′E′F′ the
solubility curve of hydrogen chloride and its hydrates. B′ and D′ are the
melting points of the hydrates HCl,3H2O and HCl,2H2O. In the space
processes usually employed for obtaining potassium chloride will be readily
intelligible.[367]
Ferric Chloride—Hydrogen Chloride—Water.—In the case of another
system of three components which we shall now describe, the relationships
are considerably more complicated than in those already discussed. They
deserve discussion, however, on account of the fact that they exhibit a
number of new phenomena.
In the system formed by the three components, ferric chloride, hydrogen
chloride, and water, not only can various compounds of ferric chloride and
water (p. 152), and of hydrogen chloride and water be formed, each of
which possesses a definite melting point, but various ternary compounds are
also known. Thus we have the following solid phases:—
2FeCl3,12H2O HCl,3H2O 2FeCl3,2HCl,12H2O
2FeCl3,7H2O HCl,2H2O 2FeCl3,2HCl,8H2O
2FeCl3,5H2O HCl,H2O 2FeCl3,2HCl,4H2O
2FeCl3,4H2O
FeCl3
From this it will be readily understood that the complete study of the
conditions of temperature and concentration under which solutions can
exist, either with one solid phase or with two or three solid phases, are
exceedingly complicated; and, as a matter of fact, only a few of the possible
equilibria have been investigated. We shall attempt here only a brief
description of the most important of these.[368]
If we again employ rectangular co-ordinates for the graphic representation
of the results, we have the two planes XOT and YOT (Fig. 115): the
concentration of ferric chloride being measured along the X-axis, the
concentration of hydrogen chloride along the Y-axis, and the temperature
along the T-axis. The curve ABCDEFGHJK is, therefore, the solubility
curve of ferric chloride in water (p. 152), and the curve A′B′C′D′E′F′ the
solubility curve of hydrogen chloride and its hydrates. B′ and D′ are the
melting points of the hydrates HCl,3H2O and HCl,2H2O. In the space
Page 242
between these two planes are represented those systems in which all three
components are present. As already stated, only a few of the possible
ternary systems have been investigated, and these are represented in Fig.
116. The figure shows the model resting on the XOT-plane, so that the
lower edge represents the solubility curve of ferric chloride, the
concentration increasing from right to left. The concentration of hydrogen
chloride is measured upwards, and the temperature forwards. The further
end of the model represents the isothermal surface for -30°. The surface of
the model on the left does not correspond with the plane YOT in Fig. 115,
but with a parallel plane which cuts the concentration axis for ferric
chloride at a point representing 65 gm.-molecules FeCl3 in 100 gm.-
molecules of water. The upper surface corresponds with a plane parallel to
the axis XOT, at a distance corresponding with the concentration of 50 gm.-
molecules HCl in 100 gm.-molecules of water.
Fig. 115.
Ternary Systems.—We pass over the binary system FeCl3—H2O, which
has already been discussed (p. 152), and the similar system HCl—H2O (see
Fig. 115), and turn to the discussion of some of the ternary systems
represented by points on the surface of the model between the planes XOT
and YOT. As in the case of carnallite, a plane represents the conditions of
concentration of solution and temperature under which a ternary solution
can be in equilibrium with a single solid phase (bivariant systems), a line
represents the conditions for the coexistence of a solution with two solid
phases (univariant systems), and a point the conditions for equilibrium with
three solid phases (invariant systems).
components are present. As already stated, only a few of the possible
ternary systems have been investigated, and these are represented in Fig.
116. The figure shows the model resting on the XOT-plane, so that the
lower edge represents the solubility curve of ferric chloride, the
concentration increasing from right to left. The concentration of hydrogen
chloride is measured upwards, and the temperature forwards. The further
end of the model represents the isothermal surface for -30°. The surface of
the model on the left does not correspond with the plane YOT in Fig. 115,
but with a parallel plane which cuts the concentration axis for ferric
chloride at a point representing 65 gm.-molecules FeCl3 in 100 gm.-
molecules of water. The upper surface corresponds with a plane parallel to
the axis XOT, at a distance corresponding with the concentration of 50 gm.-
molecules HCl in 100 gm.-molecules of water.
Fig. 115.
Ternary Systems.—We pass over the binary system FeCl3—H2O, which
has already been discussed (p. 152), and the similar system HCl—H2O (see
Fig. 115), and turn to the discussion of some of the ternary systems
represented by points on the surface of the model between the planes XOT
and YOT. As in the case of carnallite, a plane represents the conditions of
concentration of solution and temperature under which a ternary solution
can be in equilibrium with a single solid phase (bivariant systems), a line
represents the conditions for the coexistence of a solution with two solid
phases (univariant systems), and a point the conditions for equilibrium with
three solid phases (invariant systems).
Page 243
Fig. 116.
In the case of a binary system, in which 2FeCl3,12H2O is in equilibrium
with a solution of the same composition, addition of hydrogen chloride
must evidently lower the temperature at which equilibrium can exist; and
the same holds, of course, for all other binary solutions in equilibrium with
this solid phase. In this way we obtain the surface I., which represents the
temperatures and concentrations of solutions in which 2FeCl3,12H2O can
be in equilibrium with a ternary solution containing ferric chloride,
hydrogen chloride, and water. This surface is analogous to the curved
surface K1K2k4k3 in Fig. 97 (p. 256). Similarly, the surfaces II., III., IV., and
V. represent the conditions for equilibrium between the solid phases
2FeCl3,7H2O; 2FeCl3,5H2O; 2FeCl3,4H2O; FeCl3 and ternary solutions
respectively. The lines CL, EM, GN, and IO on the model represent
univariant systems in which a ternary solution is in equilibrium with two
solid phases, viz. with those represented by the adjoining fields. These lines
correspond with the ternary eutectic curves k3K1 and k4K2 in Fig. 97.
Besides the surfaces already mentioned, there are still three others, VI.,
VII., and VIII., which also represent the conditions for equilibrium between
one solid phase and a ternary solution; but in these cases, the solid phase is
not a binary compound or an anhydrous salt, but a ternary compound
containing all three components. The solid phases which are in equilibrium
with the ternary solutions represented by the surfaces VI., VII., and VIII.,
are 2FeCl3,2HCl,4H2O; 2FeCl3,2HCl,8H2O; and 2FeCl3,2HCl,12H2O
respectively.
In the case of a binary system, in which 2FeCl3,12H2O is in equilibrium
with a solution of the same composition, addition of hydrogen chloride
must evidently lower the temperature at which equilibrium can exist; and
the same holds, of course, for all other binary solutions in equilibrium with
this solid phase. In this way we obtain the surface I., which represents the
temperatures and concentrations of solutions in which 2FeCl3,12H2O can
be in equilibrium with a ternary solution containing ferric chloride,
hydrogen chloride, and water. This surface is analogous to the curved
surface K1K2k4k3 in Fig. 97 (p. 256). Similarly, the surfaces II., III., IV., and
V. represent the conditions for equilibrium between the solid phases
2FeCl3,7H2O; 2FeCl3,5H2O; 2FeCl3,4H2O; FeCl3 and ternary solutions
respectively. The lines CL, EM, GN, and IO on the model represent
univariant systems in which a ternary solution is in equilibrium with two
solid phases, viz. with those represented by the adjoining fields. These lines
correspond with the ternary eutectic curves k3K1 and k4K2 in Fig. 97.
Besides the surfaces already mentioned, there are still three others, VI.,
VII., and VIII., which also represent the conditions for equilibrium between
one solid phase and a ternary solution; but in these cases, the solid phase is
not a binary compound or an anhydrous salt, but a ternary compound
containing all three components. The solid phases which are in equilibrium
with the ternary solutions represented by the surfaces VI., VII., and VIII.,
are 2FeCl3,2HCl,4H2O; 2FeCl3,2HCl,8H2O; and 2FeCl3,2HCl,12H2O
respectively.
Page 244
The model for FeCl3—HCl—H2O exhibits certain other peculiarities not
found in the case of MgCl2—KCl—H2O. On examining the model more
closely, it is found that the field of the ternary compound
2FeCl3,2HCl,8H2O (VII.) resembles the surface of a sugar cone, and has a
projecting point, the end of which corresponds with a higher temperature
than does any other point of the surface. At the point of maximum
temperature the composition of the liquid phase is the same as that of the
solid. This point, therefore, represents the melting point of the double salt of
the above composition.
The curves representing univariant systems are of two kinds. In the one
case, the two solid phases present are both binary compounds; or one is a
binary compound and the other is one of the components. In the other case,
either one or both solid phases are ternary compounds. Curves belonging to
the former class (so-called border curves) start from binary eutectic points,
and their course is always towards lower temperatures, e.g. CL, EM, GN,
IO. Curves belonging to the latter class (so-called medial curves) would, in
a triangular diagram, lie entirely within the triangle. Such curves are YV,
WV, VL, LM, MV, NS, ST, SO, OZ. These curves do not always run from
higher to lower temperatures, but may even exhibit a point of maximum
temperature. Such maxima are found, for example, at U (Fig. 116), and also
on the curves ST and LV.
Finally, whereas all the other ternary univariant curves run in valleys
between the adjoining surfaces, we find at the point X a similar appearance
to that found in the case of carnallite, as the univariant curve here rises
above the surrounding surface. The point X, therefore, does not correspond
with a eutectic point, but with a transition point. At this point the ternary
compound 2FeCl3,2HCl,12H2O melts with separation of 2FeCl3,12H2O,
just as carnallite melts at 168° with separation of potassium chloride.
The Isothermal Curves.—A deeper insight into the behaviour of the
system FeCl3—HCl—H2O is obtained from a study of the isothermal
curves, the complete series of which, so far as they have been studied, is
given in Fig. 117.[369] In this figure the lightly drawn curves represent
isothermal solubility curves, the particular temperature being printed beside
the curve.[370] The dark lines give the composition of the univariant systems
found in the case of MgCl2—KCl—H2O. On examining the model more
closely, it is found that the field of the ternary compound
2FeCl3,2HCl,8H2O (VII.) resembles the surface of a sugar cone, and has a
projecting point, the end of which corresponds with a higher temperature
than does any other point of the surface. At the point of maximum
temperature the composition of the liquid phase is the same as that of the
solid. This point, therefore, represents the melting point of the double salt of
the above composition.
The curves representing univariant systems are of two kinds. In the one
case, the two solid phases present are both binary compounds; or one is a
binary compound and the other is one of the components. In the other case,
either one or both solid phases are ternary compounds. Curves belonging to
the former class (so-called border curves) start from binary eutectic points,
and their course is always towards lower temperatures, e.g. CL, EM, GN,
IO. Curves belonging to the latter class (so-called medial curves) would, in
a triangular diagram, lie entirely within the triangle. Such curves are YV,
WV, VL, LM, MV, NS, ST, SO, OZ. These curves do not always run from
higher to lower temperatures, but may even exhibit a point of maximum
temperature. Such maxima are found, for example, at U (Fig. 116), and also
on the curves ST and LV.
Finally, whereas all the other ternary univariant curves run in valleys
between the adjoining surfaces, we find at the point X a similar appearance
to that found in the case of carnallite, as the univariant curve here rises
above the surrounding surface. The point X, therefore, does not correspond
with a eutectic point, but with a transition point. At this point the ternary
compound 2FeCl3,2HCl,12H2O melts with separation of 2FeCl3,12H2O,
just as carnallite melts at 168° with separation of potassium chloride.
The Isothermal Curves.—A deeper insight into the behaviour of the
system FeCl3—HCl—H2O is obtained from a study of the isothermal
curves, the complete series of which, so far as they have been studied, is
given in Fig. 117.[369] In this figure the lightly drawn curves represent
isothermal solubility curves, the particular temperature being printed beside
the curve.[370] The dark lines give the composition of the univariant systems
Page 245
at different temperatures. The point of intersection of a dark with a light
curve gives the composition of the univariant solution at the temperature
represented by the light curve; and the point of intersection of two dark
lines gives the composition of the invariant solution in equilibrium with
three solid phases. The dotted lines represent metastable systems, and the
points P, Q, and R represent solutions of the composition of the ternary
salts, 2FeCl3,2HCl,4H2O; 2FeCl3,2HCl,8H2O; and 2FeCl3,2HCl,12H2O.
Fig. 117.
The farther end of the model (Fig. 116) corresponds, as already mentioned,
to the temperature -30°, so that the outline evidently represents the
isothermal curve for that temperature. Fig. 117 does not show this. We can,
however, follow the isothermal for -20°, which is the extreme curve on the
right in Fig. 117. Point A represents the solubility of 2FeCl3,12H2O in
water. If hydrogen chloride is added, the concentration of ferric chloride in
the solution first decreases and then increases, until at point 34 the ternary
curve gives the composition of the univariant solution at the temperature
represented by the light curve; and the point of intersection of two dark
lines gives the composition of the invariant solution in equilibrium with
three solid phases. The dotted lines represent metastable systems, and the
points P, Q, and R represent solutions of the composition of the ternary
salts, 2FeCl3,2HCl,4H2O; 2FeCl3,2HCl,8H2O; and 2FeCl3,2HCl,12H2O.
Fig. 117.
The farther end of the model (Fig. 116) corresponds, as already mentioned,
to the temperature -30°, so that the outline evidently represents the
isothermal curve for that temperature. Fig. 117 does not show this. We can,
however, follow the isothermal for -20°, which is the extreme curve on the
right in Fig. 117. Point A represents the solubility of 2FeCl3,12H2O in
water. If hydrogen chloride is added, the concentration of ferric chloride in
the solution first decreases and then increases, until at point 34 the ternary
Page 246
double salt 2FeCl3,2HCl,12H2O is formed. If the addition of hydrogen
chloride is continued, the ferric chloride disappears ultimately, and only the
ternary double salt remains. This salt can coexist with solutions of the
composition represented by the curve which passes through the points 173,
174, 175. At the last-mentioned point, the ternary salt with 8H2O is formed.
The composition of the solutions with which this salt is in equilibrium at
-20° is represented by the curve which passes through a point of maximal
concentration with respect to HCl, and cuts the curve SN at the point 112, at
which the solution is in equilibrium with the two solid phases 2FeCl3,4H2O
and 2FeCl3,2HCl,8H2O. The succeeding portion of the isotherm represents
the solubility curve at -20° of 2FeCl3,4H2O, which cuts the dark line OS at
point 113, at which the solution is in equilibrium with the two solid phases
2FeCl3,4H2O and 2FeCl3,2HCl,4H2O. Thereafter comes the solubility
curve of the latter compound.
The other isothermal curves can be followed in a similar manner. If the
temperature is raised, the region of existence of the ternary double salts
becomes smaller and smaller, and at temperatures above 30° the ternary
salts with 12H2O and 8H2O are no longer capable of existing. If the
temperature is raised above 46°, only the binary compounds of ferric
chloride and water and the anhydrous salt can exist as solid phases. The
isothermal curve for 0° represents the solubility curve for 2FeCl3,12H2O;
2FeCl3,7H2O; 2FeCl3,5H2O; and 2FeCl3,4H2O.
Finally, in the case of the system FeCl3—HCl—H2O, we find closed
isothermal curves. Since, as already stated, the salt 2FeCl3,2HCl,8H2O has
a definite melting point, the temperature of which is therefore higher than
that at which this compound is in equilibrium with solutions of other
composition, it follows that the line of intersection of an isothermal plane
corresponding with a temperature immediately below the melting point of
the salt with the cone-shaped surface of its region of existence, will form a
closed curve. This is shown by the isotherm for -4.5°, which surrounds the
point Q, the melting point of the ternary salt.
The following table gives some of the numerical data from which the
curves and the model have been constructed:—
chloride is continued, the ferric chloride disappears ultimately, and only the
ternary double salt remains. This salt can coexist with solutions of the
composition represented by the curve which passes through the points 173,
174, 175. At the last-mentioned point, the ternary salt with 8H2O is formed.
The composition of the solutions with which this salt is in equilibrium at
-20° is represented by the curve which passes through a point of maximal
concentration with respect to HCl, and cuts the curve SN at the point 112, at
which the solution is in equilibrium with the two solid phases 2FeCl3,4H2O
and 2FeCl3,2HCl,8H2O. The succeeding portion of the isotherm represents
the solubility curve at -20° of 2FeCl3,4H2O, which cuts the dark line OS at
point 113, at which the solution is in equilibrium with the two solid phases
2FeCl3,4H2O and 2FeCl3,2HCl,4H2O. Thereafter comes the solubility
curve of the latter compound.
The other isothermal curves can be followed in a similar manner. If the
temperature is raised, the region of existence of the ternary double salts
becomes smaller and smaller, and at temperatures above 30° the ternary
salts with 12H2O and 8H2O are no longer capable of existing. If the
temperature is raised above 46°, only the binary compounds of ferric
chloride and water and the anhydrous salt can exist as solid phases. The
isothermal curve for 0° represents the solubility curve for 2FeCl3,12H2O;
2FeCl3,7H2O; 2FeCl3,5H2O; and 2FeCl3,4H2O.
Finally, in the case of the system FeCl3—HCl—H2O, we find closed
isothermal curves. Since, as already stated, the salt 2FeCl3,2HCl,8H2O has
a definite melting point, the temperature of which is therefore higher than
that at which this compound is in equilibrium with solutions of other
composition, it follows that the line of intersection of an isothermal plane
corresponding with a temperature immediately below the melting point of
the salt with the cone-shaped surface of its region of existence, will form a
closed curve. This is shown by the isotherm for -4.5°, which surrounds the
point Q, the melting point of the ternary salt.
The following table gives some of the numerical data from which the
curves and the model have been constructed:—
Page 247
Composition of the
solution in gm.-
mols. salt
Point. Solid Phases. Temperature. to 100 gm.-mols.
water.
HCl FeCl3
A 2FeCl3,12H2O -20° — 6.56
2FeCl3,12H2O;
C 27.4° — 24.30
2FeCl3,7H2O
2FeCl3,7H2O;
E 30° — 30.24
2FeCl3,5H2O
2FeCl3,5H2O;
G 55° — 40.64
2FeCl3,4H2O
J 2FeCl3,4H2O; FeCl3 66° — 58.40
2FeCl3,12H2O;
L 2FeCl3,7H2O; -7.5° 19.22 23.72
2FeCl3,2HCl,8H2O
2FeCl3,7H2O;
M 2FeCl3,5H2O; -7.3° 23.08 28.55
2FeCl3,2HCl,8H2O
2FeCl3,5H2O;
N 2FeCl3,4H2O; -16° 28.40 31.89
2FeCl3,2HCl,8H2O
2FeCl3,4H2O;
S 2FeCl3,2HCl,8H2O; -27.5° 32.33 34.21
2FeCl3,2HCl,4H2O
2FeCl3,4H2O; FeCl3;
O 29° 33.71 49.84
2FeCl3,2HCl,4H2O
2FeCl3,7H2O;
U -4.5° 20.66 25.74
2FeCl3,2HCl,8H2O
solution in gm.-
mols. salt
Point. Solid Phases. Temperature. to 100 gm.-mols.
water.
HCl FeCl3
A 2FeCl3,12H2O -20° — 6.56
2FeCl3,12H2O;
C 27.4° — 24.30
2FeCl3,7H2O
2FeCl3,7H2O;
E 30° — 30.24
2FeCl3,5H2O
2FeCl3,5H2O;
G 55° — 40.64
2FeCl3,4H2O
J 2FeCl3,4H2O; FeCl3 66° — 58.40
2FeCl3,12H2O;
L 2FeCl3,7H2O; -7.5° 19.22 23.72
2FeCl3,2HCl,8H2O
2FeCl3,7H2O;
M 2FeCl3,5H2O; -7.3° 23.08 28.55
2FeCl3,2HCl,8H2O
2FeCl3,5H2O;
N 2FeCl3,4H2O; -16° 28.40 31.89
2FeCl3,2HCl,8H2O
2FeCl3,4H2O;
S 2FeCl3,2HCl,8H2O; -27.5° 32.33 34.21
2FeCl3,2HCl,4H2O
2FeCl3,4H2O; FeCl3;
O 29° 33.71 49.84
2FeCl3,2HCl,4H2O
2FeCl3,7H2O;
U -4.5° 20.66 25.74
2FeCl3,2HCl,8H2O
Page 248
2FeCl3,12H2O;
V 2FeCl3,2HCl,12H2O; -13° 22.40 18.00
2FeCl3,2HCl,8H2O
2FeCl3,12H2O;
X -12.5° 22.14 16.69
2FeCl3,2HCl,12H2O
Q 2FeCl3,2HCl,8H2O -3° (melting point)
Basic Salts.—Another class of systems in the study of which the Phase
Rule has performed exceptional service, is that of the basic salts. In many
cases it is impossible, by the ordinary methods of analysis, to decide
whether one is dealing with a definite chemical individual or with a
mixture. The question whether a solid phase is a chemical individual can,
however, be answered, in most cases, with the help of the principles which
we have already learnt. Let us consider, for example, the formation of basic
salts from bismuth nitrate, and water. In this case we can choose as
components Bi2O3, N2O5, and H2O; since all the systems consist of these in
varying amounts. If we are dealing with a condition of equilibrium at
constant temperature between liquid and solid phases, three cases can be
distinguished,[371] viz.—
1. The solutions in different experiments have the same composition, but
the composition of the precipitate alters. In this case there must be two solid
phases.
2. The solutions in different experiments can have varying composition,
while the composition of the precipitate remains unchanged. In this case
only one solid phase exists, a definite compound.
3. The composition both of the solution and of the precipitate varies. In this
case the solid phase is a solid solution or a mixed crystal.
In order, therefore, to decide what is the nature of a precipitate produced by
the hydrolysis of a normal salt, it is only necessary to ascertain whether and
how the composition of the precipitate alters with alteration in the
composition of the solution. If the composition of the solution is
represented by abscissæ, and the composition of the precipitate by
ordinates, the form of the curves obtained would enable us to answer our
V 2FeCl3,2HCl,12H2O; -13° 22.40 18.00
2FeCl3,2HCl,8H2O
2FeCl3,12H2O;
X -12.5° 22.14 16.69
2FeCl3,2HCl,12H2O
Q 2FeCl3,2HCl,8H2O -3° (melting point)
Basic Salts.—Another class of systems in the study of which the Phase
Rule has performed exceptional service, is that of the basic salts. In many
cases it is impossible, by the ordinary methods of analysis, to decide
whether one is dealing with a definite chemical individual or with a
mixture. The question whether a solid phase is a chemical individual can,
however, be answered, in most cases, with the help of the principles which
we have already learnt. Let us consider, for example, the formation of basic
salts from bismuth nitrate, and water. In this case we can choose as
components Bi2O3, N2O5, and H2O; since all the systems consist of these in
varying amounts. If we are dealing with a condition of equilibrium at
constant temperature between liquid and solid phases, three cases can be
distinguished,[371] viz.—
1. The solutions in different experiments have the same composition, but
the composition of the precipitate alters. In this case there must be two solid
phases.
2. The solutions in different experiments can have varying composition,
while the composition of the precipitate remains unchanged. In this case
only one solid phase exists, a definite compound.
3. The composition both of the solution and of the precipitate varies. In this
case the solid phase is a solid solution or a mixed crystal.
In order, therefore, to decide what is the nature of a precipitate produced by
the hydrolysis of a normal salt, it is only necessary to ascertain whether and
how the composition of the precipitate alters with alteration in the
composition of the solution. If the composition of the solution is
represented by abscissæ, and the composition of the precipitate by
ordinates, the form of the curves obtained would enable us to answer our
Page 249
question; for vertical lines would indicate the presence of two solid phases
(1st case), horizontal lines the presence of only one solid phase (2nd case),
and slanting lines the presence of mixed crystals (3rd case). This method of
representation cannot, however, be carried out in most cases. It is, however,
generally possible to find one pair or several pairs of components, the
relative amounts of which in the solution or in the precipitate undergo
change when, and only when, the composition of the solution or of the
precipitate changes. Thus, in the case of bismuth, nitrate, and water, we can
represent the ratio of Bi2O3 : N2O5 in the precipitate as ordinates, and N2O5
: H2O in the solution as abscissæ. A horizontal line then indicates a single
solid phase, and a vertical line two solid phases. An example of this is given
in Fig. 118.[372]
(1st case), horizontal lines the presence of only one solid phase (2nd case),
and slanting lines the presence of mixed crystals (3rd case). This method of
representation cannot, however, be carried out in most cases. It is, however,
generally possible to find one pair or several pairs of components, the
relative amounts of which in the solution or in the precipitate undergo
change when, and only when, the composition of the solution or of the
precipitate changes. Thus, in the case of bismuth, nitrate, and water, we can
represent the ratio of Bi2O3 : N2O5 in the precipitate as ordinates, and N2O5
: H2O in the solution as abscissæ. A horizontal line then indicates a single
solid phase, and a vertical line two solid phases. An example of this is given
in Fig. 118.[372]
Page 250
Fig. 118.
Bi2O3—N2O5—H2O.—Although various systems have been studied in which
there is formation of basic salts,[373] we shall content ourselves here with the
description of some of the conditions for the formation of basic salts of bismuth
nitrate, and for their equilibrium in contact with solutions.[374]
Three normal salts of bismuth oxide and nitric acid are known, viz.
Bi2O3,3N2O5,10H2O(S10); Bi2O3,3N2O5,4H2O(S4); and Bi2O3,3N2O5,3H2O(S3).
Besides these normal salts, there are the following basic salts:—
Bi2O3,N2O5,2H2O (represented by B1-1-2)
Bi2O3,N2O5,H2O ( ,, ,, B1-1-1)
6Bi2O3,5N2O5,9H2O ( ,, ,, B6-5-9)
2Bi2O3,N2O5,H2O ( ,, ,, B2-1-1)
Probably some others also exist. The problem now is to find the conditions under
which these different normal and basic salts can be in equilibrium with solutions
of varying concentration of the three components. Having determined the
equilibrium conditions for the different salts, it is then possible to construct a
model similar to that for MgCl2—KCl—H2O or for FeCl3—HCl—H2O, from
which it will be possible to determine the limits of stability of the different salts,
and to predict what will occur when we bring the salts in contact with solutions of
nitric acid of different concentrations and at different temperatures.
For our present purpose it is sufficient to pick out only some of the equilibria
which have been studied, and which are represented in the model (Fig. 119). In
this case use has been made of the triangular method of representation, so that the
surface of the model lies within the prism.
Bi2O3—N2O5—H2O.—Although various systems have been studied in which
there is formation of basic salts,[373] we shall content ourselves here with the
description of some of the conditions for the formation of basic salts of bismuth
nitrate, and for their equilibrium in contact with solutions.[374]
Three normal salts of bismuth oxide and nitric acid are known, viz.
Bi2O3,3N2O5,10H2O(S10); Bi2O3,3N2O5,4H2O(S4); and Bi2O3,3N2O5,3H2O(S3).
Besides these normal salts, there are the following basic salts:—
Bi2O3,N2O5,2H2O (represented by B1-1-2)
Bi2O3,N2O5,H2O ( ,, ,, B1-1-1)
6Bi2O3,5N2O5,9H2O ( ,, ,, B6-5-9)
2Bi2O3,N2O5,H2O ( ,, ,, B2-1-1)
Probably some others also exist. The problem now is to find the conditions under
which these different normal and basic salts can be in equilibrium with solutions
of varying concentration of the three components. Having determined the
equilibrium conditions for the different salts, it is then possible to construct a
model similar to that for MgCl2—KCl—H2O or for FeCl3—HCl—H2O, from
which it will be possible to determine the limits of stability of the different salts,
and to predict what will occur when we bring the salts in contact with solutions of
nitric acid of different concentrations and at different temperatures.
For our present purpose it is sufficient to pick out only some of the equilibria
which have been studied, and which are represented in the model (Fig. 119). In
this case use has been made of the triangular method of representation, so that the
surface of the model lies within the prism.
Page 251
Fig. 119.
This model shows the three surfaces, A, B, and C, which represent the conditions
for the stable existence of the salts B1-1-1, S10, and S3 in contact with solution at
different temperatures. The front surface of the model represents the temperature
9°, and the farther end the temperature 75.5°. The dotted curve represents the
isotherm for 20°. The prominences between the surfaces represent, of course,
solutions which are saturated in respect of two solid phases. Thus, for example,
pabc represents solutions in equilibrium with B1-1-1 and S10; and the ridge qdc,
solutions in equilibrium with S10 and S3. The point b, which lies at 75.5°, is the
point of maximum temperature for S10. If the temperature is raised above this
point, S10 decomposes into the basic salt B1-1-1 and solution. This point is
therefore analogous to the point M in the carnallite model, at which this salt
decomposes into potassium chloride and solution (p. 284); or to the point at
which the salt 2FeCl3,2HCl,12H2O decomposes into 2FeCl3,12H2O and solution
(p. 294). The curve pab has been followed to the temperature of 72° (point c).
The end of the model is incomplete, but it is probable that in the neighbourhood
of the point c there exists a quintuple point at which the basic salt B1-2-2 appears.
In the neighbourhood of e also there probably exists another quintuple point at
which S4 is formed. These systems have, however, not been studied.
The following tables give some of the numerical data:—
Isotherm for 20°.
Composition of the solution. Gram-mols.
Solid Phase. in 1000 gm.-mols. of water.
Bi2O3 N2O5
B1-1-1 10.50 38.65
— 27.20 83.84
B1-1-1; S10 30.15 97.97
This model shows the three surfaces, A, B, and C, which represent the conditions
for the stable existence of the salts B1-1-1, S10, and S3 in contact with solution at
different temperatures. The front surface of the model represents the temperature
9°, and the farther end the temperature 75.5°. The dotted curve represents the
isotherm for 20°. The prominences between the surfaces represent, of course,
solutions which are saturated in respect of two solid phases. Thus, for example,
pabc represents solutions in equilibrium with B1-1-1 and S10; and the ridge qdc,
solutions in equilibrium with S10 and S3. The point b, which lies at 75.5°, is the
point of maximum temperature for S10. If the temperature is raised above this
point, S10 decomposes into the basic salt B1-1-1 and solution. This point is
therefore analogous to the point M in the carnallite model, at which this salt
decomposes into potassium chloride and solution (p. 284); or to the point at
which the salt 2FeCl3,2HCl,12H2O decomposes into 2FeCl3,12H2O and solution
(p. 294). The curve pab has been followed to the temperature of 72° (point c).
The end of the model is incomplete, but it is probable that in the neighbourhood
of the point c there exists a quintuple point at which the basic salt B1-2-2 appears.
In the neighbourhood of e also there probably exists another quintuple point at
which S4 is formed. These systems have, however, not been studied.
The following tables give some of the numerical data:—
Isotherm for 20°.
Composition of the solution. Gram-mols.
Solid Phase. in 1000 gm.-mols. of water.
Bi2O3 N2O5
B1-1-1 10.50 38.65
— 27.20 83.84
B1-1-1; S10 30.15 97.97
Page 252
S10 29.70 96.57
— 19.65 98.76
— 10.51 162.58
— 33.51 355.87
S10; S3 51.00 403.0
S3 14.35 492.0
— 7.45 592.9
Systems in Equilibrium with B1-1-1 and S10 (Curve pabc).
Composition of the solution. Gram-mols.
Solid Phase. in 1000 gm.-mols. of water.
Bi2O3 N2O5
9° 26.7 88.2
20° (point a) 30.15 97.97
30° 33.6 112.3
50° 41.8 148.4
65° 57.21 190.8
75.5° (point b) 87.9 288.4
72° (point c) 96.0 327.0
Systems in Equilibrium with S10 and S3 (Curve qde).
Composition of the solution. Gram-mols.
Solid Phase. in 1000 gm.-mols. of water.
Bi2O3 N2O5
11.5° 44.5 396
20° 51.0 405.4
50° 66.5 444.2
65° 80.0 454.4
Basic Mercury Salts.—The Phase Rule has also been applied by A. J. Cox[375] in
an investigation of the basic salts of mercury, the result of which has been to
show that, of the salts mentioned in text-books, quite a number are incorrectly
stated to be chemical compounds or chemical individuals (p. 92). The
investigation, which was carried out essentially in the manner described above,
included the salts mentioned in the following table; and of the basic salts said to
be derived from them, only those mentioned really exist. In the following table,
— 19.65 98.76
— 10.51 162.58
— 33.51 355.87
S10; S3 51.00 403.0
S3 14.35 492.0
— 7.45 592.9
Systems in Equilibrium with B1-1-1 and S10 (Curve pabc).
Composition of the solution. Gram-mols.
Solid Phase. in 1000 gm.-mols. of water.
Bi2O3 N2O5
9° 26.7 88.2
20° (point a) 30.15 97.97
30° 33.6 112.3
50° 41.8 148.4
65° 57.21 190.8
75.5° (point b) 87.9 288.4
72° (point c) 96.0 327.0
Systems in Equilibrium with S10 and S3 (Curve qde).
Composition of the solution. Gram-mols.
Solid Phase. in 1000 gm.-mols. of water.
Bi2O3 N2O5
11.5° 44.5 396
20° 51.0 405.4
50° 66.5 444.2
65° 80.0 454.4
Basic Mercury Salts.—The Phase Rule has also been applied by A. J. Cox[375] in
an investigation of the basic salts of mercury, the result of which has been to
show that, of the salts mentioned in text-books, quite a number are incorrectly
stated to be chemical compounds or chemical individuals (p. 92). The
investigation, which was carried out essentially in the manner described above,
included the salts mentioned in the following table; and of the basic salts said to
be derived from them, only those mentioned really exist. In the following table,
Page 253
the numbers in the second column give the minimum values of the concentration
of the acid, expressed in equivalent normality, necessary for the existence of the
corresponding salts in contact with solution at the temperature given in the third
column:—
Normality of
Salt. Temperature.
acid.
HgCrO4 1.41 50°
3HgO.CrO3 2.6 × 10-4 50°
Hg(NO3)2.H2O 18.72 25°
3HgO.N2O5 0.159 25°
HgSO4 6.87 25°
3HgO.SO3 1.3 × 10-3 25°
HgF2 1.14 25°
HgNO3.H2O 2.95 25°
5Hg2O.3N2O5.2H2O ca. 0.293 25°
2Hg2O.N2O5(?) 0.110 25°
3Hg2O.N2O5.2H2O(?) 1.7 × 10-3 25°
Hg2SO4 4.2 × 10-3 25°
2Hg2O.SO3.H2O 5.6 × 10-4 25°
Mercuric fluoride does not form any basic salt.
Since two succeeding members of a series can coexist only in contact with a
solution of definite concentration, we can prepare acid solutions of definite
concentration by bringing an excess of two such salts in contact with water.
Indirect Determination of the Composition of the Solid Phase.—It has already
been shown (p. 228) how the composition of the solid phase in a system of two
components can be determined without analysis, and we shall now describe how
this can be done in a system of three components.[376]
We shall assume that we are dealing with the aqueous solution of two salts which
can give rise to a double salt, in which case we can represent the solubility
relations in a system of rectangular co-ordinates. In this case we should obtain, as
before (Fig. 120), the isotherm adcb, if we express the composition of the
solution in gram-molecules of A or of B to 100 gram-molecules of water.
of the acid, expressed in equivalent normality, necessary for the existence of the
corresponding salts in contact with solution at the temperature given in the third
column:—
Normality of
Salt. Temperature.
acid.
HgCrO4 1.41 50°
3HgO.CrO3 2.6 × 10-4 50°
Hg(NO3)2.H2O 18.72 25°
3HgO.N2O5 0.159 25°
HgSO4 6.87 25°
3HgO.SO3 1.3 × 10-3 25°
HgF2 1.14 25°
HgNO3.H2O 2.95 25°
5Hg2O.3N2O5.2H2O ca. 0.293 25°
2Hg2O.N2O5(?) 0.110 25°
3Hg2O.N2O5.2H2O(?) 1.7 × 10-3 25°
Hg2SO4 4.2 × 10-3 25°
2Hg2O.SO3.H2O 5.6 × 10-4 25°
Mercuric fluoride does not form any basic salt.
Since two succeeding members of a series can coexist only in contact with a
solution of definite concentration, we can prepare acid solutions of definite
concentration by bringing an excess of two such salts in contact with water.
Indirect Determination of the Composition of the Solid Phase.—It has already
been shown (p. 228) how the composition of the solid phase in a system of two
components can be determined without analysis, and we shall now describe how
this can be done in a system of three components.[376]
We shall assume that we are dealing with the aqueous solution of two salts which
can give rise to a double salt, in which case we can represent the solubility
relations in a system of rectangular co-ordinates. In this case we should obtain, as
before (Fig. 120), the isotherm adcb, if we express the composition of the
solution in gram-molecules of A or of B to 100 gram-molecules of water.
Page 254
Fig. 120.
Let us suppose, now, that the double salt is in equilibrium with the solution at a
definite temperature, and that the composition of the solution is represented by
the point e. The greater part of the solution is now separated from the solid phase,
and the latter, together with the adhering mother liquor, is analyzed. The
composition (expressed, as before, in gram-molecules of A and B to 100 gram
molecules of water) will be represented by a point (e.g. f) on the line eS, where S
represents the composition of the double salt. That this is so will be evident when
one considers that the composition of the whole mass must lie between the
composition of the solution and that of the double salt, no matter what the relative
amounts of the solid phase and the mother liquor.
If, in a similar manner, we analyze a solution of a different composition in
equilibrium with the same double salt (not necessarily at the same temperature as
before), and also the mixture of solid phase and solution, we shall obtain two
other points, as, for example, g and h, and the line joining these must likewise
pass through S. The method of finding the composition of an unknown double
salt consists, therefore, in finding, in the manner just described, the position of
two lines such as ef and gh. The point of intersection of these lines then gives the
composition of the double salt.
If the double salt is anhydrous, the point S lies at infinity, and the lines ef and gh
are parallel to each other.
The same result is arrived at by means of the triangular method of representation.
[377]
If we start with the three components in known amounts, and represent the
initial composition of the whole by a point in the triangle, and then ascertain the
final composition of the solution in equilibrium with the solid phase at a definite
temperature, the line joining the points representing the initial and end
concentration passes through the point representing the composition of the solid
phase. If two determinations are made with solutions having different initial and
Let us suppose, now, that the double salt is in equilibrium with the solution at a
definite temperature, and that the composition of the solution is represented by
the point e. The greater part of the solution is now separated from the solid phase,
and the latter, together with the adhering mother liquor, is analyzed. The
composition (expressed, as before, in gram-molecules of A and B to 100 gram
molecules of water) will be represented by a point (e.g. f) on the line eS, where S
represents the composition of the double salt. That this is so will be evident when
one considers that the composition of the whole mass must lie between the
composition of the solution and that of the double salt, no matter what the relative
amounts of the solid phase and the mother liquor.
If, in a similar manner, we analyze a solution of a different composition in
equilibrium with the same double salt (not necessarily at the same temperature as
before), and also the mixture of solid phase and solution, we shall obtain two
other points, as, for example, g and h, and the line joining these must likewise
pass through S. The method of finding the composition of an unknown double
salt consists, therefore, in finding, in the manner just described, the position of
two lines such as ef and gh. The point of intersection of these lines then gives the
composition of the double salt.
If the double salt is anhydrous, the point S lies at infinity, and the lines ef and gh
are parallel to each other.
The same result is arrived at by means of the triangular method of representation.
[377]
If we start with the three components in known amounts, and represent the
initial composition of the whole by a point in the triangle, and then ascertain the
final composition of the solution in equilibrium with the solid phase at a definite
temperature, the line joining the points representing the initial and end
concentration passes through the point representing the composition of the solid
phase. If two determinations are made with solutions having different initial and
Page 255
final concentrations in equilibrium with the same solid phase, then the point of
intersection of the two lines so obtained gives the composition of the solid phase.
CHAPTER XVII
ABSENCE OF A LIQUID PHASE
In the preceding chapters dealing with equilibria in three-component systems, our
attention was directed only to those cases in which liquid solutions formed one or
more phases. Mention must, however, be made of certain systems which contain
no liquid phase, and in which only solids and gases are in equilibrium. Since, in
all cases, there can be but one gas phase, four solid phases will be necessary in
order to form an invariant system. When only three solid phases are present, the
system is univariant; and when only two solid phases coexist with gas, it is
bivariant. If, however, we make the restriction that the gas pressure is constant,
we diminish the variability by one.
On account of their great industrial importance, we shall describe briefly some of
the systems belonging to this class.
Iron, Carbon Monoxide, Carbon Dioxide.—Some of the most important
systems of three components in which equilibrium exists between solid and gas
phases are those formed by the three components—iron, carbon monoxide, and
carbon dioxide—and they are of importance especially for the study of the
processes occurring in the blast furnace.
If carbon monoxide is passed over reduced iron powder at a temperature of about
600°, the iron is oxidized and the carbon monoxide reduced with separation of
carbon in accordance with the equation
Fe + CO = FeO + C
This reaction is succeeded by the two reactions
FeO + CO = Fe + CO2
CO2 + C = 2CO
intersection of the two lines so obtained gives the composition of the solid phase.
CHAPTER XVII
ABSENCE OF A LIQUID PHASE
In the preceding chapters dealing with equilibria in three-component systems, our
attention was directed only to those cases in which liquid solutions formed one or
more phases. Mention must, however, be made of certain systems which contain
no liquid phase, and in which only solids and gases are in equilibrium. Since, in
all cases, there can be but one gas phase, four solid phases will be necessary in
order to form an invariant system. When only three solid phases are present, the
system is univariant; and when only two solid phases coexist with gas, it is
bivariant. If, however, we make the restriction that the gas pressure is constant,
we diminish the variability by one.
On account of their great industrial importance, we shall describe briefly some of
the systems belonging to this class.
Iron, Carbon Monoxide, Carbon Dioxide.—Some of the most important
systems of three components in which equilibrium exists between solid and gas
phases are those formed by the three components—iron, carbon monoxide, and
carbon dioxide—and they are of importance especially for the study of the
processes occurring in the blast furnace.
If carbon monoxide is passed over reduced iron powder at a temperature of about
600°, the iron is oxidized and the carbon monoxide reduced with separation of
carbon in accordance with the equation
Fe + CO = FeO + C
This reaction is succeeded by the two reactions
FeO + CO = Fe + CO2
CO2 + C = 2CO
Page 256
Fig. 121.
The former of these reactions is not complete, but leads to a definite equilibrium.
The result of the different reactions is therefore an equilibrium between the three
solid phases, carbon, iron, and ferrous oxide, and the gas phase consisting of
carbon monoxide and dioxide. We have here four phases; and if the total pressure
is maintained constant, equilibrium can occur only at a definite temperature.
Since, under certain conditions, we can also have the reaction
Fe3O4 + CO = 3FeO + CO2
a second series of equilibria can be obtained of a character similar to the former.
These various equilibria have been investigated by Baur and Glaessner,[378] and
the following is a short account of the results of their work.
Mixtures of the solid phases in equilibrium with carbon monoxide and dioxide
were heated in a porcelain tube at a definite temperature until equilibrium was
produced, and the gas was then pumped off and analyzed. The results which were
obtained are given in the following tables, and represented graphically in Fig.
121.
Solid Phases: Fe3O4; FeO.
Duration of Percentage of
Tube filled
No. the experiment Temperature.
with CO2 CO
in hours.
The former of these reactions is not complete, but leads to a definite equilibrium.
The result of the different reactions is therefore an equilibrium between the three
solid phases, carbon, iron, and ferrous oxide, and the gas phase consisting of
carbon monoxide and dioxide. We have here four phases; and if the total pressure
is maintained constant, equilibrium can occur only at a definite temperature.
Since, under certain conditions, we can also have the reaction
Fe3O4 + CO = 3FeO + CO2
a second series of equilibria can be obtained of a character similar to the former.
These various equilibria have been investigated by Baur and Glaessner,[378] and
the following is a short account of the results of their work.
Mixtures of the solid phases in equilibrium with carbon monoxide and dioxide
were heated in a porcelain tube at a definite temperature until equilibrium was
produced, and the gas was then pumped off and analyzed. The results which were
obtained are given in the following tables, and represented graphically in Fig.
121.
Solid Phases: Fe3O4; FeO.
Duration of Percentage of
Tube filled
No. the experiment Temperature.
with CO2 CO
in hours.
Page 257
1 CO 14 600° 59.3 40.7
2 CO 15 590° 54.7 45.3
3 CO2 16 590° 64.6 35.4
4 CO 24 590° 58.4 41.6
5 CO 22 730° 67.7 32.3
6 CO2 22 730° 86.1 31.9
7 CO 22 750° 68.4 31.6
8 CO2 22 610° 64.9 35.1
9 CO 23 420° 56.0 44.0
10 CO 47 350° 65.6 34.4
11 CO2 46 350° 72.8 27.2
12 CO 53 350° 64.0 36.0
13 CO 18 570° 53.4 46.6
14 CO 19 680° 60.5 39.5
15 CO2 24 540° 55.5 44.5
16 CO 21 630° 57.5 42.5
17 CO2 17 690° 65.5 34.5
18 CO2 17 670° 67.0 33.0
19 CO2 24 410° 58.5 41.5
20 CO 24 490° 51.7 48.8
21 CO2 23 590° 54.4 45.6
22 CO2 4 950° 77.0 23.0
23 CO2 15 850° 73.4 26.6
24 CO 8 800° 71.2 28.8
25 CO2 24 540° 56.7 43.3
Solid Phases: FeO; Fe.
Duration of Percentage of
Tube filled
No. the experiment Temperature.
with CO2 CO
in hours.
I. CO 15 800° 35.2 64.8
II. CO 18 530° 29.1 70.9
III. CO 13 880° 30.2 69.6
IV. CO2 24 870° 32.3 67.7
2 CO 15 590° 54.7 45.3
3 CO2 16 590° 64.6 35.4
4 CO 24 590° 58.4 41.6
5 CO 22 730° 67.7 32.3
6 CO2 22 730° 86.1 31.9
7 CO 22 750° 68.4 31.6
8 CO2 22 610° 64.9 35.1
9 CO 23 420° 56.0 44.0
10 CO 47 350° 65.6 34.4
11 CO2 46 350° 72.8 27.2
12 CO 53 350° 64.0 36.0
13 CO 18 570° 53.4 46.6
14 CO 19 680° 60.5 39.5
15 CO2 24 540° 55.5 44.5
16 CO 21 630° 57.5 42.5
17 CO2 17 690° 65.5 34.5
18 CO2 17 670° 67.0 33.0
19 CO2 24 410° 58.5 41.5
20 CO 24 490° 51.7 48.8
21 CO2 23 590° 54.4 45.6
22 CO2 4 950° 77.0 23.0
23 CO2 15 850° 73.4 26.6
24 CO 8 800° 71.2 28.8
25 CO2 24 540° 56.7 43.3
Solid Phases: FeO; Fe.
Duration of Percentage of
Tube filled
No. the experiment Temperature.
with CO2 CO
in hours.
I. CO 15 800° 35.2 64.8
II. CO 18 530° 29.1 70.9
III. CO 13 880° 30.2 69.6
IV. CO2 24 870° 32.3 67.7
Page 258
V. CO 18 760° 36.9 63.1
VI. CO2 16 820° 34.7 65.3
VII. CO2 18 730° 41.1 58.9
VIII. CO 18 630° 34.9 65.1
IX. CO2 17 630° 61.6 58.4
X. CO 18 540° 25.0 75.0
XI. CO2 25 540° 36.5 63.5
As is evident from the above tables and from the curves in Fig. 121, the curve of
equilibrium in the case of the reaction
Fe3O4 + CO = 3FeO + CO2
exhibits a maximum for the ratio CO : CO2, at 490°, while, for the reaction
FeO + CO = Fe + CO2
this ratio has a minimum value at 680°. From these curves can be derived the
conditions under which the different solid phases can exist in contact with gas.
Thus, for example, at a temperature of 690°, FeO and Fe3O4 can coexist with a
mixture of 65.5 per cent. of CO2 and 34.5 per cent. of CO. If the partial pressure
of CO2 is increased, there occurs the reaction
3FeO + CO2 = Fe3O4 + CO
and if carbon dioxide is added in sufficient amount, the ferrous oxide finally
disappears completely. If, on the other hand, the partial pressure of CO is
increased, there occurs the reaction
Fe3O4 + CO = 3FeO + CO2
and all the ferric oxide can be made to disappear. We see, therefore, that Fe3O4
can only exist at temperatures and in contact with mixtures of carbon monoxide
and dioxide, represented by the area which lies below the under curve in Fig. 121.
Similarly, the region of existence of FeO is that represented by the area between
the two curves; while metallic iron can exist under the conditions of temperature
and composition of gas phase represented by the area above the upper curve in
Fig. 121. If, therefore, ferric oxide or metallic iron is heated for a sufficiently long
VI. CO2 16 820° 34.7 65.3
VII. CO2 18 730° 41.1 58.9
VIII. CO 18 630° 34.9 65.1
IX. CO2 17 630° 61.6 58.4
X. CO 18 540° 25.0 75.0
XI. CO2 25 540° 36.5 63.5
As is evident from the above tables and from the curves in Fig. 121, the curve of
equilibrium in the case of the reaction
Fe3O4 + CO = 3FeO + CO2
exhibits a maximum for the ratio CO : CO2, at 490°, while, for the reaction
FeO + CO = Fe + CO2
this ratio has a minimum value at 680°. From these curves can be derived the
conditions under which the different solid phases can exist in contact with gas.
Thus, for example, at a temperature of 690°, FeO and Fe3O4 can coexist with a
mixture of 65.5 per cent. of CO2 and 34.5 per cent. of CO. If the partial pressure
of CO2 is increased, there occurs the reaction
3FeO + CO2 = Fe3O4 + CO
and if carbon dioxide is added in sufficient amount, the ferrous oxide finally
disappears completely. If, on the other hand, the partial pressure of CO is
increased, there occurs the reaction
Fe3O4 + CO = 3FeO + CO2
and all the ferric oxide can be made to disappear. We see, therefore, that Fe3O4
can only exist at temperatures and in contact with mixtures of carbon monoxide
and dioxide, represented by the area which lies below the under curve in Fig. 121.
Similarly, the region of existence of FeO is that represented by the area between
the two curves; while metallic iron can exist under the conditions of temperature
and composition of gas phase represented by the area above the upper curve in
Fig. 121. If, therefore, ferric oxide or metallic iron is heated for a sufficiently long
Page 259
time at temperatures above 700° (to the right of the dotted line; vide infra),
complete transformation to ferrous oxide finally occurs.
In another series of equilibria which can be obtained, carbon is one of the solid
phases. In Fig. 121 the equilibria between carbon, carbon monoxide, and carbon
dioxide under pressures of one and of a quarter atmosphere, are represented by
dotted lines.[379]
If we consider only the dotted line on the right, representing the equilibria under
atmospheric pressure, we see that the points in which the dotted line cuts the
other two curves must represent systems in which carbon monoxide and carbon
dioxide are in equilibrium with FeO + Fe3O4 + C, on the one hand, and with Fe +
FeO + C on the other. These systems can only exist at one definite temperature, if
we make the restriction that the pressure is maintained constant (atmospheric
pressure). Starting, therefore, with the equilibrium FeO + Fe3O4 + CO + CO2 at a
temperature of about 670°, and then add carbon to the system, the reaction
C + CO2 = 2CO
will occur, because the concentration of CO2 is greater than what corresponds
with the system FeO + Fe3O4 + C in equilibrium with carbon monoxide and
dioxide. In consequence of this reaction, the equilibrium between FeO + Fe3O4
and the gas phase is disturbed, and the change in the composition of the gas phase
is opposed by the reaction Fe3O4 + CO = 3FeO + CO2, which continues until
either all the carbon or all the ferric oxide is used up. If the ferric oxide first
disappears, the equilibrium corresponds with a point on the dotted line in the
middle area of Fig. 121, which represents equilibria between FeO + C as solid
phases, and a mixture of carbon monoxide and dioxide as gas phase. If the
temperature is higher than 685°, at which temperature the curve for C—CO—
CO2 cuts that for Fe—FeO—CO—CO2; then, when all the ferric oxide has
disappeared, the concentration of CO2 is still too great for the coexistence of FeO
and C. Consequently, there occurs the reaction C + CO2 = 2CO, and the
composition of the gas phase alters until a point on the upper curve is reached. A
further increase in the concentration of CO is opposed by the reaction FeO + CO
= Fe + CO2, and the pressure remains constant until all the ferrous oxide is
reduced and only iron and carbon remain in equilibrium with gas. If the quantities
of the substances have been rightly chosen, we ultimately reach a point on the
dotted curve in the upper part of Fig. 121.
complete transformation to ferrous oxide finally occurs.
In another series of equilibria which can be obtained, carbon is one of the solid
phases. In Fig. 121 the equilibria between carbon, carbon monoxide, and carbon
dioxide under pressures of one and of a quarter atmosphere, are represented by
dotted lines.[379]
If we consider only the dotted line on the right, representing the equilibria under
atmospheric pressure, we see that the points in which the dotted line cuts the
other two curves must represent systems in which carbon monoxide and carbon
dioxide are in equilibrium with FeO + Fe3O4 + C, on the one hand, and with Fe +
FeO + C on the other. These systems can only exist at one definite temperature, if
we make the restriction that the pressure is maintained constant (atmospheric
pressure). Starting, therefore, with the equilibrium FeO + Fe3O4 + CO + CO2 at a
temperature of about 670°, and then add carbon to the system, the reaction
C + CO2 = 2CO
will occur, because the concentration of CO2 is greater than what corresponds
with the system FeO + Fe3O4 + C in equilibrium with carbon monoxide and
dioxide. In consequence of this reaction, the equilibrium between FeO + Fe3O4
and the gas phase is disturbed, and the change in the composition of the gas phase
is opposed by the reaction Fe3O4 + CO = 3FeO + CO2, which continues until
either all the carbon or all the ferric oxide is used up. If the ferric oxide first
disappears, the equilibrium corresponds with a point on the dotted line in the
middle area of Fig. 121, which represents equilibria between FeO + C as solid
phases, and a mixture of carbon monoxide and dioxide as gas phase. If the
temperature is higher than 685°, at which temperature the curve for C—CO—
CO2 cuts that for Fe—FeO—CO—CO2; then, when all the ferric oxide has
disappeared, the concentration of CO2 is still too great for the coexistence of FeO
and C. Consequently, there occurs the reaction C + CO2 = 2CO, and the
composition of the gas phase alters until a point on the upper curve is reached. A
further increase in the concentration of CO is opposed by the reaction FeO + CO
= Fe + CO2, and the pressure remains constant until all the ferrous oxide is
reduced and only iron and carbon remain in equilibrium with gas. If the quantities
of the substances have been rightly chosen, we ultimately reach a point on the
dotted curve in the upper part of Fig. 121.
Page 260
Fig. 121 shows us, also, what are the conditions under which the reduction of
ferric to ferrous oxide by carbon can occur. Let us suppose, for example, that we
start with a mixture of carbon monoxide and dioxide at about 600° (the lowest
point on the dotted line), and maintain the total pressure constant and equal to one
atmosphere. If the temperature is increased, the concentration of the carbon
dioxide will diminish, owing to the reaction C + CO2 = 2CO, but the ferric oxide
will undergo no change until the temperature reaches 647°, the point of
intersection of the dotted curve with the curve for FeO and Fe3O4. At this point
further increase in the concentration of carbon monoxide is opposed by the
reduction of ferric oxide in accordance with the equation Fe3O4 + CO = 3FeO +
CO2. The pressure, therefore, remains constant until all the ferric oxide has
disappeared. If the temperature is still further raised, we again obtain a univariant
system, FeO + C, in equilibrium with gas (univariant because the total pressure is
constant); and if the temperature is raised the composition of the gas must
undergo change. This is effected by the reaction C + CO2 = 2CO. When the
temperature rises to 685°, at which the dotted curve cuts the curve for Fe—FeO,
further change is prevented by the reaction FeO + CO = Fe + CO2. When all the
ferrous oxide is used up, we obtain the system Fe + C in equilibrium with gas. If
the temperature is now raised, the composition of the gas undergoes change, as
shown by the dotted line. The two temperatures, 647° and 685°, give, evidently,
the limits within which ferric or ferrous oxide can be reduced directly by carbon.
It is further evident that at any temperature to the right of the dotted line, carbon
is unstable in presence of iron or its oxides; while at temperatures lower than
those represented by the dotted line, it is stable. In the blast furnace, therefore,
separation of carbon can occur only at lower temperatures, and the carbon must
disappear on raising the temperature.
Finally, it may be remarked that the equilibrium curves show that ferrous oxide is
most easily reduced at 680°, since the concentration of the carbon monoxide
required at this temperature is a minimum. On the other hand, ferric oxide is
reduced with greatest difficulty at 490°, since at this temperature the requisite
concentration of carbon monoxide is a maximum.
Other equilibria between solid and gas phases are: Equilibrium between iron,
ferric oxide, water vapour, and hydrogen,[380] and the equilibria between carbon,
carbon monoxide, carbon dioxide, water vapour, and hydrogen,[381] which is of
importance for the manufacture of water gas.
ferric to ferrous oxide by carbon can occur. Let us suppose, for example, that we
start with a mixture of carbon monoxide and dioxide at about 600° (the lowest
point on the dotted line), and maintain the total pressure constant and equal to one
atmosphere. If the temperature is increased, the concentration of the carbon
dioxide will diminish, owing to the reaction C + CO2 = 2CO, but the ferric oxide
will undergo no change until the temperature reaches 647°, the point of
intersection of the dotted curve with the curve for FeO and Fe3O4. At this point
further increase in the concentration of carbon monoxide is opposed by the
reduction of ferric oxide in accordance with the equation Fe3O4 + CO = 3FeO +
CO2. The pressure, therefore, remains constant until all the ferric oxide has
disappeared. If the temperature is still further raised, we again obtain a univariant
system, FeO + C, in equilibrium with gas (univariant because the total pressure is
constant); and if the temperature is raised the composition of the gas must
undergo change. This is effected by the reaction C + CO2 = 2CO. When the
temperature rises to 685°, at which the dotted curve cuts the curve for Fe—FeO,
further change is prevented by the reaction FeO + CO = Fe + CO2. When all the
ferrous oxide is used up, we obtain the system Fe + C in equilibrium with gas. If
the temperature is now raised, the composition of the gas undergoes change, as
shown by the dotted line. The two temperatures, 647° and 685°, give, evidently,
the limits within which ferric or ferrous oxide can be reduced directly by carbon.
It is further evident that at any temperature to the right of the dotted line, carbon
is unstable in presence of iron or its oxides; while at temperatures lower than
those represented by the dotted line, it is stable. In the blast furnace, therefore,
separation of carbon can occur only at lower temperatures, and the carbon must
disappear on raising the temperature.
Finally, it may be remarked that the equilibrium curves show that ferrous oxide is
most easily reduced at 680°, since the concentration of the carbon monoxide
required at this temperature is a minimum. On the other hand, ferric oxide is
reduced with greatest difficulty at 490°, since at this temperature the requisite
concentration of carbon monoxide is a maximum.
Other equilibria between solid and gas phases are: Equilibrium between iron,
ferric oxide, water vapour, and hydrogen,[380] and the equilibria between carbon,
carbon monoxide, carbon dioxide, water vapour, and hydrogen,[381] which is of
importance for the manufacture of water gas.
Page 261
CHAPTER XVIII
SYSTEMS OF FOUR COMPONENTS
In the systems which have so far been studied, we have met with cases where two
or three components could enter into combination; but in no case did we find
double decomposition occurring. The reason of this is that in the systems
previously studied, in which double decomposition might have been possible,
namely in those systems in which two salts acted as components, the restriction
was imposed that either the basic or the acid constituent of these salts must be the
same; a restriction imposed, indeed, for the very purpose of excluding double
decomposition. Now, however, we shall allow this restriction to fall, thereby
extending the range of study.
Hitherto, in connection with four-component systems, the attention has been
directed solely to the study of aqueous solutions of salts, and more especially of
the salts which occur in sea-water, i.e. chiefly, the sulphates and chlorides of
magnesium, potassium, and sodium. The importance of these investigations will
be recognized when one recollects that by the evaporation of sea-water there have
been formed the enormous salt-beds at Stassfurt, which constitute at present the
chief source of the sulphates and chlorides of magnesium and potassium. The
investigations, therefore, are not only of great geological interest as tending to
elucidate the conditions under which these salt-beds have been formed, but are of
no less importance for the industrial working of the deposits.
It is, however, not the intention to enter here into any detailed description of the
different systems which have so far been studied, and of the sometimes very
complex relationships met with, but merely to refer briefly to some points of
more general import in connection with these systems.[382]
Reciprocal Salt-Pairs. Choice of Components.—When two salts undergo
double decomposition, the interaction can be expressed by an equation such as
NH4Cl + NaNO3 = NaCl + NH4NO3
Since one pair of salts—NaCl + NH4NO3—is formed from the other pair—
NH4Cl + NaNO3—by double decomposition, the two pairs of salts are known as
reciprocal salt-pairs.[383] It is with systems in which the component salts form
reciprocal salt-pairs that we have to deal here.
SYSTEMS OF FOUR COMPONENTS
In the systems which have so far been studied, we have met with cases where two
or three components could enter into combination; but in no case did we find
double decomposition occurring. The reason of this is that in the systems
previously studied, in which double decomposition might have been possible,
namely in those systems in which two salts acted as components, the restriction
was imposed that either the basic or the acid constituent of these salts must be the
same; a restriction imposed, indeed, for the very purpose of excluding double
decomposition. Now, however, we shall allow this restriction to fall, thereby
extending the range of study.
Hitherto, in connection with four-component systems, the attention has been
directed solely to the study of aqueous solutions of salts, and more especially of
the salts which occur in sea-water, i.e. chiefly, the sulphates and chlorides of
magnesium, potassium, and sodium. The importance of these investigations will
be recognized when one recollects that by the evaporation of sea-water there have
been formed the enormous salt-beds at Stassfurt, which constitute at present the
chief source of the sulphates and chlorides of magnesium and potassium. The
investigations, therefore, are not only of great geological interest as tending to
elucidate the conditions under which these salt-beds have been formed, but are of
no less importance for the industrial working of the deposits.
It is, however, not the intention to enter here into any detailed description of the
different systems which have so far been studied, and of the sometimes very
complex relationships met with, but merely to refer briefly to some points of
more general import in connection with these systems.[382]
Reciprocal Salt-Pairs. Choice of Components.—When two salts undergo
double decomposition, the interaction can be expressed by an equation such as
NH4Cl + NaNO3 = NaCl + NH4NO3
Since one pair of salts—NaCl + NH4NO3—is formed from the other pair—
NH4Cl + NaNO3—by double decomposition, the two pairs of salts are known as
reciprocal salt-pairs.[383] It is with systems in which the component salts form
reciprocal salt-pairs that we have to deal here.
Page 262
It must be noted, however, that the four salts formed by two reciprocal salt-pairs
do not constitute a system of four, but only of three components. This will be
understood if it is recalled that only so many constituents are taken as
components as are necessary to express the composition of all the phases present
(p. 12). It will be seen, now, that the composition of each of the four salts which
can be present together can be expressed in terms of three of them. Thus, for
example, in the case of NH4Cl, NaNO3, NH4NO3, NaCl, we can express the
composition of NH4Cl by NH4NO3 + NaCl - NaNO3; or of NaNO3 by NH4NO3 +
NaCl - NH4Cl. In all these cases it will be seen that negative quantities of one of
the components must be employed; but that we have seen to be quite permissible
(p. 12). The number of components is, therefore, three; but any three of the four
salts can be chosen.
Since, then, two reciprocal salt-pairs constitute only three components or
independently variable constituents, another component is necessary in order to
obtain a four-component system. As such, we shall choose water.
Transition Point.—In the case of the formation of double salts from two single
salts, we saw that there was a point—the quintuple point—at which five phases
could coexist. This point we also saw to be a transition point, on one side of
which the double salt, on the other side the two single salts in contact with
solution, were found to be the stable system. A similar behaviour is found in the
case of reciprocal salt-pairs. The four-component system, two reciprocal salt-pairs
and water, can give rise to an invariant system in which the six phases, four salts,
solution, vapour, can coexist; the temperature at which this is possible constitutes
a sextuple point. Now, this sextuple point is also a transition point, on the one side
of which the one salt-pair, on the other side the reciprocal salt-pair, is stable in
contact with solution.
The sextuple point is the point of intersection of the curves of six univariant
systems, viz. four solubility curves with three solid phases each, a vapour-
pressure curve for the system: two reciprocal salt-pairs—vapour; and a transition
curve for the condensed system: two reciprocal salt-pairs—solution. If we omit
the vapour phase and work under atmospheric pressure (in open vessels), we find
that the transition point is the point of intersection of four solubility curves.
Just as in the case of three-component systems we saw that the presence of one of
the single salts along with the double salt was necessary in order to give a
univariant system, so in the four-component systems the presence of a third salt is
necessary as solid phase along with one of the salt-pairs. In the case of the
reciprocal salt-pairs mentioned above, the transition point would be the point of
do not constitute a system of four, but only of three components. This will be
understood if it is recalled that only so many constituents are taken as
components as are necessary to express the composition of all the phases present
(p. 12). It will be seen, now, that the composition of each of the four salts which
can be present together can be expressed in terms of three of them. Thus, for
example, in the case of NH4Cl, NaNO3, NH4NO3, NaCl, we can express the
composition of NH4Cl by NH4NO3 + NaCl - NaNO3; or of NaNO3 by NH4NO3 +
NaCl - NH4Cl. In all these cases it will be seen that negative quantities of one of
the components must be employed; but that we have seen to be quite permissible
(p. 12). The number of components is, therefore, three; but any three of the four
salts can be chosen.
Since, then, two reciprocal salt-pairs constitute only three components or
independently variable constituents, another component is necessary in order to
obtain a four-component system. As such, we shall choose water.
Transition Point.—In the case of the formation of double salts from two single
salts, we saw that there was a point—the quintuple point—at which five phases
could coexist. This point we also saw to be a transition point, on one side of
which the double salt, on the other side the two single salts in contact with
solution, were found to be the stable system. A similar behaviour is found in the
case of reciprocal salt-pairs. The four-component system, two reciprocal salt-pairs
and water, can give rise to an invariant system in which the six phases, four salts,
solution, vapour, can coexist; the temperature at which this is possible constitutes
a sextuple point. Now, this sextuple point is also a transition point, on the one side
of which the one salt-pair, on the other side the reciprocal salt-pair, is stable in
contact with solution.
The sextuple point is the point of intersection of the curves of six univariant
systems, viz. four solubility curves with three solid phases each, a vapour-
pressure curve for the system: two reciprocal salt-pairs—vapour; and a transition
curve for the condensed system: two reciprocal salt-pairs—solution. If we omit
the vapour phase and work under atmospheric pressure (in open vessels), we find
that the transition point is the point of intersection of four solubility curves.
Just as in the case of three-component systems we saw that the presence of one of
the single salts along with the double salt was necessary in order to give a
univariant system, so in the four-component systems the presence of a third salt is
necessary as solid phase along with one of the salt-pairs. In the case of the
reciprocal salt-pairs mentioned above, the transition point would be the point of
Page 263
intersection of the solubility curves of the systems with the following groups of
salts as solid phases: Below the transition point: NH4Cl + NaNO3 + NaCl; NH4Cl
+ NaNO3 + NH4NO3; above the transition point: NaCl + NH4NO3 + NaNO3;
NaCl + NH4NO3 + NH4Cl. From this we see that the two salts NH4Cl and
NaNO3 would be able to exist together with solution below the transition point,
but not above it. This transition point has not been determined.
Formation of Double Salts.—In all cases of four-component systems so far
studied, the transition points have not been points at which one salt-pair passed
into its reciprocal, but at which a double salt was formed. Thus, at 4.4° Glauber's
salt and potassium chloride form glaserite and sodium chloride, according to the
equation
2Na2SO4,10H2O + 3KCl = K3Na(SO4)2 + 3NaCl + 20H2O
Above the transition point, therefore, there would be K3Na(SO4)2, NaCl and KCl;
and it may be considered that at a higher temperature the double salt would
interact with the potassium chloride according to the equation
K3Na(SO4)2 + KCl = 2K2SO4 + NaCl
thus giving the reciprocal of the original salt-pair. This point has, however, not
been experimentally realized.[384]
Transition Interval.—A double salt, we learned (p. 277), when brought in
contact with water at the transition point undergoes partial decomposition with
separation of one of the constituent salts; and only after a certain range of
temperature (transition interval) has been passed, can a pure saturated solution be
obtained. A similar behaviour is also found in the case of reciprocal salt-pairs. If
one of the salt-pairs is brought in contact with water at the transition point,
interaction will occur and one of the salts of the reciprocal salt-pair will be
deposited; and this will be the case throughout a certain range of temperature,
after which it will be possible to prepare a solution saturated only for the one salt-
pair. In the case of ammonium chloride and sodium nitrate the lower limit of the
transition interval is 5.5°, so that above this temperature and up to that of the
transition point (unknown), ammonium chloride and sodium nitrate in contact
with water would give rise to a third salt by double decomposition, in this case to
sodium chloride.[385]
salts as solid phases: Below the transition point: NH4Cl + NaNO3 + NaCl; NH4Cl
+ NaNO3 + NH4NO3; above the transition point: NaCl + NH4NO3 + NaNO3;
NaCl + NH4NO3 + NH4Cl. From this we see that the two salts NH4Cl and
NaNO3 would be able to exist together with solution below the transition point,
but not above it. This transition point has not been determined.
Formation of Double Salts.—In all cases of four-component systems so far
studied, the transition points have not been points at which one salt-pair passed
into its reciprocal, but at which a double salt was formed. Thus, at 4.4° Glauber's
salt and potassium chloride form glaserite and sodium chloride, according to the
equation
2Na2SO4,10H2O + 3KCl = K3Na(SO4)2 + 3NaCl + 20H2O
Above the transition point, therefore, there would be K3Na(SO4)2, NaCl and KCl;
and it may be considered that at a higher temperature the double salt would
interact with the potassium chloride according to the equation
K3Na(SO4)2 + KCl = 2K2SO4 + NaCl
thus giving the reciprocal of the original salt-pair. This point has, however, not
been experimentally realized.[384]
Transition Interval.—A double salt, we learned (p. 277), when brought in
contact with water at the transition point undergoes partial decomposition with
separation of one of the constituent salts; and only after a certain range of
temperature (transition interval) has been passed, can a pure saturated solution be
obtained. A similar behaviour is also found in the case of reciprocal salt-pairs. If
one of the salt-pairs is brought in contact with water at the transition point,
interaction will occur and one of the salts of the reciprocal salt-pair will be
deposited; and this will be the case throughout a certain range of temperature,
after which it will be possible to prepare a solution saturated only for the one salt-
pair. In the case of ammonium chloride and sodium nitrate the lower limit of the
transition interval is 5.5°, so that above this temperature and up to that of the
transition point (unknown), ammonium chloride and sodium nitrate in contact
with water would give rise to a third salt by double decomposition, in this case to
sodium chloride.[385]
Page 264
Graphic Representation.—For the graphic representation of systems of four
components, four axes may be chosen intersecting at a point like the edges of a
regular octahedron (Fig. 122).[386] Along these different axes the equivalent
molecular amounts of the different salts are measured.
To represent a given system consisting of
xB, yC, and zD in a given amount of
water (where B, C, and D represent
equivalent molecular amounts of the
salts), measure off on OB and OC lengths
equal to x and y respectively. The point of
Fig. 122.
intersection a (Fig. 122) represents a Fig. 123.
solution containing xB and yC (ab = x; ac
= y). From a a line aP is drawn parallel to OD and equal to z. P then represents
the solution of the above composition.
It is usual, however, not to employ the three-dimensional figure, but its horizontal
and vertical projections. Fig. 122, if projected on the base of the octahedron,
would yield a diagram such as is shown in Fig. 123. The projection of the edges
of the octahedron form two axes at right angles and give rise to four quadrants
similar to those employed for the representation of ternary solutions (p. 273).
Here, the point a represents a ternary solution saturated with respect to B and C;
and aP, quaternary solutions in equilibrium with the same two salts as solid
phases. Such a diagram represents the conditions of equilibrium only for one
definite temperature, and corresponds, therefore, to the isothermal diagrams for
ternary systems (p. 273). In such a diagram, since the temperature and pressure
are constant (vessels open to the air), a surface will represent a solution in
equilibrium with only one solid phase; a line, a solution with two solid phases,
and a point, one in equilibrium with three solid phases.
components, four axes may be chosen intersecting at a point like the edges of a
regular octahedron (Fig. 122).[386] Along these different axes the equivalent
molecular amounts of the different salts are measured.
To represent a given system consisting of
xB, yC, and zD in a given amount of
water (where B, C, and D represent
equivalent molecular amounts of the
salts), measure off on OB and OC lengths
equal to x and y respectively. The point of
Fig. 122.
intersection a (Fig. 122) represents a Fig. 123.
solution containing xB and yC (ab = x; ac
= y). From a a line aP is drawn parallel to OD and equal to z. P then represents
the solution of the above composition.
It is usual, however, not to employ the three-dimensional figure, but its horizontal
and vertical projections. Fig. 122, if projected on the base of the octahedron,
would yield a diagram such as is shown in Fig. 123. The projection of the edges
of the octahedron form two axes at right angles and give rise to four quadrants
similar to those employed for the representation of ternary solutions (p. 273).
Here, the point a represents a ternary solution saturated with respect to B and C;
and aP, quaternary solutions in equilibrium with the same two salts as solid
phases. Such a diagram represents the conditions of equilibrium only for one
definite temperature, and corresponds, therefore, to the isothermal diagrams for
ternary systems (p. 273). In such a diagram, since the temperature and pressure
are constant (vessels open to the air), a surface will represent a solution in
equilibrium with only one solid phase; a line, a solution with two solid phases,
and a point, one in equilibrium with three solid phases.
Page 265
Fig. 124.
Example.—As an example of the complete isothermal diagram, there may be
given one representing the equilibria in the system composed of water and the
reciprocal salt-pair sodium sulphate—potassium chloride for the temperature 0°
(Fig. 124).[387] The amounts of the different salts are measured along the four
axes, and the composition of the solution is expressed in equivalent gram-
molecules per 1000 gram-molecules of water.[388]
The outline of this figure represents four ternary solutions in which the
component salts have a common acid or basic constituent; viz. sodium chloride—
sodium sulphate, sodium sulphate—potassium sulphate, potassium sulphate—
potassium chloride, potassium chloride—sodium chloride. These four sets of
curves are therefore similar to those discussed in the previous chapter. In the case
of sodium and potassium sulphate, a double salt, glaserite [K3Na(SO4)2] is
formed. Whether glaserite is really a definite compound or not is still a matter of
doubt, since isomorphic mixtures of Na2SO4 and K2SO4 have been obtained.
According to van't Hoff and Barscholl,[389] glaserite is an isomorphous mixture;
but Gossner[390] considers it to be a definite compound having the formula
K3Na(SO4)2. Points VIII. and IX. represent solutions saturated with respect to
glaserite and sodium sulphate, and glaserite and potassium sulphate respectively.
The lines which pass inwards from these boundary curves represent solutions
containing three salts, but in contact with only two solid phases; and the points
where three lines meet, or where three fields meet, represent solutions in
Example.—As an example of the complete isothermal diagram, there may be
given one representing the equilibria in the system composed of water and the
reciprocal salt-pair sodium sulphate—potassium chloride for the temperature 0°
(Fig. 124).[387] The amounts of the different salts are measured along the four
axes, and the composition of the solution is expressed in equivalent gram-
molecules per 1000 gram-molecules of water.[388]
The outline of this figure represents four ternary solutions in which the
component salts have a common acid or basic constituent; viz. sodium chloride—
sodium sulphate, sodium sulphate—potassium sulphate, potassium sulphate—
potassium chloride, potassium chloride—sodium chloride. These four sets of
curves are therefore similar to those discussed in the previous chapter. In the case
of sodium and potassium sulphate, a double salt, glaserite [K3Na(SO4)2] is
formed. Whether glaserite is really a definite compound or not is still a matter of
doubt, since isomorphic mixtures of Na2SO4 and K2SO4 have been obtained.
According to van't Hoff and Barscholl,[389] glaserite is an isomorphous mixture;
but Gossner[390] considers it to be a definite compound having the formula
K3Na(SO4)2. Points VIII. and IX. represent solutions saturated with respect to
glaserite and sodium sulphate, and glaserite and potassium sulphate respectively.
The lines which pass inwards from these boundary curves represent solutions
containing three salts, but in contact with only two solid phases; and the points
where three lines meet, or where three fields meet, represent solutions in
Page 266
equilibrium with three solid phases; with the phases, namely, belonging to the
three concurrent fields.
If it is desired to represent a solution containing the salts say in the proportions,
51Na2Cl2, 9.5K2Cl2, 3.5K2SO4, the difficulty is met with that two of the salts,
sodium chloride and potassium sulphate, lie on opposite axes. To overcome this
difficulty the difference 51 - 3.5 = 47.5 is taken and measured off along the
sodium chloride axis; and the solution is therefore represented by the point
47.5Na2Cl2, 9.5K2Cl2. In order, therefore, to find the amount of potassium
sulphate present from such a diagram, it is necessary to know the total number of
salt molecules in the solution. When this is known, it is only necessary to subtract
from it the sum of the molecules of sodium and potassium chloride, and the result
is equal to twice the number of potassium sulphate molecules. Thus, in the above
example, the total number of salt molecules is 64. The number of molecules of
sodium and potassium chloride is 57; 64 - 57 = 7, and therefore the number of
potassium sulphate molecules is 3.5.
Another method of representation employed is to indicate the amounts of only
two of the salts in a plane diagram, and to measure off the total number of
molecules along a vertical axis. In this way a solid model is obtained.
The numerical data from which Fig. 124 was constructed are contained in the
following table, which gives the composition of the different solutions at 0°:—
[391]
Composition of solution in gram- Total
mols. number
Point. Solid phases. per 1000 gram-mols. water. of salt
Na2Cl2. K2Cl2. Na2SO4. K2SO4. molecules.
I. NaCl 55 — — — 55
II. KCl — 34.5 — — 34.5
III. Na2SO4,10H2O — — 6 — 6
IV. K2SO4 — — — 9 9
V. NaCl; KCl 46.5 12.5 — — 59
NaCl;
VI. Na2SO4,10H2O 47.5 — 8 — 55.5
VII. KCl; K2SO4 — 34.5 — 1 35.5
Glaserite;
VIII. — — 10 10 20
Na2SO4,10H2O
three concurrent fields.
If it is desired to represent a solution containing the salts say in the proportions,
51Na2Cl2, 9.5K2Cl2, 3.5K2SO4, the difficulty is met with that two of the salts,
sodium chloride and potassium sulphate, lie on opposite axes. To overcome this
difficulty the difference 51 - 3.5 = 47.5 is taken and measured off along the
sodium chloride axis; and the solution is therefore represented by the point
47.5Na2Cl2, 9.5K2Cl2. In order, therefore, to find the amount of potassium
sulphate present from such a diagram, it is necessary to know the total number of
salt molecules in the solution. When this is known, it is only necessary to subtract
from it the sum of the molecules of sodium and potassium chloride, and the result
is equal to twice the number of potassium sulphate molecules. Thus, in the above
example, the total number of salt molecules is 64. The number of molecules of
sodium and potassium chloride is 57; 64 - 57 = 7, and therefore the number of
potassium sulphate molecules is 3.5.
Another method of representation employed is to indicate the amounts of only
two of the salts in a plane diagram, and to measure off the total number of
molecules along a vertical axis. In this way a solid model is obtained.
The numerical data from which Fig. 124 was constructed are contained in the
following table, which gives the composition of the different solutions at 0°:—
[391]
Composition of solution in gram- Total
mols. number
Point. Solid phases. per 1000 gram-mols. water. of salt
Na2Cl2. K2Cl2. Na2SO4. K2SO4. molecules.
I. NaCl 55 — — — 55
II. KCl — 34.5 — — 34.5
III. Na2SO4,10H2O — — 6 — 6
IV. K2SO4 — — — 9 9
V. NaCl; KCl 46.5 12.5 — — 59
NaCl;
VI. Na2SO4,10H2O 47.5 — 8 — 55.5
VII. KCl; K2SO4 — 34.5 — 1 35.5
Glaserite;
VIII. — — 10 10 20
Na2SO4,10H2O
Page 267
IX. Glaserite; K2SO4 — — 7.5 10 17.5
Na2SO4,10H2O;
X. KCl; 51 9.5 — 3.5 64
NaCl
Na2SO4,10H2O;
XI. KCl; 40.5 13 — 3.5 57
glaserite
K2SO4; KCl;
XII. 18 23 — 3 44
glaserite
From the aspect of these diagrams the conditions under which the salts can
coexist can be read at a glance. Thus, for example, Fig. 124 shows that at 0°
Glauber's salt and potassium chloride can exist together with solution; namely, in
contact with solutions having the composition X—XI. This temperature must
therefore be below the transition point of this salt-pair (p. 314). On raising the
temperature to 4.4°, it is found that the curve VIII.—XI. moves so that the point
XI. coincides with point X. At this point, therefore, there will be four concurrent
fields, viz. Glauber's salt, potassium chloride, glaserite, and sodium chloride. But
these four salts can coexist with solution only at the transition point; so that 4.4°
is the transition temperature of the salt-pair: Glauber's salt—potassium chloride.
At higher temperatures the line VIII.—XI. moves still further to the left, so that
the field for Glauber's salt becomes entirely separated from the field for
potassium chloride. This shows that at temperatures above the transition point the
salt-pair Glauber's salt—potassium chloride cannot coexist in presence of
solution.
Fig. 125.
If it is only desired to indicate the mutual relationships of the different
components and the conditions for their coexistence (paragenesis), a simpler
diagram than Fig. 124 can be employed. Thus if the boundary curves of Fig. 124
are so drawn that they cut one another at right angles, a figure such as Fig. 125 is
obtained, the Roman numerals here corresponding with those in Fig. 124.
Na2SO4,10H2O;
X. KCl; 51 9.5 — 3.5 64
NaCl
Na2SO4,10H2O;
XI. KCl; 40.5 13 — 3.5 57
glaserite
K2SO4; KCl;
XII. 18 23 — 3 44
glaserite
From the aspect of these diagrams the conditions under which the salts can
coexist can be read at a glance. Thus, for example, Fig. 124 shows that at 0°
Glauber's salt and potassium chloride can exist together with solution; namely, in
contact with solutions having the composition X—XI. This temperature must
therefore be below the transition point of this salt-pair (p. 314). On raising the
temperature to 4.4°, it is found that the curve VIII.—XI. moves so that the point
XI. coincides with point X. At this point, therefore, there will be four concurrent
fields, viz. Glauber's salt, potassium chloride, glaserite, and sodium chloride. But
these four salts can coexist with solution only at the transition point; so that 4.4°
is the transition temperature of the salt-pair: Glauber's salt—potassium chloride.
At higher temperatures the line VIII.—XI. moves still further to the left, so that
the field for Glauber's salt becomes entirely separated from the field for
potassium chloride. This shows that at temperatures above the transition point the
salt-pair Glauber's salt—potassium chloride cannot coexist in presence of
solution.
Fig. 125.
If it is only desired to indicate the mutual relationships of the different
components and the conditions for their coexistence (paragenesis), a simpler
diagram than Fig. 124 can be employed. Thus if the boundary curves of Fig. 124
are so drawn that they cut one another at right angles, a figure such as Fig. 125 is
obtained, the Roman numerals here corresponding with those in Fig. 124.
Page 268
Ammonia-Soda Process.—One of the most important applications of the Phase
Rule to systems of four components with reciprocal salt-pairs has recently been
made by Fedotieff[392] in his investigations of the conditions for the formation of
sodium carbonate by the so-called ammonia-soda (Solvay) process.[393] This
process consists, as is well known, in passing carbon dioxide through a solution
of common salt saturated with ammonia.
Whatever differences of detail there may be in the process as carried out in
different manufactories, the reaction which forms the basis of the process is that
represented by the equation
NaCl + NH4HCO3 = NaHCO3 + NH4Cl
We are dealing here, therefore, with reciprocal salt-pairs, the behaviour of which
has just been discussed in the preceding pages. The present case is, however,
simpler than that of the salt-pair Na2SO4.10H2O + KCl, inasmuch as under the
conditions of experiment neither hydrates nor double salts are formed. Since the
study of the reaction is rendered more difficult on account of the fact that
ammonium bicarbonate in solution, when under atmospheric pressure, undergoes
decomposition at temperatures above 15°, this temperature was the one chosen
for the detailed investigation of the conditions of equilibrium. Since, further, it
has been shown by Bodländer[394] that the bicarbonates possess a definite
solubility only when the pressure of carbon dioxide in the solution has a definite
value, the measurements were carried out in solutions saturated with this gas.
This, however, does not constitute another component, because we have made the
restriction that the sum of the partial pressures of carbon dioxide and water
vapour is equal to 1 atmosphere. The concentration of the carbon dioxide is,
therefore, not independently variable (p. 10).
Rule to systems of four components with reciprocal salt-pairs has recently been
made by Fedotieff[392] in his investigations of the conditions for the formation of
sodium carbonate by the so-called ammonia-soda (Solvay) process.[393] This
process consists, as is well known, in passing carbon dioxide through a solution
of common salt saturated with ammonia.
Whatever differences of detail there may be in the process as carried out in
different manufactories, the reaction which forms the basis of the process is that
represented by the equation
NaCl + NH4HCO3 = NaHCO3 + NH4Cl
We are dealing here, therefore, with reciprocal salt-pairs, the behaviour of which
has just been discussed in the preceding pages. The present case is, however,
simpler than that of the salt-pair Na2SO4.10H2O + KCl, inasmuch as under the
conditions of experiment neither hydrates nor double salts are formed. Since the
study of the reaction is rendered more difficult on account of the fact that
ammonium bicarbonate in solution, when under atmospheric pressure, undergoes
decomposition at temperatures above 15°, this temperature was the one chosen
for the detailed investigation of the conditions of equilibrium. Since, further, it
has been shown by Bodländer[394] that the bicarbonates possess a definite
solubility only when the pressure of carbon dioxide in the solution has a definite
value, the measurements were carried out in solutions saturated with this gas.
This, however, does not constitute another component, because we have made the
restriction that the sum of the partial pressures of carbon dioxide and water
vapour is equal to 1 atmosphere. The concentration of the carbon dioxide is,
therefore, not independently variable (p. 10).
Page 269
Fig. 126.
In order to obtain the data necessary for a discussion of the conditions of soda
formation by the ammonia-soda process, solubility determinations with the four
salts, NaCl, NH4Cl, NH4HCO3, and NaHCO3 were made, first with the single
salts and then with the salts in pairs. The results obtained are represented
graphically in Fig. 126, which is an isothermal diagram similar to that given by
Fig. 124. The points I., II., III., IV., represent the composition of solutions in
equilibrium with two solid salts. We have, however, seen (p. 314) that the
transition point, when the experiment is carried out under constant pressure
(atmospheric pressure), is the point of intersection of four solubility curves, each
of which represents the composition of solutions in equilibrium with three salts,
viz. one of the reciprocal salt-pairs along with a third salt. Since, now, it was
found that the stable salt-pair at temperatures between 0° and 30° is sodium
bicarbonate and ammonium chloride, determinations were made of the
composition of solutions in equilibrium with NaHCO3 + NH4Cl + NH4HCO3 and
with NaHCO3 + NH4Cl + NaCl as solid phases. Under the conditions of
experiment (temperature = 15°) sodium chloride and ammonium bicarbonate
cannot coexist in contact with solution. These determinations gave the data
necessary for the construction of the complete isothermal diagram (Fig. 127). The
most important of these data are given in the following table (temperature, 15°):
—
Composition of solution in gram-mols.
Point. Solid phases. per 1000 gram-mols. water.
NaHCO3 NaCl NH4HCO3 NH4Cl
— NaHCO3 1.08 — — —
In order to obtain the data necessary for a discussion of the conditions of soda
formation by the ammonia-soda process, solubility determinations with the four
salts, NaCl, NH4Cl, NH4HCO3, and NaHCO3 were made, first with the single
salts and then with the salts in pairs. The results obtained are represented
graphically in Fig. 126, which is an isothermal diagram similar to that given by
Fig. 124. The points I., II., III., IV., represent the composition of solutions in
equilibrium with two solid salts. We have, however, seen (p. 314) that the
transition point, when the experiment is carried out under constant pressure
(atmospheric pressure), is the point of intersection of four solubility curves, each
of which represents the composition of solutions in equilibrium with three salts,
viz. one of the reciprocal salt-pairs along with a third salt. Since, now, it was
found that the stable salt-pair at temperatures between 0° and 30° is sodium
bicarbonate and ammonium chloride, determinations were made of the
composition of solutions in equilibrium with NaHCO3 + NH4Cl + NH4HCO3 and
with NaHCO3 + NH4Cl + NaCl as solid phases. Under the conditions of
experiment (temperature = 15°) sodium chloride and ammonium bicarbonate
cannot coexist in contact with solution. These determinations gave the data
necessary for the construction of the complete isothermal diagram (Fig. 127). The
most important of these data are given in the following table (temperature, 15°):
—
Composition of solution in gram-mols.
Point. Solid phases. per 1000 gram-mols. water.
NaHCO3 NaCl NH4HCO3 NH4Cl
— NaHCO3 1.08 — — —
Page 270
— NaCl — 6.12 — —
— NH4HCO3 — — 2.36 —
— NH4Cl — — — 6.64
I. NaHCO3; NaCl 0.12 6.06 — —
II. NaCl; NH4Cl — 4.55 — 3.72
III. NH4Cl; NH4HCO3 — — 0.81 6.40
IV. NaHCO3; NH4HCO3 0.71 — 2.16 —
NaHCO3; NH4HCO3;
P1 0.93 0.51 — 6.28
NH4Cl
P2 NaHCO3; NaCl; NH4Cl 0.18 4.44 — 3.73
With reference to the solution represented by the point P1, it may be remarked
that it is an incongruently saturated solution (p. 279). If sodium chloride is added
to this solution, the composition of the latter undergoes change; and if a sufficient
amount of the salt is added, the solution P2 is obtained.
Turning now to the practical application of the data so obtained, consider first
what is the influence of concentration on the yield of soda. Since the reaction
consists essentially in a double decomposition between sodium chloride and
ammonium bicarbonate, then, after the deposition of the sodium bicarbonate, we
obtain a solution containing sodium chloride, ammonium chloride, and sodium
bicarbonate. In order to ascertain to what extent the sodium chloride has been
converted into solid sodium bicarbonate, it is necessary to examine the
composition of the solution which is obtained with definite amounts of sodium
chloride and ammonium bicarbonate.
Fig. 127.
— NH4HCO3 — — 2.36 —
— NH4Cl — — — 6.64
I. NaHCO3; NaCl 0.12 6.06 — —
II. NaCl; NH4Cl — 4.55 — 3.72
III. NH4Cl; NH4HCO3 — — 0.81 6.40
IV. NaHCO3; NH4HCO3 0.71 — 2.16 —
NaHCO3; NH4HCO3;
P1 0.93 0.51 — 6.28
NH4Cl
P2 NaHCO3; NaCl; NH4Cl 0.18 4.44 — 3.73
With reference to the solution represented by the point P1, it may be remarked
that it is an incongruently saturated solution (p. 279). If sodium chloride is added
to this solution, the composition of the latter undergoes change; and if a sufficient
amount of the salt is added, the solution P2 is obtained.
Turning now to the practical application of the data so obtained, consider first
what is the influence of concentration on the yield of soda. Since the reaction
consists essentially in a double decomposition between sodium chloride and
ammonium bicarbonate, then, after the deposition of the sodium bicarbonate, we
obtain a solution containing sodium chloride, ammonium chloride, and sodium
bicarbonate. In order to ascertain to what extent the sodium chloride has been
converted into solid sodium bicarbonate, it is necessary to examine the
composition of the solution which is obtained with definite amounts of sodium
chloride and ammonium bicarbonate.
Fig. 127.
Page 271
Consider, in the first place, the solutions represented by the curve P2P1. With the
help of this curve we can state the conditions under which a solution, saturated
for ammonium chloride, is obtained, after deposition of sodium bicarbonate. In
the following table the composition of the solutions is given which are obtained
with different initial amounts of sodium chloride and ammonium bicarbonate.
The last two columns give the percentage amount of the sodium used, which is
deposited as solid sodium bicarbonate (UNa); and likewise the percentage amount
of ammonium bicarbonate which is usefully converted into sodium bicarbonate,
that is to say, the amount of the radical HCO3 deposited (UNH4):—
Initial composition Composition of solutions
of the solutions: obtained:
UNa UNH4
grams of salt to gram-equivalents per 1000
Point. 1000 grams per per
grams of water. of water. cent. cent.
NaCl NH4HCO3 HCO3 Cl Na NH4
P2 479 295 0.18 8.17 4.62 3.73 43.4 95.1
— 448 360 0.31 7.65 3.39 4.56 55.7 93.4
— 417 431 0.51 7.13 2.19 5.45 69.2 90.5
P1 397 496 0.92 6.79 1.44 6.28 78.8 85.1
This table shows that the greater the excess of sodium chloride, the greater is the
percentage utilization of ammonia (Point P2); and the more the amount of sodium
chloride decreases, the greater is the percentage amount of sodium chloride
converted into bicarbonate. In the latter case, however, the percentage utilization
of the ammonium bicarbonate decreases; that is to say, less sodium bicarbonate is
deposited, or more of it remains in solution.
Consider, in the same manner, the relations for solutions represented by the curve
P2IV, which gives the composition of solutions saturated with respect to sodium
bicarbonate and ammonium bicarbonate. In this case we obtain the following
results:—
Initial composition Composition of solutions
of the solutions: obtained:
UNa UNH4
grams of salt to gram-equivalents per 1000
Point. 1000 grams per per
grams of water. of water. cent. cent.
NaCl NH4HCO3 HCO3 Cl Na NH4
help of this curve we can state the conditions under which a solution, saturated
for ammonium chloride, is obtained, after deposition of sodium bicarbonate. In
the following table the composition of the solutions is given which are obtained
with different initial amounts of sodium chloride and ammonium bicarbonate.
The last two columns give the percentage amount of the sodium used, which is
deposited as solid sodium bicarbonate (UNa); and likewise the percentage amount
of ammonium bicarbonate which is usefully converted into sodium bicarbonate,
that is to say, the amount of the radical HCO3 deposited (UNH4):—
Initial composition Composition of solutions
of the solutions: obtained:
UNa UNH4
grams of salt to gram-equivalents per 1000
Point. 1000 grams per per
grams of water. of water. cent. cent.
NaCl NH4HCO3 HCO3 Cl Na NH4
P2 479 295 0.18 8.17 4.62 3.73 43.4 95.1
— 448 360 0.31 7.65 3.39 4.56 55.7 93.4
— 417 431 0.51 7.13 2.19 5.45 69.2 90.5
P1 397 496 0.92 6.79 1.44 6.28 78.8 85.1
This table shows that the greater the excess of sodium chloride, the greater is the
percentage utilization of ammonia (Point P2); and the more the amount of sodium
chloride decreases, the greater is the percentage amount of sodium chloride
converted into bicarbonate. In the latter case, however, the percentage utilization
of the ammonium bicarbonate decreases; that is to say, less sodium bicarbonate is
deposited, or more of it remains in solution.
Consider, in the same manner, the relations for solutions represented by the curve
P2IV, which gives the composition of solutions saturated with respect to sodium
bicarbonate and ammonium bicarbonate. In this case we obtain the following
results:—
Initial composition Composition of solutions
of the solutions: obtained:
UNa UNH4
grams of salt to gram-equivalents per 1000
Point. 1000 grams per per
grams of water. of water. cent. cent.
NaCl NH4HCO3 HCO3 Cl Na NH4
Page 272
P1 397 496 0.92 6.79 1.44 6.28 78.8 85.1
— 351 446 0.99 6.00 1.34 5.65 77.7 82.5
— 316 412 1.07 5.41 1.27 5.21 76.4 79.5
— 294 389 1.12 5.03 1.23 4.92 75.5 75.1
— 234 327 1.30 4.00 1.16 4.14 71.0 68.6
As is evident from this table, diminution in the relative amount of sodium
chloride exercises only a slight influence on the utilization of this salt, but is
accompanied by a rapid diminution of the effective transformation of the
ammonium bicarbonate. So far as the efficient conversion of the sodium is
concerned, we see that it reaches its maximum at the point P1, and that it
decreases both with increase and with decrease of the relative amount of sodium
chloride employed; and faster, indeed, in the former than in the latter case. On the
other hand, the effective transformation of the ammonium bicarbonate reaches its
maximum at the point P2, and diminishes with increase in the relative amount of
ammonium bicarbonate employed. Since sodium chloride is, in comparison with
ammonia—even when this is regenerated—a cheap material, it is evidently more
advantageous to work with solutions which are relatively rich in sodium chloride
(solutions represented by the curve P1P2). This fact has also been established
empirically.
When, as is the case in industrial practice, we are dealing with solutions which
are saturated not for two salts but only for sodium bicarbonate, it is evident that
we have then to do with solutions the composition of which is represented by
points in the area P1P2I,IV. Since in the commercial manufacture, the aim must be
to obtain as complete a utilization of the materials as possible, the solutions
employed industrially must lie in the neighbourhood of the curves P2P1IV, as is
indicated by the shaded portion in Fig. 127. The best results, from the
manufacturer's standpoint, will be obtained, as already stated, when the
composition of the solutions approaches that given by a point on the curve P2P1.
Considered from the chemical standpoint, the results of the experiments lead to
the conclusion that the Solvay process, i.e. passage of carbon dioxide through a
solution of sodium chloride saturated with ammonia, is not so good as the newer
method of Schlösing, which consists in bringing together sodium chloride and
ammonium bicarbonate with water.[395]
Preparation of Barium Nitrite.—Mention may also be made here of the
preparation of barium nitrite by double decomposition of barium chloride and
sodium nitrite.[396]
— 351 446 0.99 6.00 1.34 5.65 77.7 82.5
— 316 412 1.07 5.41 1.27 5.21 76.4 79.5
— 294 389 1.12 5.03 1.23 4.92 75.5 75.1
— 234 327 1.30 4.00 1.16 4.14 71.0 68.6
As is evident from this table, diminution in the relative amount of sodium
chloride exercises only a slight influence on the utilization of this salt, but is
accompanied by a rapid diminution of the effective transformation of the
ammonium bicarbonate. So far as the efficient conversion of the sodium is
concerned, we see that it reaches its maximum at the point P1, and that it
decreases both with increase and with decrease of the relative amount of sodium
chloride employed; and faster, indeed, in the former than in the latter case. On the
other hand, the effective transformation of the ammonium bicarbonate reaches its
maximum at the point P2, and diminishes with increase in the relative amount of
ammonium bicarbonate employed. Since sodium chloride is, in comparison with
ammonia—even when this is regenerated—a cheap material, it is evidently more
advantageous to work with solutions which are relatively rich in sodium chloride
(solutions represented by the curve P1P2). This fact has also been established
empirically.
When, as is the case in industrial practice, we are dealing with solutions which
are saturated not for two salts but only for sodium bicarbonate, it is evident that
we have then to do with solutions the composition of which is represented by
points in the area P1P2I,IV. Since in the commercial manufacture, the aim must be
to obtain as complete a utilization of the materials as possible, the solutions
employed industrially must lie in the neighbourhood of the curves P2P1IV, as is
indicated by the shaded portion in Fig. 127. The best results, from the
manufacturer's standpoint, will be obtained, as already stated, when the
composition of the solutions approaches that given by a point on the curve P2P1.
Considered from the chemical standpoint, the results of the experiments lead to
the conclusion that the Solvay process, i.e. passage of carbon dioxide through a
solution of sodium chloride saturated with ammonia, is not so good as the newer
method of Schlösing, which consists in bringing together sodium chloride and
ammonium bicarbonate with water.[395]
Preparation of Barium Nitrite.—Mention may also be made here of the
preparation of barium nitrite by double decomposition of barium chloride and
sodium nitrite.[396]
Page 273
The reaction with which we are dealing here is represented by the equation
BaCl2 + 2NaNO2 = 2NaCl + Ba(NO2)2
It was found that at the ordinary temperature NaCl and Ba(NO2)2 form the stable
salt-pair. If, therefore, barium chloride and sodium nitrite are brought together
with an amount of water insufficient for complete solution, transformation to the
stable salt-pair occurs, and sodium chloride and barium nitrite are deposited.
When, however, a stable salt-pair is in its transition interval (p. 315), a third salt
—in this case barium chloride—will be deposited, as we have already learned. On
bringing barium chloride and sodium nitrite together with water, therefore, three
solid phases are obtained, viz. BaCl2, NaCl, Ba(NO2)2. These three phases,
together with solution and vapour, constitute a univariant system, so that at each
temperature the composition of the solution must be constant.
Witt and Ludwig found that the presence of solid barium chloride can be
prevented by adding an excess of sodium nitrite, as can be readily foreseen from
what has been said. Since the solution in presence of the three solid phases must
have a definite composition at a definite temperature, the addition of sodium
nitrite to the solution must have, as its consequence, the solution of an equivalent
amount of barium chloride, and the deposition of an equivalent amount of sodium
chloride and barium nitrite. By sufficient addition of sodium nitrite, the complete
disappearance of the solid barium chloride can be effected, and there will remain
only the stable salt-pair sodium chloride and barium nitrite. As was pointed out by
Meyerhoffer, however, the disappearance of the barium chloride is effected, not
by a change in the composition of the solution, but by the necessity for the
composition of the solution remaining constant.
BaCl2 + 2NaNO2 = 2NaCl + Ba(NO2)2
It was found that at the ordinary temperature NaCl and Ba(NO2)2 form the stable
salt-pair. If, therefore, barium chloride and sodium nitrite are brought together
with an amount of water insufficient for complete solution, transformation to the
stable salt-pair occurs, and sodium chloride and barium nitrite are deposited.
When, however, a stable salt-pair is in its transition interval (p. 315), a third salt
—in this case barium chloride—will be deposited, as we have already learned. On
bringing barium chloride and sodium nitrite together with water, therefore, three
solid phases are obtained, viz. BaCl2, NaCl, Ba(NO2)2. These three phases,
together with solution and vapour, constitute a univariant system, so that at each
temperature the composition of the solution must be constant.
Witt and Ludwig found that the presence of solid barium chloride can be
prevented by adding an excess of sodium nitrite, as can be readily foreseen from
what has been said. Since the solution in presence of the three solid phases must
have a definite composition at a definite temperature, the addition of sodium
nitrite to the solution must have, as its consequence, the solution of an equivalent
amount of barium chloride, and the deposition of an equivalent amount of sodium
chloride and barium nitrite. By sufficient addition of sodium nitrite, the complete
disappearance of the solid barium chloride can be effected, and there will remain
only the stable salt-pair sodium chloride and barium nitrite. As was pointed out by
Meyerhoffer, however, the disappearance of the barium chloride is effected, not
by a change in the composition of the solution, but by the necessity for the
composition of the solution remaining constant.
Page 274
Fig. 128.
Barium Carbonate and Potassium Sulphate.—As has been found by
Meyerhoffer,[397] these two salts form the stable pair, not only at the ordinary
temperature, but also at the melting point. For the ordinary temperatures this was
proved in the following manner: A solution with the solid phases K2SO4 and
K2CO3.2H2O in excess can only coexist in contact either with BaCO3 or with
BaSO4, since, evidently, in one of the two groups the stable system must be
present. Two solutions were prepared, each with excess of K2SO4 +
K2CO3.2H2O, and to one was added BaCO3 and to the other BaSO4. After stirring
for a few days, the barium sulphate was completely transformed to BaCO3,
whereas the barium carbonate remained unchanged. Consequently, BaCO3 +
K2SO4 + K2CO3.2H2O is stable, and, therefore, so also is BaCO3 + K2SO4. That
BaCO3 + K2SO4 is the stable pair also at the melting point was proved by a
special analytical method which allows of the detection of K2CO3 in a mixture of
the four solid salts. This analysis showed that a mixture of BaCO3 + K2SO4, after
being fused and allowed to solidify, contains only small amounts of K2CO3; and
this is due entirely to the fact that BaCO3 + K2SO4 on fusion deposits a little
BaSO4, thereby giving rise at the same time to the separation of an equivalent
amount of K2CO3.
The different solubilities are shown in Fig. 128. In this diagram the solubility of
the two barium salts has been neglected. A is the solubility of K2CO3.2H2O;
addition of BaCO3 does not alter this. B is the solubility of K2CO3.2H2O +
Barium Carbonate and Potassium Sulphate.—As has been found by
Meyerhoffer,[397] these two salts form the stable pair, not only at the ordinary
temperature, but also at the melting point. For the ordinary temperatures this was
proved in the following manner: A solution with the solid phases K2SO4 and
K2CO3.2H2O in excess can only coexist in contact either with BaCO3 or with
BaSO4, since, evidently, in one of the two groups the stable system must be
present. Two solutions were prepared, each with excess of K2SO4 +
K2CO3.2H2O, and to one was added BaCO3 and to the other BaSO4. After stirring
for a few days, the barium sulphate was completely transformed to BaCO3,
whereas the barium carbonate remained unchanged. Consequently, BaCO3 +
K2SO4 + K2CO3.2H2O is stable, and, therefore, so also is BaCO3 + K2SO4. That
BaCO3 + K2SO4 is the stable pair also at the melting point was proved by a
special analytical method which allows of the detection of K2CO3 in a mixture of
the four solid salts. This analysis showed that a mixture of BaCO3 + K2SO4, after
being fused and allowed to solidify, contains only small amounts of K2CO3; and
this is due entirely to the fact that BaCO3 + K2SO4 on fusion deposits a little
BaSO4, thereby giving rise at the same time to the separation of an equivalent
amount of K2CO3.
The different solubilities are shown in Fig. 128. In this diagram the solubility of
the two barium salts has been neglected. A is the solubility of K2CO3.2H2O;
addition of BaCO3 does not alter this. B is the solubility of K2CO3.2H2O +
Page 275
K2SO4 + BaCO3. A and B almost coincide, since the potassium sulphate is very
slightly soluble in the concentrated solution of potassium carbonate. D gives the
concentration of the solution in equilibrium with K2SO4 + BaSO4. The most
interesting point is C. This solution is obtained by adding a small quantity of
water to BaCO3 + K2SO4, whereupon, being in the transition interval, BaSO4
separates out and an equivalent amount of K2CO3 goes into solution. C is the end
point of the curve CO, which is called the Guldberg-Waage curve, because these
investigators determined several points on it.
In their experiments, Guldberg and Waage found the ratio K2CO3 : K2SO4 in
solution to be constant and equal to 4. This result is, however, not exact, for the
curve CO is not a straight line, as it should be if the above ratio were constant; but
it is concave to the abscissa axis, and more so at lower than at higher
temperatures.
The following table refers to the temperature of 25°. The Roman numbers in the
first column refer to the points in Fig. 128. The numbers in the column Σk2 give
the amount, in gram-molecules, of K2CO3 + K2SO4 contained in 1000 gram-
molecules of water:—
Solubility Determinations at 25°.
100 gms. of the 1000 moles
solution of water
K2CO3
No. Solid phases. contain, contain, Σk2
in grams, in moles, K2SO4
K2CO3 K2SO4 K2CO3 K2SO4
K2CO3.2H2O + 147.9
I. 53.2 — — — —
BaCO3
K2CO3.2H2O
+ K2SO4 147.8
II. 53.0 0.023 0.051 — —
+ BaCO3
III. K2SO4 + 28.5 0.886 52.58 1.296 — —
IV. BaCO3 22.1 1.72 37.79 2.333 — —
BaCO3 +
V. K2SO4 + 17.81 2.485 29.11 3.220 32.32 9.03
BaSO4
slightly soluble in the concentrated solution of potassium carbonate. D gives the
concentration of the solution in equilibrium with K2SO4 + BaSO4. The most
interesting point is C. This solution is obtained by adding a small quantity of
water to BaCO3 + K2SO4, whereupon, being in the transition interval, BaSO4
separates out and an equivalent amount of K2CO3 goes into solution. C is the end
point of the curve CO, which is called the Guldberg-Waage curve, because these
investigators determined several points on it.
In their experiments, Guldberg and Waage found the ratio K2CO3 : K2SO4 in
solution to be constant and equal to 4. This result is, however, not exact, for the
curve CO is not a straight line, as it should be if the above ratio were constant; but
it is concave to the abscissa axis, and more so at lower than at higher
temperatures.
The following table refers to the temperature of 25°. The Roman numbers in the
first column refer to the points in Fig. 128. The numbers in the column Σk2 give
the amount, in gram-molecules, of K2CO3 + K2SO4 contained in 1000 gram-
molecules of water:—
Solubility Determinations at 25°.
100 gms. of the 1000 moles
solution of water
K2CO3
No. Solid phases. contain, contain, Σk2
in grams, in moles, K2SO4
K2CO3 K2SO4 K2CO3 K2SO4
K2CO3.2H2O + 147.9
I. 53.2 — — — —
BaCO3
K2CO3.2H2O
+ K2SO4 147.8
II. 53.0 0.023 0.051 — —
+ BaCO3
III. K2SO4 + 28.5 0.886 52.58 1.296 — —
IV. BaCO3 22.1 1.72 37.79 2.333 — —
BaCO3 +
V. K2SO4 + 17.81 2.485 29.11 3.220 32.32 9.03
BaSO4
Page 276
VI. K2SO4 + 12.6 3.92 19.66 4.853 — —
VII. BaSO4 5.85 6.76 8.724 7.995 — —
VIII. K2SO4 — 10.76 — 12.47 — —
IX. BaCO3 + 7.35 0.602 10.43 0.676 11.11 15.0
X. BaSO4 2.85 0.173 3.828 0.184 4.0 21.0
The Guldberg-Waage curve at 100° was also determined, and it was found that
the ratio K2CO3: K2SO4 is also not constant, although the variations are not so
great as at 25°.
Guldberg-Waage Curve at 100°.
100 moles of water
K2CO3
Solid phases. contain, in moles, Σk2
K2SO4
K2CO3 K2SO4
BaCO3 + K2SO4 + BaSO4 23.9 12.65 35.65 1.82
BaCO3 + BaSO4 6.28 2.02 8.3 3.1
" " 3.17 0.851 4.025 3.7
APPENDIX
EXPERIMENTAL DETERMINATION OF THE TRANSITION POINT
For the purpose of determining the transition temperature, a number of methods
have been employed, and the most important of these will be briefly described
here. In any given case it is sometimes possible to employ more than one method,
but all are not equally suitable, and the values of the transition point obtained by
the different methods are not always identical. Indeed, a difference of several
degrees in the value found may quite well occur.[398] In each case, therefore,
some care must be taken to select the method most suitable for the purpose.
I. The Dilatometric Method.—Since, in the majority of cases, transformation at
the transition point is accompanied by an appreciable change of volume, it is only
necessary to ascertain the temperature at which this change of volume occurs, in
order to determine the transition point. For this purpose the dilatometer is
employed, an apparatus which consists of a bulb with capillary tube attached, and
VII. BaSO4 5.85 6.76 8.724 7.995 — —
VIII. K2SO4 — 10.76 — 12.47 — —
IX. BaCO3 + 7.35 0.602 10.43 0.676 11.11 15.0
X. BaSO4 2.85 0.173 3.828 0.184 4.0 21.0
The Guldberg-Waage curve at 100° was also determined, and it was found that
the ratio K2CO3: K2SO4 is also not constant, although the variations are not so
great as at 25°.
Guldberg-Waage Curve at 100°.
100 moles of water
K2CO3
Solid phases. contain, in moles, Σk2
K2SO4
K2CO3 K2SO4
BaCO3 + K2SO4 + BaSO4 23.9 12.65 35.65 1.82
BaCO3 + BaSO4 6.28 2.02 8.3 3.1
" " 3.17 0.851 4.025 3.7
APPENDIX
EXPERIMENTAL DETERMINATION OF THE TRANSITION POINT
For the purpose of determining the transition temperature, a number of methods
have been employed, and the most important of these will be briefly described
here. In any given case it is sometimes possible to employ more than one method,
but all are not equally suitable, and the values of the transition point obtained by
the different methods are not always identical. Indeed, a difference of several
degrees in the value found may quite well occur.[398] In each case, therefore,
some care must be taken to select the method most suitable for the purpose.
I. The Dilatometric Method.—Since, in the majority of cases, transformation at
the transition point is accompanied by an appreciable change of volume, it is only
necessary to ascertain the temperature at which this change of volume occurs, in
order to determine the transition point. For this purpose the dilatometer is
employed, an apparatus which consists of a bulb with capillary tube attached, and
Page 277
which constitutes a sort of large thermometer (Fig. 129). Some of the substance to
be examined is passed into the bulb A through the tube B, which is then sealed
off. The rest of the bulb and a small portion of the capillary tube is then filled
with some liquid, which, of course, must be without chemical action on the
substance under investigation. A liquid, however, may be employed which
dissolves the substance, for, as we have seen (p. 70), the transformation at the
transition point is, as a rule, accelerated by the presence of a solvent. On the other
hand, the liquid must not dissolve in the substance under examination, for the
temperature of transformation would be thereby altered.
In using the dilatometer, two methods of procedure may be followed. According
to the first method, the dilatometer containing the form stable at lower
temperatures is placed in a thermostat, maintained at a constant temperature, until
it has taken the temperature of the bath. The height of the meniscus is then read
on a millimetre scale attached to the capillary. The temperature of the thermostat
is then raised degree by degree, and the height of the meniscus at each point
ascertained. If, now, no change takes place in the solid, the expansion will be
practically uniform, or the rise in the level of the meniscus per degree of
temperature will be practically the same at the different temperatures, as
represented diagrammatically by the line AB in Fig. 130. On passing through the
transition point, however, there will be a more or less sudden increase in the rise
of the meniscus per degree (line BC) if the specific volume of the form stable at
higher temperatures is greater than that of the original modification; thereafter,
the expansion will again be uniform (line CD). Similarly, on cooling, contraction
will at first be uniform and then at the transition point there will be a relatively
large diminution of volume.
Fig.
129.
be examined is passed into the bulb A through the tube B, which is then sealed
off. The rest of the bulb and a small portion of the capillary tube is then filled
with some liquid, which, of course, must be without chemical action on the
substance under investigation. A liquid, however, may be employed which
dissolves the substance, for, as we have seen (p. 70), the transformation at the
transition point is, as a rule, accelerated by the presence of a solvent. On the other
hand, the liquid must not dissolve in the substance under examination, for the
temperature of transformation would be thereby altered.
In using the dilatometer, two methods of procedure may be followed. According
to the first method, the dilatometer containing the form stable at lower
temperatures is placed in a thermostat, maintained at a constant temperature, until
it has taken the temperature of the bath. The height of the meniscus is then read
on a millimetre scale attached to the capillary. The temperature of the thermostat
is then raised degree by degree, and the height of the meniscus at each point
ascertained. If, now, no change takes place in the solid, the expansion will be
practically uniform, or the rise in the level of the meniscus per degree of
temperature will be practically the same at the different temperatures, as
represented diagrammatically by the line AB in Fig. 130. On passing through the
transition point, however, there will be a more or less sudden increase in the rise
of the meniscus per degree (line BC) if the specific volume of the form stable at
higher temperatures is greater than that of the original modification; thereafter,
the expansion will again be uniform (line CD). Similarly, on cooling, contraction
will at first be uniform and then at the transition point there will be a relatively
large diminution of volume.
Fig.
129.
Page 278
Fig. 130.
If, now, transformation occurred immediately the transition point was reached,
the sudden expansion and contraction would take place at the same temperature.
It is, however, generally found that there is a lag, and that with rising temperature
the relatively large expansion does not take place until a temperature somewhat
higher than the transition point; and with falling temperature the contraction
occurs at a temperature somewhat below the transition point. This is represented
in Fig. 130 by the lines BC and EF. The amount of lag will vary from case to
case, and will also depend on the length of time during which the dilatometer is
maintained at constant temperature.
As an example, there may be given the results obtained in the determination of
the transition point at which sodium sulphate and magnesium sulphate form
astracanite (p. 268).[399] The dilatometer was charged with a mixture of the two
sulphates.
Temperature. Level of oil in capillary. Rise per 1°.
15.6° 134
7
16.6° 141
7
17.6° 148
6
18.6° 154
7
19.6° 161
7
20.6° 168
73
21.6° 241
2
22.6° 243
8
23.6° 251
8
24.6° 259
The transition point, therefore, lies about 21.6° (p. 268).
The second method of manipulation depends on the fact that, while above or
below the transition point transformation of one form into the other can take
place, at the transition point the two forms undergo no change. The bulb of the
If, now, transformation occurred immediately the transition point was reached,
the sudden expansion and contraction would take place at the same temperature.
It is, however, generally found that there is a lag, and that with rising temperature
the relatively large expansion does not take place until a temperature somewhat
higher than the transition point; and with falling temperature the contraction
occurs at a temperature somewhat below the transition point. This is represented
in Fig. 130 by the lines BC and EF. The amount of lag will vary from case to
case, and will also depend on the length of time during which the dilatometer is
maintained at constant temperature.
As an example, there may be given the results obtained in the determination of
the transition point at which sodium sulphate and magnesium sulphate form
astracanite (p. 268).[399] The dilatometer was charged with a mixture of the two
sulphates.
Temperature. Level of oil in capillary. Rise per 1°.
15.6° 134
7
16.6° 141
7
17.6° 148
6
18.6° 154
7
19.6° 161
7
20.6° 168
73
21.6° 241
2
22.6° 243
8
23.6° 251
8
24.6° 259
The transition point, therefore, lies about 21.6° (p. 268).
The second method of manipulation depends on the fact that, while above or
below the transition point transformation of one form into the other can take
place, at the transition point the two forms undergo no change. The bulb of the
Page 279
dilatometer is, therefore, charged with a mixture of the stable and metastable
forms and a suitable liquid, and is then immersed in a bath at constant
temperature. After the temperature of the bath has been acquired, readings of the
height of the meniscus are made from time to time to ascertain whether expansion
or contraction occurs. If expansion is found, the temperature of the thermostat is
altered until a temperature is obtained at which a gradual contraction takes place.
The transition point must then lie between these two temperatures; and by
repeating the determinations it will be possible to reduce the difference between
the temperatures at which expansion and contraction take place to, say, 1°, and to
fix the temperature of the transition point, therefore, to within half a degree. By
this method the transition point, for example, of sulphur was found to be 95.6°
under a pressure of 4 atm.[400] The following are the figures obtained by Reicher,
who used a mixture of 1 part of carbon disulphide (solvent for sulphur) and 5
parts of turpentine as the measuring liquid.
Temperature 95.1°.
Time in minutes. Level of liquid.
5 343.5
30 340.5
55 335.75
65 333
Temperature 96.1°.
Time in minutes. Level of liquid.
5 342.75
30 354.75
55 360.5
60 361.5
Temperature 95.6°.
Time in minutes. Level of liquid.
5 368.75
100 368
110 368.75
At a temperature of 95.1° there is a contraction, i.e. monoclinic sulphur passes
into the rhombic, the specific volume of the former being greater than that of the
forms and a suitable liquid, and is then immersed in a bath at constant
temperature. After the temperature of the bath has been acquired, readings of the
height of the meniscus are made from time to time to ascertain whether expansion
or contraction occurs. If expansion is found, the temperature of the thermostat is
altered until a temperature is obtained at which a gradual contraction takes place.
The transition point must then lie between these two temperatures; and by
repeating the determinations it will be possible to reduce the difference between
the temperatures at which expansion and contraction take place to, say, 1°, and to
fix the temperature of the transition point, therefore, to within half a degree. By
this method the transition point, for example, of sulphur was found to be 95.6°
under a pressure of 4 atm.[400] The following are the figures obtained by Reicher,
who used a mixture of 1 part of carbon disulphide (solvent for sulphur) and 5
parts of turpentine as the measuring liquid.
Temperature 95.1°.
Time in minutes. Level of liquid.
5 343.5
30 340.5
55 335.75
65 333
Temperature 96.1°.
Time in minutes. Level of liquid.
5 342.75
30 354.75
55 360.5
60 361.5
Temperature 95.6°.
Time in minutes. Level of liquid.
5 368.75
100 368
110 368.75
At a temperature of 95.1° there is a contraction, i.e. monoclinic sulphur passes
into the rhombic, the specific volume of the former being greater than that of the
Page 280
latter. At 96.1°, however, there is expansion, showing that at this temperature
rhombic sulphur passes into monoclinic; while at 95.6° there is neither expansion
nor contraction. This is, therefore, the transition temperature; and since the
dilatometer was sealed up to prevent evaporation of the liquid, the pressure within
it was 4 atm.
II. Measurement of the Vapour Pressure.—In the preceding pages it has been
seen repeatedly that the vapour pressures of the two systems undergoing
reciprocal transformation become identical at the transition point (more strictly, at
the triple or multiple point), and the latter can therefore be determined by
ascertaining the temperature at which this identity of vapour pressure is
established. The apparatus usually employed for this purpose is the Bremer-
Frowein tensimeter (p. 91).
Although this method has not as yet been applied to systems of one component, it
has been used to a considerable extent in the case of systems containing water or
other volatile component. An example of this has already been given in Glauber's
salt (p. 139).
III. Solubility Measurements.—The temperature of the transition point can also
be fixed by means of solubility measurements, for at that point the solubility of
the two systems becomes identical. Reference has already been made to several
cases in which this method was employed, e.g. ammonium nitrate (p. 112),
Glauber's salt (p. 134), astracanite and sodium and magnesium sulphates (p. 268).
The determinations of the solubility can be carried out in various ways. One of
the simplest methods, which also gives sufficiently accurate results when the
temperature is not high or when the solvent is not very volatile, can be carried out
in the following manner. The solid substance is finely powdered (in order to
accelerate the process of solution), and placed in sufficient quantity along with
the solvent in a tube carefully closed by a glass stopper; the latter is protected by
a rubber cap, such as a rubber finger-stall. The tube is then rotated in a
thermostat, the temperature of which does not vary more than one or two tenths
of a degree, until saturation is produced. The solution is withdrawn by means of a
pipette to which a small glass tube, filled with cotton wool to act as a filter, is
attached. The solution is then run into a weighing bottle, and weighed; after
which the amount of solid in solution is determined in a suitable manner.
For more accurate determinations of the solubility, especially when the solvent is
appreciably volatile at the temperature of experiment, other methods are
preferable. In Fig. 131 is shown the apparatus employed by H. Goldschmidt,[401]
rhombic sulphur passes into monoclinic; while at 95.6° there is neither expansion
nor contraction. This is, therefore, the transition temperature; and since the
dilatometer was sealed up to prevent evaporation of the liquid, the pressure within
it was 4 atm.
II. Measurement of the Vapour Pressure.—In the preceding pages it has been
seen repeatedly that the vapour pressures of the two systems undergoing
reciprocal transformation become identical at the transition point (more strictly, at
the triple or multiple point), and the latter can therefore be determined by
ascertaining the temperature at which this identity of vapour pressure is
established. The apparatus usually employed for this purpose is the Bremer-
Frowein tensimeter (p. 91).
Although this method has not as yet been applied to systems of one component, it
has been used to a considerable extent in the case of systems containing water or
other volatile component. An example of this has already been given in Glauber's
salt (p. 139).
III. Solubility Measurements.—The temperature of the transition point can also
be fixed by means of solubility measurements, for at that point the solubility of
the two systems becomes identical. Reference has already been made to several
cases in which this method was employed, e.g. ammonium nitrate (p. 112),
Glauber's salt (p. 134), astracanite and sodium and magnesium sulphates (p. 268).
The determinations of the solubility can be carried out in various ways. One of
the simplest methods, which also gives sufficiently accurate results when the
temperature is not high or when the solvent is not very volatile, can be carried out
in the following manner. The solid substance is finely powdered (in order to
accelerate the process of solution), and placed in sufficient quantity along with
the solvent in a tube carefully closed by a glass stopper; the latter is protected by
a rubber cap, such as a rubber finger-stall. The tube is then rotated in a
thermostat, the temperature of which does not vary more than one or two tenths
of a degree, until saturation is produced. The solution is withdrawn by means of a
pipette to which a small glass tube, filled with cotton wool to act as a filter, is
attached. The solution is then run into a weighing bottle, and weighed; after
which the amount of solid in solution is determined in a suitable manner.
For more accurate determinations of the solubility, especially when the solvent is
appreciably volatile at the temperature of experiment, other methods are
preferable. In Fig. 131 is shown the apparatus employed by H. Goldschmidt,[401]
Page 281
and used to a considerable extent in the laboratory of van't Hoff. This consists
essentially of three parts: a, a tube in which the solvent and salt are placed; this is
closed at the foot by an india-rubber stopper. Through this stopper there passes
the bent tube cb, which connects the tube a with the weighing-tube d. At c there is
a plug of cotton wool. Tube e is open to the air. The wider portion of the tube cb,
which passes through the rubber stopper in a, can be closed by a plug attached to
a glass rod ff, which passes up through a hollow Witt stirrer, g. After being fitted
together, the whole apparatus is immersed in the thermostat. After the solution
has become saturated, the stopper of the bent tube is raised by means of the rod ff
and a suction-pump attached to the end of e. The solution is thereby drawn into
the weighing-tube d, the undissolved salt being retained by the plug at c. The
apparatus is then removed from the thermostat, tube d detached and immediately
closed by a ground stopper. It is then carefully dried and weighed.
Fig. 131.
Another form of solubility vessel, due to Meyerhoffer and Saunders, is shown in
Fig. 132.[402] This consists of a single tube, and the stirring is effected by means
of a glass screw.
essentially of three parts: a, a tube in which the solvent and salt are placed; this is
closed at the foot by an india-rubber stopper. Through this stopper there passes
the bent tube cb, which connects the tube a with the weighing-tube d. At c there is
a plug of cotton wool. Tube e is open to the air. The wider portion of the tube cb,
which passes through the rubber stopper in a, can be closed by a plug attached to
a glass rod ff, which passes up through a hollow Witt stirrer, g. After being fitted
together, the whole apparatus is immersed in the thermostat. After the solution
has become saturated, the stopper of the bent tube is raised by means of the rod ff
and a suction-pump attached to the end of e. The solution is thereby drawn into
the weighing-tube d, the undissolved salt being retained by the plug at c. The
apparatus is then removed from the thermostat, tube d detached and immediately
closed by a ground stopper. It is then carefully dried and weighed.
Fig. 131.
Another form of solubility vessel, due to Meyerhoffer and Saunders, is shown in
Fig. 132.[402] This consists of a single tube, and the stirring is effected by means
of a glass screw.
Page 282
Fig. 132.
The progress of the solution towards saturation can be very well tested by
determining the density of the solution from time to time. This is most
conveniently carried out by means of the pipette shown in Fig. 133.[403] With this
pipette the solution can not only be removed for weighing, but the volume can be
determined at the same time. It consists of the wide tube a, to which the
graduated capillary b, furnished with a cap c, is attached. To the lower end of the
pipette the tube e, with plug of cotton wool, can be fixed. After the pipette has
been filled by sucking at the end of b, the stop-cock d is closed and the cap c
placed on the capillary. The apparatus can then be weighed, and the volume of the
solution be ascertained by means of the graduations.
As has already been insisted, particular care must be paid to the characterization
of the solid in contact with the solution.
Fig. 133.
IV. Thermometric Method.—If a substance is heated, its temperature will
gradually rise until the melting point is reached, and the temperature will then
The progress of the solution towards saturation can be very well tested by
determining the density of the solution from time to time. This is most
conveniently carried out by means of the pipette shown in Fig. 133.[403] With this
pipette the solution can not only be removed for weighing, but the volume can be
determined at the same time. It consists of the wide tube a, to which the
graduated capillary b, furnished with a cap c, is attached. To the lower end of the
pipette the tube e, with plug of cotton wool, can be fixed. After the pipette has
been filled by sucking at the end of b, the stop-cock d is closed and the cap c
placed on the capillary. The apparatus can then be weighed, and the volume of the
solution be ascertained by means of the graduations.
As has already been insisted, particular care must be paid to the characterization
of the solid in contact with the solution.
Fig. 133.
IV. Thermometric Method.—If a substance is heated, its temperature will
gradually rise until the melting point is reached, and the temperature will then
Page 283
remain constant until all the solid has passed into liquid. Similarly, if a substance
which can undergo transformation is heated, the temperature will rise until the
transition point is reached, and will then remain constant until complete
transformation has taken place.
This method, it will be remembered, was employed by Richards for the
determination of the transition point of sodium sulphate decahydrate (p. 136). The
following figures give the results obtained by Meyerhoffer in the case of the
transformation:—
CuK2Cl4,2H2O CuKCl3 + KCl + 2H2O
the temperature being noted from minute to minute: 95°, 93°, 91.8°, 91.7°, 92°,
92.3°, 92.4°, 92.2°, 92.2°, 92°, 90.5°, 89°, and then a rapid fall in the temperature.
From this we see that the transition point is about 92.2°. It is also evident that a
slight supercooling took place (91.7°), owing to a delay in the transformation, but
that then the temperature rose to the transition point. This is analogous to the
supercooling of a liquid.
A similar halt in the temperature would be observed on passing from lower to
higher temperatures; but owing to a lag in the transformation, the same
temperature is not always obtained.
V. Optical Method.—The transition point can sometimes be determined by
noting the temperature at which some alteration in the appearance of the
substance occurs, such as a change of colour or of the crystalline form. Thus
mercuric iodide changes colour from red to yellow, and the blue quadratic
crystals of copper calcium acetate change, on passing the transition point, into
green rhombs of copper acetate and white needles of calcium acetate (p. 260). Or
again, changes in the double refraction of the crystals may be also employed to
ascertain the temperature of the transition point. These changes are best observed
by means of a microscope.
For the purpose of regulating the temperature of the substance a small copper air-
bath is employed.[404]
VI. Electrical Methods.—Electrical methods for the determination of the
transition point are of two kinds, based on measurements of conductivity or of
electromotive force. Both methods are restricted in their application, but where
applicable give very exact results.
which can undergo transformation is heated, the temperature will rise until the
transition point is reached, and will then remain constant until complete
transformation has taken place.
This method, it will be remembered, was employed by Richards for the
determination of the transition point of sodium sulphate decahydrate (p. 136). The
following figures give the results obtained by Meyerhoffer in the case of the
transformation:—
CuK2Cl4,2H2O CuKCl3 + KCl + 2H2O
the temperature being noted from minute to minute: 95°, 93°, 91.8°, 91.7°, 92°,
92.3°, 92.4°, 92.2°, 92.2°, 92°, 90.5°, 89°, and then a rapid fall in the temperature.
From this we see that the transition point is about 92.2°. It is also evident that a
slight supercooling took place (91.7°), owing to a delay in the transformation, but
that then the temperature rose to the transition point. This is analogous to the
supercooling of a liquid.
A similar halt in the temperature would be observed on passing from lower to
higher temperatures; but owing to a lag in the transformation, the same
temperature is not always obtained.
V. Optical Method.—The transition point can sometimes be determined by
noting the temperature at which some alteration in the appearance of the
substance occurs, such as a change of colour or of the crystalline form. Thus
mercuric iodide changes colour from red to yellow, and the blue quadratic
crystals of copper calcium acetate change, on passing the transition point, into
green rhombs of copper acetate and white needles of calcium acetate (p. 260). Or
again, changes in the double refraction of the crystals may be also employed to
ascertain the temperature of the transition point. These changes are best observed
by means of a microscope.
For the purpose of regulating the temperature of the substance a small copper air-
bath is employed.[404]
VI. Electrical Methods.—Electrical methods for the determination of the
transition point are of two kinds, based on measurements of conductivity or of
electromotive force. Both methods are restricted in their application, but where
applicable give very exact results.
Page 284
The former method, which has been employed in several cases, need not be
described here. The second method, however, is of considerable interest and
importance, and calls for special reference.[405]
If two pieces, say, of zinc, connected together by a conducting wire, are placed in
a solution of a zinc salt, e.g. zinc sulphate, the potential of the two electrodes will
be the same, and no current will be produced in the connecting wire. If, however,
the zinc electrodes are immersed in two solutions of different concentration
contained in separate vessels, but placed in connection with one another by means
of a bent tube filled with a conducting solution, the potentials at the electrodes
will no longer be the same, and a current will now flow through the connecting
wire. The direction of this current in the cell will be from the weaker to the more
concentrated solution.
The greater the difference in the concentration of the solutions with respect to
zinc, the greater will be the difference of the potential at the two electrodes, or the
greater will be the E.M.F. of the cell. When the concentration of the two solutions
becomes the same, the E.M.F. will become zero, and no current will pass.
It will be understood now how this method can be made use of for determining
the transition point of a salt, when we bear in mind that at the transition point the
solubility of the two forms becomes identical. Thus, for example, the transition
point of zinc sulphate heptahydrate into hexahydrate could be determined in the
following manner. Tube A (Fig. 134) contains, say, a saturated solution of the
heptahydrate along with some of the solid salt; tube B, a saturated solution of the
hexahydrate along with the solid salt. The tube C is a connecting tube bent
downwards so as to prevent the mixing of the solutions by convection currents.
ZZ are two zinc electrodes immersed in the solution; the cell is placed in a
thermostat and the zinc electrodes connected with a galvanometer. Since, now, at
temperatures below the transition point the solubility of the hexahydrate (the
metastable form) is greater than that of the heptahydrate, a current will be
produced, flowing in the cell from heptahydrate to hexahydrate. As the
temperature is raised towards the transition point, the solubilities of the two
hydrates also approach, and the current produced will therefore become weaker,
because the E.M.F. of the cell becomes less; and when the transition point is
attained, the E.M.F. becomes zero, and the current ceases. If the temperature is
raised above this, the solubility of the heptahydrate becomes greater than that of
the hexahydrate, and a current will again be produced, but in the opposite
direction. By noting the temperature, therefore, at which the current ceases, or the
E.M.F. becomes zero, the transition temperature can be ascertained.[406]
described here. The second method, however, is of considerable interest and
importance, and calls for special reference.[405]
If two pieces, say, of zinc, connected together by a conducting wire, are placed in
a solution of a zinc salt, e.g. zinc sulphate, the potential of the two electrodes will
be the same, and no current will be produced in the connecting wire. If, however,
the zinc electrodes are immersed in two solutions of different concentration
contained in separate vessels, but placed in connection with one another by means
of a bent tube filled with a conducting solution, the potentials at the electrodes
will no longer be the same, and a current will now flow through the connecting
wire. The direction of this current in the cell will be from the weaker to the more
concentrated solution.
The greater the difference in the concentration of the solutions with respect to
zinc, the greater will be the difference of the potential at the two electrodes, or the
greater will be the E.M.F. of the cell. When the concentration of the two solutions
becomes the same, the E.M.F. will become zero, and no current will pass.
It will be understood now how this method can be made use of for determining
the transition point of a salt, when we bear in mind that at the transition point the
solubility of the two forms becomes identical. Thus, for example, the transition
point of zinc sulphate heptahydrate into hexahydrate could be determined in the
following manner. Tube A (Fig. 134) contains, say, a saturated solution of the
heptahydrate along with some of the solid salt; tube B, a saturated solution of the
hexahydrate along with the solid salt. The tube C is a connecting tube bent
downwards so as to prevent the mixing of the solutions by convection currents.
ZZ are two zinc electrodes immersed in the solution; the cell is placed in a
thermostat and the zinc electrodes connected with a galvanometer. Since, now, at
temperatures below the transition point the solubility of the hexahydrate (the
metastable form) is greater than that of the heptahydrate, a current will be
produced, flowing in the cell from heptahydrate to hexahydrate. As the
temperature is raised towards the transition point, the solubilities of the two
hydrates also approach, and the current produced will therefore become weaker,
because the E.M.F. of the cell becomes less; and when the transition point is
attained, the E.M.F. becomes zero, and the current ceases. If the temperature is
raised above this, the solubility of the heptahydrate becomes greater than that of
the hexahydrate, and a current will again be produced, but in the opposite
direction. By noting the temperature, therefore, at which the current ceases, or the
E.M.F. becomes zero, the transition temperature can be ascertained.[406]
Page 285
Fig. 134.
In the case just described, the electrodes consisted of the same metal as was
contained in the salt. But in some cases, e.g. sodium sulphate, electrodes of the
metal contained in the salt cannot be employed. Nevertheless, the above electrical
method can be used even in those cases, if a suitable non-polarizable mercury
electrode is employed.[407]
Although, as we saw, no current was produced when two pieces of zinc were
immersed in the same solution of zinc salt, a current will be obtained if two
different metals, or even two different modifications of the same metal, are
employed. Thus an E.M.F. will be established when electrodes of grey and of
white tin are immersed in the same solution of zinc salt, but at the transition point
this E.M.F. will become zero. By this method Cohen determined the transition
point of grey and white tin (p. 42).
NAME INDEX
In the case just described, the electrodes consisted of the same metal as was
contained in the salt. But in some cases, e.g. sodium sulphate, electrodes of the
metal contained in the salt cannot be employed. Nevertheless, the above electrical
method can be used even in those cases, if a suitable non-polarizable mercury
electrode is employed.[407]
Although, as we saw, no current was produced when two pieces of zinc were
immersed in the same solution of zinc salt, a current will be obtained if two
different metals, or even two different modifications of the same metal, are
employed. Thus an E.M.F. will be established when electrodes of grey and of
white tin are immersed in the same solution of zinc salt, but at the transition point
this E.M.F. will become zero. By this method Cohen determined the transition
point of grey and white tin (p. 42).
NAME INDEX
Page 286
A
Abegg, 52
Adriani, 186, 217, 220
Alexejeff, 97, 125
Allan, 298
Allen, L. E., 109
Allen, R. W., 63
Ampolla, 213
Andreä, 109
Aristotle, 41
Armstrong, E. F., 313
Armstrong, H. E., 196
Arzruni, 33
Aten, 147, 163
Auerbach, 326
B
Babo, 126
Bancroft, 102, 104, 161, 176, 196, 202, 229, 246, 260, 261,
272, 281, 302
Barnes, 331, 339
Barschall, 318
Barus, 67
Battelli, 23
Baur, 233, 307
Beckmann, 49
Bell, 229
Berthollet, 7
Bodländer, 181, 247, 311, 321
Bogojawlenski, 72
Boudouard, 309, 311
Braun, 107
Brauns, 40, 51, 74
Bredig, 52
Bremer, 91
Brodie, 34, 47
Abegg, 52
Adriani, 186, 217, 220
Alexejeff, 97, 125
Allan, 298
Allen, L. E., 109
Allen, R. W., 63
Ampolla, 213
Andreä, 109
Aristotle, 41
Armstrong, E. F., 313
Armstrong, H. E., 196
Arzruni, 33
Aten, 147, 163
Auerbach, 326
B
Babo, 126
Bancroft, 102, 104, 161, 176, 196, 202, 229, 246, 260, 261,
272, 281, 302
Barnes, 331, 339
Barschall, 318
Barus, 67
Battelli, 23
Baur, 233, 307
Beckmann, 49
Bell, 229
Berthollet, 7
Bodländer, 181, 247, 311, 321
Bogojawlenski, 72
Boudouard, 309, 311
Braun, 107
Brauns, 40, 51, 74
Bredig, 52
Bremer, 91
Brodie, 34, 47
Page 287
Bruner, 126
Bruni, 181, 182, 256, 257
Bunsen, 67
C
Cady, 192
Calvert, 130
Cameron, 203
Carnelley, 47
Carpenter, 225
Carveth, 204, 255
Centnerszwer, 158
Chapman, 47
Chappuis, 51, 176
Charpy, 255
Churchill, 140
Coehn, 52
Cohen, 41, 72, 136, 139, 140
Cooke, 331, 339
Cox, 301
D
Dawson, 263
Debray, 74, 81, 139
Deville, 49, 74
Dewar, 26, 51, 178
Dietz, 157
Doelter, 233
Donnan, 8, 18
Dreyer, 73
Duhem, 56, 151
Dutoit, 204
E
Etard, 115, 135
F
Fahrenheit, 30
Bruni, 181, 182, 256, 257
Bunsen, 67
C
Cady, 192
Calvert, 130
Cameron, 203
Carnelley, 47
Carpenter, 225
Carveth, 204, 255
Centnerszwer, 158
Chapman, 47
Chappuis, 51, 176
Charpy, 255
Churchill, 140
Coehn, 52
Cohen, 41, 72, 136, 139, 140
Cooke, 331, 339
Cox, 301
D
Dawson, 263
Debray, 74, 81, 139
Deville, 49, 74
Dewar, 26, 51, 178
Dietz, 157
Doelter, 233
Donnan, 8, 18
Dreyer, 73
Duhem, 56, 151
Dutoit, 204
E
Etard, 115, 135
F
Fahrenheit, 30
Page 288
Faraday, 82, 89
Fath, 204
Fedotieff, 315, 320
Findlay, 111, 204, 206, 219
Foote, 69
Friedländer, 72
Fritsche, 41
Frowein, 91
Füchtbauer, 75
Fyffe, 143
G
Gattermann, 51, 52
Gautier, 222, 223
Gay-Lussac, 135
Gernez, 72
Gibbs, 7, 8, 151, 236
Glaessner, 307
Goldschmidt, E., 41
Goldschmidt, H., 335
Goldschmidt, V., 32
Goossens, 26
Gossner, 318
Graham, 178
Guertler, 73
Guldberg, 7
Guthrie, 97, 104, 117, 118, 119, 233
H
Haber, 311
Hahn, 309, 311
Hallock, 35
Hammerl, 145
Hautefeuille, 46, 49, 50, 51, 178
Heller, 311
Henry, 94
Herold, 321
Fath, 204
Fedotieff, 315, 320
Findlay, 111, 204, 206, 219
Foote, 69
Friedländer, 72
Fritsche, 41
Frowein, 91
Füchtbauer, 75
Fyffe, 143
G
Gattermann, 51, 52
Gautier, 222, 223
Gay-Lussac, 135
Gernez, 72
Gibbs, 7, 8, 151, 236
Glaessner, 307
Goldschmidt, E., 41
Goldschmidt, H., 335
Goldschmidt, V., 32
Goossens, 26
Gossner, 318
Graham, 178
Guertler, 73
Guldberg, 7
Guthrie, 97, 104, 117, 118, 119, 233
H
Haber, 311
Hahn, 309, 311
Hallock, 35
Hammerl, 145
Hautefeuille, 46, 49, 50, 51, 178
Heller, 311
Henry, 94
Herold, 321
Page 289
Hertz, 49
Heycock, 194, 221, 223
Heyn, 225, 228
Hickmans, 219
Hiorns, 228
Hissink, 115, 190
Hoitsema, 14, 90, 177, 178, 298
Hollmann, 204
Holsboer, 110
Horstmann, 8, 83, 89
Hudson, 102
Hulett, 10, 48, 52, 54, 67, 109
I
Isaac, 114
Isambert, 80, 82, 84
J
Jaffé, 74, 114
Joulin, 176
Juhlin, 23, 24, 30
von Jüptner, 225
K
Kastle, 71
Kaufler, 49
Kaufmann, 112
Kayser, 176
Keeling, 225
Kelvin, 25
Kenrick, 263, 297
Kipping, 219
Kirchhoff, 32
Knorr, 203
de Kock, 53, 182, 194
Konowaloff, 102, 103, 104
Krasnicki, 144
Heycock, 194, 221, 223
Heyn, 225, 228
Hickmans, 219
Hiorns, 228
Hissink, 115, 190
Hoitsema, 14, 90, 177, 178, 298
Hollmann, 204
Holsboer, 110
Horstmann, 8, 83, 89
Hudson, 102
Hulett, 10, 48, 52, 54, 67, 109
I
Isaac, 114
Isambert, 80, 82, 84
J
Jaffé, 74, 114
Joulin, 176
Juhlin, 23, 24, 30
von Jüptner, 225
K
Kastle, 71
Kaufler, 49
Kaufmann, 112
Kayser, 176
Keeling, 225
Kelvin, 25
Kenrick, 263, 297
Kipping, 219
Kirchhoff, 32
Knorr, 203
de Kock, 53, 182, 194
Konowaloff, 102, 103, 104
Krasnicki, 144
Page 290
Kremann, 147, 212
Kuenen, 105
Kultascheff, 233
Kuriloff, 216
Kurnakoff, 221, 222, 230
Küster, 72, 181, 183
L
Laar, 195
Labenburg, 216
Lattey, 101
Le Chatelier, 58, 81, 233
Lehfeldt, 338, 340
Lehmann, 33, 52, 53
Lidbury, 147
Loewel, 134, 135
Loewenherz, 134, 316
Lowry, 196, 198
Ludwig, 327
Lumsden, 80, 109, 110
Lussana, 68
Luther, 22
M
Mack, 67
Magnus, 22
Mathews, 221
Mellor, 80
Meusser, 142
Meyer, J., 71
Meyer, V., 47
Meyerhoffer, 158, 233, 259, 268, 271, 278, 279, 280, 284,
313, 315, 317, 319, 327, 328, 336, 337
Middelberg, 116
Miers, 114
Miller, 297
Mitscherlich, 33, 49
Kuenen, 105
Kultascheff, 233
Kuriloff, 216
Kurnakoff, 221, 222, 230
Küster, 72, 181, 183
L
Laar, 195
Labenburg, 216
Lattey, 101
Le Chatelier, 58, 81, 233
Lehfeldt, 338, 340
Lehmann, 33, 52, 53
Lidbury, 147
Loewel, 134, 135
Loewenherz, 134, 316
Lowry, 196, 198
Ludwig, 327
Lumsden, 80, 109, 110
Lussana, 68
Luther, 22
M
Mack, 67
Magnus, 22
Mathews, 221
Mellor, 80
Meusser, 142
Meyer, J., 71
Meyer, V., 47
Meyerhoffer, 158, 233, 259, 268, 271, 278, 279, 280, 284,
313, 315, 317, 319, 327, 328, 336, 337
Middelberg, 116
Miers, 114
Miller, 297
Mitscherlich, 33, 49
Page 291
Mond, 178
Moore, 72
Moss, 66
Müller, 112, 265
Mylius, 109, 142, 157
N
Naumann, 49
Neville, 194, 221, 223
O
Offer, 119
Ostwald, 8, 10, 13, 16, 22, 44, 58, 68, 70, 74, 85, 88, 92,
102, 110, 117, 125, 127, 130, 141, 198
P
Padoa, 73, 181
Parsons, 298
Pasteur, 266
Paternò, 213
Payen, 74
Pedler, 47
Pfaundler, 119
Philip, 213, 214
von Pickardt, 73
Planck, 68
Pope, 219
Poynting, 68
Preuner, 311
Puschin, 222
Q
Quincke, 52
R
Rabe, 113
Ramsay, 3, 22, 23, 24, 30, 32, 63, 64, 66, 79, 90, 165, 178
Raoult, 180
Moore, 72
Moss, 66
Müller, 112, 265
Mylius, 109, 142, 157
N
Naumann, 49
Neville, 194, 221, 223
O
Offer, 119
Ostwald, 8, 10, 13, 16, 22, 44, 58, 68, 70, 74, 85, 88, 92,
102, 110, 117, 125, 127, 130, 141, 198
P
Padoa, 73, 181
Parsons, 298
Pasteur, 266
Paternò, 213
Payen, 74
Pedler, 47
Pfaundler, 119
Philip, 213, 214
von Pickardt, 73
Planck, 68
Pope, 219
Poynting, 68
Preuner, 311
Puschin, 222
Q
Quincke, 52
R
Rabe, 113
Ramsay, 3, 22, 23, 24, 30, 32, 63, 64, 66, 79, 90, 165, 178
Raoult, 180
Page 292
Reed, 71
Regnault, 22
Reicher, 36, 37, 110, 260, 333
Reinders, 71, 185, 188
Reinitzer, 51, 52
Richards, 136, 140
Riddle, 47
Riecke, 48, 55
Roberts-Austen, 63, 194, 221, 223, 225
Roloff, 117
Roozeboom, 10, 38, 45, 47, 49, 50, 51, 54, 56, 57, 62, 63,
68, 88, 103, 126, 145, 147, 150, 151, 157, 162, 170,
174, 178, 182, 196, 201, 211, 217, 220, 225, 236,
238, 262, 264, 269, 272, 273, 281, 282, 290, 331
Rose, 223
Rotarski, 52
Rothmund, 97, 98, 100
Rutten, 298
S
Saposchnikoff, 212
Saunders, 313, 317, 319, 336, 337
Saurel, 151
Schaum, 49, 75
Scheel, 22, 23, 30
Schenck, 49, 52, 54, 311
Schneider, 52
Schönbeck, 75
Schreinemakers, 122, 126, 246, 248, 250, 252, 290, 302
Schrötter, 46
Schukowsky, 52
Schwarz, 331
Seitz, 52
Shenstone, 109, 115, 135
Shepherd, 221, 255
Shields, 178
Skirrow, 130
Regnault, 22
Reicher, 36, 37, 110, 260, 333
Reinders, 71, 185, 188
Reinitzer, 51, 52
Richards, 136, 140
Riddle, 47
Riecke, 48, 55
Roberts-Austen, 63, 194, 221, 223, 225
Roloff, 117
Roozeboom, 10, 38, 45, 47, 49, 50, 51, 54, 56, 57, 62, 63,
68, 88, 103, 126, 145, 147, 150, 151, 157, 162, 170,
174, 178, 182, 196, 201, 211, 217, 220, 225, 236,
238, 262, 264, 269, 272, 273, 281, 282, 290, 331
Rose, 223
Rotarski, 52
Rothmund, 97, 98, 100
Rutten, 298
S
Saposchnikoff, 212
Saunders, 313, 317, 319, 336, 337
Saurel, 151
Schaum, 49, 75
Scheel, 22, 23, 30
Schenck, 49, 52, 54, 311
Schneider, 52
Schönbeck, 75
Schreinemakers, 122, 126, 246, 248, 250, 252, 290, 302
Schrötter, 46
Schukowsky, 52
Schwarz, 331
Seitz, 52
Shenstone, 109, 115, 135
Shepherd, 221, 255
Shields, 178
Skirrow, 130
Page 293
Spring, 63
von Stackelberg, 107, 110
Staedel, 267
Stansfield, 194, 221
Stokes, 236
Stortenbeker, 44, 147, 161, 164, 281
T
Taber, 229
Tammann, 26, 32, 33, 37, 38, 39, 48, 52, 65, 67, 68, 72, 73,
140, 151, 176, 221, 230
Thiesen, 22, 23, 30
Thomson, J., 25, 28, 32
Thomson, W., 25
Tilden, 109, 115, 135
Trevor, 16
Troost, 46, 49, 50, 51
Tumlirz, 72
V
Van Bemmelen, 180
Van Deventer, 110, 139, 266, 267, 333
Van Eyk, 41, 63, 192, 338
Van't Hoff, 36, 38, 58, 70, 90, 92, 108, 127, 139, 140, 165,
175, 225, 258, 260, 263, 265, 266, 267, 272, 284,
290, 313, 318, 333, 340
Van Leeuwen, 259
Van Wyk, 185
Vogt, 5, 233
W
Waage, 7
Wald, 92
Walden, 158
Walker, 80, 105, 122, 126, 143
Wegscheider, 10, 49, 202
Wells, 136
von Stackelberg, 107, 110
Staedel, 267
Stansfield, 194, 221
Stokes, 236
Stortenbeker, 44, 147, 161, 164, 281
T
Taber, 229
Tammann, 26, 32, 33, 37, 38, 39, 48, 52, 65, 67, 68, 72, 73,
140, 151, 176, 221, 230
Thiesen, 22, 23, 30
Thomson, J., 25, 28, 32
Thomson, W., 25
Tilden, 109, 115, 135
Trevor, 16
Troost, 46, 49, 50, 51
Tumlirz, 72
V
Van Bemmelen, 180
Van Deventer, 110, 139, 266, 267, 333
Van Eyk, 41, 63, 192, 338
Van't Hoff, 36, 38, 58, 70, 90, 92, 108, 127, 139, 140, 165,
175, 225, 258, 260, 263, 265, 266, 267, 272, 284,
290, 313, 318, 333, 340
Van Leeuwen, 259
Van Wyk, 185
Vogt, 5, 233
W
Waage, 7
Wald, 92
Walden, 158
Walker, 80, 105, 122, 126, 143
Wegscheider, 10, 49, 202
Wells, 136
Page 294
Wenzel, 7
Wiebe, 22
Witt, 327
Wright, 241, 246, 247
von Wrochem, 109, 142
Y
Young, 3, 22, 23, 24, 30, 32, 63, 64, 66, 79, 105, 165
Z
Zacharias, 180
Zawidski, 63
Zenghelis, 35
Zimmermann, 311
Zincke, 44
Ziz, 141
SUBJECT INDEX
A
Acetaldehyde and paraldehyde, 204
Acetic acid, chloroform, water, 241
Acetone, phenol, water, 248
Adsorption, 176
Alcohol, chloroform, water, 246
——, ether, water, 246
Alloys, equilibrium curves of, 221
—— of copper and tin, liquefaction of, by cooling, 194
—— of iron and carbon, 223
—— of thallium and mercury, 222
——, ternary, 246
Ammonia compounds of metal chlorides, 82
Ammonia silver chlorides, 82
—— —— ——, dissociation pressures of, 84
Ammonia-soda process, 320
Wiebe, 22
Witt, 327
Wright, 241, 246, 247
von Wrochem, 109, 142
Y
Young, 3, 22, 23, 24, 30, 32, 63, 64, 66, 79, 105, 165
Z
Zacharias, 180
Zawidski, 63
Zenghelis, 35
Zimmermann, 311
Zincke, 44
Ziz, 141
SUBJECT INDEX
A
Acetaldehyde and paraldehyde, 204
Acetic acid, chloroform, water, 241
Acetone, phenol, water, 248
Adsorption, 176
Alcohol, chloroform, water, 246
——, ether, water, 246
Alloys, equilibrium curves of, 221
—— of copper and tin, liquefaction of, by cooling, 194
—— of iron and carbon, 223
—— of thallium and mercury, 222
——, ternary, 246
Ammonia compounds of metal chlorides, 82
Ammonia silver chlorides, 82
—— —— ——, dissociation pressures of, 84
Ammonia-soda process, 320
Page 295
Ammonium chloride, dissociation of, 3, 79
—— cyanide, dissociation of, 80
—— hydrosulphide, dissociation of, 80
—— nitrate, solubility of, 113
Aniline, phenol, water, 250
Astracanite, 260, 261, 268, 274
B
Babo, law of, 126
Barium acetate, solubility of, 143
Barium carbonate and potassium sulphate, 328
—— nitrite, preparation of, 327
Basic salts, 296
Benzaldoximes, 203
Benzene and picric acid, 216
Bismuth, effect of pressure on the melting point of, 67
——, lead, tin, 255
—— nitrates, basic, 298
Bivariant systems, 16
Bromocinnamic aldehyde and chlorocinnamic aldehyde, 183
C
Calcium carbonate, dissociation of, 3, 11, 81
—— chloride hexahydrate, solubility of, 146
—— ——, solubility of hydrates of, 148
—— ——, vapour-pressure of hydrates of, 88
Camphor oximes, 219, 257
Carnallite, 284
Carvoximes, 186, 219
Cementite, 224
Chlorine and iodine, 161
Chlorocinnamic aldehyde and bromocinnamic aldehyde, 183
Chloroform, acetic acid, water, 241
——, alcohol, water, 246
Classification of systems, 17
Component, 8, 10, 12
——, systems of one, 21, 55
—— cyanide, dissociation of, 80
—— hydrosulphide, dissociation of, 80
—— nitrate, solubility of, 113
Aniline, phenol, water, 250
Astracanite, 260, 261, 268, 274
B
Babo, law of, 126
Barium acetate, solubility of, 143
Barium carbonate and potassium sulphate, 328
—— nitrite, preparation of, 327
Basic salts, 296
Benzaldoximes, 203
Benzene and picric acid, 216
Bismuth, effect of pressure on the melting point of, 67
——, lead, tin, 255
—— nitrates, basic, 298
Bivariant systems, 16
Bromocinnamic aldehyde and chlorocinnamic aldehyde, 183
C
Calcium carbonate, dissociation of, 3, 11, 81
—— chloride hexahydrate, solubility of, 146
—— ——, solubility of hydrates of, 148
—— ——, vapour-pressure of hydrates of, 88
Camphor oximes, 219, 257
Carnallite, 284
Carvoximes, 186, 219
Cementite, 224
Chlorine and iodine, 161
Chlorocinnamic aldehyde and bromocinnamic aldehyde, 183
Chloroform, acetic acid, water, 241
——, alcohol, water, 246
Classification of systems, 17
Component, 8, 10, 12
——, systems of one, 21, 55
Page 296
Components, choice of, 12, 13, 14, 76, 313
——, determination of number of, 13
——, systems of four, 312
——, —— of three, 234
——, —— of two, 76, 207
——, variation in number of, 11, 14
Composition, determination of, without analysis, 228, 302
Concentration-temperature curve for two liquids, 101
Condensed systems, 36
Constituent, 10
Cooling curve, 230
Copper calcium acetate, 260
—— chloride, heat of solution of, 110
—— dipotassium chloride, 259
—— sulphate, 85
Critical concentration, 98, 242
—— pressure of water, 23
—— solution temperature, 98
—— temperature of water, 23
Cryohydrates, 117, 118
Cryohydric point, 117
—— ——, changes at the, 119
—— —— for silver nitrate and ice, 116
Crystals, liquid, 51
——, ——, equilibria of, 53
——, ——, list of, 54
——, ——, nature of, 52
——, mixed, 180
Crystallization, velocity of, 72, 74
——, spontaneous, 114
D
Deliquescence, 130
Devitrification, 73
Diethylamine and water, solubility of, 101
Dilatometer, determination of transition points by, 331
Dineric surface, 247
——, determination of number of, 13
——, systems of four, 312
——, —— of three, 234
——, —— of two, 76, 207
——, variation in number of, 11, 14
Composition, determination of, without analysis, 228, 302
Concentration-temperature curve for two liquids, 101
Condensed systems, 36
Constituent, 10
Cooling curve, 230
Copper calcium acetate, 260
—— chloride, heat of solution of, 110
—— dipotassium chloride, 259
—— sulphate, 85
Critical concentration, 98, 242
—— pressure of water, 23
—— solution temperature, 98
—— temperature of water, 23
Cryohydrates, 117, 118
Cryohydric point, 117
—— ——, changes at the, 119
—— —— for silver nitrate and ice, 116
Crystals, liquid, 51
——, ——, equilibria of, 53
——, ——, list of, 54
——, ——, nature of, 52
——, mixed, 180
Crystallization, velocity of, 72, 74
——, spontaneous, 114
D
Deliquescence, 130
Devitrification, 73
Diethylamine and water, solubility of, 101
Dilatometer, determination of transition points by, 331
Dineric surface, 247
Page 297
Dissociation equilibrium, effect of addition of dissociation
products on, 4
—— of ammonia compounds of metal chlorides, 82, 84
—— of ammonium chloride, 3, 79
—— —— cyanide, 80
—— —— hydrosulphide, 80
—— of calcium carbonate, 3, 81
—— of compounds, degree of, 147
—— of phosphonium bromide, 80
—— of salt hydrates, 85
——, phenomena of, 79
Dissociation pressure, 81
Distillation of supercooled liquid to solid, 32, 50
Double salt interval, 278
—— salts, crystallization from solution, 280
—— ——, decomposition by water, 267
—— ——, formation of, 258, 273, 315
E
Efflorescence, 86
Electrical methods of determining transition points, 338
Enantiotropy, 44, 51
Equilibria, Gibbs's theory of, 8
——, metastable, 69
Equilibrium apparent (false), 5, 6
—— between ice and solution, 116
—— between ice and water, 25
—— between ice, water, vapour, 27
—— between water and vapour, 21
——, chemical, 3, 16
——, heterogeneous, 5
——, homogeneous, 5
——, independence of, on amounts of phases, 9
——, law of movable, 58
——, physical, 3, 16
—— real (true), 5, 6
Ether, alcohol, water, 246
products on, 4
—— of ammonia compounds of metal chlorides, 82, 84
—— of ammonium chloride, 3, 79
—— —— cyanide, 80
—— —— hydrosulphide, 80
—— of calcium carbonate, 3, 81
—— of compounds, degree of, 147
—— of phosphonium bromide, 80
—— of salt hydrates, 85
——, phenomena of, 79
Dissociation pressure, 81
Distillation of supercooled liquid to solid, 32, 50
Double salt interval, 278
—— salts, crystallization from solution, 280
—— ——, decomposition by water, 267
—— ——, formation of, 258, 273, 315
E
Efflorescence, 86
Electrical methods of determining transition points, 338
Enantiotropy, 44, 51
Equilibria, Gibbs's theory of, 8
——, metastable, 69
Equilibrium apparent (false), 5, 6
—— between ice and solution, 116
—— between ice and water, 25
—— between ice, water, vapour, 27
—— between water and vapour, 21
——, chemical, 3, 16
——, heterogeneous, 5
——, homogeneous, 5
——, independence of, on amounts of phases, 9
——, law of movable, 58
——, physical, 3, 16
—— real (true), 5, 6
Ether, alcohol, water, 246
Page 298
——, succinic nitrile, water, 252
Ethylene bromide, picric acid, β-naphthol, 256
Eutectic mixtures, 117, 191, 209, 255, 257
—— point, 117, 209, 213, 253
F
Ferric chloride, evaporation of solutions of, 155
—— ——, hydrates of, 151, 153
—— ——, hydrogen chloride and water, systems of, 290
Ferrite, modifications of, 224
Freedom, degree of, 14
Freezing mixtures, 120
—— point, natural, 198
Fusion curve, 66
—— —— of ice, 25
—— of ice, influence of pressure on, 26
——, partial, 139
G
Glaserite, 315, 317
Glasses, 176
Glauber's salt, 13, 134
—— ——, transition curve of, 68, 140
Graphic representation in space, 77, 284
H
Hydrates, range of existence of, 89
—— chloride and water, 174
Hydrogen bromide and water, 174
Hylotropic substances, 198
I
Ice I., 32
—— II., 32
—— III., 32
——, equilibrium between water and, 25
——, influence of pressure on melting point of, 25, 26
——, sublimation curve of, 24
Ethylene bromide, picric acid, β-naphthol, 256
Eutectic mixtures, 117, 191, 209, 255, 257
—— point, 117, 209, 213, 253
F
Ferric chloride, evaporation of solutions of, 155
—— ——, hydrates of, 151, 153
—— ——, hydrogen chloride and water, systems of, 290
Ferrite, modifications of, 224
Freedom, degree of, 14
Freezing mixtures, 120
—— point, natural, 198
Fusion curve, 66
—— —— of ice, 25
—— of ice, influence of pressure on, 26
——, partial, 139
G
Glaserite, 315, 317
Glasses, 176
Glauber's salt, 13, 134
—— ——, transition curve of, 68, 140
Graphic representation in space, 77, 284
H
Hydrates, range of existence of, 89
—— chloride and water, 174
Hydrogen bromide and water, 174
Hylotropic substances, 198
I
Ice I., 32
—— II., 32
—— III., 32
——, equilibrium between water and, 25
——, influence of pressure on melting point of, 25, 26
——, sublimation curve of, 24
Page 299
——, vapour pressure of, 25, 31
Indifferent point, 150
Individual, chemical, 92
Inversion temperature, 36
Iodine and chlorine, 161
Iron—carbon alloys, 223
——, carbon monoxide and carbon dioxide, 305
Isomerides, dynamic, 195, 196
——, ——, equilibrium between, 195, 196
——, ——, equilibrium point of, 198
——, transformation of unstable into stable, 201
Isomerism, dynamic, 196
Isothermal evaporation, 278
—— solubility curves, 272
L
Lead, bismuth, tin, 255
——, desilverization of, 247
——, silver, zinc, 246
Le Chatelier, theorem of, 57
Lime, burning of, 3
Liquidus curve, 182
M
Mandelic acid, 217
Martensite, 224
Mass action, law of, 7
Melting point, influence of pressure on, 66
—— ——, congruent, 146
—— ——, incongruent, 139
—— under the solvent, 122
Menthyl mandelates, 219
Mercuric bromide and iodide, 188
Mercury salts, basic, 301
Metastable equilibria, 69
—— region, 30
—— state, 30
Indifferent point, 150
Individual, chemical, 92
Inversion temperature, 36
Iodine and chlorine, 161
Iron—carbon alloys, 223
——, carbon monoxide and carbon dioxide, 305
Isomerides, dynamic, 195, 196
——, ——, equilibrium between, 195, 196
——, ——, equilibrium point of, 198
——, transformation of unstable into stable, 201
Isomerism, dynamic, 196
Isothermal evaporation, 278
—— solubility curves, 272
L
Lead, bismuth, tin, 255
——, desilverization of, 247
——, silver, zinc, 246
Le Chatelier, theorem of, 57
Lime, burning of, 3
Liquidus curve, 182
M
Mandelic acid, 217
Martensite, 224
Mass action, law of, 7
Melting point, influence of pressure on, 66
—— ——, congruent, 146
—— ——, incongruent, 139
—— under the solvent, 122
Menthyl mandelates, 219
Mercuric bromide and iodide, 188
Mercury salts, basic, 301
Metastable equilibria, 69
—— region, 30
—— state, 30
Page 300
Methylethyl ketone and water, 100
Minerals, formation of, 232
Miscibility of liquids, complete, 95, 104, 114
—— ——, partial, 95, 96, 121
Mixed crystals, 180, 281
—— ——, changes in, with temperature, 192
—— ——, examples of, 183, 186, 187, 190, 192, 219,
223
—— ——, formation of, 181, 182
—— ——, fractional crystallization of, 188
—— ——, freezing points of, 182
—— ——, melting points of, 182, 184
—— ——, pseudoracemic, 219
Mixtures, isomorphous, 181
—— of constant boiling point, 105
—— of constant melting point, 117, 186, 187, 192, 209,
255, 257
Monotropy, 44, 51
Multivariant systems, 16
N
Naphthalene and monochloracetic acid, 192
—— and β-naphthol, mixed crystals of, 183
β-Naphthol, ethylene bromide, picric acid, 256
α-Naphthylamine and phenol, 213
Nickel iodate, solubility of, 142
o-Nitrophenol and p-toluidine, 213
O
Occlusion of gases, 176
Optical method of determining transition points, 338
Optically active substances, freezing-point curves of, 216
Order of a system, 13
Organic compounds, application of Phase Rule to, 212
P
Palladium and hydrogen, 90, 178
Minerals, formation of, 232
Miscibility of liquids, complete, 95, 104, 114
—— ——, partial, 95, 96, 121
Mixed crystals, 180, 281
—— ——, changes in, with temperature, 192
—— ——, examples of, 183, 186, 187, 190, 192, 219,
223
—— ——, formation of, 181, 182
—— ——, fractional crystallization of, 188
—— ——, freezing points of, 182
—— ——, melting points of, 182, 184
—— ——, pseudoracemic, 219
Mixtures, isomorphous, 181
—— of constant boiling point, 105
—— of constant melting point, 117, 186, 187, 192, 209,
255, 257
Monotropy, 44, 51
Multivariant systems, 16
N
Naphthalene and monochloracetic acid, 192
—— and β-naphthol, mixed crystals of, 183
β-Naphthol, ethylene bromide, picric acid, 256
α-Naphthylamine and phenol, 213
Nickel iodate, solubility of, 142
o-Nitrophenol and p-toluidine, 213
O
Occlusion of gases, 176
Optical method of determining transition points, 338
Optically active substances, freezing-point curves of, 216
Order of a system, 13
Organic compounds, application of Phase Rule to, 212
P
Palladium and hydrogen, 90, 178
Page 301
Paragenesis, 320
Paraldehyde and acetaldehyde, 204
Partial pressures of two components, 102
Pearlite, 224
Phase, 8
—— Rule, 8, 16
—— ——, deduction of, 18
—— ——, scope of, 1
Phases, formation of new, 69
——, number of, 9
Phenol, acetone, water, 248
——, aniline, water, 250
—— and α-naphthylamine, 213
—— and p-toluidine, 214
—— and water, solubility of, 97
Phosphonium bromide, dissociation of, 80
—— chloride, 65
Phosphorus, 46
——, distillation of white to red, 50
——, melting point of red, 47
——, —— —— of white, 48
——, solubility of white and red, 47
——, vapour pressure of white and red, 46
Picric acid and benzene, 216
—— ——, ethylene bromide, and β-naphthol, 256
Polymorphic forms, solubility of, 112
—— substances, list of, 63
Polymorphism, 33
Potassium nitrate and thallium nitrate, 192
Potential, chemical, 19
Pressure-concentration diagram for two liquids, 102
Pressure-temperature diagram for solutions, 126
Pseudomonotropy, 45
Pseudo-racemic mixed crystals, 21
Pyridine and methyl iodide, 147
Pyrometer, registering, 230
Paraldehyde and acetaldehyde, 204
Partial pressures of two components, 102
Pearlite, 224
Phase, 8
—— Rule, 8, 16
—— ——, deduction of, 18
—— ——, scope of, 1
Phases, formation of new, 69
——, number of, 9
Phenol, acetone, water, 248
——, aniline, water, 250
—— and α-naphthylamine, 213
—— and p-toluidine, 214
—— and water, solubility of, 97
Phosphonium bromide, dissociation of, 80
—— chloride, 65
Phosphorus, 46
——, distillation of white to red, 50
——, melting point of red, 47
——, —— —— of white, 48
——, solubility of white and red, 47
——, vapour pressure of white and red, 46
Picric acid and benzene, 216
—— ——, ethylene bromide, and β-naphthol, 256
Polymorphic forms, solubility of, 112
—— substances, list of, 63
Polymorphism, 33
Potassium nitrate and thallium nitrate, 192
Potential, chemical, 19
Pressure-concentration diagram for two liquids, 102
Pressure-temperature diagram for solutions, 126
Pseudomonotropy, 45
Pseudo-racemic mixed crystals, 21
Pyridine and methyl iodide, 147
Pyrometer, registering, 230
Page 302
Q
Quadruple point, 116
Quintuple point, 234, 261
R
Racemates, characterization of, 217, 282
Reactions, law of successive, 73
Reciprocal salt-pairs, 313
—— ——, transition point of, 314
Rubidium tartrates, 265
S
Salt hydrates, 85
—— ——, indefiniteness of vapour pressure of, 87
—— —— with definite melting point, 145
Separation of salt on evaporation, 130
Silicates, hydrated, 176
Silver, lead, zinc, 246
Silver nitrate, solubility of, 114
—— —— and sodium nitrate, 190
Single salt interval, 278
Sodium ammonium tartrates, 266
—— nitrate and silver nitrate, 190
—— sulphate and water, equilibria between, 134
Sodium sulphate and water, vapour pressures of, 138, 140
—— ——, anhydrous, dehydration by, 138
—— ——, solubility of, 135
—— —— decahydrate, solubility of, 134
—— —— ——, transition point of, 136, 139
—— —— heptahydrate, solubility of, 136
—— —— ——, transition point of, 137
Solidus curve, 182
Solubility curve at higher temperatures, 114
—— ——, form of, 108
—— —— of anhydrous salts, 111
—— ——, retroflex, 146, 151, 162
—— curves, interpolation and extrapolation of, 111
Quadruple point, 116
Quintuple point, 234, 261
R
Racemates, characterization of, 217, 282
Reactions, law of successive, 73
Reciprocal salt-pairs, 313
—— ——, transition point of, 314
Rubidium tartrates, 265
S
Salt hydrates, 85
—— ——, indefiniteness of vapour pressure of, 87
—— —— with definite melting point, 145
Separation of salt on evaporation, 130
Silicates, hydrated, 176
Silver, lead, zinc, 246
Silver nitrate, solubility of, 114
—— —— and sodium nitrate, 190
Single salt interval, 278
Sodium ammonium tartrates, 266
—— nitrate and silver nitrate, 190
—— sulphate and water, equilibria between, 134
Sodium sulphate and water, vapour pressures of, 138, 140
—— ——, anhydrous, dehydration by, 138
—— ——, solubility of, 135
—— —— decahydrate, solubility of, 134
—— —— ——, transition point of, 136, 139
—— —— heptahydrate, solubility of, 136
—— —— ——, transition point of, 137
Solidus curve, 182
Solubility curve at higher temperatures, 114
—— ——, form of, 108
—— —— of anhydrous salts, 111
—— ——, retroflex, 146, 151, 162
—— curves, interpolation and extrapolation of, 111
Page 303
—— —— of three component systems, 264
——, determination of transition points by, 335
——, influence of pressure on, 107
——, —— of subdivision on, 10
——, —— of temperature on, 109
—— of metastable forms, 47, 112, 137
Solubility of polymorphic forms, 112
—— of salt hydrates, 133, 145
—— of supercooled liquids, 125
——, retrograde, 245
Solute, 93
Solution, definition of, 92
——, heat of, 109, 110
——, saturated, 106, 108
——, supersaturated, 108
—— temperature, critical, 98
——, unsaturated, 108
Solutions, bivariant systems, 129
——, congruently saturated, 279
—— conjugate, 97, 241
——, incongruently saturated, 279, 289
——, inevaporable, 157
—— of gases in liquids, 93
—— —— in solids, 176
—— of liquids in liquids (binary), 95
—— —— —— (ternary), 240
—— ——, influence of temperature on, 247
—— of solids in liquids, 106
—— —— in solids, 180
——, solid, 175, 180
——, univariant systems, 127
Space model for carnallite, 284
Stability limit, 202
Steel, formation of, 223
Sublimation curve, 63
—— —— of ice, 24
—— without fusion, 65
——, determination of transition points by, 335
——, influence of pressure on, 107
——, —— of subdivision on, 10
——, —— of temperature on, 109
—— of metastable forms, 47, 112, 137
Solubility of polymorphic forms, 112
—— of salt hydrates, 133, 145
—— of supercooled liquids, 125
——, retrograde, 245
Solute, 93
Solution, definition of, 92
——, heat of, 109, 110
——, saturated, 106, 108
——, supersaturated, 108
—— temperature, critical, 98
——, unsaturated, 108
Solutions, bivariant systems, 129
——, congruently saturated, 279
—— conjugate, 97, 241
——, incongruently saturated, 279, 289
——, inevaporable, 157
—— of gases in liquids, 93
—— —— in solids, 176
—— of liquids in liquids (binary), 95
—— —— —— (ternary), 240
—— ——, influence of temperature on, 247
—— of solids in liquids, 106
—— —— in solids, 180
——, solid, 175, 180
——, univariant systems, 127
Space model for carnallite, 284
Stability limit, 202
Steel, formation of, 223
Sublimation curve, 63
—— —— of ice, 24
—— without fusion, 65
Page 304
Succinic nitrile and water, 122
—— ether, water, 252
Sulphur, 33, 34
—— dioxide and water, 169
—— —— and potassium iodide, 158
——, transition point of rhombic and monoclinic, 36
Supersaturation, 113, 114, 124
——, limits of, 114
Systems, condensed, 36
—— of one component, 21
—— of two components, 76, 77, 207
T
Tachydrite, influence of pressure on the transition point of,
263
Tartrate, dimethyl, 217
——, sodium potassium, 259
Tautomeric substances, 195
Tensimeter, 91
Thallium nitrate and potassium nitrate, 192
Theorem of van't Hoff and Le Chatelier, 57
Thermometric determination of transition point, 337
Tin, 41
——, lead, bismuth, 255
—— plague, 43
——, transition point of white and grey, 41
p-Toluidine and o-nitrophenol, 213
—— and phenol, 214
Transformation of optically active substances, 220
——, suspended, 37, 69, 89, 113, 137, 155
——, velocity of, 70
Transition curve, 66
—— —— of Glauber's salt, 68, 140
—— —— of rhombic and monoclinic sulphur, 37
—— interval, 270, 277, 315
—— point, 34
—— —— for double salts, 258
—— ether, water, 252
Sulphur, 33, 34
—— dioxide and water, 169
—— —— and potassium iodide, 158
——, transition point of rhombic and monoclinic, 36
Supersaturation, 113, 114, 124
——, limits of, 114
Systems, condensed, 36
—— of one component, 21
—— of two components, 76, 77, 207
T
Tachydrite, influence of pressure on the transition point of,
263
Tartrate, dimethyl, 217
——, sodium potassium, 259
Tautomeric substances, 195
Tensimeter, 91
Thallium nitrate and potassium nitrate, 192
Theorem of van't Hoff and Le Chatelier, 57
Thermometric determination of transition point, 337
Tin, 41
——, lead, bismuth, 255
—— plague, 43
——, transition point of white and grey, 41
p-Toluidine and o-nitrophenol, 213
—— and phenol, 214
Transformation of optically active substances, 220
——, suspended, 37, 69, 89, 113, 137, 155
——, velocity of, 70
Transition curve, 66
—— —— of Glauber's salt, 68, 140
—— —— of rhombic and monoclinic sulphur, 37
—— interval, 270, 277, 315
—— point, 34
—— —— for double salts, 258
Page 305
—— ——, influence of pressure on the, 68
—— points, as fixed points in thermometry, 140
—— ——, methods of determining, 331
—— —— of polymorphic substances, 63
Triangle, graphic representation by, 235
Triethylamine and water, 101
Triple point, 27, 55
—— ——, arrangement of curves round, 56
—— ——, changes at, 58
—— ——, ice, water, vapour, 27
—— ——, ice II., ice III., and water, 33
—— ——, metastable, 38
—— ——, monoclinic sulphur, liquid, vapour, 38
—— ——, monoclinic and rhombic sulphur, liquid, 38
—— ——, monoclinic and rhombic sulphur, vapour, 34
—— ——, red phosphorus, liquid, vapour, 47
—— ——, rhombic sulphur, liquid, vapour, 38
—— —— solid, solid, vapour, 62
—— ——, white phosphorus, liquid, vapour, 48
U
Univariant systems, 16
V
Van't Hoff, theorem of, 57
Vaporization curve, 63
—— ——, interpolation and extrapolation of, 66
—— —— of water, 21, 23
Vapour pressure, constancy of, and formation of compounds,
90
—— ——, dependence of, on solid phase, 88
—— ——, influence of surface tension on, 2
—— —— in three-component systems, 261
—— ——, measurement of, 91, 334
—— —— of calcium chloride solutions, 150
—— —— of ice, 25, 31
—— —— of small drops, 10
—— points, as fixed points in thermometry, 140
—— ——, methods of determining, 331
—— —— of polymorphic substances, 63
Triangle, graphic representation by, 235
Triethylamine and water, 101
Triple point, 27, 55
—— ——, arrangement of curves round, 56
—— ——, changes at, 58
—— ——, ice, water, vapour, 27
—— ——, ice II., ice III., and water, 33
—— ——, metastable, 38
—— ——, monoclinic sulphur, liquid, vapour, 38
—— ——, monoclinic and rhombic sulphur, liquid, 38
—— ——, monoclinic and rhombic sulphur, vapour, 34
—— ——, red phosphorus, liquid, vapour, 47
—— ——, rhombic sulphur, liquid, vapour, 38
—— —— solid, solid, vapour, 62
—— ——, white phosphorus, liquid, vapour, 48
U
Univariant systems, 16
V
Van't Hoff, theorem of, 57
Vaporization curve, 63
—— ——, interpolation and extrapolation of, 66
—— —— of water, 21, 23
Vapour pressure, constancy of, and formation of compounds,
90
—— ——, dependence of, on solid phase, 88
—— ——, influence of surface tension on, 2
—— —— in three-component systems, 261
—— ——, measurement of, 91, 334
—— —— of calcium chloride solutions, 150
—— —— of ice, 25, 31
—— —— of small drops, 10
Page 306
—— —— of sodium sulphate and water, 138
Vapour pressure of solid, solution, vapour, 126
—— —— of water, 21, 31
Variability of a system, 14, 16
Variance of a system, 16
Volatile components, two, 161
W
Water, 21
——, acetic acid, chloroform, 241
——, acetone, phenol, 248
——, alcohol, ether, 246
——, ——, chloroform, 246
——, aniline, phenol, 250
——, bivariant systems of, 29
——, critical pressure of, 23
——, critical temperature of, 23
——, equilibrium between ice and, 25
——, —— between vapour and, 21
——, ether, succinic nitrile, 252
——, supercooled, 30
——, ——, vapour pressure of, 31
——, vaporization curve of, 21
——, vapour pressure of, 23
Z
Zeolites, 176
Zinc, lead, silver, 246
—— chloride in water, solubility of, 157
THE END
PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, LONDON
AND BECCLES.
Vapour pressure of solid, solution, vapour, 126
—— —— of water, 21, 31
Variability of a system, 14, 16
Variance of a system, 16
Volatile components, two, 161
W
Water, 21
——, acetic acid, chloroform, 241
——, acetone, phenol, 248
——, alcohol, ether, 246
——, ——, chloroform, 246
——, aniline, phenol, 250
——, bivariant systems of, 29
——, critical pressure of, 23
——, critical temperature of, 23
——, equilibrium between ice and, 25
——, —— between vapour and, 21
——, ether, succinic nitrile, 252
——, supercooled, 30
——, ——, vapour pressure of, 31
——, vaporization curve of, 21
——, vapour pressure of, 23
Z
Zeolites, 176
Zinc, lead, silver, 246
—— chloride in water, solubility of, 157
THE END
PRINTED BY WILLIAM CLOWES AND SONS, LIMITED, LONDON
AND BECCLES.
Page 307
NOTES
[1] Except when the volume of the liquid becomes exceedingly
small, in which case the surface tension exerts an influence on the
vapour pressure.
[2] For reasons which will appear later (Chap. IV.), the volume of
the vapour is supposed to be large in comparison with that of the
solid and liquid.
[3] Ramsay and Young, Phil. Trans., 1886, 177. 87.
[4] See, more especially, Vogt, Die Silikatschmelzlösungen.
(Christiania, 1903, 1904.)
[5] Trans. Connecticut Acad., 1874-1878.
[6] Lehre von der chemischen Verwandtschaft der Körper, 1777.
[7] See Ostwald's Klassiker, No. 74.
[8] Etudes sur les affinités chimiques, 1867; Ostwald's Klassiker,
No. 104.
[9] Died April, 1903.
[10] For a mathematical treatment of the Phase Rule the reader is
referred to the volume in this series on Thermodynamics, by F. G.
Donnan.
[11] Liebig's Annalen, 1873, 170, 192; Ostwald, Lehrbuch, II. 2.
111.
[12] The action of gravity and other forces being excluded (see
p. 5).
[13] It may seem as if this were a contradiction to what was said
on p. 4 as to the effect of the addition of ammonia or hydrogen
chloride to the system constituted by solid ammonium chloride in
contact with its products of dissociation. There is, however, no
contradiction, because in the case of ammonium chloride the
[1] Except when the volume of the liquid becomes exceedingly
small, in which case the surface tension exerts an influence on the
vapour pressure.
[2] For reasons which will appear later (Chap. IV.), the volume of
the vapour is supposed to be large in comparison with that of the
solid and liquid.
[3] Ramsay and Young, Phil. Trans., 1886, 177. 87.
[4] See, more especially, Vogt, Die Silikatschmelzlösungen.
(Christiania, 1903, 1904.)
[5] Trans. Connecticut Acad., 1874-1878.
[6] Lehre von der chemischen Verwandtschaft der Körper, 1777.
[7] See Ostwald's Klassiker, No. 74.
[8] Etudes sur les affinités chimiques, 1867; Ostwald's Klassiker,
No. 104.
[9] Died April, 1903.
[10] For a mathematical treatment of the Phase Rule the reader is
referred to the volume in this series on Thermodynamics, by F. G.
Donnan.
[11] Liebig's Annalen, 1873, 170, 192; Ostwald, Lehrbuch, II. 2.
111.
[12] The action of gravity and other forces being excluded (see
p. 5).
[13] It may seem as if this were a contradiction to what was said
on p. 4 as to the effect of the addition of ammonia or hydrogen
chloride to the system constituted by solid ammonium chloride in
contact with its products of dissociation. There is, however, no
contradiction, because in the case of ammonium chloride the
Page 308
gaseous phase consists of ammonia and hydrogen chloride in
equal proportions, and in adding ammonia or hydrogen chloride
alone we are not adding the gaseous phase, but only a constituent
of it. Addition of ammonia and hydrogen chloride together in the
proportions in which they are combined to form ammonium
chloride would cause no change in the equilibrium.
[14] The vapour pressure of water in small drops is greater than
that of water in mass, and the solubility of a solid is greater when
in a state of fine subdivision than when in large pieces (cf. Hulett,
Zeitschr. physikal. Chem., 1901, 37. 385).
[15] See Ostwald, Lehrbuch, II. 2. 476, 934; Roozeboom,
Zeitschr. physikal. Chem., 1894, 15. 150; Heterogene
Gleichgewichte, I. p. 16; Wegscheider, Zeitschr. physikal. Chem.,
1903, 43. 89.
[16] Ostwald, Lehrbuch, II. 2. 478.
[17] See also Hoitsema, Zeitschr. physikal. Chem. 1895, 17. 651.
[18] The term "degree of freedom" employed here must not be
confused with the same term used to denote the various
movements of a gas molecule according to the kinetic theory.
[19] Trevor, Jour. Physical Chem., 1902, 6. 136.
[20] Ostwald, Principles of Inorganic Chemistry, translated by A.
Findlay, 2nd edit., p. 7. (Macmillan, 1904.)
[21] See the volume in this series on Thermodynamics by F. G.
Donnan.
[22] Pogg. Annalen, 1844, 61. 225.
[23] Mémoires de l'Acad., 26. 751.
[24] Phil. Trans. 1884, 175. 461; 1892, A, 183. 107.
[25] Bihang Svenska Akad. Handl. 1891, 17. I. 1.
[26] Abhandl. physikal.-tech. Reichsanstalt, 1900, 3. 71.
equal proportions, and in adding ammonia or hydrogen chloride
alone we are not adding the gaseous phase, but only a constituent
of it. Addition of ammonia and hydrogen chloride together in the
proportions in which they are combined to form ammonium
chloride would cause no change in the equilibrium.
[14] The vapour pressure of water in small drops is greater than
that of water in mass, and the solubility of a solid is greater when
in a state of fine subdivision than when in large pieces (cf. Hulett,
Zeitschr. physikal. Chem., 1901, 37. 385).
[15] See Ostwald, Lehrbuch, II. 2. 476, 934; Roozeboom,
Zeitschr. physikal. Chem., 1894, 15. 150; Heterogene
Gleichgewichte, I. p. 16; Wegscheider, Zeitschr. physikal. Chem.,
1903, 43. 89.
[16] Ostwald, Lehrbuch, II. 2. 478.
[17] See also Hoitsema, Zeitschr. physikal. Chem. 1895, 17. 651.
[18] The term "degree of freedom" employed here must not be
confused with the same term used to denote the various
movements of a gas molecule according to the kinetic theory.
[19] Trevor, Jour. Physical Chem., 1902, 6. 136.
[20] Ostwald, Principles of Inorganic Chemistry, translated by A.
Findlay, 2nd edit., p. 7. (Macmillan, 1904.)
[21] See the volume in this series on Thermodynamics by F. G.
Donnan.
[22] Pogg. Annalen, 1844, 61. 225.
[23] Mémoires de l'Acad., 26. 751.
[24] Phil. Trans. 1884, 175. 461; 1892, A, 183. 107.
[25] Bihang Svenska Akad. Handl. 1891, 17. I. 1.
[26] Abhandl. physikal.-tech. Reichsanstalt, 1900, 3. 71.
Page 309
[27] Ostwald-Luther, Physiko-chemische Messungen, 2nd edit., p.
156.
[28] Annales chim. et phys., 1892 [6], 26. 425.
[29] The vapour pressure of water at 0° has recently been very
accurately determined by Thiesen and Scheel (loc. cit.), and found
to be 4.579 ± 0.001 mm. of mercury (at 0°), or equal to 0.006025
atm.
[30] Juhlin, Bihang Svenska Akad. Handl., 1891, 17. I. 58. See
also Ramsay and Young, loc. cit.
[31] Trans. Roy. Soc. Edin., 1849, 16. 575.
[32] Proc. Roy. Soc. Edin., 1850, 2, 267.
[33] Annalen der Physik, 1899 [3], 68. 564; 1900 [4], 2. 1, 424.
See also Dewar, Proc. Roy. Soc., 1880, 30. 533.
[34] The pressure of 1 atmosphere is equal to 1.033 kilogm. per
sq. cm.; or the pressure of 1 kilogm. per sq. cm. is equal to 0.968
atm.
[35] Tammann, loc. cit., 1900, 2. 1, 424; cf. Goossens, Arch.
néerland, 1886, 20. 449.
[36] J. Thomson, Proc. Roy. Soc., 1874, 22. 28.
[37] A field is "enclosed" by two curves when these cut at an
angle less than two right angles. It may be useful to remember
that an invariant system is represented by a point, a univariant
system by a line, and a bivariant system by an area.
[38] Phil. Trans., 1724, 39. 78.
[39] Juhlin, loc. cit., p. 61; cf. Ramsay and Young, loc. cit.:
Thiesen and Scheel, loc. cit.
[40] This small difference is due to experimental errors in the
determination of the vapour pressures; a differential method
156.
[28] Annales chim. et phys., 1892 [6], 26. 425.
[29] The vapour pressure of water at 0° has recently been very
accurately determined by Thiesen and Scheel (loc. cit.), and found
to be 4.579 ± 0.001 mm. of mercury (at 0°), or equal to 0.006025
atm.
[30] Juhlin, Bihang Svenska Akad. Handl., 1891, 17. I. 58. See
also Ramsay and Young, loc. cit.
[31] Trans. Roy. Soc. Edin., 1849, 16. 575.
[32] Proc. Roy. Soc. Edin., 1850, 2, 267.
[33] Annalen der Physik, 1899 [3], 68. 564; 1900 [4], 2. 1, 424.
See also Dewar, Proc. Roy. Soc., 1880, 30. 533.
[34] The pressure of 1 atmosphere is equal to 1.033 kilogm. per
sq. cm.; or the pressure of 1 kilogm. per sq. cm. is equal to 0.968
atm.
[35] Tammann, loc. cit., 1900, 2. 1, 424; cf. Goossens, Arch.
néerland, 1886, 20. 449.
[36] J. Thomson, Proc. Roy. Soc., 1874, 22. 28.
[37] A field is "enclosed" by two curves when these cut at an
angle less than two right angles. It may be useful to remember
that an invariant system is represented by a point, a univariant
system by a line, and a bivariant system by an area.
[38] Phil. Trans., 1724, 39. 78.
[39] Juhlin, loc. cit., p. 61; cf. Ramsay and Young, loc. cit.:
Thiesen and Scheel, loc. cit.
[40] This small difference is due to experimental errors in the
determination of the vapour pressures; a differential method
Page 310
betrayed no difference between the vapour pressure of ice and of
water at 0°.
[41] Phil. Mag., 1874 [4], 47. 447; Proc. Roy. Soc., 1873, 22. 27.
[42] Pogg. Annalen, 1858, 103, 206.
[43] See Phil. Trans., 1884, 175, 461.
[44] This phenomenon of distillation from the supercooled liquid
to the solid has been very clearly observed in the case of
furfuraldoxime (V. Goldschmidt, Zeitschr. f. Krystallographie,
1897, 28. 169).
[45] Annalen der Physik, 1900 [4], 2. 1, 424.
[46] A similar triple point has been determined by Tammann in
the case of phenol (Annalen der Physik, 1902 [4], 9. 249).
[47] Annales chim. et phys., 1821, 19. 414.
[48] Lehmann, Molekularphysik, I. 153.; Arzruni, Physikalische
Chemie der Krystalle. (Graham-Otto, Lehrbuch der Chemie, I. 3.)
[49] Brodie, Proc. Roy. Soc., 1855, 7. 24.
[50] That solid sulphur does possess a certain vapour pressure has
been shown by Hallock, who observed the formation at the
ordinary temperature of copper sulphide in a tube containing
copper and sulphur (Amer. Jour. Sci., 1889 [3], 37. 405). See also
Zenghelis, Zeitschr. physikal. Chem., 1904, 50. 219.
[51] Zeitschr. für Krystallographie, 1884, 8. 593.
[52] Van't Hoff, Studies on Chemical Dynamics, p. 163.
[53] Reicher, loc. cit. See also Tammann, Annalen der Physik,
1899 [3], 68. 663.
[54] Tammann, Annalen der Physik, 1899 [3], 68. 633.
[55] Rec. Trav. Chim. Pays-Bas, 1887, 6. 314.
water at 0°.
[41] Phil. Mag., 1874 [4], 47. 447; Proc. Roy. Soc., 1873, 22. 27.
[42] Pogg. Annalen, 1858, 103, 206.
[43] See Phil. Trans., 1884, 175, 461.
[44] This phenomenon of distillation from the supercooled liquid
to the solid has been very clearly observed in the case of
furfuraldoxime (V. Goldschmidt, Zeitschr. f. Krystallographie,
1897, 28. 169).
[45] Annalen der Physik, 1900 [4], 2. 1, 424.
[46] A similar triple point has been determined by Tammann in
the case of phenol (Annalen der Physik, 1902 [4], 9. 249).
[47] Annales chim. et phys., 1821, 19. 414.
[48] Lehmann, Molekularphysik, I. 153.; Arzruni, Physikalische
Chemie der Krystalle. (Graham-Otto, Lehrbuch der Chemie, I. 3.)
[49] Brodie, Proc. Roy. Soc., 1855, 7. 24.
[50] That solid sulphur does possess a certain vapour pressure has
been shown by Hallock, who observed the formation at the
ordinary temperature of copper sulphide in a tube containing
copper and sulphur (Amer. Jour. Sci., 1889 [3], 37. 405). See also
Zenghelis, Zeitschr. physikal. Chem., 1904, 50. 219.
[51] Zeitschr. für Krystallographie, 1884, 8. 593.
[52] Van't Hoff, Studies on Chemical Dynamics, p. 163.
[53] Reicher, loc. cit. See also Tammann, Annalen der Physik,
1899 [3], 68. 663.
[54] Tammann, Annalen der Physik, 1899 [3], 68. 633.
[55] Rec. Trav. Chim. Pays-Bas, 1887, 6. 314.
Page 311
[56] Cf. van't Hoff, Lectures on Physical Chemistry, I., p. 27
(Arnold).
[57] Annalen der Physik, 1899 [3], 68. 663.
[58] Brauns, Jahrbuch für Mineralogie, 1899-1901, 13. Beilage,
p. 39.
[59] Fritsche, Ber., 1869, 2. 112, 540.
[60] De mirabilibus Auscultationibus, Cap. 51 (v. Cohen, Zeitschr.
physikal. Chem., 1901, 36. 513).
[61] E. Cohen and C. van Eyk, Zeitschr. physikal. Chem., 1899,
30. 601; Cohen, ibid., 1900, 33. 59; 35. 588; 1901, 36. 513;
Cohen and E. Goldschmidt, ibid., 1904, 50. 225.
[62] Zeitschr. physikal. Chem., 1900, 33, 58.
[63] Stortenbeker, Zeitschr. physikal. Chem., 1889, 3. 11; Rec.
Trav. Chim. Pays-Bas, 1888, 7. 152.
[64] Zincke, Ber., 1871, 4. 576.
[65] Ostwald, Zeitschr. physikal. Chem., 1897, 22. 313.
[66] Roozeboom, Das Heterogene Gleichgewicht, I. p. 177.
[67] Roozeboom, ibid., p. 179.
[68] Schrötter, Pogg. Annalen, 1850, 81. 276; Troost and
Hautefeuille, Annales de Chim. et Phys. 1874 [5], 2. 153; Ann.
Scient. École Norm. 1868 [2], II. 266.
[69] Pedler, Trans. Chem. Soc., 1890, 57. 599.
[70] Brodie, Trans. Chem. Soc., 1853, 5, 289.
[71] This is a familiar fact in the case of the solubility in carbon
disulphide.
[72] Roozeboom, Das Heterogene Gleichgewicht, I. p. 170.
(Arnold).
[57] Annalen der Physik, 1899 [3], 68. 663.
[58] Brauns, Jahrbuch für Mineralogie, 1899-1901, 13. Beilage,
p. 39.
[59] Fritsche, Ber., 1869, 2. 112, 540.
[60] De mirabilibus Auscultationibus, Cap. 51 (v. Cohen, Zeitschr.
physikal. Chem., 1901, 36. 513).
[61] E. Cohen and C. van Eyk, Zeitschr. physikal. Chem., 1899,
30. 601; Cohen, ibid., 1900, 33. 59; 35. 588; 1901, 36. 513;
Cohen and E. Goldschmidt, ibid., 1904, 50. 225.
[62] Zeitschr. physikal. Chem., 1900, 33, 58.
[63] Stortenbeker, Zeitschr. physikal. Chem., 1889, 3. 11; Rec.
Trav. Chim. Pays-Bas, 1888, 7. 152.
[64] Zincke, Ber., 1871, 4. 576.
[65] Ostwald, Zeitschr. physikal. Chem., 1897, 22. 313.
[66] Roozeboom, Das Heterogene Gleichgewicht, I. p. 177.
[67] Roozeboom, ibid., p. 179.
[68] Schrötter, Pogg. Annalen, 1850, 81. 276; Troost and
Hautefeuille, Annales de Chim. et Phys. 1874 [5], 2. 153; Ann.
Scient. École Norm. 1868 [2], II. 266.
[69] Pedler, Trans. Chem. Soc., 1890, 57. 599.
[70] Brodie, Trans. Chem. Soc., 1853, 5, 289.
[71] This is a familiar fact in the case of the solubility in carbon
disulphide.
[72] Roozeboom, Das Heterogene Gleichgewicht, I. p. 170.
Page 312
[73] Trans. Chem. Soc., 1899, 57. 734.
[74] Carnelley, Trans. Chem. Soc., 1876, 29. 489; 1878, 33. 275.
V. Meyer and Riddle, Ber., 1893, 26. 2443.
[75] Riecke, Zeitschr. physikal. Chem., 1890, 6. 411.
[76] Annalen der Physik., 1898 [3], 66. 492.
[77] Zeitschr. physikal. Chem., 1899, 28. 666.
[78] See Naumann, Ber., 1872, 4. 646; Troost and Hautefeuille,
Compt. rend., 1868, 66. 795; 1868, 67. 1345; Roozeboom, Das
Heterogene Gleichgewicht, I. pp. 62, 171.
[79] Mitscherlich, Lieb. Annalen, 1834, 12. 137; Deville and
Troost, Compt. rend., 1863, 56. 891.
[80] Beckmann, Zeitschr. physikal. Chem., 1890, 5. 79; Hertz,
ibid., 6. 358.
[81] Ber., 1902, 35. 351. Cf. also, K. Schaum, Annalen der Chem.,
1898, 300. 221; R. Wegscheider and Kaufler, Sitzungsber. kaiserl.
Akad. Wissensch. in Wien, 1901, 110, II. 606.
[82] See also Roozeboom, Das Heterogene Gleichgewicht, I. p.
177.
[83] Annales de Chim. et Phys., 1874 [5], 2. 154.
[84] Compt. rend., 1887, 104. 1505.
[85] Compt. rend., 1868, 66. 795.
[86] Phil. Mag., 1884 [5], 18. 210. See also Roozeboom, Das
Heterogene Gleichgewicht, I. p. 177.
[87] Brauns, Neues Jahrbuch für Mineralogie, 1900, 13. Beilage-
Band, p. 39; Roozeboom, Das Heterogene Gleichgewicht, I. p.
181.
[88] Monatshefte, 1888, 9. 435.
[74] Carnelley, Trans. Chem. Soc., 1876, 29. 489; 1878, 33. 275.
V. Meyer and Riddle, Ber., 1893, 26. 2443.
[75] Riecke, Zeitschr. physikal. Chem., 1890, 6. 411.
[76] Annalen der Physik., 1898 [3], 66. 492.
[77] Zeitschr. physikal. Chem., 1899, 28. 666.
[78] See Naumann, Ber., 1872, 4. 646; Troost and Hautefeuille,
Compt. rend., 1868, 66. 795; 1868, 67. 1345; Roozeboom, Das
Heterogene Gleichgewicht, I. pp. 62, 171.
[79] Mitscherlich, Lieb. Annalen, 1834, 12. 137; Deville and
Troost, Compt. rend., 1863, 56. 891.
[80] Beckmann, Zeitschr. physikal. Chem., 1890, 5. 79; Hertz,
ibid., 6. 358.
[81] Ber., 1902, 35. 351. Cf. also, K. Schaum, Annalen der Chem.,
1898, 300. 221; R. Wegscheider and Kaufler, Sitzungsber. kaiserl.
Akad. Wissensch. in Wien, 1901, 110, II. 606.
[82] See also Roozeboom, Das Heterogene Gleichgewicht, I. p.
177.
[83] Annales de Chim. et Phys., 1874 [5], 2. 154.
[84] Compt. rend., 1887, 104. 1505.
[85] Compt. rend., 1868, 66. 795.
[86] Phil. Mag., 1884 [5], 18. 210. See also Roozeboom, Das
Heterogene Gleichgewicht, I. p. 177.
[87] Brauns, Neues Jahrbuch für Mineralogie, 1900, 13. Beilage-
Band, p. 39; Roozeboom, Das Heterogene Gleichgewicht, I. p.
181.
[88] Monatshefte, 1888, 9. 435.
Page 313
[89] Gattermann, Ber., 1890, 53. 1738.
[90] Zeitschr. physikal. Chem., 1889, 4. 468; Annalen der Physik,
1900 [4], 2. 649.
[91] Quincke, Annalen der Physik, 1894 [3], 53. 613; Tammann,
Annalen der Physik, 1901 [4], 4. 524; 1902, 8. 103; Rotarski,
ibid., 4. 528.
[92] Annalen der Physik, 1900 [4], 2. 649.
[93] Annalen der Physik, 1902 [4], 8. 911.
[94] See, more especially, O. Lehmann, Annalen der Physik, 1900
[4], 2. 649; Reinitzer, Sitzungsber. kaiserl. Akad. zu Wien., 1888,
94. (2), 719; 97. (1), 167; Gattermann, loc. cit.; Schenck, Zeitschr.
physikal. Chem., 1897, 23. 703; 1898, 25. 337; 27. 170; 1899, 28.
280; Schenck and Schneider, ibid., 1899, 29. 546; Abegg and
Seitz, ibid., 1899, 29. 491; Hulett, ibid., 1899, 28. 629; Coehn,
Zeitschr. Elektrochem., 1904, 10. 856: Bredig and Schukowsky,
ibid., 3419. For a full account of the subject, the reader is referred
to the work by Lehmann, Flüssige Kristalle (Engelmann, 1904),
or the smaller monograph by Schenck, Kristallinische
Flüssigkeiten und flüssige Kristalle (Engelmann, 1905).
[95] A. C. de Kock, Zeitschr. physikal. Chem., 1904, 48. 129.
[96] On account of the fact that all grades of rigidity have been
realized between the ordinary solid and the liquid state, in the
case both of crystalline and amorphous substances, it has been
proposed to abandon the terms "solid" and "liquid," and to class
bodies as "crystalline" or "amorphous," the passage from the one
condition to the other being discontinuous; crystalline bodies
possess a certain regular orientation of their molecules and a
directive force, while in amorphous bodies these are wanting (see
Lehmann, Annalen der Physik, 1900 [4], 2. 696).
[97] Hulett, loc. cit.
[90] Zeitschr. physikal. Chem., 1889, 4. 468; Annalen der Physik,
1900 [4], 2. 649.
[91] Quincke, Annalen der Physik, 1894 [3], 53. 613; Tammann,
Annalen der Physik, 1901 [4], 4. 524; 1902, 8. 103; Rotarski,
ibid., 4. 528.
[92] Annalen der Physik, 1900 [4], 2. 649.
[93] Annalen der Physik, 1902 [4], 8. 911.
[94] See, more especially, O. Lehmann, Annalen der Physik, 1900
[4], 2. 649; Reinitzer, Sitzungsber. kaiserl. Akad. zu Wien., 1888,
94. (2), 719; 97. (1), 167; Gattermann, loc. cit.; Schenck, Zeitschr.
physikal. Chem., 1897, 23. 703; 1898, 25. 337; 27. 170; 1899, 28.
280; Schenck and Schneider, ibid., 1899, 29. 546; Abegg and
Seitz, ibid., 1899, 29. 491; Hulett, ibid., 1899, 28. 629; Coehn,
Zeitschr. Elektrochem., 1904, 10. 856: Bredig and Schukowsky,
ibid., 3419. For a full account of the subject, the reader is referred
to the work by Lehmann, Flüssige Kristalle (Engelmann, 1904),
or the smaller monograph by Schenck, Kristallinische
Flüssigkeiten und flüssige Kristalle (Engelmann, 1905).
[95] A. C. de Kock, Zeitschr. physikal. Chem., 1904, 48. 129.
[96] On account of the fact that all grades of rigidity have been
realized between the ordinary solid and the liquid state, in the
case both of crystalline and amorphous substances, it has been
proposed to abandon the terms "solid" and "liquid," and to class
bodies as "crystalline" or "amorphous," the passage from the one
condition to the other being discontinuous; crystalline bodies
possess a certain regular orientation of their molecules and a
directive force, while in amorphous bodies these are wanting (see
Lehmann, Annalen der Physik, 1900 [4], 2. 696).
[97] Hulett, loc. cit.
Page 314
[98] Roozeboom, Das Heterogene Gleichgewicht, I. p. 144. See
also Schenck, Kristallinische Flüssigkeiten und flüssige Kristalle,
p. 8 (Engelmann, 1904).
[99] The possible number of triple points in a one-component
system is given by the expression
n(n - 1)(n - 2)
,
1.2.3
where n is the number of phases (Riecke, Zeitschr. physikal.
Chem., 1890, 6, 411). The number of triple points, therefore,
increases very rapidly as the number of possible phases increases.
[100] Duhem, Zeitschr. physikal. Chem., 1891, 8. 371. Cf.
Roozeboom, Das Heterogene Gleichgewicht, p. 94 ff.
[101] Roozeboom, Das Heterogene Gleichgewicht, I. p. 99.
[102] Roozeboom, Zeitschr. physikal. Chem., 1888, 2. 474.
[103] These changes can be predicted quantitatively by means of
the thermodynamic equation,
dp Q
= ,
dt T(v2 - v1)
provided the specific volumes of the phases are known, and the
heat effect which accompanies the transformation of one phase
into the other.
[104] Studies on Chemical Dynamics, translated by Ewan, p. 218.
[105] Le Chatelier, Compt. rend., 1884, 99. 786.
[106] See Principles of Inorganic Chemistry, translated by
Findlay, 2nd edit., p. 133. (Macmillan, 1904.)
[107] Roozeboom, Zeitschr. physikal. Chem., 1888, 2. 474.
[108] Roozeboom, Das Heterogene Gleichgewicht, I. p. 189.
also Schenck, Kristallinische Flüssigkeiten und flüssige Kristalle,
p. 8 (Engelmann, 1904).
[99] The possible number of triple points in a one-component
system is given by the expression
n(n - 1)(n - 2)
,
1.2.3
where n is the number of phases (Riecke, Zeitschr. physikal.
Chem., 1890, 6, 411). The number of triple points, therefore,
increases very rapidly as the number of possible phases increases.
[100] Duhem, Zeitschr. physikal. Chem., 1891, 8. 371. Cf.
Roozeboom, Das Heterogene Gleichgewicht, p. 94 ff.
[101] Roozeboom, Das Heterogene Gleichgewicht, I. p. 99.
[102] Roozeboom, Zeitschr. physikal. Chem., 1888, 2. 474.
[103] These changes can be predicted quantitatively by means of
the thermodynamic equation,
dp Q
= ,
dt T(v2 - v1)
provided the specific volumes of the phases are known, and the
heat effect which accompanies the transformation of one phase
into the other.
[104] Studies on Chemical Dynamics, translated by Ewan, p. 218.
[105] Le Chatelier, Compt. rend., 1884, 99. 786.
[106] See Principles of Inorganic Chemistry, translated by
Findlay, 2nd edit., p. 133. (Macmillan, 1904.)
[107] Roozeboom, Zeitschr. physikal. Chem., 1888, 2. 474.
[108] Roozeboom, Das Heterogene Gleichgewicht, I. p. 189.
Page 315
[109] Roozeboom, Das Heterogene Gleichgewicht, I. p. 125. See
also Zawidski, Zeitschr. physikal. Chem., 1904, 47. 727; van Eyk,
ibid., 1905, 51. 720.
[110] Roberts-Austen, Proc. Roy. Soc., 63. 454; Spring, Zeitschr.
physikal. Chem., 1894, 15. 65. See also p. 35.
[111] Ramsay and Young, Phil. Trans., 1884, 175. 461; Allen,
Trans. Chem. Soc., 1900, 77. 413.
[112] Ramsay and Young, Phil. Trans. 1886, 177. 87.
[113] This is exemplified in the well-known experiment with the
cryophorus.
[114] Tammann has, however, found that the fusion curve (solid
in contact with liquid) of phosphonium chloride can be followed
up to temperatures above the critical point (Arch. néer., 1901 [2],
6. 244).
[115] Phil. Mag., 1886, 21. 33. See also S. A. Moss, Physical
Review, 1903, 16. 356.
[116] This is found also in the case of bismuth. See Tammann,
Zeitschr. anorgan. Chem., 1904, 40. 54.
[117] See p. 57, footnote.
[118] Pogg. Annalen, 1850, 81. 562.
[119] Barus, Amer. Jour. Sci., 1892, 42. 125; Mack, Compt. rend.,
1898, 127. 361; Hulett, Zeitschr. physikal. Chem., 1899, 38. 629.
[120] Annalen der Physik, 1899 [3], 68. 553, 629; 1900 [4], 1.
275; 2. 1; 3. 161. See also Tammann, Kristallisieren und
Schmelzen (Leipzig, 1903).
[121] Ostwald, Lehrbuch, II. 2. 373; Poynting, Phil. Mag., 1881
[5], 12. 2; Planck, Wied. Annalen, 1882, 15. 446.
[122] Bakhuis Roozeboom, Das Heterogene Gleichgewicht, I. p.
91.
also Zawidski, Zeitschr. physikal. Chem., 1904, 47. 727; van Eyk,
ibid., 1905, 51. 720.
[110] Roberts-Austen, Proc. Roy. Soc., 63. 454; Spring, Zeitschr.
physikal. Chem., 1894, 15. 65. See also p. 35.
[111] Ramsay and Young, Phil. Trans., 1884, 175. 461; Allen,
Trans. Chem. Soc., 1900, 77. 413.
[112] Ramsay and Young, Phil. Trans. 1886, 177. 87.
[113] This is exemplified in the well-known experiment with the
cryophorus.
[114] Tammann has, however, found that the fusion curve (solid
in contact with liquid) of phosphonium chloride can be followed
up to temperatures above the critical point (Arch. néer., 1901 [2],
6. 244).
[115] Phil. Mag., 1886, 21. 33. See also S. A. Moss, Physical
Review, 1903, 16. 356.
[116] This is found also in the case of bismuth. See Tammann,
Zeitschr. anorgan. Chem., 1904, 40. 54.
[117] See p. 57, footnote.
[118] Pogg. Annalen, 1850, 81. 562.
[119] Barus, Amer. Jour. Sci., 1892, 42. 125; Mack, Compt. rend.,
1898, 127. 361; Hulett, Zeitschr. physikal. Chem., 1899, 38. 629.
[120] Annalen der Physik, 1899 [3], 68. 553, 629; 1900 [4], 1.
275; 2. 1; 3. 161. See also Tammann, Kristallisieren und
Schmelzen (Leipzig, 1903).
[121] Ostwald, Lehrbuch, II. 2. 373; Poynting, Phil. Mag., 1881
[5], 12. 2; Planck, Wied. Annalen, 1882, 15. 446.
[122] Bakhuis Roozeboom, Das Heterogene Gleichgewicht, I. p.
91.
Page 316
[123] Lussana, Il nuovo Cimento, 1895 [4], 1. 105.
[124] Tammann, Zeitschr. physikal. Chem., 1903, 46. 818.
[125] Foote, Zeitschr. physikal. Chem., 1900, 33. 740.
[126] Ostwald, Zeitschr. physikal. Chem., 1897, 22. 289.
[127] Van't Hoff, Arch, néer., 1901, 6. 471.
[128] See, for example, the determinations of the solubility of
rhombic and monoclinic sulphur, by J. Meyer, Zeitschr. anorg.
Chem., 1902, 33. 140.
[129] Zeitschr. physikal. Chem., 1899, 32. 506.
[130] Kastle and Reed, Amer. Chem. Jour., 1902, 27. 209.
[131] Zeitschr. physikal. Chem., 1900, 35. 581.
[132] Compt. rend., 1882, 95. 1278; 1884, 97. 1298, 1366, 1433.
[133] Zeitschr. physikal. Chem., 1893, 12. 545.
[134] Sitzungsber. Wiener Akad., 1894, 103. IIa. 226.
[135] Zeitschr. physikal. Chem., 23-29. See also Küster, ibid., 25-
28.
[136] Zeitschr. physikal. Chem., 1897, 24. 152.
[137] Ibid., 1898, 27. 585.
[138] See W. Guertler, Zeitschr. anorgan. Chem., 1904, 40. 268;
Tammann, Zeitschr. Elektrochem., 1904, 10. 532.
[139] E. von Pickardt, Zeitschr. physikal. Chem., 1902, 42. 17.
[140] Zeitschr. physikal. Chem., 1904, 48. 467.
[141] M. Padoa, Accad. Lincei, Atti, 1904, 13. 329.
[142] Deville, Compt. rend., 1852, 34. 561; Payen, ibid., 1852,
34. 508; Debray, ibid., 1858, 46. 576. It has also been found by
[124] Tammann, Zeitschr. physikal. Chem., 1903, 46. 818.
[125] Foote, Zeitschr. physikal. Chem., 1900, 33. 740.
[126] Ostwald, Zeitschr. physikal. Chem., 1897, 22. 289.
[127] Van't Hoff, Arch, néer., 1901, 6. 471.
[128] See, for example, the determinations of the solubility of
rhombic and monoclinic sulphur, by J. Meyer, Zeitschr. anorg.
Chem., 1902, 33. 140.
[129] Zeitschr. physikal. Chem., 1899, 32. 506.
[130] Kastle and Reed, Amer. Chem. Jour., 1902, 27. 209.
[131] Zeitschr. physikal. Chem., 1900, 35. 581.
[132] Compt. rend., 1882, 95. 1278; 1884, 97. 1298, 1366, 1433.
[133] Zeitschr. physikal. Chem., 1893, 12. 545.
[134] Sitzungsber. Wiener Akad., 1894, 103. IIa. 226.
[135] Zeitschr. physikal. Chem., 23-29. See also Küster, ibid., 25-
28.
[136] Zeitschr. physikal. Chem., 1897, 24. 152.
[137] Ibid., 1898, 27. 585.
[138] See W. Guertler, Zeitschr. anorgan. Chem., 1904, 40. 268;
Tammann, Zeitschr. Elektrochem., 1904, 10. 532.
[139] E. von Pickardt, Zeitschr. physikal. Chem., 1902, 42. 17.
[140] Zeitschr. physikal. Chem., 1904, 48. 467.
[141] M. Padoa, Accad. Lincei, Atti, 1904, 13. 329.
[142] Deville, Compt. rend., 1852, 34. 561; Payen, ibid., 1852,
34. 508; Debray, ibid., 1858, 46. 576. It has also been found by
Page 317
Jaffé (Zeitschr. physikal. Chem., 1903, 43. 465) that when
spontaneous crystallization from solution occurs, the less stable
form always separates first when purification has been carried
sufficiently far.
[143] Brauns, Neues Jahrbuch für Mineralogie, 1899, 13.
(Beilage Band) 84.
[144] Lehrbuch, II. 2. 445. See also Principles of Inorganic
Chemistry, 2nd edit., p. 210 ff.
[145] Schaum and Schönbeck, Annalen der Physik, 1902 [4], 8.
652. See also Chr. Füchtbauer, Zeitschr. physikal. Chem., 1904,
48. 549.
[146] Ramsay and Young, Phil. Trans., 1886, 177. 87.
[147] See volume in this series on Chemical Dynamics, by Dr. J.
W. Mellor.
[148] Isambert, Compt. rend., 1881, 92. 919; 1882, 94. 958; 1883,
96. 643. Walker and Lumsden, Jour. Chem. Soc., 1897, 71. 428.
[149] Compt. rend., 1867, 64. 603.
[150] Compt. rend., 1883, 102. 1243.
[151] Compt. rend., 1868, 66, 1259.
[152] Horstmann, Ber., 1876, 9. 749.
[153] Loc. cit.
[154] For the reasons for choosing anhydrous salt and water
instead of salt hydrate and water as components, see p. 14.
[155] See Ostwald, Lehrbuch, II. 2. 527.
[156] Ostwald, Lehrbuch, II. 2. 538.
[157] Zeitschr. physikal. Chem., 1889, 4. 43.
[158] Ber., 1876, 9. 749.
spontaneous crystallization from solution occurs, the less stable
form always separates first when purification has been carried
sufficiently far.
[143] Brauns, Neues Jahrbuch für Mineralogie, 1899, 13.
(Beilage Band) 84.
[144] Lehrbuch, II. 2. 445. See also Principles of Inorganic
Chemistry, 2nd edit., p. 210 ff.
[145] Schaum and Schönbeck, Annalen der Physik, 1902 [4], 8.
652. See also Chr. Füchtbauer, Zeitschr. physikal. Chem., 1904,
48. 549.
[146] Ramsay and Young, Phil. Trans., 1886, 177. 87.
[147] See volume in this series on Chemical Dynamics, by Dr. J.
W. Mellor.
[148] Isambert, Compt. rend., 1881, 92. 919; 1882, 94. 958; 1883,
96. 643. Walker and Lumsden, Jour. Chem. Soc., 1897, 71. 428.
[149] Compt. rend., 1867, 64. 603.
[150] Compt. rend., 1883, 102. 1243.
[151] Compt. rend., 1868, 66, 1259.
[152] Horstmann, Ber., 1876, 9. 749.
[153] Loc. cit.
[154] For the reasons for choosing anhydrous salt and water
instead of salt hydrate and water as components, see p. 14.
[155] See Ostwald, Lehrbuch, II. 2. 527.
[156] Ostwald, Lehrbuch, II. 2. 538.
[157] Zeitschr. physikal. Chem., 1889, 4. 43.
[158] Ber., 1876, 9. 749.
Page 318
[159] See, for example, van't Hoff, Lectures on Theoretical and
Physical Chemistry, I. p. 62 (Arnold).
[160] Jour. Chem. Soc., 1877, 32. 395.
[161] Hoitsema, Zeitschr. physikal. Chem., 1895, 17. 1.
[162] Zeitschr. physikal. Chem., 1887, 1. 5; 1895, 17. 52.
[163] It is important to powder the salt, since otherwise the
dehydration of the hydrate and the production of equilibrium
occurs with comparatively great tardiness.
[164] A chemical individual is a substance which persists as a
phase of constant composition when the conditions of
temperature, pressure, and composition of the other phases
present, undergo continuous alteration within certain limits—the
limits of existence of the substance (Wald, Zeitschr. physikal.
Chem., 1897, 24. 648).
[165] Van't Hoff, Zeitschr. physikal. Chem., 1890, 5. 323;
Ostwald, Lehrbuch, I. 606.
[166] That mercury does dissolve in water can be argued from
analogy, say, with mercury and bromonaphthalene. At the
ordinary temperature these two liquids appear to be quite
insoluble in one another, but at a temperature of 280° the mercury
dissolves in appreciable quantity; for on heating a tube containing
bromonaphthalene over mercury the latter sublimes through the
liquid bromonaphthalene and condenses on the upper surface of
the tube.
[167] Phil. Mag., 1884, [5], 18. 22; 495.
[168] Wied. Annalen, 1886, 28. 305.
[169] Zeitschr. physikal. Chem., 1898, 26. 433.
[170] Rothmund, loc. cit.
[171] Rothmund, loc. cit.
Physical Chemistry, I. p. 62 (Arnold).
[160] Jour. Chem. Soc., 1877, 32. 395.
[161] Hoitsema, Zeitschr. physikal. Chem., 1895, 17. 1.
[162] Zeitschr. physikal. Chem., 1887, 1. 5; 1895, 17. 52.
[163] It is important to powder the salt, since otherwise the
dehydration of the hydrate and the production of equilibrium
occurs with comparatively great tardiness.
[164] A chemical individual is a substance which persists as a
phase of constant composition when the conditions of
temperature, pressure, and composition of the other phases
present, undergo continuous alteration within certain limits—the
limits of existence of the substance (Wald, Zeitschr. physikal.
Chem., 1897, 24. 648).
[165] Van't Hoff, Zeitschr. physikal. Chem., 1890, 5. 323;
Ostwald, Lehrbuch, I. 606.
[166] That mercury does dissolve in water can be argued from
analogy, say, with mercury and bromonaphthalene. At the
ordinary temperature these two liquids appear to be quite
insoluble in one another, but at a temperature of 280° the mercury
dissolves in appreciable quantity; for on heating a tube containing
bromonaphthalene over mercury the latter sublimes through the
liquid bromonaphthalene and condenses on the upper surface of
the tube.
[167] Phil. Mag., 1884, [5], 18. 22; 495.
[168] Wied. Annalen, 1886, 28. 305.
[169] Zeitschr. physikal. Chem., 1898, 26. 433.
[170] Rothmund, loc. cit.
[171] Rothmund, loc. cit.
Page 319
[172] A similar behaviour is found in the case of diethylamine and
water (R. T. Lattey, Phil. Mag., 1905, [6], 10, 397).
[173] C. S. Hudson, Zeitschr. physikal. Chem., 1904, 47. 113.
[174] Konowaloff, Wied. Annalen, 1881, 14. 219. Ostwald,
Lehrbuch, II. 2. 687. Bancroft, Phase Rule, p. 96.
[175] Konowaloff, loc. cit.
[176] Roozeboom, Zeitschr. physikal. Chem., 1891, 8. 526; Rec.
Trav. Chim. Pays-Bas, 1884, 3. 38.
[177] Konowaloff, loc. cit. Cf. Bancroft, Phase Rule, p. 100.
[178] Phil. Mag., 1884 [5], 18. 503.
[179] See, for example, Walker, Introduction to Physical
Chemistry, 3rd edit., p. 86 (Macmillan, 1903). Consult also
Young, Fractional Distillation (Macmillan, 1903), or Kuenen,
Verdampfung und Verflüssigung von Gemischen (Barth, 1906),
where the subject is fully treated.
[180] Since this is the only phase of variable composition present.
[181] E. von Stackelberg, Zeitschr. physikal. Chem., 1896, 20.
337. If the change of volume which accompanies solution, and
the heat effect are known, the quantitative change of the solubility
with the pressure can be calculated (Braun, Zeitschr. physikal.
Chem., 1887, 1. 259).
[182] Van't Hoff, Arch. néerland. 1901 [2], 6. 471.
[183] Tilden and Shenstone, Phil. Trans. 1884, 175. 23; Hulett
and Allen, Jour. Amer. Chem. Soc. 1902, 24. 667; Andreä, Jour.
prak. Chem. 137. 474; Lumsden, Jour. Chem. Soc., 1902, 81. 350;
Mylius and v. Wrochem, Ber. 1900, 33. 3689.
[184] E. von Stackelberg, Zeitschr. physikal. Chem. 1896, 20.
159; 1898, 26. 533; Lumsden, Jour. Chem. Soc., 1902, 81. 350;
Holsboer, Zeitschr. physikal. Chem., 1902, 39. 691.
water (R. T. Lattey, Phil. Mag., 1905, [6], 10, 397).
[173] C. S. Hudson, Zeitschr. physikal. Chem., 1904, 47. 113.
[174] Konowaloff, Wied. Annalen, 1881, 14. 219. Ostwald,
Lehrbuch, II. 2. 687. Bancroft, Phase Rule, p. 96.
[175] Konowaloff, loc. cit.
[176] Roozeboom, Zeitschr. physikal. Chem., 1891, 8. 526; Rec.
Trav. Chim. Pays-Bas, 1884, 3. 38.
[177] Konowaloff, loc. cit. Cf. Bancroft, Phase Rule, p. 100.
[178] Phil. Mag., 1884 [5], 18. 503.
[179] See, for example, Walker, Introduction to Physical
Chemistry, 3rd edit., p. 86 (Macmillan, 1903). Consult also
Young, Fractional Distillation (Macmillan, 1903), or Kuenen,
Verdampfung und Verflüssigung von Gemischen (Barth, 1906),
where the subject is fully treated.
[180] Since this is the only phase of variable composition present.
[181] E. von Stackelberg, Zeitschr. physikal. Chem., 1896, 20.
337. If the change of volume which accompanies solution, and
the heat effect are known, the quantitative change of the solubility
with the pressure can be calculated (Braun, Zeitschr. physikal.
Chem., 1887, 1. 259).
[182] Van't Hoff, Arch. néerland. 1901 [2], 6. 471.
[183] Tilden and Shenstone, Phil. Trans. 1884, 175. 23; Hulett
and Allen, Jour. Amer. Chem. Soc. 1902, 24. 667; Andreä, Jour.
prak. Chem. 137. 474; Lumsden, Jour. Chem. Soc., 1902, 81. 350;
Mylius and v. Wrochem, Ber. 1900, 33. 3689.
[184] E. von Stackelberg, Zeitschr. physikal. Chem. 1896, 20.
159; 1898, 26. 533; Lumsden, Jour. Chem. Soc., 1902, 81. 350;
Holsboer, Zeitschr. physikal. Chem., 1902, 39. 691.
Page 320
[185] Reicher and van Deventer, Zeitschr. physikal. Chem. 1890,
5. 559; cf. Ostwald, Lehrbuch, II. 2. 803.
[186] It has been shown that the formula of Ramsay and Young
(p. 66) can be applied (with certain restrictions) to the
interpolation and extrapolation of the solubility curve of a
substance provided two (or three) points on the curve are known.
In this case T, T1, etc., refer to the temperatures at which the two
substances—one the solubility curve of which is known, the other
the solubility curve of which is to be calculated—have equal
solubilities, instead of, as in the previous case, equal vapour
pressures. (Findlay, Proc. Roy. Soc., 1902, 69. 471; Zeitschr.
physikal. Chem., 1903, 42. 110.)
[187] W. Müller and P. Kaufmann, Zeitschr. physikal. Chem.
1903, 42. 497.
[188] W. O. Rabe, Zeitschr. physikal. Chem., 1901, 38. 175.
[189] With regard to the limits of supersaturation and the
spontaneous crystallization of the solute from supersaturated
solutions, see Jaffé, Zeitschr. physikal. Chem., 1903, 43. 565, and
the very interesting paper by Miers and Isaac, Trans. Chem. Soc.,
1906, 89. 413.
[190] Annales chim. phys., 1894 [7], 2. 524.
[191] Phil. Trans., 1884, 175. 23.
[192] Hissink, Zeitschr. physikal. Chem., 1900, 32. 543.
[193] Zeitschr. physikal. Chem., 1903, 43. 313.
[194] Guthrie, Phil. Mag., 1875, [4], 49. 1; 1884, [5], 17. 462.
[195] See Roloff, Zeitschr. physikal. Chem., 1895, 17. 325;
Guthrie, loc. cit.
[196] Guthrie, Phil. Mag., loc. cit. Cf. Ostwald, Lehrbuch, II. 2.
843.
5. 559; cf. Ostwald, Lehrbuch, II. 2. 803.
[186] It has been shown that the formula of Ramsay and Young
(p. 66) can be applied (with certain restrictions) to the
interpolation and extrapolation of the solubility curve of a
substance provided two (or three) points on the curve are known.
In this case T, T1, etc., refer to the temperatures at which the two
substances—one the solubility curve of which is known, the other
the solubility curve of which is to be calculated—have equal
solubilities, instead of, as in the previous case, equal vapour
pressures. (Findlay, Proc. Roy. Soc., 1902, 69. 471; Zeitschr.
physikal. Chem., 1903, 42. 110.)
[187] W. Müller and P. Kaufmann, Zeitschr. physikal. Chem.
1903, 42. 497.
[188] W. O. Rabe, Zeitschr. physikal. Chem., 1901, 38. 175.
[189] With regard to the limits of supersaturation and the
spontaneous crystallization of the solute from supersaturated
solutions, see Jaffé, Zeitschr. physikal. Chem., 1903, 43. 565, and
the very interesting paper by Miers and Isaac, Trans. Chem. Soc.,
1906, 89. 413.
[190] Annales chim. phys., 1894 [7], 2. 524.
[191] Phil. Trans., 1884, 175. 23.
[192] Hissink, Zeitschr. physikal. Chem., 1900, 32. 543.
[193] Zeitschr. physikal. Chem., 1903, 43. 313.
[194] Guthrie, Phil. Mag., 1875, [4], 49. 1; 1884, [5], 17. 462.
[195] See Roloff, Zeitschr. physikal. Chem., 1895, 17. 325;
Guthrie, loc. cit.
[196] Guthrie, Phil. Mag., loc. cit. Cf. Ostwald, Lehrbuch, II. 2.
843.
Page 321
[197] Guthrie, Phil. Mag., 1875 [4], 49. 269.
[198] Ber., 1877, 20. 2223.
[199] Silz-Ber. Wien. Akad., 1880, 81. II. 1058.
[200] Guthrie, Phil. Mag., 1875 [4], 49. 206.
[201] If in the neighbourhood of the cryohydric point solution
should be accompanied by an evolution of heat, then as the
solubility would in that case increase with fall of temperature, salt
would pass into solution.
[202] Walker, Zeitschr. physikal. Chem., 1890, 5. 193.
[203] Zeitschr. physikal. Chem., 1897, 23. 418.
[204] Provided the solid nitrile is not present in too great excess.
[205] Wied. Annalen, 1886, 28. 328. Cf. Ostwald, Lehrbuch, II. 2.
872.
[206] Walker, Zeitschr. physikal. Chem., 1890, 5. 193.
Schreinemakers, ibid., 1897, 23. 417. Roozeboom, Rec. trav.
chim. Pays-Bays, 1889, 8. 257. Bruner, Zeitschr. physikal. Chem.,
1897, 23. 542.
[207] Van't Hoff, Lectures on Theoretical Chemistry, I. p. 42.
Ostwald, Lehrbuch, II. 2. 824.
[208] Ostwald, Principles of Inorganic Chemistry, translated by
A. Findlay, 2nd edit., p. 453 (Macmillan, 1904); Skirrow and
Calvert, Zeitschr. physikal. Chem., 1901, 37. 217.
[209] Vide Loewel, Annales chim. phys., 1857 [3], 49. 32. Cf.
Löwenherz, Zeitschr. physikal. Chem., 1895, 18. 82.
[210] Loewel, loc. cit. Gay-Lussac, Annales chim. phys., 1819,
11. 296. For the solubility at higher temperatures, see Tilden and
Shenstone, Phil. Trans., 1884, 175. 23. Étard, Annales chim.
phys., 1894 [7], 2. 548.
[198] Ber., 1877, 20. 2223.
[199] Silz-Ber. Wien. Akad., 1880, 81. II. 1058.
[200] Guthrie, Phil. Mag., 1875 [4], 49. 206.
[201] If in the neighbourhood of the cryohydric point solution
should be accompanied by an evolution of heat, then as the
solubility would in that case increase with fall of temperature, salt
would pass into solution.
[202] Walker, Zeitschr. physikal. Chem., 1890, 5. 193.
[203] Zeitschr. physikal. Chem., 1897, 23. 418.
[204] Provided the solid nitrile is not present in too great excess.
[205] Wied. Annalen, 1886, 28. 328. Cf. Ostwald, Lehrbuch, II. 2.
872.
[206] Walker, Zeitschr. physikal. Chem., 1890, 5. 193.
Schreinemakers, ibid., 1897, 23. 417. Roozeboom, Rec. trav.
chim. Pays-Bays, 1889, 8. 257. Bruner, Zeitschr. physikal. Chem.,
1897, 23. 542.
[207] Van't Hoff, Lectures on Theoretical Chemistry, I. p. 42.
Ostwald, Lehrbuch, II. 2. 824.
[208] Ostwald, Principles of Inorganic Chemistry, translated by
A. Findlay, 2nd edit., p. 453 (Macmillan, 1904); Skirrow and
Calvert, Zeitschr. physikal. Chem., 1901, 37. 217.
[209] Vide Loewel, Annales chim. phys., 1857 [3], 49. 32. Cf.
Löwenherz, Zeitschr. physikal. Chem., 1895, 18. 82.
[210] Loewel, loc. cit. Gay-Lussac, Annales chim. phys., 1819,
11. 296. For the solubility at higher temperatures, see Tilden and
Shenstone, Phil. Trans., 1884, 175. 23. Étard, Annales chim.
phys., 1894 [7], 2. 548.
Page 322
[211] Richards, Zeitschr. physikal. Chem., 1898, 26. 690;
Richards and Wells, ibid., 1903, 43. 465. This temperature is not
quite the same as that of the quadruple point anhydrous salt—
hydrated salt—solution—vapour, because the latter is the
temperature at which the system is under the pressure of its own
vapour. Since, however, the influence of pressure on the solubility
is very slight (p. 107), the position of the two points will not be
greatly different. The quadruple point was found by Cohen
(Zeitschr. physikal. Chem., 1894, 14. 90) to be 32.6° and 30.8
mm. of mercury.
[212] Van't Hoff and van Deventer, Zeitschr. physikal. Chem.,
1887, 1. 185. Cf. Cohen, ibid., 1894, 14. 88.
[213] Debray, Compt. rend., 1868, 66. 194.
[214] Richards, Zeitschr. physikal. Chem., 1898, 26. 690. A
number of other salt hydrates, having transition-points ranging
from 20° to 78°, which might be used for the same purpose, have
been given by Richards and Churchill, ibid., 1899, 28. 313.
[215] Zeitschr. physikal. Chem., 1903, 46. 818.
[216] Van't Hoff, Lectures on Physical Chemistry, I. p. 67.
[217] Cohen, Zeitschr. physikal. Chem., 1894, 14. 90.
[218] Ziz, Schweigger's Journal, 1815, 15. 166. See Ostwald,
Lehrbuch, II. 2. 717.
[219] See, for example, the solubility determinations published in
Wissenschaftliche Abhandl. der physikalisch-technischen
Reichsanstalt, Vol. III., or in the Berichte, for the years 1897-
1901.
[220] Meusser, Ber., 1901, 34. 2440.
[221] Mylius and von Wrochem, Ber., 1900, 33. 3693.
[222] Walker and Fyffe, Jour. Chem. Soc., 1903, 83. 180.
Richards and Wells, ibid., 1903, 43. 465. This temperature is not
quite the same as that of the quadruple point anhydrous salt—
hydrated salt—solution—vapour, because the latter is the
temperature at which the system is under the pressure of its own
vapour. Since, however, the influence of pressure on the solubility
is very slight (p. 107), the position of the two points will not be
greatly different. The quadruple point was found by Cohen
(Zeitschr. physikal. Chem., 1894, 14. 90) to be 32.6° and 30.8
mm. of mercury.
[212] Van't Hoff and van Deventer, Zeitschr. physikal. Chem.,
1887, 1. 185. Cf. Cohen, ibid., 1894, 14. 88.
[213] Debray, Compt. rend., 1868, 66. 194.
[214] Richards, Zeitschr. physikal. Chem., 1898, 26. 690. A
number of other salt hydrates, having transition-points ranging
from 20° to 78°, which might be used for the same purpose, have
been given by Richards and Churchill, ibid., 1899, 28. 313.
[215] Zeitschr. physikal. Chem., 1903, 46. 818.
[216] Van't Hoff, Lectures on Physical Chemistry, I. p. 67.
[217] Cohen, Zeitschr. physikal. Chem., 1894, 14. 90.
[218] Ziz, Schweigger's Journal, 1815, 15. 166. See Ostwald,
Lehrbuch, II. 2. 717.
[219] See, for example, the solubility determinations published in
Wissenschaftliche Abhandl. der physikalisch-technischen
Reichsanstalt, Vol. III., or in the Berichte, for the years 1897-
1901.
[220] Meusser, Ber., 1901, 34. 2440.
[221] Mylius and von Wrochem, Ber., 1900, 33. 3693.
[222] Walker and Fyffe, Jour. Chem. Soc., 1903, 83. 180.
Page 323
[223] Monatshefte, 1887, 8. 601.
[224] The equilibria between calcium chloride and water have
been most completely studied by Roozeboom (Zeitschr. physikal.
Chem., 1889, 4. 31).
[225] Hammerl, Sitzungsber. Wien. Akad., 2te Abteil, 1878, 78. 59.
Roozeboom, Zeitschr. physikal. Chem., 1889, 4. 31.
[226] Lidbury, Zeitschr. physikal. Chem., 1902, 39. 453. The
curvature at the melting point is all the greater the more the
compound is dissociated into its components in the liquid state. If
the compound is completely undissociated, even in the vapour
phase, the two branches of the curve will intersect, (e.g. pyridine
and methyl iodide; Aten, Versl. Konink. Akad. Wetensch.
Amsterdam, 1905, 13. 462). The smaller the degree of
dissociation, therefore, the sharper will be the bend. (See
Stortenbeker, Zeitschr. physikal. Chem., 1892, 10. 194.) From the
extent of flattening of the curve, it is also possible, with some
degree of approximation, to calculate the degree of dissociation of
the substance in the fused state. (See Roozeboom and Aten,
Zeitschr. physikal. Chem., 1905, 53. 463; Kremann, Zeitschr.
Elektrochem., 1906, 12. 259.)
[227] See Roozeboom, Zeitschr. physikal. Chem., 1889, 4. 31.
[228] Tammann, Wied. Annalen, 1899, 68. 577.
[229] Duhem, Journ. Physical Chem., 1898, 2. 31.
[230] Gibbs, Trans. Conn. Acad., 3. 155; Saurel, Journ. Phys.
Chem., 1901, 5. 35.
[231] In the case of the fusion of a compound of two components
with formation of a liquid phase of the same composition, the
temperature is a maximum; in the case of liquid mixtures of
constant boiling-point, the temperature may be a minimum
(p. 105).
[224] The equilibria between calcium chloride and water have
been most completely studied by Roozeboom (Zeitschr. physikal.
Chem., 1889, 4. 31).
[225] Hammerl, Sitzungsber. Wien. Akad., 2te Abteil, 1878, 78. 59.
Roozeboom, Zeitschr. physikal. Chem., 1889, 4. 31.
[226] Lidbury, Zeitschr. physikal. Chem., 1902, 39. 453. The
curvature at the melting point is all the greater the more the
compound is dissociated into its components in the liquid state. If
the compound is completely undissociated, even in the vapour
phase, the two branches of the curve will intersect, (e.g. pyridine
and methyl iodide; Aten, Versl. Konink. Akad. Wetensch.
Amsterdam, 1905, 13. 462). The smaller the degree of
dissociation, therefore, the sharper will be the bend. (See
Stortenbeker, Zeitschr. physikal. Chem., 1892, 10. 194.) From the
extent of flattening of the curve, it is also possible, with some
degree of approximation, to calculate the degree of dissociation of
the substance in the fused state. (See Roozeboom and Aten,
Zeitschr. physikal. Chem., 1905, 53. 463; Kremann, Zeitschr.
Elektrochem., 1906, 12. 259.)
[227] See Roozeboom, Zeitschr. physikal. Chem., 1889, 4. 31.
[228] Tammann, Wied. Annalen, 1899, 68. 577.
[229] Duhem, Journ. Physical Chem., 1898, 2. 31.
[230] Gibbs, Trans. Conn. Acad., 3. 155; Saurel, Journ. Phys.
Chem., 1901, 5. 35.
[231] In the case of the fusion of a compound of two components
with formation of a liquid phase of the same composition, the
temperature is a maximum; in the case of liquid mixtures of
constant boiling-point, the temperature may be a minimum
(p. 105).
Page 324
[232] Roozeboom, Zeitschr. physikal. Chem., 1892, 10. 477. The
formula of ferric chloride has been doubled, in order to avoid
fractions in the expression of the water of crystallization.
[233] Roozeboom, Zeitschr. physikal. Chem., 1892, 10. 477.
[234] A similar series of hydrates is formed by zinc chloride and
water (Dietz and Mylius, Zeitschr. anorg. Chem., 1905, 44. 209).
[235] Meyerhoffer, Ber., 1897, 30. 1810.
[236] Walden, Ber., 1899, 32. 2863.
[237] Zeitschr. physikal. Chem., 1903, 42. 432.
[238] This composition was also confirmed by measurements of
the vapour pressure (cf. p. 90).
[239] Since all substances are no doubt volatile to a certain extent
at some temperature, it is to be understood here that the
substances are appreciably volatile at the temperature of the
experiment.
[240] For a general discussion of the partial pressures in a system
of two components, see Bancroft, Journ. Physical Chem., 1899,
3. 1.
[241] Zeitschr. physikal. Chem., 1889, 3. 11; Rec. trav. chim.
Pays-Bas, 1888, 7. 152.
[242] The composition of a solution is represented symbolically
by placing a double wavy line between the symbols of the
components, and indicating the number of atoms present in the
ordinary manner: thus, I Clx represents a solution containing
x atoms of chlorine to one atom of iodine (Roozeboom, Zeitschr.
physikal. Chem., 1888, 2. 450).
[243] Since iodine monochloride in the liquid state is only very
slightly dissociated, the bend at C is very sharp (see p. 147,
footnote). See also the investigation of the system pyridine and
formula of ferric chloride has been doubled, in order to avoid
fractions in the expression of the water of crystallization.
[233] Roozeboom, Zeitschr. physikal. Chem., 1892, 10. 477.
[234] A similar series of hydrates is formed by zinc chloride and
water (Dietz and Mylius, Zeitschr. anorg. Chem., 1905, 44. 209).
[235] Meyerhoffer, Ber., 1897, 30. 1810.
[236] Walden, Ber., 1899, 32. 2863.
[237] Zeitschr. physikal. Chem., 1903, 42. 432.
[238] This composition was also confirmed by measurements of
the vapour pressure (cf. p. 90).
[239] Since all substances are no doubt volatile to a certain extent
at some temperature, it is to be understood here that the
substances are appreciably volatile at the temperature of the
experiment.
[240] For a general discussion of the partial pressures in a system
of two components, see Bancroft, Journ. Physical Chem., 1899,
3. 1.
[241] Zeitschr. physikal. Chem., 1889, 3. 11; Rec. trav. chim.
Pays-Bas, 1888, 7. 152.
[242] The composition of a solution is represented symbolically
by placing a double wavy line between the symbols of the
components, and indicating the number of atoms present in the
ordinary manner: thus, I Clx represents a solution containing
x atoms of chlorine to one atom of iodine (Roozeboom, Zeitschr.
physikal. Chem., 1888, 2. 450).
[243] Since iodine monochloride in the liquid state is only very
slightly dissociated, the bend at C is very sharp (see p. 147,
footnote). See also the investigation of the system pyridine and
Page 325
methyl iodide (Aten, Versl. Konink. Akad. Wetensch. Amsterdam,
1905, 13. 462).
[244] This upper branch of the curve is not shown in the figure, as
the ordinate corresponding to 30° would be very great.
[245] Stortenbeker, Zeitschr. physikal. Chem., 1889, 3. 22.
[246] Ramsay and Young, Journ. Chem. Soc., 1886, 49. 458.
[247] Van't Hoff, Lectures on Physical Chemistry, I. p. 77
(Arnold).
[248] This is different from what we found in the case of non-
volatile solutes (p. 126). In the present case, the partial pressure
of the iodine in the vapour will be lowered by addition of
chlorine, but the total pressure is increased.
[249] The diminution of volume is supposed to be carried out at
constant temperature. The pressure and the composition of the
phases must, therefore, remain unchanged, and only the relative
amounts of these can undergo alteration.
[250] At point b the ratio of chlorine to iodine in the solution is
less than in the monochloride, so that by the separation of this the
excess of chlorine yielded by the condensation of the vapour is
removed.
[251] Roozeboom, Rec. trav. chim. Pays-Bas, 1884, 3. 29; 1885,
4. 65; Zeitschr. physikal. Chem., 1888, 2. 450.
[252] Two curves "enclose" a field when they form with one
another an angle less than two right angles.
[253] Roozeboom, Zeitschr. physikal. Chem., loc. cit.
[254] Van't Hoff, Zeitschr. physikal. Chem., 1890, 5. 323.
[255] Bancroft has proposed to restrict the term "occlusion" to the
formation of solid solutions, and to apply "adsorption" only to
effects which are primarily due to surface tension. Such a
1905, 13. 462).
[244] This upper branch of the curve is not shown in the figure, as
the ordinate corresponding to 30° would be very great.
[245] Stortenbeker, Zeitschr. physikal. Chem., 1889, 3. 22.
[246] Ramsay and Young, Journ. Chem. Soc., 1886, 49. 458.
[247] Van't Hoff, Lectures on Physical Chemistry, I. p. 77
(Arnold).
[248] This is different from what we found in the case of non-
volatile solutes (p. 126). In the present case, the partial pressure
of the iodine in the vapour will be lowered by addition of
chlorine, but the total pressure is increased.
[249] The diminution of volume is supposed to be carried out at
constant temperature. The pressure and the composition of the
phases must, therefore, remain unchanged, and only the relative
amounts of these can undergo alteration.
[250] At point b the ratio of chlorine to iodine in the solution is
less than in the monochloride, so that by the separation of this the
excess of chlorine yielded by the condensation of the vapour is
removed.
[251] Roozeboom, Rec. trav. chim. Pays-Bas, 1884, 3. 29; 1885,
4. 65; Zeitschr. physikal. Chem., 1888, 2. 450.
[252] Two curves "enclose" a field when they form with one
another an angle less than two right angles.
[253] Roozeboom, Zeitschr. physikal. Chem., loc. cit.
[254] Van't Hoff, Zeitschr. physikal. Chem., 1890, 5. 323.
[255] Bancroft has proposed to restrict the term "occlusion" to the
formation of solid solutions, and to apply "adsorption" only to
effects which are primarily due to surface tension. Such a
Page 326
distinction, however, would probably be very difficult to carry
through, for although adsorption may, in large measure, be due to
surface tension, the behaviour of adsorbed substances is similar to
that of substances existing in solid solutions.
[256] Tammann, Wied. Annalen, 1897, 63. 16; Zeitschr. physikal.
Chem., 1898, 27. 323.
[257] See, for example, Chappuis, Wied. Annalen, 1881, 12. 161;
Joulin, Annal. chim. phys., 1881, [5], 22. 398; Kayser, Wied.
Annalen, 1881, 12. 526.
[258] Hoitsema, Zeitschr. physikal. Chem., 1895, 17. 1.
[259] Annales chim. phys., 1874, [5], 2. 279.
[260] Hoitsema, Zeitschr. physikal. Chem., 1895, 17. 1; Dewar,
Phil. Mag., 1874, [4], 47, 324, 342; Mond, Ramsay and Shields,
Proc. Royal Soc., 1897, 62. 290.
[261] Loc. cit.
[262] It is noteworthy that the form of curve obtained for
hydrogen and palladium bears a striking resemblance to that for
the dehydration of colloids containing absorbed water, e.g. silicic
acid (vide van Bemmelen, Zeitschr. anorg. Chem., 1897-1900. Cf.
Zacharias, Zeitschr. physikal. Chem., 1902, 39. 480).
[263] Zeitschr. physikal. Chem., 1890, 5. 322.
[264] Küster, Zeitschr. physikal. Chem., 1895, 17. 367. Bodländer,
Neues Jahrbuch f. Mineralogie, 1898-99, Beilage Band, 12. 92.
[265] Bruni and Padoa, Atti Accad. Lincei, 1902 [5], 11. 1; 565.
[266] Roozeboom, Zeitschr. physikal. Chem., 1899, 30. 385;
Bruni, Rend. Accad. Lincei, 1898, 2. 138, 347. For a general
account of "solid solutions" the reader is referred to Bruni,
"Ueber feste Lösungen" (Ahrens'sche Sammlung), and to
Bodländer, loc. cit. For the formation and transformation of liquid
through, for although adsorption may, in large measure, be due to
surface tension, the behaviour of adsorbed substances is similar to
that of substances existing in solid solutions.
[256] Tammann, Wied. Annalen, 1897, 63. 16; Zeitschr. physikal.
Chem., 1898, 27. 323.
[257] See, for example, Chappuis, Wied. Annalen, 1881, 12. 161;
Joulin, Annal. chim. phys., 1881, [5], 22. 398; Kayser, Wied.
Annalen, 1881, 12. 526.
[258] Hoitsema, Zeitschr. physikal. Chem., 1895, 17. 1.
[259] Annales chim. phys., 1874, [5], 2. 279.
[260] Hoitsema, Zeitschr. physikal. Chem., 1895, 17. 1; Dewar,
Phil. Mag., 1874, [4], 47, 324, 342; Mond, Ramsay and Shields,
Proc. Royal Soc., 1897, 62. 290.
[261] Loc. cit.
[262] It is noteworthy that the form of curve obtained for
hydrogen and palladium bears a striking resemblance to that for
the dehydration of colloids containing absorbed water, e.g. silicic
acid (vide van Bemmelen, Zeitschr. anorg. Chem., 1897-1900. Cf.
Zacharias, Zeitschr. physikal. Chem., 1902, 39. 480).
[263] Zeitschr. physikal. Chem., 1890, 5. 322.
[264] Küster, Zeitschr. physikal. Chem., 1895, 17. 367. Bodländer,
Neues Jahrbuch f. Mineralogie, 1898-99, Beilage Band, 12. 92.
[265] Bruni and Padoa, Atti Accad. Lincei, 1902 [5], 11. 1; 565.
[266] Roozeboom, Zeitschr. physikal. Chem., 1899, 30. 385;
Bruni, Rend. Accad. Lincei, 1898, 2. 138, 347. For a general
account of "solid solutions" the reader is referred to Bruni,
"Ueber feste Lösungen" (Ahrens'sche Sammlung), and to
Bodländer, loc. cit. For the formation and transformation of liquid
Page 327
mixed crystals, see A. C. de Kock, Zeitschr. physikal. Chem.,
1904, 48. 129.
[267] In discussing the various systems which may be obtained
here, Roozeboom (loc. cit.) made use of the variation of the
thermodynamic potential (p. 29) with the concentration. In spite
of the advantages which such a treatment affords, the
temperature-concentration diagram has been adopted as being
more readily understood and as more suitable for an elementary
discussion of the subject.
[268] These curves are also called the "liquidus" and the "solidus"
curve respectively.
[269] Küster, Zeitschr. physikal. Chem., 1895, 17. 360.
[270] Küster, ibid., 1891, 8. 589.
[271] It should be remarked that the behaviour described here will
hold strictly only when the solid mixed crystals undergo change
sufficiently rapidly to be always in equilibrium with the liquid.
This, however, is not always the case (see Reinders, Zeitschr.
physikal. Chem., 1900, 32. 494; van Wyk, Zeitschr. anorg. Chem.,
1905, 48. 25), and complete solidification will not in this case
take place at the temperature corresponding with the line dc in
Fig. 50, but only at a lower temperature.
[272] Adriani, Zeitschr. physikal. Chem., 1900, 33. 469.
[273] Reinders, Zeitschr. physikal. Chem., 1900, 32. 494.
[274] Hissink, Zeitschr. physikal. Chem., 1900, 32. 542.
[275] Van Eyk, Zeitschr. physikal. Chem., 1899, 30. 430.
[276] Cady, Journ. Physical. Chem., 1899, 3. 127.
[277] See Roberts-Austen and Stansfield, Rapports du congrès
international de physique, 1900, I. 363.
1904, 48. 129.
[267] In discussing the various systems which may be obtained
here, Roozeboom (loc. cit.) made use of the variation of the
thermodynamic potential (p. 29) with the concentration. In spite
of the advantages which such a treatment affords, the
temperature-concentration diagram has been adopted as being
more readily understood and as more suitable for an elementary
discussion of the subject.
[268] These curves are also called the "liquidus" and the "solidus"
curve respectively.
[269] Küster, Zeitschr. physikal. Chem., 1895, 17. 360.
[270] Küster, ibid., 1891, 8. 589.
[271] It should be remarked that the behaviour described here will
hold strictly only when the solid mixed crystals undergo change
sufficiently rapidly to be always in equilibrium with the liquid.
This, however, is not always the case (see Reinders, Zeitschr.
physikal. Chem., 1900, 32. 494; van Wyk, Zeitschr. anorg. Chem.,
1905, 48. 25), and complete solidification will not in this case
take place at the temperature corresponding with the line dc in
Fig. 50, but only at a lower temperature.
[272] Adriani, Zeitschr. physikal. Chem., 1900, 33. 469.
[273] Reinders, Zeitschr. physikal. Chem., 1900, 32. 494.
[274] Hissink, Zeitschr. physikal. Chem., 1900, 32. 542.
[275] Van Eyk, Zeitschr. physikal. Chem., 1899, 30. 430.
[276] Cady, Journ. Physical. Chem., 1899, 3. 127.
[277] See Roberts-Austen and Stansfield, Rapports du congrès
international de physique, 1900, I. 363.
Page 328
[278] Heycock and Neville, Proc. Roy. Soc., 1903, 71. 409. For
the partial liquefaction of mixed crystals on cooling, see also A.
C. de Kock (Zeitschr. physikal. Chem., 1904, 48. 129).
[279] Armstrong, Watt's Dictionary of Chemistry (Morley and
Muir), III., p. 88. See also Lowry, Jour. Chem. Soc., 1899, 75.
211.
[280] See Bancroft, Journ. Physical Chem., 1898, 2. 143;
Roozeboom, Zeitschr. physikal. Chem., 1899, 28. 288.
[281] Hylotropic substances are such as can undergo
transformation into other substances of the same composition
(Ostwald, Lehrbuch, II. 2. 298).
[282] Also called Equilibrium Point (Lowry).
[283] For a discussion of these systems, see Roozeboom, Zeitschr.
physikal. Chem., loc. cit.
[284] See Bancroft, loc. cit., p. 147; Wegscheider, Sitzungsber.
Wiener Akad., 1902, 110. 908.
[285] Reference may be made here to the term "stability limit,"
introduced by Knorr (Annalen, 1896, 293. 88) to indicate that
temperature above which liquefaction and isomeric change takes
place. As employed by Knorr and others, the term does not appear
to have a very precise meaning, since it is used to denote, not the
temperature at which these changes can occur, but the
temperature at which the change is rapid (vide Annalen, 1896,
293. 91; 1899, 306. 334); and the introduction of an indefinite
velocity of change renders the temperature of the stability limit
also somewhat indefinite. The definiteness of the term is also not
a little diminished by the fact that the "limit" can be altered by
means of catalytic agents. Since, as we have seen, the stable
modification can always undergo isomeric change and liquefy at
temperatures above the natural freezing point, but not below that
point; and, further, the less stable modification can undergo
isomeric transformation and liquefy at temperatures above the
eutectic point, but will not liquefy at temperatures below that; it
the partial liquefaction of mixed crystals on cooling, see also A.
C. de Kock (Zeitschr. physikal. Chem., 1904, 48. 129).
[279] Armstrong, Watt's Dictionary of Chemistry (Morley and
Muir), III., p. 88. See also Lowry, Jour. Chem. Soc., 1899, 75.
211.
[280] See Bancroft, Journ. Physical Chem., 1898, 2. 143;
Roozeboom, Zeitschr. physikal. Chem., 1899, 28. 288.
[281] Hylotropic substances are such as can undergo
transformation into other substances of the same composition
(Ostwald, Lehrbuch, II. 2. 298).
[282] Also called Equilibrium Point (Lowry).
[283] For a discussion of these systems, see Roozeboom, Zeitschr.
physikal. Chem., loc. cit.
[284] See Bancroft, loc. cit., p. 147; Wegscheider, Sitzungsber.
Wiener Akad., 1902, 110. 908.
[285] Reference may be made here to the term "stability limit,"
introduced by Knorr (Annalen, 1896, 293. 88) to indicate that
temperature above which liquefaction and isomeric change takes
place. As employed by Knorr and others, the term does not appear
to have a very precise meaning, since it is used to denote, not the
temperature at which these changes can occur, but the
temperature at which the change is rapid (vide Annalen, 1896,
293. 91; 1899, 306. 334); and the introduction of an indefinite
velocity of change renders the temperature of the stability limit
also somewhat indefinite. The definiteness of the term is also not
a little diminished by the fact that the "limit" can be altered by
means of catalytic agents. Since, as we have seen, the stable
modification can always undergo isomeric change and liquefy at
temperatures above the natural freezing point, but not below that
point; and, further, the less stable modification can undergo
isomeric transformation and liquefy at temperatures above the
eutectic point, but will not liquefy at temperatures below that; it
Page 329
seems to the author that it would be more precise to identify these
two points—the natural freezing point and the eutectic point—
which are not altered by catalytic agents, with the "stability
limits" of the stable and unstable modification respectively. A
perfectly definite meaning would thereby be given to the term. In
the case of those substances which do not undergo appreciable
isomeric change at the temperature of the melting point, the
stability limits would be the points G and H, Fig. 60.
[286] Cameron, Journ. Physical Chem., 1898, 2. 409.
[287] Carveth, Journ. Phys. Chem., 1898, 2. 159. See also Dutoit
and Fath, Journ. chim. phys., 1903, 1. 358; Findlay, Trans. Chem.
Soc., 1904, 85. 403.
[288] Hollmann, Zeitschr. physikal. Chem., 1903, 43. 129.
[289] For other examples of the application of the Phase Rule to
isomeric substances, see Journ. Physical Chem., vols. 2. et seq.;
Findlay, Trans. Chem. Soc., 1904, 85. 403.
[290] See Roozeboom, Zeitschr. physikal. Chem., 1899, 30. 410.
[291] See also Saposchnikoff, Zeitschr. physikal. Chem., 49. 688;
Kremann, Monatshefte, 1904, 25. 1215, 1271, 1311.
[292] J. C. Philip, Journ. Chem. Soc., 1903, 83. 821.
[293] Cf. also Paterno and Ampolla, Gazzetta chim. ital., 1897,
27. 481.
[294] Philip, loc. cit., p. 826.
[295] Philip, loc. cit., p. 829. Compare curves for iodine
monochloride, Fig. 42, p. 162.
[296] Kuriloff, Zeitschr. physikal. Chem., 1897, 23. 676.
[297] Ladenburg, Ber., 1895, 28. 163; 1991.
[298] Roozeboom, Zeitschr. physikal. Chem., 1899, 28. 494;
Adriani, ibid., 1900, 33. 453.
two points—the natural freezing point and the eutectic point—
which are not altered by catalytic agents, with the "stability
limits" of the stable and unstable modification respectively. A
perfectly definite meaning would thereby be given to the term. In
the case of those substances which do not undergo appreciable
isomeric change at the temperature of the melting point, the
stability limits would be the points G and H, Fig. 60.
[286] Cameron, Journ. Physical Chem., 1898, 2. 409.
[287] Carveth, Journ. Phys. Chem., 1898, 2. 159. See also Dutoit
and Fath, Journ. chim. phys., 1903, 1. 358; Findlay, Trans. Chem.
Soc., 1904, 85. 403.
[288] Hollmann, Zeitschr. physikal. Chem., 1903, 43. 129.
[289] For other examples of the application of the Phase Rule to
isomeric substances, see Journ. Physical Chem., vols. 2. et seq.;
Findlay, Trans. Chem. Soc., 1904, 85. 403.
[290] See Roozeboom, Zeitschr. physikal. Chem., 1899, 30. 410.
[291] See also Saposchnikoff, Zeitschr. physikal. Chem., 49. 688;
Kremann, Monatshefte, 1904, 25. 1215, 1271, 1311.
[292] J. C. Philip, Journ. Chem. Soc., 1903, 83. 821.
[293] Cf. also Paterno and Ampolla, Gazzetta chim. ital., 1897,
27. 481.
[294] Philip, loc. cit., p. 826.
[295] Philip, loc. cit., p. 829. Compare curves for iodine
monochloride, Fig. 42, p. 162.
[296] Kuriloff, Zeitschr. physikal. Chem., 1897, 23. 676.
[297] Ladenburg, Ber., 1895, 28. 163; 1991.
[298] Roozeboom, Zeitschr. physikal. Chem., 1899, 28. 494;
Adriani, ibid., 1900, 33. 453.
Page 330
[299] Adriani, Zeitschr. physikal. Chem., 1900, 33. 453.
[300] A. Findlay and Miss E. Hickmans.
[301] Kipping and Pope, Journ. Chem. Soc., 1897, 71. 993.
[302] See Roozeboom, Zeitschr. physikal. Chem., 1899, 28. 512;
Adriani, ibid., 1900, 33. 473; 1901, 36. 168.
[303] In this connection reference should be made more
especially to the paper by Roberts-Austen and Stansfield, "Sur la
constitution des alliages métalliques," in the Rapports du congrès
international de physique, 1900, I. 363; J. A. Mathews, Journ. of
the Franklin Inst., 1902; Gautier, Compt. rend., 1896, 123. 109;
Roberts-Austen, "Reports of the Alloys Research Committee," in
Journ. Inst. Mechan. Engineers, from 1891 to 1904; and the
papers by Heycock and Neville, published in the Journ. Chem.
Soc., and the Trans. Roy. Soc. since 1897; also Neville, Reports of
the British Association, 1900, p. 131. Reference must also be
made to the important metallographic investigations by Tammann
and his pupils, and of Kurnakoff (Zeitschr. anorgan. Chem., vol.
40 and onwards), and also to those of Shepherd, Journ. Physical
Chem., 8. A bibliography of the alloys is given in Zeitschr.
anorgan. Chem., 1903, 35. 249.
[304] Kurnakoff and Puschin, Zeitschr. anorgan. Chem., 1902, 30.
104.
[305] Gautier, Bull. Soc. d'Encouragement, 1896 [5], 1. 1312.
[306] Heycock and Neville, Phil. Trans., 1900, 194. 201.
[307] Gautier, loc. cit. See also Roberts-Austen and Rose, Proc.
Roy. Soc., 1903, 71. 161.
[308] Heycock and Neville, Journ. Chem. Soc., 1897, 71. 414.
[309] See Roberts-Austen, Introduction to Metallurgy, 5th edit.,
p. 102; Bakhuis Roozeboom, Journ. Iron and Steel Inst., 1900, II.
311; Zeitschr. physikal. Chem., 1900, 34. 437; von Jüptner,
Siderology, p. 223 (translation by C. Salter); van't Hoff, Zinn,
[300] A. Findlay and Miss E. Hickmans.
[301] Kipping and Pope, Journ. Chem. Soc., 1897, 71. 993.
[302] See Roozeboom, Zeitschr. physikal. Chem., 1899, 28. 512;
Adriani, ibid., 1900, 33. 473; 1901, 36. 168.
[303] In this connection reference should be made more
especially to the paper by Roberts-Austen and Stansfield, "Sur la
constitution des alliages métalliques," in the Rapports du congrès
international de physique, 1900, I. 363; J. A. Mathews, Journ. of
the Franklin Inst., 1902; Gautier, Compt. rend., 1896, 123. 109;
Roberts-Austen, "Reports of the Alloys Research Committee," in
Journ. Inst. Mechan. Engineers, from 1891 to 1904; and the
papers by Heycock and Neville, published in the Journ. Chem.
Soc., and the Trans. Roy. Soc. since 1897; also Neville, Reports of
the British Association, 1900, p. 131. Reference must also be
made to the important metallographic investigations by Tammann
and his pupils, and of Kurnakoff (Zeitschr. anorgan. Chem., vol.
40 and onwards), and also to those of Shepherd, Journ. Physical
Chem., 8. A bibliography of the alloys is given in Zeitschr.
anorgan. Chem., 1903, 35. 249.
[304] Kurnakoff and Puschin, Zeitschr. anorgan. Chem., 1902, 30.
104.
[305] Gautier, Bull. Soc. d'Encouragement, 1896 [5], 1. 1312.
[306] Heycock and Neville, Phil. Trans., 1900, 194. 201.
[307] Gautier, loc. cit. See also Roberts-Austen and Rose, Proc.
Roy. Soc., 1903, 71. 161.
[308] Heycock and Neville, Journ. Chem. Soc., 1897, 71. 414.
[309] See Roberts-Austen, Introduction to Metallurgy, 5th edit.,
p. 102; Bakhuis Roozeboom, Journ. Iron and Steel Inst., 1900, II.
311; Zeitschr. physikal. Chem., 1900, 34. 437; von Jüptner,
Siderology, p. 223 (translation by C. Salter); van't Hoff, Zinn,
Page 331
Gips, und Stahl, p. 24, or Acht Vorträge über physikalische
Chemie, p. 37. Further, Roozeboom, Zeitschr. Elektrochem., 1904,
10. 489; E. Heyn, ibid., p. 491; Carpenter and Keeling, Journ.
Iron and Steel Inst., 1904, 65. 224.
[310] The melting point of pure iron is given by Carpenter and
Keeling (Journ. Iron and Steel Inst., 1904, 65. 224) as 1505°.
[311] Zeitschr. für Elektrochem., 1904, 10. 491.
[312] See also Hiorns, Journ. Soc. Chem. Ind., 1906, 25. 50.
[313] Bancroft, Jour. Physical Chem., 1902, 6. 178; Bell and
Taber, ibid., 1906, 10. 120.
[314] The method to be followed when the third component
enters into the solid phase will be explained later.
[315] Tammann, Zeitschr. anorg. Chem., 1903, 37. 303; 1905, 45.
24. Reference may be made here to the registering pyrometer of
Kurnakoff, Zeitschr. anorg. Chem., 1904, 42. 184.
[316] In this connection, see Doelter, Physikalisch-chemisch
Mineralogie (Barth, 1901); Meyerhoffer, Zeitschr. f.
Kristallographie, 1902, 36. 593; Guthrie, Phil. Mag., 1884 [5],
17. 479; Le Chatelier, Compt. rend., 1900, 130. 85; and especially
E. Baur, Zeitschr. physikal. Chem., 1903, 42. 567; J. H. L. Vogt,
Zeitschr. Elektrochem., 1903, 9. 852, and Die
Silikatschmelzlösungen, Parts I. and II. (Christiania, 1903, 1904).
See also N. V. Kultascheff, Zeitschr. anorg. Chem., 1903, 35. 187.
[317] G. G. Stokes, Proc. Roy. Soc., 1891, 49. 174; Gibbs, Trans.
Conn. Acad., 1876, 3. 176; Roozeboom, Zeitschr. physikal.
Chem., 1894, 15. 147.
[318] This figure has been taken from Ostwald's Lehrbuch, II. 2.
984.
[319] Roozeboom, Zeitschr. physikal. Chem., 1893, 12. 369.
Chemie, p. 37. Further, Roozeboom, Zeitschr. Elektrochem., 1904,
10. 489; E. Heyn, ibid., p. 491; Carpenter and Keeling, Journ.
Iron and Steel Inst., 1904, 65. 224.
[310] The melting point of pure iron is given by Carpenter and
Keeling (Journ. Iron and Steel Inst., 1904, 65. 224) as 1505°.
[311] Zeitschr. für Elektrochem., 1904, 10. 491.
[312] See also Hiorns, Journ. Soc. Chem. Ind., 1906, 25. 50.
[313] Bancroft, Jour. Physical Chem., 1902, 6. 178; Bell and
Taber, ibid., 1906, 10. 120.
[314] The method to be followed when the third component
enters into the solid phase will be explained later.
[315] Tammann, Zeitschr. anorg. Chem., 1903, 37. 303; 1905, 45.
24. Reference may be made here to the registering pyrometer of
Kurnakoff, Zeitschr. anorg. Chem., 1904, 42. 184.
[316] In this connection, see Doelter, Physikalisch-chemisch
Mineralogie (Barth, 1901); Meyerhoffer, Zeitschr. f.
Kristallographie, 1902, 36. 593; Guthrie, Phil. Mag., 1884 [5],
17. 479; Le Chatelier, Compt. rend., 1900, 130. 85; and especially
E. Baur, Zeitschr. physikal. Chem., 1903, 42. 567; J. H. L. Vogt,
Zeitschr. Elektrochem., 1903, 9. 852, and Die
Silikatschmelzlösungen, Parts I. and II. (Christiania, 1903, 1904).
See also N. V. Kultascheff, Zeitschr. anorg. Chem., 1903, 35. 187.
[317] G. G. Stokes, Proc. Roy. Soc., 1891, 49. 174; Gibbs, Trans.
Conn. Acad., 1876, 3. 176; Roozeboom, Zeitschr. physikal.
Chem., 1894, 15. 147.
[318] This figure has been taken from Ostwald's Lehrbuch, II. 2.
984.
[319] Roozeboom, Zeitschr. physikal. Chem., 1893, 12. 369.
Page 332
[320] C. R. A. Wright, Proc. Roy. Soc., 1891, 49. 174; 1892, 50.
375.
[321] The distribution coefficient will not remain constant
because, apart from other reasons, the mutual solubility of
chloroform and water is altered by the addition of the acid.
[322] Bancroft, Physical Review, 1895, 3. 21; Schreinemakers,
Zeitschr. physikal. Chem., 1897, 23. 652, and subsequent
volumes.
[323] C. R. A. Wright, Proc. Roy. Soc., 1889-1893.
[324] C. R. A. Wright, Proc. Roy. Soc., 1892, 50. 390.
[325] Bodländer, Berg- und Hüttenmänn. Ztg., 1897, 56. 331.
[326] C. R. A. Wright, Proc. Roy. Soc., loc. cit.
[327] Schreinemakers, Zeitschr. physikal. Chem., 1900, 33. 78.
[328] Schreinemakers, Zeitschr. physikal. Chem., 1898, 27. 95.
[329] Schreinemakers, Zeitschr. physikal. Chem., 1899, 29. 577.
[330] Schreinemakers, Zeitschr. physikal. Chem., 1898, 25. 543.
[331] Charpy, Compt. rend., 1898, 126. 1569. Compare the curves
for the system KNO3—NaNO3—LiNO3 (H. R. Carveth, Journ.
Physical Chem., 1898, 2. 209). Also alloys of Pb—Sn—Bi (E. S.
Shepherd, Journ. Physical Chem., 1902, 6. 527).
[332] It should be remembered that in the triangular diagram a
line parallel to one of the sides indicates, at a given temperature, a
constant amount of the component represented by the opposite
corner of the triangle; and, hence, points in a plane, parallel to
one face of a right prism, will indicate for different temperatures,
variation in the amounts of two components, but constancy in the
amount of the third.
[333] Gazzetta chim. ital., 1898, 28. II. 520.
375.
[321] The distribution coefficient will not remain constant
because, apart from other reasons, the mutual solubility of
chloroform and water is altered by the addition of the acid.
[322] Bancroft, Physical Review, 1895, 3. 21; Schreinemakers,
Zeitschr. physikal. Chem., 1897, 23. 652, and subsequent
volumes.
[323] C. R. A. Wright, Proc. Roy. Soc., 1889-1893.
[324] C. R. A. Wright, Proc. Roy. Soc., 1892, 50. 390.
[325] Bodländer, Berg- und Hüttenmänn. Ztg., 1897, 56. 331.
[326] C. R. A. Wright, Proc. Roy. Soc., loc. cit.
[327] Schreinemakers, Zeitschr. physikal. Chem., 1900, 33. 78.
[328] Schreinemakers, Zeitschr. physikal. Chem., 1898, 27. 95.
[329] Schreinemakers, Zeitschr. physikal. Chem., 1899, 29. 577.
[330] Schreinemakers, Zeitschr. physikal. Chem., 1898, 25. 543.
[331] Charpy, Compt. rend., 1898, 126. 1569. Compare the curves
for the system KNO3—NaNO3—LiNO3 (H. R. Carveth, Journ.
Physical Chem., 1898, 2. 209). Also alloys of Pb—Sn—Bi (E. S.
Shepherd, Journ. Physical Chem., 1902, 6. 527).
[332] It should be remembered that in the triangular diagram a
line parallel to one of the sides indicates, at a given temperature, a
constant amount of the component represented by the opposite
corner of the triangle; and, hence, points in a plane, parallel to
one face of a right prism, will indicate for different temperatures,
variation in the amounts of two components, but constancy in the
amount of the third.
[333] Gazzetta chim. ital., 1898, 28. II. 520.
Page 333
[334] Bruni, Gazzetta chim. ital., 1898, 28. II. 508; 1900, 30. I.
35.
[335] Zeitschr. physikal. Chem., 1900, 36. 168.
[336] For a discussion of these systems, see van't Hoff, Bildung
und Spaltung von Doppelsalzen (Leipzig, 1897).
[337] Van Leeuwen, Zeitschr. physikal. Chem., 1897, 23. 35.
[338] Meyerhoffer, Zeitschr. physikal. Chem., 1889, 3. 336; 1890,
5. 97.
[339] Reicher, Zeitschr. physikal. Chem., 1887, 1. 220.
[340] For other examples of the formation and decomposition of
double salts at a transition point, the reader is referred to the work
by van't Hoff, already cited, on the Bildung und Spaltung von
Doppelsalzen; or to Bancroft, Phase Rule, p. 180.
[341] Bancroft, Phase Rule, p. 183.
[342] Roozeboom, Zeitschr. physikal. Chem., 1888, 2. 514.
[343] The influence of pressure on the transition point in the case
of tachydrite has been determined by van't Hoff, Kenrick, and
Dawson (Zeitschr. physikal. Chem., 1901, 39. 27, 34; van't Hoff,
Zur Bildung der ozeanischen Salzablagerungen, I. p. 66—
Brunswick, 1905). This salt is formed from magnesium chloride
and calcium chloride at 22°, in accordance with the equation—
2MgCl2.6H2O + CaCl2.6H2O = Mg2CaCl6.12H2O + 6H2O
Increase of pressure raises the transition point, because the
formation of tachydrite is accompanied by increase of volume;
the elevation being 0.016° for an increase of pressure of 1 atm.
The number calculated from the theoretical formula (p. 57) is
0.013° for 1 atm.
If one calculates the influence of the pressure of sea-water on the
temperature of formation of tachydrite (which is of interest on
35.
[335] Zeitschr. physikal. Chem., 1900, 36. 168.
[336] For a discussion of these systems, see van't Hoff, Bildung
und Spaltung von Doppelsalzen (Leipzig, 1897).
[337] Van Leeuwen, Zeitschr. physikal. Chem., 1897, 23. 35.
[338] Meyerhoffer, Zeitschr. physikal. Chem., 1889, 3. 336; 1890,
5. 97.
[339] Reicher, Zeitschr. physikal. Chem., 1887, 1. 220.
[340] For other examples of the formation and decomposition of
double salts at a transition point, the reader is referred to the work
by van't Hoff, already cited, on the Bildung und Spaltung von
Doppelsalzen; or to Bancroft, Phase Rule, p. 180.
[341] Bancroft, Phase Rule, p. 183.
[342] Roozeboom, Zeitschr. physikal. Chem., 1888, 2. 514.
[343] The influence of pressure on the transition point in the case
of tachydrite has been determined by van't Hoff, Kenrick, and
Dawson (Zeitschr. physikal. Chem., 1901, 39. 27, 34; van't Hoff,
Zur Bildung der ozeanischen Salzablagerungen, I. p. 66—
Brunswick, 1905). This salt is formed from magnesium chloride
and calcium chloride at 22°, in accordance with the equation—
2MgCl2.6H2O + CaCl2.6H2O = Mg2CaCl6.12H2O + 6H2O
Increase of pressure raises the transition point, because the
formation of tachydrite is accompanied by increase of volume;
the elevation being 0.016° for an increase of pressure of 1 atm.
The number calculated from the theoretical formula (p. 57) is
0.013° for 1 atm.
If one calculates the influence of the pressure of sea-water on the
temperature of formation of tachydrite (which is of interest on
Page 334
account of the natural occurrence of this salt), it is found that a
depth of water of 1500 metres, exerting a pressure of 180 atm.,
would alter the temperature of formation of tachydrite by only 3°.
The effect is, therefore, comparatively unimportant.
[344] Roozeboom, Zeitschr. physical. Chem., 1887, 1. 227.
[345] Zeitschr. physical. Chem., 1887, 1. 227.
[346] Van't Hoff and Müller, Ber., 1898, 31. 2206.
[347] Van't Hoff and van Deventer, Zeitschr. physikal. Chem.,
1887, 1. 165.
[348] For a full discussion of the solubility relations of sodium
ammonium racemate, see van't Hoff, Bildung und Spaltung von
Doppelsalzen, p. 81.
[349] Annales chim. phys., 1848 [3], 24. 442.
[350] See Van't Hoff and van Deventer, Zeitschr. phys. Chem.,
1887, 1. 165.
[351] Meyerhoffer, Zeitschr. physikal. Chem., 1890, 5. 121.
[352] Roozeboom, Zeitschr. physikal. Chem., 1888, 2. 518.
[353] Meyerhoffer, Zeitschr. physikal. Chem., 1890, 5. 109. On
the importance of the transition interval in the case of optically
active substances, see Meyerhoffer, Ber., 1904, 37. 2604.
[354] In connection with this chapter, see, more especially, van't
Hoff, Bildung und Spaltung von Doppelsalzen, p. 3, ff.;
Roozeboom, Zeitschr. physikal Chem., 1892, 10. 158; Bancroft,
Phase Rule, p. 201; 209.
[355] The same restriction must be made here as was imposed in
the preceding chapter, namely, that the two salts in solution give a
common ion.
[356] For example, addition of ammonium chloride to solutions
of ferric chloride (Roozeboom, Zeitschr. physikal. Chem., 1892,
depth of water of 1500 metres, exerting a pressure of 180 atm.,
would alter the temperature of formation of tachydrite by only 3°.
The effect is, therefore, comparatively unimportant.
[344] Roozeboom, Zeitschr. physical. Chem., 1887, 1. 227.
[345] Zeitschr. physical. Chem., 1887, 1. 227.
[346] Van't Hoff and Müller, Ber., 1898, 31. 2206.
[347] Van't Hoff and van Deventer, Zeitschr. physikal. Chem.,
1887, 1. 165.
[348] For a full discussion of the solubility relations of sodium
ammonium racemate, see van't Hoff, Bildung und Spaltung von
Doppelsalzen, p. 81.
[349] Annales chim. phys., 1848 [3], 24. 442.
[350] See Van't Hoff and van Deventer, Zeitschr. phys. Chem.,
1887, 1. 165.
[351] Meyerhoffer, Zeitschr. physikal. Chem., 1890, 5. 121.
[352] Roozeboom, Zeitschr. physikal. Chem., 1888, 2. 518.
[353] Meyerhoffer, Zeitschr. physikal. Chem., 1890, 5. 109. On
the importance of the transition interval in the case of optically
active substances, see Meyerhoffer, Ber., 1904, 37. 2604.
[354] In connection with this chapter, see, more especially, van't
Hoff, Bildung und Spaltung von Doppelsalzen, p. 3, ff.;
Roozeboom, Zeitschr. physikal Chem., 1892, 10. 158; Bancroft,
Phase Rule, p. 201; 209.
[355] The same restriction must be made here as was imposed in
the preceding chapter, namely, that the two salts in solution give a
common ion.
[356] For example, addition of ammonium chloride to solutions
of ferric chloride (Roozeboom, Zeitschr. physikal. Chem., 1892,
Page 335
10. 149).
[357] It must, of course, be understood that the temperature is on
that side of the transition point on which the double salt is stable.
[358] Excess of the double salt must be taken, because otherwise
an unsaturated solution might be formed, and this would, of
course, not deposit any salt.
[359] Meyerhoffer, Ber., 1904, 37. 2605.
[360] Meyerhoffer, Ber., 1897, 30. 1809.
[361] Meyerhoffer, Ber., 1904, 37. 2604.
[362] Bancroft, Phase Rule, p. 203; Roozeboom, Zeitschr.
physikal. Chem., 1891, 8. 504, 531; Stortenbeker, ibid., 1895, 17.
643; 1897, 22. 60; 1900, 34. 108.
[363] Roozeboom, Zeitschr. phys. Chem., 1899, 28. 494; Ber.,
1899, 32. 537.
[364] As, for instance, strychnine racemate, a compound of
racemic acid with the optically active strychnine. This would be
resolved into strychnine d-tartrate and strychnine l-tartrate, which
are not enantiomorphous forms.
[365] Van't Hoff and Meyerhoffer, Zeitschr. physikal Chem.,
1898, 27. 75; 1899, 30. 86. Fig. 113 is taken from the latter paper.
[366] Solid models constructed of plaster of Paris can be obtained
from Max Kaehler and Martini, Berlin.
[367] Instead of the present method of obtaining potassium
chloride by decomposing carnallite with water, advantage might
be taken of the fact that carnallite when heated to 168° undergoes
decomposition with separation of three-fourths of the potassium
chloride (van't Hoff, Acht Vorträge über physikalische Chemie,
1902, p. 32).
[357] It must, of course, be understood that the temperature is on
that side of the transition point on which the double salt is stable.
[358] Excess of the double salt must be taken, because otherwise
an unsaturated solution might be formed, and this would, of
course, not deposit any salt.
[359] Meyerhoffer, Ber., 1904, 37. 2605.
[360] Meyerhoffer, Ber., 1897, 30. 1809.
[361] Meyerhoffer, Ber., 1904, 37. 2604.
[362] Bancroft, Phase Rule, p. 203; Roozeboom, Zeitschr.
physikal. Chem., 1891, 8. 504, 531; Stortenbeker, ibid., 1895, 17.
643; 1897, 22. 60; 1900, 34. 108.
[363] Roozeboom, Zeitschr. phys. Chem., 1899, 28. 494; Ber.,
1899, 32. 537.
[364] As, for instance, strychnine racemate, a compound of
racemic acid with the optically active strychnine. This would be
resolved into strychnine d-tartrate and strychnine l-tartrate, which
are not enantiomorphous forms.
[365] Van't Hoff and Meyerhoffer, Zeitschr. physikal Chem.,
1898, 27. 75; 1899, 30. 86. Fig. 113 is taken from the latter paper.
[366] Solid models constructed of plaster of Paris can be obtained
from Max Kaehler and Martini, Berlin.
[367] Instead of the present method of obtaining potassium
chloride by decomposing carnallite with water, advantage might
be taken of the fact that carnallite when heated to 168° undergoes
decomposition with separation of three-fourths of the potassium
chloride (van't Hoff, Acht Vorträge über physikalische Chemie,
1902, p. 32).
Page 336
[368] Roozeboom and Schreinemakers, Zeitschr. physikal. Chem.,
1894, 15. 588.
[369] These curves represent only portions of the isotherms, since
the systems in which a ternary solution is in equilibrium with
solid hydrogen chloride or a hydrate, have not been investigated.
[370] The numbers printed beside the points on the curves refer to
the number of the experiment in the original paper.
[371] Lash, Miller and Kenrick, Journ. Physical. Chem., 1903, 7.
259; Allan, Amer. Chem. Journ., 1901, 25. 307.
[372] Allan, Amer. Chem. Journ., 1901, 25. 307.
[373] Hoitsema, Zeitschr. physikal. Chem., 1895, 17. 651; Allan,
loc. cit.
[374] Rutten, Zeitschr. anorgan. Chem., 1902, 30. 342. Compare
the system BeO—SO3—H2O; Parsons, Zeitschr. anorgan. Chem.,
1904, 42. 250.
[375] Zeitschr. anorgan. Chem., 1904, 40. 146.
[376] Schreinemakers, Zeitschr. physikal. Chem., 1893, 11. 76;
Bancroft, Journ. Physical Chem., 1902, 6. 179.
[377] Zeitschr. anorgan. Chem., 1904, 40. 148.
[378] Zeitschr. physikal. Chem., 1903, 43. 354.
[379] These equilibria were obtained by Boudouard, Annales
chim. phys., 1901 [7], 24. 5. See also Hahn, Zeitschr. physikal.
Chem., 1903, 42. 705; 44. 513.
[380] G. Preuner, Zeitschr. physikal. Chem., 1903, 47. 385.
[381] See Hahn, Zeitschr. physikal. Chem., 1903, 42. 705; 44.
513; Boudouard, Bull. Soc. chim., [3], 25. 484; Bodländer,
Zeitschr. f. Elektrochem., 1902, 8. 833; R. Schenck and
Zimmermann, Ber., 1903, 36. 1231, 3663; Schenck and Heller,
1894, 15. 588.
[369] These curves represent only portions of the isotherms, since
the systems in which a ternary solution is in equilibrium with
solid hydrogen chloride or a hydrate, have not been investigated.
[370] The numbers printed beside the points on the curves refer to
the number of the experiment in the original paper.
[371] Lash, Miller and Kenrick, Journ. Physical. Chem., 1903, 7.
259; Allan, Amer. Chem. Journ., 1901, 25. 307.
[372] Allan, Amer. Chem. Journ., 1901, 25. 307.
[373] Hoitsema, Zeitschr. physikal. Chem., 1895, 17. 651; Allan,
loc. cit.
[374] Rutten, Zeitschr. anorgan. Chem., 1902, 30. 342. Compare
the system BeO—SO3—H2O; Parsons, Zeitschr. anorgan. Chem.,
1904, 42. 250.
[375] Zeitschr. anorgan. Chem., 1904, 40. 146.
[376] Schreinemakers, Zeitschr. physikal. Chem., 1893, 11. 76;
Bancroft, Journ. Physical Chem., 1902, 6. 179.
[377] Zeitschr. anorgan. Chem., 1904, 40. 148.
[378] Zeitschr. physikal. Chem., 1903, 43. 354.
[379] These equilibria were obtained by Boudouard, Annales
chim. phys., 1901 [7], 24. 5. See also Hahn, Zeitschr. physikal.
Chem., 1903, 42. 705; 44. 513.
[380] G. Preuner, Zeitschr. physikal. Chem., 1903, 47. 385.
[381] See Hahn, Zeitschr. physikal. Chem., 1903, 42. 705; 44.
513; Boudouard, Bull. Soc. chim., [3], 25. 484; Bodländer,
Zeitschr. f. Elektrochem., 1902, 8. 833; R. Schenck and
Zimmermann, Ber., 1903, 36. 1231, 3663; Schenck and Heller,
Page 337
ibid., 1905, 38. 2132; Zeitschr. f. Elektrochem., 1903, 9. 691;
Haber, Thermodynamik technischer Gasreaktionen, p. 293
(Munich, 1903).
[382] A very useful summary of the investigations carried out by
van't Hoff and his pupils on the formation of the Stassfurt salt-
beds is given by E. F. Armstrong, in the Reports of the British
Association for 1901, p. 262. See also van't Hoff, Zur Bildung der
ozeanischen Salzablagerungen (Brunswick, 1905).
[383] See especially Meyerhoffer, Silzungsber. Wien. Akad., 1895,
104. II. b, 840; Meyerhoffer and Saunders, Zeitschr. physikal.
Chem., 1899, 28. 453; 31. 370. The investigation of the equilibria
between reciprocal salt-pairs alone (three-component systems) is
of great importance for the artificial preparations of minerals, as
also in analytical chemistry for the proper understanding of the
methods of conversion of insoluble systems into soluble by fusion
(see Meyerhoffer, Zeitschr. physikal. Chem., 1901, 38. 307).
[384] See Meyerhoffer, Zeitschr. physikal. Chem., 1899, 28. 459.
[385] Compare the reciprocal salt-pair NaCl—NH4HCO3
(p. 321). In this case the upper limit of the transition interval was
found by extrapolation of the solubility curve for NaHCO3 +
NH4Cl + NH4HCO3 and NaHCO3 + NH4Cl + NaCl to be 32°
(Fedotieff, Zeitschr. phys. Chem., 1904, 49. 179).
[386] Löwenherz, Zeitschr. physikal. Chem., 1894, 13. 464.
[387] Meyerhoffer and Saunders, Zeitschr. physikal. Chem., 1899,
28. 479.
[388] As the quantities of the salts are expressed in equivalent
gram-molecules, the molecule of sodium and potassium chloride
must be doubled in order to be equivalent to sodium sulphate and
potassium sulphate.
[389] Sitz-Ber. der kgl. preuss. Akad. der Wiss., 1903, p. 359.
Van't Hoff, Zur Bildung der ozeanischen Salzablagerungen, I. p.
Haber, Thermodynamik technischer Gasreaktionen, p. 293
(Munich, 1903).
[382] A very useful summary of the investigations carried out by
van't Hoff and his pupils on the formation of the Stassfurt salt-
beds is given by E. F. Armstrong, in the Reports of the British
Association for 1901, p. 262. See also van't Hoff, Zur Bildung der
ozeanischen Salzablagerungen (Brunswick, 1905).
[383] See especially Meyerhoffer, Silzungsber. Wien. Akad., 1895,
104. II. b, 840; Meyerhoffer and Saunders, Zeitschr. physikal.
Chem., 1899, 28. 453; 31. 370. The investigation of the equilibria
between reciprocal salt-pairs alone (three-component systems) is
of great importance for the artificial preparations of minerals, as
also in analytical chemistry for the proper understanding of the
methods of conversion of insoluble systems into soluble by fusion
(see Meyerhoffer, Zeitschr. physikal. Chem., 1901, 38. 307).
[384] See Meyerhoffer, Zeitschr. physikal. Chem., 1899, 28. 459.
[385] Compare the reciprocal salt-pair NaCl—NH4HCO3
(p. 321). In this case the upper limit of the transition interval was
found by extrapolation of the solubility curve for NaHCO3 +
NH4Cl + NH4HCO3 and NaHCO3 + NH4Cl + NaCl to be 32°
(Fedotieff, Zeitschr. phys. Chem., 1904, 49. 179).
[386] Löwenherz, Zeitschr. physikal. Chem., 1894, 13. 464.
[387] Meyerhoffer and Saunders, Zeitschr. physikal. Chem., 1899,
28. 479.
[388] As the quantities of the salts are expressed in equivalent
gram-molecules, the molecule of sodium and potassium chloride
must be doubled in order to be equivalent to sodium sulphate and
potassium sulphate.
[389] Sitz-Ber. der kgl. preuss. Akad. der Wiss., 1903, p. 359.
Van't Hoff, Zur Bildung der ozeanischen Salzablagerungen, I. p.
Page 338
34 (Brunswick, 1905).
[390] Zeitschr. für Kristallographie, 1904, 39. 155.
[391] Meyerhoffer and Saunders, Zeitschr. physikal. Chem., 1899,
28. 479.
[392] Zeitschr. physikal. Chem., 1904, 49. 162.
[393] Another commercial process, in the study of which good
service is done by the Phase Rule, is the caustification of the
alkali salts (G. Bodländer, Zeitschr. für Elektrochem., 1905, 11.
186; J. Herold, ibid., 418).
[394] Zeitschr. physikal. Chem., 1900, 35. 32.
[395] Mention may also be made here of the equilibria between
magnesium carbonate and potassium carbonate, although these do
not form a reciprocal salt-pair (Auerbach, Zeitschr. für
Elektrochem., 1904, 10. 161).
[396] O. N. Witt and K. Ludwig, Ber., 1903, 36. 4384;
Meyerhoffer, ibid., 1904, 37. 261, 1116.
[397] Zeitschr. physikal. Chem., 1905, 53. 513. Compare also,
ibid., 1903, 38. 307.
[398] See Schwarz, Beiträge zur Kenntnis der umkehrbaren
Umwandlungen polymorpher Korper (Göttingen, 1892); or,
Roozeboom, Heterogen. Gleichgewicht, I. p. 125. Also Barnes
and Cooke, Journ. Physical Chem., 1902, 6. 172.
[399] Van't Hoff and van Deventer, Zeitschr. physikal. Chem.,
1887, 1. 173.
[400] Reicher, Zeitschr. für Krystallographie, 1884, 8. 593.
[401] Zeitschr. physikal. Chem., 1895, 17. 153.
[402] Zeitschr. physikal. Chem., 1899, 28. 464.
[403] Meyerhoffer and Saunders, ibid., p. 466.
[390] Zeitschr. für Kristallographie, 1904, 39. 155.
[391] Meyerhoffer and Saunders, Zeitschr. physikal. Chem., 1899,
28. 479.
[392] Zeitschr. physikal. Chem., 1904, 49. 162.
[393] Another commercial process, in the study of which good
service is done by the Phase Rule, is the caustification of the
alkali salts (G. Bodländer, Zeitschr. für Elektrochem., 1905, 11.
186; J. Herold, ibid., 418).
[394] Zeitschr. physikal. Chem., 1900, 35. 32.
[395] Mention may also be made here of the equilibria between
magnesium carbonate and potassium carbonate, although these do
not form a reciprocal salt-pair (Auerbach, Zeitschr. für
Elektrochem., 1904, 10. 161).
[396] O. N. Witt and K. Ludwig, Ber., 1903, 36. 4384;
Meyerhoffer, ibid., 1904, 37. 261, 1116.
[397] Zeitschr. physikal. Chem., 1905, 53. 513. Compare also,
ibid., 1903, 38. 307.
[398] See Schwarz, Beiträge zur Kenntnis der umkehrbaren
Umwandlungen polymorpher Korper (Göttingen, 1892); or,
Roozeboom, Heterogen. Gleichgewicht, I. p. 125. Also Barnes
and Cooke, Journ. Physical Chem., 1902, 6. 172.
[399] Van't Hoff and van Deventer, Zeitschr. physikal. Chem.,
1887, 1. 173.
[400] Reicher, Zeitschr. für Krystallographie, 1884, 8. 593.
[401] Zeitschr. physikal. Chem., 1895, 17. 153.
[402] Zeitschr. physikal. Chem., 1899, 28. 464.
[403] Meyerhoffer and Saunders, ibid., p. 466.
Page 339
[404] See Van Eyk, Zeitschr. physikal. Chem., 1899, 30. 446.
[405] See in this connection the volume in this series on Electro-
chemistry, by Dr. R. A. Lehfeldt.
[406] Barnes and Cooke, Journ. Physical Chem., 1902, 6. 172.
[407] For a description and explanation of these, the reader
should consult the volume in this series by Dr. Lehfeldt on
Electro-chemistry; and van't Hoff, Bildung und Spaltung von
Doppelsalzen, p. 48 ff.
[405] See in this connection the volume in this series on Electro-
chemistry, by Dr. R. A. Lehfeldt.
[406] Barnes and Cooke, Journ. Physical Chem., 1902, 6. 172.
[407] For a description and explanation of these, the reader
should consult the volume in this series by Dr. Lehfeldt on
Electro-chemistry; and van't Hoff, Bildung und Spaltung von
Doppelsalzen, p. 48 ff.
Page 340
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