The Elements of Qualitative Chemical Analysis_ vol. 1_ parts 1 and 2. Julius Stieglitz 920 downloads.pdf

The Project Gutenberg eBook of The Elements of Qualitative
Chemical Analysis, vol. 1, parts 1 and 2.

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 Elements of Qualitative Chemical Analysis, vol. 1, parts 1
and 2.

Author: Julius Stieglitz

Release date: February 23, 2014 [eBook #44986]
Most recently updated: October 24, 2024

Language: English

Other information and formats: www.gutenberg.org/ebooks/44986

Credits: Produced by Juliet Sutherland, RichardW, and the Online
Distributed Proofreading Team at http://www.pgdp.net

*** START OF THE PROJECT GUTENBERG EBOOK THE
ELEMENTS OF QUALITATIVE CHEMICAL ANALYSIS, VOL. 1,
PARTS 1 AND 2. ***

THE ELEMENTS
OF

QUALITATIVE CHEMICAL
ANALYSIS

WITH
SPECIAL CONSIDERATION OF THE APPLICATION OF
THE LAWS OF EQUILIBRIUM AND OF THE MODERN
THEORIES OF SOLUTION

BY
JULIUS STIEGLITZ
Professor of Chemistry in the University of Chicago

VOLUME I
PARTS I AND II
FUNDAMENTAL PRINCIPLES AND THEIR APPLICATION

NEW YORK
THE CENTURY CO.
1920

Copyright, 1911,
by

THE CENTURY CO.

Printed, October, 1911
Reprinted, August, 1912
Reprinted, October, 1913
Reprinted, October, 1915
Reprinted, August, 1917
Reprinted, January, 1919
Reprinted, August, 1919
Reprinted, November, 1919
Reprinted, July, 1920

PREFACE

In venturing to add another book on Qualitative Chemical Analysis to the
long list of publications on this subject, the author has been moved chiefly
by the often expressed wish of students and friends to have his lectures on
qualitative analysis rendered available for reference and for a wider circle
of instruction. Parts I and II of the present book embody these lectures in
the form to which they have developed in the course of the last sixteen
years, since, in 1894, the teaching of analytical chemistry, along the lines
followed, was first suggested by Ostwald's pioneer "Wissenschaftliche
Grundlagen der Analytischen Chemie."
The author believes that instruction in qualitative analysis, besides
teaching analysis proper, should demand of the student a very distinct
advance in the study of general chemistry, and should also, consciously,
pave the way for work in quantitative analysis, if it is not, indeed,
accompanied by work in that subject. The professional method of work,
whether routine or research work of the academic or the industrial
laboratory is involved, inevitably consists in first making an exhaustive
study of the general chemical aspects of the subject under examination: it
includes a thorough study of books of reference and of the original
literature on the subject; and when the experimental work is finally
undertaken, it is carried out with a critical, searching mind, which questions
every observation made, every process used. The method of instruction in
this book aims at developing these habits of the professional, productive
chemist. For the reasons given, a rather thorough and somewhat critical
study is first made (in Part I) of the fundamental general chemical
principles which are most widely involved in analytical work. The

applications of these principles to the subject matter of elementary
qualitative analysis are then discussed (in Part II), in closest connection
with the laboratory work covering the study of analytical reactions (in Part
III). The material is presented, not as a finished subject, but as a growing
one, with which the present generation of chemists is still busy, and which
contains many important, unsolved problems of a fundamental character.
Numerous references to standard works and to the current literature are
given, of which those suitable for reading by the young student are specially
designated. The obvious demand is thereby made on the student to aim to
remain in touch with the growth of the science, after he has completed his
studies under the guidance of an instructor. Finally, to arouse and develop
the critical, questioning attitude of the professional chemist, referred to
above, the subject matter of the laboratory work, given in Part III, is put
very largely in the form of questions, which demand not only careful
observation on the part of the student, but also a thoughtful interpretation of
the observations made.
In the experience of the author, although the majority of students
attending his lectures had already acquired some knowledge of chemical
and physical equilibrium, of the theories of solutions and of ionization and
of their applications, the more exhaustive treatment of parts of these
subjects and of related topics, to which a course in qualitative analysis lends
itself, has been of particular benefit to them, bringing them into closer touch
with the method of detailed study of a chemical topic, than the broader,
more varied work of general chemistry courses usually does. Throughout
the theoretical treatment of the subject, the attempt is made to prepare the
student for a more general quantitative expression of chemical relations.
For this reason, chemical and physical equilibrium constants are given and
used, wherever it is possible. The author is aware that these "constants"
have, in part, only a temporary standing; that more exact work will
continually modify their numerical values and, probably, limit the field for

their rigorous application. The latter facts can be impressed on the student
and still the invaluable principle be inculcated in his mind, that chemistry is
striving to express its relations, as far as possible, in mathematical terms,
exactly as its sister science, physics, has long been doing. At the same time
the treatment of physicochemical topics has been kept within the bounds set
by the subject matter, and by the chemical maturity of the students
addressed: it is elementary in form, and quantitative relations are used, in
the main, only to elucidate qualitative facts. The rigorous development of
the subjects presented and their elaboration from a purely physicochemical
standpoint are left to advanced courses. It has been found that this method
interests the better class of students in seeking such advanced courses.
The relations of qualitative to quantitative analysis are touched upon in
the theoretical treatment, where it has been feasible to do so. The laboratory
methods aim also at beginning the training of students in the habit of
accuracy demanded by quantitative analysis, by laying special emphasis on
the methods of detecting traces of a number of the common elements and
by requiring a report on the relative quantities of components found. The
study of reactions is carried out, almost wholly, with solutions of known
and uniform molar concentration. However, the actual development of
quantitative accuracy is left to the instruction in the courses in quantitative
analysis, in which a successful training in this direction is far more readily
attained. Simultaneous courses in the two branches of analysis seem to the
author to be highly desirable, whenever practicable. The study of
quantitative analysis adds neatness of manipulation and accuracy to the
work in qualitative analysis; and the latter supplies the opportunity for the
further development of a student's knowledge of general chemistry, for
which there is a much smaller scope in quantitative analysis courses, and
thus relieves a condition where a serious pedagogical defect is likely to
exist in the development of our students.

Parts III and IV of this book are published in a separate volume, as a
laboratory manual for qualitative analysis. They comprise the instructions
for laboratory work introductory to systematic analysis (the study of
reactions and of the analysis of groups, in Part III) and an outline for
elementary systematic analysis (Part IV). The attempt has been made, in
particular, to bring the laboratory work, which otherwise follows the usual
lines of instruction in systematic analysis, also into closest relations to the
development of the scientific foundations of analytical chemistry, as
represented in Parts I and II. It is believed that the subject matter lends itself
especially well to such a close interweaving of the two sides of the study,
without any special loss of time to the student, and with the result, it is
hoped, of a greatly increased interest on his part and an increased stimulus
of the habit of scientific thought.
The following plan of work is used by the author with his classes: The
first section (lasting eleven weeks) of the course in qualitative analysis is
started with some seven to ten (according to the ability of the class) lectures
or classroom exercises, given daily, and covering the first seven or the eight
chapters of Part I. At the end of the second week the laboratory work is
started. During the remainder of this section of the course, two hours of
classroom work and eight hours of laboratory work per week are required,
and, in this period, Part III, comprising the first half of the laboratory
manual, is studied in the laboratory in closest connection with the
classroom work on Part II of the book. As far as possible, the laboratory
work on a given topic precedes the classroom work. This first course is
followed by an eleven weeks' course in systematic analysis, covering Part
IV of the book. A third (graduate) course, optional for students specializing
in chemistry, is offered, in which very complex commercial and natural
products are analyzed and in which special attention is also given to rare
elements. During this course, particular care is taken to familiarize students

with other works on qualitative analysis, such as the outlines of A. A. Noyes
and Bray, and the special parts of Fresenius's manual.
Students who have been prepared in general chemistry along
physicochemical lines, as represented, for instance, by Smith's textbooks,
make more rapid and more easy progress in the first course than do students
otherwise prepared. But the treatment of the subject is intended to make it
possible for students, who have not paid particular attention to chemical
equilibrium and to the modern theories of solution in their general
chemistry course, to complete the course within the time limit indicated.
Perhaps one-third of the students in an average class, in the past, have taken
the course under these conditions and no special difficulty was encountered
by them.
In the theoretical treatment the author is particularly indebted to the
original articles and to the larger works of Arrhenius, van 't Hoff, Nernst, A.
A. Noyes, Ostwald, and Walker. For the systematic analytical material
acknowledgment is due, in particular, to Fresenius's "Qualitative Chemical
Analysis," and to the important publications by A. A. Noyes and Bray in the
Journal of the American Chemical Society. Some of the excellent methods
of the latter authors have been adopted outright, as indicated in the text. For
some special matters the author is indebted to the texts of W. A. Noyes and
of Böttger. Constant references to his sources of information have been
made by the author, partly as a matter of acknowledgment, and more
particularly to give students and teachers the opportunity for more
extended, first-hand reading on any topic of interest. References suitable for
college students are indicated by the addition of (Stud.). In two or three
instances, the original source of information has been forgotten and diligent
search has failed to trace it. For use in preparing any future edition of the
book, the author will be glad to have his attention called to the facts by
authors.

The author wishes to express here his particular appreciation of the
generous assistance given him by his former colleague, Prof. Alexander
Smith of Columbia University, whose suggestions and advice, especially in
the editing of the manuscript and proof, have been invaluable. He also
wishes to make grateful acknowledgment to his colleagues, Profs. H. N.
McCoy, H. Schlesinger, and Dr. Edith Barnard, to Prof. L. W. Jones of the
University of Cincinnati, Prof. E. P. Schoch of the University of Texas,
Prof. B. B. Freud of Armour Institute, and Prof. W. J. Hale of the University
of Michigan, who have assisted him by reading the proofs or the
manuscript, or by carrying out experimental studies underlying part of the
work, or in other ways. Corrections of his mistakes of omission and
commission, and suggestions, will be gratefully received by the author.
JULIUS STIEGLITZ.
Chicago, September, 1911.

CONTENTS

PART I
FUNDAMENTAL PRINCIPLES
CHAPTER PAGE
I. Introduction 3
II. Osmotic Pressure and the Theory of Solution, I 8
III. Osmotic Pressure and the Theory of Solution, II 21
IV. The Theory of Ionization: Ionization and Electrical
Conductivity 33
V. The Theory of Ionization, II: Ionization and Osmotic
Pressure; Ionization and Chemical Activity 67
VI. Chemical Equilibrium. The Law of Mass Action 90
VII. Physical or Heterogeneous Equilibrium.—The
Colloidal Condition 118
VIII. Simultaneous Chemical and Physical Equilibrium.—
The Solubility- or Ion-Product 139
PART II
SYSTEMATIC ANALYSIS AND THE
APPLICATION OF FUNDAMENTAL PRINCIPLES
IX. Systematic Analysis for the Common Metal Ions. The
Ions of the Alkalies and of the Alkaline Earths.
Order of Precipitation of Difficultly Soluble Salts
with a Common Ion 157
X. Aluminium; Amphoteric Hydroxides; Hydrolysis of
Salts. The Aluminium and Zinc Groups 171
XI. The Copper and Silver Groups. Precipitation with
Hydrogen Sulphide 199
XII. The Copper and Silver Groups (Continued). The Theory
of Complex Ions 216
XIII. The Arsenic Group. Sulpho-acids and Sulpho-salts 242
XIV. Oxidation and Reduction Reactions, I 251
XV. Oxidation and Reduction, II. Oxidation by Oxygen, 277
Permanganates, etc.; Oxidation of Organic

Compounds
XVI. Systematic Analysis for Acid Ions 299

LIST OF REFERENCES AND THEIR
ABBREVIATIONS

Note.—(Stud.) affixed to a reference indicates that the original article is
recommended as suitable reading for college students taking their second
year of work in chemistry.

Am. Chem. J.—American Chemical Journal.
Ann. de Chim. et de Phys.—Annales de Chimie et de Physique.
Ber. d. chem. Ges.—Berichte der deutschen chemischen Gesellschaft.
Le Blanc's Lehrbuch der Elektrochemie (1903).
Böttger's Qualitative Analyse (1908).
Compt. rend.—Comptes rendus.
Fresenius's Manual of Qualitative Chemical Analysis (1909).
Fresenius's Quantitative Chemical Analysis (1904).
Van 't Hoff's Lectures on Theoretical and Physical Chemistry (1898).
H. C. Jones's The Elements of Physical Chemistry.
J. Am. Chem. Soc.—Journal of the American Chemical Society.
J. Chem. Soc. (London).—Journal of the Chemical Society (London).
J. of Physiology.—Journal of Physiology.
J. Phys. Chem.—Journal of Physical Chemistry.
J. prakt. Chem.—Journal für praktische Chemie.
Kohlrausch und Holborn's Leitvermögen der Elektrolyte (1898).
Landolt-Börnstein-Meyerhoffer's Physikalisch-Chemische Tabellen.
Liebig's Ann.—Liebig's Annalen der Chemie.
Nernst's Theoretical Chemistry (1904).
Nernst's Theoretische Chemie (1909).
Ostwald's Lehrbuch der allgemeinen Chemie (1893).
Ostwald's Scientific Foundations of Analytical Chemistry (1908).
Ostwald's Wissenschaftliche Grundlagen der analytischen Chemie (1894).
Phil. Mag.—Philosophical Magazine.
Phil. Trans. Royal Soc.—Philosophical Transactions of the Royal Society.
Poggendorff's Ann.—Poggendorff's Annalen der Physik und Chemie.
Proc. Am. Acad.—Proceedings of the American Academy.

Remsen's Inorganic Chemistry, Advanced Course, 1904.
Smith's General Inorganic Chemistry (1909).
Smith's General Chemistry for Colleges (1908).
Treadwell's Qualitative Analyse (1902).
Walker's Introduction to Physical Chemistry (1909).
Wiedemann's Ann.—Wiedemann's Annalen der Physik und Chemie.
Z. analyt. Chem.—Zeitschrift für analytische Chemie.
Z. anorg. Chem.—Zeitschrift für anorganische Chemie.
Z. für Elektrochem.—Zeitschrift für Elektrochemie.
Z. phys. Chem.—Zeitschrift für physikalische Chemie.

QUALITATIVE CHEMICAL ANALYSIS
PART I
FUNDAMENTAL PRINCIPLES

CHAPTER I
INTRODUCTION

Qualitative chemical analysis is concerned with the determination of the
kinds of matter present in any given substance. In its broadest sense it
includes the determination of all kinds of matter, the elements, rare as well
as common, and all their combinations, organic compounds as well as
inorganic. The recognition of the presence of rare elements, such as radium,
uranium, thorium, tungsten, cerium, etc., is becoming a matter of growing
importance with the modern development of the subject of radioactivity and
the technical exploitation of the rarer elements, and it is a common
experience for an analytical chemist to be called upon to determine the
presence or absence of alcohol in beverages, of formalin in milk or other
foods, and not a rare experience to be obliged to make tests for the presence
of alkaloids like strychnine, morphine, cocaine, or for the presence of
numerous other organic compounds. In this book, however, we shall limit
our material to the more common elements and their most important
inorganic combinations, including only a few typical organic acids. The
limitation of our experimental material will make it possible to devote
special attention to the scientific principles underlying analysis, to secure a

clear and definite grasp of them, and to impart with simple material such
experience in the technique and methods of analysis as will train the student
to apply both his theoretical and practical knowledge to any field of
analysis occasion may require. Accurate qualitative analysis, [p004] in any
field, will depend on the care taken in mastering the theoretical significance
and the technique of the methods recommended for the specific problem
before the analyst; the details of the methods themselves, in any problem
involving more than elementary analysis, are sought and found by him as a
matter of practice in suitable larger works, in monographs and in the
original literature. With the object of suggesting this broader application of
the training acquired and of cultivating the invaluable habit of the
professional chemist of consulting larger works and the literature, frequent
reference will be made to such larger works, and to original papers in which
more special subjects of analysis or theory are elaborately treated.
To recognize, in a substance, the presence of any element or compound,
one must know its characteristic reactions, which will make it possible to
distinguish it from all other elements or compounds. Further, in order to
reach conclusions with the greatest possible speed, directness, and
conclusiveness, it is usually best to carry out an examination in some
systematic way, rather than in a haphazard and irregular fashion. We
distinguish, accordingly, two parts in our laboratory work: first, the study of
characteristic tests or reactions of the common elements and such of their
compounds as are of importance in elementary analysis (Part III), and,
secondly, practice in a systematic method of analysis (Part IV). In the study
of the reactions, the way will be paved for systematic analysis, by taking the
elements in the groups, which form the basis of the system of analysis
employed, and by analyses of mixtures of the elements of a group
immediately after the group has been studied.
Reliable and intelligent analysis is possible only with a clear knowledge
of the chemistry of the reactions used, and the chemistry of the most

important typical reactions will therefore be considered (in Part II),
simultaneously with the laboratory study of the reactions and of systematic
analysis.
The reactions for identifying an element or compound must bring
physical evidence which can be recognized by our senses. The sense of
touch is scarcely ever appealed to; perhaps the numbness or paralysis of the
sense of touch imparted to the tongue or eyelid by the alkaloid cocaine and
a few modern substitutes for it, and the tingling sensation produced on the
tongue [p005] by aconite and its preparations, are the most important, but
rare, instances of an appeal to this sense in analytical work. The sense of
taste is also rarely used, and always with the greatest care to prevent
poisonous effects. Acids and bases, bitter alkaloids, such as strychnine and
brucine, sweet substances, such as cane sugar, glucose, glycerine, are
instances of compounds which affect our sense of taste. In all these cases
the taste is used rather as a confirmative test than as a conclusive proof of
the identity of a suspected substance.
The sense of smell is rather more useful in qualitative analysis than that
of taste or of touch. Hydrogen sulphide and ammonia, unless present in
traces only, readily reveal themselves by their odor. Every chemist should
be familiar with the faint but very characteristic odor of hydrocyanic acid,1
which should instantly and automatically warn him of the presence of this
potent poison. Owing to partial decomposition by the moisture and carbonic
acid absorbed from the atmosphere, alkali cyanides also give this important
warning signal. Tests based on the odors of compounds are particularly
valuable in the field of organic chemistry, where the sense of smell is
extensively used for qualitative purposes; for instance, the pleasant smell of
acetic ester, and the nauseating odor of an organic arsenic derivative,
cacodyl oxide, may be used with advantage in identifying acetic acid.
But the evidence of touch, taste, and smell is, on the whole, only
occasionally available in chemical analysis—almost all the tests employed

are visual ones. A small proportion of these are color tests. The color of
iodine vapor or of the solution of iodine in chloroform, the colors of
metallic copper or gold, of copper salts in ammoniacal solutions, of
sulphides, such as the orange sulphide of antimony (exps.), may be
mentioned as instances, in which a test of identity depends on the
observation of some characteristic color. But the great majority of analytical
tests depend on observations of changes of state; evidence consisting in the
solution of solids, the formation of precipitates, the evolution of gases,
forms the most important part of the observations, [p006] on which our
conclusions are based. In organic chemistry, determinations of melting-
points and of boiling-points, which are very commonly used for the
qualitative identification of compounds, form further instances of the
application, to qualitative purposes, of observations based on changes of
state.
In very many cases, where the formation or nonformation of a precipitate
is intended to be used as an indication of the presence or absence of a given
substance, the precipitating agent may throw down one or more of several
different precipitates, which, seen without the aid of a microscope, cannot
be identified without further examination. It is, thus, commonly necessary
to use a sequence of such tests for the complete identification. For instance,
the addition of hydrochloric acid to a solution of lead, mercurous or silver
nitrate will produce a white precipitate. The precipitates may be
distinguished by a further examination of their solubilities: hot water will
dissolve the lead chloride, ammonia readily dissolves the chloride of silver
and converts the mercurous chloride into a black insoluble mixture
containing finely divided mercury (exps.). By the same means the chlorides,
if present together, may be separated from one another and subsequently
identified. Systematic analysis consists very largely in the use of a proper,
logical sequence of such precipitation and solution reactions, and in the
drawing of definite conclusions from the results obtained.

By far the greatest part of the experimental work in qualitative analysis
has to do, then, with solution and precipitation. For intelligent and accurate
analytical work a clear knowledge of the nature of solution and, in
particular, of the simple laws governing chemical action in solution, and of
those governing the formation and the solution of precipitates, is
indispensable. The discoveries of van 't Hoff, in 1885–8, concerning the
nature of solution, and the subsequent discoveries of Arrhenius, Nernst,
Ostwald and others, have advanced every branch of chemistry, but perhaps
no branch has profited quite so much as the theory of analytical chemistry,
which, as a result of these discoveries, for the first time, received a clear,
precise and satisfying scientific formulation of its empirical processes.2
[p007]

On account of the fundamental importance of this modern scientific
formulation of the principles of analytical chemistry for the proper
understanding of our subject, we shall consider first (in Part I) the modern
theories of solution, with their experimental foundations, and we shall then
develop the simpler fundamental laws governing chemical action and
physical changes in solution. The analytical reactions themselves will be
utilized as far as possible as the material for developing these general
principles, so that this study may lead to the desired grasp of the theory of
analysis and yet, at the same time, advance the student's knowledge of the
practice of analysis.

Chapter I Footnotes
[1] On account of the poisonous character of this and other vapors, the vessel containing a
substance whose odor one wishes to test is not brought to the nose, but a little of the vapor is
carefully wafted towards one by a motion of the hand, the vapor being thus greatly diluted with
air.
[2] We owe the first modern scientific treatment of the principles of Analytical Chemistry to
Ostwald's Wissenschaftliche Grundlagen der analytischen Chemie, 1894.

CHAPTER II
OSMOTIC PRESSURE AND THE THEORY OF SOLUTION
I

[p008] TOC

If a concentrated solution of a substance like sugar or cupric nitrate is
allowed to flow into a cylinder of water (exp. with cupric nitrate), we find
that the outside forces—gravity—tend to draw the solution, whose specific
gravity is greater than that of water, to the bottom of the cylinder. In this
method of proceeding there is some inevitable mixing of the solution with
the solvent, as the result of friction, but the main portion of the deep blue
solution is drawn to the bottom of the vessel and
forms a blue layer under the colorless water. A
much sharper line of separation may be obtained
by allowing the cupric nitrate solution to enter a
cylinder of water from under the water (see Fig.
1), the great density of the nitrate solution
causing it to displace the water without
perceptible mixing of the two liquids (exp.). If
these vessels are left at rest, it may be noted,
from day to day, that the copper nitrate diffuses
further and further into the pure solvent, and
careful examination would show that the solvent,
in turn, diffuses also into the copper nitrate
solution. The process is a very slow one, but it
will continue until a solution of uniform
concentration is reached, and this will be the
Fig. 1. case, whatever the shape of the vessel may be. If,

for the moment, only the copper nitrate be considered—and what we are
developing for the copper nitrate may be applied equally well, mutatis
mutandis, to the diffusion of water into the copper nitrate solution—it is
obvious then that copper nitrate in solution diffuses in all directions, even
against the force of gravity, and it is plain also, that any object, resisting or
arresting such a motion of material particles, must have a force or pressure
exerted upon it. Whatever the ultimate [p009] cause of the motion, whether it
is the result of inherent molecular velocities of the dissolved copper nitrate,
or of an attraction between the solute and the solvent, or both, it is
inevitable that a pressure must result from the impact of the moving solute
against the solvent.3
We have thus phenomena of diffusion of solutes through solvents, exactly
as we have the well-known diffusion of gases, and the two phenomena are
unquestionably very much alike, the solute, like the gas, tending to diffuse
from the place of higher, to that of lower concentration.4 Likewise, if a
solution of uniform concentration is heated in one part and not in another,
the solute,4 like a gas under similar conditions, will move from the warmer
to the colder part of the solution, as was demonstrated by Soret.5 Without
committing ourselves for the present to any given reason for the diffusion,
we note that the tendency to diffusion is a fact, and we must accept the
conclusion that every obstacle to such diffusion must have a pressure
exerted upon it.
Now, if a solution is separated from the pure solvent by means of a so-
called semipermeable membrane, some of the results of this tendency to
diffusion may be demonstrated.
Exp. A concentrated solution of cane sugar in water, colored with some aniline dye, is enclosed in
a thimble of parchment paper firmly fastened to a long narrow glass tube (see Fig. 2) and the cell is
placed in a vessel of pure water. The parchment is not absolutely semipermeable, but it is
approximately so, allowing the solvent, water, to pass, but being practically impervious to the solute
sugar. A Schleicher and Schüll diffusion-thimble, No. 579, may be used, with advantage, as the
thimble. (Cf. Smith's Introduction to Inorganic Chemistry, p. 284.) [p010]

We observe, presently, that the system is not in a
condition of equilibrium; water passes through the
thimble into the sugar solution and the latter
expands, producing a decided difference of level,
and consequently a hydrostatic pressure, between
the liquid in the cell and the solvent outside of it.
We may note two facts: first, that the change
includes an expansion of the solute,6 the sugar, in
the solution—that is, the tendency of the solute to
expand into larger volumes of the solvent is
satisfied exactly as in the experiment (Fig. 1)
described above. In the second place, like all
natural phenomena which proceed spontaneously,
the change is in the direction of equilibrium; for
when the hydrostatic pressure on the solution in
the cell becomes sufficiently great, or if it is made
sufficiently great at once by the application of
some outside pressure, a point of equilibrium is
reached, at which water will pass neither into the
cell nor out of it. At that point, the tendency to
expansion, both of the solute and of the solvent in
the solution, is just overcome by the pressure on
the solution.
Fig. 2. Definition of Osmotic Pressure.
—The hydrostatic pressure which is necessary to
bring the solution into equilibrium with the pure solvent, when the two are
separated by a semipermeable membrane, may be defined, according to
van 't Hoff, as the measure of what is called the osmotic pressure of the
solution. We note that this definition still does not commit us to any theory

as to the origin of the pressure, but merely formulates an experimental
relation.
Measurement of Osmotic Pressure.
—More perfect semipermeable membranes can be produced. These make
possible quantitative measurements of the hydrostatic pressure on a
solution, when equilibrium between the solution and the pure solvent [p011]
has been reached. Such membranes were first used by Pfeffer. They consist
of certain gelatinous precipitates, notably copper ferrocyanide. Films of
these precipitates may be formed, under proper conditions, which are
permeable to water but not to certain solutes, such as cane sugar, glucose
and galactose.
By precipitating these membranes in the pores of unglazed clay cells,
especially by the process devised by Morse,7 we may make them
sufficiently strong to resist enormous pressures—some used by the Earl of
Berkeley were found to withstand a pressure of 130 atmospheres. The
hydrostatic pressure required to produce equilibrium may then be measured
in either of two ways. The first method, used originally by Pfeffer and more
recently by Morse and Frazer8 and their collaborators in a wonderfully
conscientious study of osmotic pressures, consists in allowing the
hydrostatic pressure to establish itself by the passage of very small
quantities of the solvent, through the membrane, into the tightly closed cell
containing the solution. When the resulting pressure produces a condition of
equilibrium, it is measured9 by a manometer connected with the solution,
much as a gas pressure may be measured (Fig. 3).10 This process requires
considerable time for exact measurements—weeks, during which the cell
must be kept at a constant temperature. The second method, which has been
used by Berkeley and Hartley,11 is very much more rapid and requires only
a few hours for the measurement. It consists in having the pure solvent
within the cell, instead of outside of it, and in [p012] exerting an external
pressure on the solution outside of the cell, until a delicate manometer,

communicating with the pure solvent, shows that
water does not pass through the membrane in
either direction—equilibrium having been
reached.
Osmotic Pressure and the Laws of Gases.
—The work of van 't Hoff, which has proved of
inestimable value to the development of chemistry,
succeeded in demonstrating that, for dilute
solutions, the osmotic pressure, as defined above,
obeys the common laws of gases,12—that, in fact,
a substance in a dilute solution has an osmotic
pressure equal to the gas pressure which it would
exert if it were a gas of the same volume and at the
same temperature.13
Space does not permit the presentation of all the
details of the evidence confirming this conclusion,
but some of the most direct experimental proofs14
will be considered. [p013]
Boyle's Law.
—Boyle's law for gases states that, at a constant
temperature, the pressure of a gas changes Fig. 3.
inversely as its volume, or directly as its
concentration. Mathematically we have P : P′ = V′ : V or P V = P′ V′ = a
constant, and P : P′ = C : C′ or P : C = P′ : C′ = a constant. When van 't Hoff
published his first paper on the subject, Pfeffer's results from the direct
measurement of the osmotic pressures of cane-sugar solutions were
available, and even these, although experimentally not as exact as more
recent determinations, showed plainly that, at a given temperature, the
osmotic pressure of a sugar solution varies directly as the concentration, or

inversely as the volume containing a given weight of the sugar. At 13–16°
we have:
Osmotic Pressure. Pressure/
Concentration.
mm. Mercury. Concentration.
1.00% 535 535
2.00% 1016 508
2.74% 1518 554
4.00% 2082 521
6.00% 3075 513

The ratio of pressure to concentration varies irregularly round a mean
value of 526, and is approximately constant. The more recent, exceedingly
careful measurements of Morse and Frazer confirm the conclusion, that
Boyle's law holds for the osmotic [p014] pressures of dilute solutions; they
find that the osmotic pressures of glucose and of cane-sugar solutions vary
directly as the concentrations of the solutions, at a constant temperature.15
Gay-Lussac's Law.
—Gay-Lussac's law for gases states that, if the volume of gas is kept
constant, its pressure increases by 1 / 273 of its value for every degree
above 0° C., or Pt = P0(1 + t / 273).
Expressing the temperature in absolute degrees, we have more simply:
Pt = P0 (T / 273) or Pt / T = P0 / 273 = a constant.16
That is, the pressure of a gas varies directly as its absolute temperature, if
the volume is kept constant.
Pfeffer's results, on the osmotic pressure of sugar solutions at different
temperatures, were not sufficiently accurate to enable van 't Hoff to use
them to confirm positively the rigorous thermodynamic proof (footnote 3,
p. 12), that the osmotic pressure must increase proportionally to the
absolute temperature, as required by Gay-Lussac's law. But the data did
show, uniformly, a marked increase of the osmotic pressure with the
temperature and, frequently, excellent agreement between theory and
experiment. More striking were the results obtained by van 't Hoff in testing

the correctness of this extension of Gay-Lussac's law by means of Soret's
results on the diffusion of a solute from a warmer to a colder place. It was
found that the concentrations, obtained by Soret when equilibrium was
reached, agreed closely with the demand that the osmotic pressures in the
colder and the warmer parts of the solution should be equal, and that the
osmotic pressure of a given weight of solute in a given volume should
increase proportionally to the absolute temperature. An elevation of
temperature, in a portion of a uniform solution, will increase the osmotic
pressure of this part. Diffusion will follow, until the loss in concentration of
the solute, and therefore the loss of osmotic pressure (Boyle's law), of the
warmer part, and the increased concentration and increased pressure of the
colder portion result in all parts of the solution having the same osmotic
pressure. [p015] As an example, a concentration of 17.33% copper sulphate
at 20° was found to be in equilibrium with a concentration of 14.03% at
80°. Now, if the 17.33% solution had an osmotic pressure of P mm. at 20°,
a 14.03% solution at the same temperature would have a pressure of
(14.03 / 17.33) × P mm. (Boyle's law), and this would increase to (14.03 /
17.33) × P × (353 / 293) mm. at 80° C., or 0.975 P mm.—a result showing
that the osmotic pressure in the hot part was practically the same as that,
(P), in the cold part of the solution.17
It is a source of great satisfaction, that the recent very exact and
painstaking work of Morse and Frazer,18 in measuring osmotic pressures
directly, completely confirms this fundamentally important conclusion, that
the osmotic pressure of a solution does increase proportionally to its
absolute temperature.
The Avogadro-van 't Hoff Hypothesis.
—For chemists, the most important part of van 't Hoff's work lies in the
extension of the Avogadro Hypothesis to solutions. As van 't Hoff expresses
it, "equal volumes of the most different solutions, having the same osmotic
pressure and the same temperature, contain the same number of dissolved

molecules,—that number, namely, which would be found in the same
volume of a gas at the same gas pressure and temperature."19 [p016]
Pfeffer's measurements, with solutions of 1 g. of sugar in 100 c.c. of
water (the volume of the solution is 100.6 c.c.), were shown to prove, that
the observed osmotic pressures agreed excellently with the gas pressures,
calculated for the equimolar weight of hydrogen, in the same volume and at
the same temperature:
Osmotic Pressure
Temperature. Found. Calculated.20
Atmosphere. Atmosphere.
6.8 0.664 0.665
13.7 0.691 0.681
14.2 0.671 0.682
15.5 0.684 0.686
22 0.721 0.701
32 0.716 0.725
36 0.746 0.735

Morse's more recent and more exact results show, that the osmotic
pressure of solutions of cane sugar and of glucose (corrected for the volume
occupied by the sugar, see footnote, p. 15) agrees within 6% with the values
demanded by van 't Hoff's theory, being about 6% larger for concentrations
ranging from 0.1 to 1.0 molar. The difference of 6% is noteworthy and is
probably due to secondary causes, but suggests extended investigation of its
source.
Indirect Determinations of Osmotic Pressure.
—The experimental results given have been obtained by direct
measurements of osmotic pressures with the aid of semipermeable
membranes. [p017] Perfect membranes are very difficult to prepare, and
membranes of this kind can be used only with a few solutes. Nature offers
us, however, forms of semipermeable "walls" between solutions and pure
solvents, which in many instances are perfect. The atmosphere, above a
volatile pure solvent and a solution of a nonvolatile substance in that
solvent, when both liquids are placed side by side in a closed space, would

serve as a semipermeable wall: the solvent vaporizes and may pass freely
from solvent to solution and vice versa, but the solute, in the case under
consideration, is nonvolatile and therefore cannot pass through the
atmosphere. The vapor pressure of a pure solvent being always found to be
higher than that of a solution in this solvent, at the same temperature, the
solvent would pass in such a closed space as vapor from the pure solvent
and would condense in the solution; it thereby dilutes the solution and the
solute, and the solvent in the solution, expand, exactly as in the absorption
of a solvent by a solution through a semipermeable membrane. Again, the
vapor pressure of a solution being lower than that of the pure solvent, the
solution (of a nonvolatile solute) must be heated higher than the pure
solvent, to bring both to the boiling-point; that is, there is an elevation of the
boiling-point, when a nonvolatile solute is dissolved in a solvent. The solute
being nonvolatile, only the solvent passes off in the process of boiling, the
solute becomes more concentrated, and, according to van 't Hoff's extension
of Boyle's law, the osmotic pressure of the solution increases. Similarly,
when a solution is cooled until freezing occurs, provided the solute does not
crystallize out with the solvent, the concentration of the solute is again
increased, and therefore the osmotic pressure of the solution is also
increased. Van 't Hoff recognized the relations existing between the
freezing, boiling and vaporization of solutions, on the one hand, and the
changes of their osmotic pressures on the other. By developing rigorously
the relations between the lowering of the vapor tension, the raising of the
boiling-point, the lowering of the freezing-point of a solvent by a solute and
the osmotic pressure of the solution, he made it possible21 to use [p018]
extensive experimental material,22 on the elevation of boiling-points and the
lowering of freezing-points and of vapor tensions, to determine the osmotic
pressures of solutions. The theory of the relation of osmotic pressure to gas
pressure is fully confirmed by these measurements, for those cases to which
it may properly be applied, namely, to sufficiently dilute solutions and such

as have only negligible heats of dilution, i.e. in which dilution does not
involve chemical changes.
Apparent Exceptions.
—Instead of discussing the vast amount of material of this kind, which agrees with van 't Hoff's
theory, we may consider, more profitably, typical cases of apparent exceptions. The most important
instance of this kind, the case of solutions of compounds which undergo electrolytic dissociation or
ionization, will be separately discussed in the next chapter, and we shall find that van 't Hoff's great
generalization is a vital element in the evidence of this important form of dissociation. Of other
apparent exceptions, we may note the fact that some solutes seem to give "abnormally" low osmotic
pressures23 in certain solutions. For instance, benzoic acid, in benzene solutions, gives only a little
more than half as great an osmotic pressure as it does in aqueous solutions of the same concentration
and temperature, and as would be calculated on the basis of the Avogadro-van 't Hoff Hypothesis for
a compound of the formula C6H5COOH and the molecular weight 122. But a rigorous study24 of the
distribution of benzoic acid between water and benzene, when solutions of the acid in the two
solvents are shaken together until equilibrium is established (Chapter VIII), has proved that the
distribution is strictly in accord with the assumption that benzoic acid, in aqueous solution, has the
molecular weight 122 and the composition C6H5COOH, and that, in benzene solution, it has the
molecular weight 244 and the composition (C6H5COOH)2; only a small part of the acid
(C6H5COOH)2 is decomposed in benzene solution into the simpler molecules, of the composition
C6H5COOH. In other words, the simpler molecules C6H5COOH are polymerized or associated to
form larger molecules in benzene solution, much as the gas nitrogen dioxide NO2 goes over more or
less into the gas N2O4, especially at low temperatures, and as hydrogen fluoride at low temperatures
has the composition H2F2, while at higher temperatures it is HF. The divergence of the benzene
solutions of benzoic acid from the Avogadro-van 't Hoff principle is therefore only an apparent one,
not a real one, inasmuch as the osmotic pressure of the solutions agrees perfectly with that calculated
for solutions of a substance (C6H5COOH)2, of molecular weight 244. Such associated molecules (of
organic acids, alcohols, phenols, etc.) occur [p019] particularly readily in liquids of small dissociating
power, like benzene, and such solutions show marked absorption of heat on dilution,25 the dilution
being accompanied by a chemical change. The associated molecules are dissociated more and more
completely [(C6H5COOH)2 ⇄ 2 C6H5COOH], even in these solvents, as the solutions are diluted.
Since dilution results in a chemical increase in the number of molecules, the osmotic pressure cannot
decrease proportionally with the increase of volume in such a case as this. Nor does gas pressure, it
must be remembered, decrease proportionally to the volume in the case of gases which show
chemical changes with change of volume, e.g. in the case of nitrogen tetroxide, for which we have
N2O4 ⇄ 2 NO2.
In still other instances, apparently too high osmotic pressures, or too low molecular weights, have
been found by the application of the Avogadro-van 't Hoff Hypothesis to solutions: for instance, the
molecular weight of sodium, when dissolved in mercury, was found by Ramsay to vary from 21.6, in

dilute, to 15.1 in concentrated solutions. But Cady found that the heat of dilution of sodium in
mercury solution is considerable, and by taking this properly into account, Bancroft was able to show
that the molecular weight, correctly calculated in a given experiment, is 22.7 (agreeing well with the
theoretical weight 23), in place of 16.5, as calculated without making the required allowance for the
heat of dilution.26 These determinations are most instructive in showing that the sources of some of
the most important deviations from the van 't Hoff-Avogadro principle, deviations which have been
brought forward as arguments against its assumptions, are due, not to any untrustworthiness of the
general principle, but to the error of neglecting to observe the limiting conditions of the formulation,
or of neglecting to make corresponding corrections for the non-observance thereof.

Summary.
—Van 't Hoff's theory of solution—that the osmotic pressure of substances
in solution obeys the laws of gases, and that equal volumes of the most
varied dilute solutions, having the same temperature and osmotic pressure,
contain the same number of dissolved molecules, that number, namely,
which would be found in the same volume of a gas at the same temperature
and gas pressure,—accords thus, not only with the demands of
thermodynamics,27 but is also, within the limits demanded by the theory
itself, in agreement with the best experimental measurements of osmotic
pressures that have been made in recent years. The apparent exceptions, as
in the cases just described and, as we shall find, in the case of electrolytic
dissociation, are found to be no exceptions, when the conclusions, reached
on the assumption that [p020] the theory is correct, are tested rigorously by
independent methods of investigation.28
The fundamental laws of gases and the Avogadro Hypothesis may be condensed into the following
general equation, expressing all of the laws, viz.: P V = n R T. This equation applies equally to the
osmotic pressures of dilute solutions, the osmotic pressure being substituted for the gas pressure. In
the equation, T is the absolute temperature of the gas or solution, P the gaseous or osmotic pressure,
V the free space of the gas volume, i.e. the volume of the gas less the volume occupied by the gas
molecules, or the volume of the pure solvent in the solution used, i.e. the volume of the solution less
the volume of the solute. R is the so-called gas-constant, and represents the work done against the
external pressure when one gram molecule, or mole, of the gas is heated one degree and allowed to
expand, say at constant pressure P, against an external pressure P; n represents the number of gram
molecules or moles of gas or solute used (the total weight of solute or gas, divided by the average
weight of a mole in the gas or solute). If a given weight of a gas or solute is taken, and no
dissociation or association occurs (such as would involve appreciable heats of dilution), then n is a

given number; and, therefore, at a given temperature T, all the factors on the right side of the general
equation being given numbers, P V is a constant (Boyle's law). For a given quantity of gas or solute
(n is a given number), kept at constant volume V, the pressure must vary as the absolute temperature
(Gay-Lussac's law); P / T = n R / V = a constant. When the pressure, volume and temperature of two
gases, or two dilute solutions, are equal, n, the number of gas or solute molecules present, must be
the same (Avogadro-van 't Hoff Hypothesis); n = P V / (R T), and all the factors of the right side are
the same for the gases and solutions which we are comparing. Finally, if the pressure is expressed in
atmospheres, the volume in litres, and the temperature in absolute degrees, the gas-constant R = P V /
T = 1 × 22.4 / 273 = 0.082.

Chapter II Footnotes
[3] Even after a solution of uniform concentration of the solute is formed, the tendency toward
diffusion, and the diffusion itself, and the resulting pressure must still persist. But a state of
dynamic (or flowing) equilibrium must be considered now to exist, the loss caused by the moving
away of the solute, from a given part of the solution, being balanced by the diffusion (into that
part) of the solute from the neighboring parts. Whether one ascribes the diffusion to inherent
molecular velocities of the solute, or to an attraction between solvent and solute, the discrete
particles of the solute in a solution of uniform concentration will continue to have such inherent
velocities (Chap. III), and will also continue to be surrounded by pure solvent, exactly as in
solutions of unequal concentrations, where the diffusion may be observed, because the net result,
in such a case, is a one-sided action.
[4] This again holds equally for the solvent.
[5] See below.
[6] At the same time, the change is also in the direction of an expansion of the solvent in the
solution. The two changes are not opposed to each other, but supplementary.
[7] Am. Chem. J., 28, 1 (1902); 40, 266, 325 (1908) (Stud.).
[8] Am. Chem. J., 34, 1 (1905); 36, 39 (1906); 37, 324, 425, 558 (1907); 38, 175 (1907).
[9] The exact concentration of the solution at the point of equilibrium is determined by
subsequent analysis.
[10] Cf. Smith's Inorganic Chemistry, p. 287.
[11] Berkeley and Hartley, Phil. Trans. Roy. Soc. A, 206, 481 (1906).
[12] When appreciable heat of dilution is shown by a solution, some chemical change, resulting
from dilution, is indicated (such as, dissociation of the solute, hydration, hydrolysis, etc.). In such
a case, the Avogadro-van 't Hoff principle holds for each concentration for its actual composition,
and the principle may often be used to determine the extent of the chemical change produced by
dilution. But then the osmotic pressure will not obey Boyle's and Gay-Lussac's laws. The same
exception applies also to gases which undergo chemical changes, as the result of dilution or
change of temperature. In the case, for instance, of nitrogen tetroxide, which dissociates according
to N2O4 ⇄ 2 NO2, the extent of the dissociation varies with changes of concentration (pressure)
and of temperature, and the gas does not obey the laws of Gay-Lussac and of Boyle. In regard to

the rôle of heat of dilution in connection with osmotic pressure, see Bancroft, J. Phys. Chem., 10,
319 (1906).
[13] See p. 15 for a more rigorous statement concerning the volume. Cf. Morse and Frazer, Am.
Chem. J., 34, 1 (1905).
[14] As a result of numerous vain endeavors, as well as of much direct evidence of a positive
character, the scientific world has, for many years, held the opinion that any sort of "perpetual
motion machine" is impossible. Every one now admits that a machine which would be able to
work continuously, without consuming energy, is an impossibility—that is, that a "perpetuum
mobile of the first class," as it is called, is impossible (law of the conservation of energy or first
law of thermodynamics). From this law it does not of necessity follow, however, that it would be
impossible to make a machine or device that would convert continuously into available energy or
work, say, the enormous amounts of heat energy of the earth or of large bodies of water
("dissipated energy") which would thereby be cooled below the temperatures of their
surroundings. Such a hypothetical process has been termed a "perpetuum mobile of the second
class"; it has never been realized and is universally conceded to be an impossibility; the so-called
"second law of thermodynamics" gives expression to this fact.
Now van 't Hoff [Z. phys. Chem., 1, 481 (1887)] showed, first, that a gas like oxygen, nitrogen,
hydrogen, etc., which is soluble in proportion to its gas pressure (Henry's law), must exert, in
solution, an osmotic pressure equal to the gas pressure, which it would have, if present in the
same quantity as a gas in the same volume at the same temperature; for, if such were not the case,
the solution and gas could be used to produce a perpetuum mobile of the second class, which,
according to the above law, is an impossibility. Similar proofs were given by Rayleigh [Nature,
55, 253 (1897)] and by Larmor [Phil. Trans., 190, 266 (1897), Nature, 55, 545 (1897)] that the
principle applies to solutions of other solutes.
Provided, then, that we have (1) perfect semipermeable membranes, (2) sufficiently dilute
solutions, and (3) none but negligible heats of dilution (p. 12), van 't Hoff's generalization,
concerning the relation of osmotic pressure and the laws of gases, must hold, if the perpetuum
mobile of the second class is impossible, as is demanded by the second law of thermodynamics.
[15] See p. 15 in regard to the relation for concentrated solutions.
[16] The pressure P0 of a given quantity (weight) of a gas at 0° C., in a given constant volume, is
also a given number and consequently P0/273 is a constant under these conditions.

[17] The slight differences in the ionization of copper sulphate solutions of 14% and 17% and at
20° and 80° are not included in the calculation, ionization being unknown, when van 't Hoff made
his calculations.
[18] Am. Chem. J., 41, 258 (1909).
[19] In the light of recent work, especially by Morse and Frazer, the law would state, more
exactly, that a substance in solution produces the osmotic pressure, at a given temperature, which
it would exert, if it were contained as a gas, at the same temperature, in the volume occupied by

the pure solvent of the solution. For sufficiently dilute solutions, the volume of the solution and
the volume of the solvent may be considered identical; for more concentrated solutions, there is a
decided difference, and the correct volume to use in calculation is the volume of the solvent alone,
i.e. the volume of the solution reduced by the volume of the pure solute. This corresponds to the
correction of the volume in the more accurate expression for the behavior of gases, developed by
van der Waals; in place of v, the total gas volume, (v − b), the total volume of the gas less the
volume of the spheres of action of the gas particles, is used, especially for strongly compressed or
concentrated gases. It may be added that van 't Hoff's thermodynamic proof involves the same
correct definition of the volume that Morse and Frazer subsequently developed experimentally.
Cf. Bancroft, J. Phys. Chem., 10, 319 (1906).
[20] One gram of cane sugar, C12H22O11 (the mol. wt. is 342) corresponds to 1 / 342 gram
molecule or mole and, therefore, to 2.02 / 342 gram of hydrogen. The volume containing this
quantity of hydrogen is 100.6 c.c.; a liter would contain 2.02 / 342 × 1000 / 100.6 gram of
hydrogen. The pressure of a mole or 2.02 grams of hydrogen, contained in a liter at 0°, is 22.4
atmospheres, and the pressure of the quantity of hydrogen given above, in a liter, would be (2.02
× 1000) / (342 × 100.6) × (22.4 / 2.02) at 0°. At 36° C., for instance, the pressure would be 309 /
273 times as great, or Pcalculated = (2.02 × 1000 × 22.4 × 309) / (342 × 100.6 × 2.02 × 273) = 0.735
atmosphere.
[21] The exact relations are discussed in van 't Hoff's Lectures on Physical Chemistry, Part II, pp.
42–59, Nernst's Theoretical Chemistry (1904), pp. 142 and 148, and H. C. Jones's The Elements of
Physical Chemistry (1909), pp. 252, 271.
[22] Vide Raoult, Scientific Memoir Series, 4, 71, 127.
[23] I.e. abnormally small depressions of freezing-points or elevations of boiling-points.
[24] Nernst, Theoretical Chemistry, p. 486; Hendrixson, Z. anorg. Chem., 13, 73 (1897).
[25] Cf. Bancroft, J. Phys. Chem., 10, 319 (1906).
[26] For the discussion of other instances, vide Bancroft, loc. cit.
[27] Footnote 3, p. 12.
[28] For example, determinations of distribution coefficients (p. 18), heats of dilution (p. 19),
conductivities and chemical activity (Chapters IV–VI).

CHAPTER III
OSMOTIC PRESSURE AND THE THEORY OF SOLUTION
II

[p021] TOC

Accepting van 't Hoff's theory of solutions, then, as based on
experimental evidence as well as on sound thermodynamic reasoning, we
find a number of interesting questions still confronting us. Most insistent is
the question as to the source of the remarkable agreement between the
osmotic pressure of a solute and the gas pressure, which it would exert in
the same volume, as a gas, at the same temperature, and as to the identity of
the laws governing the two forms of pressure. Then, we may also ask, what
is the mechanism of the process by which osmotic pressure reveals itself,
especially in the case of cells with semipermeable membranes. And, finally,
we may ask what is the cause of the semipermeability of the membranes.
Semipermeability.
—Taking up the last question first, as the simplest one, we find that it was
long ago recognized that permeability depends on the power of membranes
to dissolve certain substances, or to form unstable combinations with them.
A membrane is semipermeable if it will dissolve one component only of a
solution, the solute or the solvent, and not the other.29
We find the simplest evidence of the cause of semipermeability in the
case of gases. Palladium, especially when heated, dissolves hydrogen
readily, but not nitrogen or oxygen, and a wall of palladium may be used as
a semipermeable membrane to separate a mixture of hydrogen and nitrogen
from pure hydrogen, just as copper ferrocyanide membranes are used with
aqueous sugar solutions and water. The results with the gases duplicate in
every particular the observations made on the solutions (see below, p. 24).

Certain gases, such as ammonia and hydrogen chloride, are easily soluble in
water, while others, like oxygen, nitrogen and hydrogen, are very difficultly
soluble, and a film of [p022] water may be used as a semipermeable
membrane for such gases.30
Exp. If the moist membrane of a cell (Fig. 4), containing air, is covered with an atmosphere of
hydrogen, there is no increase of pressure produced in the cell, as indicated by the column of colored
oil in the manometer in which the cell ends: hydrogen, being very little soluble in water, cannot pass
through the film of water in the few minutes it is allowed to act. If now an atmosphere of ammonia is
substituted for the hydrogen, the gas passes through the film into the cell. It turns the color of a piece
of litmus paper placed in the cell and produces an increased pressure in the cell, the air remaining in
the latter, because oxygen and nitrogen are very little soluble in water.

Membranes will be, similarly,
semipermeable to solvent or solute, when
only one of these is soluble in the
membrane, or is capable of forming an
unstable compound with it. For instance,
salts, holding water of crystallization which
is readily lost and recovered, may easily be
conceived of as assuming the rôle of
semipermeable membranes, allowing the
passage of water say from a wet atmosphere
to a dry one, or from pure water to a
solution; and Tammann31 has realized such
membranes by the use of zeolites—
silicates, which hold water of crystallization
but are insoluble in water. Kahlenberg32 has
recently used rubber membranes, that are
permeable for solvents like benzene,
pyridine, etc., which are soluble in rubber,
Fig. 4.

but not permeable for water, which is insoluble in rubber.
Osmosis.
—The recognition of this rôle of the
semipermeable membrane leads to the second
question raised, namely as to the mechanism of the
process by means of which osmotic pressures are
measured directly with the aid of such membranes
(p. 11). [p023] The answer hinges on the question of
Fig. 5.
the mechanism of the diffusion of the solvent into
the cell, a diffusion which is called its osmosis.33 If we consider the pure
solvent, say water, on one side of a semipermeable membrane, and a
solution (e.g. of sugar in water) on the other side, it is obvious that the
solvent itself has a higher concentration on the side where it is pure, than on
the side of the solution, where it is diluted—distended by the solute in it.
The solvent is soluble in the membrane, and its solubility will be
proportional34 to its own (the solvent's) concentration; it will, consequently,
be more soluble in the membrane on the side of the pure solvent than on the
side of the solution. If we bring such a membrane first into contact with the
pure solvent (Fig. 5), the membrane will take up the solvent (from the side
A) until it is saturated with it. Let the solubility, which represents the
concentration of the solvent in the membrane at this stage, be called c. The
membrane may then be considered to be taking up in unit time just as many
molecules from the solvent as it gives up to it (dynamic equilibrium),
exactly as, when water is in equilibrium with water vapor, we consider the
water to be vaporizing just as fast as vapor is condensing to form water.
Now, if a solution of sugar is placed on the other side of the membrane, the
solvent will pass out of the membrane into the solution just as fast as it
passes back into the pure solvent. At first the concentration of the solvent
on the surface B of the membrane is just as great (c) as on the surface A; but
the membrane will here receive the solvent more slowly from the solution,

which is less concentrated as to the solvent; and consequently the
membrane will lose water to the solution. The solubility (c′) of the solvent
at this surface B of the membrane, corresponding to the smaller
concentration of the solvent in the solution, will be less than the solubility
(c) at A, where the membrane is in contact with the pure solvent, and water
will pass into the solution at B, until the concentration of the water in the
membrane at B has fallen [p024] from (c) to (c′). In such a membrane, as in
every solution or gas, there must be a tendency towards the establishing of
uniform concentration by diffusion from points of higher concentration to
those of lower, and the solvent will, therefore, diffuse from points along the
surface A of the membrane to points along the surface B; the surface A will
become unsaturated and will take up solvent from the pure liquid bathing it,
and the surface B will be kept continuously supersaturated and will lose
solvent continually to the solution. Consequently, the solvent will pass
continuously through the membrane from the pure solvent to the solution.
Equilibrium will be reached, and the flow will cease, only when the solution
has become infinitely dilute, equal hydrostatic pressure obtaining on
solution and solvent, or when the disturbing influence of the solute, which
dilutes the solvent in the solution, is exactly counterbalanced by an external
hydrostatic pressure, exerted on the solution. When such a pressure on the
surface of the solution balances the force exerted against the solvent by the
solute we shall have equilibrium. It is clear, then, that the osmosis, or
passage of the solvent through the membrane, is brought about by the
unequal concentrations (or, more exactly, the resulting unequal partial
pressures) of the solvent itself. But this inequality is produced by the
presence of the solute, and it is a characteristic and significant fact, that the
effect of the latter, in dilute solutions, may be overcome by a hydrostatic
pressure, corresponding to the gas pressure which the same number of
molecules of a gas in the same volume at the same temperature would exert
against this hydrostatic pressure.

Fig. 6.
Osmosis and Gas Pressure.
—The legitimacy of the interpretation given is most strikingly shown by
experiments with a membrane, semipermeable for gases, which enables us
to measure gas pressures, that may be unknown, by exactly the same
process as is used to measure the unknown osmotic pressure of a solute in
solution. Van 't Hoff35 and Arrhenius36 predicted such a result, and
Ramsay37 proved by experiment the correctness of their assumptions. A
mixture of nitrogen and hydrogen may be enclosed in a palladium vessel
connected with a manometer (see Fig. 6).38 The partial pressure PN of the
nitrogen may be [p025] determined by surrounding the palladium vessel with
pure hydrogen, at a pressure which is known and is greater than the partial
pressure of the hydrogen in the vessel, and by observing the final total gas
pressure which is obtained in the vessel. The hydrogen diffuses from the

point of higher concentration, outside of the vessel, through the palladium,
into the interior where the concentration of the hydrogen is lower. The
experiment may be carried out at 280°, a temperature at which palladium
readily dissolves hydrogen and is permeable to it. The metal does not
dissolve nitrogen and is not permeable to it. The volume of the enclosed gas
is kept constant by raising the mercury level in the outside arm of the
manometer, and the total pressure of the enclosed gas is measured when
equilibrium is reached. If this total pressure is Pfinal and the known pressure
of the hydrogen outside of the vessel is PH, then, if equilibrium is reached
when the hydrogen on both sides of the semipermeable palladium
membrane has the same concentration (pressure), PH + PN = Pfinal and PN =
Pfinal − PH. In other words, the excess of the final combined pressure inside,
over the outside pressure of the hydrogen, is equal to the pressure of the
nitrogen in the vessel. Ramsay's results showed that the amount of hydrogen
actually entering the vessel was 90–97% of the amount predicted by the
theory on the basis of the assumption that equilibrium will be reached,
when the hydrogen has the same concentration (pressure) on both sides of
the palladium membrane.
The experiment is particularly instructive, in the first place, because it
illustrates with a gas, subject to the laws of gases, why and how osmosis
takes place through a semipermeable membrane—namely as a result of the
solubility of the diffusing substance in the membrane, and through the flow
of the diffusing substance [p026] from higher to lower concentrations. In the
second place, while the increase in total pressure in the inner chamber
undoubtedly is brought about by the osmosis of hydrogen into the chamber,
the excess pressure when equilibrium has been reached, necessarily
measures accurately the partial pressure of the nitrogen. In other words, the
semipermeable membrane is merely a means or device for measuring the
partial pressure of the nitrogen—the membrane is not the cause of the
pressure; the latter is a definite one, whether we know what it is or not, and

the osmosis of the hydrogen through the palladium merely gives us a means
of ascertaining it. Similarly, it would be wrong to consider that the osmotic
pressure of a solution is caused, or brought about, by the flow of the solvent
through a semipermeable membrane (osmosis); the latter simply is a device
which enables us to recognize and measure the pressure that exists in the
solution, both in the presence and the absence of such a membrane.
We may consider, then, that the osmosis, or migration of the solvent
through a semipermeable membrane into a solution, is the result of the
reduced concentration (or partial pressure) of the solvent in the solution,
resulting from the presence of the solute.
Inasmuch as the effect of the solute on the solvent can be overcome by a
pressure on the surface of the solution, one is led to the conclusion that the
solute acts by exerting, in turn, a force or pressure against the surfaces of
the solvent, in the directions opposite to the hydrostatic pressure required to
overcome it. The significant identity of the value of this pressure, as thus
measured, with the gas pressure that would be exerted by a gas of the same
number of molecules, in the same volume and at the same temperature,
leads us to the last of the three questions which have been raised, namely,
the question concerning the theory of the intimate relations between gas and
osmotic pressures (p. 21).
The Kinetic Theory and Osmotic Pressure.
—For an answer to this fundamentally interesting theoretical question one
turns, naturally, to the kinetic theory, which, in the hands of Clausius, Joule,
van der Waals and others, has given us a very satisfactory and essentially
complete theoretical interpretation of the behavior of gases, and of the
liquids to which they may be compressed.
The laws of gases, it is known, are in accord with the two simple
assumptions of the kinetic theory. The first assumption is that [p027] gases
consist of ultimate discrete particles (molecules), which move in all
directions through the space filled by the gas and, at ordinary pressures, are

so far apart, that the forces of molecular attraction between them are
negligible; the pressure of the gas is simply the net result of the impacts of
these flying particles upon the walls of the containing vessel. The second
assumption of the kinetic theory is that temperature is a function of the
mean kinetic energy of the moving molecules, and that the molecules of
gases of the same temperature have the same mean kinetic energy. The
kinetic energy of particles is a function of their mass m and their velocity u
(K.E. = ½ m u2). When a gas is heated, the kinetic energy of its molecules is
increased, and, since their masses remain unchanged, their velocity must
increase. As a result, the number and the force of their impacts against the
walls of a given space increase, and thus the pressure is increased.
We may ask, whether this theory cannot be used to explain the
connection between osmotic and gaseous pressure. If temperature is a
function of the kinetic energy of the molecules of which a substance
consists,—and the whole behavior of gases confirms such a conception,—
then one must conclude, that the mean kinetic energy of molecules, at a
given temperature, must always be the same, irrespective of whether they
are present in gaseous, or liquid, or solid form, or even in solution.39 The
tendency of the molecules to move, resulting from the kinetic energy
inherent at a given temperature, may be largely balanced (liquids), or
overcome (solids), by molecular attractions of surrounding particles, but
such conditions are altogether in harmony with the conception of a definite
mean molecular kinetic energy, persisting at a given temperature,
irrespective of the physical surroundings of the molecule. According to the
kinetic theory, then, when we have a dilute solution, say of alcohol in water,
the molecules of alcohol, at a given temperature, would have a given mean
kinetic energy, [p028] and would be tending to move in all directions with a
mass40 and velocity, the same as if the alcohol were present as a gas or
vapor at the same temperature. If the solution is sufficiently dilute, the
dissolved alcohol molecules are sufficiently far apart, for average time, to

make the molecular attractions between them negligible, just as is assumed
for gases. As far as the alcohol (solute) molecules alone are concerned, they
may, evidently, be assumed to be present in the solution, in the same
condition, as to number, mean kinetic energy and mean velocity, as they
would be in alcohol vapor of the same concentration and temperature. We
may ask, now, whether the osmotic pressure of the solution may not result
from the pressure on the solvent, growing out of its bombardment by the
solute molecules. And we may ask, further, what numerical relation would
subsist between such a pressure and the pressure of the solute, if the latter
were present as a gas, under the same conditions of temperature and
concentration. In order to be prepared to answer these questions, we must
consider, in what way the presence of the solvent must modify the motions
and the forces of impact of solute molecules.
One great difference between the dissolved substance and the gas would
be, that, in the solution, the solute is in intimate contact with the solvent. A
decided attraction must exist between the solute molecules and the solvent
molecules, since we could not otherwise understand how a solvent, like
water, in dissolving a nonvolatile substance like sugar, could overcome
those molecular attractions between the sugar molecules, which make sugar
a solid. But we note, that all the solute molecules in a solution, except those
at the surface, are surrounded on all sides equally by the solvent. The
attractive forces, exerted upon the single molecules of the solute by the
solvent molecules, thus sum up to zero, and need not be considered further.
Only the small number of solute molecules, which are at the surface of the
liquid, would involve a minor correction in the application of the kinetic
theory, and this need not be considered here.
A second point of difference between a substance in solution, and the
same substance as a gas or vapor at the same temperature [p029] in the same
volume, lies in the fact that a gas molecule will go a much greater distance
without colliding with some second molecule and changing its path, than

would a solute molecule, the latter molecule being closely surrounded by
the molecules of the solvent. The mean free path, as it is called, will be very
much shorter for a solute molecule than for a gas molecule, and we note, as
a matter of fact, how slow is the diffusion through a solvent (see exp. p. 8).
But the shortness of the previous path does not affect the force of a blow
resulting from the impact of a moving mass, the force of the impact being
dependent only on the mass and the change in speed of the striking particle,
at the moment of impact. Thus the short free mean path of a dissolved
molecule does not affect the mean force of the blow, delivered when it
strikes the resisting medium.
The slow diffusion of a dissolved substance represents a difference in degree, not in kind, between
gases and dissolved substances. Even in gases, we have such frequent collisions that the mean free
path of an oxygen molecule at 0° and atmospheric pressure is only 0.00001 cm., whereas the velocity,
the total path covered in one second, is 42,500 cm.
Exp. If a bulb containing a few drops of bromine is broken at the bottom of a tall cylinder, the
bromine vapor is seen to diffuse rather slowly into the upper part of the cylinder, the bromine
molecules, in their passage upward, rebounding from the air molecules, with which the cylinder is
filled. If a second cylinder is first evacuated, and the bromine bulb is broken in vacuo, the vapor is
seen to fill the cylinder instantly, the high velocity of the bromine molecules being thus revealed.

But a third question, of fundamental importance in the comparison of the
condition of a substance existing as a gas and its condition in a solution of
the same concentration and temperature, results from a consideration of the
frequency of the impacts of the solute molecules against the solvent,
growing out of the reduction of the lengths of the mean free paths of the
solute molecules.41 In order to be able to take this fact properly into
account, it will be necessary to consider somewhat more precisely the
manner in which, according to the kinetic theory, gas pressure is produced.
We may consider that we have in a cube of unit volume (1 c.c.) n
molecules of a gas, each of mass m and average velocity u cm. per second.
We may assume that one-third of the total number [p030] of molecules moves
in each of the three dimensional directions.42 A single molecule of mass m,
striking the surface with a velocity u and rebounding with the same velocity

in the opposite direction, will exert on the surface a force of 2 m u units.
But, with a velocity of u cm. per second, it will reach the opposite wall and
return to the surface we are considering, u / 2 times in one second. A single
molecule will consequently exert a force 2 m u × u / 2 or m u2 on the surface,
and the n / 3 molecules moving in the same direction will exert a force n / 3
× m u2 on the unit surface. This represents, therefore, the pressure of such a
gas, as calculated on the basis of the assumptions of the kinetic theory.
Now, when a gas is so strongly compressed, that the bulk of the molecules
is not negligible in comparison with the total volume of the gas, the number
of impacts on unit surface in unit time becomes sensibly greater than n / 3 ×
u / 2, since the distance to be covered between successive blows on the
surface will be sensibly less than 2 cm., in a cube of unit volume. If we
imagine, for the sake of a rough illustration, that one-third of the molecules
in 1 c.c. are united into one spherical mass (indicated by A in Fig. 7),
moving upwards and downwards, it is obvious that the distance covered
between two successive blows on a surface is not 2 cm., but that distance
diminished by twice the diameter of the sphere. For strongly compressed
gases, the total number of impacts on unit surface is therefore sensibly
greater than n / 3 × u / 2, and the pressure is proportionately greater.
According to van der Waal's correction for this effect, P = n / 3 × m u2 / (1 −
b), where b represents the volume actually occupied by the molecules in 1
c.c. of the gas.43
Now, for solute molecules, the "free space" of
movement, as we may call it, is, similarly, very
considerably reduced by the presence [p031] of the
solvent, and the reduction of this free space, as Nernst
has shown, will have the same effect on the pressure
produced against unit surface of the solvent by the
Fig. 7.
bombardment of the solvent by the solute, as the
reduction of the free space has on the gas pressure when a gas is strongly

compressed. The resulting pressure on unit surface of the solution must thus
be increased, from the pressure Pgas, which would be exerted by the solute
against the walls of a vessel, if it were present as a gas of the same
concentration, at the same temperature, to Pgas / (1 − v), where v represents
the real volume occupied by the solvent and (1 − v) the free space for the
solute molecules in unit volume of solution.44 If osmotic pressure is the
result of such a bombardment of the solvent by the molecules of the solute,
one might, therefore, expect to find the osmotic pressure very much greater
than the gas pressure of the same substance in the same volume at the same
temperature. However, in all the experimental determinations (by means of
semipermeable membrane, vapor pressure, boiling-point and freezing-point
measurements) of the osmotic pressure as defined on p. 10, this corrective
factor cancels out again.45 According to the kinetic theory, the osmotic
pressure of a substance in dilute solution should, consequently, be found by
experiment to be equal to the gas pressure which a gas, of the same
molecular concentration, would exert at the same temperature.46
We find thus that the significant coincidence between the osmotic
pressure of a substance in dilute solution, as defined and measured
according to van 't Hoff, and the gas pressure which the substance would
exert, if it were present as a gas in the same volume and at the same
temperature, is in agreement with the fundamental assumptions of the
kinetic theory. This theory, consequently, gives us an adequate theoretical
explanation of [p032] osmotic pressure, as it does of gas pressure. As van 't
Hoff says,47 "if the osmotic pressure follows Gay-Lussac's law and is
proportional to the absolute temperature, then, like gas pressure, it will
become zero at 0° absolute temperature and will vanish when molecular
movements come to rest. It is therefore natural to look for the cause of
osmotic pressure in kinetic phenomena and not in attractions."48

Chapter III Footnotes
[29] L'Hermite, Compt. rend., 39, 1177 (1854); van 't Hoff, Lectures on Physical Chemistry, Part
II, p. 37.
[30] Nernst, Theoretical Chemistry, p. 103.
[31] Van 't Hoff, Lectures on Physical Chemistry, Part II, p. 37.
[32] J. Phys. Chem., 10, 141 (1906).
[33] This term must not be confounded with the term osmotic pressure, which has been defined on
p. 10.
[34] See Chapter VII on the law of physical or heterogeneous equilibrium, where the relations are
discussed in detail.
[35] Z. phys. Chem., 5, 175 (1890).
[36] Ibid., 3, 119 (1889).
[37] Phil. Mag., 38, 206 (1894).
[38] Cf. van 't Hoff's Lectures on Physical Chemistry, Vol. II, 40 (1899).
[39] The molecules may have different masses in the different conditions, and the principle of the
mean kinetic energy would always apply to them as they are, in the condition under observation,
and not as they are in some other condition; any change in mass, in solution, for instance, would
show itself in the osmotic pressure measurements (see p. 18), just as it is shown in the
measurements of gases, when the gas molecules show a change in composition, as is the case with
hydrogen fluoride (H2F2 ⇄ 2 HF), nitrogen tetroxide (N2O4 ⇄ 2 NO2), phosphorus pentachloride
(PCl5 ⇄ PCl3 + Cl2) and other compounds.

[40] The molecular weight of alcohol in dilute aqueous solution is the same (46) as in vapor form.
Raoult, Z. phys. Chem., 27, 656; Loomis, ibid., 32, 592.
[41] Nernst, Theoretical Chemistry, p. 245.
[42] This assumption is not made in the rigorous development of the above relations on the basis
of the kinetic theory, but it leads to the same net result.
[43] Even for gases of ordinary concentration, the introduction of the same correction gives an
expression for the relation of pressure and volume, which is more exact than Boyle's law and is
used in all exact calculations with gases.
[44] One may imagine, first, n molecules of the solute as a gas, with the pressure Pgas, in 1 c.c.
Then, one may imagine, crudely, the n molecules of solute, in a free (gas) space of (1 − v) c.c., in
the center of 1 c.c. of the solvent, and exerting by their impacts a pressure Posm., against the

solvent. According to Boyle's law, we should then have, Pgas × 1 = Posm. × (1 − v), and therefore
Posm. = Pgas / (1 − v).

[45] Vide Nernst, Theoretical Chemistry, p. 245, for the detailed discussion of this relation.
[46] This conclusion is reached more rigorously and more simply by thermodynamic analysis.
[47] Lectures on Physical Chemistry, Part II, p. 35.
[48] Rigorous developments of the relations between solute and solvent, for dilute and
concentrated solutions, have been made by van der Waals, Z. phys. Chem., 5, 133 (1890); van
Laar, ibid., 15, 457 (1894); G. N. Lewis, J. Am. Chem. Soc., 30, 675 (1908), and Washburn, ibid.,
32, 653 (1910). An admirable review of the theories of osmotic pressure, by Lovelace, will be
found in the Am. Chem. J., 39, 546 (1908) (Stud.).

CHAPTER IV
THE THEORY OF IONIZATION; IONIZATION AND
ELECTRICAL CONDUCTIVITY

[p033] TOC

Of the laws and hypotheses concerning gases, the one that is perhaps of
most importance to chemistry is Avogadro's hypothesis. With the aid of this
hypothesis, we are able to determine the relative molecular weights49 of
such elements and compounds as are gases, or are volatile at higher
temperatures. If equal volumes of gases, under the same conditions of
temperature and pressure, contain the same number of molecules, then the
weights of such equal volumes also represent the relative weights of the
molecules composing the gases. As a standard, for expressing the relative
molecular weights in definite numbers, the molecular weight of oxygen is
taken by convention to be 32, and all other molecular weights are expressed
in terms of this standard. The density, or weight of one liter of oxygen at 0°
and 760 mm., is 1.429 grams, and the molecular weight expressed in grams
(molar weight) of oxygen, 32 grams, occupies, therefore, 32 / 1.429, or 22.4
liters. The weights of this same volume, 22.4 liters, of gases and vapors,
calculated for 0° and 760 mm. pressure,50 express then directly, in terms of
the oxygen standard, the relative molecular weights of the elements or
compounds forming the gases. The weights themselves give us directly
their gram-molecular or molar weights.
When molecular weights are determined in this way, with the aid of
Avogadro's hypothesis, results are obtained which agree [p034] perfectly with
the chemical behavior of the compounds or elements in question. The
molecular weights of hydrogen chloride, water, ammonia, and marsh gas,
for instance, are found to be 36.5, 18, 17 and 16, respectively,

corresponding to the formulæ51 HCl, H2O, NH3 and CH4, and in
confirmation of these results we find, by methods used especially in organic
chemistry, that these compounds show a chemical behavior agreeing
perfectly with the presence of one, two, three and four hydrogen atoms,
respectively, in their molecules. Marsh gas, for instance, by treatment with
chlorine, yields a monochloride, CH3Cl, a dichloride, CH2Cl2, a trichloride
(chloroform), CHCl3, and a tetrachloride, CCl4. Water, by proper treatment,
may be converted in successive stages into alcohol, (C2H5)OH, and then
into ether, (C2H5)O(C2H5), or into sodium hydroxide, NaOH, and sodium
oxide, Na2O.
It is this perfect agreement between the chemical behavior and the formulæ (as based on these
molecular weights and on the analysis of compounds), which forms the strongest experimental
evidence of the correctness of the fundamental assumption of Avogadro's hypothesis. The agreement
has been shown to hold for innumerable compounds, even for those of greatest complexity, and it
was such agreement which finally led to the general acceptance of the hypothesis. The experimental
evidence of this nature is so strong, so extensive and so completely corroborative of the hypothesis,
that many chemists, rather justly, consider the hypothesis to have been established as a law, although
the evidence is circumstantial rather than direct.

While the application of Avogadro's hypothesis thus gives results
agreeing well with the observed chemical behavior of very many important
compounds, observations have been made which, at first sight, do not
appear to agree with the requirements of the hypothesis and which seem to
raise a doubt as to the universal truth of its fundamental assumption. Thus,
if equal volumes of hydrogen chloride and ammonia, of the same
temperature and pressure, are brought together, ammonium chloride is
formed, both gases being totally consumed. Since, according to the
hypothesis, equal volumes, under the conditions obtaining, contain the same
numbers of molecules, the formation of ammonium chloride takes place
according to the equation NH3 + HCl → NH4Cl, and we should anticipate
that the molecular weight of [p035] ammonium chloride would be 17 + 36.5
or 53.5. However, when the molecular weight is determined by obtaining

the weight of a measured volume of ammonium chloride vapor, at a
temperature sufficiently high to vaporize the salt, and the observations are
reduced to standard conditions of temperature and pressure, 26.75 grams is
found as the calculated weight of 22.4 liters, and this weight, according to
this hypothesis, should be the molecular weight of the chloride. This
contradiction in two conclusions, each reached by the application of
Avogadro's hypothesis to experimental observations, would, at the first
glance, make one hesitate to accept the hypothesis as representing a
universal truth; it might seem as if in some gases, such as ammonium
chloride vapor, there might be only half as many molecules in a given
volume as in the same volume of the majority of gases.
Gaseous Dissociation.
—The discrepancy between the two conclusions and any doubt as to the
universal soundness of the great generalization expressed in Avogadro's
hypothesis disappear, however, in the light of a closer study of the
composition of ammonium chloride vapor. It was suggested simultaneously
by Cannizzaro, by Kopp and by Kékulé52 that the abnormally low result,
obtained for the molecular weight of ammonium chloride from a study of
its vapor density, is due to the dissociation of the salt at high temperatures
into its components, ammonia and hydrogen chloride, the average of whose
molecular weights is, in fact, (17 + 36.5) / 2, or 26.75, the value found
experimentally for the vapor of ammonium chloride. Proof of the
correctness of this interpretation was furnished by Pébal,53 who showed that
ammonium chloride vapor does consist of the two gases, the lighter of
which, ammonia, diffuses more rapidly through porous walls (Pébal used an
asbestos stopper) than does the heavier, hydrogen chloride. The dissociation
may be easily demonstrated by using an air cushion as a porous wall.54
From the mixture produced by vaporizing ammonium chloride,55 the
ammonia will diffuse more rapidly through the layer of air than will the

hydrogen [p036] chloride, and the gases may be recognized in succession by
their action on litmus paper (exp.).
The gaseous dissociation of other ammonium salts, of phosphorus
pentachloride and pentabromide (PX5 ⇄ PX3 + X2), and of a number of less
common compounds, has been demonstrated in similar ways. As a result of
the study of each case, the important conclusion has been reached that, as
far as our knowledge goes, there are no exceptions to Avogadro's
hypothesis, and this hypothesis seems therefore to represent a universal
truth.56
Molecular Weight Determinations in Solution.
—Van 't Hoff's extension of the Avogadro Hypothesis, so that it shall apply
to solutes in dilute solutions, is the basis of another general method of
greatest value for determining molecular weights. Equal volumes of dilute
solutions of the same osmotic pressure and the same temperature contain,
according to van 't Hoff, the same numbers of dissolved molecules,
irrespective of the solvent used. Furthermore, the number of dissolved
molecules is identical with that which a gas of the same pressure and at the
same temperature would contain in the same volume. To determine the
molecular weight of a solute, therefore, we may calculate, from the osmotic
pressure, the temperature and the concentration of the solution,57 that
weight of the solute which, in 22.4 liters of the solution, at 0° would give
760 mm. osmotic pressure; the weight found represents, in grams, the
molecular weight of the solute in the solution used. [p037]
The fact that all solvents and all solutes are included in this hypothesis,
with the sole limiting condition that the solution must be dilute, is one of
great significance and of greatest practical importance, as we may use any
suitable solvent for determinations.
When molecular weights are determined in this way, a very large number
of compounds give the same molecular weight by the solution method as by
the gas method. For instance we have:

Mol. Wt. Mol. Wt.
Substance. Solvent.
Gas Method. Sol. Method.
Chloroform, CHCl3 119.5 119.5 Benzene
Carbon bisulphide, CS2 76 76 Benzene
Methyl (wood) alcohol, CH4O 32 32 Water
Ethyl (ordinary) alcohol, C2H6O 46 46 Water
Ether, C4H10O 74 74 Acet. Acid

Further, the molecular weight of glucose is found in aqueous solutions to
be 180, conforming to the formula C6H12O6, and agreeing with the
molecular weight as obtained by a chemical study of compounds derived
from glucose.
While there are, then, very many agreements in the molecular weights
determined by the solution and by the older methods, it was recognized, at
the outset,58 that there is also a large number of apparently abnormal cases,
in which, in particular, much lower molecular weights are obtained by the
solution methods than by the gas method,—lower even than the weights
consistent with the accepted atomic weights of the elements in the
compounds in question.59 For instance, we find 36.5 to be the molecular
weight of hydrogen chloride in the gas form, but in aqueous solution its
apparent molecular weight, as determined on the basis of van 't Hoff's
hypothesis, is not even a constant; it is found to be less than 36.5 and
approaches the limit 18.25, the more dilute the solution, [p038] the lower
being the apparent molecular weight.60 For sodium chloride, the formula
weight, corresponding to the formula NaCl, is 58.5. This would also
represent its smallest molecular weight in gas form, consistent with the
accepted atomic weights for sodium and chlorine. In aqueous solution,
again, the apparent molecular weight of sodium chloride is found to be less
than 58.5, and more than 29.25, the value found depending on the
concentration of the solution used. For zinc chloride we have, likewise, in
aqueous solution values much less than 136 and tending toward the limit
45, whereas the formula weight for ZnCl2 is 136.

These are instances of a very large class of apparent gross discrepancies
between the requirements of the Avogadro-van 't Hoff principle and the
generally accepted molecular weights of common compounds. There are
three ways, in particular, in which one might be inclined to regard such
results: in the first place, one might be tempted to consider that van 't Hoff's
extension of Avogadro's hypothesis to solutions is justified in a considerable
number of cases, but not as a universal expression, applicable to all dilute
solutions. This seems, indeed, to have been van 't Hoff's own attitude
originally. Such a view, since it does not throw new light on the matter, but
simply shelves the question of the source of the discrepancy, would be
tenable only after all other explanations had been found unsatisfactory.
In the second place, we might be inclined to consider whether a molecule
like hydrogen chloride is not dissociated in aqueous solution into two
smaller molecules, hcl, in which hydrogen and chlorine would appear as
atoms with the weights h = 0.5 and cl = 17.75, which are half as large as the
atomic weights determined from a study of volatile compounds of hydrogen
and chlorine. If we remember that our atomic weights are confessedly
maximum weights, and not minimum weights—although they are almost
certainly also the true atomic weights—such a view would be, at least,
worthy of some consideration. But, in the first place, it would be
extraordinary that we should never have found, in the thousands of [p039]
hydrogen derivatives that have been investigated, any compound, the
molecule of which, in the gaseous condition, contained a single such atom
of hydrogen, with the weight 0.5, or an uneven multiple of it: that only even
multiples or pairs h2, corresponding to the atom H, should always have
been found. In the second place, such an explanation of the results of the
molecular weight determinations in aqueous solutions given above, would
soon lead to difficulties, which make the view altogether untenable. For
instance, the molecule of zinc chloride, according to the data given, would
have to break down into three molecules and, if these were of uniform

composition, we would have to assume chlorine atoms two-thirds or one-
third as large as Cl. Since a moment ago we had to assume chlorine atoms
one-half as large as Cl, we would have to conclude that the atomic weight
of chlorine could be, at most, Cl / 6, which is the largest common divisor of
Cl / 2 and Cl / 3. No chemist would seriously consider an atomic weight for
chlorine one-sixth as large as the accepted weight, for that would mean that,
in all the chlorine compounds investigated in the condition of gases, we
have always at least six such atoms occurring together, and otherwise
always multiples of six. Consequently such an interpretation of the so-
called "abnormal" behavior of solutions of hydrogen chloride, sodium and
zinc chlorides, etc., although at one time advanced by some chemists, must
be considered as altogether untenable.
A third explanation of the "abnormally" low molecular weights, which
certain substances in aqueous solutions possess, is, that the molecules of
these compounds are capable of dissociation into smaller molecules of
unlike composition, somewhat like ammonium chloride when it is heated,
and that the substances in question are dissociated more or less considerably
in this fashion in the solutions under consideration. Hydrogen chloride, for
instance, besides existing as such (as HCl), in aqueous solutions, might be
capable of dissociating, and actually be dissociated, to a considerable
degree into molecules containing either only hydrogen or only chlorine
(HCl ⇄ H + Cl); the average of the weights of the molecules in a mixture of
molecules, HCl, H, and Cl, would be less than 36.5, and, according to the
proportion of dissociated and undissociated molecules of hydrogen
chloride, the average would lie between the limits 36.5 and (1 + 35.5) / 2, or
18.25. Such an [p040] explanation,61 made with certain additions and
restrictions, was advanced in 1885 by Arrhenius, a Swedish chemist and
physicist, when he learned of the exceptional behavior of these solutions, as
noted by van 't Hoff. Although at first this interpretation occasioned
considerable criticism, it has maintained itself successfully for twenty years,

on the basis of a wide range of accumulated facts, and it has been of
remarkable value and benefit in the development of all branches of
chemistry and the allied sciences.
The Theory of Ionization.
—Arrhenius[2] made the simple observation that all those solutions, in
which the dissolved compounds seem to have abnormally low molecular
weights, are solutions through which an electric current may be readily
passed, they are electrolytes, whereas the solutions which give normal
results (see, for instance, the table on p. 37) do not allow the ready passage
of a current, they are nonelectrolytes.
Exp. The fundamental difference between the two classes of solutions may readily be
demonstrated. To water contained in an electrolytic cell, which is connected with a lighting circuit
and with an electric lamp, first some alcohol, and later a small quantity of hydrochloric acid are
added. The lamp is seen to glow, instantly, when the acid is added.

This simple fact, that the very solutions which give abnormally low
molecular weights for the dissolved compounds are also good conductors of
electricity, was explained by a theory of electrolytic dissociation or of
ionization, which Arrhenius had developed62 from a study of the
conductivity of electrolytes. The same fact has aided in establishing this
theory which has led to the elucidation of vital problems of electrical
conductivity and to a successful [p041] explanation of the problem of the
apparently abnormal osmotic pressures (and molecular weights) of
electrolyte solutes. It has thus removed the last difficulty in the way of
accepting the van 't Hoff-Avogadro Hypothesis (p. 15) as true for all dilute
solutions, exactly as the discovery of gaseous dissociation made it possible
to recognize in the original Avogadro Hypothesis a universal truth (p. 36)
about gases. And to these results was added, chiefly as the fruit of the work
of Ostwald, with the aid of the theory of Arrhenius, the most successful and
accurate formulation of the problem of the chemical activity of electrolytes,
known in the history of chemistry.
Main Assumptions of Arrhenius's Theory of Ionization.

—The main assumptions of the theory of electrolytic dissociation or
ionization are the following: (1) When an ionogen is dissolved in water, its
molecules are immediately, more or less completely, dissociated by the
water into smaller fragments or molecules of unlike composition. (2) These
new molecules are charged with electricity; the molecules of the one
product are charged with positive, the molecules of the other product63 with
negative electricity, the unit positive charge being equal in quantity, but
opposite in kind, to the unit negative charge; the sum of all the positive
charges in a solution is equal to the sum of all the negative charges, and the
whole solution is electrically neutral. (3) The dissociation is a reversible
reaction, and all electrolytes must be considered to be completely ionized at
infinite dilution. (4) Except for the dependence resulting from the electrical
charges and the consequent attractions and repulsions between ions, the
ions must be considered independent molecules with their own specific
chemical and physical properties.
When a current is passed through the solution of an ionogen, the
electrified particles carry their charges to the electrodes (see [p042] below).
They are called the ions64 of the electrolyte; the positively charged ions are
distinguished as cations from the negatively charged anions, and the
electrode toward which the cations move is called the cathode (negative
electrode), and the electrode to which the anions move is called the anode
(positive electrode).
The dissociation of hydrogen chloride may be expressed, in the terms of
the assumptions made, in the following equation: HCl ⇄ H+ + Cl−; that is,
hydrogen chloride is dissociated, to a greater or smaller extent and in
reversible fashion, into positively charged hydrogen ions H+, and negatively
charged chloride ions Cl−, and the charge on each chloride ion is equal in
quantity to the positive charge on each hydrogen ion. Zinc chloride is
dissociated according to the equation ZnCl2 ⇄ Zn2+ + 2 Cl−, and, according
to (2), the charge on each zinc ion is twice as great in quantity as the charge

on each chloride ion, and therefore twice as great also as the charge on each
hydrogen ion (see below, p. 58). It is practically certain, according to more
recent results, that the ions are combined with water to form hydrates, such
as H+(H2O)x and Cl−(H2O)y.65 This does not modify, essentially, the
fundamental assumptions of the theory, but contributes rather to a
satisfactory explanation of the rôle of water as an ionizing agent, a question
to which we shall return later.

The Theory of Ionization and the Electron Theory of Electricity and of
Matter.
66
—According to the views held by many leading physicists at the present
time, negative electricity consists of ultimate particles of matter called
electrons or corpuscles. The mass of an electron is about 1 / 1000 the mass
of an atom of hydrogen, and the electric charge of the electron is equal to
that carried by a chloride ion in solution.67 The atoms of the elements are
considered to consist of aggregations of large numbers of electrons in a kind
of "shell" or "body" of positive electricity. This positive electricity, in a
given atom, is equal in quantity to the total negative charge of the electrons
in the atom, the atoms as such [p043] containing no excess of either positive
or negative electricity. The number of electrons in the atom of an element is
considered to be definite and constant for that element, but the number
varies as we go from the atoms of one element to those of a second element,
the number increasing with the atomic weight of the element.
One of the most fundamental and most characteristic properties of
elements is considered to be the affinity which their atoms show for
electrons; thus, the atoms of metals like sodium and potassium, which are
generally called "electropositive" elements,68 show an enormous tendency
to lose one electron each and to form positively charged particles69 Na-ε
(= Na+) and K-ε (= K+).70 The atoms of strongly electronegative elements,
like chlorine, have a tremendous tendency for gaining and holding electrons
beyond the number originally in such atoms. Thus, chlorine atoms tend to
assume an electron each; they thereby become negatively charged particles,
Cl+ε ( = Cl−).
On the basis of these views, we have in sodium chloride NaCl a
substance, whose molecules contain an atom, Na, with a tremendous
tendency to lose an electron, and an atom, Cl, which has a tremendous
affinity for an electron. It is natural to suppose, then, that both tendencies
will be satisfied by the passage of an electron from the sodium to the

chlorine atom, NaCl → Na-εCl+ε. Or, if we use the sign + to designate the
positive charge produced on an atom by the loss of an electron and the sign
− to indicate the charge gained through the assumption of an electron, we
have71: NaCl is Na+Cl−. Similarly we have in hydrogen chloride H-εCl+ε or
H+Cl−. It is altogether likely, therefore, that the atoms in a molecule of
sodium chloride or of hydrogen chloride already possess electric charges,72
so that, even while combined, [p044] their tendencies to lose or gain
electrons are satisfied. It is also possible that the atoms are held together in
the molecule by the electrical attraction of the opposite charges.73 The force
with which opposite electrical charges attract each other depends, as is well
known, on the nature of the surrounding medium. Now, when molecular
sodium chloride or hydrogen chloride is dissolved in water (a favorable
medium), a decided decrease in the attraction (see p. 62), between the
charged atoms within the molecules is brought about, and a process of
ionization results: H+Cl− ⇄ H+ + Cl−. The charged particles are called ions
only after they have separated from one another and have become
independent molecules, capable, for example, of moving in opposite
directions.
While the atoms of some metallic elements tend to lose a single electron
and form ions Me+ (e.g. Na+, K+), the atoms of other elements tend to lose
two or more electrons, forming bivalent ions, Me2+ (e.g. Zn2+, Fe2+, etc.),
or trivalent ions, Me3+ (e.g. Bi3+, Fe3+), and so forth. Similarly, atoms of the
so-called negative elements may assume two or more electrons, forming
bivalent ions, X2− (e.g. S2−), and so forth.
The Validity of the Theory of Ionization.
—In determining the validity of the theory of ionization, we may consider,
first, the sufficiency of the explanations which it offers for observed facts
and important phenomena. We may then weigh, more critically, by any
evidence offering itself, the facts which will enable us to decide between
this theory and the older theory of ionization, that of Clausius (p. 51). The

latter, although displaced, is still often revived by opponents of the modern
theory. Such facts as we will consider are found, first, in the domain of
conductivity phenomena, next, in the osmotic pressure and related
properties of solutions, and, finally, in the study of the chemical activity of
electrolytes (see Chapter V).
Ionization and Electrical Conductivity.
—Turning our attention first to the field of electrical phenomena, and
developing the theory for the present descriptively, we find that the
conductivity of a solution depends, according to this theory, on the fact that
when two oppositely charged poles are placed in a solution, the [p045]
positive charge on the anode attracts all the negative particles within its
field of action, and repels all the positive particles, exactly as a positive
static charge of electricity would attract a negatively charged pith-ball and
repel a positively charged one. In the case of a solution of hydrochloric
acid, the negative charge on the cathode would attract the hydrogen ions
and repel the chloride ions, and the positive charge of the anode would
attract the chloride ions and repel the hydrogen ions. The net result would
be a migration of all the chloride ions with their negative charges toward
the anode, and of the positively charged hydrogen ions toward the cathode,
—a flow or current of electricity being thus produced. The fact, then, that a
current of electricity does readily pass through such a solution of an
ionogen, is easily understood on the basis of these views.
Exp. The migration of the ions throughout the whole solution may be demonstrated by the
passage of a current through a large U-tube containing a mixture of a cupric salt and a
permanganate,74 placed under some dilute sulphuric acid. The cupric-ion is blue, all ionized
solutions of cupric salts, with a colorless negative ion, being blue, while the permanganate-ion is of
an intense purple color. In the limb of the U-tube, in which the cathode is placed, a blue zone,
containing cupric ions, is soon seen emerging from the purple liquid and rising toward the cathode
(see Fig. 8). It will take some time for any cupric ions actually to reach the electrode and be
deposited as metallic copper. On the anode side, purple permanganate ions are seen rising toward the
positive electrode.

The movement of the electrically charged
particles in opposite directions through the
solution constitutes an electric current, and
such a current has the properties of a
current through a [p046] wire—producing,
for instance, heat, or being capable of
deflecting a magnet placed in its field of
action.75
Electrolysis.
—When ions touch an electrode, they are
discharged, and with the discharge, are
changed chemically, and, according to the
electron theory, also materially. Cupric ions,
Cu2+ or Cu−2 ε, receiving two electrons at
the cathode, are precipitated as metallic Fig. 8.
copper. When a current is passed through a
solution of hydrochloric acid, the hydrogen ions, by the pairing of the
discharged ions, yield hydrogen gas consisting of molecules, H2; the
chloride ions are converted at the anode into chlorine Cl2. The formation of
these molecules, X2, may be variously interpreted, as resulting either from
the union of two discharged or neutral atoms, or as consisting, for instance
in the case of hydrogen, in the discharge of a hydrogen ion H+, at the
negative electrode, followed by the assumption of a negative charge or
electron by the neutral atom, the new ion H− combining at once with the
positive ion H+ to form the molecule H+H−. At the positive pole, by an
analogous recharging of a discharged negative chloride-ion Cl−, we should
obtain a positive ion,76 Cl+, and immediately the formation of Cl2 or Cl+Cl−
would follow. Helmholtz advocated the latter conception of the action at the
electrodes, and, more recently, J. J. Thomson77 brings forward, as a very
important argument in favor of it, the fact that iodine, which according to

vapor density determinations dissociates into monatomic molecules at high
temperatures (I2 ⇄ 2 I), becomes, simultaneously with this dissociation, also
an excellent gaseous conductor of electricity, as would be anticipated from
a dissociation, I+I− ⇄ I+ + I−. This fact is emphasized here, because in it we
seem to have a case of conductivity coinciding with gaseous dissociation,
the existence of which is recognized by the universally accepted laws of
gases, and differing in no important respect from the dissociation assumed
for conductors in solution.
Conductivity and Dilution.
—The passage of a current through an electrolyte consists, then, in a
transfer of electricity by material particles, the ions. According to the theory
of ionization only [p047] the ionized portion of an electrolyte can carry the
current at any moment, and, consequently, a given weight of an ionogen
should, under comparable conditions, be the more efficient as a conductor,
the more completely it is dissociated into ions.
If the conductivity of a given weight of hydrogen chloride, for instance,
is measured under comparable conditions, it should be found to be greater,
the more completely the acid is ionized. Now, in aqueous solutions,
hydrogen chloride ionizes under the influence of the solvent water (pp. 41,
61), and the theory would lead us to anticipate that the greater the
proportion of water used, the more extensively will it ionize the acid.
Consequently, the addition of water to a given weight of acid should
increase the latter's efficiency as a conductor. This conclusion has been fully
verified by exact methods of measurement and may be readily
demonstrated by the following series of experiments:
Exp.78 An electrolytic cell, having the shape of a parallelopipedon and a capacity of about one
liter, is fitted with electrodes of copper, which reach from the bottom to the top of the cell and are
connected with a storage cell and an ammeter. The cell is first filled with distilled water: no
perceptible current passes through the water and the latter is therefore practically a nonconductor.
The cell is then emptied by means of a siphon and 20 c.c. of 4-molar hydrochloric acid is brought
into it. The ammeter shows that a definite current passes through the solution (0.17 ampere in an

experiment79 with a cell 4.6 cm. wide and 11.5 cm. long, with copper electrodes 4.6 cm. broad and
21 cm. high). (See Fig. 9, p. 48.) [p048]

Fig. 9.
The conductivity of a solution, like that of a metal conductor, is the
reciprocal of its resistance. Since, according to Ohm's law,80 the current for
a given potential is inversely proportional to the resistance, the current is
also directly proportional to the conductivity. The resistances of the metal
connections and of the ammeter in the experiment are very small compared
with the resistance of the solution, and they may be considered negligible
for our purpose. Thus, the current indicated by the ammeter is a closely
approximate measure of the conductivity of the solution. Now, if a volume
of water (20 c.c.) equal to the volume of acid, were to be added to the latter,
the cross section through which the current flows from plate to plate would
be doubled, and, since the conductivity of a liquid conductor, like that of a
metal, increases proportionally to the cross section, the current should be
doubled by the change in this one factor. On the other hand, the
concentration of the conducting acid is now one-half of the original
concentration, and this should in turn reduce the conductivity of the

solution to one-half. Consequently, if there were no further change in the
electrolyte, the original conductivity should be maintained when the acid is
thus diluted. But, according to the theory of ionization, as has just been
shown, the addition of [p049] water to a given weight of hydrochloric acid
should increase the proportion of ionized acid, and since the ions are the
carriers of the current, the conductivity of the solution should be increased
because of this change in the composition of the electrolyte. Experiment
shows that such is the case.
Exp. 20 c.c. of water is added to the 20 c.c. of 4-molar acid in the cell, and the mixture is stirred.
The current is decidedly increased (from 0.17 to 0.22 ampere in the experiment under discussion). If
40, 80, 160 and 320 c.c. of water are added in succession to the contents of the cell, the conductivity
is increased by every addition of water. But, while each addition dilutes the acid to one-half the
previous concentration, the increase grows proportionally smaller and smaller with increasing
dilution. In the following table, "Ratios I" are the ratios of the observed conductivities to the original
conductivity, "Ratios II" the ratio of each observed conductivity to the preceding one.

Concentration Observed
Ratios I. Ratios II.
of Acid. Conductivity.A
4-molar 0.17 1 1.
2-molar 0.22 1.30 1.30
1-molar 0.26 1.53 1.18
0.5-molar 0.30 1.76 1.15
0.25-molar 0.31 1.83 1.04
0.125-molar 0.32 B 1.03
1.88

[A] This is an artificial scale (see text) of conductivities, and does not represent reciprocal
ohms, the standard units of conductivity.
[B] In the exact data on the conductivities of 4-molar and 1/8-molar HCl (Kohlrausch and
Holborn, Leitvermögen der Elektrolyte (1898) p. 160), the ratio 348 / 181.5, or 1.92, is
found, in place of 1.88 as observed.

We should expect, further, that the increase in conductivity, being
dependent on the increased dissociation of a finite quantity of electrolyte,
should tend towards a limit, a maximum conductivity being reached when
(practically) all the acid is ionized. As a matter of experience, the
conductivity of a given quantity of an acid or other ionogen does tend
toward a limit. In the experiment just made, the conductivity of the acid

increases very rapidly at first, as the 4-molar acid is diluted by water; but
the increase in conductivity with the succeeding dilutions grows smaller
and smaller and the conductivity is plainly approaching [p050] a limit (see
the ratios I and II in the table). For hydrochloric acid at 18°, the limit for
one mole81 (36.5 grams HCl) at infinite dilution, as deduced from the curve
of conductivities at finite dilutions, is 384 reciprocal ohms.82
Degree of Ionization of an Electrolyte.
—The conductivity of a given weight of an electrolyte, for instance of its
gram-equivalent weight, depends, then, at a given temperature on the extent
to which it is ionized, the ions being the only carriers of the current in a
solution of an electrolyte. The conductivity will also depend on the friction
which the ions must overcome in moving through a solution, but, for
sufficiently dilute solutions in a given solvent, the friction may be assumed
to be approximately constant for given ions. For such solutions, then, the
conductivity of a given weight of a given electrolyte at a given temperature
may be said to depend wholly on the extent to which the electrolyte is
ionized. Thus, the proportion of ionized electrolyte in a solution may be
determined by measuring the conductivity. The extreme limit of its
conductivity, calculated for infinite dilution, represents complete ionization
of the electrolyte according to a fundamental postulate (§ 3, p. 41) of the
theory of Arrhenius, and the ratio of the conductivity in a given solution to
the conductivity of the same weight of electrolyte at infinite dilution
represents then the proportion of ionized electrolyte to the total electrolyte
used. This proportion is called its degree of ionization (commonly
designated by α). If we call Λv the conductivity of a gram-equivalent weight
of an electrolyte in a given solution, and Λ∞ the limit of its conductivity for
infinite dilution, then the degree of ionization is found from α = Λv / Λ∞.
[p051]

The method of calculation of α in a specific case may be illustrated as follows: the resistance of a
cube of 1 cm. edge of a solution of hydrochloric acid, which contains 1.825 grams hydrogen chloride
in a liter, is found to be 55.55 ohms at 18°. Its conductivity then is 1 / 55.55 reciprocal ohms. Now,

1.825 grams of hydrogen chloride is 1.825 / 36.5 or 1 / 20 gram-equivalent of the acid; a whole gram-
equivalent of the acid would be contained in 20 liters or 20,000 c.c. Then Λv = (1 / 55.55) × 20,000,
or 360 reciprocal ohms. If we use the value at infinite dilution given above, α = 360 / 384, or 93.75%.
That is, 93.75% of the hydrochloric acid is present in the ionized condition in such a solution, and
6.25% is not ionized.

By making the assumption that at infinite dilution electrolytes are
completely ionized, and by taking the ratio which the equivalent
conductivity of a given solution of an electrolyte bears to the maximum
limit-value (calculated for the conductivity at infinite dilution) to be the
degree of ionization of the electrolyte, as just explained, the theory of
Arrhenius has thus made it appear possible to determine experimentally the
proportion of ionized electrolyte present.
It is a significant fact that the equivalent conductivity of hydrochloric
acid is close to its limit even at finite dilutions, and that the same relation
holds for the strong acids and the strong bases, in general, and for most
salts. But the equivalent conductivity of weak acids, like acetic acid, and of
weak bases, like ammonium hydroxide, in finite dilutions is still far
removed from the limits which may be calculated for infinite dilutions.
Arrhenius was led then to the further important conclusion that, in the case
of the first electrolytes mentioned, a very large proportion of the electrolyte
must exist in the ionized form at finite concentrations, their equivalent
conductivities having almost reached the limit characteristic of infinite
dilution.
Clausius's Theory of Ionization and the Modern Theory.
—It is in these conclusions—in particular that the proportion of ionized
electrolyte may be determined experimentally, and that frequently a large
proportion is found to be ionized at finite concentrations,—that the modern
theory of ionization differs from the older theory of Clausius. The former is
an elaboration of the latter, and some opponents83 of the modern theory still
uphold the latter as offering an adequate explanation of the phenomena of
conductivity. All facts, then, in particular, which confirm the validity of the

conception of the degree of ionization, as introduced by Arrhenius, [p052]
must be considered as criteria favoring his theory, specifically. The
development of chemistry in the last twenty years is replete with such
evidence and we shall meet it in many connections throughout our work.
Clausius84 also assumed dissociated molecules or ions to be the real carriers of electricity in the
passage of a current through the solution of an electrolyte, but he assumed only a minute quantity of
these molecular fragments or ions to be free at any moment, their existence being supposed to be
transitory and dependent in particular on exchanges of atoms between molecules. As a result of the
oscillations of the atoms composing a molecule, oscillations comparable with the motions of
molecules assumed in the kinetic theory of gases, molecules were considered by Clausius
occasionally to reach such a condition of instability, that they dissociated into smaller particles; since
the atoms were supposed to be held in a molecule by attractions of electrical charges on the atoms
(theory of Berzelius), the fragments of the molecule would carry the charges, positive and negative
respectively, which they possessed in the molecule. Such a breaking up or dissociation of molecules
was, further, supposed to occur with particular ease during the collisions of molecules, the electrical
attractions and repulsions of the charged atoms favoring, at such moments, an exchange of atoms.
During the exchange, the atoms were considered to be free molecules, charged with electricity—
essentially ions,—capable of moving under the influence of electrical forces and of thus carrying a
current. Finally, such ions were supposed, in part, to escape recombination, and to remain free, until
each ion either collided and combined with an ion of opposite charge, or collided with a molecule
and displaced an atom of the same charge from that molecule, a new ion being thus liberated. The
theory, as usually interpreted, assumed the existence of only a very small quantity of such free ions,
that being all that was supposed to be required to explain the facts known at the time it was advanced.
In what follows, we shall confine the discussion strictly to such contrasts between the two theories
as grow out of a consideration of the phenomena of conductivity, and particularly consider some
evidence which is directly concerned with the conductivity of solutions.
In the first place, if the formation of ions occurs primarily during the exchange of atoms in
collisions of molecules, then, as Whetham85 has shown, the specific conductivity (of 1 cm.3) of an
electrolyte, like hydrochloric acid, must increase with the concentration and must increase,
approximately, as a function of the third power of the concentration. The more concentrated the
solution, the more frequent the collisions between the dissolved molecules must be. As a matter of
fact, as shown in the following table, the conductivity [p053] increases a little less than proportionally
to the first power of the concentration—which is in conflict with the assumption made in the
hypothesis of Clausius, but in perfect agreement with the hypothesis of Arrhenius. The small
decrease with increasing concentration, in the simple ratio between conductivity and concentration,
is due to the decreasing degree of ionization in the more concentrated solutions, as demanded by the
hypothesis of Arrhenius.

The table gives, in the first column, the specific conductivities of hydrochloric acid at 18°, and, in
the second column, the concentrations; these concentrations are expressed in moles or gram-
equivalents per cubic centimeter; the last column gives the ratio of conductivity to concentration.

Conductivity
Conductivity
Concentration ─────────────
of 1 c.c.
Concentration.
0.00370 0.00001 370
0.00734 0.00002 367
0.01092 0.00005 364
0.01800 0.00005 360
0.03510 0.00010 351
Furthermore, facts admitted by Clausius to be inexplicable by his own assumptions receive, in the
theory of Arrhenius, at least a quantitative formulation borne out by a mass of corroborative
evidence. The difference in conductivity between pure water and sulphuric acid is such a fact,
mentioned by Clausius. Determinations of the ionization of sulphuric acid and of water, by the
conductivity methods which are based on the theory of Arrhenius, show that, while sulphuric acid is
very considerably ionized (see p. 104), water is scarcely ionized at all. The ionization of water (see p.
104) has been determined quantitatively by at least four independent methods of examination,86 and,
minimal as the ionization is, the results agree so well with each other that van 't Hoff87 was led to
write: "If one is not previously convinced of the correctness of the theory of electrolytic dissociation,
hardly any result won by means of it is so convincing, as the agreement between the conclusions
reached in completely different ways as to the degree of dissociation of water itself. After such an
agreement, it is hardly conceivable that the basis on which all these results rest should further be
altered."
Mobilities or Partial Conductivities of Ions: Principle of Kohlrausch.
—If ions have a separate existence, each kind of ion would be expected to move through a solution
under a given electrical force at a given temperature with its own specific speed, the speed being
presumably dependent on the nature of the ion as well as on the weight of water combined with it and
dragged with it through the solution (p. 42). [p054]
Such relative speeds of ions may be demonstrated by means of an experiment: the motion of the
hydrogen ions, formed by the ionization of hydrochloric and other acids, may be observed by their
action on a reddened (alkaline) solution of phenolphthaleïn, which is decolorized by them; and the
motion of the hydroxide ions, formed by the ionization of sodium hydroxide and other bases, may be
followed by their action on colorless phenolphthaleïn, which turns red in their presence. The
hydrogen and the hydroxide ions are the fastest, in aqueous solutions, and their speeds are compared
in the next experiment with that of blue cupric ions, which have a speed roughly the same as that of
many common ions. In this experiment the hydrogen ions are readily seen to move about twice as
fast as the hydroxide ions and five to six times as fast as the cupric ions.

Fig. 10

Exp.88 Five grams of agar-agar are dissolved in 250 c.c. of boiling water. To 100 c.c. of the hot
solution, 32 c.c. of a saturated solution of potassium chloride and about 1 c.c. of phenolphthaleïn
solution are added, together with enough of a solution of potassium hydroxide, added drop by drop,
to produce a deep red tint in the phenolphthaleïn. Of this mixture 50 c.c. is treated with dilute
hydrochloric acid, added drop by drop, until the red color is just discharged, and then an excess of
acid, equal in amount to the quantity used to neutralize the 50 c.c., is added to the mixture. This
colorless solution and 50 c.c. of the red solution are poured, while still warm, into the two parts of a
wide U-tube, slowly and at equal rates, so that the level on the two sides remains the same. In this
way it is possible without difficulty to have the solution on one side red (alkaline) and on the other
side colorless (acid). The agar-agar is allowed to congeal, and then a mixture of 0.5 c.c. of
hydrochloric acid, (sp. g. 1.12), 6 c.c. of saturated cupric chloride solution and 20 c.c. of water is
poured over the red half, and a mixture of 20 c.c. of saturated [p055] potassium chloride solution and 2
c.c. of 10% potassium hydroxide solution is poured over the colorless half. The U-tube is surrounded
by ice water during the passage of the current, and the cathode is placed in the solution on the
colorless side. In Fig. 10 the ∪-tube is shown when first charged (on the left), and after the current
has been running for a short time (on the right).
The conductivity of a solution must be made up, therefore, of the sum of the shares which the
positive ions and the negative ions, respectively, take in carrying the current. This principle was first
advanced by Kohlrausch. The share of each kind of ion in conducting a current may be determined,
for hydrochloric acid for instance, in the following way: A porous diaphragm may be used to divide
the solution in an electrolytic cell into two halves, the concentration of the acid being the same in

both halves (represented, as indicated in Fig. 11, by 15 molecules89 of ionized acid in each half). A
measured current is passed through the solution, say, sufficient to liberate 3 molecules of hydrogen
H2, and 3 of chlorine Cl2, corresponding to 6 ions of each, and the concentration of the acid in each
half is then again determined by analysis. Say it is found to correspond to 14 molecules of
hydrochloric acid in the half of the solution on the side of the cathode and 10 molecules in the half on
the side of the anode (see Fig. 12). Then the anode half has lost 5 ions of hydrogen, which must have
passed through the diaphragm toward the cathode and taken the place of five of the six hydrogen ions
discharged at the cathode. Similarly, the solution around the cathode has lost one chloride ion, which
must have passed through the diaphragm toward the anode, and the hydrogen-ion corresponding to it,
remaining on the right side without a compensating negative ion, must be the sixth hydrogen-ion
discharged at the cathode. In other words, five hydrogen ions passed to the right, while one chloride
ion passed to the left. The hydrogen ions then carried five-sixths of the current through the
diaphragm, and consequently through the solution, and the chloride ions only one-sixth of the
current. Since the solutions were of equal concentration to start with, the hydrogen ions have moved
five times as fast toward the cathode as the chloride ions have moved toward the anode.

Fig. 11. Fig. 12.
The equivalent conductivity of 0.1-molar hydrochloric acid is 351 at 18°, and experiment shows
that the hydrogen-ion carries 84% of the current, the chloride-ion only 16%. The conductivity may
then be considered to be the [p056] sum of the share the hydrogen-ion has in carrying the current, i.e.
0.84 × 351, or 295, and of the share of the chloride-ion, 0.16 × 352.5, or 56. These values may be
called the equivalent partial conductivities or mobilities of the ions in this solution.
In a similar way, the conductivity of every solution of an electrolyte may be shown to represent the
sum of the mobilities of the ions carrying the current (principle of Kohlrausch). The limit of the
conductivity of one equivalent of an electrolyte is the sum of the mobilities of the ions composing the
electrolyte. The frictional forces being constant for infinitely dilute solutions, at a given temperature,
an ion will always show the same mobility, irrespective of the nature of the ion of opposite charge,
with which it forms the electrolyte. We may then put Λ∞ = (l+∞ + l−∞), if l+∞ and l−∞ are used to
designate the limits of the mobilities of gram-equivalents of the positive and negative ions forming
the electrolyte. The following table90 gives the limits of the mobilities for gram equivalents of some
of the most important ions at 18°.

Limits of Mobilities of Common Ions at 18°.
K: 65.3 ½ Ca: 53.0 I: 66.7

Na: 44.4 H: 318.0 NO3: 60.8
(NH4): 64.2 OH: 174.0 C2H3O2: 33.7
Ag: 55.7 Cl: 65.9 ½ SO4: 69.7

For quite dilute solutions, in which the friction may be assumed to be approximately constant, the
conductivity will depend, not only on the mobilities of the ions, which may be taken to be the same
as for solutions of extreme dilution, but also on the proportion of electrolyte that is ionized, i.e. on the
degree of ionization, α. Then Λv = α (l+∞ + l−∞), which is an elaboration of the original equation
given on page 50.
Now, Kohlrausch discovered the principle of the summation of the mobilities of ions a number of
years before the theory of Arrhenius was advanced, and the proportion in which the ion is present in a
given solution being unknown, the effect of what is here known as the degree of ionization was
included empirically in the value of the mobility. It is not surprising, then, that an ion was found to
have approximately the same mobility only in solutions of the same concentration of strictly
analogous and closely related salts, which, according to present methods of investigation, are now
found to have approximately the same degree of ionization. For instance, the mobility of the gram-
equivalent of the chloride-ion was found to be approximately the same, 47.3 and 50.5 respectively, in
molar solutions of sodium and potassium chloride at 18°, no account being taken of the degrees of
ionization. However, the degrees of ionization of the two salts are approximately the same, 66.9%
and 74.9% respectively, and might be ignored in a comparison of the conductivities, without affecting
the result of the comparison in any marked way. [p057]
When the conductivities of unlike electrolytes are compared, the introduction of the conception of
the degree of ionization (by Arrhenius,) into Kohlrausch's principle of the independent conductivities
of specific ions, shows most striking results and demonstrates the value of the new conception. For
instance, the equivalent conductivity of potassium chloride at 18° in 0.075 molar solution is 113.8
reciprocal ohms and the partial conductivity of the chloride-ion in the solution is 57.4. But the
conductivity of an equivalent solution of mercuric chloride at 18° is only 1.51, which is very much
less than the conductivity of the chloride-ion alone in the potassium chloride solution. Now, mercuric
chloride, according to investigations of its conductivities and of its effect in depressing the freezing-
point of water,91 is one of a very few salts that are difficultly ionizable (p. 107); according to the data
mentioned, it is ionized, at most, to the extent of 2.5 per cent in the solution in question, whereas 87.5
per cent of the potassium chloride is ionized in such a solution. When the difference in the degree of
ionization is taken into account, the conductivity which mercuric chloride should show may be
calculated, on the assumption that the chloride-ion has the same mobility in the two solutions, but
that there is less of it in the mercuric solutions. We put
ΛHgCl = α (lHg + lCl) = 0.025 (48 + 65.9) = 2.8. We thus find that the conductivity of the mercuric
2
chloride should be, approximately, only 2.8 reciprocal ohms, which is of the same order as that found
(1.51).92
In the same way, when we compare the conductivity of a strong acid, like hydrochloric acid, with
that of a weak acid, like acetic acid—the conductivity of 0.1 molar hydrochloric acid is 351, of 0.1

molar acetic acid only 4.6—the principle of the specific, characteristic mobility of the hydrogen-ion,
which is present in both solutions, has significance only if we take into account the very different
concentrations of the hydrogen-ion in the two solutions, resulting from the different degrees of
ionization of the two acids—91% for the hydrochloric and only 1.7% for the acetic acid. The same
relations hold in the comparison of the conductivity of a solution of a strong base like sodium
hydroxide with that of an equivalent solution of a weak, i.e. much less ionized base like ammonium
hydroxide, or in comparing the conductivity of a weak acid or a weak base with the conductivities of
their much more highly ionized salts.
In all these cases the use of the conception of the degree of ionization of the electrolytes makes
possible a much broader and more general application of the principle of the independent migration
or mobility of the ions than was possible before the theory of Arrhenius was proposed, and marks a
distinct advance in the theory of conductivity, over what was possible on the basis of the theory of
Clausius. [p058]

Faraday's Law.
—If a definite quantity of electricity, a faraday,93 or 96,600 coulombs, is
passed through a solution of hydrochloric acid, a definite quantity (36.5
grams, one mole) of the hydrogen chloride is decomposed, and one gram of
hydrogen and 35.5 grams of chlorine are liberated by the discharge of one
gram (i.e. one gram-ion) of the hydrogen-ion and 35.5 grams or one gram-
ion of the chloride-ion. In a solution of cupric chloride, the chloride-ion is
identical in every respect with the chloride-ion found in a solution of
hydrochloric acid. In the solution of cupric chloride, however, a molecule of
the salt, when it is completely ionized, produces two chloride ions for every
cupric ion (CuCl2 ⇄ Cu2+ + 2 Cl−). Since the solution never shows the
presence of an excess of either form of electricity, and the negative charge
on each chloride ion is the same as on a chloride ion formed by the
dissociation of hydrogen chloride, a cupric ion must hold exactly double the
positive charge that a hydrogen ion does. In modern terms, each hydrogen
atom, present as an ion, has lost one electron, and each copper atom present
in the form of a cupric ion has lost two electrons. Our unit quantity of
electricity, 96,600 coulombs, can discharge therefore only half as many of
the cupric as of the hydrogen ions, and since each cupric ion is 63.6 times
as heavy as the hydrogen-ion (Cu = 63.6, H = 1), 63.6 / 2 grams of copper,

the equivalent weight, will be deposited in place of one gram of hydrogen.
Similarly, from a solution of ferrous chloride FeCl2, 55.9 / 2 grams of iron
(Fe = 55.9) will be deposited, the ferrous ion being Fe2+; while from a
solution of ferric chloride FeCl3, only 55.9 / 3 grams of iron will be
deposited by 96,600 coulombs, the ferric ion, Fe3+, holding three times the
charge that a hydrogen ion does. In other words, a given quantity of current
will decompose equivalent quantities of electrolytes and deposit equivalent
quantities of metals. This is the well-known law of Faraday. The theory of
Arrhenius agrees with it, as did the theory of Clausius. It cannot be
considered as evidence bearing on the question of the preference to be
given to either of the theories of ionization, since the degree of ionization of
electrolytes is not involved in the relations covered by the law. But any
other relation would have been incompatible with the theory of Arrhenius.
The law is of particular importance in giving us [p059] the best clew that we
have in regard to the ultimate nature of "valence" (as shown for instance in
the difference between the ferrous, Fe2+, and the ferric ions, Fe3+). On the
basis of this law, valence may be said to consist simply in the capacity of
atoms to hold different multiples of the unit electrical charge (positive or
negative). This conception will be of especial value to us when we come to
consider the relation of the theory of ionization to oxidation and reduction
(Chapters XIV and XV).
Diffusion of Ions and Concentration Cells.
—When the, apparently, abnormally low molecular weight of ammonium
chloride was explained as being due to the dissociation of each molecule of
ammonium chloride into a molecule of ammonia and one of hydrogen
chloride, the evidence of the correctness of this interpretation was at once
forthcoming—the vapor of ammonium chloride, by the unequal rates of
diffusion of its components, was proved to be a mixture of the two gases (p.
35). Now, if an electrolyte like hydrochloric acid in aqueous solution is
dissociated more or less into separate ions, H+ and Cl−, then one may well

ask, whether the dissociation cannot be demonstrated by the same kind of
experiment, as, for instance, by showing that hydrogen and chloride ions
are molecules with unequal powers of diffusion and by separating them by
virtue of such inequality. Ions being, according to the theory under
consideration, independent molecules, except for the attractive and
repulsive forces of the electrical charges, they should have, like cane sugar,
copper nitrate and other solutes, the capacity for diffusion from regions of
higher to those of lower concentration. Further, if ions show different
degrees of mobility (p. 53), one would expect the more mobile or faster
moving one to diffuse more rapidly than a less mobile ion. Such a relation
should hold for the ions in a solution of hydrochloric acid, the hydrogen-
ion, according to the calculations of Kohlrausch94 and the observation of
Lodge,95 moving at a rate about five times as great as that of the chloride-
ion, at 18°. Thus, if a rather concentrated solution of hydrochloric acid were
covered with a layer of water, or with a very dilute solution of the acid, one
might expect the hydrogen ions to migrate faster than the chloride ions from
the [p060] point of higher to that of lower concentration, i.e. from the more
concentrated to the dilute acid. When the experiment is tried in this way, no
separation of the hydrogen from the chloride ions seems to occur. The
reason for the failure of the experiment is as follows: If any such separation
did occur, even to the extent of say one milligram-equivalent of hydrogen
and chloride ions, we would have a separation of electrostatic charges of 96
coulombs. These charges, on the small areas involved, would inevitably
produce enormous potentials, that would operate against the separation. The
hydrogen ions, which would tend to move from the concentrated to the
dilute acid, would therefore be held back by the powerful attraction
between their positive charges and the negative charges left in the
concentrated acid (on the Cl− ions). The separation of the electrical charges,
incidental to a faster diffusion of hydrogen ions, if it occurred, would result,
therefore, in the development of electrical forces of attraction, which would

prevent a separation of the oppositely charged particles beyond any but
distances too small to be measured. It would follow, however, that no
difficulty whatever should be experienced in observing such a separation,
as a result of unequal rates of migration of the ions in question, if provision
were made to preserve electrical neutrality in all zones of the two solutions,
i.e. if provision is made for the immediate discharge of the ions, as they
separate by the unequal rates of diffusion. For instance, the part of the
liquid into which the positive hydrogen ions move more rapidly, charging it
with positive electricity, may be connected, by means of a wire, with the
part of the liquid to which the chloride ions, left behind by their slower
movements, are imparting a negative charge. In such a circuit, a current of
electricity should be produced, the positive current flowing through the wire
from the dilute to the concentrated acid. As a matter of fact, we find that a
current is produced, when these conditions are observed.
Exp. The lower plate in an Arrhenius cell is covered with concentrated hydrochloric acid. Very
dilute acid is allowed to flow slowly on to the surface of the concentrated acid, from a pipette with a
curved, narrow point, until the upper plate is submerged. The two plates are connected with a
sensitive galvanometer. The current flows in the direction demanded by the observed mobilities of
the ions, the positive current entering the galvanometer from the plate covered by the dilute solution,
which is charged positively by the faster moving hydrogen ions coming from the concentrated
solution. If the cell is [p061] connected with the electrodes of a very small cell containing copper
sulphate, in the course of twenty-four hours quite a deposit of metallic copper is formed on the
electrode connected with the concentrated solution of hydrochloric acid.

The existence of the products of the electrolytic dissociation, of
hydrochloric acid may therefore be demonstrated,96 by the aid of the
individual diffusion of the products of the dissociation, in the same way as
was the coëxistence of the products of the gaseous dissociation of
ammonium chloride, when the conditions for the experiment are adapted to
the nature of the dissociation products. Cells of this type, depending for
their current on unequal concentrations of given ions, are called
"concentration cells."

If it can be shown that the flow of electricity, resulting from such unequal diffusibility of ions, is a
function not only of the difference in the total concentration of the electrolyte in the two solutions
brought into contact with each other, but is also a function of the relative degrees of ionization of the
electrolyte in the two solutions, as defined by the theory of Arrhenius, then this method of
experimentation may be used as a further test of the validity of this theory as against that of Clausius.
It is obvious that if such currents are the results of the diffusion of ions from higher to lower
concentrations, then the essential concentrations do not embrace all of the electrolyte, but only the
ionized part. W. K. Lewis97 has rather recently shown that the degrees of dissociation of electrolytes
may be measured by the use of concentration cells, and that the results agree well with the
determinations of the degree of dissociation from conductivity measurements (p. 50). From
calculations, based on Jahn's accurate measurements of the electromotive forces of concentration
cells, A. A. Noyes98 finds that "when the conductivity ratio is assumed to represent the degree of
ionization of the salt, the calculated values of the electromotive force of concentration cells exceed
the measured ones by only about one per cent, in the case of potassium and sodium chloride between
the concentrations of 1 / 600 and 1 / 20 molar."

The Rôle of the Solvent in Ionization.
—A question that has profoundly interested chemists, particularly during
the last few years, has been that of the rôle which the solvent plays in the
[p062] dissociation of electrolytes into ions. The most important ionizing

solvent is water and, of the common solvents which cause ionization, it is
the most powerful in this particular. Alcohols have also ionizing power;
methyl or wood alcohol, which stands nearest to water, has a higher
ionizing power than ordinary ethyl alcohol. The exact work99 of Franklin
and Kraus, on the conductivity of solutions of salts in liquid ammonia,
showed that the same general relations obtain for such solutions as for
solutions in water, the differences being differences of degree rather than of
kind. Salts are found to be less ionized in liquid ammonia than in equivalent
aqueous solutions, but their conductivities are higher, the result of smaller
friction in ammonia. Liquid hydrogen cyanide is also a very good ionizing
medium.
Solvents which cause ionization only to a minimal extent are benzene
(C6H6), carbon bisulphide, ether, chloroform, petroleum ether (gasoline)

and similar solvents. Hydrogen chloride dissolved in benzene has an
extremely small conductivity, indicating only a trace of ionization.100
The question may be raised, why the first solvents mentioned should
have the power to cause ionization, while the second series of solvents
named do not have this power, or have it only to a very slight extent.
Without attempting to enter into an elaborate discussion of this important
question, it may be said that J. J. Thomson101 and Nernst102 suggested that
the ionizing powers of solvents must be intimately connected with their
dielectric behavior, and this view has now been well established. It may be
said, in simple terms, that the so-called dielectric constant of a solvent
determines the force with which electrical charges will attract and repel
each other; the higher the dielectric coefficient of a medium, the smaller
will be the attraction between opposite electrical charges, other conditions
being the same. In solvents, then, of high dielectric powers, the coëxistence
of oppositely charged particles must be more favored than in solvents of
low dielectric powers. The dielectric constants of a number of solvents are
given in the following table: [p063]
Hydrogen cyanide, HNC 95
Hydrogen peroxide, H2O2 93
Water, H2O 81
Methyl (wood) alcohol, CH4O 32
Ethyl (ordinary) alcohol, C2H6O 22
Ammonia, H3N 22
Chloroform, CHCl3 5
Ether, (C2H5)2O 4
Benzene, C6H6 2

It is quite apparent that the good ionizing media have, as a matter of fact,
the highest constants; those which cause ionization, at most minimally (e.g.
benzene), the lowest.
Recent extended and exact investigations by Walden103 have succeeded in bringing the ionizing
power of solvents into definite quantitative relations to their dielectric constants, with the result that
order has been brought out of a condition of chaos that, for a number of years, existed in this field, as
the result of conclusions based on incomplete data. Conductivity being a function both of the

proportion of dissociated electrolyte and of the mobility of the ions in a given solution, Walden
determined, for a certain salt (an organic derivative of ammonium iodide, namely, tetraethyl
ammonium iodide N(C2H5)4I), for all solvents used, not only the conductivities for finite dilutions
but also, by extrapolation, the limiting values for infinite dilution. He was thus able to determine the
degree of ionization of the salt. Some of his results are particularly interesting; for instance, a poorly
conducting solution, such as that of the salt in glycol, a solvent resembling glycerine in general
character, may contain the dissolved electrolyte in a highly ionized state, while in a much better
conducting solution the degree of ionization may be much smaller—the low conductivity of the first
solution being the result of a very high friction and of the slow motion of the ions, while the well-
conducting solution might show a very high degree of mobility of the ions. The mobility changes
with the nature of the solvent, and the limit, Λ∞, of the equivalent conductivity of the salt, as found
by Walden, ranges from 8 in glycol, which is a thick, viscous oil like glycerine, to 200 in acetonitrile,
a thin mobile solvent. In the one solution, an observed conductivity of 4 represents 50% ionization of
the salt, in the other only 2%.
Now, for solutions of a given electrolyte—tetraethyl ammonium iodide was used—Walden104
found the following exceedingly interesting relation between the ionizations in, and the dielectric
constants of, various solvents:
e1 : ∛c1 = e2 : ∛c2 = a constant,

where e1 and e2 represent the dielectric constants of different solvents, and c1 and c2 represent the
concentrations of the salt in the solvents when the salt is ionized to the same degree105 in the two
solutions.
The bearing of the relation is apparent from the data in the following [p064] table.106 The upper
half of the table gives the dielectric constants (column two) of the solvents named in column one; the
concentrations which show identical degrees of ionization—47%—are given in the third column, and
the last column gives the value of the relation e : ∛c. The lower half of the table presents the same
kind of data, for the same salt, when its degree of ionization is 91%, in the different solutions
examined. It is clear that the numbers in the third column of each part represent approximately
constants.
All solutions, including aqueous solutions, are thus brought into one general relation.

Solvent. e c e : ∛c
Methyl alcohol 32.5 0.125 65
Ethyl alcohol 21.7 0.020 80
Acetyl bromide 16.2 0.010 75
Benzaldehyde 16.9 0.016 78
Acetonitril 35.8 0.100 77

Water 80 0.00910 383
Furfurol 39.4 0.00125 365
Nitromethane 40 0.00125 371
Acetonitril 36 0.00100 358

Methyl alcohol 32.5 0.00050 365

The Ionizing Power of Solvents Related to the Unsaturated Condition
of their Simple Molecules and to their Power of Association.
—A careful scrutiny of the group of highly-ionizing solvents (p. 62) brings
out another interesting relation, to which attention is called because it is a
chemical one, and which should always be considered in connection with
reactions in such solvents. It is well known that ammonia is an unsaturated
body, combining readily with all acids, and with many salts, such as copper
sulphate. The fact may be recalled, that this unsaturated condition is
ascribed to the unsaturated nitrogen atom in the molecule of ammonia, the
nitrogen showing a valence of only 3 in ammonia, whereas in the
derivatives it forms when it saturates itself with the compounds mentioned,
e.g. in H4NCl, it has five saturated valences. Assuming that a valence
consists in a unit charge, positive or negative, on the atom (pp. 42, 59), a
view which has almost become a certainty, we should decide that the two
free valences in ammonia must consist of a negative and a positive charge,
as expressed in H3N±. (We may imagine such a double [p065] charge to be
produced by the movement of one electron of the nitrogen atom to a
position in that atom which would make one point of the atom negative and
the other positive.) As a matter of fact, we find ammonia uniting with
hydrogen chloride, by absorbing a positive and a negative fragment of it—
producing H4NCl from H3N± + H+ + Cl−. It is also evident that, through
these charges, ammonia could combine with itself to form larger
complexes, +NH3-NH3−, in which we would still have two opposite
charges, presumably removed further from each other than in the simple
molecule. The new molecule could, in turn, by virtue of its charges,
combine with a further molecule to form a still larger or more associated
molecule, +NH3-NH3-NH3−, and such association could evidently go still
further. One can readily see that such molecules would be electrically
polarized, and their charges might easily have the power to cause107

electrolytic dissociation or ionization. The larger the associated molecule,
the further apart might be the positive and negative charges upon it: the
further apart the charges, the smaller would be their mutual attraction: and
the smaller the mutual attraction, the stronger, presumably, would the
dissociating power of such a molecule be. The dissociation may be effected,
possibly, by the action of these intensified charges upon charges already
existing108 within the molecule of the dissolved ionogen.
In liquid ammonia we might well have, for instance, the action +NH3-NH3− + HCl ⇄
+(NH -NH )H + Cl−, or +NH -NH − + H+Cl− ⇄ +(NH -NH )H + Cl−. Now, in liquid ammonia,
3 3 3 3 3 3
the salts NH4Cl, NH4NO3 [or, more probably, (NH3)xHCl, (NH3)x,HNO3] have the functions of the
aqueous acids109; that is, the hydrogen-ion of the acids is found combined with the solvent ammonia.
The ion +(NH3-NH3)H, and similar ions in liquid ammonia, would correspond then to what is
considered the hydrogen-ion in aqueous solutions110 (formed according to HCl ⇄ H+ + Cl−, as
ordinarily written), and the polarized charges on molecules like +NH3-NH3− appear thus as possible
active agents in this dissociation of the hydrogen chloride molecules. [p066]

Now, it is a significant fact that all the best ionizing solvents are
compounds whose simple molecules are unsaturated exactly like those of
ammonia; this is true for water H2O, the unsaturated character of whose
oxygen atom is now universally recognized. It is now a familiar fact that
liquid water is not represented by the formula H2O but consists of more
complex molecules (H2O)n. According to the most recent investigations,111
while steam is H2O, or monohydrol, ice is trihydrol (H2O)3, and liquid
water, at ordinary temperatures, a mixture consisting chiefly of dihydrol
(H2O)2, some trihydrol, and very little monohydrol. The proportion of the
last appears to increase with a rise of temperature; the proportion of
trihydrol seems to increase with a fall in temperature. One can easily see
how such aggregates would result from the saturation of the free charges on
oxygen, by further molecules of water. One can also see that such an
association of water molecules could leave a positive and a negative charge

on the associated molecules, which would be polarized and more effective
than the simple molecule would be.
That the molecule of hydrogen cyanide contains a similarly unsaturated
atom was demonstrated by Nef.112 He proved that the behavior of
hydrocyanic acid agrees with the structure expressed by the formula
HN═C═, which we may well write HN═C±. In sulphur dioxide, another
good ionizing solvent, we have, similarly, unsaturated sulphur, the sulphur
atom being here quadrivalent, whereas its maximum valence is six.
Now, the ionizing power of solvents like water, ammonia, etc., has been
ascribed, by various chemists, not only to their dielectric properties, but
also to the unsaturated condition of their molecules, and particularly to
their powers of association into large molecules. The relations developed
suggest that all three properties are most intimately related, the dielectric
properties and the powers of association being consequences, possibly, of
the fundamental condition of unsaturation, and of the great tendency toward
self-saturation,113 of the simple molecules of the best ionizing solvents.
From Walden's work it appears that the dielectric constant finally
determines the quantitative ionizing effect of a solvent.

Chapter IV Footnotes
[49] From the molecular weights of elements and compounds, the atomic weights of elements
may be determined, with the aid of analysis. (Cf. Smith, Inorganic Chemistry (1909), p. 196, or
General Chemistry for Colleges (1908), p. 130 (Stud.), or Remsen, Inorganic Chemistry,
Advanced Course (1904), pp. 71–80 (Stud.).)
[50] The weight of a small volume of a gas or vapor, at any definite temperature and pressure, is
determined. With the aid of Boyle's and Gay-Lussac's laws, this observed volume is then reduced
to standard conditions. Finally, the weight of 22.4 liters, under standard conditions, is obtained by
calculation.
[51] For the deduction of formulæ see Smith, Inorganic Chemistry, 196, 203; College Chemistry,
40; or Remsen, ibid., p. 79 (Stud.).
[52] Kopp, Liebig's Ann., 105, 390 (1858); Kékulé, ibid., 106, 143 (1858) (Stud.).
[53] Liebig's Ann., 123, 199 (1862) (Stud.).
[54] Wanklyn and Robison, Compt. rend., 52, 549 (1863) (Stud.).
[55] For instance in a test tube held in a horizontal position.
[56] By applying the corrections demanded by the kinetic theory (van der Waals's equation) to
gases even under ordinary pressures, Guye and D. Berthollet have obtained, with the aid of
Avogadro's hypothesis, values for the molecular weights of gases and for the atomic weights of
their components, which compare in accuracy with the best analytical work on solutions and
solids.
[57] The usual experimental methods consist in determining the elevation of the boiling-point, or
the lowering of the freezing-point, or the lowering of the vapor tension of a solvent by a solute,
methods which were discovered by Raoult and used empirically until van 't Hoff developed their
relations to the Avogadro principle. The calculation of a molecular weight is much simplified by
the use of the different specific constants expressing the lowering or elevation produced by one
gram-molecule or mole, dissolved either in one liter or in 100 grams of each specific solvent.
[58] See Arrhenius, Z. phys. Chem., 1, 631 (1887).
[59] Or, on the basis of the accepted molecular weights, abnormally high osmotic pressures,
abnormally great lowerings of the freezing-point, raisings of the boiling-point, etc., were
obtained. Van 't Hoff, originally, on account of these discrepancies, considered this extension of
the Avogadro Hypothesis to hold only for the "majority" of substances in solution, not for all

(Arrhenius, loc. cit.). It was considered to have universal application (for dilute solutions) only
after Arrhenius had explained the exceptions with the aid of his theory of electrolytic dissociation.
[60] That is, hydrogen chloride, in aqueous solution, depresses the vapor tension and the freezing-
point and elevates the boiling-point considerably more than an equimolecular quantity, for
instance, of glucose does, and gives a considerably higher osmotic pressure. The differences are
relatively greater, the more dilute the solutions used.
[61] A fourth interpretation advanced at one time in opposition to the theory of ionization is that
salts like sodium chloride and zinc chloride are hydrolyzed and thereby produce more solute
molecules, e.g. NaCl + H2O → NaOH + HCl. Aside from the fact that such hydrolysis of salts,
when it does occur (Chapter X.), is easily detected, and that it can be proved not to occur
appreciably in the case of sodium chloride (loc. cit.), this interpretation fails utterly to account for
the results obtained with acids, e.g. HCl, HNO3, H2SO4, and with bases, e.g. NaOH, Ba(OH)2,
which in aqueous solutions show an increase in the number of molecules as great as shown by
salts. This explanation is therefore untenable.
[62] Z. phys. Chem., 1, 631, (1887). Previous papers were published in the transactions of the
Royal Academy of Sweden (Stockholm). For a history of the theory see Ostwald, Z. phys. Chem.,
69, p. 1 (1909), and Arrhenius, The Willard Gibbs Address, J. Am. Chem. Soc., 1911 (Stud.).
[63] In the case of double salts, such as sodium-ammonium phosphate, and similar compounds,
the dissociation leads to the formation of more than two products. The molecules of two or more
different products may then be charged positively and, conversely, there may be two or more
different products of dissociation carrying negative charges. We have, for instance,
Na(NH4)HPO4 ⇄ Na+ + NH4+ + H+ + PO43− and Na(NH4)HPO4 ⇄ Na+ + NH4+ + HPO42−. In all
cases the rule concerning the sum of all the charges, as expressed in (2), must be fulfilled, the

charge on the phosphate ion, PO43−, being three times as great as that on a sodium, ammonium, or
hydrogen ion; that on the acid phosphate ion, HPO42−, being twice as great.

[64] Ion = the going or the migrating particle.
[65] See Washburn, J. Am. Chem. Soc., 31, 322 (1909), in regard to the values of x and y, the
quantities of water carried by certain ions.
[66] Vide J. J. Thomson, Electricity and Matter (1905) and Corpuscular Theory of Matter (1907)
(Stud.). Vide R. A. Millikan, Science, 32, 436 (1910), on the discrete or "granular" nature of
electricity (Stud.).
[67] See Millikan, loc. cit., as to the exact value of this "unit charge."
[68] Cf. McCoy, J. Am. Chem. Soc., 33, March, 1911, in regard to electropositive, composite (i.e.
nonelementary) "metals."
[69] The symbol ε is used to designate an electron. The loss of one electron by an atom leaves a
unit positive charge on the particle.
[70] In Chapter XV (q. v.) the affinity of the elements for electrons and the reactions, of the nature
of oxidation and reduction, depending on this affinity, are discussed in detail.
[71] J. J. Thomson, Corpuscular Theory of Matter, p. 120.
[72] A. A. Noyes (Carnegie Institution Publications, No. 63, p. 351 (1907)), believes that we may
have two kinds of molecules, HCl and H+Cl−, as well as the ions H+ and Cl−.
[73] Modern theory thus is reverting to the Berzelius theory of chemical affinity [Vide Meyer's
History of Chemistry (translated by M'Gowan) 1891, 220–265, or Ladenburg's History of
Chemistry (translated by Dobbin) 1900, 86, 88, etc.]
[74] To a saturated solution of cupric nitrate may be added a small amount of a saturated solution
of potassium permanganate, sufficient to give a decided purple color to the mixture. Potassium
chromate, as recommended by A. A. Noyes, may be used in place of the permanganate. (Cf.
Noyes and Blanchard, J. Am. Chem. Soc., 22, 726 (1900).)
[75] Exp.; cf. Eckstein, J. Am. Chem. Soc., 27, 759 (1905) (Stud.).
[76] W. A. Noyes, J. Am. Chem. Soc., 23, 460 (1901); Stieglitz, ibid., 23, 796 (1901); Walden, Z.
phys. Chem., 43, 385 (1903).
[77] Corpuscular Theory of Matter, p. 130 (1907).
[78] The experiment is an adaptation of a similar one described by A. A. Noyes and Blanchard, J.
Am. Chem. Soc., 22, 726 (1900).
[79] The copper electrodes are polarized by the formation of hydrogen on the cathode, but, in the
course of a few seconds, the current becomes rather constant and is then read. The polarization
may be considered as simply reducing the potential of the cell, and since, within the range of
concentrations of acid used,—4-molar to 1/8-molar—the polarization current does not vary

markedly, as compared with the potential of the storage cell, the total potential used through the
series of dilutions may be considered sufficiently constant for the purposes of the experiment.
Readings are made three or four seconds after each dilution, when the polarization has been fully
established. Polarization may be entirely avoided by the use of a silver nitrate solution and silver
electrodes or of a cupric salt solution and copper electrodes (Noyes and Blanchard). Hydrochloric
acid is used here in order to carry the discussion in the text as far as possible with this typical
ionogen. If one takes care to make readings as described, the result is quite satisfactory, as is
shown by the comparison of the ratios of the readings with the ratios calculated from the known
conductivities of the various dilutions (see table below).
[80] Current = (Potential Difference) / Resistance, or Current = (Potential Difference) ×
Conductivity. For a constant potential difference, then, Current ~ Conductivity.
[81] The specific conductivity of a solution (commonly designated by κ) is the conductivity of a
cube of 1 cm. edge; the molecular conductivity is the conductivity of a mole of the electrolyte; the
equivalent conductivity (designated by Λ) is the conductivity of a gram-equivalent of the
electrolyte. Λ = κ × v, where v is the volume, expressed in cubic centimeters, containing the gram-
equivalent. For instance, the resistance of 0.1 molar hydrochloric acid in a cube of 1 cm. edge is
28.5 ohms and its conductivity (κ) therefore 1 / 28.5 or 0.0351 reciprocal ohms. Since 10 liters or
10,000 c.c. of 0.1-molar hydrochloric acid is the volume (v) containing one mole of the acid (the
molar and the equivalent conductivities, for a monobasic acid being the same) Λ = 0.0351 ×
10,000, or 351.
[82] Kohlrausch and Holborn, p. 200.
[83] Cf. Kahlenberg, Transactions of the Faraday Society, 1, 42 (1905).
[84] Clausius, Poggendorf's Ann., 101, 347 (1857) (Stud.). His theory replaced the older one of
Grotthuss.
[85] Phil. Mag., 5, 729 (1903), and Transactions of the Faraday Society, 1, 55, (1905).
[86] Vide, Hudson, J. Am. Chem. Soc., 31, 1136 (1909), for a recent summary of results.
[87] Lectures on Physical Chemistry, 1, p. 131.
[88] Vide A. A. Noyes and Blanchard, J. Am. Chem. Soc., 22, 726 (1900).
[89] The concentrations are figurative, but may be taken to represent actual concentrations, such
as 0.015 molar, etc.
[90] Kohlrausch and Holborn, loc. cit., p. 200.
[91] Raoult, Ann. de Chim. et de Phys. (6), 2, 84 (1884).
[92] The degree of ionization of mercuric chloride is based on Raoult's freezing-point
measurements and is subject to revision, and the limit of the mobility of the mercuric-ion (½ Hg)

is assumed to be 48, close to the values found for the ions of zinc and cadmium, elements in the
same family as mercury.
[93] Lehfeldt's Electrochemistry, 1904, p. 3.
[94] See table, p. 56.
[95] Report of the British Association for the Advancement of Science, 1886, p. 389.
[96] With the aid of more elaborate apparatus rigorous demonstrations and measurements of such
diffusion currents of so-called "concentration cells" are made.
[97] Z. phys. Chem., 63, 174 (1908). The work was carried out in Abegg's laboratory.
[98] Report of the St. Louis Congress of Arts and Sciences, IV, 314 (1904).
[99] Am. Chem. J., 20, 21, 23 (1898–1900).
[100] Kablukoff, Z. phys. Chem., 4, 429 (1889).
[101] Phil. Mag. (5), 36, 320 (1893).
[102] Z. phys. Chem., 13, 531 (1893).
[103] Walden, Z. phys. Chem., 54, 129 (1906); McCoy, J. Am. Chem. Soc., 30, 1074 (1908).
[104] Z. phys. Chem., 54, 229 (1906).
[105] The degrees of ionization were always determined from the relation α = Λv / Λ∞ according
to the method discussed on page 50.
[106] Walden, loc. cit.
[107] Cf. Arrhenius, Theories of Chemistry, p. 83 (1907).
[108] In hydrogen chloride, the hydrogen and the chlorine atoms may be held in the molecules
H+Cl− by the electric attraction of a positive charge on the hydrogen, and a negative charge on the
chlorine atom (see p. 43).
[109] Franklin and Kraus, Am. Chem. J., 23, 305 (1900) (Stud.)
[110] It is very likely that in aqueous acids, a large proportion, at least, of the hydrogen-ion is
similarly combined with water. (Lapworth, J. Chem. Soc., (London) 93, 2187 (1908). See Chapter
XII.)
[111] Vide the discussion on the "Constitution of Water," and the summary by J. Walker,
Transactions of the Faraday Society, VI, 71–123 (1910).
[112] Proc. Am. Acad., 1892; Liebig's Ann. 287, 263 (1895).
[113] Cf. Walden, Z. phys. Chem., 55, 683 (1906).

CHAPTER V
THE THEORY OF IONIZATION. II
Ionization and Osmotic Pressure. Ionization and Chemical
Activity

[p067] TOC

We will turn now to the consideration of evidence bearing on the theory
of ionization, found in the data on osmotic pressure. The apparent
molecular weight of hydrogen chloride is found to be smaller than 36.5,
when determined in aqueous solution (p. 37), and it is found to approach the
limit 18.25 as a more and more dilute acid is used.114 The value found
represents the average molecular weight of all the molecules in any
solution, the osmotic pressure, freezing-point or boiling-point of which has
been taken. It is evident that, if there is dissociation of hydrogen chloride
into hydrogen and chloride ions, the average values found for the molecular
weight must be lower than 36.5, must be variable, and must approach the
limit 18.25, as the dissociation into the smaller molecules becomes more
and more complete. Such a result is, therefore, what we would anticipate on
the basis of the theory of ionization. For a salt like potassium chloride KCl,
a similar tendency toward a minimum, average molecular weight of
(K+ + Cl−) / 2 or (39.1 + 35.5) / 2 = 37.3 would be anticipated, and, as a
matter of fact, molecular weight determinations with potassium chloride in
aqueous solution give results agreeing with such a tendency.115 For a salt
like calcium chloride, on the other hand, we would expect that its ionization
into three ions, according to the equation CaCl2 ⇄ Ca2+ + 2 Cl−, would give
a minimum, not of one-half the formula weight, but of one-third, viz.,
(Ca2+ + 2 Cl−) / 3 or (40 + 71) / 3 = 37, when the molecular weight
determination is carried out in aqueous solution. As a matter of fact, with

salts of this type, the determinations, by osmotic pressure methods, indicate
a dissociation into three smaller components, as required by the theory. It
may be added that, for [p068] a salt, sodium mellitate, Na6(C12O12), the salt
of a hexabasic acid, Taylor found average molecular weights tending to a
minimum of one-seventh of the formula weight, as we should expect from
the ionization of the salt into seven smaller molecules, (C12O12)Na6 ⇄
6 Na+ + (C12O12)6−.
Quantitative Evidence.
—Some of the most exact quantitative evidence bearing on these relations,
such as the results of investigations, by Griffith and by Taylor, on the
freezing-point depressions of solutions of electrolytes, may be briefly
considered. The depression of the freezing-point of a given solvent by a
solute is proportional to the concentration of the solute or proportional to its
osmotic pressure. Further, according to the Van 't Hoff Hypothesis (p. 15),
the osmotic pressure at a constant temperature is dependent only on the
number of molecules present in unit volume, and not on the nature or
composition of the molecules: the freezing-point of the solvent is depressed,
likewise, proportionally to the total concentration of the solute, irrespective
of the fact whether the solution contains only one, or more than one
molecular species. The ratio, observed depression / concentration,116 or Δ /
C, should be constant,117 therefore, in a given solvent, for dilute solutions
of all kinds of solutes, simple or mixed. Griffith118 found, for a solution of
cane sugar, a non-electrolyte, in water, the ratio of the freezing-point
depression to the concentration to be 1.858°. For instance, the freezing-
point of a 0.01 molar solution of cane sugar (3.42 grams of cane sugar per
liter; C12H22O11 = 342) is found to be −0.01858°, and 0.01858 / 0.01 =
1.858. This ratio should be the same, as stated above, according to van 't
Hoff's theory of solutions, for dilute aqueous solutions of all solutes. But
the ratio Δ / C for an aqueous solution of potassium chloride, an electrolyte,
was found to increase slowly and continuously until in 0.0003 molar

solution the ratio 3.72 was found, which is exactly twice the value obtained
with cane sugar. The result indicates, therefore, a gradual dissociation of
the potassium chloride with increasing dilution, and a dissociation,
ultimately, of each molecule of the salt into two new molecules, in all
respects exactly as demanded by the theory of Arrhenius.
Loomis119 found in a similar way a ratio of 3.61 for HCl, 3.71 [p069] for
KOH, 3.60 for KCl, 3.67 for NaCl, 3.73 for HNO3, etc., when 0.01 molar
aqueous solutions were used. For similar solutions of calcium chloride
CaCl2, magnesium chloride MgCl2, and sodium sulphate Na2SO4, the value
5.07 was found as the ratio between the depressions of the freezing-point
and the concentration of the salts in extremely dilute solutions—a result
showing, plainly, a dissociation of each salt into three smaller molecules.
The limit 5.67 for such a dissociation is not quite reached in these cases,
because salts of the types Me″X2 and Me2′Y″ ionize less readily than do the
electrolytes Me′X′, a fact also shown by their conductivities.
We thus find that the most exact work on molecular weight
determinations in dilute aqueous solutions agrees excellently, as does the
conductivity of such solutions, with the demands of the theory of ionization,
a fact which is particularly impressive because osmotic pressure and
electrical conductivity are in no wise fundamentally related phenomena,
and yet each, as a measure of ionization or electrolytic dissociation, leads
independently to the same conclusion.120
The Chemical Composition of the Ions of Electrolytes.
—Accepting the theory of Arrhenius, we may now inquire more closely
than heretofore, first, what compounds are subject to electrolytic
dissociation, and then, what the chemical composition of their ions is and
how it is determined.
The compounds which are dissociated into ions, by solvents which cause
ionization (p. 62), comprise the salts, the acids and the bases; chemists are,
in fact, more inclined now to invert the statement and say that those

substances which have long been known as salts, acids and bases, owe the
essential characteristics, which led to their classification, to the fact that
they are ionizable (see pp. 72–82). The composition of the ions, formed
from the simpler of these compounds,121 may be expressed by saying that
the metal component or metal-like component (hydrogen, ammonium)
forms the positive ion (cation, metal ion) and all the rest of the [p070]
molecule forms the negative ion (anion, acid ion122). Thus, sodium
chloride, nitrate, sulphate, phosphate yield the sodium-ion, Na+, and the
chloride (Cl−), nitrate (NO3−), sulphate (SO42−), or phosphate (PO43−) ions;
cupric nitrate Cu(NO3)2 dissociates into the cupric ion (Cu2+) and the
nitrate ion, calcium sulphate CaSO4 into the calcium-ion (Ca2+) and the
sulphate-ion, aluminium sulphate Al2(SO4)3 into the aluminium-ion (Al3+)
and the sulphate-ion.
But the question arises, as to how we know that the salts mentioned
produce ions of the given composition; why, for instance, should sodium
nitrate be considered to dissociate into sodium, Na+, and nitrate ions, NO3−,
the nitrogen atom carrying all of the oxygen atoms with it in the negative
ion?
The composition of the ions of a salt can be determined
experimentally123 by devices of which the U-tube experiment (p. 45) may
be considered to be a simple type. For instance, if we wish to determine the
composition of the ions of sodium nitrate, we could cover a solution of
sodium nitrate with a solution, say, of hydrochloric acid, pass a current
through the liquids, and determine the composition of the components that
have moved to the negative and positive poles, respectively. In practice, the
device could be elaborated for the sake of convenience. Stopcocks, for
instance, might be placed in the U-tube, at the points of separation of the
nitrate solution and the hydrochloric acid (see Fig. 13), the stopcocks being
opened only during the passage of the current. Or porous plates or cells
might be used, in place of stopcocks, at these [p071] points. Now, if we

assume sodium nitrate to be dissociated, not into
Na+ and NO3−, but let us say into positive ions
NaO+ and negative ions NO2−, the changes which
would result from the passage of a current would
be as follows: starting with the action at the
positive pole, we should find chloride ions
discharged and chlorine evolved at the pole (the
evolution of chlorine could be avoided, if
considered desirable, by the use of a silver anode,
which would absorb the liberated chloride-ion to
form insoluble silver chloride on the electrode). At
the same time, hydrogen ions would move out of
the space P, being repelled by the positive pole,
and attracted by the negative. At the boundary
Fig. 13.
between the sodium nitrate solution and the
hydrochloric acid, the negative ions of sodium nitrate, which we are
supposing to have the composition NO2−, would move up from B toward
the positive pole (cf. exp., p. 45), being attracted by its charge; at any
moment we should have in any part of P as many negative ions (Cl− and
NO2−), as there are hydrogen ions, the solution showing no excess of free
electricity at any point. Now, if NO2− were the ion that moved up into the
space P, then we should presently find nitrous acid around the positive pole
in space P, H+ and NO2− combining to form nitrous acid, HNO2. But, as a
matter of experiment, although the tests for nitrous acid belong to the most
sensitive ones in chemistry, no trace of this acid is found there; what we do
find is nitric acid, HNO3, resulting obviously from the presence in space P
of both hydrogen ions and nitrate ions, NO3−, which have moved up from
space B. It is clear, that the presence of nitric acid in the region around the
positive pole means that the nitrogen atoms must have carried with them all
three of the oxygen atoms of the nitrate—in a word, that the composition of

the negative ion of sodium nitrate is NO3− and not, say, NO2−. Similarly,
considering what happens in space N, round the negative pole, we have here
an evolution of hydrogen, a migration of some chloride ions out of N into
the space C, and, at the same time, a migration of the positive ions of space
C into the division N. On examining the solution in N, we now find sodium
chloride, with unchanged hydrochloric acid, exactly what we should expect
from the migration of the ion Na+ toward the negative electrode.124 If the
positive ion were, say, [p072] NaO+, we should expect to obtain either some
of the hypochlorite NaOCl (NaO+ + Cl−), or, at least, an evolution of
oxygen in this place, since sodium chloride is formed. As a matter of
experiment, no oxygen is evolved here, and no trace of hypochlorite is
found in N round the negative pole, although the tests for hypochlorites are
extremely sensitive.
Comparatively simple methods, in principle of the nature outlined, enable
us, then, to determine experimentally the composition of the ions into which
ionizable compounds, salts, acids and bases, dissociate. Whenever any
doubt may exist about the composition of the ions of a given electrolyte,
this device may be employed to settle the matter, and there will presently be
occasion to employ the U-tube for such a purpose.
Ionization and Chemical Activity.
—The fact that the theory of ionization gives us adequate explanations of
the conductivity shown by dissolved electrolytes and of their abnormally
high osmotic pressures, would have been in itself of interest to chemists;
but, if its applications were limited to these phenomena, we should not be
considering it in connection with qualitative chemical analysis, nor would
the theory, presumably, have greatly affected the development of chemistry,
as it has done. It is the fact that the electrolytic dissociation of an electrolyte
into its ions involves chemical changes of the most profound nature, and
most intimately affects chemical reactivity, that has made it play, in the last
two decades, such a leading rôle in the development of chemistry, and that

makes it necessary to include its consequences in the consideration of
analytical problems, if one would understand, as far as present knowledge
permits, the reactions involved in chemical analysis.
Hydrogen chloride, as a perfectly dry gas, is a non-conductor of
electricity and, at the same time, it is found to be chemically inactive—it
does not combine, for instance, with dry ammonia125 or act upon dry
calcium carbonate126 or on dry litmus. Hydrogen chloride, subjected to
great pressure at a low temperature, is liquefied. The liquid is also a very
poor conductor of [p073] electricity127 and does not show the chemical
activity of ordinary, aqueous hydrochloric acid; it does not combine with
calcium oxide or attack marble, zinc, iron or even magnesium.127
A solution of hydrogen chloride in a poorly ionizing medium, like
benzene or toluene, is an extremely poor conductor. There is an extremely
small conductivity indicating only a trace of ionization.128
Exp. A solution of hydrogen chloride, prepared by passing the dried gas into benzene or toluene
(thiophene-free benzene will not become discolored), and kept anhydrous by means of fused calcium
chloride, is tested for its conductivity, by dipping into it electrodes connected with a lighting circuit
and a galvanometer.

Such a solution behaves chemically, also, quite differently from the
aqueous solutions of hydrogen chloride with which we are familiar: dry
steel nails,129 dropped into it, will remain almost unchanged—there is no
marked evolution of hydrogen (exp.). Perfectly dried marble, added to it,
will not give rise to the evolution of carbon dioxide129 (exp.). We find thus,
in all the cases discussed—the nonconducting dry gas, the anhydrous
liquefied hydrogen chloride and the anhydrous benzene solution—an
absence of ionization,130 as indicated by the lack of conductivity, and, along
with this, a lack of the familiar action of hydrochloric acid as an acid. If we
dissolve the gas in water, we obtain a well-conducting solution (exp.), in
which, according to molecular weight determinations, the [p074] hydrogen
chloride is more or less largely ionized, and this same solution has all the

well-known chemical properties of hydrochloric acid—it evolves hydrogen
liberally when given an opportunity to act upon zinc or iron (exp.), it
evolves carbon dioxide copiously when marble is brought into contact with
it (exp.). In such an aqueous solution we have both the ions of the acid and
the more or less non-ionized hydrogen chloride, the action (HCl ⇄ H+ +
Cl−) being reversible.
Now, since in those cases in which we have admittedly only non-ionized
hydrogen chloride, there is no vigorous chemical action, we are bound to
conclude that, in the aqueous solution where we have both the non-ionized
and the ionized substance, it must be the new components, the ions of the
acid, which give this solution its new qualities, the well-known properties
of a pronounced acid.131 This conclusion, that the acid properties of
hydrogen chloride in aqueous solution are due to the ionized hydrogen
chloride, rather than to the hydrogen chloride itself, is one of fundamental
importance.
Dry Salts and their Aqueous Solutions.
—If the study of the relation of ionization to chemical activity be extended,
it is found that a dry salt, such as, for example, silver nitrate, in crystals or
finely pulverized, is not perceptibly ionized, for it is a non-conductor (exp.).
The same result is obtained with potassium chromate. If the dry powders
are intimately mixed, there is no chemical action between them, no
perceptible change occurs. The aqueous solutions of the salts are excellent
conductors (exp.), as are the aqueous solutions of almost all salts; the
dissolved salts are therefore largely ionized. As soon as the ionizing
medium, water, is added to the dry, yellow mixture of silver nitrate and
potassium chromate, instantly a chemical change results—red silver
chromate, Ag2CrO4, is precipitated (exp.). Now, in the aqueous solution of
these salts we have both non-ionized molecules and their ions:
AgNO3 ⇄ Ag+ + NO3−,
K2CrO4 ⇄ 2 K+ + CrO42−.

Since there is no interaction when the dry salts, containing only the non-
ionized substances, are mixed, and since there is interaction [p075] when the
solutions are mixed, in which both the non-ionized and the ionized salts are
present, one must conclude again that the formation of silver chromate is
the result of the action of the silver ions on the chromate ions in the
solution. In point of fact, there could hardly fail to be an action, since the
positive silver ions and the negative chromate ions, moving in all directions
through the solution, must collide and be discharged, or combine, to form
molecular silver chromate. This salt happens to be very difficultly soluble,
and to be colored red, as well, so that silver chromate is precipitated and is
immediately recognizable.
The two dry powders in the experiment were allowed to be in contact for
only a few moments. It is important to note, therefore, that dry sodium acid
carbonate and dry potassium acid tartrate are also nonconductors (exp.), and
that the intimate mixture of these two powders is kept for years in the well-
known form of baking powders without appreciable decomposition—yet
best in tin vessels, to exclude moisture. The aqueous solutions, however, are
good conductors (exp.), and, when dissolved, these salts are more or less
ionized. The addition of water to the mixed salts (exp.) leads at once to the
well-known action, carbon dioxide being liberated and sodium-potassium
tartrate or Rochelle salt being formed.
Behavior of Fused Salts.
—It may be objected that there are common cases, where dry salts are
known to act upon each other; barium sulphate is fused with sodium
carbonate to convert the former into the carbonate, BaSO4 + Na2CO3 ⇄
Na2SO4 + BaCO3. Before one decides that this must be an instance of the
action of non-ionized salts on each other, the conductivity of dry salts under
the conditions of the experiment, namely at an elevated temperature, must
be examined. There is no difficulty in recognizing that while dry sodium
carbonate or potassium nitrate at ordinary temperatures does not conduct a

current, and is not perceptibly ionized, each salt, when fused, becomes an
excellent conductor (exp.,132 with potassium nitrate). It is, in fact, well
known that, in many electrolytic operations, fused salts133 are used in place
[p076] of solutions. It must be added that the heat, not the change of state,

causes the ionization, careful work having shown that conductivity begins
to be appreciable below the point of fusion.
Exp. Two platinum wires, fused, one inch apart, into a glass rod, are connected with a sensitive
galvanometer and the lighting circuit. When the glass is warmed, a current is found to pass.

The action between barium sulphate and sodium carbonate at a high
temperature does not mean, then, that the non-ionized salts interact; on the
contrary, we find that, under such conditions, coincident with the evidence
of reactivity, we have also decided conductivity—again indicating decided
ionization.
Dry Salts at Ordinary Temperatures.
—Inasmuch as ordinary temperatures are still far removed from the absolute zero, one must suppose
that dry salts must be ionized, minimally at least, even at room temperature, and should therefore
react with each other. Presumably they do, only so slowly, as a result of the minimal degrees of
ionization, and of the few chances of collision between ions of opposite charges, owing to the
restricted range of the molecular motions, that the total change is imperceptible. Critical work on the
question is most desirable. In this connection it maybe said that Spring134 found that dry salts do
interact at ordinary temperature, when subjected to great pressures, provided the volume of the
products is smaller than the volume of the initial substances. Whether this action is due to the
ionization of the salts, minimal as it is, or whether we have here a case of interaction of non-ionized
molecules, has not, it seems, been determined; it would require difficult quantitative work to settle
the question.
Influence of Light and Heat.
—It is apparent that heat, a form of energy, contributes to the dissociation of ionogens, and it is
natural that we should consider other forms of energy, e.g. light, to have the same power. One may
speculate about the possibility of light inducing chemical action (e.g. in starting the combination of
hydrogen and chlorine, or in photography) by its ionizing power, and about the possibility that rapid
combination of oxygen and hydrogen follows the application of a flame to the mixture, as the result
of increased ionization of the components at the elevated temperature of the flame and of the burning
gases. The experimental evidence shows that, in some actions of this nature, ionization is an
important factor, while in other instances it appears to be negligible.135 [p077]

Conclusions.

—It appears that we must accept the conclusion, that the reactions of salts,
acids and bases (ionogens) in aqueous solution (the so-called "salt
reactions") are the reactions of the ions and not of the non-ionized
molecules. This conclusion is of the greatest and most practical importance
in our science. It is the natural inference from the results of the qualitative
experiments described in the three preceding sections. Its final adoption,
however, is based on the existence of a great mass of quantitative evidence,
and to the consideration of some of this we now turn.
Quantitative Relations.
—If the active components in aqueous solutions of acids, bases and salts are
the ions, rather than the undissociated compounds, then quantitative data
supporting such a conclusion should be found. Such quantitative
confirmation, from the point of view of chemical activity, is not lacking.
Only a small part of the data can be considered here.
Conductivity measurements, and the lowering of freezing-points and the
elevation of boiling-points, show that there are very decided differences in
the degrees of ionization of different acids and bases in solutions of
equivalent concentration. For instance, potassium hydroxide is somewhat
more ionized than is barium hydroxide, and decidedly more so than
ammonium hydroxide, a fact that can readily be demonstrated by the
conductivities of the solutions136:
Exp. Equivalent solutions (1 / 10 normal) of the three bases are introduced into three vertical
tubes, containing electrodes connected, in parallel, with a lighting circuit and with small electric
lamps. When the two electrodes in each of the three tubes are at equal distances from each other, the
lamp connected with the potassium hydroxide solution glows most brightly, that connected with the
barium hydroxide solution a little less brightly, and the lamp connected with the ammonium
hydroxide solution does not glow at all—not enough current is carried through the ammonium
hydroxide solution to heat the filament in the corresponding lamp sufficiently to make it red. Now,
the current, for a given fall of potential, is proportional to the conductivity of a solution (p. 48) and,
in the equivalent solutions137 the conductivity depends on the proportion of charged particles (the
degree of ionization) of the base. It is clear then, that ammonium hydroxide is very much less ionized
than are the two other bases. [p078]

The resistance in a tube may be reduced, and the conductivity increased, by reducing the distance
through which the current must be carried, i.e. by bringing the electrodes closer together. In the
solution of barium hydroxide, we find that we must reduce the distance between the electrodes to
about five-sixths the corresponding distance in the potassium hydroxide solution before we obtain,
approximately, as bright a lamp from the current passing through it, and in the case of ammonium
hydroxide, we must bring the electrodes so close together that they almost touch, the distance being
only one or two hundredths of the distance between the electrodes in the potassium hydroxide
solution.
For the degrees of ionization of the three bases we have, approximately, the relation αK : αBa :
αNH :: dK : dBa : dNH , if we indicate by dK, dBa, dNH the distances between the electrodes in the
4 4 4
three solutions when the lamps are of uniform brightness, i.e. when the same quantity of current
passes through each solution. In this deduction, the conductivities of the bases at infinite dilution
(Λ∞) are taken to be the same, which is roughly true.

The experiment gives us a rough measure of the relative conductivities
and the relative degrees of ionization of the three bases. It shows that
potassium hydroxide is somewhat more ionized than is barium hydroxide,
in equivalent solution, and decidedly more than is ammonium hydroxide.
Limiting the further discussion, at this moment, to potassium hydroxide
and ammonium hydroxide, we should find that, since in equimolar
solutions, a larger portion of the former is ionized than of the latter, the
potassium hydroxide solution must contain the larger proportion or
concentration of hydroxide-ion, HO−, which is the characteristic ion of
bases. It should, therefore, show the chemical characteristics of a base
much more decidedly than the ammonium hydroxide solution. That such is
the case can be very simply shown by adding equal quantities (0.1 c.c.) of
the 0.1 molar solutions to equal volumes (50 c.c.) of water138 containing
some phenolphthaleïn. This is an indicator for bases and acids, like litmus,
but it is less sensitive to hydroxide-ion than is litmus. We find that the
potassium hydroxide causes a very decided change, producing a deep red
color with the phenolphthaleïn, whereas the ammonium hydroxide only
produces a pink hue.139 [p079]
In all the chemical changes produced by these alkalies, the same
difference in intensity of action is shown, that is here exhibited towards

indicators. If, for example, we measure the rate of change in an action,
which is slow enough to be measured [p080] and which proceeds
quantitatively in proportion to the concentration of hydroxide-ion, we find
that the measured rates of change indicate the same ratio in the
concentrations of hydroxide-ion in potassium and ammonium hydroxide
solutions, as is indicated by quantitative conductivity measurements. An
action suitable for the purpose is the saponification of an ester, such as ethyl
acetate. Under the influence of an alkali, like potassium hydroxide, ethyl
acetate is decomposed, more or less rapidly, into an acetate and alcohol: we
have, for instance,
CH3CO2C2H5 + KOH → CH3CO2K + C2H5OH.

The rate of saponification is found to be proportional to the concentration
of hydroxide-ion, and not to the total concentration of the base, and the
action may be formulated more accurately as follows:
CH3CO2C2H5 + K+ + HO− → CH3CO2− + K+ + C2H5OH
or CH3CO2C2H5 + HO− → CH3CO2− + C2H5OH.
For ammonium hydroxide we have similarly,
CH3CO2C2H5 + NH4+ + HO− → CH3CO2− + NH4+ + C2H5OH.

Now, Arrhenius140 proved that the rate of saponification of ethyl acetate by
ammonium hydroxide, which is very much slower than the rate of
saponification by potassium hydroxide of equivalent concentration, does
agree quantitatively, indeed, with the rate demanded by the theory of
ionization, when the hydroxide-ion is considered the active component of
the bases, to which the saponification is due.
Exp. A rough idea of the difference in the chemical actions of the two bases may be obtained by
observing their effects on the ester, methyl acetate, which is decomposed into an acetate and methyl
alcohol rather rapidly. To 50 c.c. of (CO2 free) water containing some phenolphthaleïn, 10 c.c. of 0.1
molar potassium hydroxide is added; a similar mixture with 10 c.c. of 0.1 molar ammonium
hydroxide solution is prepared. To each of the solutions, 2 c.c. (an excess) of methyl acetate is added

(to the ammonium hydroxide solution first), and the mixtures are shaken for a moment. At room
temperature, the mixture containing potassium hydroxide will become pale pink in a few minutes,
and colorless soon thereafter, while the mixture [p081] containing ammonium hydroxide will still be
deep red at the end of 45 minutes.141
In the following tables are summarized some of the results which have been obtained in comparing
the activity of bases, in saponifying methyl acetate, and the concentrations of the hydroxide-ion, in
the solutions of the bases, as determined by conductivity measurements. The comparisons are made
by representing the activity of the hydroxide-ion in a solution of lithium hydroxide by 100 and by
expressing the ratio of the activity of a given base to that of the lithium hydroxide in percentages of
the activity of the latter. All the bases were used in 0.025 molar concentration, and their degrees of
ionization are given in the last column of the table.

Chemical Activity of Bases and Their IonizationA
Relative
Base. Activity. Concentration
of HO−.
Lithium hydroxide 100 97
Potassium hydroxide 98 97
Sodium hydroxide 98 97
Ammonium hydroxide 2 2.5
Ethyl ammonium hydroxide 12 16.

[A] Whetham, Theory of Solutions, p. 338 (1902). (Cf. Walker, Introduction to Physical
Chemistry, p. 277 (1899).)

An ester is decomposed also under the influence of acids, in aqueous solution, into an organic acid
and an alcohol, and cane sugar is similarly decomposed into glucose and fructose (grape sugar and
fruit sugar): C12H22O11 + H2O → C6H12O6 + C6H12O6. Both actions are found to be caused by
the influence of the hydrogen ions of the acids used and to proceed, at a given temperature, with a
velocity proportional to the concentration of the hydrogen ions. Now, in 0.1 molar solution, acetic
acid is very little ionized (1.3%), as compared with hydrochloric acid (91%), the degrees of
ionization being determined by conductivity measurements (p. 50); the relation may easily be
demonstrated with the aid of the conductivity apparatus used to show the difference in ionization
between potassium hydroxide and ammonium hydroxide. In the presence of 0.1 molar hydrochloric
acid, the decomposition of cane sugar actually proceeds at 79 times the rate that it does in the
presence of 0.1 molar acetic acid. The ratio of the concentrations of the hydrogen-ion in the two [p082]
solutions is, in fact, 70 : 1. There is, therefore, close agreement142 between the relative chemical
activity of the two acids and the relation demanded, if we assume, on the basis of the theory of
ionization (p. 77), that the chemically active components of the acids are their ions and particularly
their hydrogen ions.
In the following table, the relative activities of acids, in accelerating the decomposition of methyl
acetate by water, are contrasted, in a similar fashion, with their relative conductivities. The

conductivities of acids depend to such an extent on the concentration of hydrogen-ion, which moves
five times, or more, faster than the anions and carries therefore the greater part of the current, that the
conductivities of acids, in equivalent concentrations, may be considered an approximate measure of
their relative degrees of ionization and of the concentrations of hydrogen-ion. For the purpose of
comparison the activity and the conductivity of molar hydrochloric acid are both represented by 100.
All the acids were used in normal solutions.

Chemical Activity of Acids and Their Ionization.A
Acid. Activity. Conductivity.
Hydrochloric acid 100 100
Nitric acid 92 100
Sulphuric acid 74 65
Acetic acid 0.3 0.4
Formic acid 1.3 1.7
Chloracetic acid 4.3 4.9
Tartaric acid 2.3 2.3

[A] Whetham, Theory of Solutions, p. 338.

In the following chapters and, indeed, throughout our further work, we
shall continually meet additional instances of the quantitative relation
between chemical activity and ionization. In fact, the results obtained in the
field of quantitative measurement of chemical action, of which the above
are single instances, have demonstrated, more than anything else, the value
of the theory of ionization to chemistry and the necessity of taking it into
account in expressing the results of chemical action in mathematical terms.
[p083]
Summary.
—Measurements made, then, in three great and independent fields of
investigation, electrical conductivity, osmotic pressure and the allied
relations, and chemical activity, bring independent testimony to the
correctness of the fundamental assumptions of Arrhenius's theory of
ionization. In the quantitative study of solutions of electrolytes, wherever
secondary disturbing influences are eliminated or are taken into account as
far as possible, the three lines of investigation give results which agree
satisfactorily143 as to the degree of ionization of the electrolytes under
examination. With the aid of this theory, predictions of the course of
chemical action may now be made more definitely and with more assurance
than ever before in the history of chemistry.
Chemical Activity of Non-ionized Molecules.
—The conclusion reached, on the basis both of qualitative and, particularly,
of quantitative evidence, that the reactions of salts, acids and bases
(ionogens) in aqueous solutions (the so-called salt reactions) are the actions
of the ions and not of the non-ionized molecules, does not necessarily mean
that the non-ionized molecules are altogether inactive chemically. Some
chemists believe that ions have only the advantage of an enormously
greater degree of reactivity.144 If the atoms in a molecule carry electric

charges even prior to their separation (ionization), as expressed for instance
by the formula H+Cl− for hydrogen chloride (p. 43), it can be readily seen
that an action145 resulting from the collision of a molecule of hydrogen
chloride with a molecule of potassium hydroxide H+Cl− + HO−K+ ⇄ K+Cl−
+ HO−H+ would, in some respects, resemble the ionic action H+ + Cl− + K+
+ HO− ⇄ K+ + Cl− + HOH. The latter would probably have the advantage of
a considerably smaller resistance to the action, and consequently of a far
greater speed. But the question of supreme importance and interest to
chemistry is the question as to which actions are found experimentally to be
of moment in any given case. Now, a great mass of corroborative evidence
shows that for the interactions of ionogens in aqueous solutions the ionic
actions, probably on account of their enormous speeds, are the important
ones. [p084]
On the other hand, there are large numbers of compounds, especially
among organic substances, which do not appear to ionize to a measurable
extent and whose actions, in large part at least, appear to be the actions of
non-ionized molecules. It is characteristic that most of these actions take
place at slow, very frequently easily measurable, rates of speed. Critical
study shows that even for such actions ionization often plays a very
important rôle, at least in some of their stages, and throughout the field of
organic chemistry the intimate relations between electrical phenomena and
chemical activity can be readily recognized.146 But these relations are not
obvious ones and do not, as yet, play a dominant rôle. It is because
analytical chemistry deals predominantly with the reactions of ionogens,
that the study of the reactions of ions will demand our extended attention.
Reactions in Non-aqueous Solutions.
—Kahlenberg147 has made some interesting and important, although not conclusive, contributions to
the problem of chemical activity of ionogens in non-aqueous solutions. He has found, for instance,
that zinc, left in contact with a benzene solution of hydrogen chloride carefully freed from moisture,
displaces hydrogen.148 Cadmium, aluminium and magnesium, on the other hand, do not evolve
hydrogen in such a solution.149 The solution shows an enormous resistance to the passage of an

electric current, and the conclusion is drawn by Kahlenberg that the liberation of hydrogen is due to
the action of non-ionized hydrogen chloride on the zinc.
It is evident,150 from Walden's equation showing the relation between the ionizing power and the
dielectric constant of a solvent (p. 63), that the presumption is that hydrogen chloride in benzene
solution is not absolutely non-ionized, but rather that it is ionized in traces.151 No exact
measurements of the [p085] degrees of ionization of hydrogen chloride in benzene solution have been
made; that the solution shows an enormous resistance to the passage of the electric current and can
be, at best, very little ionized, is all that has been established. In default of exact data, the
semiquantitative determination by Kablukoff, showing that a 0.25 molar solution of hydrogen
chloride in benzene has a resistance of 120 × 106 ohms, is of interest. From the meager data
concerning the dimensions of the electrodes used, one may calculate (with the aid of a not
unreasonable assumption as to the limiting value of the conductivity, at infinite solution) that the
degree of ionization of the acid in the solution is perhaps of the order 5E−9, and the concentration of
hydrogen-ion,152 consequently, roughly 10−9. Now, the evolution of hydrogen by means of zinc, in
aqueous solutions, takes place according to the equation Zn ↓, + 2 H+ ⇄ Zn2+ + H2 ↑, and depends
on a ratio of the concentrations of zinc-ion and hydrogen-ion153 (Chapters XIV and XV, q.v.). Even
if the concentration of hydrogen-ion is very small, zinc will liberate hydrogen, provided the
conditions are such that the concentration of zinc-ion cannot reach a large enough value to satisfy the
equilibrium ratio, and stop the action. Now, in an alkaline solution, zinc-ion is converted into zincate-
ion (Zn2+ + 4 HO− ⇄ ZnO22− + 2 HOH) and a large concentration of zinc-ion cannot accumulate.
The consequence is that zinc liberates hydrogen freely even from alkaline solutions, for instance
from molar solutions of potassium hydroxide, in which the concentration of hydrogen-ion, roughly
10−14, is very much smaller than that calculated for the benzene solution of hydrogen chloride
(namely, 10−9). Now, although the values of the solution-tension constants of elements change most
decidedly with a change of solvent, it seems likely154 that their ratios, on which their mutual
displacement depends, will not be found materially altered. Zinc chloride being insoluble in benzene,
the ratio for equilibrium may not be fulfilled for zinc in contact with a benzene solution of hydrogen
chloride. Hence, with that solvent, the evolution of hydrogen may, so far as it goes, very well be due
to precisely the same machinery as that operating in aqueous solution. The liberation goes on until
the metal is protected against any further action by a film of the solid chloride. It seems, therefore, at
least possible, that the evolution of hydrogen observed by Kahlenberg and his collaborators155 is a
purely ionic action, the same as the similar [p086] action in aqueous solution has been proved to be by
quantitative measurements.156 Only exact measurements, comparable with those made in aqueous
solutions, can settle the question at issue, and until such quantitative evidence is forthcoming, a
definite conclusion that the action of hydrogen chloride in benzene solution is or is not an ionic
action is not warranted by the facts.
Equally interesting are Kahlenberg's observations of interaction between hydrogen chloride in
benzene solution and a similar solution of copper oleate. Each solution shows absence of appreciable

conductivity, yet, when the solutions are mixed, precipitation of copper chloride occurs instantly.
Whether we have here an instantaneous action between non-ionized molecules, as claimed by the
observer, or whether the minimal ionization157 of the hydrogen chloride and copper oleate, the
existence of which we have a right to assume, is sufficient to account for this rapid action, both
components being in solution and intimately mixed, is a question of the greatest interest. But until
quantitative measurements of all the factors involved in chemical actions in benzene solution are
obtained, a very difficult, but necessary task, which the discoverer of the action omitted to perform,
no definite conclusion whatever can be based on such results, interesting as they are. Water, although
it is only minimally ionized (tables, Chapter VI), hydrolyzes salts like potassium cyanide and
aluminium chloride almost instantly, and it has been rigorously proved that the resulting condition of
equilibrium involves the ions of water158 (Chapter X). With the possibility that the well-known
enormous speeds of action of ions may completely offset the tremendous reduction in concentration
of the hydrogen-ion, in a benzene solution of hydrogen chloride as compared with an aqueous
solution, further analysis of the relations is imperative.159 Until such investigations have been
carried out, we must consider [p087] it possible that the reactions of hydrogen chloride in benzene
solution may be reactions of its non-ionized molecules or reactions of its ions. In view of the
undoubted minute concentrations of the latter, as compared with aqueous solutions, and in view of
the inertness of non-ionized hydrogen chloride in aqueous solutions as compared with the activity of
its ions, a benzene solution of hydrogen chloride should show far less ionic activity than an aqueous
solution, and that such is the case is brought out clearly by Kahlenberg's interesting experiments.

Some Applications of the Chemical Activity of Ions to Qualitative
Analysis.
—The knowledge that aqueous solutions of ionogens show the reactions of
the ions contained in them, gives us a clear, sharply defined interpretation
of many of the simpler facts of qualitative analysis. The elementary
observation that a large number of hydrogen derivatives show acid
properties and a considerable number of others do not (at least not to a
sufficient extent to be appreciable), finds its simplest explanation in the fact
that all solutions showing acid properties have these properties as the result
of the presence of a common component, namely the hydrogen-ion. The
acid properties are, in fact, the properties of this one substance and no other.
Thus hydrochloric, nitric, sulphuric, carbonic acids are acids because they
are dissociated more or less, liberating hydrogen ions; and compounds like
marsh-gas CH4, ammonia NH3, benzene C6H6, in spite of the presence of a
great deal of hydrogen in their molecules, are not acids, because they do

not, to an appreciable extent,160 ionize as do the first compounds
mentioned. In the same way, glycerine C3H5(OH)3, although it is a
trihydroxide, does not show the characteristic actions of the hydroxides of
potassium, barium, aluminium, of the metal hydroxides in general—the
latter are more or less ionized, forming the characteristic ion of bases, the
hydroxide-ion HO−; but glycerine does not appear to ionize into C3H53+ and
HO−. The well-known observation of qualitative analysis, that potassium
chlorate solutions do not precipitate silver chloride from silver nitrate, while
potassium chloride and other chlorides do so at once, is now understood as
being the result of the fact that the chlorates produce the chlorate-ion ClO3−
(see page 70 for the method of determining its composition), while the
chloride-ion [p088] is required for the precipitation of silver chloride.
Chlorplatinic acid H2PtCl6, in spite of the large proportion of chlorine in its
composition, does not precipitate silver chloride, but rather silver
chlorplatinate,161 a yellow salt, insoluble in ammonia, and it does so
because its ions162 are H+ and (PtCl62−).
Perhaps the most instructive case of this kind, that we can study, is that of
iron in ferrous and ferric salts. Exceedingly sensitive tests are known for the
ferrous and the ferric ions. Thiocyanates produce an intensely red salt,
Fe(SCN)3, when added, for instance, to ferric chloride; potassium
ferrocyanide, K4Fe(CN)6, precipitates ferric ferrocyanide, Fe4[Fe(CN)6]3,
Prussian blue, from ferric chloride solutions; ammonium hydroxide
precipitates quantitatively the insoluble red ferric hydroxide (exps.). With
ferrous salts, potassium ferricyanide K3Fe(CN)6 precipitates ferro-
ferricyanide Fe3[Fe(CN)6]2, Turnbull's blue; ammonium sulphide
precipitates black ferrous sulphide (exps.). Now, in two of the reagents
used, potassium ferro- and ferricyanide, iron is present according to the
formulæ given. If one should attempt to demonstrate its presence by means
of these tests—among the most sensitive and most reliable tests known in
analysis—one would fail utterly. Thiocyanates do not produce even the

faintest tinge of pink in potassium ferricyanide solution163; ammonium
hydroxide does not precipitate any ferric hydroxide (exps.). Ammonium
sulphide does not precipitate the least trace of a black sulphide from a
ferrocyanide solution, and when the latter is mixed with the ferricyanide
solution, no trace, either of Prussian or Turnbull's blue, is shown (exps.).
The contrast between the behavior of these salts and ferrous and ferric salts
is now sharply and definitely interpreted, as being the result of the contrast
in their ionization,—the color tests we use are extremely sensitive tests only
for the ferric and ferrous ions, Fe3+ and Fe2+, respectively,—but potassium
ferrocyanide ionizes into potassium ions and the negative ferrocyanide ions
Fe(CN)64−, and shows the actions of ferrous ions as little as chlorate ions
ClO3− exhibit the reactions of chloride ions Cl−. Potassium ferricyanide, in
turn, gives rise to trivalent, negative ferricyanide ions Fe(CN)63− and not to
ferric [p089] ions.164 If any doubts arise on this point, one can decide the
question readily by experiment. When a concentrated solution of potassium
ferricyanide is placed in a U-tube under a solution of some colorless
electrolyte, such as sodium sulphate, and plates connected with a battery are
inserted, there is no difficulty (exp.) in seeing that the yellow ion,165
containing the iron, moves to the positive pole and not to the negative. The
iron is, therefore, as a matter of experiment, part of a negatively charged
substance.
That iron is really present in these compounds can be shown most
effectively if we destroy the salts:
Exp. Dry, pulverized potassium ferrocyanide is intimately mixed with dry potassium carbonate
and the mixture heated in a hard glass test tube. When the whole mass has become red-hot, insuring
complete decomposition, the hot (not red-hot) tube is plunged into water; the salts are extracted and
particles of metallic iron are left undissolved. The action is
K4Fe(CN)6 + K2CO3 → 6 KCN + FeCO3
FeCO3 → FeO + CO2
and FeO + KCN → KCNO + Fe.

If the iron is dissolved in a little dilute hydrochloric acid and oxidized to the ferric condition, by the
addition of a few drops of bromine water, the intensely red solution characteristic of ferric salts may
be readily obtained, when a thiocyanate is added to the solution.

Chapter V Footnotes
[114] Loomis. (Cf. Whetham, Theory of Solution, p. 320 (1902).)
[115] Loomis; and E. H. Griffith. (Cf. Whetham, loc. cit.)
[116] Expressed in moles per liter.
[117] Δ1 : Δ2... = C1 : C2...or Δ1 / C1 = Δ2 / C2 = a constant.

[118] Cf. Whetham, loc. cit., pp. 147, 158.
[119] Ibid., p. 320.
[120] In regard to the degrees of ionization, as shown by freezing-point depressions and
conductivities of salts, see also A. A. Noyes, Report of the Congress of Arts and Sciences, St.
Louis, 1904, Vol. IV, p. 313.
[121] See Chapter XII, in regard to so-called "complex ions" and their salts.
[122] The term "acid ion" is used to designate the "acid radical," when it exists, in solution, as an
independent charged particle or ion. "Acid ion" is thus a convenient synonym for anion, just as
"metal ion," designating the metal or metal-like radical of a salt, is used as a synonym for cation.
The term, acid ion, has been found to convey more quickly and definitely to the student's mind,
than does the term anion, which component of an acid or salt is referred to. While it is not, in
some respects, an ideal term, yet its use seems justified by its very close relation to the term "acid
radical" and by its practical advantages.
[123] The principle was first applied by Hittorf.
[124] This does not preclude the possibility that the ion is combined with more or less water and
is Na(H2O)x+; see pp. 42, 65.

[125] Baker, J. Chem. Soc. (London), 65, 611 (1894), 73, 422 (1898). On page 623 of the first
article is given a list of chemical actions for which the effect of the presence of moisture has been
investigated (Stud.).
[126] Hughes, Phil. Mag., 34, 117 (1892) (Stud.).
[127] Gore, Proc. Royal Soc., 14, 204 (1841). Gore found that aluminium was dissolved and that
sodium and potassium were attacked by the gas, even before its liquefaction. It is uncertain
whether these positive reactions are reactions of absolutely anhydrous hydrogen chloride or the
result of the presence of moisture in the experiments in question, since Cohen [Chem. News, 54,
305 (1896)], drying the gas more carefully than did Gore, found, in contrast to the latter, that
metallic sodium may be exposed for several weeks to dry hydrogen chloride gas and retain its
lustre. In all experiments demanding the rigorous exclusion of moisture, more weight must be

attached to negative results (showing lack of activity) than to positive results. [Cf. the controversy
between Baker, loc. cit., and Gutmann, Liebig's Ann., 299, 3 (1898)].
[128] Nernst's Theoretical Chemistry, p. 375. Kablukoff, Z. phys. Chem., 4, 430 (1889).
[129] In regard to the behavior of zinc, see below, p. 84. (Cf. Kahlenberg, J. Phys. Chem., 6, 13
(1902) (Stud.).)
[130] For a fuller discussion of the benzene solution see p. 84.
[131] The acid character, in particular, is due to the hydrogen-ion, H+; see below.
[132] The fusion is conveniently made in a platinum dish; the dish and a platinum cathode are
connected with the lighting circuit and an electric lamp.
[133] See Smith, Inorganic Chemistry, pp. 550, 569, 578, 588, 608, 610, 683: College Chemistry,
361, 373, 380, 389, 404, 405, 443 (Stud.).
[134] J. Chem. Soc. (Abstracts) (London), 40, 504 (1881).
[135] For positive evidence of the ionizing power of light, see Haber, Z. Elektrochem., 11, 847
(1905). For evidence as to the negligible rôle of ionization in the combination of chlorine and
hydrogen, see Mellor, Chemical Statics and Dynamics (1904), p. 290.
[136] The apparatus described by A. A. Noyes and Blanchard for comparing acids is used [J. Am.
Chem. Soc., 22, 737 (1900)].
[137] The conductivity depends in this case chiefly on the migration of the fast moving hydroxide
ions (p. 56), common to the three bases. There is little difference in the rates at which the cations
move.
[138] The water should be free from carbonic acid.
[139] The various indicators show different, specific degrees of sensitiveness to acids (to
hydrogen ions) and to bases (to hydroxide ions). That is, different concentrations of hydrogen-ion
or of hydroxide-ion are required to change their colors. As they are particularly useful in
demonstrating varying concentrations of these ions, they will frequently be used in illustrating
conclusions reached in the course of our work, just as they are used extensively in practical
analysis. The following tables are intended to give some definite information on this valuable
quality. The fourth column of the first table shows the concentration of hydrogen-ion, required to
change the color of the indicator from the tint given in the second column to the tint given in the
third column. The second table gives, similarly, the concentrations of hydroxide-ion required to
produce the changes of tint indicated. The tables refer to results obtained when 0.1 c.c. (about two
drops) of a 0.1 to 0.15% solution of the indicator is added to 10 c.c. of the solution examined.
Table of Sensitiveness to Acids (to Hydrogen-ion)
Concentration
Indicator. From to
H +.
Phenolphthaleïn Pink Colorless 10E−9

AzolitminA (litmus) Violet Violet pink 1E−6
Methyl orange Yellow Reddish orange 1E−3 – 0.1E−3

[A] Azolitmin is an important component of litmus.

Table of Sensitiveness to Bases (to Hydroxide-ion)
Indicator. From to Concentration HO−.
Phenolphthaleïn Colorless Pink 10E−6
Azolitmin Violet Violet blue 1E−6 – 0.1E−6
Methyl orange Orange Yellow 1E−9
It is clear that of the three indicators given in the table, phenolphthaleïn is the most sensitive to
acids, methyl orange the most sensitive to bases. An extended table of the sensitiveness of many
indicators, on which the above tables are based, is given by Salm, Z. phys. Chem., 57, 471 (1907).
The theories (of Ostwald, Bernthsen, and others) regarding the color changes, and the theory (of
Ostwald) concerning the sensitiveness of indicators, are discussed (with references to the
literature) by Stieglitz, J. Am. Chem. Soc., 25, 1117 (1903). Later modifications of the views on
color changes are discussed in papers by Stieglitz, Am. Chem. J. 39, (1908), and by Acree, ibid.,
37, 39, 42, and in these papers references to the literature will be found. For investigations on the
sensitiveness of indicators, see McCoy, ibid., 31, 508 (1904), Salm, loc. cit., and A. A. Noyes, J.
Am. Chem. Soc., 32, 815 (1910).
[140] Z. phys. Chem., 2, 289 (1888). Note the remarks in the footnote following.
[141] The formation of an ammonium salt in the latter action still further reduces the
concentration of the hydroxide-ion (Chapter VI) and retards the action; but the solution, in equal
measure, becomes less active toward the indicator, phenolphthaleïn (p. 114). The experiment
shows, therefore, rather fairly, the relative activities of the bases. The exact work of Arrhenius
included consideration of the effect of the ammonium salt, and the clearing up of the mystery of
this effect (p. 114) formed one of the greatest triumphs of his theory.
[142] Arrhenius, Electro-chemistry, p. 184 (1902). A second accelerative factor, the so-called "salt
effect" (Chap. VI, q. v.), is more pronounced in the case of 0.1 molar hydrochloric acid than in
that of 0.1 molar acetic acid, as the result of which the activity of the hydrochloric acid should be
increased about ten per cent; the ratio, therefore, of the speeds of reaction, both the degrees of
ionization of the acids and the "salt effect" being considered, should be approximately 83 : 1,
whereas the ratio found by experiment is 79 : 1.
[143] Vide also A. A. Noyes, Report of the Congress of Arts and Science, Vol. IV, p. 311 (1904).
[144] Haber, Z. für Elektrochem., 10, 775 (1904); see Chapter XII.
[145] This is, essentially, the old Berzelius view of chemical action.
[146] Vide, for instance, Stieglitz, Report of the Congress of Arts and Sciences, St. Louis, IV, 276
(1904); W. A. Noyes, Ibid., 285; Nef, J. Am. Chem. Soc., 30, 645 (1908). For the application of

the electron theory to organic compounds, see Falk and Nelson, School of Mines Quarterly, 30,
179, and J. Am. Chem. Soc., 32, 1637 (1910). (Cf. also Chapter XV.)
[147] J. Phys. Chem., 6, 1 (1902), and other papers in the same Journal.
[148] Cf. Patten, ibid., 7, 168 (1903), and Falk and Waters, Am. Chem. J., 31, 398 (1903).
According to the latter investigators, the evolution of hydrogen is slow and weak.
[149] Patten, loc. cit.
[150] Students will not be capable of following the argument given in the succeeding passages
and would better omit this part until Chapter XV has been studied.
[151] Kablukoff, Z. phys. Chem., 4, 430 (1889). See also Nernst, Theoretical Chemistry, p. 373.
[152] In view of the low order of accuracy of the data, and of the approximate method of
calculation, this result is only qualitative, but even with an error of 102 to 104 the argument in the
text would hold.

[153] For hydrogen under atmospheric pressure, the equilibrium ratio, [Zn2+] / [H+]2, is,
approximately, 1027.
[154] Vide Sackur, Z. Elektrochem., 11, 387 (1905). Kahlenberg holds a different view; ibid.
[155] The negative results obtained with aluminium and magnesium are possibly more interesting
than the positive action observed with zinc, but their inactivity may be due to thin films of
protective chloride or oxide or to a passive condition (vide Smith's Inorganic Chemistry, pp. 723,
753; College Chemistry, p. 475).
[156] The work of Ostwald, Arrhenius, Nernst and many others shows conclusively that the
liberation of hydrogen by metals and the precipitation of metals by one another is a function of
ion concentrations (Chapter XIV). Vide Nernst, Theoretische Chemie (1905), p. 245.
[157] See above.
[158] In a 0.1 molar solution of potassium cyanide, the potassium hydroxide formed by the
decomposition of the cyanide by water is approximately 0.0013 molar and the concentration of
hydrogen-ion is reduced to 10−11 (Chapter X), a value roughly of the same order as that calculated
above as a possible concentration of hydrogen-ion in a benzene solution of hydrogen chloride. In
spite of this small concentration of hydrogen-ion in the cyanide solution, the reactions in which it
is involved are, as far as known, completed in a few moments. Only for much smaller
concentrations of ions have any doubts as to their direct action been aroused; in Chapter XII this

question, as raised by Haber, is discussed for concentrations of ions of the order of 10−23. Haber
considers that ionic concentrations of 10−14 can still account for very fast actions.
[159] Cf. Abegg., Theorie der Elektrolytischen Dissociation (1903), 255; Lehfeldt, Electro-
chemistry (1904), 87.
[160] There is probably minimal ionization in all these cases, especially in the case of ammonia
(NH3 ⇄ NH2− + H+), but not enough to yield a sufficient supply of hydrogen-ion to show its
common properties.
[161] Vide Jorgensen, J. prakt. Chem., 16, 349 (1877).
[162] See Chapter XII in regard to the stability of (PtCl62−) as a complex ion.

[163] Freshly prepared solutions must be used.
[164] See Chapter XII as to the decomposition of the "complex ions."

[165] K+ and CN− are colorless ions. The yellow color of the ion moving to the positive electrode
shows the presence of the iron in it—a fact that can be confirmed by testing the solution round the
anode for ferricyanide by the method discussed further on in the text.

CHAPTER VI
CHEMICAL EQUILIBRIUM. THE LAW OF MASS ACTION

[p090] TOC

The theory of ionization, as studied so far, gives us simple, rational
explanations of many of our qualitative reactions—explanations which
agree with phenomena taken from separate fields of investigation. But, if
our study of the theory ceased at the present stage without further
elaboration, we should fail to find in it a satisfactory explanation of a
number of other important facts of analysis—notably, why certain reactions,
the occurrence of which we might anticipate, do not take place. For
instance, the addition of a soluble carbonate to a barium chloride solution
precipitates almost all the barium as barium carbonate (exp.); we have
2 Na+ + CO32− + Ba2+ + 2 Cl− → BaCO3 ↓ + 2 Na+ + 2 Cl−. But the addition
of carbonic acid to barium chloride solutions fails to produce the slightest
precipitate (exp.), although carbonic acid also gives rise to the carbonate-
ion, CO32−. In the same way silver nitrate readily precipitates silver
phosphate from sodium phosphate solutions (exp.), but not from a solution
of phosphoric acid (exp.). Hydrogen sulphide precipitates zinc sulphide
from a zinc sulphate solution (exp.), Zn2+ + SO42− + 2 H+ + S2− →
ZnS ↓ + 2 H+ + SO42−; but the addition of hydrochloric acid effectually
prevents the precipitation (exp.), although the hydrogen sulphide is still
ionized, as is apparent from the precipitation of copper sulphide when
copper sulphate is added to the mixture (exp.). In the negative results, we
have instances of a very large number of cases which require closer study,
and a further development of the theory, if we wish to interpret them
satisfactorily. The line of development to be followed is indicated perhaps
most sharply by the following experiment.

Exp. Some sodium tetraborate (borax) is dissolved in a little water and silver nitrate is added to a
small part of the solution. A pure white precipitate (silver borate) results. Another portion of the
borate solution is diluted with a large quantity of water, and then silver nitrate is added; quite a
different result is obtained—a brown precipitate (silver oxide) is formed. [p091]

The change in the quantity of water brought about the difference in result
—the quantitative relations were altered thereby. In order to follow
intelligently this and the other actions referred to, the study of reactions in
solutions must be taken up from the quantitative side—the development
heretofore has been essentially qualitative in character. On several
occasions we have found that all electrolytes do not ionize equally well, and
that the intensity of their action, demonstrated, for instance, for potassium
and ammonium hydroxides, varies accordingly. We shall now have to study
these relations in greater detail.
For our purpose, the study of two of the fundamental quantitative laws
governing action in solution and of their application to analytical
phenomena, will be sufficient: these are, the law of chemical or
homogeneous equilibrium, in which the law of mass action is included, and
the law of physical or heterogeneous equilibrium.
The Law of Chemical Equilibrium.
—The law of chemical equilibrium may be expressed, for a simple case, by
saying that if two substances A and B interact at a constant temperature to
give two compounds C and D and, vice versa, C and D interact with each
other to produce A and B, then equilibrium will be reached when the ratio of
the product of the concentrations of A and of B to the product of the
concentrations of C and of D has a definite, constant value, which is a
value characteristic of the equilibrium between the compounds involved, at
the given temperature. The action may be expressed in the chemical
equation
A + B ⇄ C + D,

in which A, B, C and D represent four different substances reacting in the
molecular proportions indicated by their symbols, which as usual represent
molecular weights. And the condition for equilibrium may be expressed in
the mathematical equation
[A] × [B] / ([C] × [D]) = k.
[A], [B], [C] and [D] are used to represent the concentrations166 of [p092] the
four reacting substances and k is some definite number, called the
equilibrium constant.
The law was discovered by Guldberg and Waage in 1867, and, with
certain limiting conditions (see below) it has been fully established by
extensive experimental work.167 The significance of the law may be
interpreted on the basis of the following considerations. If we start with the
two substances A and B alone and have one mole of each in one liter (as gas
or in solution) at a given temperature, then, all the conditions being given,
—the temperature, the concentrations, and the nature of the substances,—
the reaction A + B → C + D, leading to the formation of C and D, will
proceed with a perfectly definite velocity. The molecules of A and of B
move in all directions (kinetic theory of gases and solutions), and molecules
of A will collide with molecules of B a definite number of times in unit time
and will form a definite number168 of molecules of C and D per minute. The
velocity of chemical change of a given substance (chemical velocity) is also
measured in terms of moles, and is represented by the number of moles or
the fraction of a mole changed per minute. If v′1 stands for the velocity of
the action between A and B, under the given conditions, then
v′1 = k1,
where k1 is some number. Now, if the concentration of one of the
components, e.g. A, should be doubled, then the chances for collision and
for action between molecules of A and B will be twice as great as before
and the velocity of the action will be doubled. If only one-tenth of the

concentration of A (one-tenth mole) is used, the velocity will only be one-
tenth as great as originally, and, in general terms, if [A] moles of A are used
per liter, the velocity of the change will be proportional to [A], and equal to
k1 × [A]. If the concentration of the other reacting component, B, is now
doubled, the chances for action are again doubled, and, in general, the
velocity of the action will be proportional also to the concentration [p093] [B]
of the second reacting substance. For the velocity, v1 of the action for any
concentrations, [A] and [B], of A and B at any moment at a given
temperature, we have
v1 = k1 × [A] × [B].
Hence, if by the symbols [A] and [B] the concentrations at any given
moment are represented, we may say that the velocity of the formation of C
and D at that moment169 is proportional to the product of the
concentrations of A and B, and to some constant, which is characteristic of
the interaction of A and B.
The validity of this conclusion has been fully verified by experiment.170
The case is an instance of the law of mass action, which states that in
chemical changes the velocity of the action is proportional at any moment
to the molecular concentrations171 of the reacting components, and to a
constant, which is characteristic of the chemical nature of the reacting
components (and of the temperature).
If we start with the reversed action
A + B ← C + D,
the relation may be developed in the same way. Thus the two substances C
and D will react upon each other, at the given temperature, with a velocity
proportional to a constant, k2, and, at any given moment, proportional also
to their respective concentrations at that moment:
v2 = k2 × [C] × [D].

Equilibrium will be reached when the substances A and B are formed at any
moment from C and D just as rapidly as they are used up to produce C and
D, and vice versa. Such is the case, [p094] when the velocities of the two
opposite reactions are equal to each other. For the condition of equilibrium,
then, v1 must be equal to v2 and therefore
k1 × [A] × [B] = k2 × [C] × [D]

or
[A] × [B] / ([C] × [D]) = k2 / k1 = kequilibrium.
In this way the meaning of the fundamental law of chemical equilibrium
may be developed from the consideration of the velocities of the reversible
actions, such as are involved in all conditions of equilibrium, and the
equilibrium constant represents the ratio of the velocity constants of the two
opposite reactions. This conclusion has been fully verified by experiment,
the equilibrium constant being, as a matter of fact, found equal to the ratio
of the velocity constants.172
The relations, so far considered, have been those of the simplest type of
reversible reaction. We may now discuss the modifications required for
other types of reaction by the law of equilibrium.
When two molecules of any reacting component take part in a reaction—
for instance, in A + 2 B ⇄ C + D—the concentration of this component is
raised to the second power in the mathematical expression of the law of
equilibrium; when three molecules of a component take part, its
concentration is raised to the third power, etc.
For instance, hydrogen iodide is decomposed, reversibly, into hydrogen
and iodine, according to 2 HI ⇄ H2 + I2. A condition of equilibrium is
reached, at a given temperature when
[H2] × [I2] / [HI]2 = K.

At 440°, the results given in the following table were obtained by
Bodenstein. The concentrations are expressed in moles per liter.173 The
constant is calcuated according to the equation just given. Analytical errors
affect the value of the constant most in the first and last experiments, as a
result of the very small concentrations of one component, I2 or H2. [p095]
[H2] [I2] [HI] K
0.0268 0.000190 0.0177 (0.016)
0.00986 0.00203 0.0328 0.019
0.00308 0.00783 0.0337 0.021
0.00175 0.0114 0.0315 0.020
0.000653 0.0204 0.0236 0.024
0.000265 0.0242 0.0202 (0.016)

The mechanical significance of the raised powers of the concentrations of
components, two or more molecules of which take part in a reaction as
indicated, will be discussed further on, in connection with a case of
equilibrium between an electrolyte and its ions (Chapter VI, p. 102).
Limitations to the Law of Chemical Equilibrium.
—Quite in agreement with the interpretation of the law of chemical equilibrium from the view-point
of the kinetic theory, it is found that, in its applications, one must take into consideration the
possibility, that molecular attractions (p. 27) or other important forces of attraction or repulsion (e.g.
electrical) of a more than negligible magnitude exist between the molecules of the components in a
reversible reaction. If such forces are involved, suitable allowance must be made for them, so that the
mathematical formulation of the law may express the facts of observation.174 For these reasons, the
law, in its simplest terms, which, alone, can be considered here, holds for the relations obtaining in
dilute systems175 (dilute solutions or gases that are not too strongly compressed), and in systems
involving only nonelectrolytes or only weak ionogens, more generally than for the relations in
concentrated solutions (or strongly compressed gases) or in systems, in which electrically charged
particles (ions) are present in large proportions (see below, p. 108).

The Factors of the Law of Chemical Equilibrium.
—Inspection of the mathematical expression of the law of chemical
equilibrium (p. 91) shows that there are two significant kinds of factors in
it: first, the equilibrium constant, whose value depends only on the nature
of the substances involved and on the temperature.176 In [p096] the second

place, we have concentration factors, which, to a large extent,177 may be
varied at will.
The following experiments may be used to illustrate the significance of
the two classes of factors: Phosphorus pentabromide is partially
decomposed by heat into the tribromide and bromine (a case of gaseous
dissociation):
PBr5 ⇄ PBr3 + Br2.
Phosphorus trichlordibromide is decomposed more or less, in a similar
fashion, into the components phosphorus trichloride and bromine,
according to the equation
PCl3Br2 ⇄ PCl3 + Br2.

For the condition of equilibrium in the two cases we have
[PBr3] × [Br2]′ / [PBr5] = k1
and [PCl3] × [Br2]″ / [PCl3Br2] = k2.
Exp. Two tubes containing equivalent quantities of the two bromides are placed side by side in
warm water.178 The tube containing the trichlordibromide is found to be much more intensely
colored by free bromine than that containing the pentabromide.

The intensity of the color of the bromine vapor shows that the
concentration of bromine, [Br2]″, in the PCl3Br2 tube, is greater than the
corresponding concentration, [Br2]′, in the PBr5 tube. As a molecule of
pentahalide PX5 dissociates into one molecule of PX3 and one molecule of
X2, [PCl3] equals [Br2]″ and is greater than [PBr3], which is equal to [Br2]′.
Further, more of the pentabromide than of the trichlordibromide must be
left undecomposed, i.e. [PCl3Br2] is smaller than PBr5. Since the factors in
the numerator of the second equation are both larger, and the factor in the
denominator smaller, than the corresponding factors in the first equation, k2
must be greater than k1. These constants are thus seen to be a measure of
the chemical stability of these pentahalides. It is evident, too, that in

reactions which depend on the presence of free bromine, such as the
bromination of many organic compounds, the trichlordibromide should be
more effective than the equivalent quantity of the pentabromide. [p097]
In the second place, if we were to introduce into either tube, for instance
into the tube containing the phosphorus trichlordibromide, an excess of one
of the dissociation products, say an excess of phosphorus trichloride, then
the condition of equilibrium would necessarily be disturbed:
y [PCl3] × [Br2]′ / [PCl3Br2] > k2,
in which the bracketed symbols represent the concentrations of the first
experiment. The velocities of the two opposite reactions would be no longer
equal, the combination of trichloride with bromine would be accelerated by
the increased concentration of the former. Here, equilibrium would only be
reëstablished when the trichloride and bromine had combined to a sufficient
extent to make
(y [PCl3] − x) × ([Br2]′ − x)
= k2,
([PCl3Br2] + x)
in which x represents the number of moles of additional phosphorus
trichlordibromide formed in unit volume by the combination of bromine
with phosphorus trichloride. The net result is seen to be that an increase in
the concentration of the one dissociation product eo ipso reduces the
concentration of the other dissociation product.
Exp. A third tube charged with the same quantity of phosphorus trichlordibromide as the tube
mentioned above, and with an added excess of phosphorus trichloride, is placed in the warm water
next to the tube containing the trichlordibromide. Its color is much paler than that of the latter, owing
to the suppression of free bromine.179

The concentration of the free bromine, ([Br2]′ − x), under the new
conditions of equilibrium, is smaller than the original concentration [Br2]′—
a result confirmed by experience. It is in our power, therefore, arbitrarily to
change the concentration of a reacting component, in a case of equilibrium,

and thus to affect the reactivity of the system; for instance, for brominating
purposes, the new system would be less effective than the original one, and
it might be of especial service where bromination is to be avoided.
In the cases studied, are found the two fundamentally important relations
expressed by the law of equilibrium: the equilibrium constant is a measure
of the stability of a certain system and, in a way, of its reactivity at a given
temperature; and the [p098] concentration factors are variables, which we
may change to a very considerable extent, so as, to a certain degree, to
subject the system to our own purposes. We shall repeatedly have occasion
to refer to these two fundamental relations and we shall use them again and
again in our analytical work.
Chemical Equilibrium of Electrolytes.
—Ionization of an electrolyte is a reversible chemical action and its relation
to the law of chemical equilibrium will now be discussed. For acetic acid,
ionization into hydrogen and acetate ions occurs thus: CH3CO2H ⇄
CH3CO2− + H+, and, in accordance with the law of equilibrium, at a given
temperature, the following relation would hold:
[H+] × [CH3CO2−] / [CH3CO2H] = Kionization.
If the total concentration of the acid is known, the concentrations of the ions
and of the non-ionized acid may be calculated from the conductivity of the
solution. For instance, if 60 grams of acetic acid (1 mole) is dissolved in
sufficient water to make 10 liters, the equivalent conductivity of the
solution (p. 50) is found to be 4.67 reciprocal ohms at 18°. The maximum
conductivity of one mole of acetic acid, at infinite dilution, when all the
acid would be ionized, would be 347. Therefore, in the acid under
examination, 4.67 / 347, or 1.34 per cent, is ionized (p. 50). Since the total
concentration of the acid is 0.1 mole per liter and 1.34 per cent is ionized,
the concentration of the hydrogen-ion, [H+], is 0.1 × 0.0134, and that of the
acetate-ion, [CH3CO2−], is the same. The concentration of the non-ionized

acetic acid, [CH3CO2H], is 0.1 × 0.9866. If these values are inserted in the
equation for the condition of equilibrium, we have
(0.1 × 0.0134)2 = K
ionization = 18.2E−6.
0.1 × 0.9866
From this experimental result, the equilibrium constant, which is called
the ionization constant of the acid, is found to have the value 18.2E−6. If
the ratio [H+] × [CH3CO2−] / [CH3CO2H] really is a constant, the same
value, within the limits of experimental errors, should be obtained from
acetic acid in other concentrations. Now, if the above solution is diluted to
ten times its volume, the concentration of the acid is made 0.01 mole per
liter, the conductivity [p099] is found to have increased to 14.5 reciprocal
ohms, and the percentage of ionized acid is then 14.5 / 347, or 4.17. Here,
[H+] and [CH3CO2−] = 0.01 × 0.0417 and [CH3CO2H] = 0.01 × 0.9583.
Inserting these values in our general equation and calculating the result, we
obtain 18.1E−6 as the value of the constant. In the following table180 are
given the molar conductivities, Λ (column 2), of acetic acid of varying
concentrations, m (column 1). The degrees of ionization, α, and the
ionization constant, calculated according to the equilibrium equation, are
given in columns 3 and 4.
Ionization of Acetic Acid. Λ∞ = 347.
m. Λ. 100 α. K.
0.1 4.67 1.34 18.2E−6
0.08 5.22 1.50 18.3E−6
0.03 8.50 2.45 18.5E−6
0.01 14.50 4.17 18.1E−6

It is evident, that a constant value is found for the ratio [H+] ×
[CH3CO2−] / [CH3CO2H] and that the ionization of acetic acid, in these
dilute solutions, obeys the law of chemical equilibrium.181 The equilibrium
constant expresses in definite, quantitative terms the tendency of acetic acid
to ionize in dilute solution. Examination of other acids shows that there is

an enormous range in the values found for their respective ionization
constants. The constants are the best measure of the strength of the acids as
acids. Obviously, the more readily acids in equivalent solutions ionize, the
greater will be the concentration of the hydrogen-ion to which the
characteristic acid properties are due, and the more pronounced (stronger)
will be the exhibition of these properties. From the ionization constants one
may calculate, for instance, the proportion in which two competing acids
will neutralize a base, when the latter is used in quantity insufficient to
neutralize both acids. [p100]
Inspection of the equation for acetic acid, which is the typical
equilibrium equation for all monobasic acids, shows that the greater the
degrees of ionization of acids are in equivalent solutions, i.e. the greater the
concentrations of the hydrogen-ion which their ionization produces in
equivalent solutions, the larger will be the values of their ionization
constants. The acids with the larger constants are, then, the stronger acids.
The Ionization of Various Acids.
—The table given on page 104 shows the ionization constants for a number
of acids of interest in analysis. Before proceeding to give the table, we must
consider further two important points.
In the first place, for the strongest acids, such as hydrochloric, nitric,
hydrobromic and similar acids, chemists have been unable to determine
ionization constants on the basis of the law of chemical equilibrium. Strong
acids, strong bases and most salts (see pp. 106–8, below), the three classes
comprising all the very readily ionizable electrolytes, do not give constants
when the values of the equilibrium ratio,182 [Cation] × [Anion] /
[Molecules], are calculated for different concentrations, and they therefore
do not ionize simply in accordance with the law of chemical equilibrium.
The reasons for this abnormal behavior will be discussed presently (p. 108),
when other necessary facts are before us. In order to have, at least, a rough
basis for comparison of these strong acids with the weak ones, which do

obey the law of chemical equilibrium, the table will give for the strong
acids the value of the above ratio as calculated from their ionization in 0.1
molar solutions.
The Ionization of Polybasic Acids.
—In the second place, the meaning of the constants for polybasic acids,
such as sulphuric, phosphoric, carbonic and similar acids, requires
explanation. The relations for carbonic acid will be first developed, as
representing a typical case. Carbonic acid, in ionizing, forms the carbonate-
ion CO32−, and the hydrogen-ion, as expressed in the [p101] equation183
H2CO3 ⇄ 2 H+ + CO32−. According to the law of chemical equilibrium for
the case where a product (here the hydrogen-ion) appears twice on one side
of the reaction equation, we have, for the condition of equilibrium (p. 94)
[H+]2 × [CO32−] / [H2CO3] = K. (1)
We may ask, however, whether both the hydrogen atoms of carbonic acid
show the same tendency to ionize, or, since there is a vast difference in the
ease of ionization of different acids, whether there is not also a difference in
the ease of ionization of the different hydrogen atoms in a polybasic acid.
As a matter of experiment, we find that a molecule of carbonic acid does
ionize, first, and more readily, into one hydrogen ion and an acid carbonate
ion HCO3−, according to H2CO3 ⇄ H+ + HCO3−.
For this reversible reaction we have184
[H+] × [HCO3−] / [H2CO3] = K1. (2)
The value of this constant,185 called the primary ionization constant of
carbonic acid, is 0.3E−6.
The acid carbonate-ion HCO3−, in turn, is ionized to a certain extent,
producing another hydrogen ion and the carbonate-ion, CO32−. We have
HCO3− ⇄ H+ + CO32−, and

[H+] × [CO32−] / [HCO3−] = K2. (3)

The value of this constant186, called the constant of the [p102] secondary
ionization of carbonic acid, is 0.07E−9, which has about one four-
thousandth of the value of the constant for the primary ionization.
If we combine equations (2) and (3) we have
[H+] × [HCO3−] × [H+] × [CO32−]
= K 1 × K2
([H2CO3] × [HCO3−]) (4)
or
[H+]2 × [CO32−] / [H2CO3] = K.

This is equation (1), derived originally by the application of the law of mass
action to the relation between the carbonate-ion, CO32−, the hydrogen-ion,
and carbonic acid, H2CO3.
This relation, and, in particular, the significant squaring of the
concentration of the hydrogen-ion, an ion which appears twice in the
equation for the formation of carbonic acid from carbonate and hydrogen
ions, (2 H+ + CO32− ⇄ H2CO3), may now be interpreted mechanically (p.
92) as follows: For the formation of carbonic acid from a carbonate ion and
two hydrogen ions, a carbonate ion must collide and combine first with one
hydrogen ion, and the velocity for the formation of this intermediate
product, HCO3−, will be proportional to the (total) concentration of the
hydrogen ions; the product, HCO3−, to form H2CO3, must collide and
combine with a hydrogen ion once more, and this combination will proceed
with a velocity again proportional to the (total) concentration of the
hydrogen ions. So the velocity for the transformation of CO32− into H2CO3
will be proportional twice over to the (total) concentration of the hydrogen
ions—as well as, in the usual fashion, to the concentration of the carbonate
ions present at any moment.
It is a general principle that the primary ionization of polyvalent acids
occurs more readily than the secondary, and this in turn more readily than

the tertiary (if a third ionizable hydrogen atom is present in the acid).
In the case of phosphoric acid, for instance, the primary ionization into the hydrogen-ion and the
dihydrogen-phosphate-ion, H2PO4−, takes place so readily that phosphoric acid reacts strongly
acid187 to methyl orange,188 the [p103] concentration of hydrogen-ion being sufficiently great to
affect this indicator (see Exp. below).
When phosphoric acid is neutralized by one equivalent of a base, say of sodium hydroxide, the salt
formed, sodium dihydrogen-phosphate, NaH2PO4, yields sodium-ion and dihydrogen-phosphate-ion,
H2PO4−. The latter is ionized somewhat into H+ and the bivalent hydrogen-phosphate-ion, HPO42−.
The ionization of the ion H2PO4− is now the chief source of supply of hydrogen-ion (the further
ionization of HPO42− is practically negligible here) and it is ionized so little that the solution of
NaH2PO4 no longer changes the color of methyl orange (see Exp. below). The solution is, however,
acid to the indicator phenolphthaleïn, which is much more sensitive to the hydrogen-ion and will
show the presence of much smaller concentrations of it than will methyl orange. The addition of a
second equivalent of sodium hydroxide to the solution converts NaH2PO4 into Na2HPO4. This salt
gives sodium-ion and the hydrogen-phosphate-ion HPO42−, which, in turn, is ionized only very
slightly, producing phosphate-ion PO43−, and again hydrogen-ion. The ionization of HPO42− is so
slight, however, and the concentration of the hydrogen-ion, therefore, so minute, that the solution
does not react acid even to the sensitive indicator phenolphthaleïn.
Exp. Methyl orange (very little) is added to 10 c.c. of a 0.1 molar solution of phosphoric acid and
10 c.c. of 0.1 molar sodium hydroxide solution is added to the mixture; the color will be found to
change from the acid to the neutral tint just as the last drop or two of the alkali are added.
Phenolphthaleïn is then added to the mixture and 10 c.c. more of the 0.1 molar sodium hydroxide
solution are required to change the color of the mixture to a pronounced pink (alkaline) tint.
Even sulphuric acid, although its two hydrogen atoms are ionized very easily, making sulphuric
acid a strong acid, shows a difference in the ease of ionization of the two hydrogen atoms. Since
ionization, in general, is favored by dilution, we find that in the case of such a strong acid the
difference is most marked in more concentrated solutions, the smaller amount of water starting the
ionization in the more favored direction and producing first, chiefly, hydrogen-sulphate ions, HSO4−.
When the solution is diluted, the hydrogen-sulphate ions are to a very considerable extent dissociated
into sulphate ions and hydrogen ions. The described change in ionization can be roughly followed
with the aid of an insoluble sulphate like barium sulphate. Barium sulphate, while very insoluble in
water, dissolves in rather strong sulphuric acid to form the acid sulphate, Ba(HSO4)2, the SO42− ion
of the sulphate being more or less suppressed by uniting with hydrogen-ion. We have the action

BaSO4 ⇄ Ba2+ + SO42− and
Ba2+ + SO42− + H+ + HSO4− ⇄ Ba2+ + 2 HSO4−.

If the solution of the acid sulphate is poured into a large volume of water, barium sulphate is
immediately reprecipitated, the hydrogen-sulphate-ion being dissociated, in the dilute solution, into
hydrogen-ion and sulphate-ion, SO42−, whose barium salt is so difficultly soluble:

Ba2+ + 2 HSO4− → Ba2+ + 2 H+ + 2 SO42− → BaSO4 ↓ + 2 H+ + SO42−.
[p104]
Exp. Finely divided barium sulphate is warmed for a moment with a few cubic centimeters of
concentrated sulphuric acid in a test tube, the mixture is allowed to settle, and some of the clear acid
is carefully decanted into a large beaker full of water.
It may be added, that while the primary ionization of sulphuric acid does not yield an equilibrium
constant for the ratio [H+] × [HSO4] / [H2SO4], even such a strong acid as is sulphuric acid is found
to give a fairly good constant189 for [H+] × [SO42−] / [HSO4−]. The value of this constant189 is
0.03.

The Ionization ConstantsA of Acids
Acid. Equilibrium Ratio. K.
Hydrochloric [H+]×[Cl−]/[HCl] (1)
Hydrobromic [H+]×[Br−]/[HBr] (1)
Hydroiodic [H+]×[I−]/[HI] (1)
Nitric [H+]×[NO3−]/[HNO3] (1)

ChromicB [H+]×[HCrO4−]/[H2CrO4] (1)

[H+]×[CrO42−]/[HCrO4−] 0.6E−6

SulphuricC,D [H+]×[HSO4−]/[H2SO4] (1)

[H+]×[SO42−]/[HSO4−] 0.3E−1

OxalicE [H+]×[C2O4−]/[H2C2O4] 3.8E−2

[H+]×[C2O42−]/[HC2O4−] 0.5E−4

PhosphoricF [H+]×[H2PO4−]/[H3PO4] 0.1E−1

[H+]×[HPO42−]/[H2PO4−] 0.2E−6

[H+]×[PO43−]/[HPO42−] 0.4E−12

ArsenicD [H+]×[H2AsO4−]/[H3AsO4] 0.5E−2

NitrousB [H+]×[NO2−]/[HNO2] 0.5E−3

AceticG [H+]×[CH3CO2−]/[CH3CO2H] 1.8E−5

CarbonicH,I [H+]×[HCO3−]/([H2CO3]+[CO2]) 0.3E−6

[H+]×[CO32−]/[HCO3−] 0.7E−10
Hydrogen [H+]×[SH−]/[H2S] 0.9E−7
SulphideJ,K 0.1E−14
[H+]×[S2−]/[SH−]
BoricB [H+]×[H2BO3−]/[H3BO3] 0.7E−9
Hydrocyanic [H+]×[CN−]/[HCN] 0.7E−9
Arsenious [H+]×[H2AsO3−]/[H3AsO3] 0.6E−9

WaterL,C [H+]×[HO−]/[H2O] at 25° 0.2E−15
at 100° 0.9E−14
+ −
[H ]×[HO ] at 25° 1.2E−14
at 100° 0.5E−11

[A] As explained on p. 100, the bracketed values given for the strong acids are not
constants, but express the values of the ratios [H+] × [Anion] / [Acid] for 0.1 molar

solutions.
[B] See references, Noyes, ibid., 32, 860 (1910).
[C] Noyes and Eastman, Carnegie Institution Publications, 63, 274 (1907).
[D] Luther, Z. Elektroch, 13, 296 (1907).
[E] Chandler (McCoy), J. Am. Chem. Soc., 30, 713 (1908).
[F] Abbot and Bray, ibid., 31, 760 (1909).
[G] See above, p. 99.
[H] Walker, J. Chem. Soc., (London), 77, 5 (1900).
[I] McCoy, Am. Chem. J., 29, 455 (1903); Stieglitz, Carnegie Institution Publications, 107,
243 (1909).
[J] Auerbach, Z. phys. Chem., 49, 220 (1904).
[K] Knox, in Abegg's laboratory, Trans. Faraday Soc., 4, 43 (1908).
[L] Vide p. 66.

[p105]

The difference in the tendencies of acids to ionize, as expressed in the
table, may be recognized in equivalent solutions by any of the properties
dependent on the ionization, such as the conductivity, the chemical activity,
the osmotic pressure and allied effects, and so forth. If the conductivities of
equal volumes of equivalent (e.g. normal) solutions of hydrochloric,
phosphoric and acetic acids are compared (exp.)190, it is readily seen that
hydrochloric acid is the best conductor, phosphoric acid a much poorer one,
and acetic acid an exceedingly poor one (the conductivity of normal acetic
acid is about 1 / 200 that of normal hydrochloric acid, and the conductivity
of normal phosphoric acid is about 1 / 14 that of normal hydrochloric acid).
Since the conductivity is approximately proportional to the concentration of
the hydrogen-ion191 in each of the solutions, it is evident that the
hydrochloric acid is ionized to a considerably greater extent than either of
the other acids—than acetic acid, in particular. Similarly, if a drop (0.05
c.c.) of molar hydrochloric acid and a drop of molar acetic acid are added to
equal volumes (50 c.c.) of a very dilute solution of methyl orange (exp.), the

color will be changed decidedly by the hydrochloric acid to a bright pink,
but by the acetic acid only to an orange hue. Again, if a precipitate of
barium chromate or calcium oxalate is treated with some strong acid,
hydrochloric or nitric, for instance, it dissolves readily, while a considerable
excess of acetic acid (exp.) only dissolves traces of either precipitate.192 In
this way, the chemical behavior of these acids differs in degree, as a result
of the different tendencies to ionize, which are expressed in the constants of
the table. Advantage is taken, in analysis, of such differences. Acetic acid,
for instance, is used when only a slight degree of acidity is desired—as in
recognizing barium-ion by its chromate, or oxalic acid by means of its
calcium salt. Hydrochloric or nitric acid is used when decided acidity is
required—as in the separation of groups by hydrogen sulphide (Chap. XI).
The Ionization of Bases.
—The same relations hold for bases as for acids: the weaker bases give
ionization constants as [p106] do the weaker acids; the strong bases, again, as
was mentioned above, do not give constants. The values for strong bases,
stated in the following table, are bracketed, and refer to the ionization in 0.1
molar solutions of the bases. Polyvalent bases, like polybasic acids, ionize
in stages, and the primary ionization is usually stronger than the secondary
ionization, and so forth. For instance, a study of ferric chloride solution
shows that the third hydroxide group of ferric hydroxide, Fe(OH)3, must
have the smallest ionization constant.193
The Ionization ConstantsA of Bases
Base. Ratio. K.
Potassium hydroxide [K+]×[HO−]/[KOH] (1)
Sodium hydroxide [Na+]×[HO−]/[NaOH] (1)
Barium hydroxide [Ba2+]×[HO−]2/[Ba(OH)2] (0.03)
Strontium hydroxide [Sr2+]×[HO−]2/[Sr(OH)2] (0.03)

Calcium hydroxideB [Ca2+]×[HO−]2/[Ca(OH)2] (0.03)

Ammonium hydroxideC,D [NH4+]×[HO−]/([NH4OH]+[NH3]) 1.8E−5

HydrazineE [N2H5+]×[HO−]/([N2H5OH]+[N2H4]) 0.3E−5

AnilineF [C6H5NH3+]×[HO−]/ 0.5E−9
([C6H5NH3OH]+[C6H5NH2])
Water [H+]×[HO−]/[H2O] at 25° 0.2E−15
at 100° 0.9E−14
+ −
[H ]×[HO ] at 25° 1.2E−14
at 100° 0.5E−11

[A] As explained above, the bracketed values under K for strong bases are not constants,
but express the values of the ratios for 0.1 molar solutions only. (For the alkaline earths
0.05 molar solutions are referred to.)
[B] Estimated value.
[C] Vide page 160.
[D] Corrected value, from Bredig's data, Z. phys. Chem., 13, 322 (1894). A. A. Noyes,
Carnegie Institution, Publication No. 63, p. 178, finds the value 17.3E−6 for 18°.
[E] Uncorrected value, Bredig, ibid.
[F] Bredig, ibid.; Stieglitz and Derby, Am. Chem. J., 31, 457 (1904).

While the constants of a large number of organic bases194 have been
determined few constants of inorganic bases are as yet known. The fact that
the majority of inorganic bases are polyvalent and difficultly soluble has
made their examination in this respect more difficult. From the study of the
decomposition of salts by water (see Chapter X), the trivalent bases, such as
[p107] ferric hydroxide and aluminium hydroxide, are found to be much

weaker than bivalent bases like cadmium, zinc and lead hydroxides,195 but
the data are not sufficient for the calculation of any constants, or for
distinguishing between the ionization of the first, second and third
hydroxide groups.
The difference in ionization and in chemical activity between a strong
base, like sodium or potassium hydroxide, and a weak base, like ammonium
hydroxide, has already been discussed and illustrated (see p. 77). In
analysis, advantage is frequently taken of these relations.196
The Ionization of Salts.

—While we read and hear a good deal about strong and weak acids, and
strong and weak bases, the expression "strong" or "weak" salt is never
heard; as a matter of fact, all salts, with very few exceptions, ionize
exceedingly readily—about as readily as the strongest acids and bases.
There are minor differences, but none of great moment—none of the kind
indicated by the wide range of constants for the acids and bases. There are
only a few important exceptions to this general rule—the most important
ones, among the common salts, being mercuric chloride and mercuric
cyanide: their exceptional behavior in regard to ionization, as indicated by
their conductivities (see below), is found side by side with an exceptional
chemical behavior, exactly as the theory of ionization would lead us to
anticipate, and it renders necessary certain precautions, particularly in
analytical work, which will be discussed later (Chap. VI). Ordinary salts are
all ionized readily: for instance, whereas acetic acid in molar solution is
ionized only to the extent of 0.37 per cent, its salts are highly ionized, the
degree of ionization of sodium acetate, for example, being 52.8% in molar
solution. As in the case of the strong acids and bases, salts of the type MeX,
which ionize according to the equation MeX ⇄ Me+ + X− and which,
according to the law of chemical equilibrium, might be expected to give a
constant ratio [Me+][X−] / [MeX], do not give a constant ratio. That is,
when the values obtained for the concentrations of the ions and of the
nondissociated molecules, in solutions of various [p108] strengths, are
substituted in this formula, different values are obtained.197 For potassium
chloride, we have the following relations:
Molar Per cent
Conductivity. Ratio.
Concentration. Ionized.
0. 131.2 100 ———
0.001 127.6 97.3 0.035
0.01 122.5 93.4 0.130
0.05 115.9 88.4 0.335
0.10 111.9 85.1 0.485
0.20 107.7 82.1 0.754
0.50 102.3 77.9 1.38

1.00 98.2 74.9 2.23

The Ionization of Strong Electrolytes and the Law of Chemical
Equilibrium.
—The fact that the ionization of good electrolytes does not seem to
conform to the law of chemical equilibrium is an exceedingly important one
—it is, perhaps, the most important problem demanding rigorous
investigation, which is before chemists at the present time. It has been used
as an argument against the whole theory of ionization, and is the most
important objection that has been urged against it. But, to the impartial
observer, this single discrepancy, between observation and what we might
have anticipated, will only prove a stronger stimulus to keener investigation
and to more rigorous analysis of relations, since the latter are more complex
than was at first expected. Without considering the mass of evidence in
favor of the theory, found in other fields of chemistry and in physics, a part
of which has been given above, we must remember that this fundamental
law of chemical equilibrium has already decided unequivocally in favor of
the theory in hundreds of cases of the ionization of weak acids and weak
bases198 and that these are the cases where the conditions are most
simple.199 [p109]
It would lead too far from our subject to enter into a full discussion of this important question. It
will be sufficient here to indicate two directions of inquiry, which promise to lead to an explanation
of the apparent contradiction between the demands of the law of chemical equilibrium and the
ionization of strong electrolytes.
In the first place, the law of chemical equilibrium is based thermodynamically, i.e. from the point
of view of the ultimate energy relations involved, on the assumption that none but negligible forces
of attraction or repulsion exist between the molecules, whose concentrations are factors in the
equilibrium equations (cf. p. 95).200 Now, in solutions of electrolytes this condition is not strictly
fulfilled under any circumstances; the attractions between ions of opposite charge and the repulsions
of ions of like charge, as well as the effect of charged particles on neutral molecules, come into play.
For strong electrolytes, where the proportion of charged particles is always a large one, the deviations
from the simpler conditions to which alone the law is really applicable must be very much greater
than for weak electrolytes. It is, therefore, probable that these electrical forces201 are the source of
the deviation of the ionization of strong electrolytes from the law of chemical equilibrium: although
ionization is a reversible reaction, forces come into play which make the simple law inapplicable,

and it is altogether likely, therefore, that we shall find, when all the factors have been investigated,
that strong electrolytes should not and cannot obey this law alone.202 In confirmation of this
conclusion, recent careful calculations203 have shown that entirely analogous deviations from the
equilibrium law become perceptible in rather concentrated solutions of weak electrolytes, such as
acetic acid, in which there is an accumulation of charged particles, more nearly akin to that present in
dilute solutions of strong electrolytes. So it appears more and more certain that the deviations are a
result of the presence of electrically charged components in the solutions, the amount of deviation
depending on their concentration.
The "Salt Effect".
—In the second place,204 it seems possible that the presence of strong electrolytes in a solution may
modify the ionizing power of the solvent in such a way as to increase it, and to increase it the more,
the more concentrated the ions are in the solution.205 The ionizing power of solvents, as has been
explained, is intimately connected with their dielectric properties. [p110]
Now, solid salts have higher dielectric constants than has206 solid water, and the dielectric
constant of a compound is usually much higher in the liquid than in the solid form.207 It is possible,
therefore, that the presence of salts in the solution increases the dielectric or, at any rate, the ionizing
power of the solvent and there are many facts which would be explained by such a behavior.
Unfortunately for any decision of the question, determinations of the dielectric constants of salt
solutions have given contradictory results; the more recent, and possibly more reliable results of
Drude208 indicate that salt solutions show approximately the same dielectric behavior as water itself.
Smale, in Nernst's laboratory, on the other hand, obtained results indicating that salt solutions have
decidedly higher dielectric constants than pure water.209 A final decision in the matter would be of
great importance.210 But, as explained before (p. 64), there are other properties of a solvent which
seem to be intimately related to its ionizing power and which may be modified by the presence of
salts, i.e. of strong electrolytes. The value obtained for the proportion [Me+] × [X−] / [MeX] grows
rapidly with increasing concentration, indicating a disproportionately large ionization in the more
concentrated solutions—which is what one would expect, if electrolytes or their ions in some way
increased the ionizing power of the medium. In agreement with such a conclusion, Arrhenius
found211 that the ionization of weak acids, like acetic acid, is increased by the presence of foreign
neutral salts, such as sodium chloride. This means, of course, that the strength of acetic acid, as an
acid, is increased likewise.
Exp. 0.5 c.c. of 0.1 molar acetic acid is added to 100 c.c. of a dilute solution of methyl orange in
each of three test glasses. When some solid sodium chloride (3 grams, and then 3 grams more—
altogether 0.1 mole) is added to the one solution, a plain increase in the intensity of the acid tint is
observed.212 The addition of cane sugar to a second solution has no such effect. The addition of
sodium chloride to a fourth portion of the methyl orange, to which no acetic acid has been added,

shows that its color remains unchanged: the effect on the indicator in the first case, then, is the result
of the action of the salt on the acetic acid.213 [p111]
The so-called "salt-effect" on the ionization of ammonium hydroxide may be illustrated in a
similar way.
Exp. 0.5 cc of 0.1 molar ammonium hydroxide is added to each of two portions (100 c.c.) of a
dilute solution of phenolphthaleïn. When some sodium chloride solution is then added to one of the
two portions, the basicity of the solution is distinctly increased. The addition of sodium chloride to a
third portion of the phenolphthaleïn solution shows that its own reaction to the indicator is neutral.
If the ionizing power of a solvent is changed by the presence of an electrolyte, then the law of
chemical equilibrium, in its simple form, would not apply to the ionization of such electrolytes in
varying concentrations—as little as we should expect to obtain the same constant for acetic acid in
aqueous solution and in alcoholic solution, the ionizing power of alcohol being much smaller than
that of water. The deviation from the law, naturally, would be most marked in the case of those
electrolytes which ionize so easily as readily to produce high concentrations of ions.

It may be said that laws based on the electrical properties of salt
solutions seem to be the predominating laws governing the ionization of
electrolytes and modifying, in certain cases, the chemical laws based on the
study of non-electrolytes.214
For the purposes of qualitative analysis, it will suffice to bear in mind the
fact that the ionization215 of salts, strong acids and strong bases does not
conform to the laws of mass action, and the fact that practically all salts
(with the notable exceptions, among common salts, given on p. 107) are
very readily ionized in aqueous solution, namely to the extent of 40 to 85%
in solutions of such moderate concentration as 0.1 molar.216
Some Applications of the Law of Chemical Equilibrium.
—According to the discussions given above, for the ionization of acetic
acid, CH3CO2H ⇄ CH3CO2− + H+ we have the relation

[CH3CO2−] × [H+] / [CH3CO2H] = Kionization.
[p112]

If the concentrations of the components are modified in any way, the
condition of equilibrium is disturbed and change will result, always toward
the restoration of equilibrium. The changes, in the case of purely ionic

actions, are found to take place with an enormous velocity, equilibrium
being restored almost instantly.
(1) If the solution of acetic acid, represented in the above equation, is
diluted by an equal volume of water, the condition of equilibrium is
disturbed:
½ [CH3CO2−] × ½ [H+] / (½ [CH3CO2H]) < Kionization.

The ratio is smaller than that required for equilibrium, and there will be a
change towards increasing the ratio. The acid will ionize more rapidly than
it will be formed from the acetate and hydrogen ions (which collide less
frequently in the diluted solution) and a new condition of equilibrium will
be reached, when more of the acid is ionized. We found, as a matter of fact,
that the more a solution of acetic acid is diluted, the larger is the proportion
of ionized acid (see p. 99).
(2) If the concentration of the acetate-ion is increased in the solution by
the addition of a salt of acetic acid, say sodium acetate, we have
x [CH3CO2−] × [H+] / [CH3CO2H] > Kionization.
The ratio is larger than allowed by the equilibrium law, and the acetate ions
will combine with the hydrogen ions to form acetic acid more rapidly than
the ions are formed from it, until equilibrium is reëstablished. In a molar
solution of acetic acid, 0.42% of the acid is ionized, and we have
[CH3CO2−] × [H+] / [CH3CO2H] =
0.0042 × 0.0042 / 0.9958 = 1.8E−5.
If an equivalent quantity of sodium acetate should be added, i.e. one mole
or 82 grams of the salt per liter, the salt being ionized to the extent of 53%,
we would have
0.534 × 0.0042 / 0.9958 > 1.8E−5.
The equilibrium constant will be satisfied (and the velocity of ionization of
the acetic acid will become equal to the velocity of its [p113] formation from

its ions) when217 [CH3CO2−] = 0.53, [H+] = 0.000,034 and [CH3CO2H] =
0.999,966. If we use two characteristic places in the decimals, we have
(0.53 × 0.000034) / 1 = 1.8E−5.
The most significant fact in the new condition of equilibrium is the
extremely small concentration of hydrogen-ion in the solution. Since the
acid properties of acetic acid are due to its forming hydrogen-ion, we would
conclude that such properties of acetic acid are very much weakened by the
presence of its own salts. This conclusion has been fully verified by careful
quantitative measurements and can be demonstrated as follows218:
Exp. To two of three portions of a dilute solution of methyl orange equal quantities of acetic acid
are added (e.g. 0.5 c.c. molar acid), the third portion being reserved to show the color of the neutral
solution of the indicator. Now, if into one of the solutions, to which acetic acid has been added, a few
crystals of sodium acetate are gradually dropped, the color reverts gradually to the color of the
original neutral solution; the concentration of hydrogen-ion becomes so small, that it does not visibly
affect this indicator, which is not very sensitive to acids, (H+).219

The solution, according to the views expressed, should still be very
slightly acid, and by the use of an indicator (litmus paper) which is much
more sensitive to the hydrogen-ion than is methyl orange, no difficulty is
found in recognizing this fact also. As a matter of experiment, then, an acid
like acetic acid is very much weaker in the presence of its own salts than in
their absence, and the equilibrium constant and the concentrations of the
components used determine the extent to which the hydrogen-ion is
suppressed. The same must be true for all weak acids and similar relations
must [p114] hold for all weak bases220—in general, weak acids and weak
bases are very much weakened by the addition of their own salts.
The importance of recognizing such changes, in considering analytical
reactions, may be illustrated as follows:
Exp. A solution of ferrous acetate (ferrous chloride with an equivalent quantity of sodium acetate)
is treated with hydrogen sulphide; a precipitate of black ferrous sulphide is formed. A second portion
of the solution is first decidedly acidified with acetic acid: hydrogen sulphide does not precipitate any
ferrous sulphide. Some crystals of sodium or ammonium acetate are added to the mixture and a black

precipitate of iron sulphide immediately appears around the salt as it dissolves, and on mixing the
contents a heavy precipitate of the sulphide throughout the vessel is formed.

It is evident that the addition of a neutral salt, containing the same
negative ion as the added acid, may completely reverse the net result of a
test with hydrogen sulphide.
(3) If the concentration of the hydrogen ions in the solution of acetic acid
is increased by the addition of hydrochloric, or some other strong acid,
equilibrium between the acetic acid and its ions will likewise be disturbed
and the new condition of equilibrium will show a suppression of the
acetate-ion. Instances of such action of a strong acid in suppressing the
characteristic ions of weaker acids will be discussed in detail in connection
with the analytical applications of hydrogen sulphide (Chap. XI), where the
action is of peculiar importance. Strong bases have a similar effect on weak
bases.
(4) If one of the ions of acetic acid is suppressed by the addition of some
agent, equilibrium is again destroyed and the resulting change is always in
the direction of reëstablishing a condition of equilibrium on the basis of the
law of equilibrium. Instances of this common case, such as the
neutralization of acetic or any other acid by a base, or the driving out of a
weak acid, from its salts, by a strong acid, or of a weak base by a strong
base, considered from the point of view of the equilibrium law, should be
worked out by the student.221 [p115]
(5) The displacement of an acid (or base) in salts by another acid (or
base) is subject always to the law that equilibrium is reached, when all the
equilibrium constants are satisfied in the system. Very frequently, the
application of the law will lead, apparently, to the incorrect conclusion that
the stronger acid (or base) will always displace, more or less completely,
the weaker222—an inference, out of which grew, indeed, the
characterization of acids and bases as strong and weak. Yet, when the laws
of equilibrium, as the result of the peculiar values of constants, demand

that, on the contrary, a strong acid or base should be displaced by a weak, or
even a feeble one, we find that the change in this direction occurs with
equal ease. Numerous instances will be given where a weak acid (or a weak
base) does this to a certain extent (Chap. X), and others where precipitation
of salts facilitates the action of weaker acids greatly by the introduction of
new, physical constants. The following case of the liberation of
hydrochloric acid by the exceedingly weak acid, hydrocyanic acid, is
important because it shows a reversal of the common action without the
formation of any precipitate, and especially because it brings out most
strikingly the relations between ionization and chemical activity in a case of
special importance to analytical chemists.
The Exceptional Ionization of Mercuric Cyanide and Its Consequences.
—We have found that practically all salts are very readily ionized. But it
was mentioned that there are a few exceptions to this rule, and mercuric
chloride and especially mercuric cyanide were named as the most important
exceptions from the point of view of analytical chemistry. The difference in
ionization between these two salts and ordinary salts may be shown readily
by the apparatus previously used to demonstrate the difference in the
ionization of various bases and acids.
Exp. Into the parallel tubes of the conductivity apparatus (p. 77) equivalent quantities223 of
solutions of mercuric cyanide224 Hg(CN)2, mercuric chloride [p116] HgCl2, and barium chloride
BaCl2, are introduced. The barium chloride represents an ordinary salt of the same type as the
mercury salts, and the current passing through its solution makes the little lamp glow. The electrodes
in the mercuric chloride solution must be brought quite close together before sufficient current will
pass through the solution to bring its little lamp to redness. In the case of the cyanide we can, at most,
get a faint, dull glow by bringing the electrodes together as closely as we can, without allowing them
to touch each other and short-circuit the current.

It is evident that these mercury salts are not as readily ionizable as are
ordinary salts. This difference, as may be anticipated, shows itself also in
the chemical behavior of their solutions and makes necessary special
precautions on the part of the analyst in examining mercury compounds.

For instance, whereas mercuric oxide is readily precipitated by the addition
of sodium hydroxide to solutions of the nitrate and even of the moderately
ionized chloride, one fails to get a precipitate of oxide from the cyanide
solution (exp.), and if we relied on this test, we should overlook the
mercury entirely. That traces of the mercuric-ion are present, as indicated
by the minimal conductivity of the cyanide, is confirmed by the fact that
from the cyanide solution the sulphide, which is much less soluble than is
the oxide, may be precipitated by the addition of ammonium sulphide
(exp.). That the sulphide is in fact less soluble225 than the oxide is shown by
the conversion of the latter into the former by the action of ammonium
sulphide (exp.).
As a further result of the abnormally slight ionization of these mercury
salts, the analyst, unless he is on his guard, may also have difficulty in
discovering the presence of their negative ions. Thus, while sodium chloride
readily gives hydrogen chloride when treated with concentrated sulphuric
acid, mercuric chloride, although it is a soluble salt, does not (exp.), and
reliance on this test alone might lead to a gross error.226 In the case of the
cyanide, it is correspondingly difficult to recognize the [p117] cyanide-ion
(see the laboratory experiment, Part III). The ordinary tests fail to show its
presence until the mercury has been removed from the solution by
precipitation as a sulphide. Mercuric cyanide being a deadly poison which
analysts are liable to meet and have met with in criminal cases, it is clear
that a knowledge of these facts is vital to analytical accuracy.
Now, the very slight ionization of mercuric cyanide enables us to realize,
in the following experiment, the case where an exceedingly weak acid
without the formation of any precipitate involving physical constants, may
displace a much stronger acid from its salts. Hydrocyanic acid is one of the
weakest acids (table, p. 104), the constant for the ratio [H+] × [CN−] /
[HNC] being 0.7E−9. It is so weak an acid that the addition of a dilute
solution to methyl orange will not redden the indicator, but will have only a

barely perceptible effect on it (exp.). Mercuric chloride solutions also are
almost neutral to methyl orange (exp.) (very slight decomposition of the salt
by water makes the solution very slightly acid, not enough to produce more
than an orange color with methyl orange). Now, mercuric chloride, while it
is not very easily ionized, is, we found, very much more readily ionized
than is mercuric cyanide. The consequence is that when we add
hydrocyanic acid to a mercuric chloride solution, the equilibrium between
mercuric chloride and its ions and between hydrocyanic acid and its ions
will be decidedly displaced, the mercuric-ion combining with the cyanide-
ion to form the scarcely ionizable mercuric cyanide. As a result, more and
more of the molecular mercuric chloride and hydrocyanic acid will be
ionized; and since the other ions, the chloride and the hydrogen ions, form a
readily ionizable electrolyte, hydrochloric acid, these ions (H+ and Cl−) will
accumulate in the solution and we shall have sufficient ionized hydrochloric
acid liberated to make the solution decidedly acid.
Exp. When the two solutions described above are mixed, a strongly acid solution, colored a bright
pink, results.

In the following equations the dark arrows indicate the direction in which
the action goes when the solutions are mixed:

HgCl2 ⥂ Hg2+ + 2 Cl−
2 HCN ⥂ 2 CN− + 2 H+
2 CN− + Hg2+ ⥂ Hg(CN)2
2 Cl− + 2 H+ ⇄ 2 HCl

Chapter VI Footnotes
[166] Concentrations are usually measured in moles or gram-molecular weights per liter, and a
gram-molecular or molar weight of a compound is its molecular weight expressed in grams.
Hence the number of grams of a given substance in a liter divided by its molecular weight
represents its concentration.
[167] Nernst, Theoretical Chemistry, 423, 433; Ostwald, Lehrbuch, II2, 104, etc., 296; Walker,
Introduction to Physical Chemistry (1909), 259, etc.
[168] Not every collision of a molecule of A with one of B is supposed to result in a chemical
interaction, but the number of collisions with such a result is considered to be directly
proportional to the total number of collisions. Van 't Hoff, Lectures on Physical Chemistry, I, 104.
[169] Since in any chemical action, which has not reached a condition of equilibrium, the
concentrations of the reacting substances change continuously, the relation between the velocity
of the action and the concentrations, for any moment, is found by the application of the calculus

to the experimental data. (Cf. Elements of Calculus, by Young and Linebarger (1900), 168, 181,
240; Mellor, Higher Mathematics for Students of Chemistry and Physics (1902), 197.)
[170] Nernst, loc. cit., 541, etc.; Ostwald, loc. cit., 107, etc.; Walker, loc. cit., 257; Smith, loc. cit.,
250, and 180 (Stud.).
[171] If a component takes part more than once in the action, its concentration is raised to the
power corresponding to the coefficient expressing the number of its molecules taking part in the
action. For instance, for A + 2 B → C + D, v1 = k1 × [A] × [B]2; (see below).

[172] Cf. Van 't Hoff, loc. cit., I, 206.
[173] The concentrations are calculated from the data given by Bodenstein, Z. phys. Chem., 22, 16
(1897). (Cf. Van 't Hoff loc. cit., I, 110.)
[174] The fundamental meaning of the law is most accurately defined in thermodynamic terms,
that is, in terms of the work or energy relations connected with changes of gaseous or osmotic
pressures.
[175] Van 't Hoff, loc. cit., I, 104, 159, etc.
[176] In regard to the variations of the equilibrium constant with changes of temperature and the
relations which govern these changes see Smith's Inorganic Chemistry (1909), p. 260.
[177] The limitations are indicated in the preceding section.
[178] Stieglitz, Am. Chem. J., 23, 406 (1900).
[179] Vide Stieglitz, loc. cit.
[180] The table is based on the results of Noyes and Cooper, given in "The Electrical
Conductivity of Aqueous Solutions," Carnegie Institution Publications, No. 63, pp. 138, 141
(1907).
[181] Ostwald [Z. phys. Chem., 2, 278 (1888)], was the first to develop this relation from the
conductivity data for so-called "weak acids," and the law of chemical equilibrium, holding in such
and similar cases, is often called Ostwald's Law of Dilution.
[182] The equilibrium ratio, used as an illustration in the text, is the equilibrium ratio for
monobasic acids. For polybasic acids, the ratio would have the form demanded by the rule given
p. 94. For instance, for H2X ⇄ 2 H+ + X2−, the expression [H+]2 × [X2−] / [H2X] should be
constant, provided the ionization occurs according to the law of chemical equilibrium in its
simplest terms. In point of fact, for strong acids, this ratio holds as little as does the equilibrium
ratio for the monobasic acids.
[183] Owing to the instability of carbonic acid, which breaks down into carbon dioxide and water
(H2CO3 ⇄ H2O + CO2), the carbonic acid is, in turn, in equilibrium with the carbon dioxide. For
the sake of simplicity, this relation is not included in the detailed discussion, and wherever the
symbols H2CO3 and [H2CO3] are used, they are intended to represent the total carbonic acid,

present as such and as carbon dioxide. The detailed discussion of the complication mentioned will
be given in connection with the analogous case of ammonium hydroxide and ammonia, and, as
will be shown there, with the significance just attached to the symbols, the relations developed in
the text are a rigorous expression of the facts.

[184] [H+], in all the equations used, represents as usual, the total concentration of hydrogen-ion.
[185] Walker and Cornack, J. Chem. Soc. (London), 77, 20 (1900).
[186] McCoy, Am. Chem. J., 29, 437 (1903); Stieglitz, Carnegie Institution Publications, No. 107,
p. 245 (1909).
[187] In a solution of phosphoric acid, all the possible forms of ionization, described in the text,
occur simultaneously, but the secondary and tertiary forms of ionization, as far as the
concentration of the hydrogen-ion is concerned, are entirely subordinate to the primary ionization.
[188] Vide footnote, p. 79.
[189] Luther, Z. Elektrochem., 3, 296 (1907). Noyes and Eastman, Carnegie Institution
Publications, 63, 274 (1907). Noyes and Stewart, J. Am. Chem. Soc., 32, 1133 (1910).
[190] The apparatus described on p. 77 is used. Vide Noyes and Blanchard, loc. cit.
[191] Hydrogen ions move five to ten times as fast as the anions and carry 80–90 per cent of the
current; see p. 56.
[192] The solution of these salts is due to the action of hydrogen ions on their anions; see Chap.
VIII.
[193] Goodwin, Z. phys. Chem., 21, 1 (1896).
[194] See Kohlrausch and Holborn, loc. cit., p. 194. Their values for K (last column) must be
divided by 100 to express the constants in terms of the same units as those used in the above
table.
[195] J. H. Long, J. Am. Chem. Soc., 18, 693 (1896). Ley, Z. phys. Chem., 30, 322 (1899); Bruner,
ibid., 32, 133 (1900); Walker, J. Chem. Soc., (London), 67, 585 (1895).
[196] Instances are found in the laboratory experiments, Parts III and IV.
[197] The ionization of salts of other types, e.g. MeX2, Me2Y, etc., likewise fails to conform to
the law of chemical equilibrium.
[198] See below (pp. 112–4), also, further, confirmatory evidence, derived from the application of
the same law to the influence upon the degree of ionization of weak acids and weak bases, exerted
by the presence of their own salts.
[199] See below, in regard to evidence that the disturbing factors, predominant with strong
electrolytes, are exhibited in much slighter, but perceptible measure in the case of the weak

electrolytes.
[200] See also the interpretation of the law of chemical equilibrium from the viewpoint of the
kinetic theory, Nernst, Theoretical Chemistry, p. 428.
[201] For a more detailed discussion of these views, see Lehfeldt's Electrochemistry (1904), pp.
78, 79.
[202] Various empirical laws, expressing the behavior of strong electrolytes, have been suggested:
see Nernst, Theoretical Chemistry, p. 498, as to Rudolphi's and van 't Hoff's rules; see also A. A.
Noyes, Report of the Congress of Arts and Science, IV, p. 316 (1904).
[203] Wegscheider, Z. phys. Chem., 70 (I), 603 (1909).
[204] It is possible that this effect is only another form of expressing the very relation discussed in
the preceding paragraph.
[205] Arrhenius, Z. Elektrochem., 6, 10 (1899); Z. phys. Chem., 31, 197 (1899).
[206] Salts have constants averaging about 7, and running from 5 to 28; the constant for ice is
about 3. Landolt, Börstein, Meyerhoffer, Tabellen, p. 766 (1905).
[207] We have: Ice, 3, water (at 0°), 80; glacial acetic acid, 2.8, acetic acid (liquid), 10; cane
sugar, 4, cane sugar in aqueous solution (40%), 67.5, (6.5%), 45.3. Ibid.
[208] Z. phys. Chem., 23, 280 (1897).
[209] Wiedemann's Ann., 60, 625 (1897).
[210] See Walden, Z. phys. Chem., 61, 636 (1908), in regard to the difficulties of the problem.
[211] Loc. cit.
[212] Cf. Szyszkowski, Z. phys. Chem., 58, 420 (1907).
[213] Arrhenius made a calculation of the effect, taking into account all the rather involved
changes produced by the salt. Loc. cit.
[214] For instance, the principle of "isohydric solutions," discovered by Arrhenius, has been
established empirically and it involves relations which are in marked disagreement with the

demands of the law of chemical equilibrium. Vide A. A. Noyes, Report of the Congress of Arts
and Sciences, IV, p. 318 (1904).
[215] The most reliable estimates of the concentrations of ions in these solutions are based on
determinations of the degrees of ionization by means of conductivity measurements (see Chap.
IV, and the previous footnote).
[216] Salts MeX ionize more readily (80–85% in 0.1 molar solution) than do salts Me″X2 or
Me2X″ (50 to 70% in 0.1 molar solution), and these, again, more readily than salts Me″X″ (about
40% in 0.1 molar solution).
[217] The calculation of the condition of equilibrium can be made, with sufficient accuracy for
our purpose, as follows: The denominator 0.9958 in the original proportion, being near its limit
(its highest possible value is 1 in a molar solution), cannot change appreciably. Consequently,
when the one factor in the numerator, [CH3CO2−], is made 0.53 / 0.0042, or 126 times as large as
it was, the other factor, [H+], to maintain a constant proportion, must be made 1 / 126th of its
original value and 0.0042 / 126 = 0.000,034. For more exact work, the new concentrations of the
three components may be found by solving a simple quadratic equation.
[218] Küster, Z. für Elektrochem., 4, 110 (1897).
[219] See note, p. 79.
[220] See Part III for the application of this principle to ammonium hydroxide and its
experimental confirmation. (Cf. Arrhenius, Z. phys. Chem., 2, 28 (1888); Stieglitz, Am. Chem. J.,
23, 406 (1900).)
[221] For instance, in the first place, the action of 0.1 mole of HCl on 0.1 mole of C2H3O2Na,
dissolved in a liter of water, and, in the second place, the action of 0.1 mole of NaOH on 0.1 mole
of NH4Cl, in a liter of water, may be considered. The strong electrolytes (HCl, C2H3O2Na, NaCl,
NH4Cl, NaOH) may be taken to be (roughly) 80% ionized. From the concentrations given and the
constants involved, the direction and the presumable intensity of the main change in each of the
two cases should be determined.
[222] Instances of such displacement are given in the footnote of the previous paragraph.
[223] E.g. 50 c.c. of 0.2 molar solutions.
[224] Mercuric cyanide and mercuric chloride are largely present in aqueous solution as
[Hg(CN)2]2 and [HgCl2]2; see Chap. XII.

[225] See Chapter VIII in regard to this proof that mercuric sulphide is less soluble than mercuric
oxide and in regard to the question how, by a continuous disturbance of the equilibrium

conditions, all the mercury may be precipitated from the cyanide solution as the sulphide, in spite
of the very slight degree of ionization of the cyanide.
[226] The chloride is, however, sufficiently ionized to make possible the precipitation of the very
insoluble silver chloride, when silver nitrate is added to its solution.

CHAPTER VII
PHYSICAL OR HETEROGENEOUS EQUILIBRIUM.—THE
COLLOIDAL CONDITION

[p118] TOC

The law governing physical or heterogeneous equilibrium applies to all
cases where, at a constant temperature, one and the same chemical
substance is present in two or more physical conditions, or "phases," in
contact and in equilibrium with each other. We have, for instance, the
common case of a liquid, say water, in contact with its vapor, or the liquid
in contact with its solid phase (ice) and its vapor; or, we may have a gas,
say oxygen, in contact with its solution in some solvent like water. We may
have a solid, like cane sugar, in contact with its solution. We may also have
a substance like bromine, which is soluble both in chloroform and in water,
present in both solutions at the same time, the two solutions being in
contact but immiscible. These cases represent the most common types of
systems to which the law of physical equilibrium may be applied, although
the list has by no means been exhausted. The law of physical or
heterogeneous equilibrium states that when one and the same chemical
compound is present in two physical states or phases, as expressed in the
equation S1 ⇄ S2, then when equilibrium is reached, at a given temperature,
the ratio of the concentrations of the substance in the two phases is some
constant number:
[S1] : [S2] = k.
The bracketed symbols denote concentrations.
It should be noted that the condition of equilibrium is independent of the
total quantity227 of substance present in either phase or in both phases; that

is, provided the ratio of the concentrations is maintained constant at a given
temperature, the quantity of substance present in both phases or in either
phase is variable. For instance, the condition of equilibrium between water
and [p119] water vapor is independent of the quantity of water or of water
vapor present: in a closed liter bottle containing water and water vapor, the
ratio of the concentrations is maintained, irrespective of the question
whether the bottle contains 10 c.c. of water and 990 c.c. of vapor or 990 c.c.
of water and 10 c.c. of vapor.
The law is one of experience; instances of its application are given below.
Its probable theoretical significance may be explained mechanically with
the aid of the kinetic theory of gases and solutions, as follows: If
chloroform is added to a solution of bromine in water, the chloroform takes
up part of the bromine and, if the mixture is vigorously shaken, a condition
of equilibrium and a definite distribution of bromine between the two
solvents will result (exp.228). Now, if one imagines a liter of the aqueous
solution to contain one mole of bromine at some given temperature and to
cover a liter of chloroform, the whole system being left to itself, then all the
conditions affecting the migration of the bromine into the chloroform will
be definite ones—the concentration of the bromine, the temperature, the
surface between the two solvents—and bromine will pass from the aqueous
solution into the chloroform solution at a definite speed. We may call the
quantity (in moles) of bromine which would enter the chloroform in one
minute, if the concentration of the bromine in the water were kept constant
(one mole) throughout the minute, the velocity of migration of the bromine
—this velocity, like chemical velocity, representing a quantity, not a
distance. The velocity being a definite one under these conditions, we have
v1 = k1. Now, if all the conditions are left unaltered, except that the
concentration of the bromine is changed, say kept at one-hundredth its
original value, then only one one-hundredth as many molecules of bromine
as in the first case will come into contact with the chloroform surface in

unit time. The chances for migration are one one-hundredth as great, and
the quantity entering the chloroform in unit time—the velocity of the [p120]
change—will be one one-hundredth of the original velocity. In general, the
velocity will be proportional to the concentration of the bromine [Br]aq. in
the water at any moment and to the characteristic constant k1.
v1 = [Br]aq. × k1.
On the other hand, if a solution of bromine in chloroform is covered with
water, bromine enters the water (exp.).229 We would find, by the method of
analysis used before, and for the same conditions, that the velocity of
migration, v2, of the bromine into the water is also proportional to a
characteristic constant, k2, and to the concentration of the bromine in the
chloroform [Br]ch.. We have, therefore v2 = [Br]ch. × k2.
Equilibrium between the two solutions will be reached when
v1 = v2 or [Br]aq. × k1 = [Br]ch. × k2,

from which follows that230 for the condition of equilibrium
[Br]aq. / [Br]ch. = k2 / k1 = k.
Applications of the Law of Physical Equilibrium.
—(1) The law of physical equilibrium may be applied first to the case of a
liquid, say chloroform, in contact with its vapor. For the condition of
equilibrium at a fixed temperature [CHCl3]vap. : [CHCl3]liq. = k.
Now, at a fixed temperature, a pure liquid has a fixed concentration, its
specific gravity being a definite one. Hence, for a fixed temperature, the
second term of the constant ratio being definite, the first term, [CHCl3]vap.,
representing the concentration of the vapor, must also have a fixed, constant
value for the condition of equilibrium, i.e. when the space above the liquid
is saturated with its vapor. This is in agreement with well-known facts. The
concentration of the vapor is usually expressed in terms of its [p121]
pressure, and is called the vapor pressure or vapor tension of the liquid at

the temperature in question. Tables giving the definite vapor pressures of
important liquids at the various fixed temperatures are in common use.
(2) For oxygen in equilibrium with its saturated solution, say in water, at
a fixed temperature, we have, according to the law, [O2]gas : [O2]solut. = k.
If the oxygen is under a given pressure at a definite temperature, its
concentration [O2]gas is fixed, and consequently the second term, [O2]solut.,
of the ratio, the concentration of the dissolved oxygen, or its solubility, must
also be definite, i.e. oxygen must have a definite solubility in water at a
given temperature under a given pressure. If the pressure on the gas is
doubled, its concentration is doubled and, to maintain the constant ratio, its
solubility must also be doubled—which is in agreement with the facts
(Henry's law). If air of the same pressure is taken, in place of pure oxygen,
then the concentration of the oxygen (first term of the above ratio) is only
about one-fifth as great as for the pure gas, and the water must be saturated
with oxygen when it has taken up only one-fifth (second term of the ratio)
as much as it would from the pure gas (Dalton's law): Each gas in a mixture
is soluble in proportion to its own partial pressure or concentration.
(3) For sugar in equilibrium with its solution in water, i.e. in contact with
its saturated solution, at a given temperature, we should have
[C12H22O11]aq. : [C12H22O11]solid = k.
Since a pure solid like sugar at a given temperature has a definite specific
gravity, the concentration of the sugar in the solid condition should also be
a definite one. Consequently, according to the law under discussion, the
first term, [C12H22O11]aq., of the ratio, the concentration of the sugar in its
saturated solution in contact with the solid phase, must also have a definite
value. This is in agreement with fact, the concentration of the sugar in the
saturated solution, termed its solubility, being a definite one for a given
temperature. (See below, p. 123, in regard to the solubility of fine powders.)
Supersaturated Solutions.

— It is well known, however, that by dissolving a substance, such as sugar,
in hot water and carefully [p122] cooling the solution, we may obtain a
solution of sugar containing much more sugar in unit volume than is
represented by its solubility at the lower temperature. The concentration of
the sugar at the temperature in question, instead of having the definite value
represented by [C12H22O11]aq., can easily have a value several times as
large. This phenomenon is not at variance with the law of physical
equilibrium, inasmuch as the law states that, when a given compound is
present in two physical states or phases, then a constant ratio between the
concentrations of the substance in the two phases is established when
equilibrium is reached at a given temperature. In the solution prepared as
described, we have the substance present only in one phase, and we have
what may be called a metastable condition, as long as the second phase is
not introduced. As soon as a minute crystal of the solid phase is added or is
formed in the solution, change immediately ensues, and the excess of solid
is deposited. If the mixture be kept perfectly quiet, the excess will in most
cases be deposited on the surfaces of the added crystal, which thereby
grows larger (rock-candy manufacture).
Exp. Supersaturated solutions of sodium sulphate and sodium thiosulphate, into which crystals of
the salts are dropped, show how the crystal starts crystallization. The crystals develop as branches
from the crystal first introduced and from the new crystals formed.

This phenomenon of supersaturation is one which analytical chemists
must always take into consideration. Tests which involve the precipitation
of substances that are merely difficultly soluble, rather than exceedingly
insoluble, or of substances present only in very small quantities, may well
lead to entirely wrong conclusions, if precautions are not taken against the
possibility of the failure of a precipitate to appear as a consequence of
persistent supersaturation. For instance, a common test for the presence of
potassium salts consists in the precipitation of potassium acid tartrate by
the addition of tartaric acid to the solution of a potassium salt (exp.). The

tartrate is somewhat soluble and tends to form supersaturated solutions; if
we proceed without due regard for this phenomenon, we may readily have a
quantity of potassium salt present and fail to obtain the test for it. Simply
mixing tartaric acid and potassium chloride solutions (exp.) may fail to
[p123] give any precipitate, and if the test is thrown away and potassium
reported absent, a glaring blunder is committed. To insure against the error
of supersaturation, we try to start crystallization by the common devices of
shaking the solution or "scratching" the walls of the vessel, the object being
to facilitate the formation of the first crystal. The surest method is to
inoculate a small portion of the mixture with a minute crystal of the
substance we expect to be formed. If no precipitate results in a short time,
the solution is not supersaturated—it may be too dilute and may require
further concentration, but the error of supersaturation has been excluded.
The relation between supersaturated solutions and crystals brings out
sharply the fact that physical equilibrium is essentially a condition of
equilibrium between the substance at the surface of the solid and the
substance in its dissolved state. In terms of the molecular theory,
equilibrium is established when the molecules of the crystal surface
dissolve as rapidly as molecules from the solution are deposited on the
surface. If the concentration of the dissolved molecules is reduced below
the point required for equilibrium, the velocity of deposition is diminished.
The velocity of solution will then be greater than the velocity of deposition
and solution will result. The reversed relations hold when the concentration
of the solution is greater than that demanded by equilibrium: the velocity of
deposition will be the greater than that of solution and precipitation
follows.231
Solubility of Fine Powders.
—Consideration of the surface forces, acting between crystals and the
liquids wetting them, led to the interesting prediction232 that the more
minute crystals of a given specimen would not only dissolve more rapidly,

on account of the larger surface exposed, but would also be more soluble
than the larger crystals, and for the same reason. Surface tension always
tends to produce the smallest possible free surface of a liquid, and the free
surface between a liquid and a given weight of solid material in a fine
powder is much larger than between the liquid and the same weight in
larger crystals. The surface tension [p124] will therefore tend to convert the
smaller crystals into larger ones, and it can do so only by means of a greater
degree of solubility of the former. This prediction has now been fully
verified by experiments on the solubility of barium sulphate and of
gypsum.233 The solubility of barium sulphate in a very fine powder (with an
average diameter of 10−4 mm.) is almost twice as great as the solubility of a
coarser material (18E−4 mm. average diameter).
The application of these relations to analysis is as follows: If a crystalline
precipitate is in contact with a solvent, e.g. if barium sulphate is in contact
with the liquid from which it has been precipitated, then this liquid must be
continually in a state of change, not of equilibrium, with respect to the
solution and the deposited barium sulphate. The more minute crystals, being
a little more soluble than the larger ones, will supersaturate the solution in
respect to the larger crystals and the excess will be deposited on these larger
crystals and make them grow still larger. This deposition will make the
solution unsaturated with respect to the smaller crystals and more of these
will dissolve. The process is obviously a continuous one, and must lead in
time to the disappearance of the minute crystals and the growth of the larger
ones. That is a result which analysts aim to attain,—which in quantitative
work it is in fact necessary to attain, since the more minute crystals are
likely to pass through filters and be lost in the analysis. The views
expressed, and the experimental confirmation of the conclusion reached,
form the theory of what is called the "digesting" of precipitates before they
are brought on filters. It is clear that every condition facilitating contact
between solvent and solid will accelerate the desired change and continuous

stirring is therefore desirable. Heating is, as a rule, also to be desired for
very insoluble precipitates, as it will, in the majority of cases, facilitate the
solution of the undesirable, finer crystals.
In conclusion, these considerations will also indicate the precautions to
be observed in the precipitation of difficultly soluble substances. If this is
not properly carried out, endless trouble in [p125] the analytical laboratory
results. Except when heating is, for some special reason, undesirable—as
inducing a chemical change (like hydrolysis) that is not wanted—solutions
are brought to the boiling-point, and the precipitant added drop by drop, in
order not to supersaturate the solution too strongly. The solution is thus
allowed time to deposit its excess as far as possible on the first crystals
formed, which it will do rather than to form new, minute ones (see
supersaturation, p. 121). Constant stirring is prescribed in order to bring
older crystals, as far as possible, into contact with all parts of the slightly
supersaturated solution. After the precipitation is complete, it is usually
desirable to allow the mixture to "digest" for some time, for the reasons
given above—stirring and a high temperature during the process being
desirable. (See further Chap. VIII, p. 147, in regard to the use of an excess
of precipitant.)
The Colloidal Condition
When a difficultly soluble substance is formed in a solution beyond the
point of saturation of the solution, the substance in question separates from
the solution in a new phase, according to the principles just laid down.
Ordinarily, if the substance is a solid, a precipitate is formed; if a gas, a gas
escapes; if a liquid, a liquid separates out, which is immiscible with the
solution in which it is formed. Occasionally, the condition of
supersaturation which precedes the separation is somewhat persistent, but
this resistance to the separation of the phase may be overcome by vigorous
agitation of the solution or, as in the case of supersaturation with a

crystallizable salt, by inoculation of the solution with a particle of the new
phase (p. 123).
Under certain conditions, however, a difficultly soluble substance may be
produced in a solution, in a concentration far beyond its solubility, without
the separation of a precipitate (evolution of a gas or formation of a separate
liquid) and also without the formation of a supersaturated solution. Thus,
when hydrogen sulphide is passed into an aqueous solution of arsenious
oxide, the liquid acquires the yellow to orange color of arsenious sulphide
and becomes opalescent. But no precipitate is seen (exp.), in spite of the
fact that the sulphide is extremely insoluble and is formed practically
quantitatively according to the equation As2O3 + 3 H2S ⇄ As2S3 + 3 H2O.
The orange liquid passes through a [p126] filter unchanged (exp.). But if
some hydrochloric acid or a salt (e.g. sodium chloride) solution is added to
a portion of it, a heavy precipitate of arsenious sulphide is immediately
produced (exp.); its quantity is a good indication of the great amount of
sulphide that is not precipitated before the addition of the acid or salt. If
some pure arsenic sulphide (solid) is added to another portion of the orange
liquid, in order to overcome any possible condition of supersaturation, the
liquid is found to remain clear (but opalescent), excepting for the few
particles of added sulphide (exp.); even when it is vigorously shaken (exp.),
or allowed to stand for days, no precipitate is formed. We are therefore not
dealing with a case of supersaturation.
A liquid, in which a very insoluble substance appears thus to be in
solution far beyond its usual degree of solubility, and yet does not show at
all the behavior of a supersaturated solution, is said to contain the substance
in the colloidal condition. After a few more instances of the colloidal
condition have been presented, the significance of the condition and the
meaning of the term used to designate it will be explained.
Colloidal Gold.

—When a solution of gold chloride234 is treated with a solution of stannous chloride which contains
a little stannic chloride,235 a purple-red, flocculent precipitate—the "purple of Cassius"—is formed;
in extremely dilute solutions only a purple-red liquid236 may be produced. If the precipitate is
collected on a filter, washed with water and then treated, on the filter, with a few drops of ammonium
hydroxide solution and some water (exp.), it is seen to dissolve and a beautifully colored liquid, of
purple-red or claret-red tint, is found to pass through the filter. In spite of the extreme insolubility of
metallic gold, the red ammoniacal solution (as well as the first red precipitate) contains metallic
gold, in the colloidal condition, formed according to the equation237 2 Au3+ + 3 Sn2+ ⥂ 2 Au + 3
Sn4+. By the careful [p127] reduction of gold chloride with phosphorus,238 or with formaldehyde in
dilute, slightly alkaline solution,239 brilliant red liquids, containing metallic gold in the colloidal
condition, may be prepared, which remain clear for months. The passage of an electric current, in the
form of an arc, between two gold points under pure water produces similar red liquids240 containing
metallic gold.
Colloidal Silver.
—Further, although silver is likewise an extremely insoluble metal, solid preparations of silver are
known which, on treatment with water, form apparently perfectly clear (opalescent) liquids or
solutions (exp.).241 From these silver is not deposited, even in the course of months. If a little of the
black solid is heated on the lid of a porcelain crucible, the metal may be readily recognized by its
white color and luster.242

Colloidal Ferric Hydroxide.
—Further, if to a solution of ferric chloride an excess of ammonium
hydroxide is added, the well-known, rust-red precipitate of very difficultly
soluble ferric hydroxide is formed: FeCl3 + 3 NH4OH ⥂ Fe(OH)3 ↓ + 3
NH4Cl. The precipitate is so insoluble that it is a favorable form for
precipitating the ferric-ion in quantitative analysis. If, however, a solution
of ferric chloride be carefully neutralized with ammonium carbonate243 and
be then placed in a vessel (called a dialyzer), in such a way that it is
separated, by an animal membrane or by parchment, from pure water, ferric
hydroxide is obtained in an apparently soluble form. The ammonium
chloride, as well as hydrochloric acid which is formed by the
decomposition of the chloride by water (FeCl3 + 3 HOH ⇄ Fe(OH)3 + 3
HCl, see Chapter X), are found to pass through the membrane readily, while
the ferric hydroxide produced does not pass through such [p128]

membranes244 and is retained in the dialyzer without forming a precipitate.
The acid and salt pass through such membranes in either direction, indeed,
but flow mainly from their solutions of higher concentration to those of
lower concentration. The water on the outside of the dialyzer is, therefore,
continuously renewed, in order to insure a concentration of these substances
on the outside of the dialyzer lower than that within it. As the hydrochloric
acid is thus removed through the membrane, the condition of equilibrium
between the ferric chloride, water, ferric hydroxide and acid is continuously
disturbed and, in the reversible reaction, expressed in the above equation,
the action is carried more and more towards the right, and more and more
ferric hydroxide is formed. The salt is, at last, practically all decomposed
and a clear red opalescent liquid, which contains ferric hydroxide in
enormous excess beyond its solubility in water, is left in the dialyzer.
Exactly as in the case of the other liquids discussed above, in which very
insoluble substances appear to be in solution far beyond their usual degree
of solubility, so the present liquid does not show the behavior of a
supersaturated solution and it is said to contain the ferric hydroxide in the
colloidal condition.245
Solution Theory of the Colloidal Condition.
—For many years the belief was prevalent among chemists that these
liquids represent true solutions of difficultly soluble substances, in the form
of soluble (colloidal) modifications of the substances. Like ordinary [p129]
solutions, the liquids are found, indeed, to show a certain osmotic pressure,
but, unlike ordinary solutions, the osmotic pressure is exceedingly small in
proportion to the quantity of the substance present. Since the osmotic
pressure is proportional to the number of molecules in unit volume (Chap.
II), this observation proved the presence of a relatively very small number
of molecules in solution, and chemists were led to assign, therefore, a
relatively very great weight to each. Hence, the data led to the assumption
that the colloidal modifications consist of molecules of very large,

sometimes enormous molecular weight. From the fact that colloids are
unable to traverse membranes, through which crystalloids readily pass,
Graham had reached the same conclusion.
The following measurements of osmotic pressures may be given:246
Osmotic
Concentration
Substance. Pressure.
Per cent.
Cm. Hg.
Gum arabic 1 6.9
Dextrin 1 16.6
As2S3 4 1.7
Fe(OH)3 1.1 0.8
2.0 2.8
3.0 5.6
5.3 12.5
8.9 22.6
The last results, obtained with special care to exclude soluble impurities, are more reliable than the
older results on gum arabic and dextrin. For the purpose of comparison it may be said that a 1%
solution of cane sugar (molecular weight = 342) has an osmotic pressure of 53 cm. Hg at 18°, a 5%
solution a pressure of 265 cm.

The Suspension Theory of the Colloidal Condition.
—On the other hand, a number of chemists considered the colloidal liquids
to represent, essentially, suspensions of minute solid particles247 in an
extreme state of subdivision, or, in some instances, perfect [p130] emulsions
of difficultly miscible liquids.248 Observations with the ultramicroscope249
finally proved,250 beyond question, the correctness of this theory of the
colloidal condition. Thus, the colloidal "solutions" of gold are seen to
contain minute solid particles of gold, the diameter of which varies251
between (approximately) 60 µµ and 6 µµ and the color of which varies with
their size. Still finer subdivisions, the diameter of whose particles cannot be
measured, are also found to exist. Colloidal silver, platinum, arsenious
sulphide and other colloidal metals and sulphides have also been shown, in
the same way, to be suspensions of solid particles.
The General Character and the Definition of the Colloidal Condition.

—Recent investigations have shown that the colloidal condition is possible,
not only for a limited class of substances, but is, in general, possible for all
substances.252 Thus, even such an eminently crystallizable, readily soluble
(in water) substance as sodium chloride may be obtained, under certain
conditions, in colloidal suspension in benzene,253 in which it is insoluble.
For our purposes it will be sufficient to define the colloidal condition, on
the basis of these results, as the condition of an insoluble substance in
which, as far as ordinary observation and the common methods for
separation of heterogeneous phases (filtration, sedimentation, etc.) are
concerned, the substance appears to be present in a homogeneous clear
solution, whereas in reality it is present in a heterogeneous mixture. An
extremely finely divided solid suspended in a liquid, or an emulsified liquid
suspended in another liquid, are the most common types254 of such
mixtures. [p131]
Relations to Analysis.
—Since the colloidal condition of insoluble substances interferes with the
precipitation of the latter, and with their separation by filtration from the
liquids in which they are suspended, and since the majority of the
separations and tests of analytical chemistry depend on the successful
formation of precipitates and on their successful separation by filtration,
analytical chemistry is primarily255 concerned with the colloidal condition
as a condition that is to be avoided as completely as possible in order to
escape error. In other fields of chemistry, notably in physiological chemistry
and in some branches of technical chemistry, it is a source of effects so
momentous and specific that a new branch of chemistry, the chemistry of
colloids,256 has grown out of the investigations of its relations and laws.
The present discussion will be limited to the presentation of such of the
fundamental facts concerning the colloidal condition as are of chief
importance in analytical work.257
Electrical Conditions of Colloids.

—One of the most important discoveries made on colloids is the
observation that the suspended particles of a large class of colloids carry
electrical charges, so that there is a potential difference between the
particles and the liquid in which the suspension exists.258 Thus, in the
colloidal suspension of arsenious sulphide (prepared as described on p. 125)
the sulphide particles carry negative charges, and the solution bathing them
is positive. Conversely, colloidal ferric hydroxide (p. 127), in water, is
charged with positive, the water with negative, electricity. The existence and
character of these charges may be readily demonstrated by the passage of a
current of electricity through the colloidal suspension in U tubes (exp.).259
Colloidal arsenious sulphide is found to migrate toward the positive pole,
ferric hydroxide [p132] to the negative pole, the movement being easily
followed by the color of the suspended particles.
The following colloids, which are of interest in analytical chemistry, are
found to carry a negative charge in pure water: Colloidal acids (silicic,
stannic), sulphides (As2S3, As2S5, CdS, etc.), salts (AgI, AgCl) and metals
(Au, Pt, Ag). It is noteworthy that the suspensions of finely divided clay,
kaolin, quartz, carbon, carry the same charge as these colloidal suspensions.
On the other hand, metal hydroxides (ferric, aluminium, chromic), and basic
substances in general, carry positive charges.
On the other hand, the colloids of one important group are found to be
almost without any electric charges;260 the passage of an electric current
through their suspensions has little or no effect on them. Perfectly neutral
albumen and gelatine are common representatives of this group.
The charge on a colloid seems to be liable to variation with the nature of the liquid in which it is
suspended. Colloidal platinum in water is negative, in a mixture of water and alcohol, positive.[2] Of
peculiar interest and importance is the fact that some colloids change the character of their charge
when the liquid, in which they are suspended, is made to pass from an acid to an alkaline condition,
and vice versa.261 For instance, albumen262, colloidal silicic acid263 and colloidal stannic acid264
are negative in alkaline liquids, positive in acid. The relation of these facts to the chemical nature of
the substances will be discussed presently.
The Source of the Electrical Charges on Colloids.

—Different views are held as to the source of electrification of colloidal suspensions. Only the two
views of most direct interest in analysis can be considered here. In the first place, it is possible that
partial ionization of the colloidal suspension produces the electrical charge. It is a significant fact
that basic colloids (metal hydroxides, some basic dyes) receive a positive charge, such as would be
left, if they were slightly ionized as bases (or salts of bases) and insoluble (suspended) [p133] positive
ions were retained by the particles. That would be the case, for instance, if particles of colloidal ferric
hydroxide, [Fe(OH)3]x, sent a few hydroxide ions into solution and the suspended particles included
positive insoluble ions. Acid colloids, on the other hand, assume a negative charge, as would be
expected from this point of view. Then, the behavior of silicic acid is particularly suggestive; in
alkaline or slightly acid liquids, in which its ionization as a weak acid is favored or predominant
(Chapter X), it carries a negative charge, the charge that would be left on it, if it ionized, in part, as an
acid or its salt. Silicic acid shows some slight tendency to ionize also as a base (see Chapter X) and
the basic form of ionization would be favored by the presence of a strong acid (Chapter X). Colloidal
silicic acid, as stated above, changes its charge from negative to positive as the solution passes from
an alkaline to a (strong) acid reaction,265 just as if, in the acid liquid, it ionized slightly as a base
(salt of a base) and retained a difficultly soluble positive ion. Albumen, which has the property of
being both a base and an acid,266 shows the same change of charge267 in the colloidal condition and
the change has been ascribed268 to the change of basic and acid functions.
According to the other of the two theories, here considered, the electrification of the colloid may
result from what is known as contact or surface electricity.269 At the surface of two different
substances there is always a potential difference.270 In the case of finely divided suspensions, like
the colloids, the contact surfaces are enormous, as compared with the surfaces involved in ordinary
contact. Whether metals (Au, Pt, Ag) owe their charges to simple contact effects or to their (minimal)
tendency to ionize (Chapters XIV and XV) is not known. In fact, no exact knowledge of the source of
electrification of any colloid has yet been obtained.

Precipitation of Colloids by Electrolytes and by Colloids.
—Substances in the colloidal condition, which carry an electrical charge,
are readily precipitated by the addition of electrolytes to the colloidal
suspensions (see the behavior of arsenious sulphide, p. 126). Negatively
charged colloids are precipitated by the action of positive ions, positively
charged colloids by the action of negative ions (Hardy's rule271). The
precipitated colloid carries [p134] with it a part of the precipitating ion272
(adsorption) and the weights of ions, carried down by a given quantity of a
given colloid, are proportional to the equivalent weights of the ions.273 The
precipitation thus appears to be intimately associated with the neutralization

of the charge on the colloid. In accordance with this conclusion, it has also
been found that a colloid may be precipitated by a colloid carrying the
opposite charge.274 Thus, colloidal arsenious sulphide, carrying a negative
charge, and colloidal ferric hydroxide, carrying a positive charge, mutually
precipitate each other (exp.275).
The purple precipitate (purple of Cassius), which is formed when stannous chloride is added to
gold chloride (p. 126), contains colloidal gold,276 which, in suspension, is charged with negative
electricity, and colloidal stannic acid,276 which in acid solution, presumably, carries a positive
charge277: these two colloids mutually precipitate each other in the presence of hydrochloric
acid.278
When the precipitate is treated with an alkaline liquid (ammonium hydroxide solution), the charge
on the stannic acid becomes negative, both colloids acquire the same charge and the precipitate
dissolves, to form the beautifully tinted suspensions of colloidal gold (p. 126). In this condition the
colloids (gold and stannic acid) are sensitive to precipitating electrolytes, and the solution is more
sensitive to a mixture of magnesium nitrate and ammonium nitrate than to ammonium nitrate alone
(exp.), as is to be expected from a negative suspension (see below).
The characteristic difference in behavior between ortho-, pyro- and metaphosphoric acids toward
albumen, which is used as a characteristic analytical test to distinguish metaphosphoric acid from the
other two acids,279 appears to be due to similar relations280: metaphosphoric acid, which
precipitates (coagulates) albumen, is colloidal, ortho- and pyrophosphoric acids are not. The [p135]
coagulation seems to be the result of the union of the negative colloid metaphosphoric acid (or a
complex negative colloidal ion thereof) with the positive colloid albumen (or a positive colloidal ion
thereof).

The Precipitating Power of Electrolytes and the Valence of their Ions.
—The complete precipitation of colloids, which carry electric charges,
depends on the concentrations of the colloid and the electrolyte; in this
connection the important observation has been made that the precipitating
power of electrolytes increases decidedly with the valence of the
precipitating ions (H. Schulze's rule281). Bivalent ions are far more efficient
than univalent; trivalent, in turn, still more effective than bivalent.
Thus, colloidal As2S3, carrying a negative charge, is precipitated by the positive ions of added
electrolytes. The addition of a few drops of a molar solution of ammonium nitrate (the precipitating
ion is NH4+) to 20 c.c. of the colloidal suspension282 produces a slight precipitate; complete
precipitation requires 3.5 to 3.6 c.c. of the ammonium nitrate solution.283 Only 0.06 c.c. of an

equivalent solution284 of magnesium nitrate (the precipitating ion is Mg2+) is required, and as little
as 0.015 c.c. of an equivalent solution of aluminium nitrate285 (the precipitating ion is Al3+) has the
same effect (exp.). An increase in valence of the negative ion, which is not the precipitating ion in
this case, does not affect the result appreciably: 3.5 c.c. of a solution286 of ammonium sulphate,
(NH4)2SO4, equivalent to the solution of NH4NO3, is also required for the complete precipitation of
the colloidal As2S3 (exp.), although the one contains the univalent ion, NO3−, the other the bivalent
ion, SO42−.
Conversely, a positively charged colloid, like ferric hydroxide, may be precipitated by much
smaller quantities287 of bivalent negative ions than of univalent ions, etc. [p136]

Nonprecipitation of Nonelectrified Colloids by Electrolytes.
—Colloids which do not carry any electric charges of moment (see p. 132)
are also not precipitated by dilute solutions of electrolytes. Heat, the
addition of concentrated salt solutions in great excess (whose effect is
probably a dehydrating one), or of other solvents (e.g. alcohol), are the
agents most commonly used to effect coagulation in such cases.
Protective Action of Colloids on Other Colloids.
—Colloids, particularly such as are not sensitive to precipitation by
electrolytes, increase in a remarkable degree the stability of the colloidal
condition of substances, that carry electrical charges and, ordinarily, would
be very sensitive to precipitation. Thus, small quantities of albumen are
used to render colloidal silver preparations more stable. Tannic acid,
gelatine and albumen and related compounds are frequently used as such
protective agents. It is supposed that they form protecting films around the
colloidal particles.
Applications in Analysis.
—From the preceding discussion we may now draw the following
conclusions concerning the consideration that is to be given to the colloidal
condition as a factor in qualitative analysis. The absence of electrolytes in
solution must favor the production of the colloidal condition, which would
result in the nonprecipitation or "solution" and consequent loss of
substances, which it is intended to precipitate. Such absence of electrolytes

in solution is most likely to be met with, in the first place, in the washing
out of precipitates. When the larger part of the mother liquor is washed
away by the use of pure water, many precipitates show a tendency to "run
through a filter," forming colloidal suspensions in the pure water in the
filter and being again precipitated as the colloid mixes with the electrolytes
in the filtrate. Precipitates, showing this tendency to assume the colloidal
condition, are therefore washed with appropriate solutions of electrolytes,
rather than with pure water. Ammonium nitrate solution is most frequently
available in qualitative analysis, because neither the ammonium-ion nor the
nitrate-ion tends to interfere with the subsequent examination of the
solution. When chloride-ion is not likely to interfere, ammonium chloride
may be used. Thus, the sulphides of the arsenic, copper and zinc groups are
washed with solutions containing ammonium nitrate (the [p137] chloride may
be used for the zinc group288) rather than with pure water (or pure hydrogen
sulphide water288). In quantitative analysis, aluminium hydroxide is also
washed with ammonium nitrate solution, silver chloride with acidulated
(nitric acid) water, lead sulphate with dilute sulphuric acid, etc.
In the second place, if precipitations are attempted either in rather dilute
solutions or in solutions of little ionized substances (arsenious acid and
hydrogen sulphide), the addition of an electrolyte is frequently required to
insure precipitation. Thus, the presence of ammonium chloride, or nitrate,
in excess, is helpful in the precipitation of the sulphides of the zinc group;
the addition of hydrochloric acid (or other electrolyte) is required to effect
the precipitation of arsenious sulphide from a solution of the oxide (p. 126).
In the next place, account must be taken, in analytical work, of the fact
that colloids carry down with them the precipitating ion by which they are
coagulated, a fact which may lead to the loss of ions which, it is intended,
should be kept in solution. To a certain extent, this loss may also be avoided
by insuring the presence of electrolytes (acids, ammonium salts) in
sufficient concentration to cause the coagulation without the aid of the ions

which, it is intended, should not be precipitated. In view of the much
weaker precipitating power of univalent ions (of hydrochloric acid,
ammonium nitrate and chloride), as compared with that of polyvalent ions,
which may be present, the acid and ammonium salts must not be used in too
small concentrations. In quantitative analysis, when conditions permit it,
ammonium or sodium sulphate is frequently substituted for the ammonium
salts of the univalent monobasic acids. The washing of the precipitated
colloid with such salt solutions gradually removes289 the ions which are
precipitated with the colloid and forms a further safeguard against their
loss. But this source of loss is avoided only with great difficulty and is
seldom absolutely removed.
Finally, the presence of protective colloids, especially of the [p138]
gelatine and albumen type, may interfere so decidedly with the common
precipitation tests for ions, that their destruction is imperative, before these
tests can be applied with any degree of confidence. Thus, the mixing of
solutions (0.1 molar) of silver nitrate and hydrochloric acid, each containing
one per cent of gelatine, fails to produce the ordinary, characteristic
precipitate290 of silver chloride, the reaction which is used to determine the
presence of the silver-ion in systematic analysis.
The mixture is opalescent and, in reflected light, looks opaque-white; on somewhat prolonged
standing a white milk is produced, but no precipitate. When the mixture is boiled, the same deep
white milk is formed, but no coagulated precipitate, the mixture running unchanged through a filter.
Hydrogen sulphide converts the mixture into a similar suspension of the black sulphide.

Chapter VII Footnotes
[227] The ratio is affected somewhat by the fineness of division of liquids and solids as a result of
surface tension phenomena, as explained below.
[228] An aqueous solution of iodine and potassium iodide shaken with chloroform gives similar
results, and the difference in color between the two layers is an advantage for a lecture
experiment. But the iodine is partially combined with the iodide, according to KI + I2 ⇄ KI3, or I−
+ I2 ⇄ I3−, and the theoretical relations are not so simple as for bromine in aqueous and
chloroform solutions.
[229] To accelerate the action, the mixture is shaken vigorously. After the separation of the layers,
the bromine may be recognized in the aqueous layer by its color, or by the addition of potassium
iodide (liberation of iodine).
[230] [Br]aq. and [Br]ch. are used to express the actual concentrations at any given moment we
wish to consider, for instance at the moment equilibrium is reached. The ratio k2 / k1 for any
substance S is found to be equal to the ratio of the solubilities of the substance in the two solvents.
That it must be so can be proved by applying the law of physical equilibrium to the mixed
solvents in contact with an excess of the substance, i.e. to its saturated solutions (see below).
[231] Similar relations hold for the condition of equilibrium between a liquid and its vapor.
[232] Curie, Bull. Soc. Min., 8, 145 (1885); Ostwald, Grundlagen der Anal. Chem., p. 22 (1894).
[233] Hulett, Z. Phys. Chem., 37, 384 (1901). See also Ostwald, ibid., 34, 495 (1900), on the
solubilities of finely divided mercuric oxide ("yellow oxide") and of larger crystals ("red oxide").
[234] A 1 / 1000 solution of AuCl3, 2 aq., and a 1.2 / 1000 solution of SnCl2, 2 aq., may be used
conveniently. When equal volumes of the solutions are mixed, the desired precipitate is formed.
[235] Stannous chloride is usually sufficiently contaminated with stannic salt. Add a few drops of
bromine- or chlorine-water to 100 c.c. of a pure stannous chloride solution.
[236] The action is an exceedingly sensitive qualitative test for gold. By a modification of the test
Donau was able to detect as little as 2E−9 gram of gold (Monatshefte f. Chem., 25, 545 (1904)).
[237] The nature of the reduction reaction is discussed in Chapters XIV and XV.
[238] Faraday, Proc. Royal Soc., 8, 356 (1857), Phil. Mag. (4), 13, 401 (1857) (Stud.).
[239] Zsigmondy, Liebig's Annalen, 301, 30 (1898).
[240] Bredig, Z. f. Elektrochem., 4, 514, 547 (1898), and Anorganische Fermente, 1901. Colloidal
preparations of platinum, silver and many other metals may be prepared in the same way. In ether,

colloidal preparations of the alkali metals may be made (Svedberg, Ber. d. chem. Ges., 38, 3616
(1905), 39, 1708 (1906)).
[241] Argentum Credé may be conveniently used. It contains, with the metallic silver, a small
percentage of albumen, which is added for reasons discussed below. Brown solutions are formed
at once.
[242] First a thin film of black carbon is produced round the metal, then the latter appears in the
form of a filigree of silver.
[243] For details of the preparation, see A. A. Noyes, J. Amer. Chem. Soc., 27, 94 (1905).
[244] This process of separation of substances, which do not pass through membranes, from such
as do, is called dialysis. It was first used by Graham, Trans. Royal Soc., London, 151, 183–224
(1861) (Stud.).
[245] Graham made the first extended investigations in this field: Trans. Royal Soc., 151, 183
(1861); J. Chem. Soc. (London), 17, 318 (1864) (Stud.). He found that amorphous, gelatinous
bodies like ferric hydroxide, aluminium hydroxide, silicic acid, gelatine, glue, dextrin, caramel,
albumen and similar bodies do not pass through membranes and may be obtained by dialysis in
the colloidal condition. Such substances were called "colloids" by Graham, the name referring to
the Latin for gelatine. Substances which pass through membranes readily were found by Graham
to resemble in behavior such bodies as are crystallizable when solid; such compounds were
classified by him as "crystalloids." That liquids containing substances in the colloidal condition
(e.g. arsenious sulphide, gold, silver and many other substances) may be prepared by methods
other than dialysis, was found later by many investigators and, in a few cases, previous to
Graham, e.g. by Faraday, loc. cit. A brief history of the chemistry of colloids is found as an
introduction to Wo. Ostwald's Kolloidchemie, pp. 1–63 (1909).
[246] Cf. Wo. Ostwald, loc. cit., p. 193.
[247] Before Graham's time, and for the few colloidal liquids then known, this view was held by
such men as J. B. Richter, Berzelius and Faraday (loc. cit.) (cf. Wo. Ostwald, loc. cit., p. 19). The
first extended experimental investigation in support of it was made by Barus and Schneider, Z.
phys. Chem., 8, 278 (1891). Bredig was also an early and consistent champion of this view (vide
his Anorganische Fermente, 1901).
[248] Cf. Wo. Ostwald, loc. cit., pp. 102–114. Graham considered "colloidal silicic acid a liquid
miscible with water in all proportions." According to modern ideas, no true miscibility exists, but
a suspension or emulsion is formed (see Ostwald, p. 237).
[249] Siedentopf and Zsigmondy, Drude's Annalen, 10, 1 (1903). Zsigmondy, Colloids and the
Ultramicroscope (1909), Chapter V.
[250] Zsigmondy, Z. für Elektrochem., 8, 684 (1902); Siedentopf and Zsigmondy, loc. cit.
[251] Zsigmondy, loc. cit., p. 161. A µµ is 1E−6 mm. The hydrogen molecule is considered to
have a diameter of 0.1 µµ (O. E. Meyer), the alcohol molecule one of 0.5 µµ (Zsigmondy, loc.

cit., plate IV, p. 157).
[252] Weimarn, Chem. Zentralblatt, 1907, II, p. 1293.
[253] Paal, Ber. d. chem. Ges., 39, 1436, 2859 (1906).
[254] Other varieties of heterogeneous colloidal mixtures are tabulated by Wo. Ostwald, loc. cit.,
p. 96.
[255] The "Cassius' purple" test for gold is an instance where the colloidal condition is used in
analysis for a positive test. See Wo. Ostwald, loc. cit., p. 68, for other, similar applications for
positive tests.
[256] Vide Wo. Ostwald's Kolloidchemie, 1909, and the references given by Noyes, loc. cit., p. 86.
[257] A general discussion of the preparation and properties of colloidal mixtures is given by A.
A. Noyes, J. Am. Chem. Soc., 27, 86–104 (1905) (Stud.).
[258] Picton and Linder, J. Chem. Soc. (London), 61, 160 (1892), 67, 63 (1895), 71, 568 (1897),
etc., and others. Wo. Ostwald, loc. cit., p. 240, gives a list of references.
[259] The arrangement of the experiment is described by Noyes, loc. cit., p. 98.
[260] Cf. Wo. Ostwald, loc. cit., p. 108. Billitzer has found that gelatine is positive in acid
solution, negative in alkaline, Z. phys. Chem., 51, 147 (1905). The charges are, however,
relatively small ones.
[261] Billitzer, Z. f. Elektrochem., 8, 638 (1902). This is probably true of all amphoteric colloids
(Chapter X); it is also true of many other substances, which are not pronouncedly amphoteric. (Cf.
Perrin, Comp. rend., 136, 1388 (1903); Billitzer, Z. phys. Chem., 51, 157 (1905).)
[262] Hardy, J. of Physiology, 24, 288 (1899); Z. phys. Chem., 33, 387 (1900).
[263] Billitzer, loc. cit., p. 159; Müller's Allgemeine Chemie der Kolloide, 1907, p. 79.
[264] See below, p. 134.
[265] In a slightly acid solution colloidal silicic acid is negatively charged; in a strong acid
solution, positively—a relation which agrees with its predominantly acid character.
[266] The general class of substances, showing both basic and acid properties, of which albumen
is a derivative, is described in a footnote on glycocoll, Chapter X, p. 188.
[267] Hardy, loc. cit.
[268] J. Loeb, University of California Publications, Physiology, 2, 149 (1904).
[269] Very little is known about the nature of contact electricity. It is even doubtful whether it is

different, in principle, from ionization.
[270] W. Ostwald, Lehrbuch der Chem., 2, (1) 553 (1903).
[271] Hardy, Proc. Royal Soc., 66, 110 (1899); Z. phys. Chem., 33, 391 (1900).
[272] Picton and Linder, J. Chem. Soc. (London), 67, 63 (1895).
[273] Whitney and Ober, J. Am. Chem. Soc., 23, 852–856 (1901) (Stud.).
[274] Picton and Linder, loc. cit. 71, 572 (1897); Lottermoser, Anorganische Kolloide, p. 76;
Biltz, Ber. d. chem. Ges., 37, 1095 (1904).
[275] Precipitation is complete only when the colloids are used in the proportions required to
neutralize each other's charges [Billitzer, Z. phys. Chem., 51, 140 (1905)]. The proportions to be
used must be determined in each case, most simply by trial (Noyes, loc. cit., p. 101), but
quantitative methods for determining the charges, by titration, are also known (cf. Billitzer, loc.
cit.).
[276] E. A. Schneider, Z. anorg. Chem., 5, 80 (1894).
[277] See the above discussion on silicic acid. Stannic acid has a greater tendency to form a base
than has silicic acid.
[278] Zsigmondy, Liebig's Annalen, 301, 361 (1898).
[279] Cf. Fresenius, p. 334, or Smith's Inorganic Chemistry, p. 468.
[280] Mylius, Ber. d. chem. Ges., 36, 775 (1903); Biltz, ibid., 37, 1116 (1904).
[281] J. für prakt. Chem., 25, 431 (1882).
[282] The suspension used is prepared by saturating, with hydrogen sulphide, an aqueous solution
of arsenious oxide. The latter is saturated on a steam bath, cooled to 20°, filtered and diluted with
an equal volume of water before it is used.
[283] Eight grams of NH4NO3 per 100 c.c.

[284] 0.6 c.c. of a tenth-normal solution is used, containing 1.28 gram Mg(NO3)2, 6 aq., in 100
c.c. Precipitation was found to be incomplete with 0.5 c.c.
[285] 0.15 c.c. of a tenth-normal solution is used, containing 1.2 gram Al(NO3)3, 4 aq., in 100 c.c.
Precipitation was found to be incomplete with 0.1 c.c. of the solution.
[286] 3.3 grams (NH4)2SO4 in 100 c.c.

[287] Freundlich found, for instance, that NaCl, KCl, BaCl2, in equivalent concentrations, had
practically the same effect on colloidal ferric hydroxide, but only one-fortieth as much of a
sulphate (the precipitating ion is SO42− versus Cl−) was required; Z. phys. Chem., 44, 129 (1903).

[288] For other reasons (e.g. to prevent oxidation of the sulphides), hydrogen sulphide is also
used in the solution for washing the arsenic group, and ammonium sulphide in that for the zinc

group (see Lab. Manual, pp. 101 and 110).
[289] Picton and Linder, loc. cit., and Whitney and Ober, loc. cit.
[290] A. A. Noyes describes a similar experiment with sodium chloride and silver nitrate, loc. cit.

CHAPTER VIII
SIMULTANEOUS CHEMICAL AND PHYSICAL
EQUILIBRIUM.—THE SOLUBILITY- OR ION-PRODUCT.

[p139] TOC

It frequently happens that we have to deal, simultaneously, with
conditions of chemical and of physical equilibrium, obtaining in the same
system. For instance, a gas like carbon dioxide, in contact with its saturated
solution in water, is in equilibrium with the dissolved carbon dioxide, and
this, in turn, is in equilibrium with its hydrate, carbonic acid. A substance
may be distributed between two solvents and show a different molecular
weight in the two (see p. 18); it may exist, in the one, primarily in
polymeric form, and only to a slight extent in the simple form, the two
forms being in equilibrium (chemical equilibrium). In the other solvent, it
may exist only in its simple molecular form, and this will be in equilibrium
with the same simple molecular form in the first solvent (physical
equilibrium). In matters dealing with the solubility of electrolytes in water,
and, therefore, in questions of their precipitation or solution, such
simultaneous conditions of chemical and physical equilibrium are
constantly occurring. Since qualitative analysis deals to a very considerable
extent with just such precipitates of salts, acids and bases, these cases are of
particular importance to us.
Earlier Derivation of the Solubility-Product Principle.
—A very simple relation was derived by Nernst291 for the combined
conditions of chemical and of physical equilibrium, where difficultly
soluble electrolytes (precipitates) were concerned. We shall develop the
relation first for a simple salt, such as silver acetate.

When water is added to solid silver acetate, the salt will dissolve. If an
excess of the acetate is used, equilibrium will result between the solid salt
and its solution, when the solution is saturated at the temperature used. As
the salt dissolves, it is more or less ionized, and in the saturated solution we
have a [p140] condition of chemical equilibrium between the salt and its ions:

CH3COOAg ⇄ CH3COO− + Ag+. (1)
If the law of chemical equilibrium is applied to this reversible action, we
have (p. 98)
[CH3COO−] × [Ag+] / [CH3COOAg] = KIonization. I
The nonionized silver acetate is present in two phases, in the solid phase
and also in solution:
CH3COOAg ↓ ⇄ CH3COOAg. (2)
Applying the law of physical equilibrium to this system, we have further (p.
121)
[CH3COOAg] / [CH3COOAg]solid = K. II
The concentration of a pure solid, as we have seen, may be considered a
constant at a given temperature. Consequently, if we consider the question
of the size of the solid particles as a minor factor and negligible, we shall
conclude, that, for saturated solutions of silver acetate, the concentration of
the solid silver acetate being a constant, the concentration of the nonionized
or molecular silver acetate, the first term of our constant ratio II, must also
have some definite, constant value at a given temperature. We may call this
concentration the "molecular solubility" of silver acetate and may put
[CH3COOAg] = Kmol. sol. III
for a saturated solution of silver acetate in water at the given temperature.
Now, since the concentration of the nonionized silver acetate,
[CH3COOAg], in the saturated solution also forms the second term of

equation I, representing the condition of chemical equilibrium between the
acetate and its ions, we obtain, by combining I and III,
[CH3COO−] × [Ag+] = KIonization × Kmol. sol. =
KSolubility-Product. IV
Further, if the assumption is made that the presence of foreign
electrolytes, in not too concentrated solutions, does not affect either the
molecular solubility, Kmol. sol., of silver acetate or its tendency to ionize—as
expressed in KIonization—then, the [p141] relation, which has been developed,
would hold for saturated aqueous solutions of silver acetate in the presence
of foreign electrolytes, as well as for a saturated, pure, aqueous solution. A
single, simple equation would thus express the conditions for simultaneous
chemical and physical equilibrium between a difficultly soluble ionogen, of
the type of silver acetate, and its saturated solutions, at a given temperature,
in the presence or the absence of foreign electrolytes.
The Solubility- or Ion-Product Principle.
—We may formulate this important conclusion by stating, that, in saturated
solutions of silver acetate, the product of the concentrations of its ions has a
constant value at a given temperature. Analogous relations may be
developed for the saturated solutions of other difficultly soluble ionogens.
The constant has been called the solubility-product constant or the ion-
product constant of the ionogen. For salts like lead iodide PbI2, silver
chromate Ag2CrO4, etc., each molecule of which forms more than one of a
given ion, the concentration of such an ion is raised, in the solubility-
product, to the power corresponding to the number of ions of this kind
formed from a single molecule of the electrolyte.292 Thus, lead iodide
ionizes according to the equation PbI2 ⇄ Pb2+ + 2 I− and, for a saturated
solution of lead iodide293 at a given temperature, [Pb2+] × [I−]2 = K. For
silver chromate, ionizing according to the equation Ag2CrO4 ⇄ 2 Ag+ +
CrO42−, the form of the solubility-product equation is [Ag+]2 × [CrO42−] =

K. In general, for a saturated solution of a difficultly soluble salt at a given
temperature the product of the ion concentrations, each raised to the power
corresponding to the number of that kind of ion formed from the ionization
of one molecule of the salt, is a constant.
Criticism of the Derivation of the Principle.
—Nernst developed this important relation in 1889, shortly after the theory
of ionization was formulated. Since then, however, the soundness of the
theoretical development, on which it was based, has been rendered open to
question in a way that could hardly have been foreseen at that early stage in
the development of the theory of ionization. In the first place, it is known
now that the ionization of easily ionizing substances (strong electrolytes)
does [p142] not conform to the law of chemical equilibrium (vide p. 108); as
far as our present knowledge goes, the ratio in equation I is not a constant,
but grows larger with an increasing total concentration of good electrolytes.
In the present case, this total concentration may be increased by the
introduction of foreign salts.294 In the second place, the second fundamental
principle used, the principle of the constant solubility of the dissolved
molecular or non-ionized salt, as expressed in equation III, was questioned
and disproved by Arrhenius in 1899. The molecular solubility depends on
the total concentration of salts in the solution and, in general, decreases
with increasing concentration of the total dissolved salts. This result does
not invalidate the law of physical equilibrium; it merely means that the
presence of salts, especially in appreciable quantities, modifies the nature of
the solvent and changes its dissolving power, much as we have different
dissolving power shown by different pure solvents, such as water and
alcohol.
It appears, however, that while the soundness of this theoretical
development of the relations expressed by the solubility-product must be
questioned, nevertheless as a matter of experiment, the product of the ion
concentrations of a difficultly soluble salt is found, in dilute solutions, to be

a constant, or sufficiently close to a constant to satisfy all but the most
rigorous requirements.295
It is, in fact, quite evident, that a decreasing value for the second term of
the ratio I—namely, for [CH3COOAg], the molecular solubility of the salt
—as the total concentration of the electrolytes present increases, together
with an increasing value for the whole ratio I under the same conditions,
are not incompatible with a constant value of the first term of the ratio. That
is, the product of the ion concentrations, [CH3COO−] × [Ag+], may well
remain constant (equation IV), or approximately constant, in dilute salt
solutions, even if equations I and III do not hold for salt solutions. [p143]
Whether in the case of all difficultly soluble salts, as the total salt
concentration increases, the increasing values of the chemical equilibrium
ratio (equation I) will be so nicely balanced by the decreasing values of the
molecular solubility, that the first term of the first ratio (the solubility-
product) will always be constant, is a question demanding further extended
investigation.296 The range of the investigation must be extensive, because
it must include several other classes297 of salts (e.g. Me2X, MeY2, etc.), for
which the first equation has a different form; for instance, for Me2X,

[Me+]2 × [X2−] / [Me2X] = K.
For the present we must remain content with the result of the past
investigations and consider the principle of the constant solubility-product
to be essentially an empirical one. It is an extremely convenient
condensation, into a very simple mathematical form, of the main factors
involved in the precipitation and solution of difficultly soluble salts, acids,
and bases. It should be used with due knowledge of its character and
limitations.
Washburn298 derives the principle of the constancy of the solubility-product, without involving in
his derivation the relation between ions and nonionized molecules—a relation which, as was stated
above, deviates from the law of chemical equilibrium. The deviation, it will be recalled (p. 109), is
generally supposed to be due to the fact that the fundamental kinetic assumption which must be made

to derive the law of chemical equilibrium from the kinetic theory, the assumption that there should be
none but negligible forces of attraction and repulsion between the molecules (of a gas or solute)
which are in equilibrium, is not fulfilled in the case of solutions of strong electrolytes (p. 109).
According to Washburn, if it is assumed that the ions of an electrolyte fulfill this fundamental
condition and that only the nonionized molecules do not—the latter causing the deviation from the
law of chemical equilibrium—then the principle of the solubility-product constant follows.299 He
sees an approximate confirmation of the assumption made, in the fact that the principle is found,
empirically, to be true, and that other relations, developed on the basis of the same assumption, agree
with the observations made. [p144]
This theoretical derivation of the principle, like the derivations of the law of chemical equilibrium
and of all our laws of dilute solutions, assumes300 that the nature of the solvent, and consequently of
the solution-process, is not changed by added substances, for instance by an excess of the
precipitating ionogen. There can be no question, however, that the nature of the solvent must change,
as a continuous function, by the addition of electrolytes to solutions. The changed solubilities of inert
gases in salt solutions,301 and a mass of other evidence,302 lead to this conclusion. The addition of a
half mole of sodium chloride to a liter of water reduces the dissolving power of the liquid towards
oxygen at 25° by 15%, i.e. by 30% per mole of salt. A weak electrolyte, such as acetic acid, has
practically no effect at this concentration, and so the effect must be chiefly due to the ions of sodium
chloride; since the salt, in half-molar solution, is ionized 73%, the reduction in the dissolving power
would be 30 / 0.73 = 41% per mole of fully ionized salt. The principle of the constant solubility-
product cannot be considered as established for solutions more concentrated than 0.2 to 0.3 molar;
but it is evident that, in any comprehensive theoretical formulation of the principle for the range in
which it is found empirically to hold, the change in the nature of the solvent, which in some cases is
conspicuous in 0.5 molar solution, must be taken into consideration as a factor even in more dilute
solutions (say 0.05 to 0.3 molar). It seems at present, quite possible, perhaps even probable, that the
constancy, in all but the most dilute solutions, is the result of the approximate balancing of two (or
more) opposing factors.303 When we leave the range of concentrations mentioned, and go to more
concentrated solutions, these factors seem to be less well balanced and the validity of the principle
ceases.304 For the present it will be safe to consider the principle as an empirical one, holding for
solutions of total salt content up to 0.25 or 0.3 molar.305 For quite dilute solutions the effect of the
electrolyte on the solvent would be negligible, and only to such solutions would the theoretical
derivation brought forward by Washburn be applicable.

Influence of a Common Ion.
—For a saturated aqueous solution of silver acetate at a given temperature,
the product of [p145] the ion concentrations may be considered a constant,
[CH3COO−] × [Ag+] = KS.P..

In such an aqueous solution, containing no foreign salts, the
concentration of the silver-ion is equal to the concentration of the acetate-
ion, since a molecule of silver acetate, when it ionizes, gives one silver ion
for every acetate ion formed. The numerical value of the solubility-product
may then be calculated, if the solubility of the salt and its degree of
ionization are known. For instance, at 16° one liter of water dissolves 10.07
grams of silver acetate, that is, 10.07 / 167, or 0.0603 gram-molecule
(mole). Conductivity measurements show that 70.8% of the salt is ionized
in such a solution, and consequently the concentration of the silver-ion is
0.708 × 0.0603, or 0.0427. The concentration of the acetate-ion is the same,
and the value of the solubility-product constant, obtained by inserting these
quantities in the above equation, is KS.P. = 0.0427 × 0.0427 = 0.00182.
Now, if, to the saturated solution of the silver acetate, there are added a
few drops of a concentrated solution of sodium acetate or some crystals of
solid sodium acetate, the concentration of the acetate-ion is thereby
increased and the condition of equilibrium in the solution is disturbed:
x [CH3COO−] × [Ag+] > KS.P..

The concentration of the acetate-ion having been increased, the ion will
combine more rapidly than before with the silver-ion, and the concentration
of the nonionized salt will be increased. The solution being already
saturated with nonionized silver acetate, the excess formed must be
precipitated. As a matter of fact, a precipitate of silver acetate is readily
obtained in this way (exp.). Precipitation will cease when sufficient silver
acetate has crystallized out to make the product of the concentrations of the
ions again equal to the solubility-product constant. If, after the
crystallization is complete and equilibrium has been reëstablished, the
acetate-ion is x′ times as concentrated as it was in the pure aqueous
solution, the concentration of the silver-ion must be reduced to 1 / x′ its
original value:

x′ [CH3COO−] × [Ag+] / x′ = KS.P..
Precipitation.
—We see thus that precipitation of a difficultly soluble ionogen will result
when the product of the ion concentrations [p146] is made greater than the
value of the solubility-product constant for that substance. In the second
place, it is seen that the concentration of an ion of an insoluble salt, which
can be present in the saturated solution of the salt, is dependent on the
concentration of the other ion (or ions) of the salt. This fact is a very
important one in analytical chemistry and it is taken advantage of in many
ways, as we shall presently see.
It is clear that a corresponding result should be obtained when, to the
saturated aqueous solution of silver acetate, an excess of the silver-ion is
added—for instance by the addition of solid silver nitrate or of a little of a
concentrated solution of this salt (exp.). Here again, the product of the ion
concentrations is greater than the constant, i.e.
[CH3COO−] × y [Ag+] > KS.P., and precipitation results. Silver acetate
therefore crystallizes out, until
([CH3COO−] / y′) × y′ [Ag+] = KS.P..
The following table shows the relations when sodium acetate is added to the saturated solution of
silver acetate. Column 1 gives the concentration of the sodium acetate in the solution saturated with
silver acetate, column 2 the percentage of the sodium acetate that is ionized, column 3 the total
concentration of silver acetate in the saturated solution, column 4 the percentage of it which is
ionized, column 5 the concentration of the acetate-ion, column 6 the concentration of the silver-ion
and column 7 the value of the solubility-product.

1 2 3 4 5 6 7
Na-Acet. 100 p. Ag-Acet. 100 p′. [CH3COO−]. [Ag+]. KS.P..
... 0.0603 70.8 0.0427 0.0427 0.00182
0.061 78.6 0.0392 64.5 0.0735 0.0258 0.00185
0.119 75.8 0.028 59.7 0.1065 0.0167 0.00179
0.239 70.8 0.0208 52.3 0.1727 0.0109 0.00188
The second table shows the relations when an excess of the silver-ion is present, silver nitrate
having been added to the saturated silver acetate solution. The columns have the same significance as

in the first table, excepting that the first column gives the concentration of silver nitrate present and
the second column its degree of ionization.306
It is clear from these results that a difficultly soluble salt is rendered less soluble (see column 3 of
the tables) by the presence of another salt, when the [p147] latter has an ion in common with the
former. This conclusion has been well established307 for a considerable number of salts.308

1 2 3 4 5 6 7
AgNO2. 100 p. Ag-Acet. 100 p′. [CH3COO−]. [Ag+]. KS.P..
0. ... 0.0603 70.8 0.0427 0.0427 0.00182
0.061 82.0 0.0417 64.0 0.0267 0.0767 0.00204
0.119 78.4 0.0341 58.6 0.0200 0.1142 0.00227
0.239 74.0 0.0195 51.7 0.0100 0.1809 0.00182

Applications in Analysis.
—A few instances of the application of this relation in analysis follow. The
determination of the sulphate-ion is based on the precipitation of barium
sulphate from solutions of sulphates. The solubility of barium sulphate in
water at 18° is 0.0023 gram, or 0.0023 / 233 = 1E−5 mole per liter. In such
an extremely dilute solution, the salt may be considered to be completely
ionized, and the value of the solubility-product constant is found from KS.P
= [Ba2+] × [SO42−] = (1E−5)2, or 1E−10. Now, the amount of sulphate-ion
left in solution, which would be about one milligram per liter of the
aqueous solution, may be reduced by the use of a small excess of the
precipitant, barium chloride. An excess of as little as 0.2 gram or 0.001
mole of BaCl2 per liter would increase the concentration of the barium-ion
about one hundredfold, and barium sulphate would be precipitated, until the
concentration of the sulphate-ion had been reduced about one hundredfold.
The loss of the sulphate-ion is thus reduced to approximately 0.01
milligram per liter.
In passing, we may ask what the approximate loss of dissolved
nonionized barium sulphate would amount to. The value of the ratio
([Ba2+] × [SO42−]) : [BaSO4], representing the ionization of barium
sulphate, is unknown for the extreme dilution represented [p148] by the
saturated solution. If we assume it to be roughly of the order 2000 : 1,309 the

solubility of nonionized barium sulphate at 18° would be roughly 0.05
milligram per liter.
As a rule, then, in the absence of complicating conditions,310 an excess of
the precipitant promotes the complete precipitation of an ionogen.
Washing of Precipitates.
311
—When barium sulphate has been brought on the filter and the excess of
precipitant is to be washed out, then, as the excess of barium chloride is
removed, the sulphate becomes more soluble again. It is advisable,
therefore, to wash the precipitate as effectively as possible with a very small
volume of water—as a rule, the water is used in a very fine stream or is
applied drop by drop.
Such precautions are still more important in the case of precipitates
which are somewhat more soluble than is barium sulphate, and in such
cases the question must be considered, whether as a washing fluid, some
solution may not be used, which contains an ion in common with the
precipitate, and which has, therefore, according to the principle of the
solubility-product, a very much smaller dissolving power for the precipitate
in question than pure water. That is a resource of the analyst to which
recourse is occasionally taken. Lead sulphate, for instance, is washed with a
very dilute solution of sulphuric acid, rather than with pure water;312
potassium cobaltinitrite, K3Co(NO2)6, which is used in the separation of
cobalt from nickel, is washed313 with a ten per cent solution of potassium
acetate, containing a little potassium nitrite. Ammonium
phosphomolybdate, used in determinations of phosphates, is washed with a
solution of ammonium nitrate. [p149]
The use of such solutions for washing precipitates is limited by the
necessity, first, of avoiding salts which interfere with subsequent operations
(e.g. which would leave nonvolatile residues in the subsequent ignition of a
precipitate, that is to be weighed after ignition) and, second, of avoiding the
loss of precipitate by the formation of complex ions between an ion of the

precipitate and a component of the washing mixture (see p. 148). But
wherever such complications can be excluded, the method is a desirable
one.
It has sometimes been recommended to wash a precipitate with a saturated aqueous solution of the
precipitate itself, in place of with pure water. It was reasoned that the solution, being already
saturated with the salt, would not be able to dissolve any of the precipitate obtained. That is true; but
if a saturated solution of a salt, MeX, is placed on a filter still holding an excess of the precipitant, i.e.
one of the ions, say X, of the precipitate, then this excess may cause supersaturation of the saturated
washing fluid and some of the salt may be precipitated out of the washing fluid. The method, as
commonly employed, has therefore the inherent fault, theoretically at least, of being liable to give too
high results. If it is to be employed without error, precautions must be taken first to remove, from the
precipitate and filter, the mother liquor (containing the excess of precipitant) as completely as
possible. If in a given case this can be accomplished, then the danger of precipitating any of the salt
(MeX) from the saturated solution is avoided, and the precipitate (MeX ↓) may then be further
washed with a saturated solution of the same salt (MeX), with advantage, in certain cases. Thus, in
the Lindo-Gladding method314 of determining potassium in the form of potassium chloroplatinate,
the source of error, just discussed, has been avoided in the following way: the excess of precipitant,
chloroplatinic acid H2PtCl6, which has the ion PtCl62− in common with the precipitate, is first
removed from the precipitate by thorough washing of the precipitate with alcohol; subsequently,
other impurities, e.g. sulphates, soluble in water but not in alcohol, are washed out with an aqueous
solution of ammonium chloride315 that has been saturated with potassium chloroplatinate. The
method gives good results.
The Solubility-Product in Volumetric Analysis.
—A final instance of the application of the solubility-product principle to the ordinary methods of
analytical chemistry, may be taken from the field of quantitative, volumetric analysis. A particularly
accurate method of determining silver consists in precipitating it as silver chloride by means of a
standardized solution of sodium chloride. The aim of the method is to recognize, as exactly as [p150]
possible, the point where the action AgNO3 + NaCl → AgCl ↓ + NaNO3 has just completed itself, i.e.
where one equivalent of sodium chloride has been added for just one equivalent of silver nitrate
present. A very sensitive method316 depends on the fact that silver chloride can be made to coagulate
by the vigorous shaking of its suspensions, and that the coagulated chloride settles rapidly, leaving a
clear supernatant liquid, in which the appearance of the faintest turbidity may be recognized, when
the sodium chloride solution is carefully added to the silver nitrate solution under investigation. Now,
when sodium chloride solution is added in this way to silver nitrate, a point is reached (called the
"neutral point"),317 where the addition of a further drop or two of sodium chloride solution will still
produce a precipitate, and where one would be inclined to decide that too little of the chloride had
been used to complete the action. But, at the same time, the addition of a few drops of silver nitrate
solution to the solution at the "neutral point" also produces a precipitate of silver chloride, seemingly

indicating that an excess of sodium chloride had been used, and apparently contradicting the previous
result. As a matter of fact, such a behavior is exactly what is to be expected from a solution, when
exactly equivalent quantities of silver nitrate and sodium chloride have been brought together in
solution. The solution is then saturated with silver chloride, KS.P. = [Ag+] × [Cl−] and [Ag+] = [Cl−],
and the further addition either of the silver-ion (silver nitrate) or of the chloride-ion (sodium
chloride) should produce a precipitate, according to the principle of the solubility-product. The
correct end-point in the determination is, thus, the "neutral point," for at that point the quantity of
silver present is equivalent to the quantity of sodium chloride added.

Effect of Electrolytes with No Ion in Common with the Precipitate.
—In the precipitation of silver acetate from its saturated solution by the
addition of sodium acetate (p. 145), it is the acetate-ion, according to the
principle of the solubility-product, which is effective—the sodium-ion has
no part in the action. Also, in a similar way, the precipitation produced by
the addition of silver nitrate is ascribed to the increased concentration of the
silver-ion—the nitrate-ion has no share in the action. We may ask, what the
effect on the solubility of silver acetate will be, if a salt, sodium nitrate,
yielding only foreign ions, and no common one, is added to its saturated
solution. The presence of sodium and of nitrate ions will not increase the
concentration of either of the ions of silver acetate, will not increase the
value of either factor in the product of ion concentrations; the addition of
sodium nitrate, therefore, should not lead to the precipitation of any silver
acetate, and as a matter of experiment it does not (exp.). A closer study [p151]
of the conditions will show, in fact, that it renders silver acetate somewhat
more soluble. The addition of the sodium-ion will lead to the suppression of
some of the acetate-ion, nonionized sodium acetate being formed to a
certain extent; the nitrate-ion will combine with some of the silver-ion to
form nonionized silver nitrate: thus the concentrations of both of the ions of
silver acetate are reduced, and the product of ion concentrations is rendered
smaller than the solubility-product constant, ([CH3COO−] − x) ×
([Ag+] − y) < KS.P..
Since the concentrations of both the silver and the acetate ions are
reduced, they will not combine as rapidly as before to form nonionized
silver acetate, and the conditions of equilibrium between the latter and its
ions must be disturbed. The nonionized salt ionizes, for a moment, more
rapidly than it is formed and its concentration will thus be reduced. We,
therefore, might expect the solution to become unsaturated in respect to the
nonionized form, and the solid salt, if present, should go into solution. In
other words, the addition of a salt with two foreign ions should increase the

solubility of a difficultly soluble salt (it is understood that no salt is used
which would precipitate a new, less soluble salt). This expectation has also
been fully confirmed by careful quantitative determinations, especially by
A. A. Noyes and his collaborators. The effect may be demonstrated more
easily by the addition to silver acetate of an electrolyte which will very
thoroughly suppress one of its ions. Nitric acid is such an agent. The
hydrogen-ion will very decidedly reduce the concentration of the acetate-
ion, acetic acid being a weak acid (table, p. 104). There is no difficulty in
recognizing the anticipated effect (exp.).
Solution of Precipitates.
—We find, then, that when the product of the ion concentrations of a
difficultly soluble salt becomes smaller than the solubility-product constant,
the solution is unsaturated in regard to the salt, and the solid salt, if present,
will go into solution.
Summary.
—The conclusions concerning the application of the solubility-product
constant may be summarized as follows: A solution is saturated with a
difficultly soluble ionogen when the product of the concentrations of the
ions of the ionogen is equal to the characteristic solubility-product constant
(at the given temperature). A solution is supersaturated and precipitation
will follow, if the product of the ion concentrations is greater than the
constant. [p152] (See p. 122 in regard to precautions against prolonged
supersaturation.) A solution is unsaturated, and the ionogen, if present, will
dissolve when the product of the ion concentrations is smaller than the
constant.
Further Considerations Concerning Precipitation and Solution.
—It is further evident that precipitation is favored, if the precipitating agent
contains an electrolyte which produces the precipitating ion readily; for
instance, carbonic acid does not precipitate any barium carbonate from a
solution of barium chloride (exp.)—carbonic acid being an exceedingly
weak acid and producing only a minute concentration of the carbonate-ion

CO32−, necessary for the precipitation; but sodium carbonate, a readily
ionized salt, will precipitate the barium carbonate quantitatively (p. 90). If
some alkali is added to the mixture of barium chloride and carbonic acid
(exp.), the latter is converted into a readily ionized salt, the concentration of
the carbonate-ion is thus decidedly increased, and the precipitate forms
instantly. In the same way, if hydrogen sulphide—a still weaker acid (table,
p. 104), which forms only minute quantities of sulphide and hydrosulphide
ions (S2− and HS−)—is passed through a solution of ferrous sulphate, it fails
to precipitate ferrous sulphide; but a salt of hydrogen sulphide, ammonium
sulphide, for instance, precipitates ferrous sulphide quantitatively (exp.).
On the other hand, solution of an ionogen is evidently favored and its
precipitation rendered more difficult, if we suppress one (or both) of its
ions. Thus barium phosphate, calcium carbonate, silver borate, and many
salts of weak acids, that are very difficultly soluble in water, are quite easily
soluble in strong acids, which suppress the anions by converting them into
little ionized acids. When a precipitate is dissolved by the addition of a
reagent, such as an acid, an alkali, ammonia, ammonium sulphide—
chemical solvents most frequently used in analytical work—we may, as a
general principle, consider that the reagent must affect one or both of the
ions of the precipitate in question, suppressing it (or them) and thereby
making solution possible. The problem of determining in what way the
suppression of the ion is effected, must then be faced. Many occasions to
determine such questions318 will arise. [p153]
We have, therefore, a certain degree of control over the precipitation and
solution of electrolytes, the control depending upon, and being limited by,
the fact that the factors of the product of ion concentrations are variables.
On the other hand, we have little control, in a given solvent, over the
question of solution or precipitation as affected by the value of the ion
product constant, the remaining term in the equation of the solubility-
product for saturated solutions. These constants cover a very wide range of

values for the various salts, which are most frequently used in analytical
work for the precipitation of the common ions.319 They are subject to
variation with the temperature, and, as a rule, as most salts are more soluble
at higher than at lower temperatures, the values of the constants increase
with the temperature. For exceedingly difficultly soluble salts, the increase
is commonly of no practical moment in analytical work, when, by an excess
of the precipitant, the ion, which is to be precipitated, can be precipitated
quantitatively; the solubility of the nonionized salt, that is precipitated, is so
minute (see p. 148) in this case, even at high temperatures, that it is
altogether negligible for ordinary purposes.320 On the other hand,
precipitates are often used which are not at all extremely insoluble but
merely rather difficultly soluble; they are used in spite of their relatively
slight insolubility because they are the best available forms for our
purposes. Such salts are, for instance, lead chloride, magnesium-ammonium
phosphate, potassium chloroplatinate. When these are precipitated, not only
must the fact that they are appreciably soluble at ordinary temperature be
taken into account, but also the fact that they are very much more soluble at
higher temperatures. Lead chloride and potassium chloroplatinate are, for
instance, quite soluble in hot water.
As a rule, we select for the form in which a given ion is to be
precipitated, a form which, in a saturated aqueous solution, shows the
smallest concentration of the ion in question. But if no form is [p154] known
which is sufficiently insoluble to give satisfactory quantitative results, then
we have recourse to a change in the solvent.
Solubility and Solvent.
—For instance, a mixture of alcohol and water may be used, or water be
excluded altogether; and either absolute (water-free) alcohol or a mixture of
alcohol and ether may be employed. In the quantitative treatment of
potassium chloroplatinate, the last-named mixture is used in place of water.
The change of solvent affects the solubility by a change both in the

solubility of the ionized portion of a salt and in that of the nonionized salt.
An important quantitative relation between the solubility of a given ionogen
in different solvents and the ionizing powers of the solvents, as determined
by their dielectric constants (p. 63), was predicted, on the basis of
theoretical considerations, by Malström321 and by Baur.322 Walden323 has
furnished experimental confirmation of the relation: The degree of
ionization of a salt is found to be the same in its saturated solutions in
different solvents, when the solutions are saturated at the same temperature.
If this relation is combined with that discussed on page 63, according to which the degree of
ionization of a given salt, in different solvents, is the same, when the cube roots of its concentrations
are directly proportional to the dielectric constants of the solvents (e1 : ∛c1 = e2 : ∛c2 = a constant),
then we find, that in saturated solutions of a given salt, in different solvents, the cube roots of the
concentrations, or solubilities, are directly proportional to the dielectric constants of the solvents, or,
the solubilities are proportional to the third powers of the dielectric constants.

e1 : ∛c1 = e2 :∛c2 = a constant, or e13 : e23 = c1 : c2,

c1 and c2 representing the solubilities, in molar concentrations, in two solvents of dielectric constants
e1 and e2.
The following table illustrates the relations for a salt examined by Walden, a derivative of
ammonium iodide, namely tetraethyl ammonium iodide (C2H5)4NI. The first column gives the name
of the solvent, the second the solubility or concentration in the saturated solution, in terms of the
proportion of moles of the solute to the total number of moles present324 [p155] (solute + solvent); the
third column gives the dielectric constant, under comparable conditions, and the last column gives
the relation e : ∛c.

Solvent. Solubility. e5 e : ∛c
Water 0.0332 75.0 50.5
Nitrobenzene 0.0020 32.2 54.8
Ethyl alcohol 0.00201 26.6 45.5
Acetone 0.00072 21.8 52.8
Amyl alcohol 0.00031 15.0 48.
In view of the difficulties in determining the values for the dielectric constant, the agreement in the
values of the last column must be considered satisfactory.325
This important principle forms another striking instance of the supreme influence of electrical
relations in determining the behavior of ionogens in solution (see p. 111).

Since, in solutions saturated at the same temperature with a given
ionogen, the degree of ionization of the ionogen is the same in both
solvents, the proportion of nonionized to ionized salt is also the same. If a
salt, e.g. calcium sulphate, is less soluble in alcohol than in water, the
alcohol must hold less of the nonionized form, as well as less of the ionized
salt, than does an equal volume of water at the same temperature.
The development of further relations, of fundamental importance to
analytical chemistry, with the aid of the laws of chemical and physical
equilibrium and of the principle of the solubility-product, will be taken up
in the study of the reactions of the various analytical groups of ions.

Chapter VIII Footnotes
[291] Z. phys. Chem., 4, 372 (1889). See also van 't Hoff, ibid., 3, 484 (1889).
[292] Cf. page 94.
[293] A. A. Noyes, Z. phys. Chem., 9, 618 (1892); Findlay, ibid., 34, 409 (1900).
[294] As foreign salts affect the ionization of poor electrolytes (p. 109), the ratio of equation I
would hold as little for poor electrolytes, and would grow larger with an increased concentration
of the foreign salts.
[295] Cf. A. A. Noyes, Congress of Arts and Sciences (St. Louis), 4, 321 (1904) and Stieglitz, J.
Am. Chem. Soc., 30, 946 (1908) (Stud.), and the references to literature given there. The
empirical relation seems to hold for dilute solutions, the total electrolyte concentration of which is

not greater than 0.2 to 0.3 gram-equivalent per liter, and, roughly, for concentrations not greater
than 0.5 gram-equivalent per liter.
[296] See Stieglitz, loc. cit.
[297] Since the writing of this it has been learned that such investigations have been carried out
by Harkins. Cf. J. Am. Chem. Soc., 1911.
[298] J. Am. Chem. Soc., 32, 488 (1910).
[299] Otherwise a perpetuum mobile of the second class (footnote 3, p. 12) could be constructed,
which is at variance with experience.
[300] This sentence is quoted from a letter from Dr. Washburn, who is at present investigating
moderately concentrated solutions of electrolytes, to determine the range of concentrations in
which it is possible to apply the laws of ideal solution.
[301] Cf. Geffcken, Z. Phys. Chem., 49, 257 (1907), and the references given there.
[302] Cf. Arrhenius, loc. cit., and similar investigations on the "salt effect" (p. 109).
[303] Vide Geffcken, loc. cit., 295, and Stieglitz, loc. cit., and p. 142.
[304] See also Hill, J. Am. Chem. Soc., 32, 1186 (1910). Hill attacks the principle as a whole, but
brings no evidence against its validity for solutions of concentrations up to 0.3.
[305] The limit of concentration depends, for constancy, upon the nature of the salts. The
calculations, on which the data in the tables on pp. 146–7 are based, involve extrapolations which
prevent the results, especially for the more concentrated solutions, being considered as final.
[306] For further illustrations, vide Stieglitz, J. Am. Chem. Soc., 30, p. 947 (1908), and the
references given there to the work of Noyes, Findlay, etc.
[307] Some instances are known where the solubility of a salt is increased by the addition of a salt
with a common ion. In such cases it is extremely likely that an ion of the salt in question forms a
complex ion with a component of the solution. Vide A. A. Noyes, Z. phys. Chem., 6, 241 (1890),
and 9, 603 (1892). In Chapter XII we shall discuss, in detail, instances of this nature where the
formation of complex ions is particularly susceptible of exact experimental verification.
[308] Especially by Noyes, loc. cit., and later papers; Findlay, loc. cit.
[309] This is the value for a similar ratio for KCl of the same concentration as found, by
extrapolation, from the data in the table on p. 108.
[310] Owing to the possibility of the formation of complex ions (Chapter XII), each individual
case must be considered by itself and the most favorable conditions for the complete precipitation
determined experimentally. The rule mentioned is to be used as a guide, and the reference to the

possibility of the formation of complex ions considered as a warning, in the planning of such
investigations.
[311] Cf. p. 136, concerning precautions used to prevent precipitates from assuming the colloidal
state.
[312] Fresenius, Quantitative Analysis, I, 355 (1904).
[313] Ibid., I, 307.
[314] Official Methods of Analysis, Bulletin 107, p. 11, U. S. Dept. of Agriculture.
[315] The excess of chloroplatinic acid is first washed out of the precipitate primarily to avoid
subsequent precipitation of ammonium chloroplatinate, but its removal also avoids the error
discussed in the text.
[316] Gay-Lussac's method.
[317] Mulder. See Sutton's Volumetric Analysis, p. 304 (1904).
[318] Vide Chapters XII and XIII.
[319] A table of exact solubilities is given at the end of the Lab. Manual, q.v.
[320] In the most exact quantitative work, as demanded in the determinations of atomic weights,
every known loss must, as far as possible, be measured and taken into account. Beautiful
instances of such work are found in T. W. Richards' classic determinations of atomic weights. See,
for instance, Richards, Carnegie Institution Publications, No. 125 (1910), Determinations of the
Atomic Weights of Silver, Lithium and Chlorine (Stud.).
[321] Z. Elektrochem., 11, 797 (1905).
[322] Ibid., 11, 936 (1905), and 12, 725 (1906).
[323] Z. phys. Chem., 55, 707 (1906), and 61, 638 (1907).
[324] If n is the number of moles of solute dissolved in N moles of solute, the concentration of the
solute may be expressed as n / (n + N), which is called its "mole fraction." This form of expressing
concentrations is in many particulars preferable to the mole / liter form. For very dilute solutions
(n is very small compared with N) the two forms become practically identical, but they are not so
for more concentrated solutions, and the mole-fraction expression is then easier to treat
rigorously.
[325] See Walden, loc cit., for more extended data.

PART II
SYSTEMATIC ANALYSIS AND THE
APPLICATION OF FUNDAMENTAL
PRINCIPLES

CHAPTER IX
SYSTEMATIC ANALYSIS FOR THE COMMON METAL
IONS. THE IONS OF THE ALKALIES AND OF THE
ALKALINE EARTHS. ORDER OF PRECIPITATION OF
DIFFICULTLY SOLUBLE SALTS WITH A COMMON ION

[p157] TOC

In systematic analysis it is most convenient to make separate
examinations for the metal and for the acid ions. The examination for metal
ions usually precedes that for the acid ions, and the scheme of analysis for
the former will be considered first.
The analytical grouping of the metallic elements is not a natural one, as
far as their chemical behavior is concerned. Such a grouping is found in the
Periodic System of Mendeléeff and is used in systematic inorganic
chemistry.326 The groups in analysis are based chiefly, but not exclusively,
on the physical property of greater or smaller solubility of certain salts of
the metals. According to the salts chosen, different systems vary somewhat
in detail. Frequently elements of the same natural family are also found in
the same analytical group, relationship in chemical properties being often
coincident with relationship in the physical behavior of the salts of the
metals.
In the following list, the common metal ions are arranged in groups,
which are given in the order in which they are precipitated in the method of
systematic analysis adopted. In each case, a group name and the
characteristic reagents used in separating a group from those following it,
are given.
The Silver Group.

—Ions whose chlorides are insoluble in dilute acid solutions. The
precipitating agent is HCl. [p158]

Pb2+ (the chloride is somewhat soluble), Ag+, Hg+.
The Copper and the Arsenic Groups.
—Ions whose sulphides are insoluble in dilute acids. The precipitating
agent for the two groups is H2S, in acid solution. The sulphides of the
arsenic group are soluble in a mixture of (NH4)2S and (NH4)2Sx and are
separated thereby from the sulphides of the copper group.
The Copper Group.—Hg2+, (Pb2+), Bi3+, Cu2+, Cd2+.
The Arsenic Group.—As3+, As5+, Sb3+, Sb5+, Sn2+, Sn4+, Pt2+, Pt4+,
Au+, Au3+.
The Aluminium and the Zinc Groups.
—Ions whose sulphides or hydroxides are insoluble in neutral or slightly
alkaline (ammonium hydroxide) solutions. The two groups are precipitated
together by a mixture of NH4Cl, NH4OH, (NH4)2S. The aluminium group
may be separated from the zinc group by treatment of solutions of the
chlorides or nitrates with barium carbonate.
The Aluminium Group.—Fe3+, Al3+, Cr3+.
The Zinc Group.—Fe2+, Ni2+, Co2+, Mn2+, Zn2+.
The Alkaline Earth Group.
—Ions whose carbonates and phosphates are insoluble in neutral or alkaline
solutions. The precipitating agent is NH4Cl, NH4OH, (NH4)2CO3 for
Ba2+, Sr2+, Ca2+, and (NH4)2HPO4 for Mg2+.327
The Alkalies.
—Ions whose chlorides, sulphides, hydroxides, carbonates and phosphates
are soluble. K+, Na+, NH4+.

In considering the analytical reactions and the analysis of these groups of
metal ions, we shall take up the groups in the order reversed to that given in
the table. We shall begin with the group of alkali metals, follow this group
with the alkaline earths, then take the aluminium and zinc groups, the
copper and silver groups, and finish with the arsenic group. This order is
chosen because the chemistry of the reactions involved is simplest in the
groups to be studied first and grows more complicated as we advance to
those to be studied later.
It is not intended to discuss in detail all the reactions and methods; our
attention will be limited rather to the study of typical general relations, and
the student is expected to acquire the power to apply the general
conclusions reached, to any specific case demanding it. [p159]
The Alkali Group.
—The group includes the ions of sodium and potassium, the most common
and most important of the alkali metals, and the ammonium-ion.
Characteristic of the ions of the group is the fact that all of their common
salts are easily soluble in water. They remain in solution in systematic
analysis, while other metal ions are removed in the form of various
insoluble precipitates.
The ammonium-ion is recognized, and may be removed from a mixture
of the salts of the group, on the basis of a fundamental distinction in its
chemical behavior, namely its instability and the instability of its
compounds. Sodium-ion and potassium-ion, are recognized, and separated
from each other, by physical methods. All ammonium compounds, NH4X,
decompose more or less readily into ammonia and the free acids,328
according to the reversible reaction,
NH4X ⇄ NH3 + HX.
The stronger the acid combined with ammonia, the more stable is the
salt, and the higher is the temperature, at which the salt decomposes readily
and rapidly. Ammonium chloride, one of the most stable of the salts, is

decomposed rapidly only at about 350°, which is, however, still below red
heat; ammonium carbonate, the salt of a very much weaker acid,
decomposes appreciably at ordinary temperatures, and exposed to the air, it
gradually disappears as ammonia, carbon dioxide and water. If the acid of
the salt is volatile at the dissociation temperature of the salt, the whole salt
is volatilized, and if the ammonia and volatile acid vapor reach a colder
space, recombination to form the original solid salt occurs to a considerable
extent (the "smoking off" of ammonium chloride). If the acid is not volatile,
the salt, nevertheless, loses its ammonia at temperatures below red heat,
while the acid remains. Sodium-ammonium phosphate, for instance, when
heated, loses its ammonia, and sodium-dihydrogen phosphate is left as a
nonvolatile residue.
Ammonium happens to form salts which closely resemble the
corresponding salts of potassium in physical properties, such as [p160]
solubility and insolubility, salts which could readily be mistaken for
potassium salts. Advantage is taken of the chemical instability of the
ammonium salts, just described, to remove ammonium completely from
mixtures, by ignition, before tests for potassium are made.
Water is a far weaker acid (see table, p. 104) than carbonic acid and it is
not surprising to find the compound formed by water and ammonia,
ammonium hydroxide, one of the least stable of the ammonium compounds.
Even at ordinary temperature, the hydroxide is more or less decomposed,
according to a reversible reaction of the same type as that found for the
ammonium salts, NH4OH ⇄ NH3 + HOH.
Chemists have always been interested in the problem of the exact degree of stability of ammonium
hydroxide, and, more particularly, in the problem whether ammonia gives solutions in water showing
very much weaker basic strength329 than equivalent solutions of potassium and sodium hydroxides,
primarily because only a small proportion of the ammonia is combined with water to form the real
base, ammonium hydroxide (which would be present then in much more dilute solution than the
alkali metal hydroxides are in the solutions with which the comparison is made), or chiefly because
ammonium hydroxide is much less readily ionizable than potassium or sodium hydroxide.

For the reversible action NH3 + HOH ⇄ NH4OH we would have, at a constant temperature,
according to the law of chemical equilibrium,
[NH3] × [HOH] / [NH4OH] = k.

For a dilute solution at a given temperature the concentration of the water may be considered a
constant, and therefore
[NH3] / [NH4OH] = k / [HOH] = kNH .
3 (I)

For the ionization of ammonium hydroxide, NH4OH ⇄ NH4+ + HO−, we would have in turn,

[NH4+] × [HO−] / [NH4OH] = kbase. (II)
This constant represents the real ionization constant of ammonium hydroxide as a base, and its
approximate value has only recently been determined by Moore330 and found to be about 5E−5. The
ratio [NH3] / [NH4OH] was found to be approximately 2 at 20°. According to this result, ammonium
hydroxide is really a much weaker, less readily ionized base than potassium or sodium hydroxide.
The efficiency of ammonium hydroxide as a base depends [p161] on both conditions of equilibrium;
the first equation states what proportion of ammonium hydroxide can exist, as such, in solution, if a
given amount of ammonia is dissolved in a given amount of water, and the second equation shows
the proportion of the hydroxide, which is ionized. The equations may be combined331 into one
expression,

[NH4+] × [HO−] / ([NH4OH] + [NH3]) = K. (III)

That is, the ratio of [NH4+] × [HO−] to the total concentration of nonionized ammonium hydroxide
and ammonia, is a constant. This constant has the value 0.000,018 at 18° (as given in the table, p.
106) and, as said, comprises in a single expression a statement measuring the efficiency, as a base, of
a solution of ammonium hydroxide and ammonia in aqueous solutions. The concentration of the
hydroxide-ion, on which the efficiency as a base depends, can be ascertained directly from the
expression, provided we know the total concentration of the ammonia and ammonium hydroxide and
the concentration and degree of ionization of any ammonium salt, which may be present with the
base (see p. 161). These data are easily obtained by direct measurement.

The instability of ammonium hydroxide is used as a means for detecting
ammonium-ion in its salts. The latter are treated with some strong base,
such as sodium or calcium hydroxide, and the ammonia, liberated by the
decomposition of its hydroxide, is recognized by its odor or by the more
sensitive test of its action on moist litmus. The delicacy of the test is
dependent on the conditions expressed in the equilibrium equation (p. 160).

Sodium and potassium resemble each other so profoundly in the
chemical behavior of their compounds, that they are recognized, and
separated from each other, by physical methods. A very simple physical test
is based on the color of their heated vapors, the color imparted to the
nonluminous bunsen flame by the introduction and volatilization of their
salts. The sodium flame is so intense that, if sodium is present in any
quantity, the color of its flame easily masks the faint color of potassium
vapor. The color of the flame is best examined, in such a case, with the aid
of a spectroscope, in which the light emitted by the two elements may be
readily recognized side by side, or with the aid of cobalt glass, which
absorbs the sodium light. [p162]
The ions of the two metals may be separated and identified by means of
difficultly soluble salts. There are so few of these in the case of both ions,
that recourse must be taken to the salts of comparatively uncommon acids.
Potassium chloroplatinate K2PtCl6, precipitated by the addition of
chloroplatinic acid H2PtCl6 to concentrated solutions of potassium salts,
gives very satisfactory results, both in qualitative and in quantitative work.
The acid tartrate, KHC4H4O6, the picrate, KC6H2N3O7, and the
cobaltinitrite, K3Co(NO2)6,332 are difficultly soluble and are sometimes
used to identify potassium-ion. The corresponding ammonium salts are also
difficultly soluble and resemble the potassium salts, and ammonium-ion
must therefore be removed, as stated above, if present, before any of these
precipitates may be used for the identification of potassium-ion. In the case
of sodium-ion, recourse is taken to the salt of a still more uncommon acid;
pyroantimonate of sodium, Na2H2Sb2O7, 6 aq., is sufficiently difficultly
soluble and characteristic to be used as a means of identifying sodium-ion.
The Alkaline Earth Group.
—This group includes magnesium, calcium, strontium, and barium.
Chemically, the analogous compounds of the four alkaline earths resemble
one another so much, that physical differences alone are used in their

separation and identification. For qualitative work, the colors of their heated
vapors,333 especially when examined in the spectroscope, give us sensitive
and reliable tests for their presence. The alkaline earth ions, especially the
ions of barium, strontium and calcium, form a great number of insoluble
salts, which may be used to separate them from each other. Salts used for
this purpose and the methods of employing them are considered in detail in
the laboratory work (see Part III). Here some general principles, only, will
be considered in connection with the behavior of some of the most
important of the precipitates.
There is a very wide range in the degree of the insolubility of such
precipitates as are used in analysis. In the table at the end of Part IV, the
exact solubilities of the most important [p163] precipitates of the alkaline
earths are given, for 18°, in grams and moles per liter. The values are
instructive in a number of respects.
Inspection of the table shows which are the least soluble (in molar terms),
and therefore the best salts, for precipitating barium, strontium and calcium,
in order to insure the use of the most sensitive tests for the ions of each of
these metals. It also shows which salts must be treated with special
precautions to escape error. It is further seen, that if the carbonates of these
alkaline earths are precipitated by a moderate excess of ammonium
carbonate, the addition of a sulphate (for instance ammonium sulphate), to
the filtrate from the precipitated carbonates, will only precipitate barium
sulphate, the only sulphate whose solubility (and solubility-product) is
smaller than that of the corresponding carbonate. In the same way, calcium
oxalate is the only oxalate of these three alkaline earths that will be
precipitated by ammonium oxalate in the filtrate from the carbonates (see
Part III in regard to precautions against difficultly soluble double oxalates
of magnesium). Again, calcium sulphate is the only one of the sulphates,
which is sufficiently soluble in water to give an immediate heavy
precipitate, when the sulphates are shaken for a few moments with water

and the filtered solution is treated with a few drops of ammonium oxalate
solution.
Fractional Precipitation.
334
—If sulphuric acid is added to a 0.5 molar solution of the chloride either
of barium, of strontium or of calcium, the corresponding sulphate is
precipitated. We may ask which sulphate will be precipitated first, when
sulphuric acid is added, drop by drop, to a solution containing the three
chlorides. This problem, a case of the fractional precipitation of salts
containing a common ion, may be treated from the point of view of the
solubility-product principle as follows, the problem being limited, for the
sake of simplicity, to only two of the sulphates, those of barium and
strontium.
For a saturated solution of barium sulphate,335 at 18°, in contact with the
solid salt, we have, according to the principle of the solubility-product,
KBaSO4 = [Ba2+] × [SO42−] = 1E−10,

[p164]

and for a saturated solution of strontium sulphate, we have similarly336
KSrSO4 = [Sr2+] × [SO42−] = 2.5E−7.

Now, we may ask what the conditions are under which both precipitates
can be present together in a condition of equilibrium with a supernatant
saturated solution. In such a solution we have simultaneously
KBaSO4 = [Ba2+]1 × [SO42−]1,
KSrSO4 = [Sr2+]1 × [SO42−]1.

New symbols, [Ba2+]1, etc., are used for expressing the concentrations, as
they are not the same as in the pure aqueous solutions. The much more
soluble strontium sulphate makes the concentration of the sulphate-ion very
much greater than it is in the saturated solution of pure barium sulphate and

diminishes the concentration of the barium-ion proportionately (p. 145).
The concentration, [SO42−]1, of the sulphate-ion, representing the actual
(total) concentration of the ion in the solution saturated with both salts,
appears in both of the new equations. Combining the two equations, we
have, for the condition of equilibrium between the two precipitates and the
supernatant liquid,
[Ba2+]1 / [Sr2+]1 = KBaSO4 / KSrSO4 = 1 / 2500.

That is, in a solution in equilibrium with both precipitates at 18°, the
strontium-ion must be about 2500 times as concentrated as is the barium-
ion. If we start with equivalent quantities of barium and strontium chlorides,
say in 0.1 molar solutions, and gradually add sulphuric acid or ammonium
sulphate, barium sulphate will be precipitated alone,337 until the strontium-
ion is in the excess [p165] indicated by the ratio given. After that, strontium
sulphate will be precipitated, with traces of barium sulphate, the ratio
expressed in the equilibrium equation being maintained in the supernatant
liquid. On the other hand, if we start with a solution containing a very large
excess of a strontium salt, more than is required by the equilibrium ratio,
then strontium sulphate will be precipitated first, until the ratio given is
reached.
Even should the more soluble salt be precipitated first from a solution
containing, say, equal concentrations of barium and strontium ions, it could
not remain in equilibrium with the supernatant liquid and would be
converted into the less soluble one, before equilibrium was reached in the
system. We can follow similar relations, experimentally, by using
precipitates of different colors. Silver chromate Ag2CrO4 is an intensely red
precipitate, that is rather difficultly soluble in water (exp.); a liter of water
dissolves338 0.0252 gram or 8E−5 mole at 18°. The concentration of the
silver-ion in the saturated solution is then 0.00016 mole.339 Silver chloride
AgCl, a white salt, is still less soluble in water, a liter of water at 18°

dissolving 0.00134 gram or 1E−5 mole, and the concentration of the silver-
ion in the saturated solution is, therefore, only 1E−5 mole, as compared
with 1.6E−4 in the saturated silver chromate solution. If a mixture of
potassium chromate and potassium chloride, containing approximately
equal (0.01 molar) concentrations of the two salts, is prepared and silver
nitrate solution added, drop by drop, to the mixture, the first permanent
precipitate is the white silver chloride (exp.). However, as the silver nitrate
solution strikes the surface of the liquid, a red precipitate of the chromate,
mixed with chloride, is momentarily seen, where the silver nitrate
temporarily produces a local excess of the precipitant. But the red
precipitate disappears rapidly and gives way to the white precipitate of the
less soluble chloride. The quantitative relations, which may be developed
with the aid of the principle of the solubility-product (see below), are such
that, if little chromate is used, it may serve as an [p166] indicator to
determine quantitatively the moment when all the chloride, within the limits
of allowed quantitative error, is precipitated, the first permanent tinge of
pink (solid Ag2CrO4), mixed with the yellow color of the solution, being
used as the indication that the precipitation of the chloride is complete.
Potassium chromate is used as a favorite indicator in quantitative analysis,
for this purpose.
The quantitative relations340 for the precipitation may be developed as follows: For a supernatant
liquid in which a precipitate of silver chromate just appears permanently, together with the chloride,
i.e. for the condition of saturation with both silver salts at 18°, we have

KAgCl = [Ag+] × [Cl−] = (1E−5)2 = 1E−10

and

KAg CrO = [Ag+]2 × [CrO42−] =
2 4

(1.6E−4)2 × (8E−5) = 2E−12,
and therefore:

[Cl−]2 / [CrO42−] = (KAgCl)2 / KAg CrO =
2 4

(1E−10)2 / 2E−12 = 1 / 2E8.

For a solution containing one or two drops (0.1 c.c.) of saturated potassium chromate solution per
100 c.c., a proportion frequently used in quantitative analysis, the concentration of the chromate-ion
is approximately 2.5E−3 and the chloride-ion will consequently be precipitated until [Cl−] = 3E−6.
The chief source of error in the method, then, will not be due to the incompleteness of the prior
precipitation of the chloride, but rather to the use of the small excess of silver nitrate required to
precipitate sufficient chromate to be visible. This error may be avoided, and is avoided in very
accurate work (e.g. in water analysis), by determining, in a blank test, the amount of silver nitrate
required to show the change of tint of a pure chromate solution of the concentration to be used in the
titration and by titrating to this tint in the determination of the chloride: the volume of silver nitrate
(e.g. 0.2 c.c. of a 0.01 molar solution), required to produce the tint in the blank test, is subtracted
from the total volume of silver nitrate used in the chloride determination.

We find thus, that the order of precipitation of difficultly soluble salts,
which contain a common ion (fractional precipitation), is subject to the
equilibrium conditions derived from the application of the principle of the
solubility-product to the salts in question.341
It should be further noted that the condition of equilibrium between two
precipitates, containing a common ion, and a supernatant liquid, depends on
the concentrations in the supernatant liquid, in the liquid phase, and not on
the quantities of the solids [p167] present. This conclusion was first reached
by Guldberg and Waage, to whom we owe the law of mass action, and was
fully confirmed by them. The modern treatment of the subject substitutes
ion concentrations, i.e. the concentrations of the active components,342 for
the total concentrations used by these investigators.343
That the condition of equilibrium is dependent on the liquid phase can
easily be demonstrated if mercurous chloride and mercurous hydroxide are
selected as the two precipitates, in order that we may follow changes of
concentration in the liquid phase by color changes. For the condition of
equilibrium between the two precipitates and the supernatant liquid we may
develop the relation
[OH−] / [Cl−] = KHgOH / KHgCl = K.
Exp. A few drops of phenolphthaleïn are added to 100 c.c. of a very dilute solution of potassium
hydroxide (1 / 500 molar); the usual indication of the presence of the hydroxide-ion is shown and the

intensity of the color will be a measure of its concentration. Three identical solutions are prepared
and then a pinch of calomel is added to two of the solutions,—their pink color fades decidedly.

Some of the calomel is decomposed into dark-colored mercurous oxide,
which is precipitated, and sufficient potassium chloride is formed to bring
the ratio [OH−] / [Cl−], in the solution, down to the value required by the
constant K. Since no chloride-ion is present at the start, this result can be
brought about only by the change indicated. Now, some chloride, say a little
of a concentrated solution of potassium chloride, which reacts perfectly
neutral, is added to one of the mixtures of the hydroxide and chloride. The
concentration of the chloride-ion is increased in the solution, the ratio
[OH−] / [Cl−] is made much too small and the condition of equilibrium is
disturbed. Consequently, mercurous oxide reacts with potassium chloride,
as expressed in the equation HgOH ↓ + KCl → HgCl ↓ + KOH, until the
ratio [OH−] / [Cl−] [p168] has the value required by the constant K. The
phenolphthaleïn is colored by the increased concentration of the hydroxide-
ion and shows the direction of the change.344
Precipitation by a Weak Base in the Presence of its Salts.
—Magnesium, in contrast to the other alkaline earth metals, forms very few
difficultly soluble compounds. Magnesium-ammonium phosphate,
Mg(NH4)PO4, a double salt, is the most characteristic precipitate for
identifying it. Magnesium hydroxide, as the table of solubilities shows, is
also very difficultly soluble. It is readily precipitated by potassium or
sodium hydroxide, but ammonium hydroxide, at best, precipitates it only
incompletely345 from solutions of its salts, and very commonly does not
precipitate it at all—namely, when ammonium salts in sufficient quantity
are present (exp.). This peculiar behavior of ammonium salts, in interfering
with the precipitation of magnesium hydroxide, puzzled chemists for many
years, and a number of "theories" were offered in explanation of it. But they
all proved untenable, and the first adequate explanation, the one in accord
with all the facts, was only found after the development of the theory of

ionization. Its quantitative application to the case in question gives a perfect
insight into the relations, and brings important confirmation of the
correctness of its fundamental assumptions.346
The fact that ammonium salts prevent the precipitation of magnesium
hydroxide was formerly explained as being due to the formation of "double
salts," such as MgCl2,NH4Cl. It is true that such double salts exist, but, if
their formation should prevent the precipitation of magnesium hydroxide,
possibly by including the magnesium as part of a negative ion or radical,347
MgCl3, then the corresponding double salts of magnesium chloride with
potassium and sodium chloride (e.g. MgCl2,KCl), which are just as stable
as the ammonium salts, should show the same behavior; but, as a matter of
fact, the addition of potassium chloride does not interfere with the
precipitation of the hydroxide by either [p169] potassium hydroxide or
ammonium hydroxide (exp.). So the explanation is untenable. Obviously, a
specific interference of ammonium salts with the precipitating power of
ammonium hydroxide is involved. But that is exactly what the law of
chemical equilibrium, applied to the ionization of ammonium hydroxide,
would demand: As a weak base, which is little ionized in pure aqueous
solutions, it is very much weaker as a base, produces a far smaller
concentration of the hydroxide-ion, when readily ionizable salts of
ammonium are added to the solution,348 and the precipitation of magnesium
hydroxide, and of metal hydroxides in general, depends on the
concentration of the hydroxide-ion, which is a factor in the solubility-
products of bases.
The precipitation of magnesium hydroxide, in particular, depends on the relation of the product
[Mg2+] × [HO−]2 to the solubility-product constant of magnesium hydroxide. For the saturated
aqueous solution, the product [Mg2+] × [HO−]2 is equal to the solubility-product constant, and from
the solubility of magnesium hydroxide (see the table) the value of the constant is found to be 15E−12
at 18°. The concentration of magnesium-ion is 0.000,154 in this solution. In a 0.1 molar solution of
magnesium sulphate, which is ionized to the extent of 37.3%, the concentration of magnesium-ion is
0.0373, and it would require a concentration greater than 2E−5 of hydroxide-ion to precipitate any

magnesium hydroxide.349 Now, the concentration of the hydroxide-ion, in an ammoniacal solution,
can easily be reduced far below this value by the addition of ammonium chloride, nitrate, sulphate or
other readily ionizable ammonium salt to the solution, and then magnesium hydroxide will not be
precipitated.
In solutions of ammonium hydroxide the concentration of hydroxide ion for 18° is found from the
relation [NH4+] × [HO−] : ([NH4OH] + [NH3]) = 18E−6 (p. 161). (1) For ammonium hydroxide, for
instance in 0.2 molar solution, and in the absence of any ammonium salt, [HO−] = [NH4+] =
0.0019.350 This concentration of the hydroxide-ion should be more than sufficient to precipitate
magnesium hydroxide in a 0.1 molar solution of the sulphate.351
Exp. 100 c.c. of a mixture which should contain magnesium sulphate in 0.1 molar solution would
require 246 / (10 × 10) or 2.46 grams of MgSO4, 7 H2O. [p170] This weight of the salt is dissolved in
50 c.c. of water and 50 c.c. of 0.4 molar solution of ammonium hydroxide is added to it. Magnesium
hydroxide is precipitated. (The precipitation is incomplete because the ammonium sulphate, formed
in the reaction, reduces the ionization of ammonium hydroxide.)
(2) In the presence of 0.25 molar ammonium chloride, the chloride being dissociated to the extent
of 80%,352 the concentration of the hydroxide-ion in a 0.2 molar ammonium hydroxide solution is
reduced to 18E−6.353 According to the above calculation this is too small a concentration to
precipitate magnesium hydroxide in a 0.1 molar solution of the sulphate.
Exp. 1.35 grams ammonium chloride (the weight corresponding to 100 c.c. of a mixture
containing ammonium chloride in 0.25 molar solution) is dissolved in 50 c.c. of 0.4 molar
ammonium hydroxide and 2.46 grams of magnesium sulphate, dissolved as before in 50 c.c. of water,
is added to the mixture. No precipitate of magnesium hydroxide is formed.

In a similar fashion and for the same reason, ammonium salts interfere
more or less with the precipitation of other hydroxides, for instance with the
precipitation of manganous, nickelous, cobaltous, ferrous, zinc, cupric and
cadmium hydroxides. But ammonium salts do not prevent the precipitation
of aluminium, chromium and ferric hydroxides, which are much less
soluble than the hydroxides just mentioned, and as much weaker bases,
(Chap. X) are also much less readily ionized. They are precipitated by
smaller concentrations of the hydroxide-ion than are the hydroxides of the
first group, and their precipitation may be made quantitative.
Exp. Ferric hydroxide is readily precipitated when 2.7 grams of ferric chloride FeCl3, 6 H2O, the
weight of the chloride required to give 100 c.c. of a 0.1 molar solution, is dissolved in as little water
as possible. The solution is added to the mixture of magnesium sulphate, ammonium chloride and

ammonium hydroxide obtained in the previous experiment, in which no magnesium hydroxide was
precipitated.

Chapter IX Footnotes
[326] See Smith, General Inorganic Chemistry, p. 414, General Chemistry for Colleges, p. 277;
Remsen, Inorganic Chemistry (advanced course), p. 158.
[327] Mg2+ may also be precipitated as a carbonate with the other ions of the group (see Part III).
[328] In the case of ammonium nitrate a different form of decomposition, namely into nitrous
oxide and water, predominates, and, in the case of ammonium nitrite, decomposition into nitrogen
and water takes place so readily, that the decomposition of the salt takes that direction chiefly.
[329] Table, p. 106.
[330] T. S. Moore, J. Chem. Soc. (London), 91, 1379 (1907).
[331] From equation (I) we obtain directly, by the application of a simple mathematical
transformation, that [NH3] + [NH4OH] / [NH4OH] = kNH3 + 1 = k′, and, therefore, [NH4OH] =
[NH3] + [NH4OH] / k′. Inserting this value for [NH4OH] in equation (II) and transferring k′, we
have [NH4+] × [HO−] / ([NH3] + [NH4OH]) = kbase / k′ = K.

[332] Water of crystallization, found in many of the precipitates used in qualitative analysis, will,
as a rule, be indicated only in the formulas used in Part III, in the study of the reactions of ions.
[333] See Part III as to the method of vaporizing magnesium.
[334] Cf. Findlay, Z. phys. Chem., 34, 409 (1900).
[335] The solubility of barium sulphate at 18°, according to the table, is 0.0023 / 233, or 1E−5
mole per liter, and the salt may be considered completely ionized at this dilution.
[336] The solubility (see the table) is 0.114 / 183.6, or 6.2E−4 mole per liter, 84% of which is
ionized (according to conductivity determinations, Kohlrausch and Holborn, loc. cit., p. 200).
Hence [Sr2+] = [SO42−] = 0.00062 × 0.84 = 0.0005.

[337] To establish equilibrium, prolonged "digesting" is sometimes required. Double salts, solid
solutions and mechanical enclosures are liable to interfere with the completeness of such
separations by fractional precipitation. Resolution and reprecipitation will then usually effect a
sufficiently accurate separation for most purposes. On account of the possibility of such

complications, the conditions for a successful separation, within limits such as those described in
the text, must in all cases be investigated.
[338] See the table at the end of Part IV.
[339] The salt may be considered completely ionized at this dilution. Each molecule of silver
chromate forms two silver ions when it is ionized. See p. 141 in regard to the form the solubility-
product takes in the case of a salt of this type.
[340] The complication, resulting from the hydrolysis of the chromate, is not included in this
calculation.
[341] Cf. Findlay, loc. cit.
[342] Even Guldberg and Waage considered the active mass to be the fundamental factor and
simply considered the total concentrations to be proportional to the "active masses," since they
had no means of determining the proportion of "active" substances in the total concentrations.
[343] See Nernst, Theoretical Chemistry, p. 533, for a fuller discussion of the relations between
the new and the old views on this subject.
[344] Dietrich and Wöhler, Z. anorg. Chem., 34, 194 (1903).
[345] On account of the formation of an ammonium salt in the reaction.
[346] Loven, Z. Anorg. Chem., 11, 404 (1896); Herz and Muks, ibid., 38, 138 (1904).
[347] In that case the salts would be called "complex" salts, salts of a complex ion, MgCl3−. See
Chapter XII. They are really "double salts"; cf. Smith, General Inorganic Chemistry, p. 536.
[348] See p. 114, and recall the laboratory experiments (Lab. Manual, p. 9, § 6), which may be
given as lecture experiments at this point.
[349] Calling x the concentration of the hydroxide-ion, required to saturate a 0.1 molar
magnesium sulphate solution with magnesium hydroxide, we have 0.0373 × x2 = 15E−12 and x =
2E−5.

[350] Putting [HO−] = [NH4+] = y, we have y2 : (0.2 − y) = 18E−6. Then y = 0.0019.

[351] 0.0373 × 0.00192 = 0.13E−6, which is considerably larger than the solubility-product
constant for magnesium hydroxide, 15E−12.
[352] Kohlrausch and Holborn, p. 159. Minor changes in the degrees of ionization of MgSO4 and
NH4Cl (and consequently of NH4OH) occur, when the salts are present together. In a rigorous
treatment, the ionization of each salt in the mixture would be calculated with the aid of
Arrhenius's principle of isohydric solutions.
[353] Vide the analogous calculation on p. 113.

CHAPTER X
ALUMINIUM; AMPHOTERIC HYDROXIDES;
HYDROLYSIS OF SALTS. THE ALUMINIUM AND ZINC
GROUPS

[p171] TOC

The chemistry of the analytical reactions of the alkalies and alkaline
earths is extremely simple,—it is essentially the chemistry of well-defined
bases and their salts,—and the separations and identifications, as we have
seen, depend almost entirely on physical differences rather than on
chemical contrasts. In the aluminium and zinc groups, which are
precipitated together and which will be discussed together, the chemistry of
the reactions becomes very much more complex. Therefore, we shall not, as
yet, consider the groups as a whole, but shall first discuss the important
analytical reactions of some compounds of aluminium.
Aluminium Hydroxide an Amphoteric Hydroxide.
—Whereas the hydroxides of the alkali and alkaline earth metals are bases,
pure and simple, aluminium hydroxide shows the properties both of a base
and of an acid; it is an amphoteric hydroxide, the term "amphoteric"
indicating the combination of acid with basic properties in any compound.
Aluminium hydroxide dissolves in acids. From its solution in hydrochloric
acid, an aluminium salt, aluminium chloride AlCl3, 6 H2O, is obtained. It
also combines with strong bases, dissolving for instance in a solution of
sodium hydroxide and forming an aluminate, NaAlO2. The two salts
mentioned are typical representatives of the two series of salts, which
aluminium hydroxide is capable of forming. This dual character of the
hydroxide raises a number of interesting questions, which one meets with
quite frequently in the study of analytical reactions. One may ask, first, how

aluminium hydroxide can ionize both as an acid and as a base; second,
whether any reason can be given, why it should show the dual nature; and
third, if it is both base and acid, why it does not neutralize itself.
According to the best knowledge we have on the subject, the molecule of
aluminium hydroxide has the following structure or arrangement of its
atoms: Al(─O─H)3.
It is readily seen that the cleavage of the molecules may produce, [p172]
either aluminium and hydroxide ions, characteristic ions of a base, or
aluminate354 and hydrogen ions, characteristic ions of an acid:
Al3+ + 3 −OH ⇄ Al(─0─H)3 ⇄ AlO2− + H+ + H2O.
The ionization of the hydroxide both as an acid and as a base is, thus,
quite possible on the basis of the molecular structure assigned to it. In fact,
all of the so-called oxygen acids are considered to be hydroxides—we have
sulphuric acid, O2S(OH)2, phosphoric acid, OP(OH)3, etc.,—exactly as the
bases, Mg(OH)2, etc., are hydroxides.
That brings us to the second question, why aluminium hydroxide should
show this dual character, whereas, for instance, sodium and magnesium
hydroxides, which have similar structures, do not show it. The best answer
to this question is found when we consider the properties of the elements
and their derivatives in connection with their position in the periodic or
natural system of elements, which shows the properties as (periodic)
functions of the atomic weights. In the second series of the elements,355
omitting the zero group element neon and taking the elements in the order
of increasing atomic weights, we have sodium (23), magnesium (24),
aluminium (27), silicon (28), phosphorus (31), sulphur (32), and chlorine
(35.5). One of the properties that are shown to be functions dependent on
the atomic weight, is the property under discussion, namely the tendency of
the (highest) hydroxides of the elements to ionize as bases or acids,
respectively. It is clear that the hydroxides of the elements with the lowest

atomic weights in the series, sodium and magnesium, show the most
pronounced tendency to ionize as bases; the hydroxides of the elements
with the highest atomic weights show the most pronounced tendency to
ionize as acids—perchloric acid, (HO)ClO3, and sulphuric acid, (HO)2SO2,
belong to the strongest acids. In accordance with the underlying principle of
the periodic system, the change of [p173] properties, in going from one
extreme to the other, is a function of the increase in atomic weight and is
not sudden but gradual. And so the basic function, the tendency to produce
the hydroxide-ion, is found to grow weaker as one goes from sodium to
magnesium and then to aluminium, hydroxide; and the acid function, the
tendency to produce the hydrogen-ion, grows markedly stronger, as one
goes from phosphoric to sulphuric and perchloric acids. It is not surprising
to find the two functions existing together, but in rather weak form, in the
case of the intermediate hydroxides, notably in aluminium hydroxide and,
to some degree, in silicic acid, the acid character beginning before the
basic function has ceased. In accordance with this view, aluminium
hydroxide is found to be only a weak, slightly ionized base, and a very
weak, even less readily ionizable acid. In the case of silicic acid, which is
the next hydroxide one meets as one goes toward the acid end of the series,
the conditions are reversed. As the name indicates, it is primarily an acid,
but it is a very weak one, and a critical scrutiny of its behavior shows it to
have very weak basic functions, much weaker than those of aluminium
hydroxide. The question may, indeed, be raised, whether either the basic or
the acid properties really die out altogether in the hydroxides, from one end
of the series to the other. In view of the small tendency toward sudden
changes found in nature, one might suspect traces of basic character to be
preserved right through the series to the strongest acids, like perchloric acid.
As a matter of fact, later (see Chapter XV), we shall be obliged to consider
possible basic functions of the strongest oxygen acids, such as nitric,
perchloric, permanganic acids, and one of their most important properties,

their behavior as oxidizing agents, will be found to be probably intimately
associated with this remnant of basic ionization. On the other hand, fused
sodium hydroxide will dissolve sodium with evolution of hydrogen, sodium
oxide, Na─O─Na, being formed; and it can readily be shown,356 that in the
fused hydroxide there must be at least a few ions NaO−, besides HO−, H+,
O2−, and Na+. [p174]
The position of aluminium in the periodic system adequately accounts,
then, for the amphoteric character of its hydroxide.357
Common Occurrence of Amphoteric Hydroxides.
—If we consider the question of amphoteric behavior a little longer—its
consequences are used extensively in analytical work—we find, in the
periodic system, two other regular changes concerning acid and basic
functions, only one of which we shall discuss here.358 While in a series of
elements the acid character of the hydroxides increases with the atomic
weight, in a family of elements the reverse relation holds. From nitrogen to
bismuth, in the nitrogen family of the sixth column of the periodic system,
the acid character of the hydroxides grows steadily weaker, the basic
character increases, and we find, again, that the intermediate elements,
notably arsenic and antimony, produce hydroxides, which show markedly
amphoteric character.
If, in the second series of the periodic group, one goes back from
aluminium to magnesium hydroxide, in accordance with the first general
principle laid down a much stronger base is found; and if one then goes, in
the magnesium family, to the hydroxide of the element of next lower atomic
weight, glucinum or beryllium, one again meets, in accordance with the
second principle laid down, a weaker basic and more acidic hydroxide than
magnesium hydroxide; in other words, the basic and acid functions revert
closely to those exhibited by aluminium hydroxide. Glucinum hydroxide is
a pronounced amphoteric hydroxide and resembles aluminium hydroxide so
closely that, in the early history of chemistry, it was mistaken for the latter.

If one goes from glucinum back to lithium, in the same series of the
periodic system, and from lithium to the element with the next lower atomic
weight in the same group, one comes to hydrogen, which forms one of the
most important and interesting of the [p175] amphoteric hydroxides, water.
The ionization of water, slight as it is, yields hydrogen-ion and hydroxide-
ion, the ions characteristic of acids and of bases, and water is placed among
the weakest of the acids (see table, p. 104) as well as among the weakest of
the bases (table, p. 106). We shall return to these relations, presently, and
shall find that the apparent weakness of water, as a base and as an acid, is
seemingly very largely due to the fact that water represents only an
extremely dilute solution (see p. 66) of the real hydroxide, HOH, or hydrol,
and consists very largely of a compound (H2O)2. H2O, or hydrol, is,
perhaps, not very much weaker as an acid or as a base, than is aluminium
hydroxide.
Lower oxides of elements in the higher (acid-forming) groups show a
less pronounced acid-forming character than the higher oxides, and a
greater tendency to produce bases as well as acids, and are often
amphoteric. Chromium hydroxide is of this type.
In view of all these facts, and in view, also, of the fact that the majority of
the seventy-odd elements cannot lie at the ends of the periodic system but
are found in the middle, it is not surprising to find that pronounced
amphoterism is shown by a large number of metal hydroxides; it is,
perhaps, the rule rather than the exception. A considerable number of the
elements in the middle of the system are rare elements and that is perhaps
the chief reason why this relation does not stand out more prominently in
the consideration of the common acids and bases.
Amphoteric Character of Hydroxides Considered in Analysis.
—The amphoteric character of hydroxides is frequently made use of in
analytical work in the separation and identification of various elements and,
when present, it must always be considered, in order to escape possible

error. The following hydroxides of the common elements show pronounced
amphoteric character: aluminium, chromic, zinc, lead, stannous,
antimonous hydroxides and arsenious, platinic, auric, antimonic and stannic
acids. Arsenic acid, ferric hydroxide and silicic acid show exceedingly
slight, but perceptible, amphoteric character, sufficient to affect, to a certain
degree, their analytical behavior.359 [p176]
Self-Neutralization of Amphoteric Substances.
360
—We may turn now to the third question raised in connection with
aluminium hydroxide, to the inquiry (p. 171), why aluminium hydroxide,
the acid, does not neutralize aluminium hydroxide, the base. In fact, the
base must and does form a salt with the acid. But the salt is formed only to
a minimal extent, as the result of the fact that the base is a very weak base,
the acid an exceedingly weak acid. Such exceedingly weak bases and acids
show little tendency to combine with each other to form salts in the
presence of water, especially if one or both are difficultly soluble in water,
as in the present instance. The behavior of aluminium hydroxide, in this
respect, is part of a much larger and more general question, growing out of
the fact that water is a very weak acid and base, as has been seen, and, to a
greater or lesser extent, reacts as such with salts, which are dissolved in it.
This action of water plays an important rôle in many analytical reactions,
and especially, also, in the reactions of aluminium salts. We shall, first,
discuss this larger question of the action of water, as an ionogen, on salts,
and then return (p. 187) to the problem of the self-neutralization of an
amphoteric hydroxide.

Hydrolysis of Salts
Ionization of Water.
—We may first consider, very briefly, the evidence that water is ionized
even to the extent indicated by the ionization constants given in our tables.
It may be said that the purest water ever prepared361 shows a minimal
conductivity, from which the concentrations of its hydrogen and hydroxide

ions and the value of the ionization constant may be calculated. For the
ionization of water we have
[H+] × [HO−] / [Nonionized water] = KIon.

As the concentration of pure water, or of the water in dilute solutions,
may be considered nearly a constant, we may put
[H+] × [HO−] = KH2O.

This is the relation most commonly, and most conveniently, used. It is
free from all assumptions as to the molecular weight of the nonionized
water, the calculation of the concentrations [p177] [H+] and [OH−] being
independent of any such assumption. The value of KH2O increases decidedly
with an increase in the temperature,362 whereas the ionization constant of an
ordinary acid, such as acetic acid, is affected very little by changes in
temperature. This peculiar increase of the ionization of water at higher
temperatures is undoubtedly due to the increasing dissociation of the
complex water molecules into hydrol molecules (see p. 66), which,
presumably, are most easily ionized. Now, the value of the constant KH2O, at
any temperature, may be determined in some half a dozen different and
independent ways, including the conductivity method mentioned, and one
of the most remarkable developments of the theory of ionization is that all
of these methods lead to concordant results.363
Aside from considerations based on its ionization, water may be shown, by its chemical behavior,
to have the functions of an acid and of a base, and the conclusions reached are in complete accord
with those reached with the aid of the theory of ionization.
Water is An Acid.
—If the oxide of a metal such as copper, lead or calcium, is treated with an acid, a salt is formed by
the combination of the two; for instance, we have
PbO + HCl → Pb(OH)Cl,
Pb(OH)Cl + HCl → PbCl2 + H2O,
PbO + 2 HCl → PbCl2 + H2O,
CaO + 2 HCl → CaCl2 + H2O.

Water will combine with a number of oxides very much in the same manner and sometimes with
such vigor, that considerable heat is evolved, as in the slaking of lime (exp.):
CaO + HOH → Ca(OH)2.

Water in this, and similar actions, takes the place of and plays the rôle of, an acid, and the metal
hydroxides or bases appear as its salts.364 It is a very weak acid, which can easily be driven out of
its salts by any stronger acid (neutralization of bases), but that does not alter the conclusions reached.
Considered from the point of view of the theory of ionization, the relation [p178] would be expressed
by saying that in the common bases the positive hydrogen ion of water has been replaced by some
other positive or metal ion. The salt of any acid could be defined in exactly the same way.
Water as a Base.
—Acid oxides, such as carbon dioxide, silicon dioxide, arsenious oxide, combine more or less readily
with bases, such as sodium hydroxide, to form salts:
CO2 + NaOH → NaHCO3,
As2O3 + 2 NaOH → 2 NaAsO2 + H2O.

A number of acid oxides combine with water in exactly the same manner, and sometimes with such
tremendous vigor, that great care must be taken in bringing the two together, as is the case when
sulphur trioxide or phosphorus pentoxide are added to water (Exp.).
We have P2O5 + HOH → 2 HPO3.

It is evident that in such actions water may take the place of, and play the rôle of, an ordinary base,
forming the acids, which may well be defined as hydrogen salts.365 It is true that the basic properties
of water are so weak, that the metal ion of even a weak base, like ammonium hydroxide, will replace
the hydrogen-ion in its salts, the acids, quite readily (HCl + NH4OH ⥂ NH4Cl + H2O). But such a
weak base, in turn, will have to give way, of course, to still stronger bases; for instances, NH4Cl +
NaOH ⥂ NaCl + NH4OH. From the point of view of the theory of ionization, the hydrogen-ion is
positive, like all the other metals ions whose hydroxides are bases.
There should be no difficulty, therefore, in considering water to have the chemical properties of a
base as well as of an acid. Its chemical activities as such, weak as they may be, must be satisfied
whenever it is present. These activities lead to the hydrolysis or the decomposition of salts by water,
in greater or lesser degree, whenever water is used as a solvent for salts.

Action of Water on a Salt of a Strong Base and a Strong Acid.
—If sodium chloride, a typical salt formed from a strong base and a strong
acid, is dissolved in water, it is ionized to a considerable extent.
Considering the solution from a mechanical point of view, we would expect
that the sodium ions, moving in all directions, would collide occasionally
with hydroxide ions, which are formed from the water and are present in

minute but definite quantity. Some of the collisions must result in the
formation of sodium hydroxide, as we have no reason to suppose that the
result would differ from that in other cases where positively charged
particles meet with negatively charged ones. However, since sodium
hydroxide is an ionogen, with a very great tendency to ionize, and since
there is present only a minute concentration of the hydroxide-ion, the [p179]
equilibrium conditions will be satisfied when only traces of the nonionized
hydroxide are formed. In a similar manner, we must expect to have traces,
and only traces, of nondissociated hydrochloric acid formed by the union of
chloride ions with some of the hydrogen ions of the water. Since hydrogen
chloride and sodium hydroxide show practically the same tendency to
ionize (tables, pp. 104 and 106), the two kinds of ions which water forms,
the hydrogen-ion and the hydroxide-ion, will be used up to a very slight and
practically equal extent to form nonionized sodium hydroxide and hydrogen
chloride, but the ions will be immediately regenerated, and in equal
concentrations, from the nonionized water which is present. All the
equilibrium requirements will be satisfied when traces of sodium chloride
have been converted into nonionized sodium hydroxide and hydrogen
chloride. Such a solution, containing no excess of the hydrogen- or the
hydroxide-ion, would react neutral. The action may be expressed by the
equation366
NaCl ⇄ Na+ + Cl−
H2O ⇄ HO− + H+
Na+ + HO− ⇄ NaOH
Cl− + H+ ⇄ HCl.
The decomposition of sodium chloride by water, which one may predict
on the basis of these theoretical considerations, may be demonstrated, slight
as it is, by the following experiment.367
Exp. A pinch of sodium chloride is brought into a platinum crucible, which is previously heated
in a blast lamp to a bright yellow heat (1100°); then 1 c.c. of water is introduced, drop by drop. A

steam cushion is formed at once (Leidenfrost's phenomenon). After about half of the water has been
evaporated (half a minute), the water is poured into a solution colored with blue litmus; it is changed
to red by an excess of hydrochloric acid in the water. The crucible is cooled, and the salt remaining in
it is dissolved in a little water and the solution poured into a red litmus solution; the latter turns blue.

The sodium chloride has obviously been partially decomposed, by the
water, into its base and its acid; the decomposition is favored by the high
temperature and by the fact that the hydrogen chloride [p180] formed can
pass through the steam cushion into the water, while the sodium hydroxide
is left behind. The removal of a product of the decomposition would favor
its progress (see. p. 114).
The conclusions concerning salts of the type of sodium chloride may then
be summarized in the statement, that salts formed by the union of a very
strong base with an equally strong acid are only very slightly decomposed
by water and their solutions show a neutral reaction.
The decomposition of a salt by water into its component base and acid is
called hydrolysis and the salt is said to be hydrolyzed in the action.
Action of Water on the Salt of a Strong Base with a Weak Acid.
—The relations are similar in principle, but quite different in degree and in
net result, when the salt of a very strong base, combined with a weak acid,
is dissolved in water. Potassium cyanide is a typical salt of this kind, and
the study of its hydrolysis will illustrate the behavior of this class of salts.
The hydrolysis takes place according to the equations
KCN ⇄ K+ + CN−
HOH ⇄ HO− + H+
K+ + HO− ⇄ KOH
CN− + H+ ⇄ HCN.
When the cyanide is dissolved in water, we must obtain, for the same
reasons as were developed in the discussion of the hydrolysis of sodium
chloride, a little nonionized potassium hydroxide, from the union of
potassium ions with hydroxide ions, formed by the water. Potassium
hydroxide being a strong, easily ionizable base, there will be only a slight

tendency towards this union. Hydrocyanic acid, on the other hand, is an
exceedingly weak acid. The value of its ionization constant KHCN = [H+] ×
[CN−] / [HCN] is only 7E−10, as compared with a similar ratio
approximating 1 for potassium hydroxide ([K+] × [HO−] / [KOH] = 1; see
the tables, p. 104 and p. 106 and see pp. 106–7). The hydrogen-ion, formed
from the water, must therefore combine with cyanide-ion, to form
nonionized hydrocyanic acid, much more completely than the hydroxide-
ion combines with potassium-ion. With the disappearance of the ions of
water, in this case notably of its hydrogen ions, more water must ionize to
satisfy the ionization constant [p181] for water (p. 176), and the formation of
hydrocyanic acid will continue, towards the satisfying of its own constant.
It is important to note that, for the reasons given, the hydrogen-ion of water
is used up to a far greater extent than is the hydroxide-ion; the latter
therefore accumulates, and this accumulation results in the formation of
smaller and smaller concentrations of the hydrogen-ion, by the water. Since
[H+] × [HO−] = 1.2E−14 (at 25°; p. 104), as [HO−] grows larger, [H+] must
grow proportionally smaller. The suppression of the hydrogen-ion by the
accumulation of the hydroxide ion will, ultimately, make [H+] so small, that
the equilibrium ratio [H+] × [CN−] / [HCN] will equal the equilibrium
constant. Since the union of the hydrogen-ion with the cyanide-ion, to form
little ionized hydrocyanic acid, is the main moving cause for the changes,
the latter will then come to a standstill and equilibrium will be established.
The net result of the action of water on potassium cyanide may be said to
consist in the formation of practically nonionized hydrocyanic acid and the
liberation of (chiefly) ionized potassium hydroxide, until all the equilibrium
constants of the system are satisfied. We note that potassium cyanide
solution must react strongly alkaline (exp.) and that a free acid (e.g. HCN)
may well exist in the presence of a free base (e.g. KOH), provided the acid
is present in a nonionized, and therefore chemically inactive, condition
(inactive as an acid).

Ignoring the (practically) unimportant formation of small quantities of
nonionized potassium hydroxide, we may summarize the action in a single
equation, which shows the main action:
CN− + HOH ⇄ HCN + HO−.
Whereas water, as an acid and as a base, is so exceedingly weak, that it
can form but traces of its own salts, sodium hydroxide and hydrochloric
acid, when acting on sodium chloride and competing for the base with such
a strong acid as hydrochloric acid and for the acid with such a strong base
as sodium hydroxide (see p. 179), the result, evidently, is quite different
when water competes for a base with so weak an acid as hydrocyanic acid.
In this case, we note that a considerable quantity of (ionized) potassium
hydroxide, the salt of water in its rôle of an acid, is formed as a result of the
action of water on potassium cyanide. [p182]
The theory of ionization, with the aid of the law of chemical equilibrium, gives us the means for
accurately defining the relative concentrations of the products, in the final condition of
equilibrium.368 For the weak acid, hydrocyanic acid, we have the condition of equilibrium

[H+] × [CN−] / [HCN] = KHCN = 7E−10.

The symbols [H+], [CN−] and [HCN] denote the final concentrations for the condition of
equilibrium, indicated in the equations on p. 180; in such a mixture [H+] is not equal to [CN−], as it
is in pure solutions of hydrocyanic acid in water. [CN−], representing the total concentration of the
cyanide-ion, is very much larger than [H+], since the salt, potassium cyanide, produces the cyanide-
ion in large concentrations.
For water, we have [H+] × [HO−] = K HOH = 1.2E−14, at 25°. Here, again, the symbols represent
the final, total concentrations of the ions in the mixture and [HO−] is much larger than [H+], since
hydroxide-ion is formed in large quantities, as described above.
Combining the two equations, we have:

[CN−] / ([HCN] × [HO−]) = KHCN / KHOH = KHydrolysis.

The cyanide-ion, whose concentration is expressed by [CN−], is formed practically altogether by
the ionization of potassium cyanide, which is an easily ionizable and almost entirely ionized salt; the
hydroxide-ion, whose concentration is expressed by [HO−], is formed by the ionization of potassium
hydroxide, which is an easily ionizable base, ionized to practically the same degree as is the

potassium cyanide in the solution. If we represent the total concentration of the potassium cyanide,
ionized and nonionized, at the point of equilibrium, by [KCN] and its degree of ionization by α1, and
if we represent, similarly, the total concentration of potassium hydroxide by [KOH] and its degree of
ionization by α2, the equilibrium equation may be written:
α1[KCN] / ([HCN] × α2[KOH]) = KHCN / KHOH = KHydrolysis.

Since the degrees of ionization of the two strong electrolytes are practically the same, we have
further simply
[KCN] / ([HCN] × [KOH]) = KHCN / KHOH = KHydrolysis.

The mathematical equations give us a measure of the extent to which water must decompose or
hydrolyze the salt in question, as expressed in the chemical equations (p. 180). The extent of the
hydrolysis, clearly, depends on the relative ionization constants of hydrocyanic acid and water, the
two acids competing for the base.
From the known values of the constants, one may calculate that, at 25°, in a solution of 6.5 grams
potassium cyanide in a liter (0.1 molar), almost 1.3% of the cyanide is decomposed into potassium
hydroxide and hydrocyanic acid. Since every molecule of hydrolyzed salt forms one molecule of
[p183] the hydroxide and one molecule of the acid, we may put [KOH] = [HCN] = x and [KCN] = 0.1
− x. The ionization constant, KHCN = 7E−10, and KHOH = 1.2E−14, at 25°. Inserting these values
into the equation [KCN] / ([HCN] × [KOH]) = KHCN / KHOH we have: (0.1 − x) / x2 = 7E−10 /
1.2E−14. Here x = 0.0013. This is 1.3% of the 0.1 mole of cyanide used.
One may convince himself, as follows, that the constants are satisfied when the decomposition of
the cyanide has proceeded to this point: the degrees of ionization of the potassium cyanide and
potassium hydroxide, α1 and α2, may be taken as 85% (the same as the degree of ionization of the
similar electrolyte KCl in 0.1 molar solution). Then [HO−] = 0.85 × 0.0013 = 0.0011; [CN−] = 0.85 ×
(0.1 − 0.0013) = 0.083; [H+] = 1.2E−14 / [HO−] = 1.1E−11. For [H+] × [CN−] / [HCN] we have then:
1.1E−11 × 0.083 / (0.0013) or 7E−10, the value for the ionization constant of hydrocyanic acid. It
should be noted that, whereas in pure water at 25° [H+] = [HO−] = √(1.2E−14) = 1.1E−7, in the
solution under consideration [HO−] has increased to the value 0.0011 and [H+] is only 1.1E−11.
The relation developed for the hydrolysis of potassium cyanide is a general one, holding for the
hydrolysis of salts, of the type MeX, of a weak acid with a strong base. It may be expressed in
general as follows: for the hydrolysis of a salt according to MeX + HOH ⇄ MeOH + HX, where HX
is a weak acid and MEOH a strong base, we have:369
[Salt] / ([Acid] × [Base]) = KAcid / KHOH.

It is clear, from the equation, that the weaker the acid of the salt (measured by the ionization
constant KAcid, the numerator on the right), the more will water, ceteris paribus, be able to drive it
out of its salt and form its own salt, the base (the smaller the numerator on the right, the larger must
be the denominator on the left).

The conclusions may be summarized in the statement that the salts of
strong bases with weak acids are more or less decomposed by water
(hydrolyzed) and the resulting solutions must react alkaline. We find, as a
matter of fact, that aqueous solutions of potassium cyanide, sodium
carbonate, sodium sulphide, borax (see the table, p. 104), all react strongly
alkaline to litmus (exp.). Conversely, it may be said, that if the sodium or
potassium salt of an acid dissolves in water with a decidedly alkaline
reaction, it is the salt of a weak, poorly ionized acid.370 [p184]
Action of Water on a Salt of a Strong Acid with a Weak Base.
—Exactly similar relations obtain in the case of salts of strong acids with
weak bases:[1] they are decomposed, to a greater or less extent, into the
free, strong, largely ionized acid and the free, scarcely ionized weak base,
the decomposition being stopped by the accumulation of the free strong acid
(more exactly, of the hydrogen-ion). Such solutions react strongly acid, as
in the case of the chloride, nitrate, sulphate of aluminium, of iron (ferric), of
chromium, and of similar salts of weak bases.
For MeX + HOH ⇄ MeOH + HX, where MeOH is a weak base and HX a strong acid, we have as
before:371

[Me+] / ([H+] × [MeOH]) =
[Salt] / ([Acid] × [Base]) = KBase / KHOH.

Action of Water on a Salt of a Base and an Acid, Both of which are
Weak.
—We will now turn to the consideration of the action of water on the fourth
class of salts, the salts of a weak base with a weak acid.372
Like all salts, such a salt, say MeX, would ionize very readily, when
dissolved in water (the few exceptions to readily ionizable salts are not
under consideration), and, in this case, both the positive and the negative
ions would have to combine respectively with the hydroxide and the
hydrogen ions of water to form the nonionized weak base and the

nonionized weak acid, and satisfy two very small constants, KBase and
KAcid:

[Me+] × [HO−] / [MeOH] = KBase
and [H+] × [X−] / [HX] = KAcid.
Both the hydrogen and the hydroxide ions of water would disappear, and in
approximately equal quantity, if the base and acid were approximately
equally weak, and the ions would be regenerated from water with no
accumulation of either one to suppress the other, as in the two previous
cases considered. Under these circumstances, the decomposition by water
must proceed very much further than in the previous cases. For instance, in
the hydrolysis of potassium cyanide in 0.1 molar solution, at 25°, we find
the concentration of the hydrogen-ion [H+] reduced373 from 1.1E−7, its
[p185] value in pure water, to 1.1E−11, as a result of the accumulation of

potassium hydroxide (the hydroxide-ion), and only this small value for [H+]
appears in the equation for the formation of the free acid, HCN (first
equation, p. 182; vide the calculation, p. 183). But, in the present case, the
factors [HO−] and [H+], in the equations on p. 184, maintain practically
their original value, about the same as in pure water, and the formation of
nonionized MeOH and HX must go correspondingly further to satisfy the
constants KBase and KAcid. Just how far the action must proceed, can be
formulated with the aid of the theory of ionization and the law of chemical
equilibrium,374 much in the same way as for the hydrolysis of potassium
cyanide.
The final equation, as developed by Arrhenius, reads:

[Me+] × [X−] α2 [Salt]2 KAcid × KBase
= = = K,
[HX] × [MeOH] [Acid] × [Base] KHOH

in which KAcid and KBase represent the ionization constants of the acid and the base, as given in the
tables (pp. 104 and 106), and α is the degree of ionization of the salt.

For the cyanide of a base, which is as weak a base as hydrocyanic acid is
an acid, we find that the decomposition by water, at 25° in a 0.1 molar
solution, must comprise 99.35%375 of the salt, in order to establish
equilibrium. In the case of potassium cyanide, in 0.1 molar solution, only
1.3% of the salt is decomposed (p. 182).
Now, if both the free base and the free acid are very difficultly soluble,
then the concentrations [MeOH] and [HX], respectively, in the solution
cannot go beyond a certain minute limit. In view,376 then, of the very small
value, KBase, of the ratio [Me+] × [HO−] / [MeOH] and the minute value that
the second term [MeOH] has under these conditions, the first term [Me+] ×
[HO−] must have a correspondingly smaller value. It is clear, therefore, that
in such a solution neither the nonionized base, MeOH, nor its ion, Me+, can
exist in more than minute quantities when the equilibrium constants are
satisfied. The same conclusion is reached regarding the [p186] possibility of
the existence of the difficultly soluble acid HX and its ion X−, in more than
minimal quantities. Since, then, neither the ion Me+ nor the ion X− can be
present in more than traces, their salt, MeX, which is considered readily
ionizable, also cannot exist in aqueous solutions, except in traces.
The quantitative relations are evident from the equilibrium equation (p. 185): [Me+] × [X−] /
([HX] × [MeOH]) = α2 [Salt]2 / ([Acid] × [Base]) = KAcid × KBase / KHOH = K. It is evident that the
concentration of the salt, [Salt], which is capable of existence in aqueous solution, is, in the first
place, the smaller the smaller the values for KAcid and KBase are, i.e. the weaker the acid and the
base are; and, in the second place, it is the smaller the smaller the values for [Acid] and [Base] are,
which, in the present instance, represent the concentrations of the difficultly soluble acid and base in
saturated solution, i.e. their solubilities.

We reach the conclusion that salts of very weak bases and very weak
acids are very considerably decomposed by water, and, if both the acid and
the base are difficultly soluble in water, the decomposition is practically
complete. Conversely, such a very weak, difficultly soluble base will not
combine with a very weak, difficultly soluble acid to form a salt in the
presence of water. An instance of the first kind is found in the case of

aluminium sulphide, the salt of a very weak, difficultly soluble base,
aluminium hydroxide, with a rather little soluble, weak acid, hydrogen
sulphide (see table, p. 104). We find that when a piece of aluminium
sulphide, prepared by dry methods, is dropped into water (exp.), a
precipitate of aluminium hydroxide is immediately formed and evolution of
hydrogen sulphide occurs. We have
Al2S3 ⇄ 2 Al3+ + 3 S2−,
6 HOH ⇄ 6 HO− + 6 H+
2 Al3+ + 6 HO− ⇄ 2 Al(OH)3 ↓
3 S2− + 6 H+ ⇄ 3 H2S ↑.

An instance where a very weak insoluble acid will not combine,
appreciably, with a very weak insoluble base, is found in the case of
aluminium hydroxide. A development of the equilibrium equations for its
ionization as a base and its ionization as an acid would show, that all the
constants would be readily satisfied, when a very minute quantity of
dissolved ionized aluminium aluminate is formed. [p187]
Self-Neutralization of Amphoteric Hydroxides.
—We may consider a saturated solution of aluminium hydroxide, in contact with the solid hydroxide.
For the acid ionization,377 Al(OH)3 ⇄ AlO2− + H+ + H2O, we have

[AlO2−] × [H+] / [Al(OH)3] = KAcid.

Similarly, for the basic ionization,378 Al(OH)3 ⇄ (AlO)+ + HO− + H2O, we have

[AlO+] × [HO−] / [Al(OH)3] = KBase.

The formation of traces of nonionized (basic) aluminium aluminate would satisfy the equilibrium
requirements for AlO+ + AlO2− ⇄ AlO(AlO2), since the aluminate, like other aluminates, is
presumably readily ionizable in aqueous solutions. Aluminium hydroxide, as a base and as an acid,
would yield in the first moment greater concentrations of the hydroxide and hydrogen ions than
would satisfy the equilibrium constant for water (p. 176); the excess of these ions must combine to
form water, until the product of their concentrations is equal to the ionization constant of water. The
neutralization of these first quantities of hydrogen and hydroxide ions would destroy the momentary
condition of equilibrium between aluminium hydroxide and its ions and would lead to its further
ionization, both as a base and as an acid, and to the solution of some aluminium hydroxide (see the

above equilibrium equations). However, since AlO+ and AlO2− remain practically uncombined and
therefore accumulate in the solution, the concentrations of the hydroxide and hydrogen ions formed
grow smaller and smaller; for an increasing excess of the ion AlO+ will allow only smaller and
smaller values for [HO−], according to the equilibrium equation for KBase, and, similarly, an
increasing excess of the ion AlO2− will permit [H+] to reach only smaller and smaller values,
according to the equilibrium equation for KAcid. When the values for [HO−] and [H+] have in this
way become small enough to make [HO−] × [H+] = KHOH, equilibrium is reached. It is evident that
in such a solution, in the condition of equilibrium, [HO−] is not equal to [AlO+], as it would
ordinarily be, according to the ionization equation Al(OH)3 ⇄ AlO+ + HO− + H2O, but is much
smaller. Similarly, [H+] is much smaller than [AlO2−].
Just how much aluminium aluminate must be formed by a self-neutralization of the amphoteric
hydroxide will depend on the values for KBase and KAcid and on the solubility of aluminium
hydroxide (nonionized Al(OH)3). The two equilibrium equations may be combined:

[AlO+] × [AlO2−] × [H+] × [HO−]
= KBase × KAcid.
[Al(OH)3]2
[p188]

Since [H+] × [HO−] = KHOH, and since [AlO+] and [AlO2−] may be taken to represent each the
concentration of the practically completely ionized aluminium aluminate AlO(AlO2), we have379

[Alum. Aluminate]2 KBase × KAcid
= ,
[Alum. Hydroxide]2 KHOH

or

[Alum. Aluminate] KBase × KAcid
=√( ).
[Alum. Hydroxide] KHOH
It is clear, that the smaller the ionization constants KBase and KAcid are, and the smaller the
solubility of nonionized aluminium hydroxide [Alum. Hydroxide] is, the smaller must be the
concentration of the aluminate formed to satisfy the conditions for equilibrium.
Aluminium hydroxide is a typical amphoteric hydroxide, and the relations developed may be
applied, mutatis mutandis, to the conditions of equilibrium for analogous amphoteric hydroxides,
such as zinc, lead, chromic hydroxides, and so forth. Salt formation or self-neutralization will
depend, in every instance, on the strength of the base and the acid formed, and on the solubility of the
hydroxide.380

With the aid of the preceding considerations the analytical reactions of
aluminium, which are used to separate it from other elements and to
identify it, may be readily understood. They will be discussed in connection
with the analysis of the "Aluminium and Zinc Groups."
The Analysis of the Aluminium and Zinc Groups.
—The groups of metals which are here called the [p189] "Aluminium and
Zinc Groups" consist of two groups, which ordinarily are precipitated
together in qualitative analysis, and which are then separated from each
other. We may distinguish the "Aluminium Group" of trivalent metal ions,
including aluminium, ferric and chromium ions, and the "Zinc Group" of
bivalent metal ions, including zinc, nickelous, cobaltous, manganous and
ferrous ions. Of the two groups, the ions of the second group, in agreement
with their lower valence (see p. 172), form the stronger bases, and, as such,
they are all capable of forming comparatively stable salts even with such
very weak acids as hydrogen sulphide and carbonic acid. Ammonium
sulphide, added to a solution of a salt of any one of the ions of the zinc
group, precipitates the corresponding sulphide, sodium or ammonium
carbonate precipitates the corresponding carbonate.381 We have, for
instance:
FeCl2 + (NH4)2S → FeS ↓ + 2 NH4Cl,
FeCl2 + Na2CO3 → FeCO3 ↓ + 2 NaCl.
Only one member of this group, zinc, forms an amphoteric hydroxide and
advantage is taken of this in identifying zinc.
The members of the aluminium group form hydroxides, which are much
weaker bases than are the hydroxides of the bivalent group just considered.
Their salts with strong acids are considerably hydrolyzed and react strongly
acid, and their salts with very weak acids, like carbonic acid and hydrogen
sulphide, are decomposed so readily by water, that only ferric sulphide is
capable of existence in its presence. When the sulphide, Al2S3, prepared by
heating aluminium with sulphur, is added to water, it is totally decomposed

into the hydroxide and hydrogen sulphide (p. 186); and if aluminium
chloride is treated with ammonium sulphide in aqueous solution, aluminium
hydroxide, and not its sulphide, is precipitated. The latter result may be
interpreted in two ways, both of which, in the ultimate analysis, mean that
hydrogen sulphide is too weak an acid to form a stable sulphide with
aluminium hydroxide in the presence of water, the difficult solubility of
aluminium hydroxide and the limited solubility of hydrogen sulphide being
favoring factors (see p. 186). In a solution of aluminium chloride, the salt of
a very weak base with a strong [p190] acid, more or less of the salt is
hydrolyzed, and we have a condition of equilibrium as expressed in the
equation AlCl3 + 3 H2O ⇄ Al(OH)3 + 3 HCl. The addition of ammonium
sulphide to such a solution would neutralize the free hydrochloric acid, and
the action would proceed to completion towards the right, hydrogen
sulphide being liberated, by the action of the acid on the ammonium
sulphide. As hydrogen sulphide is too weak an acid to combine,
appreciably, with aluminium hydroxide, and as the latter is difficultly
soluble, the hydroxide is precipitated. According to the degree of dilution,
more or less of the hydrogen sulphide also escapes. Besides this
interpretation of the precipitation of aluminium hydroxide under these
conditions, we may also consider the following: any aluminium sulphide,
formed the first moment, would remain largely ionized and would be
immediately converted, by the ions of water, into aluminium hydroxide and
hydrogen sulphide. The net result of the action is the precipitation of
aluminium hydroxide and the evolution of hydrogen sulphide:
2 AlCl3 + 3 (NH4)2S + 6 H2O →
2 Al(OH)3 ↓ + 6 NH4Cl + 3 H2S ↑ or
2 Al3+ + 3 S2− + 6 HOH → 2 Al(OH)3 ↓ + 3 H2S ↑.

A similar result is obtained when the solution of a chromium salt is
treated with a solution of ammonium sulphide. Only ferric hydroxide is

capable of forming a sulphide, ferric sulphide, Fe2S3, which is precipitated
when solutions of ferric salts are treated with ammonium sulphide.382
Ammonium sulphide will, consequently, precipitate aluminium and
chromium hydroxides and ferric, ferrous, nickel, cobalt, manganese and
zinc sulphides, from a solution of the chlorides of the metals.
Now, both the sulphides and the hydroxides of the alkaline earths and
alkalies are sufficiently soluble not to be precipitated by ammonium
sulphide, or by a mixture of it with ammonium hydroxide, if ammonium
chloride be added to the mixture to prevent the precipitation of magnesium
hydroxide (see p. 168), which is the least soluble of the hydroxides of the
alkaline earth group. [p191] A mixture of ammonium sulphide, ammonium
hydroxide and ammonium chloride will, therefore, precipitate the
aluminium and zinc groups together, separating them from the alkaline
earth and alkali groups.383

Separation of the Aluminium Group from the Zinc Group by Means of
Ammonium Chloride and Ammonium Hydroxide.
—The precipitation of the two groups together makes their subsequent
separation necessary. Some analysts attempt to avoid the extra operations
involved, by making use of the fact that the hydroxides of the bivalent
group, although difficultly soluble, are, like magnesium hydroxide, still
sufficiently soluble not to be precipitated by ammonium hydroxide in the
presence of sufficient ammonium chloride, while the hydroxides of the
trivalent metals of this group are so insoluble that they may be precipitated
quantitatively by such a mixture (p. 170). The trivalent hydroxides may be
first precipitated by ammonium hydroxide, in the presence of ammonium
chloride, and, subsequently, the sulphides of the bivalent metals may be
precipitated by ammonium sulphide, the two precipitates being collected
separately. The method has the disadvantage that it is not always accurate.
The acid character of aluminium and chromium hydroxides (and even of
ferric hydroxide, see p. 195), as well as of zinc hydroxide, leads, to a certain
extent, to the precipitation, from such alkaline solutions, of salts of these
amphoteric hydroxides with the basic hydroxides of the bivalent group; the
latter are thus liable to be lost in the analysis. It will be recalled, that the
equilibrium conditions in alkaline solutions favor the ionization of
amphoteric substances in the acid form (Part III), and alkaline solutions
would favor the precipitation of aluminates, chromites, etc., of the ions of
the zinc group. Methods have, therefore, been devised to separate the two
groups in neutral, or very slightly acid, media, and they give quantitative
separations and are preferable to the method just described. The separation
by means of suspended barium carbonate, in which carbonic acid is
liberated and the solution is practically neutral, will be discussed below on
page 193. A second method, frequently used in quantitative analysis, is

based on the [p192] decomposition of the acetates of the aluminium group by
boiling water, acetic acid being liberated.384
Separation of Cobalt and Nickel from the Other Members of the Zinc
and Aluminium Groups.
—When the aluminium and zinc groups are precipitated together, by means
of a mixture of ammonium sulphide, hydroxide and chloride, the
precipitate, obtained from a solution containing, say, the chlorides of all the
ions of the groups, would consist of the following compounds:
Aluminium Group: Fe2S3, Al(OH)3, Cr(OH)3.

Zinc Group: NiS, CoS, FeS, MnS,385 ZnS.
If such a precipitate is treated, in the cold, for a short time with quite
dilute (1 to 1.2 molar) hydrochloric acid, all of the hydroxides and
sulphides dissolve, excepting the greater part of the nickel and cobalt
sulphides, which dissolve very much more slowly than do the other
compounds. Advantage is taken of this fact, to separate these two elements
from the remaining members of these groups, and if the treatment is carried
out with care, the separation is usually satisfactory. In all cases, however,
since it is a question of delayed solution only, at least traces, and sometimes
considerably more than traces, of the sulphides of nickel and cobalt go into
solution with the other compounds. No sacrifice of analytical accuracy is
involved, if this possible loss is kept in mind and provision made for the
later detection of these small quantities of nickel and cobalt.
The question of the slow solution, or apparent lack of solubility, of nickel
and cobalt sulphides in dilute hydrochloric acid has formed an interesting
problem for investigation. While nickel and cobalt sulphides are
precipitated by ammonium sulphide, these sulphides, in common with those
of all the other members of the zinc group, are not precipitated by hydrogen
sulphide in the presence of a small excess of hydrochloric acid.386 We
would have [p193]

NiCl2 + x HCl + H2S ⥃ NiS + (x + 2) HCl

as representing the condition of equilibrium, if we start with nickel chloride,
hydrochloric acid and hydrogen sulphide; the amount of sulphide NiS,
formed, is insufficient to supersaturate the solution and form a precipitate.
In reversible reactions the final condition of equilibrium must be
independent of the order in which components are mixed (p. 91), a
conclusion which is borne out by experience. One should expect, then, that
nickel sulphide, when treated with dilute hydrochloric acid, would dissolve
and give nickel chloride, hydrogen sulphide and an excess of acid, and thus
produce the same system, found to be in equilibrium, when one starts with
the chloride, hydrogen sulphide and hydrochloric acid. As a matter of fact,
the same condition of equilibrium is finally reached, only it is reached
slowly,387 much more slowly than ordinarily in such cases, much more
slowly, for instance, than with ferrous sulphide, hydrochloric acid and
hydrogen sulphide (exp.). By taking advantage of this slow return to
equilibrium and by working with the system during the process of slow
change (collecting the undissolved nickel and cobalt sulphides on a filter),
one can separate the sulphides of nickel and cobalt from the other
components of the mixed precipitate, which dissolve much more rapidly.
Separation of the Aluminium and Zinc Groups by Means of Barium
Carbonate.
—The solution, obtained by treating the mixture of the sulphides and
hydroxides of the aluminium and zinc groups with dilute hydrochloric acid
(p. 192), contains aluminium, chromium, manganous, zinc and ferrous
chlorides, all the iron being now present in the ferrous condition because of
the reducing action of hydrogen sulphide on the ferric-ion (Part III). The
chlorides of nickel and cobalt are also present in small quantities (see
above). The further treatment of the solution is directed toward a separation
of the bivalent ions of the zinc group from the trivalent ions of the
aluminium group, and the intention is to have all the iron go with the

trivalent metals. The ferrous is, therefore, oxidized to the ferric-ion. After a
part of the solution has been tested to show the presence or absence of ferric
salts, the two groups are separated by means of a suspension, in water, of
finely [p194] divided barium carbonate. The theory of the separation may be
developed as follows:
When zinc chloride, which may be taken as a representative of the
bivalent group, is treated with sodium carbonate, a difficultly soluble
carbonate is precipitated, since zinc hydroxide, like the remaining bivalent
hydroxides, is a sufficiently strong base to form a fairly stable carbonate.388
When ferric chloride, a representative of the trivalent group, is treated with
a solution of sodium carbonate, ferric hydroxide, mixed with some basic
ferric carbonate389 Fe2(OH)4CO3, is precipitated and carbon dioxide
escapes (exp.). The trivalent hydroxides are too weak bases390 to form
stable salts with so weak an acid as carbonic acid.
2 FeCl3 + 3 Na2CO3 + 6 H2O ⥂
2 Fe(OH)3 ↓ + 3 H2CO3 + 6 NaCl
3 H2CO3 ⇄ 3 H2O + 3 CO2 ↑.

Since the bivalent metal ions are precipitated by sodium carbonate as
carbonates and the trivalent ones as hydroxides, the reagent, obviously,
cannot be used to separate the two groups. But barium carbonate is so little
soluble in water that it will not precipitate manganous, zinc, nickel,
cobalious and ferrous carbonates391 from solutions of their chlorides or
nitrates. We have, for instance, ZnCl2 + BaCO3 ↓ ⥃ BaCl2 + ZnCO3. Barium
carbonate has, however, the same effect on ferric chloride (exp.) and on the
other chlorides of the trivalent group, as has sodium carbonate, i.e. it
precipitates their hydroxides. By means of barium carbonate [p195] we can,
therefore, precipitate the hydroxides of the aluminium group without
precipitating the ions of the zinc group. The separation is carried out in a,
practically, neutral medium (free carbonic acid in excess is evolved; barium

carbonate alone, when treated with water, is slightly alkaline) and thus
avoids the error of facilitating the precipitation of the bivalent metals in the
shape of salts of the acidic forms of the trivalent metals, i.e. as aluminates,
chromites, and so forth. Manganous salts are liable to oxidation to
manganic salts, when exposed to the air, especially in alkaline, neutral or
slightly acid solutions, and prolonged exposure of the barium carbonate
mixture to the air may result in the precipitation of manganic hydroxide,
Mn(OH)3, with the other trivalent hydroxides. Provision is made for its
detection in the systematic analysis.
Analysis of the Aluminium Group.
—The precipitate of the aluminium group may contain aluminium,
chromium and ferric hydroxides (possibly traces of manganic hydroxide)
and their basic carbonates. A color test for ferric-ion has already been made
(see p. 193) and chromium (and manganese) is readily found and identified
by oxidation to the intensely colored salts of chromic (and manganic) acid
(Part III, q.v.). In ascertaining whether aluminium hydroxide is present or
not, advantage is taken of its amphoteric character. Chromium hydroxide,
like aluminium hydroxide, is amphoteric; but, in agreement with the greater
atomic weight of chromium, it is an even weaker acid than is aluminium
hydroxide. Its sodium salt, sodium chromite, is completely decomposed by
boiling water, chromium hydroxide being precipitated in a less hydrated,
insoluble form. Ferric hydroxide, whose metal has the highest atomic
weight of the three elements under consideration, has so little acid
character, that it is not perceptibly soluble in solutions of potassium or
sodium hydroxide. (That it has slight acidic properties is shown by its
capacity to form ferrites, e.g. Me(FeO2)2, which may best be obtained by
dry methods, and of which ferrous ferrite or magnetic iron ore, Fe3O4 or
Fe(FeO2)2, is the most important representative.) Of the three hydroxides,
aluminium hydroxide is, therefore, the only one that will dissolve in boiling
sodium hydroxide. In this solution we can best identify it, by converting the

aluminate into an aluminium salt, by means of an excess of acid, [p196] and
by a final precipitation of aluminium hydroxide with ammonium hydroxide.
Aluminium hydroxide is too weak an acid to form a stable aluminate with
so weak a base as ammonium hydroxide, when the latter is used only in
slight excess (p. 186). If we attempt to prepare ammonium aluminate, by
adding ammonium chloride to a solution of sodium aluminate, a precipitate
of aluminium hydroxide is obtained (exp.). For exact work, an excess of
ammonium hydroxide is to be avoided and its strength as a base should be
weakened by the addition of some ammonium chloride or nitrate (pp. 114,
169 and Lab. Manual, p. 9, § 6).
We have, in this instance, the case of a very weak, difficultly soluble acid, aluminium hydroxide,
forming a salt with a weak, soluble base, ammonium hydroxide. The conditions determining the
solubility of aluminium hydroxide in ammonium hydroxide, as an aluminate NH4AlO2, may be
shown as follows: for the acid ionization of aluminium hydroxide, Al(OH)3 ⇄ AlO2− + H+ + H2O
(p. 172); the solubility-product for a saturated solution is [AlO2−] × [H+] = KAc.S.P.. Further, from
[H+] × [HO−] = KHOH, we find [H+] = KHOH / [HO−]. Then [AlO2−] = [HO−] × KAc.S.P. / KHOH,
which shows that the solubility of aluminium hydroxide, as aluminate, is proportional to the
concentration [HO−] of the hydroxide-ion in the solution. For NH4OH we have [NH4+] × [HO−] /
([NH3] + [NH4OH]) = 0.000,018 (p. 161), and consequently, [HO−] = 0.000,018 × ([NH3] +
[NH4OH]) / [NH4+]. Then [HO−] is the smaller, the smaller the excess of ammonium hydroxide
used (which is approximately equal to ([NH3] + [NH4OH])) and the greater the concentration
[NH4+] of the ammonium-ion, i.e. of the added ammonium salt. The solubility of Al(OH)3, as
aluminate, in ammonium hydroxide and ammonium chloride is, therefore, directly proportional to the
excess of ammonium hydroxide, and indirectly proportional to the concentration of the ammonium
salt present.392
The Favorable Conditions for a Maximum Precipitation of an Amphoteric Hydroxide.
—The precipitation of aluminium hydroxide depends also on the solubility-product of aluminium
hydroxide, ionized as a base. For Al(HO)3 ⇄ Al3+ + 3 HO−, in a saturated solution, [Al3+] ×
[HO−]3 = KBas.S.P.. It is evident, that an excess of the precipitating hydroxide-ion would be
favorable to the precipitation in this form, and that the reduction of the concentration of the
hydroxide-ion, while acting favorably, as just shown, in preventing the solution of the hydroxide as
an aluminate, must be, to some extent, detrimental to a maximum precipitation of the hydroxide as a
base. One may ask, therefore, what the most favorable concentration of the hydroxide-ion must be
for a quantitative precipitation of aluminium hydroxide. The problem may be treated as follows:

According to the solubility-product relation for the basic ionization, we have, in a solution saturated
with aluminium hydroxide, [p197]

[Al3+] = KBas.S.P. × [HO−]−3. I
For the sake of a certain simplicity in the result, we will, for the moment, consider aluminium
hydroxide to ionize as an acid according to Al(HO)3 ⇄ AlO33− + 3 H+, which would resemble the
basic ionization. Then we would have [AlO33−] × [H+]3 = K′Ac.S.P., and, using the relation
[H+] = KHOH / [HO−], we have

[AlO33−] = [HO−]3 × K′Ac.S.P. × KHOH−3. II
Adding equations I and II we find

[Al3+] + [AlO33−] =
KBas.S.P. × [HO−]−3 + [HO−]3 × K′Ac.S.P. ×
KHOH−3 III

Aluminium hydroxide will be most completely precipitated when [Al3+] + [AlO33−] is a minimum,
the values [Al3+] and [AlO33−] measuring the solubility of aluminium as aluminium-ion and as
aluminate-ion. If we put [Al3+] + [AlO33−] = y and [HO−] = x, we can find the value x (the
concentration of the hydroxide-ion) for which y is a minimum. We have y = KBas.S.P. × x−3 + x3 ×
K′Ac.S.P. × KHOH−3, and find, by means of the calculus,393 that y is a minimum, when x = +
(KHOH3 × KBas.S.P. / K′Ac.S.P.)1/6.
If aluminium hydroxide were as strong an acid as it is a base, i.e. if KBas.S.P. = K′Ac.S.P., we
would have, simply, x = [HO−] = ((1.2E−14)3)1/6 = √(1.2E−14) (at 25°), which is the concentration
of the hydroxide-ion in pure water at 25° (p. 176). In other words, a perfectly neutral solution would
then give us the conditions for as complete a precipitation as possible. But aluminium hydroxide is a
stronger base than acid, KBas.S.P. > K′Ac.S.P., and consequently we find for x = [HO−] = (KHOH3 ×
KBas.S.P. / K′Ac.S.P.)1/6, a value somewhat greater than the concentration of the hydroxide-ion in
pure water, i.e. we must use a slightly alkaline medium—which agrees with common practice. In
other words, there is less danger of losing aluminium hydroxide in the form of aluminate, owing to
the weaker acid character of the hydroxide, than there is of losing it in the form of aluminium-ion.
The most favorable degree of alkalinity for the precipitation would depend on the relation of
KBas.S.P.. and K′Ac.S.P..
The exact values for KBas.S.P. and K′Ac.S.P., the two solubility-product constants, and for the
corresponding ionization constants, which would show the same ratio, are still not known. But, if, for
the sake of an illustration, we take recourse to assumed values for these constants, we find that the
solubility of aluminium, as aluminium-ion and as aluminate-ion, is, by calculation, as anticipated, a

minimum for a solution, which contains the concentration of HO− calculated (for x) in the manner
indicated above. And the further interesting conclusion is reached that this minimum loss of
aluminium [p198] hydroxide would occur when [Al3+] = [AlO33−]—which would correspond to a
saturated solution of aluminium aluminate, Al(AlO3).
When the ionization of aluminium hydroxide, as an acid, is considered to take place according to
Al(OH)3 ⇄ AlO2− + H+ + H2O, which agrees best with its real behavior (p. 172), we can find,
similarly, that [Al3+] + [AlO2−] is a minimum, when aluminium hydroxide is precipitated in such a
way, that an excess x of the hydroxide-ion is used, and x = [HO−] = (3 KHOH × KBas.S.P. /
KAc.S.P.)0.25,—where KAc.S.P. represents the solubility-product constant for [AlO2−] × [H+]. That
a minimum loss of aluminium hydroxide would be suffered when the favorable excess of the
hydroxide-ion (x) is calculated on the basis of the equation as given, may readily be seen by again
assuming definite values for KBas.S.P. and KAc.S.P.. It also appears that this minimum loss394 of
aluminium includes one-third as many Al3+ ions, as AlO2− ions—a relation corresponding, again, to
a saturated solution of aluminium aluminate, Al(AlO2)3.

Chapter X Footnotes
[354] When all three of the hydrogen atoms in the hydroxide are ionized, an aluminate ion,
AlO33− is formed: Al(OH)3 ⇄ AlO33− + 3 H+. But, as in the case of other weak polybasic acids, a
single hydrogen atom is far more readily ionized than are the remaining two (p. 102), and the ion
Al(OH)2O−, which is formed by the primary ionization, readily loses water and forms the
anhydride ion AlO2−. The most important aluminates are derivatives of this ion.

[355] See the table at the back of Smith's Inorganic Chemistry, or p. 149 of Remsen's Inorganic
Chemistry.
[356] The displacement of hydrogen by a metal, like sodium, is the result of the displacement of
the hydrogen-ion (see Chapters XIV and XV). The hydrogen-ion in fused sodium hydroxide is
probably formed chiefly by the secondary ionization of the hydroxide-ion (HO− ⇄ H+ + O2−) (see
Chap. XIII). We cannot have positive ions, Na+, with negative ions, O2−, without having some
ions NaO−. (O2− + Na+ ⥂ NaO−), NaOH, undoubtedly, is much too weak an acid to form salts
with bases in the presence of water. Such salts would be decomposed by water (see below, p.
180), as sodium oxide, indeed, is decomposed; we have Na─O─Na + HOH ⇄ 2 NaOH (see
Chapter XIII for a detailed discussion of this action). These relations sufficiently account for the
fact that salts of sodium hydroxide, in which it has the functions of an acid, are not commonly
formed. (Cf. Abegg, Anorganische Chemie, II, (1) p. 247.)
[357] See J. J. Thomson, Corpuscular Theory of Matter, pp. 103–141.
[358] See Mendeléeff, Principles of Chemistry, I, 22 (1891), in regard to the rôle of "even" and
"uneven" series in the system.
[359] In regard to the indications of the amphoteric character of stronger acids, see Chapter XV.
[360] An elaborate treatment of this problem is given by Walker, Z. phys. Chem., 49, 82 (1904),
51, 706 (1905).
[361] Kohlrausch and Heydweiller, Z. phys. Chem., 14, 317 (1894).
[362] See the table, p. 104.
[363] See p. 53 and van 't Hoff's remarks, ibid.
[364] This suggests a much broader, natural definition of a base than the conventional one. All
salts of very weak acids, to a certain degree, which is determined by the weakness of their acids,
do exactly what the ordinary bases do, e.g. neutralize acids. Metal derivatives of acids weaker
than water, metal amides, like Zn(NH2)2, metal alkyls, like zinc methyl, Zn(CH3)2, react more
vigorously than the hydroxides do, e.g. in neutralizing acids, and water attacks them and acts

upon them, exactly as ordinary acids interact with metal hydroxides. We have, for instance,
Zn(CH3)2 + 2 HOH → Zn(OH)2 + 2 CH4.

[365] See footnote, p. 177. Similar considerations apply to the conventional definition of an acid.
[366] The symbols in heavy type indicate the chief components of the final system. Vide Smith's
General Chemistry for Colleges and Inorganic Chemistry, for the form of equations used.
[367] Emich, Ber. d. chem. Ges. 40, 1482 (1901).
[368] Arrhenius, Z. phys. Chem., 5, 16 (1890); Shields, ibid., 12, 167 (1893).
[369] See below for the corresponding equation, developed by Walker for a salt of a weak base
and a strong acid.
[370] Potassium sulphate, K2SO4, reacts faintly alkaline in aqueous solution, the secondary
ionization of sulphuric acid (table, p. 104) being somewhat weaker than the ionization of
potassium hydroxide. We have: K2SO4 + HOH ⇄ KHSO4 + KOH or SO42− + HOH ⇄ HSO4− +
HO−.
[371] Walker, Z. phys. Chem., 4, 319, (1889); Arrhenius, loc. cit.; Bredig, ibid., 13, 321 (1894).
[372] Arrhenius, loc. cit.
[373] See p. 183.
[374] Arrhenius developed the relation for aniline acetate, loc. cit.

[375] Putting x = [Acid] = [Base], we have [Salt] = (0.1 − x), and (0.1 − x)2 / x2 = (7E−10)2 /
1.2E−14. Then (0.1 − x) / x = 0.0064 and x = .09935, which is 99.35% of the total salt used. The
degree of ionization, α, of the salt, in the extremely dilute solution, is taken to be 100%.
[376] See the equations for KBase and KAcid, on p. 184, and their premises.

[377] See p. 172. The concentration of water may be considered a constant and is included in
KAcid (and KBase, below).
[378] Only the primary ionization (of aluminium hydroxide) is considered in the text, because
only that is involved, as a rule, in the neutralization of very weak bases by very weak acids (see
footnote 2, p. 194). The relations are also simpler and clearer, if we limit the discussion to the
formation of a salt AlO(AlO2).

[379] See the similar equation, p. 185.
[380] Amphoteric substances of a different class are also known, which have, at the same time,
moderately strong acid and moderately strong basic functions. Glycocoll, H2N.CH2COOH, a
derivative of acetic acid and ammonia, contains an acid group, the —COOH group, the hydrogen
of which is approximately as ionizable as the hydrogen in the corresponding group in acetic acid,
CH3COOH. The ammonia residue, H2N—, in glycocoll, forms with water a hydroxide,
corresponding to ammonium hydroxide, which likewise is approximately as ionizable as is

ammonium hydroxide. In the hydroxide of glycocoll we have, consequently, both a moderately
strong acid, and a moderately strong basic, group. In this, and in similar cases, salt formation
between the acid and the basic groups of the amphoters takes place to as great an extent as if the
functions were attributes of distinct compounds. Glycocoll in aqueous solution is present, then,
H .CH2.CO O
chiefly in the form of a salt, for instance, 3N , corresponding to ammonium
└───────┘
acetate, CH3COONH4. For an elaborate discussion of the equilibrium conditions in solutions of
amphoteric compounds vide Walker, Z. phys. Chem., 49 and 51.
[381] The carbonates are occasionally partially hydrolyzed to basic carbonates.
[382] Stokes, J. Am. Chem. Soc., 29, 304 (1907).
[383] A complication, which leads to the precipitation of alkaline earths, along with these groups,
as phosphates and similar insoluble salts (not as hydroxides or sulphides), when phosphate or
certain other acid ions are present, is treated in Part IV (q.v.) under the systematic analysis of the
groups.
[384] Cf. Fresenius, Quantitative Analysis.
[385] Ammonium sulphide usually precipitates a pink hydrated sulphide of manganese, probably
Mn(SH)(OH). Under certain conditions of concentration and temperature, the dark green sulphide
MnS is precipitated. In quantitative work the chemist aims to precipitate this green sulphide,
which is more easily collected on a filter. (Cf. Fresenius, Quantitative Analysis.)
[386] We shall find that this property of the whole zinc group makes it possible to separate the
following groups, the copper and arsenic groups, from the zinc group (see p. 158). The theory of
the separation will be discussed in detail in Chapter XI.
[387] Vide Noyes, Bray and Spear, J. Am. Chem. Soc., 30, 483 (1908).
[388] See footnote, p. 189.
[389] The comparative stability of this basic salt represents an instance of the different ionizing
power, or basic strength, of the three hydroxide groups of a trivalent base (see p. 106). The
hydrolysis of ferric chloride seems to involve, primarily, only the third or least ionizable of the
hydroxide groups of ferric hydroxide, and the hydrolysis, except in extreme dilution, proceeds
chiefly according to Fe3+ + 3 Cl− + HOH ⇄ Fe(OH)2+ + 3 Cl− + H+. Vide Goodwin, Z. phys.

Chem., 21, 1 (1896). In the case of the salt of the much weaker acid, carbonic acid, the hydrolysis
goes further, involving two hydroxide groups of ferric hydroxide and, to some extent, all three.
[390] The extreme insolubility of Al(OH)3, Fe(OH)3 and Cr(OH)3, together with their weakness
as bases, facilitates their precipitation (see pp. 185–6).
[391] There is a small degree of hydrolysis (see footnote, p. 189), but the hydroxides of the zinc
group are not sufficiently insoluble to be precipitated under these conditions.
[392] Cf. A. A. Noyes, Bray and Spear, J. Am. Chem. Soc., 30, 496 (1908).
[393] Cf. The Elements of the Differential and Integral Calculus, based on Nernst and Schönflies's
Lehrbuch, etc., by Young and Linebarger, pp. 363 and 364 (1900).
[394] Losses due to the tendency of aluminium hydroxide to assume the colloidal condition (p.
136) must be guarded against by other precautions (loc. cit.).

CHAPTER XI
THE COPPER AND SILVER GROUPS. PRECIPITATION
WITH HYDROGEN SULPHIDE

[p199] TOC

The sulphides of the metal ions of the zinc group are readily precipitated
by ammonium or sodium sulphide, but hydrogen sulphide, in the presence
of a small excess of a strong acid, such as hydrochloric acid, does not
precipitate any of these sulphides (or any of the sulphides of the aluminium,
the alkaline earth and the alkali groups). Under the same conditions the
sulphides of the metal ions of the silver group, Ag+, Hg+, Pb2+, of the
copper group, Hg2+, Pb2+, Bi3+, Cu2+, Cd2+, and also of the arsenic group,
As3+, As5+, Sb3+, Sb5+, Sn2+, Sn4+, Pt2+, Pt4+, Au+, and Au3+, are
precipitated. Advantage is taken of these relations in the following way, in
systematic analysis: after the separation of the silver group, by precipitation
of the difficultly soluble chlorides, hydrogen sulphide, in the presence of an
excess of acid, is used to precipitate the sulphides of the ions of the copper
and the arsenic groups, the two groups being precipitated together.
Hydrogen sulphide, under these conditions, does not precipitate any
sulphides of the zinc group or those of any of the remaining groups.
Hydrogen sulphide is used, in this way, as one of the most valuable reagents
in analytical work, enabling the analyst to separate whole groups of metal
ions from other groups. There is also no other agent, equally important,
which is more likely to be used in a wrong way and to lead to error.
The Ionization of Hydrogen Sulphide.
—Before taking up the theory of the separation of these groups by
precipitation with hydrogen sulphide in the presence of a strong acid, a
discussion of some of the characteristics of the reagent will be in place.

Hydrogen sulphide, like carbonic acid and other dibasic acids, ionizes in
two stages; it produces first hydrogen-ion and hydrosulphide-ion, HS−, and
this ion in turn dissociates, producing hydrogen-ion and sulphide-ion, S2−.
[p200]

For the first dissociation, HSH ⇄ H+ + HS−, we have
[H+] × [HS−] / [H2S] = K1 (I)
The value of the constant395 for this primary ionization of hydrogen
sulphide is 0.91E−7. It is apparent that hydrogen sulphide, even in the
primary ionization, is a very weak acid and produces a very small
concentration of hydrosulphide-ion. In a solution, saturated at 25°, the total
concentration of hydrogen sulphide is approximately 0.1 molar, and the
concentration of hydrosulphide-ion, therefore, in the absence of any foreign
acid, at most396 0.95E−4. The concentration of the dissolved, nonionized
hydrogen sulphide, [H2S], is practically a constant, if solutions saturated
with hydrogen sulphide under a given pressure, say under atmospheric
pressure, are considered. For such solutions, then, we may put more
simply396
[H+] × [HS−] = k = (0.95E−4)2 = 0.9E−8. (II)
The concentration of hydrosulphide-ion is, therefore, inversely proportional
to the concentration of hydrogen-ion. It is clear that the addition of a strong
acid, readily yielding concentrations of hydrogen-ion very much greater
than 0.95E−4 (the value of [H+] in a saturated aqueous solution of hydrogen
sulphide) will, as the result of the greatly increased total hydrogen-ion
concentration, reduce the concentration of hydrosulphide-ion to
correspondingly low values. For instance, the presence of 0.1 molar
hydrochloric acid will increase the concentration of hydrogen-ion close to a
thousandfold and will reduce the concentration of hydrosulphide-ion to
0.9E−7.

For the secondary ionization (see p. 101) of hydrogen sulphide, HS− ⇄
H+ + S2−, we have
[H+] × [S2−] / [HS−] = K2. (III)
The value of this constant has recently been determined397 and found to
be 1.2E−15. Recalling the fact that the concentrations [H+] and [HS−] of
hydrogen-ion and hydrosulphide-ion, [p201] respectively, resulting from the
primary ionization, are each398 0.95E−4, we have for the concentration of
the sulphide-ion, in aqueous solution saturated with hydrogen sulphide at
atmospheric pressure and 25°, [S2−] = 1.2E−15.
Combining equations (II) and (III), we have, further:399
[H+]2 × [S2−] = k × K2 = k2 = 1.1E−23, (IV)
which shows, directly, the relation between the concentration of the
sulphide-ion and that of the hydrogen-ion, the relation of primary
importance in considering the precipitation of metal sulphides in acid
solutions. The concentration of the sulphide-ion is, thus, inversely
proportional to the square of the concentration of the hydrogen-ion. A
thousandfold increase in the concentration of the latter, which is very nearly
the effect produced by the presence of 0.1 molar hydrochloric acid ([H+] =
0.091), reduces the concentration of sulphide-ion in the saturated aqueous
solution a millionfold: If we call [S2−]Ac. the concentration of the sulphide-
ion in the acid solution, [S2−]Ac. = (1.1E−23) / (0.091)2 = 1.3E−21, whereas,
in the absence of acid, as found above, [S2−] = 1.2E−15.
On the other hand, the addition of alkali to hydrogen sulphide, by
neutralizing and suppressing the hydrogen-ion, and by forming the salts
MeSH and Me2S, will very greatly increase the concentrations of the
hydrosulphide-ion and of the sulphide-ion. Since the constant for the
secondary ionization of hydrogen sulphide shows that HS− is an
exceedingly weak acid, its salts, Me2S, are very largely hydrolyzed, the

constant for water being somewhat greater400 than its own. According to
Knox, in a 0.1 molar solution of Na2S about 99% of the sulphide is
hydrolyzed: Na2S + H2O ⥂ NaSH + NaOH. In spite of this almost complete
hydrolysis, sufficient sodium sulphide remains in a solution of this [p202]
substance, to yield a concentration of the sulphide-ion that is far greater
than that obtained from a solution of hydrogen sulphide. In a 0.1 molar
solution of sodium sulphide the concentration of the sulphide-ion is,
approximately, [S2−]alk. = 0.9E−3, as compared with [S2−] = 1.2E−15 in a
saturated solution of hydrogen sulphide (25°, 760 mm.), and with 1.3E−21
in the same solution in the presence of 0.1 molar hydrochloric acid.
Ammonium sulphide (NH4)2S is the salt of an extremely weak acid with
a much weaker base than sodium hydroxide, and it is correspondingly more
completely decomposed by water. In a 0.1 molar solution of the sulphide
(NH4)2S, we find the approximate concentration401 of the sulphide-ion
[S2−]am. = 1.8E−6, as compared with 0.9E−3 in a similar solution of Na2S.
But the concentration of sulphide-ion is still enormously greater than its
concentrations in hydrogen sulphide in the absence and in the presence of
acids (see above).
The following table402 contains a summary of the concentrations of
sulphide-ion in the various solutions discussed, as well as its concentration
in the presence of 0.2 molar hydrochloric acid. In the separation of the
copper and arsenic groups from the zinc and aluminium groups, a
concentration of hydrogen-ion corresponding to the presence of 0.15 to 0.25
molar hydrochloric acid is satisfactory for an accurate separation for
ordinary purposes.
Solution. [S2−]
0.1 molar Na2S: 0.9E−3
0.1 molar NaSH: 0.8E−5
0.1 molar (NH4)2S: 1.8E−6
0.1 molar (NH4)SH: 1.4E−8
0.1 molar H2S, sat. aq. sol., 25°: 1.2E−15

0.1 molar H2S, 0.1 molar HCl:403 1.3E−21
0.1 molar H2S, 0.2 molar HCl: 3.5E−22

[p203]

Precipitation of Sulphides by Hydrogen Sulphide.
—Although the hydrosulphide-ion most likely takes part in the precipitation
of sulphides, the main effect appears to be due to the sulphide-ion.404 The
sulphides seem to be both more stable and less soluble, than the
hydrosulphides. It is very likely that hydrosulphides, mixed with the
sulphides, are precipitated to a certain extent, but they are unstable, lose
hydrogen sulphide and go over into sulphides much more readily than
hydroxides, as a rule, change into oxides.405 The final condition of
equilibrium, if one waited, in a given case, until equilibrium was
established, would depend, under these conditions, rather on the
concentration of the sulphide-ion than on that of the hydrosulphide-ion,
although the latter is present in much greater concentrations than the
former. For the sake of simplifying the discussion of the theory of the
separation of metal ions by precipitation with hydrogen sulphide, the
discussion will be limited to the consideration of the sulphide-ion as the
active precipitating agent. As stated, this seems to be in accordance with the
known facts.
The absolute values of the solubilities of the various sulphides, which are
involved in the discussion, are known, with any degree of accuracy, only in
a few cases. The aim of the discussion will be, therefore, to develop, rather,
the relations in the values involved, which may be readily determined.
Wherever absolute quantities can be given, they also will be referred to.
Theory of the Separation of Sulphides by Precipitation with Hydrogen
Sulphide. I. Precipitation of Ferrous Sulphide.
—If we prepare a solution of ferrous sulphate, containing 27.8 grams of the
salt, FeSO4, 7 H2O, in one liter (0.1 molar), we may call [Fe2+] the
concentration of the ferrous-ion in the solution. If such a solution is
saturated with hydrogen sulphide, under atmospheric pressure, (exp.),

ferrous sulphide is not precipitated. We would decide, on the basis of the
principle of the solubility-product, that the reason no precipitate of ferrous
sulphide is formed is, that the product of the ion concentrations is smaller
than the [p204] solubility-product constant characteristic of the sulphide (p.
151); [Fe2+] × [S2−] < KFeS, in which [S2−] is the concentration of sulphide-
ion in the solution thus saturated with hydrogen sulphide. If an alkali,
sodium or ammonium hydroxide, is added to the solution, a heavy
precipitate of ferrous sulphide is immediately formed (exp.). The salts of
hydrogen sulphide, like all common salts, as we have just seen, are very
much more highly ionized than is hydrogen sulphide itself, and the addition
of the alkali has the effect of increasing enormously406 the concentration of
sulphide-ion, say to x [S2−] (p. 202). Under these conditions, the product of
the ion concentrations has evidently grown larger than the constant: [Fe2+]
× x [S2−] > KFeS.
II. Precipitation of Zinc Sulphide.
—Now, if a solution of zinc sulphate is prepared so as to contain 28.7
grams of ZnSO4, 7 H2O, per liter, which would make it of the same molar
concentration as the ferrous sulphate solution, we may, in view of the fact
that analogous salts ionize approximately to the same extent in solutions of
the same concentration, consider the concentration, [Zn2+], of zinc-ion to be
practically the same as the concentration, [Fe2+], of the ferrous-ion in the
ferrous sulphate solution. We may put [Zn2+] = [Fe2+].
If the solution of zinc sulphate is saturated with hydrogen sulphide, under
the same conditions as were used with the ferrous salt solution (exp.), or if
we add the zinc sulphate solution to the mixture of ferrous sulphate and
hydrogen sulphide (exp.), we immediately obtain heavy white precipitates
of zinc sulphide. We would decide, therefore, on the basis of the principle
of the solubility-product, that in this case [Zn2+] × [S2−] > KZnS. Since we
have used hydrogen sulphide under practically the same conditions, we may
consider that [S2−], in this experiment,407 is the same as in the [p205] test

with ferrous sulphate, and, by the conditions of the experiment, we have
also made [Zn2+] = [Fe2+]. The two factors of the product are, therefore, the
same, for the first moment, and we may put [Fe2+] × [S2−] = [Zn2+] × [S2−]
= P.
Since P is smaller than KFeS and larger than KZnS, it is clear that the
solubility-product constant for zinc sulphide must be smaller than that for
ferrous sulphide. The solubility-product constants, for similar salts, are a
measure of their solubilities in water. We may obtain their values by
determining the solubilities of salts in pure water, whenever the solubility is
not affected by other chemical changes. In the present instance, the
quantitative measurements, that have been made in this way, are open to
question, owing to the considerable hydrolysis which sulphides, as salts of a
very weak acid, undergo in solutions of such extreme dilution.408 Until such
relations have been taken into account quantitatively, it is better to limit
ourselves for the present to the more accessible question of relative
solubility.
It is a comparatively easy matter to determine the relative solubility of
zinc and ferrous sulphides. If equal quantities of the equivalent solutions are
mixed and a precipitant, ammonium sulphide, which would precipitate
either sulphide, if its salt were present alone, is carefully and gradually
added to the mixture, it will precipitate first the less soluble one (see p.
163); and that one alone can be present permanently (i.e. in equilibrium) in
contact with the solution containing the two salts. As a matter of fact,409
[p206] we find that zinc sulphide is precipitated first, under conditions

permitting the precipitation of ferrous sulphide if no zinc sulphate were
present, and the precipitate of zinc sulphide remains unchanged in the
presence of a mixture of the composition indicated (exp.).
It is clear, therefore, that the prediction, based on the conclusion drawn
from the application of the principle of the solubility-product, is verified by
experiment.

Now, closer examination of the solution of zinc sulphate, from which
zinc sulphide has been precipitated by the action of hydrogen sulphide,
shows, after the hydrogen sulphide has precipitated as much sulphide as it
can and the solution has been passed through a filter, that a very
considerable proportion of zinc salt is still present in the filtrate, and we
must ask why hydrogen sulphide fails to precipitate the zinc completely.
The concentration of the zinc-ion has grown somewhat smaller, but that is
not the cause of the nonprecipitation of zinc sulphide under the new
conditions, since hydrogen sulphide will precipitate the sulphide, if it is
passed into a solution of zinc sulphate which contains even a smaller
concentration of zinc-ion than the filtrate, in which it fails to give any
further precipitate. If the filtrate is examined, it is found to be strongly acid,
since sulphuric acid has been liberated by the action of hydrogen sulphide
on zinc sulphate: ZnSO4 + H2S → ZnS ↓ + H2SO4. Sulphuric acid is a
strong acid, which is very highly ionized, much more so than the
exceedingly weak acid hydrogen sulphide, and consequently, as the
precipitation of zinc sulphide proceeds, the concentration of hydrogen-ion
in the solution rapidly grows larger and larger. But, the greater the
concentration of the hydrogen-ion, the smaller is that of the sulphide-ion,
since the product [H+]2 × [S2−] is a constant [equation (IV), p. 201] for a
solution kept saturated with hydrogen sulphide. The sulphide-ion is reduced
in concentration very much more rapidly than is the zinc-ion.410 As [S2−] is
a factor in the [p207] solubility-product of zinc sulphide, it is clear that the
value of this product must grow rapidly smaller during the precipitation of
zinc sulphide from the solution, and that it may well, eventually, grow too
small to surpass the value of the solubility-product constant KZnS.
Precipitation of zinc sulphide will then cease. Obviously, the suppression of
the sulphide-ion may be accomplished by the addition of hydrochloric,
sulphuric or any other strong acid to the zinc sulphate solution in the first
place, and then hydrogen sulphide should fail to precipitate any zinc

sulphide at all. In fact, if to 50 c.c. of the 0.1 molar zinc sulphate solution 2
c.c. of hexamolar hydrochloric acid is added,411 hydrogen sulphide does not
precipitate even a trace of zinc sulphide (exp.).
We have found, then, that 0.1 molar zinc sulphate solution, acidified with
a small excess of hydrochloric acid, fails to produce a precipitate of zinc
sulphide, when it is saturated with hydrogen sulphide. We must conclude
that, under these circumstances, the product of the ion concentrations is
smaller than the solubility-product constant for zinc sulphide: ([Zn2+] ×
[S2−] / x) < KZnS, the new concentration of the sulphide-ion being
represented by the symbol [S2−] / x.
It would follow, from these considerations, that the action of
hydrochloric or sulphuric acid, in preventing the precipitation of zinc
sulphide, depends on their producing a sufficiently high concentration of
the hydrogen-ion, to keep the concentration of the sulphide-ion, in a
mixture of zinc sulphate and hydrogen sulphide, below the point where the
solution could become supersaturated with zinc sulphide. [p208] For exactly
similar reasons, none of the sulphides of the zinc group is precipitated by
hydrogen sulphide in (sufficiently) acid solutions.
It is evident, further, that, if a solution of zinc acetate (without the
addition of any acid) is substituted for the zinc sulphate solution and is
treated with hydrogen sulphide, an entirely different result, quantitatively
considered, must be obtained. By the action of hydrogen sulphide on the
acetate, acetic acid is liberated, according to Zn(CH3CO2)2 + H2S ⥂ ZnS ↓
+ 2 CH3COOH. As a weak acid, acetic acid produces much less hydrogen-
ion than is formed in equivalent solutions of sulphuric acid. Consequently, a
much slighter suppression of the sulphide-ion and a much more complete
precipitation of zinc sulphide from the acetate, than from the sulphate
solution, must result. Such is the case. Zinc sulphide is, indeed, precipitated
quantitatively by hydrogen sulphide from the acetate solution.

This behavior of zinc acetate412—and zinc salts of other weak acids
show, of course, the same behavior—represents one of the pitfalls, into
which the unwary analytical chemist is liable to fall, when he uses hydrogen
sulphide. The separation of groups by hydrogen sulphide depends, as stated,
on the fact, that, in the presence of a certain concentration of hydrogen-ion,
hydrogen sulphide will not precipitate zinc sulphide and the remaining
sulphides of the zinc group. To secure this concentration of hydrogen-ion,
some hydrochloric acid is added to solutions, from which hydrogen
sulphide is expected to precipitate none but sulphides of the copper and
arsenic groups—and, as a rule, the purpose is accomplished, as desired. It is
evident, however, that if a solution contains an acetate, say sodium acetate,
or the salt of any other weak acid, e.g. a borate or a phosphate, the addition
of hydrochloric acid will result, at least at first, in the liberation of the
weaker acid and will not produce the excess of hydrogen-ion, required for
the analysis. Zinc sulphide, and possibly nickel and cobalt sulphides,412
may, under such conditions, be precipitated with the sulphides of the groups
mentioned. Unless provision is made, therefore, to insure a certain excess
of hydrogen-ion (p. 213), or unless we are on our guard and look for zinc,
nickel and cobalt in [p209] the analysis of the precipitate formed by hydrogen
sulphide,413 serious errors obviously could result. To add an inordinately
large excess of hydrochloric acid to mixtures, in order to avoid this pitfall,
will, as we shall presently see, only throw us more certainly into still
another error, to which we are exposed in the use of this important reagent,
hydrogen sulphide.
III. Precipitation of Cadmium Sulphide.
—Now, if a 0.1 molar solution of cadmium sulphate (22.6 grams of the
salt,414 CdSO4, H2O, per liter) is prepared, equivalent, in concentration, to
the solutions of ferrous and zinc sulphates used previously, we may
consider that the concentration of cadmium-ion is, approximately, the same
as the concentrations of the ferrous-ion and zinc-ion in the solutions of their