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UNIVERSITY OF CALIFORNIA

MEDICAL CENTER LIBRARY

SAN FRANCISCO




AN INTRODUCTION



TO



PHYSICAL CHEMISTRY



MACMILLAN AND CO., LIMITED

LONDON ' BOMBAY CALCUTTA
MELBOURNE

THE MACMILLAN COMPANY

NEW YORK BOSTON CHICAGO
DALLAS SAN FRANCISCO

THE MACMILLAN CO. OF CANADA, LTD.

TORONTO



INTKODUCTION



TO



PHYSICAL CHEMISTRY



BY



JAMES WALKER, LL.D., F.R.S.

PROFESSOR OF CHEMISTRY IN THE UNIVERSITY OF EDINBURGH



SEVENTH EDITION



MACMILLAN AND CO., LIMITED

ST. MAKTIN'S STKEET, LONDON

1913



COPYRIGHT

First Edition, 1899
Second Edition, 1901

Third Edition, 1903
Fourth Edition, 1907

Fifth Edition, 1909
Reprinted 1910

Sixth Edition, 1910
Seventh Edition, 1913






Wit"






PREFACE TO THE SEVENTH EDITION

So short a time has elapsed since the appearance of the last edition,
which had undergone thorough revision, and included many new-
chapters and sections, that I have only found it necessary in the
present edition to make a few minor changes. Where recent re-
searches have afforded more accurate numerical values or better
illustrative examples than those formerly available, the newer matter
has as far as possible been incorporated.

J. W.

March 1913.



PEEFACE TO THE FIRST EDITION

THIS book makes no pretension to give a complete or even systematic
survey of Physical Chemistry; its main object is to be explanatory.
I have found, in the course of ten years' experience in teaching the
subject, that the average student derives little real benefit from reading
the larger works which have hitherto been at his disposal, owing chiefly
to his inability to effect a connection between the ordinary chemical
knowledge he possesses and the new material placed before him. He
keeps his everyday chemistry and his physical chemistry strictly apart,
with the result that instead of obtaining any help from the new
discipline in the comprehension of his descriptive or practical work,
he merely finds himself cumbered with an additional burthen on the
memory, which is to all intents and purposes utterly useless. This
state of affairs I have endeavoured to remedy in the present volume
by selecting certain chapters of Physical Chemistry and treating the
subjects contained in them at some length, with a constant view to
their practical application. In choice of subjects and mode of treatment
I have been guided by my own teaching experience. I have striven
to smooth, as far as may be, the difficulties that beset the student's
path, and to point out where the hidden pitfalls lie. If I have been
successful in my object, the student, after a careful perusal of this
introductory text-book, should be in a position to profit by the study
of the larger systematic works of Ostwald, Nernst, and van 't Hoff.

As I have assumed that the student who uses this book has already
taken ordinary courses in chemistry and physics, I have devoted little
or no space to the explanation of terms or elementary notions which



viii INTRODUCTION TO PHYSICAL CHEMISTRY

are adequately treated in the text-books on those subjects. I have
throughout avoided the use of any but the most elementary mathematics,
the only portion of the book requiring a rudimentary knowledge of the
calculus being the last chapter, which contains the thermodynamical
proofs of greatest value to the chemist.

Since it is of the utmost importance that even beginners in physical
chemistry should become acquainted at first hand with original work
on the subject, I have given a few references to papers generally
accessible to English-speaking students.

J. WALKER.

August 1899.



CONTENTS

CHAPTER I

PAGE

UNITS AND STANDARDS OF MEASUREMENT ... 1

CHAPTER II

THE ATOMIC THEORY AND ATOMIC WEIGHTS ... 8

CHAPTER III

CHEMICAL EQUATIONS . . . . . . ' 22

CHAPTER IV
THE SIMPLE GAS LAWS . . . . . .26

CHAPTER V

SPECIFIC HEATS . . . . . .29

CHAPTER VI
THE PERIODIC LAW . . . . . .38

CHAPTER VII

SOLUBILITY . . . .51



x INTRODUCTION TO PHYSICAL CHEMISTRY



CHAPTER VIII

PAGE

FUSION AND SOLIDIFICATION .... 62



CHAPTER IX

VAPORISATION AND CONDENSATION . . . .76

CHAPTER X

THE KINETIC THEORY AND VAN DER WAALS'S EQUATION . 88

CHAPTER XI
THE PHASE RULE . . . . . .103

CHAPTER XII

ALLOYS . . "7 . . . . .118

CHAPTER XIII
HYDRATES ....... 127

CHAPTER XIV

THERMOCHEMICAL CHANGE . . . . .135

CHAPTER XV

VARIATION OF PHYSICAL PROPERTIES IN HOMOLOGOUS SERIES . 145

CHAPTER XVI

RELATION OF PHYSICAL PROPERTIES TO COMPOSITION AND CONSTITUTION 155



CONTENTS xi

CHAPTER XVII

PAGE

THE PROPERTIES OF DISSOLVED SUBSTANCES . . .169

CHAPTER XVIII

OSMOTIC PRESSURE AND THE GAS LAWS FOR DILUTE SOLUTIONS 179

CHAPTER XIX

DEDUCTIONS FROM THE GAS LAWS FOR DILUTE SOLUTIONS . 190

CHAPTER XX

METHODS OF MOLECULAR WEIGHT DETERMINATION . . 197

CHAPTER XXI

MOLECULAR COMPLEXITY . . . . . 219

CHAPTER XXII

COLLOIDAL SOLUTIONS . . . * . 228

CHAPTER XXIII

DIMENSIONS OF ATOMS AND MOLECULES . . . 235

CHAPTER XXIV

ELECTROLYTES AND ELECTROLYSIS . .. , 240

CHAPTER XXV

ELECTROLYTIC DISSOCIATION . . . . .257

CHAPTER XXVI

BALANCED ACTIONS . . . .275



xii INTRODUCTION TO PHYSICAL CHEMISTRY
CHAPTER XXVII

PAGE

RATE OF CHEMICAL TRANSFORMATION . . .295

CHAPTER XXVIII

RELATIVE STRENGTHS OF ACIDS AND OF BASES . . . 306

CHAPTER XXIX

EQUILIBRIUM BETWEEN ELECTROLYTES . . . . 319

CHAPTER XXX

NEUTRALITY AND SALT-HYDROLYSIS . . . 333

CHAPTER XXXI

APPLICATIONS OF THE DISSOCIATION THEORY . . .345

CHAPTER XXXII

ELECTROMOTIVE FORCE ... 361

CHAPTER XXXIII

POLARISATION AND ELECTROLYSIS . 374

CHAPTER XXXIV

RADIO-ACTIVE TRANSFORMATIONS . . . 380

CHAPTER XXXV

THERMODYNAMICAL PROOFS . . . 389

INDEX 417



CHAPTEK I

UNITS AND STANDARDS OF MEASUREMENT

To express the magnitude of anything, we use in general a number
and a name. Thus we speak of a length of 3 feet, a temperature
difference of 18 degrees, and so forth. The name is the name of the
unit in terms of which the magnitude is measured, and the number
indicates the number of times this unit is contained in the given
magnitude. The selection of the unit in each case is arbitrary, and
regulated solely by our convenience. In different countries different
units of length are in vogue, and even in the same country it is
found convenient to adopt sometimes one unit, sometimes another.
Lengths, for example, when very great are expressed in miles ; when
small, in inches ; and we also find in use the foot and yard as units
for intermediate lengths. Such units as these British measures of
length were fixed by custom and convention, and for the purposes
of everyday life are convenient enough. When we come, however,
to the discussion of scientific problems, we find that they are un-
suitable and inconvenient, leading to clumsy calculations the greater
part of which could be dispensed with if the units of the various
magnitudes were properly selected. There is, for instance, no
simple relation between any of the British units of length and
the usual British standard of capacity the gallon. Now lengths,
volumes, and weights often enter in such a way into scientific calcula-
tions that the existence of simple relations between the units of
these magnitudes enables us to perform a calculation mentally which
would necessitate a tedious arithmetical operation were the units
not thus simply related.

The first requirement of a convenient system of measurement is
that all multiples and subdivisions of the unit chosen should be
decimal, in order to be in harmony with our decimal system of
numeration. For scientific purposes the decimal principle of measure-
ment is uniformly accepted, save in circular measure and in the
measurement of time, where the ancient sexagesimal system (of



2 INTRODUCTION TO PHYSICAL CHEMISTRY CHAP.

counting by sixties) still in part prevails. The unit of length is
subdivided into tenths, hundredths, and thousandths if we wish to
use the smaller derived units ; if we desire a larger derived unit we
take it ten, a hundred, or a thousand times greater than the funda-
mental unit. The choice of this fundamental unit is, as has been
already stated, quite arbitrary. At the time of the French Revolution,
when a decimal system was first adopted in a thoroughgoing manner,
the unit of length, the metre, was selected because it was of a
convenient length for practical measurement, and in particular because
it was supposed to have a natural relation to the size of the earth, ten
million metres measuring exactly the quadrant of a circle through the
poles. The value of the fundamental length therefore depended
theoretically on the determination of the length of the earth's
meridional quadrant. But the degree of accuracy with which this
determination can be made is far inferior to that obtainable in
comparing two short lengths (say a metre) together. If the metre
then were strictly defined by the earth's dimensions, the fundamental
unit of length would change with every fresh determination of the
polar circumference. For practical purposes the metre is legally
defined as the distance, under certain conditions, between two marks
on a rod of platinum-iridium preserved in Paris, and the supposed
exact relation to the earth's circumference has been given up. 1
Copies of this standard have been made and distributed, and the
relation between them and similar standards of length, such as the
yard, have been determined with great exactness.

For many scientific purposes, the hundredth part of the metre,
the centimetre, is a convenient unit, and in what follows we shall
generally make use of it in calculations.

The unit of mass (or weight), 2 the gram, was primarily defined
as the mass (or weight) of 1 cubic centimetre of water at the
temperature at which its density is greatest, viz. 4 C. Here we
depend on the constancy of the properties of an arbitrary substance
(pure water) to establish a relation between the units of weight and
of cubical capacity, or volume. The original Standard kilogram was
constructed in accordance with this relation, being made equal to
1000 grams as above defined, i.e. equal in weight to a cubic
decimetre of water at its maximum density point. Since it is
possible, however, to compare weights with each other with much
greater accuracy than is attainable in the measurement of volumes, the
exact relationship between the two units has been allowed to drop,
and for exact purposes the kilogram is defined as the weight of the

1 According to recent measurement, the ten-millionth part of the earth's quadrant
is nearly O'l millimetres longer than the standard metre.

2 When a chemist uses an ordinary balance he directly compares weights, but, since
at any one place weight is proportional to mass, he indirectly compares the masses of
the substances on the two pans. So far, then, as measurement of quantity of material
by means of the balance is concerned, the terms are interchangeable.



I UNITS AND STANDARDS OF MEASUREMENT 3

platinum standard kilogram kept in Paris. 1 For the purposes of the
chemist the relation between the units of weight and volume as
originally defined may be looked upon as exact, since the error is not
greater than O'Ol per cent, a degree of accuracy to which the chemist
attains only in exceptional circumstances. For measuring the volume
of liquids, the litre is defined, not as a cubic decimetre, but as the
volume occupied by a quantity of water which will balance the
standard kilogram in vacuo at 4 C.

The unit of time seldom enters into chemical calculations. The
standard for the unit is derived from the length of time necessary
for the performance of some cosmical process for example, the time
taken by the earth to perform a complete revolution on its axis. The
minute, as measured by a good-going clock or watch, is the unit
generally employed in determinations of the velocity of chemical
actions.

The units of length, weight, and time being once fixed, a great
many derived units may be fixed in their turn. The C.G.S.
system, which takes, as the letters indicate, the centimetre, the
gram, and the second for the fundamental units, is very frequently
employed, especially in theoretical calculations, and we shall often
have occasion to use it. For example, instead of expressing the
average atmospheric pressure as that of a column of mercury 76 cm.
high, it is expedient in many calculations to give the pressure in
grams per square centimetre. The conversion may easily be
performed as follows. Suppose the cross-section of the mercury
column to be 1 sq. cm., then if the height of the column is 76 cm., the
total volume of mercury is 76 cc., and the pressure per square centi-
metre is the weight of 76 cc. of mercury, viz. 1033 g. 2 The
average pressure of the atmosphere, then, is equal to 1033 g. per
square centimetre.

The specific volume of a substance may be defined as the number
of units of volume which are occupied by unit weight of the substance.
In the above system it is therefore the number of cubic centimetres
occupied by one gram. The specific weight, or density, of a substance
is the number of units of weight which occupy unit volume : in the

1 To give an idea of the difficulty of accurate measurement when volumes are con-
cerned, the following example may suffice. By Act of Parliament a gallon was denned
as equal to 4 '543458 litres, this number being derived from the weight of a cubic inch of
water in grains, and the relation between the inch and the decimetre, a litre being
supposed equal to a cubic decimetre. The original definition of the gallon is "the
volume at 62 F. of a quantity of water which balances 10 brass pound weights (true in
vacuo, and of specific gravity 8 "143) in air at 62 F. and 30 inches pressure (barometer
reduced to the freezing point) and two-thirds saturated with moisture." From this
definition, and the relation of the pound to the kilogram, Dittmar calculated that 1
gallon is equal to 4 '54585 litres, a value which differs from this statutory relation by 1
part in 2000. By an Order in Council of May 1898, the gallon was made equivalent
to 4'54596 litres.

2 This value is obtained by multiplying 76 by the specific gravity of mercury, viz.
13-59,



4 INTRODUCTION TO PHYSICAL CHEMISTRY CHAP.

above system, the number of grams which occupy one cubic centi-
metre.

These definitions are directly derived from the units of weight and
volume, and are independent of the properties of any substance save
that considered. For purposes of measurement in the case of solids
and liquids, however, it is much more convenient and accurate to com-
pare the density or specific volume of one substance with that of
another arbitrarily chosen as standard, than to effect an absolute deter-
mination by measuring both weight and volume of one and the same
substance. The substance usually chosen as the standard of com-
parison is water, and that for two reasons. In the first place, water is
easily obtained and easily purified ; in the second place, water is a
standard substance in other respects in particular it is the substance
which was used to fix the relation between the units of weight and
of volume. From this relation the density of water in our units
is 1 (cp. p. 2), so that if we take water as our standard, and refer all
densities to it as the unit, we have what are really relative densities,
although if measured at 4 the numbers obtained do not differ greatly
from the absolute densities of the substances. The actual comparison
is made in the case of liquids by weighing the same tared vessel
filled with water, and filled with the liquid whose density is to be
determined. Although the actual volume is unknown, it is known
to be the same in both cases, so that the quotient of the weight
of liquid by the weight of water gives the relative density of the
liquid.

In order to specify with exactness the density of a substance, it is
necessary to indicate at what temperature the determination or com-
parison has been made. As substances change in temperature they
invariably change in volume, so that the absolute density varies with
the temperature. In specifying the relative density, or specific gravity,
it is not only necessary to give the temperature at which the substance
is weighed, but also the temperature at which the equal volume of
water is weighed. Thus we meet with such data as the following,
15-584= 1*0653, which indicates that the weight of the substance at
15'5 is T0653 times as much as the weight of the same volume of
water at 4. As a general rule, the weights are both for the same
temperature, say 15; or the substance is weighed at this tempera-
ture and referred either directly or by calculation to water at 4, its
maximum density point. In the latter case the density given is
very nearly equal to the absolute density of the substance at the
specified temperature.

Quantities of matter may always be expressed in terms of the unit
of weight irrespective of the form in which the matter may exist.
When we come to measure energy we find no such common unit in
which its amount may be expressed. Each form of energy, such as
heat, work, electrical energy, has its own special unit, but according to



i UNITS AND STANDARDS OF MEASUREMENT 5

the Law of Conservation of Energy, a given amount of any one form of
energy is under all circumstances equivalent to constant amounts of
the other kinds of energy ; we have therefore merely to ascertain the
relation between the different special energy units in order to express
a given amount of energy in terms of any one of these units. Thus
electrical energy is usually expressed in volt-coulombs, but it may
easily be expressed in terms of the mechanical or heat units, the
numbers then indicating the amounts of mechanical or thermal energy
into which the electrical energy may be converted.

The " absolute " unit of mechanical energy, the erg, is the product
of the unit of length into the " absolute " unit of force, or dyne, i.e.
the force necessary to impart to a mass of 1 g. in a second a velocity
of 1 cm. per second. For our purposes, however, it will generally be
more convenient to use gravitation units, in the definition of which
the value of the earth's gravitational attraction for bodies on its
surface is involved. The unit of force thus defined is the weight of
1 g., and is equal to 981 dynes. The unit of mechanical energy is
therefore the product of this unit into the unit of length, i.e. the
gram-centimetre.

To obtain the unit of heat and a scale of temperature it is again
necessary to refer to the properties of some arbitrarily-chosen substance
or substances. In the construction of a scale of temperature it is
customary to fix two points by means of well-defined and presumably
constant properties of some standard substance, and divide the range
between these two points into equal arbitrary units as measured by the
change in property of some substance caused by change of temperature.
Thus in the centigrade scale the two points which are fixed are,
first, the freezing point of the standard substance water, and second,
its boiling point under a pressure of 76 cm. of mercury. When
we use a mercury thermometer it is assumed that equal changes
in volume of the mercury correspond to equal changes of
temperature, 1 so by dividing the whole change of volume of the
mercury between the freezing and boiling points of water into 100
equal portions, we obtain an ordinary centigrade thermometer.
Similarly, if we use a hydrogen thermometer, we assume that equal
increments of volume correspond to equal increments of temperature.
In each case we depend for our measurement of temperature on the
properties of some particular substance, and it does not at all follow
that the temperature as measured by one substance will exactly
coincide with the temperature as measured by another. In point of
fact, the temperatures registered by the mercury and hydrogen
thermometers never exactly agree except where the two thermometers
were originally made to correspond when their fixed points were
determined. For accurate comparative work temperatures are

1 In mercury and other liquid thermometers we really deal with the difference of the
volume change of the liquid and of the vessel containing it.



6 INTRODUCTION TO PHYSICAL CHEMISTRY CHAP.

referred to an international hydrogen scale. The " international "
hydrogen thermometer is a constant-volume instrument, that is,
instead of measuring the change of volume caused by change of
temperature, we measure the change of pressure, when the volume is
kept constant. The scale is defined as having " fixed points at the
temperature of melting ice (0) and that of the vapour of distilled
water in ebullition (100), under the normal atmospheric pressure ;
the hydrogen being taken under the manometric initial pressure
of 1 metre of mercury." For temperatures between and 100 the
maximum difference between the international and the Kew standard
mercury thermometers only amounts to a few hundredths of a degree
centigrade.

In theoretical calculations absolute temperatures are frequently
employed. The absolute scale of temperature has degrees of the
same size as centigrade degrees, but starts from a point 273 degrees
below zero centigrade. The absolute temperature is therefore
obtained by adding 273 to the temperature in the centigrade scale.

The usual unit of heat for chemical purposes is the " small calorie "
or gram calorie. It is roughly defined as the quantity of heat re-
quired to raise the temperature of one gram of water through one
degree centigrade. This quantity is not exactly the same at all tem-
peratures, e.g. the amount of heat necessary to warm a gram of water
from to 1 is somewhat different from that required to heat it from
99 to 100. It is therefore necessary to specify the temperature at
which the heating takes place. Practically the calorie measured at
the ordinary temperature, say from 15 to 16, is the most convenient.
The great or kilogram calorie is 1000 times the small calorie. A
centuple calorie has also been proposed. It is the quantity of heat
required to raise a gram of water from to 100, and is very nearly
equal to 100 small calories. It is usually denoted by the symbol K,
and we have thus the following relation of heat units : 1 Cal. =
10 K=1000 cal.

It is a matter of importance to fix the relation of the mechanical
unit of energy to the heat unit, i.e. to determine the mechanical
equivalent Of heat. Mechanical energy, e.g. the energy of a falling
body, is converted by friction or otherwise into heat, the amount of
mechanical energy and the amount of heat resulting from it being
both measured. In this way it has been found that 42,720 gram-
centimetres are equivalent to 1 gram calorie at 15, i.e. 42,720 grams
falling through a centimetre will generate enough heat in a friction
apparatus to raise the temperature of a gram of water one degree
at 15. In the sequel we shall denote this value by /.

Another unit of heat has recently been used for thermochemical
purposes. It is called a joule, and is simply related to the unit of
mechanical energy, being equivalent to 10,000,000 ergs. It is
denoted by the letter j ; a larger unit, the kilojoule, equal to 1000 j,



i UNITS AND STANDARDS OF MEASUREMENT 7

may be denoted by the symbol Kj. The relations between these and
the calorie for 15 are given by the equations

1 cal. = 4-189 j. 1 j = 0-2387 cal.

1 Cal. = 4-189 Kj. 1 Kj = 0*2387 Cal.

The relations between the units employed in electrical measure-
ments have been the subject of many accurate experimental investiga-
tions. The units have been chosen theoretically so as to give a unit
of electrical energy which bears a simple relation to the absolute unit
of mechanical energy. The theoretical unit of resistance, the ohm,
may be practically defined as the resistance at of a column of
mercury 1 sq. mm. in section, and 1*0630 metres long. A convenient
practical unit, the Siemens mercury unit, is the resistance of a similar
column exactly a metre long. Specific conductivity is expressed
in terms of the conductivity of a substance, of which a cube having
1 cm. edge shows a resistance of 1 ohm between a pair of opposite
faces. Thus the specific conductivity of mercury at is 10630 in
terms of this unit, as a reference to the practical definition of the ohm
will show. The symbol K is usually employed to denote the specific
conductivity as thus defined.

The unit quantity of electricity, the coulomb, is defined as the
quantity of electricity which will deposit 1*1180 mg. of silver from



Online LibraryJames WalkerIntroduction to physical chemistry → online text (page 1 of 43)