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STANDARD ATOMIC MASSES 1979
(Scaled to the relative atomic mass ,
A ,.(I2C) = 12)
Name
Actinium
Aluminium
Americium
Antimony
Argon
Arsenic
Astatine
Barium
Berkelium
Beryllium
Bismuth
Boron
Bromine
Cadmium
Caesium
Calcium
Californium
Carbon
Cerium
Chlorine
Chromium
Cobalt
Copper
Curium

Dysprosium
Einsteinium
Erbium
Europium
Fermium
Fluorine
Francium
Gadolinium
Gallium
Germanium
Gold
Hafnium
Helium
Holmium
Hydrogen
Indium
Iodine
Iridium
Iron
Krypton
Lanthanum
Lawrencium
Lead
Lithium
Lutetium
Magnesium
Manganese
Mendelevium
Mercury


Atomic
Symbol number
Ac
89
Al
13
Am
95
Sb
51
Ar
18
As
33
At
85
Ba
56
Bk
97
Be
4
Bi
83
B
5
Br
35
Cd
48

55
Cs
Ca
20
Cf
98
C
6
Ce
58
Cl
17
Cr
24
Co
27
Cu
29
Cm
96
Dy
66
Es
99
Er
68
Eu
63
Fm
100

F
9
Fr
87
Gd
64
Ga
31
Ge
32
Au
79
Hf
72
He
2
Ho
67
H
I
In
49
I
53
Ir
77
Fe
26
Kr
36

La
57
Lr
103
Pb
82
Li
3
Lu
71
Mg
12
Mn
25
Md
101
Hg
80

Atomic
mass
227.0278
26 .98154
(243)
121.75*
39 .948
74.9216
(210)
137 .33
(247)

9.01218
208.9804
10.81
79 .904
112.41
132 .9054
40 .08
(25 I)
12.011
140. 12
35.453
51.996
58 .9332
63 .546*
(247)
162 .50*
(252)
167.26*
151.96
(257)
18.998403
(223)
157.25 *
69.72
72 .59*
196.9665
178.49*
4.00260
164.9304
1.0079

114.82
126.9045
192 .22 *
55 .847*
83 .80
138.9055 *
(260)
207 .2
6.941 *
174 .967 *
24.305
54.9380
(258)
200 .59*

Name
Molybdenum
Neodymium
Neon
Neptunium
Nickel
Niobium
Nitrogen
Nobelium
Osmium
Oxygen
Palladium
Phosphorus
Platinum
Plutonium

Polonium
Potassium
Praseodymium
Promethium
Protactinium
Radium
Radon
Rhenium
Rhodium
Rubidium
Ruthenium
Samarium
Scandium
Selenium
Silicon
Silver
Sodium
Strontium
Sulfur
Tantalum
Technetium
Tellurium
Terbium
Thallium
Thorium
Thulium
Tin
Titanium
Tungsten
(U nnilhexium)

(Unnilpentium)
(U nnilquadium)
Uranium
Vanadium
Xenon
Ytterbium
Yttrium
Zinc
Zirconium

Atomic
Symbol number
Mo
Nd
Ne
Np
Ni
Nb
N
No
Os

0
Pd
P
Pt
Pu
Po
K
Pr

Pm
Pa
Ra
Rn
Re
Rh
Rb
Ru
Sm
Sc
Se
Si
Ag
Na
Sr
S
Ta
Tc
Te
Tb
TI
Th
Tm
Sn
Ti

W
(Unh)
(Unp)
(Unq)

U
V
Xe
Yb
Y
Zn
Zr

42
60
10
93
28
41
7
102
76
8
46
15
78
94
84
19
59
61
91
88
86
75

45
37
44
62
21
34
14
47
II
38
16
73
43
52
65
81
90
69
50
22
74
106
105
104
92
23
54
70
39
30

40

Atomic
mass
95.94
144.24*
20 . 179
237 .0482
58.69
92.9064
14 .0067
(259)
190.2
15 .9994*
106.42
30.97376
195.08*
(244)
(209)
39.0983
140.9077
(145)
231 .0359
226 .0254
(222)
186.207
102 .9055
85.4678 *
101.07*
150.36*

44.9559
78 .96*
28.0855 *
107 .868
22 .98977
87. 62
32 .06
180.9479
(98)
127.60*
158.9254
204 .383
232 .0381
168.9342
118 .69*
47 .88 *
183.85*
(263)
(262)
(261)
238.0289
50.9415
131.29*
173 .04 *
88 .9059
65.38
91.22

Source: Pure and Applied Chemistry , 51, 405 (1979 ). By permission .
Value s are considered reliable to ± I in the last digit or ± 3 when followed by an asterisk(*). Values in

parentheses are used for radioactive elements whose atomic weight s cannot be quoted precisel y without
knowledge of the origin of the elements; the value given is the atomic mass number of the isotope of th at
element of longest known half-life.

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FUNDAMENTAL CONSTANTS
(approximate values; best values are in Appendix IV)

!

,

Quantity

Symbol

Value

Gas constant
Zero of the Celsius scale
Standard atmosphere
Standard molar volume
of ideal gas
A vogadro constant
Boltzmann constant
Standard acceleration of
gravity
Elementary charge

Faraday constant
Speed of light in vacuum
Planck constant

R

8.314 J K- 1 mol-I

To

273.15 K
1.013 x 105 Pa
22.41 x 10- 3 m3 mol-I

Rest mass of electron
Permittivity of vacuum

Bohr radius
Hartree energy

Po

Vo

RTolpo

=

6.022 x 1023 mol I
1.381 x 10- 23 J K- 1

9.807 m s -2
e

F
c
Il
Ii

=

=

NAe

h121T'

In

en

41T'eo
1/41T'eo
ao = 41T'eoIi2/me2
Eh = el l41T'e oao

1.602
9.648
2.998
6.626
1.055

9.110
8.854
LIB
8.988
5.292
4.360

'>\.

X

x
x
X

X
'>\.

X

x
x
x:

10 19 C
104 C mol-I
lOR m s I
10 34 J s
10- 34 J s
10- 31 kg

10- 12 C2 N- 1 m 2
10- 10 C 2 N- I m -2
109 N m 2 C- 2
10 II m
10 I~ J

"-

CONVERSION FACTORS

i

I

1 L = 10- 3 m' (exactly) = 1 dm 3
I atm = 1.01325 Pa (exactly)
I atm = 760 Torr (exactly)
1 Torr = 1.000 mmHg
1 cal = 4.184 J (exactly)
1 erg = 1 dyne cm = 10- 7 J (exactly)
1 eV = 96.48456 kJ/mol

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1 A = 10 10 m = 0.1 nm = 100 pm
I inch = 2.54 cm (exactly)
1 pound = 453.6 g
I gallon = 3.785 L
1 Btu = 1.055 kJ
I hp = 746 W



MATHEMATICAL DATA
1T =

e = 2.7182818 ...

3.14159265 ...

In x = 2.302585 ... log x

(all x)
In I

+

x)

=x

-

Y~x"

+

x )-1

- X


(l -

x )-1

+

(I -

X)-"

+ 2x +

(l

+

X

+
+

IA\"3 -

Y4X 4

+

(x"

x" -


X3

+

(x~

<

X~

X3

+

(x"

< I)

+

3x~

+

4x 3

+ ...

(x"


< 1)

I)

<

1)

51 PREFIXES
Submultiple

Prefix

Symbol

Multiple

Prefix

Symbol

10- [

deci

d

10


deca

da

10- 2

centi

c

10"

hecto

h

10- 3
10- 6

milli

m

10 3

kilo

k

mIcro


11..

106

mega

M

nano

1}

109

giga

G

pico

10 12

tera

T

femto

P

f

10

peta

P

atto

a

10 18

exa

E

10- 9
10- [2
10 15
10 - IR

15

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Physical Chemistry


Third Edition

Gilbert W. Castellan
University of Maryland

"'

...

Addison-Wesley Publishing Company
Reading, Massachusetts

Menlo Park, California

•

London

•

Amsterdam

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•

Don Mills, Ontario

•


Sydney


To Joan and our family

Sponsoring Editor: Robert L. Rogers
Production Editor: Margaret Pinette
Copy Editor: Jerrold A. Moore
Text Designer: Debbie Syrotchen
Design Coordinator: Herb Caswell
Illustrators: YAP International Communications, Ltd.
Cover Designer: Richard Hannus, Hannus Design Associates
Cover Photograph: The Image Bank, U. Schiller

Art Coordinator: Joseph K. Vetere

Production Manager: Herbert Nolan
The text of this book was composed in Monophoto Times Roman by
Composition House Limited.

Reprinted with corrections, November 1983

Copyright © 1 983 , 1 97 1 , 1 964 by Addison-Wesley Publishing Company, Inc .

All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system, or transmitted, in any form or by any means, electronic , mechanical, photocopying,
recording, or otherwise, without the prior written permission of the publisher. Printed
in the United States of America. Published simultaneously in Canada. Library of Congress
Catalog Card No. 82-74043 .
ISBN 0-201-10386-9


BCDEFGHIJ -MA-89876543

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m

Foreword
to the Student

On most campuses the course in physical chemistry has a reputation for difficulty.
It is not, nor should it be, the easiest course available; but to keep the matter in
perspective it must be said that the IQ of a genius is not necessary for understanding
the subject.
The greatest stumbling block that can be erected in the path of learning physical
chemistry is the notion that memorizing equations is a sensible way to proceed.
Memory should be reserved for the fundamentals and important definitions. Equations
are meant to be understood, not to be memorized. In physics and chemistry an
equation is not a jumbled mass of symbols, but is a statement of a relation between
physical quantities. As you study keep a pencil and scratch paper handy. Play with
the final equation from a derivation. If it expresses pressure as a function of temperature,
turn it around and express the temperature as a function of pressure. Sketch the
functions so that you can "see" the variation. How does the sketch look if one of
the parameters is changed? Read physical meaning into the various terms and the
algebraic signs which appear in the equation. If a simplifying assumption has been
made in the derivation, go back and see what would happen if that assumption were
omitted. Apply the derivation to a different special case. Invent problems of your
own involving this equation and solve them. Juggle the equation back and forth until
you understand its meaning.

In the first parts of the book much space is devoted to the meaning of equations;
I hope that I have not been too long-winded about it, but it is important to be able
to interpret the mathematical statement in terms of its physical content.
By all means try to keep a good grasp on the fundamental principles that are
being applied; memorize them and above all understand them. Take the time to
understand the methods that are used to attack a problem.
In Appendix I there is a brief recapitulation of some of the most important
mathematical ideas and methods that are used. If any of these things are unfamiliar
to you, take the time to review them in a mathematics text. Once the relations

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vi

Foreword

between variables have been established, the algebra and calculus are simply mechanical
devices, but they should be respected as precision tools.
If problems baffle you, learn the technique of problem solving. The principles
contained in

G. Polya's book,

How to Solve It, have helped many of my students.*

It is available as a paperback and is well worth studying. Work as many problems
as possible. Numerical answers to all problems can be found in Appendix VII. Make
up your own problems as often as possible. Watching your teacher perform will not
make you into an actor; problem solving will. To aid in this, get a good "scientific"

calculator (the serious student will want a programmable one with continuous memory)
and learn how to use it to the limit of its capability. Reading the instructions will
save you hundreds of hours!
Finally, don't be put off by the reputation for difficulty. Many students have
enjoyed learning physical chemistry.
*

G . Polya,

How to Solve It.

Anchor Book No. 93. New York: Doubleday & Co . , 1 957.

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Preface

An introductory course in physical chemistry must expose the fundamental principles
that are applicable to all kinds of physicochemical systems. Beyond the exposition
of fundamentals, the first course in physical chemistry takes as many directions as
there are teachers. I have tried to cover the fundamentals and some applications in
depth. The primary aim has been to write a book that the student can, with effort,
read and understand; to provide the beginner with a reliable and understandable
guide for study in the teacher's absence. I hope that this book is readable enough
so that teachers may leave the side issues and the more elementary aspects for
assigned reading while they use the lectures to illuminate the more difficult points.
Chapters

1, 5, and 6, and most of Chapter 19 contain some general background


material and are intended exclusively for reading.
Except where it would needlessly overburden the student, the subject is presented
in a mathematically rigorous way. In spite of this, no mathematics beyond the
elementary calculus is required. The justification for a rigorous treatment is pedagogical;
it makes the subject simpler. The beginner may find it difficult at first to follow a
lengthy derivation, but

can

follow it if it is rigorous and logical. Some "simplified"

derivations are not difficult to follow, but impossible.

CHANGES IN THIS EDITION
There are several important differences between this edition and the earlier one. I
am grateful to Professor James T. Hynes, University of Colorado, who kindly supplied
the groups of questions at the end of each chapter. These are an important addition
to the book. The questions range in difficulty; some are relatively simple while others
challenge the student to take up a line of reasoning from the chapter and apply it
beyond the topics that are discussed explicitly. Many new problems have been added;
the total is over

750, about twice the number in the second edition. Answers to all

the problems are given in Appendix VII. More worked examples are included; these
are now set apart from the text, while before they were sometimes hidden in the

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viii

Preface

textual material. A separate solutions manual is in preparation in which representative
problems are worked out in detail. Certain sections of the text are marked with a
star. The star indicates that the material is either 0) an additional illustration of or
a side issue related to the topic under discussion, or (2) a more advanced topic.
In the treatment of thermodynamics, some errors have been corrected, some
passages clarified, and a few new topics introduced. The emphasis on the laws of
thermodynamics as generalizations from experience is maintained. The chapter on
electrochemical cells has been revised and a discussion of electrochemical power
sources has been added. The chapter on surface phenomena now includes sections
on the BET isotherm and on the properties of very small particles.
The chapters on the quantum mechanics of simple systems have been retained
with only minor revisions, while the chapter on the covalent bond has been extended
to include a description of molecular energy levels. The basic ideas of group theory
are introduced here and illustrated by constructing symmetry-adapted molecular
orbitals for simple molecules. There is a new chapter on atomic spectroscopy; the
chapter on molecular spectroscopy has been expanded and reorganized.
The treatment of statistical thermodynamics has been extended to include the
calculation of equilibrium constants for simple chemical reactions. At the end of the
book, new sections on photophysical kinetics, electrochemical kinetics, and a brief
chapter on polymers have been added.
TERMINOLOGY AND UNITS

With only a few exceptions I have followed the recommendations of the International
Union of Pure and Applied Chemistry (IUPAC) for symbols and terminology. I have
retained the traditional name, "advancement of the reaction" for the parameter �,

rather than''extent of reaction," which is recommended by IUPAC. The connotation
in English of the words "advancement" and "advance" when applied to chemical
reactions allow a variety of expression that "extent" and its derivatives do not. For
thermodynamic work I have retained the sign convention used in the earlier edition.
I attempted (unsuccessfully, I thought) to write a clear discussion of the Carnot
cycle and its consequences using the alternate sign convention. Then, after examining
some other recent books that use the alternate sign convention, I came to the opinion
that their discussions of the second law are not distinguished by their clarity. It
seems to me that if the subterfuges used in some of these books are· needed for
clarity, then the game is not worth the candle.
The SI has been used almost exclusively throughout the book. Except for the
thermodynamic equations that involve 1 atm or 1 mol/L as standard states (and a
few other equations that explicitly involve non-SI units), all the equations in this
book have been written in the S1, so that if the values of all the physical quantities
are expressed in the correct SI unit, the quantity desired will be obtained in the
correct SI unit. The net result is that the calculations of physical chemistry are not
just simplified, they are e normously simplified. The student no longer has to assemble
and store all the mental clutter that was formerly needed to use many of the equations
of physical chemistry. One of the great blessings conferred on the student by the
SI is that there is only one numerical value of the gas constant, R. The systematic
value of R is the only one used and the only one printed in this book. To those who
wish to use any other value, I leave the opportunity to muddle the situation and
suffer the consequences.

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Preface

ix


ACKNOWLEDGMENTS

In this third edition my aim has been to preserve the best parts of the earlier editions
and to improve the others, hoping all the while for the wisdom to know which is
which. I have been aided in this by the following individuals who reviewed either
the �ntire manuscript or major parts of it. My best thanks go to Professors Irving
Epstein, Brandeis University; James T. Hynes, University of Colorado; Paul J. Karol,
Carnegie-Mellon University; Lawrence Lohr, University of Michigan; Alden C. Mead,
University of Minnesota; Earl Mortenson, Cleveland State University. These reviews
were thorough and constructive; the final book owes much to them. I am particularly
grateful for their willingness to review a manuscript that was not always in a neat
and clean form.
My thanks are due to earlier authors in physical chemistry who have shaped my
thoughts on various topics. Most particular thanks are due to my first teachers in
the subject, Professors Karl F. Herzfeld, Walter J. Moore, and Francis O. Rice. In
addition, I am deeply indebted to Professor James A. Beattie for his kind permission
to reprint definitions from his book, Lectures on Elementary Chemical Thermody namics.
I believe that the influence of this remarkably clear exposition may be noticeable
throughout the material on thermodynamics in this book. Chapter 8 , the introduction
to the second law, is particularly indebted to Professor Beattie's Lectures.
I am grateful to all my colleagues at the University of Maryland who have made
suggestions, pointed out errors, responded to my questions, and helped in other
ways. Particular thanks go to Professors Raj Khanna and Paul Mazzocchi, who
supplied laboratory spectra for illustrations; to Professor Robert J. Munn, who wrote
the computer program to construct the index; to Professors Isadore Adler and James
M. Stewart, who read and commented on the sections dealing with x-ray spectroscopy
and x-ray diffraction; and to Professor E. C. Lingafelter, University of Washington,
who was kind enough to write detailed comments on the chapter on x-ray diffraction.
Thanks to them a number of errors have been corrected and several passages clarified.

Donald D. Wagman and David Garvin of the thermochemistry section of The National
Bureau of Standards were most helpful and patient in answering my questions and
kindly arranged for me to see a copy of NBS Technical Note 270-8 almost before
the ink was dry. Professor D. H. Whiffen, The University, Newcastle-upon-Tyne,
was most helpful in correspondence on the use of SI units in quantum mechanics.
I wish to express my appreciation to all the teachers, students, and casual readers
who have taken the time to write letters with questions, criticisms, and suggestions.
The book is much improved as a result of their comments.
I �lso wish to thank the editors and production staff of Addison-Wesley for their
excellent work. Robert L. Rogers, the Senior Science Editor, smoothed my path
throughout the preparation of the manuscript, helped with advice, secured timely
reviews, and made the necessary editorial decisions promptly and wisely. Margaret
Pinette, the Senior Production Editor, resolved all my proofreading complaints and
problems, always pleasantly and with good humor. Joseph Vetere, the Art Coordinator,
often went the extra mile to fulfill my wishes on the many illustrations in the book.
It has been a pleasure to work with all of them.
Finally, to my wife, Joan McDonald Castellan, and our children, Stephen, Bill,
David, and Susan, for their constant encouragement and patient endurance, I am
grateful in measure beyond words.
G.W.C.
October 1982

College Park, Md.

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Contents

1

1.1
1 .2
1 .3
1 .4
1 .5
1 .6
1.7
1 .8

Some Fundamental Chemical Concepts

1

Introduction
The kinds of matter
The kinds of substances
Atomic and molar masses
Symbols; Formulas
The mole
Chemical equations
The International System of Units, SI

1
1
1
2

3
4
4
6

2

Empirical Properties of Gases

2. 1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9

Boyle's law; Charles's law
Molar mass of a gas. Avogadro's law; The ideal gas law
The equation of state; Extensive and intensive properties
Properties o f the ideal gas
Determination o f molar masses o f gases and volatile
substances
Mixtures; Composition variables
Equations o f state for a gas mixture; Dalton's law
The partial-pressure concept
The barometric distribution law
Questions

Problems

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9

9
11
14
15
17
18
19
20
22
27
27


xii

Contents

3

Real Gases

33

3.1 Deviations from ideal behavior

3.2 Modifying the ideal gas equation; The van der Waals
equation
3.3 Implications of the van der Waals equation
3.4 The isotherms of a real gas
3.5 Continuity of states
3.6 The isotherms of the van der Waals equation
3.7 The critical state
3.8 The law of corresponding states
3.9 Other equations of state
Questions
Problems

4

4. 1
4.2
4.3
4.4
4.5
4.6
*4.7
4.8
4.9
*4. 1 0
4. 1 1
4. 1 2
*4.1 3
*4. 1 4
*4.1 5


34
36
40
41
42
43
45
46
48
48

The Structure of Gases

51

Introduction
Kinetic theory of gases; Fundamental assumptions
Calculation of the pressure of a gas
Dalton's law of partial pressures
Distributions and distribution functions
The Maxwell distribution
Mathematical interlude
Evaluation of A and f3
Calculation of average values using the Maxwell distribution
The Maxwell distribution as an energy distribution
Average values of individual components; Equipartition of
energy
Equipartition of energy and quantization
Calculation of vibrational heat capacity
The Maxwell-Boltzmann distribution law

Experimental verification of the Maxwell distribution law
Questions
Problems

51
51
52
57
57
58
62
66
68
69

5

5.1
5.2
5.3
5.4
5.5

33

71
74
77
80
81

82
82

Some Properties of liquids and Solids

85

Condensed phases
Coefficients of thermal expansion and compressibility
Heats of fusion; Vaporization; Sublimation
Vapor pressure
Other properties of liquids

85
86
88
88
90

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Contents

5.6 Review of structural differences between solids, liquids, and
gases
Questions
Problems

xiii


90
91
91

6

The laws of Thermodynamics: Generalities and the
Zeroth law

93

6. 1 Kinds of energy and the first law of thermodynamics
6.2 Restrictions on the conversion of energy from one form to
another
6.3 The second law of thermodynamics
6.4 The Zeroth law of thermodynamics
6.5 Thermometry
Questions
Problems

93
94
94
96
97
1 00
1 00

7


Energy and the First Law of Thermodynamics;

7. 1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.1 0
7. 1 1
7.1 2
7. 1 3
7. 1 4
7. 1 5
7. 1 6
7. 1 7
7.1 8
7. 1 9
7.20
7.21
7.22
*7.23
7.24

Thermochemistry


103

Thermodynamic terms: Definitions
Work and heat
Expansion work
Work of compression
Maximum and minimum quantities of work
Reversible and irreversible transformations
Energy and the first law of thermodynamics
Properties of the energy
Mathematical interlude; Exact and inexact differentials
Changes in energy in relation to changes in properties of the
system
Changes in state at constant volume
Measurement of (aUlaVh; Joule's experiment
Changes in state at constant pressure
The relation between Cp and Cv
The measurement of (aHlaph; Joule-Thomson experiment
Adiabatic changes in state
A note about problem working
Application of the first law of thermodynamics to chemical
reactions. The heat of reaction
The formation reaction
Conventional values of molar enthalpies
The determination of heats of formation
Sequences of reactions; Hess's law
Heats of solution and dilution
Heats of reaction at constant volume

1 03

1 04
1 06
1 09
1 10
111
1 13
1 15
1 15

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1 16
1 17
1 18
1 19
1 22
1 24
1 26
1 28
1 29
131
133
134
135
136
137


xiv


Contents

7.25 Dependence of the heat of reaction on temperature
7.26 Bond enthalpies
7.27 Calorimetric measurements
Questions
Problems
8

8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
8.16

138
141
143
144

145

Introduction to the Second law of Thermodynamics

153

General remarks
The Carnot cycle
The second law of thermodynamics
Characteristics of a reversible cycle
A perpetual-motion machine of the second kind
The efficiency of heat engines
Another impossible engine
The thermodynamic temperature scale
Retrospection
Carnot cycle with an ideal gas
The Carnot refrigerator
The heat pump
Definition of entropy
General proof
The Clausius inequality
Conclusion
Questions
Problems

153
153
155
155
155

157
157
160
161
161
162
163
164
165
167
168
168
168

9

Properties of the Entropy and the Third law of

9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12

9.13
9.14

Thermodynamics

171

The properties of entropy
Conditions of thermal and mechanical stability of a system
Entropy changes in isothermal transformations
Mathematical interlude. More properties of exact differentials.
The cyclic rule
Entropy changes in relation to changes in the state variables
Entropy as a function of temperature and volume
Entropy as a function of temperature and pressure
The temperature dependence of the entropy
Entropy changes in the ideal gas
The third law of thermodynamics
Entropy changes in chemical reactions
Entropy and probability
General form for omega
The energy distribution

171
172
172

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177
178
180
182
182
185
188
189
192
193


Contents

9.15 Entropy of mixing and exceptions to the third law of
thermodynamics
Questions
Problems
10

Spontaneity and Equilibrium

10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8

10.9
10.10

The general conditions for equilibrium and for spontaneity
Conditions for equilibrium and spontaneity under constraints
Recollection
Driving forces for natural changes
The fundamental equations of thermodynamics
The thermodynamic equation of state
The properties of A
The properties of G
The Gibbs energy of real gases
Temperature dependence of the Gibbs energy
Questions
Problems
11

11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11
11.12
11.13

11.14
*11.15
*11.16
*11.17
*11.18
11.19
11.20
11.21

xv

196
198
198

203

203
204
207
208
208
210
212
213
215
216
216
217


Systems of Variable Composition; Chemical Equilibrium

221

The fundamental equation
The properties of f.-ti
The Gibbs energy of a mixture
The chemical potential of a pure ideal gas
Chemical potential of an ideal gas in a mixture of ideal gases
Gibbs energy and entropy of mixing
Chemical equilibrium in a mixture
The general behavior of G as a function of �
Chemical equilibrium in a mixture of ideal gases
Chemical equilibrium in a mixture of real gases
The equilibrium constants, Kx and Kc
Standard Gibbs energies of formation
The temperature dependence of the equilibrium constant
Equilibria between ideal gases and pure condensed phases
The LeChatelier principle
Equilibrium constants from cal0fimetric measurements. The
third law in its historical context
Chemical reactions and the entropy of the universe
Coupled reactions
Dependence of the other thermodynamic functions on
composition
Partial molar quantities and additivity rules
The Gibbs-Duhem equation

221
222

223
224
224
226
229
230
232
234
234
235
238
240
242

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245
246
246
247
249


xvi

Contents

1 1 .22 Partial molar quantities in mixtures of ideal gases
* 1 1 .23 Differential heat of solution

Questions
Problems
12

1 2. 1
1 2.2
1 2.3
1 2.4
1 2.5
1 2.6
1 2.7
1 2.8
1 2.9

250
25 1
25 1
25 1

Phase Equilibrium i n Simple Systems; The Phase Rule

259

The equilibrium condition
Stability of the phases of a pure substance
Pressure dependence of f.L versus T curves
The Clapeyron equation
The phase diagram
The integration of the Clapeyron equation
Effect of pressure on the vapor pressure

The phase rule
The problem of components
Questions
Problems

259
259
26 1
262
266
268
270
27 1
272
274
274

13

Solutions
I. The Ideal Solution and Colligative Properties

13.1 Kinds of solutions
13.2 Definition of the ideal solution
1 3.3 Analytical form of the chemical potential in ideal liquid
solutions
13.4 Chemical potential of the solute in a binary ideal solution;
Application of the Gibbs-Duhem equation
13.5 Colligative properties
13.6 The freezing-point depression

* 1 3.7 Solubility
13.8 Elevation of the boiling point
13.9 Osmotic pressure
Questions
Problems

277

277
278
280
280
28 1
282
285
287
288
29 1
292

14

Solutions
II. More Than One Volatile Component; The Ideal Dilute

14.1
1 4.2
1 4.3
1 4.4


Solution

295

General characteristics of the ideal solution
The chemical potential in ideal solutions
Binary solutions
The lever rule

295
296
297
299

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Contents

14.5
14.6
14.7
14.8
14.9
14.10
14.11
14.12
14.13
14.14


Changes in state as the pressure is reduced isothermally
Temperature-composition diagrams
Changes in state with increase in temperature
Fractional distillation
Azeotropes
The ideal dilute solution
The chemical potentials in the ideal dilute solution
Henry's law and the solubility of gases
Distribution of a solute between two solvents
Chemical equilibrium in the ideal solution
Questions
Problems
15

15.1
15.2
15.3
15.4
15.5
*15.6
*15.7
*15.8
*15.9
*15.10
.,td5.11
*15.12
*15.13
*15.14
*15.15


xvi i

300
301
302
302
305
307
309
311
313
313
314
315

Equilibria between Condensed Phases

3 19

Liquid-liquid equilibria
Distillation of partially miscible and immiscible liquids
Solid-liquid equilibria; The simple eutectic diagram
Freezing-point diagram with compound formation
Compounds having incongruent melting points
Miscibility in the solid state
Freezing-point elevation
Partial miscibility in the solid state
Gas-solid equilibria; Vapor pressure of salt hydrates
Systems of three components
Liquid-liquid equilibria

Solubility of salts; Common-ion effect
Double-salt formation
The method of "wet residues"
" Salting out"
Questions
Problems

319
322
324
329
330
332
333
334
336
337
338
339
340
342
342
343
344

16

Equilibria i n Nonideal Systems

The concept of activity

The rational system of activities
Colligative properties
The practical system
Activities and reaction equilibrium
Activities in electrolytic solutions
The Debye-Huckel theory of the structure of dilute ionic
solutions
16.8 Equilibria in ionic solutions
Questions
Problems

16.1
16.2
16.3
16.4
16.5
16.6
16.7

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347
348
350
351
353
354
358

365
367
367


xviii

Contents

17

17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
17.10
17.11
17.12
17.13
17.14
17.15
17.16
17.17
*17.18
17.19

17.20
17.21

Equilibria in Electrochemical Cells

371

Introduction
Definitions
The chemical potential of charged species
Cell diagrams
The Daniell cell
Gibbs energy and the cell potential
The Nernst equation
The hydrogen electrode
Electrode potentials
Temperature dependence of the cell potential
Kinds of electrodes
Equilibrium constants from standard half-cell potentials
Significance of the half-cell potential
The measurement of cell potentials
Reversibility
The determination of the � o of a half-cell
The determination of activities and activity coefficients from
cell potentials
Concentration cells
Technical electrochemical processes
Electrochemical cells as power sources
Two practical power sources
Questions

Problems

371
371
372
375
375
377
378
378
380
382
383
385
387
389
389
390

18

18.1
18.2
18.3
18.4
18.5
18.6
18.7
*18.8
18.9

18.10
18.11
18.12
18.13
18.14
18.15
18.16

391
392
395
396
398
402
402

Surface Phenomena

407

Surface energy and surface tension
Magnitude of surface tension
Measurement of surface tension
Thermodynamic formulation
Capillary rise and capillary depression
Properties of very small particles
Bubbles; Sessile drops
Liquid-liquid and solid-liquid interfaces
Surface tension and adsorption
Surface films

Adsorption on solids
Physical and chemisorption
The Brunauer, Emmet, and Teller (BET) isotherm
Electrical phenomena at interfaces; The double layer
Electrokinetic effects
Colloids

407
408
409
411
413
414
417
418
420
424
426
427
428
432
434
435

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Contents

18.17 Colloidal electrolytes; Soaps and detergents

18.18 Emulsions and foams
Questions
Problems
19

19.1
19.2
19.3
19.4
19.5
19.6
19.7
19.8
19.9
19.10
19.11
*19.12
*19.13
*19.14
19.15

445

Introduction
Nineteenth century
The earthquake
Discovery of the electron
Positive rays and isotopes
Radioactivity
Alpha-ray scattering

Radiation and matter
The photoelectric effect
Bohr's model of the atom
Particles and Louis de Broglie
The classical wave equation
The Schrodinger equation
The Interpretation of I/J
Retrospection
Questions
Problems

445
445
447
448
450
450
451
452
455
456
459
460
461
463
464
465
465

Introduction to Quantum Mechanical Principles


467

Introduction
Postulates of the quantum mechanics
Mathematical interlude: Operator algebra
The Schrodinger equation
The eigenvalue spectrum
Expansion theorem
Concluding remarks on the general equations
Questions
Problems

467
467
469
470
474
476
477
478
478

21

21.1
21.2
21.3
21.4
21.5


438
439
440
440

The Structure of Matter

20

20.1
20.2
20.3
20.4
20.5
*20.6
20.7

xix

The Quantum Mechanics of Some Simple Systems

479

Introduction
The free particle
Particle in a "box"
The uncertainty principle
The harmonic oscillator


479
480
481
489
491

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xx

Contents

2 1 .6 Multidimensional problems
21.7 The two-body problem
2 1 .8 The rigid rotor
Questions
Problems
22

The Hydrogen Atom

22.1
22.2
22.3
22.4

The central-field problem
The hydrogen atom
Significance of the quantum numbers in the hydrogen atom

Probability distribution of the electron cloud in the hydrogen
atom
22.5 Electron spin and the magnetic properties of atoms
22.6 The structure of complex atoms
�22.7 Some general trends in the periodic system
Questions
Problems
23

23.1
23.2
23.3
23.4
23.5
23.6
23.7
23.8
23.9
23. 1 0
23. 1 1
23.12
23.13
23.14
23. 1 5
23. 1 6

498
500
503
508

508

511

51 1
512
516
519
523
524
527
529
530

The Covalent Bond

53 1

General remarks
The electron pair
The hydrogen molecule; Valence bond method
The covalent bond
Overlap and directional character of the covalent bond
Molecular geometry
Structures with multiple bonds
Structures involving two double bonds or a triple bond
Bond order and bond length
The covalent bond i n elements o f the second and higher
periods
Molecular energy levels

Wave functions and symmetry
Mathematical interlude
The water molecule (group CZv): Example
Representations o f a group
Reducible representations; The orthogonality theorem
Questions
Problems

53 1
532
534
538
539
543
546
549
552

24

Atomic Spectroscopy

24. 1 Spectral regions
24.2 Basic spectroscopic experiments
24.3 Origins of spectra

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554

560
56 1
562
564
569
575
575

579

579
58 1
582


Contents

24.4
24. 5
24.6
24.7
24. 8
24.9
24. 1 0
24. 1 1
24. 1 2
24. 1 3
24. 1 4
24. 1 5
24. 1 6


Light absorption; Beer's law
Theory of atomic spectra
Quantum numbers in multielectron atoms
Atomic spectroscopy; Term symbols
Atoms with closed shells
Obtaining term symbols from the electron configuration
Examples of atomic spectra
The magnetic properties of atoms
X-ray spectroscopy
X-ray fluorescence spectroscopy
X-ray microanalysis with the electron probe
X-ray photoelectron spectroscopy
Ultraviolet photoelectron spectroscopy
Questions
Problems
25

25. 1
25. 2
25. 3
25. 4
25. 5
25. 6
25. 7
25. 8
25. 9
25. 1 0
25. 1 1
25. 1 2

*25. 1 3
*25. 1 4
*25. 1 5
*25. 1 6

585
587
589
59 1
59 1
592
594
599
609
614
615
617
618
620
621

Molecular Spectroscopy

625

Nuclear motions; Rotation and vibration
Rotations
The rotational spectrum
Vibrations
The vibration-rotation spectrum

Rotational and vibration-rotation spectra of polyatomic
molecules
Applications of infrared spectroscopy
Raman effect
Electronic spectra
Electronic spectra of polyatomic molecules
Quantum mechanical description of time-dependent systems
Variation in the state of a system with time
Selection rules for the harmonic oscillator
Selection rules and symmetry
Selection rules for the hydrogen atom
Selection rules for polyatomic molecules
Questions
Problems

625
626
627
628
628

26

26. 1
26. 2
26. 3
26. 4
*26. 5
26. 6


xxi

632
636
638
64 1
646
647
648
650
65 1
655
656
657
657

Intermolecular Forces

659

Introduction
Polarization in a dielectric
Molar polarization
Intermolecular forces
Interaction energy and the van der Waals
Laws of interaction

659
659
663

668
67 1
673

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"a"


xxii

Contents

26.7 Comparison of the contributions to the interaction energy
26.8 The hydrogen bond
Questions
Problems
27

27.1
27.2
27.3
27.4
27.5
27.6
27.7
*27.8
*27.9
*27.10
*27.11

*27.12

Structure of Solids

681

The structural distinction between solids and liquids
An empirical classification of solid types
Geometrical requirements in the close-packed structures
Geometric requirements in covalent crystals
The symmetry of crystals
The crystal classes
Symmetry in the atomic pattern
The designation of crystal planes and faces
The x-ray examination of crystals
Debye-Scherrer (powder) method
Intensities and structure determination
X-ray diffraction in liquids
Questions
Problems

681
682
682
690
691
692
695
697
700

703
704
705
706
707

28

28.1
28.2
28.3
28.4
28.5
28.6
28.7

675
677
679
679

Electronic Structure and Macroscopic Properties

709

Preliminary remarks
Cohesive energy in ionic crystals
The electronic structure of solids
Conductors and insulators
Ionic crystals

Semiconductors
Cohesive energy in metals
Questions
Problems

709
709
713
715
716
716
718
719
719

29

Structure and Thermodynamic Properties

29.1 The energy of a system
29.2 Definition of the entropy
29.3 The thermodynamic functions in terms of the partition
function
29.4 The molecular partition function
29.5 The chemical potential

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721
723
724
725
726


Contents

29.6
29.7
29.8
29.9
29.10
29.11
29.12
29. 1 3
29.14

Application to translational degrees of freedom
Partition function of the harmonic oscillator
The monatomic solid
The rotational partition function
The electronic partition function
Ortho- and para-hydrogen
General expressions for the partition function
The equilibrium constant in terms of the partition functions
Conclusion
Questions
Problems

30

30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
30.9
30.10
*30.1 1
*30.12
30.13

727
728
729
731
733
735
737
738
741
741
742

Transport Properties


745

Introductory remarks
Transport properties
The general equation for transport
Thermal conductivity in a gas
Collisions in a gas; The mean free path
Final expression for the thermal conductivity
Viscosity
Molecular diameters
Diffusion
Summary of transport properties in a gas
The nonsteady state
The Poiseuille Formula
The viscosimeter
Questions
Problems

745
746
747
748
750
752
752
754
755
757
757
758

760
761
761

31

31.1
31.2
*3 1.3
31.4
31.5
31.6
3 1 .7
3 1.8
3 1 .9
3 1.10
31.11
3 1.12
*31. 1 3

xxiii

Electrical Conduction

765

Electrical transport
Conduction in metals
The Hall effect
The electrical current in ionic solutions

The measurement of conductivity in electrolytic solutions
The migration of ions
The determination of Aoc
Transference numbers
Molar ion conductivities
Applications of conductance measurements
Stokes's law
Conductivities of the hydrogen and hydroxyl ions
Temperature dependence of the ion conductivities

765
766
767
769
770
771
773
775
777
777
781
783
784

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