Introduction To Chemical Physics

538 Pages·1939·22.214 MB·English

by  John C. Slater

INTERNATIONAL SERIES IN PHYSICS
LEE A. DuBRIDGE, CONSULTING EDITOR
INTRODUCTION
TO
CHEMICAL PHYSICS
INTERNATIONAL SERIES IN PURE AND APPLIED PHYSICS
G. P. HARNWELL, CONSULTING EDITOR
ADVISORY EDITORIAL CoMMITTEE: E. U. Condon, George R. Harrison
Elmer Hutchisson, K. K. Darrow
Allis and H erlin Thermodynamics and Statistical Mechanics
Cady Piezoelectricity
Clark Applied X-rays
Edwards Analytic and Vector Mechanics
Finkelnburg Atomic Physics
Gurney Introduction to Statistical Mechanics
Hall Introduction to Electron Microscopy
Hardy and Perrin The Principles of Optics
H arnwell Electricity and Electromagnetism
H arnwell and Livingood Experimental Atomic Physics
Houston Principles of Mathematical Physics
Houston Principles of Quantum Mechanics
Hughes and DuBridge Photoelectric Phenomena
Hund High-frequency Measurements
Kemble The Fundamental Principles of Quantum Mechanics
Kennard Kinetic Theory of Gases
Marshak Meson Physics
Morse Vibration and Sound
Morse and Feshbach Methods of Theoretical Physics
M uskat Physical Principles of Oil Production
Richtmeyer and Kennard Introduction to Modern Physics
Ruark and Urey Atoms, Molecules, and Quanta
Schiff Quantum Mechanics
Seitz The Modern Theory of Solids
Slater Introduction to Chemical Physics
Slater Microwave Transmission
Slater Quantum Theory of Matter
Slater and Frank Electromagnetism
Slater and Frank Introduction to Theoretical Physics
Slater and Frank Mechanics
Smythe Static and Dynamic Electricity
Squire Low Temperature Physics
Stratton Electromagnetic Theory
Thorndike Mesons: A Summary of Experimental Facts
White Introduction to Atomic Spectra
The late F. K. Richtmyer was Consulting Editor of the series from its inception in
1929 to his death in 1939.
Lee A. DuBridge was Consulting Editor of the series from 1939 to 1946.
INTRODUCTION
TO
CHEMICAL PHYSICS
BY
J.C. SLATER
Professor of Physics
M a8sachuseUs Institute of Technology
McGRAW-HILL BOOK COMPANY, INc.
NEW YORK AND LONDON
1939
COPYRIGHT, 1939, BY THE
McGRAW-HILL BooK CoMPANY, !Ne.
PRINTED IN THE UNITED STATES OF AMERICA
All rights reserved. This book, or
parts thereof, may not be reproduced
in any form without permission of
the publishers.
IX
THE MAPLE PRESS COMPANY, YORK, PA.
PREFACE
It is probably unfortunate that physics and chemistry ever were
separated. Chemistry is the science of atoms and of the way they com
bine. Physics deals with the interatomic forces and with the large-scale
properties of matter resulting from those forces. So long as chemistry
was largely empirical and nonmathematical, and physics had not learned
how to treat small-scale atomic forces, the two sciences seemed widely
separated. But with statistical mechanics and the kinetic theory on the
one hand and physical chemistry on the other, the two sciences began to
come together. Now that statistical mechanics has led to quantum theory
and wave mechanics, with its explanations of atomic interactions, there is
really nothing separating them any more. A few years ago, though their
ideas were close together, their experimental methods were still quite
different: chemists dealt with things in test tubes, making solutions, pre
cipitating and filtering and evaporating, while physicists measured every
thing with galvanometers and spectroscopes. But even this distinction
has disappeared, with more and more physical apparatus finding its way
into chemical laboratories.
A wide range of study is common to both subjects. The sooner we
realize this the better. For want of a better name, since Physical
Chemistry is already preempted, we may call this common field Chemical
Physics. It is an overlapping field in which both physicists and chemists
should be trained. There seems no valid reason why their training in it
should differ. This book is an attempt to incorporate some of the
material of this common field in a unified presentation.
What should be included in a discussion of chemical physics? Logi
cally, we should start with fundamental principles. We should begin
with mechanics, then present electromagnetic theory, and should work
up to wave mechanics and quantum theory. By means of these we
should study the structure of atoms and molecules. Then we should
introduce thermodynamics and statistical mechanics, so as to handle
large collections of molecules. With all this fundamental material we
could proceed to a discussion of different types of matter, in the solid,
liquid, and gaseous phases, and to an explanation of its physical and
chemical properties in terms of first principles. But if we tried to do all
this, we should, in the first place, be writing several volumes which would
include almost all of theoretical physics and chemistry; and in the
second place no one but an experienced mathematician could handle the
v
.
VI PREFACE
theory. For both of these reasons the author has compromised greatly
in the present volume, so as to bring the material into reasonable com
pass and to make it intelligible to a reader with a knowledge of calculus
and differential equations, but unfamiliar with the more difficult branches
of mathematical physics.
In the matter of scope, most of the theoretical physics which forms a
background to our subject has been omitted. Much of this is considered
in the companion volume, "Introduction to Theoretical Physics," by
Slater and Frank. The effort has been made in the present work to pro
duce a book which is intelligible without studying theoretical physics
first. This has been done principally for the benefit of chemists and
others who wish to obtain the maximum knowledge of chemical physics
with the minimum of theory. In the treatment of statistical mechanics
only the most elementary use of mechanics is involved. For that reason
it has not been possible to give a complete discussion, although the parts
used in the calculations have been considered. Statistical mechanics has
been introduced from the standpoint more of the quantum theory than of
classical theory, but the quantum theory that is used is of a very elemen
tary sort. It has seemed desirable to omit wave mechanics, which
demands more advanced mathematical methods. In discussing atomic
and molecular structure and the nature of interatomic forces, descriptive
use has been made of the quantum theory, but again no detailed use of it.
Thus it is hoped that the reader with only a superficial acquaintance with
modern atomic theory will be able to read the book without great diffi
culty, although, of course, the reader with a knowledge of quantum
theory and wave mechanics will have a great advantage.
Finally in the matter of arrangement the author has departed from
the logical order in the interest of easy presentation. Logically one
should probably begin with the structure of atoms and molecules, crystals
and liquids and gases; then introduce the statistical principles that
govern molecules in large numbers, and finally thermodynamics, which
follows logically from statistics. Actually almost exactly the opposite
order has been chosen. Thermodynamics and statistical mechanics come
first. Then gases, solids, and liquids are treated on the basis of thermo
dynamics and statistics, with a minimum amount of use of a model.
Finally atomic and molecular structure are introduced, together with a
discussion of different types of substances, explaining their interatomic
forces from quantum theory and their thermal and elastic behavior from
our thermodynamic and statistical methods. In this way, the historical
order is followed roughly, and, at least for chemists, it proceeds from
what are probably the more familiar to ~he less familiar methods.
It is customary to write books either on thermodynamics or on
statistical mechanics; this one combines both. It seems hardly necessary
..
PREFACE vu
to apologize for this. Both have their places, and both are necessary in a
complete presentation of chemical physics. An effort has been made to
keep them separate, so that at any time the reader will be clear as to
which method is being used. In connection with thermodynamics, the
method of Bridgman, which seems by far the most convenient for prac
tical application, has been used.
There is one question connected with thermodynamics, that of
notation. The continental notation and the American chemical notation
of Lewis and Randall are quite different. Each has its drawbacks. The
author has chosen the compromise notation of the Joint Committee of
the Chemical Society, the Faraday Society, and the Physical Society (all
of England), which preserves the best points of both. It is hoped that
this notation, which has a certain amount of interna.tional sanction, may
become general among both physicists and chemists, whose poblems are
similar enough so that they surely can use the same language.
In a book like this, containing a number of different types of material,
it is likely that some readers and teachers will want to use some parts,
others to use other parts. An attempt has been made to facilitate such
use by making chapters and sections independent of each other as far as
possible. The book has been divided into three parts: Part I, Thermo
dynamics, Statistical Mechanics, and Kinetic Theory; Part II, Gases,
Liquids, and Solids; Part III, Atoms, Molecules, and the Structure of
Matter. The first part alone forms an adequate treatment of thermo
dynamics and statistical theory, and could be used by itself. Certain of
its chapters, as Chap. Von the Fermi-Dirac and Einstein-Bose Statistics,
Chap. VI on the Kinetic Method and the Approach to Thermal Equilib
rium, and Chap. VII on Fluctuations, can be omitted without causing
much difficulty in reading the following parts of the book (except for the
chapters on metals, which depend on the Fermi-Dirac statistics). In
Part II, most of Chap. IX on the Molecular Structure and Specific Heat
of Polyatomic Gases, Chap. X on Chemical Equilibrium in Gases, parts
of Chap. XII on Van der Waals' Equation and Chap. XIII on the
Equation of State of Solids, Chap. XV on The Specific Heat of Com
pounds, Chap. XVII on Phase Equilibrium in Binary Systems, and
Chap. XVIII on Phase Changes of the Second Order are not necessary
for what follows. In Part III, Chap. XIX on Radiation and Matter,
Chap. XX on Ionization and Excitation of Atoms, and Chap. XXI on
Atoms and the Periodic Table will be familiar to many readers. Much
of the rest of this part is descriptive; one chapter does not depend on
another, so that many readers may choose to omit a considerable portion
or all, of this material. It will be seen from this brief enumeration that
selections from the book may be used in a variety of ways to serve the
needs of courses less extensive than the whole book.
Vlll PREFACE
The author hopes that this book may serve in a minor way to fill the
gap that has grown between physics and chemistry. This gap is a
result of tradition and training, not of subject matter. Physicists and
chemists are given quite different courses of instruction; the result is
that almost no one is really competent in all the branches of chemical
physics. If the coming generation of chemists or physicists could receive
training, in the first place, in empirical chemistry, in physical chemistry,
in metallurgy, and in crystal structure, and, in the second place, in
theoretical physics, including mechanics and electromagnetic theory, and
in particular in quantum theory, wave mechanics, and the structure of
atoms and molecules, and finally in thermodynamics, statistical
mechanics, and what we have called chemical physics, they would be
far better scientists than those receiving the present training in either
chemistry or physics alone.
The author wishes to indicate his indebtedness to several of his
colleagues, particularly Professors B. E. Warren and W. B. Nottingham,
who have read parts of the manuscript and made valuable comments.
His indebtedness to books is naturally very great, but most of them are
mentioned in the list of suggested references at the end of this volume.
J. c.
SLATER.
CAMBRIDGE, MASSACHUSETTS,
September, 1939.
CONTENTS
PAGE
PREFACE .•••••••••• v
PART I
THERMODYNAMICS, STATISTICAL MECHANICS,
AND KINETIC THEORY
CHAPTER I
HEAT AS A MODE OF MOTION
INTRODUCTION .................. . 3
1. THE CONSERVATION OF ENERGY . . . . . . . . . . . 3
2. INTERNAL ENERGY, EXTERNAL WORK, AND HEAT FLOW. 6
3. THE EN'l'ROPY AND IRREVERSIBLE PROCESSES. . . . . . 9
4. THE SECOND LAw OF THERMODYNAMICS. . . 12
CHAPTER II
THERMODYNAMICS
INTRODUCTION . . . . . 16
1. THE EQUATION OF STATE . . . . . . . 16
2. THE ELEMENTARY PARTIAL DERIVATIVES 18
3. THE ENTHALPY, AND HELMHOLTZ AND GIBBS FREE ENERGIES 20
4. METHODS OF DERIVING THERMODYNAMIC FORMULAS .... 23
5. GENERAL CLASSIFICATION OF THERMODYNAMIC FORMULAS. . . . . . 27
6. COMPARISON OF THERMODYNAMIC AND GAS SCALES OF TEMPERATURE 30
CHAPTER III
STATISTICAL MECHANICS
INTRODUCTION • • • 32
1. STATISTICAL ASSEMBLIES AND THE ENTROPY . . . . . . . . 32
2. COMPLEXIONS AND THE PHASE SPACE . . . . . • • . • 36
3. CELLS IN THE PHASE SPACE AND THE QUANTUM THEORY. . 38
4. IRREVERSIBLE PROCESSES • • • • . . . ... . 43
5. THE CANONICAL ASSEMBLY . • • . . . . . . . . . . . . .. . 46
CHAPTER IV
THE MAXWELL-BOLTZMANN DISTRIBUTION LAW
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . 52
1. THE CANONICAL ASSEMBLY AND THE MAXWELL-BOLTZMANN DISTRIBUTION 52
2. MAXWELL'S DISTRIBUTION OF VELOCITIES . . . . . . . . . . . . . . . 55
3. THE EQUATION OF STATE AND SPECIFIC HEAT OF PERFECT MoNATOMic GASES 58
4. THE PERFECT GAS IN A FORCE FIELD. . . . . . . . . 62
IX