com Physical Chemistry Third Edition www.com Physical Chemistry Third Edition www. Mortimer Professor Emeritus Rhodes College Memphis, Tennessee AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an imprint of Elsevier Cover Design: Eric DeCicco Cover Image: © iStockphoto Elsevier Academic Press 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA 84 Theobald’s Road, London WC1X 8RR, UK This book is printed on acid-free paper. ∞ Copyright © 2008, Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, E-mail: permissions@elsevier. You may also complete your request on-line via the Elsevier homepage (http://elsevier.com), by www.com selecting “Customer Support” and then “Obtaining Permissions.” Library of Congress Catalog-in-Publishing Data Mortimer, Robert G. Physical chemistry / Robert G. Includes bibliographical references and index. ISBN 978-0-12-370617-1 (hardcover : alk. Chemistry, Physical and theoretical.M67 2008 541–dc22 2008007675 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-13: 978-0-12-370617-1 For information on all Elsevier Academic Press publications visit our Web site at www.com Printed in Canada 08 09 10 9 8 7 6 5 4 3 2 1 To my wife, Ann, and to my late father, William E. Mortimer, who was responsible for my taking my first chemistry course www.com Contents Periodic Table Inside front cover List of Numerical Tables in Appendix A Inside front cover www.com Information Tables Inside back cover Preface xv Acknowledgments xvii Part 1 Thermodynamics and the Macroscopic Description of Physical Systems 1 Chapter 1 The Behavior of Gases and Liquids 3 1.2 Systems and States in Physical Chemistry 12 1.4 The Coexistence of Phases and the Critical Point 27 Chapter 2 Work, Heat, and Energy: The First Law of Thermodynamics 39 2.1 Work and the State of a System 40 2.3 Internal Energy: The First Law of Thermodynamics 55 2.4 Calculation of Amounts of Heat and Energy Changes 60 2.6 Calculation of Enthalpy Changes of Processes without Chem- ical Reactions 81 2.7 Calculation of Enthalpy Changes of a Class of Chemical Reactions 86 2.8 Calculation of Energy Changes of Chemical Reactions 94 Chapter 3 The Second and Third Laws of Thermodynamics: Entropy 105 3.1 The Second Law of Thermodynamics and the Carnot Heat Engine 106 vii viii Contents 3.2 The Mathematical Statement of the Second Law: Entropy 114 3.3 The Calculation of Entropy Changes 121 3.5 The Third Law of Thermodynamics and Absolute Entropies 139 Chapter 4 The Thermodynamics of Real Systems 151 4.1 Criteria for Spontaneous Processes and for Equilibrium: The Gibbs and Helmholtz Energies 152 4.2 Fundamental Relations for Closed Simple Systems 158 4.3 Additional Useful Thermodynamic Identities 167 4.4 Gibbs Energy Calculations 175 4.6 Euler’s Theorem and the Gibbs–Duhem Relation 188 Chapter 5 Phase Equilibrium 199 www.1 The Fundamental Fact of Phase Equilibrium 200 5.2 The Gibbs Phase Rule 202 5.3 Phase Equilibria in One-Component Systems 205 5.4 The Gibbs Energy and Phase Transitions 215 5.5 Surfaces in One-Component Systems 222 5.6 Surfaces in Multicomponent Systems 230 Chapter 6 The Thermodynamics of Solutions 237 6.2 Henry’s Law and Dilute Nonelectrolyte Solutions 248 6.3 Activity and Activity Coefficients 258 6.4 The Activities of Nonvolatile Solutes 267 6.5 Thermodynamic Functions of Nonideal Solutions 275 6.6 Phase Diagrams of Nonideal Mixtures 282 6.7 Colligative Properties 292 Chapter 7 Chemical Equilibrium 303 7.1 Gibbs Energy Changes and the Equilibrium Constant 304 7.2 Reactions Involving Gases and Pure Solids or Liquids 310 7.3 Chemical Equilibrium in Solutions 315 7.4 Equilibria in Solutions of Strong Electrolytes 328 7.6 The Temperature Dependence of Chemical Equilibrium. The Principle of Le Châtelier 335 7.7 Chemical Equilibrium and Biological Systems 343 Chapter 8 The Thermodynamics of Electrochemical Systems 351 8.1 The Chemical Potential and the Electric Potential 352 8.3 Half-Cell Potentials and Cell Potentials 361 8.4 The Determination of Activities and Activity Coefficients of Electrolytes 371 8.5 Thermodynamic Information from Electrochemistry 374 Contents ix Part 2 Dynamics 381 Chapter 9 Gas Kinetic Theory: The Molecular Theory of Dilute Gases at Equilibrium 383 9.1 Macroscopic and Microscopic States of Macroscopic Systems 384 9.2 A Model System to Represent a Dilute Gas 386 9.3 The Velocity Probability Distribution 394 9.4 The Distribution of Molecular Speeds 405 9.5 The Pressure of a Dilute Gas 411 9.6 Effusion and Wall Collisions 416 9.7 The Model System with Potential Energy 418 9.8 The Hard-Sphere Gas 422 9.9 The Molecular Structure of Liquids 434 Chapter 10 Transport Processes 441 10.1 The Macroscopic Description of Nonequilibrium www.3 The Gas Kinetic Theory of Transport Processes in Hard- Sphere Gases 460 10.4 Transport Processes in Liquids 467 10.5 Electrical Conduction in Electrolyte Solutions 475 Chapter 11 The Rates of Chemical Reactions 485 11.1 The Macroscopic Description of Chemical Reaction Rates 486 11.2 Forward Reactions with One Reactant 488 11.3 Forward Reactions with More Than One Reactant 499 11.4 Inclusion of a Reverse Reaction.5 A Simple Reaction Mechanism: Two Consecutive Steps 510 11.7 The Experimental Study of Fast Reactions 515 Chapter 12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms 523 12.1 Reaction Mechanisms and Elementary Processes in Gases 524 12.2 Elementary Processes in Liquid Solutions 527 12.3 The Temperature Dependence of Rate Constants 533 12.4 Reaction Mechanisms and Rate Laws 540 12.5 Chain Reactions 556 Chapter 13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics 565 13.2 Competing Mechanisms and the Principle of Detailed Balance 583 13.3 Autocatalysis and Oscillatory Chemical Reactions 585 13.4 The Reaction Kinetics of Polymer Formation 589 x Contents 13.6 Experimental Molecular Study of Chemical Reaction Mechanisms 608 Part 3 The Molecular Nature of Matter 617 Chapter 14 Classical Mechanics and the Old Quantum Theory 619 14.4 The Old Quantum Theory 640 Chapter 15 The Principles of Quantum Mechanics. De Broglie Waves and the Schrödinger Equation 653 15.1 De Broglie Waves 654 15.2 The Schrödinger Equation 657 www.3 The Particle in a Box and the Free Particle 663 15.4 The Quantum Harmonic Oscillator 674 Chapter 16 The Principles of Quantum Mechanics. The Postulates of Quantum Mechanics 683 16.1 The First Two Postulates of Quantum Mechanics 684 16.2 The Third Postulate. Mathematical Operators and Mechanical Variables 684 16.3 The Operator Corresponding to a Given Variable 688 16.4 Postulate 4 and Expectation Values 696 16.5 The Uncertainty Principle of Heisenberg 711 16. Measurements and the Determination of the State of a System 717 Chapter 17 The Electronic States of Atoms. The Hydrogen Atom 725 17.1 The Hydrogen Atom and the Central Force System 726 17.2 The Relative Schrödinger Equation.3 The Radial Factor in the Hydrogen Atom Wave Function. The Energy Levels of the Hydrogen Atom 736 17.4 The Orbitals of the Hydrogen-Like Atom 741 17.5 Expectation Values in the Hydrogen Atom 749 17.6 The Time-Dependent Wave Functions of the HydrogenAtom 753 17.7 The Intrinsic Angular Momentum of the Electron. “Spin” 755 Chapter 18 The Electronic States ofAtoms. The Zero-OrderApproximation for Multielectron Atoms 763 18.1 The Helium-Like Atom 764 18.2 The Indistinguishability of Electrons and the Pauli Exclusion Principle 766 18.3 The Ground State of the Helium Atom in Zero Order 768 18.4 Excited States of the Helium Atom 772 18.5 Angular Momentum in the Helium Atom 774 Contents xi 18.6 The Lithium Atom 781 18.7 Atoms with More Than Three Electrons 784 Chapter 19 The Electronic States of Atoms. Higher-Order Approximations 789 19.1 The Variation Method and Its Application to the Helium Atom 790 19.2 The Self-Consistent Field Method 796 19.3 The Perturbation Method and Its Application to the Ground State of the Helium Atom 799 19.4 Excited States of the HeliumAtom. Degenerate Perturbation Theory 803 19.5 The Density Functional Method 805 19.6 Atoms with More Than Two Electrons 806 Chapter 20 The Electronic States of Diatomic Molecules 823 20.1 The Born–Oppenheimer Approximation and the Hydrogen Molecule Ion 824 www.Approximate Molecular Orbitals ThatAre Linear Combinations of Atomic Orbitals 833 20.3 Homonuclear Diatomic Molecules 838 20.4 Heteronuclear Diatomic Molecules 851 Chapter 21 The Electronic Structure of Polyatomic Molecules 867 21.1 The BeH2 Molecule and the sp Hybrid Orbitals 868 21.2 The BH3 Molecule and the sp2 Hybrid Orbitals 871 21.3 The CH4 , NH3 , and H2 O Molecules and the sp3 Hybrid Orbitals 873 21.4 Molecules with Multiple Bonds 878 21.5 The Valence-Bond Description of Polyatomic Molecules 881 21.7 The Free-Electron Molecular Orbital Method 892 21.8 Applications of Symmetry to Molecular Orbitals 894 21.9 Groups of Symmetry Operators 896 21.10 More Advanced Treatments of Molecular Electronic Structure. Computational Chemistry 904 Chapter 22 Translational, Rotational, and Vibrational States of Atoms and Molecules 915 22.1 The Translational States of Atoms 916 22.2 The Nonelectronic States of Diatomic Molecules 919 22.3 Nuclear Spins and Wave Function Symmetry 930 22.4 The Rotation and Vibration of Polyatomic Molecules 933 22.5 The Equilibrium Populations of Molecular States 942 Chapter 23 Optical Spectroscopy and Photochemistry 949 23.1 Emission/Absorption Spectroscopy and Energy Levels 950 23.2 The Spectra of Atoms 959 23.3 Rotational and Vibrational Spectra of Diatomic Molecules 961 23.4 Electronic Spectra of Diatomic Molecules 972 xii Contents 23.5 Spectra of Polyatomic Molecules 975 23.6 Fluorescence, Phosphorescence, and Photochemistry 979 23.8 Other Types of Spectroscopy 991 Chapter 24 Magnetic Resonance Spectroscopy 1001 24.1 Magnetic Fields and Magnetic Dipoles 1002 24.2 Electronic and Nuclear Magnetic Dipoles 1006 24.3 Electron Spin Resonance Spectroscopy 1010 24.4 Nuclear Magnetic Resonance Spectroscopy 1014 24.5 Fourier Transform NMR Spectroscopy 1024 Part 4 The Reconciliation of the Macroscopic and Molecular Theories of Matter 1037 Chapter 25 Equilibrium Statistical Mechanics I. The Probability Distribution for Molecular States 1039 www.1 The Quantum Statistical Mechanics of a Simple Model System 1040 25.2 The Probability Distribution for a Dilute Gas 1047 25.3 The Probability Distribution and the Molecular Partition Function 1055 25.4 The Calculation of Molecular Partition Functions 1064 Chapter 26 Equilibrium Statistical Mechanics.1 The Statistical Thermodynamics of a Dilute Gas 1082 26.2 Working Equations for the Thermodynamic Functions of a Dilute Gas 1089 26.3 Chemical Equilibrium in Dilute Gases 1101 26.4 The Activated Complex Theory of Bimolecular Chemical Reaction Rates in Dilute Gases 1106 26.5 Miscellaneous Topics in Statistical Thermodynamics 1116 Chapter 27 Equilibrium Statistical Mechanics.1 The Canonical Ensemble 1122 27.2 Thermodynamic Functions in the Canonical Ensemble 1128 27.3 The Dilute Gas in the Canonical Ensemble 1130 27.4 Classical Statistical Mechanics 1133 27.5 Thermodynamic Functions in the Classical Canonical Ensemble 1141 27.6 The Classical Statistical Mechanics of Dense Gases and Liquids 1147 Chapter 28 The Structure of Solids, Liquids, and Polymers 1153 28.1 The Structure of Solids 1154 28.3 The Electronic Structure of Crystalline Solids 1171 28.4 Electrical Resistance in Solids 1179 Contents xiii 28.5 The Structure of Liquids 1184 28.6 Approximate Theories of Transport Processes in Liquids 1188 28.8 Polymers in Solution 1198 28. Tables of Numerical Data 1209 B. Some Useful Mathematics 1235 C. A Short Table of Integrals 1257 D. Some Derivations of Formulas and Methods 1261 E. Some Mathematics Used in Quantum Mechanics 1275 G. The Perturbation Method 1283 H. The Hückel Method 1289 www. Matrix Representations of Groups 1293 J. Symbols Used in This Book 1303 K. Answers to Numerical Exercises and Odd-Numbered Numerical Problems 1309 Index 1351 www.com Preface This is the third edition of a physical chemistry textbook designed for a two-semester undergraduate physical chemistry course. The physical chemistry course is often the first opportunity that a student has to synthesize descriptive, theoretical, and mathe- www.com matical knowledge about chemistry into a coherent whole. To facilitate this synthe- sis, the book is constructed about the idea of defining a system, studying the states in which it might be found, and analyzing the processes by which it can change its state. The book is divided into four parts.
