# Physical Chemistry

**By**

- Robert Mortimer, Rhodes College, Memphis, TN, USA

This new edition of Robert G. Mortimer's Physical Chemistry has been thoroughly revised for use in a full year course in modern physical chemistry. In this edition, Mortimer has included recent developments in the theories of chemical reaction kinetics and molecular quantum mechanics, as well as in the experimental study of extremely rapid chemical reactions. While Mortimer has made substantial improvements in the selection and updating of topics, he has retained the clarity of presentation, the integration of description and theory, and the level of rigor that made the first edition so successful.

**Audience**

Undergraduate and graduate students of Physical Chemistry, professional chemists, students of Physics, Biology, and Engineering.

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Published: March 2000

Imprint: Academic Press

ISBN: 978-0-12-508345-4

## Contents

- Preface Chapter 1 Systems, States, and Processes 1.1 Scientific Inquiry 1.2 Systems and States 1.3 Units of Measurement. SI Units 1.4 State Functions 1.5 The Relationship Between Macrostates and Microstates 1.6 Processes Problems Chapter 2 The Equilibrium Macroscopic States of Gases and Liquids 2.1 Mathematical Functions and the Equilibrium Macroscopic State of a Simple System 2.2 Real Liquids and Solids 2.3 Real Gases 2.4 The Coexistence of Phases and the Critical Point Problems Chapter 3 Work, Heat, and Energy: The First Law of Thermodynamics 3.1 Work and the State of a System 3.2 Heat 3.3 Internal Energy; The First Law. 3.4 Calculation of Amounts of Heat and Energy Changes 3.5 Enthalpy - A Convenience Variable 3.6 Calculation of Enthalpy Changes for Non-chemical Processes 3.7 Calculation of Enthalpy Changes for a Class of Chemical Reactions 3.8 Energy Changes of Chemical Reactions Problems Chapter 4 The Second and Third Laws of Thermodynamics: Entropy 4.1 The Second Law of Thermodynamics and the Carnot Heat Engine 4.2 The Mathematical Statement of the Second Law. Entropy. 4.3 The Calculation of Entropy Changes 4.4 Statistical Entropy 4.5 The Third Law of Thermodynamics and Absolute Entropies Problems Chapter 5 The Thermodynamics of Real Systems 5.1 Criteria for Spontaneous Processes and for Equilibrium. The Gibbs and Helmholtz Energies. 5.2 Fundamental Relations for Closed Simple Systems 5.3 Gibbs Energy Calculations 5.4 The Description of Multicomponent and Open Systems 5.5 Additional Useful Thermodynamic Identities 5.6 Euler's Theorem and the Gibbs-Duhem Relation Problems Chapter 6 Phase Equilibrium 6.1 The Fundamental Fact of Phase Equilibrium. 6.2 The Gibbs Phase Rule 6.3 Phase Equilibria in a One-Component System 6.4 The Gibbs Energy and Phase Transitions. 6.5 Surface Structure and Thermodynamics 6.6 Surfaces in Multicomponent Systems Problems Chapter7 Multicomponent Systems 7.1 Ideal Solutions 7.2 Henry's Law and Ideally Dilute Nonelectrolyte Solutions 7.3 The Activity and the Description of General Systems 7.4 Activity Coefficients in Electrolyte Solutions 7.5 Phase Diagrams for Nonideal Mixtures 7.6 Colligative Properties Problems Chapter 8 Chemical Equilibrium 8.1 Gibbs Energy Changes and Equilibria of Chemical Reactions: The Equilibrium Constant. 8.2 Reactions involving Gases and Pure Substances. 8.3 Chemical Equilibrium in Solution 8.4 Equilibria in Solutions of Strong Electrolytes. 8.5 Acid-Base Equilibrium Calculations. 8.6 Temperature and Pressure Dependence of Equilibrium Constants: The Principle of le Chatelier. 8.7 Chemical Reactions and Biological Systems. Problems Chapter 9 The Thermodynamics of Electrochemical Systems 9.1 The Chemical Potential and the Electric Potential 9.2 Electrochemical Cells at Equilibrium 9.3 Half-Cell Potentials and Cell Potentials 9.4 The Determination of Activity Coefficients of Electrolytes 9.5 Thermodynamic Information from Electrochemistry Problems Chapter 10 Gas Kinetic Theory. The Molecular Theory of Dilute Gases at Equilibrium 10.1 The Model System for a Dilute Gas 10.2 The Velocity Probability Distribution 10.3 The Distribution of Molecular Speeds 10.4 The Pressure of an Ideal Gas 10.5 Wall Collisions and Effusion 10.6 The Model System with Potential Energy 10.7 The Hard Sphere Gas 10.9 The Molecular Structure of Liquids Problems Chapter 11 Transport Processes 11.1 The Macroscopic Description of Nonequilibrium States 11.2 Transport Processes 11.3 Transport Processes in the Hard Sphere Gas 11.4 The Structure of Liquids and Transport Processes in Liquids 11.5 Transport in Electrolyte Solutions Problems Chapter 12 The Rates of Chemical Reactions 12.1 The Macroscopic Description of Chemically Reacting Systems 12.2 Forward Reactions with one Reactant. 12.3 Forward Reactions With More than One Reactant 12.4 Inclusion of a Reverse Reaction. Chemical Equilibrium 12.5 Consecutive Reactions 12.6 The Experimental Study of Fast Reactions Problems Chapter 13 The Molecular Nature of Chemical Reactions 13.1 Elementary Processes in Gases 13.2 Elementary Reactions in Liquid Solutions 13.3 Reaction Mechanisms and Rate Laws 13.4 Some Additional Mechanisms, Including Chain and Photochemical Mechanisms. Competing Mechanisms 13.5 Catalysis 13.6 The Temperature Dependence of Rate Constants. The Collision Theory of Gaseous Reactions 13.7 Experimental Molecular Study of Chemical Reactions Problems Chapter 14 The Principles of Quantum Mechanics I: The Schrodinger Equation 14.1 Classical Mechanics 14.2 Properties of Waves in Classical Mechanics. 14.2 The Old Quantum Theory 14.4 DeBroglie Waves and the SchrÃ¶dinger Equation. 14.5 The Particle in a Box. The Free Particle. 14.6 The Harmonic Oscillator Problems Chapter 15 The Principles of Quantum Mechanics II: The Postulates of Quantum Mechanics 15.1 The First Two Postulates of Quantum Mechanics. 15.2 Mathematical Operators 15.3 Postulate III. Mathematical Operators in Quantum Mechanics 15.4 Postulate IV. Expectation Values 15.5 Postulate V. The Determination of the State of a System Problems Chapter 16 The Electronic States of Atoms I: The Hydrogen Atom and the Simple Orbital Approximation for Multi-electron Atoms 16.1 The Central Force Problem and the Hydrogen Atom. Angular Momentum 16.2 The Hydrogen-like Atom 16.3 The Helium Atom in the "Zero-order" Orbital Approximation 16.4 Atoms with More than Two Electrons Problems Chapter 17 The Electronic States of Atoms II: Higher-Order Approximations for Multi-electron Atoms 17.1 The Variation Method and its Application to the Helium Atom 17.2 The Perturbation Method and its Application to the Helium Atom 17.3 The Self-Consistent Field Method 17.4 Excited States of the Helium Atom 17.5 Atoms with More than Two Electrons Problems Chapter 18 The Electronic States of Molecules 18.1 The Born-Oppenheimer Approximation. The Hydrogen Molecule Ion. 18.2 LCAO-MO's - Molecular Orbitals That Are Linear Combinations of Atomic Orbitals 18.3 Homonuclear Diatomic Molecules 18.4 Heteronuclear Diatomic Molecules 18.5 Symmetry in Polyatomic Molecules. Groups of Symmetry Operators 18.6 Matrix Representations of Groups 18.7 Electronic Structure of Polyatomic Molecules 18.8 More Advanced Treatments of Molecular Electronic Structure Problems Chapter 19 Translational, Rotational, and Vibrational States of Atoms and Molecules 19.1 Translational Motions of Atoms 19.2 The Nonelectronic States of Diatomic Molecules 19.3 Rotation and Vibration in Polyatomic Molecules 19.4 The Equilibrium Populations of Molecular States Problems Chapter 20 Spectroscopy and Photochemistry 20.1 Spectroscopic Study of Energy Levels 20.2 Spectra of Atoms 20.3 Rotational and Vibrational Spectra of Diatomic Molecules 20.4 Electronic Spectra of Diatomic Molecules 20.5 Spectra of Polyatomic Molecules 20.6 Fluorescence, Phosphorescence, and Photochemistry 20.7 Other Types of Spectroscopy 20.8 Magnetic Resonance Spectroscopy 20.9 Fourier Transform Spectroscopy Problems Chapter 21 Equilibrium Statistical Mechanics 21.1 The Quantum Statistical Mechanics of a Sample System of Four Molecules 21.2 The Probability Distribution for a Dilute Gas 21.3 The Probability Distribution and the Molecular Partition Function 21.4 The Calculation of Molecular Partition Functions 21.5 Calculations of Thermodynamic Functions of Dilute Gases 21.6 Chemical Equilibrium in Dilute Gases 21.7 The Activated Complex Theory of Bimolecular Chemical Reactions in Dilute Gases 21.8 The Canonical Ensemble Problems Chapter 22 The Structure of Condensed Phases 22.1 General Features of Solids and Liquids 22.2 Crystals 22.3 Crystal Vibrations 22.4 The Electronic Structure of Solids 22.5 Classical Statistical Mechanics 22.6 The Structure of Liquids 22.7 Polymer Formation and Conformation 22.8 Rubber Elasticity 22.9 Polymers in Solution Problems. Chapter 23 Theories of Nonequilibrium Processes 23.1 Theories of Chemical Reactions 23.2 The Molecular Case History of a Chemical Reaction 23.3 Theories of Transport Processes in Fluid Systems 23.4 Nonequilibrium Electrochemistry 23.5 Electrical Conductivity in Solids 23.6 Oscillatory Chemical Reactions and Chemical Chaos Problems Appendixes A. Tables of Numerical Data B. Some Useful Mathematics C. A Short Table of Integrals D. Classical Mechanics E. Some Derivations of Thermodynamic Formulas and Methods F. Some Mathematics in Quantum Mechanics G. The Perturbation Method H. The HÃ¼ckel Method I. Symbols Used in this Book