F O U R T H E D I T I O N

PHYSICAL CHEMISTRY

IRA N. LEVINE Chemistry Department

Brooklyn College City University of New York

Brooklyn, New York

McGRAW-HILL, INC. New York St. Louis San Francisco Auckland Bogota Caracas

Lisbon London Madrid Mexico City Milan Montreal

New Delhi San Juan Singapore Sydney Tokyo Toronto

Preface xvii

THERMODYNAMICS 1 1.1 Physical Chemistry 1 1.2 Thermodynamics 2 1.3 Temperature 6 1.4 The Mole 8 1.5 Ideal Gases 10 1.6 Differential Calculus 17 1.7 Equations of State 21 1.8 Integral Calculus 24 1.9 Study Suggestions 28 1.10 Summary 30

THE FIRST LAW OF THERMODYNAMICS 34 2.1 Classical Mechanics 34 2.2 P-VWork 39 2.3 Heat 43 2.4 The First Law of Thermodynamics 44 2.5 Enthalpy 48 2.6 Heat Capacities 50 2.7 The Joule and Joule-Thomson Experiments 52 2.8 Perfect Gases and the First Law 54 2.9 Calculation of First-Law Quantities 59

2.10 State Functions and Line Integrals 61 2.11 The Molecular Nature of Internal Energy 63 2.12 Problem Solving 66 2.13 Summary 68

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THE SECOND LAW OF THERMODYNAMICS 73 3.1 The Second Law of Thermodynamics 73 3.2 Heat Engines 75 3.3 Entropy 79 3.4 Calculation of Entropy Changes 82 3.5 Entropy, Reversibility, and Irreversibility 87 3.6 The Thermodynamic Temperature Scale 90 3.7 What Is Entropy? 91 3.8 Entropy, Time, and Cosmology 96 3.9 Summary 98

MATERIAL EQUILIBRIUM 102 4.1 Material Equilibrium 102 4.2 Thermodynamic Properties of Nonequilibrium Systems 103 4.3 Entropy and Equilibrium 104 4.4 The Gibbs and Helmholtz Functions 106 4.5 Thermodynamic Relations for a System in Equilibrium 109 4.6 Calculation of Changes in State Functions 118 4.7 Chemical Potentials and Material Equilibrium 120 4.8 Phase Equilibrium 125 4.9 Reaction Equilibrium 127 4.10 Entropy and Life 130 4.11 Summary 131

5 STANDARD THERMODYNAMIC FUNCTIONS 0F REACTION 135 5.1 Standard States 135 5.2 Standard Enthalpy of Reaction 136 5.3 Standard Enthalpy of Formation 137 5.4 Determination of Standard Enthalpies of Formation and Reaction 139 5.5 Temperature Dependence of Reaction Heats 145 5.6 Conventional Entropies and the Third Law 147 5.7 Standard Gibbs Energy of Reaction 153 5.8 Thermodynamics Tables 154 5.9 Estimation of Thermodynamic Properties 157 5.10 The Unattainability of Absolute Zero 159 5.11 Summary 160

REACTION EQUILIBRIUM IN IDEAL GAS MIXTURES 164 6.1 Chemical Potentials in an Ideal Gas Mixture 164 6.2 Ideal-Gas Reaction Equilibrium 166 6.3 Temperature Dependence of the Equilibrium Constant 172 6.4 Ideal-Gas Equilibrium Calculations 174 6.5 Shifts in Ideal-Gas Reaction Equilibria 180 6.6 Summary 182

0NE-C0MP0NENT PHASE EQUILIBRIUM 187 7.1 The Phase Rule 187 7.2 One-Component Phase Equilibrium 191 7.3 The Clapeyron Equation 195 7.4 Solid-Solid Phase Transitions 200 7.5 Higher-Order Phase Transitions 202 7.6 Summary 203

8 REAL GASES 208 8.1 Compression Factors 208 8.2 Real-Gas Equations of State 209 8.3 Condensation 212 8.4 Critical Data and Equations of State 214 8.5 The Critical State 216 8.6 The Law of Corresponding States 216 8.7 Differences between Real-Gas and Ideal-Gas Thermodynamic Properties 218 8.8 Taylor Series 219 8.9 Summary 220

9 SOLUTIONS 224 9.1 Solution Composition 224 9.2 Partial Molar Quantities 226 9.3 Mixing Quantities 232 9.4 Determination of Partial Molar Quantities 233 9.5 Ideal Solutions 237 9.6 Thermodynamic Properties of Ideal Solutions 240 9.7 Ideally Dilute Solutions 244 9.8 Thermodynamic Properties of Ideally Dilute Solutions 245 9.9 Summary 250

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NONIDEAL SOLUTIONS 257 10.1 Activities and Activity Coefficients 257 10.2 Excess Functions 260 10.3 Determination of Activities and Activity Coefficients 261 10.4 Activity Coefficients on the Molality and Molar Concentration Scales 268 10.5 Solutions of Electrolytes 269 10.6 Determination of Electrolyte Activity Coefficients 274 10.7 The Debye-Hückel Theory of Electrolyte Solutions 276 10.8 Ionic Association 279 10.9 Standard-State Thermodynamic Properties of Solution Components 281 10.10 Nonideal Gas Mixtures 284 10.11 Summary 286

_J1 REACTI0N EQUILIBRIUM IN NONIDEAL SYSTEMS 291 11.1 The Equilibrium Constant 291 11.2 Reaction Equilibrium in Nonelectrolyte Solutions 292 11.3 Reaction Equilibrium in Electrolyte Solutions 293 11.4 Reaction Equilibria Involving Pure Solids or Pure Liquids 298 11.5 Reaction Equilibrium in Nonideal Gas Mixtures 300 11.6 Temperature and Pressure Dependences of the Equilibrium Constant 301 11.7 Summary of Standard States 303 11.8 Coupled Reactions 303 11.9 Gibbs Energy Change for a Reaction 305 11.10 Summary 306

12 MULTICOMPONENT PHASE EQUILIBRIUM 311 12.1 Colligative Properties 311 12.2 Vapor-Pressure Lowering 311 12.3 Freezing-Point Depression and Boiling-Point Elevation 312 12.4 Osmotic Pressure 316 12.5 Two-Component Phase Diagrams 321 12.6 Two-Component Liquid-Vapor Equilibrium 322 12.7 Two-Component Liquid-Liquid Equilibrium 330 12.8 Two-Component Solid-Liquid Equilibrium 332 12.9 Structure of Phase Diagrams 339 12.10 Solubility 340 12.11 Three-Component Systems 342 12.12 Summary 344

11 SURFACE CHEMISTRY 350 13.1 The Interphase Region 350 13.2 Curved Interfaces 353

13.3 Thermodynamics of Surfaces 356 13.4 Surface Films on Liquids 361 13.5 Adsorption of Gases on Solids 363 13.6 Colloids 368 13.7 Summary 371

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ELECTROCHEMICAL SYSTEMS 375 14.1 Electrostatics 375 14.2 Electrochemical Systems 378 14.3 Thermodynamics of Electrochemical Systems 380 14.4 Galvanic Cells 383 14.5 Types of Reversible Electrodes 389 14.6 Thermodynamics of Galvanic Cells 392 14.7 Standard Electrode Potentials 397 14.8 Classification of Galvanic Cells 400 14.9 Liquid-Junction Potentials 401 14.10 Applications of EMF Measurements 402 14.11 Batteries 406 14.12 Ion-Selective Membrane Electrodes 407 14.13 Membrane Equilibrium 408 14.14 The Electrical Double Layer 409 14.15 Dipole Moments and Polarization 410 14.16 Bioelectrochemistry 414 14.17 Summary 416

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KINET1C-M0LECULAR THE0RY 0F GASES 421 15.1 Kinetic-Molecular Theory of Gases 421 15.2 Pressure of an Ideal Gas 422 15.3 Temperature 425 15.4 Distribution of Molecular Speeds in an Ideal Gas 427 15.5 Applications of the Maxwell Distribution 436 15.6 Collisions with a Wall and Effusion 438 15.7 Molecular Collisions and Mean Free Path 440 15.8 The Barometric Formula 444 15.9 The Boltzmann Distribution Law 445 15.10 Heat Capacities of Ideal Polyatomic Gases 446 15.11 Summary 447

TRANSPORT PR0CESSES 452 16.1 Kinetics 452 16.2 Thermal Conductivity 453 16.3 Viscosity 457 16.4 Diffusion and Sedimentation 465

16.5 Electrical Conductivity 471 16.6 Electrical Conductivity of Electrolyte Solutions 473 16.7 Summary 487

REACTION KINETICS 493 17.1 Reaction Kinetics 493 17.2 Measurement of Reaction Rates 497 17.3 Integration of Rate Laws 498 17.4 Determination of the Rate Law 504 17.5 Rate Laws and Equilibrium Constants for Elementary Reactions 508 17.6 Reaction Mechanisms 510 17.7 Temperature Dependence of Rate Constants 517 17.8 Relation between Rate Constants and Equilibrium Constants for

Complex Reactions 521 17.9 The Rate Law in Nonideal Systems 523 17.10 Unimolecular Reactions 523 17.11 Trimolecular Reactions 525 17.12 Chain Reactions and Free-Radical Polymerizations 526 17.13 Fast Reactions 531 17.14 Reactions in Liquid Solutions 535 17.15 Catalysis 539 17.16 Enzyme Catalysis 542 17.17 Heterogeneous Catalysis 545 17.18 Nuclear Decay 549 17.19 Summary 551

18 QUANTUM MECHANICS 559 18.1 Blackbody Radiation and Energy Quantization 559 18.2 The Photoelectric Effect and Photons 561 18.3 The Bohr Theory of the Hydrogen Atom 563 18.4 The de Broglie Hypothesis 564 18.5 The Uncertainty Principle 566 18.6 Quantum Mechanics 567 18.7 The Time-Independent Schrödinger Equation 572 18.8 The Particle in a One-Dimensional Box 574 18.9 The Particle in a Three-Dimensional Box 578 18.10 Degeneracy 580 18.11 Operators 581 18.12 The One-Dimensional Harmonie Oscillator 585 18.13 Two-Particle Problems 588 18.14 The Two-Particle Rigid Rotor 589 18.15 Approximation Methods 590 18.16 Summary 593

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ATOMIC STRUCTURE 598 19.1 Units 598 19.2 Historical Background 599 19.3 The Hydrogen Atom 600 19.4 Electron Spin 610 19.5 The Helium Atom and the Pauli Principle 611 19.6 Many-Electron Atoms and the Periodic Table 618 19.7 Hartree-Fock and Configuration-Interaction Wave Functions 623 19.8 Summary 626

MOLECULAR ELECTRONIC STRUCTURE 630 20.1 Chemical Bonds 630 20.2 The Born-Oppenheimer Approximation 634 20.3 The Hydrogen Molecule Ion 638 20.4 The Simple MO Method for Diatomic Molecules 642 20.5 SCF, Hartree-Fock, and CI Wave Functions 648 20.6 The MO Treatment of Polyatomic Molecules 650 20.7 Calculation of Molecular Properties 658 20.8 Accurate Calculation of Molecular Electronic Wave Functions

and Properties 661 20.9 Semiempirical Methods 665 20.10 The Molecular-Mechanics Method 670 20.11 The Valence-Bond Method 671 20.12 The VSEPR Method 672 20.13 Future Prospects 674 20.14 Summary 674

SPECTROSCOPY AND PHOTOCHEMISTRY 678 21.1 Electromagnetic Radiation 678 21.2 Spectroscopy 681 21.3 Rotation and Vibration of Diatomic Molecules 688 21.4 Rotational and Vibrational Spectra of Diatomic Molecules 693 21.5 Molecular Symmetry 699 21.6 Rotation of Polyatomic Molecules 700 21.7 Microwave Spectroscopy 703 21.8 Vibration of Polyatomic Molecules 705 21.9 Infrared Spectroscopy 708 21.10 Raman Spectroscopy 713 21.11 Electronic Spectroscopy 716 21.12 Nuclear-Magnetic-Resonance Spectroscopy 720 21.13 Electron-Spin-Resonance Spectroscopy 732 21.14 Optical Rotatory Dispersion and Circular Dichroism 733

21.15 Photoelectron Spectroscopy 734 21.16 Photochemistry 736 21.17 Summary 741

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STATISTICAL MECHANICS 747 22.1 Statistical Mechanics 747 22.2 The Canonical Ensemble 748 22.3 Canonical Partition Function for a System of Noninteracting Particles 757 22.4 Canonical Partition Function of a Pure Ideal Gas 761 22.5 The Boltzmann Distribution Law for Noninteracting Molecules 763 22.6 Statistical Thermodynamics of Ideal Diatomic and Monatomic Gases 767 22.7 Statistical Thermodynamics of Ideal Polyatomic Gases 777 22.8 Ideal-Gas Thermodynamic Properties and Equilibrium Constants 780 22.9 Entropy and the Third Law of Thermodynamics 783 22.10 Intermolecular Forces 785 22.11 Statistical Mechanics of Fluids 791 22.12 Summary 794

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THEORIES OF REACTION RATES 800 23.1 Hard-Sphere Collision Theory of Gas-Phase Reactions 800 23.2 Potential-Energy Surfaces 803 23.3 Molecular Reaction Dynamics 810 23.4 Transition-State Theory for Ideal-Gas Reactions 816 23.5 Thermodynamic Formulation of TST 825 23.6 Unimolecular Reactions 827 23.7 Trimolecular Reactions 829 23.8 Reactions in Solution 829 23.9 Summary 834

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SOLIDS AND LIQUIDS 836 24.1 Solids and Liquids 836 24.2 Polymers 837 24.3 Chemical Bonding in Solids 838 24.4 Cohesive Energies of Solids 839 24.5 Theoretical Calculation of Cohesive Energies 840 24.6 Interatomic Distances in Crystals 843 24.7 Crystal Structures 844 24.8 Examples of Crystal Structures 850 24.9 Determination of Crystal Structures 853 24.10 Determination of Surface Structures 858 24.11 Band Theory of Solids 860 24.12 Statistical Mechanics of Crystals 862

24.13 Defects in Solids 867 24.14 Liquids 868 24.15 Summary 871

Bibliography 874

Appendix 877

Answers to Selected Problems 879

Index 885

C O N T E N T S