Physical Chemistry - Levine

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Fsico - Qumica Levine, Ira N. Physical chemistry / Ira N. Levine. -- 6th ed.



2. PHYSICAL CHEMISTRYSixth EditionIra N. LevineChemistry DepartmentBrooklyn CollegeCity University of New YorkBrooklyn, New York 3. PHYSICAL CHEMISTRY, SIXTH EDITIONPublished by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of theAmericas, New York, NY 10020. Copyright 2009 by The McGraw-Hill Companies, Inc. All rightsreserved. Previous editions 2002, 1995, 1988, 1983, and 1978. No part of this publication may bereproduced or distributed in any form or by any means, or stored in a database or retrieval system,without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, inany network or other electronic storage or transmission, or broadcast for distance learning.Some ancillaries, including electronic and print components, may not be available to customers outsidethe United States.This book is printed on recycled, acid-free paper containing 10% postconsumer waste.1 2 3 4 5 6 7 8 9 0 QPD/QPD 0 9 8ISBN 9780072538625MHID 0072538627Publisher: Thomas TimpSenior Sponsoring Editor: Tamara L. HodgeDirector of Development: Kristine TibbettsSenior Developmental Editor: Shirley R. OberbroecklingMarketing Manager: Todd L. TurnerProject Coordinator: Melissa M. LeickSenior Production Supervisor: Sherry L. KaneSenior Designer: David W. HashCover Designer: Ron E. Bissell, Creative Measures Design Inc.Supplement Producer: Melissa M. LeickCompositor: ICC Macmillan Inc.Typeface: 10.5/12 TimesPrinter: Quebecor World Dubuque, IALibrary of Congress Cataloging-in-Publication DataLevine, Ira N.Physical chemistry / Ira N. Levine. -- 6th ed.p. cm.Includes index.ISBN 9780072538625 --- ISBN 0072538627 (hard copy : alk. paper) 1. Chemistry, Physicaland theoretical. I. Title.QD453.3.L48 2009541-- dc22 4. To the memory of my mother and my father 5. Table of ContentsviPreface xivChapter 1 THERMODYNAMICS 11.1 Physical Chemistry 11.2 Thermodynamics 31.3 Temperature 61.4 The Mole 91.5 Ideal Gases 101.6 Differential Calculus 171.7 Equations of State 221.8 Integral Calculus 251.9 Study Suggestions 301.10 Summary 32Chapter 2 THE FIRST LAW OF THERMODYNAMICS 372.1 Classical Mechanics 372.2 P-V Work 422.3 Heat 462.4 The First Law of Thermodynamics 472.5 Enthalpy 522.6 Heat Capacities 532.7 The Joule and JouleThomson Experiments 552.8 Perfect Gases and the First Law 582.9 Calculation of First-Law Quantities 622.10 State Functions and Line Integrals 652.11 The Molecular Nature of Internal Energy 672.12 Problem Solving 702.13 Summary 73Chapter 3 THE SECOND LAW OF THERMODYNAMICS 783.1 The Second Law of Thermodynamics 783.2 Heat Engines 803.3 Entropy 853.4 Calculation of Entropy Changes 873.5 Entropy, Reversibility, and Irreversibility 933.6 The Thermodynamic Temperature Scale 963.7 What Is Entropy? 973.8 Entropy, Time, and Cosmology 1033.9 Summary 104 6. viiTable of ContentsChapter 4 MATERIAL EQUILIBRIUM 1094.1 Material Equilibrium 1094.2 Entropy and Equilibrium 1104.3 The Gibbs and Helmholtz Energies 1124.4 Thermodynamic Relations for a Systemin Equilibrium 1154.5 Calculation of Changes in State Functions 1234.6 Chemical Potentials and Material Equilibrium 1254.7 Phase Equilibrium 1294.8 Reaction Equilibrium 1324.9 Entropy and Life 1344.10 Summary 135Chapter 5 STANDARD THERMODYNAMIC FUNCTIONSOF REACTION 1405.1 Standard States of Pure Substances 1405.2 Standard Enthalpy of Reaction 1415.3 Standard Enthalpy of Formation 1425.4 Determination of Standard Enthalpiesof Formation and Reaction 1435.5 Temperature Dependence of Reaction Heats 1515.6 Use of a Spreadsheet to Obtain a Polynomial Fit 1535.7 Conventional Entropies and the Third Law 1555.8 Standard Gibbs Energy of Reaction 1615.9 Thermodynamics Tables 1635.10 Estimation of Thermodynamic Properties 1655.11 The Unattainability of Absolute Zero 1685.12 Summary 169Chapter 6 REACTION EQUILIBRIUM IN IDEAL GAS MIXTURES 1746.1 Chemical Potentials in an Ideal Gas Mixture 1756.2 Ideal-Gas Reaction Equilibrium 1776.3 Temperature Dependenceof the Equilibrium Constant 1826.4 Ideal-Gas Equilibrium Calculations 1866.5 Simultaneous Equilibria 1916.6 Shifts in Ideal-Gas Reaction Equilibria 1946.7 Summary 198Chapter 7 ONE-COMPONENT PHASE EQUILIBRIUMAND SURFACES 2057.1 The Phase Rule 2057.2 One-Component Phase Equilibrium 2107.3 The Clapeyron Equation 2147.4 SolidSolid Phase Transitions 221 7. viiiTable of Contents7.5 Higher-Order Phase Transitions 2257.6 Surfaces and Nanoparticles 2277.7 The Interphase Region 2277.8 Curved Interfaces 2317.9 Colloids 2347.10 Summary 237Chapter 8 REAL GASES 2448.1 Compression Factors 2448.2 Real-Gas Equations of State 2458.3 Condensation 2478.4 Critical Data and Equations of State 2498.5 Calculation of LiquidVapor Equilibria 2528.6 The Critical State 2548.7 The Law of Corresponding States 2558.8 Differences Between Real-Gas and Ideal-GasThermodynamic Properties 2568.9 Taylor Series 2578.10 Summary 259Chapter 9 SOLUTIONS 2639.1 Solution Composition 2639.2 Partial Molar Quantities 2649.3 Mixing Quantities 2709.4 Determination of Partial Molar Quantities 2729.5 Ideal Solutions 2759.6 Thermodynamic Properties of Ideal Solutions 2789.7 Ideally Dilute Solutions 2829.8 Thermodynamic Propertiesof Ideally Dilute Solutions 2839.9 Summary 287Chapter 10 NONIDEAL SOLUTIONS 29410.1 Activities and Activity Coefficients 29410.2 Excess Functions 29710.3 Determination of Activitiesand Activity Coefficients 29810.4 Activity Coefficients on the Molality and MolarConcentration Scales 30510.5 Solutions of Electrolytes 30610.6 Determination of Electrolyte Activity Coefficients 31010.7 The DebyeHckel Theory of Electrolyte Solutions 31110.8 Ionic Association 31510.9 Standard-State Thermodynamic Propertiesof Solution Components 31810.10 Nonideal Gas Mixtures 32110.11 Summary 324 8. ixTable of ContentsChapter 11 REACTION EQUILIBRIUM IN NONIDEAL SYSTEMS 33011.1 The Equilibrium Constant 33011.2 Reaction Equilibrium in Nonelectrolyte Solutions 33111.3 Reaction Equilibrium in Electrolyte Solutions 33211.4 Reaction Equilibria Involving Pure Solidsor Pure Liquids 33711.5 Reaction Equilibrium in Nonideal Gas Mixtures 34011.6 Computer Programs for Equilibrium Calculations 34011.7 Temperature and Pressure Dependences of theEquilibrium Constant 34111.8 Summary of Standard States 34311.9 Gibbs Energy Change for a Reaction 34311.10 Coupled Reactions 34511.11 Summary 347Chapter 12 MULTICOMPONENT PHASE EQUILIBRIUM 35112.1 Colligative Properties 35112.2 Vapor-Pressure Lowering 35112.3 Freezing-Point Depressionand Boiling-Point Elevation 35212.4 Osmotic Pressure 35612.5 Two-Component Phase Diagrams 36112.6 Two-Component LiquidVapor Equilibrium 36212.7 Two-Component LiquidLiquid Equilibrium 37012.8 Two-Component SolidLiquid Equilibrium 37312.9 Structure of Phase Diagrams 38112.10 Solubility 38112.11 Computer Calculation of Phase Diagrams 38312.12 Three-Component Systems 38512.13 Summary 387Chapter 13 ELECTROCHEMICAL SYSTEMS 39513.1 Electrostatics 39513.2 Electrochemical Systems 39813.3 Thermodynamics of Electrochemical Systems 40113.4 Galvanic Cells 40313.5 Types of Reversible Electrodes 40913.6 Thermodynamics of Galvanic Cells 41213.7 Standard Electrode Potentials 41713.8 Liquid-Junction Potentials 42113.9 Applications of EMF Measurements 42213.10 Batteries 42613.11 Ion-Selective Membrane Electrodes 42713.12 Membrane Equilibrium 42913.13 The Electrical Double Layer 43013.14 Dipole Moments and Polarization 43113.15 Bioelectrochemistry 43513.16 Summary 436 9. xTable of ContentsChapter 14 KINETIC THEORY OF GASES 44214.1 KineticMolecular Theory of Gases 44214.2 Pressure of an Ideal Gas 44314.3 Temperature 44614.4 Distribution of Molecular Speeds in an Ideal Gas 44814.5 Applications of the Maxwell Distribution 45714.6 Collisions with a Wall and Effusion 46014.7 Molecular Collisions and Mean Free Path 46214.8 The Barometric Formula 46514.9 The Boltzmann Distribution Law 46714.10 Heat Capacities of Ideal Polyatomic Gases 46714.11 Summary 469Chapter 15 TRANSPORT PROCESSES 47415.1 Kinetics 47415.2 Thermal Conductivity 47515.3 Viscosity 47915.4 Diffusion and Sedimentation 48715.5 Electrical Conductivity 49315.6 Electrical Conductivity ofElectrolyte Solutions 49615.7 Summary 509Chapter 16 REACTION KINETICS 51516.1 Reaction Kinetics 51516.2 Measurement of Reaction Rates 51916.3 Integration of Rate Laws 52016.4 Finding the Rate Law 52616.5 Rate Laws and Equilibrium Constantsfor Elementary Reactions 53016.6 Reaction Mechanisms 53216.7 Computer Integration of Rate Equations 53916.8 Temperature Dependence of Rate Constants 54116.9 Relation Between Rate Constants and EquilibriumConstants for Composite Reactions 54616.10 The Rate Law in Nonideal Systems 54716.11 Unimolecular Reactions 54816.12 Trimolecular Reactions 55016.13 Chain Reactions and Free-RadicalPolymerizations 55116.14 Fast Reactions 55616.15 Reactions in Liquid Solutions 56016.16 Catalysis 56416.17 Enzyme Catalysis 56816.18 Adsorption of Gases on Solids 57016.19 Heterogeneous Catalysis 57516.20 Summary 579 10. xiTable of ContentsChapter 17 QUANTUM MECHANICS 59017.1 Blackbody Radiation and Energy Quantization 59117.2 The Photoelectric Effect and Photons 59317.3 The Bohr Theory of the Hydrogen Atom 59417.4 The de Broglie Hypothesis 59517.5 The Uncertainty Principle 59717.6 Quantum Mechanics 59917.7 The Time-Independent Schrdinger Equation 60417.8 The Particle in a One-Dimensional Box 60617.9 The Particle in a Three-Dimensional Box 61017.10 Degeneracy 61217.11 Operators 61317.12 The One-Dimensional Harmonic Oscillator 61917.13 Two-Particle Problems 62117.14 The Two-Particle Rigid Rotor 62217.15 Approximation Methods 62317.16 Hermitian Operators 62717.17 Summary 630Chapter 18 ATOMIC STRUCTURE 63718.1 Units 63718.2 Historical Background 63718.3 The Hydrogen Atom 63818.4 Angular Momentum 64718.5 Electron Spin 64918.6 The Helium Atom and the SpinStatistics Theorem 65018.7 Total Orbital and Spin Angular Momenta 65618.8 Many-Electron Atoms and the Periodic Table 65818.9 HartreeFock and Configuration-InteractionWave Functions 66318.10 Summary 666Chapter 19 MOLECULAR ELECTRONIC STRUCTURE 67219.1 Chemical Bonds 67219.2 The BornOppenheimer Approximation 67619.3 The Hydrogen Molecule Ion 68119.4 The Simple MO Method for Diatomic Molecules 68619.5 SCF and HartreeFock Wave Functions 69219.6 The MO Treatment of Polyatomic Molecules 69319.7 The Valence-Bond Method 70219.8 Calculation of Molecular Properties 70419.9 Accurate Calculation of Molecular ElectronicWave Functions and Properties 70819.10 Density-Functional Theory (DFT) 71119.11 Semiempirical Methods 71719.12 Performing Quantum Chemistry Calculations 72019.13 The Molecular-Mechanics (MM) Method 723 11. xiiTable of Contents19.14 Future Prospects 72719.15 Summary 727Chapter 20 SPECTROSCOPY AND PHOTOCHEMISTRY 73420.1 Electromagnetic Radiation 73420.2 Spectroscopy 73720.3 Rotation and Vibration of Diatomic Molecules 74320.4 Rotational and Vibrational Spectra of DiatomicMolecules 75020.5 Molecular Symmetry 75620.6 Rotation of Polyatomic Molecules 75820.7 Microwave Spectroscopy 76120.8 Vibration of Polyatomic Molecules 76320.9 Infrared Spectroscopy 76620.10 Raman Spectroscopy 77120.11 Electronic Spectroscopy 77420.12 Nuclear-Magnetic-Resonance Spectroscopy 77920.13 Electron-Spin-Resonance Spectroscopy 79320.14 Optical Rotatory Dispersion and Circular Dichroism 79420.15 Photochemistry 79620.16 Group Theory 80020.17 Summary 811Chapter 21 STATISTICAL MECHANICS 82021.1 Statistical Mechanics 82021.2 The Canonical Ensemble 82121.3 Canonical Partition Function for a System ofNoninteracting Particles 83021.4 Canonical Partition Function of a Pure Ideal Gas 83421.5 The Boltzmann Distribution Law forNoninteracting Molecules 83621.6 Statistical Thermodynamics of Ideal Diatomicand Monatomic Gases 84021.7 Statistical Thermodynamics of IdealPolyatomic Gases 85121.8 Ideal-Gas Thermodynamic Properties andEquilibrium Constants 85421.9 Entropy and the Third Law of Thermodynamics 85821.10 Intermolecular Forces 86121.11 Statistical Mechanics of Fluids 86621.12 Summary 870Chapter 22 THEORIES OF REACTION RATES 87722.1 Hard-Sphere Collision Theoryof Gas-Phase Reactions 87722.2 Potential-Energy Surfaces 88022.3 Molecular Reaction Dynamics 887 12. xiiiTable of Contents22.4 Transition-State Theory for Ideal-Gas Reactions 89222.5 Thermodynamic Formulation of TST forGas-Phase Reactions 90222.6 Unimolecular Reactions 90422.7 Trimolecular Reactions 90622.8 Reactions in Solution 90622.9 Summary 911Chapter 23 SOLIDS AND LIQUIDS 91323.1 Solids and Liquids 91323.2 Polymers 91423.3 Chemical Bonding in Solids 91423.4 Cohesive Energies of Solids 91623.5 Theoretical Calculation of Cohesive Energies 91823.6 Interatomic Distances in Crystals 92123.7 Crystal Structures 92223.8 Examples of Crystal Structures 92823.9 Determination of Crystal Structures 93123.10 Determination of Surface Structures 93723.11 Band Theory of Solids 93923.12 Statistical Mechanics of Crystals 94123.13 Defects in Solids 94623.14 Liquids 94723.15 Summary 951Bibliography 955Appendix 959Answers to Selected Problems 961Index 967 13. PrefacexivThis textbook is for the standard undergraduate course in physical chemistry.In writing this book, I have kept in mind the goals of clarity, accuracy, and depth.To make the presentation easy to follow, the book gives careful definitions and expla-nationsof concepts, full details of most derivations, and reviews of relevant topics inmathematics and physics. I have avoided a superficial treatment, which would leavestudents with little real understanding of physical chemistry. Instead, I have aimed ata treatment that is as accurate, as fundamental, and as up-to-date as can readily be pre-sented Equations that students should memorizeare marked with an asterisk. These are thefundamental equations and students are cau-tionedagainst blindly memorizing the undergraduate level.LEARNING AIDSPhysical chemistry is a challenging course for many students. To help students, thisbook has many learning aids: Each chapter has a summary of the key points. The summaries list the specifickinds of calculations that students are expected to learn how to do.3.9 SUMMARYWe assumed the truth of the KelvinPlanck statement of the second law of ther-modynamics,which asserts the impossibility of the complete conversion of heat towork in a cyclic process. From the second law, we proved that dqrev/T is the differ-entialof a state function, which we called the entropy S. The entropy change in aprocess from state 1 to state 2 is S21 dqrev/T, where the integral must be eval-uatedusing a reversible path from 1 to 2. Methods for calculating S were dis-cussedin Sec. 3.4.We used the second law to prove that the entropy of an isolated system mustincrease in an irreversible process. It follows that thermodynamic equilibrium in anisolated system is reached when the systems entropy is maximized. Since isolatedsystems spontaneously change to more probable states, increasing entro...


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