xiiPrefaceThetext assumes somefamiliarity with elementarykinetics atthe level of high-school or freshman chemistry, physics at the freshman level, and mathematicsthrough calculus. Each chapter then builds upon this basis using observations, der-ivations,examples,and instructivefigures toreach clearlyidentified objectives.I am grateful to Professor T. Michael Duncan for providing some of the prob-lems used inChapters 2and 3,toBrianBocknack and JulieMuellerforassistancewiththeproblemsand solutions,toJeffrey SteinfeldandJosephFranciscoforhelp-ful suggestions, to many outside reviewers of the text, especially Laurie Butler, forgood suggestions, and to my wife, Barbara Lynch, for support and tolerance duringthe long periods when I disappeared to work on the text.Paul HoustonIthaca, NewYork
Preface The text assumes some familiarity with elementary kinetics at the level of highschool or freshman chemistry, physics at the freshman level, and mathematics through calculus. Each chapter then builds upon this basis using observations, derivations, examples, and instructive figures to reach clearly identified objectives. I am grateful to Professor T. Michael Duncan for providing some of the problems used in Chapters 2 and 3, to Brian Bocknack and Julie Mueller for assistance with the problems and solutions, to Jeffrey Steinfeld and Joseph Francisco for helpful suggestions, to many outside reviewers of the text, especially Laurie Butler, for good suggestions, and to my wife, Barbara Lynch, for support and tolerance during the long periods when I disappeared to work on the text. Paul Houston Zthaca. New York
CopyrightedMaterialsContentsxiPrefaceIntroduction:A User's Guide to Chemical Kinetics.xiiand Reaction DynamicsxviErrata.1Chapter 1Kinetic Theory of Gases11.1Introduction21.2 Pressure of an Ideal Gas41.3Temperature and Energy.1.4Distributions, Mean Values, and Distribution Functions81.5The Maxwell Distribution of Speeds1.5.1The VelocityDistribution Must Be anEven Function of u....81.5.2The Velocity Distributions Are Independent and Uncorrelated.9..91.5.3<u2> Should Agree with the Ideal Gas Law111.5.4The Distribution Depends Only on the Speed1.5.5Experimental Measurementof the.15MaxwellDistribution of Speeds. 171.6EnergyDistributions191.7Collisions: Mean Free Path and Collision Number..241.8Summary..25Appendix 1.1The Functional Form of the Velocity Distribution.26Appendix 1.2Spherical Coordinates..27Appendix 1.3The Error Function and Co-Error Function..28Appendix 1.4TheCenter-of-MassFrame.30Suggested Readings.31Problems.34The Rates of Chemical ReactionsChapter 2..342.1Introduction..352.2Empirical Observations: Measurement of Reaction Rates.352.3Rates of Reactions:Differential and Integrated Rate Laws.372.3.1First-OrderReactions.402.3.2Second-OrderReactions.442.3.3Pseudo-First-OrderReactions.472.3.4Higher-OrderReactions..482.3.5Temperature Dependence of Rate Constants..512.4ReactionMechanisms.522.4.1OpposingReactions,Equilibrium.542.4.2Parallel Reactions.Consecutive Reactions and the Steady-State Approximation...562.4.3
Contents Chapter 1 1.6 1.7 1.8 Appendix 1.1 Appendix 1.2 Appendix 1.3 Appendix 1.4 Preface . xi Introduction: A User's Guide to Chemical Kinetics . and Reaction Dynamics . xiii Errata . xvii Kinetic Theory of Gases . 1 Introduction . 1 Pressure of an Ideal Gas . 2 Temperature and Energy . 4 Distributions. Mean Values. and Distribution Functions . 5 The Maxwell Distribution of Speeds . 8 1.5.1 The Velocity Distribution Must Be an Even Function of v . 8 1 . 5.2 The Velocity Distributions Are Independent and Uncorrelated . . 9 1.5.3 <v2> Should Agree with the Ideal Gas Law . 9 1.5.4 The Distribution Depends Only on the Speed . 11 1 . 5.5 Experimental Measurement of the Maxwell Distribution of Speeds . 15 Energy Distributions . 17 Collisions: Mean Free Path and Collision Number . 19 Summary . 24 The Functional Form of the Velocity Distribution . 25 Spherical Coordinates . 26 The Error Function and Co-Error Function . 27 The Center-of-Mass Frame . 28 Suggested Readings . 30 Problems . 31 Chapter 2 The Rates of Chemical Reactions . 34 2.1 Introduction . 34 2.2 Empirical Observations: Measurement of Reaction Rates . 35 2.3 Rates of Reactions: Differential and Integrated Rate Laws . 35 2.3.1 First-Order Reactions . 37 2.3.2 Second-Order Reactions . 40 2.3.3 Pseudo-First-Order Reactions . 44 2.3.4 Higher-Order Reactions . 47 2.3.5 Temperature Dependence of Rate Constants . 48 2.4 Reaction Mechanisms . 51 2.4.1 Opposing Reactions, Equilibrium . 52 2.4.2 Parallel Reactions . 54 2.4.3 Consecutive Reactions and the Steady-State Approximation . 56
viiContents2.4.4 Unimolecular Decomposition: The Lindemann Mechanism ... 60.632.5Homogeneous Catalysis.. 632.5.1Acid-Base Catalysis.642.5.2EnzymeCatalysis.702.5.3Autocatalysis..722.6Free Radical Reactions: Chains and Branched Chains..722.6.1H, + Br2.732.6.2Rice-HerzfeldMechanism..742.6.3Branched Chain Reactions:Explosions..772.7Determining Mechanisms fromRate Laws..812.8Summary.83Suggested Readings.83Problems91Chapter3Theoriesof Chemical Reactions.913.1Introduction923.2PotentialEnergySurfaces..953.3Collision Theory..953.3.1Simple Collision Theory...993.3.2Modified SimpleCollisionTheory.1023.4ActivatedComplexTheory(ACT)1093.5Thermodynamic Interpretation of ACT.1093.6Summary.111Suggested Readings111Problems..116Chapter 4Transport Properties.1164.1Introduction.1174.2The Functional Form of the Transport Equations.1194.3The Microscopic Basis for the Transport Laws1194.3.1 Simplifying Assumptions1204.3.2The Molecular Flux1224.3.3The Vertical Distance between Collisions.1224.3.4TheGeneral Flux Equation.1244.4Thermal Conductivity..1274.5Viscosity..1314.6Diffusion.1334.7Time-Dependent Transport.1384.8Summary..139The Poiseuille FormulaAppendix 4.1..141Suggested Readings.141Problems
Contents vi i 2.4.4 Unimolecular Decomposition: The Lindemann Mechanism . 60 2.5 Homogeneous Catalysis . 63 2.5.1 Acid-Base Catalysis . 63 2.5.2 Enzyme Catalysis . 64 2.5.3 Autocatalysis . 70 2.6 Free Radical Reactions: Chains and Branched Chains . 72 2.6.1 H, + Br, . 72 2.6.2 Rice-Herzfeld Mechanism . 73 2.6.3 Branched Chain Reactions: Explosions . 74 2.7 Determining Mechanisms from Rate Laws . 77 2.8 Summary . 81 Suggested Readings . 83 Problems . 83 Chapter 3 Theories of Chemical Reactions . 91 3.1 Introduction . 91 3.2 Potential Energy Surfaces . 92 3.3 Collision Theory . 95 3.3.1 Simple Collision Theory . 95 3.3.2 Modified Simple Collision Theory . 99 3.4 Activated Complex Theory (ACT) . 102 3.5 Thermodynamic Interpretation of ACT . 109 3.6 Summary . 109 Suggested Readings . 111 Problems . 111 Chapter 4 4.4 4.5 4.6 4.7 4.8 Appendix 4.1 Transport Properties . 116 Introduction . 116 The Functional Form of the Transport Equations . 117 The Microscopic Basis for the Transport Laws . 119 4.3.1 Simplifying Assumptions . 119 4.3.2 The Molecular Flux . 120 4.3.3 The Vertical Distance between Collisions . 122 4.3.4 The General Flux Equation . 122 Thermal Conductivity . 124 Viscosity . 127 Diffusion . 131 Time-Dependent Transport . 133 Summary . 138 The Poiseuille Formula . 139 Suggested Readings . 141 Problems . 141
viliContents.144Chapter5Reactions in Liquid Solutions5.1Introduction1445.2TheCageffect,Friction,andDiffusionControl.1455.2.1The Cage Effect...1455.2.2The Langevin Equation...1455.2.3ASimpleModelforDiffusionControl..148.1485.2.4TheDiffusion-ControlledRateConstant5.3Reactions of Charged Species in Solution: onic Strength.152and Electron Transfer.5.3.1..153ReactionRatesandIonicStrength5.3.2..155Electron Transfer Reactions: Marcus Theory5.4..159Experimental Techniques..1595.4.1TheTemperatureJumpTechnique5.4.2..161UltrafastLaserTechniques5.5Summary164Appendix 5.1The Langevin Equation and the Mean Squared.165Displacement.167Appendix5.2Diffusionwithan ElectrostaticPotentialSuggested Readings169Problems.169Chapter6.171ReactionsatSolidSurfaces6.1Introduction.1716.2.174AdsorptionandDesorption6.2.1:.176TheLangmuirIsotherm6.2.2.177Competitive Adsorption6.2.3..178Heats of Adsorption6.3..179Reactions at Surfaces:Catalysis6.3.1.179Unimolecular SurfaceReactions6.3.2180BimolecularSurfaceReactions6.3.3Activated Complex Theory of Surface.181Reactions:6.3.4.182The Nature of Surface Catalytic Sites6.4.183SurfaceDiffusion..1856.5AdvancedTopicsinSurfaceReactions..1856.5.1Temperature-ProgrammedDesorption...1876.5.2ModulatedMolecularBeamMethods6.6.194Summary.196Appendix 6.1Integral Transforms.198Suggested Readings198Problems
viii Contents Chapter 5 Reactions in Liquid Solutions . 144 5.5 Appendix 5.1 Appendix 5.2 Introduction . 144 The Cage Effect. Friction. and Diffusion Control . 145 5.2.1 The Cage Effect . 145 5.2.2 The Langevin Equation . 145 5.2.3 A Simple Model for Diffusion Control . 148 5.2.4 The Diffusion-Controlled Rate Constant . 148 Reactions of Charged Species in Solution: Ionic Strength and Electron Transfer . 152 5.3.1 Reaction Rates and Ionic Strength . 153 5.3.2 Electron Transfer Reactions: Marcus Theory . 155 Experimental Techniques . 159 5.4.1 The Temperature Jump Technique . 159 5.4.2 Ultrafast Laser Techniques . 161 Summary . 164 The Langevin Equation and the Mean Squared Displacement . 165 Diffusion with an Electrostatic Potential . 167 Suggested Readings . 169 Problems . 169 Chapter 6 Reactions at Solid Surfaces . 171 6.1 . Introduction 171 6.2 Adsorption and Desorption . 174 6.2.1 The Langmuir Isotherm . 176 6.2.2 Competitive Adsorption . 177 6.2.3 Heats of Adsorption . 178 6.3 Reactions at Surfaces: Catalysis . 179 6.3.1 Unimolecular Surface Reactions . 179 6.3.2 Bimolecular Surface Reactions . 180 6.3.3 Activated Complex Theory of Surface Reactions . 181 6.3.4 The Nature of Surface Catalytic Sites . 182 6.4 Surface Diffusion . 183 6.5 Advanced Topics in Surface Reactions . 185 6.5.1 Temperature-Programmed Desorption . 185 6.5.2 Modulated Molecular Beam Methods . 187 6.6 Summary . 194 Appendix 6.1 Integral Transforms . 196 Suggested Readings . 198 Problems . 198
ixContents..204Chapter7Photochemistry.2047.1Introduction2057.2Absorption andEmissionof Light.2097.3Photophysical Processes ..2097.3.1Fluorescence and Quenching..2127.3.2IntramolecularVibrationalEnergyRedistribution7.3.31Internal Conversion, Intersystem Crossing,..215andPhosphorescence.2187.3.4Photodissociation2217.4Atmospheric Chemistry.2257.5Photodissociation Dynamics.2267.5.1The Pump-Probe Technique.2287.5.2Laser-Induced Fluorescence.2297.5.3MultiphotonIonization.2317.5.4UnimolecularDissociation.2397.5.5PhotofragmentAngularDistributions.2447.5.6Photochemistry on Short Time Scales ..2457.6Summary.248Suggested Readings.249ProblemsChapter 8257MolecularReactionDynamics8.1,257Introduction8.2.258AMolecularDynamicsExample8.3.260Molecular Collisions-A Detailed Look8.4.263Molecular Scattering.2648.4.1The Center-of-Mass FrameNewton Diagrams8.4.2Reactive Scattering: Differential Cross Section270for F + D,.2738.4.3Elastic Collisions..2788.4.4Inelastic Collisions..2818.5PotentialEnergy Surfaces..2838.5.1Trajectory Calculations by Classical Mechanics.2868.5.2Semiclassical Calculations.2898.6Molecular EnergyTransfer....2898.6.1Translational EnergyTransfer...2928.6.2Vibrational Energy Transfer.2968.6.3Rotational Energy Transfer ..2978.6.4Electronic Energy Transfer.3028.7Molecular Reaction Dynamics-SomeExamples.3028.7.1Reactive Collisions: Orientation.3048.7.2Reactive Collisions: Bond-Selective Chemistry
Contents IX Chapter 7 Photochemistry . 204 7.1 Introduction . 204 7.2 Absorption and Emission of Light . 205 7.3 Photophysical Processes . 209 7.3.1 Fluorescence and Quenching . 209 7.3.2 Intramolecular Vibrational Energy Redistribution . 212 7.3.3 Internal Conversion, Intersystem Crossing, and Phosphorescence . 215 7.3.4 Photodissociation . 218 7.4 Atmospheric Chemistry . 221 7.5 Photodissociation Dynamics . 225 7.5.1 The Pump-Probe Technique . 226 7.5.2 Laser-Induced Fluorescence . 228 7.5.3 Multiphoton Ionization . 229 7.5.4 Unimolecular Dissociation . 231 7.5.5 Photofragment Angular Distributions . 239 7.5.6 Photochemistry on Short Time Scales . 244 7.6 Summary . 245 Suggested Readings . 248 Problems . 249 Chapter 8 Molecular Reaction Dynamics . 257 8.1 Introduction . 257 8.2 A Molecular Dynamics Example . 258 8.3 Molecular Collisions-A Detailed Look . 260 8.4 Molecular Scattering . 263 8.4.1 The Center-of-Mass Frame-Newton Diagrams . 264 8.4.2 Reactive Scattering: Differential Cross Section forF+D, . 270 8.4.3 Elastic Collisions . 273 8.4.4 Inelastic Collisions . 278 8.5 Potential Energy Surfaces . 281 8.5.1 Trajectory Calculations by Classical Mechanics . 283 8.5.2 Semiclassical Calculations . 286 8.6 Molecular Energy Transfer . 289 8.6.1 Translational Energy Transfer . 289 8.6.2 Vibrational Energy Transfer . 292 8.6.3 Rotational Energy Transfer . 296 8.6.4 Electronic Energy Transfer . 297 8.7 Molecular Reaction Dynamics-Some Examples . 302 8.7.1 Reactive Collisions: Orientation . 302 8.7.2 Reactive Collisions: Bond-Selective Chemistry . 304