CopyrightedMaterialsCHEMICAL KINETICS ANDREACTION DYNAMICSPaul L. HoustonCornell UniversityDOVER PUBLICATIONS. INC.Mineola, New York
CHEMICAL KINETICS AND REACTION DYNAMICS Paul L. Houston Cornell University DOVER PUBLICATIONS, INC. Mineola, New York
CopyrightedMaterialsIntroductionA User's Guide toChemical Kineticsand ReactionDynamicsChemistry is the study of the composition, structure, and properties of substances;of the transformation between various substances by reaction; and of the energychanges that accompany reaction.In these broad terms,physical chemistry is thenthe subbranch of the discipline that seeks to understand chemistry in quantitativeand theoretical terms; it uses the tools of physics and mathematics to predict andexplain macroscopic behavior on a microscopic level.Physical chemistry can, in turn, be described by its subfields. Thermodynamicsdeals primarilywith macroscopicmanifestations of chemistry:the transformationsbetween work andheat,the stabilityofcompounds,andthe equilibriumpropertiesofreactions.Quantummechanicsand spectroscopy,ontheotherhand,dealprima-rily with microscopic manifestations of chemistry: the structure of matter, its energylevels,and the transitions between these levels.The subfield of statistical mechanicsrelates themicroscopicpropertiesof mattertothemacroscopicobservablessuchasenergy, entropy, pressure, and temperature.At their introductory level, however,all ofthese fields emphasize properties atequilibrium.Thermodynamics can be used to calculate an equilibrium constant, butit cannot be used to predict the rate at which equilibrium will be approached.Forexample,a stoichiometric mixtureof hydrogen and oxygen ispredicted bythermo-dynamics to react to water, but kinetics can be used to calculate that the reaction willtake on the order of 1025 years ( 3 × 1032 s) at room temperature, though only10-6s in the presence of a flame. Similarly,quantum mechanics can do a good jobat predicting the spacing of energy levels, but it does not do very well, at least at theelementary level,in providing simplereasons why population of some energy levelswill bepreferred over others following a reaction.Manyreactions produceproductsina Maxwell-Boltzmanndistribution,but some,such as thoseresponsibleforchemical lasers,produce an“inverteddistribution that,overa specified energy range,ischaracterized by a negative temperature.We would like to have an understanding ofwhy theratefor a reaction can be changed by 38orders ofmagnitude,or why a reac-tion yields products in very specific, nonequilibrium distributions over energy levels.Questions about the rates of processes and about how reactions take place arethe purview of chemicalkinetics and reaction dynamics.Because this subfield ofphysical chemistry isthe one most concerned with the"how,why,and when"of chem-ical reaction, it is a central intellectual cornerstone to the discipline of chemistry
Introduction A User's Guide to Chemical Kinetics and Reaction Dynamics Chemistry is the study of the composition, structure, and properties of substances; of the transformation between various substances by reaction; and of the energy changes that accompany reaction. In these broad terms, physical chemistry is then the subbranch of the discipline that seeks to understand chemistry in quantitative and theoretical terms; it uses the tools of physics and mathematics to predict and explain macroscopic behavior on a microscopic level. Physical chemistry can, in turn, be described by its subfields. Thermodynamics deals primarily with macroscopic manifestations of chemistry: the transformations between work and heat, the stability of compounds, and the equilibrium properties of reactions. Quantum mechanics and spectroscopy, on the other hand, deal primarily with microscopic manifestations of chemistry: the structure of matter, its energy levels, and the transitions between these levels. The subfield of statistical mechanics relates the microscopic properties of matter to the macroscopic observables such as energy, entropy, pressure, and temperature. At their introductory level, however, all of these fields emphasize properties at equilibrium. Thermodynamics can be used to calculate an equilibrium constant, but it cannot be used to predict the rate at which equilibrium will be approached. For example, a stoichiometric mixture of hydrogen and oxygen is predicted by thermodynamics to react to water, but kinetics can be used to calculate that the reaction will take on the order of years (= 3 X S) at room temperature, though only lop6 s in the presence of a flame. Similarly, quantum mechanics can do a good job at predicting the spacing of energy levels, but it does not do very well, at least at the elementary level, in providing simple reasons why population of some energy levels will be preferred over others following a reaction. Many reactions produce products in a Maxwell-Boltzmann distribution, but some, such as those responsible for chemical lasers, produce an "inverted" distribution that, over a specified energy range, is characterized by a negative temperature. We would like to have an understanding of why the rate for a reaction can be changed by 38 orders of magnitude, or why a reaction yields products in very specific, nonequilibrium distributions over energy levels. Questions about the rates of processes and about how reactions take place are the purview of chemical kinetics and reaction dynamics. Because this subfield of physical chemistry is the one most concerned with the "how, why, and when" of chemical reaction, it is a central intellectual cornerstone to the discipline of chemistry
xivIntroductionAnd yet it is of enormous practical importance as well. Chemical reactions controlour environment, our life processes,ourfood production, and our energyutiliza-tion. Understanding of and possible influence over the rates of chemical reactionscould provide a healthier environment and a better life, with adequate food andmoreefficientresourcemanagement.Thus, chemical kinetics is both an exciting intellectual frontierand a field thataddresses societal needs as well.At the present time both the intellectual and practi-cal forefronts of chemical kinetics are linked to a rapidly developing new set ofinstrumental techniques, including lasers that can push our time resolution to 10-15 sordetectconcentrations atsensitivitiesapproachingonepartin1o16,microscopes thatcan see individual atoms, and computers that can calculate some rate constants moreaccurately than they can be measured. These techniques are being applied to rateprocesses in all phases of matter, to reactions in solids, liquids,gases,plasmas, andeven at the narrow interfaces between suchphases.Neverbefore have we been insuch a good position to answer the fundamental question “how do molecules react?"We begin our answer to this question by examining the motions of gas-phasemolecules.What are their velocities,and what controls the rate of collisions amongthem? In Chapter I,"Kinetic Theory of Gases,"we will see that at equilibrium themolecular velocities can be described by theBoltzmann distribution and that fac-tors such as the size,relative velocity,and molecular density influence the numberof collisions per unit time. We will also develop an understanding of one of the cen-tral tools of physical chemistry, the distribution function.We then examine the rates of chemical reactions in Chapter 2, first concentrat-ing on the macroscopic observables such as the order of areaction and its rate con-stant, but then examining how the overall rate of a reaction can be broken down intoa series ofelementary,molecular steps.Alongthe waywe will develop somepow-erful tools for analyzing chemical rates, tools for determining the order of a reac-tion, tools for making useful approximations (such as the“"steady-state"approxi-mation),and toolsforanalyzingmorecomplexreaction mechanisms.InChapter3,"Theories of Chemical Reactions,"we lookatreactionrates fromamoremicroscopicpointofview,drawingonquantummechanics,statisticalmechan-ics,and thermodynamics to help us understand the magnitude of chemical rates andhowtheyvary both withmacroscopicparameters liketemperature and withmicro-scopic parameters like molecular size, structure, and energy spacing.Chapter 4, "Transport Properties,uses the velocity distribution developed inChapter1toprovidea coherentdescriptionof thermal conductivity,viscosity,anddif-fusion,that is,a descriptionofthe movementof such properties as energy,momentum,or concentration through agas.We will see that these properties are passed from onemoleculeto anotheruponcollision,and thatthemean distancebetween collisions,the"mean free path,"is an important parameter goverming the rate of such transport.Armed with the fundamental material of the first four chapters, we move tofour exciting areas of modern research:"Reactions in Liquid Solutions""(Chapter5),"Reactions at Solid Surfaces"(Chapter 6),“Photochemistry"(Chapter 7),and"MolecularReactionDynamics"(Chapter8).The material of the text can be presented in several different formats depend-ing ontheamountof timeavailable.Thecompletetext can becovered in12-14weeks assuming3hours oflectureper week.In this format, thetextmightformthebasis of an advanced undergraduate or beginning graduate level course.A morelikely scenario, given the pressures of current instruction in physical chemistry,isone in which only the very fundamental topics are covered in detail.Table 1 showsa flowchartgiving theorderofpresentation andthe numberof lectures requiredforthe fundamental material; the total number of lectures ranges between 11 and 17
Introduction And yet it is of enormous practical importance as well. Chemical reactions control our environment, our life processes, our food production, and our energy utilization. Understanding of and possible influence over the rates of chemical reactions could provide a healthier environment and a better life, with adequate food and more efficient resource management. Thus, chemical kinetics is both an exciting intellectual frontier and a field that addresses societal needs as well. At the present time both the intellectual and practical forefronts of chemical kinetics are linked to a rapidly developing new set of instrumental techniques, including lasers that can push our time resolution to 10-l5 s or detect concentrations at sensitivities approaching one part in 1016, microscopes that can see individual atoms, and computers that can calculate some rate constants more accurately than they can be measured. These techniques are being applied to rate processes in all phases of matter, to reactions in solids, liquids, gases, plasmas, and even at the narrow interfaces between such phases. Never before have we been in such a good position to answer the fundamental question "how do molecules react?" We begin our answer to this question by examining the motions of gas-phase molecules. What are their velocities, and what controls the rate of collisions among them? In Chapter 1, "Kinetic Theory of Gases," we will see that at equilibrium the molecular velocities can be described by the Boltzmann distribution and that factors such as the size, relative velocity, and molecular density influence the number of collisions per unit time. We will also develop an understanding of one of the central tools of physical chemistry, the distribution function. We then examine the rates of chemical reactions in Chapter 2, first concentrating on the macroscopic observables such as the order of a reaction and its rate constant, but then examining how the overall rate of a reaction can be broken down into a series of elementary, molecular steps. Along the way we will develop some powerful tools for analyzing chemical rates, tools for determining the order of a reaction, tools for making useful approximations (such as the "steady-state" approximation), and tools for analyzing more complex reaction mechanisms. In Chapter 3, "Theories of Chemical Reactions," we look at reaction rates from a more microscopic point of view, drawing on quantum mechanics, statistical mechanics, and thermodynamics to help us understand the magnitude of chemical rates and how they vary both with macroscopic parameters like temperature and with microscopic parameters like molecular size, structure, and energy spacing. Chapter 4, "Transport Properties," uses the velocity distribution developed in Chapter 1 to provide a coherent description of thermal conductivity, viscosity, and diffusion, that is, a description of the movement of such properties as energy, momentum, or concentration through a gas. We will see that these properties are passed from one molecule to another upon collision, and that the mean distance between collisions, the "mean free path," is an important parameter governing the rate of such transport. Armed with the fundamental material of the first four chapters, we move to four exciting areas of modern research: "Reactions in Liquid Solutions" (Chapter 5), "Reactions at Solid Surfaces" (Chapter 6), "Photochemistry" (Chapter 7), and "Molecular Reaction Dynamics" (Chapter 8). The material of the text can be presented in several different formats depending on the amount of time available. The complete text can be covered in 12-14 weeks assuming 3 hours of lecture per week. In this format, the text might form the basis of an advanced undergraduate or beginning graduate level course. A more likely scenario, given the pressures of current instruction in physical chemistry, is one in which only the very fundamental topics are covered in detail. Table 1 shows a flow chart giving the order of presentation and the number of lectures required for the fundamental material; the total number of lectures ranges between 11 and 17
IntroductionXVOf course, ifmore time is available, the instructor can supplement the funda-mental material with selected topics from later chapters. Several suggestions, includ-ing the number of lectures required, are given in Table 2 through Table 5.TABLE 1Fundamental SectionsforaCourseinKineticsSupplemental (Lectures)Most Important Sections (Lectures)1.11.6 (3)1.7 (1)4.1-4.8 (3)2.6 (2)2.12.5 (4)5.15.2 (1)3.1-3.5 (3)Total Lectures: 6Total Lectures: 11TABLE2ReactionsinLiquid SolutionsSupplemental (Lectures)Advanced (Lectures)Fundamental (Lectures)5.4 (1)5.1-5.3 (2)TABLE3An Introduction to Surface KineticsSupplemental (Lectures)Advanced (Lectures)Fundamental (Lectures)6.5 (1)6.4 (1)6.16.3, 6.6 (2)TABLE4PhotochemistryandAtmosphericChemistryAdvanced (Lectures)Fundamental (Lectures)Supplemental (Lectures)7.1, 7.2 (1)7.3.2,7.3.3 (1)7.3.1, 7.3.4 (1)7.5 (2)7.4(1)Total Lectures: 2Total Lectures: 2Total Lectures: 3TABLE5ReactionDynamicsAdvanced (Lectures)Fundamental (Lectures)Supplemental (Lectures)8.4 (1)8.1,8.2,8.3(2)8.7 (1)8.5(2)8.6 (1)Total Lectures: 2Total Lectures: 1Total Lectures: 4
Introduction Of course, if more time is available, the instructor can supplement the fundamental material with selected topics from later chapters. Several suggestions, including the number of lectures required, are given in Table 2 through Table 5. Fundamental Sections for a Course in Kinetics Most Important Sections (Lectures) Supplemental (Lectures) 1.1-1.6 (3) 1.7 (1) 4.14.8 (3) 2.1-2.5 (4) 2.6 (2) 3.1-3.5 (3) 5.1-5.2 (1) Total Lectures: 11 Total Lectures: 6 Reactions in Liquid Solutions Fundamental (Lectures) Supplemental (Lectures) Advanced (Lectures) 5.1-5.3 (2) 5.4 (1) An Introduction to Surface Kinetics Fundamental (Lectures) Supplemental (Lectures) Advanced (Lectures) 6.1-6.3, 6.6 (2) 6.4 (1) 6.5 (1) Photochemistry and Atmospheric Chemistry Fundamental (Lectures) Supplemental (Lectures) Advanced (Lectures) 7.1,7.2 (1 ) 7.3.1,7.3.4 (1 ) 7.4 (1 ) Total Lectures: 3 7.3.2, 7.3.3 (1 ) 7.5 (2 ) Total Lectures: 2 Total Lectures: 2 Fundamental (Lectures) Supplemental (Lectures) Advanced (Lectures) 8.1, 8.2, 8.3 (2 ) 8.4 (1 ) 8.5 (2 ) 8.6 (1) 8.7 (1) Total Lectures: 4 Total Lectures: 2 Total Lectures: 1
CopyrightedMaterialsPrefaceChemical Kineticsand ReactionDynamics is a textbook in modern chemicalkinet-ics.There are two operative words here,textbook and modern. It is a textbook, not areference book.While theprincipal aim of a reference book is to cover as many top-icsas possible,theprincipal aim of a textbookistoteach.Inmyview,a seriousprob-lem with modern textbooks" is that they have lost the distinction. As a consequenceof incorporating too manytopics,these booksconfusetheiraudience;students havea difficult time seeing the forest through the trees.This textbook first aims to teach,and to teach as well as possible, the underlying principles of kinetics and dynamics.Encyclopedic completeness is sacrificed for an emphasis on theseprinciples.I aimto present them in as clear a fashion as possible,using several examples to enhancebasicunderstandingratherthanracingimmediatelytomorespecializedapplications.The more technical applications are not totally neglected; many are included as sep-aratesections orappendices,andmanyarecoveredinsets ofproblems thatfolloweach chapter.But the emphasis is on making this a textbook.The second operative word is modern. Even recently written texts often use quitedatedexamples.Importantaimsofthistextbookarefirsttodemonstratethatthebasickineticprinciples are essential tothe solution ofmodernchemical problems and sec-ond to showhow theunderlying question,"howdochemical reactions occur,"leadsto exciting,vibrant fields of modern research.The first aim is achieved by using rel-evant examples in presenting the basic material, while the second is attained by inclu-sionofchaptersonsurfaceprocesses,photochemistry,andreactiondynamics.Chemical Kinetics and Reaction Dynamics provides, then, a modern textbook.In addition to teaching and showing modern relevance, any textbook should be flex-ible enough so that individual instructors may choose their own sequence of topics.In as much as possible, the chapters of this text are self-contained; when needed.material from other sections is clearlyreferenced.An introduction to each chapteridentifies the basic goals, their importance, and the general plan for achieving thosegoals.The text is designed for several possibleformats. Chapters 1,2, and 3 forma basic package for a partial semester introduction to kinetics.The basic materialcanbe expanded by inclusionof Chapter 4.Chapters 5through8can beincludedfor afull semester course.Taken in its entirety,the text is suitablefor a one-semestercourse at the third-year undergraduate level or above. I have used it for many yearsin afirst-yeargraduatecourse.While rigorous mathematical treatment of the topic cannot and should not beavoided if we are to giveprecision to thebasicprinciples,thegreatest problem stu-dents have with physical chemistry iskeeping sight of the chemistry while wadingthrough the mathematics.This text endeavors to emphasize the chemistry by twotechniques.First,the chemical objectives and thereasonsfor undertaking the mathematical routes to those objectives are clearly stated; the mathematics is treated asa means to an end rather than an end in itself. Second,the text includes several "con-ceptual"problemsinadditionto thetraditionalmethod"problems.Recentresearchontheteachingofphysicshasshownthat,whilestudentscanfrequentlymemorizetherecipefor solvingparticulartypes of problems,theyoftenfailtodevelop con-ceptual intuition.* The first few problems at the end of each chapter are designedas aconceptual self-testforthestudent.*L.A.Halloun and D.Hestenes,Am. J. Phys. 53, 1043 (1985); 53, 1056 (1985); 55,455 (1987);D.Hestenes,Am.J.Phys. 55,440 (1987):E.Mazur,Opt.Photon.News 2,38 (1992)
Preface Chemical Kinetics and Reaction Dynamics is a textbook in modern chemical kinetics. There are two operative words here, textbook and modern. It is a textbook, not a reference book. While the principal aim of a reference book is to cover as many topics as possible, the principal aim of a textbook is to teach. In my view, a serious problem with modern "textbooks" is that they have lost the distinction. As a consequence of incorporating too many topics, these books confuse their audience; students have a difficult time seeing the forest through the trees. This textbook first aims to teach, and to teach as well as possible, the underlying principles of kinetics and dynamics. Encyclopedic completeness is sacrificed for an emphasis on these principles. I aim to present them in as clear a fashion as possible, using several examples to enhance basic understanding rather than racing immediately to more specialized applications. The more technical applications are not totally neglected; many are included as separate sections or appendices, and many are covered in sets of problems that follow each chapter. But the emphasis is on making this a textbook. The second operative word is modern. Even recently written texts often use quite dated examples. Important aims of this textbook are first to demonstrate that the basic kinetic principles are essential to the solution of modem chemical problems and second to show how the underlying question, "how do chemical reactions occur," leads to exciting, vibrant fields of modern research. The first aim is achieved by using relevant examples in presenting the basic material, while the second is attained by inclusion of chapters on surface processes, photochemistry, and reaction dynamics. Chemical Kinetics and Reaction Dynamics provides, then, a modern textbook. In addition to teaching and showing modern relevance, any textbook should be flexible enough so that individual instructors may choose their own sequence of topics. In as much as possible, the chapters of this text are self-contained; when needed, material from other sections is clearly referenced. An introduction to each chapter identifies the basic goals, their importance, and the general plan for achieving those goals. The text is designed for several possible formats. Chapters 1, 2, and 3 form a basic package for a partial semester introduction to kinetics. The basic material can be expanded by inclusion of Chapter 4. Chapters 5 through 8 can be included for a full semester course. Taken in its entirety, the text is suitable for a one-semester course at the third-year undergraduate level or above. I have used it for many years in a first-year graduate course. While rigorous mathematical treatment of the topic cannot and should not be avoided if we are to give precision to the basic principles, the greatest problem students have with physical chemistry is keeping sight of the chemistry while wading through the mathematics. This text endeavors to emphasize the chemistry by two techniques. First, the chemical objectives and the reasons for undertaking the mathematical routes to those objectives are clearly stated; the mathematics is treated as a means to an end rather than an end in itself. Second, the text includes several "conceptual" problems in addition to the traditional "method" problems. Recent research on the teaching of physics has shown that, while students can frequently memorize the recipe for solving particular types of problems, they often fail to develop conceptual intuition." The first few problems at the end of each chapter are designed as a conceptual self-test for the student. *I. A. Halloun and D. Hestenes, Am. J. Phys. 53, 1043 (1985); 53, 1056 (1985); 55,455 (1987); D. Hestenes, Am. J. Phys. 55,440 (1987); E. Mazur, Opt. Photon. News 2,38 (1992)
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 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 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