ChemicalKinetics andReactionDynamicsSantosh K. UpadhyaySpringer
PrefaceReactiondynamics is thepart of chemical kineticswhich is concerned withthemicroscopic-moleculardynamicbehaviorof reactingsystems.Molecularreaction dynamics is coming of age and much more refined state-to-stateinformation is becoming available on the fundamental reactions.Thecontributionofmolecularbeamexperimentsandlasertechniquestochemicaldynamics has become very useful in the study of isolated molecules andtheir mutual interactions not only in gas surface systems, but also in solute-solution systems.This book presents the important facts and theories relatingto the rateswith which chemical reactions occur and covers main points in a manner sothat the reader achieves a sound understanding of the principles of chemicalkinetics.A detailed stereochemical discussion of the reaction steps in eachmechanismand theirrelationshipwithkineticobservations hasbeenconsidered.I wouldliketotaketheopportunitytothankProfessorR.C.Srivastavaand Professor N.Sathyamurthywith whom Ihad the privilege of workingand who inspired my interest in the subject and contributed in one way oranotherto help completethis book.I express myheavy debt of gratitudetowards ProfessorM.C.Agrawal who was gracious enoughfor sparing timeoutof hisbusyscheduletogothrough themanuscript.Hisvaluablecommentsand suggestions, of course,enhanced the value and importanceof thisbook.I also express my gratitude to my colleagues, friends and research students,especially Dr. Neelu Kambo who took all the pains in helping me in preparing,typingand checkingthemanuscript.Finally, I thank my wife Mrs. Manju Upadhyay, daughter Neha and sonAnkur for their continuous inspiration during the preparation of thetext.SANTOSHK.UPADHYAY
Preface Reaction dynamics is the part of chemical kinetics which is concerned with the microscopic-molecular dynamic behavior of reacting systems. Molecular reaction dynamics is coming of age and much more refined state-to-state information is becoming available on the fundamental reactions. The contribution of molecular beam experiments and laser techniques to chemical dynamics has become very useful in the study of isolated molecules and their mutual interactions not only in gas surface systems, but also in solutesolution systems. This book presents the important facts and theories relating to the rates with which chemical reactions occur and covers main points in a manner so that the reader achieves a sound understanding of the principles of chemical kinetics. A detailed stereochemical discussion of the reaction steps in each mechanism and their relationship with kinetic observations has been considered. I would like to take the opportunity to thank Professor R.C. Srivastava and Professor N. Sathyamurthy with whom I had the privilege of working and who inspired my interest in the subject and contributed in one way or another to help complete this book. I express my heavy debt of gratitude towards Professor M.C. Agrawal who was gracious enough for sparing time out of his busy schedule to go through the manuscript. His valuable comments and suggestions, of course, enhanced the value and importance of this book. I also express my gratitude to my colleagues, friends and research students, especially Dr. Neelu Kambo who took all the pains in helping me in preparing, typing and checking the manuscript. Finally, I thank my wife Mrs. Manju Upadhyay, daughter Neha and son Ankur for their continuous inspiration during the preparation of the text. SANTOSH K. UPADHYAY
ContentsviiPreface11.Elementary11.1Rate of Reaction21.1.1 ExperimentalDeterminationofRate31.2RateConstant41.3Order and Molecularity61.4RateEquations1.4.1IntegralEquationsfornth OrderReactionof a Single6Reactant1.4.2Integral Equations for Reactions Involving More than7OneReactants81.5Half-life of a Reaction101.6Zero OrderReactions121.7FirstOrderReactions171.8RadioactiveDecayas a FirstOrderPhenomenon201.9Second Order Reactions281.10ThirdOrderReactions301.11DeterminationofOrderofReaction301.11.1Integration Method341.11.2Half-lifePeriodMethod341.11.3 Graphical Method351.11.4DifferentialMethod351.11.5OstwaldIsolationMethod391.12Experimental MethodsofChemicalKinetics391.12.1ConductometricMethod401.12.2PolarographicTechnique411.12.3PotentiometricMethod421.12.4Optical Methods421.12.5Refractometry431.12.6Spectrophotometry44Exercises462.TemperatureEffectonReactionRate462.1Derivationof ArrheniusEquation
Contents Preface vii 1. Elementary 1 1.1 Rate of Reaction 1 1.1.1 Experimental Determination of Rate 2 1.2 Rate Constant 3 1.3 Order and Molecularity 4 1.4 Rate Equations 6 1.4.1 Integral Equations for nth Order Reaction of a Single Reactant 6 1.4.2 Integral Equations for Reactions Involving More than One Reactants 7 1.5 Half-life of a Reaction 8 1.6 Zero Order Reactions 10 1.7 First Order Reactions 12 1.8 Radioactive Decay as a First Order Phenomenon 17 1.9 Second Order Reactions 20 1.10 Third Order Reactions 28 1.11 Determination of Order of Reaction 30 1.11.1 Integration Method 30 1.11.2 Half-life Period Method 34 1.11.3 Graphical Method 34 1.11.4 Differential Method 35 1.11.5 Ostwald Isolation Method 35 1.12 Experimental Methods of Chemical Kinetics 39 1.12.1 Conductometric Method 39 1.12.2 Polarographic Technique 40 1.12.3 Potentiometric Method 41 1.12.4 Optical Methods 42 1.12.5 Refractometry 42 1.12.6 Spectrophotometry 43 Exercises 44 2. Temperature Effect on Reaction Rate 46 2.1 Derivation of Arrhenius Equation 46
Contentsx2.2Experimental Determination of Energy of Activation and48Arrhenius Factor502.3Potential Energy Surface512.4Significance of Energy of Activation53Exercises553.ComplexReactions553.1Reversible Reactions3.1.1 ReversibleReactionWhen BoththeOpposing57Processes areSecondOrder593.2ParallelReactions593.2.1DeterminationofRateConstants633.3Consecutive Reactions643.3.1Concentration-TimeRelation663.4Steady-State Treatment673.5Chain Reactions683.5.1Rate Determination693.5.2ReactionbetweenHandBr2703.5.3Chain Length703.5.4Chain Transfer Reactions703.5.5BranchingChain Explosions713.5.6Kinetics of Branching ChainExplosion723.5.7FreeRadical Chains3.5.8ChainLength andActivationEnergyinChain75Reactions76Exercises794.Theories of Reaction Rate794.1Equilibrium andRateof Reaction4.2Partition Functions and Statistical Mechanics of80Chemical Equilibrium824.3PartitionFunctions andActivatedComplex834.4Collision Theory844.4.1CollisionFrequency864.4.2EnergyFactor874.4.3OrientationFactor874.4.4Rateof Reaction884.4.5Weakness of theCollisionTheory894.5Transition StateTheory914.5.1ThermodynamicApproach934.5.2PartitionFunctionApproach4.5.3Comparison withArrhenius Equation andCollision93Theory4.5.4ExplanationforStericFactorinTermsofPartition94Function
2.2 Experimental Determination of Energy of Activation and Arrhenius Factor 48 2.3 Potential Energy Surface 50 2.4 Significance of Energy of Activation 51 Exercises 53 3. Complex Reactions 55 3.1 Reversible Reactions 55 3.1.1 Reversible Reaction When Both the Opposing Processes are Second Order 57 3.2 Parallel Reactions 59 3.2.1 Determination of Rate Constants 59 3.3 Consecutive Reactions 63 3.3.1 Concentration-Time Relation 64 3.4 Steady-State Treatment 66 3.5 Chain Reactions 67 3.5.1 Rate Determination 68 3.5.2 Reaction between H2 and Br2 69 3.5.3 Chain Length 70 3.5.4 Chain Transfer Reactions 70 3.5.5 Branching Chain Explosions 70 3.5.6 Kinetics of Branching Chain Explosion 71 3.5.7 Free Radical Chains 72 3.5.8 Chain Length and Activation Energy in Chain Reactions 75 Exercises 76 4. Theories of Reaction Rate 79 4.1 Equilibrium and Rate of Reaction 79 4.2 Partition Functions and Statistical Mechanics of Chemical Equilibrium 80 4.3 Partition Functions and Activated Complex 82 4.4 Collision Theory 83 4.4.1 Collision Frequency 84 4.4.2 Energy Factor 86 4.4.3 Orientation Factor 87 4.4.4 Rate of Reaction 87 4.4.5 Weakness of the Collision Theory 88 4.5 Transition State Theory 89 4.5.1 Thermodynamic Approach 91 4.5.2 Partition Function Approach 93 4.5.3 Comparison with Arrhenius Equation and Collision Theory 93 4.5.4 Explanation for Steric Factor in Terms of Partition Function 94 x Contents
Contentsxi954.5.5ReactionbetweenPolyatomicMolecules1004.6UnimolecularReactionsandtheCollisionTheory1004.6.1Lindemann'sMechanism1034.6.2HinshelwoodTreatment1054.6.3Rice andRamsperger, andKassel (RRK)Treatment1064.6.4MarcusTreatment1074.6.5RRKMTheory4.7109Kinetic and Thermodynamic Control1104.8Hammond'sPostulate4.9111Probing of the Transition State113Exercises1155.Kineticsof Some Special Reactions1155.1Kinetics of Photochemical Reactions1155.1.1 Grotthuss-DraperLaw1155.1.2EinsteinLawofPhotochemicalEquivalence1165.1.3PrimaryProcessinPhotochemicalReactions1185.1.4 H2-Br2Reaction1195.1.5H2andCl2Reaction1205.2OscillatoryReactions1225.2.1Belousov-ZhabotinskiiReaction5.3124Kinetics of Polymerization1255.3.1StepGrowthPolymerization5.3.2PolycondensationReactions(inAbsenceof the125Catalyst)1265.3.3AcidCatalyzedPolycondensationReaction1275.3.4ChainGrowthPolymerization1275.3.5KineticsofFreeRadicalPolymerization1305.3.6Cationic Polymerization1315.3.7AnionicPolymerization1325.3.8Co-polymerization5.4135Kinetics of Solid StateReactions5.5139Electron TransferReactions1395.5.1OuterSphereMechanism1405.5.2InnerSphereMechanism141Exercises1426.Kinetics of Catalyzed Reactions1426.1Catalysis1426.1.1 Positive Catalysis1436.1.2Negative Catalysis1436.1.3Auto Catalysis1446.1.4InducedCatalysis1446.1.5Promoters
4.5.5 Reaction between Polyatomic Molecules 95 4.6 Unimolecular Reactions and the Collision Theory 100 4.6.1 Lindemann’s Mechanism 100 4.6.2 Hinshelwood Treatment 103 4.6.3 Rice and Ramsperger, and Kassel (RRK) Treatment 105 4.6.4 Marcus Treatment 106 4.6.5 RRKM Theory 107 4.7 Kinetic and Thermodynamic Control 109 4.8 Hammond’s Postulate 110 4.9 Probing of the Transition State 111 Exercises 113 5. Kinetics of Some Special Reactions 115 5.1 Kinetics of Photochemical Reactions 115 5.1.1 Grotthuss-Draper Law 115 5.1.2 Einstein Law of Photochemical Equivalence 115 5.1.3 Primary Process in Photochemical Reactions 116 5.1.4 H2-Br2 Reaction 118 5.1.5 H2 and Cl2 Reaction 119 5.2 Oscillatory Reactions 120 5.2.1 Belousov-Zhabotinskii Reaction 122 5.3 Kinetics of Polymerization 124 5.3.1 Step Growth Polymerization 125 5.3.2 Polycondensation Reactions (in Absence of the Catalyst) 125 5.3.3 Acid Catalyzed Polycondensation Reaction 126 5.3.4 Chain Growth Polymerization 127 5.3.5 Kinetics of Free Radical Polymerization 127 5.3.6 Cationic Polymerization 130 5.3.7 Anionic Polymerization 131 5.3.8 Co-polymerization 132 5.4 Kinetics of Solid State Reactions 135 5.5 Electron Transfer Reactions 139 5.5.1 Outer Sphere Mechanism 139 5.5.2 Inner Sphere Mechanism 140 Exercises 141 6. Kinetics of Catalyzed Reactions 142 6.1 Catalysis 142 6.1.1 Positive Catalysis 142 6.1.2 Negative Catalysis 143 6.1.3 Auto Catalysis 143 6.1.4 Induced Catalysis 144 6.1.5 Promoters 144 Contents xi