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Contents Preface xiii List of Symbols xvii 1 Introduction 1 2 Experimental Procedures 5 2.1 Detection, Identification and Estimation of Concentration of Species Present 6 2.1.1 Chromatographic techniques: liquid-liquid and gas-liquid chromatography 6 2.1.2 Mass spectrometry (MS) 6 2.1.3 Spectroscopic techniques 7 2.1.4 Lasers 13 2.1.5 Fluorescence 14 2.1.6 Spin resonance methods: nuclear magnetic resonance (NMR) 15 2.1.7 Spin resonance methods: electron spin resonance (ESR) 15 2.1.8 Photoelectron spectroscopy and X-ray photoelectron spectroscopy 15 2.2 Measuring the Rate of a Reaction 17 2.2.1 Classification of reaction rates 17 2.2.2 Factors affecting the rate of reaction 18 2.2.3 Common experimental features for all reactions 19 2.2.4 Methods of initiation 19 2.3 Conventional Methods of Following a Reaction 20 2.3.1 Chemical methods 20 2.3.2 Physical methods 21 2.4 Fast Reactions 26 2.4.1 Continuous flow 27 2.4.2 Stopped flow 28 2.4.3 Accelerated flow 28 2.4.4 Some features of flow methods 29 2.5 Relaxation Methods 29 2.5.1 Large perturbations 30 2.5.2 Flash photolysis 30 2.5.3 Laser photolysis 31 2.5.4 Pulsed radiolysis 32 2.5.5 Shock tubes 32 2.5.6 Small perturbations: temperature, pressure and electric field jumps 32 2.6 Periodic Relaxation Techniques: Ultrasonics 34 2.7 Line Broadening in NMR and ESR Spectra 37 Further Reading 38 Further Problems 38 3 The Kinetic Analysis of Experimental Data 43 3.1 The Experimental Data 44 3.2 Dependence of Rate on Concentration 47 3.3 Meaning of the Rate Expression 48 3.4 Units of the Rate Constant, k 49 3.5 The Significance of the Rate Constant as Opposed to the Rate 50 3.6 Determining the Order and Rate Constant from Experimental Data 52 3.7 Systematic Ways of Finding the Order and Rate Constant from Rate/ Concentration Data 53 3.7.1 A straightforward graphical method 55 3.7.2 log/log Graphical procedures 55 3.7.3 A systematic numerical procedure 56 3.8 Drawbacks of the Rate/Concentration Methods of Analysis 58 3.9 Integrated Rate Expressions 58 3.9.1 Half-lives 59 3.10 First Order Reactions 62 3.10.1 The half-life for a first order reaction 63 3.10.2 An extra point about first order reactions 64 3.11 Second Order Reactions 66 3.11.1 The half-life for a second order reaction 67 3.11.2 An extra point about second order reactions 68 3.12 Zero Order Reaction 68 3.12.1 The half-life for a zero order reaction 70 3.13 Integrated Rate Expressions for Other Orders 70 3.14 Main Features of Integrated Rate Equations 71 3.15 Pseudo-order Reactions 73 3.15.1 Application of pseudo-order techniques to rate/concentration data 75 3.16 Determination of the Product Concentration at Various Times 77 3.17 Expressing the Rate in Terms of Reactants or Products for Non-simple Stoichiometry 79 3.18 The Kinetic Analysis for Complex Reactions 79 3.18.1 Relatively simple reactions that are mathematically complex 81 3.18.2 Analysis of the simple scheme A_! 3.18.3 Two conceivable situations 82 3.19 The Steady State Assumption 84 3.19.1 Using this assumption 84 3.20 General Treatment for Solving Steady States 86 3.21 Reversible Reactions 89 3.21.1 Extension to other equilibria 90 3.22 Pre-equilibria 91 3.23 Dependence of Rate on Temperature 92 Further Reading 95 Further Problems 96 4 Theories of Chemical Reactions 99 4.1 Collision Theory 99 4.1.1 Definition of a collision in simple collision theory 100 4.1.2 Formulation of the total collision rate 102 4.1.3 The p factor 108 4.1.4 Reaction between like molecules 110 4.2 Modified Collision Theory 110 4.2.1 A new definition of a collision 110 4.2.2 Reactive collisions 112 4.2.3 Contour diagrams for scattering of products of a reaction 113 4.2.4 Forward scattering: the stripping or grazing mechanism 116 4.2.5 Backward scattering: the rebound mechanism 118 4.2.6 Scattering diagrams for long-lived complexes 119 4.3 Transition State Theory 122 4.3.1 Transition state theory, configuration and potential energy 122 4.3.2 Properties of the potential energy surface relevant to transition state theory 123 4.3.3 An outline of arguments involved in the derivation of the rate equation 132 4.3.4 Use of the statistical mechanical form of transition state theory 135 4.3.5 Comparisons with collision theory and experimental data 136 4.4 Thermodynamic Formulations of Transition State Theory 141 4.4.1 Determination of thermodynamic functions for activation 142 4.4.2 Comparison of collision theory, the partition function form and the thermodynamic form of transition state theory 143 4.4.3 Typical approximate values of contributions entering the sign and magnitude of _S61/4_ 144 4.5 Unimolecular Theory 145 4.5.1 Manipulation of experimental results 148 4.5.2 Physical significance of the constancy or otherwise of k1, k_1 and k2 152 4.5.3 Physical significance of the critical energy in unimolecular reactions 153 4.5.4 Physical significance of the rate constants k1, k_1 and k2 153 4.5.5 The simple model: that of Lindemann 153 4.5.6 Quantifying the simple model 154 4.5.7 A more complex model: that of Hinshelwood 155 4.5.8 Quantifying Hinshelwood's theory 156 4.5.9 Critique of Hinshelwood's theory 157 4.5.10 An even more complex model: that of Kassel 158 4.5.11 Critique of the Kassel theory 159 4.5.12 Energy transfer in the activation step 159 4.6 The Slater Theory 160 Further Reading 162 Further Problems 162 5 Potential Energy Surfaces 167 5.1 The Symmetrical Potential Energy Barrier 167 5.2 The Early Barrier 169 5.3 The Late Barrier 170 5.4 Types of Elementary Reaction Studied 172 5.5 General Features of Early Potential Energy Barriers for Exothermic Reactions 173 5.6 General Features of Late Potential Energy Surfaces for Exothermic Reactions 175 5.6.1 General features of late potential energy surfaces where the attacking atom is light 176 5.6.2 General features of late potential energy surfaces for exothermic reactions where the attacking atom is heavy 178 5.7 Endothermic Reactions 180 5.8 Reactions with a Collision Complex and a Potential Energy Well 180 Further Reading 182 Further Problems 183 6 Complex Reactions in the Gas Phase 187 6.1 Elementary and Complex Reactions 187 6.2 Intermediates in Complex Reactions 190 6.3 Experimental Data 192 6.4 Mechanistic Analysis of Complex Non-chain Reactions 193 6.5 Kinetic Analysis of a Postulated Mechanism: Use of the Steady State Treatment 196 6.5.1 A further example where disentangling of the kinetic data is necessary 198 6.6 Kinetically Equivalent Mechanisms 201 6.7 A Comparison of Steady State Procedures and Equilibrium Conditions in the Reversible Reaction 205 6.8 The Use of Photochemistry in Disentangling Complex Mechanisms 207 6.8.1 Kinetic features of photochemistry 207 6.8.2 The reaction of H2 with I2 209 6.9 Chain Reactions 211 6.9.1 Characteristic experimental features of chain reactions 212 6.9.2 Identification of a chain reaction 213 6.9.3 Deduction of a mechanism from experimental data 214 6.9.4 The final stage: the steady state analysis 216 6.10 Inorganic Chain Mechanisms 216 6.10.1 The H2/Br2 reaction 216 6.10.2 The steady state treatment for the H2/Br2 reaction 217 6.10.3 Reaction without inhibition 219 6.10.4 Determination of the individual rate constants 220 6.11 Steady State Treatments and Possibility of Determination of All the Rate Constants 221 6.11.1 Important points to note 224 6.12 Stylized Mechanisms: A Typical Rice-Herzfeld Mechanism 224 6.12.1 Dominant termination steps 226 6.12.2 Relative rate constants for termination steps 227 6.12.3 Relative rates of the termination steps 227 6.12.4 Necessity for third bodies in termination 230 6.12.5 The steady state treatment for chain reactions, illustrating the use of the long chain approximation 232 6.12.6 Further problems on steady states and the Rice-Herzfeld mechanism 236 6.13 Special Features of the Termination Reactions: Termination at the Surface 243 6.13.1 A general mechanism based on the Rice-Herzfeld mechanism used previously 243 6.14 Explosions 246 6.14.1 Autocatalysis and autocatalytic explosions 247 6.14.2 Thermal explosions 247 6.14.3 Branched chain explosions 247 6.14.4 A highly schematic and simplified mechanism for a branched chain reaction 249 6.14.5 Kinetic criteria for non-explosive and explosive reaction 250 6.14.6 A typical branched chain reaction showing explosion limits 252 6.14.7 The dependence of rate on pressure and temperature 253 6.15 Degenerate Branching or Cool Flames 255 6.15.1 A schematic mechanism for hydrocarbon combustion 257 6.15.2 Chemical interpretation of 'cool' flame behaviour 260 Further Reading 262 Further Problems 263 7 Reactions in Solution 267 7.1 The Solvent and its Effect on Reactions in Solution 267 7.2 Collision Theory for Reactions in Solution 269 7.2.1 The concepts of ideality and non-ideality 271 7.3 Transition State Theory for Reactions in Solution 271 7.3.1 Effect of non-ideality: the primary salt effect 272 7.3.2 Dependence of _S61/4_ and _H61/4_ on ionic strength 282 7.3.3 The effect of the solvent 282 7.3.4 Extension to include the effect of non-ideality 286 7.3.5 Deviations from predicted behaviour 286 7.4 _S61/4_ and Pre-exponential A Factors 292 7.4.1 A typical problem in graphical analysis 295 7.4.2 Effect of the molecularity of the step for which _S61/4_ is found 295 7.4.3 Effect of complexity of structure 295 7.4.4 Effect of charges on reactions in solution 296 7.4.5 Effect of charge and solvent on _S61/4_ for ion-ion reactions 296 7.4.6 Effect of charge and solvent on _S61/4_ for ion-molecule reactions 298 7.4.7 Effect of charge and solvent on _S61/4_ for molecule-molecule reactions 299 7.4.8 Effects of changes in solvent on _S61/4_ 300 7.4.9 Changes in solvation pattern on activation, and the effect on A factors for reactions involving charges and charge-separated species in solution 300 7.4.10 Reactions between ions in solution 302 7.4.11 Reaction between an ion and a molecule 303 7.4.12 Reactions between uncharged polar molecules 303 7.5 _H61/4_ Values 305 7.5.1 Effect of the molecularity of the step for which the _H61/4_ value is found 306 7.5.2 Effect of complexity of structure 306 7.5.3 Effect of charge and solvent on _H61/4_ for ion-ion and ion-molecule reactions 306 7.5.4 Effect of the solvent on _H61/4_ for ion-ion and ion-molecule reactions 307 7.5.5 Changes in solvation pattern on activation and the effect on _H61/4_ 307 7.6 Change in Volume on Activation, _V61/4_ 307 7.6.1 Effect of the molecularity of the step for which _V61/4_ is found 310 7.6.2 Effect of complexity of structure 310 7.6.3 Effect of charge on _V61/4_ for reactions between ions 310 7.6.4 Reactions between an ion and an uncharged molecule 312 7.6.5 Effect of solvent on _V61/4_ 312 7.6.6 Effect of change of solvation pattern on activation and its effect on _V61/4_ 312 7.7 Terms Contributing to Activation Parameters 314 7.7.1 _S61/4_ 314 7.7.2 _V61/4_ 315 7.7.3 _H61/4_ 316 Further Reading 318 Further Problems 319 8 Examples of Reactions in Solution 323 8.1 Reactions Where More than One Reaction Contributes to the Rate of Removal of Reactant 323 8.1.1 A simple case 323 8.1.2 A slightly more complex reaction where reaction occurs by two concurrent routes, and where both reactants are in equilibrium with each other 327 8.1.3 Further disentangling of equilibria and rates, and the possibility of kinetically equivalent mechanisms 334 8.1.4 Distinction between acid and base hydrolyses of esters 337 8.2 More Complex Kinetic Situations Involving Reactants in Equilibrium with Each Other and Undergoing Reaction 342 8.2.1 A further look at the base hydrolysis of glycine ethyl ester as an illustration of possible problems 342 8.2.2 Decarboxylations of _-keto-monocarboxylic acids 345 8.2.3 The decarboxylation of _-keto-dicarboxylic acids 347 8.3 Metal Ion Catalysis 349 8.4 Other Common Mechanisms 352 8.4.1 The simplest mechanism 352 8.4.2 Kinetic analysis of the simplest mechanism 353 8.4.3 A slightly more complex scheme 357 8.4.4 Standard procedure for determining the expression for kobs for the given mechanism 358 8.5 Steady States in Solution Reactions 365 8.5.1 Types of reaction for which a steady state treatment could be relevant 365 8.5.2 A more detailed analysis of Worked Problem 6.5 366 8.6 Enzyme Kinetics 371 Further Reading 374 Further Problems 375 Answers to Problems 379 List of Specific Reactions 433 Index 437
Library of Congress Subject Headings for this publication: Chemical kinetics