Chemical Kinetics

Preface xi
Chapter 1
BASIC KINETIC CONCEPTS 1
1.1 Scope of Chemical Kinetics 2
1.1.1 Macroscopic and Microscopic Kinetics 3
1.2 Reaction Stoichiometry 4
1.3 Rates of Consumption and Formation 6
1.4 Extent of Reaction 7
1.5 Rate of Reaction 8
1.6 Volume Change During Reaction 9
1.7 Empirical Rate Equations JO
1.7.1 Order of Reaction 10
1.7.2 Rate Constants 11
1.7.3 Reactions Having No Order 12
1.8 Elementary, Composite, and Chain Reactions 13
1.8.1 Chain Reactions 14
1.9 Catalysis and Inhibition 14
Problems 1S
References 16
Bibliography 17
Chapter 2
ANALYSIS OF KINETIC RESULTS 18
2.1 Differential Method 18
2.2 Method of Integration 21
2.2.1 First-Order Reactions 21
2.2.2 Second-Order Reactions 23
2.2.3 Reactions of the nth Order 25
2.3 Isolation Method 26
2.4 Half-Life 26
2.5 Comparison of Methods 28
2.6 Opposing Reactions 29
2.7 Reactions in Row Systems • 31
2.8 Techniques for Very Fast Reactions 33
2.8.1 Stopped-Flow Method 34
2.8:2 Relaxation Methods 35
2.8.3 Shock-Tube Methods 39
2.8.4 Flash Photolysis 39
2.9 Influence of Temperature on Reaction Rates 39
2.9.1 Survey of Empirical Equations for Temperature Dependence 40
2.9.2 Arrhenius Equation 44
2.9.3 Improved Treatments of Temperature Dependence 45
2.9.4 Temperature Dependence of the Preexponential Factor 46
Problems 48
References 50
Bibliography 51
Chapter 3
ENERGY OF ACTIVATION 54
3.1 Statistical Distribution of Molecular Energies 55
3.1.1 Simple Statistical Expressions 5 5
3.1.2 Tolman\'s Theorem 56
3.2 Potential-Energy Surfaces 59
3.3 Ab initio Calculations of Potential-Energy Surfaces 64
3.3.1 Treatments Based on the London Equation 64
3.3.2 Variational Calculations 64
3.4 Semiempirical Calculations of Potential-Energy Surfaces 67
3.4.1 London-Eyring-Polany MLEP) Method 68
3.4.2 Sato Method 69
3.4.3 Modified LEP Methods  70
3.4.4 Bond-Energy-Bond-Order BEBO) Method 70
3.5 Empirical Treatments of Activation Energy 71 
Appendix: Statistical Distribution of Molecular Energies 74
Motion in Two Dimensions 74
Motion in Three Dimensions - 75
Motion in Many Degrees of Freedom 76
Problems 77
References 78
Bibliography 79
Chapter 4
THEORIES OF REACTION RATES 80
4.1 Kinetic Theory of Collisions 81
4.1.1 Generalized Kinetic Theory 84
4.1.2 Extensions of Collision Theory 87
4.2 Rate Theories Based on Thermodynamics 87
4.3 Rate Theories Based on Statistical Mechanics 88
4.4 Early Dynamical Theories of Rates 88
4.5 Conventional Transition-State Theory 89
4.5.1 Equilibrium Hypothesis 90
4.5.2 Statistical Mechanics and Chemical Equilibrium 93
4.5.3 Derivations of the Rare Equation 94 \\\'
4.5.4 Symmetry Numbers and Statistical Factors 98
4.6 Some Applications of Conventional Transition-State Theory 106
4.6.1 Reactions between Atoms 106
4.6.2 Reactions between Molecules 107
4.6.3 An Example: The Reaction H + HBr — H2 + Br 109
4.7 Thermodynamic Formulation of Conventional Transition-State Theory 112
4.8 Assumptions and Limitations of Conventional Transition-Stale Theory 115
4.8.1 Multiple Crossings and the Equilibrium Hypothesis 116
4.8.2 Separability of the Reaction Coordinate 119
4.8.3 Quantum Effects  21
4.9 Extensions of Transition-State Theory 123
4.9.1 Variational Transition-State Theory 124
4.9.2 Quantum-Mechanical Transition-State Theory 127
4.9.3 Muonium Kinetics 129
4.10 Microscopic Reversibility and Detailed Balance 129
Problems 131 *
References 132
Bibliography 135
Chapter 5
ELEMENTARY GAS-PHASE REACTIONS 137
5.1 Bimolecular Reactions 138
5.1.1 Reactions of the Type H + H7 138
5.1.2 Other Atom and Free-Radical Reactions 140
5.1.3 Temperature Dependence of Preexponential Factors 145
5.1.4 Ion-Molecule Reactions 146
5.2 Trimolecular Reactions 147
5.3 Unimolecular Reactions 150
5.3.1 Lindemamv-Christiansen Hypothesis 152
5.3.2 Hihshelwood\'s Treatment 155
5.3.3 Rjce-Ramsperger-Kassei (RRK) Treatment J 57
5.3.4 Slater\'s Treatment 163 -
5.3.5 Marcus\'s Extension of the RRK Treatment (RRKM) 164
5.3.6 Influence of Foreign Gases 167
5.3.7 lntermolecular Energy Transfer 168
5.3.8 Intramolecular Energy Transfer 168
5.3.9 Laser-Induced Unimolecular Reactions 170
5.3.10 Decomposition of Ions 171
5.4 Combination and Disproportionation Reactions 171
5.4.1 Mechanisms of Atom and Radical Combinations 173
Problems 176
References 177
Bibliography ISO
Chapter 6
ELEMENTARY REACTIONS IN. SOLUTION 183
6.1 Solvent Effects on Reaction Rates 183
6.1.1 Comparison between Gas-Phase and Solution Reactions 184
6.1.2 Comparison between Different Solvents 184
6.2 Factors Determining Reaction Rates in Solution 185
6.2.1 Collisions in Solution 186
6.2.2 Transition-State Theory 188
6.2.3 Influence of Internal Pressure 189
6.2.4 Influence of Solvation 190
6.3 Reactions between Ions 191
6.3.1 Influence of Solvent Dielectric Constant 191
6.3.2 Pre-exponential Factors 194
6.3.3 Single-Sphere Activated Complex 195
6.3.4 Influence of Ionic Strength 197
6.3.5 More Advanced Treatments 201
6.4 Ion-Dipole and Dipole-Dipole Reactions 203
6.4.1 Pre-exponential Factors 204
6.4.2 Influence of Ionic Strength 205
6.5 Influence of Hydrostatic Pressure 206
6.5.1 Van\'t Hoffs Equation 206
6.5.2 Volumes of Activation 207
6.6 Substituent and Correlation Effects 209
6.6.1 Hammett Equation 209
6.6.2 Compensation Effects 211
6.7 Diffusion-Controlled Reactions 212
6.7.1 Full Microscopic Diffusion Control 212
6.7.2 Partial Microscopic Diffusion Control 2I j$
6.7.3 Ionic Reactions 217
Problems 222
References 224
Bibliography 226
Chapter 7
REACTIONS ON SURFACES 229
7.1 Adsorption .230
7.2 Adsorption Isotherms 230
7.2.1 Simple Langmuir Isotherm 231
7.2.2 Adsorption with Dissociation 232
7.2.3 Competitive Adsorption 233
7.2.4 Nonideal Adsorption 234
7.2.5 Thermodynamics and Statistical Mechanics of Adsorption 235
7.3 Structures of Solid Surfaces and Adsorbed Layers 237
7.3.1 Detailed Structural Studies 238
7.3.2 Induced Heterogeneity 241
7.4 Mechanisms of Surface Reactions 241
7.4.1 Kinetic Effects of Surface Heterogeneity 243
7.4.2 Kinetic Effects of Interactions 244
7.5 Unimolecular Surface Reactions 244
7.5.1 Inhibition 246
•7.5:2 Activation Energies 246
7.6 Bimolecular Surface Reactions 248
7.6.1 Reaction between Two Adsorbed Molecules 249
7.6.2 Reaction between a Gas Molecule and an Adsorbed Molecule 250
7.6.3 Adsorption of Two Gases without Mutal Displacement 250
7.6.4 Inhibition 251
7.6.5 .Activation Energies 251
7.6.6 Parahydrogen Conversion 252
7.6.7 Combination and Formation of Atoms at Surfaces 252
7.6.8 Exchange Reactions 253
7.6.9 Addition of Hydrogen to Ethylene 257
7.7 Transition-State Theory of Surface Reactions 258
7.7.1 Rates of Chemisorption 259
7.7.2 Rates of Desorption 261
7.7.3 Unimolecular Surface Reactions 262
7.7.4 Bimolecular Surface Reactions- 264
7.7.5 Comparison of Homogeneous and Heterogeneous Reaction Rates 266
Problems 268
References 270
Bibliography 273
Chapter 8
COMPOSITE REACTIONS 276
8.1 Types of Composite Mechanism 278
8.2 Rate Equations for Composite Mechanisms 278
8.2.1 Simultaneous and Consecutive Reactions 279
8.2.2 Steady-State Treatment 282
8.2.3 Rate-Determining (Rate-Controlling) Steps 283
8.2.4 Microscopic Reversibility and Detailed Balance 285
8.3 Chain Reactions 288
8.3.1 Chain Initiation Processes 290
8.4 Some Inorganic Mechanisms 291
8.4.1 Hydrogen-Bromine Reaction 29-1
8.4.2 Hydrogen-Chlorine Reaction 295
8.4.3 Hydrogen-Iodine Reaction 298
8.4.4 Comparison of the Hydrogen-Halogen Reactions 300
8.4.5 Formation and Decomposition of Phosgene 303
8.4.6 Decomposition of Nitrogen Pentoxide 303
8.4.7 Decomposition of Ozone 305
8.4.8 Thermal Para-Ortho Hydrogen Conversion 307
8.5 Organic Decompositions 307
8.5.1 Goldfinger-Letort-Niclause Rules 311
8.5.2 Molecular Processes 314
8.5.3 Decomposition of Ethane 316
8.5.4 Decomposition of Acetaldehyde 319
8.5.5 Inhibition Mechanisms 321
8.6 Gas-Phase Combustion 322
8.6.1 Hydrogen-Oxygen Reaction 323
8.6.2 - Combustion of Hydrocarbons 328
8.7 Polymerization Reactions 330
8.7.1 Molecular Mechanisms 330
8.7.2 Free-Radical Mechanisms 332
8.7.3 Cationic Polymerization 335
8.7.4 Anionic Polymerization 338
8.7.5 Emulsion Polymerization 339
Problems 340
References. 342
Bibliography 346
Chapter 9
PHOTOCHEMICAL AND RADIATION-CHEMICAL REACTIONS . 348
9.1 Photochemical Reactions 349
9.1.1 Photochemical Primary Process 349
9.1.2 Reactions of Electronically Excited Species 353
9.1.3 Photochemical Thresholds 355
9.1.4 Law of Photochemical Equivalence 355
9.1.5 Rotating-Sector Technique 356
9.1.6 Rash Photolysis 359
9.2 Laser Photochemistry \'360
9.2.1 Pulsed Lasers 361
9.2.2 Multiphoton Excitation 362
9.3 Photosensitization 362
9.4 Radiation-Chemical Reactions 365
9.4.1 Radiation-Chemical Primary Process 366
9.4.2 Pulse Radiolysis 370
9.4.3 Hydrated Electrons 370
9.5 Chemiluminescence 371
Problems 372
References 373
Bibliography 374
Chapter 10
HOMOGENEOUS CATALYSIS 377
10.1 General Catalytic Mechanisms 379
10.1.1 Equilibrium Treatment: Arrhenius Intermediates 380
10.1.2 Steady-State Treatment: Van\'t Hoff Intermediates 382
10.1.3 Activation Energies for Catalyzed Reactions 383
10.2 Acid-Base Catalysis 384\'
10.2.1 General Acid-Base Catalysis 387
10.2.2 Mechanisms of Acid-Base Catalysis 388
10.2.3 Catalytic Activity and Acid-Base Strength 394
10.2.4 Salt Effects in Acid-Base Catalysis 396
10.2.5 Acidity Functions 397
10.3 _ Catalysis by Enzymes 399.. .
10.3.1 Influence of Substrate Concentration 400
10.3.2 Influence of pH 406
10.3.3 Influence of Temperature 409
10.3.4 Transient-Phase Kinetics 410
10.3.5 Enzyme Mechanisms 412
10.4 Catalysis in Gaseous Systems 412
10.5 Chain Mechanisms- 413
10.6 Catalysis by Ions of Variable Valency 414
10.7 Activation of Molecular Hydrogen 415
Problems 418
References 421
Bibliography 424
Chapter 11
ISOTOPE EFFECTS 427
11.1 Equilibrium Isotope Effects 428
11.l.1 Equilibria in Solution 432
11.2 Primary Kinetic Isotope Effects 433
11.2.1 Semiclassical Treatments 434
14.2.2 Quantum-Mechanical Tunneling 437
11.2.3 Reactions of the Type H + H2 438
11.2.4 Transfer of H+,H, and H\" 442
11.2.5 Reactions of Muonium 442
11.2.6 Isotope Effects with Heavier Atoms 444
11.3 Secondary Kinetic Isotope Effects 446 -
References 447
Bibliography 448
Chapter 12
REACTION DYNAMICS 449
12.1 Molecular-Dynamical Calculations 451
12.1.1- The Reaction H + H2 454
12.1.2 The Reaction Br + H2 457
12.1.3 More Complex Reactions 458
12.2 Chemiluminescence 459
12.2.1 Highly Dilute Flames 459
12.2.2 Diffusion Flames 460
12.3 Features of Potential-Energy Surfaces 460
12.3.1 Attractive Surfaces for Exothermic Reactions 461
12.3.2 Repulsive Surfaces for Exothermic Reactions 462
12.3.3 Surfaces of Intermediate Types for Exothermic Reactions
12.3.4 Selective Enhancement of Reaction 466
12.3.5 Disposal of Excess Energy 469
12.3.6 Gradual and Sudden Surfaces.. 469
12.3.7 Influence of Rotational Energy 471
12.4 Molecular Beams 472
12.4.1 Stripping and Rebound Mechanisms 475
12.5 State-to-State Kinetics 476
12.5.1 Influence of Reactant Vibrational Energy 477
12.5.2 Influence of Reactant Rotational Energy 481
12.6 Spectroscopy of Transition Species 483
References 485
Bibliography 488
Biographical Sketches 491
Answers to Problems 523
Index 525