An Introduction to Chemical Kinetics
Michel Soustelle
WWI EY Table of Contents
Preface xvii
PART 1. BASIC CONCEPTS OF CHEMICAL KINETICS 1
Chapter 1. Chemical Reaction and Kinetic Quantities 3 1.1. The chemical reaction 3 1.1.1. The chemical equation and stoichiometric coefficients 3 1.1.2. The reaction components 5 1.1.3. Reaction zones 6 1.2. Homogeneous and heterogeneous reactions 8 1.2.1. Single zone reaction 8 1.2.2. Multizone reaction 8 1.3. Extent and speed of a reaction 9 1.3.1. Stoichiometric abundance of a component in a reaction mixture 9 1.3.2. Extent of a reaction 9 1.3.3. Speed of a reaction 11 1.4. Volumetric and areal speed of a monozone reaction 12 1.5. Fractional extent and rate of a reaction 14 1.5.1. The fractional extent of a reaction 14 1.5.2. Rate of a reaction 16 1.5.3. Expression of the volumetric speed (areal) from variations in the amount of a component 16 1.6. Reaction Speeds and concentrations 18 1.6.1. Concentration of a component in a zone 18 1.6.2. Relationship between concentration and fractional extent in a closed environment 19 vi An Introduction to Chemical Kinetics
Expr n f v l tr p d rd n t v r t n n n ntr t n n l d t 8 St h tr xt r nd pr r 20 t r nfl n n r t n p d 2 Infl n f t p r t r 2 2 Infl n f th n ntr t n ( r p rt l pr r f 2 Oth r v r bl 2
Chapter 2. Reaction Mechanisms and Elementary Steps 2 2 pr f n t 2 2 2 t n h n 26 2 2 f n t n 26 2 2 2 Ex pl f h n 2 2 t n nt r d t 2 2 Ex t d t ( r l l 2 2 2 r r d l 0 2 I n 0 2 4 Ad rb d p 2 nt d f t 2 6 h ff t f nt r d t n xt nt nd p d 2 4 t n n nd S n v r pr nt t n 2 2 4 S n v d r 2 2 4 2 n r n nd lt p nt n 2 Ch n r t n 4 2 f n t n 4 2 2 h d ff r nt t r f h n r t n 2 h t p n h n r t n 2 4 S n f h n r t n 2 t n f r l l f r t n 6 2 6 C t l t r t n 2 6 n t l 8 2 6 2 t r n t l 2 I p rt nt f r n r t n h n 4
Chapter 3. Kinetic Properties of Elementary Reactions 4 Sp f n t n f n l nt r r t n 4 2 t v t nd r t f n l nt r t p 44 K n t n t nt f n l nt r t p 4 Expr n f r t v t f n t n f n ntr t n 4 2 t f t r f n l nt r r t n 46 4 Opp t l nt r r t n 4 Table of Contents vii
3.4.1. Reactivity of two opposite elementary reactions '47 3.4.2. Distance from equilibrium conditions 48 3.4.3. Principle of partial equilibria 49 3.5. Influence of temperature on the reactivities of elementary steps 49 3.5.1. Influence of temperature near the equilibrium 50 3.5.2. Activation energies of opposite elementary reactions and reaction enthalpy 50 3.6. Modeling of a gas phase elementary step 51 3.6.1. Collision theory 52 3.6.2. Theory of activated complex 54 3.7. A particular elementary step: diffusion 58 3.7.1. The diffusion phenomenon 58 3.7.2. Diffusion flux and Fick's first law 58 3.7.3. Diffusion flux in a steady state system 59 3.7.4. Reactivity and diffusion space function 60 3.7.5. Diffusion in solids 62 3.7.6. Interdiffusion of gases 63 3.7.7. Diffusion of a gas in a cylindrical pore 64 3.8. Gases adsorption onto solids 64 3.8.1. Chemisorption equilibrium: Langmuir model 65 3.8.2. Dissociative adsorption and the Langmuir model 66 3.8.3. Chemisorption of gas mixtures in the Langmuir model 68 3.8.4. Chemisorption kinetic in the Langmuir model 70 3.9. Important figures in the kinetic properties of elementary reactions 71
Chapter 4. Kinetic Data Acquisition 73 4.1. Experimental kinetic data of a reaction 73 4.2. Generalities on measuring methods 74 4.3. Chemical methods 74 4.4. Physical methods 75 4.4.1. Methods without separation of components 75 4.4.2. Physical methods with separation of components 84 4.4.3. Study of fast reactions 85 4.5. Researching the influence of various variables 87 4.5.1. Ostwald's isolation method 88 4.5.2. Variables separation 88
Chapter 5. Experimental Laws and Calculation of Kinetic Laws of Homogeneous Systems 91 5.1. Experimental laws in homogeneous kinetics 91 5.1.1. Influence of concentrations 92 viii An Introduction to Chemical Kinetics
5.1.2. Influence of temperature 94 5.2. Relationship between the speed of a reaction and the speeds of its elementary steps 95 5.3. Mathematical formulation of speed from a mechanism and experimental conditions 96 5.3.1. Example of resolution of a mechanism in a closed system 96 5.3.2. Example of resolution of a mechanism in an open system with constant concentrations 98 5.4. Mathematical formulation of a homogeneous reaction with open sequence 99 5.4.1. Mathematical formulation in a closed system 99 5.4.2. Mathematical formulation of a system with constant concentrations 100 5.5. Mathematical formulation of chain reactions 101 5.5.1. Mathematical formulation of a simple homogeneous chain reaction 101 5.5.2. Mathematical formulation of a reaction forming a macromolecule through polymerization 103
Chapter 6. Experimental Data and Calculation of Kinetic Laws of Heterogeneous Reactions 109 6.1. Heterogeneous reactions 109 6.1.1. Distinctive nature of heterogeneous systems 109 6.1.2. Rate of a heterogeneous reaction 110 6.1.3. Different kinetic classes of heterogeneous reactions 110 6.2. Experimental kinetic data of heterogeneous reactions 112 6.2.1. Catalytic reactions 113 6.2.2. Stoichiometric heterogeneous gas—solid reactions 116 6.3. Involvement of diffusion in matter balances 119 6.3.1. Balance in a slice of a volume zone 120 6.3.2. Balance in a 2D zone 122 6.3.3. Application of balances to the elementary steps of a sequence of reactions 123 6.3.4. Application to Fick's second law ...... 124 6.4. Example of mathematical formulation of a heterogeneous catalytic reaction 124 6.5. Example of the mathematical formulation of an evolution process of a phase 127 6.5.1. Balance of intermediates 129 6.5.2. Expressions of the reactivities of elementary chemical steps . . . 130 6.5.3. Expressions of the concentrations of species at the interfaces. . . 130 6.5.4. Diffusion equations of the defects 131 Table of Contents ix
6.5.5. Expressions of the variations in sizes of the zones involved in the reaction 132 6.5.6. Evolution law of the rate chosen to characterize the speed 132
Chapter 7. Pseudo- and Quasi-steady State Modes 135 7.1. Pseudo-steady state mode 135 7.1.1. Definition 135 7.1.2. Uniqueness of the reaction speed in pseudo-steady state mode . 136 7.1.3. Linear sequences in pseudo-steady state modes 137 7.1.4. Multipoint sequences in pseudo-steady state mode 140 7.1.5. Experimental research into the pseudo-steady state 141 7.2. Pseudo-steady state sequences with constant volume (or surface) — quasi-steady state 147 7.2.1. Quasi-steady state sequences 147 7.2.2. Linear sequences in quasi-steady state mode 148 7.2.3. Speed of a homogeneous linear sequence in quasi-steady state mode with invariant volume 149 7.2.4. Multipoint sequences in quasi-steady state mode 149 7.3. Pseudo- and quasi-steady state of diffusion 150 7.4. Application to the calculation of speeds in pseudo-steady state or quasi-steady state 151 7.4.1. Principle of the method 151 7.4.2. Example 1: dinitrogen pentoxide decomposition 151 7.4.3. Example 2: hydrogen bromide Synthesis 152 7.4.4. Example 3: polymerization 154 7.4.5. Example 4: application of the pseudo-steady state to a heterogeneous catalytic reaction 156 7.5. Pseudo-steady state and open or closed systems 159 7.5.1. Kinetics law in homogeneous closed systems 159 7.5.2. Kinetics law in heterogeneous closed systems 161 7.5.3. Kinetic laws of open systems with constant concentrations 162 7.6. Conclusion 162 7.7. Important figure in pseudo-steady state 163
Chapter 8. Modes with Rate-determining Steps 165 8.1. Mode with one determining step 166 8.1.1. Definition 166 8.1.2. Concentrations theorem for linear sequences 166 8.1.3. Reactivity of the rate-determining step 170 8.1.4. Rate of reaction 171 x An Introduction to Chemical Kinetics
8.1.5. Calculation of Speed of a linear sequence in pure mode determined by one step 172 8.1.6. Pure modes away from equilibrium for linear sequences 179 8.1.7. Influence of temperature on linear sequences 180 8.1.8. Cyclic sequences 182 8.1.9. Conclusion on modes with a single determining step 183 8.2. Pseudo-steady state mode with two determining steps 185 8.2.1. Definition 185 8.2.2. Mathematical formulation of a mixed pseudo-steady state mode 185 8.2.3. Linear sequences: inverse rate law or the law of slowness 186 8.2.4. Cyclic sequences 188 8.2.5. Law of characteristic times 188 8.3. Generalization to more than two determining steps 189 8.4. Conclusion to the study of modes with one or several rate-determining steps 190 8.5. First order mode changes 190 8.6. Conclusion 191
PART 2. REACTION MECHANISMS AND KINETIC PROPERTIES 193
Chapter 9. Establishment and Resolution of a Reaction Mechanism 195 9.1. Families of reaction mechanisms 195 9.2. Different categories of elementary steps 196 9.2.1. Homolytic bond breaking 196 9.2.2. Heterolytic bond breaking 196 9.2.3. Ion dissociation 196 9.2.4. Radical reactions 197 9.2.5. Ion—molecule reactions 197 9.2.6. Reactions between ions 199 9.2.7. Interface reactions 199 9.2.8. Reaction between structure elements in the solid state 200 9.2.9. Reactions between adsorbed species and point defects 200 9.3. Establishment of a reaction mechanism 201 9.3.1. Methodology 201 9.3.2. Rule no. 1: the law of elimination of intermediates 202 9.3.3. Rule no. 2: the rule of the least change of structure (in the case of a single bond) 203 9.3.4. Rule no. 3: the rule of the greatest simplicity of elementary reactions (bimolecular) 203 bl f C nt nt x
9.3.5. Rule no. 4: the rule involving a single jump into the solid state 204 9.3.6. Rule no. 5: the law of micro-reversibility 204 9.4. Research into a mechanism: intermediary reactions 205 9.4.1. Reaction filiations: primary and non-primary products 205 9.4.2. Labile intermediates 208 9.5. Back to the modes and laws of kinetics 210 9.5.1. Modes with a single rate-determining step 210 9.5.2. Modes with multiple rate-determining steps 211 9.5.3. Pseudo-steady state modes 211 9.5.4. Link between the form of the rate equation and the presence of some elementary steps 211 9.6. Experimental tests 212 9.6.1. Experimental methods 212 9.6.2. The pseudo-steady state mode test 216 9.6.3. Research into the uniqueness of the space function mechanism or 4E test 216 9.7. Looking for the type of rate law 218 9.7.1. Research into the influence of concentrations 218 9.7.2. Research into the influence of temperature 220
Chapter 10. Theory of the Activated Complex in the Gas Phase 223 10.1. The notion of molecular energy: the energy of a group of atoms 223 10.1.1. Energy of a group of two atoms 223 10.1.2. Energy of an even number of atoms 225 10.2.3. Energy of an odd number of atoms 226 10.2. Bimolecular reactions in the gas phase 227 10.2.1. Postulate of the activated molecular collision 228 10.2.2. Potential energy surface 229 10.2.3. Reaction pathways and the equivalent "mass point" 231 10.2.4. Absolute expression of the reaction rate 233 10.2.5. Partition functions of the activated complex 236 10.2.6. Evaluation of the pre-exponential factor 237 10.2.7. Activation energies 239 10.2.8. Units and other forms of the reaction rate coefficient 242 10.3. Monomolecular reactions in the gas phase 243 10.4. Photochemical elementary reactions 248 10.4.1. Grotthus—Draper quantitative law 248 10.4.2. Energetic paths of molecule dissociation 249 10.4.3. Einstein's quantitative law 250 10.4.4. Influence of temperature an photochemical reactions 251 10.5. The theory of activated complexes 252 xii An Introduction to Chemical Kinetics
Chapter 11. Modeling Elementary Reactions in Condensed Phase 253 11.1. Elementary reaction in the liquid phase 253 11.1.1. Generic expression of an elementary-step reaction rate in the liquid phase: the Bronstedt—Bjerrum law 254 11.1.2. Influence of the environment 256 11.1.3. Comparison of the reaction rate in solution and gas phases 257 11.1.4. Reactions between ions in diluted solution 258 11.1.5. Reactions in concentrated solutions: the acidity factor 262 11.2. Elementary reaction in the solid state 268 11.2.1. Potential energy of a solid 268 11.2.2. Reaction pathway 269 11.2.3. Rate of an elementary jump 270 11.2.4. Diffusion in solids 272 11.3. Interphase reactions 276 11.3.1. Gas—solid interphases: adsorption, desorption 276 11.3.2. Solid—solid interface: the concept of epitaxy 277 11.4. Electrochemical reactions 280 11.4.1. Definition 280 11.4.2. Reactivity of an electrochemical reaction 281 11.4.3. The De Donder—Pourbaix inequality 282 11.4.4. Polarization curves 282 11.4.5. Polarization curve equation 285 11.5. Conclusion 290
Chapter 12. The Kinetics of Chain Reactions 291 12.1. Definition of a chain reaction 291 12.2. The kinetic characteristics of chain reactions 292 12.3. Classification of chain reactions 293 12.3.1. Straight or non-branched chain reactions 293 12.3.2. Reactions with direct branching 294 12.3.3. Reactions with indirect branching 294 12.4. Chain reaction sequences 295 12.4.1. Initiation of a chain reaction 295 12.4.2. Propagation of a chain reaction 297 12.4.3. Chain breaking 298 12.4.4. Branching chain reaction 298 12.5. Kinetic study of straight chain or non-branch chain reactions 299 12.5.1. Mean length of the chains 299 12.5.2. Expression of the reaction rate 302 12.5.3. Calculation of the rate and mean length of chains in the reactor 303 bl f C nt nt x
12.5.4. Variation of reaction rate with temperature 310 12.5.5. Permanency of the pseudo-steady state mode and reactant consumption 310 12.6. Kinetic study of chain reactions with direct branching 311 12.6.1. Simplified representation of reactions with direct branching 312 12.6.2. Mean chain lengths: condition of the appearance of a pseudo-steady state 314 12.6.3. Example of a chain reaction with both linear branching and breaking in the bulk 316 12.6.4. Example of the calculation of the measures related to a branching chain reaction 318 12.7. Semenov and the kinetics of chain reactions 321
Chapter 13. Catalysis and Catalyzed Reactions 2 13.1. Homogenous catalysis 324 13.1.1. Specific acid—base catalysis by 11+ and OH- ions 325 13.1.2. Generic acid—base catalysis 327 13.1.3. Catalysis by Lewis acids 329 13.1.4. Redox catalysis 331 13.1.5. Autocatalytic reactions 331 13 1 6 Enzymatic catalysis 332 13.2. Heterogeneous catalysis reactions 335 13.2.1. Experimental laws in heterogeneous catalysis 335 13.2.2. Structure of the mechanism of heterogeneous catalysis 336 13.2.3. Kinetics of the catalytic act 337 13.2.4. Example of the kinetics of catalysis on a porous support 343 13.2.5. Influence of the catalyst surface area: poisoning 350 13.3. Gas—solid reactions leading to a gas 351 13.4. Conclusion on catalysis 352 13.5. Langmiur and Hinshelwood 352
Chapter 14. Kinetics of Heterogeneous Stoichiometric Reactions 353 14.1. Extent versus time and rate versus extent curves 354 14.2. The global model with two processes 355 14.3. The 4 E law 356 14.4. Morphological modeling of the growing space function 357 14.4.1. The hypothesis 357 14.4.2. Types of model involving one or two processes 360 14.4.3. Experimental research on the type of morphological model 372 xiv An Introduction to Chemical Kinetics
14.5. The nucleation process 373 14.5.1. Description of the nucleation process 373 14.5.2. Thermodynamics of nucleation 374 14.5.3. The nucleation mechanism 378 14.5.4. The nucleation rate 380 14.5.5. Surface and nucleation frequencies 383 14.6. Physico-chemical growth models 384 14.7. Conclusion on heterogeneous reactions 386 14.8. Important figures in reaction kinetics 387
Chapter 15. Kinetics of Non-pseudo-steady State Modes 389 15.1. Partial pseudo-steady state modes 389 15.2. The paralinear law of metal oxidation 392 15.3. Thermal runaway and ignition of reactions 395 15.4. Chemical ignition of gaseous mixtures 397 15.4.1. Branched chains with linear branching and chain breaking in the bulk 397 15.4.2. Branched chains with linear branching and breaking in the bulk and heterogeneous breaking on the walls 398
APPENDICES 405
Appendix 1. Point Defects and Structure Elements of Solids 407 A1.1. Point defects of solids 407 A1.2. Definition of a structural element 408 A1.3. Symbolic representation of structure elements 409 A1.4. Reactions involving structure elements in quasi-chemical reactions 411 A1.5. Equilibria and reactivities of quasi-chemical reactions 411
Appendix 2. Notions of Microscopic Thermodynamics 413 A2.1. Molecule distribution between the different energy states 413 A2.2. Partition functions 416 A2.3. Degrees of freedom of a molecule 418 A2.4. Elementary partition functions 418 A2.4.1. Vibration partition function 418 A2.4.2. Rotation partition function 419 A2.4.3. Translation partition function 420 A2.4.4. Order of magnitude of partition functions 420 Table of Contents xv
A2.5. Expression of thermodynamic functions from partition functions 420 A2.5.1. Internal energy 421 A2.5.2. Entropy 421 A2.5.3. Free energy 422 A2.6. Equilibrium constant and partition functions 422
Appendix 3. Vibration Frequency of the Activated Complex 425
Notations and Symbols 431
Bibliography 439
Index 441