An Introduction to Chemical Kinetics

Transcription

1 An Introduction to Chemical Kinetics Michel Soustelle WWILEY

2 Table of Contents Preface xvii PART 1. BASIC CONCEPTS OF CHEMICAL KINETICS 1 Chapter 1. Chemical Reaction and Kinetic Quantities The chemical reaction The chemical equation and stoichiometric coefficients The reaction components Reaction zones Homogeneous and heterogeneous reactions Single zone reaction Multizone reaction Extent and speed of a reaction Stoichiometric abundance of a component in a reaction mixture Extent of a reaction Speed of a reaction Volumetric and areal speed of a monozone reaction Fractional extent and rate of a reaction The fractional extent of a reaction Rate of a reaction Expression of the volumetric speed (areal) from variations in the amount of a component Reaction Speeds and concentrations Concentration of a component in a zone Relationship between concentration and fractional extent in a closed environment 19

3 vi An Introduction to Chemical Kinetics 1.7. Expression of volumetric speed according to variations in concentration in a closed system 1.8. Stoichiometric mixtures and progress 1.9. Factors influencing reaction speeds 1.9.L Influence of temperature Influence of the concentrations (or partial pressures of gases) Other variables Chapter 2. Reaction Mechanisms and Elementary Steps 2.1. Basic premise of kinetics Reaction mechanism Definition Examples of mechanisms Reaction intermediates Excited atoms (or molecules) Free radicals Ions Adsorbed species Point defects The effect of intermediates an extent and speeds Reaction sequences and Semenov representation Semenov diagram Linear sequences and multipoint sequences Chain reactions Definition The different categories of chain reactions The steps in a chain reaction Sequence of chain reactions Reactions of macromolecule formation Catalytic reactions Homogeneous catalysis Heterogeneous catalysis Important figures in reaction mechanisms 41 Chapter 3. Kinetic Properties of Elementary Reactions Space function of an elementary reaction Reactivity and rate of an elementary step Kinetic constants of an elementary step Expression of reactivity as a function of concentrations Rate factor of an elementary reaction Opposite elementary reactions 47 25

4 Table of Contents vii Reactivity of two opposite elementary reactions ' Distance from equilibrium conditions Principle of partial equilibria Influence of temperature on the reactivities of elementary steps Influence of temperature near the equilibrium Activation energies of opposite elementary reactions and reaction enthalpy Modeling of a gas phase elementary step Collision theory Theory of activated complex A particular elementary step: diffusion The diffusion phenomenon Diffusion flux and Fick's first law Diffusion flux in a steady state system Reactivity and diffusion space function Diffusion in solids Interdiffusion of gases Diffusion of a gas in a cylindrical pore Gases adsorption onto solids Chemisorption equilibrium: Langmuir model Dissociative adsorption and the Langmuir model Chemisorption of gas mixtures in the Langmuir model Chemisorption kinetic in the Langmuir model Important figures in the kinetic properties of elementary reactions 71 Chapter 4. Kinetic Data Acquisition Experimental kinetic data of a reaction Generalities on measuring methods Chemical methods Physical methods Methods without separation of components Physical methods with separation of components Study of fast reactions Researching the influence of various variables Ostwald's isolation method Variables separation 88 Chapter 5. Experimental Laws and Calculation of Kinetic Laws of Homogeneous Systems Experimental laws in homogeneous kinetics Influence of concentrations 91 92

5 viii An Introduction to Chemical Kinetics Influence of temperature Relationship between the speed of a reaction and the speeds of its elementary steps Mathematical formulation of speed from a mechanism and experimental conditions Example of resolution of a mechanism in a closed system Example of resolution of a mechanism in an open system with constant concentrations Mathematical formulation of a homogeneous reaction with open sequence Mathematical formulation in a closed system Mathematical formulation of a system with constant concentrations Mathematical formulation of chain reactions Mathematical formulation of a simple homogeneous chain reaction Mathematical formulation of a reaction forming a macromolecule through polymerization 103 Chapter 6. Experimental Data and Calculation of Kinetic Laws of Heterogeneous Reactions Heterogeneous reactions Distinctive nature of heterogeneous systems Rate of a heterogeneous reaction Different kinetic classes of heterogeneous reactions Experimental kinetic data of heterogeneous reactions Catalytic reactions Stoichiometric heterogeneous gas solid reactions Involvement of diffusion in matter balances Balance in a slice of a volume zone Balance in a 2D zone Application of balances to the elementary steps of a sequence of reactions Application to Fick's second law Example of mathematical formulation of a heterogeneous catalytic reaction Example of the mathematical formulation of an evolution process of a phase Balance of intermediates Expressions of the reactivities of elementary chemical steps Expressions of the concentrations of species at the interfaces Diffusion equations of the defects 131

6 Table of Contents ix Expressions of the variations in sizes of the zones involved in the reaction Evolution law of the rate chosen to characterize the speed 132 Chapter 7. Pseudo- and Quasi-steady State Modes Pseudo-steady state mode Definition Uniqueness of the reaction speed in pseudo-steady state mode Linear sequences in pseudo-steady state modes Multipoint sequences in pseudo-steady state mode Experimental research into the pseudo-steady state Pseudo-steady state sequences with constant volume (or surface) quasi-steady state Quasi-steady state sequences Linear sequences in quasi-steady state mode Speed of a homogeneous linear sequence in quasi-steady state mode with invariant volume Multipoint sequences in quasi-steady state mode Pseudo- and quasi-steady state of diffusion Application to the calculation of speeds in pseudo-steady state or quasi-steady state Principle of the method Example 1: dinitrogen pentoxide decomposition Example 2: hydrogen bromide Synthesis Example 3: polymerization Example 4: application of the pseudo-steady state to a heterogeneous catalytic reaction Pseudo-steady state and open or closed systems Kinetics law in homogeneous closed systems Kinetics law in heterogeneous closed systems Kinetic laws of open systems with constant concentrations Conclusion Important figure in pseudo-steady state 163 Chapter 8. Modes with Rate-determining Steps Mode with one determining step Definition Concentrations theorem for linear sequences Reactivity of the rate-determining step Rate of reaction 171

7 x An Introduction to Chemical Kinetics Calculation of Speed of a linear sequence in pure mode determined by one step Pure modes away from equilibrium for linear sequences Influence of temperature on linear sequences Cyclic sequences Conclusion on modes with a single determining step Pseudo-steady state mode with two determining steps Definition Mathematical formulation of a mixed pseudo-steady state mode Linear sequences: inverse rate law or the law of slowness Cyclic sequences Law of characteristic times Generalization to more than two determining steps Conclusion to the study of modes with one or several rate-determining steps First order mode changes Conclusion 191 PART 2. REACTION MECHANISMS AND KINETIC PROPERTIES 193 Chapter 9. Establishment and Resolution of a Reaction Mechanism Families of reaction mechanisms Different categories of elementary steps Homolytic bond breaking Heterolytic bond breaking Ion dissociation Radical reactions Ion molecule reactions Reactions between ions Interface reactions Reaction between structure elements in the solid state Reactions between adsorbed species and point defects Establishment of a reaction mechanism Methodology Rule no. 1: the law of elimination of intermediates Rule no. 2: the rule of the least change of structure (in the case of a single bond) Rule no. 3: the rule of the greatest simplicity of elementary reactions (bimolecular) 203

8 Table of Contents xi Rule no. 4: the rule involving a single jump into the solid state Rule no. 5: the law of micro-reversibility Research into a mechanism: intermediary reactions Reaction filiations: primary and non-primary products Labile intermediates Back to the modes and laws of kinetics Modes with a single rate-determining step Modes with multiple rate-determining steps Pseudo-steady state modes Link between the form of the rate equation and the presence of some elementary steps Experimental tests Experimental methods The pseudo-steady state mode test Research into the uniqueness of the space function mechanism or 4E test Looking for the type of rate law Research into the influence of concentrations Research into the influence of temperature 220 Chapter 10. Theory of the Activated Complex in the Gas Phase The notion of molecular energy: the energy of a group of atoms Energy of a group of two atoms Energy of an even number of atoms Energy of an odd number of atoms Bimolecular reactions in the gas phase Postulate of the activated molecular collision Potential energy surface Reaction pathways and the equivalent "mass point" Absolute expression of the reaction rate Partition functions of the activated complex Evaluation of the pre-exponential factor Activation energies Units and other forms of the reaction rate coefficient Monomolecular reactions in the gas phase Photochemical elementary reactions Grotthus Draper quantitative law Energetic paths of molecule dissociation Einstein's quantitative law Influence of temperature an photochemical reactions The theory of activated complexes 252

9 xii An Introduction to Chemical Kinetics Chapter 11. Modeling Elementary Reactions in Condensed Phase Elementary reaction in the liquid phase Generic expression of an elementary-step reaction rate in the liquid phase: the Bronstedt Bjerrum law Influence of the environment Comparison of the reaction rate in solution and gas phases Reactions between ions in diluted solution Reactions in concentrated solutions: the acidity factor Elementary reaction in the solid state Potential energy of a solid Reaction pathway Rate of an elementary jump Diffusion in solids Interphase reactions Gas solid interphases: adsorption, desorption Solid solid interface: the concept of epitaxy Electrochemical reactions Definition Reactivity of an electrochemical reaction The De Donder Pourbaix inequality Polarization curves Polarization curve equation Conclusion 290 Chapter 12. The Kinetics of Chain Reactions Definition of a chain reaction The kinetic characteristics of chain reactions Classification of chain reactions Straight or non-branched chain reactions Reactions with direct branching Reactions with indirect branching Chain reaction sequences Initiation of a chain reaction Propagation of a chain reaction Chain breaking Branching chain reaction Kinetic study of straight chain or non-branch chain reactions Mean length of the chains Expression of the reaction rate Calculation of the rate and mean length of chains in the reactor 303

10 Table of Contents xiii Variation of reaction rate with temperature Permanency of the pseudo-steady state mode and reactant consumption Kinetic study of chain reactions with direct branching Simplified representation of reactions with direct branching Mean chain lengths: condition of the appearance of a pseudo-steady state Example of a chain reaction with both linear branching and breaking in the bulk Example of the calculation of the measures related to a branching chain reaction Semenov and the kinetics of chain reactions 321 Chapter 13. Catalysis and Catalyzed Reactions Homogenous catalysis Specific acid base catalysis by 11+ and OH- ions Generic acid base catalysis Catalysis by Lewis acids Redox catalysis Autocatalytic reactions Enzymatic catalysis Heterogeneous catalysis reactions Experimental laws in heterogeneous catalysis Structure of the mechanism of heterogeneous catalysis Kinetics of the catalytic act Example of the kinetics of catalysis on a porous support Influence of the catalyst surface area: poisoning Gas solid reactions leading to a gas Conclusion on catalysis Langmiur and Hinshelwood 352 Chapter 14. Kinetics of Heterogeneous Stoichiometric Reactions Extent versus time and rate versus extent curves The global model with two processes The 4,E law Morphological modeling of the growing space function The hypothesis Types of model involving one or two processes Experimental research on the type of morphological model 372

11 xiv An Introduction to Chemical Kinetics The nucleation process Description of the nucleation process Thermodynamics of nucleation The nucleation mechanism The nucleation rate Surface and nucleation frequencies Physico-chemical growth models Conclusion on heterogeneous reactions Important figures in reaction kinetics 387 Chapter 15. Kinetics of Non-pseudo-steady State Modes Partial pseudo-steady state modes The paralinear law of metal oxidation Thermal runaway and ignition of reactions Chemical ignition of gaseous mixtures Branched chains with linear branching and chain breaking in the bulk 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 A Vibration partition function 418 A Rotation partition function 419 A Translation partition function 420 A Order of magnitude of partition functions 420

12 Table of Contents xv A2.5. Expression of thermodynamic functions from partition functions 420 A Internal energy 421 A Entropy 421 A 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