Kinetics of Chemical Reactions

Guy B. Marin is professor in Chemical Reaction Engineering at Ghent University (Belgium) and directs the Laboratory for Chemical Technology. The investigation of chemical kinetics constitutes the core of his research. He has co-authored more than 600 papers in high impact journals and is co-inventor in 3 patents. He is editor-in-chief of 'Advances in Chemical Engineering', co-editor of the 'Chemical Engineering Journal' and member of the editorial boards of 'Industrial & Engineering Chemistry Research', 'Current Opinion in Chemical Engineering' and the 'Canadian Journal of Chemical Engineering'. He is member of Scientific Advisory Boards in France, Denmark and the Netherlands. He is 'Master' of the 111 project of the Chinese Government for oversees collaborations in his field. Professor G. Yablonsky is an Associate Research Professor of Chemistry at Parks College and the College of Arts and Sciences. Previously (1997-2007), he was a Research Associate Professor in the Department of Energy, Environmental and Chemical Engineering as Washington University in St. Louis. He is a world recognized expert in the area of chemical kinetics and chemical engineering, in catalytic technology particularly, which is one of main driving forces of sustainable development. He has authored two monographs and more than 200 peer-reviewed papers on these topics. Denis Constales is associate professor of mathematical analysis at Ghent University. His work centres on the application of of integral transforms, special functions and computer algebra to problems ranging from hypercomplex analysis to applied mathematical modelling, with a strong emphasis on topics from chemical engineering and reaction kinetics. He has co-authored two monographs and more than 100 peer-reviewed papers on these subjects.

• Preface to First Edition xvPreface to Second Edition xix1 Introduction 11.1 Overview 11.2 Decoding Complexity in Chemical Kinetics 21.3 Three Types of Chemical Kinetics 21.3.1 Applied Kinetics 31.3.2 Detailed Kinetics 31.3.3 Mathematical Kinetics 31.4 Challenges and Goals. How to Kill Chemical Complexity 41.4.1 “Gray-Box” Approach 41.4.2 Analysis of Kinetic Fingerprints 51.4.3 Non-steady-state Kinetic Screening 61.5 What Our Book is Not About. Our Book among Other Books on Chemical Kinetics 61.6 The Logic in the Reasoning of This Book 71.7 How Chemical Kinetics and Mathematics are Interwoven in This Book 71.8 History of Chemical Kinetics 8References 122 Chemical Reactions and Complexity 172.1 Introduction 172.2 Elementary Reactions and the Mass-Action Law 192.2.1 Homogeneous Reactions 192.2.2 Heterogeneous Reactions 212.2.3 Rate Expressions 222.3 The Reaction Rate and Net Rate of Production of a Component – A Big Difference 232.4 Dimensions of the Kinetic Parameters and Their Orders of Magnitude 242.5 Conclusions 26Nomenclature 26References 283 Kinetic Experiments: Concepts and Realizations 293.1 Introduction 293.2 Experimental Requirements 293.3 Material Balances 303.4 Classification of Reactors for Kinetic Experiments 313.4.1 Steady-state and Non-steady-state Reactors 313.4.2 Transport in Reactors 313.4.3 Ideal Reactors 323.4.3.1 Batch Reactor 323.4.3.2 Continuous Stirred-tank Reactor 333.4.3.3 Plug-flow Reactor 343.4.4 Ideal Reactors with Solid Catalyst 343.4.4.1 Batch Reactor 343.4.4.2 Continuous Stirred-tank Reactor 353.4.4.3 Plug-flow Reactor 353.4.4.4 Pulse Reactor 353.4.5 Determination of the Net Rate of Production 363.5 Formal Analysis of Typical Ideal Reactors 363.5.1 Batch Reactor 363.5.1.1 Irreversible Reaction 363.5.1.2 Reversible Reaction 383.5.1.3 How to Distinguish Parallel Reactions from Consecutive Reactions 403.5.2 Steady-state Plug-flow Reactor 433.5.3 Non-steady-state Continuous Stirred-tank Reactor 433.5.3.1 Irreversible Reaction 433.5.3.2 Reversible Reaction 443.5.4 Thin-zone TAP Reactor 453.6 Kinetic-model-free Analysis 463.6.1 Steady State 463.6.2 Non-steady State 473.6.2.1 Continuous Stirred-tank Reactor 473.6.2.2 Plug-flow Reactor 483.7 Diagnostics of Kinetic Experiments in Heterogeneous Catalysis 493.7.1 Gradients at Reactor and Catalyst-pellet Scale 493.7.2 Experimental Diagnostics and Guidelines 493.7.2.1 Test for External Mass-transfer Effect 513.7.2.2 Test for Internal Mass-transport Effect 513.7.2.3 Guidelines 523.7.3 Theoretical Diagnostics 523.7.3.1 External Mass Transfer 533.7.3.2 External Heat Transfer 543.7.3.3 InternalMass Transport 563.7.3.4 Internal Heat Transport 593.7.3.5 Non-steady-state Operation 59Nomenclature 59References 624 Chemical Book-keeping: Linear Algebra in Chemical Kinetics 654.1 Basic Elements of Linear Algebra 654.2 Linear Algebra and Complexity of Chemical Reactions 674.2.1 Atomic Composition of Chemical Components: Molecules “Consist of” Atoms 684.2.1.1 Molecular Matrix 684.2.1.2 Linear Algebra and Laws of Mass Conservation 684.2.1.3 Key Components and Their Number 704.2.2 Stoichiometry of Chemical Reactions: Reactions “Consist of” Chemical Components 724.2.2.1 Stoichiometric Matrix 724.2.2.2 Difference and Similarity between the Conservation Law for Chemical Elements and the KineticMass-Conservation Law 744.2.2.3 Similarity and Difference between the Numbers of Key Components and the Number of Key Reactions 744.2.3 DetailedMechanism of Complex Reactions: Complex Reactions “Consist of” Elementary Reactions 754.2.3.1 Mechanisms and Horiuti Numbers 754.2.3.2 Matrices and Independent Routes of Complex Reactions 804.3 Concluding Remarks 834.A Book-Keeping Support in Python/SymPy 834.A.1 Skeleton Code Generation 834.A.2 Matrix Augmentation and Reduction 84Nomenclature 88References 905 Steady-State Chemical Kinetics: A Primer 935.1 Introduction to Graph Theory 935.2 Representation of Complex Mechanisms as Graphs 945.2.1 Single-route Mechanisms 955.2.2 Single-route Mechanism with a Buffer Step 975.2.3 Two-route Mechanisms 975.2.4 Number of Independent Reaction Routes and Horiuti’s Rule 995.3 How to Derive the Reaction Rate for a Complex Reaction 1015.3.1 Introduction 1015.3.2 Kinetic Cramer’s Rule and Trees of the Chemical Graph 1045.3.3 Forward and Reverse Reaction Rates 1105.3.4 Single-route LinearMechanism – General Case 1115.3.5 How to Find the Kinetic Equation for the Reverse Reaction: The Horiuti–Boreskov Problem 1125.3.6 What About the Overall Reaction – A Provocative Opinion 1145.4 Derivation of Steady-State Kinetic Equations for a Single-Route Mechanism – Examples 1165.4.1 Two-step Mechanisms 1175.4.1.1 Michaelis–Menten Mechanism 1175.4.1.2 Water–Gas Shift Reaction 1185.4.1.3 Liquid-phase Hydrogenation 1195.4.2 Three-step Mechanisms 1205.4.2.1 Oxidation of Sulfur Dioxide 1205.4.2.2 Coupling Reaction 1215.4.3 Four-step Mechanisms 1225.4.4 Five-step Mechanisms 1245.4.5 Single-route Linear Mechanisms with a Buffer Step 1255.5 Derivation of Steady-State Kinetic Equations for Multi Route Mechanisms: Kinetic Coupling 1265.5.1 Cycles Having a Common Intermediate 1275.5.2 Cycles Having a Common Step 1295.5.3 Cycles Having Two Common Steps 1305.5.4 Different Types of Coupling between Cycles 131Nomenclature 132References 1336 Steady-state Chemical Kinetics:Machinery 1376.1 Analysis of Rate Equations 1376.1.1 Dependence of Parameters on Temperature and Number of Identifiable Parameters 1386.1.2 Simplifying Assumptions 1406.1.2.1 Fast Step 1406.1.2.2 Rate-limiting Step 1416.1.2.3 Quasi-equilibrated Step(s) 1416.1.2.4 Irreversible Step(s) 1426.1.2.5 Dependence of the Reaction Rate on Concentrations 1436.2 Apparent Kinetic Parameters: Reaction Order and Activation Energy 1436.2.1 Definitions 1436.2.2 Two-step Mechanism of an Irreversible Reaction 1456.2.2.1 Apparent Partial Reaction Order 1456.2.2.2 Apparent Activation Energy 1466.2.3 More Examples 1476.2.3.1 Apparent Partial Reaction Order 1476.2.3.2 Apparent Activation Energy 1526.2.4 Some Further Comments 1536.3 How to Reveal Mechanisms Based on Steady-state Kinetic Data 1546.3.1 Assumptions 1546.3.2 Direct and Inverse Problems of Kinetic Modeling 1556.3.3 Minimal and Non-minimal Mechanisms 1556.3.3.1 Two-step Catalytic Mechanisms 1566.3.3.2 Three-step Catalytic Mechanisms 1566.3.3.3 Four-step Catalytic Mechanisms 1576.3.3.4 Five-step Catalytic Mechanisms 1586.3.3.5 Summary 1586.3.4 What Kind of Kinetic Model Do We Need to Describe Steady-state Kinetic Data and to Decode Mechanisms? 1596.3.4.1 Kinetic Resistance 1596.3.4.2 Analysis of the Kinetic Resistance in Identifying and Decoding Mechanisms and Models 1606.3.4.3 Concentration Terms of the Kinetic Resistance and Structure of the Detailed Mechanism 1606.3.4.4 Principle of Component Segregation 1646.4 Concluding Remarks 165Nomenclature 166References 1677 Linear and Nonlinear Relaxation: Stability 1697.1 Introduction 1697.1.1 Linear Relaxation 1717.1.2 Relaxation Times and Steady-state Reaction Rate 1737.1.2.1 Relaxation Times and Kinetic Resistance 1737.1.2.2 Temkin’s Rule. Is it Valid? 1747.1.3 Further comments 1767.2 Relaxation in a Closed System − Principle of Detailed Equilibrium 1777.3 Stability – General Concept 1807.3.1 Elements of the Qualitative Theory of Differential Equations 1807.3.2 Local Stability – Rigorous Definition 1827.3.3 Local Stability – System with two Variables 1847.3.3.1 Real Roots 1867.3.3.2 Imaginary Roots 1877.3.4 Self-sustained Oscillations and Global Dynamics 1887.4 Simplifications of Non-steady-state Models 1907.4.1 Abundance and Linearization 1907.4.2 Fast Step − Equilibrium Approximation 1917.4.3 Rate-limiting Step Approximation 1917.4.4 Quasi-steady-state Approximation 192Nomenclature 198References 2008 Nonlinear Mechanisms: Steady State and Dynamics 2038.1 Critical Phenomena 2038.2 Isothermal Critical Effects in Heterogeneous Catalysis: Experimental Facts 2058.2.1 Multiplicity of Steady States 2058.2.2 Self-sustained Oscillations of the Reaction Rate in Heterogeneous Catalytic Reactions 2078.2.3 Diversity of Critical Phenomena and Their Causes 2078.3 Ideal Simple Models: Steady State 2098.3.1 Parallel and Consecutive Adsorption Mechanisms 2098.3.2 Impact Mechanisms 2108.3.3 Simplest Mechanism for the Interpretation of Multiplicity of Steady States 2128.3.4 Hysteresis: Influence of Reaction Reversibility 2188.3.5 Competition of Intermediates 2238.4 Ideal Simple Models: Dynamics 2278.4.1 Relaxation Characteristics of the Parallel Adsorption Mechanism 2278.4.2 Catalytic Oscillators 2348.4.2.1 Simplest Catalytic Oscillator 2348.4.2.2 Relaxation of Self-sustained Oscillation: Model 2398.4.2.3 Other Catalytic Oscillators 2398.4.3 Fine Structure of Kinetic Dependences 2428.5 Structure of Detailed Mechanism and Critical Phenomena: Relationships 2448.5.1 Mechanisms without Interaction between Intermediates 2458.5.2 Horn–Jackson–Feinberg Mechanism 2478.6 Nonideal Factors 2508.7 Conclusions 251Nomenclature 251References 2539 Kinetic Polynomials 2639.1 Linear Introduction to the Nonlinear Problem: Recap 2639.2 Nonlinear Introduction 2669.3 Principles of the Approach: Quasi-Steady-State Approximation. Mathematical Basis 2679.3.1 Introduction 2679.3.2 Examples 2699.4 Kinetic Polynomials: Derivation and Properties 2709.4.1 Resultant Reaction Rate: A Necessary Mathematical Basis 2709.4.2 Properties of the Kinetic Polynomial 2729.4.3 Examples of Kinetic Polynomials 2739.4.3.1 Impact Mechanism 2739.4.3.2 Adsorption Mechanism 2749.5 Kinetic Polynomial: Classical Approximations and Simplifications 2769.5.1 Rate-limiting Step 2769.5.2 Vicinity of Thermodynamic Equilibrium 2789.5.3 Thermodynamic Branch 2799.6 Application of Results of the Kinetic-polynomial Theory: Cycles across an Equilibrium 2829.7 Critical Simplification 2899.7.1 Critical Simplification: A Simple Example 2899.7.2 Critical Simplification and Limitation 2959.7.3 Principle of Critical Simplification: General Understanding and Application 2969.8 Concluding Remarks 2979.A Appendix 298Nomenclature 299References 30110 Temporal Analysis of Products: Principles, Applications, and Theory 30710.1 Introduction 30710.2 Characteristics of TAP 30910.2.1 The TAP Experiment 30910.2.2 Description and Operation of a TAP Reactor System 31010.2.3 Basic Principles of TAP 31210.3 Position of TAP among Other Kinetic Methods 31410.3.1 Uniformity of the Active Zone 31510.3.1.1 Continuous Stirred-tank Reactor 31510.3.1.2 Plug-flow Reactor 31510.3.1.3 TAP Reactor 31510.3.2 Domain of Conditions 31510.3.3 Possibility of Obtaining Relevant Kinetic Information 31610.3.4 Relationship between Observed Kinetic Characteristics and Catalyst Properties 31610.3.5 Model-Free Kinetic Interpretation of Data 31710.3.6 Summary of the Comparison 31810.3.7 Applications of TAP 31810.4 Qualitative Analysis of TAP Data: Examples 31810.4.1 Single-pulse TAP Experiments 31910.4.2 Pump-probe TAP Experiments 32210.4.3 Multipulse TAP Experiments 32410.5 Quantitative TAP Data Description.Theoretical Analysis 32610.5.1 One-Zone Reactor 32710.5.1.1 Diffusion Only 32710.5.1.2 Irreversible Adsorption 33010.5.1.3 Reversible Adsorption 33110.5.2 Two- and Three-Zone Reactors 33210.5.3 Thin-Zone TAP Reactor Configuration 33310.5.4 Moment-Based Quantitative Description of TAP Experiments 33610.5.4.1 Moments and Reactivities 33610.5.4.2 From Moments to Reactivities 34210.5.4.3 Experimental Procedure 34510.5.4.4 Summary 34810.6 Kinetic Monitoring: Strategy of Interrogative Kinetics 34810.6.1 State-by-state Kinetic Monitoring. Example: Oxidation of Furan 34810.6.2 Strategy of Interrogative Kinetics 35210.7 Theoretical Frontiers 35310.7.1 Global Transfer Matrix Equation 35310.7.2 Y Procedure 35410.7.2.1 Principles of the Solution 35510.7.2.2 Exact Mathematical Solution 35810.7.2.3 How to Reconstruct the Active Zone Concentration and Net Rate of Production in Practice 35910.7.2.4 Numerical Experiments 36110.7.2.5 Summary of the Y Procedure 36410.7.3 Probabilistic Theory of Single-particle TAP Experiments 36610.8 Conclusions:What Next? 367Nomenclature 368References 37111 Joint Kinetics 38311.1 Events and Invariances 38311.2 Single Reaction 38411.2.1 Batch Reactor 38411.2.1.1 Basics 38411.2.1.2 Point of Intersection 38611.2.1.3 Swapping the Equilibrium 38711.2.2 Continuous Stirred-tank Reactor 38811.2.2.1 Basis 38811.2.2.2 Point of Intersection 38811.2.3 Invariances 38911.3 Multiple Reactions 39111.3.1 Events: Intersections and Coincidences 39111.3.2 Mathematical Solutions of Kinetic Models 39311.3.2.1 Batch Reactor 39311.3.2.2 Continuous Stirred-tank Reactor 39411.3.3 First Stage: Occurrence of Single Kinetic Events 39411.3.4 Second Stage: Coincidences: Ordering Events by Pairs 39711.3.5 End Products Intersection: Intersection of B and C 40211.3.6 Invariances 403Nomenclature 405References 40612 Decoding the Past 40712.1 Chemical Time and Intermediates. Early History 40712.2 Discovery of Catalysis and Chemical Kinetics 40712.3 Guldberg and Waage’s Breakthrough 40912.4 Van’t Hoff’s Revolution: Achievements and Contradictions 40912.4.1 Undisputable Achievements 40912.4.2 Contradictions 41012.5 Post-Van’t Hoff Period: Reaction is Not a Single-act Drama 41112.6 All-in-all Confusion. Attempts at Understanding 41112.7 Out of Confusion: Physicochemical Understanding 41212.8 Towards Mathematical Chemical Kinetics 414Nomenclature 418References 41913 Decoding the Future 42513.1 A Great Achievement, a Great Illusion 42513.2 A New Paradigm for Decoding Chemical Complexity 42613.2.1 Advanced Experimental Kinetic Tools 42713.2.2 New Mathematical Tools. Chemical Kinetics and Mathematics 428References 430Index 433