Table of Contents Cover Preface to First Edition Preface to Second Edition 1 Introduction 1.1 Overview 1.2 Decoding Complexity in Chemical Kinetics 1.3 Three Types of Chemical Kinetics 1.4 Challenges and Goals. How to Kill Chemical Complexity 1.5 What Our Book is Not About. Our Book Among Other Books on Chemical Kinetics 1.6 The Logic in the Reasoning of This Book 1.7 How Chemical Kinetics and Mathematics are Interwoven in This Book 1.8 History of Chemical Kinetics References 2 Chemical Reactions and Complexity 2.1 Introduction 2.2 Elementary Reactions and the MassAction Law 2.3 The Reaction Rate and Net Rate of Production of a Component – A Big Difference 2.4 Dimensions of the Kinetic Parameters and Their Orders of Magnitude 2.5 Conclusions Nomenclature References 3 Kinetic Experiments: Concepts and Realizations 3.1 Introduction 3.2 Experimental Requirements 3.3 Material Balances 3.4 Classification of Reactors for Kinetic Experiments 3.5 Formal Analysis of Typical Ideal Reactors 3.6 Kineticmodelfree Analysis 3.7 Diagnostics of Kinetic Experiments in Heterogeneous Catalysis Nomenclature References 4 Chemical Bookkeeping: Linear Algebra in Chemical Kinetics* 4.1 Basic Elements of Linear Algebra 4.2 Linear Algebra and Complexity of Chemical Reactions 4.3 Concluding Remarks BookKeeping Support in Python/SymPy Nomenclature References 5 SteadyState Chemical Kinetics: A Primer 5.1 Introduction to Graph Theory 5.2 Representation of Complex Mechanisms as Graphs 5.3 How to Derive the Reaction Rate for a Complex Reaction 5.4 Derivation of SteadyState Kinetic Equations for a SingleRoute Mechanism – Examples 5.5 Derivation of SteadyState Kinetic Equations for Multi Route Mechanisms: Kinetic Coupling Nomenclature References 6 Steadystate Chemical Kinetics: Machinery 6.1 Analysis of Rate Equations 6.2 Apparent Kinetic Parameters: Reaction Order and Activation Energy 6.3 How to Reveal Mechanisms Based on Steadystate Kinetic Data 6.4 Concluding Remarks Nomenclature References 7 Linear and Nonlinear Relaxation: Stability 7.1 Introduction 7.2 Relaxation in a Closed System − Principle of Detailed Equilibrium 7.3 Stability – General Concept 7.4 Simplifications of Nonsteadystate Models Nomenclature References 8 Nonlinear Mechanisms: Steady State and Dynamics 8.1 Critical Phenomena 8.2 Isothermal Critical Effects in Heterogeneous Catalysis: Experimental Facts 8.3 Ideal Simple Models: Steady State 8.4 Ideal Simple Models: Dynamics 8.5 Structure of Detailed Mechanism and Critical Phenomena: Relationships 8.6 Nonideal Factors 8.7 Conclusions Nomenclature References 9 Kinetic Polynomials 9.1 Linear Introduction to the Nonlinear Problem: Recap 9.2 Nonlinear Introduction 9.3 Principles of the Approach: QuasiSteadyState Approximation. Mathematical Basis 9.4 Kinetic Polynomials: Derivation and Properties 9.5 Kinetic Polynomial: Classical Approximations and Simplifications 9.6 Application of Results of the KineticPolynomial Theory: Cycles Across an Equilibrium 9.7 Critical Simplification 9.8 Concluding Remarks Appendix Nomenclature References 10 Temporal Analysis of Products: Principles, Applications, and Theory 10.1 Introduction 10.2 Characteristics of TAP 10.3 Position of TAP Among Other Kinetic Methods 10.4 Qualitative Analysis of TAP Data: Examples 10.5 Quantitative TAP Data Description. Theoretical Analysis 10.6 Kinetic Monitoring: Strategy of Interrogative Kinetics 10.7 Theoretical Frontiers 10.8 Conclusions: What Next? Nomenclature References 11 Joint Kinetics 11.1 Events and Invariances 11.2 Single Reaction 11.3 Multiple Reactions Nomenclature References 12 Decoding the Past 12.1 Chemical Time and Intermediates. Early History 12.2 Discovery of Catalysis and Chemical Kinetics 12.3 Guldberg and Waage's Breakthrough 12.4 Van't Hoff's Revolution: Achievements and Contradictions 12.5 PostVan't Hoff Period: Reaction is Not a Singleact Drama 12.6 Allinall Confusion. Attempts at Understanding 12.7 Out of Confusion: Physicochemical Understanding 12.8 Towards Mathematical Chemical Kinetics Nomenclature References 13 Decoding the Future 13.1 A Great Achievement, a Great Illusion 13.2 A New Paradigm for Decoding Chemical Complexity References Index End User License Agreement List of Tables Chapter 01 Table 1.1 Important events in the development of chemical kinetics in the nineteenth and twentieth century. Chapter 02 Table 2.1 Elementary steps in the oxidation of hydrogen. Table 2.2 Elementary steps in steam reforming of methane. Table 2.3 Dimension of the rate coefficient k for homogeneous reactions. Table 2.4 Rate coefficients for firstorder homogeneous reactions. Table 2.5 Activation energies for firstorder homogeneous reactions. Chapter 04 Table 4.1 Catalytic cycle, Horiuti numbers, and overall reaction for the twostep WGS reaction. Table 4.2 Catalytic cycle, Horiuti numbers, and overall reaction for the model isomerization reaction. Table 4.3 Catalytic cycle, Horiuti numbers, and overall reaction for the synthesis of vinyl chloride from acetylene. Table 4.4 Catalytic cycle, Horiuti numbers, and overall reaction for the synthesis of ammonia according to the dissociative mechanism. Table 4.5 Catalytic cycle, Horiuti numbers, and overall reaction for the oxidation of carbon monoxide. Table 4.6 Catalytic cycle, Horiuti numbers, and overall reaction on a catalyst with two types of active sites. Table 4.7 Catalytic cycle, Horiuti numbers, and overall reactions for steam reforming of methane. Table 4.8 Use of Horiuti's rule to determine the number of reaction routes. Chapter 05 Table 5.1 Catalytic cycle, Horiuti numbers, and overall reaction for the Michaelis– Menten mechanism. Table 5.2 Catalytic cycle, Horiuti numbers, and overall reaction for the WGS reaction. Table 5.3 Catalytic cycle, Horiuti numbers, and overall reaction for a liquidphase hydrogenation. Table 5.4 Catalytic cycle, Horiuti numbers, and overall reaction for the model isomerization reaction. Table 5.5 Catalytic cycle, Horiuti numbers, and overall reaction for the oxidation of hydrogen. Table 5.6 Catalytic cycle, Horiuti numbers, and overall reaction for the synthesis of vinyl chloride from acetylene. Table 5.7 Catalytic cycle, Horiuti numbers, and overall reactions for the reaction of NO with CO. Table 5.8 Catalytic cycle, Horiuti numbers, and overall reactions for the dehydrogenation of butane. Table 5.9 Catalytic cycle, Horiuti numbers, and overall reactions for steam reforming of methane. Table 5.10 Catalytic cycle, Horiuti numbers, and overall reactions for the catalytic a b reforming of nhexane. , Table 5.11 Sequences of reactions in catalytic reforming of nhexane. Table 5.12 Catalytic cycle, Horiuti numbers, and overall reaction for the twostep Temkin–Boudart mechanism. Table 5.13 Catalytic cycle, Horiuti numbers, and overall reaction for the twostep mechanism for the oxidation of SO . 2 Table 5.14 Catalytic cycle, Horiuti numbers, and overall reaction for a hypothetical isomerization mechanism. Chapter 08 Table 8.1 Parallel and consecutive adsorption mechanisms; A and B are gaseous m n reactants, A B and A B are gaseous products, Z is a free active site and AZ, BZ, p q p+q q and ABZ are surface intermediates. Table 8.2 Parallel adsorption mechanism for the oxidation of CO over platinum. Table 8.3 Example of an impact mechanism; A and B are gaseous reactants, A B is a m n gaseous product, and Z and AZ are surface intermediates. Table 8.4 Impact mechanism for the oxidation of CO over platinum. Table 8.5 Impact mechanism for the WGS reaction. Table 8.6 Parallel adsorption mechanism for reaction of A with B. 2 Table 8.7 Steadystate reaction rates. Table 8.8 Steady states of the parallel adsorption mechanism. Table 8.9 Characteristics of “realistic” parallel adsorption mechanisms: necessary conditions for steady states (ss) and number of steady states (for ); bss, boundary steady state; iss, internal steady state. Table 8.10 Mechanisms explaining the multiplicity of steady states. Table 8.11 Simplest consecutive adsorption mechanism exhibiting multiple steady states, with m = n = q = 1 and p = 2. Table 8.12 Possible adsorption mechanism, with a buffer step, for the overall reaction . Table 8.13 Adsorption mechanism with a buffer step. Table 8.14 Representation of the Turner–Sales–Maple mechanism for CO oxidation [41, 101–103]. Table 8.15 Representation of the mechanism for CO oxidation proposed by Ertl et al. [56–59]. Table 8.16 Representation of the mechanism for CO oxidation proposed by Vishnevskii and Savchenko [63, 152]. Table 8.17 Catalytic cycle, Horiuti numbers, and overall reaction for the oxidation of hydrogen. Chapter 09 Table 9.1 Catalytic cycle, Horiuti numbers, and overall reaction for an impact mechanism. Table 9.2 Catalytic cycle, Horiuti numbers, and overall reaction for an adsorption mechanism. Table 9.3 Catalytic cycle, Horiuti numbers, and overall reaction for a tworoute mechanism. Table 9.4 Catalytic cycle, Horiuti numbers, and overall reaction for the oxidation of carbon monoxide. Chapter 10 Table 10.1 Position of the TAP approach among other kinetic approaches. Table 10.2 Applications and theory of the TAP reactor including the corresponding catalytic materials tested. Updated from Gleaves et. al 2010 [30]. Table 10.3 Catalysts, mechanisms, and parameters derived for various oxidation reactions. Table 10.4 Catalysts, mechanisms, and parameters derived for NOx abatement reactions. Table 10.5 Basic kinetic coefficients for different detailed mechanisms. Table 10.6 Possible measurement scenarios for the reaction of A to product B. Table 10.7 Average moments and reactivities at different temperatures. Chapter 11 Table 11.1 Time invariances for some single nonlinear reversible reactions. Table 11.2 Conditions of occurrence and time values for possible events in the concentration versus time plot in the BR. Table 11.3 Conditions of occurrence and time values for possible events in the rate versus time plot in the BR. Table 11.4 Conditions of occurrence and time values for possible events in the concentration versus time plot in the CSTR. Table 11.5 Conditions of occurrence and time values for possible events in the rate versus time plot in the CSTR. Table 11.6 Color guide for the occurrence of events in the barycentric plots of Figures 11.2 and 11.3. List of Illustrations Chapter 01 Figure 1.1 Building blocks of this book. Chapter 03 Figure 3.1 Reactors for kinetic experiments: (a) batch reactor; (b) continuous stirred tank reactor; (c) continuousflow reactor with recirculation; (d) plugflow reactor; (e) differential plugflow reactor; (f) convectional pulse reactor; (g) diffusional pulse reactor or TAP reactor; and (h) thinzone TAP reactor. Figure 3.2 Temporal kinetic dependences in a batch reactor for the reaction with . Figure 3.3 Temporal kinetic dependences in a batch reactor for the reversible reaction (lower curve) compared with the irreversible reaction (upper curve); k = k + = 1 s−1, k − = 0.7 s−1. Figure 3.4 (a) Parallel reactions and (b) consecutive reactions. Figure 3.5 Qualitative temporal kinetic dependences in a batch reactor for the parallel mechanism. Figure 3.6 Qualitative temporal kinetic dependences in a batch reactor for the consecutive mechanism. Figure 3.7 Typical temperature and axial concentration profiles for an exothermic consecutive reaction in a tubular reactor; T , T , and T are the inlet, peak, and outlet temperatures, in peak out respectively. Figure 3.8 Interphase and intraparticle reactant concentration and temperature profiles for an exothermic reaction. The resistances against mass and heat transfer are completely located in a stagnant gas film surrounding the pellet; δ is the film thickness; subscripts b and s denote bulk fluid and catalyst surface, respectively. Figure 3.9 Diagnostic test for external concentration gradients. Figure 3.10 Dependence of the observed reaction rate on the diameter of the catalyst pellet. Chapter 05 Figure 5.1 Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges (left) and abstracted case (right). Figure 5.2 The “badneighbors” problem. Figure 5.3 (a) Mechanism and (b) King–Altman graph of a singleroute enzyme catalyzed reaction. Figure 5.4 Graphs of linear mechanisms. (a) Michaelis–Menten mechanism; (b) WGS reaction; (c) liquidphase hydrogenation; (d) model isomerization reaction; and (e) hydrogen oxidation. Figure 5.5 Catalytic cycle and Horiuti numbers (a) and graph (b) for the modified Michaelis–Menten mechanism. Figure 5.6 Graphs of tworoute linear mechanisms – (a) with a common intermediate: synthesis of vinyl chloride; (b) with a common step: reaction of NO with CO; (c) with a common step: dehydrogenation of butane; and (d) with a common intermediate: steam reforming of methane. Roman numbers indicate the different routes. Figure 5.7 Survey of single and tworoute mechanisms; singleroute mechanism (a) without buffer step and (b) with buffer step X  Y ; tworoute mechanism (c) with a common intermediate X, (d) with a common step, (e) with buffer step Y  Z , and (f) with “bridge” step X  Y connecting two cycles. Roman numbers indicate the different routes. Figure 5.8 Catalytic reforming of nhexane over a supported Pt catalyst: (a) graph and (b) simplified graph. The accompanying consumption or production of hydrogen is not shown. Figure 5.9 Catalytic reforming of nhexane over a supported Pt catalyst: (a) the seven independent simple cycles and (b) examples of dependent simple cycles. Figure 5.10 (a) Mechanism and (b) King–Altman graph of the model isomerization reaction. Figure 5.11 Spanning trees of the model isomerization reaction of Figure 5.10: (a) forward; (b) reverse; and (c) combined. Figure 5.12 (a) Michaelis–Menten mechanism and (b) graph. Figure 5.13 (a) Mechanism and (b) graph of the WGS reaction. Figure 5.14 (a) Mechanism and (b) graph of a liquidphase hydrogenation. Figure 5.15 (a) Possible mechanism and (b) graph for the oxidation of SO . 2 Figure 5.16 (a) Possible mechanism and (b) graph for a coupling reaction. Figure 5.17 (a) Possible mechanism and (b) graph for steam reforming of methane.