An introduction to chemical kinetics

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An Introduction to Chemical Kinetics

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www.pdfgrip.com


An Introduction
to
Chemical Kinetics

Michel Soustelle

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First published 2011 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
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© ISTE Ltd 2011
The rights of Michel Soustelle to be identified as the author of this work have been asserted by him in
accordance with the Copyright, Designs and Patents Act 1988.
____________________________________________________________________________________
Library of Congress Cataloging-in-Publication Data
Soustelle, Michel.
An introduction to chemical kinetics / Michel Soustelle.
p. cm.
"Adapted and updated from Cinétique chimique : éléments fondamentaux & Mécanismes réactionnels et
cinétique chimique published 2011 in France by Hermes Science/Lavoisier."
Includes bibliographical references and index.
ISBN 978-1-84821-302-9
1. Chemical kinetics. I. Title.
QD502.S68 2011
541'.394--dc23
2011014704
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-302-9

Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne.

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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. . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1. The chemical equation and stoichiometric coefficients. . .
1.1.2. The reaction components . . . . . . . . . . . . . . . . . . . .
1.1.3. Reaction zones . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. Homogeneous and heterogeneous reactions . . . . . . . . . . . .
1.2.1. Single zone reaction . . . . . . . . . . . . . . . . . . . . . . .
1.2.2. Multizone reaction . . . . . . . . . . . . . . . . . . . . . . . .
1.3. Extent and speed of a reaction . . . . . . . . . . . . . . . . . . . .
1.3.1. Stoichiometric abundance of a component in a reaction
mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2. Extent of a reaction . . . . . . . . . . . . . . . . . . . . . . . .

1.3.3. Speed of a reaction . . . . . . . . . . . . . . . . . . . . . . . .
1.4. Volumetric and areal speed of a monozone reaction . . . . . . .
1.5. Fractional extent and rate of a reaction. . . . . . . . . . . . . . .
1.5.1. The fractional extent of a reaction . . . . . . . . . . . . . . .
1.5.2. Rate of a reaction . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.3. Expression of the volumetric speed (areal) from variations
in the amount of a component . . . . . . . . . . . . . . . . . . . . .
1.6. Reaction speeds and concentrations . . . . . . . . . . . . . . . .
1.6.1. Concentration of a component in a zone . . . . . . . . . . .
1.6.2. Relationship between concentration and fractional extent
in a closed environment . . . . . . . . . . . . . . . . . . . . . . . . .

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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. . . . . . . . . . . . . . .
1.9.1. Influence of temperature . . . . . . . . . . . . . . . . . . .
1.9.2. Influence of the concentrations (or partial pressures
of gases) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.9.3. Other variables . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 2. Reaction Mechanisms and Elementary Steps . . . . . . . . . . . .

25

2.1. Basic premise of kinetics . . . . . . . . . . . . . . . . .
2.2. Reaction mechanism . . . . . . . . . . . . . . . . . . .
2.2.1. Definition . . . . . . . . . . . . . . . . . . . . . . .
2.2.2. Examples of mechanisms . . . . . . . . . . . . . .
2.3. Reaction intermediates . . . . . . . . . . . . . . . . . .
2.3.1. Excited atoms (or molecules) . . . . . . . . . . . .
2.3.2. Free radicals . . . . . . . . . . . . . . . . . . . . . .
2.3.3. Ions . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4. Adsorbed species . . . . . . . . . . . . . . . . . . .
2.3.5. Point defects . . . . . . . . . . . . . . . . . . . . . .
2.3.6. The effect of intermediates on extent and speeds
2.4. Reaction sequences and Semenov representation . .
2.4.1. Semenov diagram . . . . . . . . . . . . . . . . . . .
2.4.2. Linear sequences and multipoint sequences . . .
2.5. Chain reactions . . . . . . . . . . . . . . . . . . . . . . .
2.5.1. Definition . . . . . . . . . . . . . . . . . . . . . . .
2.5.2. The different categories of chain reactions . . . .
2.5.3. The steps in a chain reaction . . . . . . . . . . . .

2.5.4. Sequence of chain reactions . . . . . . . . . . . . .
2.5.5. Reactions of macromolecule formation . . . . . .
2.6. Catalytic reactions . . . . . . . . . . . . . . . . . . . . .
2.6.1. Homogeneous catalysis . . . . . . . . . . . . . . .
2.6.2. Heterogeneous catalysis . . . . . . . . . . . . . . .
2.7. Important figures in reaction mechanisms . . . . . . .

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Chapter 3. Kinetic Properties of Elementary Reactions . . . . . . . . . . . .
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3.1. Space function of an elementary reaction . . . . . . . . . . . .
3.2. Reactivity and rate of an elementary step . . . . . . . . . . . .
3.3. Kinetic constants of an elementary step . . . . . . . . . . . . .
3.3.1. Expression of reactivity as a function of concentrations .
3.3.2. Rate factor of an elementary reaction . . . . . . . . . . . .
3.4. Opposite elementary reactions. . . . . . . . . . . . . . . . . . .

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Table of Contents

3.4.1. Reactivity of two opposite elementary reactions . . . . . . .
3.4.2. Distance from equilibrium conditions . . . . . . . . . . . . . .
3.4.3. Principle of partial equilibria . . . . . . . . . . . . . . . . . . .
3.5. Influence of temperature on the reactivities of elementary steps
3.5.1. Influence of temperature near the equilibrium . . . . . . . . .
3.5.2. Activation energies of opposite elementary reactions
and reaction enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6. Modeling of a gas phase elementary step . . . . . . . . . . . . . .
3.6.1. Collision theory . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2. Theory of activated complex . . . . . . . . . . . . . . . . . . .
3.7. A particular elementary step: diffusion . . . . . . . . . . . . . . .
3.7.1. The diffusion phenomenon . . . . . . . . . . . . . . . . . . . .
3.7.2. Diffusion flux and Fick’s first law . . . . . . . . . . . . . . . .
3.7.3. Diffusion flux in a steady state system . . . . . . . . . . . . .
3.7.4. Reactivity and diffusion space function . . . . . . . . . . . . .
3.7.5. Diffusion in solids . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.6. Interdiffusion of gases . . . . . . . . . . . . . . . . . . . . . . .
3.7.7. Diffusion of a gas in a cylindrical pore . . . . . . . . . . . . .
3.8. Gases adsorption onto solids . . . . . . . . . . . . . . . . . . . . . .

3.8.1. Chemisorption equilibrium: Langmuir model . . . . . . . . .
3.8.2. Dissociative adsorption and the Langmuir model . . . . . . .
3.8.3. Chemisorption of gas mixtures in the Langmuir model . . .
3.8.4. Chemisorption kinetic in the Langmuir model . . . . . . . . .
3.9. Important figures in the kinetic properties of elementary
reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 4. Kinetic Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . .

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4.1. Experimental kinetic data of a reaction . . . . . . . . .
4.2. Generalities on measuring methods. . . . . . . . . . . .
4.3. Chemical methods . . . . . . . . . . . . . . . . . . . . . .
4.4. Physical methods . . . . . . . . . . . . . . . . . . . . . .
4.4.1. Methods without separation of components . . . .
4.4.2. Physical methods with separation of components .
4.4.3. Study of fast reactions . . . . . . . . . . . . . . . . .
4.5. Researching the influence of various variables . . . . .
4.5.1. Ostwald’s isolation method . . . . . . . . . . . . . .
4.5.2. Variables separation . . . . . . . . . . . . . . . . . .

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Chapter 5. Experimental Laws and Calculation of Kinetic Laws of
Homogeneous Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

5.1. Experimental laws in homogeneous kinetics . . . . . . . . . . . . . . . .
5.1.1. Influence of concentrations . . . . . . . . . . . . . . . . . . . . . . . .

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viii

An Introduction to Chemical Kinetics

5.1.2. Influence of temperature . . . . . . . . . . . . . . . . . . . . . . .
5.2. Relationship between the speed of a reaction and the speeds of its
elementary steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3. Mathematical formulation of speed from a mechanism and
experimental conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1. Example of resolution of a mechanism in a closed system . .
5.3.2. Example of resolution of a mechanism in an open system
with constant concentrations . . . . . . . . . . . . . . . . . . . . . . . .
5.4. Mathematical formulation of a homogeneous reaction with
open sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1. Mathematical formulation in a closed system . . . . . . . . . .
5.4.2. Mathematical formulation of a system with constant
concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5. Mathematical formulation of chain reactions . . . . . . . . . . . . .
5.5.1. Mathematical formulation of a simple homogeneous
chain reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2. Mathematical formulation of a reaction forming a
macromolecule through polymerization . . . . . . . . . . . . . . . . .

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103

Chapter 6. Experimental Data and Calculation of Kinetic Laws of
Heterogeneous Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109

6.1. Heterogeneous reactions . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1. Distinctive nature of heterogeneous systems . . . . . . . . . . .
6.1.2. Rate of a heterogeneous reaction . . . . . . . . . . . . . . . . . .
6.1.3. Different kinetic classes of heterogeneous reactions . . . . . .
6.2. Experimental kinetic data of heterogeneous reactions . . . . . . . .
6.2.1. Catalytic reactions . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2. Stoichiometric heterogeneous gas–solid reactions . . . . . . .
6.3. Involvement of diffusion in matter balances . . . . . . . . . . . . .
6.3.1. Balance in a slice of a volume zone . . . . . . . . . . . . . . . .
6.3.2. Balance in a 2D zone . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.3. Application of balances to the elementary steps of a sequence

of reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.4. Application to Fick’s second law . . . . . . . . . . . . . . . . .
6.4. Example of mathematical formulation of a heterogeneous
catalytic reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5. Example of the mathematical formulation of an evolution
process of a phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.1. Balance of intermediates. . . . . . . . . . . . . . . . . . . . . . .
6.5.2. Expressions of the reactivities of elementary chemical steps .
6.5.3. Expressions of the concentrations of species at the interfaces .
6.5.4. Diffusion equations of the defects . . . . . . . . . . . . . . . . .

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ix

6.5.5. Expressions of the variations in sizes of the zones involved
in the reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.6. Evolution law of the rate chosen to characterize the speed . . . . .

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Chapter 7. Pseudo- and Quasi-steady State Modes . . . . . . . . . . . . . . .

135

7.1. Pseudo-steady state mode . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1. Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.2. Uniqueness of the reaction speed in pseudo-steady state mode .
7.1.3. Linear sequences in pseudo-steady state modes . . . . . . . . . .
7.1.4. Multipoint sequences in pseudo-steady state mode . . . . . . . .
7.1.5. Experimental research into the pseudo-steady state . . . . . . . .
7.2. Pseudo-steady state sequences with constant volume (or
surface) – quasi-steady state. . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1. Quasi-steady state sequences . . . . . . . . . . . . . . . . . . . . .
7.2.2. Linear sequences in quasi-steady state mode . . . . . . . . . . . .
7.2.3. Speed of a homogeneous linear sequence in
quasi-steady state mode with invariant volume . . . . . . . . . . . . . .
7.2.4. Multipoint sequences in quasi-steady state mode . . . . . . . . .

7.3. Pseudo- and quasi-steady state of diffusion . . . . . . . . . . . . . . .
7.4. Application to the calculation of speeds in pseudo-steady
state or quasi-steady state . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.1. Principle of the method . . . . . . . . . . . . . . . . . . . . . . . .
7.4.2. Example 1: dinitrogen pentoxide decomposition . . . . . . . . .
7.4.3. Example 2: hydrogen bromide synthesis . . . . . . . . . . . . . .
7.4.4. Example 3: polymerization . . . . . . . . . . . . . . . . . . . . . .
7.4.5. Example 4: application of the pseudo-steady state to a
heterogeneous catalytic reaction . . . . . . . . . . . . . . . . . . . . . . .
7.5. Pseudo-steady state and open or closed systems . . . . . . . . . . . .
7.5.1. Kinetics law in homogeneous closed systems . . . . . . . . . . .
7.5.2. Kinetics law in heterogeneous closed systems . . . . . . . . . . .
7.5.3. Kinetic laws of open systems with constant concentrations . . .
7.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.7. Important figure in pseudo-steady state . . . . . . . . . . . . . . . . .

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163

Chapter 8. Modes with Rate-determining Steps . . . . . . . . . . . . . . . . .

165

8.1. Mode with one determining step . . . . . . . . . .
8.1.1. Definition . . . . . . . . . . . . . . . . . . . . .
8.1.2. Concentrations theorem for linear sequences
8.1.3. Reactivity of the rate-determining step . . . .
8.1.4. Rate of reaction . . . . . . . . . . . . . . . . . .

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171


x

An Introduction to Chemical Kinetics

8.1.5. Calculation of speed of a linear sequence in pure mode
determined by one step . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.6. Pure modes away from equilibrium for linear sequences .
8.1.7. Influence of temperature on linear sequences . . . . . . . .
8.1.8. Cyclic sequences . . . . . . . . . . . . . . . . . . . . . . . . .
8.1.9. Conclusion on modes with a single determining step . . . .
8.2. Pseudo-steady state mode with two determining steps . . . . .
8.2.1. Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.2. Mathematical formulation of a mixed
pseudo-steady state mode . . . . . . . . . . . . . . . . . . . . . . . .
8.2.3. Linear sequences: inverse rate law or the law of slowness .
8.2.4. Cyclic sequences . . . . . . . . . . . . . . . . . . . . . . . . .
8.2.5. Law of characteristic times . . . . . . . . . . . . . . . . . . .
8.3. Generalization to more than two determining steps . . . . . . .

8.4. Conclusion to the study of modes with one or several
rate-determining steps . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.5. First order mode changes . . . . . . . . . . . . . . . . . . . . . . .
8.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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190
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193

Chapter 9. Establishment and Resolution of a Reaction Mechanism . . . .

195

PART 2. REACTION MECHANISMS

AND KINETIC PROPERTIES

9.1. Families of reaction mechanisms . . . . . . . . . . . . . . . . . .
9.2. Different categories of elementary steps . . . . . . . . . . . . . .
9.2.1. Homolytic bond breaking . . . . . . . . . . . . . . . . . . . .
9.2.2. Heterolytic bond breaking . . . . . . . . . . . . . . . . . . . .
9.2.3. Ion dissociation . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.4. Radical reactions . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.5. Ion–molecule reactions . . . . . . . . . . . . . . . . . . . . .
9.2.6. Reactions between ions . . . . . . . . . . . . . . . . . . . . .
9.2.7. Interface reactions . . . . . . . . . . . . . . . . . . . . . . . .
9.2.8. Reaction between structure elements in the solid state . . .
9.2.9. Reactions between adsorbed species and point defects . . .

9.3. Establishment of a reaction mechanism . . . . . . . . . . . . . .
9.3.1. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.2. Rule no. 1: the law of elimination of intermediates . . . . .
9.3.3. Rule no. 2: the rule of the least change of structure (in the
case of a single bond) . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.4. Rule no. 3: the rule of the greatest simplicity of
elementary reactions (bimolecular) . . . . . . . . . . . . . . . . . .

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197
197
199
199
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203


Table of Contents

9.3.5. Rule no. 4: the rule involving a single jump into the
solid state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.6. Rule no. 5: the law of micro-reversibility . . . . . . . . .
9.4. Research into a mechanism: intermediary reactions . . . . .
9.4.1. Reaction filiations: primary and non-primary products.
9.4.2. Labile intermediates . . . . . . . . . . . . . . . . . . . . .
9.5. Back to the modes and laws of kinetics . . . . . . . . . . . .
9.5.1. Modes with a single rate-determining step . . . . . . . .
9.5.2. Modes with multiple rate-determining steps . . . . . . .

9.5.3. Pseudo-steady state modes . . . . . . . . . . . . . . . . .
9.5.4. Link between the form of the rate equation and the
presence of some elementary steps . . . . . . . . . . . . . . . .
9.6. Experimental tests . . . . . . . . . . . . . . . . . . . . . . . . .
9.6.1. Experimental methods . . . . . . . . . . . . . . . . . . . .
9.6.2. The pseudo-steady state mode test . . . . . . . . . . . . .
9.6.3. Research into the uniqueness of the space function
mechanism or E test . . . . . . . . . . . . . . . . . . . . . . . .
9.7. Looking for the type of rate law . . . . . . . . . . . . . . . . .
9.7.1. Research into the influence of concentrations . . . . . .
9.7.2. Research into the influence of temperature . . . . . . . .

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204
204
205
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210

210
211
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211
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212
216

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216
218
218
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
10.1.1. Energy of a group of two atoms . . . . . . . . . . . . . . . . .

10.1.2. Energy of an even number of atoms . . . . . . . . . . . . . . .
10.2.3. Energy of an odd number of atoms . . . . . . . . . . . . . . . .
10.2. Bimolecular reactions in the gas phase . . . . . . . . . . . . . . . .
10.2.1. Postulate of the activated molecular collision . . . . . . . . .
10.2.2. Potential energy surface . . . . . . . . . . . . . . . . . . . . . .
10.2.3. Reaction pathways and the equivalent “mass point” . . . . .
10.2.4. Absolute expression of the reaction rate . . . . . . . . . . . . .
10.2.5. Partition functions of the activated complex . . . . . . . . . .
10.2.6. Evaluation of the pre-exponential factor . . . . . . . . . . . .
10.2.7. Activation energies . . . . . . . . . . . . . . . . . . . . . . . . .
10.2.8. Units and other forms of the reaction rate coefficient . . . . .
10.3. Monomolecular reactions in the gas phase . . . . . . . . . . . . . .
10.4. Photochemical elementary reactions . . . . . . . . . . . . . . . . .
10.4.1. Grotthus–Draper quantitative law . . . . . . . . . . . . . . . .
10.4.2. Energetic paths of molecule dissociation . . . . . . . . . . . .
10.4.3. Einstein’s quantitative law . . . . . . . . . . . . . . . . . . . . .
10.4.4. Influence of temperature on photochemical reactions . . . . .
10.5. The theory of activated complexes . . . . . . . . . . . . . . . . . .

223
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231
233
236
237

239
242
243
248
248
249
250
251
252

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xii

An Introduction to Chemical Kinetics

Chapter 11. Modeling Elementary Reactions in Condensed Phase . . . . .
11.1. Elementary reaction in the liquid phase . . . . . . . . . . . . . .
11.1.1. Generic expression of an elementary-step reaction rate
in the liquid phase: the Brønstedt–Bjerrum law . . . . . . . . . . . .
11.1.2. Influence of the environment . . . . . . . . . . . . . . . . . .
11.1.3. Comparison of the reaction rate in solution and gas phases
11.1.4. Reactions between ions in diluted solution . . . . . . . . . .
11.1.5. Reactions in concentrated solutions: the acidity factor . . .
11.2. Elementary reaction in the solid state . . . . . . . . . . . . . . . .
11.2.1. Potential energy of a solid . . . . . . . . . . . . . . . . . . . .

11.2.2. Reaction pathway . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.3. Rate of an elementary jump . . . . . . . . . . . . . . . . . . .
11.2.4. Diffusion in solids. . . . . . . . . . . . . . . . . . . . . . . . .
11.3. Interphase reactions . . . . . . . . . . . . . . . . . . . . . . . . . .
11.3.1. Gas–solid interphases: adsorption, desorption . . . . . . . .
11.3.2. Solid–solid interface: the concept of epitaxy . . . . . . . . .
11.4. Electrochemical reactions. . . . . . . . . . . . . . . . . . . . . . .
11.4.1. Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.4.2. Reactivity of an electrochemical reaction . . . . . . . . . . .
11.4.3. The De Donder–Pourbaix inequality . . . . . . . . . . . . . .
11.4.4. Polarization curves . . . . . . . . . . . . . . . . . . . . . . . .
11.4.5. Polarization curve equation . . . . . . . . . . . . . . . . . . .
11.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

253

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280
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285
290

Chapter 12. The Kinetics of Chain Reactions . . . . . . . . . . . . . . . . . . .

291

12.1. Definition of a chain reaction . . . . . . . . . . . . . . . . . . .
12.2. The kinetic characteristics of chain reactions . . . . . . . . . .
12.3. Classification of chain reactions . . . . . . . . . . . . . . . . . .

12.3.1. Straight or non-branched chain reactions . . . . . . . . . .
12.3.2. Reactions with direct branching . . . . . . . . . . . . . . .
12.3.3. Reactions with indirect branching . . . . . . . . . . . . . .
12.4. Chain reaction sequences . . . . . . . . . . . . . . . . . . . . . .
12.4.1. Initiation of a chain reaction . . . . . . . . . . . . . . . . . .
12.4.2. Propagation of a chain reaction . . . . . . . . . . . . . . . .
12.4.3. Chain breaking. . . . . . . . . . . . . . . . . . . . . . . . . .
12.4.4. Branching chain reaction . . . . . . . . . . . . . . . . . . . .
12.5. Kinetic study of straight chain or non-branch chain reactions
12.5.1. Mean length of the chains . . . . . . . . . . . . . . . . . . .
12.5.2. Expression of the reaction rate . . . . . . . . . . . . . . . .
12.5.3. Calculation of the rate and mean length of chains in
the reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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303


Table of Contents

12.5.4. Variation of reaction rate with temperature . . . . . . . .
12.5.5. Permanency of the pseudo-steady state mode and
reactant consumption . . . . . . . . . . . . . . . . . . . . . . . . .
12.6. Kinetic study of chain reactions with direct branching . . .
12.6.1. Simplified representation of reactions with direct
branching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.6.2. Mean chain lengths: condition of the appearance of a
pseudo-steady state . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.6.3. Example of a chain reaction with both linear branching
and breaking in the bulk . . . . . . . . . . . . . . . . . . . . . . . .
12.6.4. Example of the calculation of the measures related to a
branching chain reaction . . . . . . . . . . . . . . . . . . . . . . .
12.7. Semenov and the kinetics of chain reactions . . . . . . . . .

xiii

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310

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310
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316

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318
321

Chapter 13. Catalysis and Catalyzed Reactions . . . . . . . . . . . . . . . . .

323

13.1. Homogenous catalysis . . . . . . . . . . . . . . . . . . . . . . . .
13.1.1. Specific acid–base catalysis by H+ and OH- ions . . . . .
13.1.2. Generic acid–base catalysis . . . . . . . . . . . . . . . . . .
13.1.3. Catalysis by Lewis acids . . . . . . . . . . . . . . . . . . . .
13.1.4. Redox catalysis . . . . . . . . . . . . . . . . . . . . . . . . .
13.1.5. Autocatalytic reactions . . . . . . . . . . . . . . . . . . . . .
13.1.6. Enzymatic catalysis . . . . . . . . . . . . . . . . . . . . . . .

13.2. Heterogeneous catalysis reactions . . . . . . . . . . . . . . . . .
13.2.1. Experimental laws in heterogeneous catalysis . . . . . . .
13.2.2. Structure of the mechanism of heterogeneous catalysis . .
13.2.3. Kinetics of the catalytic act . . . . . . . . . . . . . . . . . .
13.2.4. Example of the kinetics of catalysis on a porous support .
13.2.5. Influence of the catalyst surface area: poisoning . . . . . .
13.3. Gas–solid reactions leading to a gas . . . . . . . . . . . . . . .
13.4. Conclusion on catalysis . . . . . . . . . . . . . . . . . . . . . . .
13.5. Langmiur and Hinshelwood . . . . . . . . . . . . . . . . . . . .

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352

Chapter 14. Kinetics of Heterogeneous Stoichiometric Reactions . . . . . .

353

14.1. Extent versus time and rate versus extent curves . . . . .
14.2. The global model with two processes . . . . . . . . . . . .
14.3. The E law . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.4. Morphological modeling of the growing space function
14.4.1. The hypothesis . . . . . . . . . . . . . . . . . . . . . . .
14.4.2. Types of model involving one or two processes . . .
14.4.3. Experimental research on the type of morphological
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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354
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357
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372


xiv

An Introduction to Chemical Kinetics

14.5. The nucleation process . . . . . . . . . . .
14.5.1. Description of the nucleation process
14.5.2. Thermodynamics of nucleation . . . .
14.5.3. The nucleation mechanism . . . . . .
14.5.4. The nucleation rate . . . . . . . . . . .
14.5.5. Surface and nucleation frequencies .
14.6. Physico-chemical growth models . . . . .
14.7. Conclusion on heterogeneous reactions .
14.8. Important figures in reaction kinetics . . .

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373
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380
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386
387

Chapter 15. Kinetics of Non-pseudo-steady State Modes . . . . . . . . . . . .

389

15.1. Partial pseudo-steady state modes . . . . . . . . . . . . . . . . . .
15.2. The paralinear law of metal oxidation . . . . . . . . . . . . . . .
15.3. Thermal runaway and ignition of reactions . . . . . . . . . . . .
15.4. Chemical ignition of gaseous mixtures . . . . . . . . . . . . . . .
15.4.1. Branched chains with linear branching and chain breaking
in the bulk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15.4.2. Branched chains with linear branching and breaking in
the bulk and heterogeneous breaking on the walls . . . . . . . . . .

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397

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397

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398

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

405

Appendix 1. Point Defects and Structure Elements of Solids . . . . . . . . .

407

A1.1. Point defects of solids . . . . . . . . . . . . . . . . . . . . .
A1.2. Definition of a structural element . . . . . . . . . . . . . . .
A1.3. Symbolic representation of structure elements . . . . . . .
A1.4. Reactions involving structure elements in quasi-chemical
reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A1.5. Equilibria and reactivities of quasi-chemical reactions . .

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411
411

Appendix 2. Notions of Microscopic Thermodynamics . . . . . . . . . . . . .

413

A2.1. Molecule distribution between the different energy states
A2.2. Partition functions . . . . . . . . . . . . . . . . . . . . . . . .
A2.3. Degrees of freedom of a molecule . . . . . . . . . . . . . .
A2.4. Elementary partition functions . . . . . . . . . . . . . . . .
A2.4.1. Vibration partition function . . . . . . . . . . . . . . . .
A2.4.2. Rotation partition function . . . . . . . . . . . . . . . .
A2.4.3. Translation partition function . . . . . . . . . . . . . . .
A2.4.4. Order of magnitude of partition functions . . . . . . .

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Table of Contents

A2.5. Expression of thermodynamic functions from partition
functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A2.5.1. Internal energy . . . . . . . . . . . . . . . . . . . . . .
A2.5.2. Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . .
A2.5.3. Free energy . . . . . . . . . . . . . . . . . . . . . . . .
A2.6. Equilibrium constant and partition functions . . . . . . .

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Appendix 3. Vibration Frequency of the Activated Complex . . . . . . . . .

425

Notations and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

431

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

439

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

441

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xv


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Preface

This book on chemical kinetics is especially designed for undergraduate or
postgraduate students or university students intending to study chemistry, chemistry
and physics, materials science, chemical engineering, macromolecular chemistry and
combustion.
Part 1, which constists of the first eight chapters, presents the basic concepts of
chemical kinetics. Particular importance is given to definitions and the introduction
of concepts. This part includes a first approach to kinetic calculations and some
information on elementary reactions. All these models are widely adopted and
developed in the Part 2, which, in seven chapters (Chapters 9-15), deepens the
relationships between reaction mechanisms and kinetic properties.
Part 2 begins with Chapter 9, which presents the different classes of elementary
steps, the nature and identification of reaction intermediates and the principles that
must be observed to write an elementary step.
Then Chapters 10 and 11 are devoted to the modeling of elementary steps
through the activated complex theory that is presented in as complete a manner as
possible at this level, bearing in mind students who will then be confronted with
molecular dynamics. The theory is presented in gaseous phase as well as in
condensed liquid and solid phases.
Then come three chapters that deal with different specific areas (chain reactions,

catalysis and heterogeneous reactions). For each area, the application clues of basic
concepts are deepened and we introduce the specialized teachings that will be
covered at doctorate level.

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xviii

An Introduction to Chemical Kinetics

Finally, Chapter 15 addresses non-pseudo-steady state processes that are
encountered in different areas. We place particular emphasis on these modes for
combustion and explosion reactions and heterogeneous reactions.
This book is the result of extensive experience teaching this course at this level
and fundamental and applied research for over 30 years in chemical kinetics at the
highest level. These accumulated experiences have led me to a certain number of
significant modifications compared to previously published books that cover this
level of study.
First of all, the arrival and growth of computer science that has populated
laboratories should be taken into account, which implies not only unprecedented
opportunities of computation but, more significantly, changes in attitude towards the
ways of tackling problems and therefore how to teach kinetics. Thus, the sacrosanct
chapter on formal kinetics has disappeared. Indeed, there is now only the resolution
of three or four integrals that are rarely used nowadays because, unlike our
predecessors, we possess derivative curves that give the speed, as easily as integral
curves; and because modeling always leads to speed expressions (from infinitesimal
calculus), the calculation of these few particular integrals is no longer of interest in
kinetics.
The book no longer only refers to the famous “quasi-steady state approximation”

(QSSA) for several reasons:
– First, this QSSA is about the concentrations of intermediate species, which is
only applied to homogeneous systems with constant volumes, which is relatively
rare and inadequate for many gas-phase reactions carried out at constant pressure, as
is mostly the case. This is the same for reactions where a condensed phase is
created.
– Second, this QSSA is always presented as a calculus approximation that is only
justified by computations on a small number of specific cases for which it is not
even necessary. In fact, the introduction of the concept of a kinetic mode enables us
to bond the approximation level of modeling to that of the accuracy and the
reproducibility of measurements. Thus, we consider several types of kinetic modes
corresponding to multiple types of approximation in the calculation of speeds using
various mechanisms.
Among these modes, those called pseudo-steady states are very important
because they greatly simplify the calculations. These modes are characterized by the
stability of the amounts of the intermediate species and are detected by the
experiment (described in Chapter 7). Other regimes termed “with rate-determining
steps” are also used, which is still in line with the precision of the measurements.

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Preface

xix

Even if the notion of reaction order was retained for the elementary steps, for
which this notion is closely related with the mechanism, it is no longer used for
more complex reactions because the order obtained will not help us to infer the
reaction mechanism. On the contrary, the notion of separate variables of speed –

concentration, temperature, etc. – is more directly related to the mechanisms and it
should be noted that the order with respect to a concentration is only a special case
of the separation of this variable in the expression of speed.
Regarding the influence of temperature, a clear distinction is made between the
elementary steps, for which Arrhenius’ law is always true and leads to an activation
energy, and the common reactions (in general non-elementary) for which Arrhenius’
law’s experimental application leads to a “temperature coefficient”. This coefficient
can sometimes, but by no means always, be linked to magnitudes related to the
mechanism’s steps, such as activation energies and/or enthalpies. This temperature
coefficient is then called the apparent activation energy.
We retain this distinction between elementary steps to which we attribute a
reactivity that follows an order and obeys Arrhenius’ law and the multi-step
reactions for which the notion of specific speed is retained (volumetric or areal) and
whose expression of speed is far from obvious.
The importance given to the relationships between experiment and modeling
should also been noted. Very simple methods that enable us to verify, or discount, a
certain number of hypotheses are introduced: pseudo-steady state mode; and the
separation of variables.
This work has included information from many French and foreign books that
cover this subject, some of which are cited at the end of the book, retaining their
contributions and originality.
My gratitude goes to all my students who attended my classes on kinetics
because their feedback, questions and curiosity compelled me to ask myself real
questions and to deepen my reflections. I would also like to thank a number of
colleagues foremost among whom is Franỗoise Rouquerol – for the discussions,
sometimes fierce but always passionate and meaningful, that we have had. This
book owes a great deal to these people. Finally, I want to express my gratitude to
Ecole des Mines de Saint Etienne, which has for many years given me the means to
carry out my work and enabled the achievement of this book.
Michel SOUSTELLE

Saint Vallier
May 2011

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PART 1

Basic Concepts of
Chemical Kinetics

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Chapter 1

Chemical Reaction and Kinetic Quantities

This first chapter devoted to chemical kinetics, should provide us with
definitions of specific notions that are the extents and speeds of reactions every time
we approach a new field of disciplinary paradigms. This description is particularly
important in chemical kinetics because many definitions are intuitively related to the
evolution of a reaction system and the speed of this evolution and for which the
same word does not always correspond to the same definition according to authors.

Thus we encounter many “speeds” of reaction that are not expressed in the same
units and are not always linked with each other. The result is such that when starting
to read a book – or an article on kinetics – the reader needs to pay particular
attention to definitions given by the author if indeed he or she has taken the trouble
to explain them. Therefore we specially draw the reader’s attention to this chapter.
1.1. The chemical reaction
1.1.1. The chemical equation and stoichiometric coefficients
A chemical reaction is the phenomenon that turns an unstable chemical species
or mixture, under the conditions of chemical experiment, into other stable species. A
reaction is represented by its chemical equation such as reaction [1.R1], which
represents the reaction between nitric oxide and hydrogen, and produces water and
nitrogen:
2NO + 2H2 = 2H2O + N2

[1.R1]

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