V. N. Kondratiev E. E. Nikitin

Gas-Phase Reactions Kinetics and Mechanisms

With 64 Figures and 15 Tables

Springer-Verlag Berlin Heidelberg New York 1981

Professor Victor N. Kondratiev t 22. 2. 1979

Professor Evgenii E. Nikitin Institute of Chemical Physics Academy of Sciences of the USSR Vorob'evskoe shosse 2-b 117334, Moscow, USSR

ISBN-13: 978-3-642-67610-9

DOl: 10.1007/978-3-642-67608-6

e-ISBN-13: 978-3-642-67608-6

Library of Congress Cataloging in Publication Data. Kondrat'ev, Viktor Nikolaevich, 1902- • Gas-phase reactions. Bibliography: p. Includes index. 1. Chemical reaction, Rate of. 1. Nikitin, Evgenii Evgen'evich, joint author. II. Title. QD502.K64 541.3'94 80-12078

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® Springer-Verlag Berlin, Heidelberg 1981 Softcover reprint ofthe hardcover 1st edition 1981

The use of registered names, trademarks, etc. in this publication does not imply, even in the absencc of a specific statement, that such names are axempt from the relevant protective laws and regulations and therefore free for general use.

2152/3020-543210

In Memory of V. N. Kondratiev

1.2.1902 -- 22.2.1979

Foreword

The present monograph appears after the death of Professor V. N. Kondratiev, one of those scientists who have greatly contributed to the foundation of contem­porary gas kinetics. The most fundamental idea of chemical kinetics, put for­ward at the beginning of the twentieth century and connected with names such as W. Nernst, M. Bodenstein, N. N. Semenov, and C. N. Hinshelwood, was that the complex chemical reactions are in fact a manifestation of a set of simpler elementary reactions involving but a small number of species. V. N. Kondratiev was one of the first to adopt this idea and to start investigations on the elementary chemical reactions proper. These investigations revealed explicitly that every elementary reaction in turn consisted of many elementary events usually referred to as elementary processes. It took some time to realize that an elementary reaction, represented in a very simple way by a macroscopic kinetic equation, can be described on a microscopic level by a generalized Boltzmann equation. Neverheless, up to the middle of the twentieth century, gas kinetics was mainly concerned with the interpretation of complex chemical reactions via a set of elementary reactions. But later on, the situation changed drastically. First, the conditions for reducing microscopic cquations to macroscopic ones were clearly set up. These are essentially based on the fact that the small perturbations of the Maxwell-Boltzmann distribution are caused by the reaction proper.

Second, the wide research devoted to fast reactions showed that sometimes the macroscopic description was quite inadequate and the microscopic level had to be l'esorted to. For instance, only the microscopic level permits the interpre­tation of the distinctly non-equilibrium processes in the interstellar space, in the Earth atmosphere, in combustion, chemical lasers, and even in engineering.

The importance of developing an appropriate theory became increasingly evident. Although theory only provides relatively inaccurate rate constants, it nevertheless predicts the range of the rate constant variation and/or its tempe­rature dependence. This is often very helpful in the elucidation of the reaction mechanism. Equally important was the development of experimental methods of creating highly non-equilibrium conditions such as the shock tube technique, flash photolysis and various kinds of chemical activation.

The elucidation of microscopic mechanisms of the elementary reactions was facilitated by the development of kinetic spectroscopy, particularly by the use of laser excitation and detection, mass spectrometry, and the state-selected molecular beams.

VIII Foreword

All these aspects have stimulated the writing of this book, which analyzes, with allowance for recent advances, the approaches put forward in the earlier books by the same authors (V. N. Kondratiev: Chemical Kinetics of Gas Reac­tions. Pergamon, 1964. E. E. Nikitin: Theory of Elementary Atomic and Mole­cular Processes in Gases, Clarendon, 1974). Moreover, a chapter on radiation­chemical reactions has been written by Prof. V. L. Tal'roze whose contribution is highly appreciated.

Contrary to the previously attempted exhaustive list of references, such a compilation would be beyond the scope of a book of this general character. Thus, since all particular subjects are extensively treated in reviews and mono­graphs, only references to such publications are given.

Particular thanks ate due to Dr. S. Ya. Umanskii whose clatifying discussions and indispensable support greatly facilitated the writing of this book.

Immense thanks to Professor J. Troe for the reading of the whole text and for the invaluable suggestions and comments he made.

Moscow, November 1980 E. E. Nikitin

Contents

Chapter I. General Kinetic Rules for Chemical Reactions 1

1. Kinetic Equations. Rate Constants . . . . . . . 1

2. Kinctic Classification of Reactions. Simple and Complex Reactions :3

2.1 Kinetic Types of Simple Reactions 2.2 Consecutive Reactions 2.:3 Steady-State Method 2.4 Parallel Reactions . . 2.5 Coupled Reactions. Chemical Induction 2.6 Homogeneous Catalysis ..... . 2.7 Catalysis by Products (Autocatalysis)

3. Chemical Equilibrium . . . . . . . . .

Chapter n. l\'Iechanisms of Chemical Reactions

4. Macroscopic Manifestation of a Complex Reaction Mechanism

5. Intermediates

6. Atomic Reactions

6.1 Reactions in Highly-Rarefied and Diffusion Flames Reaction M + X 2 • • • • • • • • • •

6.2 Reaction M + RX and Other Reactions 6.:3 Atomic Hydrogen Reactions 6.4 Atomic Oxygen Reactions 6.5 Reactions of Atomic Halogens 6.6 Atomic Nitrogen Reactions

7. Radical Reactions

7.1 Production of Radicals .. 7.2 Reactions of Certain Radicals

Chapter III. Theory of Elementary Processes

8. Microscopic Formulation of Reaction Kinetics.

8.1 Cross Sections, Transition Probabilities and Rate Constants of Elementary Processes . . . . . . . . . . • . . . . .

:3 5 7 8 \)

9 10

11

14

14

16

20

20 22 22 24 24 25

26

26 27

28

28

30

X Contents

8.2 Kinetic Equations fo!' Unreactive Processes. . . . . 34 8.3 Translational, Rotational and Vibrational Relaxation. 37 8.4 Kinetics of Reactive Processes . . . . 39 8.5 Relation Between Rate Constants of Forward and Reverse

Non-Equilibrium Reactions. . 41

9. Dynamics of Elementary Processes 42

9.1 Adiabatic Approximation 42 9.2 Probabilities of Electronically Adiabatic Processes 44 9.3 Probabilities of Electronically Non-Adiabatic Processes 48

10. Various Types of Potential Energy Surfaces

10.1 Rectangular and Skewed Coordinates 10.2 Unreactive Interactions A + BC . . . 10.3 Reactive Interactions A + BC . . . .

52 53 54 55

11. Equilibrium Rate Constants. Transition-State Method 58

11.1 Assumptions and Derivation of the Basic Transition-State Method Expressions . . . . . . . . . . . . . . . . . . . . . . . . 59

11.2 Activation Energy and Pre-Exponential Factors in the Reaction Rate Constant Expression . . . . . . . . . . . . . . . . . . 61

Chapter IV. Energy Exchange in lUolecular Collisions

12. Experimental Methods of Studying Vibrational Relaxation

12.1 Dispersion and Absorption of Ultrasounds 12.2 The Shock-Wave Method

66

66

66 67

12.3 Spectroscopic Methods. . . . . . . . . 68 12.4 Molecular Beams . . . . . . . . . . . 69

13. Transfer of Translational and Rotational Energy 69

13.1 Translational-Translational (TT) Energy Transfer 69 13.2 Rotational-Translational (RT) Energy Transfer 71

14. Transfer of Vibrational Energy . . . . . . . . . . . 72

14.1 Exchange of Translational and Vibrational Energy (VT Process) 72 14.2 Exchange of Rotational and Vibrational Energy (VR and VRT

Processes) . . . . . . . . . . . . . . . . . . . . . . .. 77 14.3 Effect of Non-Adiabatic Coupling on Vibrational Energy Transfer 78 14.4 Vibrational Relaxation via Long-Lived Complexes and in

Symmetric Exchange Rcactions . . . . . . . . . . . 79 14.5 Intermolecular Quasi-Resonant Vibl'ational Energy Exchange

(Intermolccular VV Process) . . . . . . . . . . . . . . . 80 14.6 Intramolecular Quasi-Resonant Vibrational Energy Exchange

(Intramolecular VV Process) . . . . . . . . . . . . . 83

15. Kinetics of the Vibrational Relaxation of Diatomic Molecules. 86

16. Energy Exchange with Blectronically Excited Molecules 90

16.1 VRT Energy Transfer 90 16.2 Electronic Energy Transfer 92

Contents XI

Chapter V. Unimolecular Reactions 96

17. The TheOl'y of U nimolecular Reactions 96

17.1 Definition of Unimolecular Reactions 96 17.2 Molecular Activation and Deactivation 97 17.3 Unimolecular Conversion . . . . . . 98 17.4 Pressure Dependence of Rate-Constant of Polyatomic Molecules 99 17.5 Thermal Dissociation of Diatomic Molecules 102

18. Experimental

18.1 Pre-Exponential Factor in the koo Expression 18.2 Pre-Exponential Factor in the ko Expression . 18.3 Energy Exchange in Unimolecular Reactions 18.4 Activation Energy for Unimolecular Reactions 18.5 Boundary between High-and Low-Pressure Domains

(Fall-Off Pressure) . . . . . . . . . . . . . . .

103

103 106 106 107

108

Chal)ter VI. Combination Reactions . . . . . . . . . . . . . 109

19. Atomic and Radical Recombination and Addition Reactions 109

19.1 Radiative Stabilization . . . . . . . . . . . . . . 109 19.1.1 Recombination on a Repulsive Potential Curve 110 19.1.2 Recombination on an Attractive Potential Curve 111 19.1.3 Recombination via Inverse Predissociation 112

19.2 Collisional Stabilization 114

20. Termolecular Reactions . . 122

20.1 Number of Three-Body Collisions. 122

Chapter VII. Bimolecular Exchange Reactions 125

, 21. Theory of Bimolecular Exchange Reactions 125

21.1 Classification of Exchange Reactions 125 21.2 Cross Sections of Exchange Reactions. 127 21.3 Energy Requirements. . . . . . . . 130 21.4 Energy Disposal . . . . . . . . . . 132 21.5 Temperature Dependence of Rate Constants of Equilibrium

Bimolecular Reactions. . . . . . . . . . . . . . . . . 133 21.6 Non-Equilibrium Effects in Thermal Bimolecular Reactions 135

22. Certain Types of Bimolecular Exchange Reactions 137

22.1 Abstraction of Atoms and Radicals . . . . . 137 22.2 Isotope Exchange Reactions . . . . . . . . 138 22.3 Reactions between Atoms, Radicals and Unsaturated Molecules. 139

23. Bimolecular Reaction Rates as a Function of Molecular Structure. 139

23.1 Reactions of Atomic Sodium with Halogenated IIydrocarbons 140

XII Contents

23.2 Reactions of Hydrogen and Chlorine Atoms, and of Hydroxyl and Methyl Radicals with Hydrocarbons. . . . . . . . . . 141

23.3 Bimolecular Reactions of Electronically Excited Species. . . . . 141

Chapter vm. Photochemical Reactions 143

24. Photochemical Activation of Molecules 143

24.1 The Lambert-Beer Law . . . . . 143 24.2 Primary Photochemical Step. Quantum Yield 144 24.3 Quantum Yield a as Function of the Wavelength. 145 24.4 The Nature of Primary Centers of a Photochemical Reaction 145 24.5 Hot Particles . . . . . . . . . . . . . 148

25. Secondary Processes in Photochemical Reactions . . . . 149

25.1 Secondary Processes Involving Atoms and Radicals. 149 25.2 Secondary Processes Involving Excited Molecules 149 25.3 Fluorescence. Metastable Molecules 149 25.4 Fluorescence Quenching. . . . . 150

26. Photochemical Sensitization . . . . . 151

26.1 Photosensitization with Halogens. 152 26.2 Photosensitization with Mercury . 153

27. Temperature Dependence and Photochemical Reaction Mechanisms 155

27.1 Temperature Coefficient. . . . . . . . . . . . . . . ., 155 27.2 Formation of Hydrogen Bromide from Hydrogen and Bromine

Molecules . . . . . . . . . . . 156 27.3 The Photochemical Reaction Limit .............. 157

Chapter IX. Chemical Reactions in Electric Discharge 158

28. Activation in Elect,ric Discharge ....... 158

28.1 Excitation of Atoms and Molecules by Electron Impact. The Excitation Function. . . . . . . . . . . . . . . . . .. 158

28.2 Excitation of Molecular Vibrations and Rotations by Electron Impact . . . . . . . . . . . . . . . . . . . 161

29. Types of Electric Discharge. Low-Temperature Plasma 164

30. Certain Reactions in Electric Discharge and Their Yields . 165

30.1 Ozone Production . . . . . . . . . . . . . . 165 30.2 Ammonia Synthesis from Nitrogen and Hydrogen 166 30.3 Acetylene Production from Methane. . . . . . . 167

Chapter X. Radiation Chemical Reactions 169

31. Primary Processes ....... .

31.1 Electron Impact Ionization. Generation of Positive Ions . 31.2 Generation of Negative Ions . . . . . . :. . . . . . .

170

170 174

Contents XIII

32. Secondary Processes Specific of Radiation Chemistry. 176

32.1 Ion-Molecule Reactions . . . . . . . . . . . 176 32.2 Recombination of Charged Species . . . . . . 180 32.3 Reactions Involving Highly-Excited Neutral Particles. Hot Atoms 181

33. The Sequence of Elementary Processes in Gas Radiolysis 182

33.1 Examples of Complex Reactions 182 33.2 Radiolysis of Hydrocarbons . . . . . . . 183 33.3 Ammonia Radiolysis . . . . . . . . . . 184 33.4 Radiolysis of Nitrogen - Oxygen l\-Iixtures 185

Chapter XI. Chain Reactions . . . . 187

34. Non-chain and Chain Reactions. 187

35. Stationary Chain Reactions

35.1 Mean Chain Length .. 35.2 Time Dependence of Chain Propagation

36. Chain Generation . . . . . . . . . . . .

36.1 Thermal Gas-Phase Genel'ation of Active Centers 36.2 Gas-Phase Generation of Active Centers as a Result of Chemical

Interactions . . . . . . . . 36.3 Chain Generation at the Wall

37. Chain Termination

37.1 Homogeneous Chain Termination. 37.2 Heterogeneous Chain Termination. Diffusion and Kinetic Regions 37.3 Stationary Chain Reaction Rates

38. Branched Chains . . . . . . . . .

38.1 Limiting Phenomena. Self-Ignition Peninsula 38.2 Temperature Dependence of the Chain Reaction Rates 38.3 The Role of Impurities in Chain Reactions

39. Hydrogen Combustion as Model Reaction

39.1 Reaction Mechanism ..... . 39.2 Low-Pressure Reaction Kinetics . 39.3 Upper and Lower Ignition Limits 39.4 Induction Period . . . . . . . . 39.5 General Solution of Kinetic Problems

40. Hydrocarbon Oxidation and Combustion Mechanisms

40.1 Combustion Reactions 40.2 Slow Oxidations .

41. Fluorination Reactions

42. Radiation-Chemical Initiation of Chain Reactions

189

189 191

192

192

193 193

193

193 194 195

196

196 198 198

198

198 200 201 201 202

203

203 203

205

206

XIV

Chapter Xll. Combustion Processes

43. Self-Ignition . . . . . . .

43.1 Chain Explosion ... 43.2 Two-Stage Self-Ignition 43.3 Adiabatic Explosion. . 43.4 Account for Incomplete Combustion.

44. Non-Premixed Flames ....

44.1 Highly Rarefied Flames . 44.2 Hot Diffusion Flames

45. Premixed Flames ..

45.1 Rarefied Flames 45.2 Hot Flames . 45.3 Cool Flames . .

46. Flame Propagation .

46.1 Normal Burning Rate. 46.2 Diffusion Flame Propagation 46.3 Thermal Flame Propagation 46.4 Flammability Limits

47. Detonation .

References. .

Subject Index

Contents

209

209

209 209 210 211

212

~12

212

214

214 215 216

217

217 218 219 221

222

226

240