Chemical kinetics and reaction dynamics

265 Pages·2006·1.339 MB·English

by  Santosh K Upadhyay

Chemical Kinetics and
Reaction Dynamics
Chemical Kinetics and
Reaction Dynamics
Santosh K. Upadhyay
Department of Chemistry
Harcourt Butler Technological Institute
Kanpur-208 002, India

Anamaya
A C.I.P. catalogue record for the book is available from the Library of Congress
ISBN 1-4020-4546-8 (HB)
ISBN 1-4020-4547-6 (e-book)
Copublished by Springer
233 Spring Street, New York 10013, USA
with Anamaya Publishers, New Delhi, India
Sold and distributed in North, Central and South America by
Springer, 233 Spring Street, New York, USA
In all the countries, except India, sold and distributed by
Springer, P.O. Box 322, 3300 AH Dordrecht, The Netherlands
In India, sold and distributed by Anamaya Publishers
F-154/2, Lado Sarai, New Delhi-110 030, India
All rights reserved. This work may not be translated or copied in whole or in part
without the written permission of the publisher (Springer Science+Business Media,
Inc., 233 Spring Street, New York, 10013, USA), except for brief excerpts in connection
with reviews or scholarly adaptation, computer software, or by similar or dissimilar
methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks and similar terms,
even if they are not identified as such, is not to be taken as an expression of opinion as

to whether or not they are subject to proprietary rights.
Copyright © 2006 Anamaya Publishers
9 8 7 6 5 4 3 2 1
springeronline.com
Printed in India.
To
My Mother
Preface
Reaction dynamics is the part of chemical kinetics which is concerned with
the microscopic-molecular dynamic behavior of reacting systems. Molecular
reaction dynamics is coming of age and much more refined state-to-state
information is becoming available on the fundamental reactions. The
contribution of molecular beam experiments and laser techniques to chemical
dynamics has become very useful in the study of isolated molecules and
their mutual interactions not only in gas surface systems, but also in solute-
solution systems.
This book presents the important facts and theories relating to the rates
with which chemical reactions occur and covers main points in a manner so
that the reader achieves a sound understanding of the principles of chemical
kinetics. A detailed stereochemical discussion of the reaction steps in each
mechanism and their relationship with kinetic observations has been considered.
I would like to take the opportunity to thank Professor R.C. Srivastava
and Professor N. Sathyamurthy with whom I had the privilege of working
and who inspired my interest in the subject and contributed in one way or
another to help complete this book. I express my heavy debt of gratitude
towards Professor M.C. Agrawal who was gracious enough for sparing time
out of his busy schedule to go through the manuscript. His valuable comments
and suggestions, of course, enhanced the value and importance of this book.
I also express my gratitude to my colleagues, friends and research students,
especially Dr. Neelu Kambo who took all the pains in helping me in preparing,
typing and checking the manuscript.
Finally, I thank my wife Mrs. Manju Upadhyay, daughter Neha and son
Ankur for their continuous inspiration during the preparation of the text.

SANTOSH K. UPADHYAY
Contents
Preface vii
1. Elementary 1
1.1 Rate of Reaction 1
1.1.1 Experimental Determination of Rate 2
1.2 Rate Constant 3
1.3 Order and Molecularity 4
1.4 Rate Equations 6
1.4.1 Integral Equations for nth Order Reaction of a Single
Reactant 6
1.4.2 Integral Equations for Reactions Involving More than
One Reactants 7
1.5 Half-life of a Reaction 8
1.6 Zero Order Reactions 10
1.7 First Order Reactions 12
1.8 Radioactive Decay as a First Order Phenomenon 17
1.9 Second Order Reactions 20
1.10 Third Order Reactions 28
1.11 Determination of Order of Reaction 30
1.11.1 Integration Method 30
1.11.2 Half-life Period Method 34
1.11.3 Graphical Method 34
1.11.4 Differential Method 35
1.11.5 Ostwald Isolation Method 35
1.12 Experimental Methods of Chemical Kinetics 39
1.12.1 Conductometric Method 39
1.12.2 Polarographic Technique 40
1.12.3 Potentiometric Method 41
1.12.4 Optical Methods 42
1.12.5 Refractometry 42
1.12.6 Spectrophotometry 43
Exercises 44
2. Temperature Effect on Reaction Rate 46
2.1 Derivation of Arrhenius Equation 46
x Contents
2.2 Experimental Determination of Energy of Activation and
Arrhenius Factor 48
2.3 Potential Energy Surface 50
2.4 Significance of Energy of Activation 51
Exercises 53
3. Complex Reactions 55
3.1 Reversible Reactions 55
3.1.1 Reversible Reaction When Both the Opposing
Processes are Second Order 57
3.2 Parallel Reactions 59
3.2.1 Determination of Rate Constants 59
3.3 Consecutive Reactions 63
3.3.1 Concentration-Time Relation 64
3.4 Steady-State Treatment 66
3.5 Chain Reactions 67
3.5.1 Rate Determination 68
3.5.2 Reaction between H and Br 69
2 2
3.5.3 Chain Length 70
3.5.4 Chain Transfer Reactions 70
3.5.5 Branching Chain Explosions 70
3.5.6 Kinetics of Branching Chain Explosion 71
3.5.7 Free Radical Chains 72
3.5.8 Chain Length and Activation Energy in Chain
Reactions 75
Exercises 76
4. Theories of Reaction Rate 79
4.1 Equilibrium and Rate of Reaction 79
4.2 Partition Functions and Statistical Mechanics of
Chemical Equilibrium 80
4.3 Partition Functions and Activated Complex 82
4.4 Collision Theory 83
4.4.1 Collision Frequency 84
4.4.2 Energy Factor 86
4.4.3 Orientation Factor 87
4.4.4 Rate of Reaction 87
4.4.5 Weakness of the Collision Theory 88
4.5 Transition State Theory 89
4.5.1 Thermodynamic Approach 91
4.5.2 Partition Function Approach 93
4.5.3 Comparison with Arrhenius Equation and Collision
Theory 93
4.5.4 Explanation for Steric Factor in Terms of Partition
Function 94
Contents xi
4.5.5 Reaction between Polyatomic Molecules 95
4.6 Unimolecular Reactions and the Collision Theory 100
4.6.1 Lindemann’s Mechanism 100
4.6.2 Hinshelwood Treatment 103
4.6.3 Rice and Ramsperger, and Kassel (RRK) Treatment 105
4.6.4 Marcus Treatment 106
4.6.5 RRKM Theory 107
4.7 Kinetic and Thermodynamic Control 109
4.8 Hammond’s Postulate 110
4.9 Probing of the Transition State 111
Exercises 113
5. Kinetics of Some Special Reactions 115
5.1 Kinetics of Photochemical Reactions 115
5.1.1 Grotthuss-Draper Law 115
5.1.2 Einstein Law of Photochemical Equivalence 115
5.1.3 Primary Process in Photochemical Reactions 116
5.1.4 H -Br Reaction 118
2 2
5.1.5 H and Cl Reaction 119
2 2
5.2 Oscillatory Reactions 120
5.2.1 Belousov-Zhabotinskii Reaction 122
5.3 Kinetics of Polymerization 124
5.3.1 Step Growth Polymerization 125
5.3.2 Polycondensation Reactions (in Absence of the
Catalyst) 125
5.3.3 Acid Catalyzed Polycondensation Reaction 126
5.3.4 Chain Growth Polymerization 127
5.3.5 Kinetics of Free Radical Polymerization 127
5.3.6 Cationic Polymerization 130
5.3.7 Anionic Polymerization 131
5.3.8 Co-polymerization 132
5.4 Kinetics of Solid State Reactions 135
5.5 Electron Transfer Reactions 139
5.5.1 Outer Sphere Mechanism 139
5.5.2 Inner Sphere Mechanism 140
Exercises 141
6. Kinetics of Catalyzed Reactions 142
6.1 Catalysis 142
6.1.1 Positive Catalysis 142
6.1.2 Negative Catalysis 143
6.1.3 Auto Catalysis 143
6.1.4 Induced Catalysis 144
6.1.5 Promoters 144
xii Contents
6.1.6 Poisons 144
6.2 Theories of Catalysis 145
6.2.1 Intermediate Compound Formation Theory 145
6.2.2 Adsorption Theory 145
6.3 Characteristics of Catalytic Reactions 146
6.4 Mechanism of Catalysis 147
6.5 Activation Energies of Catalyzed Reactions 149
6.6 Acid Base Catalysis 150
6.7 Enzyme Catalysis 152
6.7.1 Influence of pH 154
6.8 Heterogeneous Catalysis 156
6.9 Micellar Catalysis 159
6.9.1 Models for Micellar Catalysis 161
6.10 Phase Transfer Catalysis 165
6.10.1 General Mechanism 166
6.10.2 Difference between Micellar and Phase Transfer-
Catalyzed Reactions 167
6.11 Kinetics of Inhibition 168
6.11.1 Chain Reactions 168
6.11.2 Enzyme Catalyzed Reactions 169
6.11.3 Inhibition in Surface Reactions 172
Exercises 173
7. Fast Reactions 175
7.1 Introduction 175
7.2 Flow Techniques 176
7.2.1 Continuous Flow Method 177
7.2.2 Accelerated Flow Method 178
7.2.3 Stopped Flow Method 178
7.3 Relaxation Method 179
7.4 Shock Tubes 181
7.5 Flash Photolysis 182
7.6 ESR Spectroscopic Technique 183
7.7 NMR Spectroscopic Techniques 183
Exerc ises 184
8. Reactions in Solutions 185
8.1 Introduction 185
8.2 Theory of Absolute Reaction Rate 185
8.3 Influence of Internal Pressure 187
8.4 Influence of Solvation 187
8.5 Reactions between Ions 187
8.6 Entropy Change 189
8.7 Influence of Ionic Strength (Salt Effect) 190
Contents xiii
8.8 Secondary Salt Effect 192
8.9 Reactions between the Dipoles 193
8.10 Kinetic Isotope Effect 195
8.11 Solvent Isotope Effect 197
8.12 Hemmett Equation 198
8.13 Linear Free Energy Relationship 199
8.14 The Taft Equation 200
8.15 Compensation Effect 201
Exercises 202
9. Reaction Dynamics 204
9.1 Molecular Reaction Dynamics 204
9.2 Microscopic-Macroscopic Relation 205
9.3 Reaction Rate and Rate Constant 207
9.4 Distribution of Velocities of Molecules 209
9.5 Rate of Reaction for Collisions with a Distribution of
Relative Speeds 209
9.6 Collision Cross Sections 210
9.6.1 Cross Section for Hard Sphere Model 210
9.6.2 Collision between Reactive Hard Spheres 211
9.7 Activation Energy 213
9.8 Potential Energy Surface 216
9.8.1 Features of Potential Energy Surface 219
9.8.2 Ab initio Calculation of Potential Energy Surface 222
9.8.3 Fitting of ab initio Potential Energy Surfaces 225
9.8.4 Potential Energy Surfaces for Triatomic Systems 226
9.9 Classical Trajectory Calculations 229
9.9.1 Initial State Properties 230
9.9.2 Final State Properties 232
9.9.3 Calculation of Reaction Cross Section 232
9.10 Potential Energy Surface and Classical Dynamics 234
9.11 Disposal of Excess Energy 239
9.12 Influence of Rotational Energy 240
9.13 Experimental Chemical Dynamics 241
9.13.1 Molecular Beam Technique 241
9.13.2 Stripping and Rebound Mechanisms 243
9.13.3 State-to-State Kinetics 244
Suggested Readings 247
Index 251