Introduction to Chemical Kinetics

Preface.

List of Symbols.

1. Introduction.

2. Experimental Procedures.

2.1 Detection, Identification and Estimation of Concentration of Species Present.

2.1.1 Chromatographic techniques: liquid-liquid and gas-liquid chromatography.

2.1.2 Mass spectrometry (MS).

2.1.3 Spectroscopic techniques.

2.1.4 Lasers.

2.1.5 Fluorescence.

2.1.6 Spin resonance methods: nuclear magnetic resonance (NMR).

2.1.7 Spin resonance methods: electron spin resonance (ESR).

2.1.8 Photoelectron spectroscopy and X-ray photoelectron spectroscopy.

2.2 Measuring the Rate of a Reaction.

2.2.1 Classification of reaction rates.

2.2.2 Factors affecting the rate of reaction.

2.2.3 Common experimental features for all reactions.

2.2.4 Methods of initiation.

2.3 Conventional Methods of Following a Reaction.

2.3.1 Chemical methods.

2.3.2 Physical methods.

2.4 Fast Reactions.

2.4.1 Continuous flow.

2.4.2 Stopped flow.

2.4.3 Accelerated flow.

2.4.4 Some features of flow methods.

2.5 Relaxation Methods.

2.5.1 Large perturbations.

2.5.2 Flash photolysis.

2.5.3 Laser photolysis.

2.5.4 Pulsed radiolysis.

2.5.5 Shock tubes.

2.5.6 Small perturbations: temperature, pressure and electric field jumps.

2.6 Periodic Relaxation Techniques: Ultrasonics.

2.7 Line Broadening in NMR and ESR Spectra.

Further Reading.

Further Problems.

3. The Kinetic Analysis of Experimental Data.

3.1 The Experimental Data.

3.2 Dependence of Rate on Concentration.

3.3 Meaning of the Rate Expression.

3.4 Units of the Rate Constant, k.

3.5 The Significance of the Rate Constant as Opposed to the Rate.

3.6 Determining the Order and Rate Constant from Experimental Data.

3.7 Systematic Ways of Finding the Order and Rate Constant from Rate/Concentration Data.

3.7.1 A straightforward graphical method.

3.7.2 log/log Graphical procedures.

3.7.3 A systematic numerical procedure.

3.8 Drawbacks of the Rate/Concentration Methods of Analysis.

3.9 Integrated Rate Expressions.

3.9.1 Half-lives.

3.10 First Order Reactions.

3.10.1 The half-life for a first order reaction.

3.10.2 An extra point about first order reactions.

3.11 Second Order Reactions.

3.11.1 The half-life for a second order reaction.

3.11.2 An extra point about second order reactions.

3.12 Zero Order Reaction.

3.12.1 The half-life for a zero order reaction.

3.13 Integrated Rate Expressions for Other Orders.

3.14 Main Features of Integrated Rate Equations.

3.15 Pseudo-order Reactions.

3.15.1 Application of pseudo-order techniques to rate/concentration data.

3.16 Determination of the Product Concentration at Various Times.

3.17 Expressing the Rate in Terms of Reactants or Products for Non-simple Stoichiometry.

3.18 The Kinetic Analysis for Complex Reactions.

3.18.1 Relatively simple reactions that are mathematically complex.

3.18.2 Analysis of the simple scheme A_!

3.18.3 Two conceivable situations.

3.19 The Steady State Assumption.

3.19.1 Using this assumption.

3.20 General Treatment for Solving Steady States.

3.21 Reversible Reactions.

3.21.1 Extension to other equilibria.

3.22 Pre-equilibria.

3.23 Dependence of Rate on Temperature.

Further Reading.

Further Problems.

4. Theories of Chemical Reactions.

4.1 Collision Theory.

4.1.1 Definition of a collision in simple collision theory.

4.1.2 Formulation of the total collision rate.

4.1.3 The p factor.

4.1.4 Reaction between like molecules.

4.2 Modified Collision Theory.

4.2.1 A new definition of a collision.

4.2.2 Reactive collisions.

4.2.3 Contour diagrams for scattering of products of a reaction.

4.2.4 Forward scattering: the stripping or grazing mechanism.

4.2.5 Backward scattering: the rebound mechanism.

4.2.6 Scattering diagrams for long-lived complexes.

4.3 Transition State Theory.

4.3.1 Transition state theory, configuration and potential energy.

4.3.2 Properties of the potential energy surface relevant to transition state theory.

4.3.3 An outline of arguments involved in the derivation of the rate equation.

4.3.4 Use of the statistical mechanical form of transition state theory.

4.3.5 Comparisons with collision theory and experimental data.

4.4 Thermodynamic Formulations of Transition State Theory.

4.4.1 Determination of thermodynamic functions for activation.

4.4.2 Comparison of collision theory, the partition function form and the thermodynamic form of transition state theory.

4.4.3 Typical approximate values of contributions entering the sign and magnitude of _S61/4_.

4.5 Unimolecular Theory.

4.5.1 Manipulation of experimental results.

4.5.2 Physical significance of the constancy or otherwise of k1, k_1 and k2.

4.5.3 Physical significance of the critical energy in unimolecular reactions.

4.5.4 Physical significance of the rate constants k1, k_1 and k2.

4.5.5 The simple model: that of Lindemann.

4.5.6 Quantifying the simple model.

4.5.7 A more complex model: that of Hinshelwood.

4.5.8 Quantifying Hinshelwood's theory.

4.5.9 Critique of Hinshelwood's theory.

4.5.10 An even more complex model: that of Kassel.

4.5.11 Critique of the Kassel theory.

4.5.12 Energy transfer in the activation step.

4.6 The Slater Theory.

Further Reading.

Further Problems.

5. Potential Energy Surfaces.

5.1 The Symmetrical Potential Energy Barrier.

5.2 The Early Barrier.

5.3 The Late Barrier.

5.4 Types of Elementary Reaction Studied.

5.5 General Features of Early Potential Energy Barriers for Exothermic Reactions.

5.6 General Features of Late Potential Energy Surfaces for Exothermic Reactions.

5.6.1 General features of late potential energy surfaces where the attacking atom is light.

5.6.2 General features of late potential energy surfaces for exothermic reactions where the attacking atom is heavy.

5.7 Endothermic Reactions.

5.8 Reactions with a Collision Complex and a Potential Energy Well

Further Reading.

Further Problems.

6. Complex Reactions in the Gas Phase.

6.1 Elementary and Complex Reactions.

6.2 Intermediates in Complex Reactions.

6.3 Experimental Data.

6.4 Mechanistic Analysis of Complex Non-chain Reactions.

6.5 Kinetic Analysis of a Postulated Mechanism: Use of the Steady State Treatment.

6.5.1 A further example where disentangling of the kinetic data is necessary.

6.6 Kinetically Equivalent Mechanisms.

6.7 A Comparison of Steady State Procedures and Equilibrium Conditions in the Reversible Reaction.

6.8 The Use of Photochemistry in Disentangling Complex Mechanisms.

6.8.1 Kinetic features of photochemistry.

6.8.2 The reaction of H2 with I2.

6.9 Chain Reactions.

6.9.1 Characteristic experimental features of chain reactions.

6.9.2 Identification of a chain reaction.

6.9.3 Deduction of a mechanism from experimental data.

6.9.4 The final stage: the steady state analysis.

6.10 Inorganic Chain Mechanisms.

6.10.1 The H2/Br2 reaction.

6.10.2 The steady state treatment for the H2/Br2 reaction.

6.10.3 Reaction without inhibition.

6.10.4 Determination of the individual rate constants.

6.11 Steady State Treatments and Possibility of Determination of All the Rate Constants.

6.11.1 Important points to note.

6.12 Stylized Mechanisms: A Typical Rice-Herzfeld Mechanism.

6.12.1 Dominant termination steps.

6.12.2 Relative rate constants for termination steps.

6.12.3 Relative rates of the termination steps.

6.12.4 Necessity for third bodies in termination.

6.12.5 The steady state treatment for chain reactions, illustrating the use of the long chain approximation.

6.12.6 Further problems on steady states and the Rice-Herzfeld mechanism.

6.13 Special Features of the Termination Reactions: Termination at the Surface.

6.13.1 A general mechanism based on the Rice-Herzfeld mechanism used previously.

6.14 Explosions.

6.14.1 Autocatalysis and autocatalytic explosions.

6.14.2 Thermal explosions.

6.14.3 Branched chain explosions.

6.14.4 A highly schematic and simplified mechanism for a branched chain reaction.

6.14.5 Kinetic criteria for non-explosive and explosive reaction.

6.14.6 A typical branched chain reaction showing explosion limits.

6.14.7 The dependence of rate on pressure and temperature.

6.15 Degenerate Branching or Cool Flames.

6.15.1 A schematic mechanism for hydrocarbon combustion.

6.15.2 Chemical interpretation of 'cool' flame behaviour.

Further Reading.

Further Problems.

7. Reactions in Solution.

7.1 The Solvent and its Effect on Reactions in Solution.

7.2 Collision Theory for Reactions in Solution.

7.2.1 The concepts of ideality and non-ideality.

7.3 Transition State Theory for Reactions in Solution.

7.3.1 Effect of non-ideality: the primary salt effect.

7.3.2 Dependence of _S61/4_ and _H61/4_ on ionic strength.

7.3.3 The effect of the solvent.

7.3.4 Extension to include the effect of non-ideality.

7.3.5 Deviations from predicted behaviour.

7.4 _S61/4_ and Pre-exponential A Factors.

7.4.1 A typical problem in graphical analysis.

7.4.2 Effect of the molecularity of the step for which _S61/4_ is found.

7.4.3 Effect of complexity of structure.

7.4.4 Effect of charges on reactions in solution.

7.4.5 Effect of charge and solvent on _S61/4_ for ion-ion reactions.

7.4.6 Effect of charge and solvent on _S61/4_ for ion-molecule reactions.

7.4.7 Effect of charge and solvent on _S61/4_ for molecule-molecule reactions.

7.4.8 Effects of changes in solvent on _S61/4_.

7.4.9 Changes in solvation pattern on activation, and the effect on A factors for reactions involving charges and charge-separated species in solution.

7.4.10 Reactions between ions in solution.

7.4.11 Reaction between an ion and a molecule.

7.4.12 Reactions between uncharged polar molecules.

7.5 _H61/4_ Values.

7.5.1 Effect of the molecularity of the step for which the _H61/4_ value is found.

7.5.2 Effect of complexity of structure.

7.5.3 Effect of charge and solvent on _H61/4_ for ion-ion and ion-molecule reactions.

7.5.4 Effect of the solvent on _H61/4_ for ion-ion and ion-molecule reactions.

7.5.5 Changes in solvation pattern on activation and the effect on _H61/4_.

7.6 Change in Volume on Activation, _V61/4_.

7.6.1 Effect of the molecularity of the step for which _V61/4_ is found.

7.6.2 Effect of complexity of structure.

7.6.3 Effect of charge on _V61/4_ for reactions between ions.

7.6.4 Reactions between an ion and an uncharged molecule.

7.6.5 Effect of solvent on _V61/4_.

7.6.6 Effect of change of solvation pattern on activation and its effect on _V61/4_.

7.7 Terms Contributing to Activation Parameters.

7.7.1 _S61/4_.

7.7.2 _V61/4_.

7.7.3 _H61/4_.

Further Reading.

Further Problems.

8. Examples of Reactions in Solution.

8.1 Reactions Where More than One Reaction Contributes to the Rate of Removal of Reactant.

8.1.1 A simple case.

8.1.2 A slightly more complex reaction where reaction occurs by two concurrent routes, and where both reactants are in equilibrium with each other.

8.1.3 Further disentangling of equilibria and rates, and the possibility of kinetically equivalent mechanisms.

8.1.4 Distinction between acid and base hydrolyses of esters.

8.2 More Complex Kinetic Situations Involving Reactants in Equilibrium with Each Other and Undergoing Reaction.

8.2.1 A further look at the base hydrolysis of glycine ethyl ester as an illustration of possible problems.

8.2.2 Decarboxylations of _-keto-monocarboxylic acids.

8.2.3 The decarboxylation of _-keto-dicarboxylic acids.

8.3 Metal Ion Catalysis.

8.4 Other Common Mechanisms.

8.4.1 The simplest mechanism.

8.4.2 Kinetic analysis of the simplest mechanism.

8.4.3 A slightly more complex scheme.

8.4.4 Standard procedure for determining the expression for kobs for the given mechanism.

8.5 Steady States in Solution Reactions.

8.5.1 Types of reaction for which a steady state treatment could be relevant.

8.5.2 A more detailed analysis of Worked Problem 6.5.

8.6 Enzyme Kinetics.

Further Reading.

Further Problems.

Answers to Problems.

List of Specific Reactions.

Index.