Preface p. xi
How to use the workbooks, exercises, and problems p. xvii
Generalities about the rates of chemical reactions p. 1
Introduction p. 1
Chemical kinetics: what is it? p. 1
The rate of a chemical reaction p. 4
How to define the rate of a reaction p. 4
The extent of reaction p. 4
The evolution of the extent of reaction p. 6
The reaction rate p. 6
Mass conservation in a chemical reaction p. 8
Example: rate of decomposition of uranyl nitrate p. 9
The general scheme of kinetics p. 11
Let us add some theory: a phenomenological approach p. 13
Testing the equation and determining the rate constant p. 14
Concentration p. 16
A summary of what you need to know about differential equations p. 18
A differential equation has an infinite number of solutions p. 19
The initial condition p. 20
How to solve differential equations: a practical guide p. 21
Systems of differential equations p. 21
Irreversible first-order reactions p. 23
Introduction p. 23
What is an irreversible first-order reaction? p. 23
Unimolecular irreversible reactions p. 23
The rate equation p. 24
Not all unimolecular reactions have a first-order rate p. 24
Solution of the rate equation p. 25
The extent of reaction p. 25
Solving the rate equation to calculate [eta](t) p. 27
The concentrations p. 27
Test whether Eq. 2.10 fits the data and determine the constant k(T, [rho]) p. 28
A crude fitting method p. 28
The least-squares method for fitting the data p. 30
The temperature dependence of the rate constant: the Arrhenius formula p. 33
Introduction p. 33
The Arrhenius formula p. 34
How to determine the parameters in the Arrhenius formula p. 35
How to determine k[subscript 0], E, and n p. 35
How to determine the constants in the Arrhenius equation: the data p. 36
A graphic method for using the Arrhenius formula p. 36
A crude determination of k[subscript 0] and E in the Arrhenius formula p. 37
The determination of k[subscript 0] and E by least-squares fitting p. 38
The activation energy p. 40
Determination of the Arrhenius parameters: a more realistic example p. 40
Fitting the data to determine k[subscript 0] and E p. 41
How do we use these results? p. 45
The decay rate p. 47
Where do these equations come from? p. 47
Why the rate law is dA/dt = -kA? p. 48
Why the Arrhenius law? p. 48
Irreversible second-order reactions p. 51
Introduction p. 51
The rate equation for an irreversible, bimolecular reaction p. 52
The rate equation for the reaction A + B to C + D p. 52
The rate equation for the reaction 2A to C + D p. 53
The rate equation for the reaction A + B to C + D in terms of the extent of reaction p. 53
The dependence of [eta](t) on time p. 54
The evolution of the concentrations p. 55
How to use these kinetic equations in practice p. 57
An example: the problem and the data p. 57
An example: setting up the equations p. 58
An example: numerical analysis of the kinetics p. 59
What controls the decay time p. 61
How to analyze kinetic data for second-order reactions p. 63
An example of analysis p. 64
Calculating k for each data point p. 66
Using a least-squares fitting p. 66
Reversible first-order reactions p. 69
Introduction p. 69
The rate equation and its solution p. 72
The rate equation for concentration p. 72
The evolution of the concentrations p. 74
The change of the extent of reaction and concentration: an example p. 74
Understanding the numerical results in the example p. 76
The connection to thermodynamic equilibrium p. 78
Equilibrium concentration by taking the long time limit in the kinetic theory p. 78
Data analysis: an example p. 80
The conversion of 4-hydroxybutanoic acid to its lactone p. 80
The equations used in analysis p. 81
A method of analysis p. 84
Reversible second-order reactions p. 87
Introduction p. 87
The rate equations p. 88
The equilibrium conditions p. 89
Mass conservation p. 90
The rate equations in terms of the extent of reaction p. 91
A general equation for the rate of change of [eta](t) p. 92
The solution of the general rate equation for [eta](t) p. 94
The solution provided by Mathematica p. 95
Solving the differential equation for [eta](t) by using the methods learned in calculus p. 96
Calculate [eta](t) for the four types of reaction p. 97
The use of these equations p. 98
Analysis of the reaction 2HI [right harpoon over left] H[subscript 2] + I[subscript 2] p. 100
A summary of the equations needed for analysis p. 102
Using the equilibrium information p. 103
Fitting the data to find k[subscript b] p. 105
How to use the results of this analysis p. 106
Coupled reactions p. 109
Introduction p. 109
First-order irreversible parallel reactions p. 111
The rate equations p. 111
Independent variables: the extents of the reactions p. 111
The change of concentration: mass conservation p. 112
The rate equations in terms of [eta subscript 1] and [eta subscript 2] p. 113
Solving the rate equations for [eta subscript 1](t) and [eta subscript 2](t) p. 114
First-order irreversible consecutive reactions p. 116
The rate equations p. 116
Mass conservation p. 117
The rate equations for [eta subscript 1] and [eta subscript 2] p. 118
Solving the rate equations to obtain [eta subscript 1](t) and [eta subscript 2](t) p. 118
The evolution of the concentrations p. 119
The analysis of the results p. 120
The steady-state approximation p. 122
Why this is called the steady-state approximation p. 124
Testing how well the approximation works p. 125
An example of a complex reaction: chain reactions p. 129
Introduction p. 129
The correct rate equation p. 130
The reaction mechanism: chain reactions p. 130
Another chain reaction: nuclear reactors' and nuclear bombs p. 132
The rate equations for the reactions involved in the mechanism p. 134
The rate of change of [HBr] p. 134
The rate of change of [Br] p. 135
The net rate of change for HBr p. 136
Using the five rate equations p. 137
The temperature dependence p. 138
Enzyme kinetics p. 141
Introduction p. 141
The Michaelis-Menten mechanism: exact numerical solution p. 143
The rate equations p. 143
The extents of reaction p. 145
Mass conservation p. 145
The rate equations for [eta subscript 1](t) and [eta subscript 2](t) p. 146
The solution of the rate equations p. 147
The Michaelis-Menten mechanism: the steady-state approximation p. 149
The differential equation for R(t) p. 151
The differential equation for the evolution of P(t) p. 152
Practical use of the steady-state approximation to determine K[subscript m] and k[subscript 2]E(0) p. 152
The evolution of the concentrations in the steady-state approximation p. 155
The evolution of R(t) p. 155
The evolution of P(t) in the steady-state approximation p. 156
The concentration of the complex and of the enzyme in the steady-state approximation p. 156
The Michaelis-Menten mechanism: how good is the steady-state approximation? p. 156
Further reading p. 161
Index p. 163