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| Preface | |
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| How to use the workbooks, exercises, and problems | |
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| Generalities about the rates of chemical reactions | |
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| Introduction | |
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| Chemical kinetics: what is it? | |
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| The rate of a chemical reaction | |
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| How to define the rate of a reaction | |
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| The extent of reaction | |
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| The evolution of the extent of reaction | |
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| The reaction rate | |
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| Mass conservation in a chemical reaction | |
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| Example: rate of decomposition of uranyl nitrate | |
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| The general scheme of kinetics | |
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| Let us add some theory: a phenomenological approach | |
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| Testing the equation and determining the rate constant | |
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| Concentration | |
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| A summary of what you need to know about differential equations | |
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| A differential equation has an infinite number of solutions | |
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| The initial condition | |
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| How to solve differential equations: a practical guide | |
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| Systems of differential equations | |
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| Irreversible first-order reactions | |
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| Introduction | |
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| What is an irreversible first-order reaction? | |
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| Unimolecular irreversible reactions | |
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| The rate equation | |
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| Not all unimolecular reactions have a first-order rate | |
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| Solution of the rate equation | |
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| The extent of reaction | |
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| Solving the rate equation to calculate [eta](t) | |
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| The concentrations | |
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| Test whether Eq. 2.10 fits the data and determine the constant k(T, [rho]) | |
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| A crude fitting method | |
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| The least-squares method for fitting the data | |
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| The temperature dependence of the rate constant: the Arrhenius formula | |
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| Introduction | |
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| The Arrhenius formula | |
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| How to determine the parameters in the Arrhenius formula | |
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| How to determine k[subscript 0], E, and n | |
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| How to determine the constants in the Arrhenius equation: the data | |
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| A graphic method for using the Arrhenius formula | |
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| A crude determination of k[subscript 0] and E in the Arrhenius formula | |
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| The determination of k[subscript 0] and E by least-squares fitting | |
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| The activation energy | |
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| Determination of the Arrhenius parameters: a more realistic example | |
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| Fitting the data to determine k[subscript 0] and E | |
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| How do we use these results? | |
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| The decay rate | |
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| Where do these equations come from? | |
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| Why the rate law is dA/dt = -kA? | |
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| Why the Arrhenius law? | |
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| Irreversible second-order reactions | |
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| Introduction | |
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| The rate equation for an irreversible, bimolecular reaction | |
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| The rate equation for the reaction A + B to C + D | |
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| The rate equation for the reaction 2A to C + D | |
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| The rate equation for the reaction A + B to C + D in terms of the extent of reaction | |
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| The dependence of [eta](t) on time | |
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| The evolution of the concentrations | |
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| How to use these kinetic equations in practice | |
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| An example: the problem and the data | |
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| An example: setting up the equations | |
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| An example: numerical analysis of the kinetics | |
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| What controls the decay time | |
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| How to analyze kinetic data for second-order reactions | |
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| An example of analysis | |
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| Calculating k for each data point | |
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| Using a least-squares fitting | |
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| Reversible first-order reactions | |
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| Introduction | |
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| The rate equation and its solution | |
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| The rate equation for concentration | |
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| The evolution of the concentrations | |
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| The change of the extent of reaction and concentration: an example | |
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| Understanding the numerical results in the example | |
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| The connection to thermodynamic equilibrium | |
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| Equilibrium concentration by taking the long time limit in the kinetic theory | |
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| Data analysis: an example | |
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| The conversion of 4-hydroxybutanoic acid to its lactone | |
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| The equations used in analysis | |
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| A method of analysis | |
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| Reversible second-order reactions | |
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| Introduction | |
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| The rate equations | |
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| The equilibrium conditions | |
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| Mass conservation | |
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| The rate equations in terms of the extent of reaction | |
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| A general equation for the rate of change of [eta](t) | |
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| The solution of the general rate equation for [eta](t) | |
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| The solution provided by Mathematica | |
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| Solving the differential equation for [eta](t) by using the methods learned in calculus | |
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| Calculate [eta](t) for the four types of reaction | |
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| The use of these equations | |
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| Analysis of the reaction 2HI [right harpoon over left] H[subscript 2] + I[subscript 2] | |
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| A summary of the equations needed for analysis | |
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| Using the equilibrium information | |
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| Fitting the data to find k[subscript b] | |
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| How to use the results of this analysis | |
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| Coupled reactions | |
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| Introduction | |
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| First-order irreversible parallel reactions | |
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| The rate equations | |
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| Independent variables: the extents of the reactions | |
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| The change of concentration: mass conservation | |
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| The rate equations in terms of [eta subscript 1] and [eta subscript 2] | |
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| Solving the rate equations for [eta subscript 1](t) and [eta subscript 2](t) | |
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| First-order irreversible consecutive reactions | |
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| The rate equations | |
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| Mass conservation | |
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| The rate equations for [eta subscript 1] and [eta subscript 2] | |
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| Solving the rate equations to obtain [eta subscript 1](t) and [eta subscript 2](t) | |
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| The evolution of the concentrations | |
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| The analysis of the results | |
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| The steady-state approximation | |
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| Why this is called the steady-state approximation | |
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| Testing how well the approximation works | |
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| An example of a complex reaction: chain reactions | |
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| Introduction | |
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| The correct rate equation | |
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| The reaction mechanism: chain reactions | |
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| Another chain reaction: nuclear reactors' and nuclear bombs | |
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| The rate equations for the reactions involved in the mechanism | |
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| The rate of change of [HBr] | |
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| The rate of change of [Br] | |
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| The net rate of change for HBr | |
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| Using the five rate equations | |
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| The temperature dependence | |
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| Enzyme kinetics | |
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| Introduction | |
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| The Michaelis-Menten mechanism: exact numerical solution | |
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| The rate equations | |
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| The extents of reaction | |
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| Mass conservation | |
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| The rate equations for [eta subscript 1](t) and [eta subscript 2](t) | |
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| The solution of the rate equations | |
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| The Michaelis-Menten mechanism: the steady-state approximation | |
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| The differential equation for R(t) | |
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| The differential equation for the evolution of P(t) | |
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| Practical use of the steady-state approximation to determine K[subscript m] and k[subscript 2]E(0) | |
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| The evolution of the concentrations in the steady-state approximation | |
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| The evolution of R(t) | |
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| The evolution of P(t) in the steady-state approximation | |
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| The concentration of the complex and of the enzyme in the steady-state approximation | |
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| The Michaelis-Menten mechanism: how good is the steady-state approximation? | |
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| Further reading | |
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| Index | |