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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 | |