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# Chemical Kinetics ## Reaction Rate * Rate determining step: the slowest step in a reaction mechanism. * Reaction rate can be expressed as the rate of disappearance of reactants or the rate of appearance of products. $aA + bB \rightarrow cC + dD$ rate $= -\frac{1}{a} \frac{\Delta [A...

# Chemical Kinetics ## Reaction Rate * Rate determining step: the slowest step in a reaction mechanism. * Reaction rate can be expressed as the rate of disappearance of reactants or the rate of appearance of products. $aA + bB \rightarrow cC + dD$ rate $= -\frac{1}{a} \frac{\Delta [A]}{\Delta t} = -\frac{1}{b} \frac{\Delta [B]}{\Delta t} = \frac{1}{c} \frac{\Delta [C]}{\Delta t} = \frac{1}{d} \frac{\Delta [D]}{\Delta t}$ ## Order of Reaction ### Rate Law Expression rate $= k[A]^x [B]^y$ * $[A]$ and $[B]$ are the concentrations of reactants. * $x$ and $y$ are the orders with respect to the reactants $A$ and $B$, respectively. * $k$ is the rate constant. * Overall order of reaction $= x + y$ * The values of $x$ and $y$ must be determined experimentally. ### Zero Order rate $= k[A]^0 = k$ * The rate of reaction is independent of the concentration of the reactant. * $[A]_t = [A]_0 - kt$ * $t_{1/2} = \frac{[A]_0}{2k}$ * Half-life is dependent on initial concentration. ### First Order rate $= k[A]^1 = k[A]$ * The rate of reaction is directly proportional to the concentration of the reactant. * $\ln[A]_t = \ln[A]_0 - kt$ * $t_{1/2} = \frac{0.693}{k}$ * Half-life is independent of initial concentration. ### Second Order rate $= k[A]^2$ * The rate of reaction is proportional to the square of the concentration of the reactant. * $\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$ * $t_{1/2} = \frac{1}{k[A]_0}$ * Half-life is inversely proportional to initial concentration. ## Activation Energy ### Arrhenius Equation $k = Ae^{-E_a/RT}$ * $k$ is the rate constant. * $A$ is the frequency factor. * $E_a$ is the activation energy. * $R$ is the gas constant ($8.314 \text{ J/mol K}$). * $T$ is the temperature in Kelvin. ### Linear Form $\ln k = -\frac{E_a}{R} (\frac{1}{T}) + \ln A$ ### Two-Point Form $\ln \frac{k_2}{k_1} = \frac{E_a}{R} (\frac{1}{T_1} - \frac{1}{T_2})$ ## Reaction Mechanisms * Elementary step: a single step in a reaction mechanism. * Molecularity: the number of molecules that participate in an elementary step. * Unimolecular: one molecule participates in the elementary step. * Bimolecular: two molecules participate in the elementary step. * Termolecular: three molecules participate in the elementary step. * Rate-determining step: the slowest step in a reaction mechanism. * The rate law for the rate-determining step determines the rate law for the overall reaction. * Intermediates: species that are formed in one step and consumed in a subsequent step. * Catalyst: a substance that increases the rate of a reaction but is not consumed in the reaction. * Homogeneous catalyst: a catalyst that is in the same phase as the reactants. * Heterogeneous catalyst: a catalyst that is in a different phase from the reactants.