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## Chemical Kinetics ### Reaction Rate * **Definition:** The rate of a chemical reaction is the change in the concentration of a reactant or product per unit time. * Units: $mol \cdot L^{-1} \cdot s^{-1}$ or M/s * **Rate Expression:** For the reaction $aA + bB \rightarrow cC + dD$ $...

## Chemical Kinetics ### Reaction Rate * **Definition:** The rate of a chemical reaction is the change in the concentration of a reactant or product per unit time. * Units: $mol \cdot L^{-1} \cdot s^{-1}$ or M/s * **Rate Expression:** For the reaction $aA + bB \rightarrow cC + dD$ $Rate = -\frac{1}{a}\frac{\Delta[A]}{\Delta t} = -\frac{1}{b}\frac{\Delta[B]}{\Delta t} = \frac{1}{c}\frac{\Delta[C]}{\Delta t} = \frac{1}{d}\frac{\Delta[D]}{\Delta t}$ ### Rate Law * **Definition:** An equation that relates the rate of a reaction to the concentrations of reactants and catalysts. * Determined experimentally * **General Form:** For the reaction $aA + bB \rightarrow cC + dD$ $Rate = k[A]^m[B]^n$ * k = rate constant (temperature dependent) * m = order with respect to A * n = order with respect to B * m + n = overall order of the reaction * The exponents m and n are not necessarily related to the stoichiometric coefficients a and b. ### Integrated Rate Laws Relate the concentration of a reactant to time. | Order | Rate Law | Integrated Rate Law | Half-Life ($t_{1/2}$) | Linear Plot | | :---- | :---------------- | :------------------------------------------------ | :----------------------- | :-------------------------- | | 0 | $Rate = k$ | $[A]_t = -kt + [A]_0$ | $ [A]_0 / 2k$ | $[A]_t$ vs t | | 1 | $Rate = k[A]$ | $ln[A]_t = -kt + ln[A]_0$ | $0.693 / k$ | $ln[A]_t$ vs t | | 2 | $Rate = k[A]^2$ | $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ | $1 / k[A]_0$ | $\frac{1}{[A]_t}$ vs t | ### Collision Theory * **Basic Idea:** Reactant molecules must collide with enough energy and proper orientation to react. * **Activation Energy ($E_a$):** The minimum energy required for a collision to result in a reaction. * **Arrhenius Equation:** $k = Ae^{-E_a / RT}$ * k = rate constant * A = frequency factor (related to the number of collisions and orientation) * $E_a$ = activation energy * R = ideal gas constant (8.314 J/mol·K) * T = temperature (in Kelvin) * **Linear Form of Arrhenius Equation:** $lnk = -\frac{E_a}{R}(\frac{1}{T}) + lnA$ * A plot of lnk vs 1/T gives a straight line with slope $-E_a/R$ and y-intercept lnA. ### Reaction Mechanisms * **Definition:** A series of elementary steps that describe the pathway of a reaction. * **Elementary Step:** A single step in a reaction mechanism. * The rate law for an elementary step can be written directly from the stoichiometry of the step. * Unimolecular: Rate = k[A] * Bimolecular: Rate = k[A][B] or Rate = k[A]$^2$ * **Rate-Determining Step:** The slowest step in a reaction mechanism. The overall rate law is determined by the rate-determining step. * **Catalyst:** A substance that speeds up a reaction without being consumed in the reaction. * Provides an alternate reaction mechanism with a lower activation energy. * Homogeneous catalyst: Present in the same phase as the reactants. * Heterogeneous catalyst: Present in a different phase as the reactants. * **Intermediate:** A species that is produced in one step of a reaction mechanism and consumed in a subsequent step. Intermediates do not appear in the overall balanced equation. ### Catalysis * Catalysts increase reaction rate by lowering the activation energy. * Catalysts are not consumed during the reaction. * Types: * **Homogeneous Catalysis:** Catalyst in the same phase as reactants. * **Heterogeneous Catalysis:** Catalyst in a different phase than reactants, often involving surface adsorption. * **Enzymes:** Biological catalysts that are highly specific. * **Michaelis-Menten Kinetics:** Describes the rate of enzyme-catalyzed reactions. ### Important Notes * Rate laws must be determined experimentally. * The rate constant k is temperature-dependent. * The activation energy $E_a$ can be determined from the slope of an Arrhenius plot. * Reaction mechanisms must be consistent with the experimentally determined rate law.