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## Chemical Kinetics ### Reaction Rates * **Definition:** Chemical kinetics is the study of reaction rates, factors affecting them, and the mechanism by which reactions occur. * **Rate of Reaction:** * The change in concentration of a reactant or product per unit time. * For the re...

## Chemical Kinetics ### Reaction Rates * **Definition:** Chemical kinetics is the study of reaction rates, factors affecting them, and the mechanism by which reactions occur. * **Rate of Reaction:** * The change in concentration of a reactant or product per unit time. * For the reaction $aA + bB \rightarrow cC + dD$: * Rate $= -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$ * Negative signs indicate reactants are disappearing. ### Rate Law * **Definition:** An equation that relates the rate of a reaction to the concentrations of reactants. * **General Form:** For the reaction $aA + bB \rightarrow cC + dD$ * Rate $= k[A]^m[B]^n$ * k = rate constant * m = order with respect to A * n = order with respect to B * m + n = overall order of the reaction * **Determining Reaction Order:** Experimentally determined; cannot be deduced from stoichiometry. ### Integrated Rate Laws Relate concentration of reactants to time. | Order | Rate Law | Integrated Rate Law | Half-Life ($t_{1/2}$) | Linear Plot | | :---- | :---------------- | :------------------------------------------------------------ | :---------------------- | :--------------------------- | | 0 | Rate = k | $[A]_t = -kt + [A]_0$ | $\frac{[A]_0}{2k}$ | $[A]_t$ vs t | | 1 | Rate = k\[A] | $ln[A]_t = -kt + ln[A]_0$ | $\frac{0.693}{k}$ | $ln[A]_t$ vs t | | 2 | Rate = k\[A]^2 | $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ | $\frac{1}{k[A]_0}$ | $\frac{1}{[A]_t}$ vs t | ### Activation Energy and Temperature Dependence * **Arrhenius Equation:** $k = Ae^{-\frac{E_a}{RT}}$ * k = rate constant * A = frequency factor * $E_a$ = activation energy * R = gas constant (8.314 J/mol·K) * T = temperature (in Kelvin) * **Activation Energy ($E_a$):** The minimum energy required for a reaction to occur. * **Effect of Temperature:** As temperature increases, the rate constant (k) increases, and the reaction rate generally increases. ### Reaction Mechanisms * **Definition:** A series of elementary steps that describe how a reaction occurs. * **Elementary Step:** A single step in a reaction mechanism. * **Rate-Determining Step:** The slowest step in a mechanism determines the overall rate of the reaction. * **Molecularity:** The number of molecules involved in an elementary step (e.g., unimolecular, bimolecular). * **Catalyst:** * Substance that speeds up a reaction without being consumed. * Provides an alternate reaction pathway with a lower activation energy. * Can be homogeneous (same phase) or heterogeneous (different phase).