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# Chemical Kinetics ### Reaction Rate $aA + bB \longrightarrow cC + dD$ $Rate = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$ ### Rate Law $aA + bB \longrightarrow cC + dD$ $Rate = k[A]^x[B]^y$ - k is the rate constant - x...

# Chemical Kinetics ### Reaction Rate $aA + bB \longrightarrow cC + dD$ $Rate = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$ ### Rate Law $aA + bB \longrightarrow cC + dD$ $Rate = k[A]^x[B]^y$ - k is the rate constant - x is the order with respect to A - y is the order with respect to B - x + y is the overall order of the reaction ### Integrated Rate Laws | Order | Rate Law | Integrated Rate Law | Linear Plot | Slope | Intercept | Half-life | | :---- | :-------------- | :-------------------------------------------------- | :--------------------------------- | :-------- | :-------- | :----------------------- | | 0 | $Rate = k$ | $[A]_t = -kt + [A]_0$ | $[A]_t$ vs t | -k | $[A]_0$ | $t_{1/2} = [A]_0/2k$ | | 1 | $Rate = k[A]$ | $ln[A]_t = -kt + ln[A]_0$ | $ln[A]_t$ vs t | -k | $ln[A]_0$ | $t_{1/2} = 0.693/k$ | | 2 | $Rate = k[A]^2$ | $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$ | $\frac{1}{[A]_t}$ vs t | k | $\frac{1}{[A]_0}$ | $t_{1/2} = 1/k[A]_0$ | | 2 | $Rate = k[A][B]$| $ln(\frac{[A]_t}{[B]_t}) = ([A]_0-[B]_0)kt + ln(\frac{[A]_0}{[B]_0})$ | $ln(\frac{[A]_t}{[B]_t})$ vs t | $([A]_0-[B]_0)k$ | $ln(\frac{[A]_0}{[B]_0})$ | N/A | ### Arrhenius Equation $k = Ae^{-\frac{E_a}{RT}}$ - k is the rate constant - A is the frequency factor - $E_a$ is the activation energy - R is the ideal gas constant (8.314 J/mol K) - T is the temperature in Kelvin $ln(k) = -\frac{E_a}{R}\frac{1}{T} + ln(A)$ $ln(\frac{k_2}{k_1}) = -\frac{E_a}{R}(\frac{1}{T_2} - \frac{1}{T_1})$ ### Reaction Mechanisms **Elementary step:** A reaction that occurs in a single step **Reaction mechanism:** A series of elementary steps that make up a complex reaction **Intermediate:** A species that is formed in one elementary step and consumed in another **Rate-determining step:** The slowest elementary step in a reaction mechanism ### Catalysis **Catalyst:** A substance that speeds up a reaction without being 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 as the reactants **Enzyme:** A biological catalyst **Inhibitor:** A substance that slows down a reaction