Rate of Reaction

$\text{rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = +\frac{1}{c}\frac{d[C]}{dt} = +\frac{1}{d}\frac{d[D]}{dt}$

Rate Law

$\text{rate} = k[A]^m[B]^n \qquad \text{overall order} = m + n$

Units of Rate Constant

$[k] = \left(\frac{mol}{L}\right)^{1-n} \cdot s^{-1}$

Integrated Rate Laws

Half-Life Formulas

$t_{1/2}^{(0)} = \frac{[A]_0}{2k}, \qquad t_{1/2}^{(1)} = \frac{0.693}{k} = \frac{\ln 2}{k}, \qquad t_{1/2}^{(2)} = \frac{1}{k[A]_0}$

Arrhenius Equation

$k = A\,e^{-E_a/RT}$

$\ln k = \ln A - \frac{E_a}{RT}, \qquad \log k = \log A - \frac{E_a}{2.303RT}$

Slope of $\ln k$ vs $1/T$: $\text{slope} = -\dfrac{E_a}{R}$

Two-temperature form:

$\log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\!\left(\frac{1}{T_1} - \frac{1}{T_2}\right), \qquad T_1 < T_2$

Activation Energy Relationship

$E_a(\text{forward}) - E_a(\text{backward}) = \Delta H$

First-Order Half-Life Chain

$[A]_t = [A]_0\left(\frac{1}{2}\right)^n \quad \text{after } n \text{ half-lives}$

Physical Constants

$R = 8.314\,J\,mol^{-1}\,K^{-1} = 1.987\,cal\,mol^{-1}\,K^{-1}$

$\ln 2 = 0.693, \qquad \log 2 = 0.301, \qquad \log 4 = 0.602$