Integrated Rate Equations
- Zero Order Reaction ($r = k$):
$$k = \frac{[R]_0 - [R]}{t}, \quad t_{1/2} = \frac{[R]_0}{2k}$$
- First Order Reaction ($r = k[R]$):
$$k = \frac{2.303}{t}\log_{10}\frac{[R]_0}{[R]}, \quad t_{1/2} = \frac{0.693}{k} \quad (\text{independent of } [R]_0!)$$
Arrhenius Equation & Activation Energy
$$k = A e^{-E_a / RT} \implies \log_{10}\frac{k_2}{k_1} = \frac{E_a}{2.303 R}\left[\frac{T_2 - T_1}{T_1 T_2}\right]$$
