Rate of reaction for $aA + bB \rightarrow cC + dD$: $\text{rate} = -\dfrac{1}{a}\dfrac{d[A]}{dt} = -\dfrac{1}{b}\dfrac{d[B]}{dt}$; always positive.

Rate law $\text{rate} = k[A]^m[B]^n$ is experimental, not derived from stoichiometry.

Overall order $= m + n$; can be 0, fractional, or any integer.

Units of $k$: zero order $= mol\,L^{-1}\,s^{-1}$; first order $= s^{-1}$; second order $= L\,mol^{-1}\,s^{-1}$; general: $(mol\,L^{-1})^{1-n}\,s^{-1}$.

Zero order: $[A] = [A]_0 - kt$; $t_{1/2} = [A]_0/(2k)$ — proportional to $[A]_0$.

First order: $k = \dfrac{2.303}{t}\log\dfrac{[A]_0}{[A]}$; $t_{1/2} = 0.693/k$ — independent of $[A]_0$.

Second order: $\dfrac{1}{[A]} = \dfrac{1}{[A]_0} + kt$; $t_{1/2} = \dfrac{1}{k[A]_0}$ — inversely proportional to $[A]_0$.

First-order half-life chain: 50% = $1t_{1/2}$; 75% = $2t_{1/2}$; 87.5% = $3t_{1/2}$; 93.75% = $4t_{1/2}$.

Arrhenius equation: $k = Ae^{-E_a/RT}$; $\ln k = \ln A - E_a/RT$.

Two-temperature form: $\log\dfrac{k_2}{k_1} = \dfrac{E_a}{2.303R}\!\left(\dfrac{1}{T_1} - \dfrac{1}{T_2}\right)$; slope of $\ln k$ vs $1/T = -E_a/R$.

Order — experimental, can be zero/fractional/integer, applies to overall reaction, can change with conditions.

Molecularity — theoretical, always positive integer 1/2/3, applies to elementary steps only, cannot change.

Rate-determining step (slowest step) controls the overall rate law for a multi-step reaction.

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

Catalyst lowers $E_a$ but does not change $\Delta H$ or the equilibrium constant $K$.

Pseudo first-order: one reactant in large excess; classic example — ethyl acetate hydrolysis in excess water.

Temperature coefficient $\approx 2$ to 3 (rate doubles or triples per 10 °C rise).

Radioactive decay, $\text{H}_2\text{O}_2$ decomposition, $\text{N}_2\text{O}_5$ decomposition — all first order.

$\text{NH}_3$ decomposition on Pt at high pressure — zero order (surface saturation).