Key Equations

relative reaction rates for a A ⟶ b B = - \frac{1}{a} \frac{Δ [A]}{Δ t} = \frac{1}{b} \frac{Δ [B]}{Δ t}

integrated rate law for zero-order reactions:

[A]_{t} = − k t + {[A]}_{0},

half-life for a zero-order reaction

t_{1 / 2} = \frac{{[A]}_{0}}{2 k}

integrated rate law for first-order reactions:

ln [A]_{t} = − k t + ln {[A]}_{0},

half-life for a first-order reaction

t_{1 / 2} = \frac{0.693}{k}

integrated rate law for second-order reactions:

\frac{1}{[A]_{t}} = k t + \frac{1}{{[A]}_{0}},

half-life for a second-order reaction

t_{1 / 2} = \frac{1}{{[A]}_{0} k}

k = A e^{− E_{a} / R T}

ln k = (\frac{− E_{a}}{R}) (\frac{1}{T}) + ln A

ln \frac{k_{1}}{k_{2}} = \frac{E_{a}}{R} (\frac{1}{T_{2}} - \frac{1}{T_{1}})