Key Equations

Key Equations

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

integrated rate law for zero-order reactions: $[A{]}_t=\text{−}kt+{\left[A\right]}_0,$

half-life for a zero-order reaction $t_{1\text{/}2}=\frac{{\left[A\right]}_0}{2k}$

integrated rate law for first-order reactions: $\text{ln}[A{]}_t=\text{−}kt+\text{ln}{\left[A\right]}_0,$

half-life for a first-order reaction $t_{1\text{/}2}=\frac{0.693}{k}$

integrated rate law for second-order reactions: $\frac{1}{[A{]}_t}=kt+\frac{1}{{\left[A\right]}_0},$

half-life for a second-order reaction $t_{1\text{/}2}=\frac{1}{{\left[A\right]}_{0}k}$

$k=A{e}^{\text{−}{E}_{\text{a}}\text{/}RT}$

$\text{ln}k=\left(\frac{\text{−}{E}_{\text{a}}}{R}\right)\left(\frac{1}{T}\right)+\text{ln}A$

$\text{ln}\frac{k_1}{k_2}=\frac{E_{\text{a}}}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$