Key Equations

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relative reaction rates for \(a \mathrm{~A} \longrightarrow b \mathrm{~B}=-\dfrac{1}{a} \dfrac{\Delta[\mathrm{~A}]}{\Delta t}=\dfrac{1}{b} \dfrac{\Delta[\mathrm{~B}]}{\Delta t}\)

integrated rate law for zero-order reactions: \([A]_t=-k t+[A]_0\),

half-life for a zero-order reaction \(t_{1 / 2}=\dfrac{[A]_0}{2 k}\)

integrated rate law for first-order reactions: \(\ln [A]_t=-k t+\ln [A]_0\),

half-life for a first-order reaction \(t_{1 / 2}=\dfrac{0.693}{k}\)

integrated rate law for second-order reactions: \(\dfrac{1}{[A]_t}=k t+\frac{1}{[A]_0}\),

half-life for a second-order reaction \(t_{1 / 2}=\dfrac{1}{[A]_0 k}\)

\(
\begin{aligned}
& k=A e^{-E_{\mathrm{a}} / R T} \\[6pt]
& \ln k=\left(\frac{-E_{\mathrm{a}}}{R}\right)\left(\dfrac{1}{T}\right)+\ln A \\[6pt]
& \ln \frac{k_1}{k_0}=\dfrac{E_{\mathrm{a}}}{R}\left(\dfrac{1}{T_0}-\frac{1}{T_1}\right)
\end{aligned}
\)

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