3.6 Summary of Reaction Profiles
| Reaction | Order | Rate Law | Integrated Rate Law | Half-life | k |
|---|---|---|---|---|---|
$$\mathrm{A \rightarrow P}$$ |
Zeroth |
$$\mathrm{rate} = k$$ |
$$\mathrm{[A]}_t = -kt + \mathrm{[A]_0}$$ |
$$t_{½} = \dfrac{[\mathrm{A}]_0}{2k}$$ |
M s–1 |
$$\mathrm{A \rightarrow P}$$ |
First |
$$\mathrm{rate} = k[\mathrm{A}]$$ |
$$\ln[\mathrm{A}]_{t} = -kt + \ln[\mathrm{A}]_0$$ |
$$t_{½} = \dfrac{\ln 2}{k} \approx \dfrac{0.693}{k}$$ |
s–1 |
$$\mathrm{A + A \rightarrow P}$$ |
Second |
$$\mathrm{rate} = k[\mathrm{A}]^2$$ |
$$\dfrac{1}{[\mathrm{A}]_t} = kt + \dfrac{1}{[\mathrm{A}]_0}$$ |
$$t_{½} = \dfrac{1}{k[\mathrm{A}]_0}$$ |
M–1 s–1 |
$$\mathrm{A + B \rightarrow P}$$ |
Second |
$$\mathrm{rate} = k[\mathrm{A}][\mathrm{B}]$$ |
$$\dfrac{1}{[\mathrm{B}]_0 - [\mathrm{A}]_0}\ln\dfrac{[\mathrm{B}][\mathrm{A}]_0}{[\mathrm{A}][\mathrm{B}]_0} = kt$$ |
$$\cdots$$ |
M–1 s–1 |