Integrated Rate Law First Order

Question

Integrated first-order rate law (A → products) is:

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1. **Differential Law**: $-\frac{d[A]}{dt} = k[A]$.
2. **Integration**: 
   - $\int \frac{d[A]}{[A]} = - \int k \, dt$
   - $\ln[A] = -kt + I$, where $I$ is the integration constant.
3. **Boundary Condition**: At $t=0, [A]=[A]_0 \implies I = \ln[A]_0$.
4. **Final Form**: **$\ln[A] = -kt + \ln[A]_0$**.
5. **Exponential Form**: $[A] = [A]_0 e^{-kt}$.

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Integrated Rate Law First Order

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