First Order Half-life

Question

Half-life (t1/2) of a first-order reaction depends on:

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1. **Integrated Rate Law**: $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$.
2. **Definition of Half-life**: Time after which $[A] = [A]_0 / 2$.
3. **Derivation**: Substituting values into the law yields $k = \frac{2.303}{t_{1/2}} \log 2 \implies k = \frac{0.693}{t_{1/2}}$.
4. **Result**: $t_{1/2} = \frac{0.693}{k}$.
5. **Conclusion**: The half-life is **independent of initial concentration**. It is determined solely by the **rate constant $k$** (which is itself dependent on temperature).

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First Order Half-life

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