The half‑life of a first‑order reaction is found to be $12\text{min}$. Calculate the rate constant $k$ in ${\text{s}}^{-1}$.

Step-by-step solution

1. Convert half‑life to seconds: $12\text{min}=720\text{s}$.
2. Use the first‑order half‑life relation: $t_{1/2}=\frac{ln2}{k}$.
3. Rearrange to find $k$: $k=\frac{ln2}{t_{1/2}}=\frac{0.693}{720}{\text{s}}^{-1}$.
4. Compute: $k=9.6\times 10^{-4}{\text{s}}^{-1}$.

Concept tested: First‑order half‑life

Published 9 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked