The half‑life of the first‑order decomposition of ${\text{N}}_2{\text{O}}_5$ at $298\text{K}$ is $30\text{min}$. Calculate the rate constant $k$ in ${\text{s}}^{-1}$.

Step-by-step solution

1. Write the first‑order half‑life expression $t_{1/2}=\frac{\ln 2}{k}$.
2. Re‑arrange to obtain $k=\frac{\ln 2}{t_{1/2}}$.
3. Convert the half‑life to seconds: $30\text{min}=30\times 60=1800\text{s}$.
4. Substitute values: $k=\frac{0.693}{1800\text{s}}$.
5. Calculate: $k=3.85\times 10^{-4}{\text{s}}^{-1}$.

Concept tested: First‑order half‑life calculation

Published 11 September 2026 · How this solution was prepared and checked