A first order reaction takes 40 min for 75 % decomposition. Calculate rate constant. [Given: log 2=0.30, log 4=0.60 ]

\[t=\frac{2.303}{\mathrm{k}} \log \frac{[A]_{0}}{A} \] \(\displaystyle 40 \mathrm{~min}=2.303 / \mathrm{k} \times \log (100 / 25)\) \[\begin{aligned} & \mathrm{k}=2.303 / 40 \mathrm{~min}^{2} \times \log 4 \\ & \mathrm{k}=2.303 / 40 \mathrm{~min}^{2} \times 0.60 \\ & \mathrm{k}=0.0345 \mathrm{~min}^{-1} \end{aligned} \]