Chemistry - Chemical Kinetics Question with Solution | TestHub

For first order reaction, $\begin{array}{rl}& t=\frac{2.303}{k}\log \frac{a}{a-x}\Rightarrow \frac{t_{30\%}}{t_{50\%}}=\frac{\frac{2.303}{k}\log \frac{100}{100-30}}{\frac{2.303}{k}\log \frac{100}{100-50}}\\ & \Rightarrow \frac{30}{t_{1/2}}=\frac{\log \frac{10}{7}}{\log 2}\Rightarrow \frac{30}{t_{1/2}}=\frac{0.1549}{0.3010}\\ & \Rightarrow t_{1/2}=\frac{0.3010\times 30}{0.1549}=58.29\min \end{array}$