The rate of first order reaction is 0 . 04 mol L - 1 s - 1 at 10 minutes and 0 . 03 mol L - 1 s - 1 at 20…

 $$\begin{gathered} \mathrm{Rate} \mathrm{r} =\mathrm{k}\left[\mathrm{A}\right] \\ 0.04=\mathrm{k}{\left[{\mathrm{A}}_0\right]}_{10} \\ 0.03=\mathrm{k}{\left[{\mathrm{A}}_{}\right]}_{20} \end{gathered}$$

$\Rightarrow \frac{{\left[{\mathrm{A}}_0\right]}_{10}}{{\left[\mathrm{A}\right]}_{20}}=\frac{0.04}{0.03}=\frac{4}{3}$

$$\begin{gathered} \mathrm{From} \mathrm{t}=\frac{2.303}{\mathrm{k}}\log \frac{{\left[\mathrm{A}\right]}_{10}}{{\left[\mathrm{A}\right]}_{20}} \\ 10= \frac{2.303}{\mathrm{k}}\log \frac{4}{3} \\ 10= \frac{2.303}{\mathrm{k}}(0.6020-0.4771) \\ \mathrm{k}= \frac{2.303}{10}\times 0.1249 \\ =2.876\times {10}^{-2} {\min }^{-1} \end{gathered}$$

$$\begin{gathered} {\mathrm{t}}_{1/2}=\frac{0.693}{k} \\ =\frac{0.693}{2.876\times {10}^{-2}} \\ =0.24\times {10}^2 \min \\ =24 \min . \end{gathered}$$