For ${\mathrm{SO}}_2{\mathrm{Cl}}_{2( \mathrm{g})}\to {\mathrm{SO}}_{2( \mathrm{g})}+{\mathrm{Cl}}_{2( \mathrm{g})}$, Pressures of ${\mathrm{SO}}_2{\mathrm{Cl}}_2$ at $\mathrm{t}=0$ and $\mathrm{t}=20$ minutes respectively are$700 \mathrm{mm} \& 350 \mathrm{mm}$. When $\log \left({\mathrm{P}}_0/\mathrm{p}\right)$is plotted against time $\left(\mathrm{t}\right)$, slope equals to

$$\begin{gathered} \mathrm{k}=\frac{2.303}{\mathrm{t}}\log \frac{{\mathrm{P}}_0}{\mathrm{P}}\text{ [1st order reaction] } \\ \text{ Plot of }\log \frac{{\mathrm{P}}_0}{\mathrm{P}}\text{ against }\mathrm{t}\text{ will give slope }=\frac{\mathrm{k}}{2.303} \\ \text{ Using given data, }\mathrm{k}=\frac{2.303}{20}\log \frac{700}{350} \\ \frac{\mathrm{k}}{2.303}=\frac{\log 2}{20}=1.5\times {10}^{-2}{\mathrm{s}}^{-1} \\ \text{ Slope }=1.5\times {10}^{-2}{\mathrm{s}}^{-1} \end{gathered}$$