For  ${\mathrm{SO}}_2{\mathrm{Cl}}_{2\left(\mathrm{g}\right)}\to {\mathrm{SO}}_{2\left(\mathrm{g}\right)}+{\mathrm{Cl}}_{2\left(\mathrm{g}\right)}$, Pressure of  ${\mathrm{SO}}_2{\mathrm{Cl}}_{2\left(\mathrm{g}\right)}$ changed from 5 atm to 4 atm in 10 min. Then, pressure of ${\mathrm{SO}}_2{\mathrm{Cl}}_2$ at the end of 30 minutes will be (in atm)

Decomposition of ${\mathrm{SO}}_2{\mathrm{Cl}}_{2\left(\mathrm{g}\right)}\to {\mathrm{SO}}_{2\left(\mathrm{g}\right)}+{\mathrm{Cl}}_{2\left(\mathrm{g}\right)}$ is a first order reaction

For same reaction as long as temperature is kept constant rate constants remains same.${\mathrm{K}}_{10\min }={\mathrm{k}}_{30\min }$

$\frac{2.303}{10}\log \frac{5}{4}=\frac{2.303}{30}\log \frac{5}{\mathrm{p}}$

$$\begin{gathered} 3\left[\log 5-\log 4\right]=\log 5-\mathrm{logp} \\ \mathrm{logp}=0.408 \\ \mathrm{p}={10}^{0.408}=2.558\cong 2.56\mathrm{atm} \end{gathered}$$