The given reaction is,
${\mathit{S}\mathit{O}}_2{\mathit{C}\mathit{l}}_2\left(\mathit{g}\right)\mathrm{}\to \mathrm{}{\mathit{S}\mathit{O}}_2\left(\mathit{g}\right)+{\mathit{C}\mathit{l}}_2\left(\mathit{g}\right)$
${\mathit{P}}_{\mathit{i}}=0.4\mathit{a}\mathit{t}\mathit{m},\mathit{P}=0.7\mathit{a}\mathit{t}\mathit{m},\mathit{t}=100\mathit{s}$
Thus, according to the integrated rate law for gas phase
$\mathit{K}=\frac{2.303}{\mathit{t}}\times {\log }_{10}\frac{{\mathit{P}}_{\mathit{i}}}{2{\mathit{P}}_{\mathit{i}}-\mathit{P}}$
$\mathit{K}=2.303\times {10}^{-2}\times {\log }_{10}\frac{0.4}{0.1}$
$\mathrm{}\mathit{K}=2.303\times {10}^{-2}\times {\log }_{10}\left(4\right)$
$\mathrm{}\mathit{K}=2.303\times {10}^{-2}\times 0.6021$
$\mathit{K}=1.3866\times {10}^{-2}\mathrm{}{\mathit{s}}^{-1}$
Thus, the rate constant for the above reaction is $1.3866\times {10}^{-2}\mathrm{}{\mathit{s}}^{-1}$.