In a first order reaction the concentration of reactant decreases from 800 $\mathrm{mol}/{\mathrm{dm}}^3$  to 50 $\mathrm{mol}/{\mathrm{dm}}^3$ in $2\times {10}^2\sec$. The rate constant of reaction in ${\sec }^{-1}$ is 

$$\begin{gathered} \mathrm{k}=\frac{2.303}{\mathrm{t}}{\log }_{10}\frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}; \\ \mathrm{t}=2\times {10}^2,\mathrm{a}=800,\mathrm{a}-\mathrm{x}=50 \end{gathered}$$

$$\begin{gathered} \mathrm{k}=\frac{2.303}{2\times {10}^2}{\log }_{10}\frac{800}{50} \\ =\frac{2.303}{2\times {10}^2}{\log }_{10}16 \end{gathered}$$

       $$\begin{gathered} =\frac{2.303}{2\times {10}^2}{\log }_{10}{2}^4 \\ =\frac{2.303}{2\times {10}^2}\times 4\times 0.301 \end{gathered}$$

       $=1.38\times {10}^{-2}{\mathrm{s}}^{-1}$