For a first order reaction A → Products, initial concentration of A is 0 . 1 M , which becomes 0 . 001 M…

The integrated rate equation for a first order reaction is given by 

$\mathrm{k}=\frac{2.303}{\mathrm{t}}\log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}$

Where 

$$\begin{gathered} \mathrm{k}=\mathrm{Rate} \mathrm{constant} \\ \mathrm{a}=\mathrm{initial} \mathrm{concentration} \mathrm{of} \mathrm{the} \mathrm{reactants} \\ \mathrm{a}-\mathrm{x}=\mathrm{concentration} \mathrm{of} \mathrm{reactants} \mathrm{left} \mathrm{after} \mathrm{time}, \mathrm{t}. \end{gathered}$$

$$\begin{gathered} \mathrm{k}=\frac{2.303}{5}\log \frac{0.1}{0.001} \\ =\frac{4.606}{5}=0.9212 {\min }^{-1} \end{gathered}$$

Hence, the rate constant of the given reaction is $0.9212 {\min }^{-1}$