If the rate constant for a first order reaction is 2 . 303 × 10 - 3   s - 1 , find the time…

According to the integrated rate law for the rate of reaction, the rate constant is:

$\mathrm{k}=\frac{1}{\mathrm{t}}\ln \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}$

Rate constant $\mathrm{k}=2.303\times {10}^{-3}{ \mathrm{s}}^{-1}$

Weight of reactant at $\mathrm{t}=0$ is $4 \mathrm{g}$. Weight after the time $\mathrm{t}=\mathrm{t}$ is $0.2\mathrm{g}$.

$\mathrm{t}=\frac{1}{\mathrm{k}}\ln \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\frac{1}{2.303\times {10}^{-3}{ \mathrm{s}}^{-1}}\ln \frac{4}{0.2}=434.22\times \ln 20=434.22\times 2.996 \mathrm{s}=1300.92 \mathrm{s}$

 $\mathrm{t}=1300.92 \mathrm{s}=\frac{1300.92}{3600}=0.36 \mathrm{hour}$

So, the time required is $0.36$ hours.