The rate constant for a first order reaction is $4.606 \times {10}^{-3}{\mathrm{s}}^{-1}$ . The time required to reduce 2.0 g of the reactant to 0.2 g is 

Given $\mathrm{k}=4.606\times {10}^{-3}{\mathrm{s}}^{-1}$
Let a = 2 g and a-x = 0.2 g
For a first order reaction,
$\begin{array}{l}\mathrm{k}=\frac{2.303}{\mathrm{t}}\log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}\\ 4.606\times {10}^{-3}=\frac{2.303}{\mathrm{t}}\log \frac{2}{0.2}\\ \mathrm{t}=\frac{2.303}{4.606\times {10}^{-3}}\log 10\\ \mathrm{t}=0.5\times {10}^3=500\mathrm{s}\end{array}$