In a first-order reaction, 0.16 moles of reactant decreases finally to 0.02 moles in 144 minutes. The half life of the given reaction is

It is given that the first order reaction, 0.16 moles of reactant decreases finally to 0.02 moles in 144 minutes.

$$\begin{gathered} \mathrm{K}=\frac{2.303}{\mathrm{t}}\log \left[\frac{{\mathrm{A}}_0}{\mathrm{A}}\right] \\ \begin{array}{rl} & =\frac{2.303}{144}\log \left[\frac{0.16}{0.02}\right] \\ & =\frac{2.303}{144}\log (2{)}^{3 } \\ & =\frac{2.303}{144}3\log 2\\ & {\mathrm{t}}_{1/2}=\frac{2.303\log 2}{\mathrm{k}}\\ & =\frac{2.303\log 2}{2.303\times 3\log 2}\times 144\min \\ & =48 \text{minutes}\end{array} \end{gathered}$$

Therefore, the correct option is (D).