The half-life of a first order reaction is 60 minutes. How long will it take to consume 90%of the reactant? [Given: log 2=0 · 3010, log 3=0 · 4771,…

\[\begin{aligned} \mathrm{t}_{1 / 2} & =\frac{0.693}{\mathrm{k}} \\ \mathrm{k} & =\frac{0.693}{60} \mathrm{~min}^{-1} \\ \mathrm{k} & =\frac{2.303}{\mathrm{t}} \log \frac{[\mathrm{R}]_{0}}{[\mathrm{R}]} \\ \frac{0.693}{60} & =\frac{2.303}{\mathrm{t}} \log \frac{100}{10} \\ \mathrm{t} & =\frac{2.303 \times 60}{0.693} \mathrm{~min} \\ \mathrm{t} & =199.3 \mathrm{~min} \end{aligned} \]