A reaction has a half life of 1 min. The time required for 99.9 % completion of the reaction is ____min. (Round off to the Nearest Integer)  [Use: In 2=0.69, In 10=2.3]

Half life expression of first order reaction:

$$\begin{gathered} \mathrm{k}=\frac{0.693}{{\mathrm{t}}_{1/2}} \\ \mathrm{k}=0.693 \end{gathered}$$

Time required for reaction to undergo 99.9% completion:

$$\begin{gathered} \mathrm{t}=\frac{2.303}{\mathrm{k}}\log \frac{100}{100-99.9} \\ \mathrm{t}=\frac{2.303}{0.693}\log \frac{100}{0.01} \\ \mathrm{t}\cong 10 \min \end{gathered}$$