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 : ln 2 = 0.69, ln 10 = 2.3]

A reaction with a constant half-life (independent of concentration) follows first-order kinetics. The rate constant is $$k = \frac{\ln 2}{t_{1/2}} = \frac{0.69}{1} = 0.69 \text{ min}^{-1}$$.

For 99.9% completion, only 0.1% of the reactant remains, so $$\frac{[A]}{[A]_0} = 0.001 = \frac{1}{1000}$$. Using the first-order integrated rate law: $$t = \frac{1}{k} \ln\frac{[A]_0}{[A]} = \frac{1}{0.69} \ln 1000$$.

Now $$\ln 1000 = \ln 10^3 = 3 \ln 10 = 3 \times 2.3 = 6.9$$. Therefore $$t = \frac{6.9}{0.69} = 10$$ min.