A reaction has a half life of 1 min.

Question:

A reaction has a half life of $1 \mathrm{~min}$. The time required for $99.9 \%$ completion of the reaction is____________ min. (Round off to the Nearest integer)

$[$ Use $: \ln 2=0.69, \ln 10=2.3]$

Solution:

(10)

$\frac{\mathrm{t}_{99.9 \%}}{\mathrm{t}_{50 \%}}=\frac{\frac{1}{\mathrm{~K}} \ln \frac{100}{0.1}}{\frac{1}{\mathrm{~K}} \ln 2}$

$=\frac{\ln 1000}{\ln 2} \times \mathrm{t}_{50 \%}$

$=\frac{3 \ln 10}{\ln 2} \times 1$

$=\frac{3 \times 2.3}{0.69}=10$