Question

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

Answer 1

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

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

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

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