Question

A first order reaction takes 40 min for 30% decomposition. Calculate $t_{\frac 12}$.

Answer 1

For a first order reaction,

$t = \frac {2.303}{k} log\ \frac { [R]_0}{[R]}$

$k= \frac {2.303}{40 \ min} log \frac {100}{100-30}$

$k= \frac {2.303}{40 \ min} log \frac {10}{7}$

$k = 8.918 \times10^{-3} min^{-1}$

Therefore, $t_{\frac 12}$ of the decomposition reaction is

$t_{\frac 12}= \frac {0.693}{k}$

$t_{\frac 12} = \frac {0.693}{8.918 \times 10^{-3}} min$

$t_{\frac 12 }= 77.7 \ min \ (approximately)$