Question

An organic compound undergoes first order decomposition. If the time taken for the $60\%$ decomposition is $540s$, then the time required for $90\%$ decomposition will be is _________$s$. (Nearest integer).
Given: $\ln 10=2.3;\log 2=0.3$

Answer 1

Answer: 1350

$\frac{t_1}{t_2}=\frac{\frac{1}{K}\ln \frac{a_0}{0.4a_0}}{\frac{1}{K}\ln \frac{a_0}{0.1a_0}}$
$\frac{540}{t_2}=\frac{\ln \frac{10}{4}}{\ln 10}$
$\frac{540}{t_2}=\frac{\log 10-\log 4}{\log 10}$
$\frac{540}{t_2}=\frac{1-0.6}{1}$
$\Rightarrow \frac{540}{t_2}=0.4$
$\Rightarrow t_2=\frac{540}{0.4}=1350\sec$