Question

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

Answer 1

$\frac{ t _1}{ t _2}=\frac{\frac{1}{ K } \ln \frac{ a _0}{0.4 a _0}}{\frac{1}{ K } \ln \frac{ a _0}{0.1 a _0}}$
$ \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$