MCQ
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 : $\ln 10=2.3 ; \log 2=0.3$
  • A
    $1351$
  • B
    $1352$
  • C
    $1353$
  • $1350$

Answer

Correct option: D.
$1350$
d
$\frac{t_1}{t_2}=\frac{\frac{1}{ K } \ln \frac{ a _0}{0.4 a _0}}{\frac{1}{ K } \ln \frac{ a _0}{0.1 a _0}}$

$\frac{540}{ t _2}=\frac{\ln \frac{10}{4}}{\ln 10}$

$\frac{540}{ t _2}=\frac{\log 10-\log 4}{\log 10}$

$\frac{540}{ t _2}=\frac{1-0.6}{1}$

$\Rightarrow \frac{540}{ t _2}=0.4$

$\Rightarrow t _2=\frac{540}{0.4}=1350\,sec$

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