The decomposition of a substance follows first order kinetics. Its concentration is reduced to $1 / 8$ th of…

The decomposition of a substance follows first order kinetics. Its concentration is reduced to $1 / 8$ th of its initial value in 24 minutes. The rate constant of the decomposition process in $\min ^{-1}$ is
  1. 0.087
  2. 0.085
  3. 0.87
  4. 0.85

Solution

$\mathrm{k}=\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\frac{2.303}{24} \log \frac{1}{\frac{1}{8}}=\frac{2.303}{24} \log 8$
$=0.087 \mathrm{~min}^{-1}$ .

Asked in: JEE-TOPICTESTS-CHEMISTRY

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