Q13 / 150 · MHT CET 2023 (12 May Shift 1) · Chemistry

Calculate the time needed for reactant to decompose $99.9 \%$ if rate constant of first order reaction is 0.576 minute $^{-1}$.

  • A
    8 minutes
  • Correct answer
    B
    12 minutes
  • C
    16 minutes
  • D
    20 minutes

Solution

$99.9 \%$ of the reaction is complete. So, if $[A]_0=100$, then $[A]_{\mathrm{t}}=100-99.9=0.1$ $$ \begin{aligned} \mathrm{t} & =\frac{2.303}{\mathrm{k}} \log _{10} \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_4} \\ & =\frac{2.303}{0.576} \log _{10} \frac{100}{0.1}=\frac{2.303}{0.576} \log _{19}(1000) \\ & =\frac{2.303}{0.576} \times 3 \\ & =11.99 \approx 12 \text { minutes } \end{aligned} $$

Hence, the correct answer is option: 'B'.

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