A first order reaction takes 23.03 minutes for $20 \%$ decomposition. Calculate its rate constant.

A first order reaction takes 23.03 minutes for $20 \%$ decomposition. Calculate its rate constant.
  1. 5:6 $6 \times 10^{-3}$ minute $^{-1}$
  2. $4.5 \times 10^{-3}$ minute $^{-1}$
  3. $6.5 \times 10^{-3}$ minute $^{-1}$
  4. $9.69 \times 10^{-3}$ minute $^{-1}$

Solution

$[A]_0=100 \%,[A]_t=100-20=80 \%$ Substitution of these in above $\begin{aligned} \mathrm{k} & =\frac{2.303}{\mathrm{t}} \log _{10} \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}} \\ \mathrm{k} & =\frac{2.303}{\mathrm{t}} \log _{10} \frac{100}{80} \\ & =\frac{2.303}{23.03 \mathrm{~min}} \log _{10}(1.25) \\ & =\frac{2.303}{23.03 \mathrm{~min}} \times 0.0969 \\ & =9.69 \times 10^{-3} \text { minute }^{-1} \end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 2)

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