A first order reaction takes 40 minute for $20 \%$ decomposition. Calculate its rate constant.

A first order reaction takes 40 minute for $20 \%$ decomposition. Calculate its rate constant.
  1. $5.6 \times 10^{-3}$ minute ${ }^{-1}$
  2. $4.5 \times 10^{-3}$ minute ${ }^{-1}$
  3. $6.5 \times 10^{-3}$ minute $^{-1}$
  4. $7.2 \times 10^{-3}$ minute ${ }^{-1}$

Solution

If $[A]_0=100$, then $[A]_t=100-20=80$ For a first order reaction, $\begin{aligned} \mathrm{k} & =\frac{2.303}{\mathrm{t}} \log _{10} \frac{[\mathrm{~A}]_0}{[\mathrm{~A}]_{\mathrm{t}}}=\frac{2.303}{40 \mathrm{~min}} \log _{10} \frac{100}{80} \\ & =\frac{2.303}{40 \mathrm{~min}} \log _{10} 1.25=\frac{2.303}{40 \mathrm{~min}} \times 0.097 \\ & =5.57 \times 10^{-3} \mathrm{minute}^{-1} \approx 5.6 \times 10^{-3} \mathrm{minute}^{-1} \end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 1)

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