What is rate constant of a first order reaction if time required to decrease concentration of reactant from…

What is rate constant of a first order reaction if time required to decrease concentration of reactant from $1.6 \mathrm{M}$ to $0.4 \mathrm{M}$ is 12 hours?
  1. 0.116 hour $^{-1}$
  2. 0.167 hour $^{-1}$
  3. 0.4 hour $^{-1}$
  4. 0.78 hour $^{-1}$

Solution

We know $\begin{aligned} \mathrm{K} & =\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{a}_0}{\mathrm{a}_{\mathrm{t}}} \\ & =\frac{2.303}{12} \log \frac{1.6}{0.4} \\ & =\frac{2.303}{12} \log ^4 \\ & =\frac{2.303}{12} \times 2 \log ^2 \\ & =0.115\end{aligned}$

Asked in: MHT CET 2022 (07 Aug Shift 2)

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