Which is rate constant of a first order reaction if 0.08 mole of reactant reduces to 0.02 mole in 23.03…

Which is rate constant of a first order reaction if 0.08 mole of reactant reduces to 0.02 mole in 23.03 minute?
  1. $0.2303 \mathrm{~min}^{-1}$
  2. $1.6021 \mathrm{~min}^{-1}$
  3. $0.4031 \mathrm{~min}^{-1}$
  4. $0.06021 \mathrm{~min}^{-1}$

Solution

$\begin{aligned} & \mathrm{K}=\frac{2.303}{\mathrm{t}} \log \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}} \\ & \mathrm{K}=\frac{2.303}{23.03} \cdot \log \frac{0.08}{0.02} \\ & \mathrm{~K}=\frac{1}{10} \log 4 \\ & =\frac{2 \log 2}{10}=0.0602 \mathrm{~min}^{-1}\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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