A first order reaction is $25 \%$ completed in 40 minutes. What is the rate constant $\mathrm{k}$ for the…

A first order reaction is $25 \%$ completed in 40 minutes. What is the rate constant $\mathrm{k}$ for the reaction?
  1. $\frac{2.303 \times \log 1 \cdot 33}{40}$
  2. $2 \cdot 303 \times \log \frac{4}{3}$
  3. $\frac{2 \cdot 303}{40} \times \log \frac{1}{4}$
  4. $\frac{2 \cdot 303 \times \log 4}{40 \times 3}$

Solution

$\begin{aligned}[\mathrm{A}]_{0} &=100,[\mathrm{~A}]_{\mathrm{t}}=100-25=75, \mathrm{t}=40 \min \\ \mathrm{k} &=\frac{2.303}{\mathrm{t}} \log _{10} \frac{[\mathrm{A}]_{0}}{[\mathrm{~A}]_{\mathrm{t}}} \\ \therefore \mathrm{k} &=\frac{2.303}{40} \log _{10} \frac{100}{75}=\frac{2.303 \times \log 1.33}{40} \end{aligned}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

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