What is rate constant of a first order reaction if $60 \%$ reactant decompose in 45 minute?

What is rate constant of a first order reaction if $60 \%$ reactant decompose in 45 minute?
  1. 0.010 minute $^{-1}$
  2. 0.015 minute $^{-1}$
  3. 0.020 minute $^{-1}$
  4. 0.025 minute $^{-1}$

Solution

If $[\mathrm{A}]_0=100$, then $[A]_t=100-60=40$ For a first order reaction, $\begin{aligned} \mathrm{k} & =\frac{2.303}{\mathrm{t}} \log _{10} \frac{[\mathrm{~A}]_0}{[\mathrm{~A}]_{\mathrm{t}}} \\ & =\frac{2.303}{45 \mathrm{~min}} \log _{10} \frac{100}{40} \\ \therefore \quad & =\frac{2.303 \times 0.397}{45 \mathrm{~min}} \\ & =0.020 \text { minute }^{-1} \end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 2)

Practice more Chemical Kinetics questions on Aicharya