Calculate the rate constant of first order reaction if the concentration of the reactant decreases by $90…

Calculate the rate constant of first order reaction if the concentration of the reactant decreases by $90 \%$ in 30 minutes.
  1. $7.7 \times 10^{-2}$ minute $^{-1}$
  2. $4.2 \times 10^{-2}$ minute $^{-1}$
  3. $2.1 \times 10^{-2}$ minute $^{-1}$
  4. $3.5 \times 10^{-2}$ minute $^{-1}$

Solution

Concentration decreases by $90 \%$. Hence, $10 \%$ reactant is left after 30 minutes. $\begin{aligned} \mathrm{k} & =\frac{2.303}{\mathrm{t}} \log _{10} \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}} \\ \mathrm{k} & =\frac{2.303}{30} \log _{10} \frac{100}{10} \\ & =\frac{2.303}{30 \mathrm{~min}} \\ & =7.7 \times 10^{-2} \mathrm{~min}^{-1} \end{aligned}$

Asked in: MHT CET 2023 (09 May Shift 2)

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