Q12 / 150 · MHT CET 2023 (09 May Shift 2) · Chemistry

Calculate the rate constant of first order reaction if the concentration of the reactant decreases by $90 \%$ in 30 minutes.

  • Correct answer
    A
    $7.7 \times 10^{-2}$ minute $^{-1}$
  • B
    $4.2 \times 10^{-2}$ minute $^{-1}$
  • C
    $2.1 \times 10^{-2}$ minute $^{-1}$
  • D
    $3.5 \times 10^{-2}$ minute $^{-1}$

Solution

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

Hence, the correct answer is option: 'A'.

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