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.
- $7.7 \times 10^{-2}$ minute $^{-1}$
- $4.2 \times 10^{-2}$ minute $^{-1}$
- $2.1 \times 10^{-2}$ minute $^{-1}$
- $3.5 \times 10^{-2}$ 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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