What is the time needed to reduce the initial concentration of reactant to $10 \%$ in a first order reaction…
What is the time needed to reduce the initial concentration of reactant to $10 \%$ in a first order reaction if its half life time is 10 minutes?
- 15 minute
- 20 minute
- 25 minute
- 33 minute
Solution
$\begin{aligned} \mathrm{k} & =\frac{0.693}{\mathrm{t}_{1 / 2}} ; \mathrm{k}=\frac{0.693}{10 \mathrm{~min}}=0.0693 \mathrm{~min}^{-1} \\ \mathrm{t} & =\frac{2.303}{\mathrm{k}} \log _{10} \frac{[\mathrm{~A}]_0}{[\mathrm{~A}]_{\mathrm{t}}} \\ \quad \mathrm{t} & =\frac{2.303}{0.0693 \mathrm{~min}^{-1}} \log _{10} \frac{100}{10}=\frac{2.303}{0.0693 \mathrm{~min}^{-1}} \times 1 \\ \therefore \quad \mathrm{t} & =33 \text { minute }\end{aligned}$
Asked in: MHT CET 2024 (11 May Shift 2)
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