In a first order reaction $87.5 \%$ of reactant is converted in to product in 15 minutes. The rate constant…

In a first order reaction $87.5 \%$ of reactant is converted in to product in 15 minutes. The rate constant for the reaction is given by
  1. $\frac{0.693}{5} \mathrm{~min}^{-1}$
  2. $\frac{0.693}{15} \mathrm{~min}^{-1}$
  3. $\frac{5}{0.693} \min ^{-1}$
  4. $0.693 \times 5 \mathrm{~min}^{-1}$

Solution

$87.5 \%$ of reactant is converted into product in 15 minutes, means $12.5 \%$ remains unreacted $[\mathrm{A}]_{0}=100, \quad[\mathrm{~A}]_{t}=100-87.5=12.5$ $k=\frac{2.303}{15} \log _{10} \frac{[A]_{0}}{[A]_{t}}$ $k=\frac{2.303}{15} \log _{10} \frac{100}{12.5}$ $k=\frac{2.303}{15} \log _{10} 8=\frac{0.693}{5} \min ^{-1}$

Asked in: MHT CET 2020 (13 Oct Shift 1)

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