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