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# The rate constant for a first order reaction is 60 s–1. How much time will it take to reduce the initial concentration of the reactant to its 1/16th value?

4.16   The rate constant for a first order reaction is $60 s^{-1}$. How much time will it take to reduce the initial concentration of the reactant to its 1/16th  value?

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We know that,
for first order reaction,
$t=\frac{2.303}{k}\log\frac{[R]_{0}}{[R]}$
$\\=\frac{2.303}{60}\log\frac{1}{1/16}\\ =\frac{2.303}{60} \log2^{4}$
$=4.6 \times 10^{-2} s$  (nearly)

Hence the time required is $=4.6 \times 10^{-2} s$

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