If the rate constant for a first order reaction is k, the time (t) required for the completion of 99% of the r

Question

If the rate constant for a first order reaction is k, the time (t) required for the completion of 99% of the reaction is given by:

Accepted Answer

First order rate constant is given as, $k = \frac{2.303}{t} \log \frac{[A_0]}{[A]_t}$. For 99% completed reaction, $k = \frac{2.303}{t} \log \frac{100}{1} = \frac{2.303}{t} \log 10^2 = \frac{2.303}{t} 	imes 2 \log 10$. $t = \frac{2.303}{k} 	imes 2 = \frac{4.606}{k}$.

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