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  4. 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 :

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Q. 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 :

NEETNEET 2019Chemical Kinetics

Solution:

First order rate constant is given as,
$ k = \frac{2.303}{t} \log \frac{\left[A_{0}\right]}{\left[A\right]_{t}} $
99% completed reaction,
$ k = \frac{2.303}{t} \log \frac{100}{1} $
$ = \frac{2.303}{t} \log10^{2} $
$ k = \frac{2.303}{t} \times2 \log 10 $
$ t = \frac{2.303}{k} \times2 = \frac{4.606}{k} $
$ t = \frac{4.606}{k} $