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  4. 50 % of a first order reaction is complete in 23 minutes. Calculate the time required to complete 90 % of the reaction

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Q. $ 50\% $ of a first order reaction is complete in $ 23 $ minutes. Calculate the time required to complete $ 90\% $ of the reaction

AMUAMU 2016Chemical Kinetics

Solution:

$t_{1/3} = 23\,$min
$\therefore k = \frac{0.693}{t_{1/2}} = \frac{0.693}{23}$
Further, for a reaction to complete $90\%$ of reaction,
$t = \frac{2.303}{k} log \frac{a}{a-0.9 a}$
$ = \frac{2.303}{0.693}\times 23 \,log \,10$
$ = 76.4$ minutes