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Q.
The half-life of a first order reaction is $30$ min. The time required for $75\%$ completion of the same reaction will be
KVPYKVPY 2009Chemical Kinetics
Solution:
Given, $t_{1/2}$ of first order reaction = $30$ min
For first order, $k=\frac{0.693}{t_{1/2}}$
$k=\frac{0.693}{30}=0.0231$
Also, if the reaction is $75\%$ completed.
$t=\frac{2.303}{k}\log \frac{a}{a-x}$
$t=\frac{2.303}{0.0231}\log\frac{100}{25}$
$=99.69\times \log\, 4$
$=99.69\times0.602$
$=60$ min