Question

The half-life of a first order reaction is $30$ min. The time required for $75\%$ completion of the same reaction will be

• A. 45 min
• B. 60 min
• C. 75 min
• D. 90 min

Answer 1

Answer: (B)

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.
$t=\frac{2.303}{k}\log \frac{a}{a-x}$
$t=\frac{2.303}{0.0231}\log \frac{100}{25}$
$=99.69\times \log 4$
$=99.69\times 0.602$
$=60$ min