Question

In a first-order reaction, $50$ minutes time is taken for the completion of $93.75$ of a reaction. What is the half life of the reaction?

• A. $25$ min
• B. $12.5$ min
• C. $20$ min
• D. $10$ min

Answer 1

The correct option is B $12.5$ min

$A$ $⟶$ $B$
$a$ $0$

$(a-0.9375a)$ $\left(0.9375a\right)$
$K=\frac{2.303}{t}log\left(\frac{a}{a-x}\right)$
$K=\frac{2.303}{50}log\left(\frac{a}{a(1-0.9375)}\right)$
$K=0.0554$
$t{}^{1{/}_2}=\frac{0.693}{k}=\frac{0.693}{0.0554}$
$t{}^{1{/}_2}=12.5min$

Hence, the correct option is $\text{B}$