Question

If a first-order reaction takes $32$ minutes for $75$% completion, then time required for $50$% completion is:

• A. $32min$
• B. $16min$
• C. $8min$
• D. $4min$

Answer 1

The correct option is B $16min$

$k=\frac{2.303}{t}\log \left(\frac{a}{a-x}\right)$

When, $a=100$, $x=75$, $t=32$

$k=\frac{2.303}{32}{\log }_{10}\left(\frac{100}{25}\right)=0.0433$ min ${}^{-1}$

Time for $50$% completion $\left(t_{1/2}\right)=\frac{0.693}{k}=\frac{0.693}{0.0433}\approx 16$ min

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