Question

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

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

Answer 1

The correct option is B 16 min

$k=\frac{2.303}{t}log\left(\frac{a}{a-x}\right)$
When, a = 100, x = 75, t = 32
$k=\frac{2.303}{32}lo{g}_{10}\left(\frac{100}{100-75}\right)$
$k=\frac{2.303}{32}lo{g}_{10}\left(\frac{100}{25}\right)=0.0433{\text{min}}^{-1}$
Time for 50% completion $\left(t_{1/2}\right)=\frac{0.693}{k}=\frac{0.693}{0.0433}\approx 16\text{min}$
Thus option (b) is correct