Question

$75\%$ of a first order reaction was completed in $32min$, when was $50\%$ of the reaction completed?

• A. 24 min
• B. 16 min
• C. 8 min
• D. 48 min

Answer 1

Answer: (B)

First order reaction,
$k=\frac{2.303}{t}\log \frac{a}{a-x}$
Here, $\therefore a=100$
$\therefore x=75$
$\because a-x=(100-75)$
$k=\frac{2.303}{32}\log \frac{100}{25}$
$=\frac{2.303}{32}\log 4$
$=\frac{2.303\times \log 2^2}{32}$
$=\frac{2.303\times 2\log 2}{32}$
$=\frac{2.303\times 2\times 0.3010}{32}$
$=\frac{2\times 0.63}{32}$
$\therefore t_{1/2}=\frac{0.693}{k}$
$\therefore t_{1/2}=\frac{0.693}{2\times 0.693/32}4$
$=16\min$