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Q.

For a reaction half-life varies with initial concentration as follows :

If time taken for 75% completion of reaction is 300 minutes, then time taken to complete 25% reaction, starting with same initial concentration at same temperature, is —

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a

l00 min.

b

33.33 min.

c

66.66 min

d

50 min.

answer is A.

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Detailed Solution

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For second order, $t_{\frac{1}{2}} = \frac{1}{{[A]}_{0} k}$
$\log t_{\frac{1}{2}} = - \log {[A]}_{0} + \log (1 / k)$
Hence reaction is second order.
$k = \frac{1}{t} [\frac{1}{{[A]}_{t}} - \frac{1}{{[A]}_{0}}]; \frac{4}{A_{0}} - \frac{1}{A_{0}} = k t_{75 %}$
$\frac{4}{3 {[A]}_{0}} - \frac{1}{{[A]}_{0}} = k t_{25 %}; t_{25 %} = \frac{300}{9} = 33.33 \min$

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