A first order reaction is 60% complete in 20 min. How long will the reaction take to be 84% complete?

60 min

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40 min

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76 min

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54 min

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Solution

The correct option is C 40 min
Case-I $k = \frac{2.303}{t} l o g \frac{a}{a - x}$
$k = \frac{2.303}{20} l o g \frac{100}{100 - 60}$
$k = \frac{2.303}{20} (l o g 10 - l o g 4)$
$= \frac{2.303}{20} (1 - 0.6020) = 0.045$
Case-II $t = \frac{2.303}{k} l o g \frac{100}{100 - 84}$
$t = \frac{2.303}{0.045} l o g \frac{100}{16}$
$= \frac{2.303}{0.045} (2 - 1.2040)$
$= 40.73 m i n \approx 40 m i n$

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