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  4. If a first order reaction takes 40 minutes for 75 % completion, then time required for 50 % completion is

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Q. If a first order reaction takes $40$ minutes for $75\%$ completion, then time required for $50\%$ completion is

UP CPMTUP CPMT 2014Chemical Kinetics

Solution:

$k=\frac{2.303}{t} log \frac{a}{a-x} $
$= \frac{2.303}{40} log \left(\frac{100}{25}\right) \quad\left(log 4 = 0.60206\right) $
$ k = 0.035\, min^{-1} $
Time for $50\%$ completion $\left(t_{1/2} \right) = \frac{0.693}{k} $
$ t_{1/2} = \frac{0.693}{0.035} = 19.8 \approx 20\, min$