A molecule undergoes two independent first order reactions whose respective half lives are 12 min and 3 min . If both the reactions are occurring then the time taken for the 50 % consumption of the re

Question

A molecule undergoes two independent first order reactions whose respective half lives are 12 min and 3 min . If both the reactions are occurring then the time taken for the 50 % consumption of the reactant is ______ min . (Nearest integer)

TestHub · Accepted Answer

For parallel reaction
When adding the rate constants of the two reactions, we need to use the formula for combining rate constants of two reactions in parallel, which is:
$k = k_{1} + k_{2}$
where $k_{1}$ and $k_{2}$ are the rate constants of the individual reactions.
In this case, the half-lives of the two reactions are $12$ min and $3$ min, respectively. The rate constants of the two reactions can be calculated using the formula for half-life of a first-order reaction:
$\frac{1}{t_{1 / 2}} = \frac{1}{12} + \frac{1}{3} = \frac{5}{12}$
Net $t_{1 / 2} = \frac{12}{5} = 2.4 \min \approx 2 \min$
Hence time taken for $50 %$ consumption of reactant will be close to $2 \min$ .

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