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  4. In a first order reaction, the concentration of reactant is reduced to 1/8 of the initial concentration in 75 minutes at 298 K. What is the half-life period of the reaction in minutes?

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Q. In a first order reaction, the concentration of reactant is reduced to $1/8$ of the initial concentration in $75$ minutes at $298 \,K$. What is the half-life period of the reaction in minutes?

KEAMKEAM 2012Chemical Kinetics

Solution:

Let $a=1$, $a-x =1 /8$, $t=75 \,min$.
$k=\frac{2.303}{t} \,log$ $\frac{a}{a-x}$ $=\frac{2.303}{75}log$ $\frac{1}{1 /8}$ $=\frac{2.303\times0.903}{75}$ $min.^{-1}$
For first order reaction,
$t_{1 /2}$$=\frac{0.693}{k}$ $=\frac{0.693\times75}{2.303\times0.903}=25 \,min$.