Question

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?

• A. 50 min.
• B. 15 min.
• C. 30 min.
• D. 25 min.

Answer 1

Answer: (D)

25 min.

Answer 2

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,
$t_{1 /2}$ $=\frac{0.693}{k}$ $=\frac{0.693\times75}{2.303\times0.903}=25 \,min$.