Question

The half life period of a first order reaction is $20$ minutes. The time required for the concentration of the reactant to change from $0.16M$ to $0.02M$ is:

• A. $80$ minutes
• B. $60$ minutes
• C. $40$ minutes
• D. $20$ minutes

Answer 1

Answer: (B)

$60$ minutes

The half life period of a first order reaction is 20 minutes.

$t_{1/2}=20$ minutes.

The rate constant, $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{20min}=0.03465/min$
The time required for the concentration of the reactant to change from 0.16M to 0.02M

is $t=\frac{2.303}{k}\log \frac{a}{a-x}=\frac{2.303}{0.03465/min}\log \frac{0.16}{0.02}=60min$

Hence, the correct option is $\text{B}$.