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 0.16 M to 0.02 M is ______.

Options

• 80 minutes

• 60 minutes

• 40 minutes

• 20 minutes

Answer 1

The half-life period of a first-order reaction is 20 minutes. The time required for the concentration of the reactant to change from 0.16 M to 0.02 M is 60 minutes.

Explanation:

Given: Half-life of a first-order reaction, t_1/2 = 20 min

Change in concentration: [A]₀ = 0.16 M → [A]_t = 0.02 M

First-order relation,

`ln ([A]_0/([A])) = kt`

Compute k from half-life: k = `0.693/t_(1//2) = 0.693/20` = 0.03465 min⁻¹

By putting these values,

t = `1/k ln (0.16/0.02)`

= `1/0.03465 ln (8)`

= `1/0.03465 xx 2.07944`

= 60 min