Question

The half-life period of a first order reaction is 10 minutes. The time required for the concentration of the reactant to change from 0.08 M to 0.02 M is ______.

विकल्प

• 10 min

• 20 min

• 30 min

• 40 min

Answer 1

The half-life period of a first order reaction is 10 minutes. The time required for the concentration of the reactant to change from 0.08 M to 0.02 M is 20 min.

Explanation:

Given: It’s a first-order reaction

Half-life t_1/2 = 10  minutes

Initial concentration: [R]₀ = 0.08 M

Final concentration: [R] = 0.02 M

By using the first-order integrated law:

\[\ce{ln\frac{[R]_0}{[R]} = kt}\]    ...(i)

And for first-order reactions, the rate constant kkk is related to half-life by:

\[\ce{k = \frac{0.693}{t_{1/2}}}\]

= \[\ce{\frac{0.693}{10}}\]

= 0.0693 min⁻¹

Putting this value of k in equation (i), we get,

\[\ce{ln\frac{0.08}{0.02} = 0.0693 \times t}\]

= ln(4) = 0.0693 × t

⇒ 1.386 = 0.0693 × t

⇒ \[\ce{t = \frac{1.386}{0.0693}}\]

t = 20 minutes