Question

The rate of a first order reaction is 0.04 mol l⁻¹ s⁻¹ at 10 seconds and 0.03 mol l⁻¹ s⁻¹ at 20 seconds after initiation of the reaction. The half-life period of the reaction is ______.

पर्याय

• 24.1 s

• 34.1 s

• 44.1 s

• 54.1 s

Answer 1

The rate of a first order reaction is 0.04 mol l⁻¹ s⁻¹ at 10 seconds and 0.03 mol l⁻¹ s⁻¹ at 20 seconds after initiation of the reaction. The half-life period of the reaction is 24.1 s.

Explanation:

For a first order reaction, \[\ce{A -> Products}\] and for concentration of the reactant at two different times,

\[\ce{k = \frac{2.303}{t_2 - t_1} log \frac{[A]_1}{[A]_2}}\]

∴ \[\ce{k = \frac{2.303}{t_2 - t_1} log \frac{(rate)_1}{(rate)_2}}\]    ...(∵ rate ∝ [A])

\[\ce{k = \frac{2.303}{20 - 10} log \frac{0.04}{0.03}}\]

\[\ce{k = \frac{2.303}{10} log 1.333}\]

k = 0.2303 × 0.12494

k = 0.02877 s⁻¹

Half-life of first order 

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

= 24.1