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The rate of a first-order reaction is 0.04 mol $L^{-1}s^{-1}$ at 10 sec and 0.03 mol $L^{-1}s^{-1}$ at 20 sec after initiation of the reaction. The half-life period of the reaction is
A
34.1 s
B
44.1 s
C
54.1 s
D
24.1 s
Explanation
For first order, rate ∝ concentration.
Detailed Solution
For a first order reaction, $K = \frac{2.303}{t_2 - t_1}\log\frac{[A]_1}{[A]_2} = \frac{2.303}{t_2 - t_1}\log\frac{[rate]_1}{[rate]_2}$
$K = \frac{2.303}{20 - 10}\log\frac{0.04}{0.03} = 0.0287\ s^{-1}$
$\therefore T_{1/2} = \frac{0.693}{K} = \frac{0.693}{0.0287} = 24.14$ s
$K = \frac{2.303}{20 - 10}\log\frac{0.04}{0.03} = 0.0287\ s^{-1}$
$\therefore T_{1/2} = \frac{0.693}{K} = \frac{0.693}{0.0287} = 24.14$ s