Chemical Kinetics - Result Question 22
####22. 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
(a) $24.1 s$
(b) $34.1 s$
(c) $44.1 s$
(d) $54.1 s$
[2016]
Show Answer
Solution:
- (a) For a first order reaction
$K=\frac{2.303}{(t_2-t_1)} \log \frac{(a-x_1)}{(a-x_2)}$
$K=\frac{2.303}{(20-10)} \log (\frac{0.04}{0.03})$
$K=\frac{2.303 \times 0.1249}{10}$
$\frac{0.6932}{t _{1 / 2}}=\frac{2.303 \times 0.1249}{10}$
$t _{1 / 2}=\frac{0.6932 \times 10}{2.303 \times 0.1249}=24.1 sec$
