Question

The rate of a first order reaction is $0.04molL-1s^{-1}$ at 10 seconds and $0.03mol{L}^{-1}{s}^{-1}$ at 20 seconds after initiation of the reaction. The half-life period of the reaction is :

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Answer 1

Given,
$T_1=10s\text{and}{T}_2=20s$
therefore,
$T_2-T_1=10s$

For first order reaction,
rate $\propto$ concentration

$\therefore \frac{r_1}{r_2}=\frac{C_1}{C_2}=\frac{0.04}{0.03}=\frac{4}{3}$

$k=\frac{2.303}{T_2-T_1}log\frac{C_1}{C_2}$
$k=\frac{2.303\times 0.125}{10}$
$k=0.0287s^{-1}$

Halflife period, $t_{1/2}=\frac{0.693}{k}$
$t_{1/2}=\frac{0.693}{0.0287}{t}_{1/2}=24.14s$