Chemical Kinetics - Result Question 32
####32. In a first order reaction the concentration of reactant decreases from $800 mol / dm^{3}$ to $50 mol / dm^{3}$ in $2 \times 10^{4} s$. The rate constant of reaction in $s^{-1}$ is
(a) $2 \times 10^{4}$
(b) $3.45 \times 10^{-5}$
(c) $1.386 \times 10^{-4}$
(d) $2 \times 10^{-4}$
$(2003,1 M)$
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Answer:
Correct Answer: 32. (a)
Solution:
- For a first order reaction, $k t=\ln \frac{[A] _0}{[A]}$
$$ \begin{aligned} \Rightarrow \quad k=\frac{1}{t} \ln \frac{[A] _0}{[A]} & =\frac{1}{2 \times 10^{4}} \ln \frac{800}{50}=\frac{4 \ln 2}{2 \times 10^{4}} s^{-1} \ & =1.386 \times 10^{-4} s^{-1} \end{aligned} $$
