Chemical Kinetics - Result Question 43
####43. For the first order reaction,
$$ 2 N _2 O _5(g) \longrightarrow 4 NO _2(g)+O _2(g) $$
(a) the concentration of the reactant decreases exponentially with time
(b) the half-life of the reaction decreases with increasing temperature
(c) the half-life of the reaction depends on the initial concentration of the reactant
(d) the reaction proceeds of $99.6 %$ completion in eight half-life duration
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Answer:
Correct Answer: 43. $(a, d)$
Solution:
- (a) For a first order reaction, the concentration of reactant remaining after time $t$ is given by $[A]=[A] _0 e^{-k t}$
Therefore, concentration of reactant decreases exponentially with time.
(b) Rise in temperature increases rate constant $(k)$ and therefore decreases half-life $\left(t _{1 / 2}\right)$ as
$$ t _{1 / 2}=\frac{\ln 2}{k} $$
(c) Half-life of first order reaction is independent of initial concentration.
(d) For a first order reaction, if 100 moles of reactant is taken initially, after $n$ half-lives, reactant remaining is given by
$$ \begin{aligned} % A & =100\left(\frac{1}{2}\right)^{n}=100\left(\frac{1}{2}\right)^{8}=0.3906 \ \Rightarrow \quad A \text { reacted } & =100-0.3906=99.6 % \end{aligned} $$
