For the first order reaction $2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \longrightarrow 4…

1. the concentration of the reactant decreases exponentially with time.
2. the half-life of the reaction decreases with increasing temperature
3. the half-life of the reaction depends on the initial concentration of the reactant.
4. the reaction proceeds of $99.6 \%$ completion in eight half-life duration.

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{\operatorname{In} 2}{k} $
(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} & \text { Percentage } A=100\left(\frac{1}{2}\right)^n=100\left(\frac{1}{2}\right)^8=0.3906 \\ & \Rightarrow \text { A reacted }=100-0.3906=99.6 \% \end{aligned} $ (c) Half-life of first order reaction is independent of initial concentration

Asked in: JEE Advanced 2011 (Paper 2)

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