Question

For the first order reaction,
$2N_2O_5(g)\rightarrow 4NO_2(g)+O_2(g)$

• 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

Answer 1

Answer: (A), (B), (D)

(a) For a first order reaction, the concentration of reactant remaining after time $t$ is given by $[A] = [A]_0 e^{-kt}$ Therefore, concentration of reactant decreases exponentially with time.
(b) Rise in temperature increases rate constant $(k)$ and therefore decreases half-life $(t_{1/2})$ as
$t_{1/2}=\frac{In 2}{k}$
(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
$\%A=100\bigg(\frac{1}{2}\bigg)^n=100\bigg(\frac{1}{2}\bigg)^8=0.3906$
$\Rightarrow $ A reacted $= 100 - 0.3906 = 99.6\%$