Question

For the first order reaction,
$2N_2{O}_5\left(g\right)\to 4N{O}_2\left(g\right)+O_2\left(g\right)$

• 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 is 99.6% completed (approximately) in eight half-life duration

Answer 1

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

The correct options are
A The concentration of the reactant decreases exponentially with time
B The half-life of the reaction decreases with increasing temperature
D The reaction is 99.6% completed (approximately) in eight half-life duration


(a) For a first order reaction, the concentration of reactant remaining after time t is given by $\left[A\right]=[A{]}_o{e}^{-kt}.$
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 $t_{1/2}=\frac{ln2}{k}$.

(c) Half-life of first order reaction is independent of initial concentration.

(d) For a first order reaction, if $100\%$ of reactant is taken initially, after n half-lives, percentage of reactant remaining is given by $\%A=100{\left(\frac{1}{2}\right)}^n=100{\left(\frac{1}{2}\right)}^8=0.3906$
$\Rightarrow$% reaction completion = $100-0.3906=99.6\%$