Question

For the reaction of first order, $2N_2{O}_5\left(g\right)\rightleftharpoons 4N{O}_2\left(g\right)+O_2\left(g\right)$, which of the following statements are correct?

• 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 to $99.6$% completion 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 proceeds to $99.6$% completion in eight half-life duration.

For 1st order reaction,

$a_t=a_0{e}^{-kt}$

Also, $t_{1/2}=\frac{In2}{k}$ or $t_{1/2}\alpha \frac{1}{k}$

As the temperature increases, value of k also increases due to which $t_{1/2}$ decreases.

For 99.6% completion, $a_t=\left(\frac{100-99.6}{100}\right)a_0=\frac{4a_0}{1000}$

$t=\frac{1}{k}In\frac{a_0}{4a-0/1000}=\frac{1}{k}In\frac{1000}{4}$

$=\left(\frac{t_{1/4}}{In2}\right).In250$

$t=8t_{1/2}$