Question

For the first order reaction given below select the set having correct statements
$2N_2{O}_5(g)\to 4N{O}_2(g)+O_2(g)$
(1) the concentration of the reactant decreases exponentially with time
(2) the reaction proceeds to 99.6 % completion in eight half life duration
(3) the half life of the reaction depends on the initial concentration of the reactant
(4) the half life of the reaction decreases with increasing temperature

• A. 1,2
• B. 1,2,3
• C. 1,2,4
• D. 1,2,3,4

Answer 1

Answer: (C)

Here for this reaction statements 1,2 and 4 are correct as follows
For first order reaction
$\left[A\right]={\left[A\right]}_0{e}^{-\text{kt}}$
Hence concentration of $\left[\text{N}{\text{O}}_2\right]$ decreases exponentially (First statement is correct).
Also, $t_{\frac{1}{2}}=\frac{0.693}{K}$ . Which is independent of concentration and $t_{\frac{1}{2}}$ decreases with the increase of temperature.
$t_{99.6}=\frac{2.303}{K}loglog\left(\frac{100}{0.4}\right)$
$t_{99.6}=\frac{2.303}{K}\left(2.4\right)=8\times \frac{0.693}{K}=8t_{\frac{1}{2}}$
So statements 2 and 4 are also correct.