Question

The reaction of NO2 (g) and O3 (g) is first-order in NO2 (g) and O3 (g)

2 NO2 (g) + O3 (g) $\longrightarrow$ N2O5 (g) + O2 (g)

The reaction can take place by mechanism :

I : NO2 + O3$\overset{\quad Slow\quad}{\rightarrow}$ NO3 + O2

NO3 + NO2$\overset{\quad fast\quad}{\rightarrow}$ N2O5

II : O3 O2 + [O]

NO2 + O $\overset{\quad Slow\quad}{\rightarrow}$ NO3

NO3 + NO2$\overset{\quad fast\quad}{\rightarrow}$N2O5

Select correct mechanism.

• A. I only
• B. II only
• C. Both I and II
• D. None of I and II

Answer 1

Answer: (C)

Both I and II

Answer 2

For Rxn rate determining step is slowest step

Then in 1st Rxn

$\text{Rate = k }\lbrack\text{N}\text{O}_{2}\rbrack\ \lbrack O_{3}\rbrack$ .....(i)

But 2nd Rxn

O3 O2 + [O] ....(1)

NO2 + O $\xrightarrow { \text { slow } }$ NO3 ....(2)

NO3 + NO2 $\xrightarrow { \text { fast } }$ N2O5 ....(3)

Then for Rxn (1)

$\frac{k_{a}}{k_{b}} = \frac{\left\lbrack O_{2} \right\rbrack\lbrack O\rbrack}{\left\lbrack O_{3} \right\rbrack} = k_{eq}$....(4)

by Rxn (2)

$\text{Rate = k }\lbrack\text{N}\text{O}_{2}\rbrack\ \lbrack O\rbrack$ ....(ii)

put value of [O] from (4) to (ii)

$\text{Rate = k }\frac{k_{\text{eq}}\left\lbrack O_{3} \right\rbrack}{\left\lbrack O_{2} \right\rbrack}\text{ × }\lbrack\text{N}\text{O}_{2}\rbrack Rate = \frac{k_{1}\left\lbrack NO_{2} \right\rbrack\left\lbrack O_{3} \right\rbrack}{\left\lbrack O_{2} \right\rbrack}$