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  4. Consider the reaction 2NO2(.g.)+O3(.g.) arrow N2O5(.g.)+O2(.g.) The reaction of nitrogen dioxide and ozone represents is first order in NO2(.g.) and in O3(.g.) . Which of these possible reaction mechanism is consistent with the rate law? <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/chemistry/68551bc82529bf54183be5073e03bdc6-.png />

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Q. Consider the reaction

$2NO_{2}\left(\right.g\left.\right)+O_{3}\left(\right.g\left.\right) \rightarrow N_{2}O_{5}\left(\right.g\left.\right)+O_{2}\left(\right.g\left.\right)$

The reaction of nitrogen dioxide and ozone represents is first order in $NO_{2}\left(\right.g\left.\right)$ and in $O_{3}\left(\right.g\left.\right)$ . Which of these possible reaction mechanism is consistent with the rate law? image

NTA AbhyasNTA Abhyas 2020Chemical Kinetics

Solution:

Mechanism I: $Rate=k\left[\right.NO_{2}\left]\right.\left[\right.O_{3}\left]\right.$ Slow step is rate determining

Mechanism II: $\text{Rate}\text{Rate}$ = $\text{k}$ ′ [ $\text{N}$ $\text{O}$ 2 ][ $\text{O}$ ] …(i)

From 1st step $K=\frac{\left[\right. O_{2} \left]\right. \left[\right. O \left]\right.}{\left[\right. O_{3} \left]\right.}$ (k = eq. constant)

$\text{[O]} \, \text{=} \, \text{k} \frac{\left[\text{O}_{\text{3}}\right]}{\left[\text{O}_{\text{2}}\right]}$ ...(ii)

From equation (i) and (ii)
Rate $= k ^{\prime}\left[ NO _{2}\right]\left[ O _{3}\right]\left[ O _{2}\right]^{-1}$

So both mechanism show that reaction is first order with respect to $NO _{2}$ and $O _{3}$.