For a reaction $\mathrm{NO}_2+\mathrm{CO} \longrightarrow \mathrm{CO}_2+\mathrm{NO}$ the possible elementary…
For a reaction
$\mathrm{NO}_2+\mathrm{CO} \longrightarrow \mathrm{CO}_2+\mathrm{NO}$ the possible elementary steps (below $500 \mathrm{~K}$ ) are
Step $1: \mathrm{NO}_2+\mathrm{NO}_2 \xrightarrow{\text { Slow }} \mathrm{NO}+\mathrm{NO}_3$
Step $2: \mathrm{NO}_3+\mathrm{CO} \xrightarrow{\text { Fast }} \mathrm{CO}_2+\mathrm{NO}_2$
It's rate expression will be
rate $=k\left[\mathrm{NO}_2\right][\mathrm{CO}]$
rate $=k\left[\mathrm{CO}_2\right][\mathrm{NO}]$
rate $=k\left[\mathrm{NO}_2\right]^2$
rate $=k[\mathrm{NO}]\left[\mathrm{NO}_3\right]$
Solution
For a reaction
$\begin{aligned} & m X+n Y \longrightarrow Z \\ & \text { rate }=k[X]^m[Y]^n\end{aligned}$
Rate of reaction is the slower step of the reaction.
$\mathrm{NO}_2+\mathrm{NO}_2 \xrightarrow{\text { Slow }} \mathrm{NO}+\mathrm{NO}_3$
$\therefore \quad$ Rate $=k\left[\mathrm{NO}_2\right]^2$.