\(\boxed{\text{bimolecular}}\)
To determine the experimental rate equation, we need to consider the rate-determining step (slow step) and how it relates to the overall reaction. The given steps are:
Step 1 (Slow):
\[
\mathrm{NO}_{2}(g) + \mathrm{NO}_{2}(g) \rightarrow \mathrm{NO}(g) + \mathrm{NO}_{3}(g)
\]
Step 2 (Fast):
\[
\mathrm{NO}_{3}(g) + \mathrm{CO}(g) \rightarrow \mathrm{NO}_{2}(g) + \mathrm{CO}_{2}(g)
\]
Since Step 1 is the slow step, it determines the rate of the overall reaction. The rate law for Step 1 is:
\[
\text{rate} = k[\mathrm{NO}_{2}]^2
\]
\(\boxed{\text{rate} = k[\mathrm{NO}_{2}]^2}\)