Step 1: Use stoichiometric coefficients.
From the balanced chemical equation:
\[
2\mathrm{N_2O_5} \rightarrow 4\mathrm{NO_2} + \mathrm{O_2}
\]
Step 2: Relate rate of formation to coefficients.
The rate of formation of products is proportional to their stoichiometric coefficients.
Thus, the rate of formation of \(\mathrm{NO_2}\) and \(\mathrm{O_2}\) is in the ratio \(4:1\).
Step 3: Express as asked ratio.
The ratio of rate of formation of \(\mathrm{O_2}\) to \(\mathrm{NO_2}\) is \(1:4\).
Step 4: Conclusion.
Hence, the required ratio is \(1:4\).