The decomposition of \(\mathrm{O}_3(g)\) follows first order kinetics and is given by \[ \mathrm{O}_3(9) \longrightarrow \mathrm{O}_2(9)+\mathrm{O}(9) \] The rate constant for this reaction is \(1.0 \times 10^{-3} \mathrm{~s}^{-1}\). The initial pressure of \(\mathrm{O}_3(g)\) is \(100 \mathrm{~atm}\). What will be the partial pressure (in atm) of \(\mathrm{O}_3, \mathrm{O}_2, \mathrm{O}\) respectively after 38.38 minutes?

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.