\(37.8 \mathrm{~g} \mathrm{~N}_2 \mathrm{O}_5\) was taken in a 1 L reaction vessel and allowed to undergo the following reaction at 500 K
\(2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightleftharpoons 2 \mathrm{~N}_2 \mathrm{O}_{4(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}\)
The total pressure at equilibrium was found to be 18.65 bar.
Then, \(\mathrm{Kp}=\) ______ \(\times 10^{-2}\) [nearest integer]
Assume \(\mathrm{N}_2 \mathrm{O}_5\) to behave ideally under these conditions.
Given: \(\mathrm{R}=0.082\) bar \(\mathrm{L} \mathrm{mol}^{-1} \mathrm{~K}^{-1}\)

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.