\( X_{2}(g) + Y_{2}(g) \rightleftharpoons 2Z(g) \),
\(X _2(g)\) and \(Y _2(g)\) are added to a 1 L flask and it is found that the system attains the above equilibrium at \(T ( K )\) with the number of moles of \(X _2(g), Y _2(g)\) and \(Z ( g )\) being 3,3 and 9 mol respectively (equilibrium moles). Under this conditions of equilibrium, 10 mol of \(Z ( g )\) is added to the flask and the temperature is maintained at \(T ( K )\). Then the number of moles of \(Z ( g )\) in the flask when the new equilibrium is established is _________ . (Nearest integer).

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.