Dissociation of a gas \(A _2\) takes place according to the following chemical reactions. At equilibrium, the total pressure is 1 bar at 300 K .
\(A_2(g) \rightleftharpoons 2 A(g)\)
The standard Gibbs energy of formation of the involved substances has been provided below:

Substance	\(\Delta G _{ t }^{\circ} / kJ mol ^{-1}\)
\(A _2\)	-100.00
\(A \)	-50.832

The degree of dissociation of \(A _2(g)\) is given by \(\left( x \times 10^{-2}\right)^{1 / 2}\) where \(x =\) _______.
(Nearest integer).
[Given: R =8 J \(mol ^{-1} K^{-1}\), log 2 = 0.3010, log 3 = 0.48]

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.