Step 1: Understanding Solvay's Process.
In the Solvay process, sodium carbonate (Na\(_2\)CO\(_3\)) is produced by reacting sodium chloride (NaCl) with calcium carbonate (CaCO\(_3\)) and carbon dioxide (CO\(_2\)) at high temperature. Carbon dioxide is bubbled through the brine solution to form sodium bicarbonate (NaHCO\(_3\)), which is then heated to produce sodium carbonate.
Step 2: Analyzing the options.
(A) CO\(_2\) (g): Correct. Carbon dioxide is the gas that is bubbled through the brine solution in the Solvay process.
(B) N\(_2\) (g): Incorrect. Nitrogen is an inert gas and does not play a role in this process.
(C) NO\(_2\) (g): Incorrect. Nitrogen dioxide is not involved in the Solvay process.
(D) O\(_2\) (g): Incorrect. Oxygen is not used in the Solvay process.
Step 3: Conclusion.
The correct answer is (A) CO\(_2\) (g), as carbon dioxide is bubbled through the brine solution in the Solvay process.