Understand that a gas-evolution reaction is a chemical reaction in which one of the products is a gas that bubbles out of the solution.
Examine each given chemical equation and identify the physical states of the products, focusing on whether any product is a gas (g).
For the equation \(\mathrm{Na_2CO_3(aq) + 2HCl(aq) \rightarrow 2NaCl(aq) + H_2O(l) + CO_2(g)}\), note that carbon dioxide (\(\mathrm{CO_2}\)) is produced as a gas, indicating gas evolution.
For the other equations, observe that the products are either aqueous (\(\mathrm{aq}\)), liquid (\(\mathrm{l}\)), or solid precipitates (\(\mathrm{s}\)), but no gases are formed.
Conclude that the equation producing \(\mathrm{CO_2(g)}\) is the gas-evolution reaction because it releases a gas as a product.