Understand what a gas-forming reaction is: it is a chemical reaction that produces a gas as one of the products, often visible as bubbles or effervescence.
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 \(\text{Ba(NO}_3)_2(aq) + \text{K}_2\text{SO}_4(aq) \rightarrow \text{BaSO}_4(s) + 2\text{KNO}_3(aq)\), note that the solid \(\text{BaSO}_4\) precipitates, but no gas is formed.
For the equation \(\text{Na}_2\text{CO}_3(aq) + 2\text{HCl}(aq) \rightarrow 2\text{NaCl}(aq) + \text{H}_2\text{O}(l) + \text{CO}_2(g)\), observe that carbon dioxide gas (\(\text{CO}_2\)) is produced, indicating a gas-forming reaction.
For the other equations, such as \(\text{AgNO}_3(aq) + \text{NaCl}(aq) \rightarrow \text{AgCl}(s) + \text{NaNO}_3(aq)\) and \(\text{HCl}(aq) + \text{NaOH}(aq) \rightarrow \text{NaCl}(aq) + \text{H}_2\text{O}(l)\), no gases are produced; one forms a precipitate and the other is a neutralization producing water.