Identify the products of each given chemical reaction and determine their physical states (solid, liquid, aqueous, or gas).
Recall that gas production in a reaction is indicated by a product with the physical state (g), which stands for gas.
Examine the first reaction: \(\mathrm{AgNO_3(aq) + NaCl(aq) \rightarrow AgCl(s) + NaNO_3(aq)}\). The products are a solid precipitate (AgCl) and an aqueous solution (NaNO3), so no gas is produced here.
Look at the second reaction: \(\mathrm{HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l)}\). The products are aqueous salt and liquid water, with no gas formed.
Analyze the last reaction: \(\mathrm{Na_2CO_3(aq) + 2HCl(aq) \rightarrow 2NaCl(aq) + H_2O(l) + CO_2(g)}\). Here, carbon dioxide (\(\mathrm{CO_2}\)) is produced as a gas, which means this reaction involves gas production.