Identify the species present in the reaction: AgNO3 and NaCl are both aqueous ionic compounds, so they dissociate completely into their ions in solution. Write the full ionic equation by splitting all strong electrolytes into their ions: \(\mathrm{AgNO_3 (aq)} \rightarrow \mathrm{Ag^+ (aq)} + \mathrm{NO_3^- (aq)}\) and \(\mathrm{NaCl (aq)} \rightarrow \mathrm{Na^+ (aq)} + \mathrm{Cl^- (aq)}\).
Write the full ionic equation by combining all ions from reactants and products: \(\mathrm{Ag^+ (aq)} + \mathrm{NO_3^- (aq)} + \mathrm{Na^+ (aq)} + \mathrm{Cl^- (aq)} \rightarrow \mathrm{AgCl (s)} + \mathrm{Na^+ (aq)} + \mathrm{NO_3^- (aq)}\).
Identify the spectator ions, which are ions that appear unchanged on both sides of the equation. In this case, \(\mathrm{Na^+ (aq)}\) and \(\mathrm{NO_3^- (aq)}\) are spectator ions because they do not participate in the formation of the precipitate.
Remove the spectator ions from the full ionic equation to write the net ionic equation. This leaves only the ions that form the precipitate: \(\mathrm{Ag^+ (aq)} + \mathrm{Cl^- (aq)} \rightarrow \mathrm{AgCl (s)}\).
Confirm that the net ionic equation represents the formation of the solid precipitate (AgCl) from its ions in solution, which is the key chemical change occurring in this reaction.