Q. \[ \mathrm{AgNO}_3 + \mathrm{HCl} \]

We are given the reactants \( \mathrm{AgNO}_3 \) and \( \mathrm{HCl} \). We will identify the ions present, predict the products, check that the equation is balanced, and write the ionic and net ionic equations, explaining each step in detail.

Step 1. Write the strong-electrolyte dissociation of each reactant, showing the ions they produce in aqueous solution. Silver nitrate is a soluble ionic compound and dissociates into silver cations and nitrate anions. Hydrochloric acid is a strong acid and dissociates into hydrogen cations and chloride anions. In chemical form, these dissociations are:
\[ \mathrm{AgNO}_3 (aq) \; \text{gives}\; \mathrm{Ag}^+ (aq) + \mathrm{NO}_3^- (aq) \]
and
\[ \mathrm{HCl} (aq) \; \text{gives}\; \mathrm{H}^+ (aq) + \mathrm{Cl}^- (aq). \]

Step 2. Predict the products by exchanging the cations between the two salts. The cation \( \mathrm{Ag}^+ \) pairs with the anion \( \mathrm{Cl}^- \) to form silver chloride, \( \mathrm{AgCl} \). The cation \( \mathrm{H}^+ \) pairs with the anion \( \mathrm{NO}_3^- \) to form nitric acid, \( \mathrm{HNO}_3 \). Writing the molecular reaction (using an equals sign rather than an arrow) gives:
\[ \mathrm{AgNO}_3 (aq) + \mathrm{HCl} (aq) = \mathrm{AgCl} + \mathrm{HNO}_3 (aq). \]

Step 3. Check that the molecular equation is balanced. Count atoms on each side. Left side: one Ag, one N, three O, one H, one Cl. Right side: in \( \mathrm{AgCl} \) there is one Ag and one Cl, and in \( \mathrm{HNO}_3 \) there is one H, one N, and three O. Every element appears once on each side, so the equation as written is already balanced. Therefore the balanced molecular equation is:
\[ \mathrm{AgNO}_3 (aq) + \mathrm{HCl} (aq) = \mathrm{AgCl} (s) + \mathrm{HNO}_3 (aq). \]

Step 4. Use solubility rules to identify the physical states and the precipitate. Nitrates are soluble, so \( \mathrm{HNO}_3 \) remains aqueous. Most silver salts are soluble except for silver halides; silver chloride, \( \mathrm{AgCl} \), is insoluble and precipitates as a white solid. Thus \( \mathrm{AgCl} \) is written as a solid in the product. The molecular equation with physical states is:
\[ \mathrm{AgNO}_3 (aq) + \mathrm{HCl} (aq) = \mathrm{AgCl} (s) + \mathrm{HNO}_3 (aq). \]

Step 5. Write the complete ionic equation by showing all strong electrolytes as ions. Dissociate the soluble species into their ions, but leave the solid precipitate intact:
\[ \mathrm{Ag}^+ (aq) + \mathrm{NO}_3^- (aq) + \mathrm{H}^+ (aq) + \mathrm{Cl}^- (aq) = \mathrm{AgCl} (s) + \mathrm{H}^+ (aq) + \mathrm{NO}_3^- (aq). \]

Step 6. Identify and remove the spectator ions. Spectator ions appear unchanged on both sides of the ionic equation. Here the nitrate ion \( \mathrm{NO}_3^- \) and the hydrogen ion \( \mathrm{H}^+ \) are present on both sides, so they are spectators. Cancel them to obtain the net ionic equation, which shows only the species that actually change:
\[ \mathrm{Ag}^+ (aq) + \mathrm{Cl}^- (aq) = \mathrm{AgCl} (s). \]

Summary. The balanced molecular equation is:
\[ \mathrm{AgNO}_3 (aq) + \mathrm{HCl} (aq) = \mathrm{AgCl} (s) + \mathrm{HNO}_3 (aq). \]
The net ionic equation, showing the precipitation of silver chloride, is:
\[ \mathrm{Ag}^+ (aq) + \mathrm{Cl}^- (aq) = \mathrm{AgCl} (s). \]