Identify the type of reaction occurring in each equation. Typically, reactions that form a solid precipitate, a gas, or a weak electrolyte proceed to a measurable extent in water.
Check the solubility rules for each product in the reactions. For example, silver chloride (AgCl) is known to be insoluble in water and will precipitate out, while most nitrates (NO_3^-) and alkali metal salts (like NaCl, KNO_3) are soluble.
For the first reaction, AgNO_3 (aq) + NaCl (aq) → AgCl (s) + NaNO_3 (aq), recognize that AgCl is a solid precipitate, indicating the reaction proceeds significantly in water.
For the second reaction, BaSO_4 (aq) + Na_2SO_4 (aq) → BaSO_4 (s) + 2 Na^+ (aq), note that BaSO_4 is sparingly soluble, but since it is already present as aqueous, the reaction does not shift significantly to form more solid.
For the third and fourth reactions, all species remain dissolved as ions in solution, so no precipitate or other driving force exists to push the reaction forward measurably.