A precipitation reaction occurs when ions that are initially dispersed in aqueous solution combine to form a sparingly soluble solid called a precipitate.

To predict a precipitation reaction qualitatively:

1. identify the ions supplied by each soluble electrolyte;
2. consider new cation-anion combinations that can form when the solutions are mixed;
3. use solubility rules to determine whether one combination is expected to be sparingly soluble;
4. write and balance the corresponding net ionic equation.

Example

Mix aqueous barium nitrate and sodium sulfate:

$$\mathrm{Ba(NO_3)_2(aq)}\qquad\text{and}\qquad\mathrm{Na_2SO_4(aq)}.$$

The dissolved ions are

$$\mathrm{Ba^{2+},\ NO_3^-,\ Na^+,\ SO_4^{2-}}.$$

Nitrates and sodium salts remain soluble, while $\mathrm{BaSO_4}$ is sparingly soluble. The predicted precipitate is therefore barium sulfate.

A molecular equation is

$$\mathrm{Ba(NO_3)_2(aq)+Na_2SO_4(aq)\rightarrow BaSO_4(s)+2NaNO_3(aq)}.$$

Expanding the soluble strong electrolytes and cancelling spectator ions gives

$$\boxed{\mathrm{Ba^{2+}(aq)+SO_4^{2-}(aq)\rightarrow BaSO_4(s)}}.$$

The sodium and nitrate ions remain dissolved and do not appear in the net ionic equation.

If every possible ionic combination is predicted to remain soluble, this simple qualitative model predicts no precipitation reaction. For example, mixing sodium nitrate and potassium chloride produces only ions whose corresponding salts are soluble, so no new solid is expected.

Solubility rules answer only the qualitative question of whether precipitation is plausible for ordinary concentrations. Near a solubility limit, actual precipitation depends on the ion concentrations and the solubility equilibrium. That quantitative decision requires comparing a reaction quotient with $K_{sp}$ and belongs to the later treatment of chemical equilibrium.