Silver chloride (AgCl) and barium chloride (BaCl2) are both insoluble in water, but they have different solubilities in other solvents. One way to separate them is to use a solvent that dissolves AgCl but not BaCl2. One such solvent is aqueous ammonia (NH3).

When AgCl is added to aqueous ammonia, it reacts to form a soluble complex ion, [Ag(NH3)2]Cl. This complex ion can then be separated from the insoluble BaCl2 by filtration. The filtrate can then be evaporated to dryness to obtain pure AgCl.

The overall reaction for the dissolution of AgCl in aqueous ammonia is:

$$\text{AgCl (s)} + 2\text{NH}_3 (\text{aq}) \rightarrow [\text{Ag}(\text{NH}_3)_2]^+ (\text{aq}) + \text{Cl}^- (\text{aq})$$

This reaction is reversible, and the equilibrium constant for the reaction is:

$$K = \frac{[\text{Ag}(\text{NH}_3)_2]^+[\text{Cl}^-]}{[\text{AgCl}]}$$

The value of K is very large, which means that the reaction proceeds almost completely to the right, resulting in the formation of the soluble complex ion [Ag(NH3)2]Cl.