Common ion effect and solubility

The presence of a common ion also affects the solubility of a sparingly soluble salt. Consider, the solubility equilibrium of AgCl,

The solubility product of AgCl is

Suppose $\mathrm{AgNO_3}$ is added to the saturated solution of AgCl. The salt $\mathrm{AgNO_3}$ being a strong electrolyte dissociates completely in the solution.

The dissociation of AgCl and $\mathrm{AgNO_3}$ produce a common $\mathrm{Ag^{+}}$ ion. The concentration of $\mathrm{Ag^{+}}$ ion in the solution increases owing to complete dissociation of $\mathrm{AgNO_3}$. According to Le-Chatelier's principle the addition of $\mathrm{Ag^{+}}$ ions from $\mathrm{AgNO_3}$ to the solution of AgCl shifts the solubility equilibrium of AgCl from right to left. The reverse reaction in which AgCl precipitates, is favoured until the solubility equilibrium is re-established. The value of $K_{sp}$, however, remains the same since it is an equilibrium constant. The solubility of a sparingly soluble compound, thus decreases with the presence of a common ion in solution.