Solubility equilibria

Hereafter we confine our attention to sparingly soluble compounds, that is, compounds those dissolve only slightly in water.

Suppose some powdered sparingly soluble salt such as AgCl is put into water and stirred vigorously. A very small amount of AgCl dissolves in water to form its saturated solution. Most of the salt remains undissolved. Thus, solid AgCl is in contact with its saturated solution. AgCl is a strong electrolyte. Hence the quantity of AgCl that dissolves in water dissociates completely into its constituent ions, $\mathrm{Ag^{+}}$ and $\mathrm{Cl^{-}}$. A dynamic equilibrium exists between undissolved solid AgCl and the dissolved ions, $\mathrm{Ag^{+}}$ and $\mathrm{Cl^{-}}$, in the saturated solution. This equilibrium, called solubility equilibrium, is represented as :

The expression for its equilibrium constant is :

The concentration of undissolved solid AgCl is constant, so we may write

Substituting in Eq. (3.27) we write

The product of $K \times K'$ is another constant and is called solubility product, that is the product of concentrations of ions in a saturated solution. It is denoted by $K_{sp}$.

For the general salt solubility equilibrium

The solubility product is

Thus, in the saturated solution of sparingly soluble salt the product of equilibrium concentrations of the constituent ions raised to the power equal to their respective coefficients in the balanced equilibrium expression at a given temperature is called solubility product.

Consider following examples.

$\text{i. } \mathrm{BaSO_4(s)} \rightleftharpoons \mathrm{Ba^{2+}(aq)} + \mathrm{SO_4^{2-}(aq)}, \quad K_{sp} = [\mathrm{Ba^{2+}}][\mathrm{SO_4^{2-}}]$ …