Relationship between solubility and solubility product:

Salts like Agl, BaS0₄, PbS0₄, Pbl₂, etc., are ordinarily considered insoluble but they do possess some solubility. These are sparingly soluble electrolytes. A saturated solution of sparingly soluble electrolyte contains a very small amount of the dissolved electrolyte. It is assumed that whole of the dissolved electrolyte is present in the form of ions, i.e., it is completely dissociated.

The equilibrium for a saturated solution of any sparingly soluble salt may be expressed as:

A_xB_y ↔ xA^y+ + yB^x-

Thus, solubility product, K_s = [A^y+]^x[B^x-]^y

Let 's' mole per litre be the solubility of the salt, then

          AxBy ↔  xA^y+ + yB^x-

                       xs       ys

So                   K_s = [xs]x[ys]y

                           = x^x.y^y(s)^x+y

(i)  1:1 type salts:

Examples: AgCl, Agl, BaSO₄, PbSO₄, etc.

Binary electrolyte: AB ↔  A⁺ + B^-

                                     s      s

Let solubility of AB be s mol litre^-1.

So               K_s = [A⁺][B^-] = s × s = s²

or                s = √H_s

(ii)  1:2 or 2:1 type salts:

Examples: Ag₂CO₃, Ag₂CrO₄, PbCl₂, CaF₂, etc.

Ternary electrolyte:

AB₂ ↔ A²⁺ + 2B^-

           s       2s

Let solubility of AB₂ be s mol litre^-1.

So          K_s = [A2⁺][B^-]² = s × (2s)² = 4s³

or           s = 3√K_s/4

              A₂B ↔ 2A⁺ + B^2-

                         s      s

      Let s be the solubility of A₂B.

                  K_s = [A⁺]²[B^2-]

                      = (2s)²(s) = 4s³

        or          s = 3√K_s/4