A sparingly soluble salt having general formula A^p+_x B^q-_y and molar solubility S is in Equilibrium with its saturated solution. Derive a relationship between the solubility and solubility product for such salt.

A relationship between the solubility and solubility product for such salt can be derived as follows-

Let the solubility be S.

Initially, assume 1 mole of A_xB_y was present. From which S moles of it was dissolved to give xS and yS moles of A^p+ and B^q- respectively. This can be understood from the following equation.

A^p+_x B^q-_y ⇋ xA^+p + yB^-q

At t=0, 1 0 0

At Equilibrium, 1-S xS yS

Solubility product is the multiplication product of concentration of products each raise to their stoichiometric coefficients.

Hence, Solubility product (K_sp) = [A^+p]^x [B^-q]^y

= (xS)^x(yS)^y

= x^xy^yS^x+y