The give compound is a sparingly soluble salt, [tex]Zn_{3}(PO_{4})_{2}[/tex]. The solubility equilibrium for this compound can be represented as:
[tex]Zn_{3}(PO_{4})_{2}(aq)<==>3Zn^{2+}(aq)+2PO_{4}^{3-}(aq)[/tex]
Initial(M) - 0 0
Change(M) - +3x +2x
Equilibrium(M) - 3x 2x
Solubility product expression for this equilibrium will be:
[tex]K_{sp}=[Zn^{2+}]^{3}[PO_{4}^{3-}]^{2}[/tex]
= [tex](3x)^{3}(2x)^{2}=108x^{5}[/tex]
Where x will be the molar solubility of the compound[tex]Zn_{3}(PO_{4})_{2}[/tex]at that given temperature.