The solubility of zinc phosphate in S `mol*L^(-1)`. Derive the mathematic expression of the solublity product of the compound .

Explanation

The following equilibrium is established by zinc phosphate, `[Zn_(3)(PO_(4))_(2)]` in its saturated aqueous solution:
`Zn_(3)(PO_(4))_(2) (s)hArr 3Zn^(2+)(aq)+2PO_(4)^(3-)(aq)`
`therefore K_(sp)=[Zn^(2+)]^(3)xx[PO_(4)^(3-)]^(2)`
As given, solublity of `Zn_(3)(PO_(4))_(2)` is S `mol*L^(-1)`. hence, `[Zn^(2+)]=3S" "mol*L^(-1) and [PO_(4)^(3-)]=2S" "mol*L^(-1)`
`therefore K_(sp)=(3S)^(3)xx(2S)^(2)=108S^(5)`, this is the mathematical expression of solublity product of zinc phosphate.