If solubility product of `Zr_(3)(PO_(4))_(4)` is denotes by `K_(sp)` and its molar solubility is denoted by S, then which of the following relation between S and `K_(sp)`­ is correct ?

Options

A. `S=(K_(sp)/144)^(1//6)`
B. `S=(K_(sp)/6912)^(1//7)`
C. `S=(K_(sp)/929)^(1//9)`
D. `S=(K_(sp)/216)^(1//7)`

Answer

B

Explanation

`Zr_3(PO_4)_4 hArr 3Zr^(4+) + 4PO_4^(3-)`
If solubility is s, then
`[Zr^(4+)]=3s, [PO_4^(3-)]=4s`
`K_(sp)=[Zr^(4+)]^3 [PO_4^(3-)]^4`
`=(3s)^3 (4s)^4`
`=27s^3xx256s^4=6912s^7`
or `s=(K_(sp)/6912)^(1//7)`