Define solubility product. Write solubility product expressions for the following:
`Zr_(3)(PO_(4))_(4)`

Explanation

Solubility product `(K_(sp))` : The product of the concentrations of the cation and the anion in a . saturated solution of a salt at room temperature is called solubility product `(K_(sp))`.
`K_(sp)=[Mn^(n+1)][A^(n-)]`
Significance of solubility product in chemical analysis: In any solution of a salt, if the product of `[M^(n+)] and [A^(n-)]` is greater than the solubility product `(K_(sp))` of the salt, then only the salt gets precipitated. For example
If the product of `[Zn^(2+)] and [S^(2-)]` in ammoniçal medium in IV group of chemical analysis exceeds the value of. `K_(sp)` of ZnS, it will be precipitated Similiar arguments apply to `Mn^(2+),Ni^(2+)`, etc.
(a) Solubility product expression for `Ag_(2)Cr_(2)O_(7)`.
`Ag_(2)Cr_(2)O_(7)hArr 2Ag_((s))^(+) +cr_(2)O_(7_((s)))^(-2)`
`K_(sp)=[Ag^(+)]^(2)[Cr_(2)O_(7)^(-2)]`
`=(2S)^(2)(S)`
`=4S^(3)`
`K_(SP)=4S^(3)`
`rArr S= ""^(3) sqrt((K_(SP))/(4))`
(b) For `Zr_(3)(P_(O_(4)))_(4)`
`Zr_(3)(PO_(4))_(4) hArr underset((3S))(3Zr^(+3)) + underset((4S))(4(PO_(4))^(-3))`
`K_(SP)=[Zr^(+3)]^(3)=[PO_(4)^(-3)]^(4)`
`=(3S)^(3) (4S)^(4)`
`:. S=((K_(SP))/(3^(3)xx4^(4)))^(1//7)`