For which of the following sparingly soluble salt the solubility (s) and solubility product `(K_(sp))` are related by the expression `s=(K_(sp)//4)^(1//3)`

Options

A. `BaSO_(4)`
B. `Ca_(3)(PO_(4))_(2)`
C. `Hg_(2)Cl_(2)`
D. `Ag_(3)PO_(4)`

Answer

C

Explanation

`BaSO_(4) hArr Ba^(2+) + SO_(4)^(2-) , K_(sp) = S^(2), S = sqrt(K_(sp))`
`Ca_(3)(PO_(4))_(2) hArr 3Ca^(2+) + 2PO_(4)^(3-), K_(sp) = (3S)^(3) xx (2S)^(2) = 108 S^(5)`
`:. S = ((K_(sp))/(108))^(1//5)`
`Hg_(2)Cl_(2) hArr Hg_(2)^(2+) + 2Cl^(-), K_(sp) = S xx (2S^(2)) = 4S^(3)`
`:. S = ((K_(sp))/(4))^(1//3)`
`Ag_(3)PO_(4)rarr 3Ag^(+) + PO_(4)^(3-), K_(sp) = (3S)^(3) xx S = 27 S^(4)`
`:. S = ((K_(sp))/(27))^(1//4)`
`CuS hArr Cu^(2+) + S^(2-), K_(sp) = S^(2), S = sqrt(K_(sp))`.