Three sparingly soluble salts `M_(2)X`, `MX` and `MX_(3)` have the same solubility product. Their solubilities will be in the order

Options

A. `MX_(3)gtMXgtM_(2)X`
B. `MX_(3)gtM_(2)XgtMX`
C. `MXgtMX_(3)gtM_(2)X`
D. `MXgtM_(2)XgtMX_(3)`

Answer

D

Explanation

`underset(s_(1))(M_(2)X) rarr underset(2s_(1))(2M^(+))+underset(s_(1))(X_(2))`
`K_(sp)=4s_(1)^(3)` or, `s_(1)=(K_(sp)//4)^(1//3)`
`MX rarr M^(+)+X^(-)`, `K_(sp)=s_(2)^(2)`
or, `s_(2)=(K_(sp))^(1//2)`
`underset(s)(MX_(3)) rarr M^(3+)+underset(3s)(3X^(-))`
`K_(sp)=27s_(3)^(4)` or, `s_(3)=(K_(sp)//27)^(1//4)`
Evidently, `s_(2)gts_(1)gts_(3)`