The solubility product constant `(K_(sp))` of salts of types `MX, MX_(2)`, and `M_(3)X` at temperature `T` are `4.0 xx 10^(-8), 3.2 xx 10^(-14)`, and `2.7 xx 10^(-15)`, respectively. The solubilities of the salts at temperature `T` are in the order

Options

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

Answer

D

Explanation

(i) `{:(MXhArr,M^(+),+X^(-)),(,S,S):}`
`:' K_(SP)= SxxS`
`:. S= sqrt(K_(SP))=sqrt(4.0xx10^(-8))=2.0xx10^(-4)`
(ii) `{:(MX_(2)hArr,M^(2+)+,2X^(-)),(,S,2S):}`
`K_(SP)= 4S^(3)`
`S= 3sqrt((K_(SP))/(4))= 3sqrt((3.2xx10^(-14))/(4)= 2.0xx10^(-5)`
(iii) `{:(M_(3)XhArr,3M^(+)+,2X^(3-)),(,3S,S):}`
`K_(SP)= 27S^(4)`
`S= 4sqrt((K_(SP))/(27))= 4sqrt((2.7xx10^(-15))/(27))=1.0xx10^(-4)`
`:. MXgtM_(3)XgtMX_(2)`