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. `MX gt MX_(2) gt M_(3)X`
B. `M_(3)X gt MX_(2) gt MX`
C. `MX_(2) gt M_(2)X gt MX`
D. `MX gt M_(3)X gt MX_(2)`

Answer

D

Explanation

`MX hArr underset((S_(1)))(M^(+)) +underset((S_(2)))(X^(-))`
`S_(1) =(K_(sp))^(1//2) =(4 xx 10^(-8))^(1//2)`
`=2xx 10^(-4).`
`MX_(2) hArr underset((S_(2)))(M^(+)) +underset((2S_(2)))(2X^(-))`
`5S_(2)^(3) =K_(sp) " or " S_(2) =((K_(sp))/(4))^(1/3)`
`S_(2) =((3.2 xx 10^(-14))/(4))^(1/3) =2xx 10^(-5)`
`M_(3)X hArr underset((3 S_(3)))(3M^(+)) + underset((S_(3)))(X^(3-))`
`27S_(3)^(4) =K_(sp) " or " S_(3) =((K_(sp))/(27))^(1/4)`
`S_(2) =((2.7 xx 10^(-5))/(27)) =10^(-4)`
The correct order is : `MX gt M_(3)X gt MX_(2)`