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. `MXgt MX_(2)gt M_(3)X`
B. `M_(3)gtMX_(2)gtMX`
C. `MX_(2)gtM_(3)XgtMX`
D. `MXgtM_(3)XgtMX_(2)`

Answer

D

Explanation

`MX rarr underset(s)(M^(+))+underset(s)(X),`
`K_(sp)=s^(2)`
or `s=sqrt(K_(sp))=sqrt(4xx10^(-8))=2xx10^(-4)M`
`MX_(x)hArr underset((s))(M^(2+))+underset((2s))(2X^(-)),`
`K_(sp)=s(2s)^(2)=4s^(3)`
`:. s=(K_(sp)//4)^(1//3)=((3/2xx10^(-14))/(4))^(1//3)=2 xx 10^(-5)M`
`M_(3)X hArr underset(3s)(3M^(+))+underset(s)(X^(3-)),`
`K_(sp)=(3s)^(3)s=27s^(4)`
`:. s=((K_(sp))/(27))^(1//4)`
`=(2.7 xx 10^(-15))/(27)=10^(-4)M`
`:. MX gt M_(3)X gt Mx_(2)`
`2 xx 10^(-4) gt 10^(-4) gt 2 xx 10^(-5)`