Solubility product constant `(K_(sp))` of salts of types `MX, MX_2 and M_3X` at temperature 'T' are `4.0 xx 10^(-8), 3.2 xx 10^(-14) and 2.7 xx 10^(-15)`, respectively. Solubilities `("mol. Dm"^(-3)` 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_(3)X gt MX`
D. `MX gt M_(3)X gt MX_(2)`

Answer

D

Explanation

`MX hArr underset(s) M^(+)+underset(x)X^(-), K_(sp)=s^(2)`
or `s=sqrt(K_(sp))=sqrt(4xx10^(-8))=2xx10^(-4)M`
`MX_(2)hArr underset(s)overset(2+)M + 2 underset(2s)X^(-), K_(sp)=s(2s)^(2)=4s^(3)`
`:. S=((K_(sp))/(4))^(1//3)=((3.2xx10^(-14))/(4))^(1//3)`
`=2xx10^(-5)M`
`M_(3)X hArr 3 underset(3s)M^(+)+ underset(s)X^(3-)`,
`K_(sp)=(3s)^(3)(s)=27s^(4)`
`:. s=((K_(sp))/(27))^(1//4)=((2.7xx10^(-15))/(27))^(1//4)=10^(-4) M`
Thus, the solubilities are in the order
`2xx10^(-4) gt 10^(-4) gt 2 xx 10^(-5)`, i.e., `MX gt M_(3)X gt MX_(2)`.