`MY` and `NY_(3)` two nearly insoluble salts, have the same `K_(sp)` values of `6.2xx10^(-13)` at room temperature. Which statement would be true in rearged to `MY` and `NY_(3)` ?

Options

A. The molar solubility of `MY` in water is less than that of `NY_(3)`.
B. The salts `MY` and `NY_(3)` are more soluble in 0.5 M `KY` than in pure water
C. The addition of the salt of `KY` to solution of `MY` and `NY_(3)` will have no effect on their solubilities
D. The molar solubilities of `MU` and `NY_(3)` in water are identical.

Answer

A

Explanation

For MY,
`underset(0)(MY)hArr underset(s)(M^(+))+underset(s)(Y^(-))`
where, s = solubility and `K_(sp)` = solubility product.
`therefore K_(sp)=[M^(+)][Y^(-)]`
`K_(sp)=s^(2)`
`s=sqrt(K_(sp))=sqrt(6.2xx10^(-13))=7.874xx10^(-7)`
Similarly, for `NY_(3)`,
`underset(0)(NY_(3))hArr underset(s)(N^(+))+underset(3s)(3Y^(-))`
`therefore K_(sp)=[N^(+)][Y^(-)]^(3)=sxx(3s)^(3)`
`K_(sp)=27s^(4)`
`therefore s= root(4)((K_(sp))/(27))=root(4)((6.2xx10^(-13))/(27))=3.89xx10^(-4)`
Therefore, molar solubility of MY in water is less than that of `NY_(3)`.