If the salts `M_(2)X,QY_(2)`, and `PZ_(3)` have the same solubilities `(lt(4)/(27))`, their `K_(sp)` values are related

Options

A. `K_(sp) (M_(2)X) = K_(sp)(QY_(2)) gt K_(sp) (PZ_(3))`
B. `K_(sp)(M_(2)X) gt K_(sp) (QY_(2)) =K_(sp) (PZ_(3))`
C. `K_(sp) (M_(2)X) = K_(sp) (QY_(2)) = K_(sp) (PZ_(3))`
D. `K_(sp)(M_(2)X) gt K_(sp) (QY_(2)) gt K_(sp) (PZ_(3))`

Answer

A

Explanation

Let `x =` solubility of each slat and `x` is small.
`{:(i.,M_(2)XhArr,2M^(o+)+,X^(2-),[K_(sp)=4x^(3)]),(,,2x,x,),(ii.,QY_(2)hArr,Q^(2+)+,2Y^(Theta),[K_(sp)=4x^(2)]),(,,x,2x,),(iii.,PZ_(3)hArr,P^(3+)+,3X^(Theta),[K_(sp)=27x^(4)]),(,,x,3x,):}`
`:. K_(sp) (M_(2)X) = K_(sp) (QY_(2)) gt K_(sp) (PZ_(3))`.