The relation between solubility and Ksp is not a fixed one, but depends on the particular solid. Here's why
If the solid is of form AX, it will dissolve, producing one cation A+ and one anion X−.
AX(s)⇌A++X−
and the Ksp expression is Ksp=[A+][X−]
If you let x be the solubility, you can show that the ion concentrations will both be equal to x, and the Ksp expression is given by x2.
On the other hand, both A2X and AX2 dissolve to form three ions, and the Ksp expression is either
Ksp=[A+]2[X−] or Ksp=[A+][X−]2
In either case, using the same assignment of x equal to the solubility, you get to the same expression, the Ksp expression is equal to 4x3.
Since all three solubilities are on the order of 10−4, the Ksp of AX will be on the order of 10−8, while the other two will be on the order of 10−12.
To break the tie, you look at the size of the numbers. AX2 at 1.20×10−4 is smaller than 1.53×10−4, and so, will generate the smaller Ksp value.
