At 25 °c only 0.0420 mol of the generic salt ab2 is soluble in 1.00 l of water. what is the ksp of the salt at 25 °c?

Solubility product constants are values to describe the saturation of ionic compounds with low solubility. A saturated solution is when there is a dynamic equilibrium between the solute dissolved, the dissociated ions, the undissolved and the compound. It is calculated from the product of the ion concentration in the solution. For the generic salt, AB2, the dissociation would  be as follows:

AB2 = A2+ + 2B-

So, the expression for the solubility product would be:

Ksp = [A2+] [B-]^2

we let x = [AB2] = [A2+] = 0.420 / 1 = 0.420 M

2x = [B-]

Ksp = x (2x)^2
Ksp= 4x^3
Ksp = 4(0.420)^3
Ksp = 0.2964

The Ksp of the salt at temperature 25 degrees Celsius would be 0.2964.