how do i determine the solubility of a substance through calculations?

Answer 1

I think you're asking how you can use Ksp values to calculate the solubility of an ionic compound, right? For a compound like Cd(OH)2, the value of Ksp is 2.5 X 10^-14. The expression of Ksp for this compound has the form:

Ksp=2.5 X 10^-14=[Cd2+][OH-]^2

So, if you let x = [Cd2+] in a saturated solution, then
2.5 X 10^-14=x(2x)^2

because the concentration of OH- will be twice the concentration of Cd2+.

By consolidating and solving for x, you find that
x=1.8 X 10^-5 mol/L.

That IS the molar solubility of Cd(OH)2. If you want to find the solubility in grams/L, you can just take that value and multiply it by the molar mass of Cd(OH)2, and you're finished.

Hope this helps...