The solubility product constant of calcium hydroxide is 6.5 x 10–6. if 0.10 mol of sodium hydroxide is added to 1 l of 0.0010m ca(oh)2, what is the final concentration of the calcium ion? show your work.

When the reaction equation is:

Ca(OH)2 → Ca2+  +  2OH-

and when we assume that the final concentration of the calcium ion is X 

and we assume [OH-] = 2 X + 0.1

and X (the molarity) = moles of Ca(OH)2 / volume L

also, we have the solubility product constant  Ksp = 6.5 x 10^-6

when the Ksp expression = [Ca2+][OH]^2

by substitution:

6.5 x 10^-6 = X*(2X+0.1)^2

∴ X = 6.3 x 10^-4  M

∴ [Ca2+] = X = 6.3 x 10^-4 M