Question

What is the molar solubility of Mg(OH)2 in a solution containing 0,10 M NH3 ?

Ksp Mg(OH)2 = 1.2x10^-11
Kp NH3 = 1.8x10^-5

Answer 1

......Mg(OH)2 ==> Mg^2+ + 2OH^-
I......solid.......0.......0
C......solid.......x.......2x
E......solid.......x.......2x

Then NH3 + HOH ==> NH4^+ + OH^-
I....0.1...........0........0
C....-x............x........x
E....0.1-x.........x........x

First, determine the OH^- from the NH3 equation.
Then Ksp = (Mg^2+)(OH^-)
You know Ksp.
(Mg^2+) = x = solubility
(OH^-) = 2x from the Mg(OH)2 dissolution and OH^- from the NH3 for a total of 2x+OH^- from NH3.
Solve for x = Mg^2+ = solubility