The solubility product of Mg(OH)2 at 25∘C is 1.4 × 10−11. The solubility of Mg(OH)2 in gm per litre is:
8.7 × 10−3
Mg(OH)2 ⇌ Mg2+(aq) + 2OH−(aq)
Ksp=[Mg2+][OH−]2
Let us take the the solubility of Mg(OH)2=S moles/litre
[Mg2+]=1 × S; [OH−]=2S and
1.4 × 10−11=4S3
Solving the cubic for S,
S=1.5 × 10−4 moles/litre
=8.7 × 10−3 gram per litre
(since Molar mass Mg(OH)2=58)