What is the pH of a saturated solution of Mg(OH)2? Ksp of Mg(OH)2 is 1.2 x 10-11?

Mg(OH)2 --> Mg+2 + 2OH-

Mg+2 = x

2OH- = 2x

Find a Ksp expression:

Ksp = [Mg+2][OH-]^2

1.2x10^-11 = [Mg+2][OH-]^2

Now plug in x for each of the concentrations in the Ksp equation, giving:

1.2x10^-11 = [x][2x]^2 simplify this equation

1.2x10^-11 = 4x^3 and solve for x,

x = 0.000144

because for every one Mg ion that is soluble, 2 OH ions are soluble, to solve for the concentration of OH (which is required to find the pH), you must multiply x by 2

[OH] = 2x, [OH] = 2(0.000144) = 0.000288

pOH = -log[OH]

pOH = -log(0.000288) = 3.54

pH = 14.00 - 3.54

pH = 10.46

x*(2x)^2 = Ksp = 1.2 x 10^-11

):

x = 1.44*10^-4

thus

OH^- = 2.88*10^-4 M

pOH = 3.54

so

pH = 10.5