Question

The pH of a saturated solution of Mg(OH)^2, whose Ksp is 7.1x10^-12, is__________.

Answer 1

In order to find the pH of a solution, you must determine the concentration of hydronium ions, H3O⁺, either directly or indirectly.

When you're dealing with a Bronsted - Lowry base, like you are here, you will be solving for the concentration of hydronium ions indirectly, i.e. by solving for the concentration of hydroxide ions, OH^-.

Magnesium hydroxide, Mg(OH)2, is insoluble in aqueous solution. This means that when you place magnesium hydroxide in water, an equilibrium will be established between the undissolved solid and the dissolved ions.

Mg(OH)2(s] Mg²⁺(aq) + 2OH⁻(aq)

The solubility product constant, Ksp, for this equilibrium is represented as

Ksp = [Mg²⁺] [OH⁻]²

Now use the Ksp to find the molar solubility, s, of magnesium hydroxide in aqueous solution;

Mg(OH)2(s] Mg²⁺(aq) + 2OH⁻(aq)
IC: 0 0
C: +s +2s
EC: s 2s

Ksp will be equal to

Ksp = s (2s)²=4s³

7.1 x 10^-12 = 4s³

s³ = 1.78 x 10^-12

s = 1.21 x 10^-4

This means that the concentration of hydroxide ions, [OH⁻] in a saturated solution of magnesium hydroxide at will be

[OH⁻] = 2s = 2 (1.21 x 10^-4) M = 2.42 x 10^-4 M

Now, the concentration of hydronium ions and the concentration of hydroxide ions have the following relationship

Kw = [H3O⁺] [OH⁻] (Kw - the ion product for water's auto-ionization)

1.0 x 10^-14 = [H₃O⁺] (2.42 x 10^-4)

  [H₃O⁺] = (1.0 x 10^-14) / (2.42 x 10^-4)

  [H₃O⁺] = 4.13 x 10^-11

This means that the pH of the solution will be

pH = - log [H₃O⁺]
= - log (4.13 x 10^-11)
= 10.38