What is the molar solubility of Mg(OH)₂ in a basic solution with a pH of 12.50? K_spfor Mg(OH)₂ is 5.6 × 10^-12. A) 1.8 × 10^-¹⁰ M B) 5.6 × 10^-⁹ M C) 2.4 × 10^-6 M D) 1.1 × 10^-4 M

Question

Quizplus · Accepted Answer

The first step is to write the balanced chemical equation for the dissolution of Mg(OH)2 in water:
Mg(OH)2(s) ⇌ Mg2+(aq) + 2OH-(aq)
The Ksp expression is:
Ksp = [Mg2+][OH-]2
Since the solution is basic, we can assume that all of the OH- ions come from the dissociation of Mg(OH)2. Therefore, [OH-] = 2x, where x is the molar solubility of Mg(OH)2.
We can use the pH to calculate [H+] and thus [OH-]:
pH = 12.50
[H+] = 10-pH = 3.2 × 10-13 M
[OH-] = Kw/[H+] = 3.1 × 10-2 M
Substituting into the Ksp expression gives:
5.6 × 10-12 = [Mg2+](3.1 × 10-2)2
[Mg2+] = 6.0 × 10-10 M
The molar solubility of Mg(OH)2 is equal to half of the [OH-] concentration, since the stoichiometry of the balanced equation is 1:2 between Mg(OH)2 and OH-.
x = [OH-]/2 = 1.6 ×10-2 M
Therefore, the best choice is B, with a molar solubility of 5.6 × 10-10 M.

What Is the Molar Solubility of Mg(OH)2 in a Basic

What Is the Molar Solubility of Mg(OH)₂ in a Basic