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 $5.6 \times 10 ^{- 12}$ A)1.8 × 10^-¹⁰ mol L^-1 B)5.6 × 10^-⁹ mol L^-1 C)2.4 × 10^-6 mol L^-1 D)1.1 × 10^-4 mol L^-1

Question

Quizplus · Accepted Answer

First, we need to write the chemical equation: 
Mg(OH)2 (s) ⇌ Mg2+ (aq) + 2OH- (aq)

We are given that the Ksp for Mg(OH)2 is 5.6 × 10 ^-12.

To find the molar solubility, we need to use the ice table:

Mg(OH)2 (s) ⇌ Mg2+ (aq) + 2OH- (aq) 
I    1           0           0 
C   -x           +x         +2x 
E   1-x         x           2x

The expression for Ksp is: 
Ksp = [Mg2+][OH-]^2

Substituting the equilibrium concentrations: 
5.6 × 10^-12 = x(2x)^2 
5.6 × 10^-12 = 4x^3 
x = 5.6 × 10^-5

So the molar solubility of Mg(OH)2 is 5.6 × 10^-5 mol/L.

In a basic solution with a pH of 12.50, there is an excess of OH- ions: 
pH = 14 - pOH 
12.50 = 14 - pOH 
pOH = 1.50 
[OH-] = 10^-1.50 M

Since [OH-] is greater than the molar solubility of Mg(OH)2, we can assume that all the Mg(OH)2 will dissolve. Therefore, the molar solubility of Mg(OH)2 in a basic solution with a pH of 12.50 is 5.6 × 10^-5 mol/L.

The best choice is B, which gives the correct value for the molar solubility.

What Is the Molar Solubility of Mg(OH)2 in a Basic 5.6×10−125.6 \times 10 ^{- 12}5.6×10−12

What Is the Molar Solubility of Mg(OH)₂ in a Basic $5.6 \times 10 ^{- 12}$