Final answer:
The solubility product constant (Ksp) for Mg(OH)2 is found by applying the expression Ksp = [Mg^2+][OH^-]^2, yielding a Ksp value of 9.0 × 10^-12 when provided with the Mg^2+ concentration in a saturated solution.
Step-by-step explanation:
To complete the solubility constant expression for Mg(OH)2, we must consider its dissociation in water:
Mg(OH)2 (s) → Mg^2+ (aq) + 2OH^- (aq)
The solubility product constant, Ksp, expression for this dissociation is:
Ksp = [Mg^2+][OH^-]^2
Given that the concentration of Mg^2+ is 1.31 × 10^-4 M in a saturated solution, and assuming the stoichiometry of the dissociation, the concentration of OH^- would be twice that of Mg^2+, which is 2 × (1.31 × 10^-4 M) = 2.62 × 10^-4 M.
Substituting these values into the Ksp expression gives us:
Ksp = (1.31 × 10^-4) × (2.62 × 10^-4)^2
Ksp = 1.31 × 10^-4 × 6.8644 × 10^-8
Ksp = 8.998644 × 10^-12
After calculating, we round off to two significant figures, to match the precision of the given concentration of Mg^2+:
Ksp = 9.0 × 10^-12