Solubility product constant Ksp for Mg(OH)2 is sought when its molar solubility in water is 1.6 × 10^−4 M. Which value is correct for Ksp?

• A. 1.6 × 10^−11
• B. 4.1 × 10^−12
• C. 2.6 × 10^−8
• D. 1.0 × 10^−12

Answer: (A)

Solubility product shows how the ions from a sparingly soluble salt come together in solution. For Mg(OH)2, dissolution gives Mg2+ and 2 OH−, so if the molar solubility is s, then [Mg2+] = s and [OH−] = 2s. The expression is Ksp = [Mg2+][OH−]^2 = s(2s)^2 = 4s^3. With s = 1.6 × 10^−4 M, Ksp = 4 × (1.6 × 10^−4)^3 = 4 × 4.096 × 10^−12 ≈ 1.64 × 10^−11, which rounds to 1.6 × 10^−11.