The literature Ksp value for Mg(OH)2 is 1.8 ✕ 10−11.

Question

The literature K_sp value for Mg(OH)₂ is 1.8 ✕ 10⁻¹¹.

(a) Calculate the theoretical [OH⁻ ] in a saturated solution of Mg(OH)_{2. Answer in M}

(b) What volume of 0.00210 M HCl would be required to neutralize the OH⁻ in 100.0 mL saturated Mg(OH)₂solution? Answer in mL.

Answer 1

Mg(OH)₂(s) <==> Mg²⁺(aq) + 2OH^-(aq)

Ksp = [Mg²⁺][OH-]²

Let x = [Mg²⁺], and then [OH-] = 2x

1.8x10^-11 = (x)(2x)²

1.8x10^-11= 4x³

x = 1.65x10^-4 M = molar solubility of Mg(OH)₂

Theoretical [OH^-] in a saturated solution = 2 x 1.65x10^-4 M = 3.3x10^-4 M = [OH-]

OH^- + H⁺ ==> H₂O

Since we already determined the [OH-] in a saturated solution of Mg(OH)₂ = 3.3x10^-4 M, we can find the moles of OH- in 100.0 mls (0.100) and then find the volume of HCl needed to provide an equal number of moles of H⁺ to neutralize the OH-.

3.3x10^-4 mol/L x 0.100 L = 3.3x10^-5 mol OH present

volume HCl needed: (x L)(0.00210 mol/L) = 3.3x10^-5 moles

x = 0.01571 L = 15.71 mls of HCl