A saturated aqueous solution of Ca(OH)2 has pH = 12.40. — Aqueous Equilibria / Solubility Chemistry Question
Problem Context
A saturated aqueous solution of Ca(OH)2 has pH = 12.40.
What is the concentration of hydroxide ion in this solution?
Model Answer
pH = 12.40, so pOH = 14.00 – 12.40 = 1.60, [OH–] = 10–pOH = 0.0251 M
What is the Ksp of Ca(OH)2?
Model Answer
[Ca2+] = 0.5[OH–] = 0.0126 M
Ksp = [Ca2+][OH–]2 = [0.0126][0.0251]2 = 7.9 × 10-6
A 100.0 mg sample of Ca(OH)2 (M = 74.09) is suspended in 100.0 mL of water. The mixture is stirred vigorously and 3 M sulfuric acid is added dropwise to it while monitoring the pH of the solution.
At the point that the pH reaches 7.00, there is solid calcium sulfate suspended in the solution. What is the concentration of Ca2+(aq) in the solution at this point? The Ksp of CaSO4 is 2.4 × 10-5.
Model Answer
When pH = 7.00, the hydroxide has been exactly neutralized by the H2SO4, so the number of moles of Ca2+ is equal to the number of moles of SO4 2- present. Some of both will have precipitated as CaSO4, but [Ca2+] is still equal to [SO4 2-] in solution. So
[Ca2+][SO4 2-] = Ksp
[Ca2+]2 = 2.4 × 10-5
[Ca2+] = 0.0049 M
Does the solution become homogeneous at any point during this titration? Justify your answer.
Model Answer
0.1000 g Ca(OH)2/(74.09 g mol-1) = 0.001350 mol Ca(OH)2. So if the solution becomes homogeneous, then [Ca2+] = (0.001350 mol)/(0.100 L) = 0.0135 M. (The volume change in the titration is negligible since less than 0.5 mL of the sulfuric acid solution is added to reach the endpoint.)
In order for the solid Ca(OH)2 to have just dissolved, [Ca2+][OH–]2 = Ksp of Ca(OH)2
[0.0135][OH–]2 = 7.9 × 10-6
[OH–] = 0.0242 M
Since the initial number of moles of hydroxide = 2(0.001350 mol) = 0.00270 mol, this means that 0.00270 mol – 0.00242 mol = 0.00028 mol hydroxide were neutralized, requiring 0.00014 mol H2SO4 and creating [SO4 2-] = (0.00014 mol)/(0.100 L) = 0.0014 M. So at this point, [Ca2+][SO4 2-] = [0.0135][0.0014] = 1.9 × 10-5. Since this ion product is less than the Ksp of CaSO4, CaSO4 will not have begun to precipitate yet, and the solution will be homogeneous at this point.