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The solubility product of calcium hydroxide

Shake excess calcium hydroxide with water, filter, and titrate the dissolved hydroxide with hydrochloric acid. The product of concentrations comes out about five times the tabulated Ksp; the bench shows step by step how ion pairs and activity coefficients bring it back to 6.5 × 10⁻⁶, and why the common ion in CaCl₂ lowers the solubility less than a constant Ksp predicts.

Difficulty ●●○ ≈ 20 min

Aim Measure the solubility of Ca(OH)₂ and its concentration product by acid–base titration, and explain how they differ from the thermodynamic Ksp.
25.0 °C · excess Ca(OH)₂ shaken and filtered · phenolphthalein · 0.0500 M HCl

The solubility product of calcium hydroxide by titration

Flask: 25.00 mL of the filtrate by pipette and 2 drops of phenolphthalein — pink. The burette holds 0.0500 M HCl.

Ca(OH)X2(s)⇌CaX2++2 OHX−\ce{Ca(OH)2(s) <=> Ca^2+ + 2OH-} OHX−+HX+→HX2O\ce{OH- + H+ -> H2O}
05101520253035404550STIR50100150200
Burette reading 0.00mL
Colourpink

Near the end the pink fades more slowly; record the volume when it has just gone and does not return on swirling.

Computed: the saturated solution is set by Ksp (pKsp 5.19, in activities), the ion pair Ca²⁺ + OH⁻ ⇌ CaOH⁺ (lg K = 1.22) and Davies activity coefficients, solved on the charge balance with the ionic strength iterated. In water this gives 20.5 mmol/kg, against 19.76 mmol/kg measured at 25 °C by Johnston and Grove (1931); without the ion pair it would be 17.5 mmol/kg. In 0.0500 M CaCl₂ the ionic strength is about 0.18 mol/kg, where the Davies equation is only approximate. HCl neutralises both the free OH⁻ and the OH⁻ in CaOH⁺, so the titration finds all of the base. The flask colour comes from the bands of phenolphthalein’s two forms; the pH from the base or acid left over. The brief colour where a drop lands is illustrative.

Procedure

  1. Choose the saturated solution: in pure water or in 0.0500 M CaCl₂. The flask holds 25.00 mL of the filtrate and 2 drops of phenolphthalein; the burette holds 0.0500 M HCl.
  2. Add 1.00 mL at a time until the pink fades quickly, then single drops until it has just gone.
  3. Work out [OH⁻] = c(HCl)·V ÷ 25.00 mL, then [Ca²⁺] and [Ca²⁺][OH⁻]², and check it on the bench.
  4. Read how ion pairs and activities bring your product down to the tabulated Ksp; then switch to the solution saturated in 0.0500 M CaCl₂ and compare the two.

What to notice

  • In water about 20.5 mL of acid is needed: [OH⁻] = 0.0410 M, a solubility of 20.5 mmol/kg (Johnston and Grove measured 19.8 mmol/kg at 25 °C).
  • 4s³ = 3.4 × 10⁻⁵, about five times the tabulated 6.5 × 10⁻⁶: about 21 % of the calcium is held as the CaOH⁺ ion pair, and at an ionic strength near 0.05, γ(Ca²⁺) ≈ 0.45 and γ(OH⁻) ≈ 0.82.
  • In 0.0500 M CaCl₂ the solubility falls only to 16.3 mmol/kg, not the roughly 12 mmol/kg a constant concentration product would predict: the extra ions lower the activity coefficients (the salt effect) and bind more CaOH⁺.

In a real lab

  • Calcium hydroxide solutions take up CO₂ from the air and precipitate CaCO₃, which lowers the hydroxide: use boiled-out water, keep the flask stoppered and titrate soon after filtering.
  • Shake for long enough (at least 30 minutes), filter through a dry paper and discard the first few millilitres; any solid that gets through would be titrated too.
  • Calcium hydroxide dissolves exothermically, so it is less soluble when warm (0.189 g per 100 g of water at 0 °C, only 0.066 g at 100 °C): keep the solution at 25 °C.
  • The alkaline solution and the acid are both corrosive: wear goggles.

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