Determining The Ksp Of Calcium Hydroxide

Determining the Ksp of calcium hydroxide is a classic laboratory exercise that illustrates how solubility equilibria can be quantified from measurable solution properties. By preparing a saturated solution of Ca(OH)₂, measuring its pH, and calculating the hydroxide ion concentration, students can derive the solubility product constant (Ksp) and compare it with literature values. This hands‑on activity reinforces concepts of ionic dissociation, equilibrium expressions, and the relationship between pH and ion concentrations in aqueous systems.

Introduction

Calcium hydroxide, commonly known as slaked lime, is a sparingly soluble base that dissociates in water according to the equilibrium

[ \text{Ca(OH)}_2(s) \rightleftharpoons \text{Ca}^{2+}(aq) + 2,\text{OH}^-(aq) ]

The solubility product constant, Ksp, expresses the product of the ion concentrations at equilibrium:

[ K_{sp} = [\text{Ca}^{2+}][\text{OH}^-]^2 ]

Because each formula unit yields one calcium ion and two hydroxide ions, the hydroxide concentration is twice the calcium concentration in a saturated solution. Determining Ksp therefore hinges on accurately measuring either [Ca²⁺] or [OH⁻] in the saturated solution. The most straightforward approach in a teaching laboratory is to measure the pH, calculate [OH⁻] from pOH, and then compute Ksp. The procedure below outlines the materials, safety considerations, step‑by‑step methodology, data treatment, and typical sources of error.

Experimental Procedure (Steps)

Materials and Reagents

• Solid calcium hydroxide (Ca(OH)₂, reagent grade)
• Deionized or distilled water (≥ 18 MΩ·cm)
• pH meter calibrated with standard buffers (pH 4.00, 7.00, 10.00)
• Magnetic stirrer and stir bar
• 250 mL beaker or Erlenmeyer flask
• Filter paper or 0.45 µm syringe filter (to remove undissolved solid) - Volumetric pipette (10 mL) and graduated cylinder
• Safety goggles, lab coat, and nitrile gloves

Safety Notes

• Calcium hydroxide is a mild irritant; avoid skin and eye contact.
• Wear eye protection and gloves throughout the experiment.
• Dispose of waste solutions according to local regulations (typically dilute with plenty of water before drain disposal).

Step‑by‑Step Method

1. Prepare the saturated solution

   • Add approximately 2 g of solid Ca(OH)₂ to 100 mL of deionized water in a 250 mL beaker.
   • Stir the mixture vigorously on a magnetic stirrer for at least 30 minutes to allow equilibrium to be reached.
   • Allow the suspension to settle for an additional 5 minutes; the supernatant should appear clear with a slight milky tint if any solid remains.

2. Filter the supernatant

   • Using a piece of filter paper fitted in a funnel, filter a portion of the supernatant into a clean 50 mL beaker.
   • Alternatively, pass the solution through a 0.45 µm syringe filter to remove any fine particulates that could interfere with the pH electrode.

3. Measure the pH

   • Rinse the pH electrode with deionized water, blot dry with lint‑free tissue, and immerse it in the filtered solution.
   • Record the stable pH reading (typically between 12.2 and 12.6 for a saturated Ca(OH)₂ solution at 25 °C).
   • Rinse the electrode again and repeat the measurement two more times to ensure reproducibility; average the three values.

4. Calculate hydroxide ion concentration - Compute pOH from the measured pH: (\text{pOH} = 14.00 - \text{pH}) (valid at 25 °C).

   • Determine ([\text{OH}^-]) using ([\text{OH}^-] = 10^{-\text{pOH}}) (units: mol L⁻¹).

5. Determine calcium ion concentration

   • From the stoichiometry of dissolution, ([\text{Ca}^{2+}] = \frac{1}{2}[\text{OH}^-]).

6. Calculate Ksp

   • Insert the ion concentrations into the expression (K_{sp} = [\text{Ca}^{2+}][\text{OH}^-]^2).
   • Report the result with appropriate significant figures (usually three).

7. Temperature correction (optional) - If the experiment is conducted at a temperature other than 25 °C, adjust the water autoprotolysis constant (Kw) accordingly before calculating pOH, or measure the temperature and apply a temperature‑dependent correction factor to Kw.

Data Treatment Example

Assume the average pH measured is 12.40.

• pOH = 14.00 – 12.40 = 1.60
• ([\text{OH}^-] = 10^{-1.60} = 2.51 \times 10^{-2},\text{M})
• ([\text{Ca}^{2+}] = \frac{1}{2}(2.51 \times 10^{-2}) = 1.26 \times 10^{-2},\text{M})
• (K_{sp} = (1.26 \times 10^{-2})(2.51 \times 10^{-2})^2 = 7.9 \times 10^{-6})

The literature value for Ksp of Ca(OH)₂ at 25 °C is approximately (5.5 \times 10^{-6}). Differences can be discussed in terms of ionic strength, temperature variations, and experimental error.

Scientific Explanation

Solubility Equilibrium and the Ksp Concept

When a sparingly soluble salt like calcium hydroxide contacts water, a dynamic equilibrium establishes between the solid phase and its constituent ions. The equilibrium constant for this process, the solubility product (Ksp, is independent of the amount of solid present, provided some solid remains. It depends only on temperature (and, to a lesser extent, on ionic strength via activity coefficients). Because the solid’s activity is taken as unity, Ksp is expressed solely in terms of the aqueous ion concentrations (or activities).

Relationship Between pH and [OH⁻]

Water autoionizes according to

[ \text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^- \quad K_w = [\text{H}^

^+][\text{OH}^-] = 1.0 \times 10^{-14} \text{ at } 25^\circ \text{C}. ]
Thus, measuring the pH of a saturated solution directly yields ([\text{H}^+]), from which ([\text{OH}^-]) is calculated via the ion product of water. For a salt like (\text{Ca(OH)}_2), which dissociates completely into ions, the hydroxide concentration is twice the calcium concentration, simplifying the Ksp determination to a single pH measurement.

Factors Influencing the Measured Ksp

While the theoretical framework is straightforward, several practical factors can cause deviations between the experimental and literature Ksp values:

• Ionic Strength and Activity Coefficients: The Ksp expression is formally defined in terms of activities, not concentrations. In a solution with significant ionic strength (such as a saturated (\text{Ca(OH)}2) solution, where ([\text{Ca}^{2+}] \approx 0.02,\text{M})), activity coefficients deviate from unity. The measured concentration-based product ((K{sp}^\text{conc})) will be lower than the thermodynamic (K_{sp}) because the effective concentrations (activities) are reduced by ion-ion interactions.
• Carbon Dioxide Absorption: Atmospheric (\text{CO}_2) can dissolve in the alkaline solution, forming carbonate ions that react with (\text{Ca}^{2+}) to precipitate (\text{CaCO}_3). This removes calcium from solution, decreasing both ([\text{Ca}^{2+}]) and, by stoichiometry, ([\text{OH}^-]), leading to an underestimation of Ksp.
• Temperature: The autoprotolysis constant of water ((K_w)) and the solubility of (\text{Ca(OH)}_2) are temperature-dependent. If the experiment is performed at a temperature different from 25 °C without correction, the calculated Ksp will reflect the conditions of that temperature, not the standard value.
• Electrode Calibration and Junction Potentials: Inaccurate pH meter calibration or liquid junction potentials between the reference electrolyte and the sample solution can introduce systematic error in the pH reading.

Conclusion

The determination of the solubility product of calcium hydroxide via pH measurement provides a clear and accessible application of equilibrium principles. The experiment illustrates how a simple physicochemical property—pH—can be leveraged to quantify the solubility of a sparingly soluble salt. Discrepancies between the calculated and accepted Ksp values serve as a valuable pedagogical tool, prompting discussion of real-world complications such as non-ideal solution behavior, contamination, and the importance of rigorous experimental technique. Ultimately, this exercise reinforces foundational concepts in analytical chemistry, including equilibrium constants, activity versus concentration, and the meticulous care required in quantitative measurements. By understanding both the ideal theory and its limitations, students gain a more nuanced appreciation for the interpretation of thermodynamic data in aqueous systems.

To obtaina reliable value for the solubility product, the experiment typically begins with the preparation of a saturated calcium hydroxide solution. A known mass of solid Ca(OH)₂ is added to de‑ionized, CO₂‑free water and stirred vigorously for at least 30 minutes to allow equilibrium to establish. The suspension is then filtered through a fine‑porosity membrane (0.45 µm) under an inert atmosphere of nitrogen to prevent further uptake of atmospheric carbon dioxide. The filtrate, now a clear alkaline solution, is transferred to a temperature‑controlled cell where a calibrated glass‑pH electrode measures the pH.

From the measured pH, the hydroxide concentration follows directly: ([{\rm OH^-}] = 10^{-(14-{\rm pH})}) at the experimental temperature. Because each formula unit of Ca(OH)₂ yields one calcium ion and two hydroxide ions, the calcium concentration is ([{\rm Ca^{2+}}] = [{\rm OH^-}]/2). The apparent solubility product is then calculated as

[ K_{sp}^{\rm conc}= [{\rm Ca^{2+}}],[{\rm OH^-}]^{2} = \frac{[{\rm OH^-}]^{3}}{2}. ]

If the experiment deviates from the standard 25 °C, the temperature dependence of both (K_w) and the intrinsic solubility must be accounted for. Applying the van’t Hoff equation

[\ln\frac{K_{sp}(T)}{K_{sp}(298\ {\rm K})}= -\frac{\Delta H^{\circ}}{R}\left(\frac{1}{T}-\frac{1}{298}\right) ]

allows conversion of the measured value to the reference temperature, provided an estimate of the enthalpy of dissolution ((\Delta H^{\circ})) is available from literature or calorimetry.

To address non‑ideality, activity coefficients can be estimated with the extended Debye–Hückel model

[\log \gamma_i = -\frac{A z_i^2 \sqrt{I}}{1 + B a_i \sqrt{I}}, ]

where (I) is the ionic strength of the saturated solution. Substituting activities ((a_i = \gamma_i [i])) into the equilibrium expression yields a thermodynamic (K_{sp}) that can be compared directly with tabulated values. In practice, the correction is modest for Ca(OH)₂ (typically a few percent) but becomes essential when comparing results across different ionic strengths or when validating the experimental protocol.

Mitigating the identified sources of error improves agreement with literature data. Performing the titration or pH measurement inside a glove box or under a continuous nitrogen stream eliminates CO₂ absorption. Using freshly prepared pH buffers (pH 4.00, 7.00, 10.00) and checking the electrode slope daily reduces calibration drift. Employing a double‑junction

or sealed reference electrode minimizes junction potential fluctuations. Finally, conducting replicate measurements at the same temperature and averaging the results reduces random scatter.

When these precautions are taken, the experimentally determined (K_{sp}) at 25 °C typically falls within 5 % of the accepted value (~5.5 × 10⁻⁶), confirming that the method is sound. The small systematic deviations that remain are usually attributable to residual CO₂ uptake or minor temperature fluctuations during measurement. By carefully controlling these variables and applying the appropriate corrections for temperature and activity, the solubility product of calcium hydroxide can be determined with high accuracy, providing a reliable basis for further thermodynamic or kinetic studies involving this important base.