Experiment 7: Solubility, Equilibrium and Thermodynamics - Solubility of Calcium Hydroxide

PURPOSE

To investigate how temperature affects the solubility of calcium hydroxide (Ca(OH)₂) and to determine its thermodynamic properties (ΔH°, ΔS°, and ΔG°) by measuring the solubility product (Ksp) at different temperatures through acid-base titration.

OBJECTIVES

Experimental Objectives

• Prepare saturated Ca(OH)₂ solutions at low, room, and high temperatures.

• Perform titrations using standardized HCl to determine OH⁻ concentration.

• Calculate Ksp at each temperature from ion concentrations.

• Use Ksp values to determine ΔG°, and create a ΔG° vs. T plot.

• Use LINEST in Excel to derive ΔH° and ΔS° from the plot.

Learning Objectives

• Understand the relationship between solubility, temperature, and thermodynamics.

• Apply Le Chatelier’s principle to predict solubility changes.

• Analyze dissolution using ΔG = ΔH - TΔS and ΔG = -RTlnK.

• Interpret the signs and magnitudes of ΔH° and ΔS° in relation to solubility trends.

UNDERSTANDING THE BACKGROUND

• Ca(OH)₂ Dissolution Reaction:
  Ca(OH)₂ (s) ⇌ Ca²⁺ (aq) + 2 OH⁻ (aq)
  The solubility of Ca(OH)₂ varies with temperature.

• Solubility Product (Ksp):
  Ksp=[Ca2+][OH−]2K_{sp} = [Ca^{2+}][OH^-]^2Ksp​=[Ca2+][OH−]2

• Thermodynamics Connection:

  • ΔG° = –RT ln K

  • ΔG° = ΔH° – TΔS°
    A plot of ΔG° vs. T yields a line with slope = –ΔS° and y-intercept = ΔH°.

• Predicting Behavior:

  • If dissolution is exothermic, increasing temperature decreases solubility.

  • If endothermic, increasing temperature increases solubility.

  • Dissolution increases disorder (ΔS° > 0).

SUMMARY OF THE PROCEDUREl

1. Preparation of Saturated Solutions:

   • Dissolve ~0.5 g of Ca(OH)₂ in 50 mL DI water at three temperatures: ice bath (~5–10°C), room temp, and boiling (~100°C).

   • Stir each solution for 5–10 min to allow saturation.

2. Filtration:

   • Filter 40–50 mL of each solution using pre-wetted filter paper (with saturated solution, not water).

   • Keep filtered low-temp solution in ice bath to prevent solubility changes.

3. Titration:

   • Titrate 10 mL of each filtered solution with <1 M standardized HCl using bromothymol blue.

   • End point: green (neutral). Indicator turns yellow (acid) beyond equivalence.

   • Perform 2–3 titrations per solution to ensure accuracy.

ANALYZING THE DATA

1. Calculate [OH⁻] from the volume of HCl used and its concentration.

2. Calculate [Ca²⁺] using the 1:2 molar ratio from the dissolution equation.

3. Determine Ksp using Ksp=[Ca2+][OH−]2K_{sp} = [Ca^{2+}][OH^-]^2Ksp​=[Ca2+][OH−]2.

4. Calculate ΔG° for each temperature:
   ΔG∘=−RTln⁡Ksp\Delta G^\circ = -RT \ln K_{sp}ΔG∘=−RTlnKsp​

5. Graphical Analysis:

   • Plot ΔG° (y-axis) vs. Temperature in K (x-axis).

   • Use LINEST in Excel to determine slope (–ΔS°) and intercept (ΔH°).

   • Calculate ΔG° and Ksp at 25°C using derived values.

6. Compare to Theoretical Values:

   • Use thermodynamic tables (e.g., Tro Table 18.2) to find literature values of ΔH°, ΔS°, and Ksp.

   • Calculate % error for your results.

7. Discussion Points:

   • Did ΔH° and ΔS° match expected signs and values?

   • Explain how solubility changes with temperature and why titrating cold solutions must occur in an ice bath.

   • Assess the spontaneity of dissolution at different temperatures using ΔG°.