Excess Ca(OH)₂ is shaken with water to produce a saturated solution. The solution is filtered, and a 50.00-mL sample is titrated with HCl, requiring 11.23 mL of 0.0983 M HCl to reach the endpoint. Calculate Ksp for Ca(OH)₂. Compare your result with that in Appendix D. Suggest a reason for any differences you find between your value and the one in Appendix D.

Verified step by step guidance

Step 1: Write the balanced chemical equation for the dissolution of Ca(OH)_2 in water: Ca(OH)_2 (s) ⇌ Ca^{2+} (aq) + 2OH^{-} (aq).

Step 2: Determine the moles of HCl used in the titration. Use the formula: \( \text{moles of HCl} = M \times V \), where \( M \) is the molarity and \( V \) is the volume in liters.

Step 3: Since HCl reacts with OH^- in a 1:1 ratio, the moles of OH^- in the solution are equal to the moles of HCl used.

Step 4: Calculate the concentration of OH^- ions in the 50.00 mL sample. Use the formula: \( [OH^-] = \frac{\text{moles of OH^-}}{\text{volume of solution in liters}} \).

Step 5: Use the concentration of OH^- to find the concentration of Ca^{2+} ions. Since the stoichiometry of the dissolution is 1:2, \( [Ca^{2+}] = \frac{1}{2} [OH^-] \). Then, calculate the K_{sp} using the expression: \( K_{sp} = [Ca^{2+}][OH^-]^2 \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that quantifies the solubility of a sparingly soluble ionic compound. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced dissolution equation. For calcium hydroxide, Ca(OH)₂, the dissolution can be represented as Ca(OH)₂(s) ⇌ Ca²⁺(aq) + 2OH⁻(aq), leading to the expression Ksp = [Ca²⁺][OH⁻]².

Titration and Stoichiometry

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. In this case, hydrochloric acid (HCl) is used to titrate the hydroxide ions (OH⁻) from the saturated calcium hydroxide solution. The stoichiometry of the reaction, which is 1:1 for HCl and OH⁻, allows for the calculation of the moles of OH⁻ present, which is essential for determining the Ksp value.

Comparison of Experimental and Literature Values

When comparing the experimentally determined Ksp value with literature values, discrepancies may arise due to factors such as temperature differences, impurities in the reagents, or measurement errors. The Ksp value is temperature-dependent, and variations in experimental conditions can lead to different solubility outcomes. Understanding these factors is crucial for interpreting results and assessing the reliability of experimental data.

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