(c) Using the appropriate Ksp value from Appendix D, calculate the pH of a saturated solution of Ca(OH)2.

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Identify the dissolution reaction for calcium hydroxide: Ca(OH)₂(s) ⇌ Ca²⁺(aq) + 2OH^-(aq).

Write the expression for the solubility product constant (K_sp) for Ca(OH)₂: K_sp = [Ca²⁺][OH^-]².

Let 's' be the solubility of Ca(OH)₂ in mol/L. Then, [Ca²⁺] = s and [OH^-] = 2s.

Substitute the expressions for [Ca²⁺] and [OH^-] into the K_sp expression: K_sp = (s)(2s)² = 4s³.

Solve for 's' using the given K_sp value, then calculate [OH^-] = 2s. Use the relation pOH = -log[OH^-] and pH + pOH = 14 to find the pH of the solution.

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 applies to the solubility of sparingly soluble ionic compounds. It quantifies the extent to which a compound can dissolve in water, represented by the concentrations of its ions at equilibrium. For calcium hydroxide, Ca(OH)2, the Ksp expression is derived from the dissociation of the compound into calcium ions and hydroxide ions.

pH and Hydroxide Ion Concentration

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. In the case of a saturated solution of Ca(OH)2, the concentration of hydroxide ions (OH-) produced will influence the pH. Since Ca(OH)2 is a strong base, the higher the concentration of OH- ions, the higher the pH, indicating a more basic solution.

Equilibrium Calculations

Equilibrium calculations involve determining the concentrations of reactants and products at equilibrium in a chemical reaction. For the dissolution of Ca(OH)2, one must set up an equilibrium expression using the Ksp value and the concentrations of Ca2+ and OH- ions. This allows for the calculation of the hydroxide ion concentration, which can then be used to find the pH of the solution.

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