Calculate the molar solubility of calcium hydroxide in a solution buffered at each pH. c. pH = 9

Verified step by step guidance

1. insert step 1> Calculate the concentration of hydroxide ions, [OH^-], in the solution using the pH value. Since pH + pOH = 14, find pOH by subtracting the given pH from 14. Then, calculate [OH^-] using the formula [OH^-] = 10^{-pOH}.
2. insert step 2> Write the balanced chemical equation for the dissolution of calcium hydroxide, Ca(OH)_2, in water: Ca(OH)_2 (s) \rightleftharpoons Ca^{2+} (aq) + 2OH^- (aq).
3. insert step 3> Write the expression for the solubility product constant, K_{sp}, of calcium hydroxide: K_{sp} = [Ca^{2+}][OH^-]^2.
4. insert step 4> Assume the molar solubility of Ca(OH)_2 is 's'. Then, [Ca^{2+}] = s and [OH^-] = 2s from the dissolution equation. However, since the solution is buffered, [OH^-] is already known from step 1.
5. insert step 5> Substitute the known [OH^-] concentration from step 1 and the expression for [Ca^{2+}] into the K_{sp} expression. Solve for 's', the molar solubility of Ca(OH)_2.

Key Concepts

Molar Solubility

Molar solubility refers to the maximum amount of a solute that can dissolve in a given volume of solvent at a specific temperature, expressed in moles per liter (M). For calcium hydroxide (Ca(OH)2), this involves determining how much of the compound can dissolve in water to reach equilibrium, which is influenced by the pH of the solution.

pH and its Relationship to Solubility

pH is a measure of the acidity or basicity of a solution, with lower values indicating acidic conditions and higher values indicating basic conditions. In the case of calcium hydroxide, which is a strong base, an increase in pH (more basic) can enhance its solubility due to the common ion effect, where the presence of hydroxide ions shifts the dissolution equilibrium.

Equilibrium and the Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the dissolution of sparingly soluble salts. For calcium hydroxide, Ksp can be expressed in terms of the concentrations of calcium ions and hydroxide ions in solution. Understanding Ksp is crucial for calculating molar solubility, especially when pH affects the concentration of hydroxide ions in the solution.