Calculate the molar solubility of calcium hydroxide in a solution buffered at each pH. b. pH = 7

검증된 단계별 안내

Identify the chemical equation for the dissolution of calcium hydroxide: \( \text{Ca(OH)}_2 (s) \rightleftharpoons \text{Ca}^{2+} (aq) + 2\text{OH}^- (aq) \).

Write the expression for the solubility product constant \( K_{sp} \) for calcium hydroxide: \( K_{sp} = [\text{Ca}^{2+}][\text{OH}^-]^2 \).

Determine the concentration of \( \text{OH}^- \) ions in the solution using the relationship between pH and pOH: \( \text{pOH} = 14 - \text{pH} \), then \( [\text{OH}^-] = 10^{-\text{pOH}} \).

Substitute the \( [\text{OH}^-] \) value into the \( K_{sp} \) expression and solve for \( [\text{Ca}^{2+}] \), which represents the molar solubility of calcium hydroxide.

Use the known \( K_{sp} \) value for calcium hydroxide to calculate the molar solubility by substituting the \( [\text{OH}^-] \) concentration into the equation and solving for \( [\text{Ca}^{2+}] \).

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주요 개념

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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 (mol/L). For calcium hydroxide (Ca(OH)2), which is a sparingly soluble salt, its molar solubility can be influenced by the pH of the solution, as it dissociates into calcium ions (Ca²⁺) and hydroxide ions (OH⁻).

pH and Hydroxide Ion Concentration

pH is a measure of the acidity or basicity of a solution, with lower values indicating higher acidity and higher values indicating higher basicity. In a buffered solution at pH 7, the concentration of hydroxide ions (OH⁻) is 1 x 10⁻⁷ M. This concentration is crucial for calculating the solubility of calcium hydroxide, as the presence of additional hydroxide ions can shift the equilibrium of the dissolution reaction.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. In the context of calcium hydroxide solubility, increasing the pH (and thus the concentration of OH⁻) will shift the dissolution equilibrium to the left, reducing the solubility of Ca(OH)2. Understanding this principle is essential for predicting how changes in pH affect solubility.