Calculate the solubility (in grams per 1.00⨉10² mL of solution) of magnesium hydroxide in a solution buffered at pH = 10. How does this compare to the solubility of Mg(OH)₂ in pure water?

Verified step by step guidance

1. Write the balanced chemical equation for the dissolution of magnesium hydroxide, Mg(OH)2, in water: \( Mg(OH)_2(s) \rightleftharpoons Mg^{2+}(aq) + 2OH^{-}(aq) \).
2. Use the given pH to find the concentration of hydroxide ions, \( OH^{-} \), in the solution. Recall that \( pH + pOH = 14 \). Calculate \( pOH \) and then use \( [OH^{-}] = 10^{-pOH} \).
3. Set up the expression for the solubility product constant (Ksp) of Mg(OH)2, which is \( K_{sp} = [Mg^{2+}][OH^{-}]^2 \).
4. Substitute the concentration of \( OH^{-} \) from step 2 into the Ksp expression and solve for \( [Mg^{2+}] \), the concentration of magnesium ions in the solution.
5. Convert the concentration of \( Mg^{2+} \) ions from moles per liter to grams per 100 mL to find the solubility of Mg(OH)2 in the buffered solution. Compare this value to the solubility in pure water by calculating or researching the Ksp value of Mg(OH)2 in pure water and following similar steps.

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For magnesium hydroxide, Mg(OH)2, the Ksp expression is Ksp = [Mg^2+][OH^-]^2, which helps determine its solubility in different conditions.

pH and its Effect on Solubility

pH is a measure of the acidity or basicity of a solution, which can significantly influence the solubility of certain compounds. In the case of magnesium hydroxide, a higher pH (more basic) increases the concentration of hydroxide ions (OH^-), which shifts the equilibrium and can lead to a decrease in solubility due to the common ion effect. Understanding how pH affects solubility is crucial for calculating solubility in buffered solutions.

Common Ion Effect

The common ion effect refers to the decrease in solubility of an ionic compound when a solution already contains one of the ions present in the compound. For magnesium hydroxide, if the solution is buffered at pH 10, the increased concentration of hydroxide ions from the buffer will reduce the solubility of Mg(OH)2 compared to its solubility in pure water, where no common ions are present. This concept is essential for understanding solubility in buffered solutions.