The pH of a sample of hard water having [Mg2+] = 2.5 x 10^-4 M is adjusted to pH 10.80. Will Mg(OH)2 precipitate?

Verified step by step guidance

Step 1: Determine the solubility product constant (K_{sp}) for Mg(OH)_2. This value is typically found in a chemistry reference table. For Mg(OH)_2, K_{sp} is approximately 1.8 \times 10^{-11} at 25°C.

Step 2: Write the equilibrium expression for the dissolution of Mg(OH)_2: Mg(OH)_2 (s) \rightleftharpoons Mg^{2+} (aq) + 2OH^{-} (aq). The expression for K_{sp} is K_{sp} = [Mg^{2+}][OH^{-}]^2.

Step 3: Calculate the concentration of OH^{-} ions at pH 10.80. Use the relationship pH + pOH = 14 to find pOH, then calculate [OH^{-}] using [OH^{-}] = 10^{-pOH}.

Step 4: Calculate the ion product (Q) for Mg(OH)_2 using the concentrations: Q = [Mg^{2+}][OH^{-}]^2. Substitute the given [Mg^{2+}] = 2.5 \times 10^{-4} M and the calculated [OH^{-}] from Step 3.

Step 5: Compare the ion product (Q) to the solubility product constant (K_{sp}). If Q > K_{sp}, Mg(OH)_2 will precipitate. If Q < K_{sp}, no precipitation will occur.

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. For magnesium hydroxide, Mg(OH)2, the Ksp expression is Ksp = [Mg2+][OH-]^2. This constant helps determine whether a precipitate will form when the product of the ion concentrations exceeds Ksp.

pH and Hydroxide Ion Concentration

pH is a measure of the acidity or basicity of a solution, with lower values indicating higher acidity. The relationship between pH and hydroxide ion concentration ([OH-]) is given by the equation [OH-] = 10^(14 - pH). At pH 10.80, the concentration of hydroxide ions can be calculated, which is crucial for assessing the potential precipitation of Mg(OH)2.

Precipitation Reaction

A precipitation reaction occurs when two soluble salts react to form an insoluble compound, or precipitate. In this case, if the product of the concentrations of Mg2+ and OH- ions exceeds the Ksp of Mg(OH)2, precipitation will occur. Understanding this concept is essential for predicting whether Mg(OH)2 will form under the given conditions.

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Textbook Question

Can Fe2+ be separated from Sn2+ by bubbling H2S through a 0.3 M HCl solution that contains 0.01 M Fe2+ and 0.01 M Sn2+? A saturated solution of H2S has [H2S] ≈ 0.10 M. Values of Kspa are 6 x 10^2 for FeS andd 1 x 10^-5 for SnS.