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Ch.17 - Applications of Aqueous Equilibria
All textbooksMcMurry 8th EditionCh.17 - Applications of Aqueous EquilibriaProblem 131
Chapter 17, Problem 131

In quantitative analysis, Al3+ and Mg2+ are separated in an NH4+ - NH3 buffer having pH approximately equal to 8. Assuming cation concentrations of 0.010 M, show why Al(OH)3 precipitates but Mg(OH)2 does not.

Verified step by step guidance
1
Step 1: Write the relevant chemical equilibrium reactions for the precipitation of Al(OH)_3 and Mg(OH)_2. For Al(OH)_3, the reaction is: Al^{3+} + 3OH^- \rightleftharpoons Al(OH)_3(s). For Mg(OH)_2, the reaction is: Mg^{2+} + 2OH^- \rightleftharpoons Mg(OH)_2(s).
Step 2: Determine the solubility product constants (K_{sp}) for Al(OH)_3 and Mg(OH)_2. These values are typically found in a chemistry reference table. For example, K_{sp} for Al(OH)_3 is approximately 1.9 \times 10^{-33} and for Mg(OH)_2 is approximately 1.8 \times 10^{-11}.
Step 3: Calculate the hydroxide ion concentration [OH^-] in the buffer solution at pH 8. Use the relationship pH + pOH = 14 to find pOH, and then calculate [OH^-] using [OH^-] = 10^{-pOH}.
Step 4: Use the K_{sp} expressions to determine the conditions for precipitation. For Al(OH)_3, the expression is K_{sp} = [Al^{3+}][OH^-]^3. For Mg(OH)_2, the expression is K_{sp} = [Mg^{2+}][OH^-]^2. Substitute the known concentrations and [OH^-] into these expressions.
Step 5: Compare the calculated ion product for each compound with its K_{sp}. If the ion product exceeds K_{sp}, precipitation occurs. Analyze the results to show that the ion product for Al(OH)_3 exceeds its K_{sp}, indicating precipitation, while the ion product for Mg(OH)_2 does not exceed its K_{sp}, indicating no precipitation.

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 a measure of the solubility of a sparingly soluble ionic compound. It represents the equilibrium between the solid and its ions in solution. For aluminum hydroxide (Al(OH)3) and magnesium hydroxide (Mg(OH)2), their Ksp values indicate the concentrations of ions at which precipitation occurs. A lower Ksp value means that the compound is less soluble, leading to precipitation at lower ion concentrations.
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pH and Hydroxide Ion Concentration

The pH of a solution is a measure of its acidity or basicity, which affects the concentration of hydroxide ions (OH-) present. In a buffer solution with a pH of approximately 8, the concentration of OH- ions is sufficient to precipitate Al(OH)3, as aluminum ions can react with hydroxide ions to form a solid. However, the concentration of OH- at this pH is not high enough to exceed the solubility of Mg(OH)2, preventing its precipitation.
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Hydroxide Ion Concentration Example

Cation Precipitation and Selectivity

Cation precipitation refers to the process where cations in solution react with anions (like hydroxide) to form an insoluble compound. The selectivity of precipitation is influenced by the Ksp values of the compounds formed. In this case, Al3+ precipitates as Al(OH)3 due to its lower Ksp compared to Mg2+, which means that at the same concentration of hydroxide ions, Al(OH)3 will form a solid while Mg(OH)2 remains dissolved.
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Related Practice
Textbook Question
Citric acid (H3Cit) can be used as a household cleaning agent to dissolve rust stains. The rust, represented as Fe(OH)3, dissolves because the citrate ion forms a soluble complex with Fe3+ (a) Using the equilibrium constants in Appendix C and Kf = 6.3 x 10^11 for Fe(Cit), calculate the equilibrium constant K for the reaction.(b) Calculate the molar solubility of Fe(OH)3 in 0.500 M solution of H3Cit.
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.
Textbook Question
Will FeS precipitate in a solution that is 0.10 M in Fe(NO3)2, 0.4 M in HCl, and 0.10 M in H2S? Will FeS precipitate if the pH of the solution is adjusted to pH 8 with an NH4+ - NH3 buffer? Kspa = 6 x 10^2 for FeS.