Multiple Choice
Calculate the solubility (in grams per 1.00×10² mL of solution) of magnesium hydroxide, Mg(OH)₂, in a solution buffered at pH = 12, given that the Ksp of Mg(OH)₂ is 1.8 × 10⁻¹¹.
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18. Aqueous Equilibrium
Solubility Product Constant: Ksp
Multiple Choice
Given a solution of 4.0 × 10⁻² M Ba(NO₃)₂, what is the minimum concentration of NaF required to cause precipitation of BaF₂, assuming the Ksp of BaF₂ is 1.7 × 10⁻⁶?
A
5.0 × 10⁻² M
B
4.3 × 10⁻⁵ M
C
1.0 × 10⁻³ M
D
2.5 × 10⁻⁴ M
Verified step by step guidance1
Understand the problem: We need to find the minimum concentration of NaF required to cause precipitation of BaF₂ from a solution of Ba(NO₃)₂. The solubility product constant (Ksp) for BaF₂ is given as 1.7 × 10⁻⁶.
Write the dissolution equation for BaF₂: BaF₂(s) ⇌ Ba²⁺(aq) + 2F⁻(aq). This equation shows that one mole of BaF₂ produces one mole of Ba²⁺ ions and two moles of F⁻ ions in solution.
Express the Ksp expression for BaF₂: Ksp = [Ba²⁺][F⁻]². This expression relates the concentrations of the ions in solution to the solubility product constant.
Substitute the concentration of Ba²⁺ from Ba(NO₃)₂ into the Ksp expression: Since the solution is 4.0 × 10⁻² M Ba(NO₃)₂, [Ba²⁺] = 4.0 × 10⁻² M. Substitute this value into the Ksp expression: 1.7 × 10⁻⁶ = (4.0 × 10⁻²)[F⁻]².
Solve for [F⁻]: Rearrange the equation to solve for the concentration of fluoride ions, [F⁻]. This will give you the minimum concentration of NaF required to cause precipitation of BaF₂.
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