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An aqueous solution contains an unknown concentration of Ba2+. When 50 mL of a 1 M solution of Na2SO4 is added, BaSO4 just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO4 is 1 × 10⁻¹⁰. What is the original concentration of Ba2+?
- 5 × 10⁻⁹ M
- 2 × 10⁻⁹ M
- 1.1 × 10⁻⁹ M
- 1.0 × 10⁻¹⁰ M
Correct answer: 1.1 × 10⁻⁹ M
Solution
The correct option is derived from the equilibrium condition for the precipitation of BaSO4, where the product of the concentrations of Ba2+ and SO4²- must equal the solubility product (Ksp). Given that the concentration of SO4²- from the Na2SO4 solution is 0.1 M after dilution, the concentration of Ba2+ that satisfies the Ksp condition is calculated to be approximately 1.1 × 10⁻⁹ M.
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