Barium sulfate, BaSO₄, is sparingly soluble in water. The solubility-product constant at 25 °C is Ksp=1.1×10−10. A student has 1.00 L of a solution that is initially saturated with respect to BaSO₄ at 25 °C. The student then adds 0.020 mol of sodium sulfate, Na₂SO₄, to the solution, and the volume change is negligible.
(a) Calculate the initial molar concentrations of Ba²⁺ and SO₄²⁻ ions in the saturated solution before the Na₂SO₄ is added.
(b) Determine the sulfate-ion concentration immediately after the Na₂SO₄ dissolves but before any precipitation or further dissolution of BaSO₄ occurs.
(c) Calculate the equilibrium molar concentration of Ba²⁺ in the solution after a new equilibrium is established.
(d) Based on your calculations, predict whether additional solid BaSO₄ precipitates, dissolves, or neither, and quantify the number of moles of BaSO₄ that change phase, if any. Justify your answer.