Two separate beakers each contain 200 mL of aqueous Ba(NO3)2, but at different concentrations. Beaker A is 0.040 M in Ba2+, whereas Beaker B is 0.010 M in Ba2+. Sodium sulfate is to be added dropwise to each beaker until BaSO4(s) first appears. The solubility product of BaSO4 is Ksp=1.1×10−10.
(a) For each beaker, calculate the threshold molar concentration of SO42− at which BaSO4 will begin to precipitate.
(b) Explain, in terms of the common-ion effect and Le Châtelier’s principle, why the required SO42− concentration differs between the two beakers.
(c) Discuss how the difference calculated in part (a) would influence the experimental design if the goal were to recover as much BaSO4 as possible from both beakers using the least total amount of Na2SO4. Provide quantitative support for your recommendation.