Final answer:
The solution that precipitates barium ions from a water sample is sodium sulfate, and the formula for the expected precipitate is BaSO4, also known as barium sulfate.
Step-by-step explanation:
To identify the precipitate for a reaction involving barium ions in a water sample, one must consider the solubility rules of the reactants involved. The precipitate is a solid that forms when two aqueous solutions react and form an insoluble product. When solutions of barium ions, such as BaCl2 (aqueous barium chloride), are mixed with a solution containing sulfate ions, like Na2SO4 (aqueous sodium sulfate), an insoluble precipitate is formed.
The formula for this precipitate, according to solubility rules, is BaSO4 (barium sulfate). Sodium chloride (NaCl) and sodium hydroxide (NaOH) do not form precipitates with barium ions, as their resulting products remain soluble in water. Therefore, the solution that could be used to precipitate the barium ion, Ba2+, in a water sample is sodium sulfate.