Final answer:
To identify the presence of an ion in the unknown aqueous sample, the student can perform a precipitation reaction using sodium sulfate, which would form a white precipitate of BaSO4 if Ba2+ is present.
Step-by-step explanation:
The student is tasked with identifying the presence of an unknown ion in an aqueous sample which could be Na+, Ba2+, or Mg2+. Given the limited sample, the student can perform only a couple of tests from a list to discern which ion, if any, is present. However, without seeing the table mentioned in the question, we cannot discern which tests will not be useful. To confirm the presence of an ion in general, the student should perform a test that applies broadly to all potential ions.
To check if the unknown sample contains an ion, a single test such as a flame test could be used for alkali metals, which would produce characteristic colors. However, this would not be useful for Ba2+ or Mg2+. Therefore, adding a reagent that forms a precipitate with one or more of the ions mentioned, such as sodium sulfate (Na2SO4), would be a good general test since Barium will form a white precipitate of barium sulfate (BaSO4), which is insoluble in water.