Final answer:
To distinguish between solutions containing ClO₄⁻ and SO₄²⁻, the use of Ba²⁺ is appropriate as it forms a precipitate of BaSO₄ with SO₄²⁻ but not with ClO₄⁻.
Step-by-step explanation:
The cation that could differentiate between a solution containing ClO₄⁻ (aq) and one with SO₄²⁻ (aq) is Ba²⁺. The reason is that BaSO₄ is insoluble in water and will precipitate out when Ba²⁺ is added to a solution containing SO₄²⁻ ions. On the other hand, when Ba²⁺ is introduced to a solution containing ClO₄⁻ ions, no precipitation occurs because all compounds containing the perchlorate ion are soluble in water. Hence, option A, Ba²⁺, could be used for the precipitation reaction to serve as a test for SO₄²⁻. The expected precipitate when Ba²⁺ is added to a solution of SO₄²⁻ is BaSO₄ (s).