Final answer:
A 0.50m solution of (NH₄)₂SO₄ will be acidic due to the ammonium ion (NH₄⁺), which is the conjugate acid of a weak base and can increase the hydrogen ion concentration in the solution.
Step-by-step explanation:
When determining if a solution of 0.50m (NH₄)₂SO₄ will be acidic or basic, we must consider the ions it forms in water. Ammonium sulfate dissociates in water to yield two ammonium ions (NH₄⁺) and one sulfate ion (SO₄²⁻).
The ammonium ion is the conjugate acid of a weak base (ammonia), and it can donate a proton to water, forming NH₃ and H₃O⁺: NH₄⁺ (aq) + H₂O (l) ⇌ NH₃ (aq) + H₃O⁺ (aq) with a Kᵗₙ value of 5.6 × 10⁻⁹. With the Kᵗₙ being greater than 1 × 10⁻⁷, this suggests that the solution will be acidic as it increases the hydrogen ion concentration in the solution.
On the other hand, sulfate is the conjugate base of a strong acid (H₂SO₄) and does not significantly contribute to the basicity of the solution. Therefore, the behavior of the ammonium ion predominates, and the solution will have an acidic character. This is consistent with the general rule that salts formed from a weak base and a strong acid yield acidic solutions.