Answer:
We should add, the KBr solution.
Step-by-step explanation:
The vial contains Ba²⁺ and Pb²⁺
Our solutions are: (NH₄)₂ SO₄, NaF and KBr
We dissociate the solutions:
(NH₄)₂ SO₄ → 2NH₄⁺ + SO₄⁻²
NaF → Na⁺ + F⁻
KBr → K⁺ + Br-
When we add ammonium sulfate and sodium fluorine, we are adding sulfates and fluorines, but these two anions make precipitate both cations, we can not determine, if the vial contains Ba²⁺ or Pb²⁺
SO₄⁻²(aq) + Ba²⁺ (aq) → BaSO₄ (s) ↓
SO₄⁻² (aq)+ Pb²⁺(aq) → PbSO₄ (s) ↓
2F⁻ (aq) + Ba²⁺ (aq) → BaF₂ (s) ↓
2F⁻ (aq) + Pb²⁺ (aq) → PbF₂ (s) ↓
When we add the KBr, bromides only make precipitate with Pb²⁺, so the vial has only Pb²⁺ cation:
2Br⁻ (aq) + Ba²⁺ (aq) → BaBr₂ (aq)
2Br⁻ (aq) + Pb²⁺ (aq) → PbBr₂ (s) ↓