When aqueous solutions of barium nitrate (Ba(NO₃)₂) and potassium carbonate (K₂CO₃) are mixed, a precipitate of barium carbonate (BaCO₃) forms.

Here's the explanation:

1. Double Displacement Reaction: The reaction is a double displacement reaction, where the positive and negative ions of the reactants switch partners.

2. Products: The products formed are barium carbonate (BaCO₃) and potassium nitrate (KNO₃).

3. Solubility: Barium carbonate is insoluble in water, meaning it forms a solid precipitate. Potassium nitrate, on the other hand, is soluble in water and remains dissolved.

The chemical equation for the reaction is:

Ba(NO₃)₂ (aq) + K₂CO₃ (aq) → BaCO₃ (s) + 2 KNO₃ (aq)

Therefore, the name of the precipitate is barium carbonate.