The balanced chemical equation for the reaction between ammonium sulfate ((NH₄)₂SO₄) and barium chloride (BaCl₂) is:

(NH₄)₂SO₄(aq) + BaCl₂(aq) → BaSO₄(s) + 2NH₄Cl(aq)

Here's a breakdown of the equation:

* (NH₄)₂SO₄(aq) : Ammonium sulfate, dissolved in water (aqueous solution)

* BaCl₂(aq) : Barium chloride, dissolved in water (aqueous solution)

* BaSO₄(s) : Barium sulfate, a white precipitate (solid)

* 2NH₄Cl(aq) : Ammonium chloride, dissolved in water (aqueous solution)

Explanation:

This reaction is a double displacement reaction where the cations and anions of the two reactants switch places.

* Barium (Ba²⁺) from barium chloride combines with sulfate (SO₄²⁻) from ammonium sulfate to form insoluble barium sulfate (BaSO₄), which precipitates out of the solution.

* Ammonium (NH₄⁺) from ammonium sulfate combines with chloride (Cl⁻) from barium chloride to form soluble ammonium chloride (NH₄Cl), which remains dissolved in the solution.

The equation is balanced because there are equal numbers of each type of atom on both sides of the equation.