Here's how to determine the balanced equation for the reaction between iron(III) chloride and copper(II) sulfate:

1. Write the reactants and products:

* Reactants:

* Iron(III) chloride: FeCl₃

* Copper(II) sulfate: CuSO₄

* Products:

* Iron(III) sulfate: Fe₂(SO₄)₃

* Copper(II) chloride: CuCl₂

2. Write the unbalanced equation:

FeCl₃ + CuSO₄ → Fe₂(SO₄)₃ + CuCl₂

3. Balance the equation:

* Iron (Fe): There are 2 Fe atoms on the product side and 1 on the reactant side. Add a coefficient of 2 in front of FeCl₃.

* Sulfate (SO₄): There are 3 SO₄ groups on the product side and 1 on the reactant side. Add a coefficient of 3 in front of CuSO₄.

* Copper (Cu): There is 1 Cu atom on the product side and 3 on the reactant side. Add a coefficient of 3 in front of CuCl₂.

* Chloride (Cl): There are 6 Cl atoms on the product side and 6 on the reactant side.

The balanced equation is:

2FeCl₃ + 3CuSO₄ → Fe₂(SO₄)₃ + 3CuCl₂