The balanced chemical equation for the reaction between iron(III) chloride (FeCl₃) and silver nitrate (AgNO₃) is:

FeCl₃(aq) + 3AgNO₃(aq) → Fe(NO₃)₃(aq) + 3AgCl(s)

Here's a breakdown:

* FeCl₃(aq): Iron(III) chloride, dissolved in water (aqueous solution).

* AgNO₃(aq): Silver nitrate, dissolved in water (aqueous solution).

* Fe(NO₃)₃(aq): Iron(III) nitrate, dissolved in water (aqueous solution).

* AgCl(s): Silver chloride, a white solid precipitate that forms out of solution.

This reaction is a double displacement reaction. The iron(III) ions (Fe³⁺) from FeCl₃ combine with the nitrate ions (NO₃⁻) from AgNO₃ to form iron(III) nitrate (Fe(NO₃)₃). The silver ions (Ag⁺) from AgNO₃ combine with the chloride ions (Cl⁻) from FeCl₃ to form silver chloride (AgCl), which is insoluble in water and precipitates out of solution.

It's important to note that the equation is balanced, meaning that the number of atoms of each element is the same on both sides of the equation.