The product of potassium carbonate (K₂CO₃) and iron(III) nitrate (Fe(NO₃)₃) is iron(III) carbonate (Fe₂(CO₃)₃) and potassium nitrate (KNO₃). This is a double displacement reaction.

Here's the balanced chemical equation:

3 K₂CO₃(aq) + 2 Fe(NO₃)₃(aq) → Fe₂(CO₃)₃(s) + 6 KNO₃(aq)

Explanation:

* In a double displacement reaction, the positive and negative ions of two reactants switch places.

* Potassium carbonate (K₂CO₃) contains potassium (K⁺) and carbonate (CO₃²⁻) ions.

* Iron(III) nitrate (Fe(NO₃)₃) contains iron(III) (Fe³⁺) and nitrate (NO₃⁻) ions.

* When these two reactants combine, the potassium ions combine with the nitrate ions to form potassium nitrate (KNO₃), which is soluble in water.

* The iron(III) ions combine with the carbonate ions to form iron(III) carbonate (Fe₂(CO₃)₃), which is insoluble in water and forms a precipitate.

Important note: The reaction is balanced, meaning there are the same number of each type of atom on both sides of the equation.