The balanced chemical equation for the reaction of solid iron(III) oxide with carbon to form iron and carbon dioxide gas is:

2 Fe₂O₃(s) + 3 C(s) → 4 Fe(s) + 3 CO₂(g)

Here's the breakdown:

* Fe₂O₃(s) represents solid iron(III) oxide.

* C(s) represents solid carbon.

* Fe(s) represents solid iron.

* CO₂(g) represents carbon dioxide gas.

This equation is balanced because:

* There are 4 iron atoms (Fe) on both sides of the equation.

* There are 6 oxygen atoms (O) on both sides of the equation.

* There are 3 carbon atoms (C) on both sides of the equation.