The given chemical equation is not balanced as the number of each type of atom on both sides of the equation does not match. A balanced equation implies the same amount of each atom on the reactant and product sides, which is not the case here. The balanced equation for the reaction of iron oxide and carbon should read 2Fe₂O₃ + 3C → 4Fe + 3CO₂.
The provided equation 4 Fe₂O₃ + C → #Fe + # CO₂ is not balanced. To answer if the equation is balanced, we need to count the atoms of each element on the reactants side and compare them to the atoms of each element on the products side. A balanced chemical equation has the same number of each type of atom on both sides of the equation.
For the iron (Fe) atoms, we have 8 Fe atoms on the reactant side (4 molecules of Fe₂O₃, each containing 2 Fe atoms), but an unspecified number of Fe atoms on the product side (#Fe).
For the oxygen (O) atoms, we have 12 O atoms on the reactant side (4 molecules of Fe₂O₃, each containing 3 O atoms), and an unspecified number of O atoms on the product side (# CO₂).
For the carbon (C) atoms, we have 1 C atom on the reactant side but an unspecified number of C atoms on the product side (# CO₂).
To properly balance the reaction, we would need to ensure the number of Fe, O, and C atoms are the same on both sides.
A correct balanced equation would look like 2Fe₂O₃ (s) + 3C (s) → 4Fe (s) + 3CO₂ (g), indicating that iron oxide reacts with carbon to produce iron and carbon dioxide. This equation shows the removal of oxygen from iron oxide, which means it is being reduced to iron, while carbon is being oxidized to carbon dioxide.