Introduction
The conversion of iron(III) oxide (Fe2O3) to iron (Fe) through the use of carbon monoxide (CO) involves a fascinating journey into chemical kinetics and stoichiometry. This process can be represented by the balanced chemical equation:

Fe2O3(s) 3CO(g) → 2Fe(l) 3CO2(g)

Analyzing the Reaction
To comprehend how half a mole of iron(III) oxide produces one mole of iron, we first need to delve into the balanced chemical equation and stoichiometric principles.

Stoichiometry of the Reaction

The coefficients in a balanced chemical equation denote the mole ratios of the reactants and products. In this particular reaction:

1 mole of Fe2O3 reacts with 3 moles of CO to produce 2 moles of Fe and 3 moles of CO2.

The mole relationship can be summarized as:

Thus, if you start with half a mole of Fe2O3, the amount of Fe produced can be calculated as follows:

Moles of Fe (2 moles of Fe / 1 mole of Fe2O3) × 0.5 moles of Fe2O3 1 mole of Fe.

Mole Relationships

The balanced chemical equation provides the molecular-scale ratio at which the reactants and products interact. In this reaction, the ratio of Fe to Fe2O3 is 2:1, meaning that for every mole of Fe2O3 that reacts, two moles of Fe are produced.

Conversely, if you start with half a mole of Fe2O3, it would produce one mole of Fe, as the equation directly states the ratio.

The balanced equation is:

Fe2O3(s) 3CO(g) ? Δ 2Fe(l) 3CO2(g)

This equation highlights that the decomposition of one formula unit of ferric oxide (Fe2O3) would require three formula units of carbon monoxide (CO) to produce two formula units of iron metal (Fe) and three formula units of carbon dioxide (CO2).

Conclusion

From the above analysis, it can be concluded that despite the half molar quantity, the stoichiometric relationship ensures the production of one mole of iron (Fe) when half a mole of iron(III) oxide (Fe2O3) undergoes the reaction.

The equation is not only balanced in terms of mass but also charge, ensuring the conservation of electrons in the reaction.

Thus, the direct relationship between the amount of reactant and the product is a fundamental principle in chemical reactions, allowing us to predict the outcome with precision.