The balanced chemical equation for the reaction of Fe2O3 (iron(III) oxide) with carbon (C) is as follows:
Fe2O3 + 3C → 2Fe + 3CO
From the equation, we can see that one mole of Fe2O3 reacts with three moles of carbon to produce two moles of iron (Fe). The molar mass of Fe2O3 is calculated as follows:
Molar mass of Fe2O3 = (2 × atomic mass of Fe) + (3 × atomic mass of O) = (2 × 55.845 g/mol) + (3 × 16.00 g/mol) = 111.69 g/mol
To determine the number of moles of Fe2O3, we divide the given mass by its molar mass:
Number of moles of Fe2O3 = Mass of Fe2O3 / Molar mass of Fe2O3 = 8 g / 111.69 g/mol ≈ 0.0716 mol
According to the balanced equation, three moles of carbon are required to react with one mole of Fe2O3. Therefore, the number of moles of carbon required is:
Number of moles of C = 3 × Number of moles of Fe2O3 = 3 × 0.0716 mol ≈ 0.2148 mol
The molar mass of carbon (C) is 12.01 g/mol. Thus, the mass of carbon required is:
Mass of C = Molar mass of C × Number of moles of C = 12.01 g/mol × 0.2148 mol ≈ 2.57 g
Since the reaction is limiting by the amount of carbon, we can determine the mass of iron (Fe) produced using the stoichiometry of the balanced equation. From the equation, we see that 1 mole of Fe2O3 reacts to produce 2 moles of Fe. Therefore, the number of moles of Fe produced is:
Number of moles of Fe = (2/1) × Number of moles of Fe2O3 = 2 × 0.0716 mol = 0.1432 mol
The molar mass of Fe is 55.845 g/mol. Hence, the mass of iron produced is:
Mass of Fe = Molar mass of Fe × Number of moles of Fe = 55.845 g/mol × 0.1432 mol ≈ 7.99 g
Therefore, approximately 8 grams of Fe2O3 can produce around 7.99 grams of iron (Fe) when reacted with carbon.