Final answer:
In a chemical reaction where 3.50 moles of iron(III) oxide reacts with carbon to produce iron and carbon monoxide, 10.5 moles of carbon are needed for a stoichiometric reaction, based on the 1:3 molar ratio from the balanced chemical equation.
Step-by-step explanation:
The question pertains to a chemical reaction in which solid iron(III) oxide reacts with carbon to produce solid iron and carbon monoxide gas. Given that 3.50 moles of iron(III) oxide react, we are asked to find out how many moles of carbon are required to react in stoichiometric proportions. Stoichiometry is a concept from chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction.
To solve this problem, we would need the balanced chemical equation for the reaction:
Fe2O3 + 3C → 2Fe + 3CO
From the balanced chemical equation, we can see that one mole of Fe2O3 reacts with three moles of carbon (C) to produce two moles of iron (Fe) and three moles of carbon monoxide (CO). This indicates a 1:3 molar ratio between iron(III) oxide and carbon.
Since we have 3.50 moles of Fe2O3, we multiply this by the molar ratio to find the moles of carbon needed:
3.50 moles Fe2O3 × (3 moles C / 1 mole Fe2O3) = 10.5 moles C
Therefore, 10.5 moles of carbon are needed to react with 3.50 moles of iron(III) oxide in stoichiometric proportions.