Stoichiometry of the Reaction Between Iron(III) Oxide and Carbon Monoxide

Stoichiometry, a fundamental concept in chemistry, helps us understand the quantitative relationships between reactants and products in chemical reactions. In this article, we will delve into the stoichiometry involved in the reaction between iron(III) oxide (Fe2O3) and carbon monoxide (CO) to produce iron (Fe) and carbon dioxide (CO2). The balanced chemical equation is given by:

Reaction Equation

3 CO Fe2O3 → 2 Fe 3 CO2

In this reaction, carbon monoxide reacts with iron(III) oxide to produce iron and carbon dioxide. By employing stoichiometry, we can determine the amount of reactants required or the products formed.

How Many Moles of Iron(III) Oxide Must React to Produce 500.0 g of Iron?

To address this question, we will utilize the following steps:

Step 1: Calculate the Moles of Iron Produced

The molar mass of iron (Fe) is approximately 55.85 g/mol.

[ text{Moles of Fe} frac{text{Mass of Fe}}{text{Molar mass of Fe}} frac{500.0 , text{g}}{55.85 , text{g/mol}} approx 8.95 , text{mol} ]

Step 2: Use Stoichiometry to Find Moles of Fe2O3 Required

From the balanced equation, 2 moles of Fe are produced from 1 mole of Fe2O3. Therefore,

[ text{Moles of Fe}_2text{O}_3 frac{text{Moles of Fe}}{2} frac{8.95 , text{mol}}{2} approx 4.48 , text{mol} ]

Therefore, approximately 4.48 moles of Fe2O3 must react to produce 500.0 g of iron.

How Many Moles of Carbon Monoxide Are Needed to React with 96 g of Fe2O3

To determine this, we follow a similar process:

Step 1: Calculate the Moles of Iron(III) Oxide (Fe2O3)

The molar mass of Fe2O3 is calculated as follows:

[ text{Molar mass of Fe}_2text{O}_3 (55.85 , text{g/mol} times 2) (16.00 , text{g/mol} times 3) 111.70 , text{g/mol} 48.00 , text{g/mol} 159.70 , text{g/mol} ]

Now, calculate the moles of Fe2O3:

[ text{Moles of Fe}_2text{O}_3 frac{text{Mass of Fe}_2text{O}_3}{text{Molar mass of Fe}_2text{O}_3} frac{96 , text{g}}{159.70 , text{g/mol}} approx 0.60 , text{mol} ]

Step 2: Use the Stoichiometry of the Reaction to Find Moles of CO Required

From the balanced equation, 1 mole of Fe2O3 reacts with 3 moles of CO. Therefore,

[ text{Moles of CO} 3 times text{Moles of Fe}_2text{O}_3 3 times 0.60 , text{mol} approx 1.80 , text{mol} ]

Therefore, approximately 1.80 moles of CO are needed to react with 96 g of Fe2O3.

Summary

Based on the stoichiometric calculations, the required amounts are as follows:

Approximately 4.48 moles of Fe2O3 must react to produce 500.0 g of iron. Approximately 1.80 moles of CO are needed to react with 96 g of Fe2O3.