Calculating the Volume of Oxygen Required for the Formation of Iron(III) Oxide: A Step-by-Step Guide

When dealing with chemical reactions, understanding how much reactant is necessary to form a specific product is crucial. This article provides a detailed guide on how to calculate the volume of oxygen required to produce 50 grams of iron(III) oxide (Fe2O3) using stoichiometry and the law of conservation of mass. The process involves several key steps that will be covered in detail.

Understanding the Chemical Reaction

The balanced chemical equation for the reaction of iron with oxygen to form iron(III) oxide is as follows:

4Fe 3O2 → 2Fe2O3

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

To determine the necessary volume of oxygen, we must first calculate the moles of iron(III) oxide (Fe2O3) produced. The molar mass of Fe2O3 can be calculated as follows:

Fe 55.85 g/mol

O 16.00 g/mol

Molar mass of Fe2O3 2(55.85) 3(16.00) 111.7 48.0 159.7 g/mol

Given 50 grams of Fe2O3, we can find the number of moles:

Moles of Fe2O3 50 g / 159.7 g/mol ≈ 0.3131 mol

Step 2: Utilize Stoichiometry to Determine the Moles of Oxygen Needed

From the balanced equation, we know that 2 moles of Fe2O3 are produced by the reaction of 3 moles of O2 with Fe. Therefore, the relationship between moles of Fe2O3 and O2 is given by:

3 moles of O2 / 2 moles Fe2O3

Using this relationship, we can calculate the moles of O2 required for 0.3131 moles of Fe2O3:

Moles of O2 0.3131 mol Fe2O3 × 3 moles O2 / 2 moles Fe2O3 0.4696 mol

Step 3: Convert Moles to Liters at Standard Temperature and Pressure (STP)

At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters (L). Therefore, to find the volume of O2 required:

Volume of O2 0.4696 mol × 22.4 L/mol ≈ 10.52 L

Conclusion

In conclusion, to produce 50 grams of iron(III) oxide at STP, approximately 10.52 liters of oxygen are required. This calculation is a practical application of stoichiometry and is essential for understanding the relationships between reactants and products in chemical reactions.