To completely react with 135 g of iron(III) oxide (Fe₂O₃), 45.6 grams of aluminum (Al) are needed.
This calculation is based on the stoichiometric principles of a balanced chemical equation, specifically the thermite reaction.
Understanding the Thermite Reaction
The reaction between iron(III) oxide and aluminum is a classic example of a single displacement reaction, commonly known as the thermite reaction. This highly exothermic process produces molten iron and aluminum oxide. The balanced chemical equation for this reaction is:
Fe₂O₃ + 2Al → 2Fe + Al₂O₃
This equation tells us the exact molar ratio in which the reactants combine and products are formed. Specifically, one mole of iron(III) oxide reacts with two moles of aluminum.
Stoichiometric Calculation for Aluminum Needed
To determine the mass of aluminum required, a step-by-step stoichiometric approach is used:
-
Calculate Moles of Fe₂O₃:
- First, the molar mass of Fe₂O₃ is determined by adding the atomic masses of its constituent elements:
- Iron (Fe): approximately 55.845 g/mol
- Oxygen (O): approximately 15.999 g/mol
- Molar mass of Fe₂O₃ = (2 × 55.845 g/mol) + (3 × 15.999 g/mol) = 111.69 g/mol + 47.997 g/mol = 159.687 g/mol
- Next, convert the given mass of Fe₂O₃ to moles:
- Moles of Fe₂O₃ = Given mass / Molar mass = 135 g / 159.687 g/mol ≈ 0.8453 moles Fe₂O₃
- First, the molar mass of Fe₂O₃ is determined by adding the atomic masses of its constituent elements:
-
Determine Moles of Al Needed:
- Using the balanced chemical equation (Fe₂O₃ + 2Al → 2Fe + Al₂O₃), the molar ratio between Fe₂O₃ and Al is 1:2.
- Moles of Al = Moles of Fe₂O₃ × (2 moles Al / 1 mole Fe₂O₃) = 0.8453 moles Fe₂O₃ × 2 ≈ 1.6906 moles Al
-
Convert Moles of Al to Grams of Al:
- The molar mass of aluminum (Al) is approximately 26.982 g/mol.
- Grams of Al = Moles of Al × Molar mass of Al = 1.6906 moles Al × 26.982 g/mol ≈ 45.6 g Al
Through these calculations, it can be determined that 45.6 g of Al is necessary to completely react with 135 g of Fe₂O₃.
Summary of Reaction Stoichiometry
| Substance | Formula | Molar Mass (g/mol) | Moles (for 135g Fe₂O₃) | Mass (g) |
|---|---|---|---|---|
| Iron(III) Oxide | Fe₂O₃ | 159.687 | 0.8453 | 135 |
| Aluminum | Al | 26.982 | 1.6906 | 45.6 |
For more detailed information on stoichiometry and chemical reactions, you can explore educational resources like Khan Academy Chemistry.
