4Al + 3O2 -> 2Al2O3 how many grams of aluminum are burned if 200.0 grams of aluminum oxide are formed?
The Correct Answer and Explanation is:
ChatGPT said:
Correct Answer:
Aluminum burned = 105.88 grams
Step-by-Step Explanation:
We are asked how many grams of aluminum are burned if 200.0 grams of aluminum oxide (Al₂O₃) are formed based on the reaction:
4Al + 3O₂ → 2Al₂O₃
Step 1: Calculate Molar Masses
- Aluminum (Al) = 27.0 g/mol
- Oxygen (O) = 16.0 g/mol
- Aluminum oxide (Al₂O₃) = (2 × 27.0) + (3 × 16.0) = 54.0 + 48.0 = 102.0 g/mol
Step 2: Determine Moles of Aluminum Oxide Formed
Given mass of Al₂O₃ = 200.0 grams
Molar mass of Al₂O₃ = 102.0 g/mol
Moles of Al₂O₃ = Mass / Molar Mass = 200.0 g / 102.0 g/mol ≈ 1.9608 moles
Step 3: Find the Moles of Aluminum Reacted Using the Balanced Equation
The balanced equation shows:
- 4 moles of Al produce 2 moles of Al₂O₃
Thus, moles of Al required = (4 moles Al / 2 moles Al₂O₃) × 1.9608 moles Al₂O₃
Moles of Al = 3.9216 moles
Step 4: Convert Moles of Aluminum to Grams
Molar mass of Aluminum = 27.0 g/mol
Mass of Aluminum = Moles × Molar Mass = 3.9216 moles × 27.0 g/mol ≈ 105.88 grams
Final Answer: Approximately 105.88 grams of aluminum are burned.
Additional Notes:
This calculation follows the stoichiometric relationships in the balanced chemical equation. The mass-to-mole and mole-to-mass conversions are essential to link the amount of product formed to the amount of reactant used. This type of problem is common in chemistry to ensure reactants are used efficiently and to predict reactant requirements for industrial or laboratory reactions.
