Final answer:
To react completely with 9.0 moles of oxygen gas in the formation of aluminum oxide according to the equation 4Al + 3O₂ → 2Al₂O₃, 12.0 moles of aluminum are required.
Step-by-step explanation:
The question is asking about the stoichiometry of a chemical reaction, specifically how many moles of aluminum (Al) are needed to react with a given amount of oxygen gas (O₂) to produce aluminum oxide (Al₂O₃). The balanced chemical equation given is: 4Al + 3O₂ → 2Al₂O₃. According to the stoichiometry of the reaction, 4 moles of Al are required to react with 3 moles of O₂.
To find out how many moles of Al are needed for 9.0 moles of O₂, we can set up a proportion because the ratio of Al to O₂ must be consistent with what's given in the balanced equation:
- (4 moles Al) / (3 moles O₂) = (x moles Al) / (9.0 moles O₂)
By cross-multiplying to solve for 'x', we get:
- x moles Al = (4 moles Al) * (9.0 moles O₂) / (3 moles O₂)
- x moles Al = 12.0 moles Al
Therefore, 12.0 moles of aluminum are required to react completely with 9.0 moles of oxygen gas to produce aluminum oxide.