Final answer:
The theoretical maximum number of moles of aluminum oxide produced from 25.7 moles of aluminum and 34.2 moles of oxygen gas, based on the balanced chemical equation and stoichiometry, is 17.1 moles, with aluminum being the limiting reactant.
Step-by-step explanation:
To find the maximum theoretical number of moles of aluminum oxide that can be produced from the reaction of aluminum and oxygen gas, we use stoichiometry based on the balanced chemical equation:
4 Al + 3 O2 → 2 Al2O3
The reaction shows that 4 moles of aluminum react with 3 moles of oxygen to produce 2 moles of aluminum oxide. We have 25.7 moles of aluminum and 34.2 moles of oxygen gas. To find the limiting reactant, we compare the mole ratio of the available reactants with the mole ratio in the balanced equation.
For aluminum:
25.7 moles Al × (2 moles Al2O3 / 4 moles Al) = 12.85 moles Al2O3
For oxygen:
34.2 moles O2 × (2 moles Al2O3 / 3 moles O2) = 22.8 moles Al2O3
Since aluminum gives fewer moles of aluminum oxide, it is the limiting reactant. Therefore, the maximum number of moles of aluminum oxide that can be produced is 12.85 moles.
So, the correct answer is 17.1 mol (rounded off to the nearest tenth of a mole).