Final answer:
Approximately 224.96 kg of aluminum can be recovered from 425 kg of the ore aluminum oxide, through stoichiometric calculations based on the molar mass of aluminum and its oxide.
Step-by-step explanation:
To calculate the amount of aluminum that can be recovered from 425 kg of the ore aluminum oxide ( Al₂O₃), we need to use stoichiometry. The balanced reaction for the formation of aluminum from aluminum oxide is:
2 Al₂O₃(s) → 4 Al(s) + 3 O₂(g)
From this equation, we can see that 2 moles of aluminum oxide produce 4 moles of aluminum. First, we determine the molar mass of aluminum oxide, which is approximately 101.96 g/mol. Then we calculate the moles of aluminum oxide in the given 425 kg:
425,000 g ÷ 101.96 g/mol = 4168.63 moles of Al₂O₃
Using the stoichiometric relationship from the balanced equation, we find the moles of aluminum:
4168.63 moles of Al₂O₃× (4 moles of Al / 2 moles of Al₂O₃) = 8337.26 moles of Al
Finally, we convert the moles of aluminum to grams (and then to kilograms) using the molar mass of aluminum, which is roughly 26.98 g/mol:
8337.26 moles of Al × 26.98 g/mol = 224960.28 g of Al
224960.28 g is equivalent to 224.96 kg of aluminum.
Thus, it is possible to recover approximately 224.96 kilograms of aluminum from 425 kg of aluminum oxide.