Final answer:
To calculate the grams of aluminum oxide produced, use the given balanced equation and molar masses. First, find the moles of aluminum and then use the molar ratio to calculate the moles of aluminum oxide. Finally, convert moles of aluminum oxide to grams using its molar mass. So, the mass of aluminum oxide is 7.29 g.
Step-by-step explanation:
To determine the grams of aluminum oxide produced, we need to use the given balanced equation and the molar masses of aluminum and aluminum oxide.
According to the equation 4Al + 3O₂ = 2Al₂O₃, the molar ratio between aluminum and aluminum oxide is 4:2 or 2:1.
So, for every 2 moles of aluminum, we get 1 mole of aluminum oxide.
First, we find the moles of aluminum (3.82 g / molar mass of Al) and then use the molar ratio to calculate the moles of aluminum oxide. Finally, we convert the moles of aluminum oxide to grams using its molar mass.
Given: Mass of aluminum = 3.82 g
Molar mass of Al = 26.98 g/mol
Molar mass of Al₂O₃ = 101.96 g/mol
Step 1: Moles of aluminum = 3.82 g / 26.98 g/mol = 0.142 mol
Step 2: Moles of aluminum oxide = (0.142 mol Al) * (1 mol Al₂O₃ / 2 mol Al) = 0.071 mol Al₂O₃
Step 3: Mass of aluminum oxide = 0.071 mol * 101.96 g/mol
= 7.29 g Al₂O₃
Thus, the mass of aluminum oxide is 7.29 g.