How many atoms of aluminum can be produced by the decomposition of 47.1 g of Al2O3? (Hint: Write and balance the equation first.) The products are oxygen gas and aluminum metal (Al)
A) 1.11 X 10^24 Al atoms
B) None of these
C) 1.39 X 10^23 Al atoms
D) 5.56 X 10^23 Al atoms
E) 2.78 X 10^23 Al atoms
1.11x 10^24
How many atoms of aluminum can be produced by the decomposition of 47.1 g of Al2O3? (Hint: Write and balance the equation first.) The products are oxygen gas and aluminum metal (Al)
To answer this question, we need to write and balance the equation for the decomposition of Al2O3.
The balanced equation is:
2 Al2O3 → 4 Al + 3 O2
According to the balanced equation, for every 2 moles of Al2O3, we get 4 moles of Al.
Now, we need to use the molar mass of Al2O3 to determine the number of moles of Al2O3 we have.
The molar mass of Al2O3 is 101.96 g/mol. Therefore, we divide the given mass by the molar mass to find the number of moles of Al2O3.
47.1 g / 101.96 g/mol = 0.4613 mol
Since 2 moles of Al2O3 produce 4 moles of Al, we multiply the number of moles of Al2O3 by the mole ratio to find the number of moles of Al.
0.4613 mol Al2O3 * (4 mol Al / 2 mol Al2O3) = 0.9226 mol Al
Finally, we need to convert the number of moles of Al to the number of atoms using Avogadro's number (6.022 x 10^23 atoms/mol).
0.9226 mol Al * (6.022 x 10^23 atoms/mol) = 5.56 x 10^23 Al atoms
Therefore, the correct answer is D) 5.56 x 10^23 Al atoms.
To answer this question, we need to first write and balance the equation for the decomposition of Al2O3.
The formula for aluminum oxide is Al2O3. When this compound decomposes, it forms aluminum metal (Al) and oxygen gas (O2). The balanced equation for this reaction is:
2 Al2O3 → 4 Al + 3 O2
Now, let's calculate the number of moles of Al2O3 using its molar mass. The molar mass of Al2O3 is 2(26.98 g/mol) + 3(16.00 g/mol) = 101.96 g/mol.
Number of moles of Al2O3 = mass of Al2O3 / molar mass
= 47.1 g / 101.96 g/mol
≈ 0.462 mol
According to the balanced equation, the mole ratio between Al2O3 and Al is 4:2. This means that for every 4 moles of Al2O3, we get 2 moles of Al.
Number of moles of Al = (0.462 mol Al2O3) x (2 mol Al / 4 mol Al2O3)
= 0.231 mol Al
To calculate the number of atoms of Al, we need to convert the moles of Al to atoms using Avogadro's number, which is 6.022 x 10^23 atoms/mol.
Number of atoms of Al = (0.231 mol Al) x (6.022 x 10^23 atoms/mol)
≈ 1.39 x 10^23 Al atoms
Therefore, the correct answer is C) 1.39 x 10^23 Al atoms.