How many kilograms of aluminum can be extracted from 2.0 metric tons of the ore 'alumina' (Al2O3)?
Would you take the percentage of aluminum in the ore:
53.96/101.96 = 52.92
then take that much out of 2.0 metric tons or 2000 kg?
So would it be 1058.40 kilograms?
Convert 2.0 metric tons Al2O3 to grams Al2O3.
Convert grams Al2O3 to mols Al2O3.
Convert mols Al2O3 to mols Al knowing that there are 2 mols Al for every mol Al2O3.
Convert mols Al to grams Al remembering that mols x atomic mass = grams.
Finally, convert grams Al to kg Al.
Check my thinking.
Post your work if you get stuck.
So.. my work wasn't right. Above your message?
No, your answer is correct. I just did it the long way. You took the short route. Very good.
Ok thanks so much.
To determine the number of kilograms of aluminum that can be extracted from 2.0 metric tons of alumina (Al2O3), we need to consider the molar mass and stoichiometry of aluminum in the compound.
First, let's calculate the molar mass of alumina (Al2O3):
- Aluminum (Al) has a molar mass of 26.98 g/mol.
- Oxygen (O) has a molar mass of 16.00 g/mol.
- Since there are two aluminum atoms and three oxygen atoms in each formula unit of alumina (Al2O3), the molar mass of alumina is:
(2 * 26.98 g) + (3 * 16.00 g) = 101.96 g/mol.
Now, let's convert 2.0 metric tons of alumina to grams:
- 1 metric ton is equal to 1000 kg.
- Therefore, 2.0 metric tons is equal to 2.0 * 1000 kg = 2000 kg.
- Since 1 kg is equal to 1000 g, 2000 kg is equal to 2000 * 1000 g = 2,000,000 g.
Next, we can use stoichiometry to determine the amount of aluminum:
- The molar ratio between aluminum and alumina is 2:1 (since there are 2 aluminum atoms in each formula unit of alumina).
- Therefore, for every 101.96 g of alumina, there are 2 * (26.98 g) = 53.96 g of aluminum.
- To find the amount of aluminum in our 2,000,000 g of alumina, we can set up the following proportion:
(53.96 g / 101.96 g/mol) = (x g / 2,000,000 g)
- Solving for x, we find x = (53.96 g / 101.96 g/mol) * 2,000,000 g = 1,057,428 g.
Finally, convert the result to kilograms:
- 1 kilogram is equal to 1000 grams.
- Therefore, 1,057,428 g is equal to 1,057,428 g / 1000 = 1057.428 kg.
So, approximately 1057.428 kilograms of aluminum can be extracted from 2.0 metric tons (2000 kg) of the ore 'alumina' (Al2O3).