Answer :
Sure! Let's go through the detailed step-by-step solution to find out how much aluminum (Al) can be produced from 6.00 tons of aluminum oxide ([tex]\(Al_2O_3\)[/tex]).
1. Determine the molar mass of [tex]\(Al_2O_3\)[/tex]:
- The molar masses of aluminum (Al) and oxygen (O) are approximately [tex]\(26.98\)[/tex] g/mol and [tex]\(16.00\)[/tex] g/mol, respectively.
- The formula [tex]\(Al_2O_3\)[/tex] contains 2 atoms of Al and 3 atoms of O.
- Therefore, the molar mass of [tex]\(Al_2O_3\)[/tex] is:
[tex]\[
(2 \times 26.98) + (3 \times 16.00) = 53.96 + 48.00 = 101.96 \text{ g/mol}
\][/tex]
2. Convert 6.00 tons of [tex]\(Al_2O_3\)[/tex] to grams:
- 1 ton is equivalent to 1,000,000 grams.
- Therefore, 6.00 tons of [tex]\(Al_2O_3\)[/tex] is:
[tex]\[
6.00 \times 1,000,000 = 6,000,000 \text{ grams}
\][/tex]
3. Determine the number of moles of [tex]\(Al_2O_3\)[/tex] in 6,000,000 grams:
- Using the molar mass of [tex]\(Al_2O_3\)[/tex], we can find the moles:
[tex]\[
\frac{6,000,000 \text{ grams}}{101.96 \text{ g/mol}} \approx 58846.61 \text{ moles of } Al_2O_3
\][/tex]
4. Determine the moles of aluminum (Al) that can be produced:
- From the chemical equation, we know that 1 mole of [tex]\(Al_2O_3\)[/tex] produces 2 moles of Al.
- Therefore, the total moles of Al produced is:
[tex]\[
58846.61 \times 2 = 117693.21 \text{ moles of } Al
\][/tex]
5. Convert moles of Al to grams of Al:
- Using the molar mass of Al (26.98 g/mol), we find:
[tex]\[
117693.21 \times 26.98 \approx 3,175,362.89 \text{ grams of } Al
\][/tex]
6. Convert grams of Al to tons of Al:
- Since 1 ton is 1,000,000 grams:
[tex]\[
\frac{3,175,362.89 \text{ grams}}{1,000,000} \approx 3.18 \text{ tons}
\][/tex]
So, from 6.00 tons of [tex]\(Al_2O_3\)[/tex], you can produce approximately 3.18 tons of aluminum (Al).
1. Determine the molar mass of [tex]\(Al_2O_3\)[/tex]:
- The molar masses of aluminum (Al) and oxygen (O) are approximately [tex]\(26.98\)[/tex] g/mol and [tex]\(16.00\)[/tex] g/mol, respectively.
- The formula [tex]\(Al_2O_3\)[/tex] contains 2 atoms of Al and 3 atoms of O.
- Therefore, the molar mass of [tex]\(Al_2O_3\)[/tex] is:
[tex]\[
(2 \times 26.98) + (3 \times 16.00) = 53.96 + 48.00 = 101.96 \text{ g/mol}
\][/tex]
2. Convert 6.00 tons of [tex]\(Al_2O_3\)[/tex] to grams:
- 1 ton is equivalent to 1,000,000 grams.
- Therefore, 6.00 tons of [tex]\(Al_2O_3\)[/tex] is:
[tex]\[
6.00 \times 1,000,000 = 6,000,000 \text{ grams}
\][/tex]
3. Determine the number of moles of [tex]\(Al_2O_3\)[/tex] in 6,000,000 grams:
- Using the molar mass of [tex]\(Al_2O_3\)[/tex], we can find the moles:
[tex]\[
\frac{6,000,000 \text{ grams}}{101.96 \text{ g/mol}} \approx 58846.61 \text{ moles of } Al_2O_3
\][/tex]
4. Determine the moles of aluminum (Al) that can be produced:
- From the chemical equation, we know that 1 mole of [tex]\(Al_2O_3\)[/tex] produces 2 moles of Al.
- Therefore, the total moles of Al produced is:
[tex]\[
58846.61 \times 2 = 117693.21 \text{ moles of } Al
\][/tex]
5. Convert moles of Al to grams of Al:
- Using the molar mass of Al (26.98 g/mol), we find:
[tex]\[
117693.21 \times 26.98 \approx 3,175,362.89 \text{ grams of } Al
\][/tex]
6. Convert grams of Al to tons of Al:
- Since 1 ton is 1,000,000 grams:
[tex]\[
\frac{3,175,362.89 \text{ grams}}{1,000,000} \approx 3.18 \text{ tons}
\][/tex]
So, from 6.00 tons of [tex]\(Al_2O_3\)[/tex], you can produce approximately 3.18 tons of aluminum (Al).
