To determine how many grams of Fe₂O₃ are required to produce 187 grams of Fe, we can follow these steps:
1. Calculate the moles of Fe needed:
- The molar mass of Fe is 55.85 g/mol.
- The mass of Fe we want to produce is 187 g.
- Moles of Fe needed = [tex]\(\frac{{\text{mass of Fe}}}{{\text{molar mass of Fe}}}\)[/tex].
[tex]\[
\text{Moles of Fe needed} = \frac{187 \text{ g}}{55.85 \text{ g/mol}} = 3.348 \, \text{mol}
\][/tex]
2. Relate the moles of Fe to the moles of Fe₂O₃ required:
- According to the balanced chemical equation:
[tex]\[
\text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2
\][/tex]
- 2 moles of Fe are produced from 1 mole of Fe₂O₃.
- Moles of Fe₂O₃ needed = [tex]\(\frac{{\text{moles of Fe}}}{2}\)[/tex].
[tex]\[
\text{Moles of Fe}_2\text{O}_3 \text{ needed} = \frac{3.348 \, \text{mol}}{2} = 1.674 \, \text{mol}
\][/tex]
3. Calculate the mass of Fe₂O₃ needed:
- The molar mass of Fe₂O₃ is 159.7 g/mol.
- Mass of Fe₂O₃ needed = moles of Fe₂O₃ needed [tex]\(\times\)[/tex] molar mass of Fe₂O₃.
[tex]\[
\text{Mass of Fe}_2\text{O}_3 \text{ needed} = 1.674 \, \text{mol} \times 159.7 \, \text{g/mol} = 267.358 \, \text{g}
\][/tex]
Therefore, to produce 187 grams of Fe, you will require approximately 267.358 grams of Fe₂O₃.
