Question
How many GRAMS of iron can be obtained from 3.0 kg of Fe₃O₄?
Answers
GPT-4o mini
To determine how many grams of iron can be obtained from 3.0 kg of Fe₃O₄ (magnetite), we first need to know the molar masses of the components involved.
1. **Calculate the molar mass of Fe₃O₄:**
- Iron (Fe): approximately 55.85 g/mol
- Oxygen (O): approximately 16.00 g/mol
The molar mass of Fe₃O₄ is calculated as follows:
\[
\text{Molar mass of Fe₃O₄} = (3 \times 55.85) + (4 \times 16.00)
\]
\[
= 167.55 + 64.00 = 231.55 \text{ g/mol}
\]
2. **Convert 3.0 kg of Fe₃O₄ to grams:**
\[
3.0 \text{ kg} = 3000 \text{ g}
\]
3. **Calculate the number of moles of Fe₃O₄ in 3000 g:**
\[
\text{Moles of Fe₃O₄} = \frac{3000 \text{ g}}{231.55 \text{ g/mol}} \approx 12.95 \text{ moles}
\]
4. **Determine the amount of iron produced from Fe₃O₄:**
The chemical formula Fe₃O₄ indicates that there are 3 moles of iron (Fe) for every mole of Fe₃O₄. Thus, for 12.95 moles of Fe₃O₄, the moles of iron produced would be:
\[
\text{Moles of Fe} = 12.95 \text{ moles Fe₃O₄} \times 3 \text{ moles Fe/mole Fe₃O₄} = 38.85 \text{ moles Fe}
\]
5. **Convert moles of iron to grams:**
\[
\text{Mass of Fe} = \text{Moles of Fe} \times \text{Molar mass of Fe}
\]
\[
= 38.85 \text{ moles} \times 55.85 \text{ g/mol} \approx 2167.84 \text{ g}
\]
Thus, from 3.0 kg of Fe₃O₄, approximately **2167.84 grams of iron** can be obtained.
1. **Calculate the molar mass of Fe₃O₄:**
- Iron (Fe): approximately 55.85 g/mol
- Oxygen (O): approximately 16.00 g/mol
The molar mass of Fe₃O₄ is calculated as follows:
\[
\text{Molar mass of Fe₃O₄} = (3 \times 55.85) + (4 \times 16.00)
\]
\[
= 167.55 + 64.00 = 231.55 \text{ g/mol}
\]
2. **Convert 3.0 kg of Fe₃O₄ to grams:**
\[
3.0 \text{ kg} = 3000 \text{ g}
\]
3. **Calculate the number of moles of Fe₃O₄ in 3000 g:**
\[
\text{Moles of Fe₃O₄} = \frac{3000 \text{ g}}{231.55 \text{ g/mol}} \approx 12.95 \text{ moles}
\]
4. **Determine the amount of iron produced from Fe₃O₄:**
The chemical formula Fe₃O₄ indicates that there are 3 moles of iron (Fe) for every mole of Fe₃O₄. Thus, for 12.95 moles of Fe₃O₄, the moles of iron produced would be:
\[
\text{Moles of Fe} = 12.95 \text{ moles Fe₃O₄} \times 3 \text{ moles Fe/mole Fe₃O₄} = 38.85 \text{ moles Fe}
\]
5. **Convert moles of iron to grams:**
\[
\text{Mass of Fe} = \text{Moles of Fe} \times \text{Molar mass of Fe}
\]
\[
= 38.85 \text{ moles} \times 55.85 \text{ g/mol} \approx 2167.84 \text{ g}
\]
Thus, from 3.0 kg of Fe₃O₄, approximately **2167.84 grams of iron** can be obtained.