Mining companies use this reaction to obtain iron from iron ore: Fe2O3(s)+3CO(g) → 2Fe(s)+3CO2(g) The reaction of 177 g of Fe2O3 with 82.8 g of CO produces 72.7 g of Fe. Calculate the theoretical yield of solid iron.
The Correct Answer and Explanation is :
To calculate the theoretical yield of solid iron ((Fe)) from the reaction of iron(III) oxide ((Fe_2O_3)) with carbon monoxide ((CO)), we will follow these steps:
- Identify the Balanced Chemical Equation:
The reaction is already balanced:
[
Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)
] - Calculate Molar Masses:
- Molar mass of (Fe_2O_3):
- (Fe: 55.85 \, g/mol)
- (O: 16.00 \, g/mol)
[
\text{Molar mass of } Fe_2O_3 = (2 \times 55.85) + (3 \times 16.00) = 159.7 \, g/mol
]
- Molar mass of (CO):
[
\text{Molar mass of } CO = 12.01 + 16.00 = 28.01 \, g/mol
]
- Convert Masses to Moles:
- Moles of (Fe_2O_3):
[
\text{Moles of } Fe_2O_3 = \frac{177 \, g}{159.7 \, g/mol} \approx 1.107 \, mol
] - Moles of (CO):
[
\text{Moles of } CO = \frac{82.8 \, g}{28.01 \, g/mol} \approx 2.957 \, mol
]
- Determine the Limiting Reactant:
From the balanced equation, (1 \, mol \, Fe_2O_3) reacts with (3 \, mol \, CO). Thus:
- For 1.107 moles of (Fe_2O_3), we need:
[
1.107 \, mol \times 3 = 3.321 \, mol \, CO
]
Since we only have 2.957 moles of (CO), (CO) is the limiting reactant.
- Calculate Theoretical Yield of Iron:
From the balanced equation, (3 \, mol \, CO) produces (2 \, mol \, Fe):
[
\text{Moles of } Fe = \frac{2}{3} \times \text{Moles of } CO = \frac{2}{3} \times 2.957 \approx 1.972 \, mol \, Fe
] The molar mass of (Fe) is (55.85 \, g/mol):
[
\text{Theoretical yield of } Fe = 1.972 \, mol \times 55.85 \, g/mol \approx 110.0 \, g
]
Conclusion
The theoretical yield of solid iron from the reaction is 110.0 grams. This calculation demonstrates the importance of determining the limiting reactant in a chemical reaction, as it dictates the maximum amount of product that can be formed. Despite having a sufficient quantity of (Fe_2O_3), the limited amount of (CO) restricts the formation of (Fe). Understanding stoichiometry allows chemists to predict yields and optimize the usage of reactants in industrial processes.