Iron metal is produced commercially by reducing iron (III) oxide in iron ore with carbon monoxide. Write down the balanced chemical equation for the above reduction of iron (III) oxide?

Options

A. Write down the balanced chemical equation for the above reduction of iron (III) oxide?
B. Enthalpies of formation for various substance at `25^(@)C` are given in the following table.
`{:(,FeO_(3(g)),CO_(g),Fe_(g),CO2_(g)),(DeltaH_(f)^(@)(KJ//"mol"),-824.2,-110.5,0,-393.5),(S[J//(K."mol")],87.5,197.6,27.3,213.6):}`
Calculate the standard free-energy change for this reaction at `25^(@)`C ?
C. Is the reaction spontaneous at `25^(@)`C ?
D. Does the reverse reaction become spontaneous at higher temperature? Explain.

Answer

To write the balanced chemical equation for the reduction of iron (III) oxide (Fe₂O₃) with carbon monoxide (CO), we can follow these steps:

### Step 1: Write the unbalanced equation
The unbalanced equation for the reaction is:
\[ \text{Fe}_2\text{O}_3 + \text{CO} \rightarrow \text{Fe} + \text{CO}_2 \]

### Step 2: Identify the number of atoms for each element
In the unbalanced equation:
- Iron (Fe): 2 atoms from Fe₂O₃
- Oxygen (O): 3 atoms from Fe₂O₃
- Carbon (C): 1 atom from CO

### Step 3: Balance the iron atoms
Since there are 2 iron atoms in Fe₂O₃, we need to place a coefficient of 2 in front of Fe on the product side:
\[ \text{Fe}_2\text{O}_3 + \text{CO} \rightarrow 2\text{Fe} + \text{CO}_2 \]

### Step 4: Balance the oxygen atoms
Now, we have 3 oxygen atoms in Fe₂O₃. On the product side, we have 2 oxygen atoms from CO₂. To balance the oxygen, we need to adjust the number of CO molecules. Since CO contributes 1 oxygen atom, we will need 3 CO to provide 3 oxygen atoms:
\[ \text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2 \]

### Step 5: Check the balance
Now, let's check the balance of each element:
- Iron: 2 on both sides
- Oxygen: 3 from Fe₂O₃ and 3 from 3 CO on the reactant side, and 6 from 3 CO₂ on the product side.
- Carbon: 3 from 3 CO on the reactant side and 3 from 3 CO₂ on the product side.

### Final Balanced Equation
The balanced chemical equation for the reduction of iron (III) oxide with carbon monoxide is:
\[ \text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2 \]

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