When `4g` of iron is burnt to ferric oxide at constant pressure, `29.28KJ` of heat is evolved. What is the enthalpy of formation of ferric oxide (At wt. of `Fe=56`)

Options

A. `-81.98 kJ`
B. `-819.8 kJ`
C. `-40.99 kJ`
D. `+819.8 kJ`

Answer

To find the enthalpy of formation of ferric oxide (Fe₂O₃) when 4 g of iron is burnt, we can follow these steps:

### Step 1: Write the balanced chemical equation
The reaction for the formation of ferric oxide from iron and oxygen can be written as:
\[ 4Fe + 3O_2 \rightarrow 2Fe_2O_3 \]

### Step 2: Calculate the number of moles of iron
To find the number of moles of iron (Fe), we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
Given that the atomic weight of iron (Fe) is 56 g/mol, we can calculate:
\[ \text{Number of moles of Fe} = \frac{4 \text{ g}}{56 \text{ g/mol}} = 0.0714 \text{ moles} \]

### Step 3: Determine the moles of ferric oxide formed
From the balanced equation, we see that 2 moles of Fe produce 1 mole of Fe₂O₃. Therefore, the moles of Fe₂O₃ formed from 0.0714 moles of Fe can be calculated as follows:
\[ \text{Moles of Fe}_2\text{O}_3 = \frac{1}{2} \times 0.0714 = 0.0357 \text{ moles} \]

### Step 4: Relate the heat evolved to the moles of ferric oxide
The heat evolved when 4 g of iron is burnt is given as 29.28 kJ. This amount of heat corresponds to the formation of 0.0357 moles of Fe₂O₃.

### Step 5: Calculate the enthalpy of formation for 1 mole of Fe₂O₃
To find the enthalpy of formation (ΔH_f) for 1 mole of Fe₂O₃, we can use the relationship:
\[ \Delta H_f = \frac{\text{Total heat evolved}}{\text{Moles of Fe}_2\text{O}_3} \]
Substituting the values:
\[ \Delta H_f = \frac{29.28 \text{ kJ}}{0.0357 \text{ moles}} \approx 819.8 \text{ kJ/mol} \]

### Step 6: State the sign of the enthalpy change
Since heat is evolved in the reaction, the enthalpy of formation is negative:
\[ \Delta H_f = -819.8 \text{ kJ/mol} \]

### Final Answer
The enthalpy of formation of ferric oxide (Fe₂O₃) is approximately:
\[ \Delta H_f = -819.8 \text{ kJ/mol} \]

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