Oxidation number of Fe in `Fe_(3) O_(4)` is fractional because -

Options

A. It is mixed `[Fe( +2) - Fe( + 4) ]` oxide
B. It is a non-stoichiometric compound
C. It is a mixed `[Fe( + 2) - Fe( + 3) ]` oxide
D. None of above

Answer

To determine why the oxidation number of iron (Fe) in Fe₃O₄ is fractional, we can follow these steps:

### Step 1: Understand the Composition of Fe₃O₄
Fe₃O₄ is a compound that consists of iron and oxygen. It can be thought of as a mixture of two iron oxides: FeO (iron(II) oxide) and Fe₂O₃ (iron(III) oxide).

### Step 2: Determine the Oxidation States of Iron in FeO and Fe₂O₃
1. **For FeO**:
- Let the oxidation state of Fe be \( x \).
- The oxidation state of O is \(-2\).
- The equation is:
\[ x + (-2) = 0 \implies x = +2 \]
- Thus, the oxidation state of Fe in FeO is +2.

2. **For Fe₂O₃**:
- Let the oxidation state of Fe be \( x \).
- For two iron atoms, the equation becomes:
\[ 2x + 3(-2) = 0 \implies 2x - 6 = 0 \implies 2x = 6 \implies x = +3 \]
- Hence, the oxidation state of Fe in Fe₂O₃ is +3.

### Step 3: Calculate the Average Oxidation State of Iron in Fe₃O₄
Fe₃O₄ can be viewed as containing:
- 1 FeO (with Fe at +2)
- 2 Fe₂O₃ (with Fe at +3)

To find the average oxidation state of the three iron atoms in Fe₃O₄:
- Total contribution from FeO: \( +2 \) (1 Fe)
- Total contribution from Fe₂O₃: \( +3 \times 2 = +6 \) (2 Fe)

Adding these contributions:
\[ \text{Total oxidation state} = +2 + +6 = +8 \]
Since there are 3 iron atoms in total, the average oxidation state (or oxidation number) is:
\[ \text{Average oxidation state} = \frac{+8}{3} = \frac{8}{3} \]

### Conclusion
The oxidation number of Fe in Fe₃O₄ is fractional (\(\frac{8}{3}\)) because it is a mixture of iron in different oxidation states (+2 and +3) from FeO and Fe₂O₃, respectively.

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