If it is known that in `Fe_(0.96)O`, Fe is present in +2 and +3 oxidation state, what is the mole fraction of `Fe^(2+)` in the compound?

Options

A. `(12)/(25)`
B. `(25)/(12)`
C. `(1)/(12)`
D. `(11)/(12)`

Answer

To find the mole fraction of `Fe^(2+)` in the compound `Fe_(0.96)O`, we can follow these steps:

### Step 1: Define Variables
Let:
- \( X \) = mole fraction of \( Fe^{2+} \)
- \( 100 - X \) = mole fraction of \( Fe^{3+} \)

### Step 2: Write the Average Oxidation State Equation
The average oxidation state (Y) of iron in the compound can be expressed as:
\[ Y = \frac{(X \cdot 2) + ((100 - X) \cdot 3)}{100} \]
This represents the contribution of both oxidation states to the average oxidation state.

### Step 3: Relate Average Oxidation State to the Compound
Since the total number of iron atoms is 0.96 and the oxidation state of oxygen is -2, we can set up the equation:
\[ Y \cdot 0.96 + (-2) \cdot 1 = 0 \]
This simplifies to:
\[ Y \cdot 0.96 = 2 \]
\[ Y = \frac{2}{0.96} \approx 2.0833 \]

### Step 4: Substitute Y into the Average Oxidation State Equation
Substituting \( Y \) back into the average oxidation state equation:
\[ 2.0833 = \frac{(X \cdot 2) + ((100 - X) \cdot 3)}{100} \]

### Step 5: Solve for X
Multiply both sides by 100:
\[ 208.33 = 2X + 300 - 3X \]
Combine like terms:
\[ 208.33 = 300 - X \]
Rearranging gives:
\[ X = 300 - 208.33 = 91.67 \]

### Step 6: Calculate the Mole Fraction
The mole fraction of \( Fe^{2+} \) is given by:
\[ \text{Mole fraction of } Fe^{2+} = \frac{X}{100} = \frac{91.67}{100} = 0.9167 \]

### Final Answer
The mole fraction of \( Fe^{2+} \) in the compound \( Fe_{0.96}O \) is approximately **0.9167**.

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