Analysis show that iron oxide consist of Iron ion with `94%` ions having `d^(6)` configuration and `6%` having `d^(5)` configuration. Which amongst the following best represents the formula of the oxide?

Options

A. `Fe_(0.97)O`
B. `Fe_(1.03)O`
C. `Fe_(0.60)O`
D. `Fe_(0.94)O_(0.94)`

Answer

To solve the problem, we need to determine the formula of the iron oxide based on the given information about the iron ions present in the oxide. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Electronic Configuration of Iron
- Iron (Fe) has an atomic number of 26, and its electronic configuration is \( [Ar] 3d^6 4s^2 \).
- When iron loses electrons to form ions:
- \( \text{Fe}^{2+} \) has the configuration \( 3d^6 \).
- \( \text{Fe}^{3+} \) has the configuration \( 3d^5 \).

### Step 2: Analyze the Given Percentages of Iron Ions
- The problem states that 94% of the iron ions are \( \text{Fe}^{2+} \) and 6% are \( \text{Fe}^{3+} \).

### Step 3: Set Up the Charge Balance Equation
- Let \( x \) be the number of iron ions per one oxygen atom (O).
- The total positive charge contributed by the iron ions can be expressed as:
\[ \text{Total positive charge} = (x \times 0.94 \times 2) + (x \times 0.06 \times 3) \]
- The negative charge from one oxygen atom is \( 2 \) (since the charge of oxide ion \( O^{2-} \) is -2).

### Step 4: Write the Charge Neutrality Equation
- Setting the total positive charge equal to the total negative charge gives us:
\[ x \times 0.94 \times 2 + x \times 0.06 \times 3 = 2 \]

### Step 5: Simplify the Equation
- Simplifying the left side:
\[ x(1.88 + 0.18) = 2 \]
\[ x \times 2.06 = 2 \]

### Step 6: Solve for \( x \)
- Rearranging gives:
\[ x = \frac{2}{2.06} \approx 0.97 \]

### Step 7: Write the Formula of the Iron Oxide
- Since \( x \approx 0.97 \), the formula for the oxide can be represented as:
\[ \text{Fe}_{0.97}O \]

### Step 8: Conclusion
- The best representation of the formula of the oxide is \( \text{Fe}_{0.97}O \).