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 determine the formula of the iron oxide based on the given information about the iron ions, we can follow these steps:

### Step 1: Identify the oxidation states of iron ions
We know that:
- 94% of the iron ions have a `d^6` configuration, which corresponds to Fe²⁺ (iron in +2 oxidation state).
- 6% of the iron ions have a `d^5` configuration, which corresponds to Fe³⁺ (iron in +3 oxidation state).

### Step 2: Set up the equations based on the percentages
Let’s denote the total number of iron ions as `n`.
- The number of Fe²⁺ ions will be 94% of `n`:
\[ \text{Number of Fe}^{2+} = 0.94n \]
- The number of Fe³⁺ ions will be 6% of `n`:
\[ \text{Number of Fe}^{3+} = 0.06n \]

### Step 3: Calculate the total positive charge contributed by the iron ions
The total positive charge from the iron ions can be calculated as follows:
- The charge from Fe²⁺ ions:
\[ \text{Charge from Fe}^{2+} = 0.94n \times 2 = 1.88n \]
- The charge from Fe³⁺ ions:
\[ \text{Charge from Fe}^{3+} = 0.06n \times 3 = 0.18n \]

### Step 4: Set up the equation for total charge
The total positive charge from both types of iron ions must equal the total negative charge from the oxide ions (O²⁻), which contributes a charge of -2 for each oxygen atom. Since we are looking for the overall charge balance in the compound:
\[ 1.88n + 0.18n = 2 \]
This simplifies to:
\[ 2.06n = 2 \]

### Step 5: Solve for `n`
Now, we can solve for `n`:
\[ n = \frac{2}{2.06} \approx 0.97 \]

### Step 6: Determine the formula of the oxide
Since we have approximately 0.97 moles of iron ions for every mole of oxide, the formula of the oxide can be represented as:
\[ \text{Fe}_{0.97}\text{O} \]

### Conclusion
The best representation of the formula of the oxide is:
\[ \text{Fe}_{0.97}\text{O} \]