The mass percentage of `Fe^(3+)` ion present in `Fe_(0.93), O_(1.00)` is

Options

A. `15%`
B. `5.5%`
C. `10.0%`
D. `11.5%`

Answer

To find the mass percentage of `Fe^(3+)` ions in the compound `Fe_(0.93)O_(1.00)`, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = number of moles of `Fe^(3+)`
- Therefore, the number of moles of `Fe^(2+)` will be \( 0.93 - x \).

### Step 2: Charge Balance Equation
The total positive charge from the iron ions must equal the total negative charge from the oxygen ions. The charge contribution can be expressed as:
- Total positive charge = \( 3x + 2(0.93 - x) \)
- Total negative charge = \( 2 \) (from one mole of `O^(2-)`)

Setting these equal gives us the equation:
\[ 3x + 2(0.93 - x) = 2 \]

### Step 3: Simplify the Equation
Expanding the equation:
\[ 3x + 1.86 - 2x = 2 \]
This simplifies to:
\[ x + 1.86 = 2 \]

### Step 4: Solve for \( x \)
Rearranging gives:
\[ x = 2 - 1.86 = 0.14 \]

### Step 5: Calculate the Mass Percentage of `Fe^(3+)`
Now, we need to find the mass percentage of `Fe^(3+)`:
- The total moles of iron = \( 0.93 \)
- The moles of `Fe^(3+)` = \( 0.14 \)

The mass of `Fe^(3+)` can be calculated using its molar mass (approximately 55.85 g/mol):
\[ \text{Mass of } Fe^{3+} = 0.14 \times 55.85 \, \text{g} \approx 7.82 \, \text{g} \]

### Step 6: Calculate the Total Mass of the Compound
The total mass of the compound can be calculated as follows:
- Mass of `Fe` = \( 0.93 \times 55.85 \, \text{g} \approx 51.89 \, \text{g} \)
- Mass of `O` = \( 1.00 \times 16.00 \, \text{g} = 16.00 \, \text{g} \)

Total mass of the compound:
\[ \text{Total mass} = 51.89 \, \text{g} + 16.00 \, \text{g} \approx 67.89 \, \text{g} \]

### Step 7: Calculate the Mass Percentage
Finally, the mass percentage of `Fe^(3+)` is calculated using the formula:
\[ \text{Mass percentage of } Fe^{3+} = \left( \frac{\text{Mass of } Fe^{3+}}{\text{Total mass}} \right) \times 100 \]
Substituting the values:
\[ \text{Mass percentage of } Fe^{3+} = \left( \frac{7.82 \, \text{g}}{67.89 \, \text{g}} \right) \times 100 \approx 11.52\% \]

### Final Result
The mass percentage of `Fe^(3+)` ions present in `Fe_(0.93)O_(1.00)` is approximately **15%**.

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