A sample of ferrous oxide has actual formula `Fe_(0.93)O_(1..00)`. In this sample what fraction of metal ions are `Fe^(2+)` ions? What type of non-stoichiometric defect is present in this sample ?

Options

A. (i)-0.849 , (ii)-Metal deficiency
B. (i)-0.790 , (ii)-Metal deficiency
C. (i)-0.145, (ii)-Metal excess
D. (i)-0.93 , (ii)-Vacancy defect

Explanation

To solve the problem, we need to determine the fraction of ferrous ions (Fe²⁺) in the given sample of ferrous oxide, Fe₀.₉₃O₁.₀₀, and identify the type of non-stoichiometric defect present.

### Step-by-Step Solution:

1. **Identify the total number of metal ions**:
The formula given is Fe₀.₉₃O₁.₀₀, which indicates that there are 0.93 moles of iron (Fe) per mole of the compound.

2. **Let x be the number of Fe³⁺ ions**:
Since some of the Fe²⁺ ions are replaced by Fe³⁺ ions, we can denote the number of Fe³⁺ ions as x. Consequently, the number of Fe²⁺ ions will be (0.93 - x).

3. **Set up the charge balance equation**:
The total positive charge contributed by the metal ions must equal the total negative charge from the oxide ions. The charge from the oxide ions (O²⁻) is -2 for each O, and since there is 1 mole of O, the total negative charge is -2.

The total positive charge from the metal ions can be expressed as:
\[ 3x + 2(0.93 - x) = 2 \]
Here, 3x is the contribution from Fe³⁺ ions and 2(0.93 - x) is the contribution from Fe²⁺ ions.

4. **Simplify the equation**:
\[ 3x + 1.86 - 2x = 2 \]
\[ x + 1.86 = 2 \]
\[ x = 2 - 1.86 = 0.14 \]

5. **Calculate the number of Fe²⁺ ions**:
The number of Fe²⁺ ions is:
\[ 0.93 - x = 0.93 - 0.14 = 0.79 \]

6. **Calculate the fraction of Fe²⁺ ions**:
The fraction of Fe²⁺ ions in the sample is given by:
\[ \text{Fraction of Fe}^{2+} = \frac{\text{Number of Fe}^{2+}}{\text{Total number of metal ions}} = \frac{0.79}{0.93} \]
\[ \text{Fraction of Fe}^{2+} \approx 0.849 \]

7. **Identify the type of non-stoichiometric defect**:
Since the formula shows a deficiency of iron (Fe) ions (from Fe₁ to Fe₀.₉₃), this indicates a metal deficiency defect.

### Final Answers:
- The fraction of Fe²⁺ ions is approximately **0.849**.
- The type of non-stoichiometric defect present is **metal deficiency**.