Experimentally it was found that a metal oxide has formula `M_(0.98)O`. Metal M, present as `M^(2+) and M^(3+)` in its oxide. Fraction of the metal which exists as `M^(3+)` would be

Options

A. `5.08%`
B. `7.01%`
C. `4.08%`
D. `6.05%`

Explanation

To solve the problem, we need to determine the fraction of the metal that exists as M^(3+) in the metal oxide M_(0.98)O. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding the Metal Oxide Composition:**
- The formula of the metal oxide is M_(0.98)O, which indicates that in 1 mole of the oxide, there are 0.98 moles of metal (M) and 1 mole of oxide (O).

2. **Defining Variables:**
- Let \( x \) be the fraction of metal that exists as M^(3+).
- Therefore, the fraction of metal that exists as M^(2+) will be \( 0.98 - x \).

3. **Setting Up the Charge Balance Equation:**
- The total positive charge contributed by the metal ions must balance the negative charge from the oxide ion.
- The charge from M^(3+) is \( 3x \) and from M^(2+) is \( 2(0.98 - x) \).
- The charge from the oxide ion (O^(2-)) is -2.
- Therefore, we can set up the equation:
\[ 3x + 2(0.98 - x) = 2 \]

4. **Expanding and Simplifying the Equation:**
- Expand the equation:
\[ 3x + 1.96 - 2x = 2 \]
- Combine like terms:
\[ x + 1.96 = 2 \]

5. **Solving for x:**
- Subtract 1.96 from both sides:
\[ x = 2 - 1.96 \]
- Thus, we find:
\[ x = 0.04 \]

6. **Calculating the Fraction of M^(3+):**
- The fraction of metal that exists as M^(3+) is \( x = 0.04 \).

7. **Converting to Percentage:**
- To find the percentage of metal that exists as M^(3+), we calculate:
\[ \text{Percentage} = \left( \frac{x}{0.98} \right) \times 100 \]
- Substituting the value of \( x \):
\[ \text{Percentage} = \left( \frac{0.04}{0.98} \right) \times 100 \approx 4.08\% \]

### Final Answer:
The fraction of the metal which exists as M^(3+) is approximately **4.08%**.