The oxide of an element possess the molecular formula `M_(2)O_(3)`. If the equivalent mass of the metal is 9, the molecular mass of the oxide will be

Options

A. 27
B. 75
C. 102
D. 18

Explanation

To find the molecular mass of the oxide with the formula \( M_2O_3 \) given that the equivalent mass of the metal is 9, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Equivalent Mass**:
- The equivalent mass of an element is given as 9. The equivalent mass can be related to the atomic mass and the n-factor (which is the change in oxidation state per atom of the element in the compound).

2. **Identifying the n-factor**:
- The molecular formula \( M_2O_3 \) indicates that there are 2 moles of metal (M) and 3 moles of oxygen (O).
- The oxidation state of oxygen is typically -2. Therefore, in \( M_2O_3 \), the total negative charge contributed by oxygen is \( 3 \times (-2) = -6 \).
- To balance this, the total positive charge from the metal must be +6. Since there are 2 moles of metal, the oxidation state of each metal atom (M) can be calculated as follows:
\[ 2x - 6 = 0 \quad \text{(where \( x \) is the oxidation state of M)} \]
\[ 2x = 6 \implies x = +3 \]
- Thus, the n-factor for the metal is 3.

3. **Calculating Atomic Mass of Metal**:
- The equivalent mass is related to the atomic mass (A) and the n-factor (n) by the formula:
\[ \text{Equivalent mass} = \frac{\text{Atomic mass}}{\text{n-factor}} \]
- Substituting the known values:
\[ 9 = \frac{A}{3} \implies A = 9 \times 3 = 27 \text{ g/mol} \]

4. **Calculating Molecular Mass of \( M_2O_3 \)**:
- The molecular mass of \( M_2O_3 \) can be calculated using the atomic mass of the metal and the atomic mass of oxygen (16 g/mol):
\[ \text{Molecular mass of } M_2O_3 = 2 \times A + 3 \times 16 \]
- Substituting the values:
\[ \text{Molecular mass} = 2 \times 27 + 3 \times 16 \]
\[ = 54 + 48 = 102 \text{ g/mol} \]

### Final Answer:
The molecular mass of the oxide \( M_2O_3 \) is **102 g/mol**.