A metal nitride `M_(3)N_(2)` contains 28 % of nitrogen. The atomic mass of metal M is

Options

A. a.24
B. b.54
C. c.9
D. d.87.62

Explanation

To find the atomic mass of the metal \( M \) in the metal nitride \( M_3N_2 \) that contains 28% nitrogen, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the total mass of the compound**:
Let's assume the total mass of the compound \( M_3N_2 \) is 100 grams for simplicity.

2. **Calculate the mass of nitrogen in the compound**:
Since the compound contains 28% nitrogen, we can calculate the mass of nitrogen:
\[ \text{Mass of } N = \frac{28}{100} \times 100 \text{ g} = 28 \text{ g} \]

3. **Calculate the mass of metal \( M \)**:
The remaining mass of the compound will be the mass of the metal \( M \):
\[ \text{Mass of } M = \text{Total mass} - \text{Mass of } N = 100 \text{ g} - 28 \text{ g} = 72 \text{ g} \]

4. **Determine the number of moles of nitrogen**:
The molar mass of nitrogen \( N \) is approximately 14 g/mol. Since there are 2 nitrogen atoms in \( M_3N_2 \):
\[ \text{Moles of } N = \frac{28 \text{ g}}{14 \text{ g/mol}} = 2 \text{ moles} \]

5. **Determine the number of moles of metal \( M \)**:
In the formula \( M_3N_2 \), there are 3 moles of metal \( M \) for every 2 moles of nitrogen. Therefore, the number of moles of metal \( M \) can be calculated as:
\[ \text{Moles of } M = \frac{3}{2} \times \text{Moles of } N = \frac{3}{2} \times 2 = 3 \text{ moles} \]

6. **Calculate the atomic mass of metal \( M \)**:
The atomic mass of metal \( M \) can be calculated using the total mass of metal and the number of moles:
\[ \text{Atomic mass of } M = \frac{\text{Mass of } M}{\text{Moles of } M} = \frac{72 \text{ g}}{3 \text{ moles}} = 24 \text{ g/mol} \]

Thus, the atomic mass of metal \( M \) is **24 g/mol**.