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

Options

A. `24`
B. `54`
C. `9`
D. `87.62`

Explanation

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

### Step 1: Assume a Sample Size
Assume we have 100 grams of the metal nitride \( M_3N_2 \). This makes calculations easier since percentages can be directly converted to grams.

### Step 2: Calculate the Mass of Nitrogen
Since the compound contains 28% nitrogen, in 100 grams of \( M_3N_2 \), the mass of nitrogen is:
\[ \text{Mass of Nitrogen} = 28\% \text{ of } 100 \text{ g} = 28 \text{ g} \]

### Step 3: Calculate the Mass of Metal
The remaining mass will be the mass of the metal \( M \):
\[ \text{Mass of Metal} = 100 \text{ g} - 28 \text{ g} = 72 \text{ g} \]

### Step 4: Determine the Moles of Nitrogen
Next, we need to calculate the number of moles of nitrogen. The atomic mass of nitrogen (N) is approximately 14 g/mol. Therefore, the number of moles of nitrogen in 28 grams is:
\[ \text{Moles of Nitrogen} = \frac{\text{Mass of Nitrogen}}{\text{Atomic Mass of Nitrogen}} = \frac{28 \text{ g}}{14 \text{ g/mol}} = 2 \text{ moles} \]

### Step 5: Relate Moles of Nitrogen to Moles of Metal
From the formula \( M_3N_2 \), we see that 2 moles of nitrogen correspond to 3 moles of metal \( M \). Thus, if there are 2 moles of nitrogen, then the moles of metal \( M \) can be calculated as follows:
\[ \text{Moles of Metal} = \frac{3}{2} \times \text{Moles of Nitrogen} = \frac{3}{2} \times 2 = 3 \text{ moles} \]

### Step 6: Calculate the Molar Mass of Metal
Now we know that 72 grams of metal corresponds to 3 moles. To find the molar mass (or atomic mass) of metal \( M \), we use the formula:
\[ \text{Molar Mass of Metal} = \frac{\text{Mass of Metal}}{\text{Moles of Metal}} = \frac{72 \text{ g}}{3 \text{ moles}} = 24 \text{ g/mol} \]

### Conclusion
The atomic mass of metal \( M \) is 24 g/mol.

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