A compound contains 28% of nitrogen and 72% of a metal by weight. 3 atoms of the metal combine with 2 atoms of nitrogen. Find the atomic weight of the metal.

Explanation

To find the atomic weight of the metal in the compound that contains 28% nitrogen and 72% metal by weight, we can follow these steps:

### Step 1: Determine the mass of nitrogen and metal in a 100 g sample
- Given that the compound contains 28% nitrogen and 72% metal by weight, in a 100 g sample:
- Mass of nitrogen = 28 g
- Mass of metal = 72 g

### Step 2: Find the number of moles of nitrogen
- The atomic weight of nitrogen (N) is 14 g/mol.
- Moles of nitrogen = mass of nitrogen / atomic weight of nitrogen
\[ \text{Moles of N} = \frac{28 \text{ g}}{14 \text{ g/mol}} = 2 \text{ moles} \]

### Step 3: Determine the number of moles of metal
- According to the problem, 3 atoms of the metal combine with 2 atoms of nitrogen. This implies a ratio of:
\[ \frac{\text{Moles of metal}}{\text{Moles of nitrogen}} = \frac{3}{2} \]
- Let the number of moles of metal be \( x \). Then:
\[ \frac{x}{2} = \frac{3}{2} \implies x = 3 \text{ moles of metal} \]

### Step 4: Find the mass of the metal
- We have 3 moles of metal corresponding to 72 g.
- Therefore, the mass of 1 mole of metal (M) can be calculated as:
\[ \text{Molar mass of metal} = \frac{\text{Mass of metal}}{\text{Moles of metal}} = \frac{72 \text{ g}}{3 \text{ moles}} = 24 \text{ g/mol} \]

### Step 5: Conclusion
- The atomic weight of the metal is 24 g/mol.