Step 1: Determine the molar mass of ammonium nitrate
The chemical formula for ammonium nitrate is \( \text{NH}_4\text{NO}_3 \). The atomic masses of its constituent elements are:
- Nitrogen (N) = 14 g/mol
- Hydrogen (H) = 1 g/mol
- Oxygen (O) = 16 g/mol
The molar mass of \( \text{NH}_4\text{NO}_3 \) is calculated as follows:
\[
M_{\text{NH}_4\text{NO}_3} = (1 \times 14) + (4 \times 1) + (1 \times 14) + (3 \times 16) = 14 + 4 + 14 + 48 = 80 \, \text{g/mol}
\]
Step 2: Calculate the mass contributed by nitrogen in ammonium nitrate
Ammonium nitrate contains two nitrogen atoms. Therefore, the total mass of nitrogen is:
\[
\text{Mass of nitrogen} = 2 \times 14 = 28 \, \text{g/mol}
\]
Step 3: Compute the percentage composition of nitrogen
The percentage of nitrogen by mass in ammonium nitrate is derived using the following formula:
\[
\text{Percentage of nitrogen} = \left( \frac{\text{Mass of nitrogen}}{\text{Molar mass of NH}_4\text{NO}_3} \right) \times 100 = \left( \frac{28}{80} \right) \times 100 = 35\%
\]
Answer: The percentage composition of nitrogen in ammonium nitrate is \( 35.0\% \). This corresponds to option (3).