To find the percent by mass of each element in the compound [tex]\(NH_4NO_3\)[/tex], we will follow these steps:
1. Find the molar mass of each element:
- Nitrogen (N) has a molar mass of 14.01 g/mol.
- Hydrogen (H) has a molar mass of 1.01 g/mol.
- Oxygen (O) has a molar mass of 16.00 g/mol.
2. Calculate the molar mass of [tex]\(NH_4NO_3\)[/tex]:
The compound [tex]\(NH_4NO_3\)[/tex] has the formula consisting of:
- 2 Nitrogens ([tex]\(N\)[/tex])
- 4 Hydrogens ([tex]\(H\)[/tex])
- 3 Oxygens ([tex]\(O\)[/tex])
Therefore, its molar mass is calculated as follows:
[tex]\[
\text{Molar mass of } NH_4NO_3 = (2 \times 14.01) + (4 \times 1.01) + (3 \times 16.00)
\][/tex]
This simplifies to:
[tex]\[
\text{Molar mass of } NH_4NO_3 = 28.02 + 4.04 + 48.00 = 80.06 \text{ g/mol}
\][/tex]
3. Calculate the percent by mass of each element in [tex]\(NH_4NO_3\)[/tex]:
- Percent by mass of Nitrogen ([tex]\(\%\text{N}\)[/tex]):
[tex]\[
\%\text{N} = \left(\frac{2 \times 14.01}{80.06}\right) \times 100 \approx 35 \%
\][/tex]
- Percent by mass of Hydrogen ([tex]\(\%\text{H}\)[/tex]):
[tex]\[
\%\text{H} = \left(\frac{4 \times 1.01}{80.06}\right) \times 100 \approx 5.0 \%
\][/tex]
- Percent by mass of Oxygen ([tex]\(\%\text{O}\)[/tex]):
[tex]\[
\%\text{O} = \left(\frac{3 \times 16.00}{80.06}\right) \times 100 \approx 60 \%
\][/tex]
Therefore, the percent by mass of each element in [tex]\(NH_4NO_3\)[/tex] is:
[tex]\[
\begin{array}{l}
\% N = 35.0 \% \\
\% H = 5.0 \% \\
\% O = 60.0 \%
\end{array}
\][/tex]
