To determine the empirical formula of a compound given the percentages of carbon (C), hydrogen (H), and nitrogen (N), we follow a series of steps:
1. Convert the percentages to masses: Assume we have 100 grams of the compound. Therefore, the masses of C, H, and N are:
- Carbon: 38.8 grams
- Hydrogen: 16.2 grams
- Nitrogen: 45.1 grams
2. Convert the masses to moles: Use the atomic masses of each element to convert the masses to moles.
- Atomic mass of Carbon ([tex]\(C\)[/tex]): 12.01 g/mol
- Atomic mass of Hydrogen ([tex]\(H\)[/tex]): 1.008 g/mol
- Atomic mass of Nitrogen ([tex]\(N\)[/tex]): 14.01 g/mol
Calculating moles:
[tex]\[
\text{Moles of C} = \frac{38.8 \text{ g}}{12.01 \text{ g/mol}} \approx 3.23 \, \text{moles}
\][/tex]
[tex]\[
\text{Moles of H} = \frac{16.2 \text{ g}}{1.008 \text{ g/mol}} \approx 16.07 \, \text{moles}
\][/tex]
[tex]\[
\text{Moles of N} = \frac{45.1 \text{ g}}{14.01 \text{ g/mol}} \approx 3.22 \, \text{moles}
\][/tex]
3. Determine the mole ratio of the elements: Divide the moles of each element by the smallest number of moles obtained.
- For C:
[tex]\[
\frac{3.23}{3.22} \approx 1
\][/tex]
- For H:
[tex]\[
\frac{16.07}{3.22} \approx 5
\][/tex]
- For N:
[tex]\[
\frac{3.22}{3.22} \approx 1
\][/tex]
4. Write the empirical formula: The ratio of C:H:N is approximately 1:5:1.
So, the empirical formula of the compound is [tex]\( \boxed{CH_5N} \)[/tex].
