What is the empirical formula for a compound containing 38.8 g of carbon, 16.2 g of hydrogen, and 45.1 g of nitrogen?

To find the empirical formula for the compound containing 38.8g of carbon, 16.2g of hydrogen, and 45.1g of nitrogen, follow these steps:

1. Determine the molar masses of each element:
- Carbon (C): approximately 12.01 grams per mole.
- Hydrogen (H): approximately 1.008 grams per mole.
- Nitrogen (N): approximately 14.01 grams per mole.

2. Convert the mass of each element to moles:
- For carbon:
[tex]\[
\text{Moles of Carbon} = \frac{38.8 \text{ g}}{12.01 \text{ g/mol}} \approx 3.23 \text{ moles}
\][/tex]
- For hydrogen:
[tex]\[
\text{Moles of Hydrogen} = \frac{16.2 \text{ g}}{1.008 \text{ g/mol}} \approx 16.07 \text{ moles}
\][/tex]
- For nitrogen:
[tex]\[
\text{Moles of Nitrogen} = \frac{45.1 \text{ g}}{14.01 \text{ g/mol}} \approx 3.22 \text{ moles}
\][/tex]

3. Determine the simplest ratio of moles between the elements:
- Divide the number of moles of each element by the smallest number of moles calculated among them:
[tex]\[
\text{Ratio for Carbon} = \frac{3.23}{3.22} \approx 1
\][/tex]
[tex]\[
\text{Ratio for Hydrogen} = \frac{16.07}{3.22} \approx 5
\][/tex]
[tex]\[
\text{Ratio for Nitrogen} = \frac{3.22}{3.22} \approx 1
\][/tex]

4. Write the empirical formula:
- Each element's ratio gives the subscript in the empirical formula, yielding:
[tex]\[
\text{Empirical formula: } \text{CH}_5\text{N}
\][/tex]

Thus, the empirical formula for the compound is [tex]$ \text{CH}_5\text{N} $[/tex].