To determine the empirical formula of a compound, follow these steps:
1. Determine the mass of each element in the compound:
- Carbon (C): 72.0 g
- Hydrogen (H): 18.0 g
- Nitrogen (N): 28.0 g
2. Find the molar mass (atomic weight) of each element:
- Molar mass of C: 12.01 g/mol
- Molar mass of H: 1.008 g/mol
- Molar mass of N: 14.01 g/mol
3. Convert the mass of each element to moles by using the formula:
[tex]\[
\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}
\][/tex]
- Moles of C:
[tex]\[
\text{Moles of C} = \frac{72.0 \text{ g}}{12.01 \text{ g/mol}} \approx 5.996 \text{ mol}
\][/tex]
- Moles of H:
[tex]\[
\text{Moles of H} = \frac{18.0 \text{ g}}{1.008 \text{ g/mol}} \approx 17.857 \text{ mol}
\][/tex]
- Moles of N:
[tex]\[
\text{Moles of N} = \frac{28.0 \text{ g}}{14.01 \text{ g/mol}} \approx 1.998 \text{ mol}
\][/tex]
4. Determine the simplest mole ratio by dividing all moles by the smallest number of moles calculated:
- The smallest number of moles is approximately 1.998 (moles of N).
- Ratio of C:
[tex]\[
\frac{5.996}{1.998} \approx 3
\][/tex]
- Ratio of H:
[tex]\[
\frac{17.857}{1.998} \approx 8.942 \approx 9
\][/tex]
- Ratio of N:
[tex]\[
\frac{1.998}{1.998} = 1
\][/tex]
5. These ratios represent the subscripts in the empirical formula:
The ratio of C:H:N is approximately 3:9:1.
Therefore, the empirical formula of the compound is [tex]\( C_3H_9N \)[/tex].
The correct answer is:
(C) [tex]\( C_3H_9N \)[/tex]
