Final answer:
The empirical formula of a compound that is 30.4% nitrogen is NO₂, as it is comprised of 1 nitrogen atom to every 2 oxygen atoms when calculating the moles of each element based on their molar masses and obtaining a simple whole number ratio.
Step-by-step explanation:
To find the empirical formula of a compound that is 30.4% nitrogen by weight, we need to calculate the moles of nitrogen and oxygen in the sample. Since the sample contains only nitrogen and oxygen, the remaining 69.6% must be oxygen by weight.
Assuming we have 100 grams of the compound (for simplicity), we would have 30.4 grams of nitrogen and 69.6 grams of oxygen. Using the molar masses of nitrogen (approximately 14.01 g/mol for N) and oxygen (approximately 16.00 g/mol for O), we can calculate the moles of each:
- Moles of N = 30.4 g / 14.01 g/mol ≈ 2.17 mol
- Moles of O = 69.6 g / 16.00 g/mol ≈ 4.35 mol
To find the simplest whole number ratio, we divide each by the smaller number of moles:
- Ratio of N = 2.17 mol / 2.17 ≈ 1
- Ratio of O = 4.35 mol / 2.17 ≈ 2
Thus, the resulting ratio is 1 nitrogen atom to 2 oxygen atoms, so the empirical formula is NO₂.