Final answer:
The molecular formula of the organic compound with the given percent composition and molar mass of 60 g/mol is CH₄N₂O. This was determined by converting the given percentages into masses, finding the mole ratio of the elements, and ensuring the molar mass matches with the empirical formula mass.
Step-by-step explanation:
Finding the Molecular Formula
To find the molecular formula of the organic compound mentioned, first, the percentages are converted to masses using the molar mass of the compound. Since the compound has a molar mass of 60 g/mol, the percentage composition by mass allows us to deduce the mass of each element in one mole of the substance:
- Carbon (C): 20.0% of 60 g/mol = 12.0 g/mol
- Hydrogen (H): 6.66% of 60 g/mol = 4.0 g/mol
- Nitrogen (N): 47.33% of 60 g/mol = 28.4 g/mol
- Oxygen (O): the rest (100% - the sum of other percentages) = 15.6 g/mol
These masses can be divided by the respective atomic masses (C = 12 g/mol, H = 1 g/mol, N = 14 g/mol, O = 16 g/mol) to find the mole ratio of the elements within the compound:
- C: 12.0 g/mol ÷ 12 g/mol = 1 mol
- H: 4.0 g/mol ÷ 1 g/mol = 4 mol
- N: 28.4 g/mol ÷ 14 g/mol = 2 mol
- O: 15.6 g/mol ÷ 16 g/mol = 0.975 mol (approximately 1 mol)
The mole ratios suggest the empirical formula of the compound is CH₄N₂O. With this empirical formula, we can find the empirical formula mass (CH₄N₂O = 60 g/mol). Since the molar mass provided for the compound is also 60 g/mol, the empirical formula is the same as the molecular formula. Therefore, the molecular formula of the compound is CH₄N₂O.