Final answer:
The molecular formula of the compound is C4H8N2O4.
Step-by-step explanation:
To determine the molecular formula of the compound, we need to find the empirical formula first. The empirical formula gives the simplest whole number ratio of atoms in a compound. To find the empirical formula, we assume 100 g of the compound, which means we have 49.48 g of carbon, 5.19 g of hydrogen, 28.85 g of nitrogen, and 16.48 g of oxygen. We can convert these masses to moles by dividing by their respective molar masses:
Carbon: 49.48 g * (1 mol/12.01 g) = 4.12 mol
Hydrogen: 5.19 g * (1 mol/1.01 g) = 5.14 mol
Nitrogen: 28.85 g * (1 mol/14.01 g) = 2.06 mol
Oxygen: 16.48 g * (1 mol/16.00 g) = 1.03 mol
We then divide these moles by the smallest number of moles to get the simplest whole number ratio:
Carbon: 4.12 mol / 2.06 mol = 2
Hydrogen: 5.14 mol / 2.06 mol = 2
Nitrogen: 2.06 mol / 2.06 mol = 1
Oxygen: 1.03 mol / 1.03 mol = 1
The empirical formula of the compound is CH2NO. The molar mass of this empirical formula is calculated as:
(12.01 g/mol * 2) + (1.01 g/mol * 2) + (14.01 g/mol * 1) + (16.00 g/mol * 1) = 45.04 g/mol
To find the molecular formula, we divide the molar mass of the compound (194.19 g/mol) by the molar mass of the empirical formula (45.04 g/mol): 194.19 g/mol / 45.04 g/mol = 4.32
Rounding to the nearest whole number, the molecular formula of the compound is C4H8N2O4.