Final answer:
The empirical formula of the compound is NO2. To find the molecular formula, we divide the given molecular weight (92.02 g/mol) by the empirical formula mass (46.02 g/mol), resulting in a factor of 2, giving the molecular formula N2O4.
Step-by-step explanation:
To determine the empirical formula for a compound with 30.45% nitrogen and 69.55% oxygen by weight, we first convert the percentage to grams; assuming 100 grams of the compound, we have 30.45 grams of nitrogen and 69.55 grams of oxygen. Next, we convert these masses to moles by dividing by the atomic mass of each element (N = 14.01 g/mol, O = 16.00 g/mol):
- Nitrogen: 30.45 g ÷ 14.01 g/mol = 2.174 moles
- Oxygen: 69.55 g ÷ 16.00 g/mol = 4.347 moles
To find the simplest whole number ratio, we divide by the smallest number of moles, which gives us:
- Nitrogen: 2.174 ÷ 2.174 = 1
- Oxygen: 4.347 ÷ 2.174 = 2
The empirical formula is NO2. For the molecular formula, we use the molecular weight provided, 92.02 g/mol, and divide it by the empirical formula mass (N = 14.01 g/mol, 2 O = 2 × 16.00 g/mol, total = 46.02 g/mol): 92.02 g/mol ÷ 46.02 g/mol = 2. Thus, the molecular formula is N2O4.