A gas is composed of 30.4%N and 69.6%O. Its density is 11.1 g/L at -20°C and 2.50 atm. What are the empirical and molecular formulas of the gas?

Answer 1

Assume you have 100 g of the unknown gas:

30.4 g N x 1 mol N / 14 g = 2.171 mols N

69.6 g O x 1 mol O / 16 g = 4.35 mols O

Ratio of O to N = 2 to 1

Empirical formula = NO₂

Molar mas NO₂ = 46 g / mol

To find the molecular formula, we need to first find the molar mass of the unknown gas:

PV = nRT and we assume a volume of 1 liter

n = PV/RT = (2.50 atm)(1 L) / (0.0821 Latm/Kmol)(253K)

n = 0.120 moles

Molar mass = g / moles = 11.1 g / 0.120 moles

Molar mass = 93.3 g / mol

Molecular formula:

Dividing molar mass of unknown by molar mass of empirical we have 93.3 / 46 = 2

Molecular formula = N₂O₄