First change percent to mass. If there was 100 grams of the sample, there would be 100 grams.
So 87.4 % nitrogen would be 87.4 grams of nitrogen.
To find the moles of nitrogen divide the mass of 87.4 grams by the molar mass of nitrogen 14 grams/ mole This gives
100 grams - 87.4 grams = 12.6 grams this would be the mass of Hydrogen. To find the moles of Hydrogen divide the mass of 12.6 by the molar mass of hydrogen.
To find the ratio of Nitrogen to Hydrogen in the empirical formula divide the moles of Hydrogen by the moles of Nitrogen
# 12.6/6.24 = 2.0 Hydrogen atoms: 1.0 Nitrogen atoms.
It would be helpful if the mass was given for the gas. Calculating the new volume using the combined gas law looks like this.
V_2 = .68 liters.
So the new density at STP is .997 grams/.68 liters. which reduces to
1.47 grams / l liter changing this to the molar volume at STP gives
1.47 x 22.4 = 32.8 grams per mole. Dividing the grams per mole by the grams per empirical formula of