Empirical and Molecular Formula

Question

A compound containing only nitrogen and oxygen was found to have 25.936% nitrogen by mass and 74.064% oxygen by mass. The molecular formula has a molar mass of 216.04 g/mol.  Determine the empirical formula and the molecular formula of the compound.

Answer 1

Assume you have 100 g of the material. This way we can convert % into grams and grams into moles.

Moles N = 25.936 g N x 1 mol/14 g = 1.853 mols N

Moles O = 74.064 g O x 1 mol/16 g = 4.629 mols O

Divide both by 1.853 to try to get whole numbers

moles N = 1.853/1.853 = 1 mol N

moles O = 4.629/1.853 = 2.5 mol O

Now multiple both by 2 to get

2 moles N

5 moles O

EMPIRICAL FORMULA = N₂O₅

The molar mass of N2O5 = 208 g/mol

Since the molar mass of the molecular formula is twice that (216 g/mol) the

MOLECULAR FORMULA = N₄O₁₀

Answer 2

Consider the total amount of the compound to be 100 g, then the mass of N is 25.936g and 74.064g for O. 

Divide each of these masses by the corresponding atomic mass.

25.936g/14.007g/mol for N and 74.064g/15.999g/mol for O to get 1.8516 for N and 4.6293 for O.

Divide each of the resulting numbers by the smallest result to get N=1 and O=2.5.

Multiply those numbers by 2 to get the smallest whole numbers N= 2 and O= 5.

The empirical formula is N2O5.

Divide the molar mass given for the compound (216.04)  by the mass determined by the empirical formula mass 108.009 = 2.000. Multiply the subscripts of the empirical formula by 2.000 to get N4O10.

Verify this is correct by calculating the molecular mass of N4O10  = 216.02 which is close enough to the molecular formula given in the problem.