Analysis of a sample of a compound, containing only carbon, nitrogen, hydrogen, and oxygen, determined that it contained 20.0% C, 6.7% H, 46.6% N and the balance O. What is the empirical formula of the compound?

CH₄N₂O

Explanation:

Let's assume 100 g of the compound, thus, the mass of each substance is it percent multiplied by 100:

C = 20.0 g (20% = 0.20, and 0.20*100 = 20.0)

H = 6.7 g

N = 46.6 g

O = 100 - (20+6.7+46.6) = 26.7 g

The number of moles of each compound is the mass divided by the molar mass. The molar masses are C = 12.011 g/mol, H = 1.00794 g/mol, N = 14.01 g/mol, and O = 15.999 g/mol, so:

nC = 20/12.011 = 1.67 mol

nH = 6.7/1.00794 = 6.65 mol

nN = 46.6/14.01 = 3.33 mol

nO = 26.7/15.999 = 1.67 mol

The empirical formula is the formula with the minimum possible number of the moles of each compound, which must be proportional to the percent of each one. So, we must divide each number of moles for the smallest, 1.67:

C = 1.67/1.67 = 1

H = 6.65/1.67 = 4

N = 3.33/1.67 = 2

O = 1.67/1.67 = 1

So, the empirical formula is CH₄N₂O.