What is the empirical formula of a substance that is 53.5% carbon (c), 15.5% hydrogen (h), and 31.1% nitrogen (n) by weight?

Empirical formula is the simplest ratio of whole numbers of components making up a compound.

since percentage compositions have been given, we can calculate the masses of elements in 100 g of the compound

carbon hydrogen nitrogen

mass 53.5 g 15.5 g 31.1 g

number of moles 53.5/12 15.5/1 31.1 / 14

= 4.46 = 15.5 = 2.22

divide by least number of moles

4.46/2.22 = 2.0 15.5/2.22 = 6.9 2.22/2.22 = 1

numbers rounded off

C - 2

H - 7

N - 1

Then empirical formula - C₂H₇N

Assuming 100 grams of the compound, we can convert the masses to the number of moles using the atomic masses:

53.5 g * 1 mol C / 12.0107 g C = 4.45 mol C

15.5 g * 1 mol H / 1.00794 g H = 15.38 mol H

31.1 g * 1 mol N / 14.0067 g N = 2.22 mol N

We divide the number of moles of each element by the lowest number of moles, in this case, we divide by 2.22:

C 4.45/2.22 = 2.00

H 15.38/2.22 = 6.93 ≈ 7

N 2.22/2.22 = 1

Therefore we can write the empirical formula using the number of moles calculated as the subscript for each element: C2H7N