Question

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?

Answer 1

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

Answer 2

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