Molecular Formula

Question

Histamine has the following percent composition: 54% C, 8.1% H, 37.9% N. The molar mass of the entire compound is 111 g/mol. what is the molecular formula of histamine?

Answer 1

When given problems that present the % composition, it is easiest to just assume 100 g of material, and calculate based on that.  Thus, in 100 g of the material, you have....

54g C = 54 g C x 1 mol/12 g = 4.5 moles C

8.1 g H = 8.1 g H x 1 mol/1 g = 8.1 moles H

37.9 g N = 37.9 g N x 1 mol/14 g = 2.7 moles N

Dividing by the smallest (2.7) in order to get whole numbers, we end up with ...

4.5 moles C/2.7 = 1.67 moles C

8.1 moles H/2.7 = 3 moles H

2.8 moles N/2.7 = 1 mole N

To get 1.67 to a whole number, we multiply by 3, and then multiply the others by 3 also.

C = 1.67 x 3 = 5 moles C

H = 3 x 3 = 9 moles H

N = 1 x 3 = 3 moles N

Empirical formula = C₅H₉N₃

Formula weight of C₅H₉N₃ = (5x12) + (9x1) + (3x14) = 60 + 9 + 42 = 111 g/mole

Since this is the same as the molar mass for the molecular formula, then this is the molecular formula, i.e. the molecular formula for histamine is C₅H₉N₃