# Derive the formula of a substance containing 93.75% – carbon and 6.25% – hydrogen, if the vapor

Derive the formula of a substance containing 93.75% – carbon and 6.25% – hydrogen, if the vapor density of this substance in the air is 4.41.

Given:

w% (C) = 93.75%

w% (H) = 6.25%

D (air) = 4.41

Find:

Formula -?

Solution:

1) Find the molecular weight of a compound by its density in air:

D (air) = Mr (HC): Mr (air), – since air does not have a certain molecular weight, it is conventionally taken as 29.

Mr (HC) = D (air) * Mr (air) = 4.41 * 29 = 128

2) Knowing the mass fraction of carbon, we find its molecular weight in the composition and the number of atoms:

128 – 100%

x – 93.75%

then x = 93.75% * 128: 100% = 120

N (C) = 120: Mr (C) = 120: 12 = 10 atoms.

3) Then the molecular weight of hydrogen accounts for 128 – 120 = 8.

N (H) = 8: Mr (H) = 8: 1 = 8 atoms.

We got a substance with the formula C10H8 – dekine or decadiene, depending on which class of hydrocarbons was considered. 