Molecular Formula of gas?

Question

For a certain gas that contains only carbon and hydrogen the mass percentage of carbon is known to be 85.62
It is also known that 2.58 g of the gas has a volume of 1.00 L and a pressure of 0.980 atm at 51.0 oC.
What is the molecular formula for the gas ?

Answer 1

First you have to find the empirical formula.
The compound has only C and H, so the percentage of H is 100-85.62= 14.38%
Divide each percentage by the respective atomic mass
C: 85.62/12 =7.135
H: 14.38/1= 14.38
Divide with the smallest number
C: 7.135/7.135=1
H: 14.38/7.135=2.01=2

Therefore the empirical formula is CH2. This means that the molecular formula is (CH2)x or CxH2x and the moleular weight
MW=12x+2x=14x. We need to find x in order to find the molecular formula.

PV=nRT and since n=mass/MW
PV=massRT/MW= massRT/14x =>
x=massRT/(14PV) =>
x =2.58*0.082*324 / (14*0.98*1)= 4.99=5
Therefore the gas is C5H10