You need to know two things to solve this problem:
- That 1 mole of any ideal gas occupies 22.4 L at STP;
- The relationship between moles and molar mass
moles=mass of substancemolar mass
So, you know that the vapor weighs 0.96 g at STP. STP conditions imply a temperature of 273.15 K and a pressure of 1.0 atm. This means that the number of moles you have is
n=VVmolar=250⋅10−3L22.4 L=0.01116 moles
SIde note - you can use the ideal gas law equation, PV=nRT, to double check this result;
Since n=mMM, you get that
n=mMM=0.01116 moles
Since m=0.96 g, the value of the molar mass will be
molar mass=mn=0.96 g0.01116 moles=86.02 g/mol
Your compound's empirical formula is (CH2)x, or CxH2x. The value of x is determined by dividing the molar mass of the compound by the molar mass of the empirical formula
x=86.02 g/mol14.0 g/mol=6.14
Ideally, x should be as close to an integer as possible; in this case, the closest integer would be 6, which would make the compound's molecular mass equal to 84.0 g/mol and the molecular formula
C6H12.
Since this problem describes the Dumas method of molecular weight determination, an experimental method used to determine molar mass, you could calculate the percent error for the result
%error=|accepted value - experimental value|accepted value⋅100
%error=|84.0−86.02|84.0⋅100=2.4%
which is a relatively small percent error → the actual molecular formula is C6H12.
