Derive an expression for the molar mass of a gas starting with its density?

The relationships between molar mass and density for a monoatomic gas can be easy.  

The Ideal Gas Law, PV = nRT can be arranged so that n moles equals the mass/molar mass of the gas to become,

PV =  

M

mRT

where m is the mass and M is the molar mass.

M =  

PV

mRT

, if you hold the temperature of the gas constant the equation reduces to the Boyle's law or  

PV

m

The mass will be constant assuming the container is closed and so the gas cannot be escaped so, PV will be constant.  

D =  

V

m

 and M =  

PV

mRT

M =  

P

DRT

The higher the density of the gas the higher the molar mass and vice versa.

Explanation:

frequency, z, and the collision density, z, in carbon dioxide (co2), r 180 pm at 30 °c and 120 kpa