The molar mass of a gas can be derived from the ideal gas law, #PV = nRT#, by using the definition of molar mass to replace #n#, the number of moles.
Molar mass is defined as the mass of a substance occupied by exactly #6.022 * 10^23# of that respective gas' atoms (or molecules). Since we know that #6.022*10^23# represents Avogadro's number, and is the equivalent of 1 mole, we can describe molar mass as being equal to
#M = m/n#, where
#m# - the gas' mass in grams;
#n# - the number of moles of gas;
We can therefore write that #n = m/M#, which can be used in the ideal gas law equation to get the value of the gas' molar mass
#PV = m/M * RT =>M = (m RT)/(PV)#, so
#M = m * (RT)/(PV)#
Here's an example of how this would look in a problem:
An unknown gas has a mass of 153 g and occupies 15.0 L at a temperature of 300.0 K and a pressure of 2.00 atm. What is its molar mass?
#M = 153g * (0.082 (L * atm)/(K * mol) * 300.0K)/(2.00atm * 15.0L) = 125# #"g/mol"#
