Question

The density of an unknown gas is found to be 4.12 g/L at standard temperature and pressure (STP). What is the molar mass of this gas?

Answer 1

The   molar  mass of this gas  is  92.3 g/mol

  Calculation

By  use  ideal gas  equation PV =nRT  where
n=mole  p=pressure V= volume R =  gas constant  T=  temperature

n =  mass /molar  mass(MM)
substitute in the equation

PV =(mass/MM)RT
mass = density  x  volume(V)

Therefore  PV =(density xV/ MM) xRT

divide both side by  by V

P=  (density/Mm) xRT

making MM  the subject  of the formula

MM = densityPRT

At  STP = P= 1 atm,  R=  0.0821 L.atm/Mol.k  T =  273 K

MM is therefore = 4.12 g/l x   1 atm x 0.081  L.atm/mol.k  x    273 K = 92.3 g/mol

Answer 2

At standard temperature and pressure, 1 mole of any gas occupies 22.4 litres. We need to find the number of grams in 22.4 litres of the unknown gas.

4.12 g/L * 22.4 = 92.288. 

92.288 or 92 grams are in one mole of the gas making the molar mass 92 g/mole.