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

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.

Answer 2

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