Using the Ideal Gas Law to Calculate Gas Densities and Molar Masses

The ideal gas law can also be used to calculate molar masses of gases from experimentally measured gas densities. To see how this is possible, we first rearrange the ideal gas law to obtain

The left side has the units of moles per unit volume (mol/L). The number of moles of a substance equals its mass (m , in grams) divided by its molar mass (M , in grams per mole):

Substituting this expression for n into Equation gives

Because m/V is the density d of a substance, we can replace m/V by d and rearrange to give

The distance between particles in gases is large compared to the size of the particles, so their densities are much lower than the densities of liquids and solids. Consequently, gas density is usually measured in grams per liter (g/L) rather than grams per milliliter (g/mL).