Gas mixtures and the ideal gas law, mass calculations, the individual gas constant and density.
Mixture of gases are common in many applications. Our most common example is air - mainly consisting of nitrogen, oxygen and water vapor - as moist air. A combustion gas with nitrogen, water vapor and carbon dioxide is an other example.
Special care must be taken for gas mixtures when using the ideal gas law, calculating the mass, the individual gas constant or the density.
The Ideal Gas Law for a Gas Mixture
The Ideal Gas Law for a perfect or ideal gas adapted for a gas mixture:
p V = mm Rm T (1)
p = absolute pressure in the mixture (N/m2, lb/ft2)
V = volume of the mixture(m3, ft3)
mm = mass of the mixture (kg, lb)
Rm = the individual gas constant for the mixture (J/kg K, ft lb/slugs oR)
T = absolute temperature in the mixture (oK, oR)
The Mass of a Gas Mixture
The mass of a gas mixture can be expressed as:
mm = m1 + m2 + .. + mn (2)
m1 + m2 + .. + mn = the mass of each gas component in the mixture
The Individual Gas Constant of a Gas Mixture
The individual gas constant of a gas mixture can be calculated as:
Rm = (R1 m1 + R2 m2 + .. + Rn mn) / (m1 + m2 + .. + mn ) (3)
The Density of a Gas Mixture
The density of a gas mixture can be calculated as:
ρm = (ρ1 v1 + ρ2 v2 + .. + ρn vn) / (v1 + v2 + .. + vn ) (4)
ρm = density of the gas mixture (kg/m3, lb/ft3)
ρ1 .. ρn = density of each of the components (kg/m3, lb/ft3)
v1 + v2 + .. + vn = volume share of each of the components (m3, ft3)