Find the apparent gas constant of an ideal gas mixture consisting of 2 kmol of N2 and 4 kmol of CO2

Gas constant = 0.499 kJ/kg. K

Explanation:

n = number of moles

nN2 = 2 kmol

nCO2 = 4 kmol

Total number of moles = 2 + 4 = 6 kmol of mixture

let y be the mole fractions of the mixture:

yN2 = number of moles of N2/total number of moles = 2/6 = 0.33 kmol/kmol

yCO2 = number of moles of CO2/total number of moles = 4/6 = 0.67 kmol/kmol

The molar mass of an ideal gas mixture is defined by the mass of mixture divided by the total number of moles of the mixure:

We assume there is 100 kg of the gas mixture if the mass is not given.

Therefore:

Molar mass of mixture = mass of mixture/total moles of mixture = 100kg/6kmol = 16.67kg/kmol

The gas constant of a mixture is defined as the universal gas constant (ideal gas constant = 8.314 kJ/kmol. K) divided by the molar mass of the mixture.

Therefore:

The gas constant of the mixture = 8.314kJ/kmol. K/16.67kg/kmol = 0.499 kJ/kmol. K