## The Equation of State of a Mixture of Gases

The equation of state of a mixture of gases may be found by making use of Dalton's law of partial pressures which states that in a given volume V, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases, if each of the gases occupied the same volume.

Let mi, m2, m3..., mk be the masses of the k gases of molecular weights Mi, M2, M3 ..., Mk contained in a given volume V. Then, if p1 is the partial pressure of the first component, p1 V = (m1/M1) RT = n1 RT where n1 is the number of mols of the first component.

Similarly, for the second and other components, p2 V =(m2/M2)RT = n2 RT p3 V =(m3/M3)RT = n3 RT

and, so on. Adding for all the components, we have from Dalton's law p V = (m1/M1 + m2/M2+)RT = nRT and, pi = nip/(n1 + n2 + +nk) (2.4.13)

Using these relationships, it can be shown that the average molecular weight M of the mixture is given by

M =(m1 + m2 + m3+)/(m1/M1 + m2/M2 + m3/M3+) (2.4.14)