The virial equation for a binary mixture is 

Here B₁₁ and B₂₂ are the second virial coefficients for pure species 1 and pure species 2, respectively, and B₁₂ is the cross second virial coefficient. For a binary mixture

a. Obtain an expression for the fugacity coefficient of a species (Eq. 9.4-6).

b. Show that the activity coefficient for species 1 is

where δ₁₂ = 2B₁₂ − B₁₁ − B₂₂. 

c. Generalize the results in part (b) to a multicomponent mixture

with PV RT 1+ Bmix V + Bmix = yB1 + y2B22 + 2y1y2B12