the average density [itex]\rho_{av}[/itex] of a gas mixture of A , B is to be calculated as follows:
[tex] \rho_{av} \ = \ \chi (A) \cdot \rho_{pure}(A) \ + \ \chi (B) \cdot \rho_{pure}(B) [/tex]
besides that, your thoughts as represented by the paper are a little hard to follow, but seem ok to me
nevertheless, you should keep in mind that the final dimension of your Kp should be [atm] in this case: the result is not a scalar (as shown)
regards
Ingo