Stat-mech: Quadratic composition dependence

[maistral]

I am quite unsure where to post this, as I am a chemical engineer and that I am working with phase equilibrium. My issue however is regarding statistical mechanics, thus me posting my problem here.

I keep on encountering that the second virial coefficient of a mixture must be quadratically composition-dependent, and that it is stipulated in statistical mechanics that it must be so.

May I know what, why, or where did this 'stipulation from statistical mechanics' come from?

 

[Chestermiller]

Since the 2nd viral coefficient relates to the effects of binary interactions between molecules, doesn't. it make sense that it should be quadratically composition-dependent?

 

[maistral]

Since the 2nd viral coefficient relates to the effects of binary interactions between molecules, doesn't. it make sense that it should be quadratically composition-dependent?

I honestly thought there was a 'deeper meaning' to this, lol. So this basically (and literally) means the 1-1, 1-2, 2-1, and 2-2 interactions.

Thanks!