I just looked at my 3rd Edition of Sherwood, Reid, and Prausnitz and I don't think you need a mixture [ω] for the original Soave modification of the Redkich-Kwong EOS. You do need pure component [ω]'s to calculate F[sub]i[/sub] and F[sub]j[/sub], which are then used to calculate F[sub]m[/sub].
However, you may be using a different modification that I don't know about. Most EOS's use a vapor fraction average, except for some EOS's that are specifically for liquid mixtures, those use a volume fraction average.
If you are going to use the Soave Redlich Kwong or the Peng Robinson equation of state, you are probably best off using the usual mixing rules for those equations rather than using pseudo critical values.
Here is an outline of what I am talking about for the SRK.
a and b would be calculated at a given temperature for both benzene and toluene using their critical temperature, critical pressure, and accentric factors.
After you have a and b for both pure benzene and toluene, mixing rules can be applied to get the mixture a and b.
The usual mixing rules are linear in b and quadratic in a, although sometimes mixing rules using quadratic bs are used, especially by Prausnitz.
For the linear b / quadratic a mixing rules:
a = sum i sum j of xi * xj * aij
where aij= (1-cij)*sqrt(ai)*sqrt(aj). cij is usally close to zero.
For your 50/50 mole % benzene and toluene case, this would give, assuming cij is 0:
a = x1*x1* a1 + 2*x1*x2 * sqrt(a1) * sqrt(a2) + x2*x2*a2
a=.25 * a1 + .5 * sqrt(a1) * sqrt(a2) + .25 * a2.
b=sum i of xi*bi
For your 50/50 mole % benzene and toluene case, this would give:
b=x1*b1 + x2*b2
b=0.5*b1+0.5*b2
