When dealing with mixtures the material-dependent constants require mixing rules due to the fact that the potential number of combinations is infinite.
The most straight-forward, and theoretically sound, mixing rules apply to the virial equation.
While not as theoretically sound the terms in the cubic equations of state have the following rough meanings:
therefore:
$a_{mix} = \sum_i\sum_j y_iy_ja_{ij}$
or
$a_{mix} = \sum_i\sum_j y_iy_j[a\alpha(T)]_{ij}$
where
$a_{ij} = \sqrt{a_ia_j}$
or (for some EOS)
$a_{ij} = \sqrt{a_ia_j}(1-k_{12})$
The excluded volume is simpler (and more "correct"), given by:
$b_{mix} = \sum_i y_ib_i$
There is no theoretically sound way to adapt the concept of corresponding states. The most commonly used is Kay's Rules, which defines "pseudo-critical" properties:
$T_{r_{mix}} = \frac{T}{T_{pc}}$, for example, where
$T_{pc} = \sum_i y_iT_{c,i}$
$P_{pc} = \sum_i y_iP_{c,i}$
$\omega_{p} = \sum_i y_i\omega_i$
Write the van der Waals mixing rules and explain their functionality in terms of molecular interactions
Write the mixing rules for the virial coefficients and for pseudo-critical properties using Kay's rule
Using mixing rules to solve for P, v, and T of mixtures
A gas mixture contains 20.0 mole % CH_{4}, 30.0% C_{2}H_{6}, and the balance C_{2}H_{4}. Ten kilograms of this gas is compressed to 200 bar at 90C. What is the volume?