It is unclear how you would use any of the non-ideal gas expressions for mixtures (since we have material-dependent quantities like $\omega$, B, a, b, etc. in each of them. How do we know which material to base these constants on?).

A variety of empirical (experience-based) rules have been developed for several of the non-ideal approaches. We will only discuss the one for the compressibility factor -- Kay's Rule -- as this has the most transparent connect with theory.

**Kay's Rule** uses pseudo-critical properties to calculate
pseudo-reduced quantities that are then used in the generalized
compressibility charts.

T'_{c} =
y_{A}T_{cA}+y_{B}T_{cB}+...

P'_{c} =
y_{A}P_{cA}+y_{B}P_{cB}+...

$\hat V_r'[ideal] = \frac{\hat V}{RT'_c/P'_c}$

Using the same procedure as with single-component systems, you can then get the pseudo-reduced quantities and obtain the (generalized) compressibility factor off of a chart.

Use equations of state for mixtures of non-ideal gases.

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?