# Non-Ideal Gas Mixtures

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.

##### DEFINITION

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

T'c = yATcA+yBTcB+...
P'c = yAPcA+yBPcB+...
$\hat V_r'[ideal] = \frac{\hat V}{RT'_c/P'_c}$

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.

##### Outcome:

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

##### Test Yourself

A gas mixture contains 20.0 mole % CH4, 30.0% C2H6, and the balance C2H4. Ten kilograms of this gas is compressed to 200 bar at 90C. What is the volume?