EoS: Equations of State for Mixtures

Equations of State for Mixtures

When dealing with mixtures the material-dependent constants require mixing rules due to the fact that the potential number of combinations is infinite.

Virial Equation for Mixtures

The most straight-forward, and theoretically sound, mixing rules apply to the virial equation.

Cubic EOS for Mixtures

While not as theoretically sound the terms in the cubic equations of state have the following rough meanings:


$a_{mix} = \sum_i\sum_j y_iy_ja_{ij}$


$a_{mix} = \sum_i\sum_j y_iy_j[a\alpha(T)]_{ij}$


$a_{ij} = \sqrt{a_ia_j}$

or (for some EOS)

$a_{ij} = \sqrt{a_ia_j}(1-k_{12})$

The excluded volume is simpler (and more "correct"), given by:

$b_{mix} = \sum_i y_ib_i$

Corresponding States for Mixtures

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

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?