The cubic equations of state are widely adopted by combustion and CFD communities due to their simplicity. The general form of the cubic equation of state can be expressed as
 | (2–58) |
In the above equation, 
is the molecular volume in cm3/mole. Five
different models of the cubic equation of state are available in Ansys Chemkin: van der Waals,
Redlich-Kwong, Soave, Aungier, and Peng-Robinson. The model parameters a, b, c, u, and w are functions
of critical temperature 
, critical pressure 
, reduced temperature 
, and the Pitzer acentric factor 
; and their expressions are given in Table 2.1: Parameters of the cubic equation of state models.
Table 2.1: Parameters of the cubic equation of state models
| Cubic EOS | u | w | a | b | c |
| van der Waals | 0 | 0 |  and  |
| 0 |
| Redlich-Kwong | 1 | 0 |  where  |
| 0 |
| Soave-Redlich- Kwong | 1 | 0 |  where
and |
| 0 |
| Aungier-Redlich- Kwong [12] | 1 | 0 |
where and |
|
|
| Peng-Robinson | 2 | -1 |
where and |
| 0 |
The expansion of the equation of state from a single real-gas species to a mixture of
real-gas species generally requires the use of a mixing rule. A mixing rule describes the
construction of mixture properties/parameters from those of pure substance components. In
general, there are two approaches to obtain the properties (P, V, or T) of a real-gas mixture: the single-fluid approach and the multi-fluid
approach. In the single-fluid approach, the real-gas mixture is treated as a pseudo-real
gas species. The parameters in the equation of state or the critical properties (used to
compute the equation of state parameters) are "mixed" first to create the
corresponding equation of state parameters of the pseudo-mixture species. The P-V-T relationship of the real- gas mixture is then determined by
the equation of state of this pseudo-mixture species. Alternatively, the multi-fluid
approach does not employ the concept of a pseudo-mixture species. The partial pressure,
molar volume, or temperature (
, 
, or 
) of a real-gas species component is determined by its respective
equation of state. The P, V, or Tof the real-gas mixture will be the
mole-fraction-weighted sum of 
, 
, or 
of all real-gas components.
The equation of state parameters or critical properties of a real-gas mixture are related to those of an individual real-gas component via a mixing rule, such as
 | (2–59) |
The interaction between the components 
can be determined by imposing a combining rule. The combining rule can
be as simple as an arithmetic or a geometric mean
The pseudocritical method treats the real-gas mixture as a pseudo real-gas species
of which the pseudocritical pressure 
and pseudocritical temperature 
are computed from the corresponding critical properties of its
components. For the pseudocritical temperature (pseudocritical compressibility factor
and pseudocritical volume), a simple mole-fraction-weighted sum (Kay's rule [13]) is applied:
 | (2–60) |
For the pseudocritical pressure, the modified Prausnitz and Gunn [13] combination is used:
 | (2–61) |
The mixture acentric factor is given by
 | (2–62) |
The commonly used mixing rule for the cubic equation of state is the single-fluid mixing rule of van der Waals:
 | (2–63) |
 | (2–64) |
 | (2–65) |
For hydrocarbon pairs, the binary interaction coefficient 
is usually zero.
The biggest limitation of the van der Waals mixing rule is that all components of
the real-gas mixture must use the same form of equation of state. For many species,
especially intermediates and radicals, the critical properties are not readily
available and the ideal gas equation of state must be used (that is, 
in Equation 2–59
and 
).