1. Definitions

Residual properties for a given thermodynamic property \(M\) are defined as

\[M = M^\text{IG} + M^\text{R}\]

where \(M^\text{IG}\) is the value of the property in the ideal gas state and \(M^\text{R}\) is the residual value of the property.

More information on residual properties can be found in standard texts [SVanNessA05]

We define partial molar property \(\bar{M}_i\) of species i in a mixture as

(1)\[\bar{M}_i = \left(\frac{\partial(nM)}{\partial n_i}\right)_{P, T, n_j}\]

The mixture property is related to the partial molar property as

\[nM=\sum_i n_i\bar{M}_i\]

or, in terms of gas-phase mole fractions \(y_i\),

\[M=\sum_i y_i\bar{M}_i\]

The following relationships also hold

(2)\[\bar{M}_i = \bar{M}^\text{IG} + \bar{M}^\text{R}\]

(3)\[M^\text{R} = \sum_i y_i\bar{M}^\text{R}\]

1.1. Nomenclature

Code	Symbol	Description
P	\(P\)	Pressure in Pa
V	\(V\)	Molar Volume in \(\text{m}^3/\text{mol}\)
R	\(R\)	gas constant SI units (\(\text{m}^3\times\text{Pa}/\text{mol}/\text{K}\))
T	\(T\)	temperature in K
T_c	\(T_\text{c}\)	critical temperature in K
P_c	\(P_\text{c}\)	critical pressure in Pa
T_r	\(T_\text{r}\)	reduced temperature (dimensionless)
V_c	\(V_\text{c}\)	Critical volume \(\text{m}^3/\text{mol}\)
w	\(\omega\)	Accentric factor
y_i	\(y_i\)	mole fraction of component i
–	\(n_i\)	number of moles of component i