3. Partial Molar Properties¶
We define partial molar property \(\bar{M}_i\) of species i in a mixture as
The mixture property is related to the partial molar property as
or, in terms of gas-phase mole fractions \(y_i\),
The following relationships also hold
3.1. Ideal Gas¶
The Gibbs theorem is
A partial molar property (other than volume) of a contituent species in an ideal-gas mixture is equal to the corresponding molar property of the species as a pure ideal gas at the mixture temperature but at a pressure equal to its partial pressure in the mixture
The partial molar volume of an ideal gas, \(\bar{V}_i^\text{IG}\), is
The partial molar enthalpy of an ideal gas, \(\bar{H}_i^\text{IG}\), is
which results from the enthalpy of an ideal gas being independent of pressure. Therefore, we can compute the ideal gas partial molar enthalpy if we have the ideal gas heat capacities, as follows
where \(T_\text{ref}\) is a reference temperature and \(T^\prime\) is a dummy variable for integration. Often times, we want to compute these quantities in dimensionless units,
or
where
is a dimensionless variable and
is a dimensionless parameter that is a function of \(T^\star\).
We note that the thermodynamic integration reference temperature does not have to be the same as the temperature for scaling, but we have made them the same here for simplicity.
Todo
Implement ideal gas partial molar entropy?? Implement ideal gas partial molar free energy?? This might not be useful though because these values seem to depend on mixture properties
3.2. Residual¶
The residual partial molar volume of component i, \(\bar{V}_i^\text{R}\), can be calculated as
Defining the dimensionless quantity
The expression in dimensionless units can be simplified to
The residual partial molar enthalpy of component i, \(\bar{H}_i^\text{R}\), can be calculated as
Defining the dimensionless quantity
The expression in dimensionless units is computed as
The residual partial molar free energy of component i, \(\bar{G}_i^\text{R}\), which defines the fugacity coefficient \(\hat{\phi}_i\), is
With these definitions, however, we note that we need an equation of state to calculate the partial molar properties. In this package, the second-order virial equation of state currently implements the necessary derivatives.
-
class
realgas.partial_molar_properties.
Mixture
(cp_args: List[dict], ideal=True, **kwargs)[source]¶ - Parameters
ideal (bool, optional) – whether or not ideal gas, defaults to True
kwargs – key-word arguments for
realgas.eos.virial.SecondVirialMixture
-
bar_Hi_IG
(cas_i: str, T, T_ref=0)[source]¶ - Parameters
T_ref – reference temperature in K for enthalpy, defaults to 0
T – temperautre in K
- Returns
\(ar{H}_i^ ext{IG}\), see Equation (5)
-
class
realgas.partial_molar_properties.
MixtureDimensionless
(cp_args: List[dict], ideal=True, **kwargs)[source]¶ Todo
add docs!
- Parameters
ideal (bool, optional) – whether or not ideal gas, defaults to True
kwargs – key-word arguments for
realgas.eos.virial.SecondVirialMixture