g ^E models

Under g ^e -models refers to methods for prediction of activity coefficients using the free excess Gibbs ( excess molar quantity with respect to the free energy ). The context is used here: ${\displaystyle \gamma }$ ${\displaystyle g^{E}}$ ${\displaystyle g}$

${\displaystyle g^{E}=R\cdot T\sum _{i}\ x_{\text{i}}\ln \gamma _{\text{i}}\ }$

There are

• ${\displaystyle R}$for the universal gas constant
• ${\displaystyle T}$for the absolute temperature
• ${\displaystyle x_{\text{i}}}$for the mole fraction of the substance i and
• ${\displaystyle \gamma _{\text{i}}\ }$ for the activity coefficient of the substance i.

Gibbs-Helmholtz

Highly parameterized g ^E models can be extrapolated more robustly to T if data on excess molar enthalpy are available: ${\displaystyle h^{E}}$

${\displaystyle \left({\frac {\partial \left({\frac {g^{E}}{T}}\right)}{\partial T}}\right)_{p,n_{j}}=-{\frac {h^{E}}{T^{2}}}}$

The derivation is analogous to the derivation of the Gibbs-Helmholtz equation .

Examples

• NRTL ( Non-Random-Two-Liquid )
• UNIQUAC ( Universal Quasi-Chemical )
• UNIFAC ( Universal Quasichemical Functional Group Activity Coefficients )
• COSMO-RS ( Conductor-like Screening Model for Real Solvents )
• Hildebrand model
• Flory Huggins model
• Wilson equation
• Porter's approach