Thermodynamics excess property, ideal mixing

Thus, an excess thermodynamic property is also the difference between the thermodynamic property for mixing the real and ideal solutions. For the Gibbs free energy, this becomes, using Eq. (3) and Eq. (35) of Chapter 8,... 

The difference between the thermodynamic function of mixing (denoted by superscript M) for an actual system, and the value corresponding to an ideal solution at the same T and jp, is called the thermodynamic excess function (denoted by superscript E). This quantity represents the excess (positive or negative) of a given thermodynamic property of the solution, over that in the ideal reference solution. nnhn< ... 

Most real solutions are neither ideal nor regular. As a result a realistic description of their thermodynamic properties must consider the fact that both the excess enthalpy of mixing, and excess entropy, are non- zero. Wilson... 

We refer to a mixture for which Equation 58 or 59 is satisfied as an ideal mixture. Clearly this concept of an ideal mixture is an idealization that is not realized in practice. Real mixtures will show deviations from the ideal results. However, the properties of an ideal mixture are convenient reference states for thermodynamic properties. For example, it is conventional to use excess thermodynamic properties of mixing that are defined as the difference between the thermodynamic property of the mixture and those of an ideal mixture of the components at the same temperature and pressure. 

We can now use the K-value expression to calculate various equilibrium properties and perform typical flash calculations. As with the simple thermodynamic approach, we can use the heat capacities, and heats of vaporization to obtain enthalpy balances for vapor and liquid streams. In addition, since we account for vapor- and liquid-phase non-ideality due to component interactions, and temperature and pressure effects, we can also apply standard thermodynamic relationships to compute excess properties for enthalpies, etc. The excess properties account for deviations from an ideal mixing behavior and the resulting deviations in equilibrium behavior. 

These solutions exhibit also a partially ideal behaviour and have specific thermodynamic properties. The excess functions, represented by the enthalpy of mixing and the excess quantities derived from it, are zero and justify considering these solutions as being almost ideal. Thus, the athermal solutions fulfil the following group of major conditions ... 

We have seen that when two pure liquids mix to form an ideal liqiud mixture at the same T and p, the total volume and internal energy do not change. A simple molecular model of a binary liquid mixture will elucidate the energetic molecular properties that are consistent with this macroscopic behavior. The model assumes the excess molar entropy, but not necessarily the excess molar internal energy, is zero. The model is of the type sometimes called the qmsicrystalline lattice model, and the mixture it describes is sometimes called a simple mixture. Of course, a molecular model like this is outside the realm of classical thermodynamics. 

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