Excess free energy of compound

As already pointed out, Yu is 1 if a compound forms an ideal solution. In this rather rare case, the term RTkiyu, which we denote as partial molar excess free energy of compound i in solution t, Gpe, is 0. This means that the difference between the chemical potential of the compound in solution and its chemical potential in the reference state is only due to the different concentration of the compound i in the two states. The term R In xtf=S 1 expresses the partial molar entropy of ideal mixing (a purely statistical term) when diluting the compound from its pure liquid (xiL =1) into a solvent that consists of otherwise like molecules. 

Substituting ptlxiL by p (the saturation vapor pressure of the pure liquid compound, since =1) and by realizing that in this case, A12G, (see Eq. 3-46) is simply given by G (the excess free energy of the compound in the gas phase see examples given in Table 3.2) we may rewrite Eq. 4-3 as ... 

Now, AfijsG, is equal to the negative excess free energy of the compound in the solid state G, , since we have chosen the liquid state as our reference state. This free energy change is given by ... 

Molecular Interpretation of the Excess Free Energy of Organic Compounds in Aqueous Solutions... 

Table 5.2 Comparison of Activity Coefficients and Corresponding Excess Free Energies of a Series of Organic Compounds in Dilute and Saturated Aqueous Solution at 25°C (recall that G, = RT In yiw)...

Before we deal with these molecular aspects in detail, it is instructive to inspect the enthalpic () and entropic (-T Sj,j,) contributions to the excess free energies of various organic compounds in aqueous solution (Table 5.3). Values representative of saturated aqueous solutions of the compounds have been derived from measurements of the enthalpies of dissolution of the liquids (i.e., = AwJ //, Fig. 5.1) or solids (// ... 

Table 53 Enthalpic (// ,) and Entropic (5 ) Contributions to the Excess Free Energy of a Series of Organic Compounds in Saturated ( Sat ) and Dilute ( Dil ) Aqueous Solution at 20 to 25°C. The Compounds are Ordered by Increasing Size Expressed by Their Molar Volume...

In summary, we can conclude that the excess free energy of an organic compound in aqueous solution, and thus its activity coefficient, depends especially on (1) the size and the shape of the molecule, and (2) its H-donor and/or H-acceptor properties. 

It should be noted that when replacing the London dispersive interactions term by other properties such as, for example, the air-hexadecane partition constant, by expressing the surface area in a more sophisticated way, and/or by including additional terms, the predictive capability could still be somewhat improved. From our earlier discussions, we should recall that we do not yet exactly understand all the molecular factors that govern the solvation of organic compounds in water, particularly with respect to the entropic contributions. It is important to realize that for many of the various molecular descriptors that are presently used in the literature to model yiw or related properties (see Section 5.5), it is not known exactly how they contribute to the excess free energy of the compound in aqueous solution. Therefore, when also considering that some of the descriptors used are correlated to each other (a fact that... 

Similarly to the fluid-fluid intermolecular potential, we split the solid-fluid intermolecular potential into repulsive hard-sphere and attractive interactions. Here Fhs Ps P is the excess free energy of the solid-fluid HS mixture, for which we employ Rosenfeld fundamental m ure functional [26] with the recent modifications that mve an accurate Carnahan-Starling equation of state in the bulk limit [27,28] r-r ) is the attractive part of the solid-fluid intermolecular potential. Since the iM>lid-soIid attraction interaction is not included, the solid is effectively modeled as a compound of... 

The third term of Eq. (14), Gxs, is the excess term of the free energy. Although several of the aluminum alloys considered here form ordered intermetallic compounds, a regular-solution type model was used to describe their excess free energy. Gxs is described by the following Redlich-Kister polynomial,... 

Table 33 Excess Free Energies, Enthalpies, and Entropies of Hexane (apolar), Benzene (monopolar), Diethylether (monopolar), and Ethanol (bipolar) in the Ideal Gas Phase, in Hexadecane, and in Water at Infinite Dilution.0 All Data at 25°C. Reference Pure Liquid Organic Compound.

Enthalpic and Entropic Contributions to the Excess Free Energy Molecular Picture of the Dissolution Process Model for Description of the Aqueous Activity Coefficient Box 5.1 Estimating Molar Volumes from Structure Illustrative Example 5.2 Evaluating the Factors that Govern the Aqueous Activity Coefficient of a Given Compound... 

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