Free excess enthalpy

AHo) is the Excess Free Enthalpy (ASo) is the Excess Free Entropy. 

The interaction parameter / can also be estimated by the use of solubility parameters (8) / is proportional to (8M — 8TS)2. But this approach has a considerable error (A8 in the range of 0.4 MPa1/2), and considers only the excess free enthalpy. For these reasons it is better to determine the miscibility window experimentally. 

In this section we shall always define the activity coefficients with respect to the symmetrical reference system. Comparing Eq. 8.7 and Eq. 8.17, we define the excess free enthalpy (excess Gibbs energy) gE per mole of a non-ideal binary solution as Eq. 8.18 ... 

The difference in thermodynamic functions between a non-ideal solution and a comparative perfect solution is called in general the thermodynamic excess function. In addition to the excess free enthalpy gE, other excess functions may also be defined such as excess entropy sE, excess enthalpy hE, excess volume vE, and excess free energy fE per mole of a non-ideal binary solution. These excess functions can be derived as partial derivatives of the excess free enthalpy gE in the following. 

We also see that the excess free enthalpy GE is differentiated with respect to the temperature and the number of moles of the solution to give the excess entropy SF and the partial molar excess free energy of mixing RTlnyi as follows ... 

A discrepancy in free enthalpy between the perfect solution and the non-ideal solution, if the reference system is symmetrical, is generally expressed by the excess free enthalpy GE, which consists of the enthalpy term HE and the entropy term -TSE i.e. GE = HE - TSE. Two situations arise accordingly in non-ideal solutions depending on which of the two terms, He and - TSE, is dominant The non-ideal solution is called regular, if its deviation from the perfect solution is caused mostly by the excess enthalpy (heat of mixing) HE ... 

According to Eq. (14) three effects contribute to the excess free enthalpy of mixing ... 

For a monosubstituted oxane, the excess free enthalpy of the conformation with an axial substituent over the conformation with an equatorial substituent is, as we know by definition, the conformational free energy (CFE) of the substituent in oxane at this position. These values, possibly measured indirectly by utilizing intennediate compounds, are shown in Table 2.2. Equatorial conformations correspond to anti conformations in butane and methoxyethane, and the axial conformations (not represented) to gauche conformations. We can observe that the environment of derivative 2.20 is closest to that of the cyclohexane and that the CFE is of the same order. On the other hand, the presence of the cyclic oxygen lowers notably the CFE of derivative 2.19. The important point is the noteworthy increase in the CFE of compound 2.18, where the methyl group is close to the cyclic oxygen and possesses, on one side, an environment similar to that of methoxyethane. Let us look at the equilibrium (2.4) of the dimethylated derivative 2.21. 

The excess free enthalpy of mixing (G ) is the difference between the actual free enthalpy of mixing (AG ,) and the ideal free enthalpy of mixing (AG j... 

The excess free enthalpy of mixing for the binary system ethanol (I)-chloroform (2) at 50°C for three different compositions is given below ... 

Ethylene vinyl acetate Ethylene vinyl alcohol Evaporation Excess free enthalpy Exclusion term... 

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