Excess free enthalpy, mixing

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 ... 

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 ... 

Thus the integral molar excess free energy of mixing as well as the enthalpy of mixing are independent of temperature for a regular solution. 

Consideration of the thermodynamics of nonideal mixing provides a way to determine the appropriate form for the activity coefficients and establish a relationship between the measured enthalpies of mixing and the regular solution approximation. For example, the excess free energy of mixing for a binary mixture can be written as... 

The regular solution approximation is introduced by assuming definition) that the excess entropy of mixing is zero. This requires that the excess free energy equal the excess enthalpy of mixing. For binary mixtures the excess enthalpy of mixing is ordinarily represented by a function of the form... 

Using an automated film balance the behavior of mixed monomolecular films exhibiting deviations from ideality was studied. Particular attention was paid to condensation effects obtained when cholesterol is mixed with a more expanded component. The deviations at various film pressures are discussed in terms of the partial molecular areas of the film components. Slope changes in these plots are caused by phase transitions of the expanded monolayer component and do not indicate the formation of surface complexes. In addition, the excess free energies, entropies, and enthalpies of mixing were evaluated, but these parameters could be interpreted only for systems involving pure expanded components, for which it is clear that the observed condensation effects must involve molecular interactions. 

AGme = excess free energy of mixing of water with the co-solvent AHme = excess enthalpy of mixing water with the co-solvent ASme = excess entropy of mixing water with the co-solvent... 

For mixed electrolyte solutions in water, the experimental excess free energy functions have been given in parameterized form by Pitzer, and excess free energies and enthalpies have been tabulated by Anderson and Wood. "" ... 

Much of the progressive development of lattice-graph theories is charted in the form attached to the final, excess free energy , term in equation (4) initially added to extend the compass of the model to systems in which the enthalpy of mixing, while small, is not zero. That is, various arrangements of the system do not have the same energy as was assumed by Flory and Huggins. The interaction function, g, taken by them to be a function of temperature alone, was shown later to require a concentration dependence also. Since then, power series representations ... 

The excess free energy of the mixture (relative to a pure polymer) is written as the sum of an entropy of mixing term, and an enthalpy term. In the latter, only a reduced energy parameter e enters, which is related to the Flory-Huggins x parameter... 

The excess functions we shall consider in this book are mainly the exce free energy, the excess enthalpy, the excess entropy and the excess volume. The excess free energy (1.7.1) is deduced from the determination of the activity coefficients (generally from vapour pressure measurements). The excess enthalpy is the heat of mixing at constant pressure per mole of solution it may be deduced either from direct measurements or from the temperature variation of the activity coefficients (cf. 1.6.6). The excess entropy is defined by (cf. 1.4.10)... 

One sees at once that the contributions of the dipolar interactions to the excess functions in such systems are always positive. This can be explained qualitatively by considering that, in the process of mixing, the stem becomes less ordered as compared to the pure polar constituent. There is therefore an increase in entropy. Also the mixing process destroys at least partially the dipolar interactions. Therefore the heat of mixing as well as the excess volume are positive. As shown by the positive value of gf in (14.4,3), the enthalpy increase gives the dominant contribution to the excess free energy. 

By simple thermodynamic arguments Brown14 has shown that, consistent with the accuracy of this second-order approximation, one may obtain from the form of Eq. (87) the form of the excess Gibbs free energy of mixing (AG ), the enthalpy of mixing of a molten salt (AHm), and the deviation of the surface tension from linearity ... 

---