Regular solution excess enthalpy

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

Still, the strain enthalpy is of particular importance. An elastic continuum model for this size mismatch enthalpy shows that, within the limitations of the model, this enthalpy contribution correlates with the square of the volume difference [41,42], The model furthermore predicts what is often observed experimentally for a given size difference it is easier to put a smaller atom in a larger host than vice versa. Both the excess enthalpy of mixing and the solubility limits are often asymmetric with regard to composition. This elastic contribution to the enthalpy of mixing scales with the two-parameter sub-regular solution model described in Chapter 3 (see eq. 3.74) ... 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

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... 

A particularly simple approximation known as regular-solution theory was developed by Hildebrand and co-workers [J. H. Hildebrand. /. Am. Chem. Soc. 51, 66-80 (1929)]. The regular-solution model assumes that the excess enthalpy of mixing can be represented as a simple one-parameter correction... 

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 ... 

The model of regular solutions is very frequently used for which the conditions expressed in Eq. (3.59) are valid. This means that the deviation from the ideal behavior is ascribed to the change in enthalpy at the interaction of the components on mixing. For the excess... 

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... 

D5.5 A regular solution has excess entropy of zero, but an excess enthalpy that is non-zero and dependent on composition, perhaps in the manner of eqn 5.30. We can think of a regular solution as one in which the different molecules of the solution are distributed randomly, as in an ideal solution, but have different energies of interaction with each other. 

Generally, therefore, these additional functions are connected with the departures from additivity shown by the volume F, the heat capacity and the chemical constant i and the enthalpy H on dilution of the solution. They find their tangible expression in volume contractions, heat effects and anomalous behavior of specific heats. Physically they should be attributed to an excess or deficiency in attraction between the molecules of solvent and solute over the cohesion of identical molecules. Hildebrand has termed solutions in which additional entropy terms such as 2, 3 and 4 are missing, regular solutions (see p. 222). In them the excess and deficiency attractions may be related quantitatively to the heat of dilution, since in the insertion of molecules of one component between those of the other, a heat effect other than zero results because the energy necessary for the separation of identical molecules differs from that obtained in bringing together dissimilar particles. 

Abe and Flory (1965) did not use this expression for X12 but instead chose to fit excess enthalpy data. Since excess enthalpy data for the styrene/ether system were not readily available, this equation was used to estimate X12. Dar (Dar, 1999 Dar and Caneba, 2002) validated the resulting value of X12 by comparing calculated excess molar enthalpy for the system using the Flory EOS (Abe and Flory, 1965, Howell et al., 1971) and the regular solution theory with solubility parameters obtained from the literature (Immergut and Brandrup, 1989). For the styrene/ether system, the two methods did not deviate by more than 10% for the entire composition range. 

The term general solution was introduced by Flory to characterize polymer solutions whose enthalpy of mixing is not zero. The model of general solutions borrows the formula of excess enthalpy from regular systems and the excess entropy from athermal solutions. Thus, a treatment of non-ideal polymer solutions arises which is simpler than the conventional methods applied to real systems this allows the deduction, on the basis of the known relationships, of the expressions of functions of deviation from ideality. Thus, for the activity coefficients of components in a binary system the following relations were established ... 

Nonideal solutions may be classified into two limiting cases. In one limiting case, called regular solutions,-AGe AHe, i.e. most of the deviation from ideality is due to the excess enthalpy of mixing. Since AGe = AI/e — TASe, it follows that for regular solutions ASe 0. Furthermore, since ASe = —(0AGe/0T), from (8.4.18) it follows that the activity coefficients are given by... 

As the enthalpy of mixing for a perfect solution is zero, the enthalpy of mixing for a strictly-regular solution is identical to its excess enthalpy, so for the the partial molar values ... 

In the same way as we defined a regular solution as one which has the same entropy of mixing as a perfect solution, we shall define an athermic solution as one which has the same enthalpy of mixing as a perfect solution - i.e. zero. Of course, its excess molar enthalpy is also null. 

Nor can the theory of regular solutions based on the simplified lattice model (cf. Ch. Ill) give any indication on the excess properties related to the equation of state such as the excess volume, the excess compressibility and hence the excess entropy and the excess specific heat all of which are closely related to the equation of state. In fact, no equation of state at all is introduced in this model. The lattice model can only be used to calculate the excess free energy and the excess enthalpy which should be equal in the zerbth approximation. However the experimental data invalidate this conclusion. 

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