Entropy excess mixing

Regular Solution Theory. The key assumption in regular-solution theory is that the excess entropy, is zero when mixing occurs at constant volume (3,18). This idea of a regular solution (26) leads to the equations ... 

It is simplest to consider these factors as they are reflected in the entropy of the solution, because it is easy to subtract from the measured entropy of solution the configurational contribution. For the latter, one may use the ideal entropy of mixing, — In, since the correction arising from usual deviation of a solution (not a superlattice) from randomness is usually less than — 0.1 cal/deg-g atom. (In special cases, where the degree of short-range order is known from x-ray diffuse scattering, one may adequately calculate this correction from quasi-chemical theory.) Consequently, the excess entropy of solution, AS6, is a convenient measure of the sum of the nonconfigurational factors in the solution. 

For a large number of the more commonly used microscopic solution models it is assumed, as we will see in Chapter 9, that the entropy of mixing is ideal. The different atoms are assumed to be randomly distributed in the solution. This means that the excess Gibbs energy is most often assumed to be purely enthalpic in nature. However, in systems with large interactions, the excess entropy may be large and negative. 

The ideal solution approximation is well suited for systems where the A and B atoms are of similar size and in general have similar properties. In such systems a given atom has nearly the same interaction with its neighbours, whether in a mixture or in the pure state. If the size and/or chemical nature of the atoms or molecules deviate sufficiently from each other, the deviation from the ideal model may be considerable and other models are needed which allow excess enthalpies and possibly excess entropies of mixing. 

The solubility parameter concept was established in the 1930s by the work of Hildebrand and Scatchard. The original concept covers regular solutions, i.e., solutions that do not show an excess entropy effect on mixing. The solubility parameter concept offers the following interesting features ... 

Starting with Equation (16.55) for Gji, derive Equations (16.60) and (16.58) for the excess entropy and enthalpy of mixing, respectively. 

At 42°C the enthalpy of mixing of 1 mole of water and 1 mole of ethanol is — 343.1 J. The vapor pressure of water above the solution is 0.821 p and that of ethanol is 0.509 P2, in which p is the vapor pressure of the corresponding pure liquid. Assume that the vapors behave as ideal gases. Compute the excess entropy of mixing. 

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... 

This conclusion implies that the excess entropy of mixing is non-zero and that the mixed micelles presumably acquire more internal order than they would by random mixing. An examination of the magnitude of the deviations from the regular solution approximation shows that there must be a large TS contribution to the excess free energy of mixing. 

According to the experiments of Campbell and Roeder (1968), at T = 1400 °C the (Mg,Ni)2Si04 mixture is virtually ideal. More recent measurements by Seifert and O Neill (1987) at T = 1000 °C seem to confirm this hypothesis. Because the intracrystalline distribution of Mg " and on Ml and Ml sites is definitely nonrandom (NP is preferentially stabilized in Ml), the presumed ideality implies that negative enthalpic terms of mixing counterbalance the positive excess entropy arising from the configurational expression... 

Haselton H. T, Hovis G. L., Hemingway B. S., and Robie R. A. (1983). Calorimetric investigation of the excess entropy of mixing in analbite-sanidine solid solutions Lack of evidence for Na, K short range order and implications for two feldspar thermometry. Amer. Mineral, 68 398-413. 

The data are then compared to predictions based on a new model which includes an excess enthalpy of mixing and two contributions to the excess entropy of mixing. 

Osborne-Lee et al. (12) have accounted for the additional contribution to the excess entropy of mixing and found the following excess free energy of mixing per amphiphile... 

Thermodynamic definitions show that the first term of Eq. (1) is the enthalpy of mixing, AHu, while the second term is the negative of the excess entropy of mixing, ASm, multiplied by T. When all four parameters are zero, the liquid is ideal with a zero enthalpy and excess entropy of mixing. What has been called the quasiregular model, a = b = 0, has been used by Panish and Ilegems (1972) to fit the liquidus lines of a number of III—V binary compounds. The particular extension of this special case of Eq. (1) to a ternary liquid given by... 

Solid-Solution Models. Compared with the liquid phase, very few direct experimental determinations of the thermochemical properties of compound-semiconductor solid solutions have been reported. Rather, procedures for calculating phase diagrams have relied on two methods for estimating solid-solution model parameters. The first method uses semiem-pirical relationships to describe the enthalpy of mixing on the basis of the known physical properties of the binary compounds (202,203). This approach does not provide an estimate for the excess entropy of mixing and thus... 

According to Hill (8), due to the small correction for excess entropy Ase, "the approximation of random mixing can appropriately be introduced, for molecules of like size, in lattice or cell solution theories that are otherwise fairly sophisticated."... 

As a demonstration of quantitative LLE calculations, we now consider in more detail some of the binary mixtures that we have discussed qualitatively in section 6.3. In Fig. 6.13 we see the excess Gibbs free energy of mixing Gex, the heat of mixing Hex, and the excess entropy of mixing Sex for mixtures of acetone and... 

The situation is quite different for a mixture of 1-propanol and n-hexane (see Fig. 6.15). Here, we find a significant positive excess heat of mixing. The excess entropy of mixing shows a change of sign at about 10% n-hexane. This feature has also been found experimentally in many alcohol-alkane mixtures. 

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