Enthalpy mixing nonideal solution

A particular type of nonideal solution is the regular solution which is characterized by a nonzero enthalpy of mixing but an ideal entropy of mixing. Thus, for a regular solution,... 

For nonideal solutions with volatile components Raoult s law is not obeyed, the enthalpy of mixing, 0, and solute-solvent interactions are different from solvent-solvent interactions. 

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... 

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

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 case of binary solid-liquid equilibrium permits one to focus on liquid-phase nonidealities because the activity coefficient of solid component ij, Yjj, equals unity. Aselage et al. (148) investigated the liquid-solution behavior in the well-characterized Ga-Sb and In-Sb systems. The availability of a thermodynamically consistent data base (measurements of liquidus, component activity, and enthalpy of mixing) provided the opportunity to examine a variety of solution models. Little difference was found among seven models in their ability to fit the combined data base, although asymmetric models are expected to perform better in some systems. 

A so-called regular solution is obtained when the enthalpy change (AHmix) is nonideal (i.e., non-zero, either positive or negative) but the entropy change (A mix) is still ideal. So on the molecular level, while an ideal solution is one in which the different types of molecules (A and B, for example) behave exactly as if they are surrounded by molecules of their own kind (that is, all intermolecular interactions are equivalent), a regular solution can form only if the random distribution of molecules persists even in the presence of A-B interactions that differ from the purely A-A and B-B interactions of the original components A and B. This concept has proved to be very useful in the development of an understanding of miscibility criteria. 

FIG U RE 10.4 Comparison between experimental (o) and calculated (solid lines) solubilities of phenacetin (S is the mole fraction of phenacetin) in the mixed solvent water/dioxane is the mole fraction of dioxane) at room temperature. The solubility was calculated using Equation 10.29. 1-activity coefficients expressed via the Flory-Huggins equation, 2-activity coefficients expressed via the Wilson equation. (From C. Bustamante, and P. Bustamante, 1996, Nonlinear Enthalpy-Entropy Compensation for the Solubility of Phenacetin in Dioxane-Water Solvent Mixtures, Journal of Pharmaceutical Sciences, 85, 1109. Reprinted from E. Ruckenstein, and I. L. Shulgin, 2003c, Solubility of Drugs in Aqueous Solutions. Part 2 Binary Nonideal Mixed Solvent, International Journal of Pharmaceutics, 260, 283, With permission from Elsevier.)... 

Some experimental heat of dilution data for NaCl are shown in Figure 10.10. The negative values show that the enthalpy of a dilute NaCl solution is less than that of a more concentrated one. The data in this diagram are an answer to the question what is the (nonideal) heat of mixing of NaCl and water In this case the NaCl is at two different concentrations - one is 1.0 molal, and the other is as shown on the x-axis. 

For solutions with nonideal behavior, the energies of the three different types of bonding between nearest neighbors in the solution, Eaa, bb and Eab, differ from each other, resulting in a nonzero enthalpy of mixing. The entropy of mixing can, but needs not necessarily, be conserved as for an ideal solution. 

If the forces between solute and solvent are somewhat weaker than between molecules of the same kind, complete mixing may still occur, the solution formed is nonideal. The solution has a higher enthalpy than the pure components, and the solution process is endothermic. This type of behavior is observed in mixtures of carbon disulfide (CS2), a nonpolar liquid, and acetone, a polar liquid. In these mixtures, the acetone molecules are attracted to other acetone molecules by dipole-dipole interactions and hence show a preference for other acetone molecules as neighbors. A possible explanation of how a solution process can be endothermic and still occur is found on page 649. 

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