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Theories of Solutions : Excess functions (and consequently activity coefficients)\ncan be obtained from equations of state. However, this approach has limited\npractical applicability.\n· Lattice Models :\nLiquid is considered to be a quasicrystalline state with molecules arranged in a\nregular array. Mixing two different liquid to obtain a solution results in the\nentropy of mixing (as lattice structure is altered) and enthalpy of mixing (due to\nintermolecular forces). The potential energy of the system is obtained by pairwise\naddition of all molecular pairs considering only the nearest neighbors. An\nexpression for Helmholtz energy can be derived in terms of the interchange\nenergy (w) which arises when a molecule of one component in the lattice is\nreplaced by the molecule of the second component. The interchange energy is\ndependent upon the difference in the potential energies of pairs 1-2, 1-1 and 2-2\n(for a binary mixture of 1 and 2). For a regular solution the excess Gibbs energy is\nequal to excess Helmholtz energy, leading to a method for calculation of activity\ncoefficients. The interchange energy can be calculated from potential functions\nand molecular properties, primarily for mixtures of nonpolar molecules similar in\nsize. This approach is not very useful for mixtures having additional complexities.\n· Non-random Mixtures:\nA solution is essentially non-random in nature as in most cases intermolecular\nforces for different compounds are not identical. So in a binary mixture of 1 and\n2, molecules of 1 either prefer 2 or 1 as immediate neighbors. The solution has\ncertain order to it resulting in sE < 0. A quasichemical theory for such solutions\ncan be developed by writing an equilibrium constant expression for the formation\nof complex 1–2 from molecules of 1 and 2. The equilibrium constant is related to\nthe interchange energy w, leading to expressions for excess Helmholtz energy,\nexcess entropy and excess Gibbs energy.\n· Two-Liquid Theory:\nSince the solutions are essentially non-random, they can be thought of as\ncomprised of 2 (or more) hypothetical fluids depending upon the nature of\ninteraction between the solution components. The thermodynamic properties of\nthe solution are then mole fraction weighted averages of the properties of the\nhypothetical fluids. Area fractions and volume fractions can be defined for each\nhypothetical fluid, and expressions developed for the excess properties of the\nsolution. The UNIQUAC equation, developed on the basis of two- liquid theory is\nquite successful, however, it may over-correct for non-randomness of the\nsolution.\n· Group Contribution Methods\nActivity coefficients can be calculated for various mixtures by considering\nindividual molecules to be comprised of different functional groups. The number\nof distinct functional groups (methyl, methylene, hydroxyl, etc.) is relatively\nsmall compared to the number of distinct compounds. The interaction between\nvarious compounds is obtained by contributions of the functional group\ninteraction for the compounds. ASOG (analytical solution of groups) and\nUNIFAC (universal functional activity coefficient) are two group contribution\nmethods that are quite useful. Group contribution methods are very rapid,\nhowever, they may not necessarily be accurate. The results of the group\ncontribution methods need to be compared with experimental data for validation.\n· Chemical Theory of Non- ideality of Liquid Solutions:\nThe non- ideality of the solutions is due to formation of new species by the\nreactions of the components. These reactions may be associations of a single\ncomponent (dimmer, trimer, polymer formation) or solvation (interactions of two\nor more components, e.g. complexation). These species are at chemical\nequilibrium with each other and form ideal solutions. Therefore, the behavior of\nthe solution can be described if the “true” composition of the solution is\ndetermined. If z1 and z2 are
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The link below should help you...
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There is a good article in wikipedia.  see link.
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