Theories of Solutions : Excess functions (and consequently activity coefficients) can be obtained from equations of state. However, this approach has limited practical applicability.
Lattice Models :
Liquid is considered to be a quasicrystalline state with molecules arranged in a
regular array. Mixing two different liquid to obtain a solution results in the
entropy of mixing (as lattice structure is altered) and enthalpy of mixing (due to
intermolecular forces). The potential energy of the system is obtained by pairwise
addition of all molecular pairs considering only the nearest neighbors. An
expression for Helmholtz energy can be derived in terms of the interchange
energy (w) which arises when a molecule of one component in the lattice is
replaced by the molecule of the second component. The interchange energy is
dependent upon the difference in the potential energies of pairs 1-2, 1-1 and 2-2
(for a binary mixture of 1 and 2). For a regular solution the excess Gibbs energy is
equal to excess Helmholtz energy, leading to a method for calculation of activity
coefficients. The interchange energy can be calculated from potential functions
and molecular properties, primarily for mixtures of nonpolar molecules similar in
size. This approach is not very useful for mixtures having additional complexities.
Non-random Mixtures:
A solution is essentially non-random in nature as in most cases intermolecular
forces for different compounds are not identical. So in a binary mixture of 1 and
2, molecules of 1 either prefer 2 or 1 as immediate neighbors. The solution has
certain order to it resulting in sE < 0. A quasichemical theory for such solutions
can be developed by writing an equilibrium constant expression for the formation
of complex 1–2 from molecules of 1 and 2. The equilibrium constant is related to
the interchange energy w, leading to expressions for excess Helmholtz energy,
excess entropy and excess Gibbs energy.
Two-Liquid Theory:
Since the solutions are essentially non-random, they can be thought of as
comprised of 2 (or more) hypothetical fluids depending upon the nature of
interaction between the solution components. The thermodynamic properties of
the solution are then mole fraction weighted averages of the properties of the
hypothetical fluids. Area fractions and volume fractions can be defined for each
hypothetical fluid, and expressions developed for the excess properties of the
solution. The UNIQUAC equation, developed on the basis of two- liquid theory is
quite successful, however, it may over-correct for non-randomness of the
solution.
Group Contribution Methods
Activity coefficients can be calculated for various mixtures by considering
individual molecules to be comprised of different functional groups. The number
of distinct functional groups (methyl, methylene, hydroxyl, etc.) is relatively
small compared to the number of distinct compounds. The interaction between
various compounds is obtained by contributions of the functional group
interaction for the compounds. ASOG (analytical solution of groups) and
UNIFAC (universal functional activity coefficient) are two group contribution
methods that are quite useful. Group contribution methods are very rapid,
however, they may not necessarily be accurate. The results of the group
contribution methods need to be compared with experimental data for validation.
Chemical Theory of Non- ideality of Liquid Solutions:
The non- ideality of the solutions is due to formation of new species by the
reactions of the components. These reactions may be associations of a single
component (dimmer, trimer, polymer formation) or solvation (interactions of two
or more components, e.g. complexation). These species are at chemical
equilibrium with each other and form ideal solutions. Therefore, the behavior of
the solution can be described if the “true” composition of the solution is determined.