Solution, ideal, regular, real

Classically, one treats phases of two components as ideal, regular, or real solutions. Usually, however, one concentrates for the non-ideal case only on solutions of salts by discussing the Debye-Huckel theory. Polymer science, in turn, adds the effect of different molecular sizes with the Hory-Huggins equation as of basic importance (Chap. 7). Considerable differences in size may, however, also occur in small molecules and their effects are hidden falsely in the activity coefficients of the general description. 

The lattice theory of solution is derived from several idealized assumptions. The assumptions that components A and B are the same size and have the same number of nearest neighbors, for example, are not applicable to real solutions. Ilie regular solution concept of Hildebrand is more versatile it takes into account a mixture of molecules of different sizes, where the principal idea is an ideal entropy of mixing at constant volume irrespective of heat. The activity coefficients in the form of (3.9) due to interaction between components A and B in a liquid mixture are derived by the following equations when the mixing term is expressed as a volume fraction ... 

The entropy of mixing of many real solutions will deviate considerably from the ideal entropy of mixing. However, accurate data are available only in a few cases. The simplest model to account for a non-ideal entropy of mixing is the quasi-regular model, where the excess Gibbs energy of mixing is expressed as... 

It is generally observed that as the temperature increases, real solutions tend to become more ideal and r can be interpreted as the temperature at which a regular solution becomes ideal. To give a physically meaningful representation of a system r should be a positive quantity and larger than the temperature of investigation. The activity coefficient of component A for various values of Q AB is shown as a function of temperature for t = 3000 K and xA = xB = 0.5 in Figure 9.3. The model approaches the ideal model as T - t. 

Chapters 17 and 18 use thermodynamics to describe solutions, with nonelectrolyte solutions described in Chapter 17 and electrolyte solutions described in Chapter 18. Chapter 17 focuses on the excess thermodynamic properties, with the properties of the ideal and regular solution compared with the real solution. Deviations from ideal solution behavior are correlated with the type of interactions in the liquid mixture, and extensions are made to systems with (liquid + liquid) phase equilibrium, and (fluid -I- fluid) phase equilibrium when the mixture involves supercritical fluids. 

For ideal solutions, A// is zero. For real solutions, however, A//m is finite and its value can be estimated by the regular solution theory of Hildebrand as described in the next section. For most vapors, cmut is negative and it dominates the value of A//j. As a result, AA/ is usually negative and the partition coefficient decreases with increasing temperature. 

Owing to their polymeric character, silicate melts belong to the solutions of type II, which do not follow Raoult s law. The classic regular solution approach is not applicable, since the limiting laws are not obeyed. The Temkin s model of ideal ionic solution, which has been widely applied in molten salt systems, cannot be used, since the real anionic composition, owing to a broad polyanionic distribution, is not known a priori. 

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... 

In this chapter, we apply some of the general principles developed heretofore to a study of the bulk thermodynamic properties of nonelectrolyte solutions. In Sec. 11-1 we discuss conventions for the description of chemical potentials in nonelectrolyte solutions and introduce the concept of an ideal component. In Sec. 11-2, we demonstrate how the concept of solution molecular weight can be introduced into thermodynamics in a natural fashion. Section 11-3 is devoted to a study of the properties of ideal solutions. In Sec. 11-4, we discuss the properties of solutions that can be considered to be ideal when they are dilute but are not necessarily ideal when they are more concentrated. In Sec. 11-5, regular solutions are defined and some of their properties are derived. Section 11-6 is devoted to a study of some of the approximations that prove useful in the derivation of the properties of real solutions. Finally, in Sec. 11-7, some of the experimental techniques utilized for the measurement of chemical potentials and activity coefficients of components in solution are described. 

Ideal liquids are mutually soluble in all proportions, while the solubilities of ideal solids in ideal liquid solvents are limited by the energy required to liquify the solute. Real solutions of non-electrolytes in non-conducting solvents can be subdivided into regular solutions and solutions in which association occurs. The former have been the subject of extensive study by Hildebrand and Scott [43], who have developed methods of predicting regular solubilities from theoretical considerations. Tliey introduced the term solubility parameter (5), which is constant for a given solute or solvent, and dependent on intermolecular attraction and molar volume. Deviation from ideal solubility is calculated from an expression containing the term (Si-Sj), where the suffixes 1 and 2 represent solvent and solute respectively. When the solubility parameters of solvent and... 

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 ... 

Equation (5.1) includes only the ideal, combinatorial entropy of mixing and the simplest conceivable regular solution type estimate of the enthalpy of mixing based on completely random mixing of monomers mm ( ) = 1 in the liquid state language i referred to as the bare chi parameter since it ignores all aspects of polymer architecture and Interchain nonrandom correlations. For these reasons, the model blend for which Eq. (5.1) is thought to be most appropriate for is an interaction and structurally symmetric polymer mixture. The latter is defined such that the only difference between A and B chains is a v (r) tall potential, which favors phase separation at low temperatures. The closest real system to this idealized mixture is an isotopic blend, where the A and B... 

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