Ideal DI Solutions

In this section, we discuss a different class of ideal solutions which have been of central importance in the study of solution thermodynamics. We shall refer to a dilute ideal (DI) solution whenever one of the components is very dilute in the solvent. The term very dilute depends on the system under consideration, and we shall define it more precisely in what follows. The solvent may have a single component or be a mixture of several components. Here, however, we confine ourselves to two-component systems. The solute, say A, is the component diluted in the solvent B. 

The fact that we make a distinction between the solute and the solvent requires separate discussion of the behavior of each of them. We shall be mainly concerned with the solute, and only briefly discuss the relevant relations for the solvent. 

The characterization of a DI solution can be carried out along different but equivalent routes. In fact, we mentioned one example already in Section 3.6, where we introduced the chemical potential of a single particle in a solvent. Here, we have chosen the Kirkwood-Buff theory to provide the basic relations from which we derive the limiting behavior of DI solutions. The appropriate relations needed from Section 4.5 are (4.50), (4.79), and (4.54) which, when specialized to a two-component system, can be rewritten as 

The term simple mixture was introduced by Guggenheim (1959). Originally, it was defined in terms of the excess Gibbs free energy. From (4.121) and (4.111), we get 

Note that the response of the chemical potential to variations in the density is different for each set of thermodynamic variables. The three derivatives in (4.123)-(4.125) correspond to three different processes. The first corresponds to a process in which the chemical potential of the solvent is kept constant (the temperature being constant in all three cases) and therefore is useful in the study of osmotic experiments. This is the simplest expression of the three, and it should be noted that if we simply drop the condition of constant, we get the appropriate derivative for the pure A component system. This is not an accidental result in fact, this is the case where strong resemblance exists between the behavior of the solute 4 in a solvent B under constant and a system 4 in a vacuum which replaces the solvent. We return to this analogy later and compare the virial expansion of the pressure with the corresponding virial expansion of the osmotic pressure. 

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The dilute-ideal (DI) solutions. This is the case which has attracted the most attention in solution chemistry. Unfortunately, this is also the case where most of the misconceptions have been involved. Here, we only focus on one aspect of the problem, namely the identification of the so-called mixing terms. Consider the case of a very dilute solution of A in B, such that NA [Pg.343]

The second class, referred to as symmetric ideal (SI) solutions, emerges whenever the various components are similar to each other. There are no restrictions on the magnitude of the intermolecular forces or on the densities. The third class, dilute ideal (DI) solutions, consists of those solutions for which at least one component is very diluted in the remaining solvent, which may be a one-component or a multicomponent system. Again, there is no restriction on the strength of the intermolecular forces, the total density, or the degree of similarity of the various components. 

In the previous two sections we have discussed deviations from ideal-gas and symmetrical ideal solutions. We have discussed deviations occurring at fixed temperature and pressure. There has not been much discussion of these ideal cases in systems at constant volume or of constant chemical potential. The case of dilute solutions is different. Both constant, T, P and constant T, pB (osmotic system), and somewhat less constant, T, V have been used. It is also of theoretical interest to see how deviations from dilute ideal (DI) behavior depends on the thermodynamic variable we hold fixed. Therefore in this section, we shall discuss all of these three cases. 

The coordinate x in eq. (5-33) appears only as a differential, so that the choice of the origin of the coordinate system for this definition is unimportant. Also, no assumption of a constant molar volume has been made. For ideal dilute solutions, 1, A2 0, and is constant. It then follows from eq. (5-33) that is equal to -5 dc2ldx. This is in agreement with eq. (5-29). It can be seen that for ideal dilute solutions the component diffusion coefficient Di and the chemical diffusion coefficient 3 are identical. 

Solution We wish to avoid as much as possible the production of di- and triethanolamine, which are formed by series reactions with respect to monoethanolamine. In a continuous well-mixed reactor, part of the monoethanolamine formed in the primary reaction could stay for extended periods, thus increasing its chances of being converted to di- and triethanolamine. The ideal batch or plug-flow arrangement is preferred, to carefully control the residence time in the reactor. 

Symmetrical Dialkyl-Substituted Polysilylenes Because of their extremely sharp order-disorder transitions, the nonpolar, symmetrical dialkyl-substituted polysilylenes are almost ideal systems with which to test the predictions discussed earlier. The predicted solvent dependence of Tc was tested by performing a series of experiments with high-molecular-weight poly(di-n-hexylsilylene) in dilute solution. Experimental results for six solvents are listed in Table II, and the theoretically defined solvation coupling constants and solvent parameters are collected in Table III. 

Garnet-structure ferrites. Garnet, ideally A3 B2[T04]3, is isometrie (Ia3d) with a straeture built of TO4 tetrahedra and BOe oetahedra linked by shared vertiees that form AOg dodeeahedra. The A-sites aeeommodate divalent (Ca, Mn, Fe) and trivalent (Y, REE) elements. The B-site may contain various di-, tri- (Fe, Al, Ga, Cr, Mn, In, Sc, Co), tetra- (Zr, Ti, Sn, Ru) and even pentavalent elements (Nb, Ta, Sb). The T-sites are filled with tetravalent (Si, Ge, Sn) but may be also occupied by trivalent (Al, Ga, Fe) and pentavalent (P, V, As) elements. Synthetic garnets form multicomponent solid solutions that provide opportunities for incorporating of HEW elements into the structure [149]. 

That double channel electrodes are ideally suited to the study of electrode reaction mechanisms involving following chemical reactions is illustrated by reference to studies on the electrochemical oxidation of 4-amino-iV, N,-di-methylaniline (ADMA) in basic solution at a platinum electrode [125], This reaction is thought to proceed via the scheme... 

Convergence is obtained when the appropriate guess for d p./di at the reactor inlet predicts the correct Danckwerts condition in the exit stream, within acceptable tolerance. To determine the range of mass transfer Peclet numbers where residence-time distribution effects via interpellet axial dispersion are important, it is necessary to compare plug-flow tubular reactor simulations with and without axial dispersion. The solution to the non-ideal problem, described by equation (22-61) and the definition of Axial Grad, at the reactor outlet is I/a( = 1, RTD). The performance of the ideal plug-flow tubular reactor without interpellet axial dispersion is described by... 

Strained cyclophanes as ligands for chromium metal, are ideal objects for investigations of the magnetic environment at the periphery of di(benzene)-chromium (52), because of the preservation of their conformation in solution. For the purpose of drawing up a map of the cone of anisotropy around 52,... 

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