Wilson equation advantage

A significant advantage of the Wilson equation is that it can be used to calculate the equilibrium compositions for multicomponent systems using only the Wilson coefficients obtained for the binary pairs that comprise the multicomponent mixture. The Wilson coefficients for several hundred binary systems are given in the DECHEMA vapour-liquid data collection, DECHEMA (1977), and by Hirata (1975). Hirata gives methods for calculating the Wilson coefficients from vapour liquid equilibrium experimental data. 

An advantage of the Wilson equation is that it involves only two parameters per binary and may be extended, without further information, to estimate multi-component phase equilibrium behavior. 

The Flory-Huggins and Wilson equations for the activity coefficients of the components of the mixed solvent were employed to correlate 32 experimental data sets regarding the solubility of drugs in aqueous mixed solvents. The results were compared with the models available in literature. It was found that the suggested equation can be used for an accurate and reliable correlation of the solubilities of drugs in aqueous mixed binary solvents. It provided slightly better results than the best literature models but has also the advantage of a theoretical basis. 

The Wilson equation will not result in the prediction of liquid-liquid phase splitting and therefore can not be used in such applications or for vapor-liquid-liquid equilibria. The NRTL model has the advantage of having three adjustable parameters that allow it to be used for fitting the phase behavior of highly nonideal mixtures, though sometimes a is set to a fixed value (usually 0.2 for liquid-liquid equilibria and 0.3 for vapor-liquid equilibria). 

Abrams and Prausnitz found that for vapor-liquid systems, the UNIQUAC equation is as accurate as the Wilson equation. However, an important advantage of the UNIQUAC equation lies in its applicability to liquid-liquid systems, as discussed in Section 5.8. Abrams and Prausnitz also give a one-parameter form of the UNIQUAC equation. The methods previously described can be used to determine UNIQUAC parameters from infinite-dilution activity coefficients or from azeotropic or other single-point data. 

For a binary mixture, (J.0.6) reduces to (J.0.1) while (J.0.7) reduces to (J.0.3) and (J.0.4). Like the Wilson equations, one advantage to the NRTL model is that all adjustable parameters are binary parameters, so no multicomponent data are needed to obtain their values. Parameter values for a few selected binaries are given in Table J.l. 

To solve these equations two terms have to be provided from experimental data, i.e., the two differences involving the interaction energies, ) i,b ab > which are generally not predictable. The variables v°l v l are the molar volumes of the pure components. The major advantage of the Wilson equations is that they render... 

For energies below the dissociation threshold we can use various coordinate systems to solve the nuclear Schrodinger equation (2.32). If the displacement from equilibrium is small, normal coordinates are most appropriate (Wilson, Decius, and, Cross 1955 ch.2 Weissbluth 1978 ch.27 Daudel et al. 1983 ch.7 Atkins 1983 ch.ll). However, if the vibrational amplitudes increase so-called local coordinates become more advantageous (Child and Halonen 1984 Child 1985 Halonen 1989). Eventually, the molecular vibration becomes unbound and the molecule dissociates. Under such circumstances, Jacobi or so-called scattering coordinates are the most suitable coordinates they facilitate the definition of the boundary conditions of the continuum wavefunctions at infinite distances which we need to determine scattering or dissociation cross sections (Child 1991 ch.l0). Normal coordinates become less and less appropriate if the vibrational amplitudes increase they are completely impractical for the description of unbound motion in the continuum. 

The NRTL equations— Eqnation (4.386), Eqnation (4.387), and Eqnation (4.391)—contain three parameters for each binary system that are adjusted to fit data. Experience indicates that a varies in the range 0.20 to 0.47. Where experimental data are scarce, the value of a can be set by referring to known valnes of similar mixtnres. Renon and Pransnitz [8] recommended values for broad classes of mixtures. A typical value of a is 0.3. The NRTL equation offers advantages over the Wilson eqnation for strongly nonideal mixtures, and especially for partially miscible systems. 

Highly promising models were obtained by using so-called G models for cubic equations of state. Apart from the description or precalculation of the behavior of highly polar systems, these models allow supercritical components to be taken into account. A further advantage of these models is that, in addition to phase equilibria, other important quantities such as densities and caloric data can be calculated. The required G values can be obtained either by fitting the parameters of proven G models (e.g., Wilson, NRTL, or UNIQUAC equation) to experimental phase equilibrium data, or with the aid of group-contribution methods such as UNIFAC. 

Local mole fractions were introduced by Wilson to define the local volume fraction, where the deviation from the macroscopic concentration is taken into account with the help of interaction energies between the different compounds using Boltzmann factors. With the introduction of the auxiliary quantities A,j the equations for and y can be derived. The great advantage of the Wilson < quation is that only binary... 

One of the disadvantages of the Free-Wilson method is that— unlike regression equations based on physicochemical parameters— it cannot be used to make predictions for substituents not included in the original analysis. The technique may break down when there are linear dependencies between the structural descriptors, for example, when two substituents at two positions always occur together, or where interactions between substituents occur. Advantages of the technique include its ability to handle data sets with a small number of substituents at a large number of positions, a situation not well handled by other analytical methods, and its ability to describe quite unusual substituents since it does not require substituent constant data. A number of variations and improvements have... 

This technique provided three advantages it increased sensitivity by 3-fold, it eliminated a concern about oxygen contamination, and it was more applicable than H2 chemisorption to used catalysts, which might have some contamination. The small amoimts of H2O formed were adsorbed by the support or by the walls of the cell if T < 273 K [27,28]. Subsequent studies indicated that for very highly dispersed Pt catalysts this titration stoichiometry could change from Oad Had Ht tr = 1 1 3 (Eq. 3.9) to 1 2 4 [60]. Wilson and Hall then showed that chemical equation 3.6 for large Pt crystallites shifts to chemical equation 3.5 for small Pt particles, which then gives a 1 2 4 ratio [51], i.e., the titration reaction becomes... 

The equation of Wilson has the advantage that for a binary mixture the experimental values can be well represented with only two constants, whereas other equations such as eq. (15) require 3 to S constants for the same accuracy. Furthermore in many cases the eq. (18) of Wilson represents the whole behaviour of a ternary mixture, if only the 3 2=6 constants are used, which are obtained for the three binary mixtures containing the same components Nevertheless small alterations of the Wdson-equation have been proposed to improve further its accuracy. 

Explain the practical advantages of Wilson s equation over that of van Laar. 

---