Redlich-Kister

Compilation of vapor-liquid equilibrium data data are correlated with Redlich-Kister equation (in Polish). 

An equivalent power series with certain advantages is known as the Redlich/Kister expansion (Redlich, Kister, and Turnquist, Chem. Eng. Progr. Symp. Ser. No. 2, 48, pp. 49-61 [1952]) qe... 

The Redlich-Kister [55, 57] equations provide a good technique for representing liquid phase activity and classifying solutions. 

A similar derivation gives equation (5.34). To use equations (5.33) and (5.34) to calculate V and 1+, must be known as a function of xj or.vi. An expression often used is the Redlich-Kister equation, given by... 

Equations (7.93) and (7.94) are usually applied to mixtures of nonelectrolytes where Raoult s law standard states are chosen for both components. For these mixtures, Hi is often expressed as a function of mole fraction by the Redlich-Kister equation given by equation (5.40). That is... 

Randall, M. 1. 264. 265 Raoult s law 268-73 and phase equilbria 419. 423 standard state 289 Rectilinear diameters, law of 393 Redlich-Kister equation 220, 362 Redlick-K wong equation 256 relative apparent molar enthalpy of solutions 356-7... 

The third term of Eq. (14), Gxs, is the excess term of the free energy. Although several of the aluminum alloys considered here form ordered intermetallic compounds, a regular-solution type model was used to describe their excess free energy. Gxs is described by the following Redlich-Kister polynomial,... 

Figure 3.11 Contributions to the molar excess Gibbs energy of mixing from the four first terms of the Redlich-Kister expression (eq. 3.76). For convenience Q - A1 - A2 - A3 1.

Guggenheim s polynomial expansion (equation 3.171 Guggenheim, 1937) and the two Redlich-Kister equations (3.172 and 3.173 Redlich and Kister, 1948) are of general applicability for any type of mixture ... 

Taking this process further, more complex composition dependencies to Q can be considered and it is straightforward to show that a general formula in terms of a power series should provide the capability to account for most types of composition dependence (Tomiska 1980). The most common method is based on the Redlich-Kister equation and Eq. (5.19) is expanded to become... 

Here the first term represents the lattice stability components of the phase , the second term the Gibbs energy contribution arising from cluster calculations and the third term is the excess Gibbs energy expressed in the form of a standard Redlich-Kister polynomial (see Chapter 5). 

The mass action model (MAM) for binary ionic or nonionic surfactants and the pseudo-phase separation model (PSM) which were developed earlier (I EC Fundamentals 1983, 22, 230 J. Phys. Chem. 1984, 88, 1642) have been extended. The new models include a micelle aggregation number and counterion binding parameter which depend on the mixed micelle composition. Thus, the models can describe mixtures of ionic/nonionic surfactants more realistically. These models generally predict no azeotropic micellization. For the PSM, calculated mixed erne s and especially monomer concentrations can differ significantly from those of the previous models. The results are used to estimate the Redlich-Kister parameters of monomer mixing in the mixed micelles from data on mixed erne s of Lange and Beck (1973), Funasaki and Hada (1979), and others. 

To this point we have used no specific mixing rule to describe the interactions of monomers of surfactants 1 and 2 in the micellar pseudophase. We have assumed, however, that only one micellar pseudo-phase exists. For our calculations we have used the Redlich-Kister expansion for w(x) with up to two parameters (10,12). Moreover, we have not yet specified the form of the function y9(x), which can be varied for modeling specific counterion association behavior. For our calculations we have used the following linear function for /3(x) ... 

Figure 1.3 for [C4CjIm][CjS04] (1) + 1-hexanol (2) mixtures at 298.15 K. Points, experimental results from Domanska, U. et al. Solid line, Redlich-Kister correlation. (Adapted from Domanska, U., Pobudkowska, A., and Wisniewska, A., /. Solution Chem., 35,311,2006.)... 

An accurate representation of the phase equilibrium behavior is required to design or simulate any separation process. Equilibrium data for salt-free systems are usually correlated by one of a number of possible equations, such as those of Wilson, Van Laar, Margules, Redlich-Kister, etc. These correlations can then be used in the appropriate process model. It has become common to utilize parameters from such correlations to obtain insight into the fundamentals underlying the behavior of solutions and to predict the behavior of other solutions. This has been particularly true of the Wilson equation, which is shown below for a binary system. 

Using the Redlich-Kister expansion (16) an expression for Y /acjj was developed at Kigh temperatures using vapor-liquid equilibrium data for... 

The Redlich/Kister expansion, the Margules equations, and the van equations are all special cases of a very general treatment based on ratio functions, i.e., on equations for Ge given by ratios of polynomials. These... 

Reaction coordinate, 497-501 Redlich/Kister expansion, 377 Redlich/Kwong equation of state, 82-86, 487-489... 

Since x2 = 1 - x, for a binary system of species 1 and 2, x, can be taken as the single independent variable. An equivalent poweT series with certain advantages is known as the Redlich/Kister expansion t... 

Such data are also often represented by equations similar to those used for GE data, in particular by the Redlich/Kister expansion (Sec. 12.4). 

Calculate the coefficients of Van Laar equations and the three-suffix Redlich-Kister equations from experimental solubility data at 70°C (158°F, or 343 K) for the water(l)/trichloroethylene(2) system. The Van Laar equations are... 

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