Redlich-Kister equations

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

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... 

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... 

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... 

The two-constant Wilson equation was chosen as the correlating equation rather than the three-constant Redlich-Kister equation (21) for two reasons. In a majority of the systems the sample deviation of vapor composition was smaller, and in certain cases the Redlich-Kister equation erroneously predicted phase separation. Figure 3 shows such an example. 

The isothermal compressibilities have been calculated with eq 5, using for the isothermal compressibilities of the pure substances the data from refs 53—56 (only the value for 2-butanol was taken as that for isobutanol). The data have been fitted using the Redlich—Kister equation.The values of D have been obtained from the activity coefficients or total pressure data by the sliding polynomials method. To check the accuracy of our calculations, the D values have been... 

The excess Gibbs energy of the ternary mixture was expressed through the Wilson [38], NRTL [39] and Zielkiewicz [32] expressions. Because of the agreement between the latter two expressions, detailed results are presented only for the more simple NRTL expression. The parameters in the NRTL equation were found by htting x-P (the composition of liquid phase-pressure) experimental data [32]. The derivatives (9 i/9xi) c2 ( IX2/dx2)xi and (diX2/dxi)x2 in the ternary mixture were found by the analytical differentiation of the NRTL equation. The excess molar volume (V ) in the binary mixtures (i-j) was expressed via the Redlich-Kister equation... 

CNIBS/R-K is the combined nearly ideal binary solvent/Redlich-Kister equations (Acree et al., 1991). The value of MPD was taken from Table 2 of the Jouyban-Gharamaleki et al. (1999) paper. 

The prediction of the solubility of poorly soluble substances of environmental significance in multicomponent (ternary and higher) aqueous mixed solvents is a difficult task because it requires the knowledge of the activity coefficient of a solute in a multicomponent mixed solvent. The method most often used for the solubility of a solid in ternary and multicomponent mixed solvents is the combined nearly ideal binary solvent/Redlich - Kister equation (33). That equation was applied to the solubility of a solid in ternary... 

In the second approach, which finds application in real systems, validity of the general Redlich-Kister equation for the excess property is supposed. For description of the composition dependence on the given property Y (molar volume, surface tension) in the system, the following equation is then used (e.g. for a ternary system)... 

A simple function of composition (in a binary mixture) satisfying this boundary condition is the Redlich-Kister equation... 

Leinonen and Mackay (5) used this method with the Redlich-Kister equation for the hydrocarbon phase activity coefficients to predict mixture solubilities. Agreement with experiment was good for mixtures of benzene with n-hexane, 1-hexane, and 2-methylpentane and for cyclohexane mixtures with the same substances. 

To begin, Vernier and coworkers reported that the excess free energy of mixing of AN + PH at 34°C could be represented across the entire composition range to a fair degree of approximation by the Redlich-Kister equation ... 

In this volume, the Redlich-Kister equation, Eq. (1.30), identifier RK2XMIN1, has been selected among the various equations which have been proposed for G (Chap. 1.5). The vapour pressure P, Eq. (1.44), the vapor... 

This four volumes series contains vapor-liquid equilibrium data (i.e., compositions of vapor and liquid phases as functions of temperature and pressure) covering the regions for which experimental measurements exi t. The systems are almost entirely organic. The data have been recalculated Into SI units and have been smoothed in many cases, often using the Redlich-Kister equation. There are detailed references to the source literature and there is an alphabetic index of the systems covered. The four volumes are ... 

If the activity data of the bulk phase are known, the value of fC can be calculated at a given value of r = Vm,2/Vm,i by means of computer iteration [71,73]. The Redlich-Kister equation has proven perfectly reliable for calculating the activities its application allows the calculation of the activity coefficients of components 1 and 2, and, on this basis, functions Uj = /(xO and U2 = /(X2) can be given [51]. The applicability of Eq. (21) is demonstrated in Fig. 13. It is revealed by the adsorption equilibrium diagrams that for the adsorption of a liquid pair made up of components significantly different in polarity covered by alkyl chains, the value of the equilibrium constant IC decreases with increasing hydrophobicity of the surface. 

Experimental values of excess molar volume and change of refractive index of binary mixtures were correlated by Redlich-Kister equation (Ottani and Comelli, 2005). The binary contribution was used to correlate the experimental ternary results with the Cibulka equation (Al-Jimaz et al., 2004). Several methods to predict density and refractive index of mixtures were applied to test their validity in the systems studied. 

Binary systems Density and refractive index Liquid mixtures Molar volume Redlich-Kister equation Ternary mixtures... 

The Guggenheim and Redlich-Kister equations (Guggenheim, 1937 Redlich and Kister, 19 8a, b King, 1969 pp.325-327) ... 

Wilson, G. M. Vapor liquid equilibria, correlation by means of a modified Redlich-Kister equation of state. Adv. Cryog. Eng. 9 168-176 (1964). 

The most formal, -power expansion is represented by the Redlich-Kister equation (which is equivalent to the Margules one), see (48RED1). For a binary 1-2 system ... 

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