Excess Gibbs energy UNIQUAC

Since the accuracy of experimental data is frequently not high, and since experimental data are hardly ever plentiful, it is important to reduce the available data with care using a suitable statistical method and using a model for the excess Gibbs energy which contains only a minimum of binary parameters. Rarely are experimental data of sufficient quality and quantity to justify more than three binary parameters and, all too often, the data justify no more than two such parameters. When data sources (5) or (6) or (7) are used alone, it is not possible to use a three- (or more)-parameter model without making additional arbitrary assumptions. For typical engineering calculations, therefore, it is desirable to use a two-parameter model such as UNIQUAC. 

We can estimate the activity coefficients by using the excess Gibbs energy models. Based on the local composition concept, the Wilson, NRTL, and UNIQUAC models for excess Gibbs energy provide relations for activity coefficient... 

The question remains, however, of whether the solution is in fact infinitely dilute at a solute concentration of xi. Only if this is true is it valid to assume that yi = y - Literature values of solubility data for several compounds in water were used to obtain parameters for the UNIQUAC and NRTL excess Gibbs energy expressions, and y values for these compounds were calculated. The calculated values are compared with inverse solubility data in Table I. The inverse solubility predicts lower values of y in all cases. However, the difference becomes smaller as the solubility decreases, and for compounds with solubility less than 0,5% the difference is less than 10%. It has been shown that these excess Gibbs energy expressions, while very useful, are not the exact representation of the composition dependence of activity coefficient all expressions have difficulty in representing liquid-liquid equilibria (43-44). Thus, extrapolating these expressions to infinite dilution may be in error. It is therefore inconclusive as to the correctness of using the inverse solubility to calculate... 

The UNIQUAC equation (Abrams and Prausnitz, 1975) is based on the two-liquid model in which the excess Gibbs energy is assumed to result from differences in molecular sizes and structures and from the energy of interaction between the molecules. 

The activity coefficients are typically computed from a model for the excess Gibbs energy g, as described in the thermodynamics chapter (Chapter 4). The most popular are the Wilson, NRTL, and Uniquac models, described in detail in many places [15, 36 0]. They contain two or three adjustable (and possibly temperature-dependent) parameters per binary. One cannot predict which model will be best for a given system however, the Wilson equation is incapable of describing LEE. 

The UNIQUAC method requires complete calculation in each specific case. Now, though, we are going to examine the concept of the contribution of groups, which can be used to calculate certain properties of the molecules a priori, using relatively small databases, and the application to a model to calculate the excess Gibbs energy a priori. 

The extension of the UNIQUAC model to ionic solutions was first envisaged by Sander et al. in 1986. The basic idea is to think of the excess Gibbs energy of an ionic solution as being the siun of two contributions ... 

More sophisticated models for have been developed from molecular principles. For example, the universal quasi-chemical theory, UNIQUAC, is an extension of the Wilson equation. It divides the excess Gibbs energy into two parts, one due to entropy, the combinatorial part, and one due to ener, the residual part ... 

The UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts, the combinatorial part and a part describing the inter-molecular forces. The sizes and shapes of the molecule determine the combinatorial part and are thus dependent on the compositions and require only pure component data. As the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. The UNIQUAC equations are about as simple for multicomponent solutions as for binary solutions. Parameters for the UNIQUAC equations can be found by Gmehling, Onken, and Arlt. ... 

In UNIQUAC the excess Gibbs free energy is computed from two contributions. The first called combinatorial part represents the influence of the structural parametejs, as size (parameter r) and shape (area parameter q). The second called the residual part account for the energy of interactions between segments. In the case of a binary mixture the expression for the excess Gibbs free energy is ... 

The name of this model is an acronym of universal quasichemical, the name of the theory used to drive it. Like the Flory-Huggins model, UNIQUAC separates nonideal contributions to the excess Gibbs free energy into a combinatorial and a residual term ... 

The model s creators showed that a certain number of classic models of solutions published previously were actually included in the UNIQUAC model, as they appear to be particular cases. By way of certain approximations performed on equations [3.152], [3.153] and [3.154], we obtain the expressions of the excess molar Gibbs energy for these different models. Table 3.3 lists some of these simplifications. 

Abrams and Prausnitz (1975) combined Guggenheim s quasi-chemical tiieory with the concept of local compositions to develop the Universal Quasi-Chemical (UNIQUAC) expression for the excess Gibbs free energy. [The equation can be also developed from the two-fluid theory (Maurer and Prausnitz, 1978).]... 

The earliest equations for Gibbs excess energy, like Margules and van Laar, were largely empirical. More recent equations and NRTL and UNIQUAC are based on a semiempirical physical model, called the two-liquid theory, based on local composition. The molecules do not mix in a random way, but because of different bonding effects, the molecules prefer a certain surrounding. This results in a composition at the molecular level, the local composition, which differs from the macroscopic composition. 

TABLE D.6 UNIQUAC Model for Binary Systems Dimensionless Gibbs excess energy... 

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