Universal Quasi-Chemical UNIQUAC Equation

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 equation, which is generalized to multi-component mixtures, requires pure component data for the van der Waals area and volume parameters, and r. Additionally, the binary interaction parameters (Uj -Uj and (Wy - are also required and are generally determined from binary phase equilibrium data. Temperature dependency is incorporated in the equation, similar to the Wilson and NRTL equations. The UNIQUAC equation is applicable to many classes of components, including mixtures containing considerably dissimilar molecules, and is also applicable to liquid-liquid equilibrium systems. It can represent temperature dependency over moderate ranges but is not necessarily more accurate than simpler equations in spite of its theoretical foundation. 

The UNIQUAC equation is the basis for the development of the group contribution method, the UNIFAC equation, which predicts liquid activity coefficients from component structures on the basis of interactions between chemical functional groups. 

Parameters for activity coefficient equations can be determined from the experimental data. Describe a procedure to calculate the Wilson equation parameters for a binary solution from infinite dilution data. 

= 0 (Xj = 1), the activity coefficient of component 1 is the infinite dilution activity coefficient, 7, . 

---

It would be desirable to apply analytical expressions for the activity coefficient, which are not only able to describe the concentration dependence, but also the temperature dependence correctly. Presently, there is no approach completely fulfilling this task. But the newer approaches, as for example, the Wilson [13], NRTL (nonrandom two liquid theory) [14], and UNIQUAC (universal quasi-chemical theory) equation [15] allow for an improved description of the real behavior of multicomponent systems from the information of the binary systems. These approaches are based on the concept of local composition, introduced by Wilson [13]. This concept assumes that the local composition is different from the overall composition because of the interacting forces. For this approach, different boundary cases can be distinguished ... 

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).]... 

These models are semiempirical and are based on the concept that intermolecular forces will cause nonrandom arrangement of molecules in the mixture. The models account for the arrangement of molecules of different sizes and the preferred orientation of molecules. In each case, the models are fitted to experimental binary vapor-liquid equilibrium data. This gives binary interaction parameters that can be used to predict multicomponent vapor-liquid equilibrium. In the case of the UNIQUAC equation, if experimentally determined vapor-liquid equilibrium data are not available, the Universal Quasi-chemical Functional Group Activity Coefficients (UNIFAC) method can be used to estimate UNIQUAC parameters from the molecular structures of the components in the mixture3. 

Modern theoretical developments in the molecular thermodynamics of liquid-solution behavior are based on the concept of local composition. Within a liquid solution, local compositions, different from the overall mixture composition, are presumed to account for the short-range order and nonrandom molecular orientations that result from differences in molecular size and intermolecular forces. The concept was introduced by G. M. Wilson in 1964 with the publication of a model of solution behavior since known as the Wilson equation. The success of this equation in the correlation of VLE data prompted the development of alternative local-composition models, most notably the NRTL (Non-Random-Two Liquid) equation of Renon and Prausnitz and the UNIQUAC (UNIversal QUAsi-Chemical) equation of Abrams and Prausnitz. A further significant development, based on the UNIQUAC equation, is the UNIFAC method,tt in which activity coefficients are calculated from contributions of the various groups making up the molecules of a solution. 

There are many other equations, which have been proposed, that do not result from Wohl s method. Two of the most popular equations are the Wilson and the universal quasi-chemical theory (UNIQUAC) by Abrams and Prausnitz.These equations are based on the concept of local composition models, which was proposed by Wilson in his paper. It is presumed in a solution that there are local compositions that differ... 

The Universal Quasi-chemical Theory or UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts. The dominant entropic contribution is described by a combinatorial part ( ). Intermolecular forces responsible for the enthalpy of mixing are described by a residual part ( ). The sizes and shapes of the molecule determine the combinatorial part, which is thus dependent on the compositions and requires only pure component data. Since the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. As the UNIQUAC equations are about as simple for multi-component solutions as for binary solutions, the UNIQUAC equations for multicomponent solutions are given below. Species are identified by subscript i, subscript j is a dummy index. Here, is a relative molecular surface area and r, is a relative molecular volume. Both of these quantities are pure-species parameters. 

Laar Margules Wilson nonrandom, two liquid phases (NRTL), or Renon-Prausnitz and Universal Quasi-Chemical Activity Coefficients (UNIQUAC). All of these equations have two constants except for the NRTL, which has three. 

Uniquac equation (universal quasi chemical) Method based on the principle of the local compositions, similar to the Wilson and NRTL equations, which are derived as special cases also describes real liquid phases only valid for small and medium operating pressures Gmehung, j., Anderson, T.F., and Prausnitz, J.M., Ind. Eng. Chem. Fund. 17 (1978) 269. 

Here yil and yi2 are the corresponding activity coefficients of component i in phase 1 and 2, xil, and xi2 are the mole fraction of components i in the system and in phase 1 and 2 respectively. The interaction parameters between cyclohexane, methanol and ethyl benzene are used to estimate the activity coefficients from the UNIQUAC groups. Equations (1) and (2) are solved for the mole fraction (x) of component i in the two liquid phase. The UNIQUAC model (universal quasi-chemical model) is given by Abrams and prausnitz (Kojima and Tochigi, 1979) as or... 

It is evidently of considerable interest to be able to predict activity coefficients without resorting to experimentation, and immense strides have in fact been made in recent decades to accomplish this goal. Among a number of promising approaches, an analytical expression known as the UNIQUAC equation (UNIversal QUAsi Chemical equation) has received the most widespread acceptance. In this model, the activity coefficient is decomposed into two constituents, one of which, termed combinatorial (C), accounts for molecular size and shape differences, while the other, denoted residual (R), expresses effects due to molecular interactions. 

In 1975, Abrams and Prausnitz published a new equation for the Gibbs free energy of mixtures which they called UNIQUAC (universal quasi-chemical). It contains two interaction parameters per binary pair in the mixture and two parameters characteristic of each component. The utility of UNIQUAC was extended considerably with the development of UNIFAC (UNIQUAC func-... 

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 ... 

---