Excess Gibbs-energy Methods

Althought originally developed for systems involving nonelectrolytes, the NRTL model has successfully been applied to correlate the UCST behaviour of binary ionic liquid with water 207,20s organics.  

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Because measurement of the phase behaviour of ionic liquid systems is time consuming, it is desirable to develop predictive methods to estimate this. Different approaches were proposed for modeling the phase behaviour of ionic liquid systems (i) molecular simulations, (ii) excess Gibbs-energy methods, (iii) equation of state modeling and (iv) quantum chemical methods. 

The relation [3.87] hnks the solutions described by the Lewis method of coefficients of activity and the excess Gibbs energy method. Both methods are therefore equivalent. 

Note.- The Van Laar law is, however, suitable for certain liquid alloys and also another model nsing an excess Gibbs energy method has been given. 

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. 

VLE data are correlated by any one of thirteen equations representing the excess Gibbs energy in the liquid phase. These equations contain from two to five adjustable binary parameters these are estimated by a nonlinear regression method based on the maximum-likelihood principle (Anderson et al., 1978). 

R. C. Pemberton and C. J. Mash. "Thermodynamic Properties of Aqueous Non-Electrolyte Mixture II. Vapour Pressures and Excess Gibbs Energies for Water-)- Ethanol at 303,15 to 363.15 K. Determined by an Accurate Static Method". J. Chem. Thermodyn., 10. 867-888 (1978). 

In many cases the CALPHAD method is applied to systems where there is solubility between the various components which make up the system, whether it is in the solid, liquid or gaseous state. Such a system is called a solution, and the separate elements (i.e., Al, Fe...) and/or molecules (i.e., NaCl, CuS...) which make up the solution are defined as the components. The model description of solutions (or solution phases) is absolutely fundamental to the CALPHAD process and is dealt with in more detail in chapter S. The present chapter will discuss concepts such as ideal mixing energies, excess Gibbs energies, activities, etc. 

With the appropriate choice of the reference state, values of the molar excess Gibbs energy can be determined over the entire range of composition of the ternary system by making studies on a set of pseudobinary systems. Values of A/if and A/iE can then be calculated by means of the usual methods. 

Pemberton R.C., Mash C.J., "Thermodynamic properties of aqueous nonelectrolyte mixtures II. Vapour pressures and excess Gibbs energies for water + ethanol at 303.15 K to 363.15 K determined by an accurate static method"., J. Chem. Therm., 1978, 10, 867-88. 

The local composition model (LCM) is an excess Gibbs energy model for electrolyte systems from which activity coefficients can be derived. Chen and co-workers (17-19) presented the original LCM activity coefficient equations for binary and multicomponent systems. The LCM equations were subsequently modified (1, 2) and used in the ASPEN process simulator (Aspen Technology Inc.) as a means of handling chemical processes with electrolytes. The LCM activity coefficient equations are explicit functions, and require computational methods. Due to length and complexity, only the salient features of the LCM equations will be reviewed in this paper. The Aspen Plus Electrolyte Manual (1) and Taylor (21) present the final form of the LCM binary and multicomponent equations used in this work. 

The problem of expressing the excess Gibbs energy as a function of composition has been researched extensively, and many methods of varying accuracy and usefulness have been proposed. An extensive discussion of these methods is given by Hala et al. (2), who show that many common expressions—e.g., those of van Laar and Margules—are deduced from the general expression of Wohl (3). 

Vapor/liquid equilibrium (VLE) block diagrams for, 382-386, 396,490 conditions for stability in, 452-454 correlation through excess Gibbs energy, 351-357, 377-381 by Margules equation, 351-357 by NRTL equation, 380 by Redlich/Kister expansion, 377 by the UNIFAC method, 379, 457, 678-683... 

Michelsen, M. L., 1990a. A method for incorporating excess Gibbs energy models in equations of state. Fluid Phase Eq 60 47—58. 

Only solid solutions were present under the conditions of the investigation of the Fe-Co [242], Ni-Cu [250], and SnTe-PbSe [262] systems given in Table 7. The thermodynamic activities, excess Gibbs energies, mixing enthalpies and excess entropies were determined by the use of the ion intensity ratio method for the Fe-Co and Ni-Cu systems as described for the melts. The partial pressure of the molecules SnTe, SnSe, PbTe, and PbSe were obtained for different compositions of the quasi-binary system SnTe-PbSe using the isothermal evaporation technique. 

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