Thermodynamic mixing model

Witlox, H. W. M., 1993, Thermodynamics Model for Mixing of Moist Air with Pollutant Consisting of HF, Ideal Gas, and Water, Shell Research Limited, Thornton Research Center, TNER.93.021,. 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

Thermodynamic models are widely used for the calculation of equilibrium and thermophysical properties of fluid mixtures. Two types of such models will be examined cubic equations of state and activity coefficient models. In this chapter cubic equations of state models are used. Volumetric equations of state (EoS) are employed for the calculation of fluid phase equilibrium and thermophysical properties required in the design of processes involving non-ideal fluid mixtures in the oil and gas and chemical industries. It is well known that the introduction of empirical parameters in equation of state mixing rules enhances the ability of a given EoS as a tool for process design although the number of interaction parameters should be as small as possible. In general, the phase equilibrium calculations with an EoS are very sensitive to the values of the binary interaction parameters. 

In several occasions the overall fit obtained by the CLS estimation could simply be found unacceptable despite the fact that the predictions of erroneous phase separation have been suppressed. In such cases, one should proceed and either modify the employed mixing rules or use a different EoS all together. Of course, the estimation should start from Step 1 once the new thermodynamic model has been chosen. Calculations using... 

However, in most aqueous electrolyte systems of industrial interest, not only strong electrolytes but also weak electrolytes and molecular nonelectrolytes are present. While the modified Pitzer equation appears to be a useful tool for the representation of aqueous strong electrolytes including mixed electrolytes, it cannot be used in the form just presented to represent the important case of systems containing molecular solutes. A unified thermodynamic model for both ionic solutes and molecular solutes is required to model these kinds of systems. 

Another type of ternary electrolyte system consists of two solvents and one salt, such as methanol-water-NaBr. Vapor-liquid equilibrium of such mixed solvent electrolyte systems has never been studied with a thermodynamic model that takes into account the presence of salts explicitly. However, it should be recognized that the interaction parameters of solvent-salt binary systems are functions of the mixed solvent dielectric constant since the ion-molecular electrostatic interaction energies, gma and gmc, depend on the reciprocal of the dielectric constant of the solvent (Robinson and Stokes, (13)). Pure component parameters, such as gmm and gca, are not functions of dielectric constant. Results of data correlation on vapor-liquid equilibrium of methanol-water-NaBr and methanol-water-LiCl at 298.15°K are shown in Tables 9 and 10. 

By using a thermodynamic model based on the formation of self-associates, as proposed by Singh and Sommer (1992), Akinlade and Awe (2006) studied the composition dependence of the bulk and surface properties of some liquid alloys (Tl-Ga at 700°C, Cd-Zn at 627°C). Positive deviations of the mixing properties from ideal solution behaviour were explained and the degree of phase separation was computed both for bulk alloys and for the surface. 

The mixed-potential model demonstrated the importance of electrode potential in flotation systems. The mixed potential or rest potential of an electrode provides information to determine the identity of the reactions that take place at the mineral surface and the rates of these processes. One approach is to compare the measured rest potential with equilibrium potential for various processes derived from thermodynamic data. Allison et al. (1971,1972) considered that a necessary condition for the electrochemical formation of dithiolate at the mineral surface is that the measmed mixed potential arising from the reduction of oxygen and the oxidation of this collector at the surface must be anodic to the equilibrium potential for the thio ion/dithiolate couple. They correlated the rest potential of a range of sulphide minerals in different thio-collector solutions with the products extracted from the surface as shown in Table 1.2 and 1.3. It can be seen from these Tables that only those minerals exhibiting rest potential in excess of the thio ion/disulphide couple formed dithiolate as a major reaction product. Those minerals which had a rest potential below this value formed the metal collector compoimds, except covellite on which dixanthogen was formed even though the measured rest potential was below the reversible potential. Allison et al. (1972) attributed the behavior to the decomposition of cupric xanthate. 

No simple thermodynamic model is yet able to explain the large decrease in conductivity when partially substituting one alkali metal for another, i.e. the so-called mixed alkali effect. Systematic analysis of the pre-... 

The finding that the assumptions of the regular solution approximation do not hold for the mixed micellar systems investigated here suggests a re-examination of how the thermodynamics of mixing enter the nonideal mixed micelle model. 

The parameters of the thermodynamic model of Lindsley et al. (1981) are reported in table 5.38. The mixing properties described are those of a regular mixture for orthopyroxene and of a subregular mixture (asymmetric with Mar-... 

The purpose of this paper will be to develop a generalized treatment extending the earlier mixed micelle model (I4) to nonideal mixed surfactant monolayers in micellar systems. In this work, a thermodynamic model for nonionic surfactant mixtures is developed which can also be applied empirically to mixtures containing ionic surfactants. The form of the model is designed to allow for future generalization to multiple components, other interfaces and the treatment of contact angles. The use of the pseudo-phase separation approach and regular solution approximation are dictated by the requirement that the model be sufficiently tractable to be applied in realistic situations of interest. 

Surfactant Activity in Micellar Systems. The activities or concentrations of individual surfactant monomers in equilibrium with mixed micelles are the most important quantities predicted by micellar thermodynamic models. These variables often dictate practical performance of surfactant solutions. The monomer concentrations in mixed micellar systems have been measured by ultraf i Itration (I.), dialysis (2), a combination of conductivity and specific ion electrode measurements (3), a method using surface tension of mixtures at and above the CMC <4), gel filtration (5), conductivity (6), specific ion electrode measurements (7), NMR <8), chromatograph c separation of surfactants with a hydrophilic substrate (9> and by application of the Bibbs-Duhem equation to CMC data (iO). Surfactant specific electrodes have been used to measure anionic surfactant activities in single surfactant systems (11.12) and might be useful in mixed systems. ... 

To this point, only models based on the pseudo—phase separation model have been discussed. Mixed micelle models utilizing the mass action model may be necessary for micelles with small aggregation numbers, as demonstrated by Kamrath and Franses ( ). However, even for large micelles, the fundamental basis for the pseudophase separation model needs to be examined. In micelles, how much solvent or how many counterions (bound or in the electrical double layer) should be included in the micellar pseudo-phase is unclear. The difficulty is normally surmounted by assuming that the pseudo—phase consists of only the surfactant components i.e., solvent or counterions are ignored. The validity of treating the micelle on a surfactant—oniy basis has not been verified. Funasaki and Hada (22) have questioned the thermodynamic consistency of such an approach. 

Osborne-Lee, I. W., and R. S. Schechter. 1986. Nonideal mixed micelles. Thermodynamic models and experimental comparisonACS Symp. Se(Phenom. Mixed Surfactant Syst.). 311 30—43. 

In addition, a model is needed that can describe the nonideality of a system containing molecular and ionic species. Freguia and Rochelle adopted the model developed by Chen et al. [AIChE J., 25, 820 (1979)] and later modified by Mock et al. [AIChE J., 32, 1655 (1986)] for mixed-electrolyte systems. The combination of the speciation set of reactions [Eqs. (14-74a) to (14-74e) and the nonideality model is capable of representing the solubility data, such as presented in Figs. 14-1 and 14-2, to good accuracy. In addition, the model accurately and correctly represents the actual species present in the aqueous phase, which is important for faithful description of the chemical kinetics and species mass transfer across the interface. Finally, the thermodynamic model facilitates accurate modeling of the heat effects, such as those discussed in Example 6. 

A new thermodynamic model for the Cu(I,II)-HC1-H20 system was developed on the basis of the representative data on GuGl(s) solubility in aqueous solutions of HC1 in a concentration interval from 1 to 6 mol kg1 HG1 (Akinfiev, 2009). The model takes into account a number of aqueous Cu(I) species [Cu+, CuOH°, Cu(OH)2, CuC1°, CuClj, HCuCL ], aqueous Cu(II) species [Cu2 CuOH+, CuO°, HCuO , CuOJ- CuCl+, CuCL , GuGlg, CuClJ)] and a mixed Cu(I)/Cu(II) chloride aqueous complex, Cu2Cl . The thermodynamic approach used a modelling approach based on i) the standard thermodynamic properties of the listed above species ii) a model for the activity coefficients iii) use of HCh software (Shvarov, 1999). 

After the seminal work of Guggenheim on the quasichemical approximation of the lattice statistical-mechanical theory[l], various practical thermodynamic models such as excess Gibbs energies[2-3] and equations of state[4-5] were proposed. However, the quasichemical approximation of the Guggenheim combinatory yields exact solution only for pure fluid systems. Therefore one has to resort to numerical procedures to find the solution that is analytically applicable to real mixtures. Thus, in this study we present a new unified group contribution equation of state[GC-EOS] which is applicable for both pure or mixed state fluids with emphasis on the high pressure systems[6,7]. 

In order to correlate the results obtained, a modified SRK equation of state with Huron-Vidal mixing rules was used. Details about the model are reported in the paper by Soave et al. [16]. This approach is particularly adequated when experimental values of the critical temperature and pressure are not available as it was the case for limonene and linalool. Note that the flexibility of the thermodynamic model to reproduce high-pressure vapor-liquid equilibrium data is ensured by the use of the Huron-Vidal mixing rules and a NRTL activity coefficient model at infinite pressures. Calculation results are reported as continuous curves in figure 2 for the C02-linalool system and in figure 3 for C02-limonene. Note that the same parameters values were used to correlated the data of C02-limonene at 45, 50 e 60 °C. 

The difference between the compound energy model and the simple two-sublattice model can be illustrated with two ternary intermetallic phases from the Al-Mg-Zn system. One of these two phases is known to contain a constant composition of 54.5 atomic percent magnesium and an extended homogeneity range of aluminum and zinc, corresponding to the formula Mg6(Al,Zn)5. However, no crystallographic data is available for this phase. Therefore, it is appropriately thermodynamically modeled by two sublattices, in which one sublattice is exclusively occupied by Mg, while A1 and Zn are allowed to randomly mix on the second sublattice (Liang et al., 1998). 

The adsorption of binary mixtures of anionic surfactants of a homologous series (sodium octyl sulfate and sodium dodecyl sulfate) on alpha aluminum oxide was measured. A thermodynamic model was developed to describe ideal mixed admicelle (adsorbed surfactant bilayer) formation, for concentrations between the critical admicelle concentration and the critical micelle concentration. Specific... 

When the components of a given chemical reaction are mixed, they will proceed, rapidly or slowly depending on the kinetics of the process, to the equilibrium position. In Chapter 6 we defined the equilibrium position as the point at which the forward and reverse reaction rates are equal. In this chapter we look at equilibrium from a thermodynamic point of view, and we find that the equilibrium point occurs at the lowest value of free energy available to the reaction system. As it turns out, the two definitions give the same equilibrium state, which must be the case for both the kinetic and thermodynamic models to be valid. 

Titration curves have the virtue of simplicity, while thermodynamic models have, at least in principle, greater capacity to be adapted to changing process conditions. In practice, the amount of effort required to develop a thermodynamic model based on real chemical species and physical properties is usually prohibitive. Semiempirical models based on notional species and concentration equilibria can be developed quite readily (Gustafsson and Waller, 1983). However, these have extrapolation properties identical to the original titration curves. In both cases the pH of a mixture of components can be predicted accurately, subject to the assumptions that mixing two solutions of equal pH results in a solution with the same pH and the pH measurement is ideal (Gustafsson, 1982 Luyben, 1990). The validity of this assumption is discussed in Walsh (1993). 

We have seen many successful industrial applications of applied electrolyte thermodynamics models. In particular, the electrolyte NRTL activity coefficient model of Chen and Evans has proved to be the model of choice for various electrolyte systems, aqueous and mixed-solvent. However, there are unmet needs that require further development. 

---