Thermodynamic model ideal solution

In many process design applications like polymerization and plasticization, specific knowledge of the thermodynamics of polymer systems can be very useful. For example, non-ideal solution behavior strongly governs the diffusion phenomena observed for polymer melts and concentrated solutions. Hence, accurate modeling of... 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

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. 

Figure 10,2 Deviations from Nernst s law in crystal-aqueous solution equilibria, as obtained from application of various thermodynamic models. (A and B) Regular solution (liyama, 1974). (C) Two ideal sites model (Roux, 1971a). (D) Model of local lattice distortion (liyama, 1974). Reprinted from Ottonello (1983), with kind permission of Theophrastus Publishing and Proprietary Co.

Kerrick D. M. and Darken L. S. (1975). Statistical thermodynamic models for ideal oxide and silicate solid solutions, with applications to plagioclase. Geochim. Cosmochim. Acta, 39 1431-1442. 

For a binary system of surfactants A and B, the mixed micelle formation can be modeled by assuming that the thermodynamics of mixing in the micelle obeys ideal solution theory. When monomer and micelles are in equilibrium in the system, this results in ... 

Scamehorn et. al. (20) also presented a simple, semi—empirical method based on ideal solution theory and the concept of reduced adsorption isotherms to predict the mixed adsorption isotherm and admicellar composition from the pure component isotherms. In this work, we present a more general theory, based only on ideal solution theory, and present detailed mixed system data for a binary mixed surfactant system (two members of a homologous series) and use it to test this model. The thermodynamics of admicelle formation is also compared to that of micelle formation for this same system. 

It is therefore essential that thermodynamic modeling be applied to obtain a simultaneous quantitative fit to the phase diagram and thermodynamic data in order to evaluate the internal consistency of the various published data. Then a reliable framework can be established for smoothing, interpolating, and extrapolating experimental data that are costly and laborious to obtain. In Chapter 3 an associated solution model is presented. This model provides a good fit to the data for the Hg-Cd-Te system as well as for the Ga-In-Sb system, which is closer to the simpler picture of an ideal solution. 

Defect thermodynamics, as outlined in this chapter, is to a large extent thermodynamics of dilute solutions. In this situation, the theoretical calculation of individual defect energies and defect entropies can be helpful. Numerical methods for their calculation are available, see [A. R. Allnatt, A. B. Lidiard (1993)]. If point defects interact, idealized models are necessary in order to find the relations between defect concentrations and thermodynamic variables, in particular the component potentials. We have briefly discussed the ideal pair (cluster) approach and its phenomenological extension by a series expansion formalism, which corresponds to the virial coefficient expansion for gases. 

The basis of the ideal solution model is that the thermodynamic activities of the components are the same as their mole fractions. Implicit in this assumption is the idea that the activity coefficients are equal to unity. This is at best an approximation and has been found to be invalid in most cases. Solutions in which activity coefficients are taken into account are referred to as "real" solutions and are described by equation 3.4. 

In example (a), the gas composition was modeled assuming ideal solution phases and neglecting known complex vapor species, such as K2SO4, K2CO3 and alkali chlorides. These serious limitations resulted from the non-availability of oxide solution-activity data, accurate vapor species thermodynamic functions, and the inability of existing computer codes to handle non-ideal solution multiphase, multicomponent equilibrium computations. 

Using our experimental activity data for Na20 in glass, we have modeled the effect of a typical combustion gas mixture on alkali vaporization ( ). For this purpose we have acquired, and adapted to our computers, a code known as SOLGASMIX (7 ) which is unique in its ability to deal with non-ideal solution multicomponent heterogeneous equilibria. Previous attempts to model this type of problem have been limited to ideal solution assumptions ( ). As is demonstrated in Table III, if solution non-ideality is neglected, drastic errors result in the prediction of alkali vapor transport processes. Table III and Figure 21 summarize the predicted alkali species partial pressures. The thermodynamic data base was constructed mainly from the JANAF (36) compilation. Additional details of this study will be presented elsewhere. 

Let us now examine the assumptions underljdng the Oncley treatment. First, thermodynamically V is defined as the increment of the volume of the solution per unit mass of the solute added and therefore is not identical with Fsp of the solute. These two quantities may be equal in magnitude if and only if the system is an ideal solution, that is, there is no solute-solvent interaction whatsoever present. To eliminate one unknown Fsp in Eq. (14) by introducing F we have at the same time added another uncertain term w into the equation. Thus this treatment offers at most a rough estimate of the shape of proteins for a chosen model, a prolate or an oblate ellipsoid. Furthermore the estimated p value corresponds only to the hydrated particle, which is slightly different from that of the unhydrated particle unless the bound water is so distributed throughout the protein molecule that it does not change its axial ratio because of hydration. 

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). 

The multiphase thermodynamic model described above has been implemented as a computational tool using the ChemSheet thermodynamic software (part of the widely used Solgasmix/ChemSage/ChemApp program family) that supports the use of the Pitzer formalism in describing ionic interactions in solutions and a number non-ideal solution models for solid phases. Despite the fact that the thermodynamic... 

In order to describe the behavior of the real solutions, i.e. the deviation of the solution from the ideal behavior, we use different thermodynamic models. 

In all calculations involving the ideal solution model, we assume that we know the molar Gibbs free energy of each of the pure species as a function of temperature and pressure. Mathematically, this means that know the form of the functions (T, p). Physically, this means that we know everything about the thermodynamics of the pure species. 

In Chapter 4, we developed the ideal solution model, which enables the estimation of the properties of mixtures from knowledge of the thermodynamic behavior of the pure species. While the ideal solution model does provide accurate predictions for mixtures of relatively similar substances, many systems do exhibit substantial deviations from the ideal solution model. 

In order to understand the thermodynamics of solubility, it is appropriate to begin with a simplihed model of solution, namely that of an ideal solution. An ideal solution is dehned as one where the activity coefficient of all components in the solution equals one. Under these stipulations, the activity of the dissolved solute, the activity of the solid, and the molar solubility of the dissolved solute would be equal. 

Do the simulation for an ideal solution and also for another choice of thermodynamic model (your choice). 

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