Solubility thermodynamic models

Thermodynamic Model. Solubility of a condensed phase, y2, in a vapor phase at supercritical conditions (12) can be defined as ... 

One of the simplest cases of phase behavior modeling is that of soHd—fluid equilibria for crystalline soHds, in which the solubility of the fluid in the sohd phase is negligible. Thermodynamic models are based on the principle that the fugacities (escaping tendencies) of component are equal for all phases at equilibrium under constant temperature and pressure (51). The soHd-phase fugacity,, can be represented by the following expression at temperature T ... 

The solubility parameter 5 of a pure solvent defined initially by Hildebrand and Scott based on a thermodynamic model of regular solution theory is given by Equation 4.4 [13] ... 

However, from our point of view, there remains a lack of sufficiently precise and reliable methods to compute thermodynamic water solubility. The majority of methods work only for congeneric series of compounds, and many have not been developed to function in areas of pharmaceutical research using drug-like molecules. Most of the methods do not use the three-dimensional structure of the compounds, while some depend on previous knowledge of certain experimental properties of the compounds of interest. Moreover, all of the methods are dependent upon the quality of solubility values in the training set used to develop the model indeed, this latter point is a critical limitation that has a major influence on solubility estimations. 

Weare, J.H., 1987, Models of mineral solubility in concentrated brines with application to field observations. In I. S.E. Carmichael and H.P Eugster (eds.), Thermodynamic Modeling of Geological Materials Minerals, Fluids and Melts. Reviews in Mineralogy 17,143-176. 

The use of thermodynamic models to correlate and predict solubility behaviour in both single solvents and mixtures can be beneficially applied at this point. This technique both validates the experimental data and minimizes the experimental workload for the design of an optimized process. These techniques are discussed further in section 5. 

The application of thermodynamic models to the correlation and prediction of pharmaceutical solubility behaviour is an underutilized technique in today s process research and development environment. This is due to the relatively poor accuracy and limited predictive ability of the previous generation of models. Recent advances in computational chemistry and an increased focus on the life science sectors has led to the development of more appropriate models with significantly improved predictive capabilities. The NRTL-SAC and Local UNIFAC approaches will be discussed here with additional examples given in section 8. 

For the purpose of this case study we will select Isopropyl alcohol as the crystallization solvent and assume that the NRTL-SAC solubility curve for Form A has been confirmed as reasonably accurate in the laboratory. If experimental solubility data is measured in IPA then it can be fitted to a more accurate (but non predictive) thermodynamic model such as NRTL or UNIQUAC at this point, taking care with analysis of the solid phase in equilibrium. As the activity coefficient model only relates to species in the liquid phase we can use the same model with each different set of AHm and Tm data to calculate the solubility of the other polymorphs of Cimetidine, as shown in Figure 21. True polymorphs only differ from each other in the solid phase and are otherwise chemically identical. 

The most important area in the pharmaceutical and related industries for the application of thermodynamic models is in solid-liquid equilibria. Once developed these same models are applicable to a range of unit operations. Aqueous solubility and concerns about pharmaceuticals in the environment is an obvious extension. Liquid-Liquid extraction and distillation are frequently used operations, and techniques that predict the partitioning and impact of... 

With liquid feed solutions, however, it is possible to work in a manner analogous to traditional solvent extraction. Pressurized columns can be of the packed-bed type or agitated by magnetic stirrers. Because of the efforts of pilot plant tests, much of the scale-up work has to be carried out in laboratory extractors. From solubility measurements, it is possible to determine parameters in thermodynamic models (e.g., equations of state), which can be used for the simulation of large-scale applications. 

Thermodynamic modelling of solution phases lies at the core of the CALPHAD method. Only rarely do calculations involve purely stoichiometric compounds. The calculation of a complex system which may have literally 100 different stoichiometric substances usually has a phase such as the gas which is a mixture of many components, and in a complex metallic system with 10 or 11 alloying elements it is not unusual for all of the phases to involve solubility of the various elements. Solution phases will be defined here as any phase in which there is solubility of more than one component and within this chapter are broken down to four types (1) random substitutional, (2) sublattice, (3) ionic and (4) aqueous. Others types of solution phase, such as exist in polymers or complex organic systems, can also be modelled, but these four represent the major types which are currently available in CALPHAD software programmes. 

Tso, N. C. (1992) Thermodynamic modelling of ternary alloy phase solubility , Ph.D. Thesis, Columbia University. 

The second important characteristic of the micellar solution that relates to solubilization is the micelle size. Poor aqueous soluble compounds are solubilized either within the hydrocarbon core of the micelle or, very commonly, within the head group layer at the surface of the micelle or in the palisade portion of the micelle. Predictions of the micelle size have relied on the use of empirical relationships employed within a thermodynamic model, for instance the law of mass action where micellization is in equilibrium with the associated and unassociated (monomer) surfactant molecules (Attwood and Florence, 1983). 

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. 

The effect of temperature on retention has been described experimentally,(4-8) but the functional dependence of k with temperature has only recently been described.W A thermodynamic model was outlined relating retention as a function of temperature at constant pressure to the volume expansivity of the fluid, the enthalpy of solute transfer between the mobile phase and the stationary phase and the change in the heat capacity of the fluid as a function of temperature.(9) The solubility of a solid solute in a supercritical fluid has been discussed by Gitterman and Procaccia (10) over a large range of pressures. The combination of solute solubility in a fluid with the equation for retention as a function of pressure derived by Van Wasen and Schneider allows one to examine the effect of solubility on solute retention. 

In this work we derive simple relationships between temperature, solute solubility and retention. The simple thermodynamic models developed predict the trend in retention as a function of pressure, given the solubility of the solute in the fluid mobile phase at constant temperature and the trend in k as a function of temperature at constant pressure. Our aim is to examine the complicated dependence of retention on the thermodynamic and physical properties of the solute and the fluid, providing a basis for consideration of more subtle effects in SFC. 

An independent means of establishing the chemical nature of the colloidal calcium phosphate is provided by the form and magnitude of the solubility product that governs the equilibrium between the ions in the milk serum and the solid phase. A thermodynamic model of the equilibria can be constructed as follows. First, ions in solution are supposed to be in equilibrium or quasi-equilibrium with a calcium... 

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). 

Kirpichtchikova, T. A., Manceau, A., Spadini, L., Panfili, F., Marcus, M. A., andjacquet, T. (2006). Speciation and solubility of heavy metals in contaminated soil using X-ray microfluorescence, EXAFS spectroscopy, chemical extraction, and thermodynamic modeling. Geochim. Cosmochim. Acta 70, 2163-2190. 

Other important applications include the generation of a model to predict thermodynamic water solubility (Cruciani et al. 2003). This model is based on consistent solubility data from literature plus additional measurements for 970 compounds. Its quality allows to differentiate between very poorly/poorly/medium/ highly and very highly soluble molecules while exact rankings within individual classes are not possible. However, given the different factors influencing experimental thermodynamic solubility data, it is not likely that significantly improved models for this key property in pharmaceutical sciences can be derived. 

Solubility data of biological compounds taken from literature are considered in this work. Different thermodynamic models based on cubic equations of state and UNIFAC are used in the correlation of experimental data. Interaction parameters are obtained by group contribution approach in order to establish correlations suitable for the prediction of the solid solubility. 

Since to measure solid solubility data is time consuming and the cost of the operation is quite high the existing data should be considered in the framework of optimizing the experimental effort and reducing the overall expenses by applying a suitable thermodynamic model. 

Thermodynamics is the basis of all chemical transformations [1], which include dissolution of chemical components in aqueous solutions, reactions between two dissolved species, and precipitation of new products formed by the reactions. The laws of thermodynamics provide conditions in which these reactions occur. One way of determining such conditions is to use thermodynamic potentials (i.e., enthalpy, entropy, and Gibbs free energy of individual components that participate in a chemical reaction) and then apply the laws of thermodynamics. In the case of CBPCs, this approach requires relating measurable parameters, such as solubility of individual components of the reaction, to the thermodynamic parameters. Thermodynamic models not only predict whether a particular reaction is likely to occur, but also provide conditions (measurable parameters such as temperature and pressure) in which ceramics are formed out of these reactions. The basic thermodynamic potentials of most constituents of the CBPC products have been measured at room temperature (and often at elevated temperatures) and recorded in standard data books. Thus, it is possible to compile these data on the starter components, relate them to their dissolution characteristics, and predict their dissolution behavior in an aqueous solution by using a thermodynamic model. The thermodynamic potentials themselves can be expressed in terms of the molecular behavior of individual components forming the ceramics, as determined by a statistical-mechanical approach. Such a detailed study is beyond the scope of this book. 

A thermodynamic model of dissolution is presented in this chapter, which relates the solubility product constant to the thermodynamic potentials and measurable parameters, such as temperature and pressure of the solution. The resulting relations allow us to develop conditions in which CBPCs are likely to form by reactions of various oxides (or minerals) with phosphate solutions. Thus, the model predicts formation of CBPCs. 

This argument has descended onto the equation of state as a principal determinant of peculiar temperature dependences of hydrophobic effects. The statistical thermodynamic model discussed above, however, started with probabilities and fluctuations. But equations of state and fluctuations are connected by the most basic of results of Gibbsian statistical mechanics, e.g. Eq. (2.24), p. 27. Ad hoc models, such as the more simplistic lattice gas models, can be adjusted to agree with solubility at a thermodynamic state point, but if they don t agree with the equation of state of liquid water more broadly they can t be expected to describe molecular fluctuations of liquid water consistently and realistically. Thus, models of that sort are unlikely to be consistent with the picture explored here. 

The predicted waste inventory for the repository indicates that potentially significant quantities of the organic ligands—acetate, citrate, oxalate, and EDTA—will be present (US DOE, 1996). Actinide interactions with these compounds were not considered in the speciation and solubility modeling, as calculations suggested that they would be mostly complexed by transition metal ions (Fe, Ni " ", Cr, and Mn " ") released by corrosion of the steel waste containers and waste components. A thermodynamic model of actinide-ligand interactions appropriate to brines will be included in solubility calculations for WIPP recertification. 

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