Multicomponent systems, solubilities

It is basically a fractionation process that depends not only on molecular size, but also on chemical composition, stereo-configuration, branching, and crosslinking. For multicomponent systems, fractionation with different ion polymolecularity, chemical heterogeneity and sequence length distribution, solubility or elution fractionation is of primary importance. Therefore, gel permeation chromatography or size exclusion chromatography is used as an important tool for the characterization of PBAs. 

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

For pharmaceutical formulations, the simplex method was used by Shek et al. [10] to search for an optimum capsule formula. This report also describes the necessary techniques of reflection, expansion, and contraction for the appropriate geometric figures. The same laboratories applied this method to study a solubility problem involving butoconazole nitrate in a multicomponent system [11],... 

Choices of precursor(s) may be dictated by solubility, reactivity, or other property. For multicomponent systems, mutual solubility is another factor that must be considered. For such solutions, the solvent selected must facilitate dissolution of all precursors. 

Whilst it is obviously valuable to measure the solubility of reagents in the SCF, it is important to be aware that the solubility in a multicomponent system can be very different from that in the fluid alone. It is also important to note that the addition of reagents and catalysts can have a profound effect on the critical parameters of the mixture. Indeed, at high concentrations of reactants, the mole fraction of C02 is necessarily lower and it may not be possible to achieve a supercritical phase at the temperature of interest. Increases in pressure (i.e. further additions of C02) could yield a single liquid phase (which would have a much lower compressibility than scC02). For example, the Diels-Alder reaction (see Chapter 7) between 2-methyl-1,3-butadiene and maleic anydride has been carried out a pressure of 74.5 bar and a temperature of 50 °C, assuming that this would be under supercritical conditions as it would if it were pure C02. However, the critical parameters calculated for this system are a pressure of 77.4bar and a temperature of 123.2 °C, far in excess of those used [41]. 

The basic problem in determining phase equilibria in multicomponent systems is the existence of a large number of variables, necessitating extensive experimental work. If ten measurements are considered satisfactory for acceptable characterization of the solubility in a two-component system in a particular temperature range, then the attainment of the same reliability with a three-component system requires as many as one hundred measurements. Therefore, a reliable correlation method permitting a decrease in the number of measurements would be extremely useful. Two different methods - the first of them based on geometrical considerations, and the second on thermodynamic condition of phase equilibria - are presented and their use is demonstrated on worked examples. 

The adjustable interaction constants Q can be evaluated from the experimental data for three-component systems these constants can then be employed for concentration of temperature interpolations and also for calculation of phase equilibria in multicomponent systems. Moreover, the constants Q usually depend very little on temperature, as the relative molalities, related to the solubility of the substance in the pure solvent, are employed hence calculations of other isotherms can be carried out easily. 

The goal of this research was to improve activity coefficient prediction, and hence, equilibrium calculations in flue gas desulfurization (FGD) processes of both low and high ionic strength. A data base and methods were developed to use the local composition model by Chen et al. (MIT/Aspen Technology). The model was used to predict solubilities in various multicomponent systems for gypsum, magnesium sulfite, calcium sulfite, calcium carbonate, and magnesium carbonate SCU vapor pressure over sulfite/ bisulfite solutions and, C02 vapor pressure over car-bonate/bicarbonate solutions. 

Calculations of the solubility with a modified Peng-Robinson-EOS lead to remarkably lower equilibrium pressures for the given temperature ranges. The reason for this effect is, that the calculations are done for two-component systems. The paraffin used for the measurements and the production of the workpieces, however, is a mixture of homologue n-alkanes, so the calculation should be done for a multicomponent system. Up to now it was not possible to find a set of thermodynamic data, which represent this n-alkane mixture and lead to two-component-calculation results according to the measurements. 

A mutual interaction of solubilities exists in all multicomponent systems. The interaction with methane is pronounced. This interdependence is treated in detail in [56], [59], [70] and [71]. 

HSD Stabilizer (Diesel Stabilizer) additive is a multicomponent, oil soluble formulation, specially designed to maintain the total sediments level in diesel fuel within the specified limits, as per ISO 1460 1995. The additive will ensure that the diesel does not deteriorate on storage and the fuel system is protected from deposit formation and corrosion. The additive consists of three major components, namely ... 

Reaction mixtures are complex multicomponent systems, and their phase behavior is dictated by the composition of the mixture and operating conditions. Organic solvents present in the reaction medium as reagents may act as cosolvents and result in solute solubility enhancement (as discussed in Section 4.2). For example, the decrease in reaction rate observed at high ethanol concentrations for the lipase-catalyzed esterification of myristic acid + ethanol in SCCO2 has been, in part, attributed to the solubility enhancement of water, resulting in drying of the enzyme... 

Surface Complex Formation, Ion Exchange, and Transport in Ground-water and Soil Systems The retardation equation can also be applied to inorganic soluble substances (ions, radionuclides, metals). But here we have to consider, in addition to the sorption or ion exchange process, that the speciation of metal ions or ligands in a multicomponent system influences the specific sorption process and varies during the pollutant transport in the groundwater chemistry then becomes an important part of the transport. 

Isolation Process in the Cross-Over Region. Chimowitz and Pennisi (13) developed a process for the separation and isolation of components from mixtures by operating in the multicomponent temperature-solubility cross-over region. The cross-over point of a pure component (dy/dT)p = 0 represents the pressure at which the dependence of solubility on temperature reverses itself. At lower pressures, the solubility is principally dependent on solvent density - raising temperature decreases density and thus solubility decreases. At higher pressures, solubility is principally dependent on solute sublimation pressure raising the temperature increases sublimation pressure and thus solubility increases. The cross-over point is therefore unique for each solute-solvent system. When there are two solutes, cross-over points occur at different pressures. At an intermediate pressure, the temperature can therefore be manipulated to deposit either component. 

The first step is preparation of the solution. Aqueous solutions are prepared by dissolving either soluble salts in solvents (usually water) or metals in acids. For multicomponent systems, the mutual solubility of the various components must be considered. For example, a solution for lead zirconate cannot be prepared from lead nitrate and zirconium sulfate, both of which are soluble in water, because lead sulfate, which is insoluble, will precipitate. A solution of nitrates of both cations is satisfactory. 

The Wilson parameters Ay and NRTL parameters Qy inherit a Boltzmann-type T dependence from the origins of the expressions for G, but it is only approximate. Computations of properties sensitive to this dependence (e.g., heats of mixing and liquid/liquid solubility) are in general only qualitatively correct. However, all parameters are found from data for binary (in contrast to multicomponent) systems, and this makes parameter determination for the local composition models a task of manageable proportions. 

We see that the shear- (i.e., tangential-) stress components are discontinuous across the interface whenever gradv y is nonzero. Now, the interfacial tension for a two-fluid system, made up of two pure bulk fluids, is a function of the local thermodynamic state - namely, the temperature and pressure. However, it is much more sensitive to the temperature than to the pressure, and it is generally assumed to be a function of temperature only. If the two-fluid system is a multicomponent system, it is often the case that there may be a preferential concentration of one or more of the components at the interface (for example, we may consider a system of pure A and pure B, which are immiscible, with a third solute component C that is soluble in A and/or B but that is preferentially attracted to the interface), and then the interfacial tension will also be a function of the (surface-excess) concentration of these solute components. Both the temperature and the concentrations of adsorbed species can be functions of position on the interface, thus leading to spatial gradients of y. 

As the first application of these criteria, consider the problem of identifying the state of equilibrium in a closed, nonreacting multicomponent system at constant internal energy and volume. To be specific, suppose N moles of species 1, moles of species 2, and so on are put into an adiabatic container that will be maintained at constant volume, and that these species are only partially soluble in one another, but do not chemically react. What we would like to be able to do is to predict the composition of each of the phases present at equilibrium. (A more difficult but solvable problem is to also predict the number of phases that will be present. This problem is briefly considered in Chapter 11.) In the analysis that follows, we develop the equation that will be used in Chapters 10, 11, and 12 to compute the equilibrium compositions. 

A. T. Anik and L. Sukumer, Extreme vertices design in formulation development solubility of butoconazole nitrate in a multicomponent system, J. Pharm. Sci. 70, 897-900 (1981). 

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