Phase equilibrium, aqueous systems

The basic principle of every measurement of the Volta potential and generally of the investigations of voltaic cells too, in contrast to galvanic cells, may thus be presented for systems containing metal/solution (Fig. 2) and liquid/liquid interfaces (Fig. 3), respectively. This interface is created at the contact of aqueous and organic solutions (w and s, respectively) of electrolyte MX in the partition equilibrium. Of course, electrolyte MX, shown in Fig. 2 and other figures of this chapter, may be different in organic (s) and aqueous (w) phases. 

Consider the following thermodynamic analysis for a reaction of the type A + B C + D conducted in a two-phase system (aqueous/organic). The equilibrium constants in the separate phases are ... 

The quantitative descriptor of lipophilicity, the partition coefficient P, is defined as the ratio of the concentrations of a neutral compound in organic and aqueous phases of a two-compartment system under equilibrium conditions. It is commonly used in its logarithmic form, logP. Whereas 1-octanol serves as the standard organic phase for experimental determination, other solvents are applied to better mimic special permeation conditions such as the cyclohexane-water system for BBB permeation. Measurement of log P is described in Chapters 12 and 13 as well as in Ref [22]. 

Fig. 2.37. Phase diagram for Ca0-Na20 Si02-(Al203)-H20 system in equilibrium with quartz at 400°C and 400 bars. Plagioclase solid solution can be represented by the albite and anorthite fields, whereas epidote is represented by clinozoisite. Note that the clinozoisite field is adjacent to the anorthite field, suggesting that fluids with high Ca/(H+) might equilibrate with excess anorthite by replacing it with epidote. The location of the albite-anorthite-epidote equilibrium point is a function of epidote and plagioclase composition and depends on the model used for calculation of the thermodynamic properties of aqueous cations (Berndt et al., 1989).

The interface separating two immiscible electrolyte solutions, e.g., one aqueous and the other based on a polar organic solvent, may be reversible with respect to one or many ions simultaneously, and also to electrons. Works by Nernst constitute a fundamental contribution to the electrochemical analysis of the phase equilibrium between two immiscible electrolyte solutions [1-3]. According to these works, in the above system electrical potentials originate from the difference of distribution coefficients of ions of the electrolyte present in the both phases. 

Depicted in Fig. 2, microemulsion-based liquid liquid extraction (LLE) of biomolecules consists of the contacting of a biomolecule-containing aqueous solution with a surfactant-containing lipophilic phase. Upon contact, some of the water and biomolecules will transfer to the organic phase, depending on the phase equilibrium position, resulting in a biphasic Winsor II system (w/o-ME phase in equilibrium with an excess aqueous phase). Besides serving as a means to solubilize biomolecules in w/o-MEs, LLE has been frequently used to isolate and separate amino acids, peptides and proteins [4, and references therein]. In addition, LLE has recently been employed to isolate vitamins, antibiotics, and nucleotides [6,19,40,77-79]. Industrially relevant applications of LLE are listed in Table 2 [14,15,20,80-90]. 

Considering only the aqueous phase of the biocatalytic system, the equilibrium constant for the reaction is given as a function of thermodynamic activities of the components shown ... 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

Phase Equilibrium Calculations by Equation of State for Aqueous Systems with Low Mutual Solubility... 

The correlation presented in this paper can be very simply applied to phase-equilibrium calculations for concentrated electrolyte systems, however, care must be taken to remember that it is basically a correlational approach and not a molecular model for aqueous electrolyte solutions. 

In a solid-fluid reaction system, the fluid phase may have a chemistry of its own, reactions that go on quite apart from the heterogeneous reaction. This is particularly true of aqueous fluid phases, which can have acid-base, complexation, oxidation-reduction and less common types of reactions. With rapid reversible reactions in the solution and an irreversible heterogeneous reaction, the whole system may be said to be in "partial equilibrium". Systems of this kind have been treated in detail in the geochemical literature (1) but to our knowledge a partial equilibrium model has not previously been applied to problems of interest in engineering or metallurgy. 

With an aqueous fluid phase of high ionic strength, the problem of obtaining activity coefficients may be circumvented simply by using apparent equilibrium constants expressed in terms of concentrations. This procedure is recommended for hydro-metallurgical systems in which complexation reactions are important, e.g., in ammonia, chloride, or sulfate solutions. 

Sorption/desorption is one of the most important processes influencing movemement of organic pollutants in natural systems. Sorption with reference to a pollutant is its transfer from the aqueous phase to the solid phase on the other hand, desorption is its transfer from the solid phase to the aqueous phase. Similar to all interphase mass-transfers, the sorption/ desorption process can be defined by the final-phase equilibrium of the pollutant at the aqueous-solid phase interface and the time required to approach final equilibrium. 

MINTEQA2 http //www.epa.gov/ceampubl/mmedia/minteq/index.htm MINTEQA2 is an equilibrium speciation model that can be used to calculate the equilibrium composition of dilute aqueous solutions in the laboratory or in natural aqueous systems. The model is useful for calculating the equilibrium mass distribution among dissolved species, adsorbed species, and multiple solid phases under a variety of conditions including a gas phase with constant partial pressures. 

In summary, whether a reaction equilibrium or a phase equilibrium approach is adopted depends on the size of the micelles formed. In aqueous systems the phase equilibrium model is generally used. In Section 8.5 we see that thermodynamic analyses based on either model merge as n increases. Since a degree of approximation is introduced by using the phase equilibrium model to describe micellization, micelles are sometimes called pseudophases. 

To assess the extent to which a compound is associated with solid phases in a given system at equilibrium (see below), we need to know the ratio of the compound s total equilibrium concentrations in the solids and in the aqueous solution. We denote this solid-water distribution coefficient as Kid (e.g., in L kg 1 solid) ... 

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