Activity coefficient aqueous systems, chemical equilibrium

The activity coefficient of the solvent remains close to unity up to quite high electrolyte concentrations e.g. the activity coefficient for water in an aqueous solution of 2 m KC1 at 25°C equals y0x = 1.004, while the value for potassium chloride in this solution is y tX = 0.614, indicating a quite large deviation from the ideal behaviour. Thus, the activity coefficient of the solvent is not a suitable characteristic of the real behaviour of solutions of electrolytes. If the deviation from ideal behaviour is to be expressed in terms of quantities connected with the solvent, then the osmotic coefficient is employed. The osmotic pressure of the system is denoted as jz and the hypothetical osmotic pressure of a solution with the same composition that would behave ideally as jt. The equations for the osmotic pressures jt and jt are obtained from the equilibrium condition of the pure solvent and of the solution. Under equilibrium conditions the chemical potential of the pure solvent, which is equal to the standard chemical potential at the pressure p, is equal to the chemical potential of the solvent in the solution under the osmotic pressure jt,... 

The need to abstract from the considerable complexity of real natural water systems and substitute an idealized situation is met perhaps most simply by the concept of chemical equilibrium in a closed model system. Figure 2 outlines the main features of a generalized model for the thermodynamic description of a natural water system. The model is a closed system at constant temperature and pressure, the system consisting of a gas phase, aqueous solution phase, and some specified number of solid phases of defined compositions. For a thermodynamic description, information about activities is required therefore, the model indicates, along with concentrations and pressures, activity coefficients, fiy for the various composition variables of the system. There are a number of approaches to the problem of relating activity and concentrations, but these need not be examined here (see, e.g., Ref. 11). 

DYNAMICS OF DISTRIBUTION The natural aqueous system is a complex multiphase system which contains dissolved chemicals as well as suspended solids. The metals present in such a system are likely to distribute themselves between the various components of the solid phase and the liquid phase. Such a distribution may attain (a) a true equilibrium or (b) follow a steady state condition. If an element in a system has attained a true equilibrium, the ratio of element concentrations in two phases (solid/liquid), in principle, must remain unchanged at any given temperature. The mathematical relation of metal concentrations in these two phases is governed by the Nernst distribution law (41) commonly called the partition coefficient (1 ) and is defined as = s) /a(l) where a(s) is the activity of metal ions associated with the solid phase and a( ) is the activity of metal ions associated with the liquid phase (dissolved). This behavior of element is a direct consequence of the dynamics of ionic distribution in a multiphase system. For dilute solution, which generally obeys Raoult s law (41) activity (a) of a metal ion can be substituted by its concentration, (c) moles L l or moles Kg i. This ratio (Kd) serves as a comparison for relative affinity of metal ions for various components-exchangeable, carbonate, oxide, organic-of the solid phase. Chemical potential which is a function of several variables controls the numerical values of Kd (41). 

The splitting of redox reaetions into two half cell reactions by introducing the symbol e is highly useful. It should be noted that the e notation does not in any way refer to solvated electrons. When calculating the equilibrium composition of a chemical system, both e , and can be chosen as components and they can be treated numerically in a similar way equilibrium constants, mass balances, etc. may be defined for both. However, while represents the hydrated proton in aqueous solution, the above equations use only the activity of e , and never the concentration of e . Concentration to activity conversions (or activity coefficients) are never needed for the electron cf. Appendix B, Example B.3). 

The EQ3/6 software package consists of several principal components. These are the EQ3NR and EQ6 codes, the EQLIB library, and the thermodynamic ta base. The EQLIB library and the thermodynamic data base support both of the main modeling codes. EQLIB contains math routines, routines that perform various computer system functions, and routines that evaluate scientific submodels, such as for activity coefficients of aqueous species, that are common to both EQ3NR and EQ6. The data base covers a wide range of chemical elements and nominally allows calculations in the temperature range 0-3(X)°C at a constant pressure of 1.013 bar from 0-l()0°C and the steam-liquid water equilibrium pressure from 1(X)-3(X)°C. 

Values of K gx for various cation exchange reactions can be shown to be related to the ratio of activity coefficients in the resin phase by means of the Donnan theory developed by describing membrane equilibria. The Donnan theory, based in thermodynamics, states that the activity product of a salt on either side of a membrane to which it is permeable, is identical. We can consider the resin phase as being separated from the aqueous phase by the equivalent of a membrane which permitted the free passage of all ions except those which are chemically bound to the polymer. Applying this to a system consisting of a resin in the hydrogen form in equilibrium... 

In order to calculate the equOibrium composition of a system consisting of one or more phases in equilibrium with an aqueous solution of electrolytes, a review of the basic thermodynamic functions and the conditions of equilibrium is important, This is particularly true inasmuch as the study of aqueous solutions requires consideration of chemical and/or ionic reactions in the aqueous phase as well as a thermodynamic framework which is, for the most part, quite different from those definitions associated with nonelectrolytes. Therefore, in this section we will review the definition of the basic thermodynamic functions, the partial molar quantities, chemical potentials, conditions of equilibrium, activities, activity coefficients, standard states, and composition scales encountered in describing aqueous solutions. 

Four equilibrium relations describe a multiphase aqueous system containing CO2 and MCO3. Equilibria for reactions in Eqs. (1-3) and (5) are written using total pressure P, gas-phase mole fraction y, liquid-phase molality m, activity fugacity coefficient and activity coefficient 7j, where i stands for a species that takes part in the chemical reaction. An activity coefficient model is needed to relate the liquid-phase activities of individual species to their molalities. 

Chemical equilibrium in a closed system at constant temperature and pressure is achieved at the minimum of the total Gibbs energy, min(G) constrained by material-balance and electro-neutrality conditions. For aqueous electrolyte solutions, we require activity coefficients for all species in the mixture. Well-established models, e.g. Debye-Htickel, extended Debye-Hiickel, Pitzer, and the Harvie-Weare modification of Pitzer s activity coefficient model, are used to take into account ionic interactions in natural systems [15-20]. 

Figure 1.1 shows chemical equilibrium model of the natural system. Variables which determine the thermochemical feature of this system include temperature, total pressure, activities of dissolved species in aqueous solution (ions, ion pairs, complexes etc.), gaseous fugacity, activities of components in solid phases and dissolved species in aqueous solution where activity of i species, is equal to Yi mj (mi is molality of i species in aqueous solution and mole fractiOTi of i component in solid solution and yi is activity coefficient of i species in aqueous solution and of each component in solid phase). 

Important to any measurement of citrus juice volatile flavor components is the presence of (i-limonene, since this compound is naturally present as the most concentrated component in all of the natural citrus oils. Also, the solubility of d-limonene in aqueous media must be considered, since after liquid phase saturation, the headspace concentration remains constant. It has long been established for d-limonene and similar nonpolar flavor compounds over water that meaningful headspace measurement techniques [e.g., solid-phase microextraction (SPME)] require equilibrium of the vapor and liquid phase concentrations. Equilibrium may take a number of hours for static (unstirred) experiments and less than 1 hr for stirred systems. These conditions have been discussed elsewhere, and solubility and activity coefficients of d-limonene in water and sucrose solutions have been determined [1,2]. More recently, the chemical and physical properties as well as citrus industry applications of d-limonene and other citrus essential oils have been compiled [3]. Although not specific to d-limonene, important relationships affecting behavior of flavor release and partitioning between the headspace and the liquid phase of a number of food systems have also been discussed [4]. 

Standard potential values are usually those of ideal unimolal solutions at a pressure of 1 atm (ignoring the deviations of fugacity and activity from pressure and concentration, respectively). A pressure of 1 bar = 10 Pa was recommended as the standard value to be used in place of 1 atm = 101 325 Pa (the difference corresponds to a 0.34-mV shift of potential). If a component of the gas phase participates in the equilibrium, its partial pressure is taken as the standard value if not, the standard pressure should be that of the inert gas over the solution or melt. In a certain case, a standard potential can be established in a system with nonunity activities, if the combination of the latter substituted in the Nemst equation equals unity. For any sohd component of redox systems, the chemical potential does not change in the course of the reaction, and it remains in its standard state. In contrast to the common thermodynamic definition of the standard state, the temperature is ignored, because the potential of the standard hydrogen (protium) electrode is taken to be zero at any temperature in aqueous and protic media. The zero temperature coefficient of the SHE corresponds to the conventional assumption of... 

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