Chemical equilibrium, aqueous systems potentials

Equation 8.173 estabhshes that in an electrolytic solution the relative proportions of oxidized and reduced species are controlled by the redox state of the system (we will see in section 8.19 that in actual fact the redox equilibrium among the various redox couples in natural, chemically complex, aqueous solutions is rarely attained). Imposing on equation 8.173 the value of the ruling redox potential (Eh)—i.e.,... 

Since natural waters are generally in a dynamic rather than an equilibrium condition, even the concept of a single oxidation-reduction potential characteristic of the aqueous system cannot be maintained. At best, measurement can reveal an Eh value applicable to a particular system or systems in partial chemical equilibrium and then only if the systems are electrochemically reversible at the electrode surface at a rate that is rapid compared with the electron drain or supply by way of the measuring electrode. Electrochemical reversibility can be characterized... 

Eh is a measure of oxidation-reduction potential in the solution. The chemical reactions in the aqueous system depend on both the pH and the Eh. While pH measures the activity (or concentration) of hydrogen ions in the solution, Eh is a measure of the activity of all dissolved species. Aqueous solutions contain both oxidized and reduced species. For example, if iron is present in the solution, there is a thermodynamic equilibrium between its oxidized and reduced forms. Thus, at the redox equilibrium, the reaction is as follows ... 

Phase equilibrium across semipermeable membranes is of special interest in biological applications. First, we will consider two-phase aqueous systems without chemical reactions, then introduce reactions, and finally electric potential differences between phases. The numbers of intensive degrees of freedom F and... 

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). 

A natural aqueous redox system may or may not be at total (internal) equilibrium (Q. How the redox status is characterized depends upon the state of the system relative to equilibrium. Regardless of whether the system is at equilibrium or not there is an individual, instantaneous pE for each redox couple in the system. Each pE corresponds to the relative concentrations of the oxidized and reduced species and is defined by Nemstian relationships (i). When a system of oxidants and reductants is at internal chemical equilibrium the pE of every couple is identical and this distinct value is the system pE. Only in this special case can the redox status be characterized by determining two of the following three factors pE, the total concentration of all components, and the relative concentrations of oxidants and reductants. When two of the factors are known, the third can be determined from Nemstian and mass balance relationships. Thus, only when the chemical system is at internal equilibrium and one of the redox couples of the system is electrochemically active and present in measurable concentrations can the system pE be calculated from an electrode potential. 

The chemical potential of the solid crystal salt B is in phase equilibrium with the dissolved salt B in the liquid or aqueous phase. In aqueous systems we are primarily dealing with salts of strong electrolytes, which in water dissociate completely to the constituent cations and anions of the salt. The chemical potential of the dissolved salt is then given by... 

With a three-component system, such as a polymer in an aqueous salt solution, preferential adsorption of one component to the polymer can affect the analysis of light-scattering data.199 Such interactions can affect the SRI. Therefore, measurements of the SRI must be made at constant chemical potential. Constant chemical potential is achieved experimentally by dialyzing the solvent and polymer solution to equilibrium through a membrane permeable to the solvent but impermeable to the polymer.199... 

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,... 

Equilibrium between simple salts and aqueous solutions is often relatively easily demonstrated in the laboratory when the composition of the solid is invariant, such as occurs in the KCI-H2O system. However, when an additional component which coprecipitates is added to the system, the solid composition is no longer invariant. Very long times may be required to reach equilibrium when the reaction path requires shifts in the composition of both the solution and solid. Equilibrium is not established until the solid composition is homogeneous and the chemical potentials of all components between solid and aqueous phases are equivalent. As a result, equilibrium is rarely demonstrated with a solid solution series. 

Earlier, Gavach et al. studied the superselectivity of Nafion 125 sulfonate membranes in contact with aqueous NaCl solutions using the methods of zero-current membrane potential, electrolyte desorption kinetics into pure water, co-ion and counterion selfdiffusion fluxes, co-ion fluxes under a constant current, and membrane electrical conductance. Superselectivity refers to a condition where anion transport is very small relative to cation transport. The exclusion of the anions in these systems is much greater than that as predicted by simple Donnan equilibrium theory that involves the equality of chemical potentials of cations and anions across the membrane—electrolyte interface as well as the principle of electroneutrality. The results showed the importance of membrane swelling there is a loss of superselectivity, in that there is a decrease in the counterion/co-ion mobility, with greater swelling. 

The thermodynamic treatment of systems in which at least one component is an electrolyte needs special comment. Such systems present the first case where we must choose between treating the system in terms of components or in terms of species. No decision can be based on thermodynamics alone. If we choose to work in terms of components, any effect of the presence of new species that are different from the components, would appear in the excess chemical potentials. No error would be involved, and the thermodynamic properties of the system expressed in terms of the excess chemical potentials and based on the components would be valid. It is only when we wish to explain the observed behavior of a system, to treat the system on the basis of some theoretical concept or, possibly, to obtain additional information concerning the molecular properties of the system, that we turn to the concept of species. For example, we can study the equilibrium between a dilute aqueous solution of sodium chloride and ice in terms of the components water and sodium chloride. However, we know that the observed effect of the lowering of the freezing point of water is approximately twice that expected for a nondissociable solute. This effect is explained in terms of the ionization. In any given case the choice of the species is dictated largely by our knowledge of the system obtained outside of the field of thermodynamics and, indeed, may be quite arbitrary. 

Thorstenson and Plummer (1977), in an elegant theoretical discussion (see section on The Fundamental Problems), discussed the equilibrium criteria applicable to a system composed of a two-component solid that is a member of a binary solid solution and an aqueous phase, depending on whether the solid reacts with fixed or variable composition. Because of kinetic restrictions, a solid may react with a fixed composition, even though it is a member of a continuous solid solution. Thorstenson and Plummer refer to equilibrium between such a solid and an aqueous phase as stoichiometric saturation. Because the solid reacts with fixed composition (reacts congruently), the chemical potentials of individual components cannot be equated between phases the solid reacts thermodynamically as a one-component phase. The variance of the system is reduced from two to one and, according to Thorstenson and Plummer, the only equilibrium constraint is IAP g. calcite = Keq(x>- where Keq(x) is the equilibrium constant for the solid, a function of... 

The calculation of the C02 solubility in aqueous solution was based upon the equations of Swope and Andersen [15]. When a chemical system is in equilibrium, the chemical potential of a gas phase particle and the particle in solution must be equal [16]. From this, we can show that the solubility of a gas particle in solution is given by ... 

Distribution potential established when ionic species are partitioned in equilibrium between the aqueous and organic phases, W and O, is a fundamental quantity in electrochemistry at liquid-liquid interfaces, through which the equilibrium properties of the system are determined. In any system composed of two immiscible electrolyte solutions in contact with each other, the equilibrium is characterized by the equality of the electrochemical or chemical potentials for each ionic or neutral species, respectively, commonly distributed in the two phases [4]. It follows from the former equality that the distribution potential Aq inner electrical potential of the aqueous phase, 0, with respect to the inner potential of the organic phase, 0°, is given by the Nernst equation [17,18],... 

---