Electric potential, aqueous systems, phase equilibrium

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... 

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. 

Example 10.1 Membrane equilibrium An aqueous solution (phase A) of 100 mmol/L of NaCl is in equilibrium across a protein-tight membrane with an aqueous solution (phase B) of NaCl and protein. The protein concentration is 5 mmol/L with a negative ionic valency of 10. Determine the difference in electric potential and hydrostatic pressure across the membrane when both solutions are assumed to be ideal and the temperature is 25°C. Figure 10.1 shows the membrane system with the phases A and B. 

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],... 

In view of the potentially important effect of the Donnan equilibrium of charged species in similar systems, for example, two-phase aqueous polymer systems (29,30), it is important to note that several observations indicate that this effect is not a dominant one in the diffusion cell experiments (24). Specifically, (i) relatively small differences in the partitioning of cytochrome-c were observed to accompany the substitution of different salt types, and (ii) the PEO concentration in the PEO-rich compartment is an order of magnitude smaller than that encountered in typical two-phase aqueous polymer systems. As a result, the effective electrical potential difference across the membrane was estimated to be 0.2mV or less (24). 

As a specific example of a Donnan membrane equilibrium, consider a system in which an aqueous solution of a polyelectrolyte with a net negative charge, together with a counterion M+ and a salt MX of the counterion, is equilibrated with an aqueous solution of the salt across a semipermeable membrane. The membrane is permeable to the H2O solvent and to the ions M+ and X , but is impermeable to the polyelectrolyte. The species in phase a are H2O, M" ", and X those in phase P are H2O, M+, X , and the polyelectrol5he. In a equilibrium state, the two phases have the same temperature but different compositions, electric potentials, and pressures. 

In an electrochemical system with phases a and p, the criterion of equilibrium should be modified due to different electric potentials cp and respectively, in phases a and p. As an example, let us consider zinc electrode of the Daniell cell, which was introduced by John Frederic Daniell in 1836. Think of a piece of zinc metal being dipped into a dilute solution of ZnS04(aq). Between the solution and metal phases, aqueous zinc ions, Zn +(aq), can be transferred. If the initial solution is extremely dilute, then the rate of transfer of ions from the metal to the solution is faster than the transfer from the solution to the metal. When Ztf+(aq) leaves the metal surface, electrons are left behind because they cannot enter the solution. This builds up a negative electric potential in the metal phase. After some time, an equilibrium state is reached between the so-called electrochemical potential of Zn +(aq) within the metal and solution phases. The electrochemical potential of the species in each phase comprises two components (1) the chemical potential of the species p, and (2) the electric... 

This equation is versatile and can describe both the ionic and neutral species (Zi = 0) encountered in the system. This model thus enables the determination of equilibrium compositions of both the gel and the bath in almost any polyelectrolyte system polyelectrolyte gels in pure water, polyelectrolyte gels in an aqueous electrolyte bath, etc. However, it does make the assumption of electroneutrality, and hence an alternative way to describe the equilibrium of a polyelectrolyte system is also commonly used wherein an electric potential difference is defined between the two phases [70, 71]. 

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