Electrochemical activity coefficient

Fig. 4. Influence of membrane potential on AT, and Kj. K, and ATj (in relative units) are plotted vs. the electrochemical activity coefficient Fi>/RT). For details see text. r=0, unloaded carrier...

Fig. 8. Influence of membrane potential on taurine transport. Influx of taurine into Ehrlich cells is plotted against the distribution ratio of the lipophilic cation tetraphenylphosphonium (TPP) as a metisure of the electrochemical activity coefficient =exp( - F li/RT). (From [50].)...

An interesting consequence of the highly nonuniform electrostatic potential and distribution of the molecular species is that the local activity coefficients of the chemical species taking part in chemical equilibria depend on their exact location at the interface. As an example, Figure 2.8 shows that the oxidation fraction of the osmium sites is a nonuniform function of the distance to the electrode. The consequences of this finding for the electrochemical response will be discussed in Section 2.3.4. 

Activity coefficients are used in calculation of equilibrium constants, rates of reactions, electrochemical phenomena, and almost all quantities involving solutes or solvents in solution. 

In addition to the foregoing, it is customary to include under electrochemistry (I) processes for which the net reaction is physical transfer, e g., concentration cells (2) electrokinetic phenomena, e.g.. electrophoresis. eleclroosmnsis, and streaming potential (3) properties ot electrolytic solutions, if they are determined by electrochemical or other means, e g.. activity coefficients and hydrogen ion concentration (4) processes in which electrical energy is first converted to heal, which in turn causes a chemical reaction that would not occur spontaneously at ordinary temperature. The... 

The adsorption of organic ligands onto metal oxides and the parameters that have the greatest effect on adsorption were also studied (Stone et al., 1993). The extent of adsorption was measured by determining the loss of the compound of interest from solution. The physical and chemical forces that control adsorption into two general categories were classified as either specific or nonspecific adsorptions. Specific adsorption involves the physical and chemical interaction of the adsorbent and adsorbate. Under specific adsorption, the chemical nature of the sites influences the adsorptive capacity. Nonspecific adsorption does not depend on the chemical nature of the sites but on characteristics such as surface charge density (Stone et al., 1993). The interactions of specific adsorption can be explained in two ways. The first approach uses activity coefficients to relate the electrochemical activity at the oxide/water interface to its electrochemical activity in bulk solution (Stone et al., 1993). This approach is useful in situations... 

Assuming that, under usual electrochemical conditions, the activity coefficient of species i does not vary significantly in the solution, the first term of the right-hand side can be written as (see also Eq. 1.11)... 

The input of the problem requires total analytically measured concentrations of the selected components. Total concentrations of elements (components) from chemical analysis such as ICP and atomic absorption are preferable to methods that only measure some fraction of the total such as selective colorimetric or electrochemical methods. The user defines how the activity coefficients are to be computed (Davis equation or the extended Debye-Huckel), the temperature of the system and whether pH, Eh and ionic strength are to be imposed or calculated. Once the total concentrations of the selected components are defined, all possible soluble complexes are automatically selected from the database. At this stage the thermodynamic equilibrium constants supplied with the model may be edited or certain species excluded from the calculation (e.g. species that have slow reaction kinetics). In addition, it is possible for the user to supply constants for specific reactions not included in the database, but care must be taken to make sure the formation equation for the newly defined species is written in such a way as to be compatible with the chemical components used by the rest of the program, e.g. if the species A1H2PC>4+ were to be added using the following reaction ... 

The effect of pore diffusion is described through the term, 5, which represents a ratio of the kinetic rate to the diffusion rate in the electrode. In general increasing the value of, v, i.e., decreasing the diffusion rate relative to the kinetic rate, has the effect of causing a significant reduction in the local current densities and that more of the electrochemical activity of the electrode is focused closer to the membrane. This is a consequence of the reduced concentration of reactant away from the membrane due to, for example, a slower diffusion rate (lower diffusion coefficient). 

Activity coefficients of ions and the pH s of solutions can also be obtained from electrochemical measurements. 

Potentiometry has found extensive application over the past half-century as a means to evaluate various thermodynamic parameters. Although this is not the major application of the technique today, it still provides one of the most convenient and reliable approaches to the evaluation of thermodynamic quantities. In particular, the activity coefficients of electroactive species can be evaluated directly through the use of the Nemst equation (for species that give a reversible electrochemical response). Thus, if an electrochemical system is used without a junction potential and with a reference electrode that has a well-established potential, then potentiometric measurement of the constituent species at a known concentration provides a direct measure of its activity. This provides a direct means for evaluation of the activity coefficient (assuming that the standard potential is known accurately for the constituent half-reaction). If the standard half-reaction potential is not available, it must be evaluated under conditions where the activity coefficient can be determined by the Debye-Hiickel equation. 

In the context of RTILs the criterion (3) raises considerable problems since the concept of activity and activity coefficients of ions is largely unexplored in such media. Accordingly, validation of the applicability of the Nernst equation in such media is a non-simple exercise, given that RTILs are likely to exhibit gross non-ideality. Rather, electrochemical measurements based on otherwise validated reference electrodes, may likely in the future provide a methodology for the study of RTIL non-ideality. 

Assuming that this constitutes the only change in the activity coefficient in comparison to the traditional approach (this point is discussed later in the paper), the equality of the electrochemical potentials (x) and pq leads to... 

Let us consider the electrode kinetics associated with charge transfer from an n-type semiconductor particle to an electrode. As indicated by Albery et al. [164], the crucial difference between the electrochemistry of a colloidal particle and an ordinary electrochemically active solution phase species is the number of electrons transferred from the particle to the electrode may be large and will depend upon the potential of the electrode. Fig. 9.5 shows the model for an encounter of a particle with an electrode used by Albery and co-workers. kD is the mass-transfer coefficient for the transport of the particles to the electrode surface. In the simplest case, wherein it is assumed that the lifetime of the transferable electrons (majority carriers of thermal or photonic origin) is greater than the time taken by a particle to traverse the ORDE diffusion layer, this is given by... 

The majority of electrochemical problems can be solved without using absolute potentials , but these quantities are of interest for the electrochemistry of -> semiconductors (for calibrating the energy levels of materials) and are related to a general problem of physical chemistry, the determination of - activity coefficients of an individual charged species. 

Formal potentials can be defined on different levels of conditions Thus the formal potential of the -> quinhydrone electrode may be defined (I) as including (a) the standard potential of the hydroquinone di-anion/quinone system, (b) the two acidity constants of the hydroquinone, and (c) the activity coefficients of the hydroquinone dianion and quinone, or, (II), it may also include (c) the pH value. In the latter case, for each pH value there is one formal potential, whereas in the first case one has one formal potential for all pH values, and an equation describing the dependence of the electrode potential as a function of that formal potential and the individual pH values. Formal potentials are strictly thermodynamic quantities, and no kinetic effects (e.g., by electrochemical -> irreversibility) are considered. 

Wagner factor — or thermodynamic factor, denotes usually the - concentration derivative of -> activity or - chemical potential of a component of an electrochemical system. This factor is necessary to describe the - diffusion in nonideal systems, where the - activity coefficients are not equal to unity, via Fick s laws. In such cases, the thermodynamic factor is understood as the proportionality coefficient between the selfdiffusion coefficient D of species B and the real - diffusion coefficient, equal to the ratio of the flux and concentration gradient of these species (chemical diffusion coefficient DB) ... 

The Nemst equation applies (if we neglect the activity coefficients of the ions, in keeping with PB theory) to the emf (electromotive force) of an electrochemical cell. The emf of such a cell and the surface potential of a colloidal particle are quantities of quite different kinds. It is not possible to measure colloidal particle with a potentiometer (where would we place the electrodes ), and even if we could, we have no reason to expect that it would obey the Nemst equation. We have been at pains to point out that all the experimental evidence on the n-butylam-monium vermiculite system is consistent with the surface potential being roughly constant over two decades of salt concentration. This is clearly incompatible with the Nemst equation, and so are results on the smectite clays [28], Furthermore, if the zeta potential can be related to the electrical potential difference deviations from Nemst behavior, as discussed by Hunter... 

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