Electrochemical systems activity coefficients

This equivalence between the charge of surface-bound molecules and the current of solution soluble ones is due to two main reasons first, in an electro-active monolayer the normalized charge is proportional to the difference between the total and reactant surface excesses ((QP/QP) oc (/> — To)), and in electrochemical systems under mass transport control, the voltammetric normalized current is proportional to the difference between the bulk and surface concentrations ((///djC) oc (c 0 — Cq) [49]. Second, a reversible diffusionless system fulfills the conditions (6.107) and (6.110) and the same conditions must be fulfilled by the concentrations cQ and cR when the process takes place under mass transport control (see Eqs. (2.150) and (2.151)) when the diffusion coefficients of both species are equal. 

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 ... 

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. 

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... 

The thermal diffusion potential, td> arises if an electrochemical system is nonisothermal. This phenomenon is due to the heat transport of ionic species and can be taken into account if the individual ion entropy of transport, conductivity, and activity coefficients of the species of interest are known. Therefore, the thermal diffusion potential depends on the temperature, pressure, and composition of the electrolyte liquid junction. Also, td is a function of the temperature gradient and can be a substantial value from tens to hundreds of millivolts [19]. 

Potentiometry may also be used to determine activity coefficients of electrolytes the measured e.m.f. of an electrochemical cell is related to the activities of the ions. These measurements can yield very accurate values near room temperature for systems where reversible and reproducible electrodes have been developed. Potentiometry at high temperatures is much more difficult this is an area of active research. 

In this equation, AG°eact is the change in the GFE for the reaction as written for reactants and products in their standard states it is calculated from Eq 2.20. The a s are the activities of the species indicated by the subscripts each activity is raised to a power equal to the stoichiometric coefficient of the species as it appears in the reaction. The activity is frequently called the effective concentration of the species because it naturally arises as a function of the concentration, that is necessary to satisfy the changes in the thermodynamic functions (here, the GFE). In electrochemical systems, the activity is usually related to the molality of the species (moles per 1000 g of solvent) by the following equation ... 

Several approaches exist for evaluating activity coefficients. For non-aqueous systems the most common method has been from electrochemical cells, (sects. 2.5-2.7). Of the remaining approaches available, the freezing point technique is most commonly employed and is considered in sects. 2.8-2.10. This gives osmotic coefficients and activity... 

Electrochemical reactions are dependent on the quantity of charged species present, but because opposite charges attract each other, the simple specification of concentration does not necessarily correlate with behavior. The concepts of ionic strength, activity, and activity coefficients help us correlate the amount of charge with the behavior of the system. 

With aqueous solutions in pressurised cells, the temperature can be varied in a very broad range. Many fundamental electrochemical data have been obtained in this medium. Thermodynamic quantities such as activity coefficients of ions [252], equilibrium double-layer capacity [261], zeta potential of metals [233], potential-pH diagrams [206] or properties of the palladium-hydrogen electrode were determined [262]. Exotic systems, e.g. the solvation of rare earth atoms in liquid gallium [234], have been studied. Main research interests in subcritical aqueous solution were focused on the kinetics, reaction mechanism and transport properties. 

This section illustrates that the thermodynamic principles we have learned so far can be applied to electrochemical systems. However, to solve Equation (9.28) in general, we need to determine the activity coefficients of the species in solution. The treatment of activity coefficients markedly differs from the nonelectrolyte solutions we have been discussing so far in the text. Charged species in solution have strong ionic interactions that are very different from other interactions in the solution. Recall from Chapter 4, these interacts vary as (l/r) in comparison to van derWaals interactions that vary as 1/ r , even in a dilute solution. 

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