Equilibrium electrode potential concentrations

The overpotential tj is defined as E — fcr, where E, is the equilibrium electrode potential at the concentration [H+] and 0H that actually pertain in the system. In fact, since ()H is unknown normally, we actually define Er with reference to the values of [H +] and pH, through the Ncrnst equation ... 

Equation (5.9) is the general Nemst equation giving the concentration dependence of the equilibrium cell voltage. It will be used in Section 5.4 to derive the equilibrium electrode potential for metal/metal-ion and redox electrodes. 

Mass transport overpotential (or concentration polarization (overpotential)) tjc — is a departure of the - electrode potential (or cell potential), E, from the - equilibrium electrode potential (or zero-current potential), Eeq, caused by a -> faradaic current flow and the associated surface concentration, Cox(x = 0), deviation from the bulk concentration, Cox(°°)> of the reacting redox species, Ox... 

Among the different surface atom positions illustrated on Fig. 2.8, the kink site position, or the half crystal position, as introduced independently by Kossel [2.12] and Stranski [2.13], has a special significance for the definition of the equilibrium conditions (vapor pressure, equilibrium concentration, equilibrium electrode potential, etc.) of the infinitely large (bulk) crystal. 

The potential of the platinum electrode in a mixture of redox couples is a poorly defined, weighted average of the potentials of all the redox couples present. The contribution of each couple to the average potential is an unknown function of its concentration, irreversibility, and equilibrium electrode potential. The potential of a nonequilibrium mixture of redox couples is not the potential of any single couple and is a mixed potential. 

Activities and/or activity coefficients are not available for ionic species in most corrosion solutions. Therefore, as a practical expedient, the concentrations of the species are used in place of the respective activities when computing equilibrium electrode potentials. ... 

In the given form, the Butler-Volmer equation is applicable rather broadly, for flat model electrodes, as well as for heterogeneous fuel cell electrodes. In the latter case, concentrations in Eq. (2.13) are local concentrations, established by mass transport and reaction in the random composite structure. At equilibrium,/f = 0, concentrations are uniform. These externally controlled equilibrium concentrations serve as the reference (superscript ref) for defining the equilibrium electrode potential via the Nernst equation. 

An important characteristic of a potentiometric indicator electrode is the response time. The response time is the time required for the establishment of an equilibrium electrode potential. According to an lUPAC recommendation [24], the response time is the time interval from the moment of inserting the potentiometric set-up into the test solution to the moment when the potential deviates from the equilibrium potential by 1 mV. This time interval can span from milliseconds to minutes or hours and depends on many conditions, e.g. concentration of the measuring ion (small exchange currents), speed of stirring, temperature, history and pretreatment of the indicator electrode and so on. 

The E° and E° values shown in parentheses are the equilibrium electrode potentials for reactions (142) and (143) at 25°C and with reactants and products at unit activity. In practice, chlor-alkali cells operate at different temperatures and concentrations, hence, the El and ° terms should be properly corrected using the Nemst equation. Typical conditions encountered in diaphragm-type chlor-alkali cells are as follows ... 

The calomel electrode is very similar in both construction and theory of operation to the silver/silver chloride electrode described below. The metal is mercury, the electrical connection being made by an inert metal wire and the salt is mercurous chloride. The equilibrium electrode potential is a function of the chloride concentration of the electrolyte. When the electrolyte is saturated potassium chloride, it is known as a saturated calomel electrode (SCE) producing an electrode potential of -1-0.224 V vs SHE. Potassium chloride is used because the ionic mobility... 

This is the famous Butler-Volmer equation. Incorporating the Nernst equation, which relates the equilibrium electrode potential to the standard equilibrium potential and to the equilibrium composition of the bulk electrolyte (concentrations with superscript b) via... 

The equilibrium electrode potential Eq depends of course on the actual concentrations c or the activities a = c/ of the dissolved species according to the Nernst equation (where / is the activity coefficient). For the discussed electrode reactions with T = 298 K and the definition pH =-log Ch... 

The Nernst equation (16) relates the equilibrium electrode potential eq (the electrical potential of the working electrode with respect to any convenient reference electrode) to the bulk solution concentrations [O] and [R] when the system is in equilibrium. As the bulk concentration [O] increases or the bulk concentration [R] decreases, the equilibrium potential becomes more positive. 

Now interpret phase X as pure solute then Cs and co become the equilibrium solubilities of the solute in solvents S and 0, respectively, and we can apply Eq. (8-58). Again the concentrations should be in the dilute range, but nonideality is not a great problem for nonelectrolytes. For volatile solutes vapor pressure measurements are suitable for this type of determination, and for electrolytes electrode potentials can be used. 

The most widely used reference electrode, due to its ease of preparation and constancy of potential, is the calomel electrode. A calomel half-cell is one in which mercury and calomel [mercury(I) chloride] are covered with potassium chloride solution of definite concentration this may be 0.1 M, 1M, or saturated. These electrodes are referred to as the decimolar, the molar and the saturated calomel electrode (S.C.E.) and have the potentials, relative to the standard hydrogen electrode at 25 °C, of 0.3358,0.2824 and 0.2444 volt. Of these electrodes the S.C.E. is most commonly used, largely because of the suppressive effect of saturated potassium chloride solution on liquid junction potentials. However, this electrode suffers from the drawback that its potential varies rapidly with alteration in temperature owing to changes in the solubility of potassium chloride, and restoration of a stable potential may be slow owing to the disturbance of the calomel-potassium chloride equilibrium. The potentials of the decimolar and molar electrodes are less affected by change in temperature and are to be preferred in cases where accurate values of electrode potentials are required. The electrode reaction is... 

Figure 2. Reactions that occur in lead-acid batteries versus electrode potential (thermodynamic situation). Their equilibrium potentials are inserted as boxed numbers. Equilibrium potentials of the charge-discharge reactions (Pb/PbS04 and PhS04/Pb02) are represented by hatched columns, to indicate their dependence on acid concentration. The inserted equilibrium potentials (-0.32 and +l. 75 V) of the charge discharge reactions correspond to an acid density of 1.23 gem 3.

Often, H+ or OH ions are involved in the electrode reactions, and the electrode potential then depends on the concentration of these ions (or solution pH). Because of the dissociation equilibrium of water, the activities of these ions are interrelated as fle+floH = = 1-27 X 10 moH/L. For this reason these reactions can be for-... 

Electrode reactions are heterogeneous since they occur at interfaces between dissimilar phases. During current flow the surface concentrations Cg j of the substances involved in the reaction change relative to the initial (bulk) concentrations Cy p Hence, the value of the equilibrium potential is defined by the Nemst equation changes, and a special type of polarization arises where the shift of electrode potential is due to a change in equilibrium potential of the electrode. The surface concentrations that are established are determined by the balance between electrode reaction rates and the supply or elimination of each substance by diffusion [Eq. (4.9)]. Hence, this type of polarization, is called diffusional concentration polarization or simply concentration polarization. (Here we must take into account that another type of concentration polarization exists which is not tied to diffusion processes see Section 13.5.)... 

Equations (6.9) and (6.10), which contain the rate constants, the electrode potential, and the concentrations, are equivalent to Eqs. (6.12) and (6.13), which contain the exchange CD and the electrode s polarization. But in the second set of equations the concentrations do not appear explicitly they enter the equations through the values of exchange CD and equilibrium potential. By convention, equations of the former type will be called kinetic equations, and those of the latter type will be called polarization equations. 

Under the effect of pure concentration polarization, when activation polarization is absent, the electrode potential retains an equilibrium value, but this is a value tied to the variable nonequilibrium values of surface concentrations... 

---