Potential determining equilibria

Pb(Hg) electrode in the presence of PbS04 and H2SO4 has been used in thermodynamic studies and equilibrium potential determination [45]. 

As argued earlier (Sect. 1.2), the initial potential Et either equals the equilibrium potential determined by eqn. (10), if the initial concentrations Cq and c are finite, or, in the case where c = 0 or Cq — 0, Ei can be fixed to a given value by means of the potentiostat. In the latter case, Ei is chosen to be in the so-called non-faradaic region where the faradaic current equals zero. For example, if only O is initially present, we take E > E°, so that the rate of reduction is negligibly small. Consequently, the boundary conditions formulated in eqn. (19c) are valid in both cases. 

Fig. 17.8. Model of a particulate redox enzyme upon which the theory of electron conduction enzymes is based. Site X in the particle acts as electrode for the redox couple X and develops an equilibrium potential determined by the extent of the reduction of X. Site Y, on the opposite side, acts in the same way for Y. The potential difference causes an electronic current between sites X and Y and within the particle (from Ref. 35 with permission).

The difference in equilibrium potentials determines the value of the change in the free energy and, therefore, the direction of the overall reaction ... 

This operation determines the values of R and C that, in series, behave as the cell does at the measurement frequency. The impedance is measured as a function of the frequency of the ac source. The technique where the cell or electrode impedance is plotted V5. frequency is called electrochemical impedance spectroscopy (EIS). In modem practice, the impedance is usually measured with lock-in amplifiers or frequency-response analyzers, which are faster and more convenient than impedance bridges. Such approaches are introduced in Section 10.8. The job of theory is to interpret the equivalent resistance and capacitance values in terms of interfacial phenomena. The mean potential of the working electrode (the dc potential ) is simply the equilibrium potential determined by the ratio of oxidized and reduced forms of the couple. Measurements can be made at other potentials by preparing additional solutions with different concentration ratios. The faradaic impedance method, including EIS, is capable of high precision and is frequently used for the evaluation of heterogeneous charge-transfer parameters and for studies of double-layer structure. 

This circuit includes multiple branches but only two nodes. Channels for different ions are equivalent to voltage sources, whose electromotive forces are equal to their respective equilibrium potentials determined by the Nemst formula and whose internal resistances depend on the permeability of the membrane for, and the diffusion coefficients as well as the concentrations of, respective ions. The ion pumps can be represented by corresponding current sources, all of which can be summed up forming one current source as shown in Fig. 1. If there exist transporters in the membrane, they can be electrically modeled (omitted in Fig. 1) in the same way as pumps. The capacitor represents the effect of the lipid bilayer of the membrane together with the extracellular solution (or the bath solution under artificial conditions) and intracellular solutiOTi. All these branches are arranged in parallel. 

If the potential of the WE is made more negative than the equilibrium potential determined by the bulk concentrations of 0 and R, equilibrium can only be reestablished when the surface concentrations of O and R have taken up the new values demanded by the Nernst equation, Equation (1.24), at the applied potential. This will require current to flow through the electrode/ solution interface. In fact, a decrease in the ratio Cq/cr is necessary, and this... 

Thus the tendency for an electrochemical reaction at a metal/solution interface to proceed in a given direction may be defined in terms of the relative values of the actual electrode potential E (experimentally determined and expressed with reference to the S.H.E.) and the reversible or equilibrium potential E, (calculated from E and the activities of the species involved in the equilibrium). 

It is apparent (Fig. 1.21) that at potentials removed from the equilibrium potential see equation 1.30) the rate of charge transfer of (a) silver cations from the metal to the solution (anodic reaction), (b) silver aquo cations from the solution to the metal (cathodic reaction) and (c) electrons through the metallic circuit from anode to cathode, are equal, so that any one may be used to evaluate the rates of the others. The rate is most conveniently determined from the rate of transfer of electrons in the metallic circuit (the current 1) by means of an ammeter, and if / is maintained constant it can eilso be used to eveduate the extent. A more precise method of determining the quantity of charge transferred is the coulometer, in which the extent of a single well-defined reaction is determined accurately, e.g. by the quantity of metal electrodeposited, by the volume of gas evolved, etc. The reaction Ag (aq.) -t- e = Ag is utilised in the silver coulometer, and provides one of the most accurate methods of determining the extent of charge transfer. 

The equilibrium potentials and E, can be calculated from the standard electrode potentials of the H /Hj and M/M " " equilibria taking into account the pH and although the pH may be determined an arbitrary value must be used for the activity of metal ions, and 0 1 = 1 is not unreasonable when the metal is corroding actively, since it is the activity in the diffusion layer rather than that in the bulk solution that is significant. From these data it is possible to construct an Evans diagram for the corrosion of a single metal in an acid solution, and a similar approach may be adopted when dissolved O2 or another oxidant is the cathode reactant. 

Equations 20.176 and 20.179 emphasise the essentially thermodynamic nature of the standard equilibrium e.m.f. of a cell or the standard equilibrium potential of a half-reaction E, which may be evaluated directly from e.m.f. meeisurements of a reversible cell or indirectly from AG , which in turn must be evaluated from the enthalpy of the reaction and the entropies of the species involved (see equation 20.147). Thus for the equilibrium Cu -)-2e Cu, the standard electrode potential u2+/cu> hence can be determined by an e.m.f. method by harnessing the reaction... 

It must be emphasised that standard electrode potential values relate to an equilibrium condition between the metal electrode and the solution. Potentials determined under, or calculated for, such conditions are often referred to as reversible electrode potentials , and it must be remembered that the Nernst equation is only strictly applicable under such conditions. 

Figure 11.5 Chloride distribution and the GABAa response. The change in membrane voltage (Fm) that results from an increase in chloride conductance following activation of GABAa receptors is determined by the resting membrane potential and the chloride equilibrium potential (Fci)- (a) Immature neurons accumulate CF via NKCC, while mature neurons possess a Cl -extruding transporter (KCC2). (b) In immature neurons GABAa receptor activation leads to CF exit and membrane depolarisation while in mature neurons the principal response is CF entry and h5q)erpolarisation. This is the classic inhibitory postsynaptic potential (IPSP)...

Fach of these reactions has its own exchange current density and its own equilibrium potential. The condition of overall balance at this electrode is determined not by Fq. (2.7) but by the equation... 

Two types of notion exist with respect to the term low concentrations [i.e., a low absolute concentration (highly dilute solutions) and a low equilibrium concentration (as in the formation of complexes or compounds of low solubility)]. In the latter case, when potential-determining substances start to be withdrawn from the solution, they re-form because of the shift in equilibrium (i.e., their potential supply is large). 

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

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.)... 

The straight lines for the partial CD t andT in Fig. 63b intersect at the equilibrium potential AE = 0. The value of CD corresponding to the point of intersection is that of the exchange CD f, according to Eq. (6.11). It follows that the exchange CD can be determined when the linear sections of the anodic or cathodic polarization curve, which have been measured experimentally and plotted as log i vs. AE, are extrapolated to the equilibrium potential. Moreover, according to Eq. (6.19) the exchange CD can be determined from the slope of the polarization curve near the equilibrium potential when the curve is plotted as i vs. AE. 

It follows that from the slope of the linear section in the polarization curve close to the equilibrium potential, we can determine the exchange CD of the overall reaction. 

In an electrochemical system, gas supersaturation of the solution layer next to the electrode will produce a shift of equilibrium potential (as in diffusional concentration polarization). In the cathodic evolution of hydrogen, the shift is in the negative direction, in the anodic evolution of chlorine it is in the positive direction. When this step is rate determining and other causes of polarization do not exist, the value of electrode polarization will be related to solution supersaturation by... 

At mercury and graphite electrodes the kinetics of reactions (15.21) and (15.22) can be studied separately (in different regions of potential). It follows from the experimental data (Fig. 15.6) that in acidic solutions the slope b 0.12 V. The reaction rate is proportional to the oxygen partial pressure (its solution concentration). At a given current density the electrode potential is independent of solution pH because of the shift of equilibrium potential, the electrode s polarization decreases by 0.06 V when the pH is raised by a unit. These data indicate that the rate-determining step is addition of the first electron to the oxygen molecule ... 

Potentiometry, which measures the open-circuit equilibrium potential of an indicator electrode, for which the substance being examined is potential determining... 

Potentiometry is suitabie for the analysis of substances for which electrochemical equilibrium is established at a suitable indicator electrode at zero current. According to the Nemst equation (3.31), the potential of such an electrode depends on the activities of the potential-determining substances (i.e., this method determines activities rather than concentrations). 

However, the equilibrium of the indicator adsorbed at an interface may also be affected by a lower dielectric constant as compared to bulk water. Therefore, it is better to use instead pH, the interfacial and bulk pK values in Eq. (50). The concept of the use at pH indicators for the evaluation of Ajy is also basis of other methods, like spin-labeled EPR, optical and electrochemical probes [19,70]. The results of the determination of the Aj by means of these methods may be loaded with an error of up to 50mV [19]. For some the potentials determined by these methods, Ajy values are in a good agreement with the electrokinetic (zeta) potentials found using microelectrophoresis [73]. It is proof that, for small systems, there is lack of methods for finding the complete value of A>. 

Another approach to stochastic processes of this kind is the observation of the system in equilibrium (for example, of an electrode in equilibrium with the potential determining system). The value of the electrode potential is not completely constant but it shows irregular small deviations from the average value E,... 

Traud1 [26], The latter reported that Zn dissolution from Zn/Hg amalgam was dependent on the amalgam electrochemical potential, but independent of the accompanying H2 evolution partial reaction. In Paunovic s and Saito s adaptation of this model, the partial electroless reactions occur simultaneously on the plating surface, resulting in the development of an equilibrium potential intermediate in value between the reversible potentials, in practice the experimentally-determined open circuit potential values, of the anodic and cathodic partial reactions. 

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