Electrode Processes at Equilibrium

It is now necessary to take a more unified view by considering situations in which the rate of the electrodic process at the interface is subject both to activation and to transport limitations. One refers to a combined activation-transport control of the electrodic reaction. Under such conditions, there will be, in addition to the overpotential T)c produced by the concentration change (from c° to c ) at the interface, an activation overpotential because the charge-transfer reaction is not at equilibrium. The total overpotential rj is the difference between the interfacial-potential difference... 

The electrode potential of a system is the electrode potential of all half-cell processes at equilibrium in the system. 

Thus, the presence of the inflection point in the calibration E-pO plots is a distinctive feature of the work on the gas membrane oxygen electrode in high-temperature ionic melts. More exactly, there are two linear sections, with slopes corresponding to values of z equal to 1 and 2. This result, noted at first in our paper [233], showed that the electrode process at the gas membrane oxygen electrode was essentially dependent not on peculiarities of the assumed potential-determining process with the participation of the given Lux base (as was considered before), but on the equilibrium concentration of oxide ion created by dissociation of this base in the ionic melt. 

Suppose a small AC signal is superimposed on the DC voltage. At equilibrium, DC voltage with no DC current, the AC current will flow in both directions because it is a reversible redox electrode process at the AgCl surface. With a DC current, the small AC current will be superimposed on the larger DC current, and thus just change the reaction rate a small amount. 

If the two half-cells are arranged oppositely, the reactions are reversed and the process refers to water electrolysis. The electrode potential at equilibrium is then negative and ARG gg is positive. Now TARS gg is positive (48.7kJ mol ) and is taken up from the environment or the electrolysis cell cools down. This effect can be compensated if the cell operates at a higher cell voltage to permit isothermal operation, and is denoted as the thermoneutral voltage ... 

In this case, spontaneous processes occur in the electrochemical cell leading to the generation of a cell potential which reaches a steady state when the net current flowing in the cell and measurement circuitry is zero, i.e. the processes occurring at the electrodes are at equilibrium. 

It is apparent from this that since the rates of the cathodic and anodic processes at each electrode are equal, there will be no net transfer of charge in fact, with this particular cell, consisting of two identical electrodes in the same electrolyte solution, a similar situation would prevail even if the electrodes were short-circuited, since there is no tendency for a spontaneous reaction to occur, i.e. the system is at equilibrium and AG = 0. 

Consider now the transfer of electrons from electrode II to electrode I by means of an external source of e.m.f. and a variable resistance (Fig.. 20b). Prior to this transfer the electrodes are both at equilibrium, and the equilibrium potentials of the metal/solution interfaces will therefore be the same, i.e. Ey — Ell = E, where E, is the reversible or equilibrium potential. When transfer of electrons at a slow rate is made to take place by means of the external e.m.f., the equilibrium is disturbed and Uie rat of the charge transfer processes become unequal. At electrode I, /ai.i > - ai.i. 3nd there is... 

Very simply these equations are valid as long as ion backspillover from the solid electrolyte onto the gas-exposed electrode surfaces is fast relative to other processes involving these ionic species (desorption, reaction) and thus spillover-backspillover is at equilibrium, so that the electrochemical potential of these ionic species is the same in the solid electrolyte and on the gas exposed electrode surface. As long as this is the case, equation (5.29) and its consequent Eqs. (5.18) and (5.19) simply reflect the fact that an overall neutral double layer is established at the metal/gas interface. 

At the extremes of pH it is common for the equilibrium to be driven completely to the left or right and then the electrode process becomes independent of pH since it is the bulk species which is electroactive. Thus the common shape of curves is shown in Fig. 7 (Zuman... 

If a system is not at equilibrium, which is common for natural systems, each reaction has its own Eh value and the observed electrode potential is a mixed potential depending on the kinetics of several reactions. A redox pair with relatively high ion activity and whose electron exchange process is fast tends to dominate the registered Eh. Thus, measurements in a natural environment may not reveal information about all redox reactions but only from those reactions that are active enough to create a measurable potential difference on the electrode surface. 

Equation (6.13), in fact, reflects the physical nature of the electrode process, consisting of the anode (the first term) and cathode (the second term) reactions. At equilibrium potential, E = Eq, the rates of both reactions are equal and the net current is zero, although both anode and cathode currents are nonzero and are equal to the exchange current f. With the variation of the electrode potential, the rate of one of these reactions increases, whereas that of the other decreases. At sufficiently large electrode polarization (i.e., deviation of the electrode potential from Eg), one of these processes dominates (depending on the sign of E - Eg) and the dependence of the net current on the potential is approximately exponential (Tafel equation). 

In order to asses the analytical aspects of the rotating electrodes we must consider the convective-diffusion processes at their bottom surface, and in view of this complex matter we shall confine ourselves to the following conditions (1) as a model of electrode process we take the completely reversible equilibrium reaction ... 

A chemical reaction subsequent to a fast (reversible) electrode reaction (Eq. 5.6.1, case b) can consume the product of the electrode reaction, whose concentration in solution thus decreases. This decreases the overpotential of the overall electrode process. This mechanism was proposed by R. Brdicka and D. H. M. Kern for the oxidation of ascorbic acid, converted by a fast electrode reaction at the mercury electrode to form dehydro-ascorbic acid. An equilibrium described by the Nernst equation is established at the electrode between the initial substance and this intermediate product. Dehydroascorbic acid is then deactivated by a fast chemical reaction with water to form diketogulonic acid, which is electroinactive. 

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