Reaction, at constant potential

Measurement of the quantity of electricity used in an electrochemical reaction at constant potential or constant current. 

Determination of the transfer coefficient from current-potential data was discussed earlier (Eq. 13b). The concentration dependence of the reaction rate can be easily obtained with simple order reactions at constant potential... 

From the electrode-kinetic point of view (Section 4), operation of electrochemical reactions at constant potential enables the rates to be treated exactly like rates of other heterogeneous processes with, e.g., corresponding evaluation of reaction orders leading to mechanism elucidation (see Section 6.3). This approach can be applied at various selected, controlled potentials. 

A number of different types of experiment can be designed, in which disc and ring can either be swept to investigate the potential region at which the electron transfer reactions occur, or held at constant potential (under mass-transport control), depending on the infomiation sought. 

Curve 1 in Fig. 6.9 shows the influence of constant k, (or of parameters or which are proportional to it) on the current density at constant potential for a reaction with an intermediate value of k°. Under diffusion control (low values of/) the current density increases in proportion to/ . Later, its growth slows down, and at a certain disk speed kinetic control is attained where the current density no longer depends on disk speed. The figure also shows curves for the kinetic current density 4 and the diffusion current density /. 

A basic defect of these ideas is their failure to provide an explanation of the substantial effects of sofution composition, in particular the pH value, on the rate of the electrochemical reaction. Since hydrogen ions are not involved in the recombination step, the rate of this step according to Eq. (15.12) should not depend on solution pH. Yet in many cases the rate of hydrogen evolution at constant potential is proportional to the hydrogen ion concentration in solution. 

Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simplified equivalent circuit for the liquid-liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clarified later, the photoinduced ET... 

The quantity kconv = exp (anFE0,/RT) is the value of the rate constant of the electrode reaction at the potential of the standard reference electrode and will be termed the conventional rate constant of the electrode reaction. It can be found, for example, by extrapolation of the dependence (5.2.36) to E = 0, as... 

Figure 8-40 shows the electron transfer current of two redox reactions (outer-sphere electron transfer) observed at constant potential for platinum electrodes covered with a thin oxide film in acidic solutions as a function of the film thickness. As e3q>ected fium Eqns. 8-84 and 8-85, a linear relationship is observed between the logarithm of the reaction ciirrents and the thicknesses of the film. 

We can define the left side of Equation 10.20 as AG, where the process described is one mole of reaction at constant chemical potential for reactants and products, that is, for a system large enough so that one mole of reaction can take place in the mixture without any significant change in composition or chemical potential, an infinite-copy model. As AG is a constant at constant temperature, the quantity in brackets is also a constant at constant temperamre, and, in particular, independent of the total pressure and the initial composition of the system. We therefore designate the quantity in brackets as Kp, which is the equilibrium constant in terms of partial pressures for a... 

From a practical point of view, which effect is responsible for the performance of an electrode material is in principle uninteresting in that both converge to improve the electrode behavior. However, from a fundamental point of view, such a distinction is essential to be able to improve and optimize the experimental situation. In terms of reaction rate (current density), only knowledge of the real surface area can allow one to separate experimentally the two factors. If a plot of j against S (real surface area) at constant potential gives a straight line, the effects are more likely to be geometric only. On the other hand, if the correlation deviates from linearity, electronic factors are most likely to operate. This approach assumes that the... 

At constant potential, in a simple reaction with no surface intermediates, the i—t line will tend to become constant after the double-layer charging is over. If at this time the current density is well below the limiting current density, iL (Section 7.9.10), there should be nothing to interfere with the continuation of the steady-state constant current. If the current density after double-layer charging is above the limiting current, the current will decline with time. This is discussed quantitatively in Chapter 8. 

Diffusion into the electrode. If the surface radical is H, there may be diffusion into the electrode and this may cause a change in the character of the surface and the atoms immediately beneath it. Hence, for surface-catalyzed reactions on real surfaces, finding the steady state in the i—t curve at constant potential may show complexities (Fig. 7.44). Where is the steady state in Fig. 7.44(b) It becomes a matter of judgment The best plan is to take the first time-invariant section and to reject the further variations, which simply indicate a nonconstant surface.44... 

Further Observations on the Technique of Steady-State Electrochemical Kinetic Measurements 1. In potentiostatic measurements, the appropriate interval of potential between each measurement depends on the total range of potential variation. It may be between 10 and 50 mV and can be automated and computer controlled (Buck and Kang, 1994). It is helpful to observe a series of steady-state currents at, say, 20 potentials taken from least cathodic to most cathodic, and the same series taken from most cathodic to the least cathodic. The two sets of current densities should be equal at each of the chosen constant potentials. In practice, with reactions involving electrocatalysis, a degree of disagreement up to 25% in the current density at constant potential is to be tolerated. 

Notice that, because of the strong dependence of the kinetics on electrode potential, the determination of the electrochemical reaction order requires that the partial cathodic or anodic current densities are measured at constant potential in addition to the activities of the other species remaining constant. 

Coulometry at constant current is often considered as being less attractive than coulometry at constant potential. However, when the current density is low, the potential of the working electrode stays almost constant until approximately 90% of the substrate is consumed. Control of the current rather than the potential has, however, a number of advantages. First, the charge consumed during the reaction is directly proportional to the electrolysis time,... 

All cathodic reductions described below were performed at mercury pool cathodes in solutions containing tetraalkylammonium (TAA+) electrolytes and most were carried out at a constant current. For preparative scale experiments, in general, the constant-current method is preferable to that of constant potential. The equipment for constant-current experiments is simpler, much less expensive and more suitable for large scale reactions. For the particular conditions described here, experiments at constant potential are difficult (except when TAA+ in small concentrations are used as catalyst, see Sect. 8). The current often varies erratically throughout constant-potential experiments, reaction times are unpredictable and often impractically long. This is the result of participation of the cathode material in the reaction sequence. The mercury pool surface is visibly disrupted, droplets of mercury separate from the surface and in many instances the black precipitate of the TAA-mercury covers the cathode surface. 

Electrochemical reduction of aryl halides in the presence of olefins (94), (equation 54) leads to the formation of arylated products (95). Electroreduction of several aralkyl halides at potentials ranging from -1.24 V to -1.54 V (see) gives products which involve dimerization, cyclization, and reduction to the arylalkanes. Carbanions and/or free radicals were again postulated as intermediates79. Aryl radicals generated from the electrochemical reduction of aryl halides have been added to carbon-carbon double bonds80,81. Electrochemical reduction of aryl halides in the presence of olefins leads to the formation of arylated products78. Preparative scale electrolyses were carried out in solvents such as acetonitrile, DMF and DMSO at constant potential or in liquid ammonia at constant current. The reaction is proposed to involve an S l mechanism. 

The electrolysis cell consists of a working-electrode at which the species to be determined is reduced or oxidized or at which a chemically reactive species is formed, and a counter-electrode. In practice electrolysis may be at constant potential, in which case the Current diminishes to zero as the reaction goes to completion, or at constant current. The quantity of electricity involved in the former is measured by means of a chemical ebuiometer or by integrating the area under the current-time curve. Constant current methods involve the generation of a titrant for a measured length of time, the completion of the reaction with the species to be determined being indicated by any of the... 

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