Electrochemically reversible reactions

Figure 2.22 shows SWV responses of electrochemically reversible reaction on stationary planar electrodes covered with a thin mercury film ... 

Unlike the table of the Electrochemical Series, which lists standard potentials, values for radicals are experimental values with experimental conditions given in the second column. Since the measurements leadingtopotentialsforionradicalsare very dependent on conditions, an attempt to report standard potentials for radicals would serve no useful purpose. For the same reason, the potentials are also reported as experimental values, usually a half-wave potential (i i/2 in polarography) or a peak potential (Ep in cyclic voltammetry). Unless otherwise stated, the values are reported vs. SCE (saturated calomel electrode). To obtain a value vs. normal hydrogen electrode, 0.241 Vhastohe added to the SCE values. All the ion radicals chosen for inclusion in the tables result from electrochemically reversible reactions. More detailed data on ion radicals can be found mHaeEncyclopedia of Electrochemistry of Elements, (A. J. Bard, Ed.), Vol. XI and XII in particular, Marcel Dekker, New York, 1978. 

Electrochemically reversible reactions produce steep curves whereas for irreversible reactions the slope may be much shallower, and it may be necessary to go to high potentials to reach the limiting current. 

From a voltammetric view point, micro- and nanoelectrode arrays con be considered as an assembly of very small electrodes separated by a nonconductive substrate. The size of the electrode affects the mass transport of redox species to and from the electrode surface, and, as a consequence, affects the observed electrochemical response. In this paragraph, we will only take into consideration voltammetric experiments performed in stagnant solutions, in the presence of excess supporting electrolyte, so that the only relevant mode of mass transport is diffusion. Let us consider a monoelectronic electrochemically reversible reaction in which the electroactive species Ox is reduced at the electrode to Red, as shown below in reaction (20.1). 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

Electrochemical Reversibility and Determination of m In deriving a relationship between 1/2 and the standard-state potential for a redox couple (11.41), we noted that the redox reaction must be reversible. How can we tell if a redox reaction is reversible from its voltammogram For a reversible reaction, equation 11.40 describes the voltammogram. 

Activation Processes. To be useful ia battery appHcations reactions must occur at a reasonable rate. The rate or abiUty of battery electrodes to produce current is determiaed by the kinetic processes of electrode operations, not by thermodynamics, which describes the characteristics of reactions at equihbrium when the forward and reverse reaction rates are equal. Electrochemical reaction kinetics (31—35) foUow the same general considerations as those of bulk chemical reactions. Two differences are a potential drop that exists between the electrode and the solution because of the electrical double layer at the electrode iaterface and the reaction that occurs at iaterfaces that are two-dimensional rather than ia the three-dimensional bulk. 

For the electrochemical cell reaction, the reaction free energy AG is the utilizable electrical energy. The reaction enthalpy AH is the theoretical available energy, which is increased or reduced by an amount TAS. The product of the temperature and the entropy describes the amount of heat consumed or released reversibly during the reaction. With tabulated values for the enthalpy and the entropy it is possible to obtain AG. ... 

The reversible reaction heat of the cell is defined as the reaction entropy multiplied by the temperature [Eq. (15)]. For an electrochemical cell it is also called the Peltier effect and can be described as the difference between the reaction enthalpy AH and the reaction free energy AG. If the difference between the reaction free energy AG and the reaction enthalpy AH is below zero, the cell becomes warmer. On the other hand, for a difference larger than zero, it cools down. The reversible heat W of the electrochemical cell is therefore ... 

The quality and quantity of sites which are capable of reversible lithium accommodation depend in a complex manner on the crystallinity, the texture, the (mi-cro)structure, and the (micro)morphology of the carbonaceous host material [7, 19, 22, 40-57]. The type of carbon determines the current/potential characteristics of the electrochemical intercalation reaction and also potential side-reactions. Carbonaceous materials suitable for lithium intercalation are commercially available in many types and qualities [19, 43, 58-61], Many exotic carbons have been specially synthesized on a laboratory scale by pyrolysis of various precursors, e.g., carbons with a remarkably high lithium storage capacity (see Secs. 

Nonpolarizable interfaces correspond to interfaces on which a reversible reaction takes place. An Ag wire in a solution containing Ag+ions is a classic example of a nonpolarizable interface. As the metal is immersed in solution, the following phenomena occur3 (1) solvent molecules at the metal surface are reoriented and polarized (2) the electron cloud of the metal surface is redistributed (retreats or spills over) (3) Ag+ ions cross the phase boundary (the net direction depends on the solution composition). At equilibrium, an electric potential drop occurs so that the following electrochemical equilibrium is established ... 

Cathodic hydrogen evolution is one of the most common electrochemical reactions. It is the principal reaction in electrolytic hydrogen production, the auxiliary reaction in the production of many substances forming at the anode, such as chlorine, and a side reaction in many cathodic processes, particularly in electrohydrometallurgy. It is of considerable importance in the corrosion of metals. Its special characteristic is the fact that it can proceed in any aqueous solution particular reactants need not be added. The reverse reaction, which is the anodic ionization of molecular hydrogen, is utilized in batteries and fuel cells. 

Two things to notice are that fc, will depend on the reference electrode chosen and secondly E° is the equilibrium potential not for the standard hydrogen electrode but rather for the electrochemical equilibrium between H+ and H ds. This can be seen by explicitly writing out the equation corresponding to the reverse reaction ... 

Sensors involving interaction with the surface of a semiconductor, or ceramic layer, e.g.(CHEMFETS and other electrochemical sensors) Low cost. Can measure total exposure over time, if a non-reversible reaction is used. Poisoning can occur. May exhibit non-reversible behaviour, which may be undesirable. May consume analyte. 

X. Mao, J.H. Jiang, J.W. Chen, Y. Huang, G.L. Shen, and R.Q. Yu, Cyclic accumulation of nanoparticles a new strategy for electrochemical immunoassay based on the reversible reaction between dethio-biotin and avidin. Anal. Chim. Acta 557, 159-163 (2006). 

At least from a theoretical viewpoint, several situations are possible depending on the extent of electrochemical reversibility of the electron transfer and on the reversibility or irreversibility of the chemical reaction following the electron transfer. 

As mentioned in the introduction to controlled potential electrolysis (Section 2.3), there are various indirect methods to calculate the number of electrons transferred in a redox process. One method which can be rapidly carried out, but can only be used for electrochemically reversible processes (or for processes not complicated by chemical reactions), compares the cyclic voltammetric response exhibited by a species with its chronoamperometric response obtained under the same experimental conditions.23 This is based on the fact that in cyclic voltammetry the peak current is given by the Randles-Sevcik equation ... 

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