Electrode potential coefficient

To calculate the open circuit voltage of the lead—acid battery, an accurate value for the standard cell potential, which is consistent with the activity coefficients of sulfuric acid, must also be known. The standard cell potential for the double sulfate reaction is 2.048 V at 25 °C. This value is calculated from the standard electrode potentials for the (Pt)H2 H2S04(yw) PbS04 Pb02(Pt) electrode 1.690 V (14), for the Pb(Hg) PbS04 H2S04(yw) H2(Pt) electrode 0.3526 V (19), and for the Pb Pb2+ Pb(Hg) 0.0057 V (21). 

Chemically, it is clear that Zn and Cd are rather similar and that Hg is somewhat distinct. The lighter pair are more electropositive, as indicated both by their electronegativity coefficients and electrode potentials (Table 29.1), while Hg has a... 

Atomic number Atomic weight Crystal structure Melting Density Thermal Electrical resistivity (at 20°C) Temperature coefficient of resistivity Specific Thermal Standard electrode potential Thermal neutron absorption cross-section. 

Generally, for ideally polarized electrodes, the plots of the electrode potential against either the chemical potential of the component in question or its activity are referred to as the Esin and Markov plots the slope of the plot is called the Esin and Markov coefficient.82 Aogaki etal.19 first established the expression of the critical pitting potential with respect to the composition of the solution (i.e., the Esin and Markov relations corresponding to the critical condition of the instability obtained in the preceding sections) and also verified them experimentally in the case of Ni dissolution in NaCl solution. 

Bet de Bethune, A.J., Swendeman Loud, N.A. Standard Aqueous Electrode Potentials and Temperature Coefficients at 25 °C, Skokie C.A. Hampel, 1964. 

In addition to the exchange current density the transfer coefficient a is needed to describe the relationship between the electrode potential and the current flowing across the electrode/solution interface. From a formal point of view a can be obtained by calculating the partial current densities with respect to the electrode potential for the anodic reaction ... 

From a kinetic point of view a describes the influence of a change of the electrode potential on the energy of activation for the charge transfer reaction which in turn influences the partial current density. The transfer coefficients % for the anodic charge transfer reaction and for the cathodic reaction add up according to... 

These relationships can be used to obtain thermodynamic data otherwise difficult to get. Vice versa they can be used to calculate the temperature coefficient of a cell voltage respectively an electrode potential based on known thermodynamic data. 

As the temperature is varied, the Galvani potentials of all interfaces will change, and we cannot relate the measured value of d"S dT to the temperature coefficient of Galvani potential for an individual electrode. The temperature coefficient of electrode potential probably depends on the temperature coefficient of Galvani potential for the reference electrode and hence is not a property of the test electrode alone. 

Thus, the temperature coefficient of Galvanic potential of an individual electrode can be neither measured nor calculated. Measured values of the temperature coefficients of electrode potentials depend on the reference electrode employed. For this reason a special scale is used for the temperature coefficients of electrode potential It is assumed as a convention that the temperature coefficient of potential of the standard hydrogen electrode is zero in other words, it is assumed that the value of Hj) is zero at all temperatures. By measuring the EMF under isothermal conditions we actually compare the temperature coefficient of potential of other electrodes with that of the standard hydrogen electrode. 

Another example are the sometimes rather complex relations existing between the potential and the reaction rate. The electrode potential influences not only the parameter h [see, e.g., Eq. (14.15)] but also the degree of surface coverage by reactant particles [i.e., the coefficients in Eq. (14.18) or (14.20)]. When a sharp drop in adsorption occurs with increasing electrode polarization (rising values of hj, the monotonic relation between reaction rate and potential may break down and the current actually may decrease within a certain region while polarization increases. 

The charge transfer reaction (5.2.39) is characterized by the formal electrode potential the conditional rate constant of the electrode reaction kf and the charge transfer coefficient aly while the reaction (5.2.40) is characterized by the analogous quantities E2y kf and a2. If the rate constants of the electrode reactions, which are functions of the potential, are denoted as in Eqs (5.2.39) and (5.2.40) and the concentrations of substances Au A2 and A3 are cly c2 and c3, respectively, then... 

The case of the prescribed material flux at the phase boundary, described in Section 2.5.1, corresponds to the constant current density at the electrode. The concentration of the oxidized form is given directly by Eq. (2.5.11), where K = —j/nF. The concentration of the reduced form at the electrode surface can be calculated from Eq. (5.4.6). The expressions for the concentration are then substituted into Eq. (5.2.24) or (5.4.5), yielding the equation for the dependence of the electrode potential on time (a chronopotentiometric curve). For a reversible electrode process, it follows from the definition of the transition time r (Eq. 2.5.13) for identical diffusion coefficients of the oxidized and reduced forms that... 

The theory also predicts that the transfer coefficient, a, should vary with the electrode potential as depicted by equation (13). 

Figure 7. Dependence of the heterogeneous transfer coefficient (5 with the applied electrode potential for the representative class of organometals I-IV.

Figure 9. The direct relationship between the homogeneous Br0nsted coefficient a(Q) and the heterogeneous transfer coefficient ft ( )) with the electrode potentials, as measured for sec-BukSn.

The quantity a is the anodic transfer coefficient-, the factor l/F was introduced, because Fcf> is the electrostatic contribution to the molar Gibbs energy, and the sign was chosen such that a is positive - obviously an increase in the electrode potential makes the anodic reaction go faster, and decreases the corresponding energy of activation. Note that a is dimensionless. For the cathodic reaction ... 

The transfer coefficient a has a dual role (1) It determines the dependence of the current on the electrode potential. (2) It gives the variation of the Gibbs energy of activation with potential, and hence affects the temperature dependence of the current. If an experimental value for a is obtained from current-potential curves, its value should be independent of temperature. A small temperature dependence may arise from quantum effects (not treated here), but a strong dependence is not compatible with an outer-sphere mechanism. 

This potential-energy surface will change when the electrode potential is varied consequently the energy of activation will change, too. These changes will depend on the structure of the double layer, so we cannot predict the value of the transfer coefficient a unless we have a detailed model for the distribution of the potential in the double layer. There is, however, no particular reason why a should be close to 1/2. Also, a temperature dependence of the transfer coefficient is not surprising since the structure of the double layer changes with temperature. 

Hydrogen evolution, the other reaction studied, is a classical reaction for electrochemical kinetic studies. It was this reaction that led Tafel (24) to formulate his semi-logarithmic relation between potential and current which is named for him and that later resulted in the derivation of the equation that today is called "Butler-Volmer-equation" (25,26). The influence of the electrode potential is considered to modify the activation barrier for the charge transfer step of the reaction at the interface. This results in an exponential dependence of the reaction rate on the electrode potential, the extent of which is given by the transfer coefficient, a. 

This result is quite in contrast to the common expectation that the electrode potential changes the activation barrier at the interface which would result in a temperature independent transfer coefficient a. Following Agar s discussion (30), such a behavior indicates a potential dependence of the entropy of activation rather than the enthalpy of activation. Such "anomalous" behavior in which the transfer coefficient depends on the temperature seems to be rather common as recently reviewed by Conway (31). 

We consider again the redox reaction Ox + ze = Red with a solution initially containing only the oxidized form Ox. The electrode is initially subjected to an electrode potential Et where no reaction takes place. For the sake of simplicity, it is assumed that the diffusion coefficients of species Ox and Red are equal, i.e., D = D()s = DRcd. Now, the potential E is linearly increased or decreased with E(t) = Ei vt (v is a potential scan rate, and signs + and represent anodic scan and cathodic scan, respectively.) Under the assumption that the redox couple is reversible, the surface concentrations of Ox and Red, i.e., c()s... 

In Section 1.4.4 we describe some typical examples of outer-sphere electron transfer kinetics, with particular emphasis on the variation of the transfer coefficient (symmetry factor) with the electrode potential (driving force). 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

---