Activation energy of the electrode reaction

The standard activation energy of the electrode reaction Hi is defined as... 

The electrode reaction occurs in the region where by the influence of the electrode charge an electric field is formed, characterized by the distribution of the electric potential as a function of the distance from the electrode surface (see Section 4.3). This electric field affects the concentrations of the reacting substances and also the activation energy of the electrode reaction, expressed by the quantities wT and wp in Eq. (5.3.13). This effect can be... 

The value of the electric potential affecting the activation enthalpy of the electrode reaction is decreased by the difference in the electrical potential between the outer Helmholtz plane and the bulk of the solution, 2, so that the activation energies of the electrode reactions are not given by Eqs (5.2.10) and (5.2.18), but rather by the equations... 

The term Eq in Equation (7.16) is the sum of anodic and cathodic overpotentials and expresses the way in which the fourth variable in electrochemistry, the electrical variable, operates to govern the rate of electrode reactions. Overpotentials are essentially determined by the activation energy of the electrode reaction. Overpotentials are the applied potential difference, in excess of the thermodynamic value, that is spent to overcome the activation energy. 

Electrode reactions are analogous to any heterogeneous chemical reaction where reaction takes place on a catalytic surface, with one important difference.37 The heterogeneous chemical reaction does not involve a net charge transfer across the interface and is potential independent, while the electrode reaction involves a net charge transfer across the interface, and therefore the reaction rate is potential-dependent. In effect, the activation energy of the electrode reaction can be controlled by varying the potential. 

The "symmetry factor fi expresses the fraction of the contribution of electrical energy to the activation energy of the electrodic reaction. Its magnitude depends on the position of the energy barrier and varies between 0 and 1. Most often, a symmetrical energy barrier is assumed, for which p - 0.5. 

Overpotential is the voltage required to overcome the activation energy of an electrode reaction. A greater overpotential is required to drive a reaction at a faster rate. 

The main catalytic influence of the nature of the electrode material is through the adsorption of intermediates of complex electrode reactions. Hortiuti and Polanyi [58] suggested that the activation energy of an electrode reaction should be related to the heat of adsorption of adsorbed intermediates by a relationship of the form of the Br0nsted rule in homogeneous solutions. This corresponds to a vertical shift of the potential energy curves by an amount j3Aif°ds with (5 a symmetry factor as discussed in Sect. 6.4 and depicted in Fig. 12. 

Pyzhov Equation. Temkin is also known for the theory of complex steady-state reactions. His model of the surface electronic gas related to the nature of adlay-ers presents one of the earliest attempts to go from physical chemistry to chemical physics. A number of these findings were introduced to electrochemistry, often in close cooperation with -> Frumkin. In particular, Temkin clarified a problem of the -> activation energy of the electrode process, and introduced the notions of ideal and real activation energies. His studies of gas ionization reactions on partly submerged electrodes are important for the theory of -> fuel cell processes. Temkin is also known for his activities in chemical -> thermodynamics. He proposed the technique to calculate the -> activities of the perfect solution components and worked out the approach to computing the -> equilibrium constants of chemical reactions (named Temkin-Swartsman method). 

In kinetic polarization, the magnitude of the current is limited by the rate of one or both of the electrode reactions—that is, the rate of electron transfer between the reactants and the electrodes. To offset kinetic polarization, an additional potential, or overvoltage, is required to overcome the activation energy of the half-reaction. 

In the periodically modulated version of this experiment (32), the laser heating is carried out sinusoidally at a frequency of 5 to 20 Hz, and the resulting sinusoidally varying current, is detected with a lock-in amplifier, as in hydrodynamic modulation. The variation of A/q with E is called thermal modulation voltammetry (TMV). Near, A/p shows a peak whose magnitude for a nemstian reaction is a function of the ratio of the en-tropic energy of the electrode reaction divided by the activation energy of the mass transport process. While the method is capable of extracting thermodynamic information about a reaction, both the theory and the experimental set-up is sufficiently complex that it has not yet found widespread use. 

Activation-related losses. These stem from the activation energy of the electrochemical reactions at the electrodes. These losses depend on the reactions at hand, the electro-catalyst material and microstructure, reactant activities (and hence utilization), and weakly on current density. 

There are two principal contributions to the overpotential. The first contribution is the concentration overpotential, which is due to changes in concentration near the surface of the electrodes due to the passage of the current. The second contribution is the activation overpotential, related to the activation energy of the chemical reaction at the electrode. 

So that the electrostatic interaction energy, for an overvoltage 17, is r F/2RT and it is by this amount that the activation energy of an electrode reaction is considered to be reduced. 

The value of < ), however, cannot be determined, and we cannot control its constancy. Indeed, measurements at constant electrode potential (when the electrode under investigation and the reference electrode are at the same temperature) would only mean that the algebraic sum of the three potential drops is constant. On the other hand, measurement against a reference electrode held at a constant temperature would introduce an error due to the fact that the temperature difference in the electrolyte solution leads to a potential difference which also cannot be measured. Thus, the activation energy of an electrode reaction, which is similar to the activation energy of a chemical reaction, cannot be determined experimentally. For this reason, this quantity is called, after Temkin[9], the ideal activation energy. 

A correlation between the electronic work function of a metal (in vacuo or in a dielectric, particularly in water, where zero-charge potentials were used) and hydrogen overpotential has been noted more than once (see, for example, [44-47]). Sometimes, this correlation was considered as a proof that the electronic work function directly influences the activation energy of an electrode reaction. It is clear from what has been said above that there is no... 

Let us now consider, using a phenomenological approach, two limiting cases, namely, highly exothermic and highly endothermic reactions. We shall proceed from the well-known dependence of the activation energy of an electrode reaction on overpotential, which has already been discussed above ... 

In addition to what has been said above, for a barrierless process to take place it is necessary that the activation barrier in the region of an ordinary discharge be not too high so that the activation energy of the reverse reaction may vanish for a not very large decrease in the electrode potential. 

The functional dependence of the activation energy of the anodic electrode reaction can be derived as follows. According to the definition of the rate of the electrode reaction, the partial current density... 

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