Real activation energy

For this reason and following a suggestion of M. I. Temkin (1948), another conventional parameter is used in electrochemistry [i.e., the real activation energy described by Eq. (14.2)], not at constant potential but at constant polarization of the electrode. These conditions are readily realized in the measurements (an electrode at zero current and the working electrode can be kept at the same temperature), and the real activation energy can be measured. 

A more detailed analysis shows that the ideal and real activation energy are interrelated as... 

In the Arrhenins eqnation, the real activation energy is combined with a real (measnrable) preexponential factor. According to Eqs. (14.1) and (14.10), this factor differs from the trne factor by the multiplicative entropy term exp( a AS /R). 

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). 

Virtual activation energies of 114.6 to 59.8 kj/mol were found, depending on catalyst particle size. Chinchen [612] found for the intrinsic reaction measured on an ICI catalyst the real activation energy to be 129.4 kj/mol. 

Let the real activation energy be Qo and Q be the activation energy calculated on the basis of equation (31) then Q/Qo may range anywhere from unity to essentially zero, depending on the degree of the diffusion effect whose magnitude is calculable on the basis of the formulas given. 

The experimental activation energy is given by equation (31) while the real activation energy is given by... 

Fig. 13. Universal relation of apparent activation energy Q, real activation energy Qo, and the diffusion parameter -q.

Using the terminology which will be considered in detail in 2.4, we can say that, with different metals, the ideal activation energy (at a constant potential drop) is different, but the real activation energy (at constant electrode potential) is the same. It is the latter that lends itself to observation. 

The activation energy found experimentally at a constant overpotential has been termed by Temkin the real activation energy... 

Thus, the foregoing shows how the real activation energies must be calculated—they can be derived from potential energy diagrams constructed on the assumption that the latent equilibrium heat of the electrode process is zero. 

For electrode reactions, as has been described above, the ideal activation energy cannot be found experimentally. However, we can measure the real activation energy A, associated with W through the above relations. If we substitute Eq. (43) into (45),... 

The real activation energies of the grafting reaction, initiated by peroxides, was calculated. The efficiency factor was calculated from a low conversion rates of monomer by comparing the theoretical curve obtained from the general expression of the monomer disappearance in function of time to the real curve. This comparison allowed authors to evaluate f and IQ. 

It should be noted that a diffusion step occurs with a null enthalpy. The sign of the apparent activation energy, if it exists, unlike the sign of a real activation energy, is not necessarily positive due to possible negative enthalpic terms, i.e. due to the presence of highly exothermic steps that precede the determining step. 

Let us consider the relationship between the ideal activation energy W and the real activation energy A. Since the current density is a function of independent variables P,T,m, and ( ). we can write the expression for the total differential... 

It is clear from the above discussion that the theoretical calculation of the ideal activation energy requires a knowledge of the latent heat q of an electrode process, which cannot be found experimentally or from thermodynamic calculations. For this reason, the ideal activation energy can neither be determined experimentally, nor strictly calculated theoretically . It turns out, however, that it is still possible to calculate theoretically the real activation energy of the process (this will be shown below). 

This line of reasoning paves the way for calculating real activation energies they are obtained from potential diagrams plotted under the assumption that the latent heat of an electrode process is zero. 

Summarizing the above arguments, we can state that the Galvani potential, the solvation energy of an ion, and the chemical potential of an electron affect not the real but the ideal activation energy, which the reaction rate as a function of overpotential is determined just by the real activation energy. 

It should be noted once more that since we are considering the real activation energy, we assume that the heat of an elementary act is the real heat, i.e. the quantity not including the equilibrium latent heat of the electrode process as a whole. If we carry out the analysis for ideal activation energies, the qualitative results would not be affected. 

In Equation (1.45), all the quantities which do not contain the temperature explicitly are independent of temperature (to within corrections of the type of difference in heat capacities, AC T). Writing the temperature-dependent part of Equation (1.45) in the form exp [-E(n)/RT], we find that the quantity E(n) is the apparent real activation energy at the overpotential and the coefficient in... 

Fig. 2.8. Potential energy curves for calculating the real activation energy Aq for a hydrogen ion discharge. Notation same as in Figures 1.3 and 1.4.

The following values of Ag have been obtained in [153] (Ag is the real activation energy at equilibrium potential) 10.7 kcal mol in sulfuric acid solution and 13.4 kcal mol in hydrochloric acid solution. 

It was shown in the preceding chapter that the real activation energy of a barrierless discharge is equal to the enthalpy of hydrogen adsorption (i.e. equal to AH for the reaction h 2... 

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