Activation energies ideal

Also presented in Fig. 18 is the ideal change in reaction rate of the spectroscopic carbon with temperature, assuming a true activation energy of 93 kcal./mole. Zone II should start at a reaction rate of ca. 6 g. of carbon per hour and knowing that t) 0.5 at the start of Zone II, the temperature can be approximated. It is of interest to note that the ideal activation energy in Zone II, 46.5 kcal./mole, is closely approximated by the change in experimental reaction rate with temperature above ca. 1250°. 

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. 

However, the magnitude of a single potential drop cannot be measured directly, therefore, it is not possible to control its constancy, i.e., we cannot conduct an experiment to determine the value similar to the energy of activation of a common chemical reaction. This value, which is impossible to measure is called, according to Temkin, the ideal activation energy. 

As can be seen from Eq. (41), the ideal activation energy cannot be found from the value of the real energy for it would require knowledge of the temperature coefficient of an individual potential drop, which is impossible to measure or to calculate a priori thermodynamically. 

Their intersection gives us the ideal activation energy Wl at 17 = 0. At any other value of 17, the initial state curve is shifted upward by rjF, and the new point of intersection determines the ideal activation energy at a given... 

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),... 

This value cannot be calculated accurately because S and S° (or at least one of them) include absolute entropies of individual ions, which cannot be determined purely thermodynamically. Therefore, the ideal preexponential factor, as well as the ideal activation energy, is impossible to calculate. 

A negative value of the true ideal activation energy has no physical meaning. Therefore, it is natural to assume (this assumption will be corroborated in what follows) that a further shift of the potential, after W (or accordingly, Wa) has become zero, will not result in any further increase in i.e., varies monotonically with the potential. A constant value of equal to zero, formally corresponds to a = 0. 

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. 

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). 

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. 

Naturally, a barrierless process takes place when the true, i.e. the ideal activation energy of the reverse reaction, vanishes. We use ever3Twhere the real quantities that are accessible to determination, but we shall take into account the difference between real and ideal parameters when it is necessary for quantitative estimates. 

The conclusion that 3 and dd cannot differ by several orders of magnitude can also be drawn on the basis of a qualitative analysis of the shape of the polarization curves in the regions of transition from an ordinary to a barrierless discharge[264]. This transition is accomplished at the value n of the overpotential for which the ideal activation energy of an ordinary discharge becomes equal to the corresponding value for a barrierless discharge. ... 

The difference in the real activation energies is mainly affected by the difference in the reorganization energies in different solvents and by a small contribution from the difference in the adsorption energies of the components, while the ideal activation energies may be considerably affected by the change in the latent equilibrium heat q = TAS of the electrode process. 

Although the rate of a cathodic reaction involving an HaO ion considerably depends on potential (a - 0.2), which does not correspond to the simplest version of an activationless process, the activation energy of this reaction for a constant potential with respect to saturated calomel electrode (s.c.e.) was found to be practically equal to zero[435]. Taking into account the temperature dependence of the potential of s.c.e. and the estimate of the temperature coefficient of the absolute potential drop, we find that these two factors nearly compensate each other, i.e. the ideal activation energy is equal to zero[438]. It should, however, be taken into account that these measurements correspond to a constant concentration of HaO ions in the bulk of solution rather than at the... 

It should be noted that at the point of transition from an ordinary to a barrierless discharge, it is the ideal activation energies W, and not the real activation energies A, which become equal to each other[265]. The relation between these energies was obtained in section 1.2 ... 

The first chapter is devoted to the phenomenological theory of an elementary act. It considers the Br insted-Polanyi relation and some of its corollaries, as well as real and ideal activation energies and preexponential factors of electrochemical reactions. 

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