Activation energy, definition

The connection with the TST expression (12.2) may be established from the definition (12.26) of the activation energy. 

Thus, In k will vary linearly with 1 fT. This plot yields A from the intercept and Ea from the slope. Equation (7-1) or (7-3) provides a definition of the Arrhenius activation energy, which is expressed as... 

As explained before, a chemical reaction can seldom be described by a single elementary step, and hence we need to adapt our definition of activation for an overall reaction. Since we are not particularly interested in the effects of thermodynamics we define the apparent activation energy as... 

Because thermodynamic quantities are commonly expressed in kj mol", we have replaced the Boltzmann constants by the gas constant, R. We calculate the activation energy (in kJ mol ) by applying the definition ... 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

Another definition of an ideal polarized electrode is based on the practical form of this electrode. At an ideal polarized electrode either no exchange of charged particles takes place between the electrode and the solution or—if thermodynamically feasible—exchange occurs very slowly as a result of the large activation energy. 

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... 

Several descriptions of electrode reaction rates discussed on the preceding pages and the difficulty to standardize electrode potential scales with respect to different temperatures imply several definitions of activation energies of electrode reactions. The easiest way to determine this quantity, for example, for an irreversible cathodic process, employs Eqs (5.2.9), (5.2.10) and (5.2.12) at a constant electrode potential,... 

Calculations carried out by Gottesfeld et al. [52], who borrowed from studies of thermal desorption of H2 from Cu [56, 57], indicate that H2 rather than H20 should be a product of formaldehyde oxidation at Cu at potentials up to ca. +0.4 V vs. RHE. This is provided conditions are such that the activation energy for hydrogen recombination and desorption does not exceed 10 kcal/mole. Obviously a relatively high activation energy (which appears never to be observed at Cu) favors eventual oxidation of adsorbed H atoms, before recombinative desorption can occur. Gottesfeld et al. s calculation is interesting, but perhaps not a definitive calculation since it is... 

Gomes, W. (1961). "Definition of Rate Constant and Activation Energy in Solid State Reactions," Nature (London) 192, 965. An article discussing the difficulties associated with interpreting activation energies for reactions in solids. 

Figure 5.8 Definition of activation energy with and without a catalyst. (Adapted with permission from Fraser, 2002)...

We use this knowledge to derive preexponential factors from (2-20) for a few desorption pathways (see Fig. 2.15). The simplest case arises if the partition functions Q and Q in (2-20) are about equal. This corresponds to a transition state that resembles the ground state of the adsorbed molecule. In order to compare (2-20) with the Arrhenius expression (2-15) we need to apply the definition of the activation energy ... 

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