Compensation effect activation energy

Figure 8.75 shows the dependence of the apparent activation energy Ea and of the apparent preexponential factor r°, here expressed as TOF°, on Uwr. Interestingly, increasing Uwr increases not only the catalytic rate, but also the apparent activation energy Ea from 0.3 eV (UWr=-2 V) to 0.9 eV (UWr-+2V). The linear variation in Ea and log (TOF°) with UWr leads to the appearance of the compensation effect where, in the present case, the isokinetic point (T =300°C) lies outside the temperature range of the investigation. 

For catalytic reactions and systems that are related through Sabatier-type relations based on kinetic relationships as expressed by Eqs. (1.5) and (1.6), one can also deduce that a so-called compensation effect exists. According to the compensation effect there is a linear relation between the change in the apparent activation energy of a reaction and the logarithm of its corresponding pre-exponent in the Arrhenius reaction rate expression. 

Figure 7.8. The compensation effect in the desorption ofAg from a ruthenium surface activation energy and pre-exponential factor depend in the same way on coverage. The...

It has been shown by several authors that a good correlation exists between activation energy (Ea) and In Aq for different reactions taking place over one catalyst [86-87]. Such a correlation is termed as compensation effect or isokinetic effect . Indeed the higher catalytic activity found with intermediate catalyst compositions on Cui.xCoxFc204 (x= 0.5) was attributed to the relatively low (Ea) for ethylation (Figure 12) on these compositions compared to the end compositions, x = 0 and 1. 

The correlation between activation energy and preexponential factor is known as the compensation effect. 

In connection with the interpretation of these trends it should be noted that in some reactions (e.g., ethylene hydrogenation) the activation energy remains substantially constant and the frequency factor changes as the metal is varied, while in other reactions (e.g., deuterium-ammonia exchange) the reverse is the case. In the exchange of deuterium with saturated hydrocarbons, a compensation effect (Cremer, 128) has been noted. The significance of these different patterns is not clear. 

Since the activation energy for ionic recombination is mainly due to viscosity we use the activation energy for viscous flow (10kJ.mol l). AH ] and 3 were determined from conductance as 44.2kJ.mol and 11,4kJ.mol From the data presented in Table III it is clear that the temperature dependence of the slope is very satisfactorily described by A% +l/2(AHd-AH3). Another, and rather critical, test for the applicability of eq. 14b is the effect of pressure since the slope of eq. 14b is largely pressure independent so that we ask here for a compensation of rather large effects. From Table III we Indeed see an excellent accordance between the experimental value and the pressure-dependence calculated from the activation volume of viscous flow (+20.3 ctPmol ), AVd (-57.3 cnAnol" ) and (-13.9 cnAnol ) the difference between the small experimental and calculated values is entirely with the uncertainties of compressibility - corrections and experimental errors. 

In many cases a compensation effect is indicated on comparison of the rates of the same reaction at the same type of catalyst after the latter has undergone special pretreatments or has been changed in its composition. In such cases the occurrence of a compensation effect may be expected if different kinds of active surface centers act simultaneously as sites of the catalytic reaction and if the proportions of these different active centers (involving different activation energies) are shifted by means of special pretreatments of the catalyst or by changes in its composition. 

An apparent compensation effect can result from errors in the experimental data used for an Arrhenium plot. Besides trivial errors, there may also occur errors in the calculation of rate constants, for instance when a homogeneous and a heterogeneous reaction occur simultaneously or when a heterogeneous reaction undergoes a change from a certain reaction order to another order. A temperature dependence of the activation energy, and the variability of the effective surface of the catalyst with temperature, especially caused by diffusion processes, may also account for apparent compensation effects. 

Compensation effects have been reported for the oxidation of ethylene on Pd-Ru and on Pd-Ag alloys (207, 254, 255) discussion of the activity patterns for these catalysts includes consideration of the influence of hydrogen dissolved in the metal on the occupancy of energy bands. Arrhenius parameters reported (208) for ethylene oxidation on Pd-Au alloys were an appreciable distance from the line calculated for oxidation reactions on palladium and platinum metals (Table III, H). Oxidation of carbon monoxide on Pd-Au alloys also exhibits a compensation effect (256). 

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