Apparent Compensation Effects

If for a given group of catalysts the Arrhenius equation strictly holds and the values of AE and A are equal from one catalyst to the next, a C.E. may also result from experimental errors. From the Arrhenius equation it follows that 

Arrhenius plot for a reaction at two different catalysts, 1 and 2, undergoing a reversible change in their effective surface areas with temperature. Dotted lines refer to the true Aff t values. The solid lines I and 2 interconnect corresponding points of the dotted lines at fc = 10 and k = 100. 

Intersections of the straight lines of an Arrhenius plot are in general obtained by extrapolation. This implies that AE is virtually constant between the experimental temperatures and the extrapolated temperature r,. The possibility that E may vary with the temperature and also with specific surface conditions, such as the density of its coverage with chemisorbed reactants, has been suggested in order to explain the existence of compensation effects (17). 

That AE may show very significant variation with temperature if the penetration of the reactants into the pores of the catalyst must be taken into account has been pointed out especially by Wicke and Brotz (30). In this case two extreme values of may be obtained Ai max if the activation energy of the chemical reaction determines the temperature 

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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. 

The activation energies for the remaining acidic and neutral catalysts show a continuous decline for the apparent activation energies in the order Pt/LTL [0.47, small] > Pt/LTL [0.47, big] > Pt/LTL [0.82] > Pt/ASA Pt/Si02 [small] Pt/Si02 [big]. The pre-exponential factor increases in the opposite direction. These observations indicate an apparent compensation effect, as will be discussed later. 

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. 

Several compensation effects have been reported for the decomposition of formic acid on metals (231) particular interest has been shown in the silver-catalyzed reaction (19, 35, 232, 233). The available data for this rate process do not, however, define a single compensation relation, and, even for groups of closely related reactions, it is difficult to decide which of the various possible calculated lines provides the most meaningful representation of the kinetic measurements. Values of B and e, obtained from various sets of reported results, extend over a significant range and, moreover, there is an apparent tendency for an increase in the value of one of these parameters to be offset by a diminution in the other. Such behavior can, in the widest sense of the word, be described as compensatory. To illustrate the difficulties inherent in this analysis of the published data, some calculated values of B and e derived from possible alternative groups of observations are discussed here. Values of (log A, E) reported by Sosnovsky (35), for the decomposition of formic acid on silver, may be considered either as the three different lines, Table III, K, L, and M for reactions on the (111), (110), and (100) planes, respectively, or as the single line,Table III, N. These combined data (Table III, N and x on Fig. 6) intersect with the line obtained from a different set of results... 

From the discussion presented in the previous paragraphs, we identify the kinetic characteristics of the hydrocarbon evolution reactions (31,291,292) and the clay dehydration processes with the common mechanistic features reversibility and similar characteristic temperatures of onset of the water evolution step. The compensation effects observed for the two groups of related reactions (Table V, R and S) were not identical, however, since the species participating in the equilibria on the surfaces (believed to be represented by the kinetic characteristics described in Appendix I) are different. Undoubtedly, the interaction of hydroxyl groups to yield water was common to both types of reaction (surface desorption and lattice dehydration) and the properties and reactivities of these species probably determine the temperature at which significant surface activity and product evolution becomes apparent. This surface reaction is... 

This paper focuses on the influence of the support on the H/D exchange of CP over supported Pt catalysts. It will be shown that kinetics and selectivities are largely affected by the support material. Particle size effects are separated from support effects. The activity shows a compensation effect, and the apparent activation energy and pre-exponential factor show an isokinetic relationship . This can be explained by different adsorption modes of the CP on the metallic Pt surface. The change in adsorption modes is attributed to a change in the electronic structure of the Pt particles, which in turn is induced by changes in the acid/base properties of the support. 

In addition to the correlation between the order in Ph2 and Eapp, the compensation effect is regularly observed for hydrogenolysis reactions48 50. The compensation effect denotes a linear relationship between the apparent activation energy and the pre-exponential factor. This relationship is also called the Constable-Cremer relation51 ... 

Let us now turn to paradox 2 (see p. 149) a lack of apparent sterio effect for 2,6-dimethylphenols in a polar medium (Fig. 2) while different Hammett equations were found for 2,6-dimethylphenols in non-polar media (e.g., Howard and Ingold, 1963b). The data of Table 6 suggest a gradation in the diminution of K when ortho substituents are introduced to phenol. Accordingly, the ratio (simple phenols while it is about 2 for 2,6-dimethylphenols. Thus equation (37) indicates a possible compensation for 2,6-disubsti-tuted phenols as K is decreased by ortho substituents, the rate constant k2 has to be multiplied by an increased factor expressing enhanced contribution of free phenol molecules to the overall rate. In case of 2,6-di-t-butylphenols, however, even the partial rate constant of free molecules ( j) is so markedly reduced that the compensation by the factor (ac + K)l(K + 1) is no longer effective. 

The greatly enhanced activity and selectivity imparted by Mo addition to Rh/Al203 is not explained by activation energy differences alone. Gilhooey, Jackson and Rigby (9) found wide variations in the apparent activation energies and pre-exponential factors for Rh on various supports. They concluded that the compensation effect, which involves the preexponential factor, made conclusions on mechanism ambiguous. 

The present theories of the effects of solvents on the rates of polar (ionic) reactions do not permit a quantitative analysis of the above cited results. Fractions of AHp and ASp, due to solvation, apparently compensate each other, because the increase in the energy needed for desolvation is just compensated by equal contributions of the entropy (a more firmly bound or larger number of molecules are desol-vated). This compensation phenomenon is well known in organic chemistry. For instance, the difference between the activation enthalpies (AAH ) of the reaction of benzyl chloride with pyridine in DMF and CH3OH is equal to -5.3 kcal mole". ... 

Kinetic parameters from selected publication on CO2 reactivity are shown in Table 1. A wide span of apparent activation energies is published for biomass chars, 80.3 kJ/mol -318 kJ/mol and for coal chars, 79 kJ/mol -359.5 kJ/mol Some of the discrepancy can be explained as due to different experimental procedures (such as sample load, particle size and sample preparation) and the application of different analysing equipment. Concerning the latter one, the potential role of systematic errors in temperature measurements among various thermobalances is evident. Variations might also be explained by different extraction procedures, lack of accuracy caused by the approximations used in the different computational methods and the kinetic compensation effect. 

It is not easy to compare the activity of the V-W-Ti catalysts here tested with the lot of chromia, Pt and Pd based catalysts previously used because they have different shapes (monoliths and spheres) and because very different particle sizes arc involved (having thus very different effectiveness factors). For conqiarison purposes, all X-T curves were adjusted to a simple fust order kinetic model (with rate based on overall volume of catalyst, both for monoliths and for fixed beds). From the kinetic constants so obtained (see details of the method in ref 7), the preexponential factors (ko) of the Arrhenius law and the apparent energies of activation (E, p) were calculated for all catalysts. One example is shown in Figure 17. By the well Imown compensation effect between ko and E,pp, the kg values so obtained were recalculated for a given E.pp value of 44 kJ/mol. Such new ko value was used [7] as an activity index of the catalyst. 

Also notable in the direction of classical catalyst improvement is the research conducted by Rhodes et al.22 A series of coprecipitated promoters were evaluated on ferrochrome catalyst activity at temperatures between 350 and 440 °C. It was found that activity decreases in the following order Hg > Ag > Ba > Cu > Pb > unpromoted > B. A noticeable compensation effect observed in the correlation between preexponential factors and apparent activation energies led the authors to conclude that these promoters might only influence the CO adsorption on catalyst rather than the course of surface reactions. 

Kinetic parameters. The hterature contains numerous reports of the rate equations identified for particular crystolysis reactions, together with the calculated Arrhenius parameters. However, reproducible values of (Section 4.1.) have been reported by independent researchers for relatively few solid state decompositions. Reversible reactions often yield Arrhenius parameters that are sensitive to reaction conditions and can show compensation effects (Section 4.9.4.). Often the influences of procedural variables have not been carefully identified. Thus, before the magnitudes of apparent activation energies can be compared, attempts have to be made to relate these values to particular reaction steps. 

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