Effect compensation

The observed linear variation in activation energy, E, and in the preexponential factor r0/ r° (Figs. 4.35 to 4.37), which conform to the equations  

All this is nicely described by the following equation, derived easily via mathematical manipulation of equations (4.49) to (4.52), which relates the NEMCA coefficient a (eq. 4.49) with the enthalpic parameter aH (eq. 4.50)  

Normally in heterogeneous catalysis compensation effect behaviour is obtained either for the same reaction upon using differently prepared catalysts of the same type, or with the same catalyst upon using a homologous set of reactants. In the case of electrochemical promotion (Figs. 4.38 and 4.39) one has the same catalyst and the same reaction but various potentials, i.e. various amounts of promoter on the catalyst surface. 

As shown in Figs. 4.38 and 4.39 there can be no doubt that the effect is real. As well known from the heterogeneous catalysis literature its existence 

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As LEED studies have shown, the stmcture of a chemisorbed phase can change with 6. In terms of transition state theory, we can write A = (I/tq) and a common observation is that while E may change with a phase change, AS will tend to change also, and similarly. The result, again known as a compensation effect, is that the product remains relatively constant... 

AG = 0 that is, all substituent (or medium) effects on the free energy change vanish at the isokinetic temperature. At this temperature the AH and TAS terms exactly offset each other, giving rise to the term compensation effect for isokinetic behavior. 

The relationship of thermodynamic functions of selective bonding of Hb to a series of carboxylic CP in the variation of the degree of ionization of carboxylic groups is expressed by the effect of enthalpy-entropy compensation (Fig. 18). The compensation effect of enthalpy and entropy components is the most wide-spread characteristic of many reactions in aqueous solutions for systems with a cooperative change in structure [78],... 

G. Parravano and M. Boudart The Compensation Effect in Heterogeneous Catalysis E. Cremer... 

The compensation effect occurs in a group of related reactions for which the influence of changes in A on reaction rate is offset to a greater or lesser extent by a sympathetic variation in E, often expressed as [36]... 

The possibility that compensation effects arise as a result of surface... 

Figure 4.38. NEMCA-induced compensation effect in the isokinetic point for C2H4 oxidation on Rh/YSZ. Conditions po2= 1-3 kPa, pC2H4 =7.4 kPa.50 Reprinted with permission from Academic Press.

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. 

Isokinetic point and compensation effect, 166 and electrochemical promotion, 164, 166 Isotherms... 

Changes in AH are paralleled by changes of AS in such a direction that the resulting effect on reactivity is less than it would be if controlled by either AH or AS alone (compensation effect). Its cause is seen in steric or solvent effects (13, 116), affecting simultaneously the geometry of the transition state and the force constants (13, 37, 116). 

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

The only solution of this differential equation is with both AH and AS constant (149). On the other hand, it was argued that a qualitative compensation effect must exist in this case since AH and AS change with temperature in the same direction (214). 

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. 

The occurrence of a compensation effect can be readily deduced from Eqs. (1.6) and (1.7). The physical basis of the compensation effect is similar to that of the Sabatier volcano curve. When reaction conditions or catalytic reactivity of a surface changes, the surface coverage of the catalyst is modified. This change in surface coverage changes the rate through change in the reaction order of a reaction. 

A consequence of the compensation effect is the presence of an isokinetic temperature. For a particular reaction, the logarithm of the rate of a reaction measured at different conditions versus 1/T should cross at the same (isokinetic) temperature. For conditions with varying n, this isokinetic temperature easily follows from Eq. (1.19) and is given by... 

It is important to realize that the compensation effect in catalysis refers to the overall catalytic reactions. 

As a further illustration of the compensation effect, we use solid-acid-catalyzed hydrocarbon activation by microporous zeolites. A classical issue in zeolite catalysis is the relationship between overall rate of a catalytic reaction and the match of shape and size between adsorbate and zeolite micropore. 

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