Isokinetic point

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.

It is worth noting that below the isokinetic point (T < T ) the reaction exhibits electrophobic behaviour, i.e. dr/dUwR > 0, while for T > T the reaction becomes electrophilic. At T = T the NEMCA effect disappears (see also the curve for T=370°C in Fig. 8.6). 

Figure 8.18. Effect of catalyst potential and work function on the apparent activation energy, E, and on the logarithm of the preexponential factor r° rfi is the open-circuit preexponential factor and T0, T are the two isokinetic points of C2H6 oxidation on Pt/YSZ for positive and negative potentials respectively.27 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... 

It follows that for a special value of one parameter, the observed value of y is independent of the second parameter. This happens at Ii= a2/ai2 or I2 = -ai/ai2 any of these values determines y= a -aia2/ai2, the so called isoparametrical point. The argument can evidently be extended to more than two independently variable parameters. Experimental evidence is scarce. In the field of extrathermodynamic relationships, i.e., when j and 2 are kinds of a constants, eq. (84) was derived by Miller (237) and the isoparametrical point was called the isokinetic point (170). Most of the available examples originate from this area (9), but it is difficult to attribute to the isoparametrical point a definite value and even to obtain a significant proof that a is different from zero (9, 170). It can happen—probably still more frequently than with the isokinetic temperature—that it is merely a product of extrapolation without any immediate physical meaning. 

A large value for the activation energy is correlated with a large prefactor and all lines in the Arrhenius plot intersect in a single point, the isokinetic point. 

Shaw calculated the isokinetic point between homolysis and elimination as 770K for mononitro- and vicinal dinitro-alkanes and as 370K for gem-dinitro species [51]. In gem-polynitro species the C-N02 bond is weaker than in mononitro compounds due to inductive effects [52] thus, homolysis is thought to be the principal decomposition pathway in 2,2 dinitropropane and hexanitroethane [48]. Octanitrocubane has recently been synthesized (Fig. 6). Its crystal density was lower (1.979 g/cm3) than the predicted 2.1 [53]. Like hexanitrobenzene, octanitrocubane has a perfect oxygen balance, but at this point it appears unlikely that further development of this compound will be undertaken. 

Such sign reversal in px at an isokinetic point is also observed in the reactions of anilines with cumyl (PhCMe2-) arenesulfonates63 (4-as) and chlorides (4-C1). Structurally, these systems correspond to R1 = R2 = Me in the general a-substituted benzylic compounds so that the reactivity and the reaction mechanism are expected to be related to those of other a-substituted benzylic series discussed above57 63. The second-order rate constants for the reactions of aniline are 33.9 x 10 3 M 1 s 1 for cumyl arenesulfonate... 

The benzylic carbocation is stabilized by resonance delocalization of the cationic charge into the ring65 and as a result the benzylic carbon becomes much less positive. As the cation stability increases the isokinetic point shifts to a more positive value. 

TABLE 5. Relationship between the isokinetic point ay (where px = 0) and the enthalpy of formation of the benzylic cation (PhC+ R R2)... 

This linear variation in E and r with e4> often leads to the appearance of the well-known compensation effect. Two typical examples, with the isokinetic point lying within the investigated temperature range, are shown in Figures 22 and 23 for the cases of C2H4 oxidation on Rh and C3H6 oxidation on Pt. The compensation effect in heterogeneous catalysis is observed either with similar reactions on the same metal or with similar cata-... 

Comparison of fep" and fep at various temperatures is given in Figure 8. At low temperature, the reactivity of ions approaches the reactivity of the ion pairs in both CH2CI2 and dimethylformamide (DMF) solvents. In DMF, a temperature could be found at which an inversion of reactivities of both species takes place (isokinetic point). Apparently at this low temperature, the solvation of ions is so strong that an additional energy is required to remove solvating molecules from... 

As a result of this. Fig. 23a presents a striking demonstration of the compensation effect with an isokinetic point at Te = 372°C. The compensation effect in heterogeneous catalysis has been the focal point of numerous studies and debates. It is usually obtained from Arrhenius plots for several similar reactions on the same catalyst or for the same reaction on several similar catalysts. In the present case, it is obtained for one reaction and one catalyst by varying its potential or, equivalently, by varying the level of promoting species (O ) on its surface. Since the isokinetic point lies usually outside the temperature range of the kinetic investigation, several authors have even questioned the existence of a true compensation effect. The results of Fig. 23 are, consequently, rather rare and show clearly that the compensation effect is a real one. 

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