Temperature effects isokinetic

It is also a point of change in control of the reaction rate by the energy of activation below it to control by the entropy of activation above it. The effect of changes in structure, solvent, etc., will depend on the relation of the experimental temperature to the isokinetic temperature. A practical consequence of knowing the isokinetic temperature is the possibility of cleaning up a reaction by adjusting the experimental temperature. Reactions are cleaner at lower temperatures (as often observed) if the decrease in the experimental temperature makes it farther from the isokinetic temperature. The isokinetic relationship or Compensation Law does not seem to apply widely to the data herein, and, in any case, comparisons are realistic if made far enough from the isokinetic temperature. 

A linear relationship between the standard enthalpies and entropies of a series of structurally related molecular entities undergoing the same reaction thus, AH° -I3AS° = constant or AAH° = (3AS°. When P > 0, this relationship is referred to as an isoequilibrium relationship. When the absolute temperature equals the factor P (often referred to as the isoequilibrium temperature), then all substituent effects on the reaction disappear (i e., AAG° = 0). In other words, a reaction studied at T = p will exhibit no substituent effects. This would suggest that, when one studies substituent effects on a reaction rate, the reaction should be studied at more than one temperature. Note also that the p factor in the Hammett equation changes sign at the isoequilibrium temperature. See Isokinetic Relationship... 

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. 

Figure 4.35. Effect of catalyst work function on the activation energy EA, preexponential factor k° and catalytic rate enhancement ratio r/r0 for C2H4 oxidation on Pt/YSZ 4 p02=4.8 kPa, Pc2H4=0-4 kPa,4,54 kg is the open-circuit preexponential factor, T is the mean temperature of the kinetic investigation, 375°C.4 T0 is the (experimentally inaccessible) isokinetic temperature, 886°C.4 25,50...

Figure 4.36. Effect of catalyst potential UWR and work function on the activation energy E (squares) and preexponential factor r° (circles) of C2H4 oxidation on Rh/YSZ. open symbols open-circuit conditions. Te is the isokinetic temperature 372°C and r is the open-circuit preexponential factor. Conditions po2=l.3 kPa, pc2n =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. 

The idea that /3 continuously shifts with the temperature employed and thus remains experimentally inaccessible would be plausible and could remove many theoretical problems. However, there are few reaction series where the reversal of reactivity has been observed directly. Unambiguous examples are known, particularly in heterogeneous catalysis (4, 5, 189), as in Figure 5, and also from solution kinetics, even when in restricted reaction series (187, 190). There is the principal difficulty that reactions in solution cannot be followed in a sufficiently broad range of temperature, of course. It also seems that near the isokinetic temperature, even the Arrhenius law is fulfilled less accurately, making the determination of difficult. Nevertheless, we probably have to accept that reversal of reactivity is a possible, even though rare, phenomenon. The mechanism of such reaction series may be more complex than anticipated and a straightforward discussion in terms of, say, substituent effects may not be admissible. 

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. 

Many workers have offered the opinion that the isokinetic relationship is confined to reactions in condensed phase (6, 122) or, more specially, may be attributed to solvation effects (13, 21, 37, 43, 56, 112, 116, 124, 126-130) which affect both enthalpy and entropy in the same direction. The most developed theories are based on a model of the half-specific quasi-crystalline solvation (129, 130), or of the nonideal conformal solutions (126). Other explanations have been given in terms of vibrational frequencies involving solute and solvent (13, 124), temperature dependence of solvent fluidity in the quasi-crystalline model (40), or changes of enthalpy and entropy to produce a hole in the solvent (87). 

Among the theories of limited applicability, those of heterogeneous catalysis processes have been most developed (4, 5, 48). They are based on the assumption of many active sites with different activity, the distribution of which may be either random (23) or thermodynamic (27, 28, 48). Multiple adsorption (46, 47) and tunnel effects (4, 46) also are considered. It seems, however, that there is in principle no specific feature of isokinetic behavior in heterogeneous catalysis. It is true only that the phenomenon has been discovered in this category and that it can be followed easily because of large possible changes of temperature. 

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... 

Figure 9 demonstrates this compensation effect by the linear relationship between AS and AH. This indicates that both activation parameters depend equally on a and that the isokinetic temperature, i.e. the slope of the line, amounts to 256°K. Thus, at -17°C the rate would become independent of a, whereas it increases with a at higher temperatures. 

The observed substituent effect on the reaction rate in the oxidation of substituted aliphatic ketoximes by /V-bromosaccharin has been rationalized in terms of a mechanism.126 The oxidation of acetophenones with N-bromophthalimidc exhibited a linear correlation with Brown s a+ with reaction constant p = —0.52. An Exner plot gave an isokinetic temperature p = 263 K. A mechanism consistent with the kinetic data has been proposed.127... 

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