Entropy, activation isokinetic

In a series of reactions for which an acceUrative decrease in the activation energy is accompanied by a decelerative decrease in the entropy of activation (Compensation Law ), or the two increase together, there wiU be an isokinetic temperature (between 0-200° C for three-fourths of the 79 reactions tabulated by Leffler ). The rate vs. temperature curves for all the reactions in the series pass through this single point. Comparisons are affected since the isokinetic temperature is a point of inversion of relative reactivity in the series. 

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. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

For simplicity we assumed that the transition states are charged. However, it is not necessary to do so because the only requirement is that the difference in entropy of forming the transition states be offset by the difference in enthalpy of activation. The transition states could have different polarities and the same result be obtained. In fact, the transition states need not have high polarity. Forming a transition state in which there is a reduction in charge separation could result in more favorable solvation when the solvent is nonpolar. For there to be an isokinetic relationship for a series of reactions, it is required only that AH and AS be related in such a way that AG be approximately constant. 

Table XV lists the isokinetic temperatures of several reactions representing a wide variety of mechanisms, these examples having been chosen because the isokinetic temperature happened to fall in the popular experimental range between 0 and 100°. There are many other polar reactions that have isokinetic temperatures well outside of the accessible temperature range there are many whose variations in activation energy and entropy are not parallel and these, of course, do not have an isokinetic temperature even approximately. When one of a series of reactions deviates markedly from a parallel trend in activation energy and entropy established by the others, it is probable that it differs in mechanism from the others. This is a better indication of a change in mechanism than either marked differences in rate or in activation energy.

The activation energies and entropies for the thermal ring opening show an isokinetic dependence indicating a common structure of the transition state in all members of the DHP series. 

The high quality (r = —0.987) of the linear correlation in Fig. 2 a, for which Eq. (1) is given in the caption, is quite surprising for several reasons. In particular, because free enthalpies of activation AG are correlated with strain enthalpies Hs despite the fact that there is neither an isoentropic (AS = const.)41) nor an isokinetic relationship (AH aAS ) 41) within this series. Indeed AS varies from 13 to 26 entropy units14). In a kind of Exner test42) it was shown, however, that the order of decreasing AG (T) values is independent of temperature and therefore significant for structural interpretation 14). 

When the temperature of the measurement (T) equals the isokinetic temperature (jS), AG is a constant. At the isokinetic temperature, a given acid will decompose at the same rate in all of the solvents for which eqn. (5) holds. In some instances the results for several acids will fall on the same line for the AH vs. AS plot. Table 52 lists the reported isokinetic temperatures for a number of systems that obey eqn. (5). The validity of the linear enthalpy-entropy of activation relationship has been questioned as an artifact due to experimental error in the enthalpy of activation. Error analysis was performed for some of the systems given in Table 52, and it was concluded that the linear enthalpy-entropy of activation relationships were valid . It has been reported that the isokinetic temperature for decarboxylation of several acids corresponds to the melting point of the acid. Our evaluation of the data, given later, does not support this conclusion. 

Some attention has been given to the effect of substituents upon the kinetics of dialkyl peroxide decomposition. The data are presented in Table 67. A linear enthalpy-entropy of activation correlation was made for the decomposition of alkyl peroxides (exclusive of the hydroxyalkyl peroxides) using data in solution and in the gas phase. The isokinetic temperature was found to be 483 °K (210 °C) . No rational explanation was advanced for the substituent effects in solution or the gas phase . However, the discussion of the effect of a chain reaction upon the activation parameters, given in the section on gas phase reactions, should be consulted. The large differences in and log A between the alkyl and the hydroxyalkyl peroxides suggests a change in mechanism. This is supported by the products from the hydroxyalkyl peroxides. A cyclic activated complex was suggested , viz. 

Fig. 5. Isokinetic plots of activation enthalpies (AHf) vs activation entropies (ASf) for PnP exclmer formation In (A) cholesteric and (B) isotropic M. Numbers In figures refer to n(40). [Reprinted with permission of the American Chemical Society.]...

The thermal decomposition reaction of 1,2,4-trioxane, along with others, was studied in toluene solution over a wide temperature range <2000MOL360>. The reaction follows a first-order kinetic law up to ca. 50% peroxide conversion. Only the linear dependence of activation enthalpies and entropies of this unimolecular reaction is reported with a slope of 130.4 °C as the isokinetic temperature . 

Cationic vesicles, for example those formed from di-n-hexadecyldimelhylammonium bromide (DHAB) accelerate the decarboxylation by a factor of about 1000 relative to pure water. Dehydration of the carboxylate group at the binding sites is most likely the main factor behind the catalysis. Different isokinetic temperatures (obtained from linear plots of enthalpies v.y. entropies of activation) have been observed above and below the main phase transition temperature. These excellent isokinetic relationships indicate that the catalytic effects are caused by a single important interaction mechanism. ... 

In the most straightforward example of a composite reaction, a substance disappears by two or more concurrent paths which are differently influenced by temperature, that is, have different energies of activation (74). If they nevertheless make comparable contributions to the observed rate, they must also have different entropies of activation. In other words, there must be some kind of compensation effect (104) between their values of AS and AH, with an isokinetic temperature (104) (the temperature at which the two paths have equal rate constants) lying in the vicinity of that at which the experiments are being performed. The two paths may lead to the same products, as envisaged by Hinshelwood (71a) or to different products (92). 

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