Enthalpy, activation isokinetic

A corollary of this pattern for parallel reactions is that the one with the larger activation enthalpy grows relatively more important at higher temperatures. Also, the reaction that is slower below the isokinetic temperature is the faster one above it. One can also show that the logarithm of product yield, ln([P]]/tP2]), is a linear function of l/T (see Problem 7-13). 

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). 

The empirical isokinetic relationship for a series of compounds, undergoing reaction by the same mechanism, suggests that there could be an empirical linear relationship between the temperature (T) at which a series of reactants decompose at a constant rate and the enthalpies of activation for that series of reactions (9,10) ... 

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. 

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. ... 

Mechanism of oxidation of purine bases (adenine and guanine) and pyrimidine bases (uracil, thymine and cytosine) in presence of NaOH by bromamine-B(BAB) has been investigated. The reactions follow identical kinetics for all the bases, being first order dependence on [BAB]o and fractional order each in [substrate]o and [NaOH]. Addition of the reaction product retards the rate and the dielectric effect is positive. Variation of ionic strength and addition of halide ions had no effect on the rate. Proton inventory studies were made in H2O-D2O mixtures for adenine and cytosine. Oxidation products were identified and activation parameters were evaluated. An isokinetic relationship is observed with p = 336 K indicated that enthalpy factors control the rate. The rate of oxidation of purines is in the order guanine > adenine while in case of pyrimidines the order is thymine > uracil > cytosine. A suitable mechanism is proposed and discussed. 

Isokinetic relationship phys chem A linear relationship that exists between the enthalpies and entropies of activation of a series of related reactions., i-s3-ki ned-ik ri la-shon.ship ... 

Figure 7.8 Isokinetic reiationship in the alkaiine hydrolysis of ethyi benzoate in water/alcohol and water/dioxane mixtures. The enthalpies and entropies of activation of the previous figure were obtained from the siope and intercept of each of the straight Unes in this figure.

Enthalpies and entropies of activation for the decarboxylation of oxalic, malonic, and acetic acids are listed in Table 1 and are shown separately on the isokinetic plots in Fig. 8. Linear trends are observed for (1) aqueous acetic acid and sodium acetate in the presence of various catalysts (2) aqueous oxalic acid at several pH values (3) oxalic acid in different solvents and (4) malonic acid in different solvents and in aqueous solutions having a different pH. Note that the isokinetic trend for the decarboxylation of malonic acid in aqueous solutions at various pH is identical to that for the reaction in nonaqueous solvents, i.e., there is one isokinetic trend for malonic acid. Moreover, the effect of pH on the activation parameters for the decarboxylation of malonic acid in aqueous solution is minimal. On the other hand, the activation data for the decarboxylation of oxalic acid in aqueous solutions determined by Crossey (1991) do not follow the same isokinetic trend as do the corresponding data for this reaction in other solvents. By contrast, activation data calculated from the rate constants determined by Dinglinger and Schroer (1937) for oxalic acid in water (pH 0.5) fall on the isokinetic trend set by the decarboxylation of oxalic acid in nonaqueous solvents, as well as the rate data determined by Lapidus et al. (1964) in the vapor phase. The cause of the disparity between the isokinetic relationships determined by Crossey (1991) and the remainder of the oxalic acid results requires further investigation. The reaction could have been surface-catalyzed, but this is doubtful because some of the oxalic acid... 

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