Activation enthalpy values

Figure 15.5 Activation enthalpy values of reaction 15.16 for different X. Data from [327]...

Figure 3. Activation enthalpy-activation entropy compensation plot. Activation enthalpy values determined at 298 K plotted as a function of activation entropy. The straight line is the result of a linear least-squares fit to all data points and has a slope of 258 6K (24). Two points, representing WT A. faecalis azurin ( ) and the V31W mutant (V), respectively, are discussed in the text.

The calculated activation enthalpy values are shown in Table 1 for a typical sample aged with the four thermal cycles. These were not the results of four separate samples, but one sample cycled through the four aging profiles. Several samples were analyzed with the four aging experiments to test for repeatability and all resulted in similar loss modulus profiles. Between each experiment the samples were dried at 190 C for more than 7 hours and quench cooled to ""reverse the previous thermal histories. This is analogous to tli rejuvenation procedures used with the glass transition. 

Typical values of the energy to form vacancies are for silver, lOSkJmol and for aluminium, 65.5kJmol These values should be compared with the values for the activation enthalpy for diffusion which are given in Table 6.2. It can also be seen from the Table 6.2 that die activation enthalpy for selfdiffusion which is related to the energy to break metal-metal bonds and form a vacant site is related semi-quantitatively to the energy of sublimation of the metal, in which process all of the metal atom bonds are broken. 

It should be noted that the experimental activation enthalpy for the Diels-Alder reaction is 33 kcal/mol (estimated from the reverse reaction and the experimental reaction energy i.e. the MP2/6-31G(d) value is 14kcal/mol too low. Similarly, the calculated reaction energy of —47 kcal/mol is in rather poor agreement with the... 

The acid hydrolysis of diaziridines has been investigated kinetic-ally. The reaction is first order and shows a relatively high temperature coefficient. Thus one finds a relatively high activation enthalpy (23-28 kcal) and a positive activation entropy (2-6 eu). The influence of substitution on nitrogen is small. The velocity of the diaziridine hydrolysis depends only in the weakly acid region on the acid concentration. Between pH 7 and 3 the fc-values rise by nearly 10 . For the... 

Further studies by Garcia, Mayoral et al. [10b] also included DFT calculations for the BF3-catalyzed reaction of acrolein with butadiene and it was found that the B3LYP transition state also gave the [4+2] cycloadduct, as happens for the MP2 calculations. The calculated activation energy for lowest transition-state energy was between 7.3 and 11.2 kcal mol depending on the basis set used. These values compare well with the activation enthalpies experimentally determined for the reaction of butadiene with methyl acrylate catalyzed by AIGI3 [4 a, 10]. 

Table 3 shows that the activation enthalpies determined by various authors can be very different. These differences cannot be correlated to discrepancies in reaction orders since, even when these are the same, activation energies can vary. Since the theoretical difference between activation enthalpy and activation energy is low (2RT = 3kJ mol"1) with regard to the differences found in experimental determinations, the values discussed below are either enthalpies or energies of activation (For more detailed information see Table 3). 

Due to the differences in the values relative to any one system, conclusions cannot easily be drawn from the activation parameters listed in Table 3. However, an analysis of the results relative to 1,2-ethanediol, 2,2-dimethyl-l,3-propanediol, 1,5-pentanediol, 1,10-decanediol and diethylene glycol shows that a slight difference can be observed between aromatic and aliphatic acids the activations enthalpies and entropies are in the ranges 70, 100 kJ mol"1 and -SO, -130 J K"1 mol-1 for aromatic acids, and in the ranges 50, 70 kJ mol"1 and -200, -100 J K"1 mol-1 for the aliphatic acids. 

Several authors studied the influence of substituents on activation parameters. Bad-dar et al.315 who studied the polyesterification of y-arylitaconic anhydrides and adds with 1,2-ethanediol found that in the non-catalyzed reaction a p-methoxy substituent decreases both the activation enthalpy and the entropy whereas an increase is observed with a p-chloro substituent. On the other hand, Huang et al., who studied the esterification of 2,2-dimethyl-l,3-propanediol with benzoic, butanedioic, hexanedioic, decanedioic and o-phthalic add found the same values since the activation enthalpy is 64 kJ mol-1 for the first reaction and 61 kJ mol-1 for the others. 

Activation energy values for the recombination of the products of carbonate decompositions are generally low and so it is expected that values of E will be close to the dissociation enthalpy. Such correlations are not always readily discerned, however, since there is ambiguity in what is to be regarded as a mole of activated complex . If the reaction is shown experimentally to be readily reversible, the assumption may be made that Et = ntAH and the value of nt may be an indication of the number of reactant molecules participating in activated complex formation. Kinetic parameters for dissociation reactions of a number of carbonates have been shown to be consistent with the predictions of the Polanyi—Wigner equation [eqn. (19)]. 

The activation parameters bring out several features. Note that the activation enthalpy and activation energy for kn, which represents a very rapid reaction, are quite small. Of course, a fast reaction can have a higher activation energy, if the value of AS is more positive, so as to compensate. The activation entropy associated with k is particularly large and negative, as is most often the case for a second-order reaction that occurs by a bimolecular step. In such cases, AS reflects the loss of entropy from the union of the two reaction partners into a single transition state. 

If AH% is negative, with an absolute value smaller than that of A//f, then the quantity of A// -I- Ais a negative number. In such a case the rate constant for the small reaction will have an apparent negative activation enthalpy (energy). That is, the rate will decrease with increasing temperature. 

Equations (7-29) and (7-32) both have the same form. It is easy to see that their temperature profiles are not linear. Their shapes are the same. Note that the temperature profile can be factored into two straight-line segments, one for each separate k. The composite will then be a line that curves upward in the usual plot. The tangent at any T can be used to obtain a value of an apparent activation enthalpy. The apparent activation enthalpy increases with temperature whenever the composite constant is a sum of the rate constants for elementary reactions. 

Table 3 shows that the small activation enthalpies of the reactions (3) and (4) are clearly affected by the zero point energy corrections. But the relative order of the activation enthalpies remains the same with or without the corrections. The activation entropies have great negative values, which is of mechanistic interest (see part 4.3.1). However, because of their similarity, when comparing the three reactions to one another they have only small importance, e.g. for estimation of copolymerization parameters (see part 4.3.2). 

The values of the apparent rate constants kj for each temperature and the activation enthalpies calculated using the Eyring equation (ref. 21) are summarized in Table 10. However, these values of activation enthalpies are only approximative ones because of the applied simplification and the great range of experimental errors. Activation entropies were not calculated in the lack of absolute rate constants. Presuming the likely first order with respect to 3-bromoflavanones, as well, approximative activation entropies would be between -24 and -30 e.u. for la -> Ih reaction, between -40 and - 45 e.u. for the Ih la reaction and between -33 and -38 e.u. for the elimination step. These activation parameters are in accordance with the mechanisms proposed above. 

From a detailed study of the exchange, at various temperatures (in the range 0 to 20 °C) and acidities at a constant ionic strength of p = 1.0 Af, the kinetic parameters were calculated, k and k 2 k 2 = k2K- have values of 0.48 l.mole". sec and 0.22 sec", respectively, at 0 °C. For the exchange pathway associated with ky, values of the activation enthalpy and entropy of 12.6 kcal.mole" and — 14 cal.deg . mole , respectively, were reported. For the second pathway... 

There was a clear linear correlation between (a + (l)-values and the differences in activation enthalpies. The absolute value of the activation enthalpy difference went through a minimum, meaning that at medium angle sum there was no distinct preference of one or the other o-QM type, whereas at extreme angle sums —either very large or very small ones—one of the o-QM types is largely preferred over the other one. 

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