Activation entropy

In order to go further in the characterisation of the processes involved in the secondary transitions, Starkweather [2-4] applied the transition state theory. It leads to expressing the motional frequency as  

A Ha and ASa are the activation enthalpy and entropy, respectively. By plotting ln(/yr) versus 1/T, one gets directly AHa and ASa. Interestingly, Starkweather differentiates between  

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Unfortunately, the number of mechanistic studies in this field stands in no proportion to its versatility" . Thermodynamic analysis revealed that the beneficial effect of Lewis-acids on the rate of the Diels-Alder reaction can be primarily ascribed to a reduction of the enthalpy of activation ( AAH = 30-50 kJ/mole) leaving the activation entropy essentially unchanged (TAAS = 0-10 kJ/mol)" . Solvent effects on Lewis-acid catalysed Diels-Alder reactions have received very little attention. A change in solvent affects mainly the coordination step rather than the actual Diels-Alder reaction. Donating solvents severely impede catalysis . This observation justifies the widespread use of inert solvents such as dichloromethane and chloroform for synthetic applications of Lewis-acid catalysed Diels-Alder reactions. 

Fig, 10. Activation entropy requireinents by reacting position as affected by previous substitutions based on Zavitsas [80], As the activation entropy becomes more negative, steric demands on the transition state are more stringent. The effect of previous or/ho-substitution on reaction at the para position is hard to explain, in light of both the reciprocal effect of para substitution on ortho and the effect seen with the d -oriho pre-substitution. 

Such plots should produce a straight line with the slope being equal to -AH /R and the intercept equal to n kB/h) + AS" /R. As the available temperature range typically is 100°, the error in AH will typically be 0.1-0.5 kcal/mol. The activation entropy is determined by extrapolating outside the data points to 7 = cxc (1/7 = 0), and is usually somewhat less well defined, a typical error may be 5 e.u. 

The rearrangement has been investigated kinetically. Hawthorne and Strahm found a reaction of the first order at 100°C in diethyl carbitol with k — 5.45 X 10", corresponding to a half-life of 212 min. The activation energy was 28 kcal, the activation entropy —3 1... 

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... 

Thermodynamic parameters have been obtained from kinetic HNMR spectroscopic studies of the thermal decomposition of ethyl 2,7-di-to7-butyl-5-methylthiepin-4-carboxylaten and two 1-benzothiepin compounds.12 The activation parameters for sulfur extrusion are AH = 93.7 kJ mol - 1 and AS = — 112.6 J Kmol-1 (in [2H18]Decalin) for the thiepin derivative,11 and AH = 75.3 and 87.9 kJ mol1 and AS = —100.4 and —104.6J Kmol-1 (in [2Hs]toluene) for the benzothiepin compounds.12 The large negative activation entropy values are consistent with a high degree of order in the anticipated thianorcaradiene transition state of the sulfur extrusion reaction. 

The rate constant increases with rising temperature and the activation parameters are AH = 80 kJ mol"1 and AS = - 100 J K-1 mol-1. According to these values the catalytic effect would result from an increase of the activation entropy. 

Both for reaction in and IV the order with respect to catalyst is 0.5. The activation enthalpies are 96.6 3.4 and 97.6 3.4 kJ mol-1 respectively when Ti(OBu)4 is used as the catalyst. This is not too far from the activation enthalpies200 for the Sn(II)-cata-lyzed esterification of B with isophthalic acid (85.1 4.9) and with 2-hydroxyethyl hydrogen isophthalate (85.8 4.2). It is also close to the Ti(OBu)4-catalyzed esterification of benzoic acid with B (85.8 2.5)49. This is probably due to the formation of analogous intermediate complexes and similar catalytic mechanisms. On the other hand, the activation entropies of reactions III and IV are less negative than those of the reaction of benzoic or isophthalic acid with B. This probably corresponds to a stronger desolvation when the intermediary complex is formed and could be due to the presence of the sodium sulfonate group. 

Habid and Malek49 who studied the activity of metal derivatives in the catalyzed esterification of aromatic carboxylic acids with aliphatic glycols found a reaction order of 0.5 relative to the catalyst for Ti(OBu)4, tin(II) oxalate and lead(II) oxide. As we have already mentioned in connection with other examples, it appears that the activation enthalpies of the esterifications carried out in the presence of Ti, Sn and Pb derivatives are very close to those reported by Hartman et al.207,208 for the acid-catalyzed esterification of benzoic and substituted benzoic acids with cyclohexanol. These enthalpies also approach those reported by Matsuzaki and Mitani268 for the esterification of benzoic acids with 1,2-ethanediol in the absence of a catalyst. On the other hand, when activation entropies are considered, a difference exists between the esterification of benzoic acid with 1,2-ethanediol catalyzed by Ti, Sn and Pb derivatives and the non-catalyzed reaction268. Thus, activation enthalpies are nearly the same for metal ion-catalyzed and non-catalyzed reactions whereas the activation entropy of the metal ion-catalyzed reaction is much lower than that of the non-catalyzed reaction. 

Structure 12.148 was already supported by results from Stamm and Zollinger s investigation (1957) in which activation entropies were determined. The mechanism was corroborated by further activation entropy studies (Demian, 1972, 1973 Demian et al., 1983) and investigations on the 2/4-ratio of coupling of 1-naphthylamine carried out by Hashida et al. (1975 b). 

Powell and Searcy [1288], in a study of CaMg(C03)2 decomposition at 750—900 K by the torsion—effusion and torsion—Langmuir techniques, conclude that dolomite and C02 are in equilibrium with a glassy phase having a free energy of formation of (73 600 — 36.8T)J from 0.5 CaO + 0.5 MgO. The apparent Arrhenius parameters for the decomposition are calculated as E = 194 kJ mole-1 and activation entropy = 93 JK-1 (mole C02)-1. 

Rate coefficients have also been measured at a range of temperatures for some aromatics in aqueous perchloric acid-trifluoroacetic acid (Table 168)468, and, surprisingly, the lower reactivity of benzene relative to toluene and /-butylbenzene appears to arise from a more negative activation entropy. This effect if real is... 

The activation entropies were considerably different from the large negative values expected for a second-order reaction and this was attributed to the effect of the internal return mechanism. 

The wide variation in the entropy factors for both the substituted phenyl and heterocyclic compounds and in particular for the methoxyphenyl and furan derivatives was considered to be strong evidence for solvent effects being predominant in determining the activation entropy. Consequently, discussion of the substituent effects in terms of electronic factors alone requires caution in this reaction. Caution is also needed since rates for the substituted phenyl compounds were only determined over a 20 °C range. The significance of entropy factors has also been indicated by the poor correlation of the data of the electrophilic reactivities of the heterocyclic compounds, as derived from protodemercuration, with the data for other electrophilic substitutions and related reactions572. 

The experimental side of the subject explores the effects of certain variables on the rate constant, especially temperature and pressure. Their variations provide values of the activation parameters. They are the previously mentioned energy of activation, entropy of activation, and so forth. The chemical interpretations that can be realized from the values of the activation parameters will be explored in general terms, but readers must consult the original literature for information about those chemical systems that particularly interest them. On the theoretical side, there is the tremendously powerful transition state theory (TST). We shall consider its origins and some of its implications. 

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. 

Baechler and coworkers204, have also studied the kinetics of the thermal isomerization of allylic sulfoxides and suggested a dissociative free radical mechanism. This process, depicted in equation 58, would account for the positive activation entropy, dramatic rate acceleration upon substitution at the a-allylic position, and relative insensitivity to changes in solvent polarity. Such a homolytic dissociative recombination process is also compatible with a similar study by Kwart and Benko204b employing heavy-atom kinetic isotope effects. 

An interesting cycloheptatriene (182) synthesis has been described using thiophene 1, 1-dioxides (180) and cyclopropenes 181 (equation 121)ns. Concerted [4 + 2]cycloaddition and subsequent cheletropic extrusion of sulfur dioxide are suggested by the second-order kinetics (first in each reactant), and by the large negative activation entropy. 

In exploring the entropic difference between a given enzyme and its reference solvent cage, we should consider the dependence of the activation barrier on the activation entropy using the relationship... 

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 insignificant alterations of the geometry, the charge distribution (see Fig. 13), the frontier orbitals, and the bond orders introduced as the educt is transferred into the activated complex point out that the latter is educt-like. However, as the activation entropies show, the reaction partners have already been arranged. For the first (AS = —161 AS° = —136 JK-1 mol-1) as well as for the second propagation... 

Most Diels-Alder reactions, particularly the thermal ones and those involving apolar dienes and dienophiles, are described by a concerted mechanism [17]. The reaction between 1,3-butadiene and ethene is a prototype of concerted synchronous reactions that have been investigated both experimentally and theoretically [18]. A concerted unsymmetrical transition state has been invoked to justify the stereochemistry of AICI3-catalyzed cycloadditions of alkylcyclohexenones with methyl-butadienes [12]. The high syn stereospecificity of the reaction, the low solvent effect on the reaction rate, and the large negative values of both activation entropy and activation volume comprise the chemical evidence usually given in favor of a pericyclic Diels-Alder reaction. 

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. 

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