Enthalpy and entropy of activation

Figure B2.4.2. Eyring plot of log(rate/7) versus (1/7), where Jis absolute temperature, for the cis-trans isomerism of the aldehyde group in fiirfiiral. Rates were obtained from tln-ee different experiments measurements (squares), bandshapes (triangles) and selective inversions (circles). The line is a linear regression to the data. The slope of the line is A H IR, and the intercept at 1/J = 0 is A S IR, where R is the gas constant. A and A are the enthalpy and entropy of activation, according to equation (B2.4.1)...

Wide variation in enthalpy and entropy of activation for different reaction systems is possible, as illustrated by the following two reactions. 

When the expanded expression for Gibb s free energy is substituted for AG. as shown in Eq. 4, it becomes possible to calculate the enthalpy and entropy of activation when rates are available across a range of temperatures. These parameters are calculated in Table 6 using the data supplied by Zavitsas and Ferrero [80,85,90]. 

Hammett originally demonstrated that the sigma-rho relation might be expected to hold if entropies of activation (or entropy changes) were constant in a series. It has since been shown that a sufficient condition is a linear relation between enthalpies and entropies of activation (or reaction), and such hnear relations are frequently encountered. Although the existence of such linear relations has always appeared somewhat mysterious, some rationale for this relationship has recently been given. 

Tautomerism of 2-substituted hexahydropyrimidines has been studied (980PP53), and free energies, enthalpies, and entropies of activation for this ring-chain tautomeric equilibrium have been measured [97JCS(P2)169]. 

The solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 13 kJ mole-1 and 200 8 J K"1 mole-1) are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 7 kJ and 257 5 J K-1, respectively, referred to 1 mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, S02 and 02. Desorption occurs over an area equivalent to about 1.4% of the total exposed crystal surface. Other possible models are discussed. 

Second-order rate coefficients have been obtained for chlorination of alkyl-benzenes in acetic acid solutions (containing up to 27.6 M of water) at temperatures between 0 and 35 °C, and enthalpies and entropies of activation (determined over 25 °C range) are given in Table 63 for the substitution at the position indicated266. 

The rates of decarboxylation of a range of 3-substituted mesitoic acids in 82.1 wt. % phosphoric and 83.0 wt. % sulphuric acids have been measured636 over a range of temperatures as indicated in Table 209, which gives the first-order rate coefficients together with the log A values and the energies, enthalpies, and entropies of activation calculated at 80 °C for sulphuric acid, and 119 °C for phosphoric acid these kinetic parameters are somewhat different from those... 

With application of reasonable values for trapping parameters and AS2, it was possible to bracket the enthalpy and entropy of activation for isomerization of cyclobutadiene. Hence, A/Zj was estimated to fall between 1.6 and lOkcal/mol, where the upper limit was consistent with theoretical predictions for square-planar cyclobutadiene. Most surprising, though, was the conclusion that AS for automeriza-tion must lie between -17 and -32cal/(molK), based on the AS values normally observed for Diels-Alder reactions as a model for AS2. ... 

In another study (see Atwood, 1985, p. 168), a series of oxad reactions was carried out at 30°C with methyl iodide and trans-[IrCl(CO)(P(p-C6H4Y)3)2]. The identities of the groups in the para position of the phosphine ligands, Y, are shown in Figure 22.4, which is a graph of the values for the enthalpy and entropy of activation for reactions. 

Electrostatically-controlled pre-association interactions have an important effect on rates for [Pd(dien)Cl]+ reacting with thione-containing nucleosides, nucleotides and oligonucleotides, as is often the case for reactions between metal complexes and this type of biological ligand. Interaction between the charged complex and the polyanionic oligonucleotide surface leads to an increase in both enthalpy and entropy of activation in the DNA or model environment (252). 

A condition said to exist for a series of structurally related molecular entities undergoing the same general reaction, wherein the enthalpies and entropies of activation can be related by the expression A// /3A5 =... 

The conclusion from these experiments is that the associated ions [RXY]-are stereochemically related to the SN2 transition state. Furthermore, little variation occurs in the stability of the associated ions for CH3C1, CH3Br and CH3I, and steric hindrance is apparently of small consequence in the enthalpic and entropic contributions of these equilibria. These data can be compared directly to the solution values for enthalpy and entropy of activation to show that solvation effects on both parameters are indeed responsible for the large variations in rates observed in solution. 

The reaction of Problem 10 was studied at two different temperatures, and, from the temperature dependence of the rate constants, the authors determined AH% and ASJ, the enthalpy and entropy of activation, respectively. The following values of these parameters were obtained in pure water and in 0.01 M sodium dodecyl sulfate (NaLS) and 0.01 M hexadecyl trimethyl ammonium bromide (CTABr) ... 

The reactions of the thiophene derivatives in both forward and reverse directions are characterized by lower enthalpies and entropies of activation than the reactions of the selenophene analogs. In the forward reactions, enthalpy and entropy changes compensate nearly exactly and result in slightly greater rates of adduct formation for the selenophene derivatives despite the higher enthalpies of activation. The higher entropies of activation for the selenophene derivatives have been attributed to less solvated transition states as compared to the reactions of the thiophene analogs (Table XXVIII). 

Many of the esters which are hydrolyzed by the AalI mechanism in acid are also hydrolyzed with alkyl-oxygen fission under neutral condi-tions60,67 74 75 84 85 88 89. These reactions have the high enthalpies and entropies of activation characteristic of unimolecular reactions, and involve the ionization of (usually) tertiary alkyl esters, to the carbonium ion and a carboxylate anion in the rate-determining step, viz. 

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