Activation parameters enthalpy

Activation parameters enthalpy expressed in kcal mol and entropy in cal K mol ... 

Figure 16. Summary plot of activation parameters (enthalpy of activation, AH entropy of activation, AS ) for oxygen isotope exehange in siUeates reacted with either pure water or salt solntions. The Eyring-Polanyi relationship (Eqn. 102) was nsed with data described by Cole et al. (1983), Cole and Ohmoto (1986), Cole et al. (1987, 1992), and in Table 2 (see Appendix). Note that data falling on a hnear trend generally indieate that a conunon leaetion meehanism predominates, ab = albite, san = sanidine, eels = celsian, qtz = qnartz, mnsc = muscovite, bio = biotite, chi = chlorite, parag = paragonite, woll = wollastonite, diop = diopside, gran = granite, bas = basalt.

Z7. The cotr arison of activation parameters for reactions in two different solvents requires consideration of differences in solvation of both the reactants and the transition states. This can be done using a potential energy diagram such as that illustrated below, where A and B refer to two different solvents. By thermodynamic methods, it is possible to establish values which correspond to the enthalpy... 

An interpretation of activation parameters has led to the conclusion that the bromination transition state resembles a three-membered ring, even in the case of alkenes that eventually react via open carbocation intermediates. It was foimd that for cis trans pairs of alkenes tiie difference in enthalpy at the transition state for bromination was greater than the enthalpy difference for the isomeric alkenes, as shown in Fig. 6.2. This... 

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. 

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. 

The activation parameters from transition state theory are thermodynamic functions of state. To emphasize that, they are sometimes designated A H (or AH%) and A. 3 4 These values are the standard changes in enthalpy or entropy accompanying the transformation of one mole of the reactants, each at a concentration of 1 M, to one mole of the transition state, also at 1 M. A reference state of 1 mole per liter pertains because the rate constants are expressed with concentrations on the molar scale. Were some other unit of concentration used, say the millimolar scale, values of AS would be different for other than a first-order rate constant. 

Clearly, the temperature profile is linear. The activation parameters are the sums shown in general, a sum of entropies and enthalpies is the result when constants are multiplied. If values of AS% and Aare known independently, from the temperature dependence of Ka for example, one can then calculate AS and AH by difference. 

Acid-base catalysis, 232-238 Brqnsted equation for, 233-236 general, 233, 237 mechanisms for, 237 specific, 232-233, 237 Activated complex (see Transition state) Activation enthalpy, 10, 156-160 for composite rate constants, 161-164 negative, 161 Activation parameters, 10 chemical interpretation of, 168-169 energy of activation, Ea, 10 enthalpy of activation (A// ), 10, 156-160... 

It should be born in mind, however, that the activation parameters calculated refer to the sum of several reactions, whose enthalpy and/or entropy changes may have different signs from those of the decrystalUzation proper. Specifically, the contribution to the activation parameters of the interactions that occur in the solvent system should be taken into account. Consider the energetics of association of the solvated ions with the AGU. We may employ the extra-thermodynamic quantities of transfer of single ions from aprotic to protic solvents as a model for the reaction under consideration. This use is appropriate because recent measurements (using solvatochromic indicators) have indicated that the polarity at the surface of cellulose is akin to that of aliphatic alcohols [99]. Single-ion enthalpies of transfer indicate that Li+ is more efficiently solvated by DMAc than by alcohols, hence by cellulose. That is, the equilibrium shown in Eq. 7 is endothermic ... 

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. 

Equation (5) holds for rate constants of the first order in sec" and of the second order in 1 mol sec". ) Therefore, no distinction will be made between the two pairs of the activation parameters in this paper the computation usually will be carried out in the simpler terms of Arrhenius theory, but all of the results will apply equally well for the activation enthalpy and activation entropy, too. Furthermore, many considerations apply to equilibria as well as to kinetics then the symbols AH, AS, AG will mean AH, AS, AG as well as AH°, AS°, AG°, and k will denote either rate or equilibrium constant. 

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). 

NMR line broadening is a suitable kinetic method for determining activation parameters for Co—C bond homolysis, and gave A//- values in the range 18-22.5 keal mol for a selection of Co(Por)R complexes containing secondary or tertiary alkyl groups.Bond dissociation enthalpies and entropies for several... 

These relations both demonstrate the inhibition of formation of the tetrahedral state which can be clearly attributed to steric crowding. Such a correlation as (5) confirms the attack at the neighbouring carbonyl group and this intramolecular catalysis for all this series. The activation parameters for the alkaline hydrolysis of these esters were also measured and are shown in Table 1. The enthalpies of activation of the 2-formyl, 2-acetyl, 2-propionyl, 2-isobutyryl and 2-pivaloyl esters are exceptionally small. These are... 

Similarly, from a plot of In (k/T) versus 1/T, the enthalpy of activation for each process may be obtained. This is also illustrated for the determination of the activation enthalpy for the propagation of degradation of a vinylidene chloride/methyl acrylate (five mole percent)/4-vinylpyridine (0.1 mole percent) copolymer in figure 7. The slope of the plot of In (kp/T) versus 1/T (figure 7) is given by -AH /R and the enthalpy of activation, AH, for the propagation reaction is calculated to be equal to 27.92 kcal/mol. The activation parameters for both the initiation and propagation reactions are recorded in table 3. 

The significance of these quantities is analogous to that for the activation parameters for homogeneous self-exchange reactions. Thus, AH equals the activation enthalpy for conditions... 

The activation parameters for the cation-independent pathway ( o) can be accounted for by a modified semiclassical Marcus-Hush theory. Lower enthalpies, and more positive volumes of activation are noted for the M +-catalyzed pathway. - ... 

Activation parameters have been determined for eliminative thermal decomposition of hexahydro-l,3,5-trinitro-l,3,5-triazine and related compounds, under high pressure in dilute solution." The negative activation volumes, low enthalpies of activation. 

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