Enthalpy of activation,

Figure C3.5.1. (a) Vibrational energy catalyses chemical reactions. The reactant R is activated by taking up the enthalpy of activation j //Trom the bath. That energy plus the heat of reaction is returned to the bath after barrier...

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. 

There are available from experiment, for such reactions, measurements of rates and the familiar Arrhenius parameters and, much more rarely, the temperature coefficients of the latter. The theories which we use, to relate structure to the ability to take part in reactions, provide static models of reactants or transition states which quite neglect thermal energy. Enthalpies of activation at zero temperature would evidently be the quantities in terms of which to discuss these descriptions, but they are unknown and we must enquire which of the experimentally available quantities is most appropriately used for this purpose. 

Arguments have been presented that this difference in changes in Gibbs function, rather than the similar difference in enthalpies of activation, AHl — AH, better represents the quantity with which... 

Additionally, the enthalpies of activation (142) for the permanganate oxidation of organic compounds is characteristically low in the range of... 

It follows from this discussion that all of the transport properties can be derived in principle from the simple kinetic dreoty of gases, and their interrelationship tlu ough k and c leads one to expect that they are all characterized by a relatively small temperature coefficient. The simple theory suggests tlrat this should be a dependence on 7 /, but because of intermolecular forces, the experimental results usually indicate a larger temperature dependence even up to for the case of molecular inter-diffusion. The Anhenius equation which would involve an enthalpy of activation does not apply because no activated state is involved in the transport processes. If, however, the temperature dependence of these processes is fitted to such an expression as an algebraic approximation, tlren an activation enthalpy of a few kilojoules is observed. It will thus be found that when tire kinetics of a gas-solid or liquid reaction depends upon the transport properties of the gas phase, the apparent activation entlralpy will be a few kilojoules only (less than 50 kJ). 

Finally from the logarithmic form of the Eyrlng equation, the free enthalpy of activation, AG, of rotation of the dimethylamino group at the coalescence temperature (318 K) can be calculated ... 

Conversely, processes which convert carbons to sfp- carbons are more favorable for five-membered than for six-membered rings. This can be illustrated by the data for acetolysis of cyclopentyl versus cyclohexyl tosylate. The former proceeds with an enthalpy of activation about 3kcal/mol less than the latter." A molecular mechanics analysis found that the difference was largely accounted for by the relief of torsional strain in the cyclopentyl case." Notice that there is an angle-strain effect which is operating in the opposite direction, since there will be some resistance to the expansion of the bond angle at the reaction center to 120° in the cyclopentyl ring. 

Reductions by NaBKt are characterized by low enthalpies of activation (8-13kcal/mol) and large negative entropies of activation (—28 to —40eu). Aldehydes are substantially more reactive than ketones, as can be seen by comparison of the rate data for benzaldehyde and acetophenone. This relative reactivity is characteristic of nearly all carbonyl addition reactions. The reduced reactivity of ketones is attributed primarily to steric effects. Not only does the additional substituent increase the steric restrictions to approach of the nucleophile, but it also causes larger steric interaction in the tetrahedral product as the hybridization changes from trigonal to tetrahedral. 

Equation (5-43) has the practical advantage over Eq. (5-40) that the partition functions in (5-40) are difficult or impossible to evaluate, whereas the presence of the equilibrium constant in (5-43) permits us to introduce the well-developed ideas of thermodynamics into the kinetic problem. We define the quantities AG, A//, and A5 as, respectively, the standard free energy of activation, enthalpy of activation, and entropy of activation from thermodynamics we now can write... 

Okamoto et al. found that A-oxidation activates 4-halogeno-quinolines in the reaction with piperidine in aqueous alcohol by kinetic factors of 9 to 25, at 100°. This rate-enhancing effect is accompanied by a fairly large decrease in the enthalpy of activation (up to 10 kcal/mole in the chloro compounds), the effect of which is partly offset by a decrease in the entropy of activation. 

The free energy of activation, is related to the heat (or enthalpy) of activation, and by the equation AF =... 

A simpler phenomenological form of Eq. 13 or 12 is useful. This may be approached by using Eq. 4 or its equivalent, Eq. 9, with the rate constants determined for Na+ transport. Solving for the AG using Eqn. (3) and taking AG to equal AHf, that is the AS = 0, the temperature dependence of ix can be calculated as shown in Fig. 16A. In spite of the complex series of barriers and states of the channel, a plot of log ix vs the inverse temperature (°K) is linear. Accordingly, the series of barriers can be expressed as a simple rate process with a mean enthalpy of activation AH even though the transport requires ten rate constants to describe it mechanistically. This... 

Fig. 16. A. Plot of log iNa as a function of T 1 (°K) using the experimental values of the rate constants and the location of the binding sites in Eq. 4. The Gibbs free energy of activation is calculated from Eq. 3 the AS are taken to be zero, and the current is calculated by means of Eq. 4. The purpose is to demonstrate that multibarrier channel transport can be seen as single rate process with average values for the enthalpies of activation. Non-linearity of such a plot is then taken to arise form the dynamic nature of the channel.

Apparently, the 1H NMR spectra of 1 //-azepines are invariant over substantial temperature ranges.61 However, temperature dependence has been noted69 in the 13CNMR spectra of some 1 -acyl-1 //-azepines, and is attributed to hindered rotation about the N-CO bond rather than to ring-inversion phenomena AG free enthalpies of activation for hindered rotation of 62-66 kJ moP1 have been calculated. E/Z-rotamcr ratios for l-aroyl-l//-azepines have been assessed and show a slight preference for the -rotamer 22 however, an X-ray structural analysis of l-(4-bromobenzoyl)-2-methyl-3.5,7-triphenyl-l//-azepine demonstrates that in the crystal state it is exclusively in the E configuration.22... 

Studies by Deathrage ef a/.137 139 revealed that most of dipeptides were hydrolyzed 100 times faster with cation exchange resins (Dowex-50) than with HC1. Deathrage etal.139 also found that the entropy of activation was significantly less than in the case of hydrolysis of the same compounds by HC1, while the enthalpies of activation for the two cases were practically the same. While the entropy changes associated with catalysis by the cationic exchange resins remain obscure, presumably the mechanism of the catalysis follows that for homogeneous acids as described here later. 

Since the enthalpy of activation of an elementary step cannot be negative, the measured negative apparent enthalpy of activation is explained by a fast pre-equilibrium... 

The vast majority of the kinetic detail is presented in tabular form. Amassing of data in this way has revealed a number of errors, to which attention is drawn, and also demonstrated the need for the expression of the rate data in common units. Accordingly, all units of rate coefficients in this section have been converted to mole.l-1.sec-1 for zeroth-order coefficients (k0), sec-1 for first-order coefficients (kt), l.mole-1.sec-1 for second-order coefficients (k2), l2.mole-2.sec-1 for third-order coefficients (fc3), etc., and consequently no further reference to units is made. Likewise, energies and enthalpies of activation are all in kcal. mole-1, and entropies of activation are in cal.deg-1mole-1. Where these latter parameters have been obtained over a temperature range which precludes the accuracy favoured by the authors, attention has been drawn to this and also to a few papers, mainly early ones, in which the units of the rate coefficients (and even the reaction orders) cannot be ascertained. In cases where a number of measurements have been made under the same conditions by the same workers, the average values of the observed rate coefficients are quoted. In many reactions much of the kinetic data has been obtained under competitive conditions such that rate coefficients are not available in these cases the relative reactivities (usually relative to benzene) are quoted. 

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... 

Enthalpy of activation, 10, 156-160 Entropy of activation, 10, 156-160 compared with AV, 169 concentration units and, 168 precision of, 168 Enzyme catalysis, 90-94 Equilibria, complexation, 145-148 Exchange reactions, kinetics of,... 

Table 17 contains the enthalpies of activation and reaction for the three propagation steps in the gas phase and in solution. They were calculated by using classical cations possessing all-trans conformation. 

The even derivatives of the interaction potential are positive, and thus the prediction in the case of biphenyl mversion is invariably that the enthalpy of activation will be greater for the protium than for the deuterium compoimd. Since no appreciable effect on the entropy of... 

The salient points in this diagram are (i) the rate-determining step in the interconversion 55 6 is the bond-making (or bond-breaking) between the secondary C+ and CO (ii) the rate of carbonylation of the secondary pentyl ion 10 (and presumably also of other secondary acyclic alkyl cations) in FHSO3—SbFs has a free-enthalpy of activation of about... 

The isomerization of 5 to 7 and 8 involves a chain-branching type rearrangement (lOis ll) (Brouwer and Oelderik 1968) and has a free-enthalpy of activation of about 22 kcal mole . This result, combined with the data of Fig, 2, the free-enthalpy of activation of 17 kcal mole for the rearrangement 9-i ll (Brouwer and Hogeveen, 1972), and an estimated difference in free-enthalpy of about 0-8 kcal mole between 10 and 11 constitutes the basis for the free-enthalpy diagram in Fig. 3. 

From Fig. 4 it is seen that the free-enthalpy of activation for the rearrangement of tertiary butyl to secondary butyl cation is 30-4 — 3.9 = 26-5 kcal mole . As the reverse rearrangement has been found by direct observation to have JG cl7-18 kcal rnole" (Saunders et al., 1968), it follows that the difference in stabilization between tertiary and secondary butyl cations is indeed 9 + 1 kcal mole . This value is in excellent agreement with a previous experimental value of 10 + 1 kcal mole (Brouwer and Hogeveen, 1972). 

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