The Enthalpy of Activation

To discuss the enthalpy of activation in electrode kinetics, we make use of the fundamental rate equation 

reference is made in the literature to the energy of activation, instead of the enthalpy of activation. It follows from elementary thermodynamics that the former applies if the reaction is conducted at constant volume, whereas the latter is applicable to conditions of constant pressure. In aqueous solutions, the difference between the two is negligible, and when measurements are made at ambient pressure, the terms can be used interchangeably. 

To be exact, it should be remembered that the frequency term, w, in Eqs. (5.19) and (6.44), is generally considered to be a function of temperature 

An inherent source of uncertainty in the calculation of the enthalpy of activation, unique to electrochemistry, is related to the temperature-dependence of the potential of the reference electrode. Thus, in order to obtain AH, we determine logj versus 1/T at a constant metal-solution potential difference, A ). Now, at any given temperature, A [) is constant, as long as the potential with respect to a given reference electrode is constant. When the temperature is changed, this is no longer true, since the metal-solution potential difference at the reference electrode has changed by an unknown amount. 

There is some merit to each of these methods, and both have been used. In isothermal mode, we estimate the change in the value of A j) with Tfor the reference electrode. In nonisothermal mode, we estimate the additional potential drop generated in the salt bridge, as a result of the thermal gradients. N either can be measured directly. Consequentiy, there is always some uncertainty in the value of the enthalpy of activation of electrode reactions. 

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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. 

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

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. 

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.

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... 

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... 

A//, the enthalpy of activation, is the difference in bond energies, including strain, resonance, and solvation energies, between the starting compounds and the transition state. In many reactions, bonds have been broken or partially broken by the time the transition state is reached the energy necessary for this is A//. It is trae that additional energy will be supplied by the formation of new bonds, but if this occurs after the transition state, it can affect only AH and not A//. ... 

The predictions of the reactivities by the geminal bond participation have been confirmed by the bond model analysis [103-105] of the transition states and the calculations of the enthalpies of activation AH of the Diels-Alder reaction [94], the Cope rearrangement [95], the sigmatropic rearrangement [96], the Alder ene reaction [100], and the aldol reaction [101] as are illustrated by the reactions of the methyl silyl derivatives in Scheme 38 [102], The bond is more electron donating than the bond. A silyl group at the Z-position enhances the reactivity. 

The empirical isokinetic relationship for a series of compounds, undergoing reaction by the same mechanism, suggests that there could be an empirical linear relationship between the temperature (T) at which a series of reactants decompose at a constant rate and the enthalpies of activation for that series of reactions (9,10) ... 

AH = 17.3 4.1 kcal.mole and ASl = —15 13 cal.deg . mole Thus the efficiency of Cu(II) as a catalyst is due to a more favourable entropy of activation. In fact the enthalpy of activation for the catalysed reaction is greater than that for the uncatalysed reaction . Recently, Espenson et have measured... 

The magnitudes of the thermodynamic parameters, A77 and AS sometimes provide evidence supporting proposed mechanisms of drug decomposition. The enthalpy of activation is a measure of the energy barrier that must be overcome by the reacting molecules before a reaction can occur. As can be seen from Eq. (28), its numerical value is less than the Arrhenius... 

The term A in Equation (2.6) is a constant known as the Arrhenius constant and E is the energy of activation derived from collision theory (Atkins, 1978). The enthalpy of activation can be calculated from transition state theory (Jencks, 1969) as... 

With the availability of stable geometric isomers of doubly bonded germanium compounds, experimental determinations of the 7r-bond strength can be made. The enthalpy of activation for double bond isomerization in Mes(Tip)Ge=Ge(Tip)Mes (Tip = 2,4,6-triisopropylphenyl) has been determined for the Z-E conversion, 22.2 . 3 kcal/mol and for the E-Z conversion, 20.0 0.3 kcal/mol.15 These values agree well with recent theoretical estimations.7 The isomerization barrier in germaphos-... 

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... 

Figure 1 Relative positions of the potential energy (E) surfaces of the electronic states involved in a hypothetical chemiluminescent reaction as a function of intemuclear separation (r). P and P represent the ground and lowest electronically excited singlet states of the product of the reaction, respectively. R represents the ground electronic state of the reactant. AH is the enthalpy of the dark reaction while AHa is its enthalpy of activation. AH is the enthalpy of activation of the photoreaction, hv denotes the emission of chemiluminescence.

From the chemical point of view, the solvent in which the CL experiment is carried out can have a dramatic influence on the efficiency of the CL reaction as solvation can alter the shapes, the depths, and the densities of the vibrational states of the potential surfaces representing the ground states of products and reactants and the lowest excited singlet state of the potential fluorophore. The alteration of the intersections of these potential energy surfaces can affect the enthalpies of reaction and the enthalpies of activation for dark and lumigenic reactions. In some cases, these changes will favor CL (if AH decreases relative to AHa) and in some cases, they will make it thermodynamically unfavorable for CL to occur. 

This result is quite in contrast to the common expectation that the electrode potential changes the activation barrier at the interface which would result in a temperature independent transfer coefficient a. Following Agar s discussion (30), such a behavior indicates a potential dependence of the entropy of activation rather than the enthalpy of activation. Such "anomalous" behavior in which the transfer coefficient depends on the temperature seems to be rather common as recently reviewed by Conway (31). 

To probe the effects of HCFC structure on toxicity the metabolism of three penta-haloethanes, HCFC-123, HCFC-124, and HCFC-125 were studied. The three compounds differ one from the other by the number of fluorine atoms present in the /3-carbon (Fig. 4.64). It was found that the enthalpies of activation, AHact, for hydrogen atom abstraction paralleled the rate of trifluoroacetic acid excretion suggesting that the more difficult it was... 

The overall enthalpy change of the insertion process contains contributions from four bonds (M-CO, M-COR, M-R and CO-R). As there is no significant difference between (Mn-R) and Zs(Mn-COR) then, at least in the case of manganese and hydrocarbon groups, R, the dominant factor will be the difference between T (Mn-CO) and E R-COX) [for R = CH3, E = 339 kJ mop1 (X = H), 370 kJ mol"1 (X = Cl) (Ref.23 )] which suggests that the insertion reaction is thermodynamically favoured with respect to decarbonylation. Kinetic studies of the carbonyl insertion reaction in solution have shown87) that the enthalpy of activation is 62 kj mol-1 for inser-... 

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