Entropy, activation reaction

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. 

Fortunately, there is evidence of a quite different kind available which at least provides a strong indication as to which mechanism is the more probable. In Table 2 are summarised the entropies of reaction (AS°ss) and activation (AS+) for the polymerisations of DXL, DXP, and THF. Four features are immediately evident (1) The AS1 is about the same for DXL and DXP initiated by perchloric acid (2) the AS+ for DXL is about the same for initiation by perchloric acid and by (VII) (3) the AS+ for DXL and DXP are much more negative than for THF and (4) for DXL and DXP the AS1 are considerably more negative than the corresponding AS°ss. 

Table 2 Entropies of reaction (AS°ss) and activation (AS ) for polymerisation of DXL, DXP, and THF in cal deg1 mol1 (rounded to nearest...

The free energy of activation is composed of an entropy activation (AS ) and an enthalpy of activation (AH ). The former is associated with the pre-exponential factor A of the Arrhenius equation and the latter with the experimental Ead, which defines the sensitivity of the reaction rate to temperature. The existence of an LFER for a set of reactants is equivalent to the statement that... 

Since hydrogen evolution is an activated reaction, an increase in temperature can only be kinetically beneficial. However, in many cases the Tafel slope has been observed not to increase linearly with T (i.e., R T/aF) but to increase at a lower rate or even to remain constant [229-232]. This has stimulated much discussion [233-240] about the fundamental significance of such an anomalous behaviour which has been interpreted in terms of a partly potential dependent entropy of activation as op-... 

This assumption is not only unjustifiable in theory, but unjustified in practice. As Hammett2 emphasized twenty years ago, the entropies of reaction or activation are not usually the same for a series of reactions of similar type. A good example is provided by the dissociation of carboxylic adds in water ... 

Secondly, we must not try to compare our calculated values for AE or AE with observed heats of reaction or activation this would clearly be gross error for reactions where the AS or AS differ in view of the compensating changes in AH or AH. It is therefore usually a waste of time to measure heats and entropies of reaction for polar reactions in solution since it is usually impossible to provide any reliable interpretation of them. The rates of reaction are the things that matter. 

In summary, zeolites have been successfully applied as catalysts or promoters in several fundamental liquid-phase organic reactions under mild reaction conditions. The functions of the zeolites in promoting the liquid-phase reactions can be characterized by (1) synergistic effects of acidic and basic sites of the zeolites on the reactants, (2) a decrease in the activation entropy of reactions owing to preadsorption of reactants in close proximity, (3) an increase in the effective surface area of the reagent owing to high dispersion... 

The ideal chemical probe for the structure of a solvent should bring into play reactants that are less volatile and more soluble in water, this being apparently incompatible with a lipophilic character. The use of a diene linked to a free sugar, according to reaction (11.7), approaches this ideal. A comparison of lines 3 and 4 of Table 11.1 shows that this reaction is also accelerated in pure water and that this is also the consequence of an increase in the entropy activation. Thus, the hydrophobic effect can take place between the diene and dienophile close to the sugar part. 

Maity, D.K. and Bhattacharyya, S.P. (1996) On the characterization of reaction paths by local descriptors the behaviour of active BO sum and local information entropy along reaction paths and some consequences. /. Mol. Struct. (Thcochcml, 367, 59-66. 

The free energy of activation is composed of an entropy activation (AS ) and an enthalpy of activation AH ). The former is associated with the pre-exponential factor A of the Arrhenius equation and the latter with the experimental act, which defines the sensitivity of reaction rate to temperature. In some reactions, substituents affect ac, (or AH ) and AH° primarily, while A (or AS ) and A S° change only slightly. In these cases, AG and In k vary in the same way as act, and In k varies linearly with AG°. Frequently, however, In k and In K are correlated, even though both A and act vary as the substituent changes. Thil can happen if AH (or act) and AS are correlated, and similar relationships are observed between the values of AH° and AS 1 for the reactions this is called the compensation effect. The net effect is a simple LFER in which the change in k in less than if E.,cl or A changed alone. It is easy to show that this situation leads to... 

Although these rate changes are small they are often the result of quite large changes in enthalpy of activation, compensated by changes in the activation entropy. The reaction... 

In the absence of noticeable strain in the metallacycle, Z)/7°(M-C) Z)/7°(M-C)i. Therefore, (JA)ptDH° (Gj-H) — Z)//°(M-C)2 —Z)/7°(M-H), a balance that is similar to the one made for the intermolecular C-H activation (reaction (60)). In the present case, however, the weight of the entropy term is expected to be smaller than for reaction (60), —44kJmoP . As entropy effects are responsible for many thermodynamically unfavorable reactions surveyed in Section 1.22.5.2, it is thus not surprising that cyclometallations are so common and that they often compete with intermolecular C-H activations. 

TABLE 8.5 The Activation Enthalpy, Activation Entropy, Activation Energy, and Rate Constants of Elementary Reaction Dnring Thiophene Pyrolysis... 

Rate laws, rate constants, activation parameters, and enthalpies and entropies of reaction have been determined for hydroxide attack at the bis-tptz complexes of cobalt(ii) and of nickel(n) (P. A. Williams, Transition Met. Chem., 1979,4,24). 

Scheme 11.35 Activation enthalpy, activation entropy and reaction enthalpy for the thio-Claisen rearrangement of allyl vinyl sulfide predicted on different levels oftheo7 (1996).

On most of the group VIII metals the heats of adsorption are comparable with their heats of dissociation. This implies that the adsorbed molecule will desorb with a rate which is 10 times faster than that for dissociation owing to the difference in the activation entropy. The reaction path that proceeds through a transition state of maximum entropy is the preferred path. For catalysis, the implication is that dissociation of adsorbed molecules will occur at those pressures and temperatures where equilibrium between the gas phase and surface maintains a significant surface concentration of the dissociated molecules. The temperature has to be chosen such that the rate constant for dissociation is in the proper time regime. The observation that for a transition-metal surface reaction, the transition entropy is low, but that for a reaction step between the surface and gas phase is large, is quite general. 

The TLM model has been applied not only to inorganic anions but also to organic species. In a study of 2,4-dichlorophenol, 2,4,6-trichlorophenol, andpentachlorophe-nol sorption in an allophanic soil (Cea et al. 2010), the isotherm experiments were well described (as shown in Figure 12.4) by the TLM in which monodentate outer and inner sphere complexes were considered to form between deprotonated organic molecules and active sites on the variable-charge soil. The calculated thermodynamic parameters suggest that chlorophenol sorption is a spontaneous (AG < 0), endothermic (AH > 0), and entropy-driven reaction (AS > 0). 

If we assume that the entropy of activation and the entropy of reaction do not change from one reaction to another among the family considered, then Eq. (2.124) becomes ... 

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