Entropy change on activation

Another criterion which may be useful for a distinction between the Al and A2 mechanisms is the evaluation of the entropy change on activation, AS. In the A2 mechanism, the loss of translational and rotational freedom of the attacking water molecule in the transition state leads to a substantial negative contribution to AS. Therefore, AS values for A2 reactions are expected to be much more negative than for Al reactions. 

Application of the AS criterion was originally suggested by Taft et al. [48]. The criterion was also employed by Long et al. [49], as well as by others in subsequent years. The subject was extensively reviewed by Schaleger and Long [50], The major portion of the examples given in Table 3 [54—67] are taken from the review article by these authors [50]. 

It can be seen from Table 3 that AS values referring to ester hydrolysis are in the range —2 to +15 eu (entropy units = cal. degree-1 ) if the mechanism is Al, or in the range —15 to —30 eu if the mechanism is A2. However, if other reactions are included the Al and A2 ranges overlap. For the acid catalyzed hydrolyses of ethylene and isobutylene oxides, the AS values are —6 and —4 eu [49], respectively. The mechanism is some form of A2 in both cases (see Sect. 6.3). On the other hand, AS = —3.8 eu has been found for the acid catalyzed hydrolysis of 2,4,4,5,5,-pentamethyl-l,3-dioxolane [51], which may be an example of an Al reaction or possibly an A2+ reaction with strong steric hindrance (see Sect. 7.4). 

As emphasized by Schaleger and Long [50], the entropy criterion must be exercised with caution . Considerable contributions to the overall AS value are due to solvation changes which take place in the formation of the transition state from the reactants. 

Solvation entropy changes are large if the reactions involve ionic charges. If opposite electric charges are created the contribution to the 

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These are only rough guides to the true entropy change on activation. Detailed calculations using spectroscopic data for the reactants and a calculated potential energy surface for the activated complex will yield accurate partition functions for the translational, rotational and vibrational terms involved. Since the quantities contributing to the partition functions for each molecule will be different, then accurate calculations will be able to differentiate between such reactions as... 

Entropy changes on activation and mechanisms of hydrolysis reactions... 

For the A-Sg2 mechanism, the entropy changes on activation are expected to be negative as translational and rotational freedom is also lost in the transition state of this mechanism. The experimental AS values for A-Sfc 2 reactions compiled by Matesich [52] (and supplemented by the writer, Table 4 [24, 44, 68—82]) are between —1 and —37 eu as far as they are concerned with reactions of H30+ with electrically neutral substrates. According to Matesich s findings [52], there is a rough linear correlation between AS and log k2 at 25 °C. The lower the second-order rate coefficient, k2, the more negative is AS. ... 

As appears from the examination of the equations (giving the best fit to the rate data) in Table 21, no relation between the form of the kinetic equation and the type of catalyst can be found. It seems likely that the equations are really semi-empirical expressions and it is risky to draw any conclusion about the actual reaction mechanism from the kinetic model. In spite of the formalism of the reported studies, two observations should be mentioned. Maatman et al. [410] calculated from the rate coefficients for the esterification of acetic acid with 1-propanol on silica gel, the site density of the catalyst using a method reported previously [418]. They found a relatively high site density, which justifies the identification of active sites of silica gel with the surface silanol groups made by Fricke and Alpeter [411]. The same authors [411] also estimated the values of the standard enthalpy and entropy changes on adsorption of propanol from kinetic data from the relatively low values they presume that propanol is weakly adsorbed on the surface, retaining much of the character of the liquid alcohol. 

The proposed mechanism of the effect of water can be supported by two other findings (i) the calculations of Maatman et al. [410] revealed that the active sites could be identified with surface silanol groups [Sect. 4.1.2.(a)] and(ii) independent studies of other authors [424—426] showed that silica gel could actually adsorb two layers of water the first layer is strongly chemisorbed whereas the second is less strongly adsorbed and retains much of the character of free water. The standard enthalpy and entropy changes on adsorption determined from kinetic adsorption coefficients, Kr and Kr, for the first and second layer, respectively [411], are consistent with this observation. 

By conservation of energy, F - F must be equal to AG° - TASe + w, where AG° is the standard Gibbs energy of reaction, ASe is any electronic entropy change on electron transfer, and w is the work required to bring the activated reactants and activated products from infinity. The second minimizing condition, i.e., 8F - 8F = 0 gives ... 

In Table XV. 1 are summarized some data for fast reactions in solution which are presumed to be diffusion-controlled. The range in rate constants of about 10 is probably a reflection of the different entropy changes on association. What is of special interest is the low values of the activation energy, which are in the range of diffusion activation energies. 

The neglect of pre-exponential factors in isotope analyses of activation energies is only valid if the entropy changes on forming the TS or the temperature dependence of the entropy change is identical for the two... 

A5 a)° entropy change on adsorption at standard state, cal or kcal/mol-K 5 surface area per unit weight of adsorbent substrate eoneentration, mass/ volume culture scaled activity variable for deactivation s n) number of molecules adsorbed per weight of adsorbate T temperature, °C or K... 

KLEIN - Yes, indeed, we are I My group Massimo Marchi and Michiel Sprik have written a constant-pressure Monte-Carlo program to study the electron-solvent system. To-date, only preliminary results are available they are sufficiently encouraging that we are actively pursuing this avenue of research. It will be necessary to compare and contrast the behaviour of hydrated and ammoniated electrons. Another quantity of interest is S, the entropy change on solvation. We are also attempting to calculate AS for the solvated electron. This story is nearly finished and will be submitted for publication shortly. 

Table IV. Preexponentials kj and activation energies of kg, k-s and kp and enthalpy and entropy change on folding for e- and t-ABPE in toluene and ethylacetate.

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). 

Theoretical aspects of the effect of ring size on the acid-catalyzed reduction of cyclic sulfoxides by iodide ions have been studied by Tamagaki et who noticed that differences in reactivity are mainly dependent on the change in activation entropy, which is correlated to the rigidity of the transition complex 220, (Eq. 59). 

According to the theory of rubber elasticity, the elastic response of molecular networks is characterized by two mechanisms. The first one is connected with the deformation of the network, and the free energy change is determined by the conformational changes of the elastically active network chains. In the early theories, the free energy change on deformation of polymeric networks has been completely identified with the change of conformational entropy of chains. The molecular structure of the chains... 

This reaction has a net increase in entropy and so it should proceed on its own. Note how the entropy change of the reaction is comparable to the entropy difference of reactants and products. FY1, this reaction has a fairly high activation energy barrier, which is why nitrogen and hydrogen don t readily react at room temperature (298 K) to form ammonia. 

From this it appears that A Eft Ea, the Arrhenius activation energy. A more correct treatment gives A Eft = Ea - RT for reactions in solution. However, since RT at 25°C is only 2.5 kj mol-1, the approximation that A Eft = Ea is often used. The preexponential term, in parentheses in Eq. 9-82, depends principally on A St, the entropy change accompanying formation of the transition state. The quantities AGt, AFft, and A St are sometimes measured for enzymatic reactions but useful interpretations are difficult. 

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