Entropy factor

In this discussion, entropy factors have been ignored and in certain cases where the difference between lattice energy and hydration energy is small it is the entropy changes which determine whether a substance will or will not dissolve. Each case must be considered individually and the relevant data obtained (see Chapter 3), when irregular behaviour will often be found to have a logical explanation. 

Entropy Factors Arising from Hydrolysis and Ionization... 

Where ortho effects and special entropy factors control the relation of the reaction rates, it seems more appropriate to evaluate relative activation from the energies of activation. 

It is more common to find that AH° and AS° have the same sign (Table 17.2, III and IV). When this happens, the enthalpy and entropy factors oppose each other. AG° changes sign as temperature increases, and the direction of spontaneity reverses. At low temperatures, AH° predominates, and the exothermic reaction, which may be either the forward or the reverse reaction, occurs. As the temperature rises, the quantity TAS° increases in magnitude and eventually exceeds AH°. At high temperatures, the reaction that leads to an increase in entropy occurs. In most cases, 25°C is a low temperature, at least at a pressure of 1 atm. This explains why exothermic reactions are usually spontaneous at room temperature and atmospheric pressure. 

As a result of thermodynamic analysis it is shown that protein bonding to carboxylic CP exhibiting a local internal chain structure is determined by the entropy factor, whereas, if the arrangement of flexible chain parts on the protein globule is possible, the energetic component predominates. 

The wide variation in the entropy factors for both the substituted phenyl and heterocyclic compounds and in particular for the methoxyphenyl and furan derivatives was considered to be strong evidence for solvent effects being predominant in determining the activation entropy. Consequently, discussion of the substituent effects in terms of electronic factors alone requires caution in this reaction. Caution is also needed since rates for the substituted phenyl compounds were only determined over a 20 °C range. The significance of entropy factors has also been indicated by the poor correlation of the data of the electrophilic reactivities of the heterocyclic compounds, as derived from protodemercuration, with the data for other electrophilic substitutions and related reactions572. 

In a reaction in which the number of product molecules is equal to the number of reactant molecules, (e.g., A + B —> C + D), entropy effects are usually small, but if the number of molecules is increased (e.g., A —> B + C), there is a large gain in entropy because more arrangements in space are possible when more molecules are present. Reactions in which a molecule is cleaved into two or more parts are therefore thermodynamically favored by the entropy factor. Conversely, reactions in which the number of product molecules is less than the number of reactant molecules show entropy decreases, and in such cases there must be a sizable decrease in enthalpy to overcome the unfavorable entropy change. 

Scheme 13 may look unfavorable on the face of it, but in fact the second two reactions are thermally allowed 10- and 14-electron electrocyclic reactions, respectively. The aromatic character of the transition states for these reactions is the major reason why the benzidine rearrangement is so fast in the first place.261 The second bimolecular reaction is faster than the first rearrangement (bi-molecular kinetics were not observed) it is downhill energetically because the reaction products are all aromatic, and formation of three molecules from two overcomes the entropy factor involved in orienting the two species for reaction. 

According to Hercules 5> a measure of the relationship between direct excitation of the first excited singlet state by radical-ion recombination and triplet-triplet annihilation is the entropy factor FAS, estimated to be on average 0.2 eV. The enthalpy of the radical cation-radical anion recombination can be measured as the difference between the redox potentials 1/2 Ar—Ar (oxidation) and 1/2 Ar—Ar<7> (reduction). This difference has to be corrected by the entropy term. If this corrected radical-ion recombination enthalpy is equal to or larger... 

The thermodynamic data presented in Table XYI are calculated for the temperature T=0K. Note that the entropy factor favors betaine decomposition via directions A and B at higher temperatures. The reactions of organoelement analogs of carbenes with phosphorus and arsenic ylides are yet poorly studied. The presented above results of calculations allow an optimistic prognosis about the possibility of developing a new method for the synthesis of elementaolefins R2E14=CH2 (E14 = Si, Ge, Sn) on the basis of these reactions. 

The ring size (degree of oligomerization x) and conformation of M-E heterocycles strongly depends on steric effects of the substituents (repulsive interactions), ring strain effects and on entropy factors. This was shown for instance by Beachley and Racette for several heterocyclic aminoalanes [R2A1NR2]X97 and confirmed by our own results. However, predictions whether four- or six-membered heterocycles will be formed are... 

More subtle arguments have been invoked to rationalize the dichotomous behavior of so-called second-generation Mn-salen catalysts of type 7 toward unfunctionalized and nucleophilic olefins. For example, higher yields and ee s are obtained with the (i ,S)-complex for the epoxidation of indene (8). However, JV-toluenesulfonyl-l,2,3,4-tetrahydropyridine (10) gave better results using the (R,/ -configuration. An analysis of the transition-state enthalpy and entropy terms indicates that the selectivity in the former reaction is enthalpy driven, while the latter result reflects a combination of enthalpy and entropy factors <00TL7053>. 

Figures 5.11 and 5.12 demonstrate that the most intense peak in the spectra is not necessarily due to a reaction with the lowest critical energy E0. For the molecular ion ABXY+ the reaction leading to ion AY+ has preferential enthalpy, while the entropy factor favors formation of ion AB+. In the former case two bonds are cleaved (AB and XY) and two bonds are formed (AY and BX), that is, the energy losses are low. In the latter case one bond (BX) is cleaved and no new bonds are formed, that is, energy restrictions are tougher. On the other hand steric requirements are stricter in the first case. Ion AB+ arises as soon as BX bond acquires an appropriate amount of...

Since there are two different connections possible for n-octane, 1,6 or 3, 8, which could lead eventually to ethylbenzene, there is a statistical entropy factor involved here which is not part of the o-xylene route. Therefore, if both closures were equally possible from an enthalpy perspective, one would predict a 2 1 ethylbenzene to o-xylene ratio. The formation of the m- and p-xylene requires prior isomerization of n-octane to 2- and 3-methylheptane, respectively. 

The equilibrium constants in Table 22 suggest that the larger the peri substituent, the less favored is the sc form. Since the phenyl group takes a conformation in which it does not directly interact with the peri CH group, this result may originate in the ease or difficulty of solvation in addition to an entropy factor due to limitations of certain conformations. 

The general equation for L is Eq. (10), and the expressions to be used for C in that equation are listed in Table 1 in terms of partition functions. But the entropies of both the activated complex and the reactants, and therefore AS, can also be expressed in terms of partition functions. Therefore, C can be expressed in terms of the entropies of the activated complex and the reactants. As we shall see, it is possible to eliminate partition functions entirely. Also, in all but one case. Step 11, the entropy factor in C can be determined if one knows only the entropy of activation in those cases the entropy of a reactant or the activated complex is not needed. 

The entropy factor should also be considered since cyclization results in a more ordered structure. The C5 cyclization of n-hexane involves an entropy decrease of about 15-17 entropy units (e.u.). The corresponding values for cyclohexane and benzene formation are about 25 and 38-45 e.u., respectively. These values are comparable with calculated values of adsorption entropy (29). Thus, adsorption of a molecule to be cyclized may supply a considerable part of the entropy change in other words, adsorption should take place in a geometry favorable for cyclization. This is one of the main roles of the catalyst. 

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