Entropy effects

In case a) deacylation is faster by a factor of 3540 since the carbonyl group is immobilized by insertion of the bulky N-acetyl-L-tyrosyl group into a hydrophobic pocket on the enzyme (Fig. 2.14a) at the correct distance from the attacking nucleophilic OH ion derived from water (cf. 2.4.2.S). In case b) the immobilization of the small acetyl group is not possible (Fig. 2.14b) so that the difference between the ground and transition states is very large. The closer the ground state is to the transition state, the more positive will be the entropy of the transition state, AS a fact that as mentioned before can lead to a considerable increase in reaction rate. The thermodynamic data in Table 2.7 show that the difference in reaction rates depends, above all, on an entropy effect the enthalpies of the transition states scarcely differ. 

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W hich leads to an isomeri/ation enthalpy of —1.7 kcal mol. ("Heat of fonnation should he taken to mean enthalpy of formation in this conte.st.) Entropy effects being... 

The quantity in parentheses is always positive for a > 1, the case of elongation, making AS < 0 for stretching. Therefore AS is positive for the opposite process, showing that entropy alone is sufficient to explain the elastomer s snap. To get an idea of the magnitude of this entropy effect, consider the following example. 

Although the right-hand sides of Eqs. (8.27) and (8.28) are the same, the former applies to the mixture (subscript mix), while the latter applies to the mixing process (subscript m). The fact that these are identical emphasizes that in Eq. (8.27) we have calculated only that part of the total entropy of the mixture which arises from the mixing process itself. This is called the configurational entropy and is our only concern in mixing problems. The possibility that this mixing may involve other entropy effects—such as an entropy of solvation-is postponed until Sec. 8.12. 

Especially for large values of Aw, there could be an additional entropy effect beyond that calculated in the last section which arises from the interaction of nearest neighbors. That is, reaction (8.A) might be characterized by both a AHp jj. and a ASp jj.. In this case Aw might be viewed as the pairwise contribution to a free energy ACpaj with... 

The equations we have written until now in this section impose no restrictions on the species they describe or on the origin of the interaction energy. Volume and entropy effects associated with reaction (8.A) will be less if x is not too large. Aside from this consideration, any of the intermolecular forces listed above could be responsible for the specific value of x- The relationships for ASj in the last section are based on a specific model and are subject to whatever limitations that imposes. There is nothing in the formalism for AH that we have developed until now that is obviously inapplicable to certain specific systems. In the next section we shall introduce another approximation... 

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

The one-pot synthesis of 9 described above appears to afford only modest yields of azacrowns. One might wonder why any crown at all would be formed under non-high dilution conditions intended to yield only open-chained material. Vogtle suggests that this can be explained in terms of template, steric and entropy effects . These factors are of doubtless significance, but it is interesting to note that in the synthesis of poly-azamacrocycles, Richman and Atkins found that there was no significant template effect observed. The question of the template effect in Ihe syntheses of 9 has recently been addressed by Kulstad and Malmsten They conclude that the formation of 9 is assisted by the presence of alkali metal cations. 

In this section we study a system with purely repulsive interactions which demonstrates the importance of entropy effects on the stability of phases when the effect of the corrugation potential due to the structured surface is completely neglected. The phase diagrams are determined by finite size scaling methods, in particular the methods of Sec. IV A. 

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

Even without a cage effect, the entropy effect will be somewhat more favorable for ortho reaction when hydrogen bonding to an azine-nitrogen atom generates the necessary nucleophile. The possibility of proton transfers between the solvent molecules (MeOH) near the reaction site and the more distant MeO is expected to produce a favorable increase (relative to other solvents) in the entropy of activation, which can reinforce the effect of a favorable point of... 

In Scheme IV, intranuclejar activation is depicted. Kinetic studies with ionic nucleophiles show a variable relationship between the rates of reaction ortho and para to an azine-nitrogen (348 vs. 353 or 349) or nitro group due to entropy effects the energy of activation is expected on further study to be consistently lower for the para-position. The relative reactivity of 2- and 4-substituted bicyclic azines... 

The results obtained demonstrate competition between the entropy favouring binding at bumps and the potential most likely to favour binding at dips of the surface. For a range of pairwise-additive, power-law interactions, it was found that the effect of the potential dominates, but in the (non-additive) limit of a surface of much higher dielectric constant than in solution the entropy effects win. Thus, the preferential binding of the polymer to the protuberances of a metallic surface was predicted [22]. Besides, this theory indirectly assumes the occupation of bumps by the weakly attracted neutral macromolecules capable of covalent interaction with surface functions. 

It is important to note that, for important sub-cases of case /), which will be discussed in more detail in Sect. 2.4, there is a low extent of disorder entropy effects, if any, are small and changes of the lattice dimensions are absent or small. These particular disordered forms are not considered as mesomorphic. In such cases, the limiting models which are fully ordered or fully disordered may be designated respectively as ordered or disordered crystalline modifications, if their consideration is useful for the structural description of a polymeric material. Note... 

Although this is true in some sort of averaged sense, in that the net forward rate is less than the net backward rate for / < lmi , the length of the individual stems may fluctuate about lmin because of surface entropy effects. Using Eq. (3.99) in Eq. (3.96) shows that ... 

FIGURE 8.33 On the left of the semipermeable membrane is the pure solvent with its characteristic molar enthalpy, entropy, and Gibbs free energy. On the right is the solution. The molar Gibbs free energy of the solvent is lower in the solution (an entropy effect), and so there is a spontaneous tendency for the solvent to flow into the solution. 

For many reactions entropy effects are small and it is the enthalpy that mainly determines whether the reaction can take place spontaneously. However, in certain... 

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. 

Although reactions in which molecules are cleaved into two or more pieces have favorable entropy effects, many potential cleavages do not take place because of large increases in enthalpy. An example is cleavage of ethane into two methyl radicals. In this case, a bond of 79 kcal mol (330 kJ mol ) is broken, and no new bond is formed to compensate for this enthalpy increase. However, ethane can be cleaved at very high temperatures, which illustrates the principle that entropy becomes more important as the temperature increases, as is obvious from the equation AG = AH — TAS. The enthalpy term is independent of temperature, while the entropy term is directly proportional to the absolute temperature. 

Another type of steric effect is the result of an entropy effect. The compound 2,6-di-fert-butylpyridine is a weaker base than either pyridine or 2,6-dimethylpyridine. The reason is that the conjugate acid (8) is less stable than the conjugate acids of nonsterically hindered pyridines. In all cases, the conjugate acids are hydrogen bonded to a water molecule, but in the case of 8 the bulky tert-butyl groups restrict rotations in the water molecule, lowering the entropy. 

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