Entropy-dominated

As described in Section 14-1. when AR and ZlS have the same sign, the spontaneous direction of a process depends on T. For a phase change, enthalpy dominates AG at low temperature, and the formation of the more constrained phase is spontaneous, hi contrast, entropy dominates AG at high temperature, and the formation of the less constrained phase is spontaneous. At one characteristic temperature, A G = 0, and the phase change proceeds in both directions at the same rate. The two phases coexist, and the system is in a state of d Tiamic equilibrium. 

Extreme cases were reactions of the least stabilized, most reactive carbene (Y = CF3, X = Br) with the more reactive alkene (CH3)2C=C(CH3)2, and the most stabilized, least reactive carbene (Y = CH3O, X = F) with the less reactive alkene (1-hexene). The rate constants, as measured by LFP, were 1.7 x 10 and 5.0 X lO M s, respectively, spanning an interval of 34,000. In agreement with Houk s ideas,the reactions were entropy dominated (A5 —22 to —29e.u.). The AG barriers were 5.0 kcal/mol for the faster reaction and 11 kcal/ mol for the slower reaction, mainly because of entropic contributions the AH components were only —1.6 and +2.5 kcal/mol, respectively. Despite the dominance of entropy in these reactive carbene addition reactions, a kind of de facto enthalpic control operates. The entropies of activation are all very similar, so that in any comparison of the reactivities of alkene pairs (i.e., ferei)> the rate constant ratios reflect differences in AA//t, which ultimately appear in AAG. Thus, car-benic philicity, which is the pattern created by carbenic reactivity, behaves in accord with our qualitative ideas about structure-reactivity relations, as modulated by substiment effects in both the carbene and alkene partners of the addition reactions. " Finally, volumes of activation were measured for the additions of CgHsCCl to (CH3)2C=C(CH3)2 and frani-pentene in both methylcyclohexane and acetonitrile. The measured absolute rate constants increased with increasing pressure Ayf ranged from —10 to —18 cm /mol and were independent of solvent. These results were consistent with an early, and not very polar transition state for the addition reaction. 

This explanation for the entropy-dominated association of surfactant molecules is called the hydrophobic effect or, less precisely, hydrophobic bonding. Note that relatively little is said of any direct affinity between the associating species. It is more accurate to say that they are expelled from the water and —as far as the water is concerned —the effect is primarily entropic. The same hydrophobic effect is responsible for the adsorption behavior of amphi-pathic molecules and plays an important role in stabilizing a variety of other structures formed by surfactants in aqueous solutions. 

Since the contribution in Eq. (6.6) is purely entropical (and large) it follows the Ge is entropy dominated. Secondly He has a different sign than one would expect intuitively. Since at 298 K, er + T — —26 the enthalpy, according to the model,... 

Entropy dominates equilibrium constants in the difference between inter- and intramolecular reactions. In Chapter 6 we explained that hcmiacetal formation is unfavourable because the C=0 double bond is more stable than two C-0 single bonds. This is clearly an enthalpy factor depending simply on bond strength. That entropy also plays a part can be clearly seen in favourable intramolecular hemiacetal formation of hydroxyaldehydes. The total number of carbon atoms in the two systems is the same, the bond strengths are the same and yet the equilibria favour the reagents (MeCHO + EtOH) in the inter- and the product (the cyclic hemiacetal) in the intramolecular case. 

NP/NP mixtures (the open circles on Fig. 16.5) tend to concentrate in Regions I and VI for such mixtures, H and are normally positive. When is positive (enthalpy domination), G /RT rarely exceeds about 0.2. If is negative (entropy domination), G / RT is rarely less than —0.2. 

Chemielowiec, J. Sawatzky, H. Entropy dominated high performance liquid chromatographic separations of polynuclear aromatic hydrocarbons. Temperature as a separation parameter. J. Chromatogr. Sci. 1979, 17, 245. 

At high temperatures the influence of reaction entropy dominates ... 

Figures 15.1b and c illustrate the two opposite cases where either enthalpy or entropy dominates the free energy function. The most difficult situation is that shown in Figure 15. Id, where entropy and enthalpy approximately balance each other. This produces a peculiar double-humped free energy curve as illustrated. Here the total free energy of the system is always lower than that of a mechanical mixture of the two pure end-members. However, this time there cannot be a complete solid solution from pure A to pure B as in the previous case. This is because we can draw a tangent (abed on the figure) that touches the free energy curve at two points (b and c). This means that two phases can coexist (having compositions and X ) in which the chemical potentials of each component are the same. That is, the chemical potential of A in both phases is given by the intercept a, and the chemical potential of B in both phases is given by the intercept at d.

In addition, the effect of temperature on column efficiency, is now being frequently exploited, particularly in size exclusion chromatography (SEC) and in other separations where the standard free entropy dominates the separation (i.e. all chiral separations and the separation of all closely eluting isomers). 

Macromolecular desorption from a surface As briefly described above, in this situation we are applying a force perpendicular to an adsorbing surface to which a polymer chain is attached. At low temperature, surface attraction dominates, but at high temperatures entropy dominates, and the polymer is free of the surface. The temperature dependent force needed to extend the polymer is calculated. Let the polymer have N monomers, of which n lie in the surface. (In two dimensions the surface is a line). Let CN n, z) be the number of such SAW whose endpoint is at perpendicular distance from the surface. The model may be described by the partition function... 

We usually assume that the intermediate is a minimum on an enthalpy surface, but that need not be the case. Tetramethylene has been reported to be an intermediate without an enthalpy minimum because it occurs in an "entropy dominated free energy minimum." Doubleday, C., Jr. Camp. R. N. King, H. F. Mclver, J. W. MullaUy, D. Page, M. /. Am. Chem. Soc. 1984,106,447 Doubleday, C., Jr. /. Am. Chem. Soc. 1993,115,11968. 

If AH and AS are both positive, then AG will be positive at low temperatures (where enthalpy dominates) and become negative at high temperatures (where entropy dominates). The temperature at which AG crosses over from positive to negative (that is, when AH = T AS) depends upon the relative magnitudes of... 

---