Entropy dissociation

Conformational Adjustments The conformations of protein and ligand in the free state may differ from those in the complex. The conformation in the complex may be different from the most stable conformation in solution, and/or a broader range of conformations may be sampled in solution than in the complex. In the former case, the required adjustment raises the energy, in the latter it lowers the entropy in either case this effect favors the dissociated state (although exceptional instances in which the flexibility increases as a result of complex formation seem possible). With current models based on two-body potentials (but not with force fields based on polarizable atoms, currently under development), separate intra-molecular energies of protein and ligand in the complex are, in fact, definable. However, it is impossible to assign separate entropies to the two parts of the complex. 

An alternative approach is to assume, in the light of the experimental evidence just mentioned, that the reactions of cations and neutral molecules have similar values of (or, equivalently, of log ( /l mol and to try to calculate the difference which would arise from the fact that the observed entropy of activation for a minority free base includes a contribution from the acidic dissociation of the conjugate acid in the medium in question (see (5) above). Consider the two following reaction schemes one (primed symbols) represents nitration via the free base, the other the normal nitration of a non-basic majority species (unprimed symbols) ... 

In a parallel study Goursot and Wadso (322) determined calorimetri-cally the free energies, enthalpies, and entropies of dissociation of the conjugate acids of thiazoles in aqueous media (Table 1-51). 

Bond dissociation energies (BDEs) for the oxygen—oxygen and oxygen— hydrogen bonds are 167—184 kj/mol (40.0—44.0 kcal/mol) and 375 kj/mol (89.6 kcal/mol), respectively (10,45). Heats of formation, entropies, andheat capacities of hydroperoxides have been summarized (9). Hydroperoxides exist as hydrogen-bonded dimers in nonpolar solvents and readily form hydrogen-bonded associations with ethers, alcohols, amines, ketones, sulfoxides, and carboxyhc acids (46). Other physical properties of hydroperoxides have been reported (46). 

In these examples tire entropy change does not vaty widely, and the value of the equilibrium constant is mainly determined by the heat of dissociation. It can be concluded, tlrerefore, that niuogen is one of the most stable diatomic molecules, and tlrat chlorine is tire most stable diatomic halogen molecule. 

The standard entropy change for the atom-molecule reactions is in the range 5-20 mole and the halogen molecule dissociation has an eiiU opy change of about 105 e.u. The halogen molecule dissociation energy decreases from chlorine to iodine, but the atom-molecule reactions become more endothermic from chlorine to iodine, and this latter effect probably influences the relative contributions to the mechanism from chain reaction and biinolecular reaction. 

AH and AS to various notional subprocesses such as bond dissociation energies, ionization energies, electron affinities, heats and entropies of hydration, etc., which themselves have empirically observed values that are difficult to compute ab initio. 

The ease of dissociation of the X2 molecules follows closely the values of the enthalpy of dissociation since the entropy change for the reaction is almost independent of X. Thus F2 at 1 atm pressure is 1% dissociated into atoms at 765°C but a temperature of 975°C is required to achieve the same degree of dissociation for CI2 thereafter, the required temperature drops to 775°C for Br2 and 575°C for I2 (see also next section for atomic halogens). 

Consider 1 mole of a completely dissociated uni-univalent solute in aqueous solution at extreme dilution at 25°C, each positive and each negative ion having a diameter equal to 3.0 angstroms. Find from (19), in calories per mole per degree, what would be the total amount of entropy lost by the solvent in the fields of all these ions, if (19) could correctly be used for a sphere as small as 3 angstroms. 

The entropy of the (OH)- ion may be obtained from the value of AS° for the self-dissociation of water. Whether this process is written in the form... 

Gas, cells, 464, 477, 511 characteristic equation, 131, 239 constant, 133, 134 density, 133 entropy, 149 equilibrium, 324, 353, 355, 497 free energy, 151 ideal, 135, 139, 145 inert, 326 kinetic theory 515 mixtures, 263, 325 molecular weight, 157 potential, 151 temperature, 140 velocity of sound in, 146 Generalised co-ordinates, 107 Gibbs s adsorption formula, 436 criteria of equilibrium and stability, 93, 101 dissociation formula, 340, 499 Helmholtz equation, 456, 460, 476 Kono-walow rule, 384, 416 model, 240 paradox, 274 phase rule, 169, 388 theorem, 220. Graetz vapour-pressure equation, 191... 

Baechler and coworkers204, have also studied the kinetics of the thermal isomerization of allylic sulfoxides and suggested a dissociative free radical mechanism. This process, depicted in equation 58, would account for the positive activation entropy, dramatic rate acceleration upon substitution at the a-allylic position, and relative insensitivity to changes in solvent polarity. Such a homolytic dissociative recombination process is also compatible with a similar study by Kwart and Benko204b employing heavy-atom kinetic isotope effects. 

From such crude data as are to be found in the literature we can calculate approximate values of the equilibrium constants, and hence of the free energies of dissociation for the various hexaarylethanes. From our quantum-mechanical treatment, on the other hand, we obtain only the heats of dissociation, for which, except in the single case of hexaphenylethane, we have no experimental data. Thus, in order that we may compare our results with those of experiment, we must make the plausible assumption that the entropies of dissociation vary only slightly from ethane to ethane. Then at a given temperature the heats of dissociation run parallel to the free energies and can be used instead of the latter in predicting the relative degrees of dissociation of the different molecules. 

NMR line broadening is a suitable kinetic method for determining activation parameters for Co—C bond homolysis, and gave A//- values in the range 18-22.5 keal mol for a selection of Co(Por)R complexes containing secondary or tertiary alkyl groups.Bond dissociation enthalpies and entropies for several... 

As regards enthalpy of dissociation A//het(R-R ) and entropy of dissociation A5het(R-R )> only a few data are available (Table 4). Bordwell (1988 ... 

Table 4 Enthalpy and entropy of dissociation for some hydrocarbons in DMSO.

Formation of the three-member ring has a higher barrier but its entropy is higher due to the remaining CO rotor. Decomposition of the three-member ring via pathway D leads to HC 02 + C O, followed by dissociation of leading to the hnal products H + C 02 + C O. 

Of course, the converse situation, in which the entropy of the transition state is lower than that of the ground state of the reactant, can also occur (Fig. 3.11). In this case, one speaks of a tight transition state tight, because rotations, vibration or motion of the activated complex are more restricted than in the ground state of the reactant. The dissociation of molecules on a surface provides an example that we shall discuss in the next section. 

Clearly, the sticking coefficient for the direct adsorption process is small since a considerable amount of entropy is lost when the molecule is frozen in on an adsorption site. In fact, adsorption of most molecules occurs via a mobile precursor state. Nevertheless, direct adsorption does occur, but it is usually coupled with the activated dissociation of a highly stable molecule. An example is the dissociative adsorption of CH4, with sticking coefScients of the order 10 -10 . In this case the sticking coefficient not only contains the partition functions but also an exponential... 

Usually, activation energies for dissociation are much higher than k T and situations like this, where the apparent activation energy becomes negative for the rate-limiting process, are rare. Nevertheless, the present case illustrates nicely that entropy changes may play an important role and that it is not always the activation energy that dominates the process. 

The simplest overall interpretation of these data is in terms of a rate-determining dissociation. Entropies of activation are positive and the solvent-dependence for a better leaving group (Cl) is less marked than for a worse one (Br) in the case of reaction (38) . For the dimeric carbonyls, [M(CO)4X]2, bridge-breaking, essentially the same dissociation, could result in a rapid pre-equilibrium. If this were followed by a second dissociative step, then the kinetics could be first-order (as for Mn), while a rate-determining entry of L could produce second-order kinetics (as for Re). 

More recently, a number of reports dealing with 1,3-sulfonyl shifts which proceed by other mechanisms have been published. For example, Baechler and coworkers suggested that the higher activation enthalpy observed for the isomerization of the deuterium labeled methallyl sulfone 72 in nitrobenzene at 150°C as compared to the corresponding sulfide, together with the positive entropy of activation may be taken as evidence for a homolytic dissociation mechanism (equation 44). A similar mechanism has also been suggested by Little and coworkers for the gas-phase thermal rearrangement of deuterium labelled allyl sec-butyl sulfone, which precedes its pyrolysis to alkene and sulfur dioxide. 

A high reaction entropy increase influences the reaction temperature of the thermochemical dissociation equilibrium. Assuming that the reaction enthalpy and the reaction entropy have no significant temperature dependence, this simplified equation can be derived. 

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