Entropic component

The natiue of the rate constants k, can be discussed in terms of transition-state theory. This is a general theory for analyzing the energetic and entropic components of a reaction process. In transition-state theory, a reaction is assumed to involve the formation of an activated complex that goes on to product at an extremely rapid rate. The rate of deconposition of the activated con lex has been calculated from the assumptions of the theory to be 6 x 10 s at room temperature and is given by the expression ... 

Examples of entropically driven separations are chiral separations and separations that are dominated by size exclusion. However, it must be emphasized that chromatographic separations can not be exclusively "energetically driven" or "entropically driven" but will always contain both components. It is by the careful adjustment of both "energetic" and "entropic" components of the distribution that very difficult and subtle separations can be accomplished. 

Hence the reduction in entropy (A5 > that results from loss of rotational and translational freedom leads to a more positive (unfavorable) value of AG. The enthaplic and entropic components of AGto, and AG, st can be determined from the temperature dependence of kcM and of kcJKs, respectively, from the Arrhenius equation... 

Where Kb is the experimental binding constant, R is the gas constant and T is the temperature. The free energy has an enthalpic and entropic component. 

The net free energy is, in the end, the thermodynamic quantity that dictates molecular behavior. However, to understand why the free energy profile for a system looks as it does, it is valuable to also determine the potential and entropic components of the net free energy ... 

Unfortunately, it is significantly more difficult to determine the component potential and entropic components of the total free energy, than it is to calculate the free energy itself. Equations that allow the entropy difference (and hence enthalpy difference via Equation 13) to be calculated at the same time we are determining the free energy have been reported. For example, for TI, the following expression can be used 9... 

The values of 0(ASD) /2.3O3 R listed in Table 5 are the entropic components of log EM. These are the log EM- alues for ideal strainless cyclisation reactions, i.e. reactions where 0AH° = 0. It is of interest to note that, as far as the entropic component is concerned, symmetry corrected effective molarities on the order of 102 106M are found. This observation leads to the important conclusion that cyclisation reactions of chains up to about 7 skeletal bonds are entropically favoured over reactions between non-connected 1 M end-groups. The intercept of 33 e.u. corresponds to an effective molarity of exp(33/R) or 107 2M, which may be taken as a representative value for the maximum advantage due to proximity of end-groups in intramolecular equilibrium reactions. It compares well with the maximum EM of about 108M estimated by Page and Jencks (1971). 

For convenience the averaged 0AS-data are tabulated (Table 19) together with the corresponding entropic components of the EM. The latter are the ideal EM-values predicted for a cyclisation reaction for which the strain is unimportant for all of the terms of the series. They can be read directly from the right-hand ordinate in Fig. 23. 

The tight and loose transition-state hypothesis is in contrast with the assumption that there is extensive cancellation of contributions due to chemical change in the entropic component of the EM (p. 81). Indeed, the uniform behaviours displayed by 0AS-data for reactions widely differing in nature (Figs 5, 23, and 24) clearly shows that no matter how loose a transition state or product is, the entropy contribution from such looseness will be cancelled out extensively by virtue of the operator 0. 

The extent of equilibrium adsorption of a given chain, thus, would depend on the counteraction between the three enthalpic and entropic components, plus the negative entropic contribution of the chain restraint. The rate of adsorption should be fairly fast, in fact, accelerated after the first segment was held, while the rate of desorption requiring simultaneous multiple desorption steps should be very slow, so slow indeed as to be barely measurable except when assisted by a displacing species. 

In addition, temperature derivatives of kcorr can be measured which allows the enthalpic and entropic components of AG ... 

Enthalpic and entropic components of nucleosome core particle (NCP) free energies [277]... 

The partitioning of free energy contributions in the explanation (and for design, the prediction) of binding constants is a subjective matter. Different workers choose different definitions, e.g. of hydrophobic binding, which may or may not include dispersion interaction, and different approaches to factorization of enthalpic and entropic components. 

The usual starting point for empirical solution models is separation of enthalpic and entropic components of G ... 

Equation (8.21) indicates the central importance of the standard Gibbs free energy difference AG° of unmixed product and reactant species at standard state conditions. As usual, this quantity can be separated into enthalpic and entropic components ... 

Equation (43) includes temperature dependent contributions from both KA and fcet. AHa and A5a are the enthalpy and entropy changes associated with the pre-association step and AH and AS are the enthalpic and entropic components of AG. ... 

For non-flexible organic compounds, only the first three entropic components must be considered. From Equation (9), the expansional entropy can be expressed as a ratio of the free volumes (Vf) to which the molecules in the solid and liquid phases have access ... 

The stronger excitonic interaction in EB assemblies than that of ACR or AMAC is apparently due to a greater hydrophobic surface area of the former, as estimated from computer modeling studies (MacSpartan). Such increased hydrophobic surface is not expected from their structures (three six-membered ring systems) it also results in an enhanced entropic contribution to the binding energy when the probe is transferred from the aqueous phase to the interior of BAZrP, where there is little or no water. Therefore, the formation of these supramolecular assemblies may indeed involve a large entropic component, but this needs to be demonstrated experimentally. 

Hydrophobic binding. The hydrophobic effect can have both enthalpic and entropic components, although the classical hydrophobic effect is entropic in origin (Section 1.9.1). Studies on the associations between planar aromatic molecules show an approximately linear relationship between the interaction energy and their mutual contact surface area with slope 64 dyn cm-1, very close to the macroscopic surface tension of water (72 dyn cm-1). Hence, in the absence of specific host or guest interactions with the solvent the hydrophobic effect can be calculated solely from the energy required to create a free surface of 1 A2 which amounts to 7.2 X 10 12 J or 0.43 kjA 2 mol. ... 

Thermodynamic factors can be divided into enthalpic and entropic components. The difference between five- and six-membered rings is shown in the formation of lactones 16 and 18 from hydroxyacids 15 and 17. Enthalpy favours the six-membered ring as the transition state is more stable but entropy favours the five-membered ring as there is a higher chance that 15 will be in a favourable conformation for cyclisation. 

It can be anticipated that the computation of A//soi and AAsoi is more delicate than the prediction of AGsoi, which benefits from the enthalpy-entropy compensation. Accordingly, the suitability of the QM-SCRF models to predict the enthalpic and entropic components of the free energy of solvation is a challenging issue, which could serve to refine current solvation continuum models. This contribution reports the results obtained in the framework of the MST solvation model [15] to estimate the enthalpy (and entropy) of hydration for a set of neutral compounds. To this end, we will first describe the formalism used to determine the MST solvation free energy and its enthalpic component. Then, solvation free energies and enthalpies for a series of typical neutral solutes will be presented and analyzed in light of the available experimental data. Finally, collected data will be used to discuss the differential trends of the solvation in water. 

Table 4-3. Enthalpic and entropic components of the electrostatic and non-electrostatic terms of the hydration free energy (kcal/mol). The non-electrostatic enthalpy and entropy were determined by subtracting the electrostatic enthalpy and entropy from the corresponding experimental data...

Finally, present results suggest that calibration of solvation models by using not only solvation free energies, but also their enthalpic and entropic components would yield to better balanced and more accurate models, which will be extremely useful to provide a more comprehensive understanding of the forces that mediate the solvation of solutes in diverse solvents. 

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