Solvent Effects on Equilibria

Solvent effects on enzymatic reactions have been most thoroughly studied for esterification reactions. It has been observed that those reactions are favorably carried out in relatively hydrophobic solvents, while the equilibrium position is less favorable for esterification in more hydrophilic solvents. Correlations between equilibrium constants and solvent parameters have been evaluated. It was shown that the solubility of water in the solvent (Sw/0) gave better correlation with esterification equilibrium constants than log P and other simple solvent descriptors [61]. 

Solvent effects on esterification equilibria have also been described using UNIFAC calculations of activity coefficients. This method was claimed to give 

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Bone, R. Cullis, R Wolfenden, R. Solvent effects on equilibria of addition of nncleophiles to acetaldehyde and the hydrophilic character of diols.. J. Am. Chem. Soc. 1983,105, 1339-1343. 

Below, solvent effects on activity and stability of enzymes will be discussed, while solvent effects on enzyme selectivity is a large topic which is treated in a separate chapter. Solvent effects on equilibria are treated in Section 1.4. 

Equation (35) is an example of a multiparametric equation17 18 64 for describing solvent effects on equilibria and is similar to the multiparametric equations used to describe solvent effects on rates. The use of these equations in describing solvent effects on equilibria involving coordination compounds is, like their application to reaction rates of coordination compounds, not common. Equilibrium (36), where L, U and X are the same as in reaction (12),... 

In studying solvent effects on equilibria, it is, in principle, not sufficient to investigate the AG° changes alone, because this term is determined by both an enthalpy and an entropy term according to Eq. (4-4). 

These same equations formally bring the quantitative study of solvent effects on equilibria and rates of elementary processes to that of solvent effects on the chemical potentials of the dissolved species or, in other words, to that of the energetics of solvent-solute interactions. In the forthcoming section, we restrict ourselves to the study of polar species (excluding free ions ) in polar... 

Insertion of the expression of the chemical potential given by Equation 14 into Equation 5 yields, in principle, the value of the electrostatic contribution to the solvent effect on equilibria. 

Solvent effects on chemical equilibria and reactions have been an important issue in physical organic chemistry. Several empirical relationships have been proposed to characterize systematically the various types of properties in protic and aprotic solvents. One of the simplest models is the continuum reaction field characterized by the dielectric constant, e, of the solvent, which is still widely used. Taft and coworkers [30] presented more sophisticated solvent parameters that can take solute-solvent hydrogen bonding and polarity into account. Although this parameter has been successfully applied to rationalize experimentally observed solvent effects, it seems still far from satisfactory to interpret solvent effects on the basis of microscopic infomation of the solute-solvent interaction and solvation free energy. 

Among many examples of the solvent effects on chemical equilibria and reactions, the solvent effect on tautomerization has been one of the most extensively studied. Experi-... 

We now consider a type of analysis in which the data (which may consist of solvent properties or of solvent effects on rates, equilibria, and spectra) again are expressed as a linear combination of products as in Eq. (8-81), but now the statistical treatment yields estimates of both a, and jc,. This method is called principal component analysis or factor analysis. A key difference between multiple linear regression analysis and principal component analysis (in the chemical setting) is that regression analysis adopts chemical models a priori, whereas in factor analysis the chemical significance of the factors emerges (if desired) as a result of the analysis. We will not explore the statistical procedure, but will cite some results. We have already encountered examples in Section 8.2 on the classification of solvents and in the present section in the form of the Swain et al. treatment leading to Eq. (8-74). 

Conformational Equilibria. The solvent effect on the conformational equilibria represents a typical problem studied using the DFT/SCRF methods. The presence of the environment may affect the free energy of a given conformer, its equilibrium conformation or even destabilize a particular conformation. The DFT/SCRF calculations have been applied to study such effects using various KS methods as well as different techniques for calculating [Pg.112]

Foresman et al.175 applied the DFT(B3LYP)/SCRF calculations to obtain the polar solvent effect on conformational equilibria in furfuraldehyde and on the C-C rotational barrier of (2-nitrovinyl)amine. The authors demonstrated that the poor results obtained using either spherical or ellipsoidal cavities can be significantly improved upon performing the SCRF calculations for the cavity of molecular shape. 

Applications to solvent effects on organic equilibria and reactions, J. Phys. Chem. B 102 1787(1998). 

Like reaction rates, the effect of solvent polarity on equilibria may be rationalized by consideration of the relative polarities of the species on each side of the equilibrium. A polar solvent will therefore favour polar species. A good example is the keto-enol tautomerization of ethyl acetoacetate, in which the 1,3-dicarbonyl, or keto, form is more polar than the enol form, which is stabilized by an intramolecular H-bond. The equilibrium is shown in Scheme 1.3. In cyclohexane, the enol form is slightly more abundant. Increasing the polarity of the solvent moves the equilibrium towards the keto form [28], In this example, H-bonding solvents will compete with the intramolecular H-bond, destabilizing the enol form of the compound. 

The second important solvent effect on Lewis acid-Lewis base equilibria concerns the interactions with the Lewis base. Since water is also a good electron-pair acceptor129, Lewis-type interactions are competitive. This often seriously hampers the efficiency of Lewis acid catalysis in water. Thirdly, the intermolecular association of a solvent affects the Lewis acid-base equilibrium242. Upon complexation, one or more solvent molecules that were initially coordinated to the Lewis acid or the Lewis base are liberated into the bulk liquid phase, which is an entropically favourable process. This effect is more pronounced in aprotic than in protic solvents which usually have higher cohesive energy densities. The unfavourable entropy changes in protic solvents are somewhat counterbalanced by the formation of new hydrogen bonds in the bulk liquid. 

In 1976, Kamlet and Taft introduced their solvatochromic comparison method [25, 26], The hydrogen-bond donor acidity a and basicity /3 together with the solvent polarity and polarizability jv were employed to correlate the solvent effects on reaction rates, equilibria, and spectroscopic properties XYZ according to equations of the form... 

For a complete quantitative description of the solvent effects on the properties of the distinct diastereoisomers of dendrimers 5 (G = 1) and 6 (G = 1), a multiparameter treatment was used. The reason for using such a treatment is the observation that solute/solvent interactions, responsible for the solvent influence on a given process—such as equilibria, interconversion rates, spectroscopic absorptions, etc.—are caused by a multitude of nonspecific (ion/dipole, dipole/dipole, dipole/induced dipole, instantaneous dipole/induced dipole) and specific (hydrogen bonding, electron pair donor/acceptor, and chaige transfer interactions) intermolecular forces between the solute and solvent molecules. It is then possible to develop individual empirical parameters for each of these distinct and independent interaction mechanisms and combine them into a multiparameter equation such as Eq. 2, "... 

Thermodynamic Equilibrium, Kinetics, Activation Barriers, and Reaction Mechanisms for Chemical Reactions in Karst Terrains (White, 1997) Solvent Effects On Isomerization Equilibria—an Energetic Analysis in the Framework of Density Functional Theory (Lelj and Adamo, 1995)... 

Contemporary computer-assisted molecular simulation methods and modern computer technology has contributed to the actual numerical calculation of solvent effects on chemical reactions and molecular equilibria. Classical statistical mechanics and quantum mechanics are basic pillars on which practical approaches are based. On top of these, numerical methods borrowed from different fields of physics and engineering and computer graphics techniques have been integrated into computer programs running in graphics workstations and modem supercomputers (Zhao et al., 2000). 

Comparison of Ionic Solvation Energies in Different Solvents and Solvent Effects on Ionic Reactions and Equilibria... 

We can use the transfer activity coefficients to predict solvent effects on chemical reactions and equilibria [22]. Some examples are shown below. 

The use of the Gutmann41 donor and acceptor numbers for describing solvent effects on rates, equilibria and other physicochemical properties has met with some success in organic chemistry. 62 63 However, because the donor and acceptor numbers of mixtures of solvents can not be inferred from the values of the pure solvents but must be determined experimentally, and also because the relationships describing the effects of solvent on chemical reactions were found to apply to non-associated solvents of medium to high dielectric constant, there has been very little attempt to introduce this approach into inorganic systems where the commonly used solvents are protic, i.e. associated. However, one such reaction that has been studied was63 equation (34) ... 

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