Quantitative treatments of rates and equilibria

Micellar effects upon reaction rates and equilibria have generally been discussed in terms of a pseudophase model, and this approach will be followed here. 

Provided that equilibrium is maintained between the aqueous and micellar pseudophases (designated by subscripts W and M) the overall reaction rate will be the sum of rates in water and the micelles and will therefore depend upon the distribution of reactants between each pseudophase and the appropriate rate constants in the two pseudophases. Early studies of reactivity in aqueous micelles showed the importance of substrate hydrophobicity in determining the extent of substrate binding to micelles for example, reactions of a very hydrophilic substrate could be essentially unaffected by added surfactant, whereas large effects were observed with chemically similar, but hydrophobic substrates (Menger and Portnoy, 1967 Cordes and Gitler, 1973 Fendler and Fendler, 1975). 

Ester saponifaction was a favoured reaction for this type of study, because the hydrophobicity of the acyl moiety could easily be controlled by increasing the length of an n-alkyl group, and saponification of p-nitrophenyl n-alkanoates could be followed with very dilute substrate. Substrate concentration is an important factor, because provided that it is kept low it is reasonable to assume that the micelle structure is relatively unperturbed. 

Menger and Portnoy (1967) developed a quantitative treatment which adequately described inhibition of ester saponification by anionic micelles. Micelles bound hydrophobic esters, and anionic micelles excluded hydroxide ion, and so inhibited the reaction, whereas cationic micelles speeded saponification by attracting hydroxide ion (Menger, 1979b). 

The concentration of micellized surfactant is that of total surfactant less that of monomer which is assumed to be given by the critical micelle concentration (cmc). The overall first-order rate constant is then given by (1). 

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This section is concerned with the quantitative correlation of reaction rates and equilibria of organic reactions with the structure of the reactants. We will restrict the discussion to benzene derivatives. The focus is on a remarkably simple treatment developed by L. P. Hammett in 1935, which has been tremendously influential. Hammett s correlation covers chemical reactivity, spectroscopy and other physical properties, and even the biological activity of drugs. Virtually all quantitative treatments of reactivity of organic compounds in solution start with the kinds of correlations that are discussed in this section. 

There has been a decisive evolution in the treatment of steric effects in heteroaromatic chemistry. The quantitative estimation of the role of steric strain in reactivity was first made mostly with the help of linear free energy relationships. This method remains easy and helpful, but the basic observation is that the description of a substituent by only one parameter, whatever its empirical or geometrical origin, will describe the total bulk of the substituent and not its conformationally dependent shape. A better knowledge of static and dynamic stereochemistry has helped greatly in understanding not only intramolecular but also intermolecular steric effects associated with rates and equilibria. Quantum and molecular mechanics calculations will certainly be used in the future to a greater extent. 

The quantitative treatment of mass transfer is based on material and energy balances, equilibria, and rates of heat and mass transfer. Certain concepts applicable generally are discussed here. The individual operations are discussed in the following chapters. 

Quantitative treatments of micellar rate effects in aqueous solution The development of quantitative models of micellar effects upon reaction rates and equilibria was based on the concept that normal micelles in aqueous, or similar associated, solvents behave as a separate medium from the body of the solvent. 

We have seen numerous examples of substituent effects on rates and equilibria of organic reactions and have developed a qualitative feel for various groups as electron-donating or electron-withdrawing. Beginning in the 1930s, Lewis P. Hammett of Columbia University developed a quantitative treatment of substituent effects represented in the equations ... 

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, "... 

Examples of reactions in which acid-base catalysed dehydration was combined with acid-base equilibria either preceding or subsequent to the dehydration process are quoted for the waves of pyridine aldehydes (Tirouflet and Laviron, 1959 Volke, 1958 ManouSek and Zuman, 1964) and of glyoxalic acid (Kuta, 1959). Different dehydration rates were found for pyridinium ions and free pyridine derivatives, as well as for the free glyoxalic acid and its anion. For numerous aldehydic substances the effect of hydration has been observed but a quantitative treatment has not yet been applied. 

Marcia-Rio et al. used this W/O AOT microemulsion as the medium for nitroso transfer to secondary amines from A-methyl-/V-nitroso-/ -toluenesulfonamide (8). Their quantitative treatment, which includes consideration of reactant solubilities, shows that reaction occurs at the microemulsion interface, where it is slower than in water. This rate difference is understandable on the very reasonable assumption that the polarity of the microemulsion interface is lower than that of water [99-101]. These kinetic data indicate that the interfacial regions of the water pool microdroplets in O/W microemulsions and reverse micelles can be regarded as reaction media corresponding to descriptions applied to normal aqueous association colloids. This concept has also been applied to acid-base equilibria, especially by El Seoud and his group [112,116,117]. 

Effects of association colloids on rates of reactions that are slow relative to diffusion are understandable on the assumption that these colloidal aggregates provide reaction media distinct from bulk solvent. Rate constants depend on the transfer equilibria and the individual rate constants in the colloidal aggregates and in bulk solvent. The quantitative treatments developed for reactions mediated by aqueous micelles are applicable to other association colloids including microemulsions. The phase volumes provided by O/W microemulsions contain contributions of surfactant, cosurfactant, and oil and are typically much larger than those provided by aqueous micelles. Bimolecular reactions in O/W... 

The dinuclear Sr complex of the ditopic ligand 17 increases the rate of basic ethanolysis ofthe malonate derivative 19 by a surprising 5700-fold, but increases by only 9.5-fold the rate of cleavage of 14 [28]. It is remarkable that such a huge rate-enhancement occurs under extremely dilute conditions, namely 15 pM 19 and 30 pM 17-Sr2. A slightly lower rate enhancement is observed in the presence of 17-Ba2. It seems likely that under the dilute conditions of the catalytic experiments several crown-complexed metal species occur simultaneously (Scheme 5.4). Given the plethora of species involved in such a complicated system of multiple equilibria, quantitative kinetic treatment is out of reach. Nevertheless, a comparison with the reactivity of model compounds, particularly that of the malonate derivative 20, provides insight into the composition of the reactive intermediate (Table 5.8),... 

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