Koppel-Palm equation

According to the Lorentz-Lorenz equation (4.3.21) for the molar refraction at optical frequencies, Y is directly proportional to the molecular polarizability p. The Koppel-Palm equation has also been applied to the analysis of solvent effects on thermodynamic quantities related to the solvation of electrolytes [48, 49]. In the case of the systems considered in table 4.11, addition of the parameter X to the linear equation describing the solvent effect improves the quality of the fit to the experimental data, especially in the case of alkali metal halide electrolytes involving larger ions. The parameter Y is not important for these systems but does assist in the interpretation of other thermodynamic quantities which are solvent dependent [48, 49]. Addition of these parameters to the analysis is only possible when the solvent-dependent phenomenon has been studied in a large number of solvents. 

In an analysis of the solvolysis of tert-butyl chloride in terms of equation 3, Abraham et al. (9) found that the specific rates could be correlated against tt and a, without the need to include a term relating to basicity (P) values. However, a new analysis with inclusion of the cavity term has indicated (II) a minor contribution from the fop term. Conversely, an analysis (12) in terms of the Koppel-Palm equation, with inclusion of a cavity term, did not find any dependence on nucleophilicity (basicity). 

It was determined by us at the attempts to describe the gasses dissolving processes into liquids with the use of the equation (5) that to obtain of satisfactory results the Koppell Palm .s equation should be expanded by fifth term, which takes into account the density of the... 

Recently the data concerning to interaction of propanthiole with chlorine dioxide in 8 solvents have been published [1], In this work it was shown, that the dependence of process rate from solvents properties is satisfactory described for seven solvents, after the exclusion of data for ethyl acetate, by the Koppel-Palm four parameters equation (coefficient of multiple correlation R 0,96) at determining role of medium polarity (coefficient of pair correlation between lg(k) and (s - l)/(2e + 1) - r 0.90). Chemical mechanism of the reaction including the formation of ion-radical RS H and radical RS has been proposed by authors [ ] ... 

Correlation analysis of solvent effects on the heterolysis of p-methoxyneophyl tosyl-ate has been performed by using the Koppel-Palm and Kamlet-Taft equations. The reaction rate is satisfactorily described by the electrophilicity and polarity parameters of solvents, but a possible role for polarizability or nucleophilicity parameters was also examined. 

Equations containing a number of solvent parameters in linear or multiple linear regression and expressing the effect of the solvent on the rate of the reaction or the thermodynamic equilibrium constant. See Ej Values Kamlet-Taft Solvent Parameter Koppel-Palm Solvent Parameter Z Value... 

ENZYME KINETIC EQUATIONS MICHAELIS CONSTANT UNI UNI MECHANISM Koppel-Palm solvent parameters,... 

GRUNWALD-WlNSTEIN EQUATION KAMLET-TAFT SOLVENT PARAMETERS KOPPEL-PALM SOLVENT PARAMETERS SOLVOPHOBICITY PARAMETER Z-VALUE. 

The Swain Equation (34) provides very accurate predictive power for a limited range of solvents and processes based on a statistical analysis of a five-parameter equation. The origins of the Swain parameters are not explicit, although the acity (A) and basity (B) coefficients are related to electrophilic and nucleophilic processes respectively. Many fundamental processes have been implicated in solvent effects and the equation of Koppel and Palm (Equation 37) incorporates the major factors thought to be involved. 

Krygowski and Fawcett described the variation of the physico-chemical parameter g, reflecting the solvent effect, in an analogous manner to that in the first half of the equation of the Koppel-Palm model, but as a linear function of only two independent complementary terms ... 

With taken into account, that the constants of the reaction rates are determined via the equilibrium constants of the activated reactive complex formation, and the last in part depend on the solvation processes, it was proposed by Koppell and Palm [22] the following equation in order to determine the influence of medium properties on the reaction rates of processes proceeding in it ... 

Palm s group has continued to develop statistical procedures for treating solvent effects. In a previous paper, a set of nine basic solvent parameter scales was proposed. Six of them were then purifled via subtraction of contributions dependent on other scales. This set of solvent parameters has now been applied to an extended compilation of experimental data for solvent effects on individual processes. Overall, the new procedure gives a signiflcantly better flt than the well-known equations of Kamlet, Abboud, and Taft, or Koppel and Palm. 

Use of the Palm-Koppel equation (72MI1 77MI1 88MI1) led to a good correlation (r = 0.986) (91ZPK1052) between the constants of the ring-chain equilibrium 13A 13B (X = H) measured ( H-NMR) in ten deuter-ated solvents and the sum of solvent polarity, polarizability, general acidity,... 

A more rigorous approach has been suggested by Koppel and Palm [6, 112], who argue that a complete description of all solute/solvent interactions must include both non-specific and specific effects. They proposed the general four-parameter equation (7-50), which relates the variation of a given property A to two non-specific (T and P) and two specific characteristics of the solvent E and B). 

Another important treatment of multiple interacting solvent effects, in principle analogous to Eq. (7-50) but more precisely elaborated and more generally applicable, has been proposed by Kamlet, Abboud, and Taft (KAT) [84a, 224, 226], Theirs and Koppel and Palm s approaches have much in common, i.e. that it is necessary to consider non-specific and specific solute/solvent interactions separately, and that the latter should be subdivided into solvent Lewis-acidity interactions (HBA solute/HBD solvent) and solvent Lewis-basicity interactions (HBD solute/HBA solvent). Using the solvato-chromic solvent parameters a, and n, which have already been introduced in Section 7.4 cf. Table 7-4), the multiparameter equation (7-53) has been proposed for use in so-called linear solvation energy relationships (LSER). 

Koppel and Palm (27) theoretically justified the application of multiparameter correlations based on LFER in a quantitative expression of several types of interactions between the solvent and substrate. Their conclusion was that effects of the solvent on the chemical reactivity and on various physical and physicochemical phenomena are of similar nature and that there exist only several types of physical interactions between the solvent and substrate. Then it is possible to find a general approach to the evaluation of experimental data, that is, to express these interactions quantitatively. For this purpose they suggested a four-parameter equation (27) in... 

A more general relationship for analyzing solvent effects for thermodynamic quantities was given by Koppel and Palm [51]. They extended equation (4.9.9) to include non-specific solvent effects related to solvent permittivity and polarizability. Their equation can be written as... 

For the analysis of SN1 solvolyses, Abraham et al. (9) have proposed an equation (equation 3) based on sensitivities toward solvatochromatic properties. In equation 3, tr is a measure of solvent dipolarity-polarization, a is a measure of solvent hydrogen bond donor acidity, and P is a measure of solvent hydrogen bond acceptor basicity. More recently, a term governing cavity effects has been added, and this term is considered to represent an important contribution (10, 11). The cavity term can be directly related to the square of the Hildebrand solubility parameter (10-12). A similar analysis by Koppel and Palm (13, 14) involves terms governed by solvent polarity, solvent polarizability, electrophilic solvation ability, and nucleophilic solvation ability. Recently, a cavity term has also been added to this analysis (12). 

Koppel and Palm used an equation with four parameters... 

Drago s concept has the merit that two specific factors governing the solvent effect are written together in one common equation. As seen above, characterization of the solvent effect by means of this model succeeded well in certain systems, and less well in others. It appeared that replacement of the two-parameter approach by several parameters might lead to a more generally valid solution. For a joint description of non-specific and specific effects, Koppel and Palm [Ko 72] proposed the introduction of the following four-parameter equation ... 

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