Thermodynamic partitioning coefficient

Our present topic is the relationship between permeability and lipophilicity (kinetics), whereas we just considered a concentration and lipophilicity model (thermodynamics). Kubinyi demonstrated, using numerous examples taken from the literature, that the kinetics model, where the thermodynamic partition coefficient is treated as a ratio of two reaction rates (forward and reverse), is equivalent to the equilibrium model [23], The liposome curve shape in Fig. 7.20 (dashed-dotted line) can also be the shape of a permeability-lipophilicity relation, as in Fig. 7.19d. 

It assumes that there are no significant solute-solute interactions and no strong solute-solvent interactions which would influence the distribution process. Concentrations are expressed as mass/unit volume, and usually C1 refers to an aqueous phase and C2 to a non-aqueous phase. The equilibrium constant (P or K) defining this system is referred to as the partition coefficient or distribution ratio. The thermodynamic partition coefficient (P ) is given by the ratio of the respective mole fractions as follows ... 

Equation (5) is greatly simplified the true thermodynamic partition coefficient would be the quotient of analyte activities, not concentrations. Furthermore, the equation assumes that analyte A is present in only one form (one molecular structure or ion). When this is not realized in practice, a more complex equilibrium constant must be used. 

Validity of the Method. The feasibility of the method was demonstrated (2 by measuring diffusion coefficients and thermodynamic partition coefficients for... 

The distribution of lomefloxacin between 1-octanol and aqueous buffers was studied at 25°C, pH 5,7 and 9 (17). The apparent partition coefficients of lomefloxacin as determined by the analysis of both the organic and aqueous phases using spectrophotometry were 0.118 0.001,0.139 0.004 and 0.112 0.002, respectively. The thermodynamic partition coefficient was determined to be 0.146 0.005. Takacs-Novac, et al. (18) measured the octanol-water partition coefficient spectrophotometrically by analysis of the aqueous phase only and obtained a value of 0.150. It was found that the presence of metal ions (Al3+, Ca2+, Mg2+, Bi3+ and Fe3+) decreased the partition coefficient of lomefloxacin. (15, 19). 

Extraction is the first step of pesticide residue analysis of water samples. Any pesticide residue technique of water samples should include the development of a dependable quantitative extraction procedure. The pitfalls of liquid-liquid extraction as now used are explained. A theoretical approach for quantitation of the extraction step based upon the thermodynamic partition coefficient as a p-value is proposed. The p-value approach is discussed to enable choosing the best solvent, water quality parameters, and solvent water ratios for serial analysis of water samples containing pesticides. 

Lipophilicity is an important determinant of the suitability of a compound as a drug candidate, as it is directly linked to absorption, permeation, disposition and bioavailability. " Lipophilicity is related to the thermodynamic partition coefficient, P, which is the ratio of the equilibrium activity (or concentration in dilute solution, i.e., <10 M) of the neutral species in a water-immiscible organic solvent to the equilibrium activity of the neutral species in water. Usually the partition coefficient is expressed as the form of logarithm, logP. The desirable logP values of drug candidates are less than 5. ... 

The thermodynamic partition constant, Ki, has to be employed for calculating the free energy of adsorption of any adsorbate, which differs in nature from the chromatographic partition constant, K. Actually, the thermodynamic partition coefficient, Ki, is the ratio of the partial pressure of the chromatographed solute p, to its molar fraction in the stationary phase, jc,-. For designing chemical processes the thermodynamic Ki values are usually expressed as ... 

Thermodynamic partition coefficient. In chromatographic applications the Nernst distribution constant it of a component i, referred to as the... 

The thermodynamic partition coefficient. A, defined by eqn (2.17) is of the first kind. 

Up to this point we have discussed the optimization of gas chromatographic separations by manipulation of the column variables that do not affect peaks relative retentions. Changing the column dimensions, the stationary-phase film thickness or the carrier-gas velocity will affect retention times, but the peaks thermodynamic partition coefficients (K) remain constant a long as the colunm temperature and the stationary-phase chemistry remain unchanged. As a result, the peaks relative retentions—the ratios of their adjusted retention times (t )—also will not be affected by such manipulations, and so the peaks elution order and relative separations remain unchanged. This makes prediction of the effects of modifying these variables fairly simple to compute using relationships such as those presented thus far in this chapter. 

For the PC model, adsorption can be seen as purely partitioning behavior. This model ascribes a thermodynamic partitioning coefficient ( adsorption separation factor ) to each solute to describe adsorption quantitatively. No explicit thermodynamic contribution of the surface site to the adsorption process nor competitive adsorption effects are considered. 

Many additional consistency tests can be derived from phase equiUbrium constraints. From thermodynamics, the activity coefficient is known to be the fundamental basis of many properties and parameters of engineering interest. Therefore, data for such quantities as Henry s constant, octanol—water partition coefficient, aqueous solubiUty, and solubiUty of water in chemicals are related to solution activity coefficients and other properties through fundamental equiUbrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equiUbrium models may permit a missing property value to be calculated from those values that are known (2). 

Matsui and Mochida24) have determined the thermodynamic stabilities (log 1 /Kd) for a- and P-cyclodextrin complexes with a variety of alcohols (Table 2) and analyzed the results in connection with the physicochemical properties of the guest molecules by the multivariate technique. The log 1/Kd values were plotted against log Pe, where Pe is the partition coefficient of alcohol in a diethyl ether-water system. The plots for the a- and P-cyclodextrin complexes with eight 1-alkanols gave approximately straight lines with slopes of around one. 

If the substance shared between two solvents can exist in different molecular states in them, the simple distribution law is no longer valid. The experiments of Berthelot and Jungfleiscli, and the thermodynamic deduction show, however, that the distribution law holds for each molecular state separately. Thus, if benzoic acid is shared between water and benzene, the partition coefficient is not constant for all concentrations, but diminishes with increasing concentration in the aqueous layer. This is a consequence of the existence of the acid in benzene chiefly as double molecules (C6H5COOH)2, and if the amount of unpolymerised acid is calculated by the law of mass action (see Chapter XIII.) it is found to be in a constant ratio to that in the aqueous layer, independently of the concentration (cf. Nernst, Theoretical Chemistry, 2nd Eng. trans., 486 Die Verteilnngssatz, W. Hertz, Ahrens h annulling, Stuttgart, 1909). 

Lipophilicity is a molecular property expressing the relative affinity of solutes for an aqueous phase and an organic, water-immiscible solvent. As such, lipophilicity encodes most of the intermolecular forces that can take place between a solute and a solvent, and represents the affinity of a molecule for a lipophilic environment. This parameter is commonly measured by its distribution behavior in a biphasic system, described by the partition coefficient of the species X, P. Thermodynamically, is defined as a constant relating the activity of a solute in two immiscible phases at equilibrium [111,112]. By convention, P is given with the organic phase as numerator, so that a positive value for log P reflects a preference for the lipid phase ... 

Nevertheless, ionization often complicates the measurement and interpretation of partition coefficient because of the charge distribution it generates across the interface. It is therefore necessary to briefly recall the fundamentals of partition thermodynamics at the ITIES. 

FIG. 4 Thermodynamic equilibria for the interfacial distribution of a solute X which can be ionized n times, and X being its most acidic (or deprotonated) and its most basic (or protonated) forms, respectively. X and are the dissociation constants in the aqueous and organic phase, respectively, and P is the partition coefficient of the various species between the two phases. 

The pKa of a molecule, a charge-state-related parameter, is a descriptor of an acid-base equilibrium reaction [34,35]. Lipophilicity, often represented by the octanol-water partition coefficient Kp is a descriptor of a two-phase distribution equilibrium reaction [36]. So is solubility [37-39]. These three parameters are thermodynamic constants. On the other hand, permeability Pe is a rate coefficient, a kinetics parameter, most often posed in a first-order distribution reaction [40-42]. 

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