Distribution constant/ratio

It was experimentally established by Berthelot and Jungfleisch (1872), that a body brought in contact with two liquids, in each of which it is soluble, always divides itself between them in a simple ratio, how ever great may be its solubility in one of them, and the excess of the volume of this same solvent. The quantities dissolved simultaneously by the two liquids stand to one another in a constant ratio which is independent of the relative volumes of the two liquids. This ratio is called the coefficient of distribution, or the partition coefficient, k. 

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substance shared between two solvents can exist in different molecular states in them, the simple distribution law is no longer valid.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). 

However, not withstanding the above objections, further discussion of the Snyder solvent triangle classification method is justified by its common use in many solvent optimization schemes in liquid chromatography. The polarity index, P, is given by the sum of the logarithms of the polar distribution constants for ethanol, dioxane and nltromethane and the selectivity parameters, X, as the ratio of the polar distribution constant for solute i to... 

The average distribution constant, calculated from the ratio of soil concentration (moles/kg)tsolution concentration (moles/L). 

A review of several classic equilibrium equations is in order. The Nernst distribution law states that a neutral species will distribute between two immiscible solvents with a constant ratio of concentrations. 

The equilibrium condition for the distribution of one solute between two liquid phases is conveniently considered in terms of the distribution law. Thus, at equilibrium, the ratio of the concentrations of the solute in the two phases is given by CE/CR = K, where K1 is the distribution constant. This relation will apply accurately only if both solvents are immiscible, and if there is no association or dissociation of the solute. If the solute forms molecules of different molecular weights, then the distribution law holds for each molecular species. Where the concentrations are small, the distribution law usually holds provided no chemical reaction occurs. 

When M is present in various differently complexed forms in the aqueous phase and in the organic phase, [M]t refers to the sum of the concentrations of all M species in a given phase (the subscript t indicates total M). It is important to distinguish between the distribution constant, K, which is valid only for a single specified species (e.g., MAj), and the distribution ratio, D, which may involve sums of species of the kind indicated by the index, and thus is not constant. 

These equations allow definition of a distribution constant for the species AB, [see Eq. (4.15c)]. Distribution constants can also be defined for each of the species A, B and AB (Kd a, etc.) but this is of little interest as the concentration of these species is related through A large for the system indicates that large distribution ratios Da can be obtained in practice. As shown in Eq. (4.15), the concentration of B influences the distribution ratio Da. 

This is shown by the horizontal trends in Fig. 4.6, for which Eq. (4.17) is valid i.e., the distribution constant equals the measured distribution ratio. When... 

Fig. 4.15 The system La(III) acetylacetone (HA) - IM NaC104/benzene at 25°C as a function of lanthanide atomic number Z. (a) The distribution ratio Hl (stars, right axis) at [A ] = 10 and [HA] rg = 0.1 M, and extraction constants (crosses, left axis) for the reaction Ln + 4HA(org) LnA3HA(org) + 3FE. (b) The formation constants, K , for formation of LnA " lanthanide acetylacetonate complexes (a break at 64Gd is indicated) circles n = 1 crosses n = 2 triangles w = 3 squares w = 4. (c) The self-adduct formation constants, for the reaction of LnA3(org) + HA(org) LnA3HA(org) for org = benzene. (A second adduct, LnA3(HA)2, also seems to form for the lightest Ln ions.) (d) The distribution constant Ajc for hydrated lanthanum triacetylacetonates, LnAs (H20)2 3, between benzene and IM NaC104. (From Ref. 28.)...

Dyrssen and Sill6n [68] pointed ont that distribntion ratios obtained by conventional batchwise techniques are often too scattered to allow the determination of as many parameters as used in Examples 15 and 16. They suggested a simplified graphic treatment of the data, based on the assnmption that there is a constant ratio between successive stability constants, i.e., KJK i = 10 , and that all distribntion cnrves can be normalized so that A log Pn = where N is the number of ligands A in the extracted complex. Thns, the distribution curve log Du vs. log[A ] is described by the two parameters a and b, and the distribution constant of the complex, Tdc- The principle can be nsefnl for estimations when there is insnfficient reliable experimental data. 

Vo is the interstitial volume of a column filled with the (particulate) packing K is the distribution constant described as a ratio of solute concentration in the stationary and the mobile phase cjc ... 

Consider a fluidized bed operated at an elevated temperature, e.g. 800°C, and under atmospheric pressure with ah. The scale model is to be operated with air at ambient temperature and pressure. The fluid density and viscosity will be significantly different for these two conditions, e.g. the gas density of the cold bed is 3.5 times the density of the hot bed. In order to maintain a constant ratio of particle-to-fluid density, the density of the solid particles in the cold bed must be 3.5 times that in the hot bed. As long as the solid density is set, the Archimedes number and the Froude number are used to determine the particle diameter and the superficial velocity of the model, respectively. It is important to note at this point that the rale of similarity requires the two beds to be geometrically similar in construction with identical normalized size distributions and sphericity. It is easy to prove that the length scales (Z, D) of the ambient temperature model are much lower than those in the hot bed. Thus, an ambient bed of modest size can simulate a rather large hot bed under atmospheric pressure. 

The linear isotherm is obtained when the ratio of the concentration of substance adsorbed per unit mass and the concentration of the substance in solution remains constant. This means the partition coefficient or distribution constant, K (see Section 1.4) is a constant over all working concentration ranges. Thus, the front and rear boundaries of the band or zone will be symmetrical. 

This is the most direct and simple theory of chromatography. The transport of the solute down the column will depend upon the distribution constant (partition coefficient), K, and the ratio of the amounts of the two phases in the column. Band (zone) shape does not change during this movement through the column. The system could be visualized as illustrated in Figures 1.10, 1.11. 

Distribution constant. KQ(K). The ratio of the concentration of a sample component in a single definite form in the stationary phase to its concentration in the mobile phase at equilibrium. Both concentrations should be calculated per unit volume of the phase. IUPAC recommends this term rather than partition coefficient. 

Thus the selectivity a has a thermodynamic interpretation as the ratio of two distribution constants. Consequently a is itself a constant, independently from the injected concentrations of the analyte and the interferent, respectively. 

From the Boltzmann distribution, the ratio of pressures (assuming constant temperature) should be Since mg/ksT = 1.26 x 10-4m-1 (see text), at... 

Both primary and secondary electron models (Atoyan Voelk 2000, Brunetti et al. 2001, Blasi Colafrancesco 1999, Miniati et al. 2001) have been analyzed to reproduce the spectral and spatial features of the EUV excess in Coma without a definite solution. Additional experimental information has been recently added to the complexity of the problem in particular, the EUV intensity distribution seems to be highly correlated with the thermal X-ray intensity and produce a constant ratio between the azimuthally averaged EUV and X-ray intensifies (Bowyer et al. 2004). Specific secondary models seem, at present, one of the few viable possibilities to reproduce the EUV emission features of Coma. 

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