Distribution coefficient theoretical

In extraction (qv), the distribution coefficient value is the slope of the equiUbrium line. In practice, the slope of the operating line is set at a value somewhat less than the distribution coefficient to provide driving force and fix the required theoretical extraction stages at some reasonable number. 

Nonideal Separations. In numerous iastances, the ideal equations 2 and 4 have been verified experimentally. However, ia other experiments different results were obtained, reflecting failure of one ore more of the assumptions made ia deriving equations 2 and 4. Likewise, much theoretical work is concerned with modified assumptions, iucluding varyiag distribution coefficient k (19), eutectic-forming phase behavior (4,20—21), varyiag mass of 2one (22), and soHd-state diffusion (23). 

The distribution-coefficient concept is commonly applied to fractional solidification of eutectic systems in the ultrapure portion of the phase diagram. If the quantity of impurity entrapped in the solid phase for whatever reason is proportional to that contained in the melt, then assumption of a constant k is valid. It should be noted that the theoretical yield of a component exhibiting binary eutectic behavior is fixed by the feed composition and position of the eutectic. Also, in contrast to the case of a solid solution, only one component can be obtained in a pure form. 

In fundamental SEC studies retention is often described in terms of a distribution coefficient. The theoretical distribution coefficient Kg is defined as the ratio of solute concentration inside and outside of the packing pores under size exclusion conditions. The experimental distribution coefficient as defined in Equation 1, is a measurable quantity that can be used to check the theory. 

The Langmuir equation has a strong theoretical basis, whereas the Freundlich equation is an almost purely empirical formulation because the coefficient N has embedded in it a number of thermodynamic parameters that cannot easily be measured independently.120 These two nonlinear isotherm equations have most of the same problems discussed earlier in relation to the distribution-coefficient equation. All parameters except adsorbent concentration C must be held constant when measuring Freundlich isotherms, and significant changes in environmental parameters, which would be expected at different times and locations in the deep-well environment, are very likely to result in large changes in the empirical constants. 

Potential error in the measurement of tissue to blood distribution coefficients in physiological pharmacokinetic modeling residual tissue blood. 1. Theoretical considerations, Drug Metab. Dispos. 1991, 19, 478—485. 

Indium, cadmium and silver can be extracted into chloroform as their 8-hydroxyquinoline complexes, and the pH1/2 values for these metals are 2.1, 6.3 and 8.8 respectively. Plot a graph of theoretical percent extraction against pH over the range 0 to 9 for each metal. Deduce the pH of incipient extraction (0.01%) and complete extraction (99.99%) for each metal, and comment on the feasibility of separating each from the other assuming that all the distribution coefficients are sufficiently high. 

Mark-Houwink-Sakurada constant Mass transfer coefficient around gel Fractional reduction in diffusivity within gel pores resulting from frictional effects Solute distribution coefficient Solvent viscosity nth central moment Peak skewness nth leading moment Viscosity average molecular weight Number of theoretical plates Dimensionless number... 

The theory of solute retention, as controlled by molecular Interactions between the solutes and the phase system is, in fact, not germane to the subject of this book. Nevertheless, as distribution and distribution coefficients together with retention volumes and capacity ratios will be discussed or used in the subsequent theoretical development of column theory, the basic principles of molecular interaction will be given. 

The concept of plate theory was originally proposed for the performance of distillation columns (12). However, Martin and Synge (13) first applied the plate theory to partition chromatography. The theory assumes that the column is divided into a number of zones called theoretical plates. One determines the zone thickness or height equivalent to a theoretical plate (HETP) by assuming that there is perfect equilibrium between the gas and liquid phases within each plate. The resulting behavior of the plate column is calculated on the assumption that the distribution coefficient remains unaffected by the presence of other... 

In order to permit sizing a tower, data must be available of the height of a transfer unit (HTU). This term often is used interchangeably with the height equivalent to a theoretical stage (HETS), but strictly they are equal only for dilute solutions when the ratio of the extract and raffinate flow rates, E/R, equals the distribution coefficient, K = xE/xR (Treybal, 1963, p. 350). Extractor performance also is expressible in terms of mass transfer coefficients, for instance, KEa, which is related to the number and height of transfer units by... 

Figure 1. Theoretical plots of distribution coefficient vs concentration of NaCl for sorption of Cs(I), Sr(II), and Hu (III) on a hypothetical clay with a capacity of one equivalent per kilogram.

In Figure 6, we show a theoretical calculation using Equations 3-6 of the effect of pH on the distribution coefficient for a case where the principal adsorbent is a hypothetical clay which contains a total of 0.8% oxides. In this case, we chose a mixture of three oxides as follows oxide 1, 0.1%, Kox =. 01, C =. 5 oxide 2, 0.2%, -. 005,... 

Figure 6. Theoretical distribution coefficients for trivalent ion sorption on sorbent containing 99.2% clay and 0.8% oxide. Arbitrary constants (see text).

For further consideration it is necessary to take into account that the distribution coefficient is never zero, so that theoretically the conditions for a single-step quantitative extraction cannot be set. It is well known from theory [16] that the extraction yield is much greater in repeated extractions with smaller volumes of extraction agent than in a single-step extraction with the whole volume. This consideration can easily be derived from the relationship for the concentration of the compound under extraction in the... 

Solute retention in reversed-phase HPLC is dependent on the different distribution coefficients established between a polar mobile and a nonpolar stationary phase by the peptidic components of a mixture. Although there are many similarities between reversed-phase HPLC separations of peptides and the classical liquid-liquid partition chromatographic methods, it is debatable whether the sorption process in reversed-phase HPLC arises due to partition or adsorption events, i.e., whether the nonpolar stationary phase functions as a bulk liquid or as an adsorptive monolayer. These aspects and the theoretical models for reversed-phase HPLC are discussed in a subsequent section. 

These are only the theoretical dependencies real behavior of actual molecule usually is significantly altered due to different types of intermolecular interactions. Molecular solvation, association, hydrogen bonding, and counterions all have a significant effect on drug ionization constant and partitioning and distribution coefficients. Detailed and comprehensive discussion of these effects could be found in the book by Avdeef [22]. 

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