Solid-liquid distribution ratios

It has already been noted (Section 13.2) that the determination of solid-liquid distribution ratios (Kds) and, to a lesser extent, biological concentration factors 

Concentration per kg of suspended particulate matter Concentration per litre of water 

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The stability constants of nickel carbonate complexes were investigated by measuring the solid/liquid distribution ratio of Ni in the absence and presence of varying carbonate concentrations. For this purpose a Ni tracer method was employed. A considerable part of the uncertainty (log, K°, for the reaction Ni " + CO3 NiC03(aq), is calculated to be (4.2 0.4)) inherent in this method arises from the poorly known formation constants of neutral and anionic hydroxo complexes of nickel. 

Extraction Between Two Phases When the sample is initially present in one of the phases, the separation is known as an extraction. In a simple extraction the sample is extracted one or more times with portions of the second phase. Simple extractions are particularly useful for separations in which only one component has a favorable distribution ratio. Several important separation techniques are based on simple extractions, including liquid-liquid, liquid-solid, solid-liquid, and gas-solid extractions. 

The observed distribution can be readily explained upon assuming that the only part of polymer framework accessible to the metal precursor was the layer of swollen polymer beneath the pore surface. UCP 118 was meta-lated with a solution of [Pd(AcO)2] in THF/water (2/1) and palladium(II) was subsequently reduced with a solution of NaBH4 in ethanol. In the chemisorption experiment, saturation of the metal surface was achieved at a CO/Pd molar ratio as low as 0.02. For sake of comparison, a Pd/Si02 material (1.2% w/w) was exposed to CO under the same conditions and saturation was achieved at a CO/Pd molar ratio around 0.5. These observations clearly demonstrate that whereas palladium(II) is accessible to the reactant under solid-liquid conditions, when a swollen polymer layer forms beneath the pore surface, this is not true for palladium metal under gas-solid conditions, when swelling of the pore walls does not occur. In spite of this, it was reported that the treatment of dry resins containing immobilized metal precursors [92,85] with dihydrogen gas is an effective way to produce pol-5mer-supported metal nanoclusters. This could be the consequence of the small size of H2 molecules, which... 

The term two-phase flow covers an extremely broad range of situations, and it is possible to address only a small portion of this spectrum in one book, let alone one chapter. Two-phase flow includes any combination of two of the three phases solid, liquid, and gas, i.e., solid-liquid, gas-liquid, solid-gas, or liquid-liquid. Also, if both phases are fluids (combinations of liquid and/or gas), either of the phases may be continuous and the other distributed (e.g., gas in liquid or liquid in gas). Furthermore, the mass ratio of the two phases may be fixed or variable throughout the system. Examples of the former are nonvolatile liquids with solids or noncondensable gases, whereas examples of the latter are flashing liquids, soluble solids in liquids, partly miscible liquids in liquids, etc. In addition, in pipe flows the two phases may be uniformly distributed over the cross section (i.e., homogeneous) or they may be separated, and the conditions under which these states prevail are different for horizontal flow than for vertical flow. 

FIG. 16-13 Effect of Re Sc group, distribution ratio, and diffusivity ratio on height of a transfer unit. Dotted lines for gas and solid lines for liquid-phase systems. 

The heat transfer across the vapor layer and the temperature distribution in the solid, liquid, and vapor phases are shown in Fig. 13. In the subcooled impact, especially for a droplet of water, which has a larger latent heat, it has been reported that the thickness of the vapor layer can be very small and in some cases, the transient direct contact of the liquid and the solid surface may occur (Chen and Hsu, 1995). When the length scale of the vapor gap is comparable with the free path of the gas molecules, the kinetic slip treatment of the boundary condition needs to be undertaken to modify the continuum system. Consider the Knudsen number defined as the ratio of the average mean free path of the vapor to the thickness of the vapor layer ... 

This problem requires specific techniques not developed in this chapter, such as Laplace transforms, and the reader interested in the derivation of the solution may refer to the textbook of Crank (1976). Defining a as the final distribution ratio, i.e., the amount of solute contained in the solid divided by the amount contained in the liquid when t- co... 

However, the temperature also affects the solute partitioning between the mobile and stationary phase and therefore also the chromatographic retention. The distribution of the solute between the mobile and stationary phases is a function of (i) its solubility in the liquid phase and (ii) its adsorption on the solid phase. This is characterized by the distribution ratio K defined as the ratio of the concentration of the solute in the stationary phase to its concentration in the mobile phase. The higher this ratio, the longer the retention. According to the Van t Hoff equation... 

This diversity in solvent properties results in large differences in the distribution ratios of extracted solutes. Some solvents, particularly those of class 3, readily react directly (due to their strong donor properties) with inorganic compounds and extract them without need for any additional extractant, while others (classes 4 and 5) do not dissolve salts without the aid of other extractants. These last are generally used as diluents for extractants, required for improving then-physical properties, such as density, viscosity, etc., or to bring solid extractants into solution in a liquid phase. The class 1 type of solvents are very soluble in water and are useless for extraction of metal species, although they may find use in separations in biochemical systems (see Chapter 9). 

Note that is not necessarily constant with varying p,. In fact, evaluation of the air-water equilibrium distribution ratio as a function ofp, is one of the methods that can be used to assess the concentration dependence of y-w of an organic compound, regardless whether the compound is a gas, liquid, or solid at the temperature considered (see below). 

Impregnation by Soaking, or with an Excess of Solution [2]. Excess liquid is eliminated by evaporation or by draining. Deposition of the active element is never quantitative. The quantity deposited depends on the solid/liquid ratio. Deposition is slow, requiring several hours or days. Extensive restructuring of the surface (loss of surface area, etc.) may occur. However, the method allows the distribution of the species to be very well controlled and high dispersions may be obtained. The method works best if ion/solid interactions are involved. 

The rheological phase reaction method is the process of preparing compounds or materials from a solid-liquid rheological mixture. That is, the solid reactants are fully mixed in a proper molar ratio, and made up by a proper amount of water or other solvents to a solid-liquid rheological body in which the solid particles and liquid substance are uniformly distributed, so that the product can be obtained under suitable experimental conditions. 

An adaptation of the distribution constant defined in Equation (23-3) could be made for solutes in chromatojp-aphy. As in liquid-liquid extraction, however, solutes may be present in several chemical forms, and therefore a quantity analogous to the distribution ratio (Section 23-1), called the partition ratio, is preferred. The partition ratio must be a somewhat more broadly defined term than the distribution ratio in liquid-liquid extraction for two reasons. First, in chromatography, concentrations of solute in the two phases are usually unknown and may be unmeasurable, as when adsorption is important. Second, instead of the two phases being merely an aqueous phase and an immiscible organic solvent, in chromatography they can be any one of innumerable combinations of solid or liquid stationary phases and liquid or gas... 

Planning to optimize slurry preparation. The slurries must have analyte concentrations that are appropriate for the analyte line selected. The factors of interest include homogeneity of the solid, distribution of the analyte in the solid, density, particle size and analyte partitioning in the slurry. If the analyte distribution in the solid is heterogeneous, one must strive for very small (< 10 pm) particles. The minimum mass required for analysis based on particle size and density should be computed. The volume-to-volume ratio (solid volume/liquid volume ratio) should be computed in order to ensure that it is lower than 0.25. 

Another form of equation (36.15) may be obtained by writing k for the distribution ratio N /Na of the solute between solid and liquid phases the result is... 

DYNAMICS OF DISTRIBUTION The natural aqueous system is a complex multiphase system which contains dissolved chemicals as well as suspended solids. The metals present in such a system are likely to distribute themselves between the various components of the solid phase and the liquid phase. Such a distribution may attain (a) a true equilibrium or (b) follow a steady state condition. If an element in a system has attained a true equilibrium, the ratio of element concentrations in two phases (solid/liquid), in principle, must remain unchanged at any given temperature. The mathematical relation of metal concentrations in these two phases is governed by the Nernst distribution law (41) commonly called the partition coefficient (1 ) and is defined as = s) /a(l) where a(s) is the activity of metal ions associated with the solid phase and a( ) is the activity of metal ions associated with the liquid phase (dissolved). This behavior of element is a direct consequence of the dynamics of ionic distribution in a multiphase system. For dilute solution, which generally obeys Raoult s law (41) activity (a) of a metal ion can be substituted by its concentration, (c) moles L l or moles Kg i. This ratio (Kd) serves as a comparison for relative affinity of metal ions for various components-exchangeable, carbonate, oxide, organic-of the solid phase. Chemical potential which is a function of several variables controls the numerical values of Kd (41). 

From the above examples, it can be seen that an extraction is the transfer of a compound from one liquid to another or from a solid to a liquid. This transfer is seldom ever complete in a single operation. Generally, a small amount of the compound is always left behind. Because the compound divides between the two layers, it is called a partition. The usual way to express the extent of this partition is the partition coefficient, P, or the distribution ratio, D. 

The major difficulties with a liquid-solid extraction were that the distribution ratios of the desired products were low the process was slow and large amounts of solvent were required, which then had to be removed. What was desired was an apparatus that could (1) hold finely divided solid particles so a large surface area could be exposed, (2)... 

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