Distribution coefficients adsorbate-solid

The partitioning of As in the aquifer solid-water interface can best be explained with the distribution coefficient, Kd (a ratio of solute adsorbed in sediment to that of dissolved in groundwater). Due to being simplistic in nature, Kd has long been well appreciated as well as applied by geochemical modelers. 

The semi-empirical descriptions of adsorbate/solid interactions are based on net changes in system composition and, unlike surface complexation models, do not explicitly identify the details of such interactions. Included in this group are distribution coefficients (Kp) and apparent adsorbate/proton exchange stoichiometries. Distribution coefficients are derived from the simple association reaction... 

Distribution coefficient (Kd) In a system at equilibrium, the distribution coefficient (Kd) is a constant that results from taking the ratio of the concentration of a chemical species in a solid or adsorbed onto it with the species concentration in the host solution of the solid. 

Enhanced HOC solubility in surfactant systems generally has been quantified by a distribution coefficient that only considers HOC partitioning to surfactant micelles that exist above the critical micelle concentration (CMC). Although surfactants can form a mobile micellar pseudophase that leads to the facilitated transport of solubilized HOCs, they also can be adsorbed by the solid matrix and thereby lead to HOC partitioning to immobile sorbed surfactants and, thus, enhanced HOC retardation. Therefore, the effectiveness of a remediation scheme utilizing surfactants depends on the distribution of an HOC between immobile compartments (e.g., subsurface solids, sorbed surfactants) and mobile compartments (e.g., water, micelles). 

Material balance calculations on separation processes follow the same procedures used in Chapters 4 and 5. If the product streams leaving a unit include two phases in equilibrium, an equilibrium relationship for each species distributed between the phases should be counted in the degree-of-freedom analysis and included in the calculations. If a species is distributed between gas and liquid phases (as in distillation, absorption, and condensation), use tabulated vapor-liquid equilibrium data, Raoult s law, or Henry s law. If a solid solute is in equilibrium with a liquid solution, use tabulated solubility data. If a solute is distributed between two immiscible liquid phases, use a tabulated distribution coefficient or equilibrium data. If an adsorbate is distributed between a solid surface and a gas phase, use an adsorption isotherm. 

Figure 9.28. The distribution of nonpolar organic substances between aquatic solids and water (as given by the distribution coefficient Kp) is dependent upon the lipophilicity of the compound and the organic C content of the adsorbing material (foe = weight fraction). The solid phases considered here are coastal sea and lake sediments, river sediments, solids from aquifers and biomass (activated sludge). The octanol/water distribution coefficients are, respectively 500, 2400, 11,200 and 52,000 for chlorobenzene, 1,4-dichlorobenzene, 1,2,4-trichlorobenzene and 1,2,4,5-tetrachlorobenzene. (Modified from Schwarzenbach and Westall, 1980).

The other common representation of the uptake studies is in form of percentage of uptake (pH) or distribution coefficient (pH) curves at constant initial concentration of the adsorbate and solid to liquid ratio. The typical course of the percentage of uptake (pH) curves for cations and anions is presented in Fig. 4.5-4.7. In a few publications the dissolved fraction rather than uptake is plotted as a function of pH. In such a representation anion type curves look like the cation type curves shown in Fig. 4,5 (A) and vice versa. The typical uptake curves for cations (A) and anions (B) (for low concentration of the solute) are shown in Fig. 4.5. The uptake... 

Zirconium is polyvalent, but only the 4- - valence state is observed in aqueous environments. In common with other polyvalent elements, it is adsorbed rapidly and relatively intensely by soils and sediments, rendering it relatively poorly available for biological absorption in the terrestrial environment. Solid-liquid distribution coefficients quoted for Zr by Sheppard and Thibault (1990) range from 600 L kg for sandy soil to 7300 L kg for organic soil. 

By defining a distribution coefficient Kj such that = CEC vKs/N, we finally obtain a simple relationship between the quantity of Cs" adsorbed on the soil solids (mmoles/kg) and the concentration of Cs in solution (mmoles/kg) ... 

Dipole interact ions,. tee Electrostatic forces Dispersion forces (energies), 44-47 on alumina, 245 in gas-solid adsorption, 243-245 Displacement chromatography, 34-36 Distribution coefficient A, lOi-ll calculation (examples), 385-396 correlation between different adsorbent batches, 148-149... 

The Langmuir isotherm is by definition free from interactions between adsorbate molecules (2) and surface heterogeneity (3). It is therefore an ideal model for illustrating the contribution of surface saturation (1) to isotherm nonlinearity. Beginning with the Langmuir isotherm for liquid-solid systems [Eq. (3-5a)], we can define a distribution coefficient K equal to S/iVa , so that ... 

Pj (g/cm ) is the bulk density of the packed bed, 0 (no units) is the porosity, and (cmVg) is the distribution coefficient. See Zheng and Beimett (1995) for a derivation of this equation. It is related to the (mol/g-soHd/ mol/kg-water) derived in Chapter 6 by a units transformation involving the molecular weight of the adsorbing species and the density of water. Because Kspecific surface area of the solid. 

Methods The measurements were carried out by batch equilibration, most by an isotope dilution technique. Samples of clay were pre-equilibrated several times with NaCl-CaCl2 solutions of fixed compositions, until successive equilibrations showed no change in concentration. To separate samples (separate because of he difficulty of discriminating between the gamma emission of Na and Ca radioisotopes) were added known amounts of Na and Ca tracers, and the solutions were allowed to equilibrate for 2-5 days. The solid was centrifuged down, and aliquots of the supernatant solutions were counted. By material balance, the fractions of the activity adsorbed were computed, and, from these, the distribution coefficients, D... 

Nolan et al. [107] reported the adsorption of chloro dibenzo-p-dioxins on polyhydroxoaluminum montmorillonite. High distribution coefficients (ATp(ml/g) = amount X adsorbed per g solid (mg/g)/amount X in solution (mg/ml)) are obtained (octachloro dibenzodioxin on montmorillonite 2800 ml/g, on polyhydroxoaluminum montmorillonite 94000 ml/g). The distribution coefficient decreases sharply when the interlamellar polyhydroxoaluminum complexes are dehydrated to polyoxoaluminum pillars Kq = 1100 and 1800 ml/g for polyhydroxoaluminum montmorillonite heated to 170° and 550°C). 

At any instant, the adsorbed solute concentration within the solid is X mass solute/mass solute-free solid, and since the solid-phase r sistance is negligible, this will be taken as uniform throughout the solid. The distribution coefficient tn is then defined as... 

Lateral density fluctuations are mostly confined to the adsorbed water layer. The lateral density distributions are conveniently characterized by scatter plots of oxygen coordinates in the surface plane. Fig. 6 shows such scatter plots of water molecules in the first (left) and second layer (right) near the Hg(l 11) surface. Here, a dot is plotted at the oxygen atom position at intervals of 0.1 ps. In the first layer, the oxygen distribution clearly shows the structure of the substrate lattice. In the second layer, the distribution is almost isotropic. In the first layer, the oxygen motion is predominantly oscillatory rather than diffusive. The self-diffusion coefficient in the adsorbate layer is strongly reduced compared to the second or third layer [127]. The data in Fig. 6 are qualitatively similar to those obtained in the group of Berkowitz and coworkers [62,128-130]. These authors compared the structure near Pt(lOO) and Pt(lll) in detail and also noted that the motion of water in the first layer is oscillatory about equilibrium positions and thus characteristic of a solid phase, while the motion in the second layer has more... 

The soil aggregates are assumed to be spherical in form and to have constant temperature and to contain initially uniform distributions of substrate (contaminant) and biomass. The external concentrations of biomass and substrate are assumed to be zero and the external oxygen concentration is constant. Substrate is adsorbed onto the solid phase to an extent determined by an equilibrium partition coefficient. 

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