Distribution coefficient overall

After phase separation, two sets of equations such as those in Table A-1 describe the polymerization but now the interphase transport terms I, must be included which couples the two sets of equations. We assume that an equilibrium partitioning of the monomers is always maintained. Under these conditions, it is possible, following some work of Kilkson (17) on a simpler interfacial nylon polymerization, to express the transfer rates I in terms of the monomer partition coefficients, and the iJolume fraction X. We assume that no interphase transport of any polymer occurs. Thus, from this coupled set of eighteen equations, we can compute the overall conversions in each phase vs. time. We can then go back to the statistical derived equations in Table 1 and predict the average values of the distribution. The overall average values are the sums of those in each phase. 

The relative basicities of the hydrocarbons may be determined from the result of partition between aqueous sulfuric acid and cyclohexane, the reasonable assumption being made that the degree of conversion to conjugate acid, rather than the distribution coefficient of the neutral olefin, is the major factor determining the overall distribution. The resulting order of basicities is ... 

The first of these environmentally-important parameters can be expressed as a partition coefficient. In aqueous solution many, but not all pesticide compounds exhibit strong affinity for soil organic matter or concentrate in the lipid phase of soil organisms. Some, notably the cationic group, also exhibit marked affinity for clay or other mineral surfaces. An overall partition (or distribution) coefficient (kD) can be defined ... 

Pertechnetate in neutral and alkaline media can be extracted into solutions of tetra-alkylammonium iodides in benzene or chloroform. With tetra-n-heptylammo-nium iodide (7.5 x 10 M) in benzene distribution coefficients up to 18 can be obtained . A solution of fV-benzoyl-iV-phenylhydroxylamine (10 M) in chloroform can be used to extract pertechnetate from perchloric acid solution with a distribution coefficient of more than 200, if the concentration of HCIO is higher than 6 M The distribution of TcO between solutions of trilauryl-ammonium nitrate in o-xylene and aqueous solutions of nitrate has been measured. In 1 M (H, Li) NOj and 0.015 M trilaurylammonium nitrate the overall equilibrium constant has been found to be log K = 2.20 at 25 °C. The experiments support an ion exchange reaction . Pertechnetate can also be extracted with rhodamine-B hydrochloride into organic solvents. The extraction coefficient of Tc (VII) between nitrobenzene containing 0.005 %of rhodamine-B hydrochloride and aqueous alcoholic " Tc solution containing 0.0025 % of the hydrochloride, amounts to more than 5x10 at pH 4.7 . 

This reaction is suppressed by using a large excess of Cl ion in the stripping phase. Furthermore, the extraction equilibrium constant of the above reaction is much lower than that of reaction given by Eq. (4). The overall distribution coefficient of CPC, mg (defined as Cqp/Cp) is given by [50]... 

So the assumption about the constancy of Kid is equivalent to presuming either (a) the overall process is described by a linear isotherm (n, - 1= 0), or (b) the relative concentration variation, (concentration range is less than a factor of 10, when multiplied by (n, - 1) with an n, value of 0.7, then the solid-water distribution coefficient would vary by less than a factor of 3. 

In all of these cases, the structure of the organic sorbate, the composition of the surface, and the conditions of the vapor or solution exchanging with the solid must be considered. However, it is important to note that with some experience in thinking about the organic chemicals and environmental situation involved, we can usually anticipate which one or two sorption mechanisms will predominate. For example, in Chapter 9 we wrote an expression reflecting several simultaneously active sorption mechanisms, each with their own equilibrium descriptor, to estimate an overall solid-water distribution coefficient for cases of interest (Eq. 9-16) ... 

To find the overall goethite-water distribution coefficient for benzoic acid (HBz), assume that only adsorption of the deprotonated species (benzoate, Bz") is important ... 

Any chromatographic process is associated with the distribution of the analyzed substance between the mobile and the stationary phase. In liquid chromatography the solvent, with the volume V0 in the interparticle space, moving along the column at a certain speed, is the mobile phase, and a porous adsorbent, with an overall pore volume of V, is the stationary phase. The distribution coefficient, Kd, equal to the ratio between the concentration of the substance in the stationary and the mobile phase, determines the retention volume, VR, of a given substance in the column according to the basic chromatographic equation... 

Such reactions can take place predominantly in either the continuous or disperse phase or in both phases or mainly at the interface. Mutual solubilities, distribution coefficients, and the amount of interfadal surface are factors that determine the overall rate of conversion. Stirred tanks with power inputs of 5-10 HP/1000 gal or extraction-type equipment of various kinds are used to enhance mass transfer. Horizontal TFRs usually are impractical unless sufficiently stable emulsions can be formed, but mixing baffles at intervals are helpful if there are strong reasons for using such equipment. Multistage stirred chambers in a single shell are used for example in butene-isobutane alkylation with sulfuric acid catalyst. Other liquid-liquid processes listed in Table 17.1 are numbers 8, 27, 45, 78, and 90. 

Complexity in multiphase processes arises predominantly from the coupling of chemical reaction rates to mass transfer rates. Only in special circumstances does the overall reaction rate bear a simple relationship to the limiting chemical reaction rate. Thus, for studies of the chemical reaction mechanism, for which true chemical rates are required allied to known reactant concentrations at the reaction site, the study technique must properly differentiate the mass transfer and chemical reaction components of the overall rate. The coupling can be influenced by several physical factors, and may differently affect the desired process and undesired competing processes. Process selectivities, which are determined by relative chemical reaction rates (see Chapter 2), can thenbe modulated by the physical characteristics of the reaction system. These physical characteristics can be equilibrium related, in particular to reactant and product solubilities or distribution coefficients, or maybe related to the mass transfer properties imposed on the reaction by the flow properties of the system. 

HOC distribution coefficients (KD) between the immobile and mobile compartments varied as a function of solution chemistry and surfactant dose, KD values increased with increasing surfactant dose at low surfactant concentrations, but decreased at higher doses. This trend indicates that competition for HOC partitioning occurs between sorbed- and micellar-phase surfactants. Overall, the results of this study demonstrate that retardation of HOCs by surfactants sorbed to the solid phase can be significant and must be considered for proper evaluation of treatment/remediation alternatives that use surfactants. 

The increase in extraction efficiency, evaluated by the distribution coefficients DM, is often considered to be the result of an increase in the overall lipophilicity of a system. Synergism has been studied systematically using four types of extractant combinations 1) chelating extractant/neutral extractant 2) acidic extractant/neutral extractant 3) two neutral extractants 4) two chelating extractants, with the observed synergistic effect generally decreasing from class 1 to 4. [49]... 

In deriving the shapes of these isotherms, we first must define isotherms for ideal clays and ideal oxides. We then combine these ideal functions into overall isotherms and compare the derived functions to experimental isotherms determined for various adsorbents. We will show that observations which have been said to preclude ion exchange are, in fact, quite consistent with ion-exchange behavior. We will not attempt to derive actual values of equilibrium distribution coefficients, but rather we seek only to define the shapes of the isotherms. 

Modeling of H F contactors is in most papers based on a simple diffusion resistance in series approach. In many systems with reactive extractants (carriers) it could be of importance to take into account the kinetics of extraction and stripping reactions that can influence the overall transport rate, as discussed in refs. [30,46], A simple shortcut method for the design and simulation of two-phase HF contactors in MBSE and MBSS with the concentration dependent overall mass-transfer and distribution coefficients taking into account also reaction kinetics in L/L interfaces has been suggested [47]. 

The overall low solubility of nitro compounds in the acids causes the distribution coefficient of dinitrotoluene being very low (0.3-0.4). The distribution coefficient of dinitrotoluene when a 50 50 mixture of 2,4-dinitrotoluene and a- trinitrotoluene was... 

Since the equilibrium distribution coefficient Kassoc l is related to the overall energy change in Gibbs free energy AGassoc, for the separation process carried out at constant pressure P and constant molar volume V of the solvent, then the capacity factor K, also takes on the well-known fundamental thermodynamic dependency through the relationships ... 

Partition or distribution coefficients Environmental phenomena frequently involve the transfer of a substance, i (or solute) from one medium (phase 1) into another (phase 2). The amount transferred can be quantified by measuring the equilibrium concentration of i in both media (phases). If the overall attraction between i and phase l is weaker than that between i and phase 2, the substance will prefer to be in phase 2. The resulting distribution or partitioning of i can be estimated quantitatively by defining a partition or distribution coefficient (K np) as follows ... 

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