Equilibrium distribution coefficient

Selection of Solubility Data Solubility values determine the liquid rate necessaiy for complete or economic solute recoveiy and so are essential to design. Equihbrium data generally will be found in one of three forms (1) solubility data expressed either as solubility in weight or mole percent or as Heniy s-law coefficients, (2) pure-component vapor pressures, or (3) equilibrium distribution coefficients (iC values). Data for specific systems may be found in Sec. 2 additional references to sources of data are presented in this section. 

Whenever data are available for a given system under similar conditions of temperature, pressure, and composition, equilibrium distribution coefficients (iC = y/x) provide a much more rehable tool for predicting vapor-liquid distributions. A detailed discussion of equilibrium iC vahies is presented in Sec. 13. 

The compositions of CE in the gaseous and liquid effluents of the ethyl chloride reactor are related through an equilibrium distribution coefficient as follows ... 

Kj = equilibrium distribution coefficient for component, i Kf = equilibrium distribution coefficient for component to which relative volatilities are referred... 

Sablani, S.S. and Rahman Shafiur, M. 2003. Effect of syrup concentration, temperature and sample geometry on equilibrium distribution coefficients during osmotic dehydration of mango. Food Res. Int. 36, 65-71. 

Table VI summarizes values of the activity coefficient ratio Ygr-/YC].- in the saturated solution for each average solid composition (as calculated from the model of Table II), the calculated provisional equilibrium distribution coefficient (Equation 12) and the provisional equilibrium aqueous solution activity ratio of Br to Cl- (Equation 13) based on the data of Table V.

Thus the equilibrium distribution coefficient for a CAC experiment is given by... 

This equation allows the retention time (or solute band velocity) to be calculated from the equilibrium distribution coefficient K, and vice versa. 

Celorie, J.A., Woods, S.L., Vinson, T.S., and Istok, J.D. A comparison of sorption equilibrium distribution coefficients using... 

Gan, D.R. and Dnpont, R.R. Mnltiphase and multicompound measnrements of batch equilibrium distribution coefficients for six volatile organic componnds, Haz. Waste Haz. Mater., 6(4) 363-383, 1989. 

The term within the square brackets in equation 11.79 is the normalized (equilibrium) distribution coefficient between the minerals a and )3 (cf section 10.8) at the closure condition of the mineral isochron. Ganguly and Ruitz (1986) have shown it to be essentially equal to the observed (disequilibrium) distribution coefficient between the two minerals as measured at the present time. can be assumed to be 1, within reasonable approximation. Equation 11.79 can be calibrated by opportunely expanding AG° over P and T ... 

Barbari TA, King CJ. 1982. Equilibrium distribution coefficients for extraction of chlorinated hydrocarbons and aromatics from water into undecane. Environ Sci Technol 16(9) 624-627. 

In most mathematical analyses used to establish bounds for radionuclide migration rates through the abyssal red clays, the sorption properties of the sediment are generally represented mathematically by the sorption equilibrium distribution coefficients for each of the species involved. These coefficients are usually denoted by Kp. and are defined by... 

Therefore, the preliminary investigation described herein examined several aspects of the behavior of the equilibrium distribution coefficients for the sorption of rubidium, cesium, strontium, barium, silver, cadmium, cerium, promethium, europium, and gadolinium from aqueous sodium chloride solutions. These solutions initially contained one and only one of the nuclides of interest. For the nuclides selected, values of Kp were then... 

First, consider the diffusion of an organic compound across the boundary between two environmental systems, A and B. Imagine that at time 1 = 0, the surface of system A (e.g., an air bubble, a silt particle, etc.) is suddenly juxtaposed to a (very large) system B (e.g., the water of a lake, Fig. 18.5a). Mixing in system B is sufficient that the concentration of the selected compound at the boundary of the injected medium is kept at the constant value, Cg. This concentration is different from the initial concentration in A, CA. In system A, transport occurs by diffusion only. We want to calculate the concentration in system A as it evolves in space and time, CA(x,t). For the time being, we will assume that the equilibrium distribution coefficient between A and B is 1. Hence, the concentration of A seeks to change to be equal to that of system B. 

Thus, the sorption of chemicals on the surface of the solid matrix may become important even for substances with medium or even small solid-fluid equilibrium distribution coefficients. For the case of strongly sorbing chemicals only a tiny fraction of the chemical actually remains in the fluid. As diffusion on solids is so small that it usually can be neglected, only the chemical in the fluid phase is available for diffusive transport. Thus, the diffusivity of the total (fluid and sorbed) chemical, the effective diffusivity DieS, may be several orders of magnitude smaller than diffusivity of a nonsorbing chemical. We expect that the fraction which is not directly available for diffusion increases with the chemical s affinity to the sorbed phase. Therefore, the effective diffusivity must be inversely related to the solid-fluid distribution coefficient of the chemical and to the concentration of surface sites per fluid volume. 

In Section 19.2 we treated the phase problem by choosing a reference system (for instance, water) to which the concentrations of the chemicals in other phases are related by equilibrium distribution coefficients such as the Henry s law constant. Here we employ the same approach. The following derivation is valid for an arbitrary wall boundary with phase change. The mixed system B is selected as the reference system. In order to exemplify the situation, Fig. 19.9 shows the case in which system A represents a sediment column and system B is the water overlying the sediments. This case will be explicitly discussed in Box 19.1. 

Dif is molecular diffusivity of compound i in the film, 8f is surface film thickness, and KWvj is the nondimensional equilibrium distribution coefficient of substance i in the film relative to the water. 

Of course, the first question is, where must the system go This is formally answered by chemical thermodynamics in terms of equilibrium-distribution coefficients or Henry s Law constants. For our purposes these are well described from the elementary viewpoint by MacDougall (8) and from the viewpoint of practical application by Norman (9). 

EQUILIBRIUM OF SEPARATION. If we allow a system of two immiscible liquids, containing a solute (i) to come to equilibrium, we can express our equilibrium distribution coefficient, Kc, as... 

The equations used to describe dopant incorporation are identical to those used to describe the deposition of the semiconductor. Thus equations 12-14 are applicable to a diflusion-limited model, with the number of components, n, increased by the number of dopants added. The equilibrium distribution coefficient, ki9 is defined as... 

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. 

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