Distribution coefficient, thermodynamic properties

By measuring the retention volume of a solute, the distribution coefficient can be obtained. The distribution coefficient, determined over a range of temperatures, is often used to determine the thermodynamic properties of the system this will be discussed later. From a chromatography point of view, thermodynamic studies are also employed as a diagnostic tool to examine the actual nature of the distribution. The use of thermodynamics for this purpose will be a subject of discussion in the next chapter. It follows that the accurate measurement of (VV) can be extremely... 

To a first approximation the three terms in equation (1.46) and (1.47) can be treated as independent variables. For a fixed value of n Figure 1.8 Indicates the influence of the separation factor and capacity factor on the observed resolution, when the separation factor equals 1.0 there is no possibility of any separation. The separation factor is a function of the distribution coefficients of the solutes, that is the thermodynamic properties of the system, and without some... 

Finally, it is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be shown independently that equilibrium has been established. One possible exception applies to trace substitution where the assumptions of stoichiometric saturation and unit activity for the predominant component allow close approximation of equilibrium behavior for the trace components (9). The method of Thorstenson and Plummer (10) based on the compositional dependence of the equilibrium constant, as used in this study, is well suited to testing equilibrium for all solid solution compositions. However, because equilibrium has not been found, the thermodynamic properties of the KCl-KBr solid solutions remain provisional until the observed compositional dependence of the equilibrium constant can be verified. One means of verification is the demonstration that recrystallization in the KCl-KBr-H20 system occurs at stoichiometric saturation. 

In application of this method to solubility data (8) in the KCl-KBr- O system at 25°C, it is found that equilibrium is in general not attained, though some mid-range compositions may be near equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. It is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be demonstrated that equilibrium has been attained. 

Hill, J.O., Worsley, EG., and L.G. Hepler. Calorimetric determination of the distribution coefficient and thermodynamic properties of bromine in water and carbon tetrachloride, J. Phys. Chem., 72(10) 3695-3697, 1968. 

Theory. The most widely accepted mechanism of size separation is based on steric exclusion (1). In terms of thermodynamic properties, the distribution coefficient consists of enthalpic and entropic contributions ... 

MD and MC simulations have provided data on layer spacings, thermodynamic properties, as well as interlayer water configurations, interlayer-species self-diffusion coefficients, and total radial distribution functions that are consistent with experimental data. Most of the clay surface is relatively... 

One of the most successful applications of crystal field theory to transition metal chemistry, and the one that heralded the re-discovery of the theory by Orgel in 1952, has been the rationalization of observed thermodynamic properties of transition metal ions. Examples include explanations of trends in heats of hydration and lattice energies of transition metal compounds. These and other thermodynamic properties which are influenced by crystal field stabilization energies, including ideal solid-solution behaviour and distribution coefficients of transition metals between coexisting phases, are described in this chapter. 

In Chapter 8, Zuyi Tao, in order to provide a better understanding of the ion-exchange behavior of amino acids, has compiled their particular acid-base properties, their solubility in water, their partial molal volumes, and their molal activity coefficients in water at 25 C. This information has been used in Gibbs-Donnan-based equations to facilitate a better understanding of the mechanism of amino acid uptake by ion exchangers at low and high solution concentration levels. Measurement of distribution coefficients and separation factors are also described. The eventual resolution of thermodynamic ion-exchange functions (AG, AH, and AS) is provided for the reader. 

Methodology for acquiring such information is relatively well-established and interpretations are typically noncontroversial. Results, however, are limited to the system studied. This may be adequate for the task at hand, but the prospect of individually describing every sorbate/sorbent combination usually encourages attempts toward predictive modeling whereby applicability is broadened to systems not actually studied. Prediction, in turn, requires information not directly available from empirical studies sorption mechanisms must be deduced and system parameters such as rate constants and distribution coefficients must be defined. In many cases, thermodynamic properties of the system are also useful for modeling input. 

In order to define the quantitative relationships among the various parameters in a nnit operation, a mathematical model is employed, in which the physical relationships are expressed as mathematical equations. Thus, the equilibrium stage may be simulated by a model for which the mathematical solution represents physical performance. When physical relations are translated into analytical expressions, certain assumptions mnst be made and the accuracy of the simulation model depends on the validity of these assumptions. For an equilibrium stage model, it is assumed that the stage is essentially at equilibrium. Additionally, it is assumed that the models used for predicting the thermodynamic properties, namely the distribution coefficients and enthalpy, are accurate. To the extent that these assumptions are met, the performance of the equilibrium stage can be accurately predicted. 

For multicomponent mixtures, graphical representations of properties, as presented in Chapter 3, cannot be used to determine equilibrium-stage requirements. Analytical computational procedures must be applied with thermodynamic properties represented preferably by algebraic equations. Because mixture properties depend on temperature, pressure, and phase composition(s), these equations tend to be complex. Nevertheless the equations presented in this chapter are widely used for computing phase equilibrium ratios (K-values and distribution coefficients), enthalpies, and densities of mixtures over wide ranges of conditions. These equations require various pure species constants. These are tabulated for 176 compounds in Appendix I. By necessity, the thermodynamic treatment presented here is condensed. The reader can refer to Perry and Chilton as well as to other indicated sources for fundamental classical thermodynamic background not included here. 

A better insight into composition of phases along the separation process is provided by multicomponent process simulation as it can be carried out with commercial process simulating programs, such as ASPEN-h. As usual, the process is separated into theoretical stages. Normally, ASPEN+ provides thermodynamic models and calculates thermodynamic properties such as the distribution coefficients and separation factors. As the accuracy of these results is not sufficient for a design analysis in many cases, distribution coefficients (and if necessary solubilities) can be provided by a user-defined module which uses empirical correlations for these values. 

These properties can be characterized by the distribution coefficient of each adsorbing component i. This parameter can be denned as the ratio between the equilibrium eon-centrations of the surfactant in the two phases, and ean be expressed in terms of basic thermodynamic parameters [ef Eq. (10)]. In fact, considering a solute in two liquids a and P, under the hypothesis of dilute and ideal solutions, the ratio between the equilibrium concentrations and P ean be written as (163) ... 

It is seen that if the standard entropy change and standard enthalpy change for the distribution of any given solute between two phases can be calculated, then the distribution coefficient (K) and, consequently, its retention volume can also be predicted. Unfortunately, these properties of a distribution system are bulk properties, that include, in a single measurement, the effect of all the different types of molecular interactions that are taking place between the solute and the two phases. As a result it is often difficult to isolate the individual interactive contributions in order to estimate the magnitude of the overall distribution coefficient, or identify how it can be controlled. Nevertheless, there are a number of ways in which this can be done and, in any event, the thermodynamic approach can provide valuable information with regard to the nature of the distribution. 

The Thermodynamic Properties of the Distribution Coefficient The Availability of the Stationary Phase Synopsis References Chapter 3... 

Identify relevant thermodynamic properties, such as distribution coefficients. 

Equation (154) represents a solution to our kinetic model equation when the explicit expressions given in this section are used to avaluate the thermodynamic properties and transport coefficients. The solution is known to be valid at long wavelengths, or more precisely when Tk c. At the opposite extreme of very short wavelengths all the collision effects become unimportant compared to free molecular flow. Then all kinetic model solutions will tend to the distribution... 

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