Thermodynamic Distribution Constant

A solute undergoing chromatographic migration partitions between the stationary and mobile phases, a process driven by thermodynamic equilibrium. At equilibrium (established fully only at the zone center), the concentration in the stationary phase (c,) relative to that in the mobile phase (cm) is given by the thermodynamic distribution constant K, as shown by comparing Eqs. 2.18 and 2.19. Thus... 

A thermodynamic approach has just been used to show what is important analytically, that is, LLE enables an analyte to be transferred from the sample to the extracting solvent and remain at a fixed concentration over time in the extractant. This ratio of activities is defined as the thermodynamic distribution constant, K°, so that... 

It becomes important to TEQA to relate the thermodynamic distribution constant, Z , to measurable concentrations of dissolved solute in both phases. Because the chemical potential for a given solute must be the same in both immiscible phases that are in equilibrium, Eq. (3.2) can be rewritten in terms of activity coefficients and concentration according to... 

Upon substituting Eq. (3.6) into Eq. (3.7), we obtain the relationship between the partition ratio and the thermodynamic distribution constant according to... 

Equation (3.8) is the desired outcome. In many cases with respect to TEQA, the activity coefficients of solutes in both phases are quite close to unity. The partition ratio and thermodynamic distribution constant can be used interchangeably. 

This relationship resulted from the spontaneous tendency for the analyte, initially solubilized in an aqueous matrix, to partition into the surface monolayer of hydrophobic octadecyl- or octyl-bonded silica. Organic compounds as analytes will have a unique value for the thermodynamic distribution constant. One fundamental difference between LEE and SPE stands out Partition or adsorption of solute molecules onto a solid surface follows the principles of the Eangmuir adsorption isotherm, whereas EEE does not. We will briefly develop the principles below. This model assumes that an analyte A combines with a site of adsorption, S, in which there is a finite number of such sites according to... 

It is the adjusted retention volume which is directly proportional to the thermodynamic distribution constant and therefore the parameter often used in theoretical equations. In essence it is the retention time measured from the nonretained peak (air or methane) as was shown in Figure 1.5. 

Distribution coefficients on pure-phase R or S Thermodynamic distribution constant. Equation 11.5 Distribution constant in which the concentration in the stationary phase is expressed as weight of substance per weight of the dry solid phase... 

Batch adsorption experiments by Yee and Fein (2002) using aqueous Cd, B. subtilis, and quartz as a function of pH showed that the thermodynamic stability constants, determined from binary systems, could successfully describe the distribution of Cd between the aqueous phase and the bacterial and mineral surfaces. The constants could also be used to estimate the distribution of mass in systems, and construct a surface complexation model. 

As regards the effect of temperature on the distribution constant, if both phases are ideal, the distribution constant is equivalent to the thermodynamic constant, and we can write... 

Medium-chain alcohols such as 2-butoxyethanol (BE) exist as microaggregates in water which in many respects resemble micellar systems. Mixed micelles can be formed between such alcohols and surfactants. The thermodynamics of the system BE-sodlum decanoate (Na-Dec)-water was studied through direct measurements of volumes (flow denslmetry), enthalpies and heat capacities (flow microcalorimetry). Data are reported as transfer functions. The observed trends are analyzed with a recently published chemical equilibrium model (J. Solution Chem. 13,1,1984). By adjusting the distribution constant and the thermodynamic property of the solute In the mixed micelle. It Is possible to fit nearly quantitatively the transfer of BE from water to aqueous NaDec. The model Is not as successful for the transfert of NaDec from water to aqueous BE at low BE concentrations Indicating self-association of NaDec Induced by BE. The model can be used to evaluate the thermodynamic properties of both components of the mixed micelle. 

The chemical equilibrium model of Roux et al (6) is a powerful tool for the study of the thermodynamics of mixed micellar solutions. It can estimate the distribution constant of the surfactant 3 between water and micelles of the surfactant 2 and the thermodynamic properties of the surfactant 3 in the mixed micelles. For this it is necessary to obtain reliable data over a large concentration range of solute 2. 

The magnitude and sign of the distribution constants and of the thermodynamic functions of the transfered solute to the mixed micelle, when compared with those predicted from the binary systems, indicate that the formation of a mixed micelle between BE and NaDec is a highly favorable event. 

In Section 2.1.3 we discussed extractions from the viewpoint of one substance being transferred from one phase to another or the separation of two solutes by selective extraction. When we have a system in which the distribution constants (K) or distribution coefficients (ftc) differ by 103, we can only recover the extracted solute in about 97% purity. Continued extractions will increase yield but not purity. Good separations, with high purity, of two or more solutes can be achieved when there is a difference in the thermodynamic behavior of the various solutes, that is, a difference in the distribution constants (K) or coefficients (Kc). A measure of this degree of separation is the separation factor, a, for pairs of solutes which is defined as... 

Thus the selectivity a has a thermodynamic interpretation as the ratio of two distribution constants. Consequently a is itself a constant, independently from the injected concentrations of the analyte and the interferent, respectively. 

These programs are able to model the geological systems soil/rock-aqueous solution systems that is the concentration and distribution of the thermodynamically stable species can be determined based on the total concentrations of the components and the parameters just mentioned. In addition, the programs can also be used to estimate thermodynamic equilibrium constants and/or surface parameters from the concentrations of the species determined through experiments. Thermodynamic equilibrium constants can be found in tables (Pourbaix 1966) or databases (e.g., Common Thermodynamic Database Project, CHESS, MINTEQ, Visual MINTEQ, NEA Thermodynamical Data Base Project (TDB), JESS, Thermo-Calc Databases). Some programs (e.g., NETPATH, PHREEQC) also consider the flowing parameters. 

This distribution law applies only to the distribution of a definite chemical species, as does Henry s law. The distribution constant is not a true thermodynamic equilibrium constant, since it involves concentrations rather than activities. Thus it may vary slightly with the concentration of the solute (particularly because of the relatively high concentration of I2 in the CCI4 phase) it is therefore advantageous to determine 1 at a number of concentrations. It can be determined directly by titration of both phases with standard thiosulfate solution when I2 is distributed between CCI4 and pure water. Once k is known, (I2) in an aqueous phase containing I3 can be obtained by means of a titration of the I2 in a CCI4 layer that has been equilibrated with this phase. The use of a distribution constant in this manner depends upon the assumption that its value is unaffected by the presence of ions in the aqueous phase. 

The use of a typical equilibrium constant K in chromatographic theory indicates that the system can be assumed to operate at equilibrium. As the analyte (X) proceeds through the system, it partitions between the two phases and is retained in proportion to its affinity for the stationary phase. At any given time, a particular analyte molecule is either in the mobile phase, moving at its velocity, or in the stationary phase and not moving at all. The individual properties of each analyte control its thermodynamic distribution and retention, and result in differential migration of the components in the mixture—the basis of the chromatographic separation. The effectiveness of the separation, however, is a function of both thermodynamics and kinetics. 

The K value for the silver complex of an acetylene, hex-3-yne, as determined by the distribution method 14>, was found to be 19.1, i.e. smaller than those of alkenes such as the pentenes and cyclohexene, but greater than those of aromatic hydrocarbons 1S). A later study of silver-acetylene complexes 16> using the more rapid solubility technique of Andrews and Keefer 1S> gave rise to quasi thermodynamic equilibrium constants , Ka (as opposed to K) for various methyl substituted hex-3-ynes and hept-2-yne. There was good agreement for the K values for hex-3-yne for the two different methods in each case, replacement of an a-hydrogen atom by a methyl group caused a decrease in the value of Ka, similar to that observed in alkenes. Values of AH approximated to 19-21 kJ mole-1. 

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