Equilibrium constants chromatography

Figure 4.17 General phenonenaloglcal retention model for a solute that participates in a secondary chemical equilibrium in liquid chromatography. A - solute, X - equilibrant, AX analyte-equilibrant coeplex, Kjq - secondary chemical equilibrium constant, and and are the primary distribution constants for A and AX, respectively, between the mobile and stationary phases.

It is desirable that the equilibrium constant for a solute be not zero or very large lest there be no net retention or near infinite retention. The catch comes in the fact that liquids, which are relatively good solvents for a given type of molecule are also solvents for each other. This means the risk involved is by washing off the stationary phase with the mobile phase. Yet liquid-liquid methods offer much promise for relatively nonvolatile but soluble molecules and their separation of one from the other. The discovery of liquid-liquid chromatography earned Martin and Synge the Nobel Prize when they applied it to amino acids with water mobile phases and organic liquid stationary phases. 

Isotopes of hydrogen. Three isotopes of hydrogen are known H, 2H (deuterium or D), 3H (tritium or T). Isotope effects are greater for hydrogen than for any other elements (and this may by a justification for the different names), but practically the chemical properties of H, D and T are nearly identical except in matters such as rates and equilibrium constants of reactions (see Tables 5.1a and 5.1b). Molecular H2 and D2 have two forms, ortho and para forms in which the nuclear spins are aligned or opposed, respectively. This results in very slight differences in bulk physical properties the two forms can be separated by gas chromatography. 

Figure 4.2 Protein transformations in reversed-phase chromatography for a two-state model. The native folded state can exist in either the mobile phase (Fm) or the stationary phase (Fs), as can the unfolded state (Um, Us). The equilibrium constants (k) for interconversions of the four species are indicated. (Reproduced from X.M. Lu, K. Benedek, and B.L. Karger, J. Chromatogr., 359 19 [1986]. With permission from Elsevier Science.)...

In Equation 1.15, q represents the adsorbed amount of solute, ns and qs are the saturation capacities (number of accessible binding sites) for site 1 (nonstereoselect-ive, subscript ns) and site 2 (stereoselective, subscript s), and fens and bs are the equilibrium constants for adsorption at the respective sites [54]. It is obvious that only the second term in this equation is supposed to be different for two enantiomers. Expressed in terms of linear chromatography conditions (under infinite dilution where the retention factor is independent of the loaded amount of solute) it follows that the retention factor k is composed of at least two distinct major binding increments corresponding to nonstereoselective and stereoselective sites according to the following... 

On the contrary, a more advanced methodology makes use of nonlinear chromatography experiments If the adsorption isotherms are measured under variable temperatures, the corresponding thermodynamic parameters for each site can be obtained in view of the van t Hoff dependency (site-selective thermodynamics measurements) [51,54]. Thus, the adsorption equilibrium constants of the distinct sites bi a = ns, s) are related to the enthalpy (A// ) and entropy (A5j) according to the following equation [54] ... 

Ackers, G. K., and T. E. Thompson Determination of stoichiometry and equilibrium constants for reversible associating systems by molecular sieve chromatography. Proc. Natl. Acad. Sci. 53, 342 349 (1965). 

Uioxane. 72.166, 174-176 Dipeptkles. 263 Diphenyidichlorosilane. 133 Dipole moment. 208.217 Diprotic acids, equilibrium constants and retention bctors in hetaeric chromatography. 241... 

Chromatography and thermodynamics. Thermodynamic relationships can be applied to the distribution equilibria defined in chromatography. /C(= Cs/Cm), the equilibrium constant defining the concentration C of analyte in the mobile phase (M) and stationary phase (S) can be determined from chromatographic experiments. If the temperature of the experiment is known, it is possible to determine the variation of the standard free energy AG° for this transformation ... 

Adsorption Chromatography. In a linear multicomponent system (several sorbates at low concentration in an inert carrier) the wave velocity for each component depends on its adsorption equilibrium constant. Thus, if a pulse of the mixed sorbate is injected at the column inlet, the different species separate into bands which travel through the column at their characteristic velocities, and at the outlet of the column a sequence of peaks corresponding to the different species is detected. Measurement of the retention time (7) under known flow conditions thus provides a simple means of determining the equilibrium constant (Henry constant). 

A characteristic of small-molecule liquid chromatography is the reversibility of their contacts with the stationary phase. The distribution equilibrium constant determines the duration of the stationary periods and, thus, the retention of the solute. With polymers, isocratic retention factors of normal degree (i.e., 1 gk 10) generally do not occur. A fractional alteration of elution conditions may cause transition from zero retention to infinity. As a rule of thumb, polymers either pass without retention or remain in the column. This off or on behavior produces the impression of irreversible fixation under the conditions of retention. 

The good agreement of the equilibrium constants with the values for ideal randomness (Table II) confirms Calingaert s conclusions. Analyses of tetramethyl- and tetraethyllead redistribution mixtures today may be performed conveniently by gas chromatography (20, 67, 232). 

On heating Ni(CO)4 and Ni(PF3)4 or any of the intermediates having mixed ligands at 75° C, a mixture of all five redistribution compounds Ni(CO)4 n(PF3) (n=0, 1, 2, 3, and 4) is obtained. Quantitative separation has been accomplished by gas chromatography and a nearly random distribution has been observed. However, the authors claim that the study was not performed with sufficient accuracy to determine equilibrium constants or to judge how closely this system comes to being truly random. 

Similarly, the reaction of phosphorus trifluoride and iron pentacarbonyl 59) at elevated temperatures and pressures results in a mixture of compounds of the general formula Fe(CO)5 B(PF3)B, where n=0-5. All of these compounds were isolated from the reaction mixture by gas chromatography. However, it is stated that equilibrium was most probably not reached and thus no efforts were made to calculate equilibrium constants. Similar studies have been mentioned to be in progress with molybdenum carbonyls (5). 

We will first approach liquid chromatography by assuming that both phases are bulk fluids (i.e. LLC), and generalize our approach later. For LLC we can define a thermodynamic equilibrium constant (Klh) as... 

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