Equilibrium constants chromatographic methods

Garst, J.E. (1984) Accurate, wide-range, automated, high-performance chromatographic method for the estimation of octanol/water partition coefficients. II Equilibrium in partition coefficient measurements, additivity of substituent constants, and correlation of biological data. J. Pharm. Sci. 73, 1623-1629. 

The reaction between cellulose and acrylamide was studied by quantitative, chromatographic separation of the substituted D-glucoses obtained on acid hydrolysis of the reaction product,320 followed by an analysis by Spurlin s method.249 Although, apparently, no check was made on the stability of the ethers to the conditions of hydrolysis, it might be expected that the ethers would isomerize only under basic conditions. The ratios of the relative equilibrium-constants for reaction at 0-2, 0-3, and 0-6 were 9 1 19, and these are attributable to the high, relative stability of the primary ether, together with the low reactivity of 0-3, also observed in rate-controlled reactions. 

The equilibrium constant can be derived from free energy considerations of gas chromatographic data. It may also be obtained directly from the measurement of all concentrations at the specified temperature by selection of a column that can separate each component and by a quantitative method of detection. 

Finally, the validity of the chromatographic methods for the determination of isotherms is based on the assumption that phase equilibrium is reached rapidly during the experiment. The rate constant for phase equilibration must be large enough for the experimental results to be independent of the mobile phase velocity. When carrying out FA, FACP, or ECP measurements on proteins that tend to equilibrate slowly, it is advisable to check the influence of the flow velocity on the isotherms (Figures 3.15 and 3.44 [38]). 

The most complete study of silver olefin complexes was made by Muhs and Weiss 21), who used a simple, rapid gas chromatographic technique. The method made use of the relationship between the complexing equilibrium constants and the retention times for olefins, using a silver nitrate-ethylene glycol stationary phase on the column. The reaction followed was... 

Another method is to independently measure the adsorption equilibrium constants of the components involved, and use them in determining the rate equation. Since the adsorption equilibrium values are very different under actual reaction conditions than under the conditions they are normally determined, care must be taken to ensure their measurement under reaction conditions. A chromatographic method based on the use of central moments appears to be particularly useful (Kubin, 1965 Kucera, 1965 Schneider and Smith, 1968). A combination of this method with statistical analysis is a sound strategy for determining the rate equation for a given reaction. This method has been successfully employed by Raghavan and Doraiswamy (1977) for the isomerization of butenes. 

The method described here is used for determining the equilibrium constant of the reaction catalyzed by ion exchange resin. It consists in preparing a reaction mixture of definite molar composition and in introducing it into a reactor (column) with ion exchange resin. Once the equilibrium between reactants of the catalytic reaction is obtained, carrier gas is passed through the column and the composition of the equilibrium mixture is analyzed by gas chromatograph. 

As a result of the continuity condition a binary isothermal system with two adsorbable components (no carrier) has a single mass transfer zone which propagates with velocity given by Eq. (8.22). This provides the basis of a simple chromatographic method for the experimental determination of binary equilibrium isotherms. The propagation velocity for a small perturbation is measured over a range of compositions for the binary mixture. The variation with composition of the apparent equilibrium constant defined by... 

Surfactant solutions above the cmc may be considered as made up of two species in equilibrium, i.e. monomers and micelles. Chromatographic methods may indicate how the monomer concentration, C., varies with the total concentration above the cmc. The concentration of monomers, C, above cmc is often assumed to be constant, as indicated surface tension [54] or from equilibrium dialysis [55]. This question was recently investigated by the use of chromatography [47]. In Fig. 14 the equilibria between the various species are depicted. Before elution the surfactant solution above cmc consists of micelles and monomers. These investigations were carried out where the eluant contained only monomers, C, somewhat lower than cmc. In order to calculate the magnitude of the monomer concentration, C, in equilibrium with micelles, when the total surfactant concentration, C, is larger than cmc, the following analytical procedure was carried out. The situation of the elution process is shown in Fig. 14b. 

Where y is the contribution of dispersive forces and y is the contribution of specific interaction forces such as H-bonding, dipole-dipole, acid-base, etc. The IGC method was successfully applied in recent years to determine the surface properties of divided solids 45,46), From gas chromatographic measurements, Vg is determined by using equation (1). Vg relates to the equilibrium constant K between the adsorbed solute and the polymer surface as follows ... 

Compositional control for other than azeotropic compositions can be achieved with both batch and semibatch emulsion processes. Continuous addition of the faster reacting monomer, styrene, can be practiced for batch systems, with the feed rate adjusted by computer through gas chromatographic monitoring during the course of the reaction (54). A calorimetric method to control the monomer feed rate has also been described (8). For semibatch processes, adding the monomers at a rate that is slower than copolymerization can achieve equilibrium. It has been found that constant composition in the emulsion can be achieved after ca 20% of the monomers have been charged (55). 

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