16] Determination of equilibrium constants by countercurrent distribution

Abstract

Three procedures have been outlined which may be used to obtain chemical equilibrium constants from countercurrent distribution experiments. The first, which has been used experimentally and is likely to be the most sensitive, depends on fitting predictions computed from a model to the experimental zonal countercurrent distribution pattern. The fit is optimized by variation in succession of the unknown parameters, such as equilibrium constants. For this procedure, it is necessary to perform iterative computations with the aid of a digital computer, to make the necessary predictions. The second procedure consists of measuring directly the weight-average rate factor { K (1+K) } w from the countercurrent distribution pattern in moving boundary experiments. This is done at different loading concentrations or compositions, and the data are combined with individual rate factors for the species present, to obtain equilibrium constants. The third procedure is to study the movement of differential moving boundaries between two large regions of constant composition. Such data, in the case of only one reacting solute, which is a single thermodynamic component, gives rise to the Z -average rate factor. In the case of a monomer-single polymer equilibrium, the use of this quantity, together with the weight-average rate factor and the rate factor for monomer, leads very directly to the equilibrium constant for the reaction. There is an important potential advantage in the use of the counter-current distribution technique rather than continuous transport methods in such determinations. Even if the reactions are quite slow, one can allow the system to come to equilibrium at each stage in countercurrent distribution with no loss in resolution whatsoever, and one can also test quite carefully to assure that equilibrium has been achieved. However, due to the effects of diffusion in continuous transport methods, resolution is impaired by decreasing the field responsible for migration. Moreover, if the speed of reaction is slow enough so that appreciable migration takes place before chemical equilibrium is locally reestablished, a wide variety of artifacts can also occur, which seriously complicate the possibility of achieving any meaningful equilibrium measurements. 23