Practice of Chromatography: Deriving Isotherms from Elution Curves.

Sorption isotherms are essential when describing cation‐exchange processes. This study tested the usefulness of chromatographic principles for calculating isotherms from column elution curves obtained for a series of miscible‐displacement column experiments in which K was exchanged with Ca. The isotherms were obtained from nonlinear, least‐squares inversion of elution curves, using a numeric procedure. These data served as control for two analytic approximations: the classical approximation (which is based on the difference in moment of breakthrough between retarded and non‐reactive species) and an approximation based on the quotient of the two moments. All these data were controlled for one experimental series by the incremental step method, which yields stable plateau values from mass balance. The methods agree reasonably; the results indicate that the chromatographic technique is useful for deriving isotherms, especially when combined with the incremental step method. The applicability of the technique improves with increasing column Peclet number. Specific results show that the numeric method and/or the analytic approximations, together with the incremental step method, offer an easy and reliable way to check the validity of the local equilibrium assumption: disequilibrium is indicated by a discontinuity in derivative between the end of an experiment and the beginning of the next experiment.