The problem of substantiating a pseudo-second order equation in the kinetics of sorption processes is considered. A simple way is presented of transforming the Langmuir kinetic equation written for a process within a limited volume into a polynomial relation in the form of the sum of difference terms of first- and second-order kinetic equations. It is shown that such a relation is reduced to a good approximation of a pseudo-second order equation over a much wider range of conditions determined by the equilibrium and kinetic characteristics of the sorbent and the experimental parameters than was predicted earlier. It is established that the errors of such a theoretical approximation are either negligible or do not exceed the corresponding errors at the initial stage of kinetic experiments within a confined space. It is concluded that the applicability of the pseudo-second order model is independent of the mechanisms determining the rate of sorption and does not require concepts of chemisorption or special equations of kinetics controlled via chemical reactions or diffusion.

The batch sorption kinetics described by a nonlinear equation with a variable equilibrium parameter for the interface was considered. It was shown that a difference equation of this type can...

The paper describes the new phenomenon called Ion-Exchange Isothermal Supersaturahon (IXISS). This effect is observed for a number of ion-exchange systems, where frontal or reverse frontal separation is accompanied by the formation of stable supersaturated solutions of slightly soluble substances in the interstitial space of ion-exchange columns. After leaving the column a supersaturated solution crystallizes spontaneously, which allows for designing practically ideal ion-exchange process where a crystalline product is obtained right after the ion-exchange purification cycle. The paper comprises results on experimental investigation of IXISS of amino acids (e.g., such as glutamic, aspartic and some others), calcium and magnesium salts (sulfates and carbonates), and some other substances. The mechanisms of stabilization of supersaturated amino acid solutions in the interstitial space is proposed and confirmed experimentally. Methods for identification of substances exhibiting the IXISS effect and practical application of the IXISS phenomenon for separation and ion-exchange synthesis of substances and some other problems are discussed.

The effect of high supersaturation of magnesium carbonate solutions in an ion-exchange bed is displayed on treatment of (Mg²⁺-Na⁺) forms of carboxylic resins in the column with solutions of sodium carbonate and sodium bicarbonate. Upon leaving the column the supersaturated eluate decomposes with formation of coarse-grained crystals of nesquegonite: MgCO₃·3H₂O. The sorption scheme of isolating pure magnesium compounds from seawater by means of the effect of isothermal supersaturation was advanced and tested on a pilot-plant scale. The proposed process includes stages of isolation of calcium using natural and manufactured zeolites and isolation of magnesium using carboxylic ion-exchange resins. The mathematical model of the dynamics of the ion-exchange process with super-saturation is developed.