Rare earth elements (REEs) are valuable and strategically important in many high-technology areas, such as laser technology, pharmacy and metallurgy. The main methods of REE recovery are precipitation, extraction and sorption, in particular ion exchange using various sorbents, which allow to perform selective recovery and removal of associated components, as well as to separate rare earth metals with similar chemical properties. The paper examines recovery of ytterbium in the form of coordination compounds with Trilon B on weakly basic anion exchange resin D-403 from nitrate solutions. In order to estimate thermodynamic sorption parameters of ytterbium anionic complexes, ion exchange process was carried out from model solutions under constant ionic strength specified by NaNO3, optimal liquid to solid ratio, pH level, temperatures 298 and 343 K by variable concentrations method. Description of thermodynamic equilibrium was made using mass action law formulated for ion exchange equation and mathematically converted to linear form. Values of equilibrium constants, Gibbs free energy, enthalpy and entropy of the sorption process have been calculated. Basing on calculated values of Gibbs energy, a sorption series of complex REE ions with Trilon B was obtained over anion exchange resin D-403 from nitrate solutions at temperature 298 K. Sorption characteristics of anion exchange resin have been estimated: total capacity, limiting sorption of complex ions, total dynamic capacity and breakthrough dynamic capacity.

A complex heterogeneous process of ion exchange can be defined with an isotherm-isobar equation of the chemical reaction, which describes differential affinity between the process and its effect - the law of mass action. Ion exchange includes processes accompanied by changes in the charge of ions and functional groups caused by the passing of ionic bond into covalent one. Hence isotherm equations of ion exchange for such processes must differ from conventional stoichiometric equations, but they can be obtained by classical study approaches to ion exchange equilibrium. The paper describes a new thermodynamic model, based on linearization of mass action law, modified for the ion exchange equation. The application of this model allows to define stoichiometry of ion exchange and the shape of ions adsorbed by the solid phase of ion-exchange resins, as well as to estimate equilibrium constant and Gibbs free energy of the process. Comparative analysis has been carried out for the thermodynamic model of cerium sorption in the form of anionic complex with Trilon B from a multisalt solution with ionic strength of 1 mol/kg (NaNO3) under PH= 3 and temperature 298 K on a test sample of weak-base anion-exchange resin Cybber EV009. Experimental isotherm of the sorption has been obtained. Calculations of thermodynamic parameters have been performed using Langmuir, Freundlich, Dubinin -Radushkevich, Temkin and Flory - Huggins models, as well as thermodynamic model of linearized mass action law, proposed by the authors. Calculated values of the equilibrium constant and Gibbs energy - K = 9.0 +/- 0.5 and Delta rG(298)(0) = -5.54 +/- 0.27 kJ/mol - characterize the sorption of EDTA cerate ions by ion-exchange resin. The shape of adsorbed ions has been defined in Stern-Helmholtz layer of CeTr, and total capacity of anion resin EV009 for EDTA cerate ions has been estimated as q(infinity) = 2.0 +/- 0.1 mol/kg.