Theoretical and experimental justification of kinetic and isotherm equations for gold adsorption from solutions onto activated carbon considering intraparticle mass transfer

This study continues the research presented in our previous article [1], which examined the process of gold adsorption from gold cyanide solutions onto activated carbon (AC) over a relatively short time interval – up to 40 h – during which adsorption occurred predominantly within the near-surface layer of the sorbent. The aim of the present work was to improve the previously developed mathematical model of gold adsorption onto activated carbon from gold cyanide solutions [1] by incorporating the intraparticle mass transfer stage into the model. This goal was achieved by adding an additional term to the adsorption kinetics equation that accounts for gold sorption driven by intraparticle mass transfer. This modification preserved the entire theoretical framework of adsorption described by the earlier kinetics equation, incorporating it as a special case within a more general sorption model based on the improved kinetics equation. An analytical solution to the modified equation was derived, from which a new-type adsorption isotherm was obtained in analytical form. The paper presents the derivation and analysis of this new-type isotherm equation and its identification based on experimental data.