Development and solution of the kinetics equation and adsorption isotherm for gold adsorption from cyanide solutions onto activated carbon

This paper presents the results of theoretical and experimental studies on the process of gold adsorption from cyanide solutions onto activated carbon (AC). One of the objectives of the study was to identify the functional relationship between the mass loading of AC in the volume of the adsorption column solution and the kinetics of the process. To achieve this, a modified adsorption kinetics equation (considering the heterogeneity of the process) was proposed, which incorporates the solid phase of the carbon sorbent in the unit volume of solution as a third intermediate agent of adsorption interaction between the adsorbate ions and the free active sites of the AC. As a result, a modified third-order adsorption kinetics equation for gold adsorption on AC was derived, taking into account the solid phase loading of AC in the solution volume, along with its analytical solutions under conditions of constant gold content in the initial solution and the process conducted in a closed volume with varying gold concentrations in the solution according to the material balance equation. The relationship between the solutions of the kinetic equation and the adsorption isotherm equation was established. From the solutions of the kinetic equation, a modified Langmuir isotherm equation was derived, which allows determining the equilibrium concentrations of gold on the AC and in the solution a priori under the condition that the process is conducted in a closed volume, with known initial gold contents in the solution and on the AC, as well as with a known AC loading in the adsorber volume. The theoretical dependencies of the adsorption and desorption rate constants on temperature, convective, and diffusion parameters are discussed. The presented mathematical model of adsorption kinetics is valid under the conditions of gold adsorption on AC from gold cyanide solutions with an adsorption time of up to 2 days and a sorbent capacity utilization degree of 40–60%.