Mathematical modelling for copper and lead adsorption on coffee grounds

Abstract

Research studies on the adsorption kinetics are conducted in order to determine the absorption time of heavy metals on coffee grounds from liquid. The models of adsorption kinetics and adsorption diffusion are based on mathematical models (Cho et al. 2005). The adsorption kinetics can provide information on the mechanisms occurring between adsorbates and adsorbents and give an understanding of the adsorption process. In the mathematical modelling of processes, Lagergren's pseudo-first- and pseudo-second-order kinetics and the intra-particle diffusion models are usually applied. The mathematical modelling has shown that the kinetics of the adsorption process of heavy metals (copper (Cu) and lead (Pb)) is more appropriately described by the Lagergren's pseudo-second-order kinetic model. The kinetic constants (k2Cu = 0.117; k2Pb = 0,037 min −1 ) and the sorption process speed (k2qeCu = 0.0058-0.4975; k2qePb = 0.021-0.1661 mg/g per min) were calculated. After completing the mathematical modelling it was calculated that the Langmuir isotherm better reflects the sorption processes of copper (Cu) (R 2 = 0.950), whilst the Freundlich isotherm - the sorption processes of lead (Pb) (R 2 = 0.925). The difference between the mathematically modelled and experimentally obtained sorption capacities for removal of heavy metals on coffee grounds from aqueous solutions is 0.059-0.164 mg/l for copper and 0.004-0.285 mg/l for lead. Residual concentrations of metals in a solution showed difference of 1.01 and 0.96 mg/l, respectively.