Application of the Nernst-Planck approach to lead ion exchange in Ca-loaded Pelvetia canaliculata

Ca-loaded Pelvetia canaliculata biomass was used to remove Pb²⁺ in aqueous solution from batch and continuous systems. The physicochemical characterization of algae Pelvetia particles by potentiometric titration and FTIR analysis has shown a gel structure with two major binding groups - carboxylic (2.8 mmol g⁻¹) and hydroxyl (0.8 mmol g⁻¹), with an affinity constant distribution for hydrogen ions well described by a Quasi-Gaussian distribution. Equilibrium adsorption (pH 3 and 5) and desorption (eluents: HNO₃ and CaCl₂) experiments were performed, showing that the biosorption mechanism was attributed to ion exchange among calcium, lead and hydrogen ions with stoichiometry 1:1 (Ca:Pb) and 1:2 (Ca:H and Pb:H). The uptake capacity of lead ions decreased with pH, suggesting that there is a competition between H⁺ and Pb²⁺ for the same binding sites. A mass action law for the ternary mixture was able to predict the equilibrium data, with the selectivity constants α_Ca^H = 9 ± 1 and α_Ca^Pb = 44 ± 5, revealing a higher affinity of the biomass towards lead ions. Adsorption (initial solution pH 4.5 and 2.5) and desorption (0.3 M HNO₃) kinetics were performed in batch and continuous systems. A mass transfer model using the Nernst-Planck approximation for the ionic flux of each counter-ion was used for the prediction of the ions profiles in batch systems and packed bed columns. The intraparticle effective diffusion constants were determined as 3.73 × 10⁻⁷ cm² s⁻¹ for H⁺, 7.56 × 10⁻⁸ cm² s⁻¹ for Pb²⁺ and 6.37 × 10⁻⁸ cm² s⁻¹ for Ca²⁺.