Modeling mass transfer for adsorptive removal of Pb(II) onto phosphate modified ordered mesoporous carbon (OMC)

Phosphate modified ordered mesoporous carbon (MOMC-NP) has been synthesized and proven to be an effective adsorbent for Pb(II) removal from aqueous solutions. However, the key application components of the mass transfer operations and diffusion coefficient have not been determined. In this study, a modified Finite Bath Diffusion Control Model was mathematically developed containing a constant related to the radius of the adsorbent particle and the fractional attainment of adsorption. The adsorption experiments were conducted under various initial Pb(II) concentrations ranging from 60 mg L^-1 to 100 mg L^-1. The results suggested that the modified Finite Bath Diffusion Control Model was more applicable to the experimental data than the original Finite Bath Diffusion Control Model. The average value of the diffusion coefficient (λD¯) obtained from the modified finite bath diffusion control model was 1.63 × 10^-2 cm² s^-1 indicating the effective diffusivity in the adsorption of Pb(II) on MOMC-NP. Overall, the modified Finite Bath Diffusion Control Model exhibited the precise description and simulation of the mass transfer kinetics for Pb(II) adsorption onto MOMC-NP. Therefore, the modified Finite Bath Diffusion Control Model could be effectively used to investigate the mass transfer kinetics of the adsorption process.