A kinetic modeling study of phosphate adsorption onto Phoenix dactylifera L. date palm fibers in batch mode

The removal of phosphates from aqueous solutions by adsorption onto date palm fibers (DPF) has been studied in batch mode. The aim of this study was to understand the mechanisms that govern phosphate sorption and find an appropriate model for the kinetics of removal. In order to investigate the mechanism of sorption and potential rate controlling steps, pseudo first-order, pseudo second-order, intra-particle diffusion and the Elovich equations have been used to test experimental data. Kinetic analysis of the four models has been carried out for initial phosphate concentration in the range of 30-110 mg/L. The rate constants for the four models have been determined and the correlation coefficients have been calculated in order to assess which model provides the best fit predicted data with experimental results. Seven statistical functions were used to estimate the error deviations between experimental and theoretically predicted kinetic adsorption values, including the average relative error deviation (ARED), Marquardt's percent standard error deviation (MPSED), the hybrid fractional error function (HYBRID), the sum of the squares of the errors (SSE) and three alternative statistical functions, including the Chi-square test, the F-test and Student's T-test. The results showed that, both Elovich equation and pseudo second-order equation provide the best fit to experimental data for different initial phosphate concentrations.