In this study, the synthesis and characterization of cerium oxide nanoparticles (CeO(2)-NPs) and their adsorption potential for removing phosphate from water was evaluated using a multi-factor experimental design to explore the effect of various factors on adsorption. The objective function selected was the percentage of phosphate removed from water, in which the phosphate concentration and the CeO(2)-NP concentration are quantitative variables (factors in the experimental design). A lineal polynomial fitted the experimental results well (R(2) = 0.9803). The nanostructure was studied by transmission electron microscopy (TEM) and high-resolution TEM techniques before and after the adsorption process. During the adsorption and desorption processes several changes in the morphology and surface chemistry of the CeO(2)-NPs were observed.