A simple equation to describe sorption of anions by goethite

A simple equation to describe sorption of anions by goethite would be useful as a means of characterizing batches of goethite and in studies of plant uptake of anions from the sorbed form. A suitable relationship between solution concentration (c) of phosphate or citrate and their sorption (S) by goethite at a constant pH or at different pH Values is c = a exp(b S)S/(S-Max -S), where b is a parameter, S-Max is the maximum sorption, and a is a parameter at constant pH. In the middle range of sorption (from about 30% to about 70% of maximum sorption) this equation approximated to a Tempkin equation, but the full equation is more useful as it applied over the whole sorption range. The values of a varied with pH. This variation could be explained by changes in the electric potential of the adsorbing surfaces and in the degree of dissociation of the anions. The parameter a could therefore be replaced by a function of pH. The effects were consistent with formation of bidentate phosphate complexes and tridentate citrate complexes with the goethite surface.