Simplification of the IAST for activated carbon adsorption of trace organic compounds from natural water

Recent studies have shown that the ideal adsorbed solution theory (IAST) coupled with the concept of equivalent background compound (EBC) can be simplified for describing trace organic compound adsorption from natural water, provided that the adsorbent surface loading is dominated by competing natural organic matter. The resulting simplified IAST has been used to reduce the complexity of kinetic models for various dynamic adsorption processes. In order to be correctly applied, however, the simplified IAST requires some additional clarification and a quantitative evaluation of the deviation caused by the simplifying assumption. In this study, we derive a simple equation that relates the relative deviation of the simplified IAST directly to the molar ratio of EBC and trace organic compound surface loadings and their Freundlich isotherm exponents. We then verify the simplified IAST using the original IAST and experimental isotherm data from the literature for trace organic compounds at various initial concentrations in natural water. By further assuming that the adsorbed amount of the EBC is substantially greater than what remains in solution, a new pseudo single-solute isotherm equation is derived and a simple relation is subsequently established between the carbon dose and the remaining trace compound concentration. The results show that the adsorption capacity and relative removal of a trace organic compound at any carbon dose can be estimated directly with the simple equations developed here and data from a single isotherm experiment for the target compound conducted in the natural water of interest.