Multifactor Kinetics of Phosphate Reactions with Minerals in Acidic Soils: I. Modeling and Simulation

Abstract

Abstract A mathematical model was developed to simulate phosphate reactions with minerals in acidic soils. Phosphate in solution was assumed to react with kaolinite, gibbsite, and goethite simultaneously. Each reaction had a two‐step sorption mechanism, i.e., mineral + solution P ⇄ labile P ⇄ nonlabile P, where labile and nonlabile forms are defined as isotopically exchangeable and nonexchangeable, respectively. The first step of the sorption mechanism followed the kinetic version of the Langmuir adsorption isotherm and was a second‐order reaction in nature. The second step of the sorption mechanism was a linear reversible kinetic equation. Seven ordinary differential equations describing the system were solved by numerical methods. The model effectively simulated the trend of phosphate reactions with soil minerals. Using the model to study the adsorption isotherm, we found that the Langmuir plot, i.e., concentration/adsorption vs. concentration, was linear when minerals had relatively homogeneous adsorption rates (or adsorption energies) and was nonlinear for widely differing rates, implying that a homogeneous surface provides a sufficient condition but not a necessary condition for a linear Langmuir plot. Simulation and analysis of a two‐surface Langmuir equation supported this finding.