Kinetics of Soil Chemical Reactions: Relationships between Empirical Equations and Diffusion Models

Abstract

A variety of kinetic equations such as zero‐order, first‐order, second‐order, Elovich, fractional‐power, and parabolic‐diffusion equations have been used to describe the kinetics of soil chemical processes. Often, several of these expressions seem to equally well describe the kinetics of a particular reaction. In this research, it is shown that the kinetics of phosphate sorption/release can be described by an expression that is approximated at beginning times by a fractional‐power equation, at intermediate times by the Elovich equation, and at long times by an apparent first‐order equation. Such kinetics, which can be characterized by a sigmoidal z(t) plot of the reciprocal of the rate against the time [(dq/dt)⁻¹ vs. t], are consistent with theoretical homogeneous and heterogeneous models based on diffusion of the sorbate in the solid phase or at the solid/liquid interface. These models were applied to data from the published literature on sorption and release of phosphates by soils. For some soils, the experimental results were accounted for by assuming a constant diffusion coefficient. For other soils, it was assumed that diffusion processes with various diffusion coefficients take place simultaneously. Using these models, diffusion parameters can be estimated.