We present an analytical model describing solute transport subject to nonlinear solute adsorption and demonstrate the exact correspondence of the model with water infiltration. The model is applied to experimental data from a laboratory Ca-K exchange experiment in which a solution containing Ca is passed through a column filled with K- saturated soil. The model, which is based on the assumption of local equilibrium of the solute between the adsorbed and liquid phases, fails to predict the spreading of the experimental breakthrough curve. Further analysis, however, suggests that chemical kinetic non- equilibrium exchange is occuring, thus violating the model assumption of local equilibrium.