Reacting, nonlinearly adsorbing solute transport in chemically heterogeneous soils is studied. Assuming adsorption is adequately described with the Freundlich equation, random variation of the adsorption coefficient is assumed to describe the heterogeneity. In a homogeneous case, traveling wave fronts develop, characterized by a constant velocity and a constant front shape. Using the method of moments, an analytical expression is derived to describe the constant variance of the traveling wave front. Deviations from the analytical variance and velocity, both calculated with an average adsorption coefficient, show that column scale heterogeneity has significant effects on front spreading and front movement. Expected values of front velocity and variance are computed as averages of values of 600 randomly generated columns. The nonlinear process causes small deviations from the case with average parameters. The ensemble average concentration front, representing an average front for the flow domain, shows that three mechanisms are responsible for the front spreading. At early displacement times the front spreading is caused by the thickness of the individual traveling waves. Subsequently, the effect of the internal variation of the adsorption coefficient (column scale heterogeneity) increases, whereas at large displacement times the front spreading is dominated by the different retardation coefficients of the different columns. The latter effect causes the variance to increase in proportion tot2. An analytical approximation is derived for the ensemble average front, ignoring column scale heterogeneity.