In this paper we consider the large time structure of reactive solute plumes in two dimensional, macroscopically homogeneous, flow domains. The reactions between the dissolved chemicals and the porous matrix are equilibrium adsorption reactions, given by an isotherm of Freundlich type. We also incorporate the effect of partial and full decay. We use the method of asymptotic balancing to obtain, to leading order, the large time behaviour of the solute concentration and the relevant moments (mass, centre of mass,variance). The method of balancing is based on certain conjectures about the form of the temporal decay and partial spreading of the solute. These conjectures are verified numerically.