Mass conservation in the extended coordinates of space, time, and one or more exposure-time dimensions is used as a basis for the development of equations that govern the evolution of residence-time distributions of material undergoing convective-dispersive reactive transport to particular phases or states involved in the mass transfer reactions. The validity of using a continuous motion in the new exposure-time coordinate for tracking material residence-time distributions is placed in the context of the no-recrossing rule of transition state theory and arises from the representation of the reaction as a series of Bernoulli trials. A set of constitutive laws are given for describing some of the different ways in which material residence times and thus memory may be accounted. The model approach is illustrated through generalization of the conventional two-site reactive transport model to include memory of phase association. The resulting forms of the two-site model with memory are expressed and examined in light of the no-recrossing assumption. ¿ 2000 American Geophysical Union