A methodology is presented for evaluating the temporal moments of solutes undergoing linear rate-limited mass transfer processes based on a Lagrangian approach to solute transport in heterogeneous media. The temporal moments of sorbing solutes are written as a function of those of conservative tracers. The general continuous diffusion rate model that has recently appeared in the hydrologic literature is used to model the rate-limited mass transfer processes. The methodology is also applied to desorption from an initially uniformly contaminated aquifer, and the concentration expected value and variance are found quasi-analytically. The conditional temporal moments of sorbing solutes can be written as a function of the conditional moments of conservative tracers. Conditioning results in a reduction of the variance of travel time. The amount of reduction depends on the chemical model selected.