Analytical expressions are derived for the zeroth, first, and second spatial moments of sorbing solutes that follow a linear reversible kinetic mass transfer model. We determine phase-transition probabilities and closed-form expressions for the spatial moments of a plume in both the sorbed and aqueous phases resulting from an arbitrary initial distribution of solute between the phases. This allows for the evaluation of the effective velocity and dispersion coefficient for a homogeneous domain without resorting to numerical modeling. The equations for the spatial moments and the phase-transition probabilities are used for the development of a new random-walk particle-tracking method. The method is tested against three alternate formulations and is found to be computationally efficient without sacrificing accuracy. We apply the new random-walk method to investigate the possibility of a double peak in the aqueous solute concentration resulting from kinetic sorption. The occurrence of a double peak is found to be dependent on the value of the Damköhler number, and the timing of its appearance is controlled by the mass transfer rate and the retardation factor. Two ranges of the Damköhler number leading to double peaking are identified. In the first range (DaI ≤ 1), double peaking occurs for all retardation factors, while in the second range (1 ≤ DaI ≤ 3), this behavior is most significant for R > 12.