The problem analyzed in this paper is a specific application of the general M-layered composite reaction/diffusion/convection formulation given by Locke and Arce. The analysis considers electrophoretic transport of a single solute species across a one-dimensional three-layered system and the solution is obtained using operator-theoretic methods. The geometrical structure of the spectrum of the operator is determined for the complete range of the various parameters including the distribution coefficients, applied electric field, electrophoretic mobilities, and diffusion coefficients. The structure of the spectrum allows a complete characterization of all the eigenvalues of the system in terms of all of these physical parameters. Calculation of the first eigenvalue for a number of cases shows its variation with the applied electrical field for various medium porosities and allows a priori estimates of the dynamics of the process. Concentration profiles are given to illustrate the solution.