  The Poisson-Nernst-Planck (PNP) diffusional model for the immittance or
impedance spectroscopy response of an electrolytic cell in a finite-length
situation is extended to a general framework. In this new formalism, the bulk
behavior of the mobile charges is governed by a fractional diffusion equation
in the presence of a reaction term. The solutions have to satisfy a general
boundary condition embodying, in a single expression, most of the surface
effects commonly encountered in experimental situations. Among these effects,
we specifically consider the charge transfer process from an electrolytic cell
to the external circuit and the adsorption-desorption phenomenon at the
interfaces. The equations are exactly solved in the small AC signal
approximation and are used to obtain an exact expression for the electrical
impedance as a funcion of the frequency. The predictions of the model are
compared to and found to be in good agreement with the experimental data
obtained for an electrolytic solution of CdCl2H20.
