In this contribution, the dynamic (or alternating current (AC)) electrophoretic mobility of spherical colloidal particles in a realistic salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Such a suspension is a concentrated one (in charged solid particles) in an aqueous solution without any electrolyte added during the preparation. The ionic species in solution can solely be: (i) the "added counterions" stemming from the particles (for example, by ionization of particle surface ionizable groups), (ii) the H+ and OH-ions from water dissociation, and (iii) the ions produced by the atmospheric CO2 contamination. The corrections related to water dissociation and CO2 contamination in suspensions open to the atmosphere have turned out to be tremendous in many of the experimental situations of interest in direct current (DC) electric fields, Thus, it is mandatory to explore their influence in the more complex situation of AC electrophoresis. The results confirm the importance of ions produced by water dissociation and those originated by the acidification of the aqueous solution in suspensions contaminated with atmospheric CO2, for low to moderate particle volume fractions, where the role of the added counterions is screened by the other ionic species. It is worth mentioning that, for high particle charges, two Maxwell-Wagner processes develop in the mobility frequency spectrum, respectively linked to the diffuse layer relaxation and to the relaxation of a condensed layer of counterions located very close to the particle surface. This is the so-called ionic condensation effect for highly charged particles, already described in the literature, and which for the first time will be studied in detail in realistic salt-free systems. The dynamic electrophoretic mobility will be numerically computed throughout a wide frequency range and compared with the cases of pure and realistic salt-free conditions. In addition, the competition between different relaxation processes associated to the complex electric dipole moment induced on the particles by the field, the particle inertia, as well as their influence on the dynamic response, will be explored for pure and realistic cases.