We show that colloidal suspensions that acquire a surface charge by capturing ions from the surrounding solution display unexpected and remarkable phoretic behavior. Depending on suspension volume fraction, a critical zeta potential ζ exists where the effective electrophoretic mobility diverges, becoming virtually infinite. Beyond such critical value, a ζ-range is identified where mobility reversal occurs, i.e., the effective mobility becomes negative. This counterintuitive behavior is due to the salt gradient engendered by phoretic drift of this kind of particles, which capture and release ions (salt), respectively, at the start and the end of the phoretic path. This salt gradient deeply influences the electric field in the bulk electrolyte where the particles migrate: it can make the field vanish, hence the mobility divergence, or even entail inversion of the field, which is reflected in the mobility reversal. These findings should spur new concepts in a variety of traditional and emerging technologies involving, for example, the separation or targeting of colloids as well as in applications where the creation or manipulation of chemical gradients or electric fields in solution is critical.