We study the effect of nonbinding Na(+) ions on the kinetics of rupture of alginate gels cross-linked by Ca(2+). Wetting a crack tip with a saline solution at physiological concentrations is found to be able to induce a quasi-instantaneous, 10-fold velocity jump. This effect is analyzed with a phenomenological model for the rate-dependent fracture energy in physical gels, extended here to account for the role of ions on the rate of cross-link ``unzipping''. Ionic interaction is found to act cooperatively with mechanical tension, leading to an enhanced rate of rupture. The kinetics turns out to be second order in counterion concentration. The definition of the reference state requires to take into account counterion condensation due to long-range interactions in the polyelectrolyte gel. Surprisingly, the contribution of the Na(+) ions to the free energy of the activated state is essentially entropic, suggesting that the displacement of Ca(2+) is primarily a steric process, electrostatic interactions being reduced to the constraint of charge conservation. This phenomenon may have important consequences on the rate of degradation of alginate based scaffolds for in vivo tissue regeneration.