Using quasielastic neutron scattering spectroscopy, we measured the averaged translational diffusion of water in solutions of biologically relevant salts, NaCl, a kosmotrope, and KCl, a chaotrope. The analysis revealed the striking difference in the influence of these ions on water dynamics. While the averaged water diffusion slows down in the presence of the structure making (kosmotrope) Na+ ion, the diffusion becomes faster in the presence of the structure breaking (chaotrope) K+ ion. The latter means that, despite strong Coulombic interactions introduced by the K+ ions, their disruption of the hydrogen-bonding network is so significant that it leads to faster diffusion of the water molecules.