The hopping mechanism of electrolytic conductivity is analyzed, employing mixtures of two solvents: one that sustains the hopping mechanism and the other that does not inhibit it directly, but interferes with it by diluting the solvent that sustains hopping. Measurement of the equivalent conductivity shows that the excess proton conductivities of H3O+ and OH- increases with increasing temperature, although the number of hydrogen bonds is known to decrease. In mixtures of acetonitrile with water, proton hopping does not start until a threshold concentration of about 20 vol.% water has been reached, while no such threshold concentration is observed upon addition of methanol to acetonitrile. It is concluded that in the former the proton is transferred to a cluster of water molecules, which can be formed only if there is enough water in the solvent mixture. This observation leads to the concept of mono-water, which is the state of water molecules when they constitute a small minority in the solvent mixtures, as opposed to bulk water, which consists of clusters of variable sizes. Systems in which a hopping mechanism of heavy ions has been observed include Br-/Br-2 and I-/I-2, In these cases the triple ions Br-3(-) and I-3(-), respectively are formed, and serve as the mediators for the transfer of the simple halogen ion. A very large increase of conductivity was observed upon solidification of the Br-/Br-3 system, probably caused by favorable linear alignment of ions in the solid. The conductivity of acidified methanol decreases upon addition of water, because the affinity of the proton to water is higher than to methanol, thus water can act as a scavenger for protons. This behavior exemplifies a general observation, namely that conductivity by hopping can only occur when the Gibbs energy of the system does not change significantly following ion transfer; otherwise the ions would be trapped in the more stable state, hindering further propagation by hopping. The dependence of the Walden product on temperature can serve as an experimental criterion for hopping. A distinct decline of the product lambda(0) x n with increasing temperature is a clear indication of the occurrence of a hopping (non-Stokesian) mechanism of electrolytic conductivity. (c) 2006 Elsevier Ltd. All rights reserved.