There is little known about the transport behavior of ions in electrolyte solutions at very high concentrations and there is currently no one widely-accepted theory or equation to describe it over the whole concentration range. In this work, the ionic conductivity (kappa) of lithium salts in aqueous and non-aqueous electrolyte solutions have been measured as a function of concentration (C) and have been fitted to known theoretical and empirical equations. A new, isothermal, semi-empirical equation based on free volume theory: kappa = AC exp[ -gamma V-o/V-f C] where V-o and V-f are the occupied and unoccupied "free" volume, respectively, gives better fit over the whole concentration range than the known equations. V-f and V-2,phi(0), the apparent molar volume of the salt, were calculated from density measurements and it is found that free volume decreases with concentration in both the aqueous and non-aqueous solutions over the whole range. We hypothesize that the changes to transport properties in solution with concentration are caused by structural changes that switches the conductivity mechanism from vehicular to a Grotthuss-type or a mixture of both. We, for the first time, correlate the origin of C-max, the concentration of highest conductivity, to the eutectic composition in the salt-solvent phase diagram. (C) 2017 The Electrochemical Society. All rights reserved.