A new theoretical development of the limiting electric conductivity of ions in solution

The physical interpretation of the limiting equivalent conductivity of binary electrolytes in solution, Λ0 (=Σi = +,– λ0i), has been a challenge for almost a century. Here, as a follow-up on a preliminary communication [D. Fraenkel, Mol. Phys. 115, 2944 (2017)], a quantitative theoretical treatment is offered and fully developed for the limiting ionic equivalent conductivity, λ0i, based on assuming that around any singled-out ion i in solution, there is an electrostatic atmosphere that includes oriented solvent dipoles and the counterion as ‘charge density’. This leads to a simple mathematical expression for λ0i as the result of the tandem operation of the dipole viscosity and dipole relaxation forces on the drifting ion. Contrary to literature teaching, λ0i is found proportional to the effective ionic radius, ri. An ‘electric ion-radius scale’ derived from experimental λ0i’s for aqueous solutions, compares reasonably well with known ion-size scales. A newly defined solvent-specific dipole random-walk correction factor, ξ, is used for nonaqueous solvents as an adjustable parameter, to attain a parallel electric ion-size scale. The new theory provides overall a comprehensive view of the limiting ion mobility in solution, based on the ionic properties, solvent variables and universal constants.