Theoretical interpretation of the limiting electric conductivity in ionic solution

The physical essence of the limiting equivalent ionic conductivity in solution, λ⁰_i, has been a continuing challenge over almost a century. Here I briefly present an ab initio theoretical treatment providing (1) a new insight into the nature of λ⁰_i, and (2) a mathematical formula for computing λ⁰_i. In the new treatment, one assumes that any chosen ion i is surrounded by a spherical body of oriented solvent dipoles carrying the charge of the counterion, and the bulk solvent is a continuum with no molecular detail. λ⁰_i is thus the result of the tandem operation, at hydrodynamic equilibrium, of the dipole body's electrophoretic and relaxation forces exerted on the drifting ion. λ⁰_i is found to be proportional to the radius of ion i, and independent of the ionic charge. From experimental λ⁰_i's, the ion radius can be computed as ‘electric radius.’ An electric ion-radius scale so derived compares well with other ion-size scales. The current theory expresses λ⁰_i using only universal constants and unitary factors of the ionic solution, and it sheds new light on the fundamental nature of ion and charge transport in a polar liquid medium.