Ion mobility is related to molar conductivity by the equations:
which allows the mobilities, u+ and u- of the cation and anion to be determined from molar conductivity measurements at and away from infinite dilution. z+ and z- are the formal charges of the cation and anion respectively, so z+F and |z-F| are the magnitudes of the charges on a mole of cations and anions. The mobility is always positive (+) and is a measure of the terminal migration speed of an ion per unit applied electric field. This limiting speed is accelerating due to the field is exactly balanced by the viscous drag of the ions moving through the solution which for a spherical ions lead to the equations:
where e is the charge on the electron (-), so ze is the charge on the ions, η is the viscosity, a constant for any solvents which determines how easy it is for the ion to part the solvent molecule and move through solution and a is the hydrodynamic radius of the solvated ion.
Hydroxide and Protons ions have anomalously high ionic molar conductivities and mobilities in comparison to all ions, and in particular for their size. That is as a result of the mechanism by which they move through solution, called the Grotthus mechanism (Fig. 1).
Fig. 1. The Grotthus mechanism for (a) H+; (b) OH- ion motion in water. The arrows indicate the concerted proton movement when the field is applied.