Page 161 - Instant notes

E7
MOLECULAR ASPECTS OF IONIC
MOTION

Key Notes
The mobility of an ion is its terminal speed in a unit applied field.
The mobility can be calculated from the ionic molar conductivity
and also varies with concentration. The limiting mobility as c→0
can be used to determine the hydrodynamic radius of the ion.
The hydrodynamic radius is the radius of the ion as it moves
through solution with its solvation shell. This radius is
significantly larger than the ion radius in the gas phase. The
solvation shell size can dominate the hydrodynamic radius for
ions which are small and highly charged when unsolvated. This
can lead to a larger hydrodynamic radius for these ions compared
with intrinsically larger or less charged ions.
+
−
H and OH have anomalously high mobilities for ions of their
+
−
size in water. This is because movement of H and OH ions
through solution is achieved by bond rearrangement in the
hydrogen-bonded water framework of the solvent. This is a much
faster process than the physical movement of ions through the
solution.
Related topic Ions in aqueous solution (E1)

Ion mobility

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 field. This limiting
speed is attained when the acceleration due to the field is exactly balanced by the viscous
drag of the ion moving through the solution, which for a spherical ion leads to the
equations: