Page 162 - Instant notes

Physical chemistry 148

where e is the charge on the electron, so ze is the charge on the ion, η is the viscosity, a
constant for any solvent which determines how easy it is for the ion to part the solvent
molecules and move through solution and a is the hydrodynamic radius of the solvated
ion.

Hydrodynamic radius
The hydrodynamic radius is the radius of the ion as it migrates through solution. At the
low applied fields typically used for conductivity measurements, this closely mirrors the
radius of the solvated ion (see Topic E1), as the forces between ion and solvent in the
solvation shell are sufficiently strong to ensure the ion moves with its solvation shell.
This means that the hydrodynamic radius is typically much larger than the ion radius in
−
3+
+
the gas phase. The smallest, most highly charged ions (such as Li , Al and F ) before
solvation have the largest solvation shells (see Topic E1). Since the overall radius of the
solvated ion is the sum of the ionic radius plus the solvation shell radius, the smallest
unsolvated cations often have the largest radii when solvated and move slowest through
solution. Singly-charged anions often have similar hydrodynamic radii, as they tend to be
larger than singly-charged cations, have smaller solvation shells, and the effect of a
change in the size of the ion is often counterbalanced by the change in the solvation shell
radius.

+
−
H /OH mobility
Protons and hydroxide ions have anomalously high ionic molar conductivities and
mobilities in comparison to all other ions, and in particular for their size. This is as a
result of the mechanism by which they move through solution, often 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.