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70 CHAPTER 2

activity coefficient and the concentration will be developed. In it, the unknown is
the hydration number of the electrolyte. The sum of the hydration number of the cation
and anion will be found and so a measurement of the activity coefficient at a particular
concentration (from, e.g., 0.1 mol up to 10 mol ) will yield the hydration
number at that concentration.
A second difficulty is more subtle. The activity coefficient is determined not only
by water that is adhering to ions, but also by increasing interionic effects, and our
ability to allow for these at very high concentrations such as 5 mol is not good.
Spectroscopy tells us also that ionic association is occurring in these high ranges, but
there is not much information on this association for ions that do not have IR spectra
–
(e.g., and Cl ). These matters will be discussed again quantitatively in Chapter 3.

2.10. TRANSPORT

2.10.1. The Mobility Method

The mobility method is a rough-and-ready method for obtaining information on
the number of solvent molecules that accompany an ion in motion. Its basic theory is
really quite simple. One equates the electrostatic force pulling the ion forward,
= charge of the ion; X = electric field gradient), to the viscous resistance to
the ion’s flow. This view neglects all interionic interactions (Chapter 4) but would
apply at sufficiently high dilution. This viscous resistance is given by Stokes’ law,
where r is the radius of the entity moving through a liquid of viscosity and
at a velocity v. The bulk viscosity is used. However, in reality an ion breaks up the
solvent near it as it darts from here to there in the solution, so that a viscosity less than
that of the undisturbed bulk water should be used with Stokes’ law. Again, to determine
the radius of the ion plus the adherent solvent and to determine how many water
molecules fit in, one has to know the volume of water attached to the ion. This is not
the ordinary bulk volume but a compressed value arising from the effect of the ion’s
field on normal water.
Finally, the validity of using Stokes’ law to find the force of viscous resistance
against movement in a liquid has to be questioned. In the original derivation of this
formula, the model used was that of a solid sphere passing in a stately way in a straight
line through a viscous fluid like molasses. The extrapolation to atomic-sized particles
that move randomly in a solvent which itself has innumerable complex, dynamic
movements might be thought to stretch the equation so far from its original model that
it would become inapplicable. Nevertheless, tests (Chapter 5) show that Stokes’ law
does apply, although, depending on the shape of the particle, the 6 (which is valid for
spheres) might have to be modified for other shapes (e.g., 4 for cylinders).
Now, from the equivalent conductivity of an electrolyte (Chapter 4, Section
4.3.7) at concentrations low enough so that the ions are virtually free from the influence