Page 354 - MODERN ELECTROCHEMISTRY

290 CHAPTER 3

In order to test these predictions, attention was drawn to an empirical treatment
of ionic solutions. For solutions of noninteracting particles, the chemical-potential
change in going from a solution of unit concentration to one of concentration is
described by the equation

However, in the case of an electrolytic solution in which there are ion–ion
interactions, it is experimentally observed that

If one is unaware of the nature of these interactions, one can write an empirical equation
to compensate for one’s ignorance

and say that solutions behave ideally if the so-called activity coefficient is unity, i.e.,
and, in real solutions, It is clear that corresponds to a coefficient
to account for the behavior of ionic solutions, which differs from that of solutions in
which there are no charges. Thus, accounts for the interactions of the charges, so that

Thus arose the Debye–Hückel expression for the experimentally inaccessible
individual ionic-activity coefficient. This expression could be transformed into the
Debye–Hückel limiting law for the experimentally measurable mean ionic-activity
coefficient

which would indicate that the logarithm of the mean activity coefficient falls linearly
with the square root of the ionic strength which is a measure of the total
number of electric charges in the solution.
The agreement of the Debye–Hückel limiting law with experiment improved with
decreasing electrolyte concentration and became excellent for the limiting tangent to
the versus curve. With increasing concentration, however, experiment
deviated more and more from theory and, at concentrations above 1 N, even showed
an increase in with an increase in concentration, whereas theory indicated a
continued decrease.