الفهرس 
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Abstract
I’
1. Historical background;’
The modem theory of electrolytes dates from the work of Debye and Huckel in
1923, although it had begun to take shape many years earlier when Bjerrum, Jahn, Noyes
and Sutherland realized the importance of the electrostatic forces between free ions, and
gave the first quantitative treatment of them. Debye and Huckel assumed that an
electrolyte is completely dissociated into rigid, spherically symmetrical ions. The inter-
action between these was computed by Coulomb’s law, assuming the medium to have the
dielectric constant of the pure solvent. The theory led to an equation for the mean activity
coefficient of an electrolyte in dilute solution. This familiar equation, the Debye--Huckel
limiting law is predicted from the principles of the thermodynamic behavior of a dilute
electrolyte and its dependence on valency, temperature and the properties of the solvent.
The conducting power of an electrolyte also is influenced by inter-ionic forces, and here
the treatment, modified by Onsager, led to another limiting law for dilute solutions--the
Onsager equation. The main achievement of the Debye-Huckel-Onsager treatment was to
draw attention to, and to show how to calculate, the effects of the long-range electrostatic
interactions in dilute electrolyte solutions. The idea of complete dissociation was also
fostered, no doubt, by the suspicion that apparent deviations from the Debye-Onsager
theories would find a physical explanation, and would not require a return to the idea of
un-ionized salt molecules.
It was known that such deviations were not uncommon; Onsager in his early
papers quoted approximate dissociation constants for potassium nitrate and other
electrolytes. Moreover, the cause, or at least one possible cause, of such deviations was
clearly appreciated. In the mathematical simplification of the Debye-Huckel treatment it
had to be asswned that the electrical interaction energy of an ion is small compared with its
mean thermal energy. This will be untrue for small ions which can approach one another
very closely, as can. easily be seen by remembering that two point charges that came
together would need infinite work to separate them again. It will be especially untrue for
small ions of high valency and for solutions in organic media of low dielectric constant.
Methods of allowing for these complications were proposed by Bjerrum (1926), Muller
(1927) and Gronwall and LaMer (1928). Using the same model as Debye and Huckel,
Bjerrum plotted for dilute solutions the probability of finding an oppositely charged ion at
a given distance from a central ion. The distribution curve shows a flat minimum at a
distance where the work of separating the two oppositely charged ions is four times as
great as the mean kinetic energy per degree of freedom. This distance is 3.5 AO for
univalent ions in water at 25°C. For ions that are so large, that their centers cannot
approach more closely than this it is assumed that the Debye-Huckel limiting equation
should be satisfactory. However, small ions will be able to approach to distances varying
from r = 3.5 A ° to r = a, where a is the sum of the radii of the ions- distances at which the
work of separation increases rapidly and can become very large. Bjerrum regarded a pair
of ions within this range as associated to form an ’ ion-pair’. The associated ion-pairs.