Two kinds of equilibrium constants were discussed based on a thermodynamic cycle of overall extraction equilibrium. Consequently, it was clarified that the individual distribution constants of cation and anion into an organic (o) phase is controlled by an equilibrium potential at the water/o solution interface.
Keywords: individual distribution constant, interfacial equilibrium potential, two kinds of equilibrium constants, extraction constant, dissociation of extracted ion pair
An extraction constant with the dissociation of the ion pair has been defined as
(1)
in a molar concentration unit.1,2 where
, L, and
refer to a univalent metal ion, a ligand such as crown ethers, and a pairing anion as picrate and permanganate ions, respectively. This equation corresponds to the overall extraction equilibrium,
.1,2 and is expressed by the product of
.1
(2)
at given values of ionic strength. The constants,
and
, are the functions of an interfacial equilibrium-potential difference (
).3,4 as follows:
(3)
with
(3a)
.5 (4)
The symbols,
, and
, in Eqs. (3)-(4) denote the individual distribution constant,
, of
into an o phase, that of
into the o phase, the complex formation constant,
, for
in the o phase (
because of the reaction in the homogeneous phase), a standard formal potential for the
transfer across the water/o solution interface, and that for
across the interface, respectively.3,4,6
Combinations of the experimental
and
values are infinite in the variation of
. On the other hand, the combination of the
and
values which are defined as the
and
ones at
is only one. However, their products, Eq. (2), have to equal with each other by a compensation of the two
terms between Eqs. (3) and (4).4,6
Also, Eq. (3) is showing us an interesting fact in an equilibrium condition of the extraction system. For example, the log
value is not generally equal to the log
one. This reason is because the
value is of the condition of
, while the
ones are of that of certain
values. The latter value (or also
) becomes a constant only under the condition that all the
and
values are fixed. That is, there are two kinds of equilibrium constants,
(
,
= constant) and
(
= constant) or
, in the extraction system.
Moreover, this means that zero of the
or
value, which corresponds to the overall extraction system of Eq. (1) and is related with
, is not necessarily agreeable to zero of the
value at the water/o solution interface. In other words, the condition of
(5)
Should be satisfied at the extraction equilibrium.3,4,6 That is, the relation,
, holds in the extraction system.3,4,6 Here, the symbols,
and
, denote the
value evaluated from the
and
ones, respectively; the front sign of
in Eq. (5) shows the formal charge of A− with the sign.5
Consequently, we can see that the two kinds of equilibrium constants,
, are present in an extraction system at the same time. With respect to this fact,
controls magnitudes of
and
at least.