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D = (D° + ¨
1
+ ¨
2
) [1 + c (d lng
/ d c)]
(16)
±
D = (D° + ¨
1
) [1 + c (d lng
/ d c)]
(17)
±
The theory of mutual diffusion in binary electrolytes, developed by Pikal [24], includes
the Onsager-Fuoss equation, but has new terms resulting from the application of the
Boltzmann exponential function for the study of diffusion. The eventual formation
of ion pairs is taken into account in this model, not considered in the Onsager-Fuoss.
1
D =
(10
3
R T v ) [1 + c (d lng
/ d c)]
(18)
M
Δ
1
M
±
(1
−
)
0
0
Data from these models for different types of electrolytes in dilute aqueous solutions
have been presented in the literature [25, 26]. From those data we conclude that for
symmetrical uni-univalent, both theories (Onsager and Pikal) give similar results, and
they are consistent with experimental ones. In fact, if Pikal's theory is valid, ¨M
0F
must be the major term, all other terms are much smaller and they partially cancel each
other. Concerning symmetrical but polyvalent electrolytes [25, 26], we can well see
that Pikal's theory is a better approximation than the Onsager-Fuoss'. The ion associa-
tion, taken into account in this model [27] can justify this behavior.
In polyvalent nonsymmetrical electrolytes, agreement between experimental data
and Pikal calculations is not so good, eventually because of the full use of Boltzmann's
exponential in Pikal's development.
Although no theory on diffusion in electrolyte solutions is capable of giving gen-
erally reliable data on
D
, we suggest, for estimating purposes, when no experimental
data are available, the calculations of
D
OF
and
D
Pikal
for hundreds of electrolytes al-
ready made by Lobo et al. [25, 26]. That is, for symmetrical uni-univalent electrolyte
(1:1) we suggest the application of Onsager-Fuoss equation with any
a
(ion size) from
the literature (e.g., Lobo's publication), because
a
parameter has little effect on ¿ nal
conclusions of
D
OF
; for symmetrical polyvalent (basically 2:2), we suggest the applica-
tion of Pikal equation. In this case, because
D
Pikal
is strongly affected by the choice of
a,
we suggest calculation with two (or more) reasonable values of
a
, assuming that the
actual value of
D
should lie between them, for nonsymmetrical polyvalent, we sug-
gest both Onsager-Fuoss and Pikal theories, assuming the actual value of
D
should lie
between them. Now, the choice of
a
is irrelevant, within reasonable limits.
Concerning more concentrated solutions, no de¿ nite conclusion is possible. In
fact, the results predicted from these models differ from experimental observation
(ca>4%). This is not surprising if we take into account the change with concentration
of parameters such as viscosity, dielectric constant, hydration, and hydrolysis, which
are not taken into account in these models [20-28].
For example, the experimental diffusion coef¿ cient values of CrCl
3
in dilute solu-
tions at 298.15K [6] are higher than the calculated ones (
D
OF
).This can be explained
not only by the initial CrCl
3
gradient and the formation of complexes between chloride
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