Journal of Electroanalytical Chemistry 460 (1999) 100 – 104
Activity coefficients of Al(ClO
4
)
3
in aqueous solutions: a reexamination
M. Molero, D. Gonza ´lez-Arjona, J.J. Calvente, G. Lo ´ pez-Pe ´rez *
Department of Physical Chemistry, Uniersity of Seille, E-41071 Seille, Spain
Received 6 January 1998; received in revised form 8 September 1998
Abstract
A reexamination of the published activity coefficients of Al(ClO
4
)
3
in aqueous solutions (E. Ka ´lma ´n, G. Horn, K. Schwabe, Z.
Phys. Chem. (Leipzig), 244 (1970) 106) is given. A procedure for the estimation of activity coefficients of electrolytes is proposed.
The method combines experimental osmotic coefficients and a theory based on the primitive model. This strategy provides suitable
results, especially for asymmetrical electrolytes. © 1999 Elsevier Science S.A. All rights reserved.
Keywords: Activity coefficients; Thermodynamic analysis; Interfacial chemistry
1. Introduction
The activity coefficient is a very important magni-
tude, as it is well known, specially in the thermody-
namic analysis of electrolyte solutions and interfacial
electrochemistry.
Although there are a lot of bibliographic references
and reviews about activity coefficients [1 – 3], published
data are scarce for asymmetrical electrolytes. There is
only one data set for species such as Al(ClO
4
)
3
[4], in
the concentration range from 0.3 mol kg
-1
up to
saturation (3.14 mol kg
-1
).
From this data set, plotted in Fig. 1, it is difficult to
extrapolate to more diluted solutions. For the sake of
comparison, in the same figure other published activity
coefficients of 1 – 3 electrolytes (perchlorates of La
3 +
[5]
and Ga
3 +
[1], AlCl
3
[6] and Al(ClO
3
)
3
[7]) are included
also. The corresponding data for Al(ClO
4
)
3
look some-
what higher compared with the other ones.
The goal of this work is to obtain the data of activity
coefficients of Al(ClO
4
)
3
for diluted solutions, between
10
-3
and 0.3 mol kg
-1
. For this purpose, the calcula-
tions were supported by the experimental osmotic co-
efficients measured by Ka ´lma ´n [8].
2. Theory
A usual procedure to determine activity coefficients
of solutes involves the measurement of vapor pressures
of the solution to obtain the solvent activity. For
aqueous solutions of single salts, solvent activities (a
w
)
can be expressed by means of the osmotic coefficient
( ), defined as:
=-
55.509 ln a
w
m
i
i
(1)
where
i
is the number of particles i into which the salt
of molality m dissociates.
Activity coefficients of the solute can be calculated
on the basis of the integration of the well-known
Gibbs – Duhem relationship. This integration requires
the knowledge of osmotic (
Ref
) and activity coeffi-
cients (
Ref
) at a given reference solution of molality,
m
Ref
.
ln
=ln
Ref
-
Ref
+ +
m
m
Ref
-1
m
dm (2)
where m is the integration molality variable.
A possible source of error in the estimation of activ-
ity coefficients from osmotic coefficients is the evalua-
tion of the integration constant (A ), defined as: * Corresponding author.
0022-0728/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved.
PII:S0022-0728(98)00353-2