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Polyhedron 19 (2000) 2493 – 2500
Activity coefficients of 3:3 electrolytes in aqueous solutions
Francesco Malatesta *, Sara Trombella, Ambrogio Giacomelli, Massimo Onor
Dipartimento di Chimica e Chimica Industriale, Uniersita ` di Pisa, Via Risorgimento 35, 56126 Pisa, Italy
Dedicated to the memory of Professor Sergio Cabani.
Abstract
Activity coefficients of 3:3 electrolytes have not been liable to determination until 1994, when one of the authors devised a new
type potentiometric cell able to trace La[Fe(CN)
6
] down to about 5 ×10
-6
mol kg
-1
. La[Co(CN)
6
], [Co(en)
3
][Co(CN)
6
], and
[Co(en)
3
][Fe(CN)
6
], are now studied by the same method. Like La[Fe(CN)
6
], these electrolytes display in the dilute regions large
negative deviations from the limiting slope instead of the moderate positive deviations predicted by the Debye – Hu ¨ ckel theory.
Although the negative deviations can be easily interpreted in terms of only a partial dissociation, one should not conclude that
the 3:3 salts are only sparingly dissociated. Theoretical calculations are presented, showing how long-range interactions, in a
population of non associated +3 and -3 charged spheres, are able to produce effects that simulate the behaviour of a weak
electrolyte. Preliminary information is provided of an unexplored method, here devised, to determine the mean activity coefficients
in mixed electrolyte solutions. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: 3:3 Electrolytes; Activity coefficients; Electrolytic solutions; High-charge salts; High valency electrolytes; Mixed electrolytes
1. Introduction
About 1 century since Lewis’ concept of the activity
coefficient [1] and 76 years since the Debye–Hu ¨ ckel
theory [2], experimental and theoretical information
regarding 3:3 electrolytes is still lacking. Only in the last
few years have potentiometric cells suitable for such
salts and for the high dilution levels required become
available [3 – 11], and only La[Fe(CN)
6
] has been stud-
ied appropriately [6]. Owing to the paucity of experi-
mental data, essentially all restricted to La[Fe(CN)
6
],
theoretical treatments have not been able to reach
ultimate conclusions either. For instance, the conduc-
tivity data for La[Fe(CN)
6
] have long been interpreted
as evidence of a significant association of the elec-
trolyte, comparable to formic acid [12]; conversely, the
activity coefficients recently determined with the
method of the liquid membrane cells [6] have proved
identical to those expected for a theoretical model of
charged spheres free from any association, the so-called
‘primitive’ model [6,7]. (The only partial dissociation of
La[Fe(CN)
6
] evidenced from the conductivity data re-
lies on a theoretical framework that is incorrect for
high-charge electrolytes).
As no general value can be obtained from
La[Fe(CN)
6
] alone, three more salts of the same 3:3
type, lanthanum hexacyanocobaltate(III), tris(ethylene-
diamine)cobalt(III) hexacyanocobaltate(III), and tris-
(ethylenediamine)cobalt(III) hexacyanoferrate(III) are
now examined. These salts are sparingly soluble, e.g.
[Co(en)
3
][Fe(CN)
6
] does not reach 5 ×10
-4
mol kg
-1
,
but this does not represent a problem, as the liquid
membrane cells in many electrolytes are able to provide
stable and reproducible emf values down to 1 ×10
-5
mol kg
-1
and less. Moreover, a later reported thermo-
dynamic relationship (Eq. (3)), allows us to derive the
values of the activity coefficients of a 3:3 electrolyte
from the corresponding relative activity coefficients,
regardless of the ability of directly performing extrapo-
lation to zero for the 3:3 electrolyte.
* Corresponding author. Fax: +39-050-918-260.
E-mail address: franco@dcci.unipi.it (F. Malatesta).
0277-5387/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.
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