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calculated from the exact compressibility route from liquid state theory match
experiments for salt concentrations up to 2 M.
3.1.2 Hofmeister Series of the Osmotic/Activity Coefficient
Ion-specific effects often give rise to changes in thermodynamic observables that
follow a particular ion series [
50
,
51
,
53
]. These series are known as Hofmeister
series or lyotropic series. Osmotic coefficients (or the related salt activity coeffi-
cients) depend on the ion types at finite salt concentration, while being independent
of the ion type in the limit of infinite dilution, where simple electrostatic models
(for example the Debye-H
uckel limiting law) can be used to describe them.
Because small ion-ion separation distances are rarely sampled at low salt concen-
trations, short-range ion-ion interactions are unimportant relative to the electro-
static forces operative at larger distances. Short-range interactions, however, start
playing an important role at finite salt concentrations, leading to the formation of
ion pairs which we examine here. It is well-known that osmotic coefficients follow
a Hofmeister series as shown in Fig.
5
[
74
]. When activity coefficients are presented
instead, this series remains qualitatively the same. The law of matching water
affinities [
63
,
64
] predicts that activity and osmotic coefficients of aqueous alkali
bromide solutions decrease in the order Li
þ
>
€
Cs
þ
,as
observed in Fig.
5a
. In LiBr solution, a small (“hard”) cation (Li
þ
) combines with
a large (“soft”) anion (Br
); because small ions and large ions remain solvent
separated, the osmotic coefficient of this system is high. In CsBr solution, on the
other hand, two large ions are combined; these two ions favor forming contact ion
pairs with a corresponding reduction of the osmotic (and salt activity) coefficient.
Qualitatively similar ion series are obtained if the bromide anion is replaced by
chloride or iodide. Interestingly, a reversed Hofmeister series is obtained upon
replacing bromide with the molecular anion CH
3
CO
2
Na
þ
>
K
þ
>
Rb
þ
>
(acetate) as shown in Fig.
5b
.
Fig. 5 (a) Experimental osmotic coefficients [
74
] of aqueous alkali bromides and (b) aqueous
alkali acetates as a function of salt molality at 298 K
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