Comments on the Competitive Preferential Solvation Theory Page: 308
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J. CHEM. SOC. FARADAY TRANS., 1990, VOL. 86
Table 1. Comparison of experimental carbazole solubilities to calculated values based on the competitive preferential solvation and extended
NIBS models
eqn (2) eqn (7) eqn (9)
solvent (B)-solvent (C) ratio dev. ratio dev. ratio dev. KOc dev.
n-hexane-dibutyl etherc 1.00 31.8 1.88 3.2 0.35 6.6 24.0 2.0
n-heptane-dibutyl ether 1.00 31.4 1.88 3.5 0.39 5.7 22.0 1.8
n-octane-dibutyl ether 1.00 25.4 1.77 2.5 0.37 6.1 25.0 1.7
cyclohexane-dibutyl ether 1.00 11.8 1.26 1.9 0.26 6.6 24.0 2.2
methylcyclohexane-dibutyl ether 1.00 12.9 1.30 2.6 0.29 5.3 26.0 1.8
cyclo-octane-dibutyl ether 1.00 3.7 0.91 2.3 0.25 3.1 25.0 2.1
iso-octane-dibutyl ether 1.00 37.4 2.17 4.5 0.39 5.6 30.0 1.7
n-hexadecane-dibutyl ether 1.00 22.7 1.75 1.3 0.52 3.9 24.0 1.4
squalane-dibutyl ether 1.00 23.3 2.11 2.2 0.79 3.8 23.0 1.7
t-butylcyclohexane-dibutyl ether 1.00 12.4 1.33 1.6 0.32 4.4 30.0 1.5
In(XAQA /A ). Experimental data taken from papers
Affinity constant ratios, PB) (C), used in the calculations. b Deviations = 100/N ncl/Xp . C Experimental data taken from papers
by McCargar and Acree.2-that eqn (7) provides very reasonable predictions for naph-
thalene, anthracene, biphenyl, iodine, benzoic acid, benzil, p-
benzoquinone and pyrene solubilities in binary solvent
systems that are free of association when weighting factors
are approximated by molar volumes.3-20 Justification for
approximating weighting factors with molar volumes can be
found in the literature in the form of comparisons between
the basic NIBS model and the Scatchard-Hildebrand solu-
bility parameter theory.2" The majority of solvent systems
studied thus far were nearly ideal, and contributions from the
FAAG c/(XB + XOccXRT) 'unmixing" term amounted to
only a few per cent of the predicted value. Through judicious
selection of the affinity constant ratio, the COPS model
should also be able to describe these solubility data.
Similarities between eqn (1H)-(4), and eqn (7) and (8) suggest
that the COPS model may be applicable to a much larger
number of thermodynamic and physical properties than
hitherto envisioned. However, the model is not expected to
describe all systems which might be encountered. As an
example, the basic NIBS model is limited in application to
systems containing only non-specific interactions. Expres-
sions for systems containing solute complexation with a
single solvent22-25
At + CI AC; Kc JAC(qA, IC,)
In 4&2' = 4 In(ltf), + 4{ ln(4')A
+ ln[1 + VA KAC /(VA +c)]
- + (9) n[1 + A K ( A C
R T(Xg B + xg Vc)
and for systems where the solute complexes with both solvent
components26,27
At + CtAC; KAc = 'AC/PA, &Cs)
AI + B, AB; KO = 4AB/(A1 Bi)
In 4' = 4o ln(q/t'), + 4 ln(os')c
- 4 In[1 + VA Kis/( VA + VB)]
- In[il + VA Kicd( A + c)]
+ In[1 + VAK0A8t/(VA+ VB)
+ PAK4c4#/(VA + c)I
_( +A G M
+T VA Cg (10)
R T(X VPB + X0 c)have much different mathematical forms. It is doubtful
whether eqn (6) will be able to imitate the behaviour of the
extended NIBS and competitive associated NIBS models, eqn
(9) and (10), respectively.
Table 1 summarizes the ability of the COPS model to
describe published carbazole solubilities in ten binary dibutyl
ether-alkane solvent mixtures. The various affinity constant
ratios were selected so as to reduce differences between the
calculated and observed values. For completeness, we have
included calculations based on the extended NIBS model.
Inspection of the first six columns of table 1 reveals that the
COPS model fails to describe the measured solubility data.
Absolute average deviations for the 'most realistic' of the
three additive equations, eqn (7), are on the order of 4-8%.
Eqn (5) grossly overpredicts the observed solubilities. It is
only by assuming that carbazole is preferentially solvated by
the inert hydrocarbon cosolvent B, PA(B) > PA(C), can the
deviations of eqn (2) be reduced. This assumption is com-
pletely inconsistent with the experimental data. Carbazole is
over 15 times more soluble in dibutyl ether than in any of the
hydrocarbon cosolvents studied. Furthermore, spectroscopic
studies of carbazole with similar ethers, such as
tetrahydrofuran2829 and dipropyl ether,30 also suggest com-
plexation between carbazole and dibutyl ether. In compari-
son, the extended NIBS model [eqn (9)] described the
carbazole solubilities to within an average deviation of 2%
using a single carbazole-dibutyl ether association constant,
which varied from K"c = 22 for n-heptane to Ktc = 30 for
iso-octane. The success of eqn (9) is even more remarkable if
one realizes that the mole fraction solubilities covered up to a
25-fold range, and the inert cosolvents included both small
(cyclohexane, n-hexane) and large (n-hexadecane, squalane)
saturated hydrocarbon molecules. Expressed in terms of
molar concentrations, the magnitude of the carbazole-dibutyl
ether association constant of Kc = 1.76-2.39 does indicate a
very weak molecular complex. Failure of the COPS model to
describe these ten non-electrolyte systems documents that the
model does have its limitations. Recalling that the COPS
model was developed specifically as an alternative thermody-
namic treatment for systems having weak molecular com-
plexation, its failure in the present study is particularly
disturbing. One naturally must wonder if published affinity
constant ratios are meaningful. For example, in the recent
study of the electronic spectroscopic behaviour of copper
chloride with both 4-ethylpyridine and 2,4-dimethylpyridine
Szpakowska and B. Nagy2 noted an unusual order of inter-
acting power of the inert cosolvents, namely benzene > n-
heptane > n-hexane > cyclohexane > chlorobenzene. Of the308
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Acree, William E. (William Eugene); Zvaigzne, Anita I. & Tucker, Sheryl A. (Sheryl Ann). Comments on the Competitive Preferential Solvation Theory, article, 1990; [Cambridge, England]. (https://digital.library.unt.edu/ark:/67531/metadc157300/m1/2/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.