Association and transport properties in solvents of medium and low relative permittivity: Quaternary ammonium picrates in acetone-n-hexane mixed solvents

Article abstract of DOI:10.1016/j.molliq.2010.10.004

The behavior of tetra-n-butylammonium picrate, TBAPic, in acetone-n-hexane mixed solvent, with the relative permittivity changing gradually from ε_r = 20.53 to 4.99 and only slightly changing viscosity, was studied at 25.0 °C using conductometry

Full text of DOI:10.1016/j.molliq.2010.10.004

Journal of Molecular Liquids 158 (2011) 33–37
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Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Association and transport properties in solvents of medium and low relative
permittivity: Quaternary ammonium picrates in acetone–n-hexane mixed solvents
⁎
Irina N. Palval, Alexander V. Lebed, Nikolay O. Mchedlov-Petrossyan
Department of Physical Chemistry, Kharkov V.N. Karazin National University, 61077, Kharkov, Ukraine
a r t i c l e i n f o
a b s t r a c t
Article history:
The behavior of tetra-n-butylammonium picrate, TBAPic, in acetone–n-hexane mixed solvent, with the
relative permittivity changing gradually from εr =20.53 to 4.99 and only slightly changing viscosity, was
studied at 25.0 °C using conductometry. The association constants (TBA++Pic– ⇄TBA+Pic–, KA) and the
limiting molar conductivities were determined using the Lee–Wheaton equation. At acetone content 50 mass
% (εr =8.76) and higher, the 1:1 association model is still able to describe the conductance data at the salt
concentrations 3×10−5–0.02 M. These results are in line with the data for some other quaternary ammonium
picrates. However, at higher contents of n-hexane, this simple model becomes invalid. Therefore, symmetrical
ion triplets were involved into the equilibrium scheme. The relation between the mobility of ions and that of
the triplets, as calculated conjointly with the equilibrium constants, is close to the common equation:
ΛT0 =0.693Λ0. The Walden product Λ0η, being almost constant up to 50 mass % of acetone, drops at lower εr
values. The plot of log KA vs. ε−r 1 is linear. However, the KA value at 27 mass % acetone is 3 times lower as
compared with that published earlier for an isodielectric solvent, pure n-butylacetate, due to the presence of
an “active” dipolar co-solvent. Summarizing of the data for acetone–n-hexane system with those for acetone–
n-butylacetate solutions studied earlier allows concluding that at εr around 7, the existence of ion triplets
becomes doubtless.
Received 14 August 2010
Received in revised form 7 October 2010
Accepted 8 October 2010
Available online 16 October 2010
Keywords:
Tetra-n-butylammonium picrate
Quaternary ammonium picrates
Acetone–n-hexane mixtures
Conductance
Ion pairs
Triplets
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
The viscosity of this binary mixture stays practically constant.
Thus, the alterations of the Walden product (if any) occurring along
In the previous paper [1], the conductance data for tetra-n-
butylammonium picrate (TBAPic) in acetone–n-butylacetate (AC–BA)
solvent system at 25 °C have been analyzed. It has been demonstrated,
that for this organic electrolyte with relatively poor solvated ions, not
inclined to specific interactions, the simple 1:1 ion association model
allows to describe adequately the conductance data only at the
relative permittivity range εr N9 [1]. The approaches for estimation of
the constants of triplets and even quadruplet formation have been
developed for lower εr values. Ibidem, a brief review of the problem
can be found [1].
with εr decrease should be ascribed to the decrease in limiting
conductivity, Λ∘.
Also, three other alkylammonium picrates were involved in the
experimental study.
Finally, we recalculated some well-known precise data on TBAPic
conductance in binary organic solvent systems, available in literature,
by using the contemporary methods.
2. Experimental section
The aim of the present work was to verify these findings by
studying the TBAPic in another solvent system, acetone–n-hexane
(AC–Hex). The solvents AC and Hex, non-hydrogen bond donors
(ENT =0.355 and 0.009, respectively [2]), were used to create mixtures
with gradually changing εr values. The lowest content of AC was 27
mass %. This corresponds to the εr =4.99 value, which is close the
εr =5.10 value of pure BA, where the ionic equilibrium of TBAPic was
studied previously [1].
2.1. Materials
The synthesis, purification, and characterization of TBAPic and
tetraethylammonium picrate, TEAPic, was described previously [1].
Cetyltrimethylammonium picrate, CTAPic, was prepared from picric
acid (reagent grade, purified by re-crystallization) and cetyltrimethy-
lammonium bromide (Merck, purity 99%). The initial reagents with
molar ratio 1.12:1 were dissolved in appropriate amount of distilled
water; the mixture was heated to 70–80 °C, cooled, stored 20–24 h,
and filtrated the precipitate. The dried precipitate was re-crystallized
successively from AC and methanol, and dried at 60–80 °C to constant
mass. The melting point was 128.3–128.5 °C; elemental analysis: % N
calc. 10.93, found 10.90, 10.96; % C calc. 58.57, found 58.65, 58.73; % H
⁎
Corresponding author.
E-mail address: mchedlov@univer.kharkov.ua (N.O. Mchedlov-Petrossyan).
0167-7322/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.molliq.2010.10.004

34
I.N. Palval et al. / Journal of Molecular Liquids 158 (2011) 33–37
Table 1
calc. 8.65, found 8.73, 8.73. N-cetylpyridinium picrate, CPPic, was
prepared from picric acid and N-cetylpyridinium chloride (×1 mol
H2O, Merck, purity 99%). The initial reagents with molar ratio 1.2:1
were dissolved in appropriate amount of distilled water; the mixture
was heated to 50–55 °C, cooled, stored 20–24 h, and filtrated the
precipitate. The latter was dried at room temperature and then twice
re-crystallized from AC. The salt was dried and stored at room
temperature in the desiccator over silicagel. The melting point was
49.2–49.6 and 48.7–49.1 °C, as measured with two samples within a
month; elemental analysis: % N calc. 10.52, found 10.47; % C calc.
60.89, found 60.79; % H calc. 7.57, found 7.60.
Physico-chemical properties of AC–Hex mixtures at 25 °C.
Content of AC/mass %
εr
103η/Pa s
ρ/g cm−3
100
80
70
60
50
40
27
20.53
15.23
12.88
10.72
8.76
0.3030
0.2896
0.2851
0.2818
0.2798
0.2791
0.2804
0.7845
0.7505
0.7350
0.7206
0.7071
0.6946
0.6799
6.99
4.99
AC was stored with KMnO4 and after distilling it was boiled 4–5 h
with dried K2CO3 or MgSO4, again distilled and the middle fraction
was used. The reagent grade Hex was purified as described in the
literature [2], after making sure of the absence of unsaturated
hydrocarbons [3]. After distillation, the middle fraction was
collected. The purity of solvents was checked by conductivity and
density.
in media with very low polarity (εr b10) the formation of ion triplets
becomes possible [7]:
Ctþ + CtþAn–⇄ CtþAn–Ctþ; KT+
An– + CtþAn–⇄ An–CtþAn–; KT−
ð2aÞ
ð2bÞ
:
2.2. Apparatus and procedure
Electrical resistance of solutions was measured using an automatic
digital AC bridges R5058, R5083 or Precision LCR Meter GW Instek
LCR-817 at 25.0 0.05 °C at a frequency of 1000 Hz. Conductance cells
were calibrated using a set of aqueous KCl solutions within the
concentration range of c=2×10−4–6×10−3 M.1 The temperature
For AC–Hex mixtures with AC content of 80 and 70%, we took into
account only the equilibrium [Eq. (1)]; this variant of calculations is
designated here as type “A”. Therefore, three parameters (Λ∘, KA and
R) were to be fitted in this case. By this type of calculations we also
processed the experimental data of Reynolds and Kraus [8] for pure
AC. The calculations were successful, but estimation errors of R
parameter were considerable in all the cases. Additionally we
performed series of testing calculations with two (Λ∘, KA) fitted
parameters and several fixed R values in the range of 0.8–2.0 nm. The
results indicated that the influence of R value on the calculation
results is negligible, if the body of the experimental data in the series
is big enough. Finally, the Λ∘ and KA values were calculated with the
constant value of R=1.0 nm as a mean value for all the above
systems.
For AC–Hex mixtures with AC content of 60% (εr =10.72) and less,
we used a more complex procedure of data processing (type “B”). As a
first step, the preliminary three-parameter (Λ∘, KA and R) optimization
(type “A”) was performed using data for the diluted concentration
range. Then the formation of ion triplets [Eqs. (2a), (2b)] was taken
into account. For simplifying, the assumption KT+ =KT− =KT [7,9]
was used. Therefore, only a sole value of the limiting conductivity of
triplets (ΛT∘ =Λ∘T + +ΛT∘ −) can be used. Consequently, four para-
meters (Λ∘,ΛT∘, KA and KT) were to be fitted, while the value of R
parameter was taken from preliminary calculation. The results of
was maintained with an accuracy of
0.05 °C using an aqueous
thermostat. The correction for pure solvent conductance was used in
the calculations of molar conductance values, Λ; the last-named were
obtained with uncertainty of (0.05–0.1) %. The values of relative
permittivity, viscosity, and density of pure solvents at 25.0 °C were
taken from the literature [4]. The kinematic viscosity of AC–Hex
mixtures was determined using a capillary viscosimeter VPZh-2,
utilizing freshly distilled water, AC, Hex, and BA as reference liquids.
The density of the mixed solvents was measured by picnometric
method. All the stock and working solutions were prepared directly
before measurements and kept protected from light before
measurements.
3. Results
3.1. Physico-chemical properties of mixed solvent
The known literature data [5] on the physico-chemical properties
of AC–Hex mixed solvent were compiled together with our experi-
mental data. The interpolated equations were obtained to calculate
density (ρ), viscosity (η) and εr values of AC–Hex mixtures (see
Supplementary data). The values necessary for conductance data
processing are gathered in Table 1.
2.4
2.0
1.6
1.2
0.8
0.4
0.0
3.2. Conductance data processing
The experimental data on molar conductivities are deposited in
the Appendix A: Supplementary data. The phoreograms are typified in
Fig. 1.
The main principles of data processing have been described earlier
[1]. The extended version of Lee–Wheaton conductance equation [6]
and the second approach of Debye–Hückel theory for ionic activity
coefficients were used in all calculations. Depending on εr value of the
solvent, various models of the ion equilibrium can be used. Along with
generally known ion association equilibrium,
0
3
6
9
12
15
Ctþ + An–⇄ CtþAn–; KA
ð1Þ
c
100
Fig. 1. The dependence of molar conductivities of TBAPic on concentration in AC–Hex
mixtures: ⋄ — 70 mass % AC; □ — 50 mass % AC; × — 27 mass % AC.
1
1 M=1 mol dm−3
.

I.N. Palval et al. / Journal of Molecular Liquids 158 (2011) 33–37
35
Table 2
Limiting conductivities/S cm2 mol−1 and equilibrium constants of TBAPic in AC–Hex mixtures at 25.0 °C.
a
b
Acetone/%
εr
cctr×104/M
Type of calc.
c ×104/M
Λ ∘
Λ ∘T
Λ ∘η
log KA
1.93 0.01
log KT
R/nm
σ
100
80
70
60
60
50
50
40
40
27
27
20.53
15.23
12.88
10.72
10.72
8.76
8.76
6.99
6.99
4.99
27.3
11.1
6.75
3.88
3.88
2.12
2.12
1.076
1.076
0.395
0.395
A
A
A
A
B
A
B
A
B
A
B
0.40–4.0
0.37–90
0.29–98
0.32–210
0.32–210
0.54–10
0.54–140
0.32–14
0.32–190
0.34–14
0.34–190
152.4 0.1
158.8 1.1
170.4 2.9
150.4 1.8
150.4 2.0
154.6 3.1
161.9 0.1
46.3
46.0
48.6
42.4
42.4
43.3
45.3
31.0
35.0
10.3
25.4
1.0
1.0
1.0
1.0 0.3
1.0
1.2 0.4
1.2
1.5 0.5
1.5
2.2 0.6
2.2
0.11
1.27
2.33
2.28
2.27
1.69
0.55
0.89
0.34
0.51
0.20
–
2.50 0.02
2.95 0.03
3.40 0.03
3.40 0.03
4.11 0.03
4.187 0.004
4.84 0.06
4.99 0.03
5.7 0.6
–
–
–
–
–
104 4.0
–
0.69 0.15
–
108.7 0.5
–
2.03 0.13
–
111
125.5 3.4
6
86.9 0.2
–
1.89 0.07
–
36 23
4.99
90
6
49.6 0.2
6.60 0.06
2.37 0.06
a
cctr =1.19×10−14 (εrT)−concentration of triplet formation by Fuoss [7,9]; T — absolute temperature.
b
Dispersion/S cm2 mol−1
.
calculations are summarized in Table 2. The preliminary versions are
given in italic in the Tables.
calculated according to Fuoss (Table 2). Indeed, the account of the
triplets did not refine the fitting, and the KT value is below 10.
The plot of log KA vs. the reciprocal relative permittivity for TBA++Pic−
in AC–Hex solvent system is linear (Fig. 2, Eq. (3)):
It should be noted, that almost in all cases the optimized ΛT∘ values
are very close to calculated ones by using the relation ΛT∘ =0.693Λ∘
[10]. Thus, using of this relation seems to be worthwhile in other
cases, when four-parameter optimization gets unstable or physically
unreasonable results.
log KA = 0:521 + 30:84εr−1
;
r = 0:998:
ð3Þ
The results of data processing for three other picrates are compiled
in Table 3.
For the system AC–BA [1], the dependence within the same εr
range is successfully described by Eq. (4):
log KA = 0:269 + 34:63εr−1
;
r = 0:999:
ð4Þ
4. Discussion
The processing of conductance data for TBAPic in AC–Hex (present
work) as well as AC–BA [1] solvent systems at the concentration range
of (3×10−5–0.02 M) and εr =20.53 to (4.99–5.10) allows to reveal
some regularities.
The detailed discussion of the plots log KA vs. ε−r 1 was given in our
previous paper [1]. The constants calculated in solutions with low εr
values without taking into account equilibria (2a) and (2b), are
underestimated.
At εr around 5, the phoreograms exhibit an evident minimum, and
the data processing without constants taking into account the ion
triplets is impossible. The calculated triplet formation constants are
well above 102.
At εr =6.7–7.0, the aforementioned minimum is absent. However,
the consideration of the triplets improves the fitting of the
experimental curves and is still necessary. The log KT values equal to
1.9–2.0.
At εr =8.8–9.1, the calculation of the Λ∘ and KA values (1:1
association, Eq. (1)) both with and without the triplet formation
results in close values. However, the conjoint estimation of KA and KT
again improves the data fitting. This εr region can be considered as an
intermediate one.
In order to examine the validity of this statement, we studied the
equilibria of three other picrates in the AC–Hex mixture with εr =8.76
(Table 3). The results are in line with those obtained with TBAPic.
Moreover, the KA values for all the four picrates are rather close: 4.19
(TBAPic), 4.21 (TEAPic), 4.44 (CTAPic), and 4.48 (CPPic).
If εr did not sink below 10 the triplet formation can be ignored,
though the working concentrations exceed the “threshold” value
It should be noted, that the KT values exhibit a slight increase along
with decrease in εr (Table 2 and ref. [1]). Chen and Hojo [7e] also
observed some increase for TBAPic in different solvents: log KT =1.76
(in tetrahydrofuran, εr =7.58), 1.78 (in dimethoxyethane, εr =7.2),
and 2.29 (in trichloromethane, εr =4.8).
In addition to our results, we also processed the data of Hirsch and
Fuoss for TBAPic in nitrobenzene–CCl4 system [11]. Though in this
work the concentration ranges were rather narrow, the number of
mixed solvent compositions was large, and the εr range was from
34.69 to 4.96. The algorithm was as described above for treating our
experimental data. The results are depicted in Fig. 3.
The KA values thus estimated agree with the results of Hirsch
and Fuoss in outline. If the formation of ion triplets at low εr values
was ignored (calculations by type “A”), the calculated KA and Λ∘
values were lower than by using type “B”. However, it should be
noted that the experimental data of these authors [11] refer to
relatively diluted solutions, where the contribution of triplets is
much less. Therefore, the differences between the results obtained
using two different models, as well as by our procedure and by
Hirsch–Fuoss method, are not so marked as in our case (Fig. 2). The
Table 3
Limiting conductivities/S cm2 mol−1 and equilibrium constants of picrates in AC–Hex (1:1) mixture at 25.0 °C; εr =8.76.
Type of calc
Λ ∘
193
195
123
131.5 0.4
134
143.4 0.3
Λ ∘T
Λ ∘η
log KA
log KT
R/nm
σ
TEAPic
CTAPic
CPPic
A
B
A
B
A
B
4
3
4
–
54.0
54.6
34.4
36.8
37.5
40.2
4.20 0.04
4.21 0.02
4.35 0.08
4.44 0.01
4.38 0.11
4.48 0.01
–
1.1 0.4
1.1
1.2 0.6
1.2
1.2 0.6
1.2
1.47
1.35
1.32
0.38
1.71
0.89
131
–
1
4
8
1.3 0.3
–
74
–
2.05 0.13
–
4
105
1.8 0.4

36
I.N. Palval et al. / Journal of Molecular Liquids 158 (2011) 33–37
Table 4
Association (TBA+ +Pic−) constants in isodielectric solvents at 25 °C.
8.5
6.0
3.5
1.0
Reference
Solvent
εr
log KA
Chen and Hojo [7e]
Fuoss, D'Aprano [12]
Hirsch and Fuoss [11]
Mchedlov-Petrossyan et al. [1]
Present paper
Trichloromethane
4.80
4.84
4.96
5.10
4.99
7.40
7.07
7.33
7.10
6.60
p-Nitroaniline-1,4-dioxane
Nitrobenzene–CCl4 , 10:90
BA
AC–Hex, mass ratio 27:73
which better solvate ions as compared with pure BA. The fraction of
nitrobenzene in its mixture with tetrachloromethane (Table 4) is
substantially lower.
At higher εr values, the independence of the KA value for TBAPic on
the individuality of the solvent is even more expressed. So, in a
number of isodielectric mixtures of n-butyronitrile or iso-butyronitrile
with 1,4-dioxane, benzene, CCl4, and tetrahydrofurane, at εr from
10.14 to 10.79, log KA varies from 3.88 to 3.62 at 25 °C [13]. In our
AC–Hex system, at εr =10.72 log KA =3.40 (Table 2).
In the both systems studied by us (Table 2 and ref. [1]), a distinct
decrease in the Walden product is registered at εr≤7 (Fig. 4).
Such effect was numerously reported in the literature [1,4c,11,14]
and was described both theoretically [4c,15] and semi-empirically
[16]. In the last case, Eq. (6) was proposed by Shkodin [16]:
4
8
12
16
20
100/
εr
Fig. 2. The dependence of log KA on 100/εr in AC–BA (×) and AC–Hex (□) solvent
systems.
dependence log KA versus εr− 1 is quite linear if the points with εr
from 16.2 to 4.96 are used:
log KA = 0:751 + 33:11εr−1
;
r = 0:998:
ð5Þ
Λ∘η = A expð−B = εrÞ
ð6Þ
Some deviations from linearity at higher εr values may be
explained by the elevated content of the “active”, highly polar solvent
(nitrobenzene). Note, that the slope ∂(log KA)/∂(ε−r 1) of the plots (3),
(4), and (5) lies within the range from ≈31 to ≈35.
The data for TBAPic in different solvent systems compiled in
Table 4 demonstrate that in isodielectric non-hydrogen bond donor
(or “aprotic”) solvents, the KA values of the salt under study are rather
close. At this, the influence of the calculation algorithm on the final
result should be kept in mind for such low εr range [1]. This is in
accordance with the character of the tetra-n-butylammonium and
picrate ions, which are not inclined to specific interactions.
The data for TBAPic in nitrobenzene–CCl4 system obtained by
Hirsch and Fuoss [11] also clearly bring out the decrease in Λ∘η
(Fig. 5).
Because the η value in the AC–Hex system is practically constant,
Fig. 4 actually refer in this case to the variations of the Λ∘ value along
with the decrease in εr. This feature should be considered as a
confirmation of the theoretical “dielectric friction” concept, in line
with the work of Fuoss [15] and the theory proposed by Zwanzig [17],
Hubbard and Onsager and others [18].
Our log KA value in 27% AC–73% Hex is 0.5 units lower as compared
with the value in the isodielectric solvents, pure BA [1]). This should
be explained by the influence of the “active” dipolar co-solvent, AC,
Appendix A. Supplementary data
Supplementary data to this article can be found online at
doi:10.1016/j.molliq.2010.10.004.
1.8
1.6
1.4
1.2
8.0
6.0
4.0
2.0
0.0
0
5
10
15
20
100/εr
4
8
12
16
20
100/εr
Fig. 3. The dependence of log KA on 100/εr in nitrobenzene–carbon tetrachloride
mixtures at 25 °C: × — values reported by Hirsch and Fuoss [11]; □ — values, calculated
by us using the 1–1 association model; ▲ — values, calculated by us using the model of
ion pairs and triplets formation.
Fig. 4. The dependence of log(Λ0η) on 100/εr in AC–BA (×) and AC–Hex (□) solvent
systems.

I.N. Palval et al. / Journal of Molecular Liquids 158 (2011) 33–37
37
1.8
1.7
1.6
1.5
1.4
1.3
1.2
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[18] (a) J.B. Hubbard, L. Onsager, J. Chem. Phys. 67 (1977) 4850;
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Fig. 5. The dependence of log(Λ0η) on 100/εr in nitrobenzene–carbon tetrachloride
mixtures at 25 °C: × — values reported by Hirsch and Fuoss [11]; □ — values, calculated
by us using the 1–1 association model; ▲ — values, calculated by us using the model of
ion pairs and triplets formation.
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