Thermodynamic studies of ionic interactions in aqueous solutions of N-butyl-pyridinium bromide at 298.15 K

Article abstract of DOI:10.1016/j.molliq.2013.04.027

Density and osmotic coefficient measurements for aqueous solutions of N-butyl-pyridinium bromide [Bpy][Br] in concentration range ~ 0.019 to ~ 0.39 mol·kg^{- 1} at 298.15 K are reported. The density data are used to obtain apparent molar volume (_V), partial molar volume of solute and solvent V?₂andV?₁ respectively as well the limiting partial molar volume ?V0=V?20 of the solute [Bpy][Br] (by appropriate extrapolation). The experimental osmotic coefficient data are used to determine the activity and mean ionic activity coefficients of solute and solvent respectively. Experimental activity coefficient data are compared with those obtained from Debye-Hu?ckel and Pitzer models. The activity data have been further processed to obtain the Gibbs free energy change due to mixing (ΔG_m) and excess Gibbs free energy change (ΔG ^E). The aggregation number (n) and critical micelle concentration (cmc) are obtained for ionic salt in solution phase by applying pseudo-phase separation model to and_V data respectively. Application of McMillan-Mayer theory of solutions to the data is made. The results have been interpreted on the basis of structural characteristic of salt, ion-solvent and ion-ion interactions.

Full text of DOI:10.1016/j.molliq.2013.04.027

Journal of Molecular Liquids 186 (2013) 14–22
Contents lists available at SciVerse ScienceDirect
Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Thermodynamic studies of ionic interactions in aqueous solutions of
N-butyl-pyridinium bromide at 298.15 K
a
b
a
a
a,
Vasim R. Shaikh , Santosh S. Terdale , Gaurav R. Gupta , Dilip G. Hundiwale , Kesharsingh J. Patil ⁎
a
School of Chemical Sciences, North Maharashtra University, Jalgaon 425001, India
Department of Chemistry, University of Pune, Pune 411007, India
b
a r t i c l e i n f o
a b s t r a c t
Article history:
Density and osmotic coefficient measurements for aqueous solutions of N-butyl-pyridinium bromide [Bpy]
Received 23 February 2013
Received in revised form 30 April 2013
Accepted 30 April 2013
−1
[
Br] in concentration range ~0.019 to ~0.39 mol·kg
at 298.15 K are reported. The density data are used
ꢀ
ꢁ
to obtain apparent molar volume (ϕ
as well the limiting partial molar volume
The experimental osmotic coefficient (ϕ) data are used to determine the activity and mean ionic activity
coefficients of solute and solvent respectively. Experimental activity coefficient data are compared with
V
), partial molar volume of solute and solvent V 2 andV 1 respectively
ꢂ
ꢃ
0
0
ϕ
¼ V 2 of the solute [Bpy][Br] (by appropriate extrapolation).
V
Available online 14 May 2013
Keywords:
Ionic liquids
those obtained from Debye–Hückel and Pitzer models. The activity data have been further processed to
E
Apparent molar volume
Osmotic coefficient
Activity coefficient
McMillan–Mayer theory of solutions
Pitzer model
obtain the Gibbs free energy change due to mixing (ΔG
m
) and excess Gibbs free energy change (ΔG ). The
aggregation number (n) and critical micelle concentration (cmc) are obtained for ionic salt in solution phase
by applying pseudo-phase separation model to ϕ and ϕV data respectively. Application of McMillan–Mayer
theory of solutions to the data is made. The results have been interpreted on the basis of structural characteristic
of salt, ion–solvent and ion–ion interactions.
©
2013 Elsevier B.V. All rights reserved.
1
. Introduction
monograph are now available [6–9]. To date, a number of researchers
have studied the thermophysical properties of aqueous solutions of
imidazolium-based ionic liquids. The thermodynamic studies (density,
speed of sound and osmotic coefficient) of ionic interactions in aqueous
solutions of 1-ethyl-3-methylimidazolium bromide and 1-butyl-3-
methylimidazolium chloride at 298.15 K are reported [10]. Similarly,
the measurements for speed of sound and density of aqueous solutions
of imidazolium chloride, 1-methyl imidazolium chloride and 1-butyl-
3-methylimidazolium chloride at 298.15 K are reported and discussed
in terms of hydrophobic hydration, hydrophobic interactions, and water
structural changes in aqueous medium [11]. The electrical conductivity
was measured for aqueous solutions of long-chain imidazolium
ionic liquids (1-alkyl-methylimidazolium bromides) with C12–C16
chains and further the data were used for the determination of ag-
gregation number, critical micelle concentration and degree of coun-
ter ion binding [12]. For the systems involving imidazolium based
ionic liquids and water, the measurements of density, refractive index,
viscosity, specific conductance and surface tension have been studied
[13]. Osteryoung et al. pioneered the first room temperature pure elec-
trolyte of pyridine family in 1975 [14,15]. Thereafter very few research
articles which deal with the physical properties of pyridinium-based
ionic liquids have been reported [16–19].
Ionic liquids (ILs) have attracted much attention over the past de-
cade due to their large variety of applications in industry and applied
chemistry [1,2]. The journey of ionic liquids started from molten salts
or fused salts which are composed entirely of ions; their conductivity
is considerable and higher than that of water [3,4]. Ionic liquids are
termed room-temperature ionic liquids (RTILs) if they are composed
of a salt that is liquid at room temperature. ILs almost always contain
an organic ion as either the cation or the anion. These neoteric mate-
rials provide a feasibility of changing ion either cation or anion in ac-
cordance with the conditions. Such designing ability is the key reason
as these materials are popular solvents for organic reactions [5].
Reliable knowledge of thermodynamic and thermophysical prop-
erties for both the pure ILs and their mixtures is a prerequisite for
the design and optimization of different processes. Most of the ILs
have negligibly low vapor pressures, high thermal decomposition
temperatures, wide liquid temperature ranges and excellent stability
in air and water. These features make ILs suitable for the application
of IL + water mixtures as heat transfer fluids [4].
The ionic liquids mainly consist of ammonium, sulfonium and
phosphonium cations. Furthermore, the applications of imidazolium
and pyridinium-based ionic liquids are increased by many folds in
recent years; large number of research articles, reviews, books and
Our literature survey revealed that N-butyl pyridinium bromide
salt has different freezing and melting points [20]. As such the salt
exists at room temperature in a glassy state of which properties are
difficult to determine. It is also known in literature [21,22] that
pyridinium salts exert water structure breaking effect in aqueous
⁎
Corresponding author.
E-mail address: patilkesharsingh@hotmail.com (K.J. Patil).
0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.molliq.2013.04.027

V.R. Shaikh et al. / Journal of Molecular Liquids 186 (2013) 14–22
15
solutions as well some have reported micellization when the non-
polar residues are substituted on the pyridinium nitrogen center
Digital Densitometer (Model: DMA-5000) at 298.15 ± 0.001 K. After
applying the humidity and lab pressure corrections, the uncertainty in
−
3
−3
[23]. Considering these aspects, in order to study the effects due
the density measurements was found to be ± 5 · 10
kg·m . The
to hydrophobic substituent such as N-butyl group, we focused our
attention on N-butyl pyridinium bromide salt.
details about the density measurements have been reported earlier
[27]. The reliability of the density data was ascertained by making the
measurements of binary aqueous solutions of alkali halides (NaCl and
Recently, we have developed a rapid and simple method for the
synthesis of the substituted imidazolium ionic liquids. Considering
the applications for the devised method, we undertook the work of
synthesis of N-butyl pyridinium bromide [Bpy][Br]. We could synthe-
size the compound successfully, however its identification was biased
because of differing freezing and melting behavior (as well its highly
hygroscopic nature). Therefore, a program was embarked to investi-
gate the structural properties of aqueous pyridinium-based ionic
liquid solutions, for the studies of hydrophobic interaction amongst
pyridinium-based ionic liquids, their hydration properties i.e. ionic
liquid–water interactions and water structural effects (structure
making and breaking effect). For this the knowledge of partial vol-
umes, free-energy and entropy changes at infinite as well as at finite
concentrations is essential. It is suspected that ionic liquid depending
upon the hydrophobic moieties may exhibit micelle type or aggregation
equilibria in solution phase. To probe such an equilibria in solution
phase, the measurements of density and osmotic coefficient properties
of [Bpy][Br] in aqueous solutions at 298.15 K were carried-out. The
results are being reported below and discussed in terms of water struc-
tural effects and presence of micellar type of equilibria in solution phase.
KCl) at 298.15 K and comparing the data with literature [28]. Also, the
0
limiting apparent molar volumes (ϕ
V
) for these standards are in good
agreement with the literature data [29].
The osmotic coefficients (ϕ) of aqueous ionic salt solutions were
measured using a Knauer Vapor Pressure Osmometer (Model: K-7000)
at 298.15 ± 0.001 K. The instrument was calibrated using aqueous
NaCl solutions taking water as a reference. The required osmotic coeffi-
cient data for aqueous NaCl solutions were taken from literature [30].
−
3
The uncertainty in ϕ measurements was found to be ± 1 · 10 at the
lowest concentration studied. The details about the calibration, mea-
surements and error analysis of vapor pressure osmometer were de-
scribed earlier [31–33].
3. Results
3.1. Molecular weight determination of [Bpy][Br] by vapor
pressure osmometry
We have used aqueous NaCl solutions of known osmolality for the
calibration and hence determined the instrumental constant (Kcalib).
The Kcalib is represented by the slope of the regression curve
2
. Experimental procedure
(
measurement value as a function of osmolality of aqueous NaCl
Synthesis of N-butyl-pyridinium bromide [BPy][Br] was carried-out
solutions) passing through origin and is represented by the equation:
by a simple and efficient method, previously reported by us [24]. It
consists of reacting alkyl-halide and pyridine in appropriate amounts
in the presence of molten-tetra-butyl-ammonium-bromide for about
half an hour. On cooling the reaction mixture, the white product
obtained was separated and purified with the help of tetrahydrofuran.
The product [BPy][Br] was dried in vacuum-oven and identified by
mass and spectral analysis [24–26]. It was stored in vacuum. However,
it was found that the salt is very much hygroscopic (absorbs water),
making the measurements of weight etc. difficult. Therefore, it was
decided to determine the water content of the stored salt by Karl Fischer
Kcalib ¼ measurement value=knownosmolality:
ð1Þ
The osmolality of the sample solution can be calculated with the
following equation:
osmolality ¼ measurement value=Kcalib
:
ð2Þ
The osmotic pressure (π) is calculated by the following equation:
ꢂ
ꢃ
ꢂ
ꢃ
πðatmÞ ¼ osmolality mosmol⋅kg−1 ⋅0:082056 L⋅atm⋅K−1⋅mol−1 ⋅298:15ðKÞ:
ð3Þ
(
KF) and Thermo-Gravimetric Analysis (TGA) and also estimating with
the osmometry (to be discussed later). The structure of the studied ionic
liquid is shown in Fig. 1. The salt NaCl of AR grade (Merck) was dried
under vacuum at 393 K for 24 h before use.
All the solutions were prepared on molality basis using quartz
doubly distilled water and were converted to molarity scale whenever
required with the help of density data at 298.15 K. A Shimadzu
AUW220D balance having a readability of 0.01 mg was used for
weighing. The density measurements were made using an Anton Paar
The concentration c in (g·cm−3) is calculated with the help of
density and weight fraction data.
The values of parameter (π/cRT) are estimated with help of the
following equation:
ꢂ
ꢃ
h ꢂ
ꢃ
ꢂ
ꢃ
i
−1
−3
⋅82:056 cm ⋅atm⋅K−1⋅mol−1 ⋅298:15ðKÞ :
3
π=cRT mol⋅g
¼ πðatmÞ= c g⋅cm
ð4Þ
In Fig. 2, parameter π/cRT is plotted as a function of concentration
−
3
(
c in g·cm ) for the studied compound. The intercept of the said
plot yielded the value of reciprocal of molecular weight while the
slope value gave the measure of osmotic second virial coefficient.
The intercept of the plot reveals that the molecular weight of studied
−
1
compound is 283.53 g·mol . The theoretical molecular weight of
−
1
the compound is 216.12 g·mol . Therefore, we concluded that the
salt contains four water molecules as water of hydration. This conclu-
sion is also supported by our KF titrimetry and TGA analysis [25]. The
calculated molecular weight was used to correct the molalities and
reported in Table 1 as well as in Table 3.
+
-
C H3
N
Br
3.2. Volumetric properties
The density (d) data as a function of concentration of ionic salt
Fig. 1. Molecular structure of the compound studied.
molecule in aqueous solutions at 298.15 K are reported in Table 1.

16
V.R. Shaikh et al. / Journal of Molecular Liquids 186 (2013) 14–22
Fig. 3. Variation of (ϕ
Bpy][Br] in aqueous solutions at 298.15 K.
V
− 1.868c1/2) as a function of concentration (c/mol·dm−3) of
[
Fig. 2. The plot of parameter (π/cRT) against concentration (gm·cc−1) of [Bpy][Br] in
aqueous [Bpy][Br] solutions at 298.15 K.
The partial molar volume of the ionic salt (V2) has been computed
from ϕ
V
data by using the following equation [36]
2
3
The apparent molar volume (ϕ
salt molecules was calculated by using the following equation:
V
) as a function of molality of the ionic
1
000−c ϕ
pffiffi
pffiffi dϕ
V
dϕV
d
V
4
5
V2
¼
ϕV
þ
c⋅ pffiffi :
ð7Þ
2
000 þ c c⋅ pffiffi
d
c
c
ϕV ¼ 1
000ðd −dÞ
þ
M2
d
ð5Þ
0
The partial molar volume of solvent ( V1) is calculated using
equation
mdd
0
"
#
M1
d−c⋅ δδ dc
where m is the molality of ionic salt molecules in aqueous solution
V1
¼
ꢀ
ꢁ
ð8Þ
−
1
(
mol·kg ), d and d
0
are the densities of solution and solvent respec-
−
3
−1
tively in kg·m
2
and M is the molar mass of the solute (kg·mol ).
The ϕ
V
data can also be expressed as [29,34,35]
where M1 is the molecular weight of the solvent and c is the con-
centration in mol·dm
−
3
.
The data of ϕ , V 2 and V 1 for aqueous solutions of [Bpy][Br] at
298.15 K are reported in Table 1.
V
1
0
V
=2
ϕV ¼ ϕ þ AV c þ BV c
ð6Þ
Vikingstad et al. [37] have calculated the volume of the surfactant
in the micellar state (V
using the following equation:
m
) directly from the apparent molal volume by
0
where ϕ
V
is the apparent molar volume of the salt at infinite dilution, A
V
is the Debye–Hückel limiting law coefficient (1.868 for 1:1 electrolyte
solutions at 298.15 K), B is the deviation parameter and c is
the concentration of the salt on molarity scale. The variation of
(ϕ − 1.868c ) parameter as a function of concentration of ionic
salt (c/mol·dm ) in aqueous solutions at 298.15 K is shown in
V
cmc
m
m−cmc V
ϕV
¼
V þ
ð9Þ
s
m
m
1
/2
V
−3
where V
and V is the molar volume of drugs in the micellar state. The data of
are plotted against 1/m as suggested by Taboada et al. [38] (Fig. 4).
Using Eq. (9) and the data shown in Fig. 4, we estimated the values of
s
is the molar volume of the surfactant in the dispersed state
1
/2
Fig. 3. When (ϕ
V
− 1.868c ) values are extrapolated to infinite
m
0
dilution, they yield limiting apparent molar volumes (ϕ ) of ionic
salt. The values of ϕ and B parameter of Eq. (6) are collected in
V V
V
ϕ
V
0
−
1
Table 2.
aggregation number (n) and cmc value as 6 and 0.17 mol·kg
Table 1
ꢀ
ꢁ
Molality (m), density (d), concentration (c), apparent molar volume (ϕ
V
), partial molar volumes of solute and solvent V 2 andV 1 for Aqueous solutions of [Bpy][Br] at 298.15 K.
a
−1
b
−3
c/mol·dm−3
103 · ϕc
3
−1
3
3
−1
3
3
−1
m /mol·kg
d /kg·m
V
/mm ·mol
10 ⋅V 2/mm ·mol
10 ⋅V 1/mm ·mol
0.00000
0.01984
0.02735
0.04333
0.05223
0.06294
0.07738
0.09862
0.12224
0.16454
0.23438
0.31217
0.39501
0997.043
0998.117
0998.523
0999.388
0999.870
1000.450
1001.231
1002.381
1003.659
1005.949
1009.729
1013.394
1018.424
0.00000
0.01972
0.02715
0.04290
0.05164
0.06212
0.07620
0.09679
0.11653
0.15984
0.22525
0.29652
0.37065
162.03a
162.14
162.07
161.93
161.85
161.76
161.63
161.45
161.24
160.88
160.27
159.61
158.90
162.03a
161.96
161.82
161.54
161.38
161.19
160.93
160.57
160.16
159.46
158.33
157.13
155.90
18.068
18.068
18.069
18.069
18.069
18.069
18.069
18.070
18.071
18.073
18.077
18.083
18.092
a) The uncertainty in molality m is of the order of ± 5 · 10− mol·kg−1
5
.
−
3
kg·m−3.
b) The error involved in density determination at lowest concentration is of the order of ± 5 · 10
c) The errors in ϕ
3
3
−1
V
were obtained using the method of propagation of errors and found to be ± 0.25 · 10 mm ·mol
at the lowest concentration studied.
a
Extrapolated value at infinitely dilute solution of [Bpy][Br] at 298.15 K.

V.R. Shaikh et al. / Journal of Molecular Liquids 186 (2013) 14–22
17
Table 2
The limiting partial molar volume (V 2), deviation parameter (B
centration (cmc), molar volume of the ionic salt in the dispersed state (V
aggregation number (n) data for [Bpy][Br] in aqueous solutions at 298.15 K.
Substituting Eq. (13) into Eq. (12) and considering higher order
interaction terms A , which are expected to be appreciable at higher
concentrations, one can write Eq. (12) as [37]
0
v
), critical micelle con-
i
s
) and
03 · V
0
2
/
103 · B
mm ·mol
/
cmc/mol·kg−1
103 · V
mm ·mol
n
X
n
1
v
s
/
pffiffiffiffi
2:303
3
i=2
3
−1
6
−2
3
−1
mm ·mol
ϕ ¼ 1−
A z z
þ −
γ
m þ
Aim
ð14Þ
i¼2
1
62.03 ± 0.25
−11.64
0.17 ± 0.01
940
6
γ
where A is the Debye–Hückel limiting slope for aqueous solutions
and its value is 0.5115 at 298.15 K.
Eq. (14) can be written as
respectively and these are collected in Table 2. The calculation details
of n and cmc were described earlier [27].
n
X
i=2
ϕ ¼ 1 þ
Aim
ð15Þ
3
.3. Osmotic and activity coefficients
i¼1
The osmotic coefficient (ϕ) values of N-butyl-pyridinium bromide
where A
1
is the Debye–Hückel constant equal to −0.3927 for 1:1
represents the term
) / 3], assuming the ionic salt studied as 1:1
= z = 1), and A = 0.5115 at 298.15 K.
The experimentally observed osmotic coefficient values were fitted
according to Eq. (15) and the corresponding values of A coefficients
[
Bpy][Br] in aqueous solutions were determined over the concentra-
electrolyte at 298.15 K. The coefficient A
(−2.303 A
electrolytes (z
1
−
1
tion range of ~0.019 to ~0.39 mol·kg
at 298.15 K.
[
γ + −
z z
Using the osmotic coefficient (ϕ) values obtained for aqueous
+
−
γ
w
binary electrolyte solutions, the water activity (a ) values have been
calculated using the equation
i
ꢄ
ꢅ
have been determined by least square fit method. The A coefficients
in Eq. (15) are collected in Table 4.
i
x2
x1
lnaw ¼ −ϕ
ð10Þ
For further processing, we applied the pseudo-phase separation
model to ϕ data as suggested by Desnoyers et al. [39]. When ϕ values
are plotted against 1/m (Fig. 6) it leads to the simultaneous determi-
nation of aggregation number n (by linear extrapolation in the high
concentration region) and critical micelle concentration cmc according
to equation [39,40]
where x
ous solutions respectively.
Further the (a ) data were utilized to calculate the solvent activity
) using the equation:
1 2
and x are the mole fractions of water and the salt in the aque-
w
coefficient (γ
1
aw
x1
ꢄ
ꢅ
γ1
¼
:
ð11Þ
1
n
1
n
cmc :
ϕ ¼
þ
1−
ð16Þ
m
The data of ϕ and a
w
are collected in Table 3. The variation of ϕ as a
Using Eq. (16) and the data shown in Fig. 6, we calculated the
function of square root of solute molality is shown in Fig. 5.
The experimental osmotic coefficient data for 1:1 type electrolyte
has been expressed as [34]
−
1
values of n and cmc values as 1.4 and 0.15 mol·kg
for [Bpy][Br] in
aqueous solutions at 298.15 K respectively.
The mean molal activity coefficient of the solute (γ
±
) in binary
aqueous solutions can be expressed in terms of osmotic coefficient
using the equation [36]
ϕ ¼ 1 þ 1 lnγ
ð12Þ
ꢀ
3
pffiffiffi
m
where γ
According to Debye–Hückel limiting law, the solute activity coeffi-
cient (γ ) is given as:
±
represents the mean molal activity coefficient of solute.
ðϕ−1Þ
pffiffiffiffi
lnγ ¼ ðϕ−1Þ þ 2 ∫ pffiffiffiffi
d
m
ð17Þ
ꢀ
m
0
±
pffiffiffiffi
m:
This equation can be processed as:
lnγ ¼ 2:303 logγꢀ ¼ −2:303A z z
ð13Þ
ꢀ
γ þ −
n
X
i=2
ϕ−1 ¼
Aim
(From Eq. (15))
i¼1
Substituting m1/2 = x
n
X
i
ϕ−1 ¼
A x :
ð18Þ
i
i¼1
Solving the right hand side integral of Eq. (17) and using Eq. (18),
one can write [36]
n
X
2
þ i
i=2
lnγ
¼
Aim
:
ð19Þ
ꢀ
i
i¼1
The mean molal activity coefficient (γ
±
) values are calculated
using Eq. (19) and the data are collected in the Table 3. The variation
of ln γ as a function of square root of ionic liquid concentration is
±
shown in Fig. 7. The calculation details can be obtained from our
Fig. 4. Variation of apparent molar volumes (ϕ
V
) as a function of reciprocal of molality
(1/m) of [Bpy][Br] in aqueous solutions at 298.15 K.
earlier reported studies [41–44].

18
V.R. Shaikh et al. / Journal of Molecular Liquids 186 (2013) 14–22
Table 3
Molality (m), mole fraction (x ), osmotic coefficient (ϕ), water activity (a ), solvent activity coefficient (γ ), activity coefficient (γ ), free energy change due to mixing (ΔG ) and
2
w
1
±
m
E
excess Gibbs free energy change (ΔG ) data for aqueous solutions of [Bpy][Br] at 298.15 K.
m/mol·kg−
1
x
ϕ
a
a
w
b
γ
1
b
γ
ΔG
m
d
/J·mol−1
0.00
ΔG /J·mol−1
Ed
2
±
0.00000
0.01984
0.02735
0.04333
0.05223
0.06294
0.07738
0.09862
0.12224
0.16454
0.23438
0.31217
0.39501
0.00000
0.00071
0.00098
0.00156
0.00188
0.00226
0.00278
0.00354
0.00438
0.00589
0.00837
0.00111
0.00140
1.0000
0.9772
0.9759
0.9726
0.9702
0.9667
0.9611
0.9513
0.9387
0.9140
0.8738
0.8363
0.8037
1.0000
0.9993
0.9990
0.9985
0.9982
0.9978
0.9973
0.9966
0.9959
0.9946
0.9926
0.9906
0.9886
1.0000
1.0000
1.0000
1.0000
1.0000
1.0001
1.0001
1.0002
1.0003
1.0005
1.0010
1.0018
1.0027
1.0000
0.9093
0.9014
0.8879
0.8811
0.8729
0.8616
0.8442
0.8239
0.7867
0.7280
0.6727
0.6242
0.00
−0.13
−0.39
−0.70
−0.89
−1.14
−1.50
−2.09
−2.83
−4.41
−7.76
−12.52
−18.64
−14.72
−19.53
−29.19
−34.32
−40.33
−48.19
−59.33
−71.28
−91.77
−123.82
−157.71
−192.26
a) The uncertainty in ϕ values at the lowest concentration is of the order ± 1 · 10−
b) The uncertainty in the water activity (a ) and solvent activity coefficient (γ
) are of the order of ± 1 · 10−4.
c) The mean ionic activity coefficient (γ
) of the [Bpy][Br] at the lowest concentration studied are accurate up to ± 1 · 10−3.
and ΔG are estimated to be of the order of ± 0.05 J·mol−1
3
.
w
1
±
E
d) The errors in ΔG
m
.
The activity coefficient data which have been converted to mole
where, a is the distance of the closest approach of oppositely charged
ions and h is the hydration number of the electrolyte.
fraction scale and were used to calculate the Gibbs free energy change
E
due to mixing (ΔG
m
) and excess Gibbs free energy change (ΔG ) of
Our attempt to obtain hydration number values were hampered
by the difficulty in choosing the value of a, the distance of the closest
approach of oppositely charged ions. The standard value of 3.6 Å for
closest ion approach yields a value of 5.4 for hydration number; how-
ever this does not reproduce the activity coefficient data, meaning
in addition to ion–solvent interaction, other types of interactions
i.e. hydrophobic cation–cation, stacking micellar type all are contribut-
ing to the deviation from Debye–Hückel limiting law for 1:1 electrolyte.
binary aqueous drug solutions at 298.15 K using equations
2
X
ΔGm ¼ RT
xi lna
ð20Þ
i
i¼1
2
X
E
ΔG ¼ RT
xi lnγi
ð21Þ
i¼1
4
. Discussion
where x
i
, a
i
and γ
i
are the mole fraction, activity and activity coeffi-
cient of ith component.
The values for ΔG
The variation of ΔG
E
4.1. Volumetric properties
m
and ΔG parameters are collected in Table 3.
E
m
and ΔG as a function of square root of ionic liq-
It is observed from Table 1 and Fig. 3 that the apparent molar volume
± m
uid concentration is shown in Fig. 8. The corrections to ln γ , ΔG and
E
V
(ϕ ) of [Bpy][Br] in aqueous solutions decreases as concentration of salt
ΔG data due to hydrolysis in low concentration region are assumed
to be negligible.
0
2
increases. The value of limiting partial molar volumes (V ) is found to
3
3
−1
be 162.03 · 10 mm ·mol . The deviation parameter (B
V
) is negative
Taking into the account the hydration effect, the mean molal activity
3
6
−2
(
−11.64 · 10 mm ·mol ) for [Bpy][Br]. In general for structure
±
coefficient γ for aqueous 1:1 electrolyte solutions then can be
making ions, B
V
is negative due to overlap of cosphere effect. The cal-
expressed as [30,36]
ꢀ
ꢁ
culations of partial molar volumes of solute and solvent V2 andV1
respectively have been made and are reported in Table 1. The aggre-
gation number (n) and critical micelle concentration (cmc) are found
to be 6 and 0.17 mol·kg
pffiffiffiffi
Aγ
m
h
υ
logγ ¼ − 1
pffiffiffiffi − loga −log½1−0:018 ðh−υÞmꢁ
ð22Þ
ꢀ
w
þ 0:3286a
m
−1
respectively for the studied ionic liquid
by applying pseudo-phase separation model to ϕ
V
data (Fig. 4).
pffiffi
The negative values of the slope of V 2−2:802 c against concen-
−
3
tration (c in mol·dm ), suggest solute–solute (solvent induced)
Table 4
Coefficients A in Eq. (15).
i
A
A
A
A
A
A
A
A
A
A
A
1
−0.3927
2.5709
−7.1211
2.9719
3.8835
1.3611
−0.8042
−1.8019
−1.9113
−1.5594
−1.0505
2
3
4
5
6
7
8
9
10
11
a
a
We stopped up to the coefficient A11, since
Fig. 5. Variation of experimental osmotic coefficient (ϕ) as a function of square root of
molality of ionic salt in aqueous ionic salt solutions at 298.15 K: –●–●–, [Bpy][Br]; - - -,
Debye–Hückel limiting law.
the experimental data gets well fitted within
the experimental uncertainties and requires
no higher order terms.

V.R. Shaikh et al. / Journal of Molecular Liquids 186 (2013) 14–22
19
respectively for the ionic liquid (Fig. 6). We note that the extrapolation
at 1/m = 0 is difficult because of limited number of measurements in
high concentration region. However, we are certain that, the n value sig-
nifies the formation of dimeric as well higher order aggregates in these
solutions. Thus, the solution behavior is similar to that of systems
exhibiting micellar type equilibria.
±
The variation of mean molal activity coefficient γ with concen-
tration is shown in Fig. 7 and which shows the similar effect observed
in the variation of ϕ data. The nature of the curve is similar to the var-
iation observed in aqueous solutions of cationic surfactant solutions
[38,47].
It is observed that the Gibbs free energy change due to mixing
E
(
ΔG
m
) and excess Gibbs free energy change (ΔG ) are negative over
E
the studied concentration range. The ΔG
m
and ΔG values decrease
Fig. 6. Variation of experimental osmotic coefficient (ϕ) as a function of reciprocal of
molality (1/m) of [Bpy][Br] in aqueous [Bpy][Br] solutions at 298.15 K.
with increase in concentration of ionic liquid (Fig. 8). The excess
free energy change values are small negative meaning in the solution
process excess entropies are importantly contributing. However, due
to the absence of excess enthalpy data, we could not able to do calcu-
lations of excess entropies.
interactions as has been observed for aqueous solutions of tetra-
alkylammonium halides [45].
4.3. Application of the McMillan–Mayer theory
The apparent molar volume behavior for various substituents on
pyridine ring and substituents on nitrogen up to methyl group has
been reported [21,22] and discussed in terms of electrostriction and
water structure breaking properties of pyridinium salt. However, in
present case of n-butyl group substitution on charged nitrogen cen-
ters, the volumetric behavior indicates negative magnitude for the
limiting slope after Debye–Hückel correction meaning that the salt
exerts a water structure making effect in solution. This is also similar
to the volume behavior exhibited by 1-ethyl-3-methylimidazolium
bromide and 1-butyl-3-methylimidazolium chloride salts in water
An application of McMillan–Mayer theory of solutions to aqueous
electrolytic solutions yields information about relative non-electrolytic
contribution to the solute–solvent and solute–solute interactions. In
dilute solutions of up to 0.1 mol·kg , if the Debye–Hückel electro-
static contribution is subtracted from the thermodynamic parameter,
−
1
i.e. from ln γ , then the remainder will be linear in the molality, similar
±
to what is being observed for aqueous non-electrolyte solutions [48].
The mean molal activity coefficient of the solute (γ ) in dilute
±
concentration range can be represented as
[
10]. These salt ions have a very small hydration number and hence
ꢂ
ꢃ
exhibit cation–cation interaction (hydrophobic in solution). The
pyridinium salt is having four water molecules in its hydration
sphere, still exhibit cation–cation (solvent induced) interaction,
probably through the mechanism of solvent shared ion-pair forma-
tion [46].
1=2
1=2 −1
lnγ ¼ −αm
1 þ bm
þ ωm
ð23Þ
ꢀ
where α = 1.173 kg1/2·mol−1/2 at 25 °C and b = 1.0 kg1/2·mol−1/2
and ω is non-electrolyte solute–solute interaction parameter.
According to McMillan–Mayer [49],
4
.2. Osmotic and activity coefficient
π
n þ Bꢂ n þ B n þ …
2
ꢂ
3
¼
ð24Þ
2
2
222
kT
It is observed from Fig. 5 that the osmotic coefficient (ϕ) for aque-
ous [Bpy][Br] solutions, decreases as a function of the square root of
concentration and ϕ data show the positive deviation from Debye–
Hückel limiting law. We applied the pseudo-phase separation model
to ϕ data. The ϕ varies linearly in lower concentration region and
after a certain concentration shows a break with increase in concentra-
tion and the values of n and cmc are found to be 1.4 and 0.15 mol·kg−1
where n is number density of the solute and B2 2⁎ and B222 are
the osmotic second and third virial coefficients for solute–solute
interaction.
⁎
Fig. 7. Variation of the mean activity coefficient of a ionic salt (lnγ
of square root of molality of ionic salt in aqueous ionic salt solutions at 298.15 K:
●–●–, [Bpy][Br]; - - -, Debye–Hückel limiting law.
±
) as a function
Fig. 8. Variation of Gibbs free energy change due to mixing (ΔG
energy change (ΔG ) of ionic salt as a function of square root of molality of [Bpy][Br] in
aqueous [Bpy][Br] solutions at 298.15 K: –■–■–, ΔG ; ▲–▲– ΔG .
m
m
) and excess Gibbs free
E
E
–

20
V.R. Shaikh et al. / Journal of Molecular Liquids 186 (2013) 14–22
The total Gibbs free energy of solution can be expressed as a
where
function of mole ratio m (ratio of moles of solute to solvent) using
the equation
pffiffi
Aϕ
I
ϕ
f
¼ −
pffiffi :
ð31Þ
1
þ b
I
0
1
0
2
G
μ
μ
1
2
2
1
3
3
¼
þ
m−m þ m lnm þ A22
m
þ
B222
m
þ …
ð25Þ
n1kT kT kT
Here, A
ϕ
is the Debye–Hückel constant for the osmotic coeffi-
cient which is equal to 0.3927 for aqueous solutions at 298.15 K,
0
0
1/2
−1/2
where μ
1
and μ
2
are the chemical potential of pure solvent and solute
b is an adjustable parameter having a value of 1.2 kg ·mol
,
2
ϕ
respectively, whereas A22 and B222 are the pair and triplet interaction
term for solute particles.
Hill [50,51] has shown that the coefficient A22 in the free energy
expression (Eq. (25)), may be related to the coefficient B22 through
and I = [(1/2)∑ m
i
·z
are the second virial and third virial type coefficients for the os-
motic coefficient.
The coefficient B depends on concentration and is generally
expressed as
i
] is the ionic strength of solution. B and
ϕ
C
ϕ
⁎
the relation
pffi
ϕ
¼ βð0Þ þ βð1Þ
−α
I
0
1
¼ 2Bꢂ0 −v þ b
0
0
B
e
ð32Þ
A22
v
ð26Þ
22
2
11
β(0) and β(1) are the Pitzer ion interaction parameters, whereas α is
0
0
2
where v
1
and v are the molecular volume of the pure solvent and
1
/2
−1/2
the adjustable parameter having a value of 2.0 kg ·mol
the help of the nonlinear least-squares fit method, the experimental
osmotic coefficient data have been fitted using Eqs. (31)–(33) to ob-
. With
partial molecular volume of the solute at infinite dilution respectively
and b 10 1 = (−B11 ) is the solute–solvent cluster integral. The solute–
⁎
0
0
solvent cluster integral b11 is related to the partial molecular volume
(
0)
(1).
tain the Pitzer ion interaction parameters β
and β
The values
of the solute at infinite dilution by [52]
(
0)
(1)
obtained for β and β are included in Table 5. The standard devi-
ation in osmotic coefficient obtained from the least-squares fit is also
given in the last column of Table 5 and is calculated using the equation
0
1
0
2
b
¼ −v þ kTκT
ð27Þ
1
where k is the Boltzmann constant, T is the absolute temperature, and
2
ꢂ
ꢃ 3
1
2
=2
exp
cal
∑
ϕ
−ϕ
κ
T
is the isothermal compressibility coefficient for the pure solvent.
6
7
5
σðϕÞ ¼ 4
:
ð33Þ
For a 1:1 electrolyte [48],
n−m
ꢂ
2
2
lnγ ¼ A22m þ B222
m
ð28Þ
2
(
0)
(1)
We observe from Table 5 that when β and β values are com-
pared with those reported by Pitzer and Mayorga [53] for 1:1 electro-
⁎
where γ
2
is the nonelectrolyte contribution to the solute mean molal
(
0)
(1)
lytes, these are highly negative and highly positive for β and β
activity coefficient.
ϕ
respectively while the C coefficient is also high. The positive value
From Eqs. (23) and (28), ω = (A22·M
mass of solvent in kg·mol ).
Thus from Eqs. (26) and (27)
1
) / 2 (where M
1
is molar
ϕ
−
1
of 1.9639 for the parameter C implies that there is a contribution
to ln γ
±
because of third virial coefficient. Thus, our interpretation
of the presence of multiple cation–cation interaction equilibria is
being supported. It is pleasing that these observations based upon
the application of Pitzer approach are in close agreement with the re-
sults discussed earlier based on the application of MacMillan–Mayer
A22V01
RTkT
2
ꢂ0
0
NB
¼
þ V −
ð29Þ
2
2
2
2
(
0)
theory. The ‘ω’ parameter is negative and closely agrees with β
.
where N is the Avogadro constant.
Using the Eq. (29), the value of solute–solute (osmotic second)
virial coefficient (NB22 ) has been calculated for the studied ionic
⁎
0
While the osmotic second virial coefficient NB22 in solution is nega-
tive implying affinity between the solute–solute i.e. cation–cation in-
teraction as well as having some additional cation–anion–cation
affinity contribution in the form of third virial coefficient.
⁎
0
salt in aqueous solutions at 298.15 K and reported in Table 5 along
⁎0
with the corresponding values of ω and A22. The NB22 value
which is a measure of the solute cation–solute cation interactions)
is large negative.
Earlier, we discussed the activity coefficient profiles as a function
of concentration for few ionic liquids (imidazolium salts) in water
(
[11]. We noted therein that the concentration dependence can be
⁎0
The value of solute–solvent (NB11 ) virial coefficient obtained
using the McMillan–Mayer theory is also given in Table 5. We calcu-
accounted for in terms of hydrophobic hydration of the ions similar
to that of aqueous solutions of tetra-alkylammonium salts. The limiting
properties however indicate a resemblance with aqueous solutions
of simple alkali halide. We observe the similar type of interactions in
water due to addition of ionic pyridyl salt.
late the NB11 value as 161 · 103 mm ·mol
3
−1
which is similar to
⁎0
0
that of ϕ
V
.
4
.4. Application of the Pitzer model
When we compare the osmotic coefficient (ϕ) and mean molal ac-
tivity coefficient (γ
imidazolium salt ions [10], it is noted that the former exhibits positive
deviations from Debye–Hückel limiting law for both ϕ and γ as a
±
) behavior of studied pyridinium salt ions with
According to the Pitzer model [53–55] the osmotic coefficient for
:1 electrolyte can be expressed as
1
±
function of concentration. In case of imidazolium salt ions, the
ϕ
ϕ
2 ϕ
Debye–Hückel limiting law is obeyed up to ~0.05 mol·kg− and
1
ϕ−1 ¼ f þ mB þ m C
ð30Þ
Table 5
⁎0
Nonelectrolyte solute–solute interaction parameter (ω), pair interaction terms for solute particles (A22), solute–solute (osmotic second) virial coefficients (NB22 ) and solute–solvent
virial coefficient (NB11 ) and Pitzer interactions parameters for [Bpy][Br] in aqueous solutions at 298.15 K.
⁎0
ω/kg·mol−
2.09
1
A
10 ·NB22 /mm ·mol
3
⁎ 0
3
−1
10 ·NB11 /mm ·mol
3
⁎ 0
3
−1
β
(0)/kg·mol−1
−2.2085
β
(1)/kg·mol−1
4.5462
σ(ϕ)
22
−
−232.03
−1935
161
0.0008

V.R. Shaikh et al. / Journal of Molecular Liquids 186 (2013) 14–22
21
thereafter the negative deviation from the limiting law for γ
±
and
work. Mr. Vasim R. Shaikh acknowledges the University Grants
Commission, New Delhi (India), for financial assistance through the
Maulana Azad National Fellowship (MANF) for Minority Students.
positive deviation for ϕ has been observed. We feel that these are
the important differences between hydration and hydrophobic ef-
fects exhibited by imidazolium and pyridinium salt ions. The positive
deviation from the limiting law and negative virial coefficient ob-
served for the studied salt indicates the aggregation (with limited
number of solute molecule), similar to that of small sized micellar
systems probably exhibiting stacking type equilibria in solution
phase. The application of Pitzer model to the solution of pyridinium
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