Studies of Volumetric and Viscosity Properties in Aqueous Solutions of Imidazolium Based Ionic Liquids at Different Temperatures and at Ambient Pressure

Article abstract of DOI:10.1007/s10953-019-00845-7

The ionic liquids (ILs) 1,3-dimethyl imidazolium methyl sulfate [MIm][MeSO₄] and 1-ethyl-3-methyl imidazolium ethyl sulfate [EMIm][EtSO₄] have been synthesized and characterized by ¹H NMR, ¹³C NMR, mass spectrometry, TGA and DSC methods. The densities and viscosities of binary aqueous solutions of [MIm][MeSO₄] (0.02458 to 0.18922?mol·kg^?1) and [EMIm][EtSO₄] (0.01044 to 0.21261?mol·kg^?1) are reported at (293.15, 298.15 and 303.15) K and at ambient pressure. Apparent and partial molar volumes of the studied ILs are calculated at the studied concentrations. The limiting partial molar volumes of the studied ILs were obtained using an appropriate extrapolation method. The limiting apparent molar expansivity values at 298.15?K are also obtained. The relative viscosity data are analyzed by applying the Jones–Dole equation and Vand’s equations. Positive viscosity A and B coefficients were observed for both studied ILs, while the D coefficients were also found to be necessary, showing specific behavior depending upon the solute–solute interactions. Calculations of the B coefficients for anions are reported. The application of Vand’s equation to the viscosity data enabled us to calculate the Einstein–Simha factor (ν) and particle interaction coefficient (Q) for the ion-pairs. The calculated ν values are found to be less than Einstein’s value of 2.5. The results are discussed from the points of view of the water structure making effect, solute–solvent hydrogen bond interaction and the presence of hydrophobic interaction.

Full text of DOI:10.1007/s10953-019-00845-7

Journal of Solution Chemistry
https://doi.org/10.1007/s10953-019-00845-7
Studies of Volumetric and Viscosity Properties in Aqueous
Solutions of Imidazolium Based Ionic Liquids at Diꢀerent
Temperatures and at Ambient Pressure
1
1
2
1
Pankaj D. Patil · Vasim R. Shaikh · Gaurav R. Gupta · Dilip G. Hundiwale ·
1
Kesharsingh J. Patil
Received: 29 January 2018 / Accepted: 8 October 2018
©
Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract
The ionic liquids (ILs) 1,3-dimethyl imidazolium methyl sulfate [MIm][MeSO ] and
4
1
-ethyl-3-methyl imidazolium ethyl sulfate [EMIm][EtSO ] have been synthesized and
4
1
13
characterized by H NMR, C NMR, mass spectrometry, TGA and DSC methods. The
densities and viscosities of binary aqueous solutions of [MIm][MeSO ] (0.02458 to
4
−
1
−1
0
.18922 mol·kg ) and [EMIm][EtSO ] (0.01044 to 0.21261 mol·kg ) are reported at
4
(
293.15, 298.15 and 303.15) K and at ambient pressure. Apparent and partial molar vol-
umes of the studied ILs are calculated at the studied concentrations. The limiting partial
molar volumes of the studied ILs were obtained using an appropriate extrapolation method.
The limiting apparent molar expansivity values at 298.15 K are also obtained. The relative
viscosity data are analyzed by applying the Jones–Dole equation and Vand’s equations.
Positive viscosity A and B coeꢀcients were observed for both studied ILs, while the D
coeꢀcients were also found to be necessary, showing speciꢁc behavior depending upon the
solute–solute interactions. Calculations of the B coeꢀcients for anions are reported. The
application of Vand’s equation to the viscosity data enabled us to calculate the Einstein–
Simha factor (ν) and particle interaction coeꢀcient (Q) for the ion-pairs. The calculated ν
values are found to be less than Einstein’s value of 2.5. The results are discussed from the
points of view of the water structure making eꢂect, solute–solvent hydrogen bond interac-
tion and the presence of hydrophobic interaction.
Keywords Aqueous solutions of ILs · Partial molar volumes · Viscosity B and D
coeꢀcients · Vand’s theory · Particle interaction coeꢀcients
*
Kesharsingh J. Patil
patilkesharsingh@hotmail.com
1
2
School of Chemical Sciences, North Maharashtra University, Jalgaon, Maharashtra 425001, India
Institute of Chemical Technology, Matunga, Mumbai, Maharashtra 400019, India
Vol.:(0123
1
456789)
3

Journal of Solution Chemistry
1
Introduction
Ionic liquids (ILs) are a new class of neoteric solvents (containing an organic ion as
either the cation or an anion) that provides the feasibility of changing the cation or the
anion. In general, ILs are organic salts with melting temperatures below a conventional
temperature of 373 K and can act as green solvents and catalysts. ILs have unique prop-
erties like signiꢁcant solubility in water, non-ꢃammability, negligible vapor pressure,
low melting temperature, wide liquid temperature ranges and high thermal stability.
Over the past decades, ILs have received attention of the scientiꢁc community due to
their immense applications in industries and applied chemistry [1–4].
In general, because of the importance of ILs technologically, a huge literature is
available on aqueous solutions of ILs, mostly over the whole mole-fraction region, espe-
cially with respect to properties like conductance, density, viscosity coeꢀcient, etc.
A large number of research articles are available in the literature on physico-chemical
properties of aqueous solutions of imidazolium based ILs [5–14]. Our literature survey
revealed that studies on imidazolium ethyl sulfate ILs are rather limited [1, 6, 14]. The
density and viscosity data for 1-ethyl-3-methyl imidazolium ethyl sulfate in various sol-
vents have been reported at very high concentrations [14]. Such data may not yield use-
ful information about ion–solvent and ion–ion interactions, as we need to use theories
that require proper extrapolation to inꢁnitely dilute solution.
We are interested in obtaining information about the eꢂect of the anion on
anion–water interactions in solutions of ILs. Considering these factors, we have chosen
two ILs, namely, 1,3-dimethyl imidazolium methyl sulfate [MIm][MeSO ] and 1-ethyl
4
3
-methyl imidazolium ethyl sulfate [EMIm][EtSO ], which were synthesized and char-
4
acterized. In the present article we report the studies of volumetric and viscosity prop-
erties for aqueous solutions of [MIm][MeSO ] and [EMIm][EtSO ] in the dilute con-
4
4
−
1
centration range (0.01044 to 0.21261 mol·kg ) at (293.15, 298.15 and 303.15) K. The
density data have been utilized to obtain the apparent molar volumes (V ), and the par-
ꢀ
̄
̄
1
tial molar volumes of the ILs and of water (V and V ) at ꢁnite concentrations of ILs.
2
The viscosity data are subjected to analysis by applying the Jones–Dole, Vand’s and
Huggins’ equations [15–20]. Viscosity A, B and D coeꢀcients are obtained. The den-
sity and relative viscosity coeꢀcient data also helped us to obtain the volume-fraction
of the ILs, which facilitated the data analysis in a much simpler way by applying the
Einstein and Einstein–Simha equations [21–25] to the viscosity data. All the results are
presented and discussed in following manuscript.
2
Experimental Procedure
2
.1 Materials
1
-Methylimidazole (Sigma Aldrich, ≥ 99.8%), diethyl sulfate (Sigma Aldrich, ≥ 99.8%),
dimethyl sulfate (Sigma Aldrich, ≥ 99.8%) and toluene (≥ 98.0%) were used without
further puriꢁcation.
1
3

Journal of Solution Chemistry
2
.2 Synthesis of the ILs
Ionic liquids were synthesized by using the method developed by Holbrey et al. [26].
A dialkyl sulfate (0.5 mol) was added drop wise to a solution of 1-methylimidazole
(
0.5 mol) in toluene (150 mL), while cooled in an ice bath. The reaction mixture yielded
ILs immediately with the formation of a biphasic system. After complete addition of
dialkyl sulfate the reaction mixture was stirred overnight. Thereafter, the upper organic
phase was decanted and the lower IL phase was washed with toluene (75 mL), then
dried with heating at 353 K under reduced pressure to remove residual solvent. The
1
13
synthesized ILs were characterized by NMR ( H and C), mass spectrometry and by
thermal methods (TGA–DSC). The molecular structures of the studied ILs are given in
Fig. 1.
2
.3 Preparation of Solutions
All aqueous solutions of the studied ILs were prepared using double-distilled (in quartz)
water, on a molality basis, in standard glass joint stoppered conical ꢃasks so that atmospheric
humidity and air contacts were avoided. An analytical balance (Shimadzu AUW220D) having
a readability of 0.01 mg was used for the weighings. As ILs are hygroscopic in nature, correc-
tions incorporating their amount of water needs to be made for the calculations of molality.
For this purpose, TGA analyses of the ILs were made and the amount of water was estimated.
The water content estimated for [MIm][MeSO ] and [EMIm][EtSO ] are of the order of 2.5%
4
4
and 4%, respectively. These water contents were taken into account to calculate the molalities
of the solutions.
2
.4 Density Measurements
The densities of aqueous solutions of ILs at (293.15, 298.15 and 303.15) K have been meas-
ured using a high precision digital densimeter—Anton PAAR DMA-5000. The densimeter
was calibrated by using water and air at the studied temperatures. The reliability of the den-
sity data was ascertained by making measurements on binary aqueous solutions of NaCl at
298.15 K and comparing the results with literature data [27].
2
.5 Viscosity Measurements
The ꢃow-time technique was used to measure the viscosity data using an Ubbelohde capillary
3
viscometer. The constant temperature bath was constructed with a capacity of 60 dm . Con-
stant temperature water was circulated inside the bath using a German-made Julabo F-32 cry-
ostat having accuracy ± 0.02 K. The viscometer was placed in the bath in such a manner that
the capillary of the viscometer was vertical and straight and leveled by using a leveling device.
1, 3–dimethyl imidazolium methyl sulfate 1–ethyl 3–methyl imidazolium ethyl sulfate
Fig. 1 Molecular structures of the studied ILs
1
3

Journal of Solution Chemistry
Flow-time measurements were repeated seven times for every solution and at each temper-
ature (i.e., 293.15, 298.15 and 303.15 K). Two diꢂerent viscometers were used. The times
of ꢃow for water at (293.15, 298.15 and 303.15) K for ꢁrst viscometer (which was used for
aqueous solutions of [MIm][MeSO ]) were 459.67, 413.23 and 371.10 s, respectively, while
4
those for second viscometer (which was used for aqueous solutions of [EMIm][EtSO ]) were
4
5
46.83, 487.56 and 435.16 s, respectively. The ꢃow time data were processed to calculate rela-
tive viscosity values using density data at all the studied temperatures. The viscometers were
fabricated in such a way, i.e., by having standard joints for closing (avoiding air contact), that
they were opened only at the time of actual measurements.
The kinetic energy correction factor (K) was calculated by making time of ꢃow meas-
urements for water at (293.15, 298.15 and 303.15) K, using the expression:
ꢃꢂ
ꢀ
= ꢁꢂ t −
(1)
t
where ꢀ and ꢀ are instrumental constant for the viscometer while t and ꢀ represent the ꢃow
time and density of water. It was observed that the kinetic energy correction was negligible
for the two viscometers.
For the check of the reliability of data produced from our experimental set-up, we have
ꢀ
ꢂ
ꢁ
ꢀ
carried out relative viscosity
measurements for aqueous NaCl solutions at 298.15 K.
ꢀ
0
The experimental value obtained for the B coeꢀcient of aqueous NaCl solutions,
3
−1
3
−1
0
.077 dm ·mol , is in good agreement with literature values [28] (0.078 dm ·mol ).
These reproducibility tests yielded the required conꢁdence for us regarding the accuracy
and precision of our data. Considering the temperature accuracy, uncertainty in time and
concentration measurements, the estimated standard uncertainty of our relative viscosity
measurements of a given solution is of the order of ± 0.0005.
3
Results
3
.1 Density and Apparent Molar Volume
−
1
The densities of aqueous solutions of [MIm][MeSO ] (0.02458 to 0.18922 mol·kg ) and
4
−
1
[
EMIm][EtSO ] (0.01044 to 0.21261 mol·kg ) at (293.15, 298.15 and 303.15) K are
4
reported in Tables 1 and 2, respectively.
The experimental density data obtained were utilized to calculate apparent molar vol-
umes (V ) as a function of the molality of the IL using the following equation [12, 29, 30]:
ꢀ
(
ꢁ0 − ꢁ)
M
Vꢀ =
+
(2)
mꢁꢁ0
ꢁ
−
3
where ꢀ and ꢀ are the densities of solvent and solution, respectively, in kg·m , m is the
0
−
1
molality of the solute in aqueous solutions (mol·kg ), and M is the molar mass of the
−
1
solute in kg·mol . The obtained values of V for the [MIm][MeSO ] and [EMIm][EtSO ]
ꢀ
4
4
aqueous solutions at the studied temperatures are given in Tables 1 and 2, respectively.
The V data can be represented adequately by using the Debye–Hückel limiting law with
ꢀ
an additional linear term [12, 29, 30]:
0
ꢀ
1∕2
V = V + A c
ꢀ
+ BV c
V
(3)
1
3

Journal of Solution Chemistry
Table 1 Molality (m), density (ꢀ), apparent molar volume (V ) (V −Α ×c ), partial molar volume of sol-
1/2
ꢀ
ꢀ
V
̄
̄
1
ute and solvent (V and V ) Data for aqueous solutions of [MIm][MeSO ] at (293.15, 298.15, and 303.15) K
2
4
and at ambient pressure of 101.325 kPa
a
m (mol·kg−1) ꢀa (kg·m−3
10 V (m ·mol−1) 10
6
3
6
10 V̄ (m ·mol−1) 10 V̄ (m ·mol−1)
6
3
6
3
)
ꢀ
2
1
(
(
V − Α ·c1/2)
ꢀ
V
3
−1
m ·mol
)
T=293.15 K
0.0000
0.0246
0.0456
0.0526
0.0891
0.1031
0.1249
0.1727
0.1863
0.1892
998.21
999.40
158.46b
159.56
156.68
158.11
156.68
156.30
156.63
156.13
156.26
156.29
18.047
18.049
18.047
18.049
18.048
18.047
18.048
18.047
18.047
18.047
159.84± 0.12
157.05± 0.07
158.51± 0.06
157.21± 0.03
156.87± 0.03
157.25± 0.02
156.86± 0.02
157.02± 0.02
157.05± 0.02
159.26
156.27
157.67
156.12
155.70
155.97
155.38
155.48
155.50
1000.53
1000.81
1002.71
1003.44
1004.48
1006.88
1007.51
1007.65
T=298.15 K
0.0000
0.0246
0.0456
0.0526
0.0891
0.1031
0.1249
0.1727
0.1863
0.1892
997.05
998.22
999.32
159.40b
160.21
157.84
159.08
157.30
157.16
157.54
156.94
156.94
156.93
18.068
18.070
18.069
18.070
18.068
18.068
18.069
18.068
18.068
18.068
160.51± 0.12
158.24± 0.07
159.51± 0.06
157.86± 0.03
157.75± 0.03
158.20± 0.02
157.70± 0.02
157.73± 0.02
157.73± 0.02
159.88
157.40
158.60
156.69
156.50
156.83
156.11
156.08
156.07
999.60
1001.50
1002.20
1003.21
1005.59
1006.24
1006.38
T=303.15 K
0.0000
0.0246
0.0456
0.0526
0.0891
0.1031
0.1249
0.1727
0.1863
0.1892
995.65
996.79
997.95
160.07b
161.96
157.51
159.35
157.95
157.36
157.62
157.41
157.19
157.44
18.094
18.096
18.094
18.095
18.094
18.093
18.094
18.094
18.093
18.094
162.27± 0.12
157.93± 0.07
159.80± 0.06
158.53± 0.03
157.98± 0.03
158.30± 0.02
158.21± 0.02
158.02± 0.02
158.27± 0.02
161.51
156.90
158.70
157.12
156.46
156.64
156.27
156.02
156.26
998.20
1000.06
1000.80
1001.82
1004.14
1004.82
1004.91
Standard uncertainties u are u(Τ)=0.01 K and u(p)=0.3 kPa
a
Standard uncertainties u are u(m)=0.00005 mol·kg and u(ρ)=3×10 kg·m−3
Extrapolated value at inꢁnitely dilute solution of ILs in water at 293.15, 298.15 and 303.15 K
−1
b
where A is Debye–Hückel limiting law coeꢀcient (1.782, 1.868, and 1.955)×10−
6
V
−
3 −3/2
(
mol·mm )
for 1:1 electrolyte solutions at (293.15, 298.15, and 303.15)K, B is a devi-
V
6
−2
ation parameter due to solute–solute interaction (m ·mol ) and c is the concentration of
1
3

Journal of Solution Chemistry
1
/2
Table 2 Molality (m), density (ꢀ), apparent molar volume (V ), (V −Α ×c ), and partial molar volume
ꢀ
ꢀ
V
̄
̄
1
of solute and solvent (V and V ): data for aqueous solutions of [EMIm][EtSO ] at (293.15, 298.15, and
2
4
3
03.15) K and ambient pressure of 101.325 kPa
a
m (mol·kg−1) ꢀa (kg·m−3
10 V (m ·mol−1) 10 (V − Α ·c1/2) 10 V̄ (m ·mol−1) 10 V̄ (m ·mol−1)
6
3
6
3
6
3
6
3
)
ꢀ
ꢀ
V
2
1
−1
(
m ·mol )
T=293.15 K
0.0000
0.0104
0.0206
0.0412
0.0625
0.0830
0.1043
0.1364
0.1581
0.1906
0.2126
998.21
998.62
999.02
196.56b
196.94
196.67
195.38
195.88
195.35
195.13
195.07
194.81
194.40
194.44
18.047
18.048
18.048
18.048
18.048
18.048
18.048
18.048
18.048
18.047
18.047
197.12± 0.29
196.93± 0.15
195.74± 0.07
196.32± 0.05
195.86± 0.04
195.70± 0.03
195.72± 0.02
195.51± 0.02
195.17± 0.02
195.25± 0.01
196.87
196.56
195.23
195.69
195.14
194.90
194.82
194.54
194.12
194.15
999.88
1000.69
1001.53
1002.38
1003.63
1004.50
1005.81
1006.64
T=298.15 K
0.0000
0.0104
0.0206
0.0412
0.0625
0.0830
0.1043
0.1364
0.1581
0.1906
0.2126
997.05
997.44
997.85
998.67
999.51
1000.32
1001.15
1002.41
1003.26
1004.55
1005.35
197.70b
198.85
197.18
196.74
196.28
196.13
195.99
195.70
195.52
195.10
195.22
18.068
18.069
18.069
18.069
18.069
18.069
18.069
18.069
18.069
18.067
18.068
199.05± 0.29
197.45± 0.15
197.12± 0.07
196.74± 0.05
196.66± 0.04
196.58± 0.03
196.38± 0.02
196.25± 0.02
195.89± 0.02
196.06± 0.01
198.69
196.96
196.43
195.90
195.70
195.51
195.16
194.95
194.47
194.57
T=303.15 K
0.0000
0.0104
0.0206
0.0412
0.0625
0.0830
0.1043
0.1364
0.1581
0.1906
0.2126
995.65
996.05
996.44
997.26
998.09
998.89
999.71
1000.87
1001.77
1003.09
1003.83
197.92b
198.10
197.93
197.26
196.98
196.76
196.61
196.96
196.29
195.64
195.99
18.094
18.094
18.094
18.094
18.094
18.094
18.094
18.095
18.094
18.092
18.093
198.30± 0.29
198.21± 0.15
197.66± 0.07
197.47± 0.05
197.31± 0.04
197.24± 0.03
197.67± 0.02
197.05± 0.02
196.47± 0.02
196.87± 0.01
198.09
197.91
197.23
196.94
196.71
196.57
196.91
196.24
195.59
195.94
Standard uncertainties u are u(Τ)=0.01 K; u(p)=0.3 kPa
a
Standard uncertainties u are u(m)=0.00005 mol·kg and u(ρ)=3× 10−3 kg·m−3
Extrapolated value at inꢁnitely dilute solution of ILs in water at 293.15, 298.15 and 303.15 K
−1
b
1
3

Journal of Solution Chemistry
−
3
the solute (mol·dm ). We have converted our molality scale data to molarity using the
appropriate density data.
1
∕2
−3
By plotting graphs of (V − A c ) as a function of concentration (c/mol·dm ) of the
ꢀ
V
0
studied solutions, the intercept and slope of the lines result in values of V and B , respec-
ꢀ
V
0
tively. The obtained values of V and B for [MIm][MeSO ] and [EMIm][EtSO ] in aqueous
ꢀ
V
4
4
solutions at all studied temperatures are given in Table 3.
̄
The partial molar volumes of the studied ILs (V ) and partial molar volumes of solvent
2
0
dV
ꢀ
̄
0
ꢀ
water (V ), and the apparent molar expansivities at inꢁnite dilution. E =
, were calculated
1
dT
̄
̄
0
ꢀ
using equations given in our earlier work [12, 29, 30]. The V , V and E values for the aque-
2
1
ous solutions of studied ILs are collected in Tables 1, 2 and 3, respectively.
3
.2 Viscosity Measurements
ꢀ
The relative viscosities ꢀ = for aqueous solutions of the studied ILs at (293.15, 298.15 and
r
ꢀ0
3
03.15) K were determined by using the expression [12]:
ꢀ
ꢁ
ꢀ
tꢁ
ꢀr
=
=
K
(4)
ꢀ0
t ꢁ
0
0
where ꢀ and ꢀ are the viscosity of solution and solvent, respectively, ꢀ and ꢀ are the den-
0
0
sity of the solution and solvent, respectively, while t and t are the times of ꢃow of solution
0
and solvent, respectively. The kinetic energy correction was found to be negligible, hence
K is assumed to be unity.
The ꢀ values of the studied solutions are reported in Table 4. The variation of ꢀ as a
r
r
−3 1/2
function of the square root of concentration (c/mol·dm ) of [MIm][MeSO ] and [EMIm]
4
[
EtSO ] in aqueous solutions is depicted in Figs. 2, 3, 4.
4
The viscosity data also can be represented by the following Jones-Dole equation [12, 15,
1
6, 20, 27]:
ꢀ
1∕2
ꢀr
=
= 1 + Ac + Bc
(5)
ꢀ0
0
Table 3 Limiting apparent molar volumes (V ) and deviation parameter (B ) values for aqueous solutions
ꢀ
V
of [MIm][MeSO ] and [EMIm][EtSO ] at (293.15, 298.15, and 303.15) K and limiting apparent molar
4
4
0
expansivity (E ) values of [MIm][MeSO ] and [EMIm][EtSO ] at 298.15 K and ambient pressure of
ꢀ
4
4
1
01.325 kPa
[
MIm][MeSO4]
93.15 K 298.15 K
[EMIm][EtSO4]
293.15 K
2
303.15 K
298.15 K
303.15 K
6
0
̄ 0
2
1
0 V (=V ) 158.46± 0.12 159.40± 0.12 160.07± 0.12 196.56± 0.29 197.70± 0.29 197.92± 0.29
ꢀ
3
−1
−2
−1
/
m ·mol
6
1
0 B
−14.0
−15.2
0.161
−17.5
−11.6
−14.5
0.136
−10.8
V
6
/
m ·mol
6
0
1
0 E
ꢀ
3
/
m ·mol
Standard uncertainties u are u(Τ)=0.01 K and u(p)=0.3 kPa
1
3

Journal of Solution Chemistry
1
3

Journal of Solution Chemistry
Fig. 2 Variation of relative
viscosity coeꢀcient (ꢀ ) against
r
square root of concentration (c/
−
3 1/2
mol·dm
)
of the studied ILs
in aqueous solutions at 293.15 K:
ꢁ
lled circle [MIm][MeSO ];
4
4
open circle [EMIm][EtSO ]
Fig. 3 Variation of the relative
viscosity coeꢀcient (ꢀ ) against
r
square root of concentration (c/
−
3 1/2
mol·dm
)
of the studied ILs
in aqueous solutions at 298.15 K:
ꢁ
lled circle [MIm][MeSO ];
4
4
open circle [EMIm][EtSO ]
where A is a constant characterizing ion–ion interactions and B is an adjustable parameter
related to the size of the ions, which is proportional to the partial molar entropies of the
ions and is additive.
The viscosity A and B coeꢀcients of Eq. 5 were determined with the help of a plot
ꢀ
ꢁ
1
∕2
1/2
of ꢀ − 1 ∕c
against c . The values of viscosity A and B coeꢀcients of [MIm]
r
[
MeSO ] and [EMIm][EtSO ] in aqueous solutions at the studied temperatures are given
4
4
in Table 5.
The Jones-Dole equation (Eq. 5) is limited to very low concentrations of solutes
−
1
(
<0.1 mol·kg ), while for slightly higher concentrations an additional parameter may be
needed [12, 15, 16, 20, 27]:
ꢀ
1∕2
2
ꢀr
=
= 1 + Ac + Bc + Dc
(6)
ꢀ0
where D is a constant that is probably related to solute–solute association eꢂects.
1
3

Journal of Solution Chemistry
Fig. 4 Variation of the relative
viscosity coeꢀcient (ꢀ ) against
r
the square root of concentration
−
3 1/2
(
c/mol·dm
)
of studied ILs in
aqueous solutions at 303.15 K:
ꢁ
lled circle [MIm][MeSO ];
4
open circle [EMIm][EtSO ]
4
Table 5 Viscosity A coeꢀcient, viscosity B coeꢀcient, viscosity D coeꢀcient, temperature coeꢀcient of B
(
dB/dT), Arrhenius viscosity A and B coeꢀcient, Einstein–Simha factor (ꢀ), and particle interaction coef-
ꢁ
cient (Q) at (293.15, 298.15 and 303.15) K and at ambient pressure of 101.325 kPa
A/dm3/2·mol−1/2 B coeꢀcient B coeꢀcient
a
c
D
νd
ν (calcu-
Qd
1000B
T (K)
3
−1
3
−1
c
−2
(
dm ·mol
)
(dm ·mol
)
coeꢀcient
lated)=
V̄
0
6
2
(
dm ·mol
)
[
MIm][MeSO4]
293.15
298.15
303.15
0.001a
0.294
0.230
0.351
0.279
0.220
0.357
0.109
0.074
−0.027
1.80 1.76
1.42 1.38
2.29 2.23
4.9
3.2
−0.7
a
0.001
0.001a
[
EMIm][EtSO4]
a
b
293.15
298.15
303.15
0.001 (0.010) 0.465
0.001 (0.009) 0.424
0.001 (0.005) 0.430
0.460
0.416
0.446
0.035
0.049
−0.099
2.39 2.35
2.15 2.10
2.31 2.25
−0.01
1.45
−4.00
a
b
a
b
Standard uncertainties u are u(T)=0.005 K and u(p)=0.3 kPa
a
The values of A and B coeꢀcients were calculated by using Eq. 5
The values of A coeꢀcients were calculated by using Eq. 10
The values of B and D coeꢀcients were calculated by using Eq. 6
The values of ν and Q were calculated by using Eq. 9
b
c
d
By using values of the viscosity A coeꢀcient of Eq. 5, the viscosity B and D coeꢀcients of
ꢀ
ꢁ
1
∕2
Eq. 6 have been estimated with the help of a plot of (ꢀ − 1) − Ac
∕cagainst c (Figs. 5, 6, 7).
r
The obtained values of the viscosity B and D coeꢀcients of [MIm][MeSO ] and [EMIm]
4
[
EtSO ] in aqueous solutions at the studied temperatures are given in Table 5.
4
The volume fraction ꢀ values were calculated by using the partial molar volumes of the
2
components of the binary solution using the equation:
̄
x V
2
2
ꢀ2
=
(7)
̄
̄
1
x V + x V
2
2
1
1
3

Journal of Solution Chemistry
Fig. 5 Variation of the
ꢀ
ꢁ
1
∕2
(
ꢀ − 1) − Ac
∕c parameter as
r
a function of concentration of the
studied ILs in aqueous solutions
at 293.15 K: ꢁlled circle [MIm]
[
[
MeSO ]; open circle [EMIm]
4
EtSO ]
4
Fig. 6 Variation of the
ꢀ
ꢁ
1
∕2
(
ꢀ − 1) − Ac
∕c parameter
r
as a function of concentration of
studied ILs in aqueous solutions
at 298.15 K: ꢁlled circle [MIm]
[
[
MeSO ]; open circle [EMIm]
4
EtSO ]
4
Fig. 7 Variation of the
ꢀ
ꢁ
1
∕2
(
ꢀ − 1) − Ac
∕c parameter
r
as a function of concentration of
studied ILs in aqueous solutions
at 303.15 K: ꢁlled circle [MIm]
[
[
MeSO ]; open circle [EMIm]
4
EtSO ]
4
1
3

Journal of Solution Chemistry
̄
̄
1
where x and x are mole fraction of the IL and water, respectively, while V and V are the
2
1
2
partial molar volumes of IL and water, also respectively. The ꢀ values of the studied solu-
2
tions at (293.15, 298.15 and 303.15) K are collected in Table 4.
Based on Einstein’s equation for viscosity,
ꢀr − 1 = 2.5 ⋅ ꢁ2
(8)
the ꢁrst-order coeꢀcient, the so called viscosity increment designated as ꢀ, should be equal
to 2.5. Deviations from Einstein’s ꢀ=2.5 have been attributed to various causes includ-
ing the eꢂects of hydration [28], water structure formation and breaking [15, 24, 29, 30],
and hydrophobic interaction [27, 31–33]. These are discussed below. One additional eꢂect
inꢃuencing ꢀ is the deviation of the particle from the assumed spherical shape [15, 23, 34].
Rewriting Vand’s equation [17, 18, 35] in the form
ln ꢀr
=
ꢂ + Q ⋅ ln ꢀr
(9)
ꢁ2
where ꢀ is the Einstein–Simha factor and Q is the particle interaction coeꢀcient, we
ln ꢀ
r
obtained values of ꢀ and Q by plotting the graphs of ꢁ as a function of ln ꢀ . The values of
r
2
ꢀ
and Q are collected in Table 5.
4
Discussion
1
∕2
Examination of the data from Tables 1 and 2 reveals that (V − A c ) is more or less
ꢀ
V
constant for [[MIm][MeSO ] and [EMIm][EtSO ] in aqueous solutions in the stud-
4
4
ied concentration range at all studied temperatures. The limiting partial molar volumes
of [MIm][MeSO ] and [EMIm][EtSO ] in aqueous solutions at 298.15 K are found to
4
4
−
6
3
−1
−6
3
−1
be (159.40± 0.12)×10 m mol
and (197.70± 0.29)×10 m ·mol , respectively
0
ꢀ
(
Table 3). Observations from Table 3 reveal that, for both studied ILs, the values of V
increases with increase in temperature. Using the previously reported data for [EMIm][Br]
+
−6
3
−1
[
8], we calculated the ionic partial molar volume of [EMIm] ion as 106.87×10 m ·mol
at 298.15 K. Using this value, we estimate the limiting partial molar volume of the
−
3
−6
3
−1
CH − CH − O − SO anion as being 90.83×10 m ·mol . Similar calculations were
3
2
−
carried out with our previous data on 1-methtyl imidazolium chloride [7] and using the Cl
−
6
3
−1
ion value of 23×10 m ·mol , and by adding the contribution of one more methyl group
−
−
6
3
−1
3
as 16×10 m ·mol , we calculate the limiting partial molar volume of HC − O − SO
3
3
−
6
−1
as being 75×10 m ·mol .
The deviation parameters B of Eq. 3 for [MIm][MeSO ] and [EMIm][EtSO ] in aque-
V
4
4
ous solutions at the studied temperatures are small and negative, meaning that the ions of
these electrolytes are water structure making (kosmotropic eꢂect) due to solute-induced
water interactions in the co-sphere of the cations, and water–water interactions similar
to those of solutions of alkylammonium salts [36]. However, the extent of such an eꢂect
appears to be small because of the hydrophilic nature of the imidazolium cation.
0
The apparent molar expansivities at inꢁnite dilution (E ) of [MIm][MeSO ] and
ꢀ
4
−6
3
−1
[
EMIm][EtSO ] in aqueous solutions at 298.15 K are found to be 0.161×10 m ·mol
4
−
6
3
−1
and 0.136×10 m ·mol , respectively. These values are similar to those of simple 1:1
electrolytes [37] and this indicates that these electrolytes are not strong water structure
makers such as tetraalkylammonium salts [38].
1
3

Journal of Solution Chemistry
The ꢀ values of solutions increase with increase in the concentration of the ILs (Figs. 2,
r
3
, 4). This increase is much greater for [EMIm][EtSO ] than for [MIm][MeSO ], indicating
4 4
the eꢂect of additional methylene groups in the ILs.
The viscosity A coeꢀcient value can be calculated by using the Falkenhagen and Dole
equation [39, 40]:
ꢀ
ꢁ
ꢂ
ꢃ
2
0
1
0
2
0
1
0
2
ꢀ
+ ꢀ
ꢀ − ꢀ
ꢁ
A = 0.7536
−
ꢂ
(10)
0
1
0
2
0
1
0
2
0
1
0
2
4ꢀ ꢀ
4.41ꢀ ꢀ ꢀ + ꢀ
0
0
where ꢀ and ꢀ denote the limiting equivalent conductances of the cations and anions,
1
2
respectively, and the required splitting of equivalent conductance into individual ionic
parts was made using data for a chloride salt [13].
Electrical conductance data for aqueous solutions of [EMIm][EtSO ] are available [6];
4
therefore, we calculated the viscosity A coeꢀcient for [EMIm][EtSO ] by using Eq. 10 and
4
these values are collected in Table 5 along with the values calculated by using Eq. 5. The
conductance data yield A coeꢀcient values higher than the values obtained from the vis-
cosity data. We will use our A coeꢀcient values for further scrutiny.
For aqueous [MIm][MeSO ] solutions, precise conductance data is not available, hence
4
we could not calculate theoretical A coeꢀcient values for it. Therefore, we calculated the
viscosity A coeꢀcient for [MIm][MeSO ] in aqueous solutions with the help of Eq. 5 by
4
ꢀ
ꢁ
1∕2
1/2
plotting the graphs of ꢀ − 1 ∕c against c . The obtained values of viscosity A coeꢀ-
r
cients of [MIm][MeSO ] and [EMIm][EtSO ] in aqueous solutions at the studied tempera-
4
4
tures are given in Table 5. The viscosity A coeꢀcient values are very small but positive as
required. Using these viscosity A coeꢀcient values, and with help of Eq. 6 and graphs of
ꢀ
ꢁ
1
∕2
(
ꢀ − 1) − Ac
∕c plotted against c (Figs. 5, 6, 7), the viscosity B and D coeꢀcient val-
r
ues were calculated.
The B coeꢀcient values are positive for both studied ILs (Table 5). The variation of vis-
cosity B coeꢀcients as a function of temperature for [MIm][MeSO ] and [EMIm][EtSO ]
4
4
in aqueous solutions is shown in Fig. 8. The temperature coeꢀcient of B (dB/dT) is non-
linear, showing a minimum at 298.15 K for both studied ILs and the extent of lowering is
comparatively more for the [MIm][MeSO ] solutions. These ꢁndings may be interpreted as
4
+
the [EMIm] cations being solvated in water with a hydrophobic interaction eꢂect.
Fig. 8 Variation of the viscosity
B coeꢀcient as a function of
temperature: ꢁlled circle [MIm]
[
[
MeSO ]; open circle [EMIm]
4
EtSO ]
4
1
3

Journal of Solution Chemistry
+
The small sized [MIm] cation exhibits a negative particle interaction coef cient (Q)
+
only at 303.15 K, while ꢀo r the [EMIm] cation its value is positive only at 298.15 K.
+
This clearly demonstrates the ef ects due to hydrophobic hydration oꢀ the [EMIm] cat-
+
ion. The Q values can be interpreted in terms oꢀ substitutional dissolution oꢀ the [MIm]
cation in water’s structural cavities, as has been postulated by Franks and Ives [37] and
Kaulgud and Patil [41] ꢀo r small sized solutes such as methanol and methylamine in
water, respectively. The values oꢀ the Einstein–Simha coef cient (ꢀ) is near about 2.5
+
ꢀ
or the [EMIm] cation, which may be seen as a result oꢀ these cations interacting nei-
ther as water structure makers nor as water structure breakers. It is dif cult to comment
on the temperature variation oꢀ Q as we do not yet know how to isolate the volume ef ect
ꢀr om the total ef ect that includes that ꢀr om the energetics [42].
In this context, the ef ect oꢀ anion structural interaction with water is also interesting.
The B-coef cient values can be split at 298.15 K by obtaining ionic B coef cient values
ꢀ
or the studied ILs. The data oꢀ Tamaki et al. [43] were used to estimate B coef cients
−
−
3
−1
3
−1
oꢀ the anions [MeSO ] and [EtSO ] as 0.102 dm ·mol and 0.197 dm ·mol , respec-
4
4
+
+
tively. Thus, the ionic B coef cients ꢀo r the [MIm] and [EMIm] cations are ꢀo und
3
−1
3
−1,
to be 0.118 dm ·mol and 0.237 dm ·mol respectively, while the ionic B coef cient
+
3
−1
value ꢀo r the Na ion is 0.0863 dm ·mol [15]. The positive B coef cient value ꢀo r the
−
CH COO anion has been interpreted by Gurney [44] in terms oꢀ H-bonding by the
3
anion with surrounding water molecules. Seen in this light, the alkyl sul ꢀa te group can
interact by ꢀo rming hydrogen bond with water molecules, threby exhibiting quite high
ionic B coef cient values. More systematic work with aqueous ILs containing dif er-
ent anions is in progress, to ꢁnd better evidences about the water structure making and
breaking properties oꢀ anions containing alkyl residues.
5
Conclusions
The viscosity coef cient and density properties oꢀ two ILs containing alkylsul ꢀa te ani-
ons in aqueous solutions have been studied. The values oꢀ Jones–Dole viscosity A, B
and D coef cients have been obtained. The calculated hydration numbers are ꢀo und to
be negligible ꢀo r both oꢀ the ILs. Values oꢀ the apparent molar expansivity have been
ꢀ
ound to be positive, indicating that these electrolytes are also oꢀ the 1:1 type. Using
the volume ꢀr action data and Vand’s equation, ꢀ (the Einstein–Simha coef cient) along
with Q (particle interaction coef cient) have been determined. The ꢀ values are speciꢁc,
+
+
−
−
smaller than 2.5 ꢀo r [MIm] [MeSO ] while near about 2.5 ꢀo r [EMIm] [EtSO ] , and
4
4
4
are attributed to the borderline water structure making/breaking action oꢀ [EtSO ] ions.
The limiting partial molar volume data and viscosity B coef cient data ꢀo r both electro-
lytes have been split into individual ionic contributions due to their cation and anion in
aqueous solutions. Values oꢀ the ionic B coef cients at 298.15 K ꢀo r both cations and
anions are ꢀo und to be positive. On the basis oꢀ these observations, it has been inter-
−
−
preted that the anions [MeSO ] and [EtSO ] can interact with surrounding water mol-
4
4
ecules by ꢀo rming hydrogen bonds in the solution phase.
Acknowledgements P. D. P. acknowledges University Grants Commission, New Delhi (India) ꢀo r providing
ꢁ
nancial assistance through a UGC-BSR Fellowship ꢀo r Science Meritorious Students.
1
3

Journal of Solution Chemistry
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