Indian Journal of Pure & Applied Physics
Vol. 50, March 2012, pp. 161-166
Molecular interaction parameters of binary mixtures of diethyl ether and
apolar solvents using ultrasonic probe
S K Pradhan1, S K Dash2, L Moharana3 & B B Swain4*
1
Department of Physics, Nayagarh Autonomous College, Nayagarh 752 069
2
DESM, Regional Institute of Education (NCERT), Bhubaneswar 751 022
3
Post Graduate Department of Physics, Utkal University, Bhubaneswar 751 004
4
Plot No. 15, Chintamaniswar Area, Bhubaneswar 751 006
*E-mail: [email protected]
Received 29 September 2011; revised 30 November 2011; accepted 9 January 2012
Ultrasonic velocity (u), density (ρ) and co-efficient of viscosity (η) of pure and binary mixtures of diethyl ether with
carbon tetrachloride, carbon disulphide and benzene have been measured at 303.15 K using an ultrasonic interferometer,
pyknometer and Ostwald viscometer, respectively. Molecular interaction parameters i.e isentropic compressibility (βs),
intermolecular free length (Lf), molar volume (Vm), acoustic impedance (Z), available volume (Va), free volume (Vf), internal
pressure (πi) and the relaxation time (τ) have been calculated and interpreted for the intra and intermolecular association
among like and unlike molecules. Dipole-induced dipole type of interaction is found to be stronger in case of CCl4 mixture.
Keywords : Diethyl ether, Binary mixtures, Ultrasonic studies, Dipole-induced dipole interaction
1 Introduction
Diethyl ether (DEE) is one of the solvent extraction
reagent employed for the extraction and separation of
zirconium and hafnium in reaction technology1. For
extraction of actinides and lanthanides, the
commercial extractants such as tri-n-butyl phosphate
(TBP), di-2-ethyl hexyl phosphoric acid (DEPHA),
tri-octyl phosphoric oxide (TOPO) etc are used in
atomic energy industry. However, for greater
dispersal and more rapid phase disengagement, the
extractants are blended with appropriate polar and
apolar diluents. This facilitates in the elimination of
the third organo-aqueous phase which contains some
of the metal ions2. As such the molecular interaction
among the component molecules in the complexes
plays a significant role in the selection of the
diluents/modifiers. Ultrasonic investigation of liquid
mixtures is one of the available tool in this direction
and useful in giving insight into the structure and
bonding of resulting molecular complexes3. The
concentration dependence of ultrasonic velocity and
other thermoacoustic parameters along with their
excess values in binary as well as ternary liquid
mixtures have been investigated by several
researchers4.
Arce et al.5 have studied the thermodynamic
properties of hydrocarbons/alcohols with ether
systems. In view of usefulness of ethers as
oxygenating agent in gasoline technology, the
molecular interaction in binary mixtures with DEE as
one of the component is of particular interest in
reactor technology. DEE is a self-associated liquid
having three dimensional network of hydrogen bond
that can be associated with any other group having
some degree of polarity. Although several
investigations were carried out in liquid mixtures
involving the extractants like TBP, DEPHA6 as one of
the component, a systematic ultrasonic study in the
binary mixtures involving DEE is scarce. However,
the data for density, refractive index and speed of
sound in the binary mixtures of diethyl either with nhexane at 298.15 K are available in the literature7.
The present study is undertaken with some more
binary systems that is DEE + carbon tetrachloride
(CCl4), DEE + carbon disulphide (CS2) and DEE +
benzene at 303.15 K. The interaction parameters such
as isentropic compressibility (βs), intermolecular free
length (Lf) molar volume (Vm), acoustic impedance
(Z), available volume (Va), free volume (Vf), internal
pressure (πi) and the relaxation time (τ) have been
computed for such binary mixtures and are used for
assessing the nature of molecular interaction.
2 Theory
The experimental values of density (ρ), ultrasonic
velocity (u) and co-efficient of viscosity (η) have
INDIAN J PURE & APPL PHYS, VOL 50, MARCH 2012
162
been used to calculate the thermoacoustic parameters
such as isentropic compressibility (βs), acoustic
impedance (Z), intermolecular free length (Lf), free
volume (Vf), molar volume (Vm), available volume
(Va), internal pressure (πi) and relaxation time (τ)
using the following standard expressions8.
βs =
1
ρ u2
… (1)
Z = ρu
… (2)
L f = K β s1/ 2
… (3)
Vm =
M eff
… (4)
ρ
ª
u º
Va = Vm «1 − »
¬ u∞ ¼
ªM uº
V f = « eff »
¬ kη ¼
… (5)
3/2
… (6)
3 Experimental Details
All the organic liquids used in this investigation are
of analytical reagent grade and obtained from EMerck Chemicals Ltd. India. These chemicals were
further purified by standard procedures10. The purity
of chemicals was checked by comparing measured
densities and viscosities with those reported in the
literature11. The ultrasonic velocities of the binary
mixtures have been measured with single crystal
variable path ultrasonic interferometer at 2 MHz with
an accuracy of ±0.05 m/s. The temperature of the
liquid was maintained at 303.15 K with an accuracy
of ±0.1 K in an electronically controlled thermostatic
water bath. The binary mixture of DEE+carbon
tetrachloride, DEE+carbon disulphide, DEE+ benzene
was prepared by weight and kept in special air tight
bottle. The weighing of sample was done by
SHIMADZU BL-200H digital top loading balance
with a precision of ±0.001 g. The densities of pure
liquids and their binary mixtures have been measured
using a single stem pyknometer of 25 mL capacity.
The marks on the stem have beencalibrated with triple
distilled water. The viscosities have been determined
using Ostwald viscometer. The accuracy of
measurement of density was ±0.03 kg/m3 and that of
viscosity was ±0.0004 Nsm–2.
1/2
2/3
§ kη · § ρ ·
¨
7/6 ¸
πi = bRT ¨© u ¸¹
© M eff ¹
τ=
4η
3ρ u 2
… (7)
… (8)
where K is the Jacobson’s temperature dependent
constant and T is the experimental temperature in
n
absolute scale, M eff = ¦ x i M i with xi is the mole
i =1
fraction and Mi is the molar mass of ith component9,
u∞ is 1600 ms–1, b the cubical packing fraction taken
as 2 for all the liquids, Vm the molar volume, R the
universal gas constant and k is a constant equal to
4.28 ×109.
Excess value (AE) of the interaction parameter was
obtained by Eq. (9):
n
AE = Aexp −¦ xi Ai
… (9)
i =1
Aexp is the experimental value and Ai is the interaction
parameter of the ith pure liquid component.
4 Results and Discussion
The ultrasonic velocity, density and viscosity of the
binary liquid mixtures of DEE with three nonpolar
solvents such as carbon tetrachloride, carbon
disulphide and benzene have been measured at
303.15 K. The experimental data have been used to
compute the values of the interaction parameters such
as isentropic compressibility (βs), intermolecular free
length (Lf), acoustic impedance (Z), internal pressure
(πi), free volume (Vf), available volume (Va),
relaxation time (τ) and are presented in Table 1. Some
of the excess molecular interaction parameters are
displayed graphically in Figs (2-9).
Perusal of Table 1 reveals that the values of
ultrasonic velocity (u), isentropic compressibility (βs),
intermolecular free length (Lf), increases while
viscosity (η) and acoustic impedance (Z) decreases
non-linearly with the increase in mole fraction of
DEE in the binary mixtures of CCl4. On the other
hand, in the binary mixtures of carbon disulphide and
benzene the values of ultrasonic velocity (u), viscosity
(η) and acoustic impedance (Z) decrease while those
of βs and Lf increase non-linearly with the increase in
mole fraction of DEE. The variation of u in a mixture
PRADHAN et al.: MOLECULAR INTERACTION PARAMETERS OF BINARY MIXTURES
163
Table 1 — Variation in the values of ultrasonic velocity (u), density (ρ), viscosity (η), and acoustic impedance (Z), isentropic
compressibility (βs) intermolecular free length (Lf), internal pressure (πi), free volume (Vf), available volume (Va) and molar volume (Vm)
with molefraction (X1) of DEE
u
(ms−1)
(kg m−3)
η×105
(Nm−2 s)
βs×109
(m2 N−1)
0.00
0.09
0.18
0.25
0.32
0.45
0.53
0.72
0.82
0.89
1.00
926.1
930.3
936.2
942.2
946.1
956.1
962.3
968.2
972.1
978.2
985.1
1596
1250
1440
1340
1280
1200
1110
930
830
810
721
91.00
83.21
81.43
70.15
62.41
54.12
45.33
39.14
32.81
27.62
21.93
0.731
0.761
0.792
0.841
0.873
0.912
0.973
1.147
1.275
1.291
1.429
DEE + carbon tetrachloride
9.638
14.779
5.611
9.622
14.136
5.724
9.686
13.478
5.843
9.992
12.621
6.019
10.025
12.109
6.133
9.830
11.472
6.268
10.052
10.678
6.476
10.370
9.002
7.031
10.659
8.068
7.412
10.233
7.921
7.457
10.280
7.102
7.848
0.00
0.06
0.11
0.16
0.30
0.37
0.48
0.61
0.75
0.86
1.00
1140.1
1138.1
1110.2
1100.3
1084.1
1072.3
1060.1
1040.1
1022.2
1004.1
985.1
1261.0
1235.0
1192.3
1149.2
1054.4
991.2
923.9
867.8
820.4
770.0
721.0
36.00
34.10
33.82
31.13
29.82
27.73
26.12
24.89
23.78
22.18
21.93
0.610
0.625
0.681
0.719
0.807
0.878
0.963
1.065
1.167
1.288
1.429
DEE + carbon disulphide
6.038
14.375
5.127
6.155
14.054
5.190
6.367
13.234
5.415
6.597
12.641
5.566
7.164
11.430
5.897
7.606
10.626
6.150
8.136
9.793
6.442
8.632
9.025
6.775
9.096
8.384
7.090
9.663
7.731
7.450
10.280
7.102
7.848
0.00
0.08
0.16
0.25
0.35
0.45
0.54
0.64
0.73
0.82
1.00
1295.3
1270.1
1230.2
1196.1
1140.2
1116.1
1090.1
1070.3
1040.2
1010.2
985.1
881.0
869.9
816.6
800.3
779.5
769.5
761.6
749.4
740.8
731.9
721.0
60.10
54.68
52.60
48.86
45.58
42.82
40.33
37.55
33.29
29.31
21.93
0.677
0.738
0.809
0.873
0.987
1.043
1.105
1.165
1.248
1.339
1.429
5.400
5.639
5.905
6.134
6.520
6.705
6.900
7.086
7.333
7.596
7.848
X1
ρ
Vf×103
(m3 mol−1)
πi×10−6
τ×1012
(Pa)
(s)
4.060
4.029
4.020
4.109
4.110
4.098
3.956
4.096
4.183
3.978
3.951
6.994
7.463
7.250
8.610
9.687
10.741
13.013
13.155
15.153
17.957
21.694
20.526
19.123
18.173
15.607
14.283
13.062
11.142
9.092
7.590
7.178
5.966
0.886
0.844
0.861
0.787
0.726
0.658
0.588
0.599
0.558
0.475
0.418
1.736
1.777
1.950
2.062
2.310
2.510
2.746
3.021
3.286
3.599
3.951
13.371
14.431
14.047
15.660
16.249
17.770
19.028
19.776
20.513
22.074
21.694
16.651
15.705
15.082
13.733
11.839
10.418
9.109
8.172
7.413
6.560
5.966
0.293
0.284
0.307
0.298
0.321
0.324
0.335
0.353
0.370
0.381
0.418
1.690
1.910
2.194
2.433
2.829
3.000
3.179
3.340
3.553
3.770
3.951
7.798
8.673
8.708
9.262
9.492
10.018
10.504
11.282
12.859
14.790
21.694
10.330
9.292
8.974
8.608
8.333
8.094
7.918
7.599
7.227
6.848
5.966
0.542
0.538
0.568
0.569
0.599
0.596
0.594
0.583
0.554
0.523
0.418
Z×102
Vm×102
Va×102
Lf×1011
(m)
(kg m−2 s−1) (m3 mol−1) (m3 mol−1)
DEE + benzene
11.410
10.667
10.044
9.571
8.887
8.588
8.301
8.018
7.704
7.392
7.102
depends upon the increase or decrease of
intermolecular free length, Lf after mixing of the
components. According to the Eyring and Kincaid
model12, ultrasonic velocity varies inversely with the
intermolecular free length in the liquid mixtures. Our
results for DEE + carbon disulphide and DEE +
benzene agree with it. But for DEE + carbon
tetrachloride binary mixture both the values of u and
Lf increase with the increase in the mole fraction of
DEE showing a deviation from Eyring and Kincaid
model. It will be rather more appropriate to infer that
density also has a role to play in the relative increase
or decrease in the values of u and Lf . The non-linear
variation in the values of Lf and βs indicate significant
interactions13 between liquid molecules in all binary
8.866
9.262
9.487
9.635
9.840
9.917
9.973
10.082
10.151
10.225
10.280
mixtures containing DEE. Further, it is also observed
that the values of Vf, Va and Vm increase non-linearly
with the mole fraction of DEE in the DEE + carbon
tetrachloride binary mixtures. This behaviour may be
attributed to solute-solvent interaction14 in the systems
which is different from the ideal mixture behaviour.
Furthermore, the nature of variation of Lf and βs
strongly depends on the size of molecules of both the
components. If the molecular size of both components
is equal, then the curve for Lf and βs with the mole
fraction of the solute is linear. The nature as well as
degree of molecular interaction between the
component molecules of the liquid mixture have been
speculated through the sign and extent of deviation of
the excess parameters. If the size of the solvent
164
INDIAN J PURE & APPL PHYS, VOL 50, MARCH 2012
molecule is increased the deviation is positive and if it
is decreased then the deviation is negative15. In
general βEs, LEf and VEm can be considered from two
types of interactions between the component
molecules such as physical interaction arising from
dispersion forces or weak dipole-dipole interactions
making a positive contribution to LEf , βEs and VEm
and chemical or specific interactions which include
charge transfer, hydrogen-bond formation and other
complex forming interactions, resulting in negative
values 16 of LEf , βEs and VEm. Palani et al.17 have
reported similar observation on the basis of excess of
βEs and VEm.
DEE is a polar liquid having dipole moment
µ=1.18 D, dielectric constant ε=4.138. The
Kirkwood-Föhlich linear correlation factor g=1.55 for
it, which indicates that short-range specific dipolar
interaction between DEE molecules is leading to
preferential dipolar alignment. Reinforcement of
angular correlation among the polar molecules of
similar nature results in parallel dipolar alignment
leading to the formation of α-multimers where the
Kirkwood-Föhlich linear correlation factor, g is
greater than unity whereas anti-parallel dipolar
alignment results in β-multimers, for g < 1. As DEE is
known to be a mildly associated polar liquid having
g>1, it can remain in head-tail arrangement with αmultimerization (Fig. 1).
With addition of apolar liquids like carbon
tetrachloride, carbon disulphide and benzene in our
present study the increase in the values of βs, Lf and Vf
may be due to breaking of α-multimers in DEE. It
may result in new associated complexes with the
possibility of hydrogen-bonding between Hδ+ of DEE
with Clδ–, Sδ– and π-electron cloud of CCl4, CS2 and
benzene, respectively through dipole-induced dipole
type of interaction.
Fig. 1 — Head-tail arrangement in DEE leading to αmultimerization
Perusal of Figs (2-9) shows that the values of βEs,
L f VEf and VEm are negative while that of πEi, ZE and
ηE are positive for the entire compositional range of
DEE. However, its magnitude decreases in the order
CCl4 > CS2 > benzene
E
Fig. 2 — Variation of ηE with mole fraction (X1) DEE
Fig. 3 — Variation of βEs with mole fraction (X1) DEE
Fig. 4 — Variation of LEf with mole fraction (X1) DEE
PRADHAN et al.: MOLECULAR INTERACTION PARAMETERS OF BINARY MIXTURES
Fig. 5 — Variation of πEi with mole fraction (X1) DEE
165
Fig. 8 — Variation of ZE with mole fraction (X1) DEE
Fig. 6 — Variation of VEf with mole fraction (X1) DEE
Fig. 9 — Variation of VEm with mole fraction (X1) DEE
Fig. 7 — Variation of VEa with mole fraction (X1) DEE
A stronger molecular interaction through charge
transfer, dipole-induced dipole and dipole-dipole
interaction,
interstitial
accommodation
and
orientational ordering18 lead to a more compact
structure making βEs negative. The magnitude of such
contributions depends on the relative molecular size
of the components. Fort and Moore19 have suggested
that the values of βEs and LEf become increasingly
negative with increase in the strength of interaction
between components of binary mixture. In the present
study, negative values of βEs and LEf in carbon
tetrachloride, carbon disulphide and benzene mixtures
containing DEE can be attributed to formation of
molecular ring-like structure through dipole-induced
dipole interaction. As such considerable increase in
intermolecular spaces in the presence of apolar
solvents in DEE result in an increase in Vm, Vf and
decrease in η, Z, Va, π and τ values. The relaxation
time (τ) which is in the order of 10–12s, is due to
structural relaxation process and in such situation it is
suggested that the molecules get rearranged due to cooperative process. Among the three apolar solvents,
carbon tetrachloride molecule is nearly a spherical
one which can be trapped easily inside the interstitial
166
INDIAN J PURE & APPL PHYS, VOL 50, MARCH 2012
voids of DEE. At low DEE molefraction region, CCl4
molecules surround the scarce DEE molecules
inhibiting the dipole-dipole interaction among DEE
molecules.
However,
at
about
equimolar
concentration region of DEE the dipole-induced
dipole interaction is predominant in three dimensional
network of the DEE+CCl4 mixtures. This may be
responsible for giving maximum negative value of βEs
and LEf in the binary mixture with CCl4. Further, the
dipole-dipole interaction among DEE molecules is
reinforced by the solute-solvent interaction at very
high concentration of DEE.
In carbon disulphide and benzene mixture, similar
screening effect results in reduction of molecular
interaction at low DEE concentration region. Increase
in molefraction of DEE in the mixture with carbon
disulphide, the Sδ– species interact with Oδ– of DEE
while in the mixture with benzene, π-electron cloud in
benzene-ring interact with Oδ– of DEE. Here in both
the cases,the pushing effect of Sδ– and π-electron
clouds with Oδ– of DEE probably dominates over
dipole-induced dipole interaction and may result in
low negative values of βEs and LEf which agrees with
our findings for positive values of ηE (Fig. 2).
The positive values of ηE are an indication of stronger
interaction among component molecules containing
DEE. The excess value is maximum at equimolar
concentration range in the mixture containing CCl4.
This corroborates our findings from other excess
parameters. Apart from dipole-induced dipole
interaction, the interaction due to dispersive forces
and realignment of α-multimers cannot be ruled out in
the study for which the magnitude of the excess
interaction parameters is affected at lower and higher
concentration of DEE, respectively.
5 Conclusions
The present report based on the study of the
acoustic properties shows that the nature of molecular
interaction of DEE with carbon tetrachloride, carbon
disulphide and benzene molecules may be nonspecific-dipole-induced dipole, dispersive and dipoledipole type. The strength of molecular interaction is
relatively higher in carbon tetrachloride compared to
carbon disulphide and benzene mixture. As such
carbon tetrachloride may be used as an effective
diluent/modifier in comparison to the solvent
extraction process using diethyl ether.
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