Indian Journal of Pure & Applied Physics
Vol. 48, December 2010, pp. 875-880
Acoustic behaviour of citric acid in aqueous and partial aqueous media
J Ishwara Bhata, M N Manjunathab & N S Shree Varaprasadc
a
Department of Chemistry, Mangalore University, Mangalagangothri 574 199, India
b
S J C Institute of Technology, Chickballapur 562 101, India
c
Reva College of Engineering and Technology, Bangalore, India
E-mail: [email protected]
Received 4 November 2009; revised 24 June 2010; accepted 11 October 2010
Measurement of ultrasonic velocity, density and viscosity at different concentrations of citric acid in water,
dimethylformamide, dimethylsulphoxide, and their mixtures have been carried out at 303 K using ultrasonic interferometer
at frequency 2 MHz. The data obtained are used to evaluate various acoustic parameters in view of identification of the
presence of ion-solvent interaction under prevailing conditions. Ultrasonic velocity has been found to increase with increase
in the composition of DMSO and to decrease with DMF in water. The compressibility has been found to decrease with the
increase in concentration for all compositions indicating the increase in ion-solvent interaction.
Keywords: Acoustic, Citric acid, Ultrasonic velocity, Ion-solvent interaction
1 Introduction
Ion-solvation is the back bone of solution
chemistry1,2. Ultrasonic velocity studies3,4 in aqueous
and several non-aqueous electrolyte solutions have
led to new insights in the solvation process. Acoustic
parameters such as adiabatic compressibility,
intermolecular free length, specific acoustic
impedance, relative association, viscous relaxation
time,
solvation
number,
apparent
molar
compressibility, apparent molar volume, free volume
and available volume are useful parameters in
elucidating ion-solvent interaction5-8. Citric acid
(2-hydroxy-propane-1,2,3-tricarboxylic acid) is a
hydroxy tricorboxylic acid which occurs widely in
lemon, lime and other citrus fruits. It is an important
intermediate in carbohydrate metabolism. It can be
used as plasticizers, in the manufacture of soft drinks
and candies9. It also finds wide applications in the dye
industry. It is a white crystalline compound, soluble in
water and some non-aqueous solvents. There are no
reports available on ultrasonic behaviour of citric acid
except some work on viscosity of citric acid in
water+ethanol10. In the present paper, ultrasonic
behaviour of citric acid in water and different
compositions of water+ DMF/DMSO at 303 K ±
0.01°C has been studied.
2 Experimental Details
Commercially available citric acid (Merck make,
AR grade) was used as such and its stock solution (0.5
mol dm-3) in water, DMF, DMSO and different
compositions (v/v) of water + DMF and water +
DMSO were prepared. Triply distilled water was used
throughout the experiment. Non-aqueous solvents
DMF and DMSO were purified as proposed
earlier11.
The ultrasonic velocity was measured using
ultrasonic interferometer (M-81, Mittal enterprises,
New Delhi) at a frequency of 2 MHz. The frequency
was measured with an accuracy of 0.03%. The
accuracy of the instrument was checked by comparing
the experimental sound velocity of triply distilled
water (1494 ms−1) with the theoretical sound
velocity12 (1496 ms−1) at 298 K. The velocity
measurements were carried out for six solutions of
citric acid of different concentrations (0, 0.05, 0.1,
0.2, 0.3, 0.4 and 0.5 mol dm−3) in water, DMF,
DMSO and their mixtures (v/v), (0, 10, 20, 40, 60, 80
and 100%). The experiment was repeated at least
twice and the average value is reported. Density and
viscosity of all the solutions were determined using
pyknometer of 10 cc capacity and Ostwald`s
viscometer, respectively at a known temperature.
3 Results and Discussion
Acoustic
parameters
such
as
adiabatic
compressibility (βad ), apparent molar compressibility
(Фk ), intermolecular free length (Lf), specific acoustic
impedance (Z), relative association (RA), apparent
molar volume (Фv), solvation number (Sn) and free
INDIAN J PURE & APPL PHYS, VOL 48, DECEMBER 2010
876
volume (VF) were obtained for different
concentrations of citric acid in water, DMF, DMSO
and their mixtures (v/v) at 303K ± 0.01°C using the
following relations13:
U=λF
β ad =
… (1)
1
… (2)
U 2d
Lf = k βad
… (3)
Z=Ud
… (4)
d U 0 
RA =
d 0  U 
1/ 3
… (5)
φk =
1000
M
d 0β ad − dβ 0ad + β ad
d × d0
d
… (6)
φv =
M 1000  d − d 0 
−


d0
C  d0 
… (7)
Sn =
n1  β ad 
1 −

n2  β 0ad 
… (8)
(
M U 
VF =  eff1 
 K η 
)
the increased co-solvent. In other words density
decreased with the decrease in dielectric constant in
case of water+DMF and increased for the increased
amount of DMSO with water. Variation in density
with the increased amount of either DMF or DMSO
with water is shown in Fig. 1. The decrease in density
in case of water+ DMF indicates the decrease in
solvent-solvent or ion-solvent interaction or the
structure breaking property of citric acid. But addition
of DMSO to water has rigidified the three
dimensional structure of water forming a strong
hydrogen bond between solvent molecules14,15. It also
indicates the structure forming property of citric acid
in water+DMSO system, which is contrary to
water+DMF system.
Viscosity of citric acid solution in various
compositions of water + DMF and water + DMSO
were measured with usual procedure. Viscosity
increased with the increase in concentration of citric
acid in all the cases of solvent mixtures. Viscosity
increased from 0 to 60% (v/v) co-solvent with a latter
decrease indicating the formation of a complex at
3/ 2
... (9)
where λ is the wave length, F is the frequency
(2MHz), d and d0 are the measured densities of
solution and solvent, U and U0 are the experimental
ultrasonic velocities, respectively, of the solution and
solvent. M is the molecular weight of the solute, βad0
and βad are the adiabatic compressibility of the solvent
and solution, C is concentration in mol dm-3, n1 and n2
are the number of moles of solvent and solute,
respectively.
Density of citric acid solution in water, DMF and
DMSO and their mixtures (v/v) was determined at
303K ± 0.01°C with the usual procedure. Density is
known to be the measure of ion-solvent and solventsolvent interactions. As expected, for a given
composition, density increased with the increase in
concentration of citric acid due to increased
electrostriction in the system. For a given
concentration of citric acid the density decreased with
Fig. 1 — (A) Plot of percentage composition of DMF or DMSO
versus density at 303K ± 0.01°C; (B) Plot of percentage
composition of DMF or DMSO versus viscosity at 303K ± 0.01°C
BHAT et al.: ACOUSTIC BEHAVIOUR OF CITRIC ACID
60% in both the cases of solvent mixtures as shown in
Fig. 1. This indicates the increase in ion-solvent
interaction and also the effect of the formed complex
(DMF: 3H2O16-18 or DMSO: H2O19) on the viscosity
under existing conditions.
Ultrasonic velocity of citric acid in different
compositions of water+DMF/DMSO (v/v) has been
determined at 303K ±0.01°C. The resulted values are
shown in Table 1. This velocity represents the
magnitude of movement of sound velocity in that
medium.
Sound velocity increased with the increase in the
amount of co-solvent (DMF or DMSO) in water and
reaches maximum at 60%, indicating the formation of
a complex at 60% region. Probably, this formed
complex is not allowing the sound wave to travel
freely in solution and hence sound velocity decreases.
Sound velocity increased with increase in
concentration of citric acid in water+DMSO and
water+DMF except at 40% to 60% DMF where it
decreases.
The adiabatic compressibility (βad ) is a measure of
intermolecular association or repulsion calculated
from the measured ultrasonic velocity (U) and density
(d). Ultrasonic velocity decreased (Table 1) with the
877
increase in concentration of citric acid for all the
compositions of DMF or DMSO in water. βad is found
to decrease with the increase in composition of DMF
or DMSO till 60% and thereafter increased, since βad
is inversely related to the product of density and
ultrasonic velocity. Based on this the compressibility
is expected to decrease, which has been observed in
the present case. The variation in βad indicates the
increased ion-solvent interaction. Such trend supports
the formation of certain complex at 60% co-solvent.
Decrease in adiabatic compressibility13 in the
beginning might be due to the close association
between the two solvents under consideration i.e.,
solvent-solvent
interaction
and
and
also
electrostriction. This trend continued till 60%
co-solvent. Probably, from this stage solvent-solvent
interaction decreases due to the complete filling up of
the interstitial spaces of water.
Intermolecular free length (Lf) denotes the
magnitude of either the ion-ion interaction or the ionsolvent interactions or both of the system. The
calculated values of Lf for all the concentrations and
compositions are presented in Table 1. At a given
composition, Lf is found to decrease with the increase
in concentration indicating the small inter ionic
Table 1 — Experimental values of ultrasonic velocity (U), adiabatic compressibility (βad) and intermolecular free length (Lf) at different
concentrations of citric acid in water+DMF and water+DMSO at 303 K ± 0.01°C
c: mol dm−3
0.0
0.05
0.1
0.2
0.3
0.4
0.5
0
10
20
40
60
80
1504
1508
1510
1514
1523
1523
1524
1554
1554
1558
1560
1563
1568
1567
1603
1602
1602
1602
1602
1603
1602
1668
1664
1662
1661
1658
1654
1652
1675
1674
1672
1669
1667
1664
1662
1605
1607
1606
1608
1610
1610
1611
U (ms-1)
100%
0
DMF
1445
1445
1451
1455
1462
1468
1472
10
20
40
60
80
100%
DMSO
1554
1556
1556
1568
1561
1564
1565
1600
1604
1603
1601
1604
1603
1603
1683
1683
1679
1673
1670
1667
1668
1700
1699
1696
1690
1697
1690
1687
1623
1628
1624
1630
1633
1634
1636
1480
1483
1490
1493
1494
1505
1515
4.43
4.39
4.36
4.30
4.23
4.18
4.16
4.09
4.07
4.05
4.01
3.97
3.93
3.89
3.80
3.78
3.77
3.76
3.72
3.70
3.68
3.35
3.34
3.34
3.33
3.33
3.32
3.31
3.20
3.19
3.18
3.18
3.17
3.16
3.15
3.47
3.44
3.44
3.40
3.37
3.35
3.32
4.17
4.15
4.10
4.05
4.03
3.94
3.87
0.1328
0.1322
0.1317
0.1308
0.1297
0.1290
0.1286
0.1276
0.1272
0.1269
0.1263
0.1257
0.1250
0.1244
0.1230
0.1226
0.1225
0.1223
0.1217
0.1213
0.1210
0.1154
0.1153
0.1152
0.1151
0.1150
0.1149
0.1148
0.1128
0.1127
0.1126
0.1125
0.1123
0.1122
0.1121
0.1175
0.1172
0.1170
0.1163
0.1158
0.1154
0.1149
0.1288
0.1285
0.1277
0.1269
0.1266
0.1252
0.1241
1504
1508
1510
1514
1523
1523
1524
βad (10−10 m2 N−1)
0.0
0.05
0.1
0.2
0.3
0.4
0.5
4.43
4.39
4.36
4.30
4.23
4.18
4.16
4.17
4.15
4.11
4.06
4.02
3.96
3.95
3.92
3.90
3.89
3.86
3.83
3.80
3.77
3.62
3.61
3.60
3.59
3.57
3.56
3.55
3.60
3.59
3.58
3.57
3.55
3.54
3.53
3.99
3.95
3.94
3.90
3.86
3.83
3.80
5.08
5.07
5.00
4.93
4.83
4.75
4.69
Lf (Å)
0.0
0.05
0.1
0.2
0.3
0.4
0.5
0.1328
0.1322
0.1317
0.1308
0.1297
0.1290
0.1286
0.1288
0.1285
0.1279
0.1271
0.1265
0.1255
0.1254
0.1249
0.1246
0.1244
0.1239
0.1234
0.1230
0.1225
0.1200
0.1198
0.1197
0.1195
0.1192
0.1190
0.1188
0.1197
0.1195
0.1193
0.1192
0.1188
0.1187
0.1185
0.1260
0.1254
0.1252
0.1246
0.1239
0.1234
0.1230
0.1422
0.1420
0.1410
0.1401
0.1386
0.1375
0.1366
878
INDIAN J PURE & APPL PHYS, VOL 48, DECEMBER 2010
distance. Intermolecular free length further decreased
with the increase in concentration due to the increase
in the number of ions in a given volume or due to
increase in compressibility.
According to Eyring and Kincaid20, intermolecular
free length (Lf) is a predominant factor in solvation
Chemistry21 and inversely related to ultrasonic
velocity. In the present investigation the
intermolecular free length is found to decrease with
increase in concentration of citric acid at all
compositions indicating a significant molecular
interactions. Therefore, the electrolyte may be
considered as structure promoter under the existing
condition. Lf decreased with the increase in the
amount of co-solvent till 60% and then increased.
When the sound wave travels through a solution
certain part of it travels through the medium and rest
gets reflected by the ion5,7 i.e., restriction for the free
flow of sound velocity by the ions. The character that
determines this restriction/backward movement of
sound waves is known as acoustic impedance (Z). It
has been estimated for citric acid solution in different
compositions of water+DMF and water+DMSO
system which is found to increase with the increase in
concentration of citric acid till 60% co-solvent with a
later decrease (values are not shown). As anticipated,
acoustic impedance appears almost reciprocal to
adiabatic compressibility, which further proves the
formation of complex at 60% co-solvent. The higher
impedance indicates the presence of bulkier/solvated
ion due to ion-solvent/solvent-solvent interactions
which restricts the free flow of sound waves.
Relative association (RA ) denotes magnitude of the
association between two species. This Process is
influenced by polarization22 of the solvent species by
the electrolyte or the electrolyte species by the solvent
molecules. RA increases with increase in concentration
due to the decrease in intermolecular free length and
also increase in electrostatic attraction (values are not
shown). From this data it can be said that ion-ion
interaction overcomes the ion-solvent interaction.
The apparent molar compressibility φk, was
calculated using the Eq. 6. All the terms on the right
hand side of that equation are constant except βad and
it depends on concentration. Hence it can be said that
φk is also related to concentration. φk is found to
decrease with increase in concentration of citric acid
at all compositions of water+DMF or water+DMSO.
It represents the magnitude of ion-solvent interaction.
Gucker23 related apparent molar compressibility and
concentration of the solution by:
Fig. 2 — Plot of apparent molar compressibility (Фk: 10−12 m2
mol−1) versus C1/2 for citric acid in various compositions (v/v) of:
A- water+DMF at 303 K ± 0.01°C; B- water+DMSO at 303 K ±
0.01°C
Table 2 — Computed values of limiting apparent molar
compressibility (Ф0k: m2 mol−1) and Sk for citric acid in
water+DMF and water+DMSO at 303K ± 0.01°C
Water+DMF
%comp
Ф0k × 10−12
0
1092
10
1024
20
941
40
847
60
832
80
955
100
1449
φ k = φ 0k + S k C
Sk × 10−12
968
842
643
461
425
721
1496
Water+DMSO
Ф0k × 10−2 Sk × 10−12
1092
968
992
743
891
530
724
273
685
287
737
455
973
829
… (10)
The parameters φk0 and Sk were evaluated from the
intercept and slope of the linear plot of φk versus C
(Fig. 2) and are presented in Table 2. φk0 and Sk are
the indicators of the magnitude of ion-solvent and
ion-ion interactions existing in the system. Both φk0
and Sk increased for water+DMF system and
BHAT et al.: ACOUSTIC BEHAVIOUR OF CITRIC ACID
879
decreased for water+DMSO system. But φk0 appears
to be larger than Sk indicating the predominance of
ion-solvent interaction over ion-ion interaction. The
values increases with the increase in the amount of
DMF in water indicating the increased ion-solvent/
ion-ion interaction, which might be due to the
structure breaking property of either the solvent or
solute. In case of DMSO both the values decreases
continuously.
The apparent molar volume φv is defined as the
change in volume of the solution for the added one
mole of a particular component at constant
temperature and pressure without any appreciable
change in the concentration. It is a thermodynamic
property which helps in elucidating solvation
behaviour of electrolyte in solution. φv was evaluated
from the density of the solution and solvent (Eq. 7).
The limiting molar volume φv0 was obtained from the
plot based on the following Masson’s equation24:
φv = φ0v + Sv C
… (11)
where Sv is obtained from the slope of the plot φv
versus C which represents the measure of ionsolvent interaction in the system. φv0 is the intercept
of the plot (Fig. 3) and the values are given in
Table 3. Sv found to be smaller than φv0.
Solvation number is the number of solvent
molecules associated and taking part in the formation
of primary shell with the central ion25. Solvation
number of the cation is found to decrease from water
to water+co-solvent mixture (values are not shown).
In case of pure water it was found to be around 8 and
about 2 in case of pure non-aqueous solvent
indicating the presence of solvent separated ion-pair.
Free volume (VF), is the average volume into which
the molecules can move due to the repulsion by the
surrounding molecules26. VF can be calculated from
the Eq. (9), where Meff is the effective molecular
weight which is expressed as Meff = (X1M1 + X2M2) X
is the mole fraction and M is the molecular weight of
the individual component in the mixture. K1 is the
temperature independent constant19 (4.28×109) and η
is the viscosity of the solution. VF decreased with the
increase in the volume of co-solvent to water till 60%
with a sharp increase then onwords in both the cases
(values are not shown).
The decrease in free volume indicates strong
intermolecular
attraction
between
dissimilar
molecules. Above 60% co-solvent, where it is the co-
Fig. 3 — Plot of apparent molar volume (Фv : 10−12 m3 mol−1)
versus C1/2 for citric acid in various compositions (v/v) of: A—
water+DMF at 303 K ± 0.01°C; B—water+DMSO at 303 K ±
0.01°C
Table 3 — Computed values of limiting apparent molar volume
(Ф0v: m3 mol−1) and Sv for citric acid in water+DMF and
water+DMSO at 303K ± 0.01°C
Water+DMF
%comp
Ф 0v
0
10
20
40
60
80
100
76
82
72
60
62
66
122
Sv
82
74
90
107
96
93
14
Water+DMSO
Ф 0v
Sv
76
116
113
115
100
-
83
26
38
31
58
-
solvent rich region, the solvent-solvent interaction is
not much. After the formation of a complex at 60%
there may be a wide gap or weak bond between two
solvent molecules which might have led to increased
free volume. This increase indicates the removal of
initially occupied solvent molecules on an ion by the
incoming solvent molecules.
880
INDIAN J PURE & APPL PHYS, VOL 48, DECEMBER 2010
4 Conclusions
Density of citric acid increase with the increase in
the amount of DMSO and decreased with the increase
in amount of DMF in water indicating the structure
formation ability of citric acid in DMSO and structure
breaking property of it in DMF. Around 60%
water+DMF or water+DMSO complex was formed.
DMSO preferentially solvates the species of citric
acid over either water or DMF. Solvation number
decrease with the increase in the co-solvent amount
but indicate the formation of solvent separated ion
pair.
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