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34
CHAPTER 3
ULTRASONIC STUDY OF MOLECULAR INTERACTIONS
OF BINARY LIQUID MIXTURES
3.1 INTRODUCTION
Considerable scientific and practical interest has been stimulated by
the investigation of inorganic liquids by ultrasonic measurements. A liquid is
of cohesive nature. Important physicochemical properties of solutions such as
adiabatic compressibility, viscosity, internal pressure, relaxation time etc may
be computed from ultrasonic velocity and density data. The extent to which
the cohesive forces are disturbed depends on the nature of the solute and
solute-solvent interactions. When an electrolyte is dissolved in a solvent, the
cations and anions from the crystal go into the solutions.
Basically, a binary mixture is formed by the replacement of like
contacts in the pure liquids. Ultrasound velocity measurements have been
extensively applied to assess the molecular interactions in pure and binary
liquid mixtures. Ultrasonic velocities of binary mixtures can be calculated
theoretically from Jacobsons free length theory, Schaaff’s collision factor
theory and empirical relations of Nomoto. The extent of deviation from the
theoretical values can be used to access molecular interactions in liquid
mixtures. In the binary mixtures containing non-polar liquids there can be
only induced dipole-induced dipole interactions, which arise due to polarity
aspects. The forces of attraction due to induced dipole-induced dipole are
very weak.
35
In this chapter, ultrasonic velocity, density and viscosity measurements have been employed to access the interactions existing between the molecules of the components in three binary liquid mixtures. The systems chosen are:
a. ammonium chloride : ammonium sulphate b. ammonium oxalate : ammonium formate c. zinc sulphate : zinc nitrate
The experimental values of ultrasonic velocity, density and viscosity for above three systems are discussed.
3.2 DENSITY (ρ) Density of mixed salts solution of binary mixture of ammonium chloride: ammonium sulphate, ammonium oxalate: ammonium formate and zinc sulphate: zinc nitrate were measured in different concentration at 303 K. As the number of particles increases, the density is also increases. Density increases with increasing the concentration due to the presence of ions or particles. The density of a mixed salt solution is increased with the increase in composition of ammonium sulphate, whereas they decrease with ammonium chloride (Kalidass et al., 1999). The measured density values of ammonium chloride and ammonium sulphate solution are given in Table 3.1. But, the density of a solution is found to be increases with increase in the concentration of ammonium oxalate and it is found to be maximum at 90:10 with a mole fraction of 0.8181, whereas they decrease with the increase in concentration of ammonium formate. It may be decreasing with further increase the concentration of ammonium oxalate. Similarly, a non-linear variation is found with the increase the concentration of zinc nitrate. The density of mixed salt solution shows a sharp increase which confirms the structural rearrangement of molecules (Ali et al., 2002).
36
Table 3.1 Experimental values of ultrasonic velocity (U), density (), acoustic impedance (Z), adiabatic compressibility (ad), intermolecular free length (Lf), molar sound velocity (R) and molar compressibility (W) of ammonium sulphate and ammonium chloride mixed salt solution in different concentrations at 303 K
Composition of ammonium chloride +
ammonium sulphate
Mole fraction (X1 ) of
(NH4)2 SO4
Velocity(U) ms-1
Density ()
kgm-3
Acoustic impedance
(Z) × 106
kg m-2s-1
Adiabatic compressibility
(ad )× 10-10
kg-1 ms2
Intermolecular free length
(Lf )x 10-10
m
Molar sound velocity
(R)
m3mol-1(ms-1)1/3
Molar compressibility
(W)
m3mol-1Pa1/7
100 : 00 0.0000 1542 1018 1.569 4.133 0.0129 0.607 1.150
90 : 10 0.0526 1550 1022 1.584 4.073 0.0128 0.653 1.238
80 : 20 0.1111 1568 1028 1.611 3.958 0.0126 0.703 1.334
70 : 30 0.1764 1579 1032 1.632 3.886 0.0125 0.760 1.443
60 : 40 0.2500 1590 1039 1.652 3.808 0.0124 0.822 1.560
50 :50 0.3333 1600 1043 1.669 3.744 0.0123 0.894 1.697
40 : 60 0.4285 1557 1049 1.634 3.931 0.0126 0.963 1.833
30 : 70 0.5385 1595 1055 1.683 3.726 0.0122 1.061 2.019
20 : 80 0.6666 1610 1060 1.707 3.639 0.0121 1.171 2.228
10 : 90 0.8181 1617 1066 1.723 3.588 0.0120 1.297 2.470
00 : 100 1 1625 1071 1.734 3.538 0.0119 1.451 2.764
37
3.3 VELOCITY (U)
A plot of ultrasonic velocity against mole fraction of ammonium
sulphate in different concentration at 303 K is shown in Figure 3.1. The
variation of ultrasonic velocity in a solution depends upon the increase or
decrease of intermolecular free length (Lf) after mixing the component.
According to Eyring and Kinchaid (1938), velocity increases if the
intermolecular free length decreases and vice-versa as a result of mixing
component. It is seen that, the ultrasonic velocity increases initially with the
increase of concentration of ammonium sulphate. It attains a maximum at a
concentration of 50:50 with a mole fraction of 0.3333 (Table 3.1). The
increase in the concentration of ammonium sulphate weakens the molecular
forces and hence the abrupt change in velocity is obtained. This non-linear
variation of velocity with increase in concentration indicates the complex
formation between the constituents of the mixture (Manisha Gupta and Shukla
1996).
While in the case of ammonium oxalate and ammonium formate
salt solution, when the concentration is increased, the plots are linear up to the
concentration of 80:20 (Figure 3.2). At the composition of 90:10, the
ultrasonic velocity decreases with increase the concentration. It is observed
that, the mixed salt solution shows a critical characteristics at a mole fraction
of 0.8181. The positive or negative slop indicating the existence of very weak
intermolecular attractions in these systems and there is little deviation from
ideal behavior. This may be due to induced dipole-induced dipole type. The
abrupt variation in velocity at the concentration of 90:10 indicates the
formation of complex (Ali and Nain 1994; Tabhane and Patki 1985).
38
Similarly, the ultrasonic velocity decreases with the increase of
concentration of zinc nitrate. It attains a minimum at a mole fraction of
0.6928. The increase in the concentration of zinc nitrate weakens the
molecular forces and hence the abrupt change in velocity is obtained at a mole
fraction of 0.7945 (Figure 3.3). This non-linear variation of velocity with
increase in concentration indicates critical characteristics at a particular
composition (Muraliji et al., 2002a,b).
0.0 0.2 0.4 0.6 0.8 1.0
1540
1560
1580
1600
1620
1640
U (m
/s)
Mole fraction of Ammonium Sulphate
( (NH4 )SO4)2+(NH4)Cl2
Figure 3.1 Variation of ultrasonic velocity with mole fraction of
ammonium sulphate of a mixed salt solution at 303 K
Ultr
ason
ic v
eloc
ity (U
) ms-1
Mole fraction of ammonium sulphate
39
0.0 0.2 0.4 0.6 0.8
1550
1555
1560
1565
1570
1575
Ultr
ason
ic v
eloc
ity (U
) ms-1
Mole fraction of ammonium oxalate
(NH 4)2C 2O 4+HC OO NH 4
Figure 3.2 Variation of ultrasonic velocity with mole fraction
of ammonium oxalate of a mixed salt solution at 303 K
0.0 0.2 0.4 0.6 0.8 1.01570
1575
1580
1585
1590
1595
1600
1605
ultra
soni
c ve
loci
ty(U
) ms-1
mole fraction of zinc Nitrate
ZnSO4+Zn(NO3)
Figure 3.3 Variation of ultrasonic velocity with a mole fraction
of zinc nitrate of a mixed salt solution at 303 K
Ultr
ason
ic v
eloc
ity (U
) ms-1
Mole fraction of zinc nitrate
Ultr
ason
ic v
eloc
ity (U
) ms-1
Mole fraction of ammonium oxalate
40
3.4 INTER MOLECULAR FREE LENGTH (Lf)
Intermolecular free length in binary liquid mixtures can be used to
access the attraction between the component molecules. Increase in
concentration leads to decrease in gap between two species and it is referred
as intermolecular free length. On the basis of sound propagation in liquid
(Karthikeyan and Palaniappan 2005) the increase in free length after mixing,
decreases the sound velocity. The intermolecular free length has an inverse
behavior of ultrasonic velocity. The intermolecular free length is found to be a
predominant factor in determining the nature of sound velocity variation in
liquid mixtures (Karthikeyan and Palaniappan 2005; Eyring and Kinchaid
1938). Table 3.1 shows the values of intermolecular free length of ammonium
sulphate and ammonium chloride solution. It shows that the decrease of
intermolecular free length with the increase of concentration of ammonium
sulphate and reaches minimum value (Figure 3.4). The value of
intermolecular free length in a binary mixture depends on concentration. It is
observed that, a sudden increase in length with decrease in velocity at a mole
fraction of 0.4285 of ammonium sulphate. This indicates that there is a
significant interaction present between the solute molecules due to which
structural arrangement molecules are considerably affected (Ishwara Bhat and
Shree Varaprasad 2003).
In the mixed solution of ammonium oxalate and ammonium
formate, intermolecular free length decreases with increase the concentration
of ammonium oxalate and reaches a minimum (Figure 3.5). An increase in
intermolecular free length produces a decrease in velocity. This indicates that,
there is a significant interaction between solute molecules. Thus, the structural
arrangements are considerably affected (Manisha Gupta and Shukla 1996;
Karunanidhi et al., 1999). A sudden change in free length at a given
concentration may be due to weakening of intermolecular attraction.
41
0.0 0.2 0.4 0.6 0.8 1.00.0118
0.0120
0.0122
0.0124
0.0126
0.0128
0.0130
L f x 1
0-10 m
Mole fraction of Ammonium Sulphate
((NH4)2SO4)2+NH4Cl2
Figure 3.4 Variation of intermolecular free length with mole fraction of
ammonium sulphate of a mixed salt solution
0.0 0.2 0.4 0.6 0.8 1.0
0.01255
0.01260
0.01265
0.01270
0.01275
0.01280
Lf A
Mole fraction of Ammonium oxalate
Amm.oxalate+Amm.formate
Figure 3.5 Variation of intermolecular free length with mole fraction of
ammonium oxalate of a mixed salt solution
Inte
rmol
ecul
ar fr
ee le
ngth
(Lf )
x 1
0-10 m
Mole fraction of ammonium sulphate
Inte
rmol
ecul
ar fr
ee le
ngth
(Lf )
x 1
0-10 m
Mole fraction of ammonium oxalate
(NH4)2C2O4 + HCOO NH4
42
Similarly, it is seen that the concentration of zinc nitrate increases
the intermolecular length and sudden decrease at a mole fraction of 0.7945 of
zinc nitrate (Figure 3.6). It indicates that there is a significant presence in
between the molecules due to the dipole induced dipole or dipole-dipole
interaction leads structural rearrangement as described earlier (Nikam et al.,
2004; Rama Rao et al., 2004). It may be pointed out here that the free length
values at a given concentration in different systems can be used to compare
the induced ionic-ionic interactions in the above three systems investigated.
3.5 ADIABATIC COMPRESSIBILITY (βad)
Adiabatic compressibility (βad) values were calculated for three
mixed salt solution. Adiabatic compressibility is inversely proportional to U2
and the trend in adiabatic compressibility with concentration is the reverse of
the trend in U with concentration in all the three system.
The adiabatic compressibility decreases with increases in
concentration. This is an ideal trend. In the mixed ammonium chloride and
ammonium sulphate salt solution, the compressibility decreases with increase
in concentration of ammonium sulphate (Table 3.1). And it attains sudden
increases at a mole fraction of 0.4285 of ammonium sulphate (Figure 3.7). It
means, ion-solvent interaction increases at a given composition (Varma and
Surendar Kumar 2000; Kalidass et al., 1999).
43
0.0 0.2 0.4 0.6 0.8 1.0
0.1150
0.1155
0.1160
0.1165
0.1170
0.1175
0.1180
0.1185
L f A
Mole fraction of Zinc Nitrate
ZnSO4+Zn(NO
3)2
Figure 3.6 Variation of intermolecular free length with mole fraction of
zinc nitrate of a mixed salt solution
0.0 0.2 0.4 0.6 0.8 1.0
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
x1
0-10 kg
m-2S
-1
Mole fraction of Ammonium Sulphate
(NH4)2SO
4+NH
4)Cl
2
Figure 3.7 Variation of adiabatic compressibility with mole fraction of
ammonium sulphate of a mixed salt solution
Inte
rmol
ecul
ar fr
ee le
ngth
(Lf )
x 1
0-10 m
Mole fraction of zinc nitrate
Adi
abat
ic c
ompr
essi
bilit
y (
ad )
x 10
-10 k
g-1 m
s2
Mole fraction of ammonium sulphate
(NH4)2SO4 + (NH4)Cl2
44
Every solvent has a limit for compression called the limiting a
compressibility value. The compressibility of a solvent is higher than that of
a solution and it decreases with increases in concentration. In the mixed
solution of ammonium oxalate and ammonium formate, the compressibility
decreases with increase in concentration of ammonium oxalate solution
(Figure 3.8). At a mole fraction of 0.8181 of ammonium oxalate, it is found to
increases. That means ion-solvent interaction increases (Ravinder Reddy and
Linga Reddy 1999). Similar non-linear variation of compressibility is also
occurs in the zinc nitrate and zinc sulphate salt solution (Figure 3.9). It shows
that the reverse effect as that of impedance (Nikam et al., 2004). The
variations of adiabatic compressibility with concentration indicate that the
strength of induced ionic-ionic interactions concentration is dependent.
0.0 0.2 0.4 0.6 0.8 1.03.92
3.94
3.96
3.98
4.00
4.02
4.04
4.06
4.08
4.10
adx1
0-10 k
g-1m
s2
Mole fraction Ammonium oxalate
Amm.oxalate+Amm.formate
Figure 3.8 Variation of adiabatic compressibility with mole fraction of
ammonium oxalate of a mixed salt solution
Adi
abat
ic c
ompr
essi
bilit
y (
ad )
x 10
-10 k
g-1 m
s2
Mole fraction of ammonium oxalate
(NH4)2C2O4 + HCOONH4
45
0.0 0.2 0.4 0.6 0.8 1.03.28
3.30
3.32
3.34
3.36
3.38
3.40
3.42
3.44
3.46
3.48
3.50
ad
x 10
-10 k
g -1m
s2
Mole fraction of Zinc Nitrate
Zn(NO3)2+ZnSO4
Figure 3.9 Variation of adiabatic compressibility with mole fraction of zinc nitrate of a mixed salt solution
3.6 ACOUSTIC IMPEDANCE (Z)
The variation of acoustic impedance and mole fraction of ammonium sulphate is shown in Table 3.1. In the aqueous solution of ammonium sulphate and ammonium chloride, acoustic impedance increases with increase the concentration of ammonium sulphate suggesting that the ion-solvent interaction increases till the mole fraction of 0.3333. But it decreases at mole fraction of 0.4285. And again it is increases with concentration. It may be due to the complex formation in the solution and this may be on the basis of the interaction between solute and solvent molecules (Ravindra Natha Reddy and Ramamurthy 1995). As the concentration of ammonium oxalate increases, acoustic impedance increases, whereas compressibility decreases and it is shown in Table 3.2. The usual behavior of the linear increase of acoustic impedance is noticed in the solution. This behavior of linear variation is observed till the
Adi
abat
ic c
ompr
essi
bilit
y (
ad )
x 10
-10 k
g-1 m
s2
Mole fraction of zinc nitrate
46
mole fraction of 0.6666. The value of impedance is suddenly decreases at a mole fraction of 0.8181. The variation of acoustic impedance shows dips at a given concentration again support the existence of molecular interaction. The decrease in impedance with increase in concentration can be explained on the basis of interaction between ion-solvent, which increases the intermolecular free length (Madhu Rastogi et al., 2002). Similarly, in the mixed solution of zinc sulphate and zinc nitrate, the acoustic impedance decreases with increases in the concentration of zinc nitrate, till the mole fraction of 0.6928. The variation of impedance is shown in Table 3.3. The sudden increase in impedance at a mole fraction of 0.7945 of zinc nitrate may be due to the critical characteristics in the solution and this may be on the basis of the interaction between solute and solvent complex (Ravinder Reddy and Linga Reddy 1999). 3.7 VISCOSITY (η)
Viscosity depends mainly on the availability of bulky or less mobile entities of salt solution. The viscosity is related to normal forces in the liquids. The variation of viscosity of ammonium sulphate and ammonium chloride mixed salt solution at 303 K is shown in Figure 3.10. The changes in density and viscosity can be correlated to hydrophilic (Hydrogen bond forming or structure making) or hydrophobic (Hydrogen bond disrupting or structure breaking) character of solute. The viscosity is gradually increases and suddenly decreases with the increase concentration of ammonium sulphate. A dip is shown at a mole fraction of 0.8181 of ammonium sulphate and again it increases. Similarly, in the case of ammonium oxalate and ammonium formate solution, the values of viscosity increases and attains the maximum values of 0.25 and 0.6666 mole fraction of ammonium oxalate (Figure 3.11) and then decreases with further increase in concentration which indicates the weakening of intermolecular interaction between the component molecules (Prasad 2003).
47
Table 3.2 Experimental values of density (), ultrasonic velocity (U), adiabatic compressibility (ad), acoustic
impedance (Z), free length (Lf), molar volume (V), molar sound velocity (R), molar compressibility (W)
and molar volume (V) of ammonium oxalate and ammonium formate in different concentrations at 303 K
Composition of ammonium
chloride + ammonium
sulphate
Mole fraction of
ammonium oxalate (X1)
Ultrasonic
velocity(U) ms-1
Density
() kg m-3
Adiabatic compressibility
ad ×10-10
kg-1 ms2
Acoustic impedance
(Z)
kg m-2s-1
Intermolecular
Free length(Lf) ×10-10m
Molar sound
velocity
(R)
m3 mol-1
(ms-1)1/3
Molar compressibility
(W)
m3 mol-1Pa1/7
Molar volume
(V) m3 mol-1
100 : 00 0.000 1551 1018 4.085 1578562 0.01280 0.717 1.360 0.0619
90 : 10 0.053 1555 1018 4.064 1582634 0.01277 0.755 1.430 0.0651
80 : 20 0.111 1554 1020 4.062 1584713 0.01276 0.793 1.503 0.0685
70 : 30 0.177 1554 1020 4.059 1585243 0.01276 0.838 1.589 0.0724
60 : 40 0.250 1557 1021 4.040 1589697 0.01273 0.889 1.685 0.0767
50 :50 0.333 1559 1022 4.027 1593145 0.01271 0.946 1.793 0.0816
40 : 60 0.429 1563 1023 4.003 1598540 0.01267 1.012 1.918 0.0872
30 : 70 0.539 1574 1025 3.938 1613350 0.01257 1.088 2.063 0.0935
20 : 80 0.667 1575 1025 3.935 1613965 0.01256 1.177 2.231 0.1012
10 : 90 0.818 1556 1026 4.025 1596538 0.01271 1.275 2.419 0.1101
00 : 100 1.000 1567 1025 3.972 1606513 0.01262 1.405 2.665 0.1210
48
Table 3.3 Experimental values of ultrasonic velocity (U), density (), specific acoustic impedance (Z), adiabatic
compressibility (ad), intermolecular free length (Lf), viscosity () of zinc sulphate and zinc nitrate at
different concentration at 303 K
Composition of zinc
sulphate + zinc nitrate
Mole fraction
of
(ZnSO4)
Mole fraction of
(Zn(NO3)2)
(X1)
Ultrasonic velocity (U)
ms-1
Density (ρ)
kgm-3
Acoustic impedance
(Z)
kgm-2s-1
Adiabatic compressibility
( βad) × 10-10
kg-1ms2
Intermolecular
free length
(Lf ) × 10-10 m
Viscosity
(η)×10-3
Nsm-2
90 : 10 0.903 0.0970 1604 1176 1886737 3.304 0.1151 1.597
80 : 20 0.8054 0.1946 1600 1170 1871200 3.340 0.1157 1.529
70 : 30 0.7071 0.2929 1597 1168 1864961 3.358 0.1160 1.497
60 : 40 0.6081 0.3919 1595 1166 1859930 3.371 0.1163 1.427
50 : 50 0.5085 0.4915 1590 1164 1851396 3.397 0.1167 1.562
40 :60 0.4082 0.5918 1585 1163 1843228 3.422 0.1172 1.603
30 : 70 0.3072 0.6928 1573 1161 1826285 3.481 0.1182 1.621
20 : 80 0.2055 0.7945 1581 1164 1840932 3.436 0.1174 1.631
10 : 90 0.1031 0.8969 1577 1159 1828248 3.468 0.1170 1.632
49
0.0 0.2 0.4 0.6 0.8 1.0
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
(Vis
cosi
ty) 1
0-3N
sm-2
Mole fraction of ammonium sulphate
(NH4)(SO
4)
2+(NH
4)CL
2
Figure 3.10 Variation of viscosity with mole fraction of ammonium
sulphate of a mixed salt solution at 303 K
0.0 0.2 0.4 0.6 0.8 1.01.13
1.14
1.15
1.16
1.17
1.18
1.19
x 1
0-3N
sm-2
mole fraction of ammonium oxalate
amm oxalate + amm formate
Figure 3.11 Variation of viscosity with mole fraction of ammonium
oxalate of a mixed salt solution at 303 K
Visc
osity
() x
10-3
Nsm
-2
Visc
osity
() x
10-3
Nsm
-2
(NH4)2C2O4 + HCOONH4
50
Similarly the variation of viscosity with the concentration of zinc
nitrate is shown in Figure 3.12. The viscosity decreases with the increase in
the concentration of zinc nitrate reaches its minimum at a mole fraction of
0.3919 and increases on further increase in concentration of nitrate, which is
due to the less cohesive force between them (Subramanyam Naidu and
Ravindra Prasad 2004). From the observed viscosity values, it is confirmed
that, viscosity is more sensitive to structural changes because of
solvent-solute interactions (Rajkotia and Parsania 1998).
0.0 0.2 0.4 0.6 0.8 1.01.40
1.45
1.50
1.55
1.60
1.65
x10
-3 N
sm-2
Mole fraction of Zinc nitrate
ZnSo4+Zn(NO3)2
Figure 3.12 Variation of viscosity with mole fraction of Zinc nitrate of a
mixed salt solution at 303 K
3.8 INTERNAL PRESSURE (i)
Internal pressure in binary mixtures can used to assess the
intermolecular attraction between the components. Internal pressure is a
energy volume co-efficient and is a measure of the attractions and repulsions
Vis
cosi
ty (
) x 1
0-3 N
sm-2
51
of the molecules in the liquid systems. Its measurements are significant in the
evaluation of thermodynamic properties of liquid because it is closely related
to ultrasonic velocity, viscosity and compressibility in the liquid phase. The
internal pressure values reflect the net cohesive/adhesive forces available in
the medium. Such forces will drastically change if mole fraction of
components is changed (Figure 3.13).
0.0 0.2 0.4 0.6 0.8 1.0
1000
1200
1400
1600
1800
2000
2200
2400
2600
Pre
ssur
e(P
a) x
102
mole fraction of ammonium sulphate
NH4Cl2+NH4SO4
Figure 3.13 Variation of internal pressure with mole fraction of
ammonium sulphate of a mixed salt solution
The internal pressure is linearly decreasing with concentration of
ammonium oxalate which shows that the attractive force increases
(Figure 3.14) (Sabesan et al., 1980). A decrease in internal pressure with
concentration confirms that the presence of solvent-solute interactions (Raj
Kotia et al., 1999). Similarly, the same linear variation is observed in the case
of ammonium sulphate and ammonium chloride salt solution (Tables 3.4-3.6).
Inte
rnal
pre
ssur
e (
i) x
102
Pa
Mole fraction of ammonium sulphate
52
Table 3.4 Computed values of mole fraction, molar volume (V), available volume (Va), attenuation (α), relaxation time (), internal pressure (πi), viscosity (η) and free volume (Vf) of mixed salt solution of ammonium chloride and ammonium sulphate solution in different concentrations
Composition of Ammonium Chloride +
Ammonium Sulphate
Mole fraction (X1) of
ammonium sulphate
Molar
volume (V) m3mol-1
Available volume (Va)
m3mol-1
Attenuation
(α)
Np m-1
Relaxation
time ()
10-13 sec
Pressure (πi) 102 ×Pa
Viscosity
(η)
10-3 NSm-2
Free volume(Vf)
10-3
m3
100 : 00 0.000 0.053 0.051 0.0292 5.708 2562 1.036 2.536
90 : 10 0.053 0.056 0.055 0.0295 5.748 2434 1.059 2.767
80 : 20 0.111 0.061 0.059 0.0287 5.714 2252 1.083 3.047
70 : 30 0.176 0.065 0.064 0.0286 5.730 2070 1.106 3.369
60 : 40 0.250 0.070 0.070 0.0280 5.651 1888 1.113 3.814
50 :50 0.333 0.076 0.076 0.0330 6.696 1874 1.341 3.311
40 : 60 0.429 0.083 0.081 0.0374 7.385 1760 1.409 3.378
30 : 70 0.539 0.091 0.091 0.0370 7.487 1616 1.507 3.648
20 : 80 0.667 0.010 0.101 0.0396 8.083 1511 1.666 3.699
10 : 90 0.818 0.111 0.112 0.0280 5.755 1135 1.203 7.118
00 : 100 1.000 0.123 0.125 0.0319 6.564 1069 1.392 6.840
53
Table 3.5 Experimental values of viscosity (), relaxation time () , internal pressure (i), available value (Va), free volume (Vf) and attenuation () of ammonium oxalate and ammonium formate in different concentrations at 303 K
Composition of ammonium formate +
ammonium oxalate
Mole fraction of
ammonium oxalate
(X1)
Mole fraction of
ammonium formate
(X2)
Viscosity ()
10- 3 Nsm-2
Relaxation time ()
10 – 13 sec
Internal pressure (i) Pa
Available volume
(Va) m3 mol-1
Free volume (Vf) m3
Attenuation () 10-7 Np m-1
100 : 00 0.0000 1.0000 1.179 6.421 2313 0.0600 0.6128 0.1633
90 : 10 0.0526 0.9481 1.152 6.243 2155 0.0633 0.6609 0.1584
80 : 20 0.1111 0.8888 1.168 6.323 2045 0.0665 0.6862 0.1605
70 : 30 0.1765 0.8235 1.174 6.355 1920 0.0703 0.7216 0.1613
60 : 40 0.2500 0.7500 1.182 6.358 1799 0.0746 0.7618 0.1613
50 :50 0.3333 0.6666 1.143 6.137 1644 0.0795 0.8399 0.1553
40 : 60 0.4286 0.5714 1.158 6.179 1529 0.0851 0.8892 0.1560
30 : 70 0.5385 0.4615 1.146 6.019 1395 0.0920 0.9740 0.1509
20 : 80 0.6666 0.3333 1.173 6.156 1288 0.0995 1.0281 0.1542
10 : 90 0.8181 0.1818 1.134 6.086 1154 0.1070 1.1447 0.1543
00 : 100 1.0000 0.0000 1.146 6.071 1035 0.1185 1.2522 0.1528
54
Table 3.6 Computed values of molar volume (V), molar sound velocity (R), molar compressibility (W), available volume (Va), relaxation time (τ), attenuation constant and internal pressure in ZnSO4 and Zn (NO3)2 in different concentrations
Composition of zinc sulphate +
zinc nitrate
Mole fraction of
Zn(NO3)2
(X1)
Molar volume (V)
m3mol-1
Molar sound velocity
(R)
m3mol-1(ms-1)1/3
Molar compressibility
(W)
m3mol-1Pa1/7
Available volume(Va)
m3mol-1
Relaxation
time (τ)
10-13 sec
Attenuation
(α) 10-15
Nepm-1
Internal pressure
(i) 10-5
90 : 10 0.0970 0.2453 2.871 5.547 0.2459 7.034 2.754 1.393
80 : 20 0.1946 0.2475 2.895 5.589 0.2475 6.807 2.672 1.362
70 : 30 0.2929 0.2487 2.907 5.612 0.2482 6.701 2.635 1.346
60 : 40 0.3919 0.2499 2.920 5.636 0.2491 6.414 2.525 1.311
50 : 50 0.4915 0.2511 2.931 5.657 0.2496 7.074 2.794 1.372
40 :60 0.5918 0.2524 2.943 5.679 0.2500 7.316 2.898 1.391
30 : 70 0.6928 0.2536 2.949 5.693 0.2493 7.522 3.003 1.408
20 : 80 0.7945 0.2537 2.956 5.706 0.2507 7.472 2.968 1.397
10 : 90 0.8969 0.2557 2.976 5.743 0.2520 7.547 3.006 1.396
55
0.0 0.2 0.4 0.6 0.8 1.0
1000
1200
1400
1600
1800
2000
2200
2400
i a
tm
Mole fraction of Ammonium oxalate
Amm.oxalate+Amm.formate
Figure 3.14 Variation of internal pressure with mole fraction of
ammonium oxalate of a mixed salt solution
The variation of the internal pressure with the increase in the
concentration of zinc nitrate is shown in Figure 3.15. The primary effect of
dissolving zinc nitrate is lowers the compressibility of the solvent molecules.
The lowering of compressibility results in the increase of ultrasonic velocity
and hence pressure increases with concentration. With reference to the
Figure 3.15, the pressure decreases up to the mole fraction of 0.3919 and then
increases reaching the maximum at 0.6928 again decreases (Rajendran and
Marikani 1994). The internal pressure values are less in mixed solution
ammonium oxalate and ammonium formate systems suggesting the presence
of weak induced ionic-induced ionic interactions.
Inte
rnal
pre
ssur
e (
i) Pa
Mole fraction of ammonium oxalate
(NH4)2C2O4 + HCOONH4
56
0.0 0.2 0.4 0.6 0.8 1.01.30
1.32
1.34
1.36
1.38
1.40
1.42
i 10-5
Mole fraction of Zinc Nitrate
ZnSO4+Zn(NO3)2
Figure 3.15 Variation of internal pressure with mole fraction of zinc
nitrate of a mixed salt solution
3.9 MOLAR VOLUME (V)
A small quantity of ammonium sulphate is added to the mixed
solution (Table 3.4), ion-solvent interaction occurs resulting considerable
increase intermolecular spaces between the molecules as suggested by
Jacobson (Jacobson 1952). This contributes to increase in molar volume. It
is also noted that, an increase in molar volume decreases the intermolecular
interactions. This trend shows that bonding length decrease with the increase
in concentration and hence the intermolecular interaction decreases. Similar
trend occurs in the case of ammonium oxalate: ammonium formate and zinc
nitrate: zinc sulphate mixed salt solution. From the results it shows that the
complex has formed almost constant molar volume which indicating that
every molecules present in the complex has same molar volume (Viswanadha
Sastry et al., 2003).
Inte
rnal
pre
ssur
e (
i) x
10-5
Pa
Mole fraction of zinc nitrate
57
3.10 MOLAR SOUND VELOCITIES (R) AND MOLAR
COMPRESSIBILITY (W)
Molar sound velocity is an additive function of the chemical bonds
in the molecule and it is useful in correlating molecular structure with
ultrasonic velocity. The linear variation in the Rao constant values with
concentration suggests that the interactions are concentration dependent. The
values of molar sound velocity and molar compressibility are computed of the
liquid mixtures given by Nomoto (Adgankar et al., 1988) is based on the
assumption of linearity of variation of the molecular sound velocity with mole
fractions and further on the additively of the molar volume in the liquid
mixtures. The values of R & W are indicating the linear variation for above
three mixed salts solution. Therefore, the values of velocities increase with
increasing the concentration (Gour et al., 1986). Thus, the linearity
considered here, can be attributed to the intermolecular interactions between
the component molecules of the mixtures.
3.11 AVAILABLE VOLUME (Va)
The available volume is increases with concentration of ammonium
sulphate and it shows a linear variation. But in the case of zinc sulphate and
zinc nitrate, it is observed as a non-linear variation. From the values, it is
inferred that the available volume is directly proportional to velocity. The
values show a sudden decrease at a concentration of 0.6928 which confirms
that the complex formed has less available volume (Ramanathan and
Ravichandran 2004). The same linear variation is also absorbed in the
ammonium oxalate and ammonium sulphate salt solution. Available volume
shows that the non-linear values indicating the structural variations at
molecular levels inside the liquid system (Muraliji et al., 2002a).
58
3.12 ATTENUATION (α)
The attenuation is increase with the concentration of ammonium
sulphate and it shows a sudden decrease at a mole fraction of 0.8181, while,
the variation of attenuation with the concentration of ammonium oxalate in
the mixed salt solution is non linear. It shows a non-linear variation.
Similarly, in the case of zinc nitrate and zinc sulphate salt solution, the
attenuation value decreases up to the concentration of 0.3919 again increases
reaching the maximum at the mole fraction of 0.6929 and again it decreases
(Tables 3.4-3.6). It confirms that the complex formed has high attenuation
value (Muraliji et al., 2002 a,b).
3.13 RELAXATION TIME (τ)
Acoustical relaxation time depends upon viscosity and
compressibility. Relaxation time of a system can be used to characterize the
intermolecular interactions. The values are calculated for three systems at
different concentration. Relaxation process leads to absorption of the waves,
which is related to structural changes in the liquids (Kannappan and
Rajendran 1992).
The relaxation time shows a non-linear variation. It shows a dips at
a mole fraction of 0.33 and 0.5385 with increase the concentration of
ammonium oxalate. Similarly, in the case of zinc nitrate and zinc sulphate
mixed salt solution, the relaxation time is decreases with concentration of
zinc nitrate. It is decreases up to the mole fraction of 0.3919 and above that it
increases. The variation of relaxation time reaches minimum and then
increases as the concentration of zinc nitrate. The increases of relaxation time
with concentration support the solute-solvent interactions (Muraliji et al.,
2002a) (Tables 3.5 and 3.6).
59
3.14 FREE VOLUME (Vf)
The free volume is the effective volume in which the molecules in
the liquid can move and obey perfect gas law. In the mixed solution of
ammonium sulphate and ammonium chloride, the free volume is increases
with concentration of ammonium sulphate. It sudden increases at two points
with a mole fraction of 0.25 and 0.8181 and hence a non-linear variations are
absorbed. It decreases on further increases in the concentration.
Similarly, in the study of ammonium oxalate and ammonium
formate solution, the increase in free volume with concentration indicates the
variations in cohesive forces of this liquid system with changes in solute
concentration. The change in size and shape of the molecules results in the
structural rearrangements of the molecules in the mixture. The structural
changes features are as a result of the reaction between like and unlike
molecules during the mixing of liquids.
In this case, free volume increases with increase in concentration
suggest that the packing of molecules becomes loose. The trend is found to
be opposite to that of internal pressure observation (Kannappan and
Rajendran 1992). But in the case of zinc nitrate and zinc sulphate salt solution
it shows a maximum at a mole fraction of 0.3919 and on again increasing
with concentration. Its value seems to be decreasing which shows that
cohesive force varies with the changes in the solute concentration
(Pauling 1960; Muraliji et al., 2002 c).
3.15 DISCUSSION
The two salts, ammonium sulphate and ammonium chloride, are
dissolved in water to form NH4++, SO4
- and Cl- ions. These ions are strongly
60
bonded with water molecules. NH4+ ion is always bonded with metal ion.
The ionic radii of SO4- and Cl- are 1.4 and 1.81 Å respectively (Pauling
1960). From the literature (Kavanau 1964) it can be seen that the relatively
small ion like SO4 induces higher order in the water structure. It is explained
that the observed non-linear increase in ultrasonic velocity and decrease in
ultrasonic absorption in the aqueous solutions of the ammonium salts based
on the flickering cluster model and Hall’s two state models for liquid water.
According to the Flicker cluster model, NH4+ ions have a structure breaking
property which results in the increase in closely packed structures of water
which in turn leads to an increase in cohesion. This causes increase in velocity
and decrease in compressibility (Subramaniam Naidu and Ravindra Prasad
1996). In the case of ammonium oxalate solution, the absorption is maximum
at a particular concentration because of oxalate ions (anions).
The increase in structural order of water may result in more
cohesion at higher concentration and hence leads to decrease in
compressibility. The decrease in compressibility results an increase in
velocity. Such a possibility doesn’t exist in this case. But, from the velocity
curve, it is observed that there is a sudden decrease in velocity at a
composition of 60:40. From this, it concluded that, some complex molecules
may be formed. The above conclusion is similar to the one drawn by
Ragouramane and Srinivasa Rao (1998).
A similar effect is also observed in solutions of aqueous urinal
chloride, nitrate, strontium iodide, lead acetate, lead nitrate, cadmium bromide
and iodide (Kavanau 1964).
The ammonium oxalate and ammonium formate are freely soluble
in water. As a result of hydration, oxalate ion can form much unequal
distribution of water, by which regions with more density of water and less
61
density of water can be form. The region in which the oxalate ion is present
is to have higher density of water that those in which oxalate ions are absent.
This property is more important for oxalate ions than the formate ions.
Hence, as a result of introducing the oxalate ion, in the beginning, there is
increase in ultrasonic velocity. But at 0.1111 mole fraction of ammonium
oxalate; the value is less implying uniform distribution. But above this value,
gradual increases in the mole fraction of oxalate increases the velocity up to
the mole fraction of 0.6666. Hence, at mole fraction of 0.8181 implies, there
might be uniform distribution of oxalate ions and formate ions through the
matrix in order to have sudden drop in velocity. Pure ammonium oxalate at
mole fraction of 1.000, exhibits velocity is higher than ammonium format at a
mole fraction of 1.00. Since, ammonium oxalate yields 3 moles of ion per
mole. It can yield more heterogeneity in the distribution of water than
ammonium formates which scan furnish two moles of ions. It is to be said
that, multicharged “anions” in aqueous solution can show higher velocity,
than non-negative ion. When the negative charges are closes, the associated
solvent molecules are to be closer. It leads to the formation of higher and less
dense regions in water.
Similarly, the ultrasonic velocity of the solution derived from zinc
sulphate and zinc nitrate decreases with increasing the mole fraction of zinc
nitrate up to 0.6928. Since, zinc sulphate can furnish only 2 ions whereas
zinc nitrate can furnish 3 ions. Ultrasonic velocity is expected to be largely
influenced by the addition of zinc nitrate. Each ion, either Zn++, SO4= or NO3
-
can better organize solvents around them. The ultrasonic velocity is to
decrease with increase in the concentration of any ionic spaces. At the mole
fraction of zinc nitrate 0.7945, there is a increase in velocity. It illustrates,
organization of zinc nitrate themselves rejecting more water of hydration. But
at a mole fraction of 0.8969, there is a decrease in velocity. Hence, at this
mole fraction, the organized ions at 0.7945 must segregate. So this study
62
illustrates that the complete dissolution of zinc nitrate up to the mole fraction
of 0.6928. But association of ions begins at mole fraction of 0.7945.
Suppression of association begins at mole fraction of 0.8969.
This suppression could be possible by charging individual neutral
ionic clusters. The density of mixture also decreases with increasing the mole
fraction of zinc nitrate up to 0.6928. So this clearly supports complete
dissolution of zinc nitrate, thus weakening the force between free water
molecules by adding zinc nitrate. At the mole fraction of 0.7945, since there
is a association of ions partly rejecting water at hydration, the density
increases. In other words, they release the water and enhance the hydrogen
bonding interaction. The density of the solution is decreased at the mole
fraction of 0.8969, since the association is suppressed by charging neutral
clusters. The water is to be taken for salvation. Hence, there may be weak
hydrogen bonding interaction in the water thus reducing its density. The data
and free length also supports the above view. With increase of mole fraction
of zinc nitrate, there is decreasing the hydrogen bonding interaction in water.
Hence, the free length is increases up to the mole fraction of 0.6928 of zinc
nitrate but at 0.7945, water is released, so there is more hydrogen bonding
interaction. This results in decrease in free length.
The viscosity of the solution increases with increase in the mole
fraction of zinc nitrate up to 0.6928. Since, water is being used more and
more for hydration. The free water has reduced hydrogen bonding
interaction. Hence, a decrease in viscosity is absorbed.
3.16 CONCLUSION
The ultrasonic study of 1N mixed salts solution of ammonium
sulphate and ammonium chloride, ammonium oxalate and ammonium
63
formate and zinc sulphate and zinc nitrate solution have been carried out. It
shows that the process of ion association and complex formation at the
concentration of 60:40. The same complex indications are absorbed at a mole
fraction of 0.0526 and 0.8181 of ammonium oxalate and at a mole fraction of
0.7945 of zinc nitrate salt solution.
Ultrasonic investigations on three binary liquid systems reveals
that, the liquid mixtures containing inorganic salts solutions exist some
complex formations at a particular concentration. This is due to induced
dipole-induced dipole attraction in the ammonium binary mixtures. While in
the case of zinc solutions, the compounds have weak intermolecular
attractions. These conclusions are supported by the trend in the acoustical
parameters and molecular interaction parameters.