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Ultrasonic Velocity in Binary Liquid IMixtures
3.1 Introduction
The study of physiochemical behaviour and molecular interactions in
liquid mixhues is of considerable importance and a number of experimental techniques
have been used to investigate the interactions between the components of binary liquid
mixtures [I-51. In recent years, the measurement of ultrasonic velocity has been
extensively applied in understanding the nature of molecular systems,
physicochemical behaviour and molecular interactions in liquid mixtures [6-81.
Rout and Chakravortty [9] studied the molecular interactions in binary mixtures of
acetyl acetone with isoamyl alcohol, benzene and carbon tetrachloride at 30, 35,
40 and 4 5 ' ~ and showed that due to dipole-induced dipole interactions between
unlike molecules, a relatively stronger interaction is present in the mixtures of acetyl
acetone and carbon tetrachloride system than in the other two systems. Ultrasonic
velocity studies of Nikam et al. [ 101 in binary liquid mixtures of nibbenzene with
several alcohols at 25 and 30% showed that strong dipole-dipole interactions are
present in the liquid mix-. Ramababu et al. [ l 11 discussed extensive application
of isentropic compressibilities of liquid mixtures in characterising molecular
association, dissociation and complex formation. This chapter (Chapter 3) deals
with the experimental study of ultrasonic velocity, density and viscosity in a few
binary organic liquid mixtures at different temperatures. Organic solvents can be
classified on the basis of their structure and dielectric constants. On the basis of
structure they are classified as aliphatic and aromatics. Aliphatic has an open
chain structure and aromatics have a closed chain structure. Polar solvents are
those having high dielectric constants, which produce effects on reaction rates that
are different h m those produced by non-polar solvents (having very low dielectric
constants). There are important difference between protic solvents- solvents
containing hydrogen that is attached to oxygen or nitrogen and hence acidic enough
to form hydrogen bonds-and aprotic solvents which do not contain acidic hydrogen
and in which all hydrogen are bonded to carbon [12]. Methyl ethyl ketone,
nitrobenzene, chlorobenzene and bromobenzene are polar aprotic solvents while
benzene and toluene are non-polar aprotic solvents.
When discussing solvent effects, it is important to distinguish between the
macroscopic effects of the solvent and effects that depend upon the details of the
structure. Macroscopic properties refer to properties of the bulk solvent. An
important example is the dielectric constant, which is a measure of the availability
of the bulk material to increase the capacitance of a condenser. In terms of
structure, dielectric constant is a function of both the permanent dipole moments
of the molecule and its polarizability. Polarizability refers to the distortion of
molecule's electron density. Dielectric constant increases with both dipole
moment and polarizability. An important property of solvent molecules with
regard to reactions is the response of the solvent to changes in charge distribution
as the reaction occurs. The dielechic constant of a solvent is a good indicator of
the ability of the solvent to accommodate separation of charges [12].
A literature survey shows that ultrasonic studies have been made in a large
number of binary liquid mixtures [13-201. But a comparative study of the binary
mixtures of aliphatic compounds, aromatic compounds and mixtures of both
aliphatic and aromatic compounds are rare in the literature. A comparative study
of 'binary mixtures of these compounds is of importance from the viewpoint of
molecular interactions that may takes place between molecules of the same type
and those of different types. This chapter deals with a detailed study of ultrasonic
velocity in binary liquid mixtures of nitrobenzene, chlorobenzene, bromobenzene,
toluene and benzene with methyl ethyl ketone as a common component.
The binary system chosen for the present study are
1. Methyl Ethyl Ketone (MEK) + Nitrobenzene
2. Methyl Ethyl Ketone (MEK) + Bromobenzene
3. Methyl Ethyl Ketone (MEK) + Chlorobenzene
4. Methyl Ethyl Ketone (MEK) + Toluene
5 . Methyl Ethyl Ketone (MEK) + Benzene
These systems of binary mixtures were chosen to study the relative
strength of intermolecular interactions existing in binary mixtures of aliphatic and
aromatic liquids. The mixtures chosen were of polar + polar and polar + non-polar
type. A study of such systems may throw light on the nature of interactions
between two polar components, and between a polar and a non-polar component.
Ultrasonic velocity, density and viscosity measurements were made in the five
binary mixtures at four different temperatures. The sign and magnitude of excess
thermodynamic functions reflect the nature and type of interactions existing in
liquid mixtures. Therefore a systematic study of excess functions that yield
important information on the intermolecular interactions in the mixtures was made
in the five binary mixtures. Other usem thermo acoustical parameters which can
compliment the study of inter molecular interactions in the binary mixtures were
also determined.
3.2 Experimental
The liquids used for the present investigation (benzene, toluene, bromobenzene
and chlorobenzene were of SRL AR grade, and nitrobenzene and MEK were of Merck
synthesis grade) and were used as supplied. The liquid mixtures of different
composition were prepared by mixing calculated volumes of each component.
The liquid cell (described in Section 2.3 of Chapter 2) was filled with the sample.
A PZT transducer of resonant frequency 2MHz was attached to the liquid cell.
This transducer was coupled to the Matec ultrasonic velocity measuring system
(described in Section 2.2.2 of Chapter 2) and the velocity was measured by pulse
echo overlap method (described in Section 2.2.1 of Chapter 2). The experiment
was done at four different temperatures 30,40, 50 and ~o'c, each temperature
being kept constant with in 0.1 '~ using a laboratory made temperature
controller [21]. The highest temperature was limited to 6 0 ' ~ since the boiling
point of methyl ethyl ketone is 7 9 ' ~ . The density of the sample was measured
using lOml pyknometer (described in Section 2.4 of Chapter 2) and the viscosity
was measured using Ostwald viscometer (described in Section 2.5 Chapter 2).
3.3 Thermo Acoustical Parameters
Ultrasonic velocity can be used to calculate several thermodynamic and
acoustic parameters, which are very useful in the study of molecular interactions
in binary liquid mixtures.
3.3.1 Compressibility
Compressibility of a liquid is one of the important physical quantities in
fluid mechanics. It depends on the structure of the liquid. If the temperature is
kept constant during compression then the compressibility of the liquid is called
isothermal compressibility (KT) and if compression is carried out reversibly
without heat exchange with surroundings then we obtain isentropic (adiabatic)
compressibility (K,). Ultrasonic methods always yield isentropic (adiabatic)
compressibility.
Knowing the ultrasonic velocity (C) and density (p) of the liquid or liquid
mixture. the adiabatic compressibility can be computed using the formula [22].
3.3.2 Internal Pressure
In the Van der Waal's equation
the term containing a / v 2 is due to intermolecular forces and is referred to as
the intemal pressure ( r r i ) . In fact internal pressure is a broader concept and is a
measure of the totality of forces of dispersion, repulsion, ionic and dipolar
interactions that contribute to the overall cohesion of a liquid.
Differentiation of equation 3.2 with respect to temperature at constant
volume gives [23]
where E is the internal energy.
On the other hand internal pressure is a measure of change in intemal
energy of a liquid as it undergoes a very small isothermal expansion[24]
where V, T and P have their usual meanings as in thermodynamics. P i s the
thermal expansion coefficient and K is the isothermal compressibility. To T
understand the physical significance of ni, one must consider a liquid undergoing a
small isothermal expansion. The small expansion does not disrupt intermolecular
interactions. The most important contributions to rri will come h m those interactions
varying most rapidly near the equilibrium separation in the liquid. Dispersion,
repulsion and dipole-dipole interaction all vary rapidly with intermolecular
separation and so we might expect ni to reflect mainly these interactions.
There are many equations to calculate the internal pressure (ni) of liquids
and liquid mixtures 125-271. Panday et al. [27] compared the different equations
and concluded that Suryanarayana's formula [28] is suitable for the estimation of
internal pressure (n, )
According to Suryanarayana [28], internal pressure is given by
where b' is the packing factor of liquid which is equal to 1.78 for close packed
hexagonal structure and 2 for cubic packing. For many liquids, b' is equal to 2. K' is a
dimensionless constant having a value of 4.28 x lo9 independent of temperature
and nature of liquid. q is the coefficient of viscosity, R is the universal gas
constant and M is the molecular weight of the liquid. The molecular weight of the
binary liquid mixture is calculated by using the relation
where M I , M, are respectively the molecular weights of the pure first and second
liquids and x, , x, are their mole fractions.
To compute the internal pressure of a liquid system directly we need only
to measure the density, viscosity and ultrasonic velocity. Ultrasonic velocity in a
liquid system depends on the structure and molecular properties. In addition to
temperature, ultrasonic velocity in a liquid system is responsive to external
pressure. Thus equation 3.8 has in it parameters which respond uniquely to
molecular interactions, temperature and pressure. This shows that computed
internal pressure is sensitive to all the physico chemical characteristics of the
liquid system. Using equation 3.8 one gets the value of internal pressure in liquid
systems that decreases with an increase of temperature either for pure liquids or
for any homogeneous solutions of electrolytes or non electrolytes [28].
3.3.3 Inter molecular free length
Intermolecular free length (L ) is the distance between the surfaces of the I
molecules. According to Jacobson [29-321 intermolecular free length is given by
where V is the molar volume at temperature T and V, that at absolute zero. Y is
the surface area per mole of the liquid and is given by Y =
N is the Avogadro number. A
The greater importance of intermolecular free length compared to the
distance between centres of two molecules is that the intermolecular forces, which
determine the properties of fluids consists of attractive and repulsive forces. These
forces have opposite directions but are numerically equal under given external
conditions. The attractive forces are dependent on the distance between what are
called the centres of attraction of the molecules, where as the repulsive forces are
dependent on the distance between the surfaces of the molecules. The distance
between centres of attraction is a property extremely difficult to define, one
reason being that these centres do not coincide with the geometrical centres of the
molecules of the liquid. The distance between the surfaces of the molecules on the
other hand, have a clear physical significance, and this lend themselves more
easily to clear definitions. Also, the inter molecular free length is a predominant
factor in determining the sound velocity variations in liquid mixtures.
Inter molecular free length can also be calculated using adiabatic
compressibility by Jacobson's empirical relation [29]
L,. = k' K~ ---------------- (3.1 1)
where k' is the Jacobson's constant which is temperature dependent and is
obtained from the literature 1291.
3.3.4 Specific acoustic impedance
There are some analogies between acoustics and electricity. One of the
most fruitful of these has been the direct impedance analogy. Acoustic pressure P,
is the analogue of voltage, acoustic velocity C is the analogue of current and
specific acoustic impedance Zi is the analogue of resistance. Specific acoustic
impedance (Zi) is defined by Ohms analogue [33].
Beyer and Letcher [33] considered the case of plane harmonic wave and
obtained a relation for Zi as
zi= p c ---------------- (3.13)
where p is the density and C is the ultrasonic velocity
The mathematical relations for specific acoustic impedance and adiabatic
compressibility show that their behaviour is opposite.
3.3.5 Enthalpy
According to Suryanarayana [34-361, the energy of vaporisation per mole
can be replaced by the Eyring's rate theory. Since PV term is negligible for
liquids [37] the cohesive energy can be equated to the internal energy (niV) as
given by
F.:Hyr,V + (PV,, - pviq k i v ---------------- (3.14)
where F' and H are Helmholtz free energy and enthalpy, respectively.
3.3.6 Rao's Constant
Rao [38-401 noted that the ratio of temperature coefficient of sound
velocity C - I (32 / 8 ~ ) to the expansion coefficient V - I (dV 1 d ~ ) is virtually same
for all unassociated organic liquids
This equation can be integrated to get a simple relation [33]
where V is the molar volume and C is the sound velocity. R' is a constant
independent of temperature and called Rao's constant.
3.3.7 Wada's constant
In the study of sound velocity in liquids, another constant has been
suggested by Wada [41]. According to Wada
where B' is a constant called Wada's constant or molecular compressibility which
is independent of temperature and pressure.
3.3.8 Van der Waal's constant @)
Van der Waal's constant (b) also called co-volume in the Van der Waal's
equation is given by the formula 1421
where R is the gas constant, M is the molecular weight, p is the density, C is the
velocity of sound and T is the temperature.
3.3.9 Excess functions
Excess functions ( A ~ ) for binary liquid mixtures are calculated by a
formula
where xl and x2 are the mole fractions of first and second liquid components
respectively. In the case of enthalpy (H) this formula takes the form[43]
where HI and H2 are enthalpies of first and second liquid component and H,,t is
the enthalpy of the mixture determined experimental.
The excess Gibb's free energy for binary liquid mixture is given by the
formula [44]
where q and V are the viscosity and molar volume of the binary liquid mixtures and
q ,q , V , V are the viscosities and molar volumes of pure liquids respectively. 1 2 1 2
3.4 Results and Discussions
The experimentally determined values of ultrasonic velocity, density and
viscosity are given in table 3.1. A graph of ultrasonic velocity against mole
fraction of MEK at 3 0 ' ~ is shown in figure 3.1.
Table 3.1 Experimental values of Ultrasonic velocity(U), Density(p) and Viscosity (q) of the binary mixtures at different tempaatures
Mole Fraction MEK
X
0.0000
0.2211
0.3271
0.4308
0.5316
0.6300
0.7259
0.8195
1 .om0
0.0000
0.2258
0.3333
0.4375
0.5385
0.6364
0.7313
0.8235
1.0000
0.0000
0.2204
0.3265
0.4299
0.5307
0.6291
0.7252
0.8189
1 .0000
40°C
P 'l u MEK + Nitrobenzene
1.1796 1.4485 1370
1.1102 1.3061 1322
1.0592 1.2373 1279
1.0347 1.0132 1257
0.9964 0.8431 1234
0.9543 0.8143 1200
0.8998 0.7062 1164
0.8721 0.6341 1142
0.7849 0.3422 1085
MEK + Bromobenzene
1.4681 0.8550 1070
1.3545 0.5650 1061
1.2911 0.5450 1058
1.2199 0.5050 1064
1.1341 0.4740 1068
1.0342 0.4370 1074
0.9716 0.4080 1076
0.9017 0.3720 1079
0.7849 0.3422 1085
MEK + Chlorobenzene
1.0848 0.6310 1169
1.0332 0.6096 1154
0.9993 0.5335 1149
0.9715 0.5051 1143
0.9299 0.4850 1138
0.9095 0.4612 1131
0.8762 0.4417 1121
0.8354 0.4113 1104
0.7849 0.3422 1085
MEK + Toluene
0.8485 0.4710 1204 0.8371 0.4580 1190 0.8304 0.4480 1178 0.8252 0.4270 1171 0.8185 0.4070 1161 0.8129 0.3930 1149 0.8067 0.3710 1136 0.7991 0.3540 1121 0.7849 0.3422 1085
MEK + Benzene 0.8573 0.5010 1181 0.8422 0.4930 1170 0.8361 0.4790 1167 0.8284 0.4570 1159 0.8206 0.4360 1151 0.8138 0.4120 1143 0.8060 0.3970 1126 0.7971 0.3650 1112 0.7849 0.3422 1085
J -
I I I I I I
Mole fraction of MEK
Figure3.1 Ultrasonic velocity vs mole fraction of MEK in binary liquid mixtures at 3 0 ' ~
From table 3.1 and figure 3.1 it is clear that as the mole fraction of MEK
increases, ultrasonic velocity decreases except for MEK + bromobenzene binary
liquid mixture. In MEK + bromobenzene system velocity at first show a decreeing
trend and then it increases with increase in the mole fraction of MEK. Also the
density and viscosity of the liquid mixture show similar type variation, viz.,
molefraction of MEK. Moreover, as the temperature is increased ultrasonic
velocity of all the systems decreases.
The variations of isentropic (dabatic) compressibility, intermolecular free
length, internal pressure and specific acoustic impedance of the binary liquid systems
with mole M o n of MEK at different temperatures are shown in tables 3.2 and 3.3.
Also, the variations of these parameters with mole fixtion of MEK at 3 0 ' ~ are shown
Table 3.2 Isentropic compressibility(K,), Intermolecular free length (Lf),Specific acoustic impedance (Zi) of binary mixtures at different temperatures
Mole Fraction of 30" C 40°C 50°c 60°c
MEK x K, Lf Z, Ks Lf Z, K, Lr Zi K, Lr Zi
MEK + Nitrobenzene 0.0000 395 0.3967 1738 426 0.4117 1664 456 0.4261 1600 486 0.4400 1542 0.2211 449 0.4225 1598 492 0.4424 1503 521 0.4585 1442 565 0.4742 1388 0.3271 500 0.4406 1523 542 0.4645 1398 584 0.4822 1339 626 0.4992 1288 0.4308 529 0.4590 1439 572 0.4773 1345 618 0.4961 1286 664 0.5141 1236 0.5316 575 0.4783 1347 617 0.4954 1271 667 0.5152 1215 718 0.5345 1167 0.6300 635 0.5026 1248 679 0.5197 1186 736 0.5411 1133 793 0.5619 1087 0.7259 706 0.5301 1167 765 0.5517 1085 830 03746 1036 898 0.5978 991 0.8195 764 0.5514 1068 816 0.5699 1034 887 0.5942 987 961 0.6183 944 1.0000 915 0.6035 931 I001 0.6311 886 1093 0.6595 843 1194 0.6894 801
MEK + Bromobenzene 0.0000 514 0.4522 I698 554 0.4695 1628 601 0.4890 1555 654 0.5103 1483 0.2258 561 0.4726 1561 ti09 0.4922 1492 662 0.5132 1424 720 0.5353 1359 0.3333 591 0.4851 1484 642 0.5053 1419 699 0.5274 1353 763 0.5512 1288 0.4375 622 0.4977 1406 673 0.5176 1346 730 0.5391 1287 794 0.5622 1228 0.5385 664 0.5140 1309 719 0.5348 1256 780 0.5573 1200 849 0.5812 1145 0.6364 722 0.5276 1203 '782 0.5577 1150 849 0.5812 1097 918 0.6045 1049 0.7313 742 0.5434 1128 828 0.5741 1083 928 0.6078 1001 1042 0.6439 924 0.8235 795 0.5625 1048 890 0.5953 1006 996 0.6296 930 1104 0.6630 870 1.0000 915 0.6034 932 1001 0.6311 886 1093 0.6595 843 1194 0.6894 801
MEK + Chlorobenzene
0.0000 589 0.4842 1364 633 0.5021 1309 681
0.2204 628 0.4999 I289 678 0.5196 1234 734
0.3265 656 0.51 11 1240 708 0.5309 1188 765
0.4299 680 0.5202 1193 735 0.5409 1150 795
0.5307 718 0.5299 1144 776 0.5557 1095 839
0.6291 738 0.5421 1096 801 0.5645 1066 870
0.7252 782 0.5578 1052 847 0.5806 1017 919
0.8189 839 0.5733 1003 912 0.6025 957 993
1.0000 915 0.6034 932 1001 0.6311 886 1093
MEK + Toluene
0.0000 699 0.5274 1120 757 0.5487 1059 823
0.2281 728 0.5383 1087 787 0.5595 1032 854
0.3363 745 0.5444 1070 807 0.5668 1014 878
0.4408 762 0.5506 1055 823 0.5724 1001 895
0.5418 781 0.5576 1038 845 0.5798 984 916
0.6394 800 0.5642 1021 868 0.5877 968 943
0.7339 822 0.5721 1004 894 0.5965 950 973
0.8254 854 0.5831 977 927 0.6075 928 1006
1.0000 915 0.6035 931 1001 0.6311 886 1093
MEK + Benzene
0.0000 707 0.5304 1108 772 0.5543 1054 846
0.2004 741 0.5431 1072 801 0.5646 1025 877
0.2974 754 0.5478 1059 817 0.5702 1012 888
0.3976 772 0.5542 1042 837 0.5771 995 909
0.4975 792 0.5614 1024 856 0.5839 979 931
0.5976 810 0.5617 1009 877 0.5909 963 952
0.6979 835 0.5763 989 908 0.6011 942 990
0.7984 866 0.5869 965 943 0.6127 919 1027
1.0000 915 0.6035 931, 1001 0.6311 886 1093
K, ( T P ~ ) 1% (m) 1u3z @gm2s-')
Table 3.3 Internal pressure (n;),Enthalpy (H) of the binary mixtures at Different tempratures
Internal pressure (atm) Enthalpy (kcal) Mole
fraction of MEK
30°c 4 0 ' ~ 5 0 " ~ 60°c 30°c 40°c 50°c 60°c
X
MEK t Nitrobenzene 0.0000 4528 4436 4340 4264 196 194 196 200 0.2212 4387 4283 4189 4094 190 195 205 209 0.3273 4329 4213 4111 4024 189 197 206 214 0.43111 4250 4143 4043 3948 176 183 189 192 0.5318 4194 4071 3980 3874 166 172 178 185 0.6303 4120 3994 3896 3785 170 175 181 184 0.7257 4039 3909 3783 3684 164 171 177 183 0.8195 3925 3796 3689 3557 165 166 170 171 1.0000 3491 3430 3371 3301 130 132 135 138
MEK + Bromobenzene 0.0000 3448 3349 3311 3262 153 150 150 149 0.2259 3449 3352 3302 3258 134 129 128 134 0.3332 3450 3355 3303 3259 133 130 130 134 0.4375 3450 3358 3306 3262 132 129 128 128 0.5383 3453 3366 3314 3267 131 129 126 129 0.6362 3458 3374 3320 3271 131 129 129 132 0.7310 3464 3386 3331 3283 129 129 131 135 0.8236 3475 3398 3343 3292 125 128 131 137 1.0000 3491 3430 3371 3317 130 132 135 138
MEK + Chlorobenzene 0.0002 3420 3364 3292 3232 148 145 142 142 0.2206 3436 3379 3311 3257 146 147 145 146 0.3267 3445 3387 3322 3270 142 141 140 140 0.4299 3453 3394 3333 3284 140 140 140 140 0.5307 3460 3397 3342 3294 139 140 142 143 0.6291 3467 3405 3347 3299 137 139 141 143 0.7252 3473 3407 3356 3305 138 140 141 144 0.8189 3481 3413 3359 3310 136 139 141 142 1.0000 3491 3430 3371 3317 130 132 135 138
MEK + Toluene 0.0000 3075 3044 3020 3005 138 138 139 142
0.2283 3174 3157 3133 3117 138 139 139 141 0.3362 3214 3198 3179 3154 136 139 140 141 0.4411 3247 3228 3210 3189 136 137 135 138 0.5419 3278 3256 3232 3214 134 135 136 138 0.6397 3316 3282 3257 3234 132 134 136 138 0.7340 3351 3307 3286 3259 129 132 134 136 0.8253 3389 3343 3310 3282 127 131 133 136 1.0000 3491 3430 3371 3317 130 132 135 138
MEK + Benzene 3969 3888 3782 3678 3896 3819 3719 3634 3836 3765 3676 3604 3768 3701 3620 3554 3718 3657 3558 3514 3656 3602 3518 3473 3607 3542 3471 3421 3569 3498 3418 3363 3491 3430 3371 3317
Mole fraction of MEK
Figure 3.2 Adiabatic corn ressibility vs mole fraction of MEK in binary liquid 2 mixtures at 30 C
I I I I 1 0.0 0.2 0.4 0.6 0.8 1.0
Mole fraction of MEK
Figure 3.3 Intermolecular. free length vs mole fraction of MEK in binary liquid mixtures at 3 0 ' ~
Figure mixtures
em! , , , , , , , , , , , 0.0 0.2 0.4 0.6 0.8 1 .O
Mole fraction of MEK
Figure 3.5 Specific acoustic impedance vs mole fraction of MEK in binary liquid mixtures at 3 0 ' ~
Out of all the five binary systems none exhibited a maximum in velocity
curve and dip in compressibility curve. This indicates the absence of complex
formation [45-481. The absence of complex formation is also confirmed by the
linear variation of specific acoustic impedance [49, 501. It is clear from figure 3.5
that specific acoustic impedance is linear and hence no indication of complex
formation.
Inter molecular free length increases with mole fractions of MEK in all the
present systems. This indicates that the distance between surfaces of molecules
increases, there by reducing the ordering of molecules. According to the observation of
Tabhane and Patki [51], an increase in the adiabatic compressibility shows a
tendency towards less ordering resulting in a decrease of ultrasonic velocity with
molefraction of one component. Thus the variation of intermolecular free length
and adiabatic compressibility with mole tkaction of MEK suggests that molecular
arrangement becomes less ordered as the mole fraction of MEK increases.
The intermolecular free length increases with temperature for all the
binary system in the present study. These results are supported by Pandey's [52]
view that, in liquids, increase in temperature results in an increase of inter
molecular distance. Therefore the liquid becomes less packed, and hence the
density and ultrasonic velocity decreases and the compressibility increases.
The mathematical relations for specific acoustic impedance (Zi = pC)
and adiabatic compressibility ( K ' = " P C ' ) show that they must exhibit
opposite behaviour and the behaviour is observed in all the liquid mixtures studied
(figures 3.2 and 3.5). The variation of internal pressure with mole fraction of
MEK at 3 0 ' ~ is shown in figure 3.4. The change in intemal pressure with mole
fraction of MEK suggest that molecular interactions vary in the binary mixtures
and the different types of interactions will be discussed in the next section.
Suryanarayana [53] reported that an increase of tempemtux would result in a decrease of
internal pressure in liquids and liquid mixtures. Table 3.3 shows that as temperature
increases intemal pressure daxases in the present binary systems also.
Enthalpy values at different temperatures are shown in table 3.3.
Variation of enthalpy values of the binary systems with mole fraction of
MEK at 3 0 ' ~ is shown in figure 3.6.
Mole fraction of MEK
Figure 3.6 Enthalpy vs mole hction of MEK in binary liquid mixtures at 30°c
From the figure 3.6 it is clear that enthalpy shifts from the value of one
component to that of the other as the mole fraction changes. Enthalpy values are
used to calculate excess enthalpy of the binary mixtures, which is a usehl
parameter to study molecular interactions.
The values of Rao's constant, Wada's constant and Van der Waal's constant
for the present binary systems are shown in table 3.4 and the variations of these
quantities with mole fraction of MEK at 3 0 ' ~ are shown in figures 3.7 - 3.9.
Table 3.4 Rao's constant(R1) ,Wadas constant (Bt),Van der Waals the binary mixtures at different temperatures
Mole fract~on
of 3 0 ' ~ 4 0 ' ~ 50°c
ME K x R' B' b R' B' b R' B'
MEK + Nitrobenzene 0.0000 1168 2274 98 1169 2274 99 1170 2274 0.2211 1113 2151 93 1114 2152 95 1114 2152 0.3271 1100 2117 93 1102 2117 95 1102 2118 0.4308 1066 2042 91 1066 2043 92 1067 2044 0.5316 1043 1992 90 1044 1993 91 1044 1993 0.6300 1025 1944 89 1024 1945 89 1023 1943 0.7259 1017 1916 88 1018 1919 89 1017 1918 0.8195 985 1852 87 986 1853 87 985 1853 1.0000 957 1773 84 956 1773 85 954 1772
MEK + Bromobenzene 0.0000 1108 2250 100 1107 2249 101 1106 2251 0.2258 1052 2109 95 1050 2108 96 1049 2110 0.3333 1030 2054 93 1029 2056 94 1028 2054 0.4375 1019 2007 92 1018 2008 92 1018 2008 0.5385 1017 1991 91 1017 1992 92 1016 1990 0.6364 1013 1986 92 1014 1987 93 1015 1985 0.7313 1010 1937 88 1009 1935 91 1010 1936 0.8235 1001 1896 86 1001 1897 90 1000 1897 1.0000 957 1773 84 956 1773 85 954 1772
MEK + Chlorobenzene 0.0000 1105 2139 97 1104 2138 98 1104 2137 0.2204 1066 2050 94 1065 2049 94 1063 2047 0.3265 1054 2018 93 1053 2016 93 1051 2017 0.4299 1037 1979 91 1036 1976 92 1035 1977 0.5307 1035 1962 91 1034 1961 92 1033 1960 0.6291 1010 1909 89 1009 1908 89 1008 1907 0.7252 998 1878 88 998 1877 89 997 1876 0.8189 995 1861 88 994 1860 88 993 1862 1.0000 957 1773 84 956 1773 85 954 1772
MEK + Toluene 0.0000 1170 2183 101 1169 2181 102 1170 2183 0.2281 1121 2090 97 1121 2090 98 1122 2091 0.3363 1099 2048 95 1099 2047 96 1098 2046 0.4408 1076 2003 94 1076 2004 94 1076 2003 0.5418 1056 1964 92 1056 1964 93 1055 1963 0.6394 1034 1923 90 1034 1922 91 1033 1921 0.7339 1014 1884 89 1013 1883 89 1013 1882 0.8254 995 1847 87 994 1846 88 994 1845 1.0000 957 1773 84 956 1773 85 954 1772
constant (b) of
b R' B ' b
MEK + Benzene 1825 85 1819 85 1814 85 1810 85 1807 85 1801 85 1795 85 1790 85 1773 85
Mole fraction of MEK
Figure 3.7 Rao's constant vs mole fraction of MEK in binary liquid mixtures at 30°c
10 0 0 0 2 0 4 06 OX 10
Mole fiaction of MEK
Figure 3.8 Wadas constant vs mole w o n of MEK in binaty liquid mixtures at 3 0 ' ~
0.0 0.2 0.4 0.6 0.8 1 .O
Mole fraction of MEK
Figure 3.9 Van der Waal's constant vs mole fraction of MEK in binary liquid mixtures at 3 0 ' ~
From table 3.3 it is clear that Rao's constant, Wada's constant and Van der
Waal's constants are independent of temperature and the variations of these
constants with mole fractions of MEK is linear. It was reported that in a binary
liquid mixture, a linear variation of Rao's constant and Wada's constant with
change in mole fraction of one component indicates the absence of complex
formation [54, 551. In the present case also there is no indication of complex
formation in any of the binary system. Tong et a/. [56] showed that Van der
16 Waal's constant b=-m 3~~ where NA is the Avogadro number and ro is the
3 0
molecular radius. Ernst and Glinski [57] reported that molecular radius is
independent of temperature. Present study (table 3.4) showed that Van der Waal's
constant is also independent of temperature.
Excess thermodynamic functions
The excess values of the velocity cE isentropic compressibility K , ~ ,
intermolecular free length ~f~ and specific acoustic impedance zE at different
temperatures are shown in table 3.5 and 3.6. The variation of these excess
functions with mole fraction of MEK at 3 0 ' ~ are shown in figures 3.10 - 3.13.
Table 3.5 Excess velocity (uE) and Excess isentropic compressibility (K:) of the binary mixtures at different temperatures
Mol fraction of
MEK X uE ( d s )
MEK + Nitrobenzene 0.00 0.00 0.00 0.00 16.08 16.85 14.56 -61.38 18.40 18.97 21.99 -64.75 23.58 23.20 26.22 -89.76 26.24 25.11 27.13 -96.61 23.62 26.01 23.83 -87.81 19.80 22.78 21.07 -66.31 15.48 18.16 13.76 -57.34 0.00 0.00 0.00 0.00
MEK + Bromobenzene 0.(H 0.00 0.00 14.16 10.65 -43.48 15.61 15.39 -56.30 19.87 20.32 -67.11 22.86 21.70 -66.12 22.39 21.43 -47.66 19.46 16.85 -65.34 16.27 11.16 -49.32 0.00 0.00 0.00
MEK + Chlorobenzene 0.00 0.00 0.00 10.29 8.17 -32.98 12.66 12.33 -39.04 14.56 15.73 -49.33 16.27 17.25 -44.07 16.68 15.98 -55.65 14.41 14.16 -43.80 9.30 6.52 -16.63 0.00 0.00 0.00
MEK + Toluene 0.00 0.00 0.00 8.77 5.81 -20.18 10.90 9.68 -26.97 13.21 12.21 -32.48 14.69 13.38 -34.85 14.54 13.32 -37.25 12.13 8.98 -35.31 7.23 5.49 -22.89 0.00 0.00 0.00
MEK + Benzene 0.00 0.00 0.00 4.96 2.90 -7.60 7.27 5.56 -14.83 9.92 7.79 -18.12 11.91 9.89 -18.63 12.08 9.38 -21.58 9.34 5.66 -17.63 4.34 3.57 -7.53 0.00 0.00 0.00
Table 3.6 Excess acoustic impedance (zE), excess intermolecular free length ( ~ f ~ ) of the binary mixtures at different temperatures
Mole fraction 30~C of MEK 4 0 ' ~
i (kg m2 st) MEK + Nitrohenzene
0.00 0.00 0.0000 30.91 29.68 -0.0199 38.56 35.67 -0.0238 40.14 42.16 -0.0268 38.65 39.76 -0.0284 30.14 31.28 -0.0244 33.01 31.29 -0.0167 24.15 20.73 -0.0149 0.00 0.00 0.0000
MEK + Bromobenzene 0.00 0.00 0.0000 29.65 28.75 -0.0138 35.03 32.49 -0.0175 43.15 42.62 -0.0207 27.92 25.95 -0.0196 32.14 30.51 -0.0208 25.46 25.48 -0.0194 15.89 14.71 -0.0142 0.00 0.00 0.0000
MEK + Chlorohenzene 0.00 0.00 0.0000 15.85 15.83 -0.0106 15.91 15.06 -0.0120 22.21 20.20 -0.0153 19.13 19.52 -0.0175 20.81 18.37 -0.0171 14.59 14.66 -0.0129 5.69 4.29 -0.0085 0.00 0.00 0.0000
MEK + Toluene 0.00 0.00 0.0000 12.98 14.52 -0.0064 13.70 13.37 -0.0086 19.10 22.00 -0.0103 20.57 21.63 -0.0110 20.43 17.77 -0.0119 18.10 18.25 -0.0112 13.92 11.53 -0.0072 0.00 0.00 0.0000
loa L: (m)
MEK + & 0.00 0.00 0.00 0.00 2.82 5.22 5.60 6.90 4.63 7.70 11.54 12.08 4.99 8.01 11.92 11.51 5.74 8.62 11.19 13.32 6.21 9.74 12.37 14.40 3.66 5.75 6.40 7.00 2.08 0.29 0.71 1.48 0.00 0.00 0.00 0.00
Mole fraction of MEK
Figure 3.10 Excess velocity vs mole fraction of MEK in binary liquid mixtures at 30°c
Figure 3.11
I 00 0.2 0.4 0.6 08 1.0
Mole fraction of MEK
Excess compressibility vs mole fraction of MEK in mixtures at 30'~
binary liquid
J 0.0 0.2 0.4 0.6 0.8 1 .o
Mole fraction of MEK
Figure3.12 Excess intermoliculm freelength vs mole fraction of MEK in binary liquid mixtures at 3 0 ' ~
Figure 3.13 Excess acoustic impedance vs mole fraction of MEK in binary liquid mixtures at 3 0 ' ~
The intermolecular interaction occurring in the liquid mixtures might result in the
decrease of the inter space between molecules and this might lead to a decrease in
intermolecular free length producing negative values of the excess intermolecular
freelength. The decrease of intermolecular free length result in a decrease of
compressibility and an increase of velocity. This produces negative values of
excess compressibility and positive values of excess velocity in the binary
mixtures. As a result the graph of the variation of excess compressibility with
mole fiaction of MEK must show the same trend as that of the excess
intermolecular free length (figures 3.1 1 and 3.12) and excess velocity graph
(figure 3.10) must show the reverse trend as that of the excess compressibility
It was shown earlier (Section 3.3.4) that specific acoustic impedance and
adiabatic compressibility exhibit opposite trend. A similar trend is expected in the
corresponding excess functions also. An analysis of figures 3.1 1 and 3.13 shows
that the excess specific acoustic impedance and excess compressibility are
exhibiting opposite behaviour. These results point out the fact that the variation of
excess velocity and excess specific acoustic impedance must show a reverse trend
as that of the excess intermolecular free length and excess compressibility versus
mole fraction of MEK which is obtained the present study.
From table 3.5 it may be noted that the values of excess compressibility
becomes more negative with increase of temperature. The values of the excess
intermolecular free length also became more negative with increase of
temperature. These observations in conjunction with Fort and Moore's [58] result
that the values of excess compressibility should become increasingly negative as
the strength of interaction between unlike molecules increase, indicates that the
strength of interaction between unlike molecules in the present study increases
with temperature in all the binary mixtures.
According to Fort and Moore [58] a negative excess compressibility is an
indication of strong hetromolecular interaction in the liquid mixtures which is
attributable to charge transfer, dipole-dipole, dipole-induced dipole interactions,
and hydrogen bonding between unlike components, while a positive sign indicates
weak interaction and is attributed to dispersion forces (London forces), which are
likely to be operative in every cases. The magnitude of the contributions made by
these different types of interactions will very with the components and
composition of the mixture. In the present study, the excess compressibility is
negative in all the binary mixtures. This observation together with Fort and
Moore's result suggests the existence of strong intermolecular interactions in all
the mixtures.
The structure and dipole moment of the liquids chosen for the present
study are given below
Dipole Name Chemical Formula Structure moment
(Debey) 1 Methyl Ethyl CH3CH2COCH3 0 Ketone II 2.75
H3C-C-CH2-CH3
2 Nitrobenzene
3 Chlorobenze
4 Bromobenzene C6H5Br 1.70
5 Toluene C6H5CH3
0.45
6 Benzene
Comparing the dipole moments of the above five liquids, toluene and
benzene can be considered as non-polar in nature and the rest of the four liquids
are polar. The binary mixtures chosen are of polar + polar and polar + non-polar
type. The common component in the present five binary mixtures is methyl ethyl
ketone, which is polar in nature. In the carbonyl group of methyl ethyl ketone, the
carbon atom and the more electronegative oxygen atom are joined together by
o bond. Due to inductive effect in the o bond joining the two atoms, the more
readily polarisable n electrons are shifted more towards oxygen atom. Hence its
structure can be best represented as [59] shown below.
Consider the system methyl ethyl ketone + nitrobenzene which is polar +
polar in nature. Due to the electron withdrawing nature of NO2 group in
nitrobenzene a slight positive charge is developed in the benzene ring which can
interact with oxygen of methyl ethyl ketone hence a sort of dipole induced dipole
interaction will result.
It is possible that there is a dipoldipole interaction existing in this
mixture between the carbonyl group (-C=O) of MEK and NO2 group of
nitrobenzene as shown below.
Both dipole-dipole and dipoleincluded dipole interactions are considered
to be strong [58].
In MEK + bromobenzene and MEK + chlorobenzene systems, which are
polar + polar in nature, due to resonance effect a slight positive charge is
developed in the C1 atom of cholrobenzene and Br atom of bromobenzene. These
positive charges interact with carbonyl group of methyelthyl ketone resulting in a
dipole-dipole interaction. Which is considered to be strong. This interaction is
shown below
Consider the case of Methyl ethyl ketone + toluene binary system. Toluene
is a non-polar aprotic solvent, and solvents that fall in the nonpolar aprotic class are
not effective in stabilising the development of charge separation. In toluene molecules,
there is a possibility of interaction between the o and n electrons. In the valance band
theory a special type of resonance called hyperconjugation is used to describe such
interactions [59]. In valance bond language "no bond" resonance structure are
introduced to indicate this electronic interaction as shown below.
Due to this resonance, the negative charge on the methylene group of
toluene molecule is stabilised so that hydrogen atom has a positive charge. Thus
in methyl ethyl ketone + toluene mixtures there may be an interaction between the
hydrogen atom of toluene molecule with the oxygen atom of methyl ethyl ketone,
as shown below, which is expected to be strong.
In methyl ethyl ketone + benzene system which is a polar + non polar
mixture, there is an interaction of TC electron of benzene with carbon atom in
carbonyil group of methyl ethyl ketone, which is a sort of strong interaction
shown below
In the above fow binary systems with methyl ethyl ketone as a common
compound, nitrobenzene has the largest dipole moment and hence methyl ethyl
ketone + nitrobenze should have the greatest molecular interaction. Thus
molecules with large value of dipole moment interact strongly and the magnitude
of interaction in the present study is in the order nitrobenzene < bromobenzene
< chlorobenzene < toluene < benzene with methyl ethyl ketone. The graphical
representation of the excess compressibility at a particular temperature (figure 3.11)
supports this observation that MEK + nitrobenzene have the largest and MEK +
benzene has the least negative values of excess compressibility.
It was reported [60j that positive values of excess enthalpy and negative
values of excess internal pressure and viscosity indicate the absence of complex
formation in binary liquid mixtures. Representative plots of the excess value of
internal pressure, enthalpy and viscosity against mole fraction of methyl ethyl
ketone at a given temperature are shown in figures 3.14 -3.16, which show that
there is no indication of complex formation in the present five binary systems.
Mole fraction of MEK
Figure 3.14 Excess internal pressure vs mole fraction of MEK in binary liquid mixtures at 3 0 ' ~
Mole fraction of MEK
Figure 3.15 Excess enthalpy vs mole fraction of MEK in binary liquid mixtures at 30°c
""E l 4 MEK+C,H,NO, --t MEK+C,H,Br
6.16 A MEK+C.H.CI
Mole fraction of MEK
Figure 3.16 Excess viscosity vs mole fraction of MEK in binary liquid mixtures at 30°c
Reddy et al. [61] reported that positive values of excess velocity and
negative values of excess compressibility are attributable to molecular association
and complex formation where as negative values of excess velocity and positive
values of excess compressibility are attributable to molecular dissociation. In the
present study excess compressibility values are negative and excess velocity
values are positive which indicates molecular association or complex formation.
However the results obtained from the studies of excess internal pressure, excess
viscosity and excess enthalpy, Rao's constant and Wada's constant shows that
cotnplex formation is not present in the mixtures. Thus there exists interaction due
to dipole-dipole and hyper conjugation that lead to molecular association in the
binary mixtures.
3.5 Conclusion
Ultrasonic velocity, density and viscosity were measured in binary
mixtures of nitrobenzene, chlorobenzene, bromobenzene, toluene and benzene
with methyl ethyl ketone as a common component, at four different temperatures.
Various thennoacoustical parameters and excess thermodynamical functions were
evaluated. An analysis of these results suggests the presence of strong
intermolecular interactions resulting from dipole-dipole interactions and
hyperconjugation in all the binary mixtures.
It was found that the intermolecular interaction is very strong in MEK-
nitrobenzene system and weak in MEK-benzene system. The study of
temperature variation of excess thermo dynamical functions of the binary
mixtures indicates that the strength of intermolecular interactions increases with
temperature. Rao's constant, Wada's constant and Van der Wall's constant were
found to be independent of temperature. The study of excess velocity, excess
specific acoustic impedance, excess enthalpy and excess Gibb's free energy
showed that there is no complex formation in the binary liquid systems studied.
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