Ultrasonic velocity and density measurements have been undertaken for a number of binary liquid mixtures involving different commercial solvent extractants, LIX reagents. The binary mixtures under investigation have been classified under two categories such as polarpolar, and polarnonpolar types. Different theories and relations such as Schaaff’s Collision Factor Theory (CFT), Nomoto’s relation (NOM), and Van Dael & Vangeel ideal mixing relation (IMR) have been used to evaluate the velocity theoretically for all these binary systems. The relative merits of aforementioned theories and relations compared to experimental values of velocity have been discussed in terms of percentage variations. However, the CFT and Nomoto’s relation show better agreement with the experimental findings than the ideal mixing relation for all the systems under investigation.
INTRODUCTION
Theoretical evaluation of sound velocity in liquids has been investigated by many workers employing various Factors. Schaaffs,
1
,
2
on the basis of collision factor theory (CFT), developed a relation for the evaluation of sound velocity in pure liquids. The theory was extended to binary liquid mixtures by NutschKuhnkies,
3
Sheshadri et al..
4
,
5
Basing on the assumption of linearity of molar sound velocity, Nomoto
6
established an empirical formula for sound velocity in binary mixtures and Bhimsenachar et al.
7
computed the ultrasonic velocity using this relation. Besides, Van Dael and Vangeel
8
established ideal mixing relation (IMR) for evaluating sound velocity. Review of literatures
9

17
shows that many successful attempts have been made to compute ultrasonic velocity for quite a number of binary liquid systems employing the aforesaid relations. But, however, the binary mixtures involving commercial extractants are scarce in literature.
Commercially available LIX reagents are the substituted acetophenone oximes
18
,
19
and are widely used as extractants for the extraction of nuclear strategic metals like uranium and thorium.
20
Besides, TBP is also used as an effective extractant for the separation and isolation of plutonium and uranium from the fission products and other nuclides. In the chemical processing of nuclear fuels (PUREX process) and with suitable diluents and modifiers, TBP has shown its utility for the extraction of various metal ions.
21
All these binary systems can effectively be employed as the organic phase of solvent extraction during the extraction of various metals. In the present study, special efforts have been made to evaluate the sound velocity in different binary liquid mixtures involving commercial solvent extractants and diluents. Commercially available LIX reagents (Liquid Ion Exchanger) such as LIX 84, LIX 622, LIX 860 and LIX 980 have been taken with amyl alcohol, TBP and benzene for investigation at 303.15 K temperature. The binary mixtures of different LIX reagents with amyl alcohol and trinbutyl phosphate (TBP) fall under polarpolar category whereas LIX reagents with benzene come under the category polar  nonpolar type. The theoretical values of sound velocity have been compared with the experimental values and the deviations in values may indicate the existence of molecular interactions.
EXPERIMENTAL
The LIX reagents were supplied by Henkel Corporation, Ireland and were used as received. TBP (SRL), benzene and amyl alcohol (Merk), analytical reagent grade (AR) were used. The solutions were prepared on percentage basis (v/v) by dissolving known volumes of LIX reagents in appropriate volumes of benzene, amyl alcohol and TBP, and measuring their masses on MetlerToledo AB 54 electronic balance.
The densities of all the mixture solutions were measured by a bicapillary pyknometer calibrated with deionised double distilled water with 0.996×10
^{3}
kg m
^{3}
as its density at 303.15K. The precision of density measurement was within ±0.0003 kg m
^{3}
. The ultrasonic velocity of the mixtures as well as of the pure ones were measured at 303.15K by a single crystal variable path ultrasonic interferometer operating at 5 MHz frequency supplied by Mittal Enterprise, N. Delhi. The temperature of the solution was maintained constant within ±0.01K by circulation of water from thermostatically regulated water bath through the waterjacketed cell. The velocity measurement was precise up to ±0.5 ms
^{1}
.
RESULTS AND DISCUSSIONS
The theoretical values of ultrasonic velocity in the present binary mixtures were calculated using Schaaff’s collision factor theory (CFT), Nomoto’s relation (NOM), and Van Dael and Vangeel ideal mixing relation (IMR) by the following expressions:
Here
S
_{1}
,
S
_{2}
and
B
_{1}
,
B
_{2}
are the respective collision factors and geometrical volumes of the molecules per mole of components 1 & 2 having mole fractions
x
_{1}
&
x
_{2}
.
U_{∞}
is taken to be 1600 ms
^{1}
. Geometrical volume B can be obtained by using the equation.
12
where
N
is the Avogadro’s number and
r
is the molecular radius.
where
R
_{1}
,
R
_{2}
and
V
_{1}
,
V
_{2}
are the molar sound velocity and molar volume of component 1 and 2, respectively
where
M
_{1}
,
M
_{2}
are the molecular masses of corresponding components. Various parameters like geometrical volume, molecular radius, etc. have been calculated from the measured values of density and ultrasonic velocity for pure liquids and which are in turn employed to find collision factor of liquid mixtures to evaluate sound velocities using collision factor theory. Experimentally observed ultrasonic velocity,
U_{EXP}
and theoretically computed values obtained from the aforesaid relations,
U_{CFT}
,
U_{NOM}
,
U_{IMR}
along with their percentage variations from the experimental velocity have been summarised in
1
to
3
. Comparison of experimentally observed ultrasonic velocities with those obtained theoretically in all the above binary systems have been displayed graphically [
1

12
].
A close perusal of
1
for the velocities of different LIX reagents with amyl alcohol indicate that Nomoto’s relation, with minimum percentage variations fits the experimental data well, followed by collision factor theory and then by ideal mixing relation, which is found to show the maximum variations from the experimental values. In the binary mixtures of LIX reagents with TBP and with benzene [in
2
&
3
], both Nomoto’s relation as well as CFT are almost equally suited with the experimental results well followed by the ideal mixing relation showing maximum percentage variations. But, however, the percentage difference obtained in
U_{IMR}
for these binary systems are comparatively low to those obtained for LIX reagents with amyl alcohol.
From Figures, it reveals that the experimental velocities are in a regular increase with the concentrations for all the systems under investigation. Both
U_{CFT}
and
U_{NOM}
values show approximately similar trends with
U_{EXP}
data, whereas those for
U_{IMR}
decrease first with concentration and then increase giving minima at around 0.30.5 mole fraction for all the binary systems, which indicates that Nomoto’s relation and collision factor theory are quite satisfactory and seem to be equally good in predicting the experimental data, rather there is not any remarkable deviation between the experimental velocity values and those calculated from both the theories. But, however, the ideal mixing relation is on the other hand shown to deviate more from the experimental findings than the aforesaid two theories for all the systems. The limitations and approximation incorporated in the ideal mixing theory is supposed to be responsible for such variations. According to the assumption for the formation of ideal mixing relation, the ratio of specific heats of the components is equal to the ratio of specific heats of ideal mixtures, indicating the equality in volumes.
17
This implies that no interaction should be entitled here. But, on mixing of components, specially polarpolar and nonpolarpolar types of components there is the probability of various types of forces like hydrogen bonding, dipoledipole, dipoleinduceddipole, dispersion forces, charge transfer etc. operating in them, which may result in violating the assumption. The deviations in the ideal mixing relation is therefore, supposed to indicate as the presence of intermolecular interaction in these binary mixtures and this interaction may result in treating the component molecules to be elastic spheres, which is, in fact the basic concept for collision factor theory, corroborated from the similar trends of
U_{CFT}
and
U_{EXP}
in all the Figures. On the other hand the ultrasonic velocities obtained from Nomoto’s relation are better fitted to the experimental values having minimum percentage of variations. Thus, the linearity of molar sound velocity as suggested by Nomoto
6
in deriving the empirical relation is rather more appropriate for the binary liquid mixtures studied.
Theoretical values of ultrasonic velocities calculated from CFT(UCFT), Nomoto’s (UNOM) and Van Dael & Vangeel’s ideal mixing relation (UIMR) along with experimental values of ultrasonic velocity (UEXP) and percentage difference for the binary liquid systems
Theoretical values of ultrasonic velocities calculated from CFT(U_{CFT}), Nomoto’s (U_{NOM}) and Van Dael & Vangeel’s ideal mixing relation (U_{IMR}) along with experimental values of ultrasonic velocity (U_{EXP}) and percentage difference for the binary liquid systems
Theoretical values of ultrasonic velocities calculated from CFT(UCFT), Nomoto’s (UNOM) and Van Dael & Vangeel’s ideal mixing relation (UIMR) along with experimental values of ultrasonic velocity (UEXP) and percentage difference for the binary liquid systems
Theoretical values of ultrasonic velocities calculated from CFT(U_{CFT}), Nomoto’s (U_{NOM}) and Van Dael & Vangeel’s ideal mixing relation (U_{IMR}) along with experimental values of ultrasonic velocity (U_{EXP}) and percentage difference for the binary liquid systems
Theoretical values of ultrasonic velocities calculated from CFT(UCFT), Nomoto’s (UNOM) and Van Dael & Vangeel’s ideal mixing relation (UIMR) along with experimental values of ultrasonic velocity (UEXP) and percentage difference for the binary liquid systems
Theoretical values of ultrasonic velocities calculated from CFT(U_{CFT}), Nomoto’s (U_{NOM}) and Van Dael & Vangeel’s ideal mixing relation (U_{IMR}) along with experimental values of ultrasonic velocity (U_{EXP}) and percentage difference for the binary liquid systems
Variation of ultrasonic velocities as a function of mole fraction of LIX 84 in the mixture LIX 84 + amyl alcohol [○EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as a function of mole fraction of LIX 622 in the mixture LIX 622 + amyl alcohol [○  EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as a function of mole fraction of LIX 984 in the mixture LIX 984 + amyl alcohol [○ EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as a function of mole fraction of LIX 860 in the mixture LIX 860 + amyl alcohol [○ EXP, □□ CFT, △△ NOM, ×× IMR]
Variation of ultrasonic velocities as a function of mole fraction of LIX 84 in the mixture LIX 84 + TBP [○ EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as a function of mole fraction of LIX 622 in the mixture LIX 622 + TBP [○ EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as a function of mole fraction of LIX 860 in the mixture LIX 860 + TBP [○ EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as a function of mole fraction of LIX 984 in the mixture LIX 984 + TBP [○ EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as afunction of mole fraction of LIX 84 in the mixture LIX 84 + benzene [○ EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as a function of mole fraction of LIX 622 in the mixture LIX 622+ benzene [○ EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as a function of mole fraction of LIX 860 in the mixture LIX 860 + benzene [○ EXP, □□ CFT, △△ NOM, ×× IMR].
Variation of ultrasonic velocities as a function of mole fraction of LIX 984 in the mixture LIX 984+ benzene [○ EXP, □□ CFT, △△ NOM, ×× IMR].
It is, however, concluded that there is intermolecular interaction present in all the binary mixtures under investigations and the interaction is supposed to be more in case of LIX reagents with amyl alcohol and benzene relative to TBP (%Variations of
U_{IMR}
from
1

3
). This investigation may further be extended by measuring other parameters like density, viscosity, refractive indices, surface tension etc., of these binary systems to study the type and strength of interactions present and accordingly it can be correlated with the extraction behaviours of these systems.
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