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Ultrasonic velocity (u) and density (ρ) has been measured for binary liquid mixture of Benzonitrile with Amyl alcohol at 298.15K, 303.15K, 308.15K over the entire range. Isentropic compressibility (βs), intermolecular free length (Lf), molar sound velocity (Rm), specific acoustic independence (Z) and molar volume (Vm) and their excess values has been calculated using experimental data of ultrasonic velocity and density. The variation of these properties helps us to understand the strength of intermolecular interaction in the liquid mixture.

The study of thermodynamic properties of binary liquid mixtures has proved to be a useful tool in elucidating the interactions that are operating between component molecules[2]. Excess thermodynamic functions, which depend on the composition, temperature, and pressure of the system, are of great importance to a chemical engineer in the design of industrial separation process and to a chemist for arriving at theories of liquid mixtures. The primary objective is to measure the speeds of sound and densities of liquid systems in order to estimate the value of isentropic compressibility, intermolecular free length and molar volume which in turn is widely used to study the molecular interactions through its excess value.

The physical and chemical properties of liquid mixtures are influenced by intermolecular forces[3-7]. Study of the ultrasonic velocity in liquids and liquid mixtures and its influence on the molecular structure was studied by several researchers [8-17]. Ultrasonic investigations of liquid mixtures consisting of polar and non-polar components enable us to understand the molecular interactions and structural behavior of molecules and their mixtures 18-20. Dipole-dipole, dipole–induced dipole, charge transfer interaction, and hydrogen bonding between unlike molecules are responsible for possessing negative excess values [21-23].

Experimental Details

The ultrasonic velocities is measured by using a single crystal ultrasonic interferometer (M/S Mittal Enterprises, New Delhi) operating at 2 MHz frequency with an accuracy of ±0.05% (Model F-81), which is calibrated with water and benzene.  The temperature stability is maintained within 0.1K by circulating thermostat water around interferometer cell that contains the liquid with a circulating pump. In order to minimize the error of measurements several maxima of ultrasonic velocity are allowed to pass and their number n is counted. All maxima are recorded with highest swing of the needle on the micrometer scale of the interferometer.  The total distance d moved by the reflector of the interferometer cell is given by

d = n λ/2 ----------------------------(1)

Where λ is wavelength of ultrasonic wave. The frequency ν of the interferometer crystal is accurately known (2 MHz) and using λ from eq 1, the ultrasonic velocity v m/s is calculated by the relation

v = ν λ------------------------------ (2)

Employing the measurement values of velocity (v) and density (ρ) some thermodynamic properties such as isentropic compressibility (βs), intermolecular free length (L_f) and molar volume (V_m) have been computed through the following expressions[24-25]. 

Molar volume                     ...… (1)                      

V_m = [M^-/e]

Isentropic compressibility               …… (2)                      

βs = 1/V²ρ

Intermolecular free length              …… (3)

Lf = [K √β_s]

High purity chemicals (E. Merck and S.D. fine) are used and purified by the standard methods[26].

Excess values of various parameters are computed using the following relation: -

A^E = (A) exp – (X₁A₁ + X₂A₂) where A^E is excess function (A) exp is experimental value of the mixture, A₁ and A₂ are the values for the pure components 1 and 2 whose mole fractions are X₁ and X₂.

The results obtained from these investigations have been incorporated in Table (1-3) and in Graph (1-4).

The measured values of ultrasonic velocity (u), density (ρ) and computed values of molar volume (Vm), excess molar volume (V_m^E), isentropic compressibility (β_s), excess isentropic compressibility(β_s^E), intermolecular free length (L_f), excess value of intermolecular free length (L_f^E) for the binary liquid mixture of Benzonitrile with Amyl alcohol at different temperature are presented in table 1,2 and 3.

The variation of ultrasonic velocity, excess isentropic compressibility(β_s^E), excess value of intermolecular free length (L_f^E) and excess molar volume (V_m^E) are shown in figure 1,2,3 and 4.

Table 1‒Experimentally determined ultrasonic velocity, density, calculated excess values of isentropic compressibility, intermolecular free length and molar volume for Benzonitrile with Amyl alcohol at 298.15K

Mole fraction X1	Ultrasonic velocity (u) ms-1	Density (ρ) gml-1	Excess isentropic Compressibility (BSE) cm2 dyne-1 X1012	Excess intermolecular freelength (LfE) Ao	Excess molar volume (VmE) ml mole-1
1.0000	1416	1.0012	0.0000	0.0000	0.0000
0.9048	1400	0.9844	-0.5478	-0.0013	-0.2377
0.8086	1386	0.9674	-1.1562	-0.0030	-0.4649
0.7113	1374	0.9509	-1.8866	-0.0054	-0.7572
0.6129	1360	0.9324	-2.2453	-0.0064	-0.8396
0.5136	1346	0.9140	-2.5159	-0.0072	-0.9376
0.4131	1334	0.8949	-2.8164	-0.0083	-0.9580
0.3115	1320	0.8755	-2.7601	-0.0082	-0.8947
0.2088	1304	0.8546	-2.2928	-0.0068	-0.7400
0.1050	1288	0.8335	-1.5815	-0.0048	-0.4982
0.0000	1268	0.8106	0.0000	0.0000	0.0000

Table 2‒Experimentally determined ultrasonic velocity, density, calculated excess values of isentropic compressibility, intermolecular free length and molar volume for Benzonitrile with Amyl alcohol at 303.15K

Mole fraction X1	Ultrasonic velocity (u)  ms-1	Density (ρ) gml-1	Excess isentropic Compressibility (BSE) cm2 dyne-1 X1012	Excess intermolecular freelength (LfE) Ao	Excess molar volume (VmE) ml mole-1
1.0000	1400	0.8864	0.0000	0.0000	0.0000
0.9047	1388	0.9804	-0.8159	-0.0025	-0.3088
0.8084	1376	0.9649	-1.6051	-0.0050	-0.6850
0.7111	1362	0.9476	-2.0636	-0.0062	-0.8799
0.6128	1352	0.9292	-2.7132	-0.0083	-0.9601
0.5134	1338	0.9114	-2.9662	-0.0090	-1.1135
0.4129	1326	0.8922	-3.2034	-0.0099	-1.1089
0.3113	1312	0.8728	-3.1120	-0.0096	-1.0793
0.2087	1296	0.8525	-2.5872	-0.0080	-0.9350
0.1049	1284	0.8313	-2.2446	-0.0073	-0.6649
0.0000	1260	0.8073	0.0000	-0.0000	0.0000

Table 3‒Experimentally determined ultrasonic velocity, density, calculated excess values of isentropic compressibility, intermolecular free length and molar volume for Benzonitrile with Amyl alcohol at 308.15K

Mole fraction X1	Ultrasonic velocity (u)  ms-1	Density (ρ) gml-1	Excess isentropic Compressibility (BSE) cm2 dyne-1 X1012	Excess intermolecular freelength (LfE) Ao	Excess molar volume (VmE) ml mole-1
1.0000	1382	0.9918	0.0000	0.0000	0.0000
0.9047	1374	0.9771	-1.1614	-0.0040	-0.4386
0.8084	1362	0.9621	-1.9502	-0.0046	-0.8627
0.7111	1352	0.9452	-2.7376	-0.0090	-1.0951
0.6127	1340	0.9266	-3.1775	-0.0102	-1.1459
0.5133	1328	0.9090	-3.5939	-0.0115	-1.3152
0.4129	1316	0.8897	-3.7943	-0.0122	-1.2906
0.3113	1304	0.8708	-3.9103	-0.0127	-1.3134
0.2087	1290	0.8515	-3.6526	-0.0120	-1.2867
0.1050	1274	0.8299	-2.7962	-0.0093	-0.9594
0.0000	1248	0.8038	0.0000	0.0000	0.0000

In the present study, the data of Ultrasonic velocity, density, and related thermodynamic parameters with their excess values suggest the existence of a strong intermolecular interaction. The negative values indicate a strong intermolecular interaction in the component of a binary liquid mixture of Benzonitrile with Amyl alcohol over the entire range.

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