Theoretical evaluation of internal pressure in ternary and sub-binary liquid mixtures at various temperatures

The Internal pressures of Ternary and their sub-Binary liquid mixtures of benzene(1) + hexane(2) + sec-butyl alcohol(3) were calculated using density, velocity and molar refraction from the temperature range of 303.15K-318.15K. For the Binary liquid mixtures, the Experimental Internal pressure values were correlated through an equation proposed by Andiappan et.al. For the Ternary liquid mixture, the Experimental Internal pressure values were correlated through an equation proposed by us. The Experimental values and the Theoretical values are in close agreement with each other


INTRODUCTION
The Internal pressure is the cohesive force, which is a resultant of forces of attraction and forces of repulsion between molecules in a liquid, and considerable importance can be gained by simply observing and comparing internal pressure-volume curves for pure liquids 1 .The term a/v 2 in Vander waals 2 equation being the measure of attractive force of the molecule is called the cohesive or internal pressure. The intermolecular forces give a liquid its cohesion and it creates a pressure of thousand to ten thousands atmospheres within a liquid. Cohesion creates a pressure within a liquid of between 10 3 to 10 4 atmospheres. The internal pressure thus depends markedly on the molar volume, and also on the external pressure. It should be emphasized that the internal pressure is also sensitive to the repulsive component in a liquid 3 .
Non-polar liquids have low internal pressures of the order of 2000 to 3000 atm; polar liquids have somewhat larger values, hydrogen bonding still increasing the value, water having a value around twenty thousand atmospheres 3,4 . The importance of internal pressure in understanding the properties of liquids and the full potential of internal pressure as a structural probe did become apparent with the Pioneering work of Hildebrand 5,6 . In an  Dack 7 reviewed the importance of solvent internal pressure and cohesion to solution phenomena. The internal pressure is a single factor which varies due to all type of solvent-solute, solute-solute and solvent-solvent interactions.The Various thermodynamic properties and molecular interactions involving self-associated alcohols and phenols helps in understanding the inter and intramolecular interactions.
Stavely et al 8 compared the internal pressure of individual liquid components and predicted the interaction in liquid mixtures. Richards 9 pointed out the importance of internal pressure in understanding the physical properties of liquids and solids. An extensive list of values of internal pressure for liquids has been given by Allen et al 10 .

MATERIALS AND METHODS
The chemicals used in the present work are Analar grade and purified by the standard methods 11 . The purity of samples are checked out by measuring their density, boiling point and refractive index ( Table 1.). Ultrasonic velocities of pure liquids and liquid mixtures from the temperature range of 308K to 318K were measured using Ultrasonic Interferometer operating at 3 MHz. The density was determined at the experimental temperatures using 10 ml capacity specific gravity bottle immersed in a thermostatic bath (accuracy + 0.01 °C). The volume of the bottle at the experimental temperature, viz. 308K-318K was ascertained using doubly distilled water.
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THEORY AND CALCULATION
Srivastava and Berkowitz Equation 12 equation was used to compute internal pressure from the measurement of ultrasonic velocity, density and refractive index.

Srivastava and Berkowitz Equation is
i Where U 12 =Ultrasonic velocity of the binary mixture  Evaluation of Rm: Where x 1 and π 1 are the mole fraction and internal pressure of the component 1 and x 2 and π 2 are the mole fraction and internal pressure of the component 2. The equation (4) containing only one constant β, has been employed for correlating the experimental data.
The experimentally determined internal pressure data for all the three binary systems have been correlated through equation (4) at temperatures 303.15K to 318.15K (Table 3). Constant β has been determined through a least square method at all the temperatures. Srivastava and Berkowitz equation for the Ternary liquid mixture is written as In the present work, the equation (4) for ternary system is modified as The constants β 12 , β 23 and β 31 are determined from equation (4) using least square method. Constant C has been determined through a least square method at all the temperatures.

RESULTS AND DISCUSSION
For the Ternary and sub-binary systems, the internal pressure values are evaluated from the temperature range of 303.15K to 318.15K. These values are correlated through equations (4) and (6) is shown in Tables (2 & 3).  Both the Experimental and Theoretical Internal pressure values are represented in the tables (2 & 3). It is known from the tables that both the experimental and the theoretical internal pressure values are more comparable with each other. By using least square method, the Interaction constants (β) and (C) are evaluated from the temperature range of 303.15K to 318.15K. The absolute average deviation between the experimental and correlated Internal Pressure values for all the binary systems varies from 0.17% to 0.38%. The Interaction constant (β) evaluated for all the binary systems varies from 0.02 to 0.08.

Experimental and Calculated Internal pressures(in atm) for the system benzene(1) + hexane(2) + sec-butyl alcohol(3)
It is known from the tables (2) & (3) that the increase in internal pressure values with increase of alcohol concentration is probably due to Hydrogen bonding. Since alcohols are strongly self-associated liquid having a three dimensional network of Hydrogen bond 14 . So it is apparent that when two interacting molecules are having some sort of attractive forces like that of hydrogen bonding should result in increase of internal pressure 15 . The hydrogen bonding arises from short range interaction augmented by the fact that Hydrogen bond distance (A-H--B) is greater than Vander Waals radii. The short range forces arise when the molecules come close enough together causing a significant overlap of electron clouds and are often highly directional 16 .
The non-linear relationship is more obvious for sec-butyl alcohol and benzene. This may be due to the interaction of the delocalized π-bond electron cloud with the sec-butyl alcohol. Benzene is a non-polar and an inert aromatic solvent. The dissociation effect of benzene molecule prevents self-association in associated alcohol molecules. The π-electron cloud of benzene is responsible for the dissociation effect.
The Internal pressure varies with respect to the concentration and Temperature. This is shown in graph. Figures 1-3 shows a linear variation of internal pressure with the concentration for binary liquid mixtures from the temperature range of 303.15K to 318.15K.

Fig. 3.
From the Tables 2 & 3 it is known that the decrease in internal pressure values with increase of temperature is due to the decrease in cohesive forces. The reduction in internal pressure may be due to the loosening of cohesive forces leading to breaking the structure of the solute.

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When the temperature is increased, there is a tendency for the solute molecules to move away from each other, reducing the possibility for the interaction, which may further reduce the cohesive forces 17 . Due to weakening of intermolecular forces of attraction the internal pressure should fall. This is an important observation which we have made and which is to be expected theoretically also as cohesive forces between molecules becoming less with increasing temperature 18 . Figures (4-6) shows a linear variation of internal pressure with the reciprocal of temperature for binary liquid mixtures from the temperature range of 303.15K-313.15K. The absolute average deviation between the experimental and correlated values for the Ternary system varies from 0.98% to 1.37%.
The evaluated Interaction constant (C) for the Ternary system varies from 0.89 to 1.03.

Fig. 4.
The average absolute deviation for the Ternary system is greater than that for the sub-binary system. This may be due to the Interaction between the three components. Among the three components, one of the component is self associated alcohol (sec-butyl alcohol). While the other two components (benzene and hexane) which are non-polar in nature.
Hexane is a non-polar chain molecule; only Vander Waals type interactions are present in hexane, while alcohol molecule is polar and associate strongly through hydrogen bonding. The alcohol molecule associate in inert hexane medium and form clusters. An associated molecular cluster in a liquid may be called as a quasi-molecule or a pseudo molecule 19 . While with benzene, π-bond interaction takes place with alcohol.
Due to these strong interactions among the components in a ternary liquid mixture, the interaction constant values for the Ternary liquid mixture increases than that of the 92 ILCPA Volume 4 Binary liquid mixtures. This increase in Interaction constant values leads to increase in absolute average deviation for the Ternary system than that of the Binary system.

CONCLUSION
It is evident from the present work, that  The absolute average deviation between the experimental and correlated values for the Binary system and Ternary system varies from 0.17% to 1.37% indicating the applicability of equations (4) and (5).  Internal pressure and their use in the study of molecular interactions.  The character of association of alcohols makes the study of interactions particularly interest.  The cohesive forces are of primary importance.