Thermodynamic and interaction studies of binary liquid mixtures on the basis of Flory's statistical theory and empirical relations

Accepted Manuscript Thermodynamic and interaction studies of binary liquid mixtures on the basis of Flory's statistical theory and empirical relations

Vinay Sanguri, Rupali Sethi, Sunil, J.D. Pandey PII: DOI: Reference:

S0167-7322(18)32482-6 doi:10.1016/j.molliq.2018.09.039 MOLLIQ 9645

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

13 May 2018 19 August 2018 8 September 2018

Please cite this article as: Vinay Sanguri, Rupali Sethi, Sunil, J.D. Pandey , Thermodynamic and interaction studies of binary liquid mixtures on the basis of Flory's statistical theory and empirical relations. Molliq (2018), doi:10.1016/j.molliq.2018.09.039

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ACCEPTED MANUSCRIPT Thermodynamic and interaction studies of binary liquid mixtures on the basis of Flory’s statistical theory and empirical relations Vinay Sanguri1*, Rupali Sethi2, Sunil2, J. D. Pandey2 Department of Chemistry, S. P. M. Government Degree College, (University of Allahabad) Allahabad-211013, India

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1

2

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E-mail: [email protected]

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Department of Chemistry, University of Allahabad, Allahabad- 211002, India

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Abstract

A number of important and useful thermodynamic properties of seven binary liquid mixtures namely

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DPGDME + methanol, 1-propanol, 1-pentanol, 1-heptanol at 298.15K and oxolane + aniline, N-methyl aniline, N-ethyl aniline at 303.15K, 313.15K & 323.15K have been computed on the basis of the most

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widely accepted Flory’s statistical Theory (FST). The component DPGDME is basically dipropylene glycol

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dimethyl ether and oxolane known as tetrahydofuran are the key ethereal liquids with which the interactions of popular solvents are analyzed. Also, some thermodynamics properties of aforesaid mixtures were

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calculated from the recently proposed empirical correlations using density and ultrasonic velocity. The theoretical results are compared with the experimental findings yielding quite satisfactory agreement. The

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results are discussed in the light of interactions operating in the systems.

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Keywords: Thermodynamic properties, Binary mixtures, FST, empirical correlations, interactions.

1. Introduction

The key factor in determining the thermodynamic properties of any pure substance is the intermolecular forces viz. electrostatic forces, induction forces, chemical forces and dispersion forces prevalent between the molecules of a substance depending on the type of molecules in the vicinity of each other. The study of thermodynamic properties of mixture of pure components is intricate and cumbersome due to interaction between similar and dissimilar components which *Corresponding author. Tel.: +91-9415253608. E-mail address: [email protected] (V. Sanguri).

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ACCEPTED MANUSCRIPT causes innumerable minute variations for consideration. In a liquid mixture of two or more pure liquids, the intermolecular forces and the liquid structure are the key factors to express the properties of liquid mixtures. The properties of a mixture can be calculated from the properties of pure components [1-10]. The mixture of non-polar liquids, having complex structure, varying in

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size and shape can well be studied from its excess thermodynamic properties [11-12]. The most

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widely accepted Flory’s statistical theory (FST) has been successfully applied to evaluate various

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important thermodynamic properties of liquid mixtures due to its simplicity and validity [13-18]. It is best applicable to pure liquids, binary and multi-component liquid systems of metallic,

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molecular nature and ionic liquids [19-26]. During the recent past industrial and biological

velocity and density measurements.

Highly sophisticated instruments are employed to get

accurate results.

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importance of binary liquid mixtures has gained exceeding importance on the basis of ultrasonic

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Recently, accurately and precisely measured values of density (ρ) and ultrasonic velocity

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(u) of DPGDME (dipropylene glycol dimethyl ether) with 1-alkanols at 298.15K by Pal and Gaba [27] and the work of Oswal et al [28] on binary mixtures of oxolanes with aniline and substituted

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anilines at 303.15K, 313.15K and 323.15K has been an area of key interest to calculate the

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thermodynamic properties through our established relations of FST and empirical relations and its comparison with experimental values have been done so that more light can be thrown on the properties of binary mixtures and the system finds multifaceted industrial and biological applications. DPGDME [29] is a propylene based diether, a versatile and environmental friendly solvent, hygroscopic in nature. The system (ether + alcohol) has great relevance in industry as a

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ACCEPTED MANUSCRIPT water entrainer as they form an excellent azeotropic mixture thereby enhancing the solubility of the monomers. Ethers and alcohols are preferred solvents in chemical industry especially for acrylic paints as a binder and coalescing agent, electronic cleaner, in wood and furniture coating. They are a perfect solvent and the combination increases the octane rating of oil and petrol. The

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chemical structure of DPGDME reveals that it is an aprotic solvent (inert) as it does not have free

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hydroxyl groups that readily donate or accept protons (finds use in electro deposition coating) but

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its interaction with alcohols, a protic solvent with labile hydrogen is due to strong hydrogen bonds. As the size of the alkyl groups of alcohol increases (from –CH3 to –C7H15), the van der

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Waals interaction increases to a point where they can dominate the hydrogen bonding and thereby

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making the alcohols largely hydrophobic or lipophilic in nature.

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Oxolane (popularly Tetrahydrofuran, THF) [30], a cyclic ether with oxygen as hetero atom is an aprotic solvent with no labile hydrogen, moderately polar, water miscible, finds use in permeation

chromatography

for

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gel

dissolving

polymers,

in

reversed-phase

liquid

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chromatography, biofuels while amines have labile hydrogen atoms which forms strong hydrogen bonds with oxygen of oxolane. The donating tendency of hydrogen in amines depends on electron

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displacement effects viz. +I effect (inductive effect) and steric hindrance which in turns either

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enhances or diminishes the inductive effect residing on the molecule. In the present work we have calculated various important thermodynamic properties of binary mixtures [viz. dipropylene glycol dimethyl ether (DPGDME) + aliphatic primary alcohol and oxolane + aniline and N-substituted anilines] at different temperatures by using Flory’s statistical theory and with the help of empirical relations. The obtained theoretical results are compared with experimental findings.

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ACCEPTED MANUSCRIPT 2. Theoretical In recent past Flory’s statistical theory [13-26] has been applied for computing various thermodynamic and transport properties of liquids and solution. The equilibrium properties of a liquid are strongly dependent on what may be loosely called its local structure, often expressed in

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terms such as packing density, free volume or, more exactly, in terms of radial distribution

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function. Flory et al used a simple partition function proposed by Erying and Hirschfelder to get

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the reduced equation of state, which is based on van der Waals potential energy model. They assume that the intermolecular energy depends only on the volume.

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For computing various thermodynamic properties of ternary and binary liquid mixtures,

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~ ~ the required parameters V , V*, P*, T and T* of pure components can be obtained from the knowledge of   and V of pure components. Segment fraction  Ψ site fraction (θ) and reduced

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~ volume ( V ) of the mixture are calculated by the method described by earlier workers [19]. With the help

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of reduced volume of mixture various thermodynamic properties viz. thermal expansivity (α),

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density (ρ), isothermal compressibility (βT), internal pressure (Pi), heat capacity at constant pressure (CP), adiabatic compressibility (βS), ultrasonic velocity (u), heat capacity ratio (γ), heat

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capacity at constant volume (CV), Gruneisen parameter (Г) and non-linearity parameter (B/A) of binary mixtures (DPGDME + methanol, 1-propanol, 1-pentanol and 1-heptanol and oxolane +

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aniline, N-methyl aniline and N-ethyl aniline) have been calculated using Flory’s statistical theory at 298.15, 303.15K, 313.15Kand 323.15K with the help of Eqs. (1) to (11). The detailed methods for computing the aforesaid properties are given in our earlier papers [20-26].



3(V1/3  1) T (1  3(V 1/3  1))

(1)

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ACCEPTED MANUSCRIPT x1 M 1  x 2 M 2 ~ x1V1*  x 2V2* V



T 

(2)

TV 2 P*

(3)

T

T T

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Pi 



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

𝛼2 𝑇𝑉 𝐶𝑃

)

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𝛽𝑆 = 𝛽𝑇 − (

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CP  (x1CP,1  x 2 CP,2 )  C EP

1/ 2

CP



 1 T

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

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CV 

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T S

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

(5)

(6)

(7)

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 1   u    S 

(4)

(8)

(9)

(10)

General formulation for the non-linearity parameter in terms of the acoustical parameters of liquids has been made using the expression for the sound velocity (u), and introducing the contribution due to isobaric acoustic parameters (K) and the isothermal acoustic parameter (K). The expression for the calculation of B/A of mixture has been expressed as [31]

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ACCEPTED MANUSCRIPT B  2 K  2K " A

(11)

Computations of K and K require only the knowledge of thermal expansion coefficient, (. Detailed method of calculation is given in literature [32-33].

velocity,

thermal

expansion

coefficient,

isothermal

compressibility,

adiabatic

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sound

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We have also calculated different thermodynamic properties of mixtures (viz. density,

compressibility, internal pressure , heat capacity at constant pressure , heat capacity ratio, heat

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capacity at constant volume and pseudo Gruneisen parameter under the present investigation from the sound velocity and the density data on the basis of recently developed empirical relations for α

1.71X 103 T 4/9 u 2  4/3

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T 

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5715.36 X 104 MuT 11/9 CP  (17.1   2/3 )T 4/9 Pi  44.2 XT 4/3u 3/2 





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75.6 X 103 T 1/9u1/2  1/3

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  (0.0191X T )1/4 

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and βT in terms of u and ρ by the aid of the Eqs. (12) to (17).

(12)

(13)

(14)

(15)

1.71X 103 T 4/9  1/3

(16)

 1 T

(17)

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ACCEPTED MANUSCRIPT where u is in m sec-1 and  in g cm-3. These relations have been obtained on the dimensional basis and applied successfully to various class of organic liquids and solutions during recent years [3439]. Marcus highlighted these relations very recently in his review [40].

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3. Results and discussion

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The target of the most widely accepted Flory statistical theory here is to estimate a number

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of important and useful thermodynamic properties of dipropylene glycol dimethyl ether (DPGDME) + 1ο alcohols ( methanol, propanol, pentanol, heptanol) mixture at 298.15K and

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oxolane + amines (aniline, N-methyl aniline and N-ethyl aniline) over a wide range of

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compositions. An interesting application of this theory is to assess ultrasonic propagation parameters of such systems. The calculated properties include density (ρ), sound velocity (u),

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thermal expansion coefficient (α), isothermal compressibility (βT), adiabatic compressibility (βS),

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internal pressure (Pi), heat capacity at constant pressure (CP), heat capacity ratio (γ), heat capacity at constant volume (CV) and pseudo Gruneisen parameter (Г) and non-linearity parameter B/A.

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The theoretical results were compared with the experimental findings of recent paper of Pal and

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Gaba [27] and Oswal et al [28]. In another attempt we have also calculated thermal expansion coefficient (α) and isothermal compressibility (βT), internal pressure (Pi), heat capacity ratio (γ),

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Gruneisen parameter (Г) and heat capacity at constant pressure (CP), of binary liquid mixtures using recently proposed empirical Eqs. (12) to (17) respectively. The empirical relations are calculated from experimental ultrasonic velocity (u) and density (ρ) data in both the above systems. The results are found to be quite satisfactory.

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ACCEPTED MANUSCRIPT Table 1 enlists all the required parameters of pure components diproylene glycol dimethyl ether (DPGDME), methanol, 1-propanol, 1-pentanol, 1-heptanol at 298.15K and oxolane, aniline, N-methyl aniline, N-ethyl aniline at 303.15K, 313.15K and 323.15K. The necessary data needed, for the calculation, have been taken from different sources [27,28,41].The most widely accepted

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Flory’s statistical theory (FST) has been employed to evaluate theoretically density, ultrasonic

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velocity, thermal expansivity, isothermal compressibility, adiabatic compressibility, internal

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pressure, heat capacity at constant pressure, heat capacity ratio, heat capacity at constant volume, Grunisen parameter and non-linearity parameter B/A at 298.15K of binary system of DPGDME

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with methanol, 1-propanol, 1-pentanol and 1-heptanol respectively in Table 2. Table 3 lays its

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emphasis on percentage deviation of density, ultrasonic velocity and adiabatic compressibility, alongwith (APD) average percentage deviation values of binary system DPGDME and primary

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alcohols at 298.15K. Table 4 compiles the calculated values of α, βT, Pi, γ, Г and Cp through

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empirical relations of binary system (DPGDME + methanol, 1-propanol, 1-pentanol and 1-

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heptanol) at 298.15K.

The structure of DPGDME (commonly known as Purum), Bis (methoxypropyl) ether as

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obtained by the software ChemDraw Ultra 10.0 are represented in 2D and 3D form in Figure 1

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and Figure 2 respectively where red balls are the oxygen atoms, dark grey balls are the carbon atoms and light grey balls are the hydrogen atoms.

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ACCEPTED MANUSCRIPT O

T

O

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O

Figure 2:

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Figure 1:

Structure of DPGDME in 3D

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Structure of DPGDME in 2D

The interaction study of intermolecular hydrogen bond between, two similar electronegative

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atoms, oxygen atom of DPGDME and the oxygen atom of 10 alcohols (O……H……..O) viz. methanol, propanol, pentanol, heptanol has been clearly explained by 2D (Figure 3) and 3D

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(Figure 4) structures.

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O

O

H O

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O

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R

R

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H

O

O

H

R

Figure 3: Interaction of DPGDME+alkanols in 2D

Figure 4: Interaction of DPGDME+alkanols in 3D

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ACCEPTED MANUSCRIPT The values of ultrasonic velocity and density increase whereas βs decrease as the mole fraction of DPGDME increases in the binary mixture as calculated by FST and empirical relations as compared to experimental values computed in Table 3 which indicates as the mole fraction of DPGDME increases its bonding with alcohol molecules increases, leading to more compact and

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highly dense structure which is viscous in flow. Since βS is inversely proportional to density and

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ultrasonic velocity it decreases proportionally. In case of DPGDME and 10 alcohols (methanol,

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propanol, pentanol, heptanol) as the size of alkyl (R = -CH3, -C3H7, -C5H11, -C7H15) group increases the hydrogen bonding decreases which eventually decreases the dipole-dipole attraction.

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Thus density and ultrasonic velocity decreases on increasing numbers of alkyl (–CH2) group. The

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APD values of u, βS and ρ are in excellent agreement with the experimental values.

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Table 5 compiles the calculated values of ρ, u, α, βT, βS, Pi, γ, Г CV, Cp and B/A through FST of binary system (oxolane + aniline, N-methyl aniline and N-ethyl aniline) at 303.15K,

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313.15K and 323.15K. Table 6 lays its emphasis on percentage deviation of density (ρ), ultrasonic

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velocity (u) and adiabatic compressibility (βs), alongwith APD values of binary system (oxolane+ aniline, N-methyl aniline and N-ethyl aniline) at 303.15K, 313.15 and 323.15K. Table 7 compiles

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the calculated values of α, βT, Pi, γ, Г and Cp through empirical relations of binary system (oxolane

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+ aniline, N-methyl aniline and N-ethyl aniline) at 303.15K, 313.15K and 323.15K. The structure of oxolane in 2D and 3D are represented in Figure 5 and Figure 6 respectively where red balls indicate the oxygen atom, blue balls are the nitrogen atoms, pink balls are the alkyl groups –CH3, -C2H5. The interaction of oxolane with amines namely aniline, Nmethyl aniline, N-ethyl aniline is depicted diagrammatically in 2D and 3D form in Figure 7 and Figure 8.

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O Figure 6: Structure of oxolane in 3D

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Figure 5: Structure of oxolane in 2D

O H

R

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N

Figure 8: Interaction of oxolane + N-substituted aniline in 3D

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aniline in 2D

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Figure 7: Interaction of oxolane + N-substituted

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In the binary system of oxolane with aniline, N-methyl aniline and N-ethyl aniline the value of ultrasonic velocity and density, decreases whereas βs increases as the mole fraction of oxolane

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increases in the binary mixture as calculated by FST and empirical relations and compared to

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experimental values computed in Table 6. As the mole fraction of oxolane increases its binding with aniline and substituted anilines decreases making it less dense, lighter, less viscous, easy in flow. Since βs is inversely proportional to u and ρ thus correspondingly it increases. In addition in case of oxolane and amines (aniline, N-methyl aniline, N-ethyl aniline) the order of decreasing hydrogen bonding is aniline > N-methyl aniline > N-ethyl aniline. As the +I effect is maximum in

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ACCEPTED MANUSCRIPT N-ethyl aniline more electron pairs are available on nitrogen which decreases the polarity between hydrogen and oxygen atom of oxolane which results in δ-

δ+

δ-

diminished hydrogen bonding (N…..H….O) between oxolane and N-ethyl aniline. Similar is

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the case of N-methyl aniline while in case of aniline maximum hydrogen bond strength as no inductive effect is prevalent. The APD values are in excellent agreement with the experimental

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values hence prove that the desired parameter fit well in the proposed equations of FST and

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empirical relations. It is closely observed that with increasing temperature the value of u, ρ decreases while βS increases remarkably, indicates that rise in temperature leads to less

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interactions, increased bond length, more hydrogen bonding as expected in the aforesaid system.

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4. Conclusions

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As the average percentage deviation (APD) values is in quite good agreement keeping in view the various approximations and uncertainties in the experimental values FST gives quite satisfactory

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results for all the binary systems undertaken. The variation of other properties (α, βT, CP, Cv, Pi, ϒ

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and Г) with composition and temperature is highly satisfactory. The empirical relations 100% satisfy and support the experimental data in all the binary systems. The results have been

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confirmed and supported by diagrammatic illustrations of hydrogen bonding in two and three dimensional forms and inductive effect of alkyl groups between binary liquids which are in vicinity of each other. This work enhances the understanding and critical thinking in chemistry, throw light on the use of software to determine the structure and interaction relationship which is highly

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ACCEPTED MANUSCRIPT supported by data calculations of FST and empirical relations. This is a stepping stone in collaboration of liquid state, thermodynamic and software ChemDraw Ultra 10.0 and we will further incorporate softwares like SPSS 10.0 to make interpretation of interactions more strongly

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supportive.

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ACCEPTED MANUSCRIPT

Internal pressure

CP

Heat capacity at constant pressure

CV

Heat capacity at constant volume

CPE

Excess heat capacity at constant pressure

u

Ultrasonic velocity

V

Molar volume

V*

Characteristic Volume

𝑉̃

Reduced Volume

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Excess Volume

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VE

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Pi

T

Nomenclature

Temperature in Kelvin

𝑇̃

Reduced temperature

T*

Characteristic Temperature

P*

Characteristic Pressure

x1

Mole fraction of Component 1

x2

Mole fraction of Component 2

M1

Molecular weight of Component 1

M2

Molecular weight of Component 2

Vmix

Molar Volume of Mixture

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T

B/A Non-linearity parameter K

Isobaric acoustic parameter

Kʹʹ Isothermal acoustic parameter

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ACCEPTED MANUSCRIPT

Abbreviations Flory’s statistical theory

DPGDME

Dipropylene glycol dimethyl ether

THF

Tetrahydrofuran

T

FST

ρ

Density

βT

Isothermal compressibility

βs

Adiabatic compressibility

γ

Heat capacity ratio

Г

Gruneisen parameter

Ψ

Segment fraction



Site fraction

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Thermal expansivity

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α

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Greek letters

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ACCEPTED MANUSCRIPT References [1]

W. E. Acree Jr., J. Phys. Chem. 86 (1982) 1461-1465.

[2]

W. E. Acree Jr., Thermodynamic properties of non-electrolyte solutions. Academic Press, New York, 1984. G. L. Bertrand, W. E. Acree Jr., J. Phys. Chem. 83 (1979) 2355-2558.

[4]

E. L. Taylor, G. L. Bertrand, J. Solution Chem. 3 (1974) 479-491.

[5]

G. L. Bertrand, W. E. Acree Jr., T. E. Burchfield, J. Sol. Chem. 12 (1983) 327-346.

[6]

W. Brostow, J. S. Sochanski, J. Material Sci. 10 (1975) 2134-2145.

[7]

J. D. Pandey, T. Bhatt, R. L. Mishra, Acustica 38 (1977) 83-85.

[8]

J. D. Pandey, R. D. Rai, R. K. Shukla, J. Chem Soc. Faraday Trans.1 85 (1989) 331-341.

[9]

J. D. Pandey, A. K. Shukla, R. K. Shukla, R. D. Rai, J. Chem. Thermodyn. 21 (1989)125-

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[3]

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129.

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[10] P. P. Singh, V. K. Sharma, Can. J. Chem. 61 (1983) 2321-2328. [11] K. Arakawa, O. Kiyohara, Bull. Chem. Soc. Jpn. 43 (1970) 975-984.

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[12] J. S. Rowlinson, Liquids and Liquid Mixtures, second ed., Butterworth, London, 1969.

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[13] P. J. Flory, R. A. Orwoll, A. Vrij, J. Am. Chem. Soc. 86 (1964) 3507–3514. [14] P. J. Flory, J. Am. Chem. Soc. 87 (1965) 1833-1838.

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[15] A. Abe, P. J. Flory, J. Am. Chem. Soc. 87 (1965) 1838-1846. [16] V. A. Bloomfeld, R. K. Dewan, J. Phys. Chem. 75 (1971) 3113-3119. [17] R. K. Dewan, V. A. Bloomfeld, P. B. Berget, J. Phys. Chem. 75 (1971) 3120-3124. [18] J. D. Pandey, D. M. Alec David, J. Phys. Chem. 85 (1981) 3151-3152.

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ACCEPTED MANUSCRIPT [19] J. D. Pandey, N. Pant, J. Am. Chem. Soc. 104 (1982) 3299-3302. [20] J. D. Pandey, V. Sanguri, Phys. Chem. Liq. 46 (2008) 417-432. [21] J. D. Pandey, V. Sanguri, J. Chem. Research (S) (2001) 344-345. [22] V. Sanguri, Nidhi Singh, J. Ind. Chem. Soc. 88 (2011) 163-171.

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[23] J. D. Pandey, S. B. Tripathi, V. Sanguri, J. Mol. Liq. 100/2 (2002) 153-161.

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[24] J. D. Pandey, V. Sanguri, B. D. Bhatt, J. Chem. Research(S) (2003) 430-432.

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[25] R. Dey, N. K. Soni, R. K. Mishra, V. Sanguri, J. D. Pandey, J. Mol. Liq. 124 (2006) 102105.

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[26] Vinay Sanguri, Jyotsna Chhabra, A. K. Srivastava, J. D. Pandey, J. Mol. Liq. 206 (2015)

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300-308.

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[27] A. Pal, R. Gaba, J. Chem. Thermodyn. 40 (2008) 818-828.

508 (2010) 27-34.

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[28] S. L. Oswal, V. Pandiyan, B. Krishnakumar, P. Vasantharani, Thermochimica Acta 507-

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[29] M. Tejraj, Aminabhavi, H. T. S. Phayde, R. S. Khinnavar, B. Gopalakrishana, K.C. Hansen, J. Chem. Eng. Data 39(2) (1994) 251-260.

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[30] Muller, Herbet, THF, Ulmann’s Encylopedia of Industrial Chemistry, Weinhein WeileyVCH 2005. [31] B. K. Sharma, Pramana – J Phys, 37 (1991) 489-496. [32] J. D.Pandey, R. Dey, B. D. Bhatt, PhysChemComm., 5(6), (2002) 37-39. [33] J. D. Pandey, R. Dey , J. Chhabra, PhysChemComm 6(14), (2003), 55-58. [34] J. D. Pandey, R. Verma, Chem. Phys. 270 (2001) 429-438. [35] J. D. Pandey, R. Dey, M. Upadhaya, Acoustics Letters 21 (1997) 120-125. [36] J. D. Pandey, J. Chhabra, R. Dey, V. Sanguri, R. Verma, Pramana – J. Phys 55 (2000) 433-439.

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ACCEPTED MANUSCRIPT [37] J. D. Pandey, V. Sanguri, M. K. Yadav, A. Singh, Ind. J. Chem. 47A (2008) 1020-1025. [38] B. B. Nanda, Binita Nanda, P. C. Mohanty, J. Mol. Liq. 171 (2012) 50-53. [39] J. D. Pandey, A. K. Singh, Ranjan Dey, Ind. J. Chemical Technology 12 (2005) 588-592. [40] Y. Marcus, Chemical Reviews, 113 (2013) 6536-6551.

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[41] CRC Handbook of Chem. & Phys. seventy eighth ed., CRC Press, Boca Raton, New York,

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1997-98.

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ACCEPTED MANUSCRIPT Table 1:

~ Value of molar volume V, thermal expansivity α, reduced volume V , characteristic volume V*, reduced

~

temperature T , characteristic temperature T*, isothermal compressibility  T, characteristic pressure P*, density ρ, heat capacity at constant pressure CP and ultrasonic velocity u of pure components at different temperatures.

K-1

K

DPGDME

180.54 32

298. 15

1.0 50

1.25 79

143.53 11

0.05 85

5094. 04

96.2 3

Methanol

40.735 0

298. 15

1.2 01

1.28 75

31.638 4

0.06 27

4751. 61

1-propanol

75.156 4

298. 15

1.0 03

1.24 83

60.206 0

0.05 71

1-pentanol

108.69 28

298. 15

0.8 93

1.22 53

88.703 7

1-heptanol

141.90 62

298. 15

0.8 45

1.21 50

116.79 15

Oxolane

82.195 4

303. 15

1.2 48

83.152 7

313. 15

N-methyl aniline

~ T

T*

P* x 10-6 N m2

x 10-3/ kg m-3

514. 74

CP / J mol-1 K-1

u/ m s-1

0.898 6

303.08

1204. 97

470. 56

0.786 5

81.21

1102. 62

5222. 50

101. 63

458. 51

0.799 7

144.01

1206. 00

0.05 35

5577. 85

88.0 1

454. 21

0.811 0

208.40

1277. 00

0.05 17

5762. 80

80.4 4

462. 37

0.818 9

271.70

1327. 27

63.209 5

0.06 45

4702. 70

103. 31

619. 21

0.877 3

125.00

1255. 90

1.31 22

63.369 5

0.06 60

4745. 74

111. 30

614. 77

0.867 2

128.00

1211. 70

1.2 91

1.32 42

63.571 4

0.06 75

4788. 84

120. 03

609. 49

0.856 6

130.00

1170. 90

1.2 69

AN

M

ED

PT

1.30 04

US

126. 15

CE

Aniline

323. 15

AC

84.181 6

V* x 106/ m3 mol-1

T

K

Component

T x 1011/ m2 N-1

~ V

IP

T

x 103/

CR

Vx 106/ m3 mol-1

91.953 0

303. 15

0.8 51

1.21 94

75.407 6

0.05 25

5777. 41

48.4 2

792. 32

1.012 8

191.00

1615. 20

92.675 9

313. 15

0.8 58

1.22 71

75.525 4

0.05 37

5827. 54

50.7 4

797. 26

1.004 9

194.00

1582. 60

93.279 2

323. 15

0.8 66

1.23 50

75.530 9

0.05 50

5874. 56

52.7 3

809. 48

0.998 4

197.00

1558. 20

109.53 79

303. 15

0.8 16

1.21 17

90.399 3

0.05 12

5924. 14

53.1 2

683. 69

0.978 2

211.00

1548. 30

19

ACCEPTED MANUSCRIPT

0.8 22

1.21 90

90.637 1

0.05 24

5975. 83

56.0 0

682. 98

0.969 8

214.00

1512. 40

111.49 84

323. 15

0.8 30

1.22 67

90.889 3

0.05 37

6019. 73

59.0 7

683. 37

0.961 0

218.00

1477. 30

127.30 33

303. 15

0.8 85

1.22 68

103.76 84

0.05 37

5646. 27

60.1 7

671. 09

0.951 9

227.00

1497. 40

128.32 79

313. 15

0.8 93

1.23 48

103.92 29

0.05 50

5695. 15

63.4 6

671. 89

0.944 3

230.00

1462. 20

129.47 96

323. 15

0.9 02

1.24 31

104.15 86

0.05 63

5741. 31

66.8 3

674. 03

0.935 9

233.00

1430. 50

CE

PT

ED

M

AN

US

CR

IP

T

313. 15

AC

N-ethyl aniline

110.48 67

20

ACCEPTED MANUSCRIPT

S x 1011/

Pi x 106 /

 x 103 /

K-1

m2 N-1

m2 N-1

J mol-1 K-1

N m-2

kg m-3

86.32

284.62

96.86

286.89

98.68

110.31

290.38

97.15

117.39

292.29

95.05

127.61

93.27

136.90

297.44

91.32

148.05

300.19

89.30

160.88

303.16

87.92

170.57

305.25

86.46

181.93

307.54

85.22

192.41

309.52

84.20

201.87

311.19

82.65

217.84

313.80

82.01

225.05

314.90

80.95

238.13

316.77

CP /

DPGDME + methanol

u/



1.211 0 1.218 9 1.226 5 1.229 7 1.233 6 1.236 6 1.239 6 1.242 4 1.244 2 1.246 0 1.247 4 1.248 6 1.250 3 1.250 9 1.252 0

1100.8 4 1101.9 1 1108.1 2 1112.4 3 1119.1 6 1125.4 8 1133.0 2 1141.4 0 1147.4 4 1154.1 7 1160.0 4 1165.0 5 1172.9 2 1176.2 5 1181.9 6

Cv /

B/A

J mol-1 K-1

m s-1

US

0.795 3 0.810 3 0.825 3 0.831 8 0.840 0 0.846 4 0.853 0 0.859 5 0.863 8 0.868 3 0.872 0 0.875 0 0.879 4 0.881 3 0.884 3

AN

M 295.03

ED

103.7 6 101.6 4

PT

125.6 5 123.8 9 121.0 3 119.4 6 117.2 5 115.3 4 113.2 0 110.9 5 109.3 9 107.7 2 106.3 1 105.1 3 103.3 4 102.5 9 101.3 4

CE

1.20 0 1.19 2 1.17 9 1.17 1 1.16 0 1.15 1 1.14 0 1.12 8 1.12 0 1.11 1 1.10 4 1.09 7 1.08 8 1.08 4 1.07 7

AC

0.023 0 0.070 5 0.131 2 0.163 2 0.209 4 0.251 4 0.301 8 0.359 8 0.403 6 0.454 9 0.502 2 0.544 9 0.616 9 0.649 4 0.708 3



IP

T x 1011/

CR

x1

x 103/

T

Table 2: Calculated values of density ρ, ultrasonic velocity u, thermal expansivity α, isothermal compressibility T, adiabatic compressibility  S, internal pressure Pi, heat capacity at constant pressure CP, heat capacity ratio , heat capacity at constant volume CV, Grünisen parameter  and non-linearity parameter (B/A) of binary mixtures (DPGDME + methanol, 1-propanol, 1-pentanol, 1-heptanol) calculated through Flory theory at 298.15 K

0.590 0 0.616 0 0.644 6 0.657 9 0.675 3 0.689 6 0.705 0 0.720 6 0.731 2 0.742 5 0.752 0 0.759 8 0.771 7 0.776 6 0.784 9

71.28 79.46 89.93 95.46 103.44 110.71 119.44 129.49 137.10 146.01 154.24 161.68 174.23 179.91 190.21

7.32 6 7.33 1 7.33 5 7.33 7 7.33 9 7.34 1 7.34 2 7.34 3 7.34 4 7.34 5 7.34 5 7.34 6 7.34 7 7.34 7 7.34 7

21

80.15

248.73

318.18

99.41

79.31

261.05

319.72

98.70

78.71

270.47

320.82

97.90

78.04

281.83

322.08

97.43

77.64

288.89

322.83

97.22

77.47

292.17

323.16

86.05

154.49

296.31

85.91

161.47

297.78

85.70

167.27

299.03

85.16

178.03

84.61

187.14

303.36

84.25

192.67

304.55

0.886 5 0.888 9 0.890 6 0.892 4 0.893 5 0.894 0

1.252 7 1.253 5 1.254 0 1.254 6 1.254 9 1.255 0

0.812 3 0.819 7 0.825 4 0.834 9 0.842 0 0.846 1 0.849 5 0.855 2 0.861 2 0.865 1 0.868 7 0.873 7 0.876 3 0.880 0 0.883

1.191 4 1.197 0 1.201 3 1.208 5 1.214 0 1.217 1 1.219 8 1.224 2 1.228 8 1.231 9 1.234 6 1.238 5 1.240 5 1.243 4 1.245

AN

301.38

ED

PT

102.5 2 102.8 3 102.9 4 102.9 2 102.7 2 102.5 4 102.3 4 101.9 5 101.4 2 101.0 3 100.6 3 100.0 1

83.90

197.74

305.63

83.28

206.57

307.48

82.54

216.89

309.59

82.01

224.19

311.03

81.50

231.24

312.39

80.75

241.96

314.39

99.66

80.34

247.89

315.46

99.14 98.69

79.73 79.22

256.88 264.68

317.03 318.34

CE

1.01 9 1.02 7 1.03 2 1.04 0 1.04 5 1.04 7 1.04 9 1.05 1 1.05 3 1.05 4 1.05 4 1.05 5 1.05 4 1.05 4 1.05

AC

0.065 3 0.108 9 0.145 1 0.212 4 0.269 4 0.304 1 0.335 9 0.391 3 0.456 1 0.502 0 0.546 4 0.613 9 0.651 3 0.708 0 0.757

US

DPGDME + 1propanol

1186.2 9 1191.0 1 1194.4 1 1198.3 0 1200.6 0 1201.6 4

0.791 0 0.797 5 0.802 1 0.807 3 0.810 4 0.811 7

T

100.4 1

IP

1.07 2 1.06 6 1.06 2 1.05 8 1.05 5 1.05 4

CR

0.756 0 0.811 4 0.853 7 0.904 7 0.936 4 0.951 1

M

ACCEPTED MANUSCRIPT

1196.0 9 1191.6 8 1189.0 3 1185.9 4 1184.7 3 1184.4 6 1184.4 7 1184.9 6 1186.1 0 1187.2 0 1188.4 4 1190.5 6 1191.8 3 1193.8 4 1195.6

0.630 0 0.643 3 0.653 8 0.672 2 0.686 8 0.695 2 0.702 7 0.715 1 0.728 8 0.737 9 0.746 4 0.758 6 0.765 0 0.774 4 0.782

198.55 208.26 215.68 224.64 230.21 232.80

129.67 134.90 139.25 147.32 154.15 158.30 162.11 168.75 176.50 181.99 187.30 195.36 199.83 206.60 212.47

7.34 7 7.34 8 7.34 8 7.34 8 7.34 8 7.34 8

7.33 3 7.33 3 7.33 3 7.33 4 7.33 6 7.33 6 7.33 7 7.33 8 7.34 0 7.34 1 7.34 2 7.34 3 7.34 4 7.34 5 7.34

22

ACCEPTED MANUSCRIPT

78.69

273.01

319.70

97.88

78.33

278.69

320.61

97.35

77.75

288.34

322.09

96.91

77.28

296.38

323.28

96.76

77.13

299.07

323.67

94.62

82.04

209.78

283.00

95.24

82.28

212.65

284.37

96.27

82.61

218.46

287.16

96.92

82.73

223.05

289.36

97.57

82.74

229.04

97.80

82.70

231.74

293.49

98.16

82.54

237.05

295.98

98.35

82.36

241.18

297.91

7 1.248 1 1.249 6 1.252 0 1.254 0 1.254 6

0.812 8 0.816 4 0.823 4 0.828 7 0.835 2 0.838 1 0.843 5 0.847 6 0.850 5 0.853 0 0.857 5 0.861 6 0.863 9 0.869 4 0.873 2

1.153 4 1.157 4 1.165 4 1.171 5 1.179 3 1.182 6 1.189 1 1.194 0 1.197 6 1.200 6 1.206 3 1.211 3 1.214 3 1.221 2 1.226 1

AN

M 292.21

ED

PT

CE

0.89 8 0.90 8 0.92 7 0.94 1 0.95 6 0.96 3 0.97 4 0.98 3 0.98 8 0.99 3 1.00 1 1.00 8 1.01 2 1.02 0 1.02 5

98.45

82.20

244.23

299.32

98.51

82.05

246.88

300.53

98.57

81.71

251.92

302.83

98.56

81.37

256.56

304.91

98.53

81.14

259.36

306.15

98.40

80.58

265.97

309.05

98.25

80.13

270.86

311.16

AC

0.014 3 0.044 1 0.104 5 0.152 3 0.214 9 0.243 1 0.298 6 0.341 9 0.374 0 0.401 8 0.454 9 0.503 8 0.533 4 0.603 4 0.655 3

US

DPGDME + 1pentanol

6 1197.6 4 1199.0 2 1201.3 7 1203.3 4 1203.9 9

2 0.790 1 0.795 3 0.803 8 0.810 6 0.812 8

T

98.21

0 0.886 0 0.888 0 0.891 1 0.893 6 0.894 4

IP

4 1.05 3 1.05 3 1.05 2 1.05 1 1.05 0

CR

2 0.809 8 0.845 7 0.906 7 0.957 6 0.974 6

1224.6 3 1220.1 1 1212.5 1 1207.7 5 1202.9 1 1201.1 7 1198.4 3 1196.8 6 1195.9 7 1195.3 7 1194.6 2 1194.3 5 1194.3 5 1194.7 9 1195.4 6

0.572 8 0.581 3 0.598 4 0.611 7 0.628 7 0.636 3 0.651 0 0.662 3 0.670 6 0.677 7 0.691 1 0.703 2 0.710 4 0.727 3 0.739 5

218.74 223.02 230.29 236.36 238.38

181.88 183.72 187.45 190.39 194.23 195.95 199.34 201.98 203.93 205.62 208.84 211.80 213.58 217.80 220.91

5 7.34 6 7.34 7 7.34 7 7.34 8 7.34 8

7.36 2 7.35 8 7.35 1 7.34 7 7.34 4 7.34 2 7.34 1 7.34 0 7.33 9 7.33 9 7.33 9 7.33 9 7.33 9 7.34 0 7.34 1

23

ACCEPTED MANUSCRIPT

274.76

312.82

97.89

79.28

279.80

314.93

97.68

78.85

284.09

316.70

97.40

78.33

289.20

318.78

97.10

77.80

294.44

320.87

96.86

77.41

298.21

322.35

96.79

77.29

299.36

322.80

70.15

273.65

313.78

83.01

70.86

275.43

314.33

83.85

71.34

276.73

84.95

71.96

278.47

315.30

85.86

72.46

279.97

315.80

86.87

72.99

281.69

316.37

87.59

73.36

282.98

316.81

88.50

73.81

284.63

317.38

89.28

74.19

286.12

317.91

90.12

74.58

287.77

318.49

90.84

74.89

289.22

319.01

91.45

75.16

290.52

319.48

92.00 93.14

75.39 75.83

291.71 294.27

319.92 320.87

314.74

ED

PT

0.824 5 0.829 6 0.833 2 0.837 9 0.841 9 0.846 4 0.849 7 0.853 9 0.857 5 0.861 5 0.865 0 0.868 1 0.870 8 0.876

AN

81.81

CE

0.86 1 0.87 5 0.88 5 0.89 8 0.90 9 0.92 2 0.93 1 0.94 2 0.95 2 0.96 3 0.97 2 0.98 0 0.98 7 1.00

AC

0.060 9 0.116 4 0.157 0 0.211 7 0.259 0 0.313 2 0.353 9 0.406 0 0.453 3 0.505 6 0.552 0 0.593 5 0.631 6 0.713

M

DPGDME + 1heptanol

0.876 2 0.879 9 0.883 0 0.886 5 0.890 0 0.892 5 0.893 2

1.229 9 1.234 7 1.238 7 1.243 4 1.248 1 1.251 3 1.252 3

1196.1 8 1197.3 3 1198.4 7 1200.0 1 1201.7 6 1203.1 2 1203.5 4

0.749 2 0.761 5 0.771 8 0.784 0 0.796 2 0.804 9 0.807 6

1314.8 4 1304.3 1 1297.0 5 1287.8 4 1280.3 5 1272.2 9 1266.5 7 1259.6 5 1253.7 3 1247.5 6 1242.4 1 1238.0 3 1234.2 0 1226.5

0.647 3 0.657 0 0.664 2 0.673 9 0.682 2 0.691 8 0.699 1 0.708 4 0.716 8 0.726 2 0.734 5 0.742 0 0.748 9 0.763

T

79.77

IP

98.10

CR

1.02 9 1.03 4 1.03 8 1.04 1 1.04 5 1.04 7 1.04 8

US

0.696 8 0.750 5 0.796 2 0.850 9 0.907 1 0.947 6 0.960 0

1.166 2 1.171 4 1.175 3 1.180 5 1.185 0 1.190 1 1.194 0 1.199 0 1.203 5 1.208 4 1.212 8 1.216 8 1.220 4 1.228

223.40 226.61 229.33 232.59 235.92 238.31 239.05

234.66 235.12 235.45 235.89 236.27 236.69 237.00 237.40 237.75 238.13 238.47 238.76 239.03 239.59

7.34 2 7.34 3 7.34 4 7.34 5 7.34 6 7.34 7 7.34 8

7.37 6 7.36 9 7.36 5 7.36 0 7.35 7 7.35 3 7.35 1 7.34 9 7.34 7 7.34 6 7.34 5 7.34 4 7.34 4 7.34

24

ACCEPTED MANUSCRIPT

295.91

321.48

94.32

76.25

297.12

321.94

94.85

76.42

298.47

322.46

95.48

76.61

300.10

323.08

95.78

76.70

300.92

323.40

96.04

76.77

301.64

323.68

1 1221.9 5 1218.7 4 1215.3 6 1211.4 7 1209.6 1 1208.0 3

7 0.773 3 0.780 5 0.788 5 0.798 2 0.803 1 0.807 4

T

76.08

2 1.233 3 1.237 0 1.241 2 1.246 2 1.248 7 1.251 0

IP

93.83

6 0.880 3 0.883 0 0.885 9 0.889 3 0.891 1 0.892 6

239.94 240.19 240.48 240.81 240.98 241.12

4 7.34 4 7.34 4 7.34 5 7.34 6 7.34 7 7.34 7

CE

PT

ED

M

AN

US

CR

2 1.01 2 1.01 8 1.02 6 1.03 5 1.03 9 1.04 3

AC

7 0.766 6 0.805 9 0.849 5 0.902 6 0.929 3 0.952 7

25

ACCEPTED MANUSCRIPT Table 3: Percentage deviation values of density ρ, ultrasonic velocity u and adiabatic compressibility βs, of binary mixtures (DPGDME + methanol, 1-propanol, 1-pentanol, 1-heptanol) calculated through Flory theory at 298.15 K alongwith APD values. x1

u/ ms

S x 1011/ m2 N-1

 x 10-3/ kg m-3

exp

exp

exp

% Deviation

CE AC

 

1.38 3.21 4.33 4.61 4.78 4.78 4.64 4.39 4.16 3.84 3.54 3.26 2.76 2.53 2.13 1.79 1.39 1.09 0.72 0.47 0.38 2.87

-3.35 -8.02 -11.03 -11.81 -12.28 -12.27 -11.90 -11.24 -10.61 -9.77 -8.98 -8.25 -6.98 -6.40 -5.44 -4.57 -3.60 -2.87 -2.00 -1.41 -1.20 7.33

0.52 1.19 1.60 1.70 1.77 1.77 1.72 1.65 1.57 1.48 1.38 1.30 1.14 1.07 0.97 0.85 0.73 0.64 0.53 0.47 0.44 1.17

0.8152 0.8240 0.8306 0.8411

1.23 1.74 2.05 2.41

-2.87 -4.12 -4.90 -5.78

0.36 0.52 0.63 0.74

AN

US

0.7994 0.8201 0.8387 0.8462 0.8551 0.8616 0.8680 0.8739 0.8776 0.8813 0.8842 0.8864 0.8896 0.8908 0.8930 0.8941 0.8954 0.8963 0.8972 0.8977 0.8979 APD

CR

ED

M

100.39 94.09 88.88 86.88 84.65 83.08 81.61 80.28 79.49 78.76 78.20 77.79 77.26 77.08 76.77 76.65 76.55 76.51 76.51 76.56 76.55

PT

1116.23 1138.44 1158.23 1166.24 1175.36 1181.96 1188.14 1193.87 1197.26 1200.27 1202.61 1204.27 1206.21 1206.79 1207.74 1207.93 1207.84 1207.56 1206.96 1206.22 1206.17

IP

DPGDME + methanol 0.0230 0.0705 0.1312 0.1632 0.2094 0.2514 0.3018 0.3598 0.4036 0.4549 0.5022 0.5449 0.6169 0.6494 0.7083 0.7560 0.8114 0.8537 0.9047 0.9364 0.9511

S  

u

T

-1

DPGDME + 1-propanol 0.0653 0.1089 0.1451 0.2124

1210.93 1212.77 1213.96 1215.21

83.66 82.51 81.70 80.51

26

ACCEPTED MANUSCRIPT

CE

AC

CR

-6.19 -6.22 -6.20 -6.09 -5.85 -5.63 -5.27 -4.72 -4.37 -3.85 -3.29 -2.71 -2.28 -1.52 -0.89 -0.71

0.79 0.81 0.81 0.81 0.80 0.79 0.77 0.74 0.71 0.67 0.62 0.56 0.51 0.43 0.37 0.35

T

IP

2.57 2.58 2.56 2.52 2.41 2.31 2.16 1.92 1.77 1.54 1.30 1.05 0.87 0.54 0.26 0.17

US

0.8488 0.8529 0.8565 0.8622 0.8682 0.8720 0.8754 0.8802 0.8826 0.8859 0.8885 0.8910 0.8925 0.8950 0.8969 0.8976 APD

1.70

4.17

0.64

0.8132 0.8177 0.8260 0.8321 0.8395 0.8426 0.8486 0.8529 0.8560 0.8586 0.8634 0.8675 0.8699 0.8752 0.8789 0.8817 0.8850 0.8877 0.8908 0.8938 0.8959

3.91 4.08 4.27 4.33 4.32 4.29 4.18 4.06 3.94 3.85 3.62 3.42 3.27 2.88 2.53 2.27 1.95 1.65 1.25 0.76 0.46

-8.38 -8.85 -9.48 -9.71 -9.79 -9.75 -9.56 -9.32 -9.07 -8.88 -8.40 -7.94 -7.61 -6.74 -5.95 -5.35 -4.63 -3.94 -3.03 -1.97 -1.31

0.06 0.16 0.32 0.41 0.51 0.54 0.59 0.63 0.65 0.66 0.68 0.69 0.69 0.67 0.65 0.62 0.58 0.54 0.48 0.42 0.38

AN

75.70 75.59 75.46 75.41 75.36 75.35 75.34 75.34 75.37 75.36 75.39 75.38 75.40 75.49 75.63 75.71 75.77 75.86 76.03 76.29 76.41

PT

DPGDME + 1-pentanol 0.0143 1274.51 0.0441 1271.97 0.1045 1266.64 0.1523 1262.41 0.2149 1257.22 0.2431 1254.96 0.2986 1250.68 0.3419 1247.45 0.3740 1244.96 0.4018 1243.17 0.4549 1239.54 0.5038 1236.62 0.5334 1234.72 0.6034 1230.26 0.6553 1226.53 0.6968 1223.96 0.7505 1221.20 0.7962 1218.59 0.8509 1215.14 0.9071 1211.00 0.9476 1208.65

79.68 79.31 79.01 78.49 77.97 77.64 77.43 77.11 76.98 76.78 76.70 76.61 76.59 76.58 76.60 76.59

M

1215.98 1215.81 1215.64 1215.56 1215.44 1215.32 1214.62 1213.86 1213.24 1212.51 1211.39 1210.35 1209.51 1207.87 1206.44 1206.10

ED

0.2694 0.3041 0.3359 0.3913 0.4561 0.5020 0.5464 0.6139 0.6513 0.7080 0.7572 0.8098 0.8457 0.9067 0.9576 0.9746

27

ACCEPTED MANUSCRIPT 0.9600

1207.77

76.47

0.8965

0.35

-1.07

0.37

APD

2.98

6.85

0.51

0.8251 0.8307 0.8346 0.8397 0.8440 0.8487 0.8522 0.8565 0.8603 0.8644 0.8679 0.8710 0.8739 0.8797 0.8834 0.8861 0.8890 0.8926 0.8942 0.8956

0.22 0.41 0.45 0.59 0.68 0.73 0.77 0.86 0.88 0.89 0.89 0.89 0.90 0.79 0.74 0.64 0.55 0.38 0.28 0.22

-0.53 -0.96 -1.08 -1.40 -1.63 -1.76 -1.86 -2.04 -2.12 -2.14 -2.16 -2.16 -2.18 -1.95 -1.85 -1.65 -1.47 -1.13 -0.91 -0.78

0.07 0.13 0.17 0.21 0.24 0.27 0.29 0.30 0.32 0.33 0.34 0.34 0.35 0.35 0.35 0.35 0.35 0.36 0.34 0.34

1.59

0.29

IP

CR

US

AN M

ED

69.79 70.19 70.58 70.96 71.30 71.72 72.02 72.33 72.65 73.01 73.31 73.57 73.78 74.38 74.70 75.01 75.31 75.76 76.01 76.17

APD

0.64

CE

PT

1317.80 1309.65 1302.97 1295.47 1289.17 1281.70 1276.44 1270.52 1264.90 1258.76 1253.61 1249.18 1245.39 1236.22 1231.03 1226.59 1222.12 1216.11 1213.01 1210.68

AC

0.0609 0.1164 0.1570 0.2117 0.2590 0.3132 0.3539 0.4060 0.4533 0.5056 0.5520 0.5935 0.6316 0.7137 0.7666 0.8059 0.8495 0.9026 0.9293 0.9527

T

DPGDME + 1-heptanol

28

ACCEPTED MANUSCRIPT Table 4: Calculated values of thermal expansivity α, isothermal compressibility  T, internal pressure Pi, heat capacity ratio , Grünisen parameter  and heat capacity at constant pressure CP of binary mixtures (DPGDME + methanol, 1-propanol, 1pentanol, 1-heptanol) calculated through empirical relations at 298.15 K kg m-3





-2

CP / J mol-1 K-1

Nm

exp

1.295 1.271 1.251 1.243 1.234 1.227 1.221 1.215 1.212 1.208 1.206 1.204 1.202 1.201 1.199 1.199 1.198 1.198 1.198 1.198 1.198

147.01 136.62 128.08 124.84 121.22 118.66 116.28 114.12 112.84 111.65 110.73 110.05 109.18 108.87 108.35 108.14 107.94 107.85 107.81 107.87 107.84

0.8152 0.8240 0.8306 0.8411

1.235 1.229 1.226 1.220

121.71 119.61 118.12 115.92

IP

0.7994 0.8201 0.8387 0.8462 0.8551 0.8616 0.8680 0.8739 0.8776 0.8813 0.8842 0.8864 0.8896 0.8908 0.8930 0.8941 0.8954 0.8963 0.8972 0.8977 0.8979

PT

100.39 94.09 88.88 86.88 84.65 83.08 81.61 80.28 79.49 78.76 78.20 77.79 77.26 77.08 76.77 76.65 76.55 76.51 76.51 76.56 76.55

CE

1116.23 1138.44 1158.23 1166.24 1175.36 1181.96 1188.14 1193.87 1197.26 1200.27 1202.61 1204.27 1206.21 1206.79 1207.74 1207.93 1207.84 1207.56 1206.96 1206.22 1206.17

m N

-1

262.47 277.32 291.06 296.72 303.34 308.23 312.95 317.37 320.07 322.63 324.64 326.14 328.10 328.78 329.97 330.45 330.91 331.12 331.21 331.09 331.15

1.4644 1.4520 1.4411 1.4369 1.4319 1.4283 1.4248 1.4215 1.4195 1.4176 1.4160 1.4148 1.4131 1.4125 1.4113 1.4108 1.4101 1.4096 1.4091 1.4089 1.4087

1.2032 1.1928 1.1830 1.1791 1.1743 1.1707 1.1670 1.1636 1.1613 1.1589 1.1570 1.1554 1.1530 1.1520 1.1502 1.1492 1.1477 1.1467 1.1455 1.1446 1.1443

46.97 56.93 69.66 76.38 86.06 94.84 105.34 117.42 126.51 137.10 146.87 155.65 170.37 176.99 189.00 198.59 209.70 218.14 228.26 234.46 237.40

302.42 306.39 309.28 313.69

1.4549 1.4497 1.4458 1.4398

1.2355 1.2267 1.2201 1.2092

97.85 104.99 110.91 121.85

AC

0.0230 0.0705 0.1312 0.1632 0.2094 0.2514 0.3018 0.3598 0.4036 0.4549 0.5022 0.5449 0.6169 0.6494 0.7083 0.7560 0.8114 0.8537 0.9047 0.9364 0.9511

2

Pi x 10-6/

T

exp exp DPGDME + methanol

K

-1

T x 1011/

CR

m N

-1

 x 103/

US

ms

2

 x 10-3/

AN

-1

S x 1011/

M

u/

ED

x1

DPGDME + 1-propanol 0.0653 0.1089 0.1451 0.2124

1210.93 1212.77 1213.96 1215.21

83.66 82.51 81.70 80.51

29

ACCEPTED MANUSCRIPT

0.8132 0.8177 0.8260 0.8321 0.8395 0.8426 0.8486 0.8529 0.8560 0.8586 0.8634 0.8675 0.8699 0.8752 0.8789 0.8817 0.8850 0.8877 0.8908 0.8938 0.8959

1.205 1.204 1.202 1.201 1.200 1.200 1.199 1.198 1.198 1.198 1.197 1.197 1.197 1.196 1.197 1.197 1.196 1.196 1.197 1.197 1.198

ED

PT

CE

75.70 75.59 75.46 75.41 75.36 75.35 75.34 75.34 75.37 75.36 75.39 75.38 75.40 75.49 75.63 75.71 75.77 75.86 76.03 76.29 76.41

AC

1274.51 1271.97 1266.64 1262.41 1257.22 1254.96 1250.68 1247.45 1244.96 1243.17 1239.54 1236.62 1234.72 1230.26 1226.53 1223.96 1221.20 1218.59 1215.14 1211.00 1208.65

M

DPGDME + 1-pentanol 0.0143 0.0441 0.1045 0.1523 0.2149 0.2431 0.2986 0.3419 0.3740 0.4018 0.4549 0.5038 0.5334 0.6034 0.6553 0.6968 0.7505 0.7962 0.8509 0.9071 0.9476

114.38 113.67 113.06 112.09 111.08 110.45 110.00 109.35 109.07 108.65 108.43 108.21 108.11 108.01 107.95 107.91

316.84 318.33 319.60 321.69 323.87 325.26 326.25 327.71 328.35 329.30 329.80 330.30 330.53 330.76 330.89 330.99

1.4354 1.4331 1.4311 1.4279 1.4247 1.4226 1.4207 1.4182 1.4169 1.4151 1.4137 1.4124 1.4116 1.4103 1.4093 1.4089

1.2013 1.1967 1.1927 1.1866 1.1801 1.1760 1.1720 1.1666 1.1638 1.1599 1.1567 1.1535 1.1515 1.1482 1.1455 1.1447

131.11 136.69 141.80 150.73 161.18 168.58 175.66 186.46 192.40 201.44 209.17 217.45 223.06 232.54 240.42 243.08

110.22 109.86 109.30 108.96 108.57 108.42 108.16 107.97 107.88 107.76 107.60 107.42 107.35 107.25 107.31 107.31 107.25 107.27 107.39 107.65 107.73

325.76 326.56 327.83 328.58 329.47 329.81 330.42 330.84 331.04 331.34 331.71 332.12 332.27 332.50 332.38 332.37 332.51 332.46 332.18 331.59 331.41

1.4560 1.4534 1.4485 1.4450 1.4407 1.4389 1.4356 1.4331 1.4314 1.4299 1.4273 1.4250 1.4237 1.4208 1.4188 1.4174 1.4156 1.4141 1.4125 1.4109 1.4098

1.2698 1.2635 1.2514 1.2425 1.2317 1.2271 1.2185 1.2121 1.2076 1.2038 1.1970 1.1911 1.1876 1.1797 1.1740 1.1699 1.1650 1.1609 1.1561 1.1510 1.1477

137.47 140.90 147.78 153.19 160.27 163.45 169.71 174.59 178.17 181.32 187.28 192.81 196.12 203.92 209.58 214.16 220.15 225.18 231.10 237.03 241.41

T

1.216 1.214 1.212 1.210 1.207 1.205 1.204 1.202 1.201 1.200 1.200 1.199 1.199 1.198 1.198 1.198

IP

0.8488 0.8529 0.8565 0.8622 0.8682 0.8720 0.8754 0.8802 0.8826 0.8859 0.8885 0.8910 0.8925 0.8950 0.8969 0.8976

CR

79.68 79.31 79.01 78.49 77.97 77.64 77.43 77.11 76.98 76.78 76.70 76.61 76.59 76.58 76.60 76.59

US

1215.98 1215.81 1215.64 1215.56 1215.44 1215.32 1214.62 1213.86 1213.24 1212.51 1211.39 1210.35 1209.51 1207.87 1206.44 1206.10

AN

0.2694 0.3041 0.3359 0.3913 0.4561 0.5020 0.5464 0.6139 0.6513 0.7080 0.7572 0.8098 0.8457 0.9067 0.9576 0.9746

30

ACCEPTED MANUSCRIPT 0.9600 1207.77

76.47

0.8965

1.198

107.78

331.28

1.4095 1.1466

242.72

0.8251 0.8307 0.8346 0.8397 0.8440 0.8487 0.8522 0.8565 0.8603 0.8644 0.8679 0.8710 0.8739 0.8797 0.8834 0.8861 0.8890 0.8926 0.8942 0.8956

1.179 1.180 1.181 1.182 1.183 1.184 1.185 1.186 1.187 1.188 1.189 1.189 1.190 1.191 1.192 1.193 1.194 1.196 1.196 1.197

101.12 101.48 101.88 102.23 102.53 102.96 103.25 103.52 103.82 104.17 104.46 104.70 104.88 105.50 105.80 106.14 106.45 106.94 107.23 107.40

347.51 346.60 345.56 344.69 343.92 342.85 342.13 341.47 340.72 339.86 339.16 338.57 338.12 336.64 335.92 335.12 334.38 333.24 332.57 332.16

1.4490 1.4458 1.4435 1.4406 1.4382 1.4355 1.4335 1.4311 1.4290 1.4267 1.4248 1.4231 1.4216 1.4184 1.4164 1.4150 1.4134 1.4116 1.4107 1.4099

190.72 194.15 196.51 199.88 202.78 206.03 208.49 211.75 214.64 217.81 220.64 223.19 225.56 230.44 233.67 235.94 238.53 241.55 243.02 244.39

IP

CR

US

AN

M

ED

69.79 70.19 70.58 70.96 71.30 71.72 72.02 72.33 72.65 73.01 73.31 73.57 73.78 74.38 74.70 75.01 75.31 75.76 76.01 76.17

1.2774 1.2672 1.2595 1.2501 1.2422 1.2334 1.2270 1.2194 1.2125 1.2051 1.1988 1.1933 1.1884 1.1778 1.1714 1.1664 1.1613 1.1547 1.1515 1.1489

CE

PT

1317.80 1309.65 1302.97 1295.47 1289.17 1281.70 1276.44 1270.52 1264.90 1258.76 1253.61 1249.18 1245.39 1236.22 1231.03 1226.59 1222.12 1216.11 1213.01 1210.68

AC

0.0609 0.1164 0.1570 0.2117 0.2590 0.3132 0.3539 0.4060 0.4533 0.5056 0.5520 0.5935 0.6316 0.7137 0.7666 0.8059 0.8495 0.9026 0.9293 0.9527

T

DPGDME + 1-heptanol

31

ACCEPTED MANUSCRIPT Table 5: Calculated values of density ρ, ultrasonic velocity u, thermal expansivity α, isothermal compressibility  T, adiabatic compressibility S, internal pressure Pi, heat capacity at constant pressure CP, heat capacity ratio , heat capacity at constant volume CV, Grünisen parameter  and non-linearity parameter (B/A) of binary mixtures (Oxolane + aniline, N-methyl aniline, N-ethyl aniline) calculated through Flory theory at different temperatures. S x 1011/

CP /

K-1

m2 N-1

m2 N-1

J mol-1 K-1

Pi x 106 /

 x 103 /

N m-2

kg m-3



u/



T

T x 1011/

m s-1

Cv /

B/A

J mol-1 K-1

CR

Oxolane+anili ne

IP

x1

x 103/

0.873

50.93

0.1803

0.898

53.91

0.2735

0.925

57.21

0.3573

0.951

60.50

0.4556

0.985

64.83

0.5638

1.025

70.26

0.6708

1.070

76.48

0.8169

1.141

86.70

0.8812

1.176

91.98

1.0000

1.248

103.32

50.74

39.7 3

CE

AC

166.93

476.49

160.39

460.39

153.24

442.36

146.21

424.19

136.72

398.85

132.58

387.50

125.00

366.19

529.48

1.004 9

532.84

185.10

519.42

178.80

504.82

172.54

AN

0.0870

191.00

M

48.42

490.01

ED

0.851

1.012 8 1.003 2 0.992 6 0.981 5 0.971 2 0.958 6 0.944 0 0.929 0 0.907 1 0.896 9 0.877 3

PT

0.0000

37.8 5 39.5 8 41.6 1 43.8 3 46.0 2 48.8 6 52.3 6 56.2 8 62.5 4 65.6 9 72.2 7

US

At T=303.15 K

1.279 3 1.286 8 1.295 6 1.305 2 1.314 6 1.326 8 1.342 0 1.359 0 1.386 3 1.400 2 1.429 6

1615.1 5 1586.9 1 1556.0 4 1524.5 9 1495.7 6 1461.2 5 1422.3 7 1383.0 0 1327.6 9 1302.7 9 1255.9 0

1.082 5 1.084 0 1.086 1 1.088 6 1.091 3 1.095 1 1.100 2 1.106 4 1.117 2 1.122 9 1.135 6

1.277 2

1582.6 0

1.031 6

87.43

7.35 7 7.35 5 7.35 4 7.35 6 7.35 9 7.36 5 7.37 5 7.39 0 7.42 0 7.43 8 7.47 9

151.90

7.35 5

149.31 143.85 138.01 132.19 126.98 120.88 114.19 107.59 98.62 94.68

At T=313.15 K

0.0000

0.858

194.00

32

0.906

56.69

0.2735

0.934

60.28

0.3573

0.961

63.87

0.4556

0.995

68.59

0.5638

1.037

74.56

0.6708

1.084

81.41

0.8169

1.157

92.73

0.8812

1.193

98.61

1.0000

1.269

111.30

188.08

515.53

181.77

500.35

175.50

484.98

169.89

470.96

163.34

454.28

156.19

435.61

149.17

416.84

139.69

390.68

135.56

378.97

128.00

357.04

0.0870

0.889

55.68

0.1803

0.915

59.19

0.2735

0.943

63.11

0.3573

0.971

67.04

0.4556

1.007

72.23

0.5638

1.050

78.82

0.6708

1.098

86.42

0.8169

1.174

99.07

0.8812

1.212

105.67

1.0000

1.291

120.03

AC

197.00

530.74

ED

52.73

190.98

515.76

184.56

499.50

178.18

483.06

172.48

468.09

165.83

450.32

158.57

430.48

151.45

410.58

141.84

382.95

137.65

370.62

130.00

347.58

PT

0.866

CE

0.0000

M

At T=323.15 K 41.2 5 43.3 4 45.7 9 48.5 0 51.2 0 54.7 1 59.1 1 64.1 0 72.2 0 76.3 5 85.1 5

0.995 2 0.984 3 0.973 1 0.962 6 0.949 8 0.935 1 0.919 8 0.897 5 0.887 2 0.867 2

1.284 3 1.292 5 1.301 5 1.310 4 1.321 8 1.335 9 1.351 7 1.377 1 1.390 0 1.417 1

1553.6 0 1521.8 9 1489.5 5 1459.8 8 1424.3 3 1384.2 4 1343.5 7 1286.3 1 1260.4 8 1211.7 0

1.031 3 1.031 2 1.031 3 1.031 8 1.032 6 1.034 2 1.036 4 1.040 9 1.043 5 1.049 6

0.998 4 0.988 4 0.977 2 0.965 6 0.954 8 0.941 7 0.926 5 0.910 7 0.887 8 0.877 2 0.856 6

1558.2 0 1527.9 7 1494.9 1 1461.1 8 1430.2 4 1393.1 6 1351.3 2 1308.8 4 1249.0 0 1221.9 7 1170.9 0

0.994 0 0.991 9 0.989 8 0.987 8 0.986 1 0.984 3 0.982 7 0.981 6 0.980 8 0.980 9 0.981 8

T

0.1803

41.6 3 43.8 6 46.3 2 48.7 4 51.9 0 55.8 1 60.2 3 67.3 4 70.9 4 78.5 4

IP

53.47

CR

0.880

AN

0.0870

US

ACCEPTED MANUSCRIPT

1.278 2 1.284 9 1.292 6 1.301 1 1.309 5 1.320 2 1.333 4 1.348 3 1.372 1 1.384 2 1.409 6

146.45 140.63 134.84 129.65 123.58 116.92 110.36 101.44 97.53 90.32

154.13 148.64 142.78 136.95 131.72 125.61 118.92 112.33 103.37 99.45 92.23

7.35 5 7.35 5 7.35 8 7.36 2 7.36 9 7.38 1 7.39 7 7.42 9 7.44 7 7.49 0

7.35 4 7.35 5 7.35 7 7.36 1 7.36 6 7.37 5 7.38 8 7.40 6 7.44 0 7.45 9 7.50 4

33

ACCEPTED MANUSCRIPT

Oxolane + N-methyl aniline At T=303.15 K

58.04

0.2813

0.892

60.99

0.3782

0.923

64.38

0.4714

0.957

68.09

0.5746

0.998

72.80

0.6956

1.055

79.34

0.7823

1.101

84.89

0.8882

1.166

92.91

1.0000

1.248

103.32

CE

At T=313.15 K

0.834

57.05

0.0831

0.854

59.27

0.1864

0.882

62.34

0.2813

0.910

65.51

0.3782

0.941

69.16

0.4714

0.975

73.15

AC

0.0000

194.57

451.10

186.26

443.14

177.82

434.59

169.74

425.91

160.85

415.75

150.51

403.00

143.16

45.8 0 47.3 0 49.3 6 51.4 5 53.8 2 56.3 7

393.26

134.27

380.59

125.00

366.19

214.15

457.63

206.79

451.22

197.67

442.87

189.34

434.80

180.87

426.13

172.78

417.35

0.967 7 0.962 0 0.954 4 0.946 9 0.938 7 0.930 2

1548.3 0 1528.2 4 1502.3 9 1477.6 9 1451.4 9 1425.2 8 1395.0 7 1357.9 4 1330.1 6 1294.8 5 1255.9 0

0.993 4 0.999 6 1.008 1 1.016 9 1.026 8 1.037 6 1.051 2 1.069 7 1.085 2 1.107 4 1.135 6

1502.1 5 1482.4 6 1457.0 6 1432.7 5 1406.9 0 1381.0 1

0.941 3 0.946 1 0.952 7 0.959 4 0.967 1 0.975 3

T

0.864

459.33

1.245 7 1.253 4 1.264 0 1.274 8 1.287 3 1.300 9 1.318 1 1.342 1 1.362 3 1.391 6 1.429 6

IP

0.1864

203.66

0.978 2 0.972 4 0.964 8 0.957 3 0.949 0 0.940 5 0.930 4 0.917 3 0.907 0 0.893 3 0.877 3

CR

55.19

465.65

US

0.836

211.00

AN

0.0831

42.6 4 44.0 3 45.9 2 47.8 4 50.0 1 52.3 4 55.2 3 59.1 2 62.3 1 66.7 7 72.2 7

M

53.12

ED

0.816

PT

0.0000

1.245 8 1.253 0 1.263 0 1.273 3 1.285 0 1.297 8

169.38 162.49 153.94 146.11 138.13 130.48 122.03 112.15 105.09 96.49 87.43

171.91 165.03 156.51 148.70 140.76 133.14

7.36 8 7.36 3 7.35 8 7.35 5 7.35 5 7.35 7 7.36 4 7.38 0 7.39 8 7.43 0 7.47 9

7.36 0 7.35 7 7.35 4 7.35 4 7.35 5 7.36 0

34

ACCEPTED MANUSCRIPT

78.23

0.6956

1.074

85.30

0.7823

1.121

91.30

0.8882

1.186

99.99

1.0000

1.269

111.30

59.5 4 63.8 4 67.3 8 72.3 5 78.5 4

163.87

407.07

153.52

394.19

146.16

384.35

137.27

371.56

128.00

357.04

215.46

455.93

208.17

448.98

199.15

439.92

190.89

431.17

182.50

421.78

0.920 1 0.907 0 0.896 8 0.883 2 0.867 2

1.313 9 1.336 2 1.355 0 1.382 1 1.417 1

1351.0 7 1314.1 6 1286.4 2 1251.0 1 1211.7 0

0.985 7 0.999 8 1.011 6 1.028 4 1.049 6

T

1.017

124.72 114.89 107.87 99.32 90.32

7.36 9 7.38 8 7.40 7 7.44 0 7.49 0

IP

0.5746

0.1864

0.870

63.94

0.2813

0.901

67.50

0.3782

0.935

71.62

0.4714

0.971

76.14

0.5746

1.017

81.92

0.6956

1.079

90.02

0.7823

1.130

96.91

0.8882

1.201

106.94

1.0000

1.291

120.03

165.63

401.15

155.35

387.26

148.05

376.69

139.21

363.01

130.00

347.58

445.89

0.951 9

174.47

412.26

1.239 0 1.246 2 1.256 2 1.266 4 1.278 1 1.290 9 1.307 0 1.329 3 1.348 0 1.374 9 1.409 6

1488.5 9 1466.9 1 1438.9 1 1412.1 2 1383.6 5 1355.1 7 1322.3 1 1281.9 2 1251.6 9 1213.2 8 1170.9 0

0.902 8 0.906 1 0.910 6 0.915 3 0.920 7 0.926 7 0.934 2 0.944 5 0.953 3 0.965 8 0.981 8

1.284 2

1497.3 9

1.059 3

US

60.53

AN

0.841

0.962 9 0.956 9 0.948 8 0.940 9 0.932 2 0.923 2 0.912 4 0.898 6 0.887 8 0.873 4 0.856 6

M

0.0831

46.8 6 48.5 7 50.9 0 53.3 0 56.0 3 58.9 8 62.6 8 67.7 2 71.8 9 77.7 8 85.1 5

ED

58.07

PT

0.819

92.23

7.35 9 7.35 5 7.35 3 7.35 2 7.35 5 7.36 0 7.37 1 7.39 1 7.41 3 7.44 9 7.50 4

176.76

7.35 5

173.90 167.04 158.54 150.74 142.79 135.16 126.73 116.87 109.83 101.25

AC

CE

0.0000

CR

At T=323.15 K

Oxolane+ N- ethyl aniline At T=303.15 K

0.0000

0.885

60.17

46.8 5

227.00

35

0.923

64.32

0.2813

0.946

66.82

0.3782

0.971

69.70

0.4714

0.999

72.84

0.5746

1.034

76.86

0.6956

1.081

82.46

0.7823

1.120

87.23

0.8882

1.176

94.19

1.0000

1.248

103.32

218.32

441.24

207.57

435.10

197.74

429.08

187.76

422.51

178.19

415.74

167.66

407.68

155.39

397.37

146.66

389.33

136.07

378.65

125.00

366.19

0.0831

0.910

65.37

0.1864

0.932

68.00

0.2813

0.955

70.73

0.3782

0.982

73.89

0.4714

1.010

77.35

0.5746

1.046

81.78

0.6956

1.095

87.98

0.7823

1.136

93.29

0.8882

1.194

101.05

1.0000

1.269

111.30

AC

230.00

440.63

ED

63.46

221.31

435.74

210.54

429.29

200.70

422.96

190.71

416.06

181.14

408.96

170.61

400.51

158.34

389.70

149.62

381.27

139.05

370.08

128.00

357.04

PT

0.893

CE

0.0000

M

At T=313.15 K 49.5 3 50.7 9 52.5 1 54.2 9 56.3 1 58.5 0 61.2 6 65.0 5 68.2 2 72.7 5 78.5 4

0.948 1 0.942 9 0.937 7 0.932 0 0.926 0 0.918 6 0.908 8 0.901 0 0.890 3 0.877 3

1.290 3 1.298 6 1.307 2 1.317 0 1.327 7 1.341 2 1.360 1 1.376 1 1.399 3 1.429 6

1482.6 2 1463.2 4 1444.3 5 1423.8 8 1402.9 9 1378.3 2 1347.1 5 1323.1 6 1291.7 7 1255.9 0

1.062 5 1.066 9 1.071 3 1.076 4 1.082 0 1.089 0 1.098 9 1.107 3 1.119 5 1.135 6

0.944 3 0.940 3 0.935 0 0.929 7 0.923 8 0.917 5 0.909 9 0.899 8 0.891 7 0.880 6 0.867 2

1462.2 0 1447.0 3 1427.0 9 1407.6 3 1386.5 3 1364.9 5 1339.4 3 1307.0 8 1282.1 1 1249.3 4 1211.7 0

1.005 9 1.007 8 1.010 2 1.012 7 1.015 6 1.018 7 1.022 7 1.028 3 1.033 1 1.040 2 1.049 6

T

0.1864

47.9 8 49.5 3 51.1 2 52.9 2 54.8 7 57.3 0 60.6 3 63.3 9 67.3 1 72.2 7

IP

61.91

CR

0.901

AN

0.0831

US

ACCEPTED MANUSCRIPT

1.281 3 1.287 0 1.294 9 1.303 0 1.312 2 1.322 3 1.335 0 1.352 6 1.367 5 1.389 0 1.417 1

169.21 159.85 151.28 142.56 134.21 125.00 114.25 106.58 97.25 87.43

179.51 171.95 162.59 154.03 145.33 136.99 127.80 117.07 109.41 100.11 90.32

7.35 5 7.35 5 7.35 7 7.36 1 7.36 7 7.37 6 7.39 3 7.40 9 7.43 7 7.47 9

7.35 4 7.35 5 7.35 7 7.36 0 7.36 5 7.37 1 7.38 2 7.40 0 7.41 8 7.44 7 7.49 0

36

ACCEPTED MANUSCRIPT

At T=323.15 K

0.942

72.07

0.2813

0.966

75.05

0.3782

0.993

78.51

0.4714

1.022

82.31

0.5746

1.059

87.19

0.6956

1.110

94.04

0.7823

1.152

99.92

0.8882

1.213

108.56

1.0000

1.291

120.03

429.19

213.32

422.49

203.38

415.91

193.28

408.75

183.61

401.38

172.97

392.61

160.60

381.40

151.80

372.66

141.13

361.07

130.00

347.58

0.954 6 0.955 7 0.957 2 0.958 7 0.960 4 0.962 3 0.964 7 0.968 2 0.971 2 0.975 7 0.981 8

T

0.1864

224.21

IP

69.19

1426.5 0 1411.1 0 1390.8 5 1371.0 7 1349.6 1 1327.6 4 1301.6 3 1268.6 2 1243.1 0 1209.5 4 1170.9 0

CR

0.919

434.28

1.278 3 1.283 8 1.291 4 1.299 3 1.308 2 1.317 9 1.330 2 1.347 2 1.361 6 1.382 4 1.409 6

US

0.0831

233.00

AN

67.12

M

0.902

0.935 9 0.931 8 0.926 4 0.920 9 0.914 8 0.908 4 0.900 5 0.890 2 0.881 9 0.870 4 0.856 6

182.28 174.64 165.18 156.53 147.74 139.32 130.03 119.20 111.48 102.09 92.23

7.35 4 7.35 5 7.35 8 7.36 2 7.36 8 7.37 6 7.38 8 7.40 8 7.42 7 7.45 8 7.50 4

AC

CE

PT

ED

0.0000

52.5 1 53.9 0 55.8 0 57.7 7 60.0 1 62.4 6 65.5 4 69.8 0 73.3 8 78.5 3 85.1 5

37

ACCEPTED MANUSCRIPT Table 6: Percentage deviation values of density ρ, ultrasonic velocity u and adiabatic compressibility βs, of binary mixtures (Oxolane + aniline, Nmethyl aniline, N-ethyl aniline) calculated through Flory theory at different temperatures alongwith APD values. x1

u/

S x 1011/

exp

exp

1615.00 1592.00 1565.00 1535.00 1509.00 1476.00 1438.00 1393.00 1334.00 1306.00 1256.00

37.86 39.28 41.04 43.10 45.02 47.61 50.88 55.12 61.74 65.24 72.26

1.0128 1.0044 0.9948 0.9848 0.9754 0.9641 0.9505 0.9350 0.9101 0.8987 0.8773

-0.01 0.32 0.57 0.68 0.88 1.00 1.09 0.72 0.47 0.25 0.01

0.02 -0.76 -1.38 -1.71 -2.22 -2.62 -2.91 -2.11 -1.29 -0.69 -0.02

0.00 0.12 0.23 0.34 0.43 0.57 0.68 0.65 0.33 0.20 0.00

APD

0.66

1.74

0.39

1.0049 0.9975 0.9882 0.9785 0.9694 0.9578 0.9439 0.9287 0.9040 0.8922

0.03 0.47 0.60 0.70 0.89 1.09 1.27 1.14 0.98 0.51

-0.05 -1.19 -1.60 -1.97 -2.52 -3.07 -3.55 -3.30 -2.72 -1.61

0.00 0.23 0.39 0.55 0.70 0.83 0.93 0.96 0.72 0.56

T

u

AN

M

ED

PT CE 1583.00 1561.00 1531.00 1500.00 1473.00 1440.00 1402.00 1359.00 1299.00 1267.00

AC

0.0000 0.0870 0.1803 0.2735 0.3573 0.4556 0.5638 0.6708 0.8169 0.8812

39.71 41.14 43.17 45.42 47.54 50.35 53.90 58.30 65.56 69.82

CR

US

At T=303.15 K

At T=313.15 K



exp

kg m-3

Oxolane+aniline

0.0000 0.0870 0.1803 0.2735 0.3573 0.4556 0.5638 0.6708 0.8169 0.8812 1.0000

S

m N

IP

-1

% Deviation

-1

ms

2

 x 10-3/

38

ACCEPTED MANUSCRIPT 1.0000

1212.00

78.50

0.8672

0.02

-0.05

0.00

APD

0.85

2.39

0.65

0.9984 0.9915 0.9816 0.9718 0.9624 0.9516 0.9379 0.9226 0.8985 0.8850 0.8566

-0.01 0.59 1.00 1.14 1.36 1.68 2.01 1.89 1.50 1.21 0.01

0.03 -1.51 -2.49 -2.97 -3.60 -4.54 -5.42 -5.24 -4.31 -3.39 -0.02

0.00 0.32 0.45 0.63 0.79 1.04 1.22 1.29 1.19 0.88 0.00

1.38

3.72

0.87

0.9782 0.9731 0.9660 0.9591 0.9515 0.9435 0.9332 0.9194 0.9082 0.8934 0.8773

-0.02 -0.02 -0.03 0.02 0.10 0.19 0.07 -0.07 -0.09 -0.14 0.01

0.04 -0.04 -0.07 -0.23 -0.47 -0.70 -0.44 -0.09 0.04 0.28 -0.02

0.00 0.07 0.12 0.19 0.26 0.31 0.30 0.23 0.13 0.01 0.00

APD

0.08

0.26

0.18

0.9698

0.65

-1.54

0.22

APD

42.66 44.01 45.89 47.73 49.78 51.98 54.99 59.07 62.34 66.95 72.26

AC

CE

PT

1548.00 1528.00 1502.00 1478.00 1453.00 1428.00 1396.00 1357.00 1329.00 1293.00 1256.00

ED

At T=303.15 K 0.0000 0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

IP

M

Oxolane + N-methyl aniline

CR

41.26 42.69 44.68 47.11 49.42 52.34 56.07 60.91 69.22 73.84 85.13

US

1558.00 1537.00 1510.00 1478.00 1450.00 1417.00 1379.00 1334.00 1268.00 1237.00 1171.00

AN

0.0000 0.0870 0.1803 0.2735 0.3573 0.4556 0.5638 0.6708 0.8169 0.8812 1.0000

T

At T=323.15 K

At T=313.15 K 0.0000

1512.00

45.10

39

46.49 48.55 50.55 52.83 55.30 58.56 63.11 66.81 72.03 78.50

0.9649 0.9583 0.9514 0.9440 0.9360 0.9260 0.9122 0.9008 0.8857 0.8672

0.71 0.61 0.64 0.64 0.65 0.51 0.29 0.20 0.08 0.02

APD

0.48

0.30 0.41 0.48 0.56 0.62 0.64 0.56 0.44 0.28 0.00

1.46

0.48

-0.78 -0.54 -0.41 -0.36 -0.19 -0.09 -0.02 0.01 0.02 -0.02 0.01

1.75 1.10 0.71 0.46 0.00 -0.28 -0.44 -0.46 -0.42 -0.23 -0.02

-0.20 -0.03 0.11 0.27 0.39 0.45 0.49 0.44 0.37 0.27 0.00

APD

0.19

0.46

0.31

0.9519 0.9478 0.9438 0.9395 0.9345 0.9293 0.9219 0.9131

-0.03 -0.04 0.39 0.53 0.64 0.78 0.63 0.94

0.05 0.11 -0.88 -1.25 -1.56 -1.94 -1.63 -2.40

0.00 -0.03 0.09 0.19 0.27 0.36 0.36 0.47

AN

0.9610 0.9566 0.9499 0.9434 0.9358 0.9274 0.9169 0.9026 0.8911 0.8758 0.8566

M

47.70 49.11 51.27 53.54 56.03 58.82 62.40 67.41 71.59 77.60 85.13

ED

1477.00 1459.00 1433.00 1407.00 1381.00 1354.00 1322.00 1282.00 1252.00 1213.00 1171.00

CE

PT

0.0000 0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

US

At T=323.15 K

-1.74 -1.65 -1.78 -1.87 -1.94 -1.68 -1.16 -0.85 -0.44 -0.05

IP

1493.00 1466.00 1442.00 1416.00 1390.00 1358.00 1318.00 1289.00 1252.00 1212.00

CR

0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

T

ACCEPTED MANUSCRIPT

Oxolane+ N- ethyl aniline

AC

At T=303.15 K

0.0000 0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956

1497.00 1482.00 1469.00 1452.00 1433.00 1414.00 1387.00 1360.00

46.88 48.04 49.10 50.49 52.11 53.82 56.38 59.21

40

ACCEPTED MANUSCRIPT 1326.00 1291.00 1256.00

63.05 67.35 72.26

0.9021 0.8908 0.8773

0.21 -0.06 0.01

-0.55 0.06 -0.02

0.12 0.06 0.00

APD

0.47

1.15

0.22

AC

CE

PT

ED

M

AN

US

CR

IP

T

0.7823 0.8882 1.0000

41

ACCEPTED MANUSCRIPT At T=313.15 K -0.01 0.20 0.55 0.73 0.89 1.02 0.86 1.20 0.38 0.13 0.02

APD

0.66

0.9359 0.9328 0.9291 0.9252 0.9206 0.9157 0.9081 0.8995 0.8877 0.8742 0.8571 APD

M

52.18 53.17 54.60 56.10 58.13 60.28 63.49 67.22 72.10 77.49 85.09

CE

PT

ED

1431.00 1420.00 1404.00 1388.00 1367.00 1346.00 1317.00 1286.00 1250.00 1215.00 1171.00

0.00 0.05 0.18 0.29 0.41 0.55 0.58 0.73 0.41 0.24 0.00

1.73

0.38

0.31 0.63 0.94 1.22 1.27 1.36 1.17 1.35 0.55 0.45 0.01 0.99

-0.63 -1.37 -2.20 -2.96 -3.24 -3.61 -3.23 -3.83 -1.78 -1.34 -0.08 2.62

0.00 0.10 0.29 0.46 0.63 0.80 0.83 1.03 0.66 0.43 0.06 0.58

AC

0.0000 0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

AN

At T=323.15 K

0.03 -0.46 -1.29 -1.77 -2.23 -2.63 -2.33 -3.20 -1.18 -0.51 -0.05

T

0.9443 0.9408 0.9367 0.9324 0.9276 0.9226 0.9152 0.9064 0.8954 0.8828 0.8672

IP

49.54 50.56 51.84 53.34 55.08 57.00 59.87 63.03 67.43 72.38 78.50

CR

1462.00 1450.00 1435.00 1418.00 1399.00 1379.00 1351.00 1323.00 1287.00 1251.00 1212.00

US

0.0000 0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

Table 7: Calculated values of thermal expansivity α, isothermal compressibility  T, internal pressure Pi, heat capacity ratio , Grünisen parameter  and heat capacity at constant pressure CP of binary mixtures (Oxolane + aniline, N-methyl aniline, N-ethyl aniline) calculated through empirical relations at different temperatures. x1

m s-1

S x 1011/ m2 N-1

exp

exp

u/

 x 10-3/

 x 103/

kg m-3

K-1

T x 1011/ m2 N-1

Pi x 10-6/ N m-2





CP / J mol-1 K-1

exp

42

ACCEPTED MANUSCRIPT

1.0128 1.0044 0.9948 0.9848 0.9754 0.9641 0.9505 0.9350 0.9101 0.8987 0.8773

0.993 1.003 1.015 1.028 1.040 1.056 1.075 1.098 1.132 1.149 1.181

39.71 41.14 43.17 45.42 47.54 50.35 53.90 58.30 65.56 69.82 78.50

1.0049 0.9975 0.9882 0.9785 0.9694 0.9578 0.9439 0.9287 0.9040 0.8922 0.8672

1.002 1.011 1.024 1.038 1.051 1.067 1.087 1.110 1.146 1.165 1.203

52.72 54.75 57.64 60.84 63.88 67.92 73.06 79.46 90.16 96.44 109.46

1.008 1.018 1.030 1.045 1.058 1.074 1.094 1.119 1.158

54.14 56.14 58.95 62.36 65.64 69.77 75.11 82.04 94.07

0.0000 0.0870 0.1803 0.2735 0.3573 0.4556 0.5638 0.6708 0.8169

AC

At T=323.15 K

1558.00 1537.00 1510.00 1478.00 1450.00 1417.00 1379.00 1334.00 1268.00

41.26 42.69 44.68 47.11 49.42 52.34 56.07 60.91 69.22

M

ED

PT

1583.00 1561.00 1531.00 1500.00 1473.00 1440.00 1402.00 1359.00 1299.00 1267.00 1212.00

CE

0.0000 0.0870 0.1803 0.2735 0.3573 0.4556 0.5638 0.6708 0.8169 0.8812 1.0000

AN

At T=313.15 K

0.9984 0.9915 0.9816 0.9718 0.9624 0.9516 0.9379 0.9226 0.8985

50.85 52.92 55.47 58.44 61.25 65.02 69.81 76.04 85.96 91.20 101.83

591.67 574.28 554.38 533.10 514.65 492.10 466.54 437.56 399.14 381.79 351.51

1.3434 1.3471 1.3514 1.3560 1.3603 1.3656 1.3721 1.3796 1.3921 1.3980 1.4092

1.1409 1.1419 1.1426 1.1424 1.1429 1.1425 1.1422 1.1407 1.1426 1.1427 1.1431

211.37 203.19 194.29 185.25 177.42 168.20 158.12 147.59 133.91 127.94 117.52

594.89 578.24 556.42 534.31 515.11 491.94 465.74 437.32 397.81 378.20 343.93

1.3276 1.3309 1.3350 1.3394 1.3436 1.3490 1.3556 1.3630 1.3753 1.3813 1.3944

1.0443 1.0448 1.0444 1.0439 1.0440 1.0443 1.0447 1.0442 1.0461 1.0451 1.0475

223.87 215.34 205.38 195.54 187.02 177.08 166.21 155.15 140.37 133.51 121.61

601.80 585.60 564.54 541.23 520.84 497.51 470.76 440.60 397.64

1.3120 1.3150 1.3195 1.3239 1.3282 1.3332 1.3396 1.3470 1.3589

0.9575 0.9580 0.9596 0.9593 0.9597 0.9596 0.9603 0.9597 0.9594

238.10 229.11 218.67 207.87 198.49 187.86 176.15 163.96 147.39

T

37.86 39.28 41.04 43.10 45.02 47.61 50.88 55.12 61.74 65.24 72.26

IP

1615.00 1592.00 1565.00 1535.00 1509.00 1476.00 1438.00 1393.00 1334.00 1306.00 1256.00

US

0.0000 0.0870 0.1803 0.2735 0.3573 0.4556 0.5638 0.6708 0.8169 0.8812 1.0000

CR

Oxolane+aniline At T=303.15 K

43

ACCEPTED MANUSCRIPT 0.8812 1.0000

1237.00 1171.00

73.84 85.13

0.8850 0.8566

1.178 1.224

100.86 117.55

377.39 336.44

1.3658 1.3807

0.9608 0.9625

139.98 125.76

42.66 44.01 45.89 47.73 49.78 51.98 54.99 59.07 62.34 66.95 72.26

0.9782 0.9731 0.9660 0.9591 0.9515 0.9435 0.9332 0.9194 0.9082 0.8934 0.8773

1.026 1.034 1.046 1.057 1.069 1.081 1.097 1.119 1.135 1.157 1.181

57.98 59.92 62.62 65.29 68.28 71.49 75.91 81.95 86.85 93.78 101.83

536.27 523.17 506.15 490.54 474.36 458.28 438.13 413.69 396.07 373.89 351.51

1.1545 1.1525 1.1504 1.1486 1.1471 1.1458 1.1439 1.1425 1.1425 1.1426 1.1431

228.16 218.42 206.36 195.54 184.69 174.37 162.68 149.24 139.90 128.70 117.52

45.10 46.49 48.55 50.55 52.83 55.30 58.56 63.11 66.81 72.03 78.50

0.9698 0.9649 0.9583 0.9514 0.9440 0.9360 0.9260 0.9122 0.9008 0.8857 0.8672

47.70 49.11 51.27 53.54 56.03 58.82

0.9610 0.9566 0.9499 0.9434 0.9358 0.9274

1.037 1.046 1.058 1.069 1.082 1.095 1.111 1.134 1.151 1.175 1.203

60.59 62.57 65.49 68.34 71.62 75.17 79.89 86.53 91.99 99.74 109.46

535.92 523.20 505.59 489.67 472.78 455.92 435.56 410.26 391.83 368.80 343.93

1.3434 1.3457 1.3488 1.3520 1.3555 1.3594 1.3643 1.3711 1.3769 1.3847 1.3944

1.0573 1.0558 1.0531 1.0517 1.0498 1.0484 1.0466 1.0452 1.0453 1.0455 1.0475

240.31 230.11 217.16 205.63 193.95 182.83 170.42 155.99 145.93 133.91 121.61

1.049 1.057 1.069 1.081 1.094 1.109

63.38 65.36 68.39 71.59 75.12 79.09

534.67 522.53 505.06 488.01 470.73 452.89

1.3288 1.3308 1.3340 1.3370 1.3406 1.3447

0.9700 0.9686 0.9667 0.9644 0.9631 0.9621

252.78 242.16 228.51 215.97 203.50 191.48

ED

PT

CE

1512.00 1493.00 1466.00 1442.00 1416.00 1390.00 1358.00 1318.00 1289.00 1252.00 1212.00

AC

0.0000 0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

M

At T=313.15 K

IP

T

1.3590 1.3614 1.3647 1.3680 1.3716 1.3755 1.3805 1.3874 1.3931 1.4007 1.4092

CR

1548.00 1528.00 1502.00 1478.00 1453.00 1428.00 1396.00 1357.00 1329.00 1293.00 1256.00

AN

0.0000 0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

US

Oxolane + N-methyl aniline At T=303.15 K

At T=323.15 K 0.0000 0.0831 0.1864 0.2813 0.3782 0.4714

1477.00 1459.00 1433.00 1407.00 1381.00 1354.00

44

ACCEPTED MANUSCRIPT 0.5746 0.6956 0.7823 0.8882 1.0000

1322.00 1282.00 1252.00 1213.00 1171.00

62.40 67.41 71.59 77.60 85.13

0.9169 0.9026 0.8911 0.8758 0.8566

1.126 1.150 1.168 1.194 1.224

84.23 91.47 97.56 106.36 117.55

431.98 406.09 386.93 362.65 336.44

0.9611 0.9606 0.9606 0.9605 0.9625

178.22 162.84 152.03 139.04 125.76

46.88 48.04 49.10 50.49 52.11 53.82 56.38 59.21 63.05 67.35 72.26

0.9519 0.9478 0.9438 0.9395 0.9345 0.9293 0.9219 0.9131 0.9021 0.8908 0.8773

1.053 1.060 1.066 1.074 1.083 1.092 1.105 1.120 1.139 1.159 1.181

64.29 65.98 67.53 69.54 71.91 74.40 78.16 82.34 88.03 94.44 101.83

496.28 486.73 478.31 467.89 456.30 444.76 428.64 412.22 392.07 371.94 351.51

1.3714 1.3734 1.3753 1.3774 1.3799 1.3825 1.3861 1.3906 1.3962 1.4021 1.4092

1.1639 1.1625 1.1618 1.1597 1.1575 1.1555 1.1523 1.1505 1.1478 1.1445 1.1431

245.62 234.41 221.77 209.57 197.09 185.25 171.59 156.72 144.43 130.96 117.52

49.54 50.56 51.84 53.34 55.08 57.00 59.87 63.03 67.43 72.38 78.50

0.9443 0.9408 0.9367 0.9324 0.9276 0.9226 0.9152 0.9064 0.8954 0.8828 0.8672

1.064 1.070 1.077 1.085 1.094 1.104 1.119 1.134 1.155 1.177 1.203

67.15 68.61 70.46 72.60 75.10 77.86 81.99 86.61 93.02 100.33 109.46

496.16 488.25 478.60 467.96 456.23 444.07 427.16 409.97 388.58 367.15 343.93

1.3554 1.3571 1.3591 1.3611 1.3635 1.3660 1.3696 1.3740 1.3796 1.3862 1.3944

1.0664 1.0657 1.0645 1.0627 1.0606 1.0582 1.0551 1.0532 1.0500 1.0481 1.0475

258.48 247.18 233.42 220.47 207.26 194.58 179.95 164.07 150.79 136.33 121.61

52.18 53.17 54.60

0.9359 0.9328 0.9291

1.075 1.081 1.088

69.95 71.35 73.38

496.57 489.23 479.08

1.3406 1.3421 1.3439

0.9803 0.9797 0.9779

272.16 260.42 245.72

PT

CE

1462.00 1450.00 1435.00 1418.00 1399.00 1379.00 1351.00 1323.00 1287.00 1251.00 1212.00

AC

0.0000 0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

ED

At T=313.15 K

IP

CR

US

AN

1497.00 1482.00 1469.00 1452.00 1433.00 1414.00 1387.00 1360.00 1326.00 1291.00 1256.00

M

0.0000 0.0831 0.1864 0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

T

Oxolane+ N- ethyl aniline At T=303.15 K

1.3498 1.3569 1.3627 1.3706 1.3807

At T=323.15 K 0.0000 0.0831 0.1864

1431.00 1420.00 1404.00

45

ACCEPTED MANUSCRIPT 56.10 58.13 60.28 63.49 67.22 72.10 77.49 85.09

0.9252 0.9206 0.9157 0.9081 0.8995 0.8877 0.8742 0.8571

1.096 1.106 1.117 1.132 1.149 1.171 1.194 1.224

75.50 78.36 81.40 85.97 91.32 98.37 106.27 117.46

468.94 456.06 443.22 425.41 406.59 384.53 362.89 336.64

1.3457 1.3480 1.3504 1.3541 1.3584 1.3644 1.3714 1.3805

0.9763 0.9735 0.9710 0.9681 0.9651 0.9632 0.9629 0.9620

232.20 217.88 204.29 188.60 171.42 157.25 142.00 125.80

CE

PT

ED

M

AN

US

CR

IP

T

1388.00 1367.00 1346.00 1317.00 1286.00 1250.00 1215.00 1171.00

AC

0.2813 0.3782 0.4714 0.5746 0.6956 0.7823 0.8882 1.0000

46

ACCEPTED MANUSCRIPT Highlights

 Seven binary solutions at different temperatures are studied.  Flory’s Statistical Theory (FST) has been applied to the seven binary liquid mixtures.  Empirical relations are used for comparison with FST in the aforesaid systems.

AC

CE

PT

ED

M

AN

US

CR

IP

T

 Various important thermodynamic properties are also calculated.

47