HUNGARIAN JOURNAL OF 
INDUSTRY AND CHEMISTRY 

Vol. 52(1) pp. 19–27 (2024) 

hjic.mk.uni-pannon.hu 
DOI: 10.33927/hjic-2024-04 

MOLECULAR INTERACTION STUDIES OF BINARY MIXTURES OF 
DIETHYL OXALATE WITH BUTYL VINYL ETHER, DIISOPROPYL ETHER, 
ANISOLE AND DIBUTYL ETHER IN TERMS OF THERMODYNAMIC, 
TRANSPORT AND ACOUSTIC PROPERTIES 

AJIT BHUMKAR1* AND PRALHAD WAGH1 

1 Department of Chemistry, VPM’s B.N. Bandodkar College of Science (Autonomous), Thane, 
400601, INDIA 

Viscosity, the speeds of sound and density were measured in the binary mixtures of diethyl oxalate with butyl vinyl 
ether, diisopropyl ether, anisole and dibutyl ether at T = 303.15, 308.15 and 313.15 K. The experimental data 
were used to calculate the excess molar volume 𝑉𝑚

𝐸 ,deviation in viscosity Δη and the acoustical parameters, 
namely isentropic compressibility (KS), free volume (Vf ), free length (Lf ) and internal pressure (πi). The excess or 
deviation properties were fitted to the Redlich-Kister polynomials and the results interpreted in terms of the 
molecular interactions present in mixtures. Theoretical viscosities were calculated using the Grunberg-Nissan, 
Lobe and Krishnan-Laddha models before their merits were studied in terms of interaction parameters. 

Keywords: diethyl oxalate, density, viscosity, speeds of sound, isentropic compressibility  

1. Introduction 

Thermodynamic, transport and ultrasonic properties of 

liquid-liquid mixtures are essential theoretically and in 

terms of process design. Density, viscosity and speeds of 

sound as well as their excess or deviation properties are 

mostly useful in engineering design processes in addition 

to the chemical and biological industries [1]. The analysis 

of these properties provides detailed information on the 

intermolecular interactions present in the liquid mixtures. 

Further excess properties provide key values for 

calculating the properties of multicomponent mixtures 

from the data of pure components. They can also provide 

data to evaluate parameters characterizing interactions 

between unlike molecules. 

Diethyl oxalate (DEO) is a colorless organic 

compound and the diethyl ester of oxalic acid. DEO is 

used in active pharmaceutical ingredients, polymers and 

intermediates for dyestuffs as well as a solvent to make 

esters, resins, fragrances and electronic lacquers. 

Tremendous growth has been seen in the pharmaceutical 

industry attributed to the high consumption of DEO. 

Demand for drugs such as steroids and barbiturates has 

led to an increase in the usage of DEO. While ethers are 

a class of organic compounds that contain an oxygen 

between two alkyl groups, they are relatively unreactive 

so are useful as solvents for fats, oils, waxes, perfumes, 

resins, dyes, gums and hydrocarbons. Vapors of certain 

 

Received: 14 Nov 2023; Revised: 18 Dec 2023; 
Accepted: 5 Jan 2024 
*Correspondence: ajitnanabhumkar@gmail.com  

ethers are used as insecticides, mildewcides and 

fumigants for soil. These numerous applications of ethers 

have sparked the present study to know more about their 

possible molecular interactions when mixed with DEO. 

A literature review uncovered several studies on the 

thermodynamic, transport and volumetric properties of 

binary mixtures of esters with different organic liquids 

[2]-[6]. Likewise, few studies have been undertaken on 

the density, viscosity and speeds of sound [7]-[11] of 

binary mixtures containing DEO with ethers as well as 

polar and non-polar solvents. However, it has been 

observed that to the best of our knowledge, except for the 

system of DEO with anisole (AS), no studies have been 

found in the literature concerning any of the other binary 

systems undertaken in our present study. The study of the 

thermodynamic and transport properties of binary 

mixtures containing esters with ethers contributes to the 

understanding of the theory of the liquid state [12]-[17]. 

In this paper, the densities, viscosities and speeds of 

sound of the binary mixtures of DEO with butyl vinyl 

ether (BVE), diisopropyl ether (DIPE), AS and dibutyl 

ether (DBE) at T = 303.15, 308.15 and 313.15 K were 

reported. From the above experimental data, several 

excess or deviation parameters were evaluated at the 

respective temperatures which are important in industrial 

processes. These excess or deviation properties were 

fitted to the Redlich-Kister polynomial equation [18] to 

derive the binary coefficients and estimate the standard 

https://doi.org/10.33927/hjic-2024-04
mailto:ajitnanabhumkar@gmail.com


  BHUMKAR AND WAGH 

Hungarian Journal of Industry and Chemistry 

20 

errors. The experimental viscosity data were used to test 

correlations between viscosity models proposed by 

Grunberg-Nissan [22], Lobe [23] and Krishnan-Laddha 

[24]. 

2. Experimental 

2.1. Materials 

DEO, BVE, DIPE, AS and DBE all with a mass fraction 

purity of >0.990 were supplied by Sigma-Aldrich and 

purified by vacuum distillation. The filtrates of these 

chemicals were collected in dark bottles over molecular 

sieve 0.4 nm beads to remove any water then degassed 

just before their use. Gas chromatography (GC) detected 

no traceable amounts of impurities in the filtrates. The 

stated purities of these filtered chemicals and their final 

purities as estimated by GC (HP 8610) analysis are 

shown in Table 1. 

2.2. Methods 

The binary liquid mixtures were arranged by mixing 

known masses of pure liquids in airtight stoppered 

bottles. All mass measurements were made using a 

Mettler single-pan digital balance with an accuracy of 

+0.01mg (AE240, Switzerland). The resulting mole 

fraction uncertainty was calculated to be less than 

1×10-4. The densities of the pure chemicals and their 

binary mixtures were fixed by using a density meter 

(Rudolph Research Analytical DDM 2910). The 

instrument contains a high-precision platinum 

thermometer in the density sensor to accurately measure 

the temperature. The instrument was calibrated 

frequently before each experiment was started using 

deionized double distilled water and dry air. The 

uncertainty in the densities was within 0.0004 g·cm-3. 

The viscosities of the pure liquids and their mixtures 

were measured by using a Ubbelohde viscometer [17]. 

The viscometer was calibrated using double distilled 

water. The uncertainty in the viscosities was estimated to 

be within 0.10 mPa·s. 

The speeds of sound of the pure liquids and liquid 

mixtures were calculated by using a Mittal Enterprises 

model F-81 single-crystal variable path interferometer 

(New Delhi, India) operating at a frequency of 2 MHz 

and with an accuracy of + 0.01ms-1. The instrument was 

calibrated by measuring the velocity in standard liquids, 

i.e. AR grade benzene and carbon tetrachloride. The 

estimated uncertainty in the speeds of sound was found 

to be within 1%. All measurements were taken at a 

constant temperature in an INSREF model IRI-016C 

constant low temperature bath (India) by circulating 

water from a thermostat around the cell containing the 

liquid. 

3. Results and discussion 

The experimental values of the density (ρ), viscosity (η), 

speeds of sound (U) and isentropic compressibility (KS) 

were determined for the studied binary mixtures over the 

entire composition range expressed as a function x1 of 

DEO at 303.15, 308.15 and 313.15 K. A large number of 

data are not reported in this paper but are available from 

the editorial office of this journal.  

From the density data, excess molar volumes (𝑉𝑚
𝐸) 

and deviations in viscosity (∆η) were calculated using the 

following relations: 

𝑉𝑚
𝐸 = (𝑥1𝑀1 + 𝑥2𝑀2)/𝜌12 − (𝑥1𝑀1/𝜌1 + 𝑥2𝑀2/𝜌2) (1) 

∆𝜂 = 𝜂12 − (𝑥1𝜂1 + 𝑥2𝜂2) (2) 

where x, M, η and ρ are the mole fraction, molar mass, 

viscosity and density, respectively, of the pure 

components 1 and 2. ρ12 denotes the density and η12 the 

viscosity of the binary mixture. 

Isentropic compressibility (KS), deviation in 

isentropic compressibility (∆KS), intermolecular free 

length (Lf), internal pressure (πi) and free volume (Vf) are 

calculated using the following equations: 

𝐾𝑆 = [1/(𝑈2𝜌)] (3) 

∆𝐾𝑆 = (𝐾𝑆)12 − [𝑥1(𝐾𝑆)1 + 𝑥2(𝐾𝑆)2] (4) 

𝐿𝑓 = 𝐾 ∙ (𝐾𝑆)1/2 (5) 

𝜋𝑖 = 𝑏𝑅𝑇(𝐾𝜂/𝑈)1/2 (𝜌2/3 / 𝑀𝑒𝑓𝑓
7/6

) (6) 

𝑉𝑓 = (𝑀𝑒𝑓𝑓𝑈/𝜂𝐾)
3/2

 (7) 

In Equations 5-7, K denotes the temperature-

dependent Jacobson’s constant and b stands for the cubic 

packing fraction taken as 2 for all the liquids, while R 

represents the universal gas constant and T refers to the 

experimental temperature. Meff = ∑ximi. where xi denotes 

the mole fraction and mi stands for the molecular weight 

of the ith component. These calculated properties are also 

available at the editorial office. 

Furthermore, the excess or deviation properties (Y) 

recorded were fitted to the following Redlich-Kister 

polynomial equation by the method of least squares to 

derive the binary coefficients: 

∆𝑌 = 𝑥1𝑥2[𝐴0 + 𝐴1(𝑥1 − 𝑥2) + 𝐴2(𝑥1 − 𝑥2)2] (8) 

Table 1: Chemical Specifications and Purity 

Estimation 

Chemical Source Initial 
mole 

fraction 

purity 

Purification 
method 

Analysis 
method 

Final 
mole 

fraction 

purity 

DEO Sigma-

Aldrich 

0.990 None GC-8610 > 0.996 

BVE Sigma-
Aldrich 

0.980 Distillation GC-8610 > 0.984 

DIPE Sigma-

Aldrich 

0.980 None GC-8610 > 0.984 

AS Sigma-

Aldrich 

0.997 None GC-8610 > 0.997 

DBE Sigma-

Aldrich 

0.993 Distillation GC-8610 > 0.995 

GC* - Gas-liquid chromatography 



MOLECULAR INTERACTION STUDIES OF BINARY MIXTURES 

52(1) pp. 19–27 (2024) 

21 

where ΔY represents the relevant excess or deviation 

property. The standard deviations of 𝑉𝑚
𝐸, ∆η, ∆KS, excess 

free volume (𝑉𝑓
𝐸), excess intermolecular free length (𝐿𝑓

𝐸) 

and excess internal pressure (𝜋𝑖
𝐸) were calculated using 

the following equation: 

𝜎(𝑌) = [∑(𝑌𝑒𝑥𝑝 − 𝑌𝑐𝑎𝑙)
2

/(𝑁 − 𝑛)]
1/2

 (9) 

where N denotes the number of data points, n represents 

the number of coefficients, while Yexp and Ycal denote 

experimentally obtained and theoretically calculated 

excess or deviation properties, respectively. The 

calculated values of the polynomial coefficients A0, A1 

and A2 along with their standard deviations σ are given in 

Table 2, moreover, the results of the excess or deviation 

properties calculated by Equation 8 are graphically 

represented in Figures 1-6. 

As shown in Figure 1, the 𝑉𝑚
𝐸 values for the binary 

mixtures of DEO with BVE, DEO with DIPE and DEO 

with AS are negative, whereas for DEO with DBE it is 

positive over the entire range of composition at all the 

studied temperatures. Furthermore, the 𝑉𝑚
𝐸  values 

decrease as the temperature increases for the mixtures of 

DEO with BVE, DIPE and DBE, while for DEO with AS, 

these 𝑉𝑚
𝐸  values increase as the temperature increases, 

indicative of the effect of the temperature. The 𝑉𝑚
𝐸 values 

are found to be more negative for DIPE with minima in 

the isotherm at x1 = 0.5018, while for DBE, the 𝑉𝑚
𝐸 values 

are positive and the maximum for the excess volume 

observed at x1 = 0.5018. These 𝑉𝑚
𝐸 values can be ordered 

as follows: 

DBE > AS > BVE > DIPE 

The negative 𝑉𝑚
𝐸  may be due to the interstitial 

accommodation of the ester molecules with an associated 

structure, the formation of weak molecular complexes 

through hydrogen bonds, π-π interactions and dipole-

dipole interactions. While positive 𝑉𝑚
𝐸  values may be 

attributed to the breaking of the molecular association of 

the components. In our present study, the molar masses 

of DEO, BVE, DIPE, AS and DBE are 146.14, 100.16, 

102.18, 108.14 and 130.23 g·mol-1, respectively. The 

molar volumes of DEO at T = 303.15, 308.15 and 313.15 

K are 137.04, 137.79 and 138.52 cm3·mol-1, respectively. 

Furthermore, the molar volumes for the studied ethers - 

namely BVE, DIPE, AS and DBE - are (130.25, 131.12, 

132.00), (143.28, 144.34, 145.45), (109.85, 110.37, 

110.91) and (170.45, 172.44, 173.45) cm3·mol-1, 

respectively. These molar volumes of DEO differ slightly 

to those of BVE, DIPE and AS, indicating that the 

molecules of DEO are interstitially accommodated into 

clusters of BVE, DIPE and AS leading to negative 𝑉𝑚
𝐸 

values. The increase in 𝑉𝑚
𝐸  values for AS as the 

temperature increases may confirm the presence of 

stronger dispersion forces or dipole–dipole interactions 

between the component molecules leading to greater 

contraction in volumes as the temperature rises. The 

positive 𝑉𝑚
𝐸 values observed for DEO and DBE may 

indicate weak molecular interactions.  

The variation in the deviation in viscosity (∆η) as a 

function of the mole fraction (x1) of DEO at the studied 

temperatures is shown in Figure 2. It was observed that 

for all the systems of DEO, ∆η was found to be negative 

throughout and at the studied temperatures. These 

negative ∆η values suggest the presence of weak dipolar 

forces in mixtures of liquids. It is found that ∆η is large 

and negative for the mixtures of DEO with DIPE but less 

negative for the DEO with AS ones. As suggested by 

Hasan et al. [19], the destruction of the short-range 

orientation structural order in pure liquids as a result of 

hydrogen bonds and dipolar interactions causes 

dispersive interactions between unlike molecules giving 

rise to negative deviations in viscosity of liquid mixtures. 

A graphical comparison of the values of the density, 

viscosity and excess volume at T = 303.15 and 308.15 K 

of the DEO with AS system recorded by Baragi et al. [8] 

 
Figure 1: 𝑉𝑚

𝐸 vs. x 1 for the binary mixtures of: 

DEO with BVE at □ 303.15, ◊ 308.15 and Δ 313.15 K; 

DEO with DIPE at × 303.15, җ 308.15 and ▬ 313.15 K; 

DEO with AS at ● 303.15, + 308.15 and ■ 313.15 K; 

DEO with DBE at ◊ 303.15, ▲ 308.15 and O 313.15 K 

-1,2

-0,8

-0,4

0

0,4

0 0,2 0,4 0,6 0,8 1

V
m

E
/(

cm
3
m

o
l-1

)

x1

 
Figure 2: Δη vs. x1 for the binary mixtures of: 

DEO with BVE at □ 303.15, ◊ 308.15 and Δ 313.15 K; 

DEO with DIPE at × 303.15, җ 308.15 and ▬ 313.15 K; 

DEO with AS at ● 303.15, + 308.15 and ■ 313.15 K; 

DEO with DBE at ◊ 303.15, ▲ 308.15 and O 313.15 K 

-0,32

-0,24

-0,16

-0,08

0

0 0,2 0,4 0,6 0,8 1

Δ
η
/(

m
P

a
.s

)

x1



  BHUMKAR AND WAGH 

Hungarian Journal of Industry and Chemistry 

22 

is presented in Figures 7-9, respectively. 

 

 

 

 

 

 

 

 

  

 
Figure 3: ΔKS vs. x1 for the binary mixtures of: 

DEO with BVE at × 303.15, җ 308.15 and ▬ 313.15 K; 

DEO with DIPE at □ 303.15, 308.15 and Δ 313.15 K; 

DEO with AS at ● 303.15, + 308.15 and ■ 313.15 K; 

DEO with DBE at  303.15, ▲ 308.15, O 313.15 K 

 
Figure 4: 𝑉𝑓

𝐸 vs. x1 for the binary mixtures of: 

DEO with BVE at ♦ 303.15, ■ 308.15 and Δ 313.15 K; 

DEO with DIPE at җ 303.15, O 308.15 and + 313.15 K; 

DEO with AS at ▬ 303.15, ◊ 308.15 and □ 313.15 K; 

DEO with DBE at × 303.15, җ 308.15 and ● 313.15 K 

-0,105

-0,085

-0,065

-0,045

-0,025

-0,005

0 0,2 0,4 0,6 0,8 1

V
fE

/m
3
.m

o
l 

-1

x1

 
Figure 5: 𝐿𝑓

𝐸 vs. x1 for the binary mixtures of: 

DEO with BVE at □ 303.15, ◊ 308.15 and Δ 313.15 K; 

DEO with DIPE at × 303.15, җ 308.15 and ▬ 313.15 K; 

DEO with AS at O 303.15, + 308.15 and ■ 313.15 K; 

DEO with DBE at ♦ 303.15, ▲ 308.15, ● 313.15 K 

 
Figure 6: π𝑖

𝐸 vs. x1 for the binary mixtures of: 

DEO with BVE at ♦ 303.15, ■ 308.15 and Δ 313.15 K; 

DEO with DIPE at җ 303.15, O 308.15 and + 313.15 K; 

DEO with AS at ▬ 303.15, ◊ 308.15 and □ 313.15 K; 

DEO with DBE at × 303.15, җ 308.15 and ● 313.15 K 

-0,28

-0,19

-0,1

-0,01

0 0,2 0,4 0,6 0,8 1

π
i

E
/c

m
3
.m

o
l 

-1

x1



MOLECULAR INTERACTION STUDIES OF BINARY MIXTURES 

52(1) pp. 19–27 (2024) 

23 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

Table 2: Parameters of Equation 8 for various functions and the corresponding standard deviations (σ) of the binary 

mixtures at 303.15, 308.15 and 313.15 K  

Binary mixture  T (K) Excess property Ao A1 A2 𝜎 

DEO + BVE 303.15 𝑉𝑚
𝐸  (cm3·mol-1) -1.6578 -0.2804 1.0443 0.008 

  𝛥𝜂 (mPa·s) -0.9331 -0.2035 0.0142 0.001 

  ΔKs (TPa-1) 1.7257 0.0902 0.6977 0.002 

  Vf
E × 10-6 (m3·mol-1) -0.2483 0.01275 0.0028 0.000 

  𝐿𝑓
𝐸 × 10-8  (cm) 0.0335 0.0056 0.0029 0.000 

  𝜋i
E × 10-6   (Nm-2) -0.3006 0.1191 0.0761 0.001 

 308.15 𝑉𝑚
𝐸  (cm3·mol-1) -1.7406 -0.2060 0.7103 0.013 

  𝛥𝜂 (mPa·s) -0.8227 -0.2035 -0.0003 0.001 

  ΔKs (TPa-1) 1.6081 0.1759 0.4717 0.005 

  Vf
E × 10-6 (m3·mol-1) -0.2268 0.0014 0.0173 0.001 

  𝐿𝑓
𝐸 × 10-8 (cm) 0.0322 0.0053 0.0090 0.000 

  𝜋i
E × 10-6 (Nm-2) -0.2768 0.0957 0.1158 0.002 

 313.15 𝑉𝑚
𝐸 (cm3·mol-1) -1.8354 -0.1895 0.4415 0.012 

  𝛥𝜂 (mPa·s) -0.7656 -0.1767 -0.0294 0.001 

  ΔKs (TPa-1) 1.4733 0.2236 0.3123 0.006 

  Vf
E × 10-6 (m3·mol-1) -0.2223 -0.0150 0.0275 0.000 

  𝐿𝑓
𝐸 × 10-8 (cm) 0.0321 0.0050 -0.0004 0.000 

  𝜋i
E × 10-6 (Nm-2) -0.3246 0.0949 0.0019 0.001 

DEO + DIPE 303.15 𝑉𝑚
𝐸  (cm3·mol-1) -3.8814 -0.1995 0.1160 0.016 

  𝛥𝜂 (mPa.s) -1.1946 -0.3873 -0.0850 0.000 

  ΔKs (TPa-1) -6.4274 0.9665 0.1169 0.013 

  Vf
E × 10-6 (m3·mol-1)  -0.3899 0.03931 0.0134  0.001 

  𝐿𝑓
𝐸 × 10-8 (cm) 0.04034 0.0121 0.0028 0.000 

  𝜋i
E × 10-6 (Nm-2) -0.5095 0.0779 0.0665 0.001 

 308.15 𝑉𝑚
𝐸 (cm3·mol-1) -4.0847 -0.0394 -0.2515 0.014 

  𝛥𝜂 (mPa·s) -1.0418 -0.3387 -0.0976 0.000 

  ΔKs (TPa-1) -7.0499 1.2347 -0.2205 0.012 

  Vf
E × 10-6 (m3·mol-1) -0.3978 0.0481 0.0185 0.001 

  𝐿𝑓
𝐸 × 10-8 (cm) 0.04374 0.0117 0.0003 0.000 

  𝜋i
E × 10-6  (Nm-2) -0.3914 0.0831 0.0838 0.001 

 313.15 𝑉𝑚
𝐸 (cm3·mol-1) -4.2667 0.0259 -0.5911 0.018 

  𝛥𝜂 (mPa·s) -0.9175 -0.2913 -0.0746 0.001 

  ΔKs (TPa-1) -7.7585 1.4416 -0.5426 0.017 

  Vf
E × 10-6 (m3·mol-1) -0.4054 0.0682 0.0011 0.000 

  𝐿𝑓
𝐸 × 10-8 (cm) 0.04370 0.0136 0.0039 0.000 

  𝜋i
E × 10-6 (Nm-2) -0.3220 0.0624 0.0375 0.001 

DEO + AS 303.15 𝑉𝑚
𝐸  (cm3·mol-1) -0.8468 0.0252 -0.2574 0.004 

  𝛥𝜂 (mPa·s) -0.1699 -0.0186 -0.0318 0.000 

  ΔKs (TPa-1) 0.7685 0.0434 -0.0821 0.003 

  Vf
E × 10-6 (m3·mol-1) -0.0244 0.0016 0.0064 0.000 

  𝐿𝑓
𝐸 ×10-8 (cm) 0.0042 -0.0002 -0.0007 0.000 

  𝜋i
E × 10-6 (Nm-2) -0.0244 0.0016 0.0064 0.000 

 308.15 𝑉𝑚
𝐸  (cm3·mol-1) -0.7708 0.1124 -0.0633 0.002 

  𝛥𝜂 (mPa·s) -0.1491 -0.0181 -0.0306 0.000 

  ΔKs (TPa-1) 0.3415 -0.2199 0.0768 0.005 

  Vf
E × 10-6 (m3·mol-1)       -0.0277 0.0026 0.0082 0.000 

  𝐿𝑓
𝐸 × 10-8 (cm) 0.0041 -0.0037 -0.0052 0.000 

  𝜋i
E × 10-6 (Nm-2)        -0.0277 0.0026 0.0082 0.000 

 313.15 𝑉𝑚
𝐸 (cm3·mol-1) -0.7053 0.1648 0.1500 0.004 

  𝛥𝜂 (mPa·s) -0.1336 -0.0183 -0.0041 0.000 

  ΔKs (TPa-1) 0.1518 -0.1619 -0.1085 0.002 

  Vf
E ×10-6 (m3·mol-1) -0.0304 0.0049 0.0016 0.000 

  𝐿𝑓
𝐸 × 10-8 (cm) 0.0018 -0.0006 -0.0003 0.000 

  𝜋i
E × 10-6 (Nm-2) -0.0489 -0.0134 -0.0172 0.001 

 



  BHUMKAR AND WAGH 

Hungarian Journal of Industry and Chemistry 

24 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

Table 2 (continued): Parameters of Equation 8 for various functions and the corresponding standard deviations (σ) of the 

binary mixtures at 303.15, 308.15 and 313.15 K  

Binary mixture  T (K) Excess property Ao A1 A2 𝜎 

DEO + DBE 303.15 𝑉𝑚
𝐸 (cm3·mol-1) 1.2523 -0.4768 -0.1035 0.005 

  𝛥𝜂 (mPa·s) -0.8823 -0.3128 -0.1872 0.002 

  ΔKs (TPa-1) -4.5150 -0.0774 0.1275 0.005 

  Vf
E × 10-6 (m3·mol-1) -0.0167 -0.0595 0.0480 0.001 

  𝐿𝑓 
𝐸 × 10-8 (cm) 0.0027 0.0001  0.0003 0.000 

  𝜋i
E ×10-6 (Nm-2) -1.0201 -0.2342 -0.1808 0.001 

 308.15 𝑉𝑚
𝐸 (cm3·mol-1) 1.1863 -0.4387 -0.3837 0.005 

  𝛥𝜂 (mPa·s) -0.7694 -0.2750 -0.1056 0.001 

  ΔKs (TPa-1) -4.7739 -0.0111 -0.2990 0.002 

  Vf
E ×10-6 (m3·mol-1) -0.0196 -0.0437 0.0106 0.001 

  𝐿𝑓
𝐸×10-8 (cm) 0.0035 -0.0001 -0.0095 0.000 

  𝜋i
E ×10-6 (Nm-2) -0.9246 -0.2237 -0.0097 0.001 

 313.15 𝑉𝑚
𝐸 (cm3·mol-1) 1.0757 -0.4354 -0.4843 0.002 

  𝛥𝜂 (mPa·s) -0.6759 -0.2224 -0.0089 0.000 

  ΔKs (TPa-1) -4.9529 0.0234 -0.2893 0.003 

  Vf
E ×10-6 (m3·mol-1) -0.0324 -0.0315 -0.0314 0.001 

  𝐿𝑓
𝐸 × 10-8 (cm) 0.0017 0.0004 -0.0005 0.000 

  𝜋i
E × 10-6 (Nm-2) -0.8775 -0.2027 0.0535 0.001 

 

 

 
Figure 7: Comparison between the densities (ρ) for the 

binary mixtures of: 

AS with DEO at ■ 303.15 and ▲ 308.15 K (values 

measured by Baragi et al. [8]) 

DEO with AS at ● 303.15 and ▼ 308.15 K (present study) 

 
Figure 8: Comparison between the viscosities (η) for the 

binary mixtures of: 

AS with DEO at ■ 303.15 and ▲ 308.15 K (values 

measured by Baragi et al. [8]) 

DEO with AS at ● 303.15 and ▼ 308.15 K (present study) 

 
Figure 9: Comparison between the excess molar volumes 

(𝑉𝑚
𝐸) for the binary mixtures of: 

AS with DEO at ■ 303.15 and ▲ 308.15 K (values 

measured by Baragi et al. [8]) 

DEO with AS at ● 303.15 and ▼ 308.15 K (present study)  



MOLECULAR INTERACTION STUDIES OF BINARY MIXTURES 

52(1) pp. 19–27 (2024) 

25 

Close observation of these figures reveals that these 

values agree with each other quite satisfactorily. The 

variation in ΔKS with regard to the composition of the 

mixtures (x1 of DEO) at 303.15, 308.15 and 313.15 K is 

presented in Figure 3. It was observed that ΔKS is positive 

for the mixtures of DEO with BVE and AS, while 

negative throughout for the mixtures of DEO with DIPE 

and DBE at all studied temperatures. Strong 

intermolecular interactions due to dipole-dipole 

interactions and interstitial accommodation result in the 

reduction in the deviations in the isentropic 

compressibility leading to negative deviations, while 

positive deviations indicate weak intermolecular 

interactions. 

The variation in 𝑉𝑓
𝐸 for the studied DEO mixtures is 

plotted in Figure 4. It is observed that the values of 𝑉𝑓
𝐸 

exhibit negative deviations for the mixtures of DEO with 

BVE, DIPE and AS, while for the mixtures of DEO with 

DBE, 𝑉𝑓
𝐸  showed both positive and negative deviations 

throughout. The change from positive to negative 

deviations occurs at x1 = 0.3965. This deviation in 𝑉𝑓
𝐸  

depends on the relative strength between the contractive 

and expansive forces. The factors responsible for volume 

contraction are specific interactions between the 

component molecules, namely weak physical forces such 

as dipole-dipole or Van der Waals forces. The negative 

values of 𝑉𝑓
𝐸  suggest the existence of strong dipole-

dipole interactions. Furthermore, the absolute values of 

𝑉𝑓
𝐸  increase in the mixture of DEO with BVE as the 

temperature increases, suggesting the strengthening of 

intermolecular interactions between unlike molecules 

due to thermal energy. However, for the mixtures of DEO 

with DIPE, AS and DBE, 𝑉𝑓
𝐸  decreases as the 

temperature increases. 

Figure 5 shows that 𝐿𝑓
𝐸  is positive for all the 

systems. For the mixture of DEO with DIPE, 𝐿𝑓
𝐸  

increases as the temperature increases, while for those of 

DEO with BVE, AS and DBE, it decreases throughout at 

all studied temperatures. The negative values of 𝐿𝑓
𝐸  show 

that sound waves cover long distances due to a decrease 

in the intermolecular free length given the strength of 

interactions between hydrogen bonds of unlike 

molecules [20]. Positive 𝐿𝑓
𝐸  values may be attributed to 

the dispersion forces [21].  

The plots of the 𝜋𝑖
𝐸  against the mole fraction of 

DEO (x1) are shown in Figure 6. It was observed from 

the plots that the values of 𝜋𝑖
𝐸  for all the systems are 

negative throughout, while for the mixture of DEO with 

DBE, 𝜋𝑖
𝐸 is more negative. The internal pressure values 

are a reflection of the net cohesive or adhesive forces 

available in the medium.  

3.1. Estimation of the theoretical viscosity of 
mixtures 

The theoretical viscosity of binary mixtures was 

calculated using the following semi-empirical relations. 

Grunberg-Nissan [22] proposed the following 

relation:  

ln 𝜂𝑚𝑖𝑥 = 𝑥1 ln 𝜂1 + 𝑥2 ln 𝜂2 + 𝑥1𝑥2𝑑12 (10) 

where d12 denotes an interaction parameter. 

 

Lobe [23] represented a two-parameter relation as 

follows: 

𝑉 = 1𝑣1 ∙ 𝑒𝑥𝑝(2𝛼𝐴) + 2𝑣2 ∙ 𝑒𝑥𝑝(1𝛼𝐵) (11) 

where v, v1 and v2 denote the kinematic viscosities of the 

mixtures as well as of pure liquids 1 and 2, respectively. 

1 and 2 stand for the volume fractions of the pure 

components. A, and B represent the interaction 

parameters A = AB ln(v2/v1) and B = BA ln(v2/v1) 

where AB and BA denote parameters to fit the 

experimental data. 

A three-parameter relation proposed by Krishnan-

Laddha [24] is represented as follows: 

ln 𝜐 = ln 𝜐1 + 𝑥2 ln 𝜐2 + 𝑥1 ln 𝑀1 + 𝑥2 ln 𝑀2 −
ln[𝑥1𝑀1 + 𝑥2𝑀2] − 2.303𝑥1𝑥2[𝐵12 + 𝐶12(𝑥1 − 𝑥2) +

𝐷12(𝑥1 − 𝑥2)2] (12) 

where υ, υ1 and υ2 refer to kinematic viscosities, while 

B12, C12 and D12 are binary coefficients. 

The predictive ability of Equations 10-12 was tested 

by estimating the percentage standard deviation σ(%) 

between the experimental and determined viscosities as 

follows: 

𝜎(%) = [1/(𝑛 − 𝑘) ∑{100(𝑛𝑒𝑥𝑝 − 𝑛𝑐𝑎𝑙)/𝑛𝑒𝑥𝑝}
2

]
1/2

 (13) 

where n represents the number of data points in each set 

and k denotes the number of numerical coefficients in the 

equation, while nexp and ncal denote experimentally 

obtained and theoretically calculated mixtures 

viscosities, respectively. 

The values of the interaction parameters measured 

from the above relations together with the percentage 

standard deviations σ(%) are reported in Table 3. A close 

examination of the values of σ(%) reveals that the σ(%) 

values for one parameter of the Grunberg-Nissan 

equation fall between 0.01 and 0.05, for two of the Lobe 

equation between 0.00 and 0.04, while for 3 of the 

Krishnan–Laddha equation between 0.00 and 0.01. From 

these σ(%) values, it can be concluded that the three 

parameters of the Krishnan-Laddha relation calculate the 

theoretical viscosity more satisfactorily than the other 

two models. 

4. Conclusions 

The density, viscosity and speed of sound data have been 

described for binary mixtures of diethyl oxalate with 

butyl vinyl ether, diisopropyl ether, anisole and dibutyl 

ether at 303.15, 308.15 and 313.15 K over the whole 

range of the composition. Using the experimental data, 

the various excess or deviation properties - namely 𝑉𝑚
𝐸, 

∆η, ΔKS, 𝑉𝑓
𝐸 , 𝐿𝑓

𝐸  and 𝜋𝑖
𝐸  - were assessed. All the 

calculated excess or deviation properties exhibited either 

positive or negative deviations as a result of the effect of 

the temperature. These excess parameters are indicative 

of the weak interactions (dispersion forces) between 



  BHUMKAR AND WAGH 

Hungarian Journal of Industry and Chemistry 

26 

DEO and DBE, while for the other mixtures the strong 

interactions of charge transfer and dipole-induced dipole 

forces are implied. It may be suggested that molecular 

interactions between esters and ethers through hydrogen 

bonding and dipole-dipole interactions may be present.  
In comparison with our earlier work [25], the 

present reported system of DEO with ethers was found to 

yield stronger molecular interactions perhaps due to the 

molecular weight of vinyl acetate being less than that of 

DEO, resulting in a reduction in the flow time observed 

for vinyl acetate because smaller molecules are not 

resistant to flow. Therefore, in the case of vinyl acetate, 

thinner and less viscous substances are produced. 

Additionally, it can be concluded that the carbonyl 

oxygen of DEO may interact with the hydrogen of ethers, 

resulting in stronger hydrogen bonding. 

Nomenclature 

ρ density (g·cm-3) 

∆η deviation in viscosity (mPa·s) 

∆KS deviation in isentropic compressibility 

 (TPa-1) 

𝑉𝑚
𝐸 excess molar volumes (cm3·mol-1) 

𝑉𝑓
𝐸 excess free volume (m3·mol-1) 

𝐿𝑓
𝐸  excess intermolecular free length (cm) 

𝜋𝑖
𝐸 excess internal pressure (Nm-2) 

Vf free volume (m3·mol-1) 

KS isentropic compressibility (TPa-1) 

Lf intermolecular free length (cm) 

πi internal pressure (Nm-2) 

x1 mole fraction of component 

η viscosity (mPa·s) 

U speeds of sound (ms-1) 

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308.15 -0.3902 0.03 0.8762 -0.4831 0.02 0.1540 0.0173 0.0099 0.01 

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