Research Journal of Recent Sciences _________________________________________________ ISSN 2277-2502
Vol. 1 (ISC-2011), 224-231 (2012)
Res.J.Recent Sci.

Surface Tension of Binary Liquid Mixtures at
298.15, 303.15 and 313.15 K
Shukla R.K., Awasthi Naveen, Gangwar V.S. Singh, S.K. and Srivastava Kirti
Department of Chemistry, V.S.S.D.College, Kanpur-208002, INDIA

Available online at, www.isca.in
(Received 16th November 2011, revised 2nd Februry 2012, accepted 2nd Februry 2012)

Abstract
Densities and surface tensions were measured for the binary liquid mixtures formed by benzonitrile, and benzyl alcohol with
benzene at 298.15, 303.15 and 313.15 K and atmospheric pressure over the whole concentration range. Prigogine-Flory-Patterson
model (PFP), Ramaswamy and Anbananthan (RS), model derived by Glinski, Sanchez equation, Goldsack relation and Eberhart
models were utilized to predict the associational behavior of weakly interacting liquids. The measured properties were fitted to
Redlich-Kister polynomial relation to estimate the binary coefficients and standard errors. Furthermore, McAllister multi body
interaction model was also used to correlate the binary properties. These non-associated and associated models were compared
and tested for different systems showing that the associated processes yield fair agreement between theory and experiment as
compared to non-associated processes.
Keywords: Surface Tension, Binary Prigogine-Flory-Patterson, McAllister, Sanchez, Eberhart

Introduction
Prediction of surface tension is of outstanding importance
in many scientific and technological areas such as liquidliquid extraction, gas absorption, distillation, condensation,
environmental sciences, material sciences, process
simulation, molecular dynamics etc and play a significant
role in several industries such as paints, detergents,
agrochemicals and petroleum. As a fundamental parameter,
surface tension is the single most accessible experimental
parameter that describes the thermodynamic state and
contains at least implicit information on the internal
structure of a liquid interface. Apart from this theoretical
interest, a detailed understanding of the behavior of a
vapor-liquid interface, such as enrichment of one
component in a liquid surface is important for modeling a
distillation process.
Surface tensions have been measured for a long time and
collections of experimental data for pure, binary and multi
component liquid mixtures1-4. A critical review reveals that
systematic theoretical and experimental investigations of
vapor-liquid interfaces for the prediction of associational
behavior are rare, especially in a wide temperature and
concentration range. High quality of experimental data of
surface tensions forms the basis for a successful modeling
and for theoretical calculations of surface properties5-6.
In continuation of our work, we present the experimental
data on density and surface tension of binary liquid mixtures
formed by banzonitrile and benzyl alcohol with benzene at
298.15, 303.15 and 313.15 K and atmospheric pressure over

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the whole concentration range. These data were analyzed in
terms of Ramaswamy and Anbananthan (RS) model model
derived by Glinski, Prigogine-Flory-Patterson (PFP) model,
Sanchez model, Goldsack model and Eberhart Model 7-14.
First two models, RS and model devised by Glinski
(associated) are based on the association constant as an
adjustable parameters where as PFP and others (nonassociated) are based the additivity of liquids. For that
purposes, we selected the liquids containing poor interacting
properties. From these results, deviations in surface tension,
 were calculated and fitted to the Redlich-Kister
polynomial equation to derive the binary coefficients and the
standard errors13. An attempt has also been made to correlate
the experimental data with the McAllister multi body
interaction model. This is our first attempt to correlate all the
models (associated and non-associated) simultaneously in
predicting the associational behavior of binary liquid
mixtures from surface tension data.

Material and Methods
High purity and AR grade samples of banzonitrile, and
benzyl alcohol with benzene at 298.15, 303.15 and 313.15
K used in this experiment were obtained from Merck Co.
Inc., Germany and purified by distillation in which the
middle fraction was collected. The liquids were stored in
dark bottles over 0.4nm molecular sieves to reduce water
content and were partially degassed with a vacuum pump.
The purity of each compound was checked by gas
chromatography and the results indicated that the mole
fraction purity was higher than 0.99. The purity of
chemicals used was confirmed by comparing the densities

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Vol. 1 (ISC-2011), 224-231 (2012)
Res.J.Recent Sci.
and viscosities with those reported in the literature as
shown in table 1.
Apparatus and Procedure: Before each series of
experiments, we calibrated the instrument at atmospheric
pressure with doubly distilled water. The uncertainty in the
density measurement was within ± 0.5 kg.m-3. The densities
of the pure components and their mixtures were measured
with the bi-capillary pyknometer. The average uncertainty
in the composition of the mixtures was estimated to be less
than ± 0.0001.
Surface tension was measured by the differential capillary
rise method. A well stirred water bath (Raga Industries)
was used with temperature control to ±0.01 K. The
diameters of the precision bore capillaries were confirmed
at several points along the length of each capillary by
mercury weighing. The diameter of the capillaries were
found to be 0.01 and 0.02 cm. At equilibrium, the
difference in the level of menisci in both the capillaries, h,
was constant within the precision of the cathetometer, ±
0.001 cm. Each experiment was repeated three times at
each temperature for all compositions and results were
averaged. The estimated uncertainty in surface tension
measurements was within ± 1.9 X 10-4 Nm-1. The surface
tension of the mixture,, was calculated using the relation;
r r g[3h  ( r2  r1 )]
(1)
  1 2
6( r2  r1 )
where r1 and r2 are the radii i of the capillaries, g is the
gravitational acceleration and  , the density of the
mixture. The angle of contact was assumed to be zero,
which was supported by visual observations. The results
are listed in table 1 together with literature values for
comparison15.
Modeling: Ramswamy and Anbananthan proposed the
model based on the assumption of linearity of acoustic
impedance with the mole fraction of components 7. Further it
is assumed, that an equilibrium physical property such as
viscosity, refractive index, surface tension etc which are
based on linearity can be predicted11-14. Further Glinski
assumed that when solute is added to solvent the molecules
interact according to the equilibrium as:
A+B = AB
(2)
By applying the condition of linearity with composition
obs = xA A + xAB AB
(3)
Where xA, xAB, A and AB and obs are the mole fraction of
A, mole fraction of associate AB, surface tension of A,
surface tension of associate AB and observed surface
tension respectively. The component AB can not be
obtained in its pure form. Following simplifications have
been made, firstly, concentration term should be replaced
by activities for concentrated solution and second, there are
also molecules of non associated components in the liquid
mixture. The eq (3) takes the form,

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obs = [xA A + xB B + xAB AB] 
(4)
where  is a temperature dependent adjustable parameter
which changes with the changing temperature conditions.
The general idea of this model can be, however, exploited
as;
[ AB ]
(5)
K

as

(C A  [ AB ])(CB  [ AB ])

where CA and CB are initial molar concentrations of the
components. One can take any value of Kas and calculate
the equilibrium value of [AB] for every composition of the
mixture as well as [A] =CA-[AB] and [B] =CB-[AB].
Replacing molar concentration by activities for
concentrated solution, eq (5) becomes,

K as 

a AB
(a A  a AB )(aB  a AB )

(6)

where aA, aB and aAB are the activity of component A,
Component B and associate, AB respectively. Taking
equimolar activities which are equal to;
a´A=aA-aAB and a´B = aB-aAB
(7)
where a´A and a´B are the activities of [A] and [B] in equi
molar quantities respectively.
From eq (7) one can obtain the value of Kas as;

K as 

a AB
2
a A aB  a A a AB  aB a AB  a AB

a AB
(8)
a ' A .a ' B
Now, assuming any value of surface tension in the pure
component AB, AB, it is possible to compare the surface
tension calculated using eq (4) with the experimental
values. On changing both the adjustable parameters Kas and
AB gradually, one can get different values of the sum of
squares of deviations,
S = (obs - cal) 2
(9)


On inspecting the results obtained from Ramaswamy and
Anbananthan model, Glisnki suggested the equation
assuming additivity with the volume fraction,  as;
 1 2
(10)
 cal 
1 2  2 1
Where cal is the theoretical surface tension of binary liquid
mixture, 1, 2 are the volume fractions of component 1 and
2 and 1 and 2 are the surface tensions of pure component
liquids. The numerical procedure and determination of
association constant, Kas, were similar to that described
before. Flory and collaborators used the cell partition
function of Hirschfelder and Eyring and a simple Van der
Waals energy- volume relation, by putting m=3, n so
that the Flory equations for the mixing functions and partial
molar quantities may be obtained from the general
corresponding states equations given by making this
particular choice of (m,n). Patterson et al have drawn
attention to the close connection between the Flory theory
and corresponding state theory of Prigogine employing a

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Vol. 1 (ISC-2011), 224-231 (2012)
Res.J.Recent Sci.
simple cell model of the liquid statea11. The equation of
state for the materials conforming to the principle of
corresponding states can be expressed in a universal form
through the use of suitable characteristic values i.e.
(reduction parameters) P,V,T for the pressure, volume and
temperature respectively.
In order to extend corresponding state theory to deal with
the surface tension, Patterson and Rastogi11 used the
reduction parameters as,
(11)
 *  k 1/ 3 P 2 / 3T 1/ 3
called the characteristic surface tension of the liquid. Here k
is the boltzmann constant. Paterson and Rastogi extended
the simple cell model theory of the surface tension of
spherical molecules by Prigogine and Saraga to the case of
chain molecules16. A segment experiences an increase in the
configurational energy due to the loss of a fraction, M, of its
nearest neighbors at the surface while moving from the bulk
phase to the surface phase. It’s most suitable value ranges
from 0.25 to 0.29. In the present case the value of M is taken
as 0.29 throughout the calculation. The cell partition
function of a segment at the surface is increased due to the
loss of constraining nearest neighbors in one direction. With
the particular (3,∞) choice of m,n potential, the Flory model
takes the form as;
~

~

~ 5 / 3

 (V )  [ M V

~ 1/ 3

(

 1.0

V

~
2

~ 1/ 3

) ln(

V

V
~ 1/ 3

V

 0.5

)]

 1.0

Thus on the basis of flory theory, surface tension of liquid
mixture is given by the expression,
~

~

   *  (V )

(13)

All the notations used in the above equations have their
usual significance as detailed out by Flory. The relationship
between surface tension, isothermal compressibility, T,
and density,  of a liquid was obtained by Sanchez and
applied successfully to binary liquids12.
(14)
 (  T /  )1 / 2  A01/ 2
Goldsack and Sarvas used the mole fraction and volume
fraction statistics to obtain the expression surface tension
and applied to various systems as;
A
(15)
xi , S  xi , B [(   i ) i ]  1
RT

where xi, S and xi, B are the mole fraction of the component
in surface and bulk phase respectively and Ai is the molar
surface area of the component for binary liquids.
Eberhart assumed that the surface tension of binary liquids is
a linear function of surface layer mole fractions as;
(16)
  y1 1  y2 2
Using a semi-empirical constant, S, which is defined as the
surface enrichment factor for the component having the
lower surface tension,

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S  ( y 2 / y1 ) /( x2 / x1 )

(17)

where y1 and y2 are surface mole fractions and x1 and x2 are
bulk mole fractions and where y1+y2=1 and x1+x2=1,  can
be expressed in terms of bulk liquid composition of the
mixture.
(18)
  ( x1 1  x2 S 2 ) /( x1  Sx2 )

Results and Discussion
Relations between associations phenomenon in liquids were
analyzed earlier by considering van der Waals equation of
state which was based only on simple averaged geometrical
deviations without analyzing the system in terms of
equilibrium17. The association phenomenon has been related
usually the deviation of different quantities from additivity.
Ramaswamy and Anbananthan derived the model based on
the assumption of linearity of acoustic impedance with the
mole fraction of components which was corrected and tested
to predict the associational behavior8,18. The quantities
analyzed were refractive index, molar volume, viscosity,
intermolecular free length and many others19-22. Prediction
of surface tension from this approach is our first attempt.
The results of fittings obtained from the model were utilized
properly. The calculations were performed using a computer
program which allows fittings easily both the adjustable
parameters simultaneously or the parameters were changed
manually.
Values of thermal expansion coefficient () and isothermal
compressibility needed in the PFP model were obtained
from the equation which have already been tested in many
cases by us18. The mixing function  can be represented
mathematically by Redlich-Kister polynomial equation for
correlating the experimental data as18;
p

y  xi (1  x1 )  Ai (2 x1  1)i

(19)

i 0

where y refers to deviation in surface tension (), x1 is the
mole fraction and Ai is the coefficient. The values of
coefficients were determined by a multiple regression
analysis based on the least square method and are
summarized along with the standard deviations between the
experimental and fitted values of the respective function in
Table 2. The standard deviation is defined by,
1/ 2

 m ( yexp  yCal ) 2

  

(
m

p
)
i 1


(20)

where m is the number of experimental points and p is the
number of adjustable parameters. The values of standard
deviation lie 0.0551 to 0.4217.Multibody interaction model
of McAllister is widely used for correlating the viscosity of
liquid mixtures with mole fraction which is based on the
assumption of additivity19.

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Res.J.Recent Sci.

T=298.15 K

T= 303.15 K
7

7

5

5
3

1
-1

Δσ

Δσ

3

0

0.2

0.4

0.6

0.8

1

1

-3

-1 0

-5

0.2

0.4

0.6

0.8

1

-3
X1

X1

-5

Bez+Benzonitrile
7

T=298.15

T=303.15

7
5
3
1
-1
0
-3
-5

3
Δσ

Δ σ

5

0.2

0.4

0.6

0.8

1

1
-1 0

0.2

0.4

0.6

0.8

1

-3
X1

-5

X1

Figure-2
Plot of surface tension deviations, with mole fraction x, for benzene + (1-x) benzyl alcohol at 298.15 and 303.15 K and
benzene + (1-x) benzonitrile at 298.15 and 303.15 K: , PFP((eq.19), ■,Sanchez (22) ,▲, Goldsack and sarvas(eq.25) ,
Eberhart (eq.29), *,RS(eq.5) ,, model devised by Glinski((eq.10)
Table-1
Comparison of density (ρ) and Surface tension (σ) with literature data for pure components at 298.15, 303.15, and 313.15
K
Components
T/K
V/ cm3
σexp/
σ
 x 10-3
 x 1012
exp /
lit /
lit
mole-1
mN.m-1
/mN.m-1
K
Pa
g.cm-3
g.cm-3
Benzene
298.15
1.218023 94.60978
89.32
0.8732
0.8736b
28.20b
28.02
b
303.15
1.21875
94.77915
89.94
0.8680
0.8683
27.56b
27.38
b
313.15
1.24239
100.4023
91.13
0.8575
0.8576
26.79
Benzonitrile
298.15
0.997994 52.04158
103.08
1.0003
1.0006b
38.33
303.15
1.008302 53.67095
103.56
0.9976
0.9978b
38.38b
38.19
313.15
1.016819 55.04248
105.24
0.9919
38.03
Benzyl alcohol
298.15
1.015504 54.82925
103.82
1.0412
1.0413b
39.03
b
303.15
1.021907 55.87294
104.24
1.0376
1.0376
38.94b
38.81
313.15
1.063372 62.95392
107.98
1.0366
38.31
a Ref 23 b Ref 15

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Vol. 1 (ISC-2011), 224-231 (2012)
Res.J.Recent Sci.
Table-2
Coefficients of the Redlich-Kister equation and standard deviations ( ) for surface tension
of binary liquid mixtures at various temperatures
Benzene+Benzonitrile

/mN.m-1

T
298.15

A0
12.6428

A1
-1.2057

A2
-1.2846

A3
4.9859

Std dev()
0.0551

303.15

7.5091

-3.5624

-2.5595

8.6404

0.0832

313.15

4.3350

-0.5640

-4.3693

2.0337

0.1343

Benzene+Benzylalcohol
 /mN.m

-1

298.15

12.7894

10.0663

10.0663

0.3097

0.1998

303.15

17.1911

7.0611

-8.9754

3.8436

0.1620

313.15

7.5755

4.4203

-2.5178

-1.4961

0.1122

Table-3
Parameters of McAllister Three body and Four body Interaction
Models and Standard Deviations () for Surface Tension of Binary Liquid
Mixtures at Various Temperatures

Component

Temp
298.15

Benzene+Benzonitrile

Benzene+Benzylalcohol

McAllisterThreeBody (/m N.m-1)
a
b
()
36.7411
38.7966
0.0873

McAllister Four Body (/m N.m-1)
a
34.4134

b
37.4648

c
38.8202

()
0.0876

303.15

33.7796

37.3544

0.1391

31.8587

35.8572

37.2830

0.1325

313.15

32.2240

35.8585

0.1837

29.8686

36.0244

34.9991

0.1010

298.15

42.1778

33.6207

0.4234

29.1982

33.4461

33.0062

0.1825

303.15

39.5465

35.7636

0.2514

28.3772

33.1275

32.9763

0.1046

313.15

34.0128

33.7965

0.1125

27.7798

32.6639

31.2272

0.1597

Table-4
Comparison of absolute average deviation values obtained from various liquid state models
Component
Liquids

Temp (K)

Kas

σab(RS)/
mN.m-1

σ Eq.4/
mN.m-1

σab(Glin) /
mN.m-1

σ Eq.10/
mN.m-1

σ Eq.13/
mN.m-1

σ Eq.14/
mN.m-1

σ Eq.15/
mN.m-1

σ Eq.16/
mN.m-1

298.15

0.9990

37.80

4.87

25.00

1.43

2.86

2.66

2.99

0.72

303.15

0.0010

37.00

1.25

37.00

1.60

1.57

1.70

2.09

0.66

313.15

0.0050

36.50

0.64

36.50

0.99

0.94

1.14

1.50

0.38

298.15

0.0014

35.00

2.91

35.00

3.08

3.46

3.15

3.47

0.59

303.15

0.0015

35.10

2.91

35.10

3.09

2.86

3.15

3.46

1.84

313.15

0.0002

35.30

1.33

35.30

3.37

1.85

1.94

1.86

1.00

Benzene+Benzon
itrile

Benzene+Benzyl
alcohol

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Res.J.Recent Sci.
Table -5
Experimental densities (), experimental surface tensions (σexp), theoretical surface tension from
PFP model (σEq.19),Sanchez method,(σEq.22), Goldsack model, (σEq.25), Eberhart model, (σEq.29),
RS model (σEq.5), Glinski model (σEq.10) of binary liquid mixtures and their percent deviations
(% Δσ) at various temperatures.
Benzene+Benzonitrile
X1

ρ/gm.
cm-3

σ exp/
mN.m-1

σEq.13/
mN.m-

σ Eq.14/
mN.m-

1

1

σ Eq.15/
mN.m-1

σ Eq.16/
mN.m-1

σ Eq.4/
mN.m-1

σ Eq.10/
mN.m-1

%ΔσEq./
13/

%ΔσEq.14/
mN.m-1

-1

mN.m

%ΔσEq./
15

%ΔσEq.16/
mN.m-1

%ΔσEq.5
/
mN.m-1

%ΔσEq.
10 /
mN.m-1

-1

mN.m

298.15
0.1681

0.9987

38.20

36.95

36.17

35.81

37.47

34.53

38.32

3.26

5.31

6.26

1.91

9.62

-0.33

0.3126

0.9875

37.78

35.14

34.50

34.02

36.58

31.86

37.78

6.98

8.68

9.96

3.18

15.68

0.01

0.4381

0.9765

37.01

33.56

33.15

32.66

35.65

30.05

36.82

9.33

10.43

11.76

3.67

18.80

0.52

0.5481

0.9645

35.83

32.17

32.05

31.59

34.69

28.89

35.59

10.21

10.56

11.83

3.18

19.36

0.66

0.6453

0.9568

34.40

30.94

31.11

30.72

33.69

28.20

34.24

10.05

9.55

10.69

2.06

18.02

0.46

0.7318

0.9423

33.20

29.85

30.32

30.00

32.65

27.83

32.86

10.09

8.67

9.63

1.66

16.17

1.01

0.8093

0.9356

31.96

28.87

29.63

29.39

31.56

27.69

31.52

9.67

7.30

8.04

1.25

13.35

1.37

0.8792

0.9156

30.66

27.99

29.03

28.87

30.43

27.71

30.26

8.71

5.33

5.84

0.75

9.63

1.31

0.9423

0.8876

29.37

27.23

28.50

28.42

29.25

27.83

29.09

7.32

2.99

3.26

0.41

5.25

0.95

0.1681

0.9825

37.26

36.54

35.95

35.51

36.78

36.37

36.07

1.94

3.51

4.68

1.28

2.39

3.19

0.3126

0.9758

36.45

34.82

34.20

33.63

35.47

34.80

34.36

4.46

6.17

7.75

2.69

4.51

5.74

0.4381

0.9678

35.43

33.33

32.79

32.20

34.23

33.45

32.95

5.95

7.46

9.12

3.39

5.60

7.00

0.5481

0.9587

34.18

32.01

31.63

31.09

33.08

32.26

31.77

6.34

7.47

9.04

3.22

5.62

7.06

0.6453

0.9564

32.61

30.85

30.64

30.18

31.99

31.21

30.76

5.40

6.02

7.43

1.90

4.30

5.67

0.7318

0.9356

31.43

29.81

29.81

29.43

30.96

30.27

29.90

5.15

5.17

6.35

1.50

3.68

4.88

0.8093

0.9152

30.46

28.89

29.08

28.80

29.99

29.44

29.15

5.17

4.54

5.45

1.54

3.36

4.32

0.8792

0.9056

29.44

28.05

28.44

28.26

29.07

28.68

28.48

4.72

3.40

4.02

1.26

2.57

3.24

0.9423

0.8768

28.46

27.30

27.88

27.79

28.21

28.00

27.90

4.06

2.02

2.33

0.88

1.61

1.96

0.1681

0.9642

36.49

36.31

35.66

35.25

36.32

36.12

35.82

0.48

2.27

3.39

0.47

1.01

1.83

0.3126

0.9523

35.19

34.53

33.82

33.28

34.79

34.49

34.04

1.87

3.89

5.42

1.14

2.00

3.26

0.4381

0.9487

34.13

32.98

32.35

31.81

33.43

33.07

32.58

3.35

5.20

6.80

2.05

3.10

4.55

0.5481

0.9356

33.20

31.62

31.14

30.64

32.20

31.83

31.35

4.75

6.19

7.68

3.01

4.11

5.58

0.6453

0.9365

31.62

30.41

30.13

29.70

31.08

30.74

30.30

3.82

4.72

6.06

1.71

2.77

4.17

0.7318

0.9136

30.45

29.34

29.27

28.93

30.07

29.78

29.40

3.64

3.88

5.00

1.25

2.21

3.43

0.8093

0.9

29.31

28.38

28.52

28.27

29.14

28.91

28.62

3.17

2.70

3.56

0.58

1.36

2.34

0.8792

0.8865

28.34

27.52

27.87

27.71

28.29

28.13

27.94

2.90

1.66

2.25

0.18

0.73

1.42

0.9423

0.8658

27.56

26.75

27.30

27.22

27.51

27.43

27.33

2.97

0.95

1.25

0.18

0.47

0.83

303.15

313.15

International Science Congress Association

229

Research Journal of Recent Sciences ____________________________________________________________ ISSN 2277-2502
Vol. 1 (ISC-2011), 224-231 (2012)
Res.J.Recent Sci.
Benzene+Benzylalcohol
X1
298.15
0.1749
0.3229
0.4498
0.5598
0.6561
0.741
0.8166
0.8841
0.945
303.15
0.1749
0.3229
0.4498
0.5598
0.6561
0.741
0.8166
0.8841
0.945
313.15
0.1749
0.3229
0.4498
0.5598
0.6561
0.741
0.8166
0.8841
0.945

ρ/gm.
cm-3

σ exp/
mN.m-

σEq.13/
mN.m-

σ Eq.14/
mN.m-

1

1

1

σ Eq.15/
mN.m-1

σ Eq.16/
mN.m-

σ Eq.4/
mN.m-1

%ΔσEq./13/
mN.m-1

%ΔσEq.14/
mN.m-1

%ΔσEq./15
mN.m-1

%ΔσEq.16/
mN.m-1

%ΔσEq.5
/
mN.m-1

%ΔσEq.10
/
mN.m-1

1.0008
0.9935
0.9825
0.9601
0.9445
0.9236
0.9001
0.8935
0.8801

36.54
36.04
35.84
35.19
34.98
34.70
33.14
31.87
30.19

35.75
34.11
32.70
31.47
30.38
29.43
28.57
27.81
27.12

34.99
33.60
32.46
31.52
30.72
30.04
29.44
28.91
28.44

34.67
33.15
32.00
31.08
30.34
29.72
29.20
28.75
28.36

36.36
35.91
35.39
34.79
34.10
33.30
32.34
31.20
29.79

35.23
33.94
32.82
31.86
31.02
30.28
29.62
29.03
28.50

35.09
33.72
32.58
31.62
30.81
30.10
29.48
28.93
28.45

2.16
5.35
8.77
10.58
13.14
15.20
13.79
12.73
10.15

4.23
6.78
9.42
10.42
12.17
13.44
11.19
9.28
5.79

5.12
8.01
10.72
11.67
13.27
14.34
11.90
9.78
6.05

0.48
0.37
1.27
1.14
2.51
4.03
2.41
2.10
1.33

3.58
5.84
8.42
9.46
11.32
12.74
10.63
8.91
5.60

3.97
6.44
9.09
10.13
11.94
13.26
11.05
9.21
5.76

0.9998
0.9874
0.9754
0.9564
0.9354
0.9002
0.8897
0.8845
0.8789

35.75
35.99
36.23
35.87
34.70
33.23
31.65
30.36
28.87

35.53
33.95
32.59
31.40
30.36
29.43
28.61
27.88
27.21

34.34
32.95
31.82
30.88
30.08
29.39
28.79
28.27
27.80

34.02
32.51
31.36
30.45
29.70
29.08
28.56
28.11
27.72

35.25
34.39
33.53
32.67
31.80
30.93
30.05
29.16
28.27

34.57
33.28
32.17
31.21
30.37
29.63
28.97
28.39
27.86

34.41
33.05
31.91
30.96
30.14
29.44
28.83
28.29
27.81

0.62
5.68
10.06
12.46
12.52
11.42
9.59
8.19
5.75

3.95
8.46
12.18
13.91
13.31
11.53
9.01
6.90
3.72

4.84
9.68
13.46
15.12
14.40
12.47
9.75
7.42
3.99

1.40
4.45
7.45
8.92
8.36
6.92
5.06
3.95
2.08

3.30
7.54
11.21
13.00
12.48
10.83
8.46
6.50
3.51

3.74
8.18
11.92
13.70
13.14
11.41
8.93
6.83
3.68

0.9745
0.9683
0.9512
0.9354
0.9102
0.8754
0.8563
0.8365
0.8236

34.54
33.84
33.38
32.73
31.67
30.60
29.70
28.84
27.67

33.62
32.29
31.14
30.13
29.25
28.46
27.75
27.12
26.55

29.91
32.41
31.29
30.35
29.54
28.85
28.24
27.70
27.22

33.41
31.92
30.78
29.86
29.12
28.50
27.98
27.53
27.13

34.19
33.04
32.01
31.06
30.20
29.40
28.67
28.00
27.37

33.94
32.66
31.56
30.61
29.77
29.03
28.38
27.79
27.27

16.94
32.45
31.32
30.37
29.56
28.86
28.24
27.70
27.22

2.67
4.59
6.70
7.93
7.64
7.01
6.56
5.94
4.03

13.39
4.23
6.24
7.27
6.70
5.74
4.93
3.95
1.63

3.26
5.68
7.79
8.76
8.04
6.87
5.81
4.55
1.94

1.01
2.36
4.10
5.10
4.64
3.92
3.47
2.91
1.08

1.73
3.49
5.46
6.49
6.00
5.12
4.45
3.63
1.46

50.96
4.11
6.16
7.20
6.66
5.70
4.91
3.95
1.63

1

The coefficients a,b, and c were calculated using the least
square procedure and the results of estimated parameters and
standard deviation between the calculated and experimental
values are presented in table 3. It is observed that four body
model is correlated the mixture surface tension to a
significantly higher degree of accuracy for all the systems
than the three body model. Generally McAllister model is
adequate in correlating the systems having small deviations.
Mixture data are presented in table 4-5.

σ Eq.10/
mN.m1

surface tension in a hypothetical pure associate and observed
dependence of concentration on composition of a mixture.

Acknowledgement
R.K.Shukla is very thankful to U.G.C., New Delhi for
financial support (Grant-34-332/2008(SR) and Department
of Chemistry, V.S.S.D. College, for cooperation

References
With the increase of mole fraction, the values of surface
tension obtained from all the models decrease at all
temperatures except at few places. The absolute average
deviations (AAD) in surface tension obtained from different
models are provided in table 4 It is observed that all the
equations are equally good and provide fairly good results.
Higher deviation values in PFP model (eq 13) can be
explained as the model was developed for non-electrolyte meric spherical chain molecules and the system under
investigation have interacting and associating properties.
Moreover, the expression used for the computation of  and
T are also empirical in nature.

Conclusion
Associated process give more reliable results as compared to
non-associated processes and helpful in deducing the
internal structure of associates through the fitted values of

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