Study the Effect of Chemical Structures of Solvent on the

Journal of A pplied Sciences Res earch, 5(6): 605-612, 2009
© 2009, INSInet Publication
Study the Effect of Chemical Structures of Solvent on the
Excess Free Energies of Solution
Farid M. Farag and Sahar M. Taw fik
Egyptian Petroleum Research Institute (EPRI), Cairo, Egypt.
Abs tract: Vis cos ities and refractive indices of the mixtures of benzene with the s olvents Triethyleneglycol
(TEG), Tetraethyleneglycol (TETEG), N-me t h y lpyrrolidone (NM P), Triethyleneglycol-dimethylether
(T EGD M E), D ie t h y le n e g ly c o l-dimethylether (D EGD M E), D ime t h y lfo rma mid e (D M F ) a n d
Dimethyls ulphoxide (DM SO) at 30o C and atmos pheric pres s ure have been meas ured at t h e entire
compos ition range mixtures . Exces s free energies Ä GE and exces s refractive indices n ED were determined
to unders tand the interaction patterns between molecules and the effect of the s tructure on it. The ÄGE are
+ve for all s olvents with benzene except for the s olvents DM SO and DM F are –ve. For exce s s re fra ctive
indices
all are -ve deviation except of DEGDM E, DM SO and DM F are +ve.
Key words : Exces s free energy, refractive index, kinematic vis cos ity, s olvents .
INTRODUCTION
Vis cometric properties of mixed s olvent s ys tems
and their dependence on compos ition find applications
in many important chemic a l, indus trial and biological
proces s es . The s tudy of functions s uch as deviation in
vis cos ity and exces s free energy of activation of
vis cous flow, deviation in re fra ctive index, etc. of
binary liquid mixtu re s are us eful in unders tanding the
nature and s trength of molecular interaction between
the component molecules [1-2]. Benzene is a non-polar
and unas s ociated liquid w h e reas glycols are polar and
s e lf-as s ociated through hydrogen bonding in the pure
s tate. The mixtures are interes ting becaus e o f t he
pos s ibility of weak hydro g e n bonding involving ðelectrons o f the benzene ring and the proton of the
hydroxyl group of glycols . W eak hydrogen bonding of
aromatic ring with proton donors appears to play an
important rule in the s tructure of certain bimolecules
[3 ,4 ]
DM F is approtic and unas s ociate d in its pure liquid
s tate [5]. It belongs to the s o-called s u per s olvents ,
owing to its mis c ib ility with all common polar and
non-polar s olvents [6], probably to its high polarity with
large dipole moment (µ = 3.8D) and moderately h igh
dielectric cons tant (ª = 36.76) a t 298.15K. The s olvent
DM SO was particularly chos e n due to its high polarity
[7]
. NM P is a heterocyclic polar s olvent u s ed for the
extraction o f lo w mo le c u la r w e ig h t a romatic
compounds from petroleum feed s tock [ 8 ]. The pres ent
work is devoted to s tudy the exces s fre e energies ÄGE
and exces s refra c t iv e index
of the s olvents TEG,
TEGD M E, T ET EG, DEGDM E, NM P, DM F and
DM SO with benzene as aromatic hydro carbon mixtures
Corresponding Author:
where the s olvent cou ld b e us ed as s elective s olvents
for aromatic hydrocarbons .
In this s t u d y we us ed the data of vis cos ity and
refractive ind e x which are publis hed before by us but
not calculated for ÄGE or n ED. He re w e c ollect the data
o f vis cos ity ç and refractive index n D [9 ,1 0 ] and calculate
the ÄGE and n ED .The ÄGE for TETEG was calculated
before but we us e it here for comparis on [1 1 ].
MATERIALS AND METHODS
Experimental: The liquids us ed were of analytical
grade and mixtures were prepared by mixing ca lc u lated
volumes to get mixtures of different compos itions .
The kinematics vis cos it y meas urements of pure liquids
and their mixtures were made with an a u t o matic Schott
Gerate A VS 400 vis cos ity meas uring s ys tem equipped
with s eries of ubbelhode Vis cometers . Refractive
indices are at th e s o dium D-line, n D was meas ured
us ing a thermos t a t ed A bbe refractometer (carlizeis s ,
les s than ±0.0001 units ).
RES ULTS AND DIS CUS S ION
The exces s free energies for vis cous flow at 300 c
were obtained [1 2 -1 5 ] by us ing the equation:
Ä GE = RT [ ln( ç m Vm / h N A ) –
hNA) ]
i
ln (ç i Vi /
(1)
W here R is the gas cons tant, T is the abs olute
temperature, h is Plank's cons tant (6.626 x 103 4 J.S).
Farid M . Farag, Egyptian Petroleum Research Institute, Cairo, Egypt.
E-mail: [email protected]
605
J. App. Sci. Res., 5(6): 605-612, 2009
NA is A vogadro's number, ç m a n d Vm are the vis cos ity
a n d t h e molar volume of the binary mixtu re
res pective ly , ç i and Vi the vis cos ity and the molar
volume of the ith pure components .
F ig. (1) and Table (1) s how that the values of Ä GE
are pos itive for all mixtu res over the entire compos ition
range except that for DM F and DM SO are negative.
The va lues are increas e in the s equence: TETEG >
TEGDM E > TEG > DEGDM E > NM P > DM F >
DM SO s ugges ts t h a t t h ey are attributed to the large
s ize and cohes ive energy diffe re n c e between the two
unlike components . From the me as ured refractive
indices (n D) at 300 c t h e exces s refractive indices (n ED)
were calculated us ing the equation:
The negativity for all mixture in t h e s equence :
NM P > TEGDM E > TETEG > DM F >T EG and the
maximum negativity for n ED for all mixt u re is at x1 .0.4
except for NM P at x1 .0.85.
In general, the magnitude of n ED increas es with
decreas es in the s trength of interaction between the
component mole c u le s in the mixture [1 6 ], it means more
negative
, more s trength of interaction.
For ÄGE the maximum is a ls o at x1 .0.4 (it means
that is the bes t concentration for extraction). A ccording
to Reed and Taylor, Pos itive ÄGE values indicate
s pecific interactions , while negative value s indicate the
dominance of dis pers ion forces [1 7 ].
In th e p res ent work and in the work reported by
others [1 8 ,1 9 ]. The mole fraction bas is has b e e n u s e d to
calculate
values . Thus , the functions ÄGE and
truly complemen t each other in des cribing the
behaviors of the pres ent binary liquid mixtures .
(2)
W here x1 , x2 , n 1 , n 2 are t h e molar fraction and
refractive indices of the firs t and s econd s olvents in
their mixtures res pectively and n m is the refractive
index of the s olvent mixtures .
F ig. (2) and Table (2) s how that the exc e s s
re fra c t iv e indices
are negative for all mixtures for
the entire compos ition range except for DEGDM E has
p o s itive deviation and DM SO has pos itive deviation
tell x1 . 0.505 after that it going as negative.
The exces s refractive indices n ED s how that
s olvent-s olvent interaction proces s es depend on t h e
nature of s olvent and on its phys ical properties s uch as
the dielectric cons tant, dipole moment,and donor
number, and it is indicates maximum s olvent -s o lvent
interaction proces s es and s o define the s uitable s olvent
mixture with the high effective properties [2 0 ].
Fig. 1: Exces s Free Energy ÄGE vs the M ole Fraction X1 of Benzene with Different Solvents .
606
J. App. Sci. Res., 5(6): 605-612, 2009
Table 1: Mole fractions (x 1 , x 2), kinematic viscosity (ç) at 30 oc and the excess free energy ÄG E of benzene with different solvents.
Benzene+T EG
X2
çm
Vm
ÄGE
X1
1.0000
0.0000
24.3800
134.640
6.29E-09
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8570
0.1430
18.0154
125.770
5.03E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7271
0.2729
11.7000
119.010
5.81E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.4997
0.5003
5.1000
111.390
6.07E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3997
0.6003
3.4800
107.150
5.51E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3075
0.6925
2.5125
103.100
5.59E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.2223
0.7777
1.8118
99.500
5.02E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1429
0.8571
1.2613
95.560
2.85E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0689
0.9310
0.8508
92.400
-4.18E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
0.6581
92.514
-1.06E-08
Benzene+DMSO
1.0000
0.0000
1.7294
73.672
-8.53E-09
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.9185
0.0815
1.5100
75.118
-1.41E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7450
0.2551
1.2490
78.257
-2.00E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.6048
0.3952
1.1530
80.757
-5.48E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5450
0.4550
1.0710
81.856
-9.54E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.4549
0.5451
0.9791
83.467
-1.05E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3560
0.6440
0.9180
85.366
-2.64E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1221
0.8780
0.7920
89.956
1.62E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
0.6581
92.514
-1.06E-08
Benzene+NMP
1.0000
0.0000
1.5595
99.538
4.50E-09
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8929
0.1071
1.4504
98.566
4.51E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7810
0.2190
1.3550
97.432
1.08E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.6836
0.3164
1.2600
96.330
1.26E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5309
0.4691
1.0980
94.370
8.79E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3817
0.6183
0.9680
93.650
1.03E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.2730
0.7270
0.8770
93.232
9.92E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0933
0.9067
0.7410
92.773
8.60E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
0.6581
92.514
-1.06E-08
Benzene+T EGDME
1.0000
0.0000
1.6860
182.560
1.07E-08
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8156
0.1844
1.6060
170.056
4.52E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7110
0.2890
1.5230
160.072
5.93E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5342
0.4658
1.3620
143.158
7.52E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3753
0.6248
1.2040
128.066
8.03E-01
607
J. App. Sci. Res., 5(6): 605-612, 2009
Table 1: Continue
0.2468
0.7532
1.0575
115.902
7.56E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1540
0.8460
0.9182
105.900
5.51E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0518
0.9482
0.7367
96.000
1.66E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
0.6581
92.514
-1.06E-08
Benzene+DMF
1.0000
0.0000
0.8759
78.345
-1.76E-09
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.9122
0.0878
0.8375
80.240
-2.63E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7292
0.2708
0.7896
83.099
-3.13E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.6780
0.3220
0.7770
83.821
-3.46E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5852
0.4148
0.7622
85.000
-1.99E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.4349
0.5651
0.7418
86.840
1.11E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.2630
0.7370
0.7206
89.060
5.35E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1137
0.8863
0.6941
90.903
5.57E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
0.6581
92.514
-1.06E-08
Benzene+T ET G
1
0
0.6580
89.988
0
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.9459
0.0541
0.8320
94.510
0.0948
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8861
0.1139
1.1400
99.532
0.3332
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8194
0.1806
1.6500
105.062
0.6357
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7446
0.2553
2.2200
111.370
0.6801
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.6603
0.3397
3.2000
118.452
0.7824
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5644
0.4355
5.2200
126.470
1.0884
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.4545
0.5455
8.2200
135.621
1.1406
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3271
0.6729
13.6300
146.248
1.2005
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1776
0.8224
20.6700
158.977
0.6888
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1
32.2300
174.088
0.0000
Benzene+DEGDME
1.0000
0.0000
1.0020
143.261
5.28E-07
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8493
0.1507
0.9820
135.179
1.29E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7000
0.3000
0.9520
128.320
2.42E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5934
0.4066
0.9150
121.433
2.33E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3851
0.6149
0.8550
110.338
2.71E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.2116
0.7884
0.7820
101.055
2.00E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1400
0.8600
0.7390
97.620
1.25E-01
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0651
0.9349
0.6990
94.300
5.93E-02
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
0.6581
92.514
0.00E+00
608
J. App. Sci. Res., 5(6): 605-612, 2009
Table 2: Mole fractions (x1 , x 2 ), refractive indices (nD) at 30 oC and excess refractive indices (n E E ) of benzene with different solvents.
Benzene + T EG
X2
nD
nE E
X1
1.0000
0.0000
1.4508
0.0000
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8866
0.1134
1.4547
-0.0006
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7427
0.2573
1.4593
-0.0017
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.6732
0.3268
1.4618
-0.0019
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5795
0.4205
1.4653
-0.0022
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.4669
0.5331
1.4700
-0.0019
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3543
0.6457
1.4744
-0.0020
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.2000
0.8000
1.4815
-0.0010
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
1.4904
0.0000
Benzene + DMSO
1.0000
0.0000
1.4745
0.0000
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.9185
0.0815
1.4758
-0.0002
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7450
0.2550
1.4777
-0.0016
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.6048
0.3952
1.4811
-0.0009
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5450
0.4550
1.4835
0.0004
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.4549
0.5451
1.4864
0.0015
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3560
0.6440
1.4890
0.0023
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1221
0.8779
1.4925
0.0013
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
1.4935
0.0000
Benzene + NMP
1.0000
0.0000
1.4953
0.0000
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8929
0.1071
1.4687
-0.0263
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7810
0.2190
1.4690
-0.0257
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.6836
0.3164
1.4707
-0.0237
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5309
0.4691
1.4742
-0.0197
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3817
0.6183
1.4773
-0.0162
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.2730
0.7270
1.4799
-0.0133
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0933
0.9067
1.4862
-0.0065
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
1.4924
0.0000
Benzene+T EGDME
1.0000
0.0000
1.4200
0.0000
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8156
0.1844
1.4237
-0.0097
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7110
0.2890
1.4262
-0.0147
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5342
0.4658
1.4322
-0.0215
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3753
0.6247
1.4404
-0.0248
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.2468
0.7532
1.4557
-0.0188
609
J. App. Sci. Res., 5(6): 605-612, 2009
Table 2: Continue
0.1540
0.8460
1.4673
-0.0140
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0518
0.9482
1.4835
-0.0051
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
1.4924
0.0000
Benzene+DMF
1.0000
0.0000
1.4279
0.0000
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.9122
0.0878
1.4322
-0.0014
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7292
0.2708
1.4405
-0.0049
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.6780
0.3220
1.4429
-0.0058
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5852
0.4148
1.4490
-0.0057
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.4349
0.5651
1.4612
-0.0031
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.2630
0.7370
1.4751
-0.0003
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1137
0.8863
1.4851
0.0000
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
1.4924
0.0000
Benzene+T ET EG
1.0000
0.0000
1.4555
0.0000
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.9459
0.0541
1.4570
-0.0030
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8860
0.1140
1.4599
-0.0052
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8193
0.1807
1.4628
-0.0069
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7446
0.2554
1.4674
-0.0077
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.6603
0.3397
1.4717
-0.0080
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5644
0.4356
1.4751
-0.0088
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.4545
0.5455
1.4786
-0.0094
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3270
0.6730
1.4828
-0.0076
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1776
0.8224
1.4872
-0.0050
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
1.4922
0.0000
Benzene+DEGDME
1.0000
0.0000
1.4045
0.0000
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.8493
0.1507
1.4215
0.0038
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.7000
0.3000
1.4391
0.0082
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.5934
0.4066
1.4488
0.0086
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.3851
0.6149
1.4663
0.0078
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.2116
0.7884
1.4776
0.0038
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.1400
0.8600
1.4822
0.0021
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0651
0.9349
1.4866
-0.0001
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------0.0000
1.0000
1.4924
0.0000
610
J. App. Sci. Res., 5(6): 605-612, 2009
Fig. 2: Exces s Referactive Indices (n ED) vs the M ole Fraction X1 of Benzene with the Solvents .
Conclus ion: The ÄGE was calculated from t he vis cos ity
ç , a ll values are +ve except for DM F and DM SO a re
–ve. Pos itive value indicates that the s trength of
interaction are s tronger which coming in the order
TETEG> TEGDM E > TEG > DEGDM E > NM P >
DM F > DM SO all s olvents has a polarity.
The n ED als o calculated and s ho w negative
deviation and as we s aid before the more negative
means more s trength interactio n w hich give the s ame
explanation as ÄGE for our s tudied s olvents .
The interactions include formatio n o f hydrogen
bonds and other comp le x fo rming interactions .
Structure contributions aris ing from geometrical fitting
of one component into the other becaus e of differences
in molar volume and free volume between components ,
that is the molar volume of pure s olvent is t h e s u m of
the actual molecular volumes plus t h e “empty” volume
that aris es from hydrogen bonded s tructure.
This finding reveals that t h e s trength of
intermolecular hydrogen bonding is not only the fac tor
in fluencing the ÄGE of liquid mixtures but the s ize a n d
s hapes of the components are als o equally important.
It is clear that the big ger the s olvent molecule the
s tronger t h e s t rength of the interaction, that is explain
the rule of the chemical s tructure, in s trength of
interaction and +v e value of exces s free energies of
s olution.
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ACKNOWLEDGMENTS
The authors wis h to expres s their deep gratitude to
M r. M us tafa F . Farag for his kind as s is tance in
technical computing.
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