A new theoretical approach for estimating excess internal pressure
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Transcript of A new theoretical approach for estimating excess internal pressure
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Journal of Molecular Liqui
A new theoretical approach for estimating excess internal pressure
Ranjan Dey *, A.K. Singh, J.D. Pandey
Department of Chemistry, University of Allahabad, Allahabad, 211002, India
Received 13 April 2005; accepted 5 September 2005
Abstract
Over the years, internal pressure has proven to be an important tool for the study of intermolecular interactions in binary and multicomponent
liquid mixtures. Hence prediction of this property and its corresponding excess parameters assumes paramount significance in the light of
intermolecular interactions. In this regard, the assumption of mole fraction additivity of internal pressure for the ideal mixture is somewhat
erroneous. In this context, a corrected and modified expression for a recently proposed relation has been presented and a comparative study carried
out thereof. For this, three binary mixtures of dimethylsulphoxide(DMSO)+1-alkanol(1-butanol, 1-hexanol and 1-octanol) at 303.15 K have been
put to test.
D 2005 Elsevier B.V. All rights reserved.
Keywords: Internal pressure; Excess; Intermolecular interactions
1. Introduction
The study of internal pressure of binary liquid mixtures has
been carried out by several workers [1–3]. It has been exten-
sively used as a tool to study the intermolecular interactions,
internal structure, clustering phenomenon, ordered structure,
etc. [4–6]. Correlations with the liquid state model in case of
binary mixtures have been also made [7–9], and this
investigation has been further extended to multicomponent
mixtures in recent past [10].
2. Formula derivation
Internal pressure of the mixture may be defined in terms
of the influence of the volume on the internal energy of the
liquid. Thermodynamically, the isothermal internal energy and
molar volume coefficients of real fluids measure the internal
pressure(Pint) as
Pint ¼ BU=BVð ÞT ð1Þ
where U is the internal energy, V the volume and T the
temperature.
0167-7322/$ - see front matter D 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.molliq.2005.09.005
* Corresponding author.
E-mail address: [email protected] (R. Dey).
Assuming the thermodynamic equation of state,
BU=BVð ÞT ¼ T BP=BTð ÞV � P ð2Þ
where P is the pressure.
Employing the expression of thermal expansion coefficient
(a) and isothermal compressibility(KT), internal pressure can
be expressed as [11]
Pint ¼ BU=BVð ÞT ¼ aTjT
� P
��ð3Þ
where all the symbols have their usual meaning.
The excess internal pressure, PintE of liquid mixture is given
by
PEint ¼ Pint � Pid
int ¼ Pint �X
Pint iIxi ð4Þ
Where x is mole fraction and i, id denote the ith component
and the ideal mixture, respectively. The quantity calculated by
Eq. (4) is sometimes called the deviation of internal pressure
[12].
Very recently, Marczak [13] proposed an idea for computing
excess internal pressure. In his approach, he computed ideal
internal pressure by making use of mole fraction additivity in
terms of thermal expansion coefficient (a) and isothermal
compressibility (jT). This is evidently erroneous since both
thermal expansion coefficient and isothermal compressibility
ds 124 (2006) 121 – 123
www.elsev
DMSO+1-butanol
-800.00
-600.00
-400.00
-200.00
0.00
200.00
400.00
600.00
-800.00
-600.00
-400.00
-200.00
0.00
200.00
400.00
600.00
-800.00
-600.00
-400.00
-200.00
0.00
200.00
400.00
600.00
0.00 0.19 0.37 0.53 0.67 0.80 0.93 1.00
Pin
tE(a
tm)
Pin
tE(a
tm)
Pin
tE(a
tm)
eqn-4 eqn-8
DMSO+1-hexanol
0.00 0.19 0.36 0.52 0.67 0.80 0.92 1.00
eqn-4 eqn-8
DMSO+1-octanol
0.00 0.19 0.36 0.52 0.66 0.80 0.92 1.00
x1
x1
x1
eqn-4 eqn-8
a
b
c
Fig. 1. Excess internal pressure of DMSO+1-butanol (a), DMSO+1-hexanol
(b) and DMSO+1-octanol (c) at 303.15 K vs mole fraction.
R. Dey et al. / Journal of Molecular Liquids 124 (2006) 121–123122
are very well known volume fraction additive quantities [14].
Since such a wrongful assumption results in major computa-
tional error, the aim of the present investigation is an attempt to
rectify the error and obtain a corrected and modified expression
for the computation of internal pressure of a thermodynami-
cally ideal mixture. This ideal value has then been employed
for computation of excess internal pressure.
For the calculation of Pintid , various authors have assumed
[6,15–17] that
Pidint ¼
XPint iIxi ð5Þ
which is erroneous and Pintid can be given as
Pidint ¼
aidT
jidT
� P
��ð6Þ
where
aid ¼X
/iai
jidT ¼
X/ijTi
/i ¼xiViXxiVi
where /i is the volume fraction. Now from Eq. (6) we have
Pidint ¼
X/iaiTXuijTi
� P ð7Þ
using Eqs. (3) and (7) in Eq. (4) we have
PEint ¼
aTjT
� P
���
X/iaiTX/ijTi
� P
! ð8Þ
PEint ¼
aTjT
�X
/iaiTX/ijTi
! ð9Þ
where thermal expansion coefficient and isothermal compress-
ibility have been computed through the recently developed
relation [18–20].
3. Results and discussion
Excess internal pressure of three binary systems as
dimethylsulphoxide (DMSO)+1-butanol, DMSO+1-hexanol
and DMSO+1-octanol have been calculated using Eqs. (4)
and (9) at 303 K. Necessary data needed for computation
have been taken from the literature [21]. The excess internal
pressure obtained via the two approaches have been plotted
graphically against the mole fraction and the graphical
representations have been shown in Fig. 1(a–c). In all the
three systems under investigation we find that the plots show
contrasting trends. While the excess internal pressure values
obtained from the previous method (Eq. (4)) show negative
values over the entire mole fraction range, those given by the
proposed method show positive values over the entire
concentration range. This trend is seen in all the systems
under investigation.
In all the three systems under investigation, the excess
internal pressure values obtained via the corrected method are
found to be positive. It is a well known fact that while negative
values of excess functions indicate strong interactions and are
observed when intermolecular complexes are formed, positive
values are indicative of weak interactions. Previously reported
values [21] of variation of excess velocity, uE, excess specific
acoustic impedance, ZE and excess adiabatic compressibility,
bSE, point out towards weak interactions between the compo-
nent molecules and this interaction shows a decrease with
increase in the carbon chain length from 1-butanol to 1-octanol.
These literature values further strengthen the validity of the
modified and the corrected expression for evaluation of excess
internal pressure as compared to the one proposed earlier [13].
Further, it also proves that the excess internal pressure
computed with the mole fraction additivity (Eq. (4)) is
definitely erroneous, since the negative values of internal
pressure obtained thereof indicate presence of strong interac-
R. Dey et al. / Journal of Molecular Liquids 124 (2006) 121–123 123
tions which are in complete contradiction to literature values
[21]. The proposed relation receives further credence from the
fact that positive values of excess properties can be interpreted
as being due to dispersion forces. Experimental findings and
literature survey reveals that structure breaking effect and weak
interactions between unlike molecules predominate in all the
DMSO+1-alkanol (1-butanol, 1-hexanol and 1-octanol) sys-
tems due to rupture of hydrogen bonded chains of the alkanols
and loosening of dipolar interactions and decrease in strength
of interaction between unlike molecules. The observed excess
free energy of activation of viscous flow, GE, and excess
viscosity values, gE values (reported earlier) both suggest that
dispersion forces are operative between unlike molecules for all
the binary systems under investigation.
Thus we conclude that the proposed relation in the present
investigation definitely proves its suitability and credibility for
computation of excess internal pressure over the previously
developed methods.
References
[1] M.R.J. Dack, Aust. J. Chem. 281 (1975) 643.
[2] J.D. Pandey, R.L. Mishra, Acustica 33 (1981) 200.
[3] J.D. Pandey, J. Chem. Soc., Faraday Trans. II 76 (1980) 1215.
[4] J.D. Pandey, B.R. Chaturvedi, N. Pant, Chem. Scr. 18 (1981) 224.
[5] J.D. Pandey, U. Gupta, Z. Physik. Chemie. (Leipzig) 268 (1987) 477.
[6] J.D. Pandey, R. Dey, Acoust. Lett. 24 (2000) 105.
[7] S.V. Subrahmanyam, V. Hyder Khan, K. Malakondaiah, Acustica 45
(1980) 196.
[8] J.D. Pandey, N. Dubey, D.K. Dwivedi, R. Dey, Phys. Chem. Liq. 39
(2001) 781.
[9] Amalendu Pal, Harsh Kumar, Phys. Chem. Liq. 41 (2003) 415.
[10] J.D. Pandey, A.K. Shukla, Neelima Tripathi, G.P. Dubey, Pramana J. Phys.
40 (1993) 81.
[11] J.A.R. Renuncio, G.J.F. Breedveld, J.M. Prausnitz, J. Phys. Chem. 81
(1977) 324.
[12] T.M. Aminabhavi, V.B. Patil, K. Banerjee, R.H. Balundgi, Bull. Chem.
Soc. Jpn. 72 (1999) 1187.
[13] W. Marczak, Phys. Chem. Chem. Phys. 4 (2002) 1889.
[14] M.H. Blandemer, M.J. Davis, G. Douheret, J.C.R. Reis, Chem. Soc. Rev.
30 (2001) 6.
[15] V. Rajendran, Ind. J. Pure Appl. Phys. 31 (1993) 812.
[16] L. Acevedo, G.C. Pedrosa, M. Katz, J. Solution Chem. 19 (1990) 911.
[17] I.M. Aralaguppi, T.M. Aminabhavi, R.H. Balundgi, S.S. Joshi, J. Phys.
Chem. 95 (1991) 5299.
[18] J.D. Pandey, R. Dey, M. Upadhyaya, Acoust. Lett. 21 (6) (1997) 120.
[19] J.D. Pandey, R. Verma, Chem. Phys. 270 (3) (2001) 429.
[20] J.D. Pandey, R. Dey, R. Verma, Phys. Chem. Liq. 14 (2) (2003) 145.
[21] A. Ali, K. Tiwari, A.K. Nain, V. Chakravortty, Phys. Chem. Liq. 38
(2000) 459.