Journal of Structural Chemistry, Vol. 47, Supplement, pp. S66-S72, 2006
Original Russian Text Copyright © 2006 by Yu. G. Bushuev and V. P. Korolev
WATER–METHANOL–BENZENE TERNARY SYSTEM.
THERMOCHEMICAL EXPERIMENT AND COMPUTER SIMULATION
Yu. G. Bushuev1 and V. P. Korolev2
UDC 544.355-122: 544.33:519.245
Solution heats have been measured for benzene dissolved in mixtures of water with methanol at 25qC. The
resulting values are compared with data for water–methanol–aniline, water–acetonitrile–benzene, and
water–acetonitrile–aniline systems. Computer simulations have been performed for binary mixtures of
water with methanol and dilute solutions of benzene in these mixtures. Thermodynamic and structural
characteristics of solutions were obtained by calculations. The enthalpy of benzene transfer from water into
a mixed solvent correlates with the relative deviation of the local composition from the mean composition
of the mixture.
Keywords: nonelectrolyte solutions, thermal effects, computer simulation.
INTRODUCTION
Water has a number of specific properties compared to other liquids. Its structural characteristics depend on the
ability of molecules to form directed hydrogen bonds, leading to the formation of a three-dimensional net with complex
topology. Aqueous solutions also possess anomalous properties. These peculiarities are most conspicuous in solutions of
hydrophobic substances.
Hydrophobic substances typically have extremely low solubility in water, which hinders experimental determination
of the properties of solutions. The methanol molecule has a hydrophobic methyl group and a hydrophilic OH group. Water
and methanol are mixed in any proportion. In liquid water, ɇ bonds form a 3D net; in methanol, molecules associate into
slightly branched chains [1-3]. Rearrangement of the system of ɇ bonds during the formation of mixtures shows itself as
extrema on the concentration dependences of the thermodynamic and physicochemical properties of mixed solvents.
Studies of benzene solutions are of great interest for several reasons. The benzene molecule can form weak H bonds
with water [4, 5], increasing the solubility of benzene approximately 35-fold compared to the solubility of hydrophobic
cyclohexane, whose molecule has dimensions similar to those of the benzene molecule. The properties of aqueous solutions
of benzene are more liable to experimental determination than the properties of solutions of typical hydrophobic substances.
The benzene molecule is the simplest representative of the wide class of aromatic compounds. The benzene ring is part of
many organic molecules possessing biological activity. Investigations of benzene solvation provide insight into the nature of
interactions of fullerenes and carbon nanotubes with solvents. These nanotubes exhibit unusual properties. For example,
electric current has been found in carbon nanotubes placed in a flow of liquid [6].
The aim of the present work is to correlate the experimental thermochemical properties of infinitely dilute solutions
of benzene in water–methanol mixtures with the peculiarities of solvation of benzene molecules.
1
Ivanovo State Chemical Technological University. 2Institute of Solution Chemistry, Russian Academy of Sciences,
Ivanovo; [email protected]. Translated from Zhurnal Strukturnoi Khimii, Vol. 47, Supplement, pp. S70-S76. Original article
submitted July 5, 2005.
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0022-4766/06/47 Supplement-0066 © 2006 Springer Science+Business Media, Inc.
EXPERIMENTAL
The integrated solution heat of benzene in mixtures of water with methanol was measured at 25qC in a hermetically
sealed variable-temperature ampule calorimeter with an isothermal shell and a reactor volume of 60 cm3. The instrument
error of measurements was up to 0.6%. For the initial state of the system, the thermal value of the calorimeter was determined
by electric current calibration. Benzene of reagent grade designed for chromatography was employed. Methanol of reagent
grade was dried using Mg(OCH3)2. Mixed solvents were prepared gravimetrically to an accuracy of 0.001 mole fraction.
Potentials and computer simulation procedure. The key problem of computer simulation is the choice of a
procedure for describing intermolecular interactions because several calculated characteristics may depend significantly on
the potential used. In the simplest version we should specify the geometrical parameters of molecular structure, the force
centers, and the analytical form of the potential. We considered molecules having no internal degrees of freedom. The
interaction energy was calculated by formula (1) whereby the universal interactions were determined by the Lennard-Jones
formula and electrostatic interactions, by the Coulomb formula:
U
4¦ Hij [(Vij / rij )12 (Vij / rij )6 ] 1389.09 ¦ qk qm / rkm .
ij
(1)
k ,m
Here H, V are the parameters of the Lennard-Jones potential; and q is the charge. The indices denote the force centers. To
describe the interactions of water molecules we used the SPC/E potential (rOH = 1 Å, H–O–H bond angle is 109.47q,
HOO = 0.650 kJ/mole, VOO = 3.166 Å, qH = 0.4238 ɟ) [7].
The methanol molecule had three centers of interaction, lying on the ɋ and Ɉ atoms and on the hydroxyl H atom.
The ɋ–O and O–ɇ bond lengths were found to be 1.43 Å and 0.945 Å, respectively; the ɋ–O–ɇ angle was 108.5q. The force
constants were chosen such that the thermodynamic properties of methanol could be reproduced: VOO = 3 Å, Vɋɋ = 3.7 Å,
VOɋ = 3.35 Å, HOO = Hɋɋ = HOɋ = 0.7531 kJ/mole, qC = 0.278e, qH = 0.418e, qO = –0.696e. The benzene molecule had 12
interaction centers lying on ɋ and ɇ atoms. The C–ɋ and C–ɇ bond lengths were 1.394 Å and 1.084 Å, respectively. We
chose the following parameters of potential (1): Vɋɋ = 3.55 Å, Vɇɇ = 2.42 Å, Hɋɋ = 0.2929 kJ/mole, Hɇɇ = 0.1255 kJ/mole,
qC = –0.115e, qH = 0.115e. The standard combination rules Vij = (Vii + Vjj)/2, Hij = (Hii Hjj)0.5 were used to determine the
parameters of interaction of force centers belonging to different molecules.
The calculations were performed by the Monte Carlo method using the NPT ensemble and an original program for
liquids of the following composition: x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.7, 1. Here and below x is the mole fraction of methanol in
its mixtures with water. For simulation of benzene solutions, one of the water molecules (or one of the methanol molecules
for x = 1) was replaced by a benzene molecule, and calculations were repeated. In each case, the cubic unit cell contained
1000 molecules. Periodic boundary conditions were used; the field of the potential was restricted by a sphere with distances
rOO of more than 10 Å. The interactions between the benzene and solvent molecules were calculated by formula (1) if the
distance between the center of the benzene molecule and the O atom of the methanol and water molecules did not exceed
15 Å, and were set to zero otherwise. Calculations were carried out provided that the maximal shift of the molecule was up to
0.13 Å and that rotation by each Euler angle was up to 0.13 rad. Tentative variation of the cell volume was performed after
each 2000th adopted displacement of a randomly chosen molecule. Variation of the edge length of the cell was up to 0.1 Å.
The total length of the Markov chain depended on the rate of convergence and amounted to 1.5-2.5˜109 configurations. The
ratio of adopted configurations to the total number of configurations generated was 0.4-0.5. The calculated characteristics
were averaged over several thousands configurations selected for the equilibrium segment of the Markov chain.
DISCUSSION OF RESULTS
Table 1 lists the solution enthalpies of benzene dissolved in mixtures of water with methanol. Our data are in good
agreement with the literature data: 1.51r0.08 kJ/mole for benzene solutions in methanol [8] and 2.08r0.04 kJ/mole [9],
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TABLE 1. Solution Enthalpies ('H m, kJ/mole) of Benzene in Water–Methanol Mixtures at 25qC
Mole
fraction of m˜104
methanol
0
62
40
27
'H m
Mole
fraction of m˜104
methanol
2.03
2.16
2.24
0.025
0.050
0.100
88
119
63
'H m
5.12
7.67
13.0
Mole
fraction of m˜104
methanol
0.150
0.200
0.250
0.301
158
69
186
84
'H m
15.8
17.4
17.1
16.2
Mole
fraction of m˜104
methanol
0.501
0.700
0.900
1.0
313
546
712
836
'H m
8.84
5.20
2.50
1.56
Note: m is molality, mole of benzene/kg of solvent.
2.21r0.01 kJ/mole [10], 2.05r0.06 kJ/mole [11], and 2.03 kJ/mole [12] for benzene solutions in water.
Solvation of benzene and aniline with mixtures of water with methanol and acetonitrile. At first we compare
the thermochemical data obtained in this work with the literature data for other waterorganic solvent–aromatic solute
systems [11-15]. For comparison we chose two solvents (watermethanol and water–acetonitrile) and two solutes (benzene
and aniline).
The acetonitrile molecule is small. Its molar volume (52.9 cm3/mole) is only 1.3 times larger than that of methanol
(40.7 cm3/mole). Mixing of water with acetonitrile is endothermal over the whole range of compositions except the region
with a very low content of CH3CN. ɇȿ > 0 means that water mixing with acetonitrile is controlled by the entropy component
of the Gibbs energy. Note that the ɇ2Ɉ–CH3CN binary mixture is a system with UCST. The results of computer simulation
for this mixture [16] are consistent with the microheterogeneous structure concept of aqueous organic mixtures [17].
Aniline solvation with aqueous organic solvents is well defined [11, 13-15]. Aniline has a higher donor number
(DN) than DMSO [15] and a slightly higher acceptor number (AN) than tert-butanol [15] and is capable of specific
interactions with solvents, acting as both ɇ-donor and ɇ-acceptor. In the condensed state, aniline is strongly associated.
Therefore the standard heat of solution of liquid aniline in water (1.8 kJ/mole [14, 15]) differs but slightly from the heat of
solution of benzene in water, although aniline evidently has much stronger interactions with water than benzene.
Figure 1 shows the standard heats of the transfer of benzene and aniline from water into mixtures of water with
methanol or acetonitrile calculated from the data of Table 1 and [11, 14, 15]. Minor additions of CH3CN to water are more
effective than CH3OH additions in decreasing the exothermal character of solvation (making the transfer more endothermal)
of both benzene and aniline. The maximum is reached more quickly in water–acetonitrile systems. The maximum of the
transfer enthalpy lies at ɯ = 0.075 ppm for aniline and at ɯ = 0.1 ppm of acetonitrile for benzene. For the watermethanol
solvent, maximum is observed at ɯ = 0.2 ppm of methanol in both cases (Fig. 2).
Figure 3 shows the differences between the solution heats of benzene and aniline in water–methanol and water–
acetonitrile solvents, i.e., the heats of the transfer of benzene or aniline from the ɇ2Ɉ–ɋɇ3CN mixture to the ɇ2Ɉ–CH3OH
mixture. When ɯ < 0.075 for benzene and ɯ < 0.1 for aniline, solvation with aqueous methanol is slightly more exothermal. At
higher contents of the organic cosolvent, solution with a wateracetonitrile mixture is more exothermal. In this range of
compositions, the weaker water–acetonitrile interaction probably favors solvation of both benzene and aniline (compared to
the water–methanol mixture).
From the equation [11]
'H 0
'ɇ 0(ɯ = 0) + 2(h23 /M1) x,
(2)
where M1 is the molar mass of water, and ɯ = 0 – 0.1 ppm of methanol, we calculated the enthalpy coefficient h23 of the pair
interaction of benzene with methanol in aqueous solution. Below this value (h23 r standard error, J˜kg/mole2) is compared
with data obtained earlier [11, 15]:
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C6H6
C6H5NH2
CH3OH
CH3CN
971r18
505r15
1916r225
1034r160
The positive values of h23 indicate that the pair interactions of the aromatic compounds with methanol and
acetonitrile in aqueous solution are hydrophobic and unfavorable from the viewpoint of enthalpy (repulsive); the coefficients
are doubled from methanol to acetonitrile system. The pair interaction coefficient of the NH2 group of aniline
h23 (NH 2 )
h23(C6H5NH2) – h23(C6H6)
(3)
is –466 J˜kg/mole2 and –882 J˜kg/mole2, respectively, for methanol–NH2 and acetonitrile–NH2 interactions. These are
attractive hydrophilic interactions that are favorable from enthalpy viewpoint. The coefficient h23 (NH2) is also doubled in
magnitude from methanol to acetonitrile system. Acetonitrile is less hydrated than methanol; this facilitates its specific
interactions with the aniline NH2 group in aqueous solution.
Computer simulation of the water–methanol–benzene system. For multicomponent systems, computer
simulation encounters serious difficulties. Major challenge is due to the action of the fundamental principle of identity of
particles. In the case of the one-component system, rearrangement of particles does not lead to a new configuration, which
shows itself as a combinatorial factor in the expression for the statistical sum. Rearrangement of particles of different sorts
yields a new configuration of the multicomponent system. During mixing, the accessible region of the configuration space
increases considerably. This means that computer simulation should generate much more configurations than in the case of
the individual solvent.
In the case of the molecular dynamics method, this leads to increased structural relaxation times; in the case of the
Monte Carlo method, this hinders convergence of the structural and thermodynamic characteristics to the equilibrium values.
Despite great progress in computing technology, ergodicity of simulation is still a challenge even for one-component liquids.
Another problem is dictated by the necessity to find the difference between large numbers determined with a finite
accuracy to find many thermodynamic characteristics of solutions. Thus for calculating the solvation enthalpy one should
Fig. 1. Standard heats of the
transfer of benzene (solid lines)
and aniline (dashed lines) from
water to its mixtures with
methanol (1) and acetonitrile (2) at
25qC.
Fig. 2. Standard heats of the
transfer of benzene (solid line)
and aniline (dashed line) from
water to its mixtures with
methanol at 25qC.
Fig. 3. Standard heats of the transfer
of benzene (solid line) and aniline
(dashed
line)
from
water–
acetonitrile to water–methanol at
25qC.
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subtract the solvent enthalpy from the enthalpy of an infinitely dilute solution. The mixing enthalpy is found as the difference
between the solution enthalpy and the enthalpies of the individual components taken in an appropriate ratio. In the case of a
ternary system, simulation should be performed for both infinitely dilute solution in a mixed solvent and for the mixed
solvent.
The indicated adverse effects lead to large errors in calculating the thermodynamic characteristics of ternary
systems. The errors cannot be evaluated because of the failure to reach convergence and ergodicity of simulation. These
factors account for the lack of papers devoted to simulation of multicomponent liquid systems. Reproduction (at a qualitative
level) of the dependences of the experimental properties of multicomponent systems and solutions on the state parameters is
already considered good progress.
The results of computer simulation also depend on the choice of the potentials. According to the data of our
simulation, the SPC/E density of water is 1.013 g/cm3, and the configuration energy is –48.1 kJ/mole. For methanol, the
corresponding characteristics are 0.7907 g/cm3 and –35.32 kJ/mole. These values are close to the literature data [7, 18].
Figure 4 presents the calculated and experimental curves of the concentration dependence of the mixing enthalpy
[19] and excess volumes [20] for water–methanol mixtures. In this context, one can speak about qualitative reproduction of
the experimental dependences. The deviation of the calculated values from the experimental ones is up to 0.4 cm3/mole and
0.2 kJ/mole, which are good results. Worse agreement between the calculated and experimental values was obtained for the
enthalpy of benzene transfer from water to the mixed solvent (Fig. 5). Here we can speak about correlation of values and
about experimental concentration dependence reproduced only at a qualitative level. The extent and character of agreement
between the calculated and experimental thermodynamic functions gives us grounds to hope that the real structure of solutions
will be correctly reproduced by the calculated structural characteristics.
To determine the local composition of a mixed solvent in the solvation shells of benzene, we calculated the number
of molecules of each sort within a sphere of radius r whose center coincided with the geometrical center of the benzene
molecule. In Fig. 6, the local composition of a mixed solvent is plotted versus the distance to the center of the benzene
molecule. For all compositions of the mixed solvent under study, there are ranges of distances where the methanol content in
the solvation shells exceeds the stoichiometric value typical of the pure solvent. The solvation shells with a preferable content of
methanol are rather large. For all compositions, the radius is at least 13 Å. Thus benzene is essentially solvated by methanol.
Maximal deviations from the composition of pure solvent are observed for r ~ 6.5 Å. Figure 7 presents the
concentration dependences of absolute deviations from the solvent composition Gx = xL – x and the relative deviations Gx/x.
The deviations Gx are maximal at x = 0.4, while Gx/x are maximal at x = 0.2. The deviations Gx were calculated from the
experimental data on the concentration dependence of the enthalpy of benzene transfer from water to the mixed solvent; for
this we employed the simple phenomenological model of solvation [21]. The values obtained by the two methods differ, but
Fig. 4. Redundant enthalpies (ɚ) and volumes (b) of water-methanol mixtures. Symbols —
computer simulation, solid line — polynomial approximation, dashed line —
approximation of experimental data.
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Fig. 5. Standard heats of the transfer of benzene
from water to its mixtures with methanol. Symbols
— computer simulation (right scale), solid line —
approximation of experimental data (left scale).
Fig. 6. Composition of the
solvation shells of benzene versus
shell radius (solid lines). Dashed
lines — average composition of
the mixture.
Fig. 7. Absolute (ɚ) and relative (b) deviations of the composition of the solvation shells
of benzene from the average composition of the mixture. Symbols — computer
experiment, solid line — approximation, dashed line — calculation using the model of
[21].
the character of the concentration dependence remains the same in both cases. As follows from Fig. 7b, the enthalpy of
benzene transfer from water to the mixed solvent correlates with the relative preferable solvation. We can again speak only
about qualitative agreement because of the large errors in determining Gx and Gx/x.
CONCLUSIONS
Thus the concentration dependence of the experimental enthalpy of benzene transfer from water to a mixed
watermethanol solvent has large deviations toward the endothermal region. The maximal deviations are observed for
x = 0.2. The results of computer simulation of water–methanol mixtures and infinitely dilute solutions of benzene in these
mixtures showed that the calculated values of the concentration dependence of enthalpy and excess volumes are in
satisfactory agreement with the experimental data. At the same time, for the ternary system, we have only partial agreement
between the calculated and experimental enthalpies of benzene transfer from water to the mixed solvent. For all
compositions, benzene is preferably solvated by methanol, which is a consequence of hydrophobic interactions between
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benzene molecules and the methyl groups of methanol molecules. It has been found that the transfer enthalpy correlates with
the relative values of the maximal deviation of the local composition from the stoichiometric values.
This work was supported by RFBR grant No. 04-03-32363ɚ.
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