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Molar excess enthalpies and volumes of binary fluorobenzene systems at 298.15 K
Fluid Phase Equilibria, 3 (1979) 93-112 0 Elsevier Scientific Publishing Company,
Amsterdam
- Printed in The Netherlands
MOLAR EXCESS ENTHALPIES AND VOLUMES FLUOROBENZENE SYSTEMS AT 298.15 K
FUMIO KIMURA
OF BINARY
and SACHIO MURAKAMI
Department of Chemistry, Osaka, 558 (Japan) (Received
93
November
Faculty
6th, 1978;
of Science,
accepted
Osaka City
University,
in revised form February
Sumiyoshi-ku, 23rd,
1979)
ABSTRACT Kimura, F. and Murakami, S., 1979. Molar excess enthalpies and volumes of binary fluor&benzene systems at 298.15 K. Fluid Phase Equilibria, 3: 93-112. Molar excess enthalpies and molar excess volumes of a series of fluorobenzene-alicyclic hydrocarbon and fluorobenzen&aromatic hydrocarbon systems were measured at 298.15 K. The experimental results iKere analyzed by using the Flory theory and the Sanchez-Lacombe theory of nonelectrolyte solutions to discuss the intermolecular interactions in the systems, and the necessity of considering ‘the solution structure’ in the systems was also discussed.
INTRODUCTION It is generally known that solutions containing fluorine compounds show some characteristic thermodynamic properties. Many thermodynamic studies have been carried out for such solutions, especially the hexafluorobenzenem -aromatic hydrocarbon systems (e.g. Duncan et al., 1966; Fenby et al., 1967; Andrews et al., 1970; Powell et al., 1970; Fenby, 1972; Skillerne et al., 1974; Chen et al., 1975), for which very large enthalpic stabilization was observed. However, there have been only a few systematic investigations for systems containing a few fluorine substituted benzenes (e.g. Anantaraman et al., 1963; Fenby et al., 1967; Bhattacharyya et al., 1968). In this investigation, in order to investigate the thermodynamic properties of fluorobenzene (mono fluorine substituted benzene) solutions, molar excess enthalpies HE and molar excess volumes VE of the systems of fluorobenzene with cyclohexane, methylcyclohexane, benzene, toluene and isomeric xylene were measured and the Flory theory (1965) and the Sanchez--Lacombe theory (1976) of nonelectrolyte mixtures were applied to the experimental results to discuss the intermolecular interactions in such systems. EXPERIMENTAL
Fluorobenzene from Wako Pure Chemical Industries Ltd. or Aldrich Chepicals Company Inc. was purified by fractional distillation without any
94 TABLE
1
Densities
of component
Component
liquids
at 298.15
Density
K
p (g cmM3)
Experiment Fluorobenzene Cyclohexane Methylcyclohexane Benzene Toluene o-Xylene m-Xylene p-Xylene * Riddick
1.01893 0.77387 0.76514 0.87359 0.86226 0.87592 0.85984 0.85670
+ f + * t f f f
Literature 0.00001 0.00001 0.00001 0.00001 0.00002 0.00001 0.00002 0.00001
*
0.77389 0.76506 0.87370 0.86231 0.87596 0.85990 0.85669
et al., (1970).
chemical treatment. Cyclohexane, methylcyclohexane, benzene, toluene and isomeric xylenes from Wako Pure Chemical Industries Ltd. were purified by the conventional method (Riddick et al., 1970). All materials were checked with a Shimadzu analytical gas chromatograph (Model GC-3BT) with a column packed with Silicone on Teflon and they were estimated to be more than 99.9% pure, though small peaks which seemed to show the existence of isomers were observed for isomeric xylenes. Densities at 298.15 K of the materials used are shown along with literature values in Table 1.
Fig. 1. Comparison of experimental results for the molar excess volume of cyclohexane(1)-benzene(2) system at 298.15 K. Points and curves represent deviations from eqn. (1). o present work. The solid curves represent the smoothed results by (a) Stokes et al. and (b) Tanaka et al.. The broken curves correspond to deviations of +l%.
95
Molar excess enthalpies HE were determined at 298.15 K using a isothermal displacement calorimeter described previously (Tanaka et al., 1972). The reproducibility of the calorimeter is estimated to be +0.5% in a molar excess enthalpy of 100 J mol-’ for an equimolar mixture. Molar excess volumes VE were determined at 298.15 K from the density measurements using an Ostwald type pycnometer. The volume of the pycnometer is about 10 cm3 and was calibrated by measuring the density of water. The temperature of the measurements was (298.15 f 0.01) K and was determined with a Hewlett-Packard thermometer calibrated at the factory. The bath temperature was controlled within *O.OOl K. In order to test the accuracy of our measurements, VE for the cyclohexane( l)-benzene( 2) system which has been frequently used as a standard system by many investigators was measured. The results are given in Table 3 and also in Fig. 1 along with the results obtained by Stokes et al. (1970) and Tanaka et al. (1975), and our results are believed to be as good as the results from densimetry. RESULTS
The experimental results from measurements of HE and VE at 298.15 K are listed in Tables 2 and 3, and graphical representations of the results are also given in Figs. 2-7. In all cases, x1 is the mole fraction of fluorobenzene. Each set of results was fitted to the following equation XE = XlXz i:
Cj (Xz - Xl)‘-l
i=l
(I)
where XE is either HE or VE. Values of the coefficients Cj were determined by the method of least squares with all points weighted equally. Choice of the appropriate number n of coefficients was based on the variation of the standard deviation,
(2) where the sum extends over the m results in a set. Table 4 summarizes the results of Cj and u obtained from this analysis. The smoothed representations of the results by eqn. (1) are shown as solid curves in Figs. 2-7. The HE result for the benzene system obtained by Fenby et al. (1967) and those of the toluene system and the methylcyclohexane system obtained by Bhattacharyya et al. (1968) are also shown as broken curves in Figs. 2 and 3. The resuit of the benzene system by Fenby et al. is a little more endothermic than ours, and those of the toluene system and the methylcyclohexane system by Bhattacharyya et al. are more exothermic than ours. It is clear from the figures that there is a distinct difference in the magnitudes of HE and VE between the fluorobenzene-alicyclic hydrocarbon sys-
96
TABLE2 Experimental Xl
values of HE at298.15 K
HE
Xl
HE
Xl
(J mol-l)
(J mol-l)
HE
(J mol-l)
Fluorobenzene(1) -cyclohexane(2) 0.0378 0.0872 0.1448 0.2071 0.2659 0.3217 0.3777
137.9 298.0 456.7 596.5 700.2 775.2 826.2
0.4279
0.4852 0.6210 0.5317 0.5447 0.5669 0.6182
0.6703 0.7230 0.7789 0.8343 0.8871 0.9344 0.9724
746.5 673.2 575.2 459.0 330.8 201.3 87.3
822.1 815.3 812.1 805.0 793.4 776.8 734.3
0.7093
680.7 610.6 526.6 418.9 300.6 181.9 74.7
-1.1 0.1 1.1 1.0 2.1 3.2 4.3
0.6907
853.7 863.6 861.8 855.2 850.3 642.8 804.7
FZuorobenzene(1) -methylcyelohexane(2) 0.0418 0.0979 0.1643 0.2326 0.3020 0.3719 0.4313
134.0 297.7 460.9 595.5 700.0 770.7 807.9
0.4906
0.5432 0.5586 0.5750 0.5911 0.6190 0.6649
0.7564 0.8017 0.8525 0.9000 0.9423 0.9772
Fluorobenzene(l)--benzene(2) 0.0311 0.0746 0.1263 0.1811 0.2311 0.2921 0.3521
-1.3 -2.8 -4.0 -4.3 -4.1 -3.4 -2.3
0.4080 0.4597 0.4846 0.4958 0.5321 0.5827 0.6314
0.7438 0.6001 0.6623 0.9176 0.9668
4.7 4.9 4.8 4.0 2.8 1.4
FluorobenzenP(l)--toluene(2) 0.0366 0.0856 0.1462 0.2077 0.2711 0.3353 0.3941
-6.6 -19.4 -30.2 -38.5 -45.1 -49.2 -51.3
0.4489
0.5011 0.5156 0.5362 0.5479 0.5820 0.6301
-51.8 -50.8 -49.9 -49.3 -46.8 -47.0 -43.8
0.6802 0.7236 0.7726 0.6288 0.8824 0.9311 0.9704
-39.6 -35.3 -30.0 -23.3 -16.4 -9.8 -4.3
Fluorobenzene(l)--o-xylene(2) 0.0415 0.0993 0.1618 0.2294 0.2974 0.3536 0.4100 0.4618
0.3 0.6 1.0 1.4 1.9 2.3 2.6 2.9
0.5116 0.5474 0.5575 0.5666 0.6113 0.6571 0.7008 0.7490
3.2 2.9 3.4 2.8 3.0 3.1 3.1 3.0
0.7947
0.8383 0.8856 0.9271 0.9628 0.9869
2.8 2.5 2.0 1.4 0.8 0.4
97
TABLE
2(continued) _ HE (J mol-I)
Xl
HE
x1
HE
x1
(Jmol-l)
(Jmol-l)
Fluorobenzene(l)-m-xylene(2) 0.0019
-0.1 -2.1 -4.5 -6.5 -7.4 -7.6 -7.1
0.0455 0.1020 0.1676 0.2372 0.3065 0.3660
Fluorobenzene(l)0.0095 0.0539 0.1131 0.1744 0.2409
0.3072 0.3785 0.4306
0.4117 0.4674 0.5189 0.5653 0.5753 0.6208 0.6679
-6.5 -5.7 -4.6 -3.6 -2.3 -1.1 0.1
0.7119 0.7601 0.8092 0.8487 0.8979 0.9403 0.9753
1.0 2.0 2.5 2.6 2.4 1.7 0.8
0.7891 0.8389 0.8895 0.8965 0.9366 0.9748
-0.5 0.4 0.9 0.9 0.8 0.4
p-xylene(2)
-0.7 -3.7 -7.6 -10.2
-11.9 -12.6 -12.3 -11.5
0.4763 0.5296 0.5553 0.5724 0.5934 0.6408
0.6901 0.7372
-10.5
-9.2 -7.7 -7.7 -6.6 -5.0 -3.3 -1.8
TABLE3 Experimental Xl
values of VE at 298.15 K VE (cm3 mol-l)
Xl
VE
Xl
VE
(cm3mol-l)
(cm3molV1)
Cyclohexane(l)-benzene(2) 0.1024
0.1493 0.1967 0.2681 0.2925 0.3426
0.234 0.323 0.402
0.3878 0.4352 0.5094
0.619 0.642 0.653
0.7021 0.7507
0.553 0.499
0.506 0.530 0.581
0.5591 0.6083 0.6525
0.646 0.628 0.599
0.8011 0.8487 0.8945
0.427 0.342 0.249
0.3912 0.4911 0.6107 0.7052
0.676 0.688 0.629 0.540
0.7135 0.8006 0.8978
0.536 0.403 0.227
0.3966 0.4898 0.6110 0.7063
0.560 0.555 0.518 0.449
0.8004 0.8973
0.340 0.190
Fluorobenzene(l)-cyclohexane(Z) 0.1055
0.294
0.2017 0.2956 0.3912
0.481 0.609 0.671
Fluorobentelie(l)-methylcyclohexane(2)
0.1090 0.2059 0.3004 0.3966
0.233 0.387 0.489 0.546
98
TABLE3(continued) Xl
VE (cd
Xl
VE (cm3
0.5840
0.067 0.070 0.074 0.073
0.7041 0.7041 0.7994 0.8710
0.068 0.065 0.050 0.037
0.3919 0.3950 0.4404 0.4896 0.4910 0.5092 0.6100
0.025 0.022 0.023 0.024 0.025 0.026 0.029
0.6111 0.7045 0.7059 0.8001 0.8989 0.8989
0.031 0.028 0.028 0.020 0.011 0.009
0.076 0.090 0.093 0.090
0.7529 0.8702 0.9224
0.072 0.044 0.028
0.105 0.110 0.105
0.7052 0.8013 0.8954
0.098 0.077 0.049
0.091 0.094 0.081 0.084
0.8059 0.9133
0.070 0.037
Xl
mC1)
VE (cm3
mol--1)
mole1
Fluoroben.zene(l)-benzene(2) 0.1043 0.2007 0.2973 0.2973
0.030 0.045 0.056 0.058
0.3940 0.3945 0.4938
Fluorobenzene(l)-toluene(2) 0.0615 0.1260 0.1339 0.2076 0.2963 0.2981 0.3455
-0.004 0.004 0.005 0.011 0.020 0.018 0.021
Fluorobenzene(l)-o-xylene(2) 0.1232 0.1645 0.1656 0.3048
0.036 0.047 0.045 0.069
0.3084 0.4509 0.5617 0.6102
Fluorobenzene(l)-m-xylene(2) 0.1110 0.2032 0.3018
0.041 0.063 0.087
0.3948
0.4917 0.6106
Fluorobenzene(l)-p-xylene(2) 0.1049 0.2029 0.3008 0.3953 -
0.028 0.047 0.069 0.086
0.5030 0.6055 0.7068 0.7068
terns and the fluorobenzene--aromatic hydrocarbon systems,namely, the magnitudes ofHE and VE of alicyclichydrocarbon solutions are fairlylarge but those of aromatic hydrocarbon solutions are small or,in some cases, negative. Such arelationshipis also generally observed between usual aromatic hydrocarbon-alicyclic hydrocarbon systems and usual aromatic hydrocarbon-aromatic hydrocarbon systems. It is also foundthattheHE curves of fluorobenzene-aromatic hydrocarbon systems are skewed towardlowhydrocarbon mole fractions.More especially,the HE of systems containing benzene, m- andp-xylenes show a change of sign at intermediate composition. A similar change of sign on the HE
)
-40
-50
0.2
0,6
0.4
X1
0.8
0.2
0.4
r1
0.6
0.8
Fig. 2. Molar excess enthalpies of fluorobenzene( 1 )--alicyclic hydrocarbon(2) systems at 293.15 K. o fluorobenzene-cyclohexane, l fluorobenzene-methylcyclohexane. The solid curves are smoothed results calculated from eqn. (1) with coefficients from Table 4. The broken curve is smoothed result of methylcyclohexane mixture by Bhattacharyya et al.. Fig. 3. Molar excess enthalpies of fluorobenzene(l)--aromatic hydrocarbon(2) systems at 298.15 K. o fluorobenzene-benzene, l fluorobenzene-toluene. The solid curves are smoothed results calculated from eqn. (1) with coefficients from Table 4. The broken curves are smoothed results of (a) benzene mixture by Fenby et al. and (b) toluene mixture by Bhattacharyya et al..
curves has also been found in some poly-fluorinated benzene-aromatic hydrocarbon systems (Fenby et al., 1967). Fenby et al. (1967) explained this as follows. Assuming that HE observed as a macroscopic property consists of the sum of a positive contribution due to the non-specific ‘physical’ interaction and a negative one due to the specific ‘chemical’ interaction, they concluded that the change of sign on the HE curves is attributed to the different composition dependence of these two contributions. According to their explanation, when HE values are plotted against the mole fraction, their maximum should be shifted toward solutions rich in the component of smaller molar volume. However, for the fluorobenzene-benzene system measured in this investigation, the endothermic maximum exists in the region of solutions rich in the component of larger molar volume, fluorobenzene, and hence’the above explanation is not available in this system. In the case of fluorobenzene-aromatic hydrocarbon systems, the V”
100
0.6
0.5 A'-IO.4 B J ,;0.3
0.2
0.1 -151
,
, 0.2
,
,
,
0.4
, 0.6
,
,
,
0
0.8
0.2
0.4
0.6
0.8
X1
X1
Fig. 4. Molar excess enthalpies of fluorobenzene(l)-xylene(2) systems at 298.15 K. fluorobenzene-o-xylene, A fluorobenzene-m-xylene, l fluorobenzene-p-xylene. The solid curves are smoothed results calculated from eon. (1) with coefficients from Table 4. 0
Fig. 5. Molar excess volumes of fluorobenzene( 1)-alicyclic hydrocarbon( 2) systems at 298.15 K. o fluorobenzene-cyclohexane, l fluorobenzene-methylcyclohexane. The solid curves are smoothed results calculated from eon. (1) with coefficients from Table 4.
0.10 0.08 r: d P.$ 0.06 Y
0,011 0.02
0.2
0.4
x1
0.6
0.8
n 0.2
0.4
0.6
0.8
Xl
Fig. 6. Molar excess volumes of fluorobenzene( 1)-aromatic hydrocarbon(2) systems at 298.15 K. o fluorobenzene-benzene, l fluorobenzene--toluene. The solid curves are smoothed results calculated from eon. (1) with coefficients from Table 4. Fig. 7. Molar excess volumes of fluorobenzene(l)-xylene(2) systems at 298.15 K. fluorobenzene-o-xylene, A fluorobenzene-m-xylene, l fluorobenzene-pxylene. The solid curves are smoothed results calculated from eon. (1) with coefficients from Table 4.
o
101 TABLE
4
Coefficients -
and standard
deviations
for representation
System
Function *
Cyclohexane( l)benzene( 2)
VE
2.6166
Fluorobenzene(l)cyclohexane( 2)
HE
VE
3454.38 2.7436
Fluorobenzene(l)methylcyclohexane( 2)
HE
3290.49
Fluorobenzene( benzene( 2)
l)--
Fluorobenzene( toluene(2)
l)-
Fluorobenzene( o-xylene( 2)
l)-
Fluorobenzene( m-xylene( 2)
l)-
Fluorobenzene( p-xylene( 2)
l)-
* Units:
Cl
c2
results by eqn. (1)
c3
c4
u
-
VE
2.2434
HE
5.15 0.2926
-0.0898 224.81 0.3858 21.07 0.2169
-0.0216 90.00 0.0757
0.002 76.47
106.63
1.0 0.003 0.9
0.0041
0.006
-49.43 -0.0373
-9.73 0.0306
4.71
0.1 0.002
-57.73 --0.0578
3.18 -0.0493
3.40
0.1 0.002
11.68 0.3658
-6.12 -0.0489
2.34 -0.009
-18.60 0.4385
-51.06 -0.0658
12.72 0.0188
6.49
VE
0.2 0.002
HE VE
-39.09 0.3656
-59.28 -0.1024
11.07 0.0051
9.87
0.2 0.002
VE
HE VE
HE
VE
HE (J mol-l);
of experimental
HE
-202.68 0.1096
-4.22
0.1 0.002
VE (cm3 mol-I).
curves show asymmetrical character as well, but its extent is less remarkable than that of HE curves. DISCUSSION
In order to consider the relation between the thermodynamic properties of fluorobenzene solutions and the relevant intermolecular interactions, experimental H” and VE values for fluorobenzene solutions were analyzed using the Flory solution theory and the Sanchez--Lacombe solution theory. Floly theory
of mixtures
The free volume theory by Flory (1965) has been applied to various nonelectrolyte solutions by many investigators to date (eg. McLure et al., 1965; Benson et al., 1969; Murakami et al., 1969). According to the Flory theory, the equation of state, HE and VE are represented respectively as follows y =
(3)
(~1/3_1)/~4/3
HE = x1 v;e2x,2v-1 vz = (xiv;
+ XlP; v; (;l-l-
+ X2V,*)(v” ~- P)
C-r)
+ XzP; v; (VT1 -E-l)
(4) (5)
where the notation follows closely that of Flory. The interaction parameter
102
Xl2 was determined using the experimental Hh data of each system in such a way that the following integral was minimized,
stand for HE obtained experimentally and that where ffh,,, and H&,.(4) calculated from eqn. (4), respectively. As c in eqn. (5) depends on X1,, theoretical VE values can be calculated using the values of Xl2 obtained from HE calculations. Sanchez-Lacombe
theory
of mixtures
Only the equations needed for the present application are summarized here. The notation follows that of Lacombe et al. (1976). The equation of state is p+P+F[ln(l-_)+(l-l/r);]=0
(7)
Values of molecular parameters of pure substances are determined by applying this equation to their vapor pressure data. HE and VE for binary mixtures are given by following equations HE = ru*]P&&APZ2 VE = ru*~-&Gl AP;,
+ (isi -
i$@iP;
+ (5s -
(8)
i%2P~l + PVE
-q52V2]
(9)
is defined as
P* = @,P;
+
@2G
+
4142APT
(10)
2
where P* is a characteristic pressure of a solution (I.C. Sanchez, personal communication, 1977). APi defined by eqn. (10) has a similar physical meaning to Xl2 of the Flory theory, and is treated as an interaction parameter. When VE is small, eqn. (8) is also rewritten in the form, HE = rv* ji,$,
q5,AP;,
+ [Fo(@,P; + 62%
+ rv* [@lP;Gl -
4142APT2)
-
Co> + +
42PHG52
PI VE
-
PO)1 (11)
where p”, = U(@,lP,
+
@2/P2).
(12)
The first term represents the contribution from the contact interaction energy, the second term represents the contribution due to the difference in the reduced densities and the characteristic pressures of the pure components, and this term is negative for ordinary mixtures. The last term represents the contribution due to the effect of the volume change when the mixture is formed. The sign of HE depends on the relative magnitudes of these three contributions.
103
In the Sanchez-Lacombe theory, it is assumed that the effective number of segments ri of a molecule i in a solution state is different from rp which is that in its pure state, but is related to rp by ‘a combining rule (1)’ as, ri = t-$.$+/v*
(13)
C $Ni = C riNi
(14)
where r$; is the close-packed volume of a molecule i in its pure state, v* is the average close-packed volume of a segment in the mixed state, and Ni is the number of molecule i, respectively, and then ri is regarded as a quantity which depends on the extent of the interaction surface and the volume of the molecule i in solution. The combining rule takes only the relative size of component molecules into consideration, because, in the Sanchez-Lacombe theory, uniformity of the interaction surface of each molecule and random mixing of component molecules in solution is assumed. However, the effective surface area and volume of each molecule should not in practice depend only on the relative size of the component molecules in the solution in which ‘a local order’ exists. The following modification was made. A quantity r: is used to signify the effective value of ri in the mixture, and a supplemental parameter qi which represents the extent of deviation of ri from rj given by eqn. (13) is introduced. The extent of the ‘deviation’ is considered to depend on the composition of the mixture. Now, it is assumed that the deviation which refers to a molecule i becomes greater when the number of molecules j surrounding molecule i increases, and if the assumption of random mixing of component molecules is satisfied, r-i is also assumed to be of the form
r’=l2
CXiri xiri(l
+ xjqi)
ri(l+xjyi)
(13’ 1
where xi and xi are mole fractions of molecules i and j, respectively. The factor 2ciri/Cifjxiri(l + x,qi) is introduced so that the ri satisfies the relation Cr:Ni
= CryNi
(14’)
which is similar to eqn. (14) for ri. When qi = 0, eqn. (13’) reduces to eqn. (13). The supplemental parameter qj which refers to a molecule j is determined simultaneously in the case of the binary mixture, because qj is a variable parameter which depends on qi through the relations eqn. (13’) and eqn. (14’). In this paper, the parameter qi which is determined explicitly refers to the alicyclic hydrocarbon or aromatic hydrocarbon in the mixture, and is denoted as q2. Values of the interaction parameter API, and the supplemental parameter y2 were determined using the experimental HE data so that they minimized
104 the integral
where H&,n.(~)stands for HE calculated from eqn. (8). As the value of 6 in eqn. (9) depends on the values of AP i2 and q2, theoretical vahres of VE were calculated by using the values of APT2 and qz determined from HE calculations. Values of molar volumes V, thermal expansion coefficients CYand isothermal compressibilities /3 of pure components used in the application of the Flory theory, and molecular parameters c*, U* and r of pure components used in the application of the Sanchez-Lacombe theory are summarized in Table 5. The interaction parameters X1 a and AP;, determined by using the experimental HE data are listed in Tables 6 and 7. The parameter APT, of the Sanchez-Lacombe theory was determined in two ways, the first is the case where the parameter q2 is introduced so that the most suitable fit of eqn. (8) to the experimental HE curve is obtained, and the second is the case where the parameter q2 is not introduced. The comparison of the calculated results with the experimental ones was made for the various fluorobenzene systems and examples are shown in Figs. 8 to 11. For the fluorobenzene-alicyclic hydrocarbon system, agreement between the calculated and observed results is fairly good, and in addition, better agreement is obtained by introducing the parameter q2 in the SanchezLacombe theory. On the other hand, the agreement is poor for the fluoroTABLE
5
Properties
of component
Component
Fluorobenzene Cyclohexane Methylcyclohexane Benzene Toluene o-Xylene m-Xylene p-Xylene
liquids
V
10301
1060
E*
(cm3 mo1-1)
(K-l)
(atm-l
94.32 108.75 128.33 89.42 106.86 121.21 123.48 123.93
1.16 a 1.261 c 1.18 a 1.217 c 1.071 c 0.963 1.004 1.017
99.09 b 155.1 c 112.4 b 98.12 ’ 95.0 c 83.1 88.5 92.0
)
(J mol-l)
4380.6 4129.6 4347.2 4518.7 4748.8 4661.0 4665.2
__~
*
r
Fcm3 mo1-1) d
10.39 10.79 9.80 11.22 12.03 12.11 12.24
d
8.05 8.65 8.02 8.50 9.14 9.21 9.14
V: based on densities measured in this work. aandfl: a SCEJ Data Book (1963). b Estimated Prom data for molecular acoustics c McLure et al. (1965), others; (Schaaffs, 1967) and heat capacities (Riddick et al., 1970), Singh et al. (1968). others; Sanchez et al. (1976). I?*, u* and r: d I.C. Sanchez, personal communication (1977),
d
105
TABLE
6
Summary of calculations
of fluorobenzene
System
systems using the Flory theory
X12 (J cmP3)
OH
VE (x1 = 0.5) (cm3 mol-I)
(J mol-I) Calc.
Expt.
0.664 0.638 0.013 4.022 0.019 0.023 0.033
0.686 0.561 0.073 0.027 0.092 0.110 0.091
Fluorobenzene(1) -cyclohexane( 2) -methylcyclohexane(2) -benzene( 2) -toluene( 2) -o-xylene( 2) --m-xylene(2) --p-xylene( 2)
42.74 38.53 0.08 -2.42 0.53 0.04 -Q.24
26.76 24.57 3.33 4.59 0.52 3.55 4.16
benzene-aromatic hydrocarbon systems. More especially, the calculated VE values seem to be small compared with the experimental ones and this tendency is remarkable in the case of the Sanchez-Lacombe theory. However, if the parameter q2 is introduced, the calculated HE curves reproduce the skewed shape of the experimental one fairly well, and the magnitude of VE is improved to some extent and the asymmetrical character of the calculated
TABLE
7
Summary of calculations System
of fluorobenzene Ap;, (J cm -3)
systems using the Sanchez-Lacombe
42
OH
VE (x1 = 0.5) (cm3 mol-l)
(J mold1 )
~-
Calc.
Expt.
Fluorobenzene(1) -cyclohexane( -benzene(2) -toluene(
2)
--o-xylene(2)
2)
32.93 33.71
0 -0.16
28.80 13.66
0.706 0.689
0.686
0.04 -0.43
0 -0.14
3.33 0.29
0.003 0.028
0.073
0 0.24
4.89 0.89
-0.033 0.023
0.027
0 0.004
0.27 0.06
-0.006 --0.004
0.092
-1.82 -2.75 0.66 0.63
--m-xylene(2)
0.25 -0.24
0 0.06
3.47 0.20
0.003 0.042
0.110
--p-xylene(
0.08 -0.53
0 0.07
4.17 0.24
0.016 0.052
0.091
2)
theory
106
-15 0 0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
X1 Fig. 8. Experimental and calculated HE results of fluorobenzene(l)-cyclohexane(2) system at 298.15 K. o experimental results. The broken curve is calculated from the Flory theory and the Sanchez-Lacombe theory (92 = 0). The solid curve is calculated from the Sanchez-Lacombe theory (42 = -0.16). Fig, 9. Experimental and calculated HE results of fluorobenzene( 1)--p-xylene( 2) system at 298.15 K. o experimental results. The broken curve is calculated from the Flory theory. The solid curves (a) and (b) are calculated from the Sanchez-Lacomhe theory (q2 = 0) and (42 = 0.07). respectively.
VE curve is in agreement with that of the experimental one, but its extent seems to be greatly overestimated. The fluorobenzene-p-xylene system appears to be almost athermal. It may be thought of as arising from the balance of the three contributions corresponding to the terms of the r.h.s. of eqn. (11). Curves (l), (2) and (3) in Fig. 12 correspond to the contributions of the first, second and the last terms in eqn. (ll), respectively. It is found from this figure that the introduction of parameter qs enlarges the asymmetrical character of the VE effect corresponding to the last term of eqn. (ll), and then such an effect seems to reflect the asymmetrical HE curve of the fluorobenzene-p-xylene system. This is true for the other aromatic hydrocarbon systems showing skewed HE curves. From the asymmetrical composition dependence of VE, it can be supposed that the packing of the component molecules in the mixture is not completely random and there exists a local order which depends on the solution composition. Both in the Flory theory and the Sanchez-Lacombe theory, the random mixing of component molecules is assumed and any effect depending on the solution composition is not allowed for. Introduction of parameter q2 in the Sanchez-Lacombe theory takes such an effect into account to some extent, in that it adjusts the effective size of component molecules so that they depend on the solution composition. A theory which can reflect the state of packing of component molecules in a mixture,
107
0.10
0.08
0.02
0 0.2
004
0.6
0.8
x1
Fig. 10. Experimental and calculated VE results of fluorobenzene(l)-cyclohexane( 2) system at 298.15 K. o experimental results. The broken curve is calculated from the Flory theory. The solid curves (a) and (b) are calculated from the Sanchez-Lacombe theory (q2 = 0) and (q2 = -0.16) respectively. Fig. 11. Experimental and calculated VE results of fluorobenzene(l)-p-xylene(2) system at 298.15 K. o experimental results. The broken curve is calculated from the Flory theory. The solid curves (a) and (b) are calculated from the Sanchez-Lacombe theory (42 = 0) and (42 = 0.07), respectively.
so-called ‘solution structure’, may be needed to account consistently for various thermodynamic properties of any system. In order to explain the intermolecular interactions in the fluorobenzene solutions, HE and VE results for the toluene-cyclohexane and toluene-aromatic hydrocarbon systems were also analyzed in a similar manner to those of the fluorobenzene systems. Toluene was chosen because the size and symmetry of the toluene molecule is similar to that of the fluorobenzene molecule. Experimental HE and VE values of the toluene systems used here are collected from the literature data (Watson et al., 1965; Murakami et al., 1969). The results are summarized in Tables 8 and 9. Values of XI2 and APT2 of the fluorobenzene-aromatic hydrocarbon systems and those of the toluene-aromatic hydrocarbon systems are also shown in Fig. 13. As shown in this figure, XI2 of the Flory theory and APT2 of the Sanchez-Lacombe theory have a similar tendency for both series. Hence, these two theories are regarded as qualitatively equivalent when considering intermolecular interactions.
-i 0.2
0.4
0.6
0.8
x1 Fig. 12. Calculated HE result of fluorobenzene(l)-p-xylene(2) system at 298.15 K from the Sanchez-Lacombe theory. The broken and solid curves correspond to 42 = 0 and 42 = 0.07, respectively. Curves lahelled (l), (2) and (3) represent the contributions from the first, second and third terms of eqn. (11). o experimental results.
TABLE Summary
8 of calculations
System
Toluene(
of toluene Xl!2 (J cm-‘)
systems
using the Flory OH
(J mol-I)
theory
VE (xl
-
= 0.5) (cm3 mol-‘)
Calc.
Expt.
0.312 0.105 0.021 0.029 0.019
0.570 0.088 0.042 0.051 0.018
1)
-cyclohexane( -benzene( 2) -o-xylene( 2) --mxylene(2) -p-xylene( 2)
2)
28.37 3.70 2.15 1.88 0.84
12.22 0.17 0.45 0.05 0.37
109 TABLE
9
Summary
of calculations
System
of toluene AP;, (J cmA3)
systems 42
using the Sanchez-Lacombe VE (xl
OH
theory
= 0.5)(cm3
mol.-l)
(J mol-I)
Calc
Expt.
0.437 0.070 0.021 0.034 0.020
0.570 0.088 0.042 0.051 0.018
Toluene( 1) -cyclohexane( -benzene( 2) -0.xylene( 2) --m-xylene( 2) -p-xylene(2)
2)
22.77 2.82 1.77 1.52 0.73
0 0 0 0 0
9.63 0.59 0.85 0.39 0.18
Generally speaking, the intermolecular interactions in an aromatic hydrocarbon such as toluene consist mainly of the dispersion force and the electrostatic interaction. The dispersion interaction should exist in all systems consisting of any molecule. The crystal structure of an aromatic compound such as benzene can be explained by the intermolecular electrostatic interaction, which affects the orientation of the molecule (Kihara, 1966). It may be rea-
A
TOLUENE
O_XYLENE
M-XYLENE
P-XYLENE
COMPONENT(2)
Fig. 13. Interaction parameters Xl2 and APT2 for fluorobenzene-aromatic hydrocarbon systems and toluene-aromatic hydrocarbon systems. A X12, o A&(q2 = 0), a APT2 (obtained by introducing q2 listed in Table 7) for fluorobenzene mixtures. A X12, l APi2(q2 = 0) for toluene mixtures.
110
sonable to consider that such an interaction exists not only in the solid state but in the liquid state. On the other hand, aliphatic hydrocarbons hardly participate in such electrostatic interactions (Hanna, 1968). The values of X1, and AP;z for the toluene-cyclohexane system are much larger than those of other toluene solutions. It means that the electrostatic interactions among toluene molecules are broken by mixing with cyclohexane molecules. This seems to be true also for the fluorobenzene-cyclohexane system. Both X1 z and APT2 of this system are larger than those of the toluene-cyclohexane system. In a similar comparison of both aromatic hydrocarbon series, the values of the interaction parameters of each fluorobenzene system are smaller than those of the corresponding toluene system. From these facts, it can be concluded that the attractive interaction between fluorobenzene and aromatic hydrocarbon is stronger than that between toluene and aromatic hydrocarbon. It is found from Fig. 13 that the relative magnitude of the interaction parameters is identical for all corresponding systems of the two series. It suggests that the nature of the interactions which contributes dominantly to these two series is essentially alike. In systems such as the toluene systems, the dispersion interaction and the electrostatic interaction may be supposed to be the principal intermolecular interactions as mentioned above. Hence, these interactions may also be presumed to contribute considerably to overall intermolecular interactions in the fluorobenzene systems. The contribution from the dispersion interaction in the fluorobenzene systems seems not to be so different from that in the toluene systems. However, the character of the electrostatic interaction in the former should be clearly distinct from that in the latter. Namely, the quadrupolar interaction will be the principal electrostatic interaction in usual aromatic hydrocarbon systems, because the dipole moments of common aromatic hydrocarbons are zero or negligibly small. On the other hand, the dipolar interaction cannot be negligible in the fluorobenzene systems. Moreover, as the relative magnitude of each component of the quadrupole moment belonging to each coordinate axis of the fluorobenzene molecule is considerably different from that of usual aromatic hydrocarbon molecules (Gierke et al., 1972), the orientational dependence of the quadrupolar interaction in the fluorobenzene systems should not be similar to that in the usual aromatic hydrocarbon systems. If there is local order in the packing of molecules in these solutions as discussed earlier, then the difference of the orientational dependence of the electrostatic interaction in each system should play a significant role in the thermodynamic properties. Because of the large electronegativity of the fluorine and the existence of the r-electrons in the aromatic hydrocarbon molecules, there may be a charge transfer interaction between the fluorobenzene acting as a x-electron acceptor and the aromatic hydrocarbon acting as a n-electron donor. It is generally known that such an interaction increases with a decrease in the ionization potential of the aromatic hydrocarbons acting as r-electron donors. From the relative magnitude of the ionization potential, the strength of the charge
111
transfer interaction between the fluorobenzene and these aromatic hydrocarbons may be in the order of benzene < toluene < each isomeric xylene system. However, as shown in Fig. 13, the difference in the interaction parameters of the fluorobenzene systems from those of the corresponding toluene systems is large for the benzene systems and small for the isomeric xylene systems. This means that the characteristic interaction between fluorobenzene and aromatic hydrocarbon is large for the benzene system and small for the isomeric xylene systems. It may be concluded that the contribution of the charge transfer interaction to the overall interaction in such a system is negligible, even though it actually exists. CONCLUSIONS
Attractive intermolecular interactions which contribute dominantly in the fluorobenzene-aromatic hydrocarbon systems were attributed to the dispersion interaction and the electrostatic dipolar and quadrupolar interactions. It was also recognized that a consideration of ‘the solution structure’ was essentially necessary to estimate consistently any thermodynamic property in the system. ACKNOWLEDGMENTS
The authors are indebted to the Japanese Ministry of Education which supported this work in part through a grant. The authors wish to thank Dr. I.C. Sanchez, National Bureau of Standards, for valuable discussions. REFERENCES Anantaraman, A.V., Bhattacharyya, S.N. and Parit, S.R., 1963. Excess thermodynamic functions of binary mixtures. System: cyclohexane + fluorobenzene. Trans. Faraday sot., 59: 1101-1109. Andrews, A., Morcom, K.W., Duncan, W.A., Swinton, F.L. and Pollock, J.M., 1970. The thermodynamic properties of fluorocarbon + hydrocarbon mixtures. 2. Excess enthalpies of mixing. J. Chem. Thermodyn., 2: 95-103. Benson, G.C., Murakami, S., Lam, V.T. and Singh, J., 1969. Molar excess enthalpies and volumes of cyclohexane-isomeric decalin systems at 25°C. Can. J. Chem., 48: 211-218. Bhattacharyya, S.N. and Mukherjee, A., 1968. Excess thermodynamic functions of some binary nonelectrolyte mixtures. I. Measurements of excess Gibbs free energy, enthalpies, and volumes of mixing. J. Phys. Chem., 72: 56-63. Bhattacharyya, S.N., Mitra, R.C. and Mukherjee, A., 1968. Excess thermodynamic functions of some binary nonelectrolyte mixtures. II. Analysis of gE, hE, and uE data in terms of a generalized quasi-lattice theory. J. Phys. Chem., 72: 63-67. Chen, S.-S. and Zwolinski, B.J., 1975. Excess thermodynamic functions of mixtures of hexafluorobenzene-toluene. J. Chem. Thermodyn., 7: 251-256. Duncan, W.A. and Swinton, F.L., 1966. Thermodynamic properties of binary systems containing hexafluorobenzene, Part 1. Phase diagrams. Trans. Faraday Sot., 62: 1082-1089. Fenby, D.V., 1972. Hexafluorobenzene-benzene and related systems. Rev. Pure and Appl. Chem., 22: 55-65.
112 Fenby, D.V. and Scott, R.L., 1967. Heats of mixing of nonelectrolyte solutions. IV. Mixtures of fluorinated benzenes. J. Phys. Chem., 71: 4103-4110. Flory, P.J., 1965. Statistical thermodynamics of liquid mixtures. J. Am. Chem. Sot., 87: 1833-1846. Gierke, T.D., Tigelaar, H.L. and Flygare, W.H., 1972. Calculation of molecular electric dipole and quadrupole moments. J. Am. Chem. Sot., 94: 330-338. Hanna, M.W., 1968. Bonding in donor-acceptor complexes. I. Electrostatic contributions to the ground-state properties of benzene-halogen complexes. J. Am. Chem. Sot., 90: 285-291. Kihara, T., 1966. Self-crystallizing molecular models. II. Acta Cryst., 21: 877-879. Lacombe, R.H. and Sanchez, I.C., 1976. Statistical thermodynamics of fluid mixtures. J. Phys. Chem., 80: 2568-2580. McLure, I.A., Bennett, J.E., Watson, A.E.P. and Benson, G.C., 1965. Excess properties of some aromatic-alicyclic systems. II. Analyses of HE and VE data in terms of three different theories of molecular solutions. J. Phys. Chem., 69: 2759-2765. Murakami, S., Lam, V.T. and Benson, G.C., 1969. The thermodynamic properties of binary aromatic systems. II. Excess enthalpies and volumes of benzene + toluene and toluene + isomeric xylene mixtures at 25OC. J. Chem. Thermodyn., 1: 397-407. Powell, R.J. and Swinton, F.L., 1970. The thermodynamic properties of fluorocarbon + hydrocarbon mixtures. 1. Excess volumes of mixing. J. Chem. Thermodyn., 2: 87-93. Powell, R.J., Swinton, F.L. and Young, C.L., 1970. The thermodynamic properties of fluorocarbon + hydrocarbon mixtures. 3. Gas-liquid critical temperatures and a comparison with the theory of Rowlinson and Sutton. J. Chem. Thermodyn., 2: 105-115. Riddick, J.A. and Bunger, W.B., 1970. Techniques of Chemistry, Vol. 2, Organic Solvents, 3rd edn, Wiley-Interscience, New York. Sanchez., I.C. and Lacombe, R.H., 1976. An elementary molecular theory of classical fluids. Pure fluids. J. Phys. Chem., 80: 2352-2362. SCEJ Data Book, Bussei Teisu (in Japanese), Vol. 1, 1963. The Society of Chemical Engineers (Japan) Maruzen, Tokyo. Schaaffs, W., 1967. Landolt-Bornstein New Series Group II Vol. 5, Molecular Acoustics, Springer Verlag, Berlin. Skillerne de Bristowe, B.J. and Stubly, D., 1974. Excess enthalpies of liquid mixtures of an aromatic fluorocarbon + a hydrocarbon. Analysis in terms of lattice theory. J. Chem. Thermodyn., 6: 581-585. Stokes, R-H., Levien, B.J. and Marsh, K.N., 1970. A continuous dilution dilatometer: The excess volume for the system cyclohexane + benzene. J. Chem. Thermodyn., 2: 43-52. Tanaka, R., Murakami, S. and Fujishiro, R., 1972. An isothermal displacement calorimeter for measuring enthalpies of mixing. Bull. Chem. Sot. Jpn., 45: 2107-2110. Tanaka, R., Kiyohara, O., D’Arcy, P.J. and Benson, G.C., 1975. A micrometer syringe dilatometer: Application to the measurement of the excess volumes of some ethylbenzene systems at 298.15 K. Can. J. Chem., 53: 2262-2267. Watson, A.E.P., McLure, IA., Bennett, J.E. and Benson, G.C., 1965. Excess properties of some aromatic-alicyclic systems. I. Measurements of enthalpies and volumes of mixing. J. Phys. Chem., 69: 2753-2758.
Amsterdam
- Printed in The Netherlands
MOLAR EXCESS ENTHALPIES AND VOLUMES FLUOROBENZENE SYSTEMS AT 298.15 K
FUMIO KIMURA
OF BINARY
and SACHIO MURAKAMI
Department of Chemistry, Osaka, 558 (Japan) (Received
93
November
Faculty
6th, 1978;
of Science,
accepted
Osaka City
University,
in revised form February
Sumiyoshi-ku, 23rd,
1979)
ABSTRACT Kimura, F. and Murakami, S., 1979. Molar excess enthalpies and volumes of binary fluor&benzene systems at 298.15 K. Fluid Phase Equilibria, 3: 93-112. Molar excess enthalpies and molar excess volumes of a series of fluorobenzene-alicyclic hydrocarbon and fluorobenzen&aromatic hydrocarbon systems were measured at 298.15 K. The experimental results iKere analyzed by using the Flory theory and the Sanchez-Lacombe theory of nonelectrolyte solutions to discuss the intermolecular interactions in the systems, and the necessity of considering ‘the solution structure’ in the systems was also discussed.
INTRODUCTION It is generally known that solutions containing fluorine compounds show some characteristic thermodynamic properties. Many thermodynamic studies have been carried out for such solutions, especially the hexafluorobenzenem -aromatic hydrocarbon systems (e.g. Duncan et al., 1966; Fenby et al., 1967; Andrews et al., 1970; Powell et al., 1970; Fenby, 1972; Skillerne et al., 1974; Chen et al., 1975), for which very large enthalpic stabilization was observed. However, there have been only a few systematic investigations for systems containing a few fluorine substituted benzenes (e.g. Anantaraman et al., 1963; Fenby et al., 1967; Bhattacharyya et al., 1968). In this investigation, in order to investigate the thermodynamic properties of fluorobenzene (mono fluorine substituted benzene) solutions, molar excess enthalpies HE and molar excess volumes VE of the systems of fluorobenzene with cyclohexane, methylcyclohexane, benzene, toluene and isomeric xylene were measured and the Flory theory (1965) and the Sanchez--Lacombe theory (1976) of nonelectrolyte mixtures were applied to the experimental results to discuss the intermolecular interactions in such systems. EXPERIMENTAL
Fluorobenzene from Wako Pure Chemical Industries Ltd. or Aldrich Chepicals Company Inc. was purified by fractional distillation without any
94 TABLE
1
Densities
of component
Component
liquids
at 298.15
Density
K
p (g cmM3)
Experiment Fluorobenzene Cyclohexane Methylcyclohexane Benzene Toluene o-Xylene m-Xylene p-Xylene * Riddick
1.01893 0.77387 0.76514 0.87359 0.86226 0.87592 0.85984 0.85670
+ f + * t f f f
Literature 0.00001 0.00001 0.00001 0.00001 0.00002 0.00001 0.00002 0.00001
*
0.77389 0.76506 0.87370 0.86231 0.87596 0.85990 0.85669
et al., (1970).
chemical treatment. Cyclohexane, methylcyclohexane, benzene, toluene and isomeric xylenes from Wako Pure Chemical Industries Ltd. were purified by the conventional method (Riddick et al., 1970). All materials were checked with a Shimadzu analytical gas chromatograph (Model GC-3BT) with a column packed with Silicone on Teflon and they were estimated to be more than 99.9% pure, though small peaks which seemed to show the existence of isomers were observed for isomeric xylenes. Densities at 298.15 K of the materials used are shown along with literature values in Table 1.
Fig. 1. Comparison of experimental results for the molar excess volume of cyclohexane(1)-benzene(2) system at 298.15 K. Points and curves represent deviations from eqn. (1). o present work. The solid curves represent the smoothed results by (a) Stokes et al. and (b) Tanaka et al.. The broken curves correspond to deviations of +l%.
95
Molar excess enthalpies HE were determined at 298.15 K using a isothermal displacement calorimeter described previously (Tanaka et al., 1972). The reproducibility of the calorimeter is estimated to be +0.5% in a molar excess enthalpy of 100 J mol-’ for an equimolar mixture. Molar excess volumes VE were determined at 298.15 K from the density measurements using an Ostwald type pycnometer. The volume of the pycnometer is about 10 cm3 and was calibrated by measuring the density of water. The temperature of the measurements was (298.15 f 0.01) K and was determined with a Hewlett-Packard thermometer calibrated at the factory. The bath temperature was controlled within *O.OOl K. In order to test the accuracy of our measurements, VE for the cyclohexane( l)-benzene( 2) system which has been frequently used as a standard system by many investigators was measured. The results are given in Table 3 and also in Fig. 1 along with the results obtained by Stokes et al. (1970) and Tanaka et al. (1975), and our results are believed to be as good as the results from densimetry. RESULTS
The experimental results from measurements of HE and VE at 298.15 K are listed in Tables 2 and 3, and graphical representations of the results are also given in Figs. 2-7. In all cases, x1 is the mole fraction of fluorobenzene. Each set of results was fitted to the following equation XE = XlXz i:
Cj (Xz - Xl)‘-l
i=l
(I)
where XE is either HE or VE. Values of the coefficients Cj were determined by the method of least squares with all points weighted equally. Choice of the appropriate number n of coefficients was based on the variation of the standard deviation,
(2) where the sum extends over the m results in a set. Table 4 summarizes the results of Cj and u obtained from this analysis. The smoothed representations of the results by eqn. (1) are shown as solid curves in Figs. 2-7. The HE result for the benzene system obtained by Fenby et al. (1967) and those of the toluene system and the methylcyclohexane system obtained by Bhattacharyya et al. (1968) are also shown as broken curves in Figs. 2 and 3. The resuit of the benzene system by Fenby et al. is a little more endothermic than ours, and those of the toluene system and the methylcyclohexane system by Bhattacharyya et al. are more exothermic than ours. It is clear from the figures that there is a distinct difference in the magnitudes of HE and VE between the fluorobenzene-alicyclic hydrocarbon sys-
96
TABLE2 Experimental Xl
values of HE at298.15 K
HE
Xl
HE
Xl
(J mol-l)
(J mol-l)
HE
(J mol-l)
Fluorobenzene(1) -cyclohexane(2) 0.0378 0.0872 0.1448 0.2071 0.2659 0.3217 0.3777
137.9 298.0 456.7 596.5 700.2 775.2 826.2
0.4279
0.4852 0.6210 0.5317 0.5447 0.5669 0.6182
0.6703 0.7230 0.7789 0.8343 0.8871 0.9344 0.9724
746.5 673.2 575.2 459.0 330.8 201.3 87.3
822.1 815.3 812.1 805.0 793.4 776.8 734.3
0.7093
680.7 610.6 526.6 418.9 300.6 181.9 74.7
-1.1 0.1 1.1 1.0 2.1 3.2 4.3
0.6907
853.7 863.6 861.8 855.2 850.3 642.8 804.7
FZuorobenzene(1) -methylcyelohexane(2) 0.0418 0.0979 0.1643 0.2326 0.3020 0.3719 0.4313
134.0 297.7 460.9 595.5 700.0 770.7 807.9
0.4906
0.5432 0.5586 0.5750 0.5911 0.6190 0.6649
0.7564 0.8017 0.8525 0.9000 0.9423 0.9772
Fluorobenzene(l)--benzene(2) 0.0311 0.0746 0.1263 0.1811 0.2311 0.2921 0.3521
-1.3 -2.8 -4.0 -4.3 -4.1 -3.4 -2.3
0.4080 0.4597 0.4846 0.4958 0.5321 0.5827 0.6314
0.7438 0.6001 0.6623 0.9176 0.9668
4.7 4.9 4.8 4.0 2.8 1.4
FluorobenzenP(l)--toluene(2) 0.0366 0.0856 0.1462 0.2077 0.2711 0.3353 0.3941
-6.6 -19.4 -30.2 -38.5 -45.1 -49.2 -51.3
0.4489
0.5011 0.5156 0.5362 0.5479 0.5820 0.6301
-51.8 -50.8 -49.9 -49.3 -46.8 -47.0 -43.8
0.6802 0.7236 0.7726 0.6288 0.8824 0.9311 0.9704
-39.6 -35.3 -30.0 -23.3 -16.4 -9.8 -4.3
Fluorobenzene(l)--o-xylene(2) 0.0415 0.0993 0.1618 0.2294 0.2974 0.3536 0.4100 0.4618
0.3 0.6 1.0 1.4 1.9 2.3 2.6 2.9
0.5116 0.5474 0.5575 0.5666 0.6113 0.6571 0.7008 0.7490
3.2 2.9 3.4 2.8 3.0 3.1 3.1 3.0
0.7947
0.8383 0.8856 0.9271 0.9628 0.9869
2.8 2.5 2.0 1.4 0.8 0.4
97
TABLE
2(continued) _ HE (J mol-I)
Xl
HE
x1
HE
x1
(Jmol-l)
(Jmol-l)
Fluorobenzene(l)-m-xylene(2) 0.0019
-0.1 -2.1 -4.5 -6.5 -7.4 -7.6 -7.1
0.0455 0.1020 0.1676 0.2372 0.3065 0.3660
Fluorobenzene(l)0.0095 0.0539 0.1131 0.1744 0.2409
0.3072 0.3785 0.4306
0.4117 0.4674 0.5189 0.5653 0.5753 0.6208 0.6679
-6.5 -5.7 -4.6 -3.6 -2.3 -1.1 0.1
0.7119 0.7601 0.8092 0.8487 0.8979 0.9403 0.9753
1.0 2.0 2.5 2.6 2.4 1.7 0.8
0.7891 0.8389 0.8895 0.8965 0.9366 0.9748
-0.5 0.4 0.9 0.9 0.8 0.4
p-xylene(2)
-0.7 -3.7 -7.6 -10.2
-11.9 -12.6 -12.3 -11.5
0.4763 0.5296 0.5553 0.5724 0.5934 0.6408
0.6901 0.7372
-10.5
-9.2 -7.7 -7.7 -6.6 -5.0 -3.3 -1.8
TABLE3 Experimental Xl
values of VE at 298.15 K VE (cm3 mol-l)
Xl
VE
Xl
VE
(cm3mol-l)
(cm3molV1)
Cyclohexane(l)-benzene(2) 0.1024
0.1493 0.1967 0.2681 0.2925 0.3426
0.234 0.323 0.402
0.3878 0.4352 0.5094
0.619 0.642 0.653
0.7021 0.7507
0.553 0.499
0.506 0.530 0.581
0.5591 0.6083 0.6525
0.646 0.628 0.599
0.8011 0.8487 0.8945
0.427 0.342 0.249
0.3912 0.4911 0.6107 0.7052
0.676 0.688 0.629 0.540
0.7135 0.8006 0.8978
0.536 0.403 0.227
0.3966 0.4898 0.6110 0.7063
0.560 0.555 0.518 0.449
0.8004 0.8973
0.340 0.190
Fluorobenzene(l)-cyclohexane(Z) 0.1055
0.294
0.2017 0.2956 0.3912
0.481 0.609 0.671
Fluorobentelie(l)-methylcyclohexane(2)
0.1090 0.2059 0.3004 0.3966
0.233 0.387 0.489 0.546
98
TABLE3(continued) Xl
VE (cd
Xl
VE (cm3
0.5840
0.067 0.070 0.074 0.073
0.7041 0.7041 0.7994 0.8710
0.068 0.065 0.050 0.037
0.3919 0.3950 0.4404 0.4896 0.4910 0.5092 0.6100
0.025 0.022 0.023 0.024 0.025 0.026 0.029
0.6111 0.7045 0.7059 0.8001 0.8989 0.8989
0.031 0.028 0.028 0.020 0.011 0.009
0.076 0.090 0.093 0.090
0.7529 0.8702 0.9224
0.072 0.044 0.028
0.105 0.110 0.105
0.7052 0.8013 0.8954
0.098 0.077 0.049
0.091 0.094 0.081 0.084
0.8059 0.9133
0.070 0.037
Xl
mC1)
VE (cm3
mol--1)
mole1
Fluoroben.zene(l)-benzene(2) 0.1043 0.2007 0.2973 0.2973
0.030 0.045 0.056 0.058
0.3940 0.3945 0.4938
Fluorobenzene(l)-toluene(2) 0.0615 0.1260 0.1339 0.2076 0.2963 0.2981 0.3455
-0.004 0.004 0.005 0.011 0.020 0.018 0.021
Fluorobenzene(l)-o-xylene(2) 0.1232 0.1645 0.1656 0.3048
0.036 0.047 0.045 0.069
0.3084 0.4509 0.5617 0.6102
Fluorobenzene(l)-m-xylene(2) 0.1110 0.2032 0.3018
0.041 0.063 0.087
0.3948
0.4917 0.6106
Fluorobenzene(l)-p-xylene(2) 0.1049 0.2029 0.3008 0.3953 -
0.028 0.047 0.069 0.086
0.5030 0.6055 0.7068 0.7068
terns and the fluorobenzene--aromatic hydrocarbon systems,namely, the magnitudes ofHE and VE of alicyclichydrocarbon solutions are fairlylarge but those of aromatic hydrocarbon solutions are small or,in some cases, negative. Such arelationshipis also generally observed between usual aromatic hydrocarbon-alicyclic hydrocarbon systems and usual aromatic hydrocarbon-aromatic hydrocarbon systems. It is also foundthattheHE curves of fluorobenzene-aromatic hydrocarbon systems are skewed towardlowhydrocarbon mole fractions.More especially,the HE of systems containing benzene, m- andp-xylenes show a change of sign at intermediate composition. A similar change of sign on the HE
)
-40
-50
0.2
0,6
0.4
X1
0.8
0.2
0.4
r1
0.6
0.8
Fig. 2. Molar excess enthalpies of fluorobenzene( 1 )--alicyclic hydrocarbon(2) systems at 293.15 K. o fluorobenzene-cyclohexane, l fluorobenzene-methylcyclohexane. The solid curves are smoothed results calculated from eqn. (1) with coefficients from Table 4. The broken curve is smoothed result of methylcyclohexane mixture by Bhattacharyya et al.. Fig. 3. Molar excess enthalpies of fluorobenzene(l)--aromatic hydrocarbon(2) systems at 298.15 K. o fluorobenzene-benzene, l fluorobenzene-toluene. The solid curves are smoothed results calculated from eqn. (1) with coefficients from Table 4. The broken curves are smoothed results of (a) benzene mixture by Fenby et al. and (b) toluene mixture by Bhattacharyya et al..
curves has also been found in some poly-fluorinated benzene-aromatic hydrocarbon systems (Fenby et al., 1967). Fenby et al. (1967) explained this as follows. Assuming that HE observed as a macroscopic property consists of the sum of a positive contribution due to the non-specific ‘physical’ interaction and a negative one due to the specific ‘chemical’ interaction, they concluded that the change of sign on the HE curves is attributed to the different composition dependence of these two contributions. According to their explanation, when HE values are plotted against the mole fraction, their maximum should be shifted toward solutions rich in the component of smaller molar volume. However, for the fluorobenzene-benzene system measured in this investigation, the endothermic maximum exists in the region of solutions rich in the component of larger molar volume, fluorobenzene, and hence’the above explanation is not available in this system. In the case of fluorobenzene-aromatic hydrocarbon systems, the V”
100
0.6
0.5 A'-IO.4 B J ,;0.3
0.2
0.1 -151
,
, 0.2
,
,
,
0.4
, 0.6
,
,
,
0
0.8
0.2
0.4
0.6
0.8
X1
X1
Fig. 4. Molar excess enthalpies of fluorobenzene(l)-xylene(2) systems at 298.15 K. fluorobenzene-o-xylene, A fluorobenzene-m-xylene, l fluorobenzene-p-xylene. The solid curves are smoothed results calculated from eon. (1) with coefficients from Table 4. 0
Fig. 5. Molar excess volumes of fluorobenzene( 1)-alicyclic hydrocarbon( 2) systems at 298.15 K. o fluorobenzene-cyclohexane, l fluorobenzene-methylcyclohexane. The solid curves are smoothed results calculated from eon. (1) with coefficients from Table 4.
0.10 0.08 r: d P.$ 0.06 Y
0,011 0.02
0.2
0.4
x1
0.6
0.8
n 0.2
0.4
0.6
0.8
Xl
Fig. 6. Molar excess volumes of fluorobenzene( 1)-aromatic hydrocarbon(2) systems at 298.15 K. o fluorobenzene-benzene, l fluorobenzene--toluene. The solid curves are smoothed results calculated from eon. (1) with coefficients from Table 4. Fig. 7. Molar excess volumes of fluorobenzene(l)-xylene(2) systems at 298.15 K. fluorobenzene-o-xylene, A fluorobenzene-m-xylene, l fluorobenzene-pxylene. The solid curves are smoothed results calculated from eon. (1) with coefficients from Table 4.
o
101 TABLE
4
Coefficients -
and standard
deviations
for representation
System
Function *
Cyclohexane( l)benzene( 2)
VE
2.6166
Fluorobenzene(l)cyclohexane( 2)
HE
VE
3454.38 2.7436
Fluorobenzene(l)methylcyclohexane( 2)
HE
3290.49
Fluorobenzene( benzene( 2)
l)--
Fluorobenzene( toluene(2)
l)-
Fluorobenzene( o-xylene( 2)
l)-
Fluorobenzene( m-xylene( 2)
l)-
Fluorobenzene( p-xylene( 2)
l)-
* Units:
Cl
c2
results by eqn. (1)
c3
c4
u
-
VE
2.2434
HE
5.15 0.2926
-0.0898 224.81 0.3858 21.07 0.2169
-0.0216 90.00 0.0757
0.002 76.47
106.63
1.0 0.003 0.9
0.0041
0.006
-49.43 -0.0373
-9.73 0.0306
4.71
0.1 0.002
-57.73 --0.0578
3.18 -0.0493
3.40
0.1 0.002
11.68 0.3658
-6.12 -0.0489
2.34 -0.009
-18.60 0.4385
-51.06 -0.0658
12.72 0.0188
6.49
VE
0.2 0.002
HE VE
-39.09 0.3656
-59.28 -0.1024
11.07 0.0051
9.87
0.2 0.002
VE
HE VE
HE
VE
HE (J mol-l);
of experimental
HE
-202.68 0.1096
-4.22
0.1 0.002
VE (cm3 mol-I).
curves show asymmetrical character as well, but its extent is less remarkable than that of HE curves. DISCUSSION
In order to consider the relation between the thermodynamic properties of fluorobenzene solutions and the relevant intermolecular interactions, experimental H” and VE values for fluorobenzene solutions were analyzed using the Flory solution theory and the Sanchez--Lacombe solution theory. Floly theory
of mixtures
The free volume theory by Flory (1965) has been applied to various nonelectrolyte solutions by many investigators to date (eg. McLure et al., 1965; Benson et al., 1969; Murakami et al., 1969). According to the Flory theory, the equation of state, HE and VE are represented respectively as follows y =
(3)
(~1/3_1)/~4/3
HE = x1 v;e2x,2v-1 vz = (xiv;
+ XlP; v; (;l-l-
+ X2V,*)(v” ~- P)
C-r)
+ XzP; v; (VT1 -E-l)
(4) (5)
where the notation follows closely that of Flory. The interaction parameter
102
Xl2 was determined using the experimental Hh data of each system in such a way that the following integral was minimized,
stand for HE obtained experimentally and that where ffh,,, and H&,.(4) calculated from eqn. (4), respectively. As c in eqn. (5) depends on X1,, theoretical VE values can be calculated using the values of Xl2 obtained from HE calculations. Sanchez-Lacombe
theory
of mixtures
Only the equations needed for the present application are summarized here. The notation follows that of Lacombe et al. (1976). The equation of state is p+P+F[ln(l-_)+(l-l/r);]=0
(7)
Values of molecular parameters of pure substances are determined by applying this equation to their vapor pressure data. HE and VE for binary mixtures are given by following equations HE = ru*]P&&APZ2 VE = ru*~-&Gl AP;,
+ (isi -
i$@iP;
+ (5s -
(8)
i%2P~l + PVE
-q52V2]
(9)
is defined as
P* = @,P;
+
@2G
+
4142APT
(10)
2
where P* is a characteristic pressure of a solution (I.C. Sanchez, personal communication, 1977). APi defined by eqn. (10) has a similar physical meaning to Xl2 of the Flory theory, and is treated as an interaction parameter. When VE is small, eqn. (8) is also rewritten in the form, HE = rv* ji,$,
q5,AP;,
+ [Fo(@,P; + 62%
+ rv* [@lP;Gl -
4142APT2)
-
Co> + +
42PHG52
PI VE
-
PO)1 (11)
where p”, = U(@,lP,
+
@2/P2).
(12)
The first term represents the contribution from the contact interaction energy, the second term represents the contribution due to the difference in the reduced densities and the characteristic pressures of the pure components, and this term is negative for ordinary mixtures. The last term represents the contribution due to the effect of the volume change when the mixture is formed. The sign of HE depends on the relative magnitudes of these three contributions.
103
In the Sanchez-Lacombe theory, it is assumed that the effective number of segments ri of a molecule i in a solution state is different from rp which is that in its pure state, but is related to rp by ‘a combining rule (1)’ as, ri = t-$.$+/v*
(13)
C $Ni = C riNi
(14)
where r$; is the close-packed volume of a molecule i in its pure state, v* is the average close-packed volume of a segment in the mixed state, and Ni is the number of molecule i, respectively, and then ri is regarded as a quantity which depends on the extent of the interaction surface and the volume of the molecule i in solution. The combining rule takes only the relative size of component molecules into consideration, because, in the Sanchez-Lacombe theory, uniformity of the interaction surface of each molecule and random mixing of component molecules in solution is assumed. However, the effective surface area and volume of each molecule should not in practice depend only on the relative size of the component molecules in the solution in which ‘a local order’ exists. The following modification was made. A quantity r: is used to signify the effective value of ri in the mixture, and a supplemental parameter qi which represents the extent of deviation of ri from rj given by eqn. (13) is introduced. The extent of the ‘deviation’ is considered to depend on the composition of the mixture. Now, it is assumed that the deviation which refers to a molecule i becomes greater when the number of molecules j surrounding molecule i increases, and if the assumption of random mixing of component molecules is satisfied, r-i is also assumed to be of the form
r’=l2
CXiri xiri(l
+ xjqi)
ri(l+xjyi)
(13’ 1
where xi and xi are mole fractions of molecules i and j, respectively. The factor 2ciri/Cifjxiri(l + x,qi) is introduced so that the ri satisfies the relation Cr:Ni
= CryNi
(14’)
which is similar to eqn. (14) for ri. When qi = 0, eqn. (13’) reduces to eqn. (13). The supplemental parameter qj which refers to a molecule j is determined simultaneously in the case of the binary mixture, because qj is a variable parameter which depends on qi through the relations eqn. (13’) and eqn. (14’). In this paper, the parameter qi which is determined explicitly refers to the alicyclic hydrocarbon or aromatic hydrocarbon in the mixture, and is denoted as q2. Values of the interaction parameter API, and the supplemental parameter y2 were determined using the experimental HE data so that they minimized
104 the integral
where H&,n.(~)stands for HE calculated from eqn. (8). As the value of 6 in eqn. (9) depends on the values of AP i2 and q2, theoretical vahres of VE were calculated by using the values of APT2 and qz determined from HE calculations. Values of molar volumes V, thermal expansion coefficients CYand isothermal compressibilities /3 of pure components used in the application of the Flory theory, and molecular parameters c*, U* and r of pure components used in the application of the Sanchez-Lacombe theory are summarized in Table 5. The interaction parameters X1 a and AP;, determined by using the experimental HE data are listed in Tables 6 and 7. The parameter APT, of the Sanchez-Lacombe theory was determined in two ways, the first is the case where the parameter q2 is introduced so that the most suitable fit of eqn. (8) to the experimental HE curve is obtained, and the second is the case where the parameter q2 is not introduced. The comparison of the calculated results with the experimental ones was made for the various fluorobenzene systems and examples are shown in Figs. 8 to 11. For the fluorobenzene-alicyclic hydrocarbon system, agreement between the calculated and observed results is fairly good, and in addition, better agreement is obtained by introducing the parameter q2 in the SanchezLacombe theory. On the other hand, the agreement is poor for the fluoroTABLE
5
Properties
of component
Component
Fluorobenzene Cyclohexane Methylcyclohexane Benzene Toluene o-Xylene m-Xylene p-Xylene
liquids
V
10301
1060
E*
(cm3 mo1-1)
(K-l)
(atm-l
94.32 108.75 128.33 89.42 106.86 121.21 123.48 123.93
1.16 a 1.261 c 1.18 a 1.217 c 1.071 c 0.963 1.004 1.017
99.09 b 155.1 c 112.4 b 98.12 ’ 95.0 c 83.1 88.5 92.0
)
(J mol-l)
4380.6 4129.6 4347.2 4518.7 4748.8 4661.0 4665.2
__~
*
r
Fcm3 mo1-1) d
10.39 10.79 9.80 11.22 12.03 12.11 12.24
d
8.05 8.65 8.02 8.50 9.14 9.21 9.14
V: based on densities measured in this work. aandfl: a SCEJ Data Book (1963). b Estimated Prom data for molecular acoustics c McLure et al. (1965), others; (Schaaffs, 1967) and heat capacities (Riddick et al., 1970), Singh et al. (1968). others; Sanchez et al. (1976). I?*, u* and r: d I.C. Sanchez, personal communication (1977),
d
105
TABLE
6
Summary of calculations
of fluorobenzene
System
systems using the Flory theory
X12 (J cmP3)
OH
VE (x1 = 0.5) (cm3 mol-I)
(J mol-I) Calc.
Expt.
0.664 0.638 0.013 4.022 0.019 0.023 0.033
0.686 0.561 0.073 0.027 0.092 0.110 0.091
Fluorobenzene(1) -cyclohexane( 2) -methylcyclohexane(2) -benzene( 2) -toluene( 2) -o-xylene( 2) --m-xylene(2) --p-xylene( 2)
42.74 38.53 0.08 -2.42 0.53 0.04 -Q.24
26.76 24.57 3.33 4.59 0.52 3.55 4.16
benzene-aromatic hydrocarbon systems. More especially, the calculated VE values seem to be small compared with the experimental ones and this tendency is remarkable in the case of the Sanchez-Lacombe theory. However, if the parameter q2 is introduced, the calculated HE curves reproduce the skewed shape of the experimental one fairly well, and the magnitude of VE is improved to some extent and the asymmetrical character of the calculated
TABLE
7
Summary of calculations System
of fluorobenzene Ap;, (J cm -3)
systems using the Sanchez-Lacombe
42
OH
VE (x1 = 0.5) (cm3 mol-l)
(J mold1 )
~-
Calc.
Expt.
Fluorobenzene(1) -cyclohexane( -benzene(2) -toluene(
2)
--o-xylene(2)
2)
32.93 33.71
0 -0.16
28.80 13.66
0.706 0.689
0.686
0.04 -0.43
0 -0.14
3.33 0.29
0.003 0.028
0.073
0 0.24
4.89 0.89
-0.033 0.023
0.027
0 0.004
0.27 0.06
-0.006 --0.004
0.092
-1.82 -2.75 0.66 0.63
--m-xylene(2)
0.25 -0.24
0 0.06
3.47 0.20
0.003 0.042
0.110
--p-xylene(
0.08 -0.53
0 0.07
4.17 0.24
0.016 0.052
0.091
2)
theory
106
-15 0 0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
X1 Fig. 8. Experimental and calculated HE results of fluorobenzene(l)-cyclohexane(2) system at 298.15 K. o experimental results. The broken curve is calculated from the Flory theory and the Sanchez-Lacombe theory (92 = 0). The solid curve is calculated from the Sanchez-Lacombe theory (42 = -0.16). Fig, 9. Experimental and calculated HE results of fluorobenzene( 1)--p-xylene( 2) system at 298.15 K. o experimental results. The broken curve is calculated from the Flory theory. The solid curves (a) and (b) are calculated from the Sanchez-Lacomhe theory (q2 = 0) and (42 = 0.07). respectively.
VE curve is in agreement with that of the experimental one, but its extent seems to be greatly overestimated. The fluorobenzene-p-xylene system appears to be almost athermal. It may be thought of as arising from the balance of the three contributions corresponding to the terms of the r.h.s. of eqn. (11). Curves (l), (2) and (3) in Fig. 12 correspond to the contributions of the first, second and the last terms in eqn. (ll), respectively. It is found from this figure that the introduction of parameter qs enlarges the asymmetrical character of the VE effect corresponding to the last term of eqn. (ll), and then such an effect seems to reflect the asymmetrical HE curve of the fluorobenzene-p-xylene system. This is true for the other aromatic hydrocarbon systems showing skewed HE curves. From the asymmetrical composition dependence of VE, it can be supposed that the packing of the component molecules in the mixture is not completely random and there exists a local order which depends on the solution composition. Both in the Flory theory and the Sanchez-Lacombe theory, the random mixing of component molecules is assumed and any effect depending on the solution composition is not allowed for. Introduction of parameter q2 in the Sanchez-Lacombe theory takes such an effect into account to some extent, in that it adjusts the effective size of component molecules so that they depend on the solution composition. A theory which can reflect the state of packing of component molecules in a mixture,
107
0.10
0.08
0.02
0 0.2
004
0.6
0.8
x1
Fig. 10. Experimental and calculated VE results of fluorobenzene(l)-cyclohexane( 2) system at 298.15 K. o experimental results. The broken curve is calculated from the Flory theory. The solid curves (a) and (b) are calculated from the Sanchez-Lacombe theory (q2 = 0) and (q2 = -0.16) respectively. Fig. 11. Experimental and calculated VE results of fluorobenzene(l)-p-xylene(2) system at 298.15 K. o experimental results. The broken curve is calculated from the Flory theory. The solid curves (a) and (b) are calculated from the Sanchez-Lacombe theory (42 = 0) and (42 = 0.07), respectively.
so-called ‘solution structure’, may be needed to account consistently for various thermodynamic properties of any system. In order to explain the intermolecular interactions in the fluorobenzene solutions, HE and VE results for the toluene-cyclohexane and toluene-aromatic hydrocarbon systems were also analyzed in a similar manner to those of the fluorobenzene systems. Toluene was chosen because the size and symmetry of the toluene molecule is similar to that of the fluorobenzene molecule. Experimental HE and VE values of the toluene systems used here are collected from the literature data (Watson et al., 1965; Murakami et al., 1969). The results are summarized in Tables 8 and 9. Values of XI2 and APT2 of the fluorobenzene-aromatic hydrocarbon systems and those of the toluene-aromatic hydrocarbon systems are also shown in Fig. 13. As shown in this figure, XI2 of the Flory theory and APT2 of the Sanchez-Lacombe theory have a similar tendency for both series. Hence, these two theories are regarded as qualitatively equivalent when considering intermolecular interactions.
-i 0.2
0.4
0.6
0.8
x1 Fig. 12. Calculated HE result of fluorobenzene(l)-p-xylene(2) system at 298.15 K from the Sanchez-Lacombe theory. The broken and solid curves correspond to 42 = 0 and 42 = 0.07, respectively. Curves lahelled (l), (2) and (3) represent the contributions from the first, second and third terms of eqn. (11). o experimental results.
TABLE Summary
8 of calculations
System
Toluene(
of toluene Xl!2 (J cm-‘)
systems
using the Flory OH
(J mol-I)
theory
VE (xl
-
= 0.5) (cm3 mol-‘)
Calc.
Expt.
0.312 0.105 0.021 0.029 0.019
0.570 0.088 0.042 0.051 0.018
1)
-cyclohexane( -benzene( 2) -o-xylene( 2) --mxylene(2) -p-xylene( 2)
2)
28.37 3.70 2.15 1.88 0.84
12.22 0.17 0.45 0.05 0.37
109 TABLE
9
Summary
of calculations
System
of toluene AP;, (J cmA3)
systems 42
using the Sanchez-Lacombe VE (xl
OH
theory
= 0.5)(cm3
mol.-l)
(J mol-I)
Calc
Expt.
0.437 0.070 0.021 0.034 0.020
0.570 0.088 0.042 0.051 0.018
Toluene( 1) -cyclohexane( -benzene( 2) -0.xylene( 2) --m-xylene( 2) -p-xylene(2)
2)
22.77 2.82 1.77 1.52 0.73
0 0 0 0 0
9.63 0.59 0.85 0.39 0.18
Generally speaking, the intermolecular interactions in an aromatic hydrocarbon such as toluene consist mainly of the dispersion force and the electrostatic interaction. The dispersion interaction should exist in all systems consisting of any molecule. The crystal structure of an aromatic compound such as benzene can be explained by the intermolecular electrostatic interaction, which affects the orientation of the molecule (Kihara, 1966). It may be rea-
A
TOLUENE
O_XYLENE
M-XYLENE
P-XYLENE
COMPONENT(2)
Fig. 13. Interaction parameters Xl2 and APT2 for fluorobenzene-aromatic hydrocarbon systems and toluene-aromatic hydrocarbon systems. A X12, o A&(q2 = 0), a APT2 (obtained by introducing q2 listed in Table 7) for fluorobenzene mixtures. A X12, l APi2(q2 = 0) for toluene mixtures.
110
sonable to consider that such an interaction exists not only in the solid state but in the liquid state. On the other hand, aliphatic hydrocarbons hardly participate in such electrostatic interactions (Hanna, 1968). The values of X1, and AP;z for the toluene-cyclohexane system are much larger than those of other toluene solutions. It means that the electrostatic interactions among toluene molecules are broken by mixing with cyclohexane molecules. This seems to be true also for the fluorobenzene-cyclohexane system. Both X1 z and APT2 of this system are larger than those of the toluene-cyclohexane system. In a similar comparison of both aromatic hydrocarbon series, the values of the interaction parameters of each fluorobenzene system are smaller than those of the corresponding toluene system. From these facts, it can be concluded that the attractive interaction between fluorobenzene and aromatic hydrocarbon is stronger than that between toluene and aromatic hydrocarbon. It is found from Fig. 13 that the relative magnitude of the interaction parameters is identical for all corresponding systems of the two series. It suggests that the nature of the interactions which contributes dominantly to these two series is essentially alike. In systems such as the toluene systems, the dispersion interaction and the electrostatic interaction may be supposed to be the principal intermolecular interactions as mentioned above. Hence, these interactions may also be presumed to contribute considerably to overall intermolecular interactions in the fluorobenzene systems. The contribution from the dispersion interaction in the fluorobenzene systems seems not to be so different from that in the toluene systems. However, the character of the electrostatic interaction in the former should be clearly distinct from that in the latter. Namely, the quadrupolar interaction will be the principal electrostatic interaction in usual aromatic hydrocarbon systems, because the dipole moments of common aromatic hydrocarbons are zero or negligibly small. On the other hand, the dipolar interaction cannot be negligible in the fluorobenzene systems. Moreover, as the relative magnitude of each component of the quadrupole moment belonging to each coordinate axis of the fluorobenzene molecule is considerably different from that of usual aromatic hydrocarbon molecules (Gierke et al., 1972), the orientational dependence of the quadrupolar interaction in the fluorobenzene systems should not be similar to that in the usual aromatic hydrocarbon systems. If there is local order in the packing of molecules in these solutions as discussed earlier, then the difference of the orientational dependence of the electrostatic interaction in each system should play a significant role in the thermodynamic properties. Because of the large electronegativity of the fluorine and the existence of the r-electrons in the aromatic hydrocarbon molecules, there may be a charge transfer interaction between the fluorobenzene acting as a x-electron acceptor and the aromatic hydrocarbon acting as a n-electron donor. It is generally known that such an interaction increases with a decrease in the ionization potential of the aromatic hydrocarbons acting as r-electron donors. From the relative magnitude of the ionization potential, the strength of the charge
111
transfer interaction between the fluorobenzene and these aromatic hydrocarbons may be in the order of benzene < toluene < each isomeric xylene system. However, as shown in Fig. 13, the difference in the interaction parameters of the fluorobenzene systems from those of the corresponding toluene systems is large for the benzene systems and small for the isomeric xylene systems. This means that the characteristic interaction between fluorobenzene and aromatic hydrocarbon is large for the benzene system and small for the isomeric xylene systems. It may be concluded that the contribution of the charge transfer interaction to the overall interaction in such a system is negligible, even though it actually exists. CONCLUSIONS
Attractive intermolecular interactions which contribute dominantly in the fluorobenzene-aromatic hydrocarbon systems were attributed to the dispersion interaction and the electrostatic dipolar and quadrupolar interactions. It was also recognized that a consideration of ‘the solution structure’ was essentially necessary to estimate consistently any thermodynamic property in the system. ACKNOWLEDGMENTS
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