J. Phys. Chem. 1989,93, 4973-4981
4973
Equation of State of Mixtures of Simple Molecular Fluids. The CS,
+ CH,Ci,
System
A. Compostizo, A. Crespo Colin, M. R. Vigil, R. G. Rubio,* and M. Diaz Peiia Departamento de Quimica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense, 28040 Madrid, Spain (Received: August 9, 1988; In Final Form: January 25, 1989)
The equation of state of CS, + CH2C12has been studied over the whole composition range and for 298.15 C T/K d 319.15 and 0.1 C p/MPa C 40.0. The results indicate that the system shows a higher degree of nonideality than CS2 + CCI4, as well as larger pressure dependences of GE,p,and TSE.While the Gubbins-Gray perturbation theory leads to conclusions in agreement with the data, the Deiters equation of state gives worse results than for CS2 + CC14.
Introduction There is a great deal of interest in the prediction of the structure and thermodynamic properties of molecular fluids, both for technological and theoretical reasons. Perturbation theories lead to the conclusion that the structure of the fluids is mostly determined by the packing effects (repulsive part of the potential) and that this is also the most important contribution to the thermodynamic properties, at least far from critical points.’ However, currently our predictive ability is small, mainly because as one introduces many details into the reference system, it is almost as difficult to calculate its properties as those of the whole system (reference perturbation). The anisotropy of the intermolecular pair potential can arise either from the shape of the molecular core and/or from multipolar interactions, and so far theories that include the latter can only be applied to molecules with low anisotropies of shape,2 while higher departures from sphericity can only be dealt with when no permanent electrical moments are p r e ~ e n t . ~Therefore, the study of molecular fluids is an open field in which much advance is still necessary before current theories can be applied to the mixtures of complex fluids usually present in chemical processes. Besides computer simulations, carefully chosen experimental data are helpful in testing theoretical approaches. The fluids must be formed by rigid molecules, the size, shape, and multiples of which should be changed in order to cover any aspect of the theory. Derivatives of methane seem ideal fluids for this purpose. In a previous paper4 we studied the excess properties of CS, CCl, over the pressure interval 0.1 C p/MPa < 40. The results indicate that p,GE,and HE are very weakly dependent upon p , which contrasts with the results of other mixtures of simple fluids, like Ar Kr or Kr + CH,, for which p changes more than 200% over the same pressure range.s The different behavior should be traced back to packing effects and the correlations of order that exist in the pure component^.^ Recently, Siddiqi and Lucas reported on HEfor the system CS2 CH2C12,6and found that the pressure dependence of HE is small and linear, but HE itself is much larger than for CS2 CCI4. The high degree of nonideality has been confirmed by a value of GE0, 0.1 MPa) which is almost 4 times that of CS2 CCI4.’ From a microscopic viewpoint the main differences between the two systems are that
+
+
+
+
+
-
+
~
~~
CC14 is a tetrahedral molecule with a permanent octupole while CH2C12is triangular (neglecting the H atoms!) and has a permanent dipole. Differences in packing between a linear a tetrahedral and a linear + a triangular molecules and quadrupole octupole and quadrupole dipole interactions should justify the high difference in nonideality between the two systems. It is known that the pressure may have a noticeable influence on packing effects, especially when there are order correlations between the molecules of the pure components. Since they exist in CS2 and some halo derivatives of methane: it seemed interesting to carry out a study of the p-p-T surface of CS2 CH2C12to compare the resulting p ( x , p , T ) with those of C S , + CC14 and other mixtures of simple fluids.
+
+
+
+
Experimental Section The p-p-T data have been measured with a high-pressure vibrating-tube densitometer. Since the whole apparatus has been described in detail in a previous work: only a brief description will be included here for the convenience of the reader. The experimental setup is similar to that of Matsuo and van Hook,g the main difference being that the pressure is directly applied to the sample by a screw pump; thus there is no need for oil-sample separators. The strain-gauge pressure transducers were calibrated against a dead-weight gauge, and the calibration was checked after the experiments on each substance were completed; this has allowed the pressure to be measured within fO.OO1 MPa. The temperature of the U-tube was kept constant within f0.5 mK, and it was measured with a quartz thermometer, whose calibration was checked weekly against a Ga melting point standard. The temperature of the whole apparatus was kept constant to fO.O1 K of that of the sample. The densitometer was calibrated with different substances of well-known densities. It constrast with previous we have found the period of vibration 7 vs density relationship to be nonlinear; thus we have used p-p-T relationships reported in the literature for N2,12C02,13and CCl: for establishing a calibration curve. The calibration was tested after the experiments on each pure substance were carried out. No hysteresis was found within f5 X lo-’ in 7 when measuring at low pressure after the vibrating tube was subjected to high pressure. In the previous conditions p can be obtained within f104 g cm-3 for 0.1 4 p/MPa 4 40.
~~
(1) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids; Academic Press: London, 1976. (2) Gray, C. B.; Gubbins, K. E. Theory of Molecular Fluids; Clarendon Press: Oxford, 1984. (3) Kohler, F.; Marius, W.; Quirke, N . ; Perram, J. W.; Hoheisel, C.; Breithenfelder-Manske, H. Mol. Phys. 1979, 38, 2057. Fischer, J. J . Chem. Phys. 1980, 72, 5371. Fischer, J.; Lago, S . J . Chem. Phys. 1983, 78, 5750. (4) Compostizo, A.; Crespo Colin, A,; Vigil, M. R.; Rubio, R. G.; Diaz Pefia, M. J . Phys. Chem. 1988, 92, 3998. (5) Calado, J. C. G.; Guedes, M. J. R.; Nunes da Ponte, M.; Rebelo, L. P. N.; Streett, W. B. J . Phys. Chem. 1986, 90, 1892. Barreiros, S. F.; Calado, J. C. G.; Nunes da Ponte, M.; Streett, W. B. J. Chem. Soc., Faraday Trans. I 1983, 79, 1869. (6) Siddiqi, M. A.; Lucas, K. Fluid Phase Equilib. 1985, 20, 297. (7) Aracil, J.; Luengo, G.; Almeida, B. S.; Telo da Gama, M. M.; Rubio, R. G.; Diaz Peiia, M. J . Phys. Chem., in press.
0022-3654/89/2093-4973$01.50/0
(8) Swinton, F. L. Pure Appl. Chem. 1987, 59, 35. Montague, D. C.; Chowdhury, M. R.; Dore, J. C.; Reed, J. Mol. Phys. 1983, 50, 1. Narten, A. H. J . Chem. Phys. 1976,65, 573. Enciso, E.; Lombardero, M.; Dore, J. C. Mol. Phys. 1986,59,941. Enciso, E.; Martin, C.; Deraman, M. B.; Dore, J. C. Mol. Phys. 1987, 60, 541. (9) Matsuo, S.; van Hook, A. J . Phys. Chem. 1984, 88, 1032. (10) Albert, H. J.; Wood, R. H. Reu. Sci. Instrum. 1984, 55, 589. ( 1 1) Eckert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J . Phys. Chem. 1986, 90, 2738. (1 2) Angus, S.; de Reuck, K. M.; Armstrong, B.; Jacobsen, R. T.; Stewart, R. B. Nitrogen; IUPAC Thermodynamic Tables Project Centre; Pergamon Press: Oxford, 1978; Vol. 6. (13) Angus, S.; Armstrong, B.; de Reuk, K. N . Carbon Dioxide, International Thermodynamic Tables of the Fluid State, No. 3; Pergamon Press: Oxford, 1976.
0 1989 American Chemical Society
4974
The Journal of Physical Chemistry, Vol. 93, No. 12. 1989
The pure components were Fluka of the highest punty available, they were dried over 4-A molecular sieves, and CH2C12was purified according to recommended methods immediately before use.14 The densities at 298.15 K under orthobaric conditions were 1.255 68 g for CS2 and 1.3 16 43 g cmW3for CH2CI2,which compare well with the literature values of 1.255 85 g cm-3 for CS, - ~ CH2C1,.'s and 1.31630 g c ~ n for
Compostizo et al.
Ix
I
I A I
I
I
Results Table I shows the p-p data at three temperatures for xCS2 + (1 - x)CH2CI2over the whole composition range. The results at each composition were fitted to a generalized Tait equation of the form P =
Po/[1
- B4 In [(B + P I / @ + P0)ll
(1)
where po
= B1
+ B2T + B3'P
(2)
and B = BS exp(-B6Tj
(3)
where B,, i = 1-6 are parameters independent of T and p . Table I1 shows the values of B, for the different compositions and the corresponding standard deviations. From eq 1-3 the isobaric expansivities ap and the isothermal compressibilities K~ shown in Table I were calculated. The excess volumes are defined by P ( ~ , T , P )= V~(X,T,P)- xvi(T,p) - (1
c
4
0.3
IO
0
20 p/MPa
30
LO
- x)V2(T9p) (4)
where subscripts m, 1, and 2 refer to mixture, component 1, and component 2 , respectively. Figure 1A shows the pressure dependence of r/E at 318.15 K, while Figure 1B shows the temperature dependence of p at 0.1, 10, and 40 MPa. As can be observed, p decreases with increasing pressure. This tendency 0 at high pressures is common to the behavior of toward mixtures of simpler f l ~ i d s .( ~d p / d T ) , shows a rather complicated dependence upon pressure and composition; however, one should notice that, for those isopleths for which ( d P / d T ) , looks negative (p = 40 MPa), it is so small that it may be considered zero within the experimental uncertainty (see below). Comparing the present p results with those for CS2 CC14,4 one confirms the higher degree of nonideality of the CS2 + CH2Clz system since the maxima of the P vs x curves are twice those for CS2 CC14 system, the curves being slightly more symmetric for the present system. Two more differences can be mentioned with respect to the system with CCl4 the first is that in the present system P decreases faster with increasing the pressure. However, the dependence of on p is almost linear for 0.1 < p/MPa 6 40 as in CS2 + C C 4 , which is different from the behavior found in other simple fluids for which the magnitude of P changes almost 200% over the same pressure range and the pressure dependence is highly nonlinear. The second difference with respect to the CS, + CC14 system is that (dP/aT), is not negligible. A larger temperature dependence should not be a suprise since multipolar interactions are stronger in the CS2 C H CI s stem, and multipolar interactions are temperature dependent. The effect of pressure upon GE is given by
-
+
+
+
2R
where p o is a reference pressure taken as 0.1 MPa in this work. We have assumed GE(x,T,po)= GE(~,T,pa),where u means orthobaric conditions. This introduces a negligible error due to the high volatility of the pure components. GE(x,T,p,,) was taken from (14) Riddick, J. A., Bunger, N. B. Organic Soluents; Wiley Interscience: New York, 1970. (1 5) Dreisbach, R. R. Physical Properties of Chemical Compounds-III; Advances in Chemistry Series 29; American Chemical Society: Washington, DC, 1961. (16) Reed, T. M.; Gubbins, K. E. Applied Statistical Mechanics; McGraw-Hill Kogakusha: Tokyo, 1973.
298 15
308 15
318 15
T/K
+
Figure 1. (A) Pressure dependence of the excess volume of xCS2 (1 - x)CH2CI, for several compositions. The approximated value of the composition is indicated near each line. (B) Temperature dependence of the excess volume of xCS2 (1 - x)CH2C12for x 0.2,0.4,0.6, and 0.8 at 0.1 (-),
+
10 (---), and 40
(-e-)
MPa.
-
Aracil et a!.' Figure 2 shows GE at 308.15 K as a function of p . Though GE for CS2 + CH2CI2is more than twice that for CS2 + CC14, its pressure dependence is the same: GE slightly increases linearly with p ; H E shows the same behavior.6 A H E and are related through (aArP/ap)T=
P - T(aP/aT),
(6)
where A H E is defined in a similar way to AGE. From eq 1 and the parameters in Table I1 one can calculate p at a given p . The results over the whole composition range can be fitted to a Redlich-Kister equation
VE
= x ( l - x)[Ao + A,(2x - 1)
+ A2(2x - 1123
(7)
Equation of State of the CS2 + CHzClz System T = 308.15K X -
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 4975 I
I
I
/
0.5
r 700
-
1
I
--
E .
7
W I/)
+
500
300
I
0
I
I 20
IO
I
30
Lo
p/MPa
300
I
1
I
IO
20
30
1 I
p/MPa
Figure 2. Pressure dependence of the excess Gibbs energy calculated according to eq 5 for several compositions.
Figure 3. Pressure dependence of TSe calculated from eq 1 and experimental HE data.
We have carried out such fittings for several isobars, the results being shown in Table 111. As can be observed, the average scattering of the VE data for a given p is of the order of f3 X cm3 mol-', which will turn out to be relevant for the calculation of M. In effect, for an intermediate value of VE, namely, = 0.41 cm3 mol-' at T 300 K, ( ~ 3 A @ / a p > ) ~0 only if (aP/aT), < 1.1 X cm3 mol-' K-'. Given the present scattering in P, one must expect an uncertainty in (aVE/aT), larger than 3.3 X lo-) cm3 mol-' K-I. Thus within the precision of the present experiments both ( d A @ / a p ) , > 0 and < 0 are compatible with the present experimental p-p-T-x data, and hence much more precise data are necessary for estimating the pressure dependence of HE,which, at high pressures, is a difficult experimental challenge. has been frequently calculated from P ( x , T , p ) data for mixtures of simple fluid^.^ Even though the magnitude of VE at low pressures is larger than in the present system (up to -2 cm3 mol-' for Kr + Xe!), also (aP/aT), is much larger at those pressures. Unfortunately, most frequently no error analysis is done; therefore it is difficult to know the reliability of the AHEvalues reported. In conclusion, except for systems with large and small 1(8P/dT),I, the @ values calculated from P ( x , T , p ) must be used with great care. Figure 3 shows TSEcalculated from the present GEvalues and the experimental @ of Siddiqi and Lucas.6 As can be observed, TSEalso increases linearly with p . Considering that the uncertainties in GE and in HE are never larger than * 5 J mol-', the dependence of TSEupon p is outside the experimental uncertainty. This result stresses again the difficulty of obtaining reliable ( a P / d T ) , data, since as can be observed in Table I and Figure lB, ( d p / d T ) , shows a very small temperature dependence, which would lead to pressure-independent TSE values, in clear discrepancy with the results of Figure 3. In CS2 + CCl., we concluded that TSEwas independent of p4 This different behavior might be traced back to the fact that the anisotropies of shape and multipolar interactions of CH2C12are larger than those of CC14, and the larger the anisotropy, the larger the effect of pressure on the packing of the molecules.
portant contributions to the mixing functions. One of the properties that is a quite sensitive order indicator is the dependence of energy on relative compression:
-
Discussion The Quantity A(yVT). As already said, some degree of orientational correlations exist in CSz and in some halo derivatives of methane.8 Breaking order correlations upon mixing has im-
V ( a E / a v ) , = yVT (8) and more especially its change upon mixing A(yVT),I7y being the thermal pressure coefficient. Many of the theories for complex fluids assume that the components and the solution are liquids of the van der Waals type; i.e., the configurational energy is E =ap/V (9) as indeed shown to hold under quite general conditions18 and especially at high densities. This assumption leads to A ( y V T ) = -HE + pVE + TACO (10) ( A ( y V T ) / J mol-') X lo3 ranges from 1.51 to -1.17 for x 0.4 and 0.1 < p / M P a 6 40, while (HE- p p ) is not lower than 1000 J mol-'. Many van der Waals theories of the liquid state, e.g., that of Flory,19 lead to AC, = 0, according to which one should conclude that eq 10 cannot be applied to this mixture. A similar 0 discrepancy between A(yVT) and HE has been found at p for systems including n-alkanesz0 and has been attributed to breaking correlations of molecular order, Le., packing effects. However, Kohler and Svejda21have shown that, under generalized conditions, eq 10 becomes invalid due to the density dependence of the constant a in eq 9, which contributes to the excess properties of mixtures. Semiempirical Equations of State. Perturbation theories are often complicated and always computer-time-consuming, and so far, they are only applicable to simple molecular fluids. It has been foundZZthat the Deiters equation of state23 gives quite satisfactory results when compared with some perturbation theories
-
-
(17) Costas, M.;Bhattacharyya, S . M.; Patterson, D. J . Chem. SOC., Faraday Trans. I 1987, 81, 381. (18) Widom, B. J . Chem. Phys. 1963, 39, 2808. (19) Flory, P. J. J . Am. Chem. SOC.1965, 87, 1833. (20) Tardajos, G.;Aicart, E.; Costas, M.;Patterson, D. J . Chem. SOC., Faraday Trans. 1 1986, 82, 2917. (21) Kohler, F.;Svejda, P. Ber. Bunsen-Ges. Phys. Chem. 1984,88, 101. (22) Palanco, J. M.G.; Rubio, R. G.; Diaz Pefia, M.; Prolongo, M.Mafer. Chem. Phys. 1987, 18, 325. (23) Deiters, U . Chem. Eng. Sci. 1981, 36, 1139.
4976 The Journal of Physical Chemistry, Vol. 93, No. 12, 1989
Compostizo et al.
+
TABLE I: Experimental Data of xCS, ( 1 - x)CHzCI* at Three Temperatures over the Whole Composition Range, Excess Volumes, Isothermal Compressibilities, K~ and Isobaric Expansion Coefficients, aP
VE,
1
lo5KT/
io3(u /
MPa-’
K-f
PI
g cm-3
PI
MPa
VEI
cm3 mo1-l
1 0 5 4
MPa-’
1 0 3 ~
K-f
PI
g cm-’
MPa
PI
VEI cm3 mol-’
x1 = 0.20256
1.296 15 1.297 14 1.299 22 1.301 64 1.304 00 1.306 34 1.308 73 1.31082 1.31248 1.31436 1.31620 1.318 I O 1.31964
0.9 16 1.631 3.132 4.908 6.664 8.434 10.272 11.902 13.208 14.716 16.207 17.773 19.058
0.432 0.430 0.425 0.419 0.413 0.407 0.401 0.396 0.392 0.387 0.383 0.379 0.375
103.5 102.8 101.6 100.1 98.7 97.3 95.9 94.7 93.8 92.7 91.7 90.6 89.8
T = 298.15 K 1.39 1.321 46 1.38 1.32404 1.37 1.326 68 1.35 1.328 38 1.34 1.330 14 1.32 1.33201 1.31 1.33350 1.30 1.33534 1.29 1.337 17 1.28 1.337 74 1.27 1.33961 1.26 1.341 03 1.25 1.34221
20.597 22.814 25.134 26.655 28.257 29.997 31.394 33.156 34.947 35.510 37.382 38.825 40.047
0.372 0.367 0.362 0.360 0.357 0.356 0.354 0.353 0.353 0.353 0.354 0.354 0.355
88.8 87.4 86.0 85.1 84.2 83.3 82.5 81.6 80.6 80.3 79.4 78.7 78.1
1.24 1.22 1.21 1.20 1.19 1.18 1.17 1.16 1.15 1.15 1.14 1.13 1.12
1.277 33 1.282 38 1.286 36 1.289 45 1.29I 90 1.29440 1.29701 1.299 49 1.30207 1.30441
0.23 1 3.629 6.415 8.615 10.468 12.371 14.433 16.382 18.342 20.257
0.450 0.437 0.430 0.422 0.421 0.419 0.419 0.417 0.408 0.406
113.5 110.0 107.3 105.3 103.7 102.1 100.4 98.8 97.3 95.9
1.41 1.38 1.36 1.34 1.32 1.31 1.29 1.28 1.26 1.25
T = 308.15 K 1.306 86 1.30941 1.31202 1.31441 1.31673 1.31891 1.321 48 1.323 40 1.32605 1.327 57
22.274 24.372 26.509 28.481 30.417 32.341 34.538 36.261 38.522 39.492
0.403 0.397 0.390 0.382 0.374 0.370 0.360 0.356 0.343 0.318
94.4 92.9 91.5 90.2 89.0 87.8 86.5 85.4 84.2 83.6
1.23 1.22 1.21 1.19 1.18 1.17 1.16 1.15 1.13 1.13
1.259 78 1.262 65 1.265 5 1 1.26907 1.272 83 1.27644 1.280 16 1.283 53 1.28702
0.184 2.189 4.045 6.502 9.120 1 1.750 14.443 16.901 19.568
0.437 0.447 0.443 0.445 0.443 0.445 0.440 0.434 0.430
123.8 121.4 119.2 116.4 1 13.6 110.9 108.3 106.0 103.7
T = 318.15 K 1.43 1.290 60 1.41 1.293 88 1.39 1.29744 1.37 1.30073 1.35 1.304 14 1.32 1.307 29 1.30 1.31064 1.28 1.31384 1.26
22.428 24.686 27.417 30.093 32.730 35.346 38.043 40.323
0.431 0.405 0.391 0.384 0.366 0.356 0.338 0.303
101.3 99.5 97.4 95.4 93.6 91.8 90.0 88.6
1.24 1.22 1.20 1.19 1.17 1.15 1.14 1.13
x1 = 0.29098
1.287 50 1.289 88 1.291 74 1.293 77 I .295 88 1.297 80 1.299 77 1.301 73 1.304 18 1.30623 1.308 1 1 1.30979
0.245 1.943 3.291 4.776 6.343 7.791 9.289 10.804 12.726 14.359 15.880 17.264
0.561 0.553 0.547 0.541 0.534 0.527 0.521 0.514 0.507 0.500 0.495 0.490
105.3 103.8 102.7 101.4 100.2 99.0 97.9 96.7 95.3 94.2 93.1 92.2
T = 298.15 K 1.38 1.31144 1.37 1.313 39 1.36 1.315 18 1.35 1.31703 1.34 1.318 74 1.33 1.32064 1.32 1.322 37 1.30 1.324 08 1.29 1.326 13 1.28 1.32829 1.21 1.33020 1.26 1.331 89
18.630 20.277 21.813 23.422 24.930 26.637 28.221 29.804 31.746 33.834 35.718 37.422
0.485 0.480 0.476 0.472 0.468 0.465 0.462 0.459 0.457 0.456 0.455 0.455
91.3 90.2 89.3 88.3 87.4 86.4 85.4 84.6 83.5 82.4 81.4 80.5
1.25 1.24 1.24 1.23 1.22 1.21 1.20 1.19 1.18 1.17 1.16 1.15
1.269 67 1.270 71 1.274 60 1.278 8 I 1.28202 1.286 1 1 1.28935 1.291 91 1.29431 1.296 80
0.231 0.942 3.465 6.341 8.603 1 1.766 14.241 16.432 18.338 20.305
0.594 0.592 0.571 0.555 0.543 0.541 0.534 0.540 0.535 0.528
113.8 113.0 110.5 107.8 105.7 103.0 101.0 99.3 97.8 96.4
1.40 1.39 1.37 1.35 1.33 1.30 1.29 1.27 1.26 1.25
T = 308.15 K 1.29921 1.301 70 1.304 16 1.30661 1.308 83 1.3 1 1 53 1.31378 1.31598 1.31787 1.321 46
22.302 24.368 26.319 28.385 30.338 32.440 34.425 36.317 37.792 40.262
0.524 0.518 0.506 0.499 0.495 0.474 0.468 0.458 0.441 0.392
94.9 93.5 92.2 90.8 89.6 88.3 87.1 86.0 85.2 83.9
1.23 1.22 1.21 1.20 1.19 1.18 1.17 1.16 1.15 1.14
1.252 5 1 1.255 18 1.258 90 1.262 60 1.265 85 1.269 54 1.27348 1.277 29
0.180 1.992 4.511 7.098 9.289 1 1.977 14.918 17.800
0.581 0.583 0.582 0.581 0.571 0.569 0.566 0.561
123.0 120.8 118.0 115.2 1 12.9 110.3 107.5 105.0
1.41 1.39 1.37 1.35 1.33 1.31 1.29 1.27
T = 318.15 K 1.28037 1.283 80 1.28848 1.292 26 1.295 75 1.29943 1.301 96
20.179 22.689 26.183 29.276 3 1.960 35.245 37.108
0556 0.539 0.5 15 0.507 0.486 0.486 0.462
102.9 100.9 98.2 96.0 94.1 91.9 90.7
1.25 1.23 1.21 1.19 1.18 1.16 1.15
Equation of State of the CSz
+ CHzClzSystem
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 4977
TABLE I (Continued)
PI
PI
1 0 3 ~/
g cm-3
MPa
cm3 mol-'
VEI
105KT/ MPa-'
1.281 39 1.282 83 1.285 07 1.287 48 1.290 02 1.291 88 1.29361 1.295 32 1.297 09 1.299 38 1.301 31 1.303 05 1.30481 1.307 03
1.665 2.710 4.350 6.144 8.060 9.486 10.832 12.173 13.579 15.434 17.020 18.470 19.963 21.871
0.647 0.642 0.633 0.623 0.613 0.606 0.600 0.593 0.586 0.578 0.572 0.566 0.561 0.555
101.7 L00.9 99.7 98.4 97.0 96.1 95.2 94.3 93.4 92.2 91.2 90.4 89.5 88.4
g cm-3 x , = 0.396 11 T = 298.15 K 1.38 1.308 67 1.37 1.309 87 1.36 1.311 62 1.34 1.31283 1.33 1.31433 1.31 1.31607 1.30 1.31767 1.29 1.31920 1.28 1.321 15 1.27 1.322 33 1.26 1.323 96 1.25 1.325 22 1.24 1.326 08 1.22
1.262 09 1.265 60 1.268 90 1.273 04 1.277 28 1.28089 1.284 20 1.28647 1.28909 1.291 36
0.233 2.643 4.826 7.762 11.051 13.768 16.504 18.414 20.464 22.392
0.683 0.672 0.653 0.637 0.633 0.621 0.621 0.621 0.609 0.607
112.2 110.0 108.1 105.6 103.0 101.0 99.0 97.6 96.2 94.9
1.39 1.37 1.35 1.32 1.29 1.27 1.25 1.24 1.22 1.21
1.245 16 1.247 38 1.25099 1.254 08 1.258 37 1.262 16 1.265 48 1.269 08 1.272 22
0.180 1.769 4.182 6.4 17 9.329 11.937 14.583 17.230 19.657
0.681 0.687 0.679 0.682 0.665 0.649 0.655 0.643 0.636
122.6 120.9 118.3 116.0 113.2 110.8 108.5 106.3 104.3
1.39 1.38 1.35 1.33 1.30 1.28 1.26 1.23 1.21
PI
K- f
vel
cm3 mol-'
105KT/ MPa-'
1 0 3 ~1
MPa
23.308 24.367 25.938 27.042 28.424 30.063 31.587 33.068 34.992 36.184 37.855 39.161 40.069
0.551 0.548 0.544 0.541 0.538 0.536 0.534 0.532 0.531 0.531 0.531 0.532 0.533
87.6 87.0 86.1 85.6 84.8 84.0 83.2 82.5 81.6 81.0 80.2 79.6 79.2
1.21 1.21 1.20 1.19 1.18 1.17 1.16 1.15 1.14 1.14 1.13 1.12 1.11
24.360 26.373 28.367 30.407 32.546 34.520 36.412 38.602 40.075
0.597 0.599 0.586 0.572 0.553 0.547 0.540 0.522 0.482
93.7 92.4 91.2 90.0 88.8 87.7 86.7 85.5 84.7
1.19 1.18 1.17 1.15 1.14 1.13 1.12 1.10 1.10
22.360 24.920 27.238 30.279 32.736 35.595 38.351 40.542
0.629 0.623 0.603 0.577 0.553 0.532 0.515 0.461
102.3 100.4 98.7 96.6 95.0 93.2 91.5 90.3
1.19 1.18 1.16 1.14 1.12 1.10 1.09 1.07
21.615 23.762 25.689 27.934 31.441 33.050 34.684 36.367 38.167 39.528 40.271
0.601 0.597 0.598 0.621 0.581 0.575 0.575 0.564 0.550 0.528 0.499
90.4 89.0 87.8 86.4 84.3 83.4 82.5 81.6 80.6 79.9 79.5
1.18 1.17 1.16 1.15 1.13 1.12 1.12 1.11 1.10 1.10 1.09
PI
K-p
T = 308.15 K 1.293 78 1.295 99 1.298 44 1.30094 1.30361 1.305 83 1.307 94 1.31056 1.31289
T = 318.15 K 1.27566 1.278 81 1.281 92 1.285 92 1.289 17 1.292 74 1.296 06 1.299 49 XI
= 0.502 72
T = 298.15 K 1.27 1 60 1.271 76 1.272 87 1.275 55 1.278 98 1.281 80 1.284 91 1.287 40 1.289 89 1.292 06 1.294 52 1.29671
0.182 0.255 0.920 2.550 4.880 6.869 9.359 11.332 13.458 15.303 17.475 19.475
0.723 0.719 0.706 0.674 0.647 0.626 0.619 0.610 0.608 0.604 0.602 0.602
107.8 107.7 107.1 105.5 103.4 101.6 99.5 97.9 96.3 94.9 93.3 91.9
1.31 1.31 1.30 1.29 1.28 1.26 1.25 1.24 1.22 1.21 1.20 1.19
1.299 06 1.301 43 1.30343 1.305 26 1.309 68 1.31 142 1.31304 1.31492 1.316 96 1.31876 1.32009
1.255 08 1.258 80 1.261 74 1.26441 1.267 23 1.270 23 1.272 53 1.275 08 1.277 58 1.280 03 1.28251
0.207 2.615 4.581 6.443 8.391 10.576 12.439 14.411 16.390 18.382 20.464
0.733 0.708 0.689 0.676 0.658 0.645 0.644 0.635 0.628 0.622 0.618
115.3 112.6 110.6 108.7 106.8 104.8 103.1 101.4 99.8 98.2 96.5
1.34 1.32 1.31 1.30 1.28 1.27 1.26 1.24 1.23 1.22 1.21
1.284 99 1.287 44 1.289 97 1.292 00 1.293 86 1.29676 1.298 74 1.301 00 1.303 35 1.305 66 1.307 18
22.488 24.624 26.696 28.503 30.377 32.460 34.258 36.241 38.087 39.820 40.498
0.609 0.606 0.593 0.590 0.597 0.563 0.558 0.548 0.525 0.498 0.459
95.0 93.5 92.0 90.8 89.5 88.2 87.1 85.9 84.8 83.8 83.4
1.20 1.19 1.18 1.17 1.16 1.15 1.14 1.13 1.13 1.12 1.12
1.239 18 1.239 39 1.241 69 1.24429 1.247 44 1.25023 1.253 21 1.255 98 1.259 14
0.180 0.236 1.936 4.015 6.486 8.467 10.521 12.436 14.644
0.701 0.694 0.701 0.7 18 0.730 0.724 0.710 0.696 0.678
123.3 123.2 121.1 118.6 115.8 113.6 111.4 109.5 107.4
T = 318.15 K 1.37 1.26 1 90 1.37 1.264 61 1.36 1.266 83 1.34 1.269 90 1.33 1.272 23 1.31 1.274 84 1.30 1.276 98 1.28 1.280 28 1.27 1.282 43
16.605 18.439 20.473 22.751 24.498 26.415 28.345 30.983 32.802
0.662 0.639 0.652 0.634 0.620 0.600 0.604 0.586 0.579
105.5 103.9 102.1 100.2 98.8 97.3 95.8 93.9 92.6
1.26 1.25 1.24 1.22 1.21 1.20 1.19 1.18 1.17
T = 308.15 K
The Journal of Physical Chemistry, Vol. 93, No. 12, I989
4978
Compostizo et al.
TABLE I (Continued) g
Pi
cni3
Pl
MPa
VEi cm3 mol-'
105KT/ MPa-I
10%
K-f
1
MPa
cm3 mol-'
VEl
105KT/ MPa-'
22.896 23.947 25.086 26.108 27.128 28.157 29.236 30.222 30.961 32.01 1 32.927 34.171 34.931 36.074 37.535 38.970 39.870
0.530 0.528 0.525 0.523 0.521 0.520 0.518 0.518 0.517 0.516 0.516 0.516 0.516 0.517 0.518 0.519 0.520
86.4 85.7 85.0 84.4 83.9 83.3 82.7 82.1 81.7 81.2 80.7 80.0 79.6 79.0 78.3 77.6 77.2
1.18 1.18 1.17 1.16 1.16 1.15 1.15 1.14 1.14 1.13 1.13 1.12 1.12 1.11 1.10 1.10 1.09
22.332 24.430 26.427 28.389 30.517 32.407 34.369 36.402 38.298 40.626
0.578 0.574 0.562 0.557 0.549 0.541 0.537 0.524 0.503 0.464
92.8 91.3 90.0 88.7 87.4 86.2 85.1 83.9 82.8 81.6
1.16 1.15 1.14 1.12 1.11 1.10 1.09 1 .OS 1.07 1.06
21.615 24.466 27.545 30.321 33.762 36.517 40.21 1
0.597 0.585 0.569 0.551 0.526 0.497 0.483
99.8 97.5 95.2 93.2 90.8 89.1 86.8
1.14 1.12 1.10 1.09 1.07 1.05 1.03
16.762 18.266 19.929 21.411 22.812 24.609 25.968 27.648 29.361 31.561 33.128 35.092 36.808
0.486 0.481 0.477 0.473 0.469 0.466 0.464 0.462 0.460 0.459 0.459 0.460 0.462
89.6 88.8 87.9 87.1 86.4 85.4 84.8 83.9 83.1 82.1 81.4 80.5 79.7
1.19 1.18 1.17 1.16 1.15 1.14 1.14 1.13 1.12 1.1 1 1.10 1.09 1.08
1.275 74 1.27780 1.28045 1.282 46 1.28455 1.286 31 1.28906 1.290 26 1.293 39
24.388 26.335 28.465 30.274 32.092 33.726 36.293 37.102 39.150
0.518 0.520 0.501 0.496 0.486 0.482 0.475 0.457 0.405
91.3 90.1 89.0 88.0 87.0 86.2 84.9 86.5 83.5
1.15 1.13 1.12 1.11 1.10 1.09 1.08 1.08 1.07
T = 318.15 K 1.241 05 1.243 49 1.246 26 1.248 13
8.505 10.415 12.541 14.503
0.583 0.583 0.577 0.575
109.0 107.4 105.7 104.2
1.26 1.24 1.23 1.21
/
g .
Pi
cm-3
1.26474 1.267 23 1.268 75 1.270 84 1.272 54 1.274 20 1.275 66 1.277 19 1.278 59 1.280 04 1.281 71 1.283 43 1.285 08 1.286 43 1.287 48 1.288 96 1.290 20 1.291 61
0.201 2.029 3.164 4.748 6.046 7.333 8.468 9.678 10.798 11.976 13.336 14.762 16.149 17.298 18.201 19.489 20.577 21.829
0.637 0.625 0.618 0.609 0.601 0.594 0.588 0.582 0.576 0.571 0.564 0.558 0.552 0.548 0.545 0.540 0.537 0.533
103.1 101.5 100.5 99.2 98.2 97.1 96.3 95.3 94.5 93.6 92.7 91.7 90.7 89.9 89.3 88.5 87.8 87.0
= 0.64459 T = 298.15 K 1.34 1.292 79 1.32 1.29395 1.32 1.295 18 I .30 1.296 28 1.29 1.297 37 1.28 1.298 45 1.28 1.299 57 1.27 1.300 58 1.26 1.301 33 1.25 1.302 39 1.24 1.303 30 1.23 1.304 53 1.305 26 1.22 1.22 1.306 36 1.21 1.307 75 1.20 1.309 08 1.20 1.30991 1.19
1.248 38 1.251 44 1.254 01 1.256 90 1.259 46 1.262 33 1.264 62 1.267 07 1.269 75 1.271 92 1.27441
0.237 2.445 4.403 6.399 8.377 10.538 12.363 14.437 16.362 18.290 20.361
0.664 0.655 0.652 0.633 0.628 0.616 0.61 1 0.61 1 0.590 0.592 0.585
111.7 109.5 107.6 105.7 103.9 102.0 100.4 98.7 97.2 95.7 94.2
T = 308.15 K 1.33 1.276 75 1.31 1.279 14 1.29 1.28 1 55 1.27 1.283 75 1.26 1.286 17 1.24 1.288 3 1 1.23 1.29041 1.21 1.292 74 1.20 1.295 11 1.19 1.298 23 1.17
1.232 79 1.237 03 1.241 37 1.24541 1.249 20 1.253 25 1.256 90
0.204 3.351 6.606 9.566 12.422 15.506 18.304
0.640 0.646 0.648 0.639 0.631 0.620 0.608
121.2 117.4 113.8 110.7 107.9 105.0 102.5
1.31 1.28 I .25 I .23 1.21 1.18 1.16
Pi
10%
K-f
XI
T = 318.15 K 1.261 03 1.264 57 1.268 38 1.271 84 1.27609 1.27961 1.283 75
1.261 69 1.262 43 1.263 49 1.265 44 1.267 25 1.268 04 1.269 56 1.270 60 1.27231 1.274 32 1.276 25 1.277 80 1.279 36 1.280 59
0.201 0.747 1.539 3.006 4.390 4.997 6.178 6.996 8.351 9.965 11.535 12.813 14.112 15.151
0.567 0.564 0.559 0.550 0.543 0.539 0.533 0.529 0.522 0.514 0.507 0.502 0.496 0.492
100.1 99.7 99.1 98.1 97.2 96.8 96.0 95.5 94.6 93.6 92.7 91.9 91.1 90.5
= 0.71701 T = 298.15 K 1.30 1.282 47 1.30 1.284 20 1.29 1.28608 1.28 1.287 74 1.27 1.289 28 1.27 1.291 22 1.26 1.292 66 1.25 1.294 42 1.24 1.296 18 1.23 1.298 39 1.22 1.299 93 1.21 1.301 83 1.20 1.303 45 1.20
1.245 75 1.250 36 1.25390 1.256 76 1.260 52 1.263 88 1.266 53 1.268 74 1.27I 42 1.273 64
0.227 3.633 6.239 8.361 1 1.406 12.645 16.564 18.332 20.568 22.460
0.583 0.572 0.558 0.546 0.541 0.448 0.542 0.532 0.524 0.518
107.9 105.2 103.2 101.6 99.5 98.6 96.0 94.9 93.5 92.4
1.31 1.29 1.21 1.25 1.23 1.22 1.19 1.18 1.17 1.16
1.23001 1.232 89 1.235 61 1.238 22
0.182 2.558 4.499 6.423
0.579 0.599 0.593 0.590
116.5 114.2 112.4 110.8
1.33 1.31 1.29 1.21
x,
T = 308.15 K
Equation of State of the CS2
+ CH2Cl2 System
The Journal of Physical Chemistry, Vol. 93, No. 12, 1989 4979
TABLE I (Continued)
1
PI
PI MPa
MPa-'
1 0 3 ~1
K- f
PI
g cm-'
PI MPa
lob
cm3 mol-'
105KT/
105KT/
g cni3
cm3 mol-!
MPa-'
K- f
1.25105 1.25345 1.25645 1.259 58 1.263 57
16.341 18.237 20.655 23.422 26.128
0.571 0.564 0.557 0.560 0.515
102.8 101.5 99.8 97.9 96.1
1.20 1.19 1.17 1.15 1.14
1.267 19 1.270 87 1.276 37 1.28041
28.954 32.029 36.446 39.840
0.492 0.475 0.437 0.412
94.4 92.5 90.0 88.2
1.12 1.10 1.08 1.06
21.387 22.988 24.798 26.421 28.055 29.582 31.501 33.297 35.287 36.647 37.553 39.022 39.828
0.374 0.371 0.369 0.367 0.366 0.366 0.366 0.367 0.370 0.372 0.373 0.376 0.378
85.3 84.5 83.6 82.9 82.1 81.4 80.6 79.8 78.9 78.4 78.0 77.4 77.1
1.18 1.17 1.16 1.15 1.14 1.13 1.12 1.11 1.10 1.09 1.09 1.08 1.08
24.243 26.100 28.080 30.198 32.052 34.106 35.985 38.144 39.667 40.141
0.43 1 0.422 0.409 0.404 0.397 0.390 0.383 0.373 0.351 0.325
89.7 88.7 87.7 86.6 85.7 84.7 83.8 82.8 82.1 81.9
1.12 1.11 1.10 1.09 1.08 1.07 1.06 1.05 1.04 1.04
23.605 26.486 29.421 32.454 35.514 38.523 40.941
0.445 0.436 0.404 0.392 0.368 0.357 0.302
96.3 94.5 92.8 91.0 89.4 87.8 86.6
1.09 1.07 1.06 1.04 1.02 1.01 0.99
VEI
1.258 91 1.260 12 1.261 70 1.264 02 1.26607 1.267 88 1.269 64 1.27 1 87 1.273 92 1.276 07 1.276 86 1.278 99 1.28 1 02 1.28281
0.203 1.117 2.327 4.127 5.736 7.176 8.600 10.431 12.141 13.958 14.633 16.483 18.274 19.883
0.455 0.450 0.443 0.434 0.426 0.420 0.4 13 0.406 0.400 0.393 0.391 0.385 0.380 0.377
97.4 96.8 96.0 94.9 93.9 93.0 92.2 91.1 90.1 89.1 88.8 87.8 86.9 86.0
xl = 0.79866 T = 298.15 K 1.32 1.28445 1.31 1.286 18 1.30 1.288 i o 1.29 1.289 79 1.28 1.29 1 46 1.27 1.293 00 1.26 1.294 89 1.24 1.296 63 1.23 1.298 51 1.22 1.299 77 1.22 1.300 60 1.21 1.301 93 1.19 1.302 64 1.18
1.243 02 1.246 42 I .249 47 1.25 1 92 1.255 11 1.25865 1.260 53 1.26331 1.26564 1.267 92 1.270 05
0.21 1 2.730 5.168 6.9 12 9.330 12.355 13.794 16.448 18.468 20.494 22.334
0.479 0.470 0.470 0.454 0.441 0.443 0.433 0.446 0.443 0.442 0.437
105.3 103.4 101.6 100.4 98.7 96.8 95.8 94.2 93.0 91.8 90.8
T = 308.15 K 1.29 1.272 25 1.27 1.27441 1.25 1.276 79 1.24 1.279 11 1.22 1.281 18 1.20 1.28341 1.19 1.285 47 1.17 1.287 82 1.16 1.289 80 1.15 1.29080 1.14
1.227 89 1.231 18 1.23494 1.23861 1.242 68 1.246 09 1.250 I O 1.253 87
0.170 2.720 5.668 8.535 1 1.643 14.352 17.603 20.742
0.457 0.465 0.472 0.472 0.464 0.459 0.454 0.449
113.9 111.7 109.2 106.9 104.5 102.5 100.2 98.1
1.27 1.25 1.22 1.20 1.18 1.16 1.13 1.11
VEI
T = 318.15 K 1.257 23 1.260 66 1.264 55 1.268 07 1.271 81 1.275 17 1.278 79
TABLE 11: Characteristics of the Fittings of the Experimental Data to Eq 1
0.202 56 0.290 98 0.396 11 0.502 72 0.644 59 0.71701 0.798 66
1.8331 1.8586 1.9173 1.6861 1.9454 1.7764 1.9803
-0.1799 -0.2047 -0.249 3 4.1111 -0.2867 -0.1808 -0.3176
TABLE 111: Characteristics of the Fittings of Different Pressures and Temperatures AQ/
T/K
cm3 mol-'
298.15 308.15 318.15
2.7020 2.8356 2.9367
298.15 308.15 318.15 298.15 308.15 318.15
10All
V E vs x to Eq 7 at
10A2/
cm3 mol-' cm3 mol-' p = 0.1 MPa 0.7041 1.3194 1.3898
-0.0130 0.4422 1.1903 -0.9 309 1.9643 0.2786 2.5434
103u(VE)/ cm3 mol-l
-2.8245 -0.4007 -0.1081
8.7 3.9 2.9
2.5482 2.6730 2.7654
p = 10 MPa 0.4563 -0.0823 0.8932 1.9014 0.7621 1.6890
1.9 5.7 5.9
2.0566 2.1431 2.1944
p = 40 MPa 0.7536 1.1507 0.9570 1.3432 0.5915 -0.8585
9.6 8.3 6.7
1.0873 1.1090 1.1865 1.0624 1.0655 1.2329 1.2550
0.1394 0.1056 0.1588 0.0733 0.1155 0.1 177 0.1329
0.8697 0.7741 0.8800 0.6737 0.8101 0.7576 0.7831
2.2 2.4 3.0 11.3 2.7 4.0 3.4
and that it also leads to satisfactory predictions for mixtures of nonpolar molecular fluids, e.g., CS2 + cc14.4For the sake of brevity, we will not describe the equation but refer the reader to the original p a p e r ~ . ~There ~ J ~ are three characteristic parameters per pure substance and two binary parameters involved in the mixing rules for the energy and the core volume. The parameters for CS2 and CH2C12were fitted to the p-p data of a given isotherm. The results indicate that the three parameters are slightly dependent upon temperature, as expected from ihe approximated character of the equation of state. Figure 4 shows the prediction of the p - p isotherms of CS2 and CH2C12when the parameters that best fit the 308.15 K isotherm are used. It is obvious that the equation fails to describe (~3p/C37')~,the results being worse (24) Deiters, U. Fluid Phase Equilib. 1983, 12, 193. Deiters, U.; Swaid, I. Ber. Bunsen-Ges. Phys. Chem. 1984, 88, 791.
4980 The Journal of Physical Chemistry, Vol. 93, No. 12, 1989
r
16
I
I
I
Compostizo et al.
1
i
CIb
4
16.51-
0
1
1
I
J
10
20
30
LO
plMPa
Figure 4. Comparison between experimental data and Deiters equation of state predictions. Symbols, experimental data: 0,298.15 K; A, 308.15
K;m,
318.15 K.
Lines: equation of state predictions.
for CH2C12than for CS2. One could be tempted to justify this fact in terms of the polarity of CH2CI2,since the equation of state is based on an isotropic square-well potential; however, more evidence seems necessary. The two binary parameters have been fitted to a p-p-x isotherm. The results for a given composition show a temperature dependence similar to that of the pure components. Figure 4 shows the results for x 0.50 at the three temperatures using the binary parameters obtained at 308.15 K. The predictions are similar to those for the pure components. In addition, the parameters show a slight composition dependence for a given temperature. Figure 5 shows the results obtained for x 0.2, x 0.5, and x 0.8 and 308.15 K when the parameters obtained from the data of x = 0.5 and T = 308.15 K are used. The failure of the equation of state in describing the composition dependence of the p - p data is similar to that on the temperature dependence. Although the results are not unsatisfactory, the equation of state leads to predictions that are worse than those for CS2+ CC14.4 Bulk Modulus. Using Pople's expansion for the intermolecular potential and a reference system characterized by the angular average of the full intermolecular potential
p1MPa
Figure 5. Comparison between experimental data and Deiters equation of state predictions for the pressure and composition dependence of p for xCSz (1 - x)CH2CI2.Symbols: experimental results. Lines: Deiters'
+
predictions. I
I
36
-
- -
u'(r) = (u(r,w,,wz)w,.w,)
-
(11)
where wi denotes the orientation of molecule i, and ( ) indicates a canonical average, Gubbins and O ' C ~ n n e l lhave ~ ~ shown that
-m
3 L
L
-
1
C
32
30
.,
c 95
09
-
-
IC5
10
P'
-
+
Figure 6. Bulk modulus vs reduced density for xCS2 (1 - x)CH2CI2. x = 0; A,x 0.2; A,x 0.5; V,x 0.8; 0 ,x = 1. Lines calculated from Huang and OConne11.26
(14)
which expresses a law of corresponding states as far as the different fluids may be described by the same reference system. Huang and O'Conne1126have been able to find correlations, for the bulk modulus B = ( p k , T ~ , ) - ' ,which are valid for a great variety of molecular fluids, ranging from Ar to n-CI,Hz4. The apparent lack of sensitivity of B to molecular details can be related to the fact that B depends only on the direct pair correlation function, which has a much shorter range than the radial distribution function; thus the behavior of B should be mainly described by the reference system. We have calculated B for CS2 and CH2CI2as well as for three mixtures of x 0.2, x 0.5, and x 0.8, the results being plotted in Figure 6, with p* = pu3. The values of u and t / k Bfor a (1 2,6) potential given by Mouritz
( 2 5 ) Gubbins, K. E.; O'Connell, J. P. J . Chem. Phys. 1974, 60, 3449.
( 2 6 ) Huang, Y . H.; O'Connell, J. P. Fluid Phase Equilib. 1987, 37, 75.
with kB being the Boltzmann constant and K ~ ' the isothermal compressibility of the reference system. G, involves integrals over the anisotropic part of the intermolecular potential and the center pair correlation function of the reference system. For a variety of anisotropic contributions to the potential, e.g., dipole-dipole, G, 1 , thus leading to
-
pkBTKT
%
pkBTKT' = f x " ( p ~ ' , k ~ T / t )
(13)
where u and t are the parameters of a (n,m) Mie-like potential. Furthermore, f," was found to show a very weak temperature dependence for p > 2p,, p c being the criticial density; hence
-
P ~ B T K T f,"(pu3)
-
-
-
J. Phys. Chem. 1989, 93, 4981-4985
and Rummensz7have been used. It can be observed that a slight temperature dependence exists in each set of points corresponding to the three isotherms, in agreement with the results of Huang and O’Connell.26 However, within each set of points, the pure components and the mixtures show the same density dependence; thus a good description of In (1 B ) can be made by using the master curve fitted by Huang and OConnell.
+
Conclusions The p-p-T-x data obtained for CS2 + CHzC12confirm that the degree of nonideality of this system is much greater than that (27) Mouritz, F. M.; Rummens, F. H. A. Can. J. Chem. 1977,55, 3007.
498 1
+
of CS2 CCl,. Also, the pressure dependence of the excess functions GE,p,and TSEis greater than for the system with CCl,. The bulk modulus of the mixture shows the same temperature and density dependence as those of the pure components and can be satisfactorily calculated from the correlation of Huang and OConnell. Even though the Deiters equation leads to reasonably good predictions, these are worse than those previously reported for the CS2 CCl, system.
+
Acknowledgment. This work was supported in part by CAICYT under Grant PB-85/0016 and by Universidad Complutense under a grant for Grupos Precompetitivos. Registry No. CS2, 75-15-0; CH2C12,75-09-2.
A Glass Formation Study of Aqueous Tetraalkylammonlum Halide Solutions H. Kanno,* Department of Chemistry, The National Defence Academy, Yokosuka, 239 Kanagawa, Japan
K. Shimada, and T. Katoh Department of Chemistry, Meisei University, Hino, 191 Tokyo, Japan (Received: March 24, 1988; In Final Form: December 7, 1988)
The glass-forming composition regions of aqueous tetraalkylammonium halide solutions (alkyl = methyl, ethyl, and n-propyl; halide = chloride and bromide) were determined by a simple DTA method with a cooling rate of about 600 K/min. It is shown that the glass-forming behavior is primarily controlled by cations in these solutions. A liquid-liquid immiscibility is observed in tetraethyl- and tetra-n-propylammoniumhalide solutions at low temperatures. The glass transition temperature ( Tg)of an aqueous tetra-n-propylammonium halide solution shows a very anomalous concentration dependence.
Introduction Aqueous solutions of tetraalkylammonium salts have been extensively studied from various points of view’+ since they are an attractive target for investigating hydrophobic interactions in aqueous solutions and since they provide us a good chance to see the effects of cation size on solution properties5 beyond the region covered by alkali-metal ions. Although there have been many studies’-5 devoted to aqueous tetraalkylammonium halide solutions at ordinary temperatures, there remains much to be explored in supercooled and glassy aqueous solutions of tetraalkylammonium salts. In this paper we expand our preliminary reports6s7on the glass formation of aqueous tetraethylammonium and tetrapropylammonium chloride solutions by describing the glass-forming behavior of tetraalkylammonium halide solutions (alkyl = methyl, ethyl, n-propyl; halide = chloride, bromide) and thereby examining of hydrophobic interactions of tetraalkylammonium ions with water molecules at low temperatures. Experimental Section Sample solutions with various tetraalkylammonium halide concentrations were prepared from vacuum-dried tetraalkylammonium halide and distilled water. Tetraalkylammonium (1) Frank, H. S.; Evans, M. W. J. Chem. Phys. 1945, 13, 507. (2) Kay, R.L.; Evans, D. F. J. Phys. Chem. 1%5,69,4216; 1966,70,366, 2325. (3) Jeffrey, G. A.; McMullan, R. K. Prog. Inorg. Chem. 1967, 8, 43. (4) Wen, W.-Y. In Water and Aqueous Solutions: Structure, Thermodynamics and Transport Processes; Horne, R. A,, Ed.; Wiley-Interscience: New York, 1972; Chapter 15. (5) Krishnan, C. V.;Friedman, H. L. J. Phys. Chem. 1%9,73, 1572,3934; 1971, 75, 361 1, 3609. (6) Kanno, H.; Shimada, K.; Katoh, T. Chem. Phys. Lett. 1983,103,219. (7) Kanno, H.; Shimada, K.; Yoshino, K.; Iwamoto, T. Chem. Phys. Lett. 1984, 112, 242.
0022-3654/89/2093-4981$01.50/0
halides used in this study were tetramethylammonium, tetraethylammonium, tetra-n-propylammonium, and tetra-n-butylammonium halides (halide = chloride and bromide). Here the concentration of the solution is expressed by R (moles of water/moles of salt). A simple, conventional DTA technique was used to measure the glass transition temperature (Tg)of these aqueous solutions.8 An aliquot of the sample solution in a 2 mm diameter glass tube with one end sealed, in which an alumelchrome1 thermocouple junction was inserted, was vitrified in liquid nitrogen. The cooling rate of the solution was approximately 600 K/min. Glass formation was checked visually and transparency is a good indicator for vitrification. Any incomplete vitrification is usually associated with a loss of transparency and is easily detected visually. Benzene was used as a reference material. DTA measurements were carried out at a heating rate of about 5 K/min in the glass transition temperature region. Several annealing experiments were carried out for the quenched samples in which a phase separation was expected to occur in a quenching process: a sample quenched in liquid nitrogen was heated up to a temperature of about 10 K below Tg,annealed at the temperature for several hours and then requenched to liquid nitrogen temperature for a DTA measurement.
Results and Discussion The Tgresults for the aqueous (CH3),NC1 solution are shown in Figure 1. Glass formation was observed between R = 3 and 6.5. Tgdecreases monotonically with decrease in the (CHJ4NC1 concentration from R = 3 to 6.5. Here some comment must be made about the dilute side (water-rich side) of the glass-forming composition region. As noted briefly in the Experimental Section, the edge of a glass-forming composition region for a given aqueous solution is usually determined sharply because partial vitrification (8) Akama, Y.; Kanno, H. Bull. Chem. Soc. Jpn. 1982, 55, 3308.
0 1989 American Chemical Society
