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Temperature dependence of the excess molar volume of (dimethyl carbonate, or diethyl carbonate + toluene) fromT = 278.15 K to 323.15 K
J. Chem. Thermodynamics 2000, 32, 743–754 doi:10.1006/jcht.1999.0644 Available online at http://www.idealibrary.com on
Temperature dependence of the excess molar volume of (dimethyl carbonate, or diethyl carbonate + toluene) from T = 278.15 K to 323.15 K ˜ E. R. L´opez, L. Lugo, M. J. P. Comunas, Laboratorio de Propiedades Termofisicas, Departamento de F´ısica Aplicada, Facultad de F´ısica, Universidad de Santiago, E-15706 Santiago de Compostela,
J. Garc´ıa, Laboratorio de Propiedades Termofisicas, Departamento de F´ısica Aplicada, Facultad de F´ısica, Universidad de Santiago, E-15706 Santiago de Compostela, and Departamento de F´ısica Aplicada, Facultad de Ciencias, Universidad de Vigo, E-36200 Vigo,
and J. Fern´andeza Laboratorio de Propiedades Termofisicas, Departamento de F´ısica Aplicada, Facultad de F´ısica, Universidad de Santiago, E-15706 Santiago de Compostela The experimental densities ρ and excess molar volumes VmE of (dimethyl carbonate + toluene) at the temperatures (278.15, 288.15, 298.15, 308.15, 318.15, and 323.15) K and of (diethyl carbonate + toluene) at the temperatures (288.15, 298.15, 308.15, 318.15, and 323.15) K were determined using an Anton-Paar DMA602HP densimeter. For (dimethyl carbonate + toluene) the excess molar volumes were positive over the whole composition range and at all temperatures. On the contrary, for (diethyl carbonate + toluene) the excess molar volumes were negative. The experimental data were used for the calculation by analytical differentiation of the following quantities: the cubic expansion E /∂ p) . coefficient, the excess cubic expansion of coefficient, (∂ VmE /∂ T ) p and (∂ Hm T c 2000 Academic Press
KEYWORDS: excess molar volume; organic carbonate; toluene; molecular interaction; cubic expansion coefficient
a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/00/060743 + 12 $35.00/0
c 2000 Academic Press
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1. Introduction The problem of the replacement of chlorofluorocarbons (CFCs) by new refrigerants has been only partially solved. The requirements of suitable lubricants for the new refrigerants are not fulfilled by mineral oils, which were used for CFCs. In the last few years new oils based on carbonate molecules have been proposed(1, 2) for stationary air conditioners as candidates because of their thermal stability, miscibility with HFCs and lubricity. The lubricant carbonate molecules include alkyl groups (which contribute to the thermal stability) a carbonate group (which provides lubricity and miscibility) and an alkyl benzene group (which contributes to lubricity). To find the best lubricant properties for the carbonates, experimental data on the thermophysical properties as well as prediction methods such as group contribution models are needed. In previous papers(3, 4) we have determined the characteristic parameters for carbonate and methyl, or methylene groups of the UNIFAC model (in the versions of Dang and Tassios,(5) Larsen et al.(6) and Gmehling et al.(7) ) and the Nitta–Chao(8) model. Our next step is to determine the carbonate-aromatic parameters for several group contribution models. For this purpose an updated database is necessary. Up to now, we have found in the literature (vapour + liquid) equilibrium data,(9–12) excess molar enthalpies(13–15) at T = 298.15 K, and excess molar volumes(12, 16, 17) at T = 298.15 K for (di-n-alkyl carbonate + benzene) as well as activity coefficients at infinite dilution(18) at T = 318 K, excess molar enthalpies(13–15) and excess molar volumes(16, 17) at T = 298.15 K for (di-n-alkyl carbonate + toluene). To the best of our knowledge, we are not aware of any VmE measurements on (di-nalkyl carbonate + toluene) at temperatures other than T = 298.15 K. In order to calculate reliable interaction parameters between the carbonate and aromatic groups for the Nitta– Chao model, it is necessary to have experimental data at several temperatures. For this reason, we report in this paper excess molar volumes of (dimethyl carbonate + toluene) at the temperatures (278.15, 288.15, 298.15, 308.15, 318.15 and 323.15) K and of (diethyl carbonate + toluene) at the temperatures (288.15, 298.15, 308.15, 318.15 and 323.15) K. In addition, using the excess molar volumes at different temperatures, the cubic expansion coefficients α, excess cubic expansion coefficients α E , and values of (∂ VmE /∂ T ) p and (∂ HmE /∂ p)T were calculated.
2. Experimental MATERIALS
Diethyl carbonate (Fluka, puriss, mole fraction purity >0.995), Dimethyl carbonate (Fluka, puriss, mole fraction purity >0.99) and toluene (Aldrich, puriss, mole fraction purity >0.998), were subjected to no further purification other than drying with 0.4 nm Union Carbide molecular sieves. The products were partially degassed before use with a Branson 2210 ultrasonic bath. The purity of the chemical products was verified by measuring their densities at several temperatures, which were found to be in agreement with literature values, as can be seen in table 1. The cubic expansion coefficients α determined by
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
745
TABLE 1. Experimental and literature densities ρ, and cubic expansion coefficients α, of the pure compounds at several temperatures and at atmospheric pressure.
T /K
Compound toluene
dimethyl carbonate
diethyl carbonate
ρ/(g · cm−3 ) This work Literature
278.15 288.15 298.15 308.15 318.15 323.15
0.88069 0.87142 0.86216 0.85281 0.84327 0.83864
278.15 288.15 298.15 308.15 318.15 323.15
1.08983 1.07646 1.06338 1.05004 1.03670 1.02994
288.15 298.15 308.15 318.15 323.15
0.98027 0.96916 0.95790 0.94643 0.94077
0.8712(19) 0.86220(20) , 0.86215(21) 0.85282(21) 0.84342(21) 0.8387(20)
α/(10−3 · K−1 ) This work Literature
1.083
1.080(25)
1.07656(22) 1.06342(22) , 1.06340(23) 1.05011(22)
1.241
1.243(22)
0.98035(22) 0.96906(22) , 0.96923(24) 0.95779(22)
1.157
1.159(22)
analytical differentiation at T = 298.15 K are also in agreement with the literature values, as shown in table 1. APPARATUS
Excess molar volumes were determined with an Anton-Paar 60/602HP vibrating-tube digital densimeter. The temperature was controlled to within ±1·10−3 K using a thermostat (Polyscience) and was measured with a digital calibrated thermometer CKT100 with a precision of ±0.01 K. Before each series of measurements the densimeter was calibrated with heptane and water, which was purified using a Milli-Q Plus System. Liquid mixtures were prepared by weight using a precision digital Sartorius 210-P balance with an accuracy of ±10−5 g. The estimated uncertainties associated with the mole fraction and with the excess volumes were (10−5 and 2 · 10−3 ) cm3 · mol−1 , respectively.
3. Results and discussion Excess molar volumes,
VmE ,
were calculated from the measured densities according to:
VmE = x M1 {(1/ρ) − (1/ρ1 )} + (1 − x)M2 {(1/ρ) − (1/ρ2 )},
(1)
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0.4
0.4
a
–0.02 VmE /(cm3 · mol–1)
VmE /(cm3 · mol–1)
0.3
0.2
0.1
0
b
–0.04
–0.06
0
0.2
0.4
0.6
0.8
1
–0.08
x
0
0.2
0.4
0.6
0.8
1
x
FIGURE 1. Excess molar volumes VmE for a, {(1 − x)(CH3 O)2 CO + xC7 H8 }; and b, {(1 − x)(C2 H5 O)2 CO + xC7 H8 } at different temperatures T : , T = 278.15 K; •, T = 288.15 K; 4, T=298.15 K; , T = 308.15 K; N, T = 318.15 K; , T = 323.15 K. Solid lines equation (2).
where Mi and ρi denote, respectively, the molar mass and the density of the pure liquids and x and ρ the mole fraction and the density of the mixture, respectively. The experimental values of the density ρ and excess molar volumes VmE at several temperatures for (dimethyl, or diethyl carbonate + toluene) are listed in tables 2 and 3, respectively. In order to calculate the second order properties, the excess molar volumes of (dimethyl carbonate + toluene) and (diethyl carbonate + toluene) were fitted to the following polynomial: VmE /(cm3 · mol−1 ) = x(1 − x)
3 X 3 X
Ai j (2x − 1)i−1 (T − T0 ) j−1 ,
(2)
i=1 j=1
where x is the mole fraction of toluene, T0 = 278.15 K and T is the absolute temperature. The coefficients Ai j and the standard deviations s are given in table 4. They were obtained by an optimization process which employed a Marquardt’s algorithm.(26) Figure 1 shows the values found for the experimental excess molar volumes together with the calculated VmE (x, T ) values obtained using equation (2). Our values at T = 298.15 K are in agreement with those reported by Garc´ıa de la Fuente et al.(16, 17) At x = 0.5, the present results differ from theirs by 0.6 per cent for (dimethyl carbonate + toluene) and by 1.6 per cent for (diethyl carbonate + toluene). The excess molar volumes of (dimethyl carbonate + toluene) are positive over the whole composition range and at all temperatures. However, for (diethyl carbonate + toluene) the excess molar volumes are negative, but small. Garc´ıa de la Fuente et al.(13–15) have found
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
747
TABLE 2. Experimental densities ρ and excess molar volumes VmE of {(1 − x)(CH3 O)2 CO + xC7 H8 } at temperatures from T = 278.15 K to T = 323.15 K at atmospheric pressure x
ρ VmE −3 3 g · cm cm · mol−1
x
ρ VmE −3 3 g · cm cm · mol−1
0.00708 0.04964 0.07081 0.12365 0.16351 0.19990
1.08782 1.07616 1.07055 1.05662 1.04641 1.03739
0.011 0.054 0.070 0.122 0.159 0.184
0.28887 0.37292 0.47660 0.51396 0.66703 0.72760
T = 278.15 K 1.01610 0.237 0.99718 0.258 0.97510 0.262 0.96740 0.264 0.93765 0.228 0.92654 0.201
0.02886 0.05869 0.08390 0.15003 0.18194 0.25558
1.06856 1.06058 1.05397 1.03717 1.02934 1.01188
0.038 0.073 0.100 0.160 0.182 0.225
0.40893 0.44724 0.58589 0.65319 0.70526
0.06295 0.09352 0.13304 0.14759 0.19567 0.24461
1.04679 0.03892 1.02907 1.02549 0.01392 1.00252
0.071 0.107 0.143 0.156 0.194 0.224
0.02196 0.07645 0.08636 0.11099 0.19182 0.25363
1.04425 0.03030 1.02776 1.02162 1.00250 0.98836
0.05562 0.09564 0.14230 0.19947 0.25187 0.27400 0.27690 0.03067 0.03917 0.11517 0.13999 0.19845 0.19974 0.29887
x
ρ VmE −3 3 g · cm cm · mol−1
0.79398 0.84610 0.86182 0.93347 0.97126
0.91474 0.90582 0.90318 0.89132 0.88527
0.167 0.129 0.116 0.060 0.023
T = 288.15 K 0.97798 0.270 0.96997 0.274 0.94243 0.261 0.92981 0.240 0.92042 0.211
0.80094 0.86773 0.91707 0.95608 0.98713
0.90369 0.89251 0.88448 0.87827 0.87340
0.160 0.113 0.074 0.040 0.013
0.33919 0.42027 0.49623 0.53326 0.57345 0.63045
T = 298.15 K 0.98150 0.263 0.96441 0.277 0.94908 0.283 0.94188 0.276 0.93421 0.269 0.92366 0.249
0.69735 0.74453 0.79506 0.83908 0.89548 0.96070
0.91164 0.90340 0.89480 0.88752 0.87840 0.86814
0.222 0.200 0.171 0.139 0.095 0.041
0.030 0.095 0.111 0.140 0.193 0.237
0.31582 0.39200 0.42650 0.52228 0.56756 0.59342
T = 308.15 K 0.97474 0.265 0.95872 0.289 0.95169 0.296 0.93297 0.294 0.92448 0.285 0.91969 0.281
0.64870 0.72086 0.77943 0.86898 0.91040 0.95428
0.90977 0.89719 0.88734 0.87284 0.86639 0.85967
0.258 0.228 0.192 0.127 0.088 0.046
1.02245 1.01255 1.00144 0.98821 0.97647 0.97167 0.97105
0.078 0.127 0.169 0.217 0.255 0.265 0.267
0.34544 0.38332 0.39628 0.43565 0.50322 0.59963 0.62852
T = 318.15 K 0.95656 0.295 0.94881 0.305 0.94616 0.311 0.93835 0.316 0.92536 0.316 0.90768 0.296 0.90257 0.285
0.64927 0.68907 0.68953 0.76260 0.80614 0.85702 0.93246
0.89894 0.89210 0.89205 0.87987 0.87277 0.86474 0.85324
0.277 0.258 0.254 0.211 0.186 0.146 0.071
1.02205 1.01995 1.00146 0.99556 0.98217 0.98185 0.96032
0.050 0.058 0.144 0.172 0.223 0.227 0.285
0.34034 0.39994 0.48600 0.51085 0.60585 0.67105 0.72229
T = 323.15 K 0.95163 0.307 0.93962 0.322 0.92297 0.331 0.91835 0.326 0.90119 0.305 0.88993 0.277 0.88136 0.248
0.76957 0.78598 0.83667 0.89484 0.91372 0.97011
0.87364 0.87103 0.86307 0.85407 0.85124 0.84296
0.218 0.203 0.160 0.117 0.098 0.034
748
E. R. L´opez et al. TABLE 3. Experimental densities and excess molar volumes of {(1 − x)(C2 H5 O)2 CO + xC7 H8 } at temperatures from T = 288.15 K to T = 323.15 K at atmospheric pressure x
ρ VmE −3 3 g · cm cm · mol−1
x
ρ VmE −3 3 g · cm cm · mol−1
x
ρ VmE −3 3 g · cm cm · mol−1
0.07483 0.10476 0.18132 0.19792 0.24053 0.27597
0.97319 0.97031 0.96283 0.96120 0.95694 0.95336
−0.017 −0.022 −0.033 −0.037 −0.041 −0.046
0.35460 0.44737 0.53971 0.58838 0.64550 0.76800
T = 288.15 K 0.94530 −0.053 0.93555 −0.059 0.92558 −0.062 0.92022 −0.062 0.91382 −0.061 0.89974 −0.054
0.79172 0.84747 0.87414 0.91566 0.96431
0.89694 0.89029 0.88707 0.88198 0.87593
−0.050 −0.041 −0.037 −0.026 −0.013
0.02096 0.06753 0.09390 0.12269 0.16480 0.17960
0.96722 0.96287 0.96039 0.95764 0.95360 0.95217
−0.004 −0.013 −0.017 −0.021 −0.028 −0.030
0.31680 0.38350 0.44370 0.57500 0.69080 0.77680
T = 298.15 K 0.93860 −0.046 0.93182 −0.053 0.92557 −0.056 0.91158 −0.059 0.89877 −0.056 0.88895 −0.048
0.81970 0.86390 0.87570 0.92870 0.97530
0.88396 0.87873 0.87732 0.87094 0.86521
−0.042 −0.035 −0.032 −0.021 −0.006
0.02977 0.09272 0.12411 0.19602 0.24169
0.95519 0.94938 0.94644 0.93963 0.93523
−0.005 −0.015 −0.019 −0.029 −0.035
0.37533 0.41107 0.50780 0.57181 0.58945
T = 308.15 K 0.92205 −0.049 0.91843 −0.052 0.90847 −0.058 0.90170 −0.059 0.89981 −0.058
0.79839 0.82836 0.87334 0.92536 0.97533
0.87667 0.87321 0.86798 0.86182 0.85582
−0.043 −0.038 −0.030 −0.019 −0.007
0.05077 0.10815 0.18969 0.25750 0.28227 0.32623
0.94187 0.93665 0.92909 0.92267 0.92030 0.91606
−0.008 −0.016 −0.027 −0.035 −0.039 −0.044
0.44542 0.49667 0.56958 0.62594 0.68148 0.76474
T = 318.15 K 0.90425 −0.054 0.89905 −0.056 0.89150 −0.057 0.88556 −0.056 0.87959 −0.054 0.87044 −0.044
0.82981 0.85611 0.90924 0.93339 0.95925
0.86313 0.86013 0.85400 0.85117 0.84812
−0.036 −0.032 −0.022 −0.016 −0.010
0.03223 0.15909 0.18418 0.25950 0.29023
0.93791 0.92642 0.92411 0.91707 0.91415
−0.005 −0.020 −0.024 −0.035 −0.038
0.33261 0.38431 0.55561 0.63658 0.74580
T = 323.15 K 0.91008 −0.043 0.90506 −0.048 0.88784 −0.056 0.87938 −0.055 0.86761 −0.045
0.84539 0.85651 0.89274 0.85112 0.95738 0.84365
−0.029 −0.020 −0.009
a similar behaviour for the excess enthalpies. For dimethyl carbonate HmE is positive and for diethyl carbonate the HmE (x) curve presents an s-shape form. The behaviour of this type of mixtures is quite different from that of (di-alkyl carbonate + alkane)(4) for which the HmE and VmE values are higher and positive. This means
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
749
TABLE 4. Parameters Ai j of equation (2), together with the standard deviation s 1−j
Ai j /cm3 · mol−1 · K 2 3
s/cm3 · mol−1
i
1
1 2 3
1.0699 −0.1322 0.0067
(1 − x)(CH3 O)2 CO + xC7 H8 0.00039 0.000110 −0.00179 0.000028 0.00394 −0.000078
1 2 3
−0.2541 −0.0599 −0.1000
(1 − x)(C2 H5 O)2 CO + xC7 H8 0.00117 −0.000011 −0.00055 0.000012 0.00353 −0.000001
0.0031
0.0008
TABLE 5. Number of contacts Ni j between groups: CHi –CH j , CHi –OCOO and OCOO–OCOO, with i, j = 2, 3. 1Ni j is the change in the number of contacts during the mixing process
Dimethyl carbonate Diethyl carbonate Hexane Dodecane
0.5 (CH3 O)2 CO + 0.5 C6 H14 + 0.5 C12 H26 0.5 (C2 H5 O)2 CO + 0.5 C6 H14 + 0.5 C12 H26
NCHi –CH j
NCHi –OCOO
NOCOO–OCOO
4.61 8.43 15.24 28.05 1NCHi –CH j
4.20 5.09
2.33 1.89
1NCHi –OCOO
1NOCOO–OCOO
−0.54 −0.70
1.09 1.40
−0.54 −0.70
−0.39 −0.51
0.78 1.02
−0.39 −0.51
that the n-π complex formation between the free electrons of the –O–CO–O group and the aromatic ring(17) is very important. Evidence of n-π interactions in (alkanone,(27) alkyl alkanoate,(28, 29) propylene carbonate,(30) or alkyl carbonate(17) + toluene) has been previously reported. The trends of HmE and VmE with the alkyl chain length of a carbonate are identical for (an organic carbonate + an alkane) and (an organic carbonate + an aromatic compound). The reason for these trends is that a pure dimethyl carbonate has more interactions between the carbonate groups than a pure ethyl carbonate. This means that during mixing the toluene or the alkane molecules can destroy a larger number of dipole–dipole interactions in the case of dimethyl carbonate, and, therefore, for the mixtures containing dimethyl carbonate the disruption of the dipolar order is higher. Thus, the excess molar enthalpies and excess molar
750
E. R. L´opez et al.
0.40
–0.05
a
b
VmE /(cm3 · mol–1)
VmE /(cm3 · mol–1)
0.35
0.30
–0.06
0.25
0.20 270
290
310
330
–0.07 270
290
T /K
310
330
T /K
FIGURE 2. Temperature dependence of the excess molar a, {0.5(CH3 O)2 CO + 0.5C7 H8 }; and b, {0.5(C2 H5 O)2 CO + 0.5C7 H8 }.
volumes
VmE
for:
volumes are larger for dimethyl carbonate. This behaviour can be shown theoretically by determining the number of contacts Ni j and the increment in the number of contacts 1Ni j during mixing for (an organic carbonate + an alkane) using the Nitta–Chao model and the parameters of Garc´ıa et al.(4) The resulting values of Ni j and 1Ni j are shown in table 5. For (an alkyl carbonate + an aromatic hydrocarbon) the contact numbers cannot be obtained because there are no published parameters. Figure 2 shows how the VmE values increase with temperature for (dimethyl, or diethyl carbonate + toluene) at x = 0.5. It can be also observed that the change in VmE with the temperature is more important for (dimethyl carbonate + toluene). TEMPERATURE DEPENDENCE OF THE EXCESS VOLUMES AND PRESSURE DEPENDENCE OF THE EXCESS ENTHALPIES
The values of (∂ VmE /∂ T ) p of (dimethyl carbonate + toluene) and (diethyl carbonate + toluene) were obtained by analytical derivation of equation (2). Figures 3a and b show that (∂ VmE /∂ T ) p is positive in all cases and decreases with increase in the chain of the organic carbonate. In addition, for (dimethyl carbonate + toluene) the curves present a unique maximum although when the temperature decreases the curves’ shapes become flat. In the case of diethyl carbonate, (∂ VmE /∂ T ) p presents a double maximum. Figure 3 also shows that (∂ VmE /∂ T ) p increases when the temperature increases for (dimethyl carbonate + toluene) and when the temperature decreases in the case of (diethyl carbonate + toluene). Figure 4 shows the pressure dependence of the excess enthalpies determined from the excess volumes by using the equation: (∂ HmE /∂ p)T = VmE − T (∂ VmE /∂ T ) p .
(3)
(∂ VmE /∂ T ) p
are both positive for all
For (dimethyl carbonate + toluene)
VmE
and
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
0.5
a
2
103(∂VmE/∂T )p /(cm3 · mol–1 · K–1)
103(∂VmE/∂T )p /(cm3 · mol–1 · K–1)
2.5
T = 318.15 K
1.5
T = 308.15 K
1
T = 298.15 K
0.5
T = 288.15 K
751
b
0.4 0.3 T = 298.15 K
0.2 T = 308.15 K
0.1 T = 318.15 K
0
0 0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
x
0.6
0.8
1
x
FIGURE 3. (∂ VmE /∂ T ) p against the mole fraction x for: a, {(1 − x)(CH3 O)2 CO + xC7 H8 }; and b, {(1 − x)(C2 H5 O)2 CO + xC7 H8 } at different temperatures T . 0.2
0
a
b
E /∂p) /(J · MPa–1) (∂Hm T
E /∂p) /(J · MPa–1) (∂Hm T
T = 288.15 K
0 T = 298.15 K
T = 308.15 K
–0.2
T = 318.15 K
–0.04 T = 318.15 K
–0.08 T = 308.15 K
–0.12 T = 298.15 K
–0.4 –0.16
–0.6 0
0.2
0.6
0.4 x
0.8
1
–0.2 0
0.2
0.4
0.6
0.8
1
x
E /∂ p) against the mole fraction x for: a, {(1 − x)(CH O) CO + xC H }; and FIGURE 4. (∂ Hm 7 8 T 3 2 b, {(1 − x)(C2 H5 O)2 CO + xC7 H8 } at different temperatures T .
temperatures and of similar magnitude. As a consequence (∂ HmE /∂ p)T is small and its sign depends on the composition and temperature. This fact implies that a little change in the VmE fitting equation can cause a relatively strong variation in (∂ HmE /∂ p)T . However, for (diethyl carbonate + toluene), VmE is negative and T (∂ VmE /∂ T ) p is positive, which implies that
752
E. R. L´opez et al.
1.25
a
b
x=0
1.3
x = 0.25
x=0
1.20
x = 0.25
1.2 x = 0.75 x=1
103 α /K–1
103 α /K–1
x = 0.50
1.1
1.0 280
x = 0.50
1.15
x = 0.75 x=1
1.10
290
300 310 T /K
320
330
1.05 290
300
310 T /K
320
330
FIGURE 5. Cubic expansion coefficients α for the pure liquids and for the mixtures: a, {(1 − x)(CH3 O)2 CO + xC7 H8 }; and b, {(1 − x)(C2 H5 O)2 CO + xC7 H8 } as a function of temperature T and the mole fraction x. , this work; , Sun et al.(25)
(∂ HmE /∂ p)T is negative. For both systems we conclude that the excess enthalpies change slightly with pressure within the studied temperature range. Bhattacharyya and Patterson(31) and Costas et al.(32) have suggested that the properties (∂ VmE /∂ T ) p and (∂ HmE /∂ p)T can be employed as indicators of changes of order in a solution. A destruction of order during mixing implies a negative contribution to (∂ VmE /∂ T ) p and a positive contribution to VmE , HmE and (∂ HmE /∂ p)T . In the present case for both systems (∂ VmE /∂ T ) p is positive and is larger for the system containing dimethyl carbonate. It is interesting to note that for (diethyl carbonate + toluene) all the properties, VmE , HmE , (∂ VmE /∂ T ) p and (∂ HmE /∂ p)T have very small values. This means that this system behaves as almost ideal due to a compensation of opposite effects. For (dimethyl carbonate + toluene) all these properties are higher except (∂ HmE /∂ p)T . CUBIC EXPANSION COEFFICIENTS
Figure 5 shows the cubic expansion coefficients α for the mixtures investigated at several mole fractions and temperatures. We can see that α increases with the temperature and decreases when the mole fraction of the toluene increases. Furthermore, a diminution of α is observed when the length of the organic carbonate chain increases as for HmE , and VmE . The excess cubic expansion coefficient α E , is obtained by subtracting from the observed value of α of the mixture the ideal value α id given by: α id = ϕ1 α1∗ + ϕ2 α2∗ ,
(4)
where the ∗ refers to the pure substance, and the volume fraction ϕi is given by: ∗ ϕi = xi Vm,i /Vmid ,
(5)
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
753
and ∗ ∗ Vmid = x1 Vm,1 + x2 Vm,2 .
(6)
The excess cubic expansion coefficient α E is given by: α E = {(∂ VmE /∂ T ) p − VmE α id }/(Vmid + VmE ).
(7)
For (dimethyl carbonate + toluene) at T = 318.15 K, α E is positive up to 1.9·10−5 K−1 , and for (diethyl carbonate + toluene) it is also positive and an order of magnitude lower. For the first system α E increases when the temperature increases, whereas for the second the opposite occurs, and similarly for (∂ VmE /∂ T ) p . This work was carried out under the CICYT QUI98-1071-C02-01 Research Project-Spain. The authors wish to express their gratitude to Miss Silvia Miramontes for her experimental assistance. REFERENCES 1. Takahata, K.; Tanaka, M.; Hayashi, T.; Sakamoto, N. Proceedings of 1994 International Refrigeration Conference at Purdue. Purdue University, W. Lafayette, IN, USA. 1994, 141–146. 2. Hayashi, T.; Tanaka, M.; Takeuchi, K.; Takahata, K.; Sakamoto, N. Proceedings of 1996 International Refrigeration Conference at Purdue. Purdue University, W. Lafayette, IN, USA. 1996, 285–290. 3. Garc´ıa, J.; L´opez, E. R.; Fern´andez, J.; Legido, J. L. Thermochim. Acta 1996, 286, 321–332. 4. Garc´ıa, J.; Lugo, L.; Comu˜nas, M. J.; L´opez, E. R.; Fern´andez, J. J. Chem. Soc. Faraday Trans. 1998, 94, 1707–1712. 5. Dang, D.; Tassios, P. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 22–31. 6. Larsen, B. L.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Res. 1987, 26, 2274–2286. 7. Gmehling, J.; Li, J.; Schiller, M. Ind. Eng. Chem. Res. 1993, 32, 178–193. 8. Nitta, T.; Turck, E. A.; Greenkorn, R. A.; Chao, K. C. AIChE. J. 1977, 23, 144–160. 9. Cocero, M. J.; Mato, F.; Garc´ıa, I.; Cobos, J. C.; Kehiaian, H. V. J. Chem. Eng. Data 1989, 34, 73–76. 10. Cocero, M. J.; Mato, F.; Garc´ıa, I.; Cobos, J. C.; Kehiaian, H. V. J. Chem. Eng. Data 1989, 34, 443–445. 11. Cocero, M. J.; Gonz´alez, J. A.; Garc´ıa, I.; Cobos, J. C.; Mato, F. Int. DATA Ser. Sel. Data Mixtures, Ser. A 1991, 112–129. 12. Negadi, L.; Blondel, A.; Mokbel, I.; Ait-Kaci, A.; Jose, J. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1993, 21, 169–194. 13. Garc´ıa, I.; Cobos, J. C.; Gonz´alez, J. A.; Casanova, C. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1987, 3, 164–173. 14. Garc´ıa, I.; Cobos, J. C.; Gonz´alez, J. A.; Casanova, C. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1987, 4, 245–253. 15. Garc´ıa, I.; Cobos, J. C.; Gonz´alez, J. A.; Casanova, C.; Cocero, M. J. J. Chem. Eng. Data 1988, 33, 423–426. 16. Garc´ıa de la Fuente, I.; Gonz´alez, J. A.; Cobos, J. C.; Casanova, C. J. Chem. Eng. Data 1992, 37, 535–537. 17. Garc´ıa de la Fuente, I.; Gonz´alez, J. A.; Cobos, J. C.; Casanova, C. J. Sol. Chem. 1995, 24, 827–835. 18. Orye, R. V.; Prausnitz, J. M. Trans. Faraday Soc. 1965, 61, 1338–1346. 19. Moumouzias, G.; Ritzoulis, G. J. Chem. Eng. Data 1992, 37, 482–483. 20. TRC Thermodynamics Tables, Texas A&M University,College Station, Table 23-2-(33.11000)d, Texas. 1994.
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21. Gamboa, I.; Tardajos, G.; D´ıaz Pe˜na, M.; Aicart, E. J. Chem. Thermodynamics 1986, 18, 885– 890. 22. Pardo, J. M.; Tovar, C. A.; Cerdeiri˜na, C. A.; Carballo, E.; Roman´ı, L. J. Chem. Thermodynamics 1999, 31, 787–796. 23. Gonzalez, J. A.; Garc´ıa, I.; Cobos, J. C.; Casanova, C. J. Chem. Eng. Data 1991, 36, 162–164. 24. Francesconi, R.; Comelli, F. J. Chem. Eng. Data 1997, 42, 45–48. 25. Sun, T. F.; Bominaar, S. A. R. C.; ten Seldam, C. A.; Biswas, S. N. Ber. Bunsen-Ges. Phys. Chem. 1991, 95, 696–704. 26. Marquardt, D. W. J. Soc. Indust. Appl. Math. 1963, 11, 431–441. 27. Shen, S.; Wang, Y.; Shi, J.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1990, 22, 387–392. 28. Grolier, J.-P. E.; Ballet, D.; Viallard, A. J. Chem. Thermodynamics 1974, 6, 895–908. 29. Jim´enez, E.; Roman´ı, L.; Wilhelm, E.; Roux-Desgranges, G.; Grolier, J.-P. E. J. Chem. Thermodynamics 1994, 26, 817–827. 30. Wilhelm, E.; Jim´enez, E.; Roux-Desgranges, G.; Grolier, J.-P. E. J. Sol. Chem. 1991, 20, 17–28. 31. Bhattacharyya, S. H.; Patterson, D. J. Chem. Soc. Faraday Trans. I 1985, 81, 375–385. 32. Costas, M.; Bhattacharyya, S. H.; Patterson, D. J. Chem. Soc. Faraday Trans. I 1985, 81, 387– 395. (Received 24 June 1999; in final form 10 December 1999)
WA 99/036
Temperature dependence of the excess molar volume of (dimethyl carbonate, or diethyl carbonate + toluene) from T = 278.15 K to 323.15 K ˜ E. R. L´opez, L. Lugo, M. J. P. Comunas, Laboratorio de Propiedades Termofisicas, Departamento de F´ısica Aplicada, Facultad de F´ısica, Universidad de Santiago, E-15706 Santiago de Compostela,
J. Garc´ıa, Laboratorio de Propiedades Termofisicas, Departamento de F´ısica Aplicada, Facultad de F´ısica, Universidad de Santiago, E-15706 Santiago de Compostela, and Departamento de F´ısica Aplicada, Facultad de Ciencias, Universidad de Vigo, E-36200 Vigo,
and J. Fern´andeza Laboratorio de Propiedades Termofisicas, Departamento de F´ısica Aplicada, Facultad de F´ısica, Universidad de Santiago, E-15706 Santiago de Compostela The experimental densities ρ and excess molar volumes VmE of (dimethyl carbonate + toluene) at the temperatures (278.15, 288.15, 298.15, 308.15, 318.15, and 323.15) K and of (diethyl carbonate + toluene) at the temperatures (288.15, 298.15, 308.15, 318.15, and 323.15) K were determined using an Anton-Paar DMA602HP densimeter. For (dimethyl carbonate + toluene) the excess molar volumes were positive over the whole composition range and at all temperatures. On the contrary, for (diethyl carbonate + toluene) the excess molar volumes were negative. The experimental data were used for the calculation by analytical differentiation of the following quantities: the cubic expansion E /∂ p) . coefficient, the excess cubic expansion of coefficient, (∂ VmE /∂ T ) p and (∂ Hm T c 2000 Academic Press
KEYWORDS: excess molar volume; organic carbonate; toluene; molecular interaction; cubic expansion coefficient
a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/00/060743 + 12 $35.00/0
c 2000 Academic Press
744
E. R. L´opez et al.
1. Introduction The problem of the replacement of chlorofluorocarbons (CFCs) by new refrigerants has been only partially solved. The requirements of suitable lubricants for the new refrigerants are not fulfilled by mineral oils, which were used for CFCs. In the last few years new oils based on carbonate molecules have been proposed(1, 2) for stationary air conditioners as candidates because of their thermal stability, miscibility with HFCs and lubricity. The lubricant carbonate molecules include alkyl groups (which contribute to the thermal stability) a carbonate group (which provides lubricity and miscibility) and an alkyl benzene group (which contributes to lubricity). To find the best lubricant properties for the carbonates, experimental data on the thermophysical properties as well as prediction methods such as group contribution models are needed. In previous papers(3, 4) we have determined the characteristic parameters for carbonate and methyl, or methylene groups of the UNIFAC model (in the versions of Dang and Tassios,(5) Larsen et al.(6) and Gmehling et al.(7) ) and the Nitta–Chao(8) model. Our next step is to determine the carbonate-aromatic parameters for several group contribution models. For this purpose an updated database is necessary. Up to now, we have found in the literature (vapour + liquid) equilibrium data,(9–12) excess molar enthalpies(13–15) at T = 298.15 K, and excess molar volumes(12, 16, 17) at T = 298.15 K for (di-n-alkyl carbonate + benzene) as well as activity coefficients at infinite dilution(18) at T = 318 K, excess molar enthalpies(13–15) and excess molar volumes(16, 17) at T = 298.15 K for (di-n-alkyl carbonate + toluene). To the best of our knowledge, we are not aware of any VmE measurements on (di-nalkyl carbonate + toluene) at temperatures other than T = 298.15 K. In order to calculate reliable interaction parameters between the carbonate and aromatic groups for the Nitta– Chao model, it is necessary to have experimental data at several temperatures. For this reason, we report in this paper excess molar volumes of (dimethyl carbonate + toluene) at the temperatures (278.15, 288.15, 298.15, 308.15, 318.15 and 323.15) K and of (diethyl carbonate + toluene) at the temperatures (288.15, 298.15, 308.15, 318.15 and 323.15) K. In addition, using the excess molar volumes at different temperatures, the cubic expansion coefficients α, excess cubic expansion coefficients α E , and values of (∂ VmE /∂ T ) p and (∂ HmE /∂ p)T were calculated.
2. Experimental MATERIALS
Diethyl carbonate (Fluka, puriss, mole fraction purity >0.995), Dimethyl carbonate (Fluka, puriss, mole fraction purity >0.99) and toluene (Aldrich, puriss, mole fraction purity >0.998), were subjected to no further purification other than drying with 0.4 nm Union Carbide molecular sieves. The products were partially degassed before use with a Branson 2210 ultrasonic bath. The purity of the chemical products was verified by measuring their densities at several temperatures, which were found to be in agreement with literature values, as can be seen in table 1. The cubic expansion coefficients α determined by
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
745
TABLE 1. Experimental and literature densities ρ, and cubic expansion coefficients α, of the pure compounds at several temperatures and at atmospheric pressure.
T /K
Compound toluene
dimethyl carbonate
diethyl carbonate
ρ/(g · cm−3 ) This work Literature
278.15 288.15 298.15 308.15 318.15 323.15
0.88069 0.87142 0.86216 0.85281 0.84327 0.83864
278.15 288.15 298.15 308.15 318.15 323.15
1.08983 1.07646 1.06338 1.05004 1.03670 1.02994
288.15 298.15 308.15 318.15 323.15
0.98027 0.96916 0.95790 0.94643 0.94077
0.8712(19) 0.86220(20) , 0.86215(21) 0.85282(21) 0.84342(21) 0.8387(20)
α/(10−3 · K−1 ) This work Literature
1.083
1.080(25)
1.07656(22) 1.06342(22) , 1.06340(23) 1.05011(22)
1.241
1.243(22)
0.98035(22) 0.96906(22) , 0.96923(24) 0.95779(22)
1.157
1.159(22)
analytical differentiation at T = 298.15 K are also in agreement with the literature values, as shown in table 1. APPARATUS
Excess molar volumes were determined with an Anton-Paar 60/602HP vibrating-tube digital densimeter. The temperature was controlled to within ±1·10−3 K using a thermostat (Polyscience) and was measured with a digital calibrated thermometer CKT100 with a precision of ±0.01 K. Before each series of measurements the densimeter was calibrated with heptane and water, which was purified using a Milli-Q Plus System. Liquid mixtures were prepared by weight using a precision digital Sartorius 210-P balance with an accuracy of ±10−5 g. The estimated uncertainties associated with the mole fraction and with the excess volumes were (10−5 and 2 · 10−3 ) cm3 · mol−1 , respectively.
3. Results and discussion Excess molar volumes,
VmE ,
were calculated from the measured densities according to:
VmE = x M1 {(1/ρ) − (1/ρ1 )} + (1 − x)M2 {(1/ρ) − (1/ρ2 )},
(1)
746
E. R. L´opez et al.
0.4
0.4
a
–0.02 VmE /(cm3 · mol–1)
VmE /(cm3 · mol–1)
0.3
0.2
0.1
0
b
–0.04
–0.06
0
0.2
0.4
0.6
0.8
1
–0.08
x
0
0.2
0.4
0.6
0.8
1
x
FIGURE 1. Excess molar volumes VmE for a, {(1 − x)(CH3 O)2 CO + xC7 H8 }; and b, {(1 − x)(C2 H5 O)2 CO + xC7 H8 } at different temperatures T : , T = 278.15 K; •, T = 288.15 K; 4, T=298.15 K; , T = 308.15 K; N, T = 318.15 K; , T = 323.15 K. Solid lines equation (2).
where Mi and ρi denote, respectively, the molar mass and the density of the pure liquids and x and ρ the mole fraction and the density of the mixture, respectively. The experimental values of the density ρ and excess molar volumes VmE at several temperatures for (dimethyl, or diethyl carbonate + toluene) are listed in tables 2 and 3, respectively. In order to calculate the second order properties, the excess molar volumes of (dimethyl carbonate + toluene) and (diethyl carbonate + toluene) were fitted to the following polynomial: VmE /(cm3 · mol−1 ) = x(1 − x)
3 X 3 X
Ai j (2x − 1)i−1 (T − T0 ) j−1 ,
(2)
i=1 j=1
where x is the mole fraction of toluene, T0 = 278.15 K and T is the absolute temperature. The coefficients Ai j and the standard deviations s are given in table 4. They were obtained by an optimization process which employed a Marquardt’s algorithm.(26) Figure 1 shows the values found for the experimental excess molar volumes together with the calculated VmE (x, T ) values obtained using equation (2). Our values at T = 298.15 K are in agreement with those reported by Garc´ıa de la Fuente et al.(16, 17) At x = 0.5, the present results differ from theirs by 0.6 per cent for (dimethyl carbonate + toluene) and by 1.6 per cent for (diethyl carbonate + toluene). The excess molar volumes of (dimethyl carbonate + toluene) are positive over the whole composition range and at all temperatures. However, for (diethyl carbonate + toluene) the excess molar volumes are negative, but small. Garc´ıa de la Fuente et al.(13–15) have found
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
747
TABLE 2. Experimental densities ρ and excess molar volumes VmE of {(1 − x)(CH3 O)2 CO + xC7 H8 } at temperatures from T = 278.15 K to T = 323.15 K at atmospheric pressure x
ρ VmE −3 3 g · cm cm · mol−1
x
ρ VmE −3 3 g · cm cm · mol−1
0.00708 0.04964 0.07081 0.12365 0.16351 0.19990
1.08782 1.07616 1.07055 1.05662 1.04641 1.03739
0.011 0.054 0.070 0.122 0.159 0.184
0.28887 0.37292 0.47660 0.51396 0.66703 0.72760
T = 278.15 K 1.01610 0.237 0.99718 0.258 0.97510 0.262 0.96740 0.264 0.93765 0.228 0.92654 0.201
0.02886 0.05869 0.08390 0.15003 0.18194 0.25558
1.06856 1.06058 1.05397 1.03717 1.02934 1.01188
0.038 0.073 0.100 0.160 0.182 0.225
0.40893 0.44724 0.58589 0.65319 0.70526
0.06295 0.09352 0.13304 0.14759 0.19567 0.24461
1.04679 0.03892 1.02907 1.02549 0.01392 1.00252
0.071 0.107 0.143 0.156 0.194 0.224
0.02196 0.07645 0.08636 0.11099 0.19182 0.25363
1.04425 0.03030 1.02776 1.02162 1.00250 0.98836
0.05562 0.09564 0.14230 0.19947 0.25187 0.27400 0.27690 0.03067 0.03917 0.11517 0.13999 0.19845 0.19974 0.29887
x
ρ VmE −3 3 g · cm cm · mol−1
0.79398 0.84610 0.86182 0.93347 0.97126
0.91474 0.90582 0.90318 0.89132 0.88527
0.167 0.129 0.116 0.060 0.023
T = 288.15 K 0.97798 0.270 0.96997 0.274 0.94243 0.261 0.92981 0.240 0.92042 0.211
0.80094 0.86773 0.91707 0.95608 0.98713
0.90369 0.89251 0.88448 0.87827 0.87340
0.160 0.113 0.074 0.040 0.013
0.33919 0.42027 0.49623 0.53326 0.57345 0.63045
T = 298.15 K 0.98150 0.263 0.96441 0.277 0.94908 0.283 0.94188 0.276 0.93421 0.269 0.92366 0.249
0.69735 0.74453 0.79506 0.83908 0.89548 0.96070
0.91164 0.90340 0.89480 0.88752 0.87840 0.86814
0.222 0.200 0.171 0.139 0.095 0.041
0.030 0.095 0.111 0.140 0.193 0.237
0.31582 0.39200 0.42650 0.52228 0.56756 0.59342
T = 308.15 K 0.97474 0.265 0.95872 0.289 0.95169 0.296 0.93297 0.294 0.92448 0.285 0.91969 0.281
0.64870 0.72086 0.77943 0.86898 0.91040 0.95428
0.90977 0.89719 0.88734 0.87284 0.86639 0.85967
0.258 0.228 0.192 0.127 0.088 0.046
1.02245 1.01255 1.00144 0.98821 0.97647 0.97167 0.97105
0.078 0.127 0.169 0.217 0.255 0.265 0.267
0.34544 0.38332 0.39628 0.43565 0.50322 0.59963 0.62852
T = 318.15 K 0.95656 0.295 0.94881 0.305 0.94616 0.311 0.93835 0.316 0.92536 0.316 0.90768 0.296 0.90257 0.285
0.64927 0.68907 0.68953 0.76260 0.80614 0.85702 0.93246
0.89894 0.89210 0.89205 0.87987 0.87277 0.86474 0.85324
0.277 0.258 0.254 0.211 0.186 0.146 0.071
1.02205 1.01995 1.00146 0.99556 0.98217 0.98185 0.96032
0.050 0.058 0.144 0.172 0.223 0.227 0.285
0.34034 0.39994 0.48600 0.51085 0.60585 0.67105 0.72229
T = 323.15 K 0.95163 0.307 0.93962 0.322 0.92297 0.331 0.91835 0.326 0.90119 0.305 0.88993 0.277 0.88136 0.248
0.76957 0.78598 0.83667 0.89484 0.91372 0.97011
0.87364 0.87103 0.86307 0.85407 0.85124 0.84296
0.218 0.203 0.160 0.117 0.098 0.034
748
E. R. L´opez et al. TABLE 3. Experimental densities and excess molar volumes of {(1 − x)(C2 H5 O)2 CO + xC7 H8 } at temperatures from T = 288.15 K to T = 323.15 K at atmospheric pressure x
ρ VmE −3 3 g · cm cm · mol−1
x
ρ VmE −3 3 g · cm cm · mol−1
x
ρ VmE −3 3 g · cm cm · mol−1
0.07483 0.10476 0.18132 0.19792 0.24053 0.27597
0.97319 0.97031 0.96283 0.96120 0.95694 0.95336
−0.017 −0.022 −0.033 −0.037 −0.041 −0.046
0.35460 0.44737 0.53971 0.58838 0.64550 0.76800
T = 288.15 K 0.94530 −0.053 0.93555 −0.059 0.92558 −0.062 0.92022 −0.062 0.91382 −0.061 0.89974 −0.054
0.79172 0.84747 0.87414 0.91566 0.96431
0.89694 0.89029 0.88707 0.88198 0.87593
−0.050 −0.041 −0.037 −0.026 −0.013
0.02096 0.06753 0.09390 0.12269 0.16480 0.17960
0.96722 0.96287 0.96039 0.95764 0.95360 0.95217
−0.004 −0.013 −0.017 −0.021 −0.028 −0.030
0.31680 0.38350 0.44370 0.57500 0.69080 0.77680
T = 298.15 K 0.93860 −0.046 0.93182 −0.053 0.92557 −0.056 0.91158 −0.059 0.89877 −0.056 0.88895 −0.048
0.81970 0.86390 0.87570 0.92870 0.97530
0.88396 0.87873 0.87732 0.87094 0.86521
−0.042 −0.035 −0.032 −0.021 −0.006
0.02977 0.09272 0.12411 0.19602 0.24169
0.95519 0.94938 0.94644 0.93963 0.93523
−0.005 −0.015 −0.019 −0.029 −0.035
0.37533 0.41107 0.50780 0.57181 0.58945
T = 308.15 K 0.92205 −0.049 0.91843 −0.052 0.90847 −0.058 0.90170 −0.059 0.89981 −0.058
0.79839 0.82836 0.87334 0.92536 0.97533
0.87667 0.87321 0.86798 0.86182 0.85582
−0.043 −0.038 −0.030 −0.019 −0.007
0.05077 0.10815 0.18969 0.25750 0.28227 0.32623
0.94187 0.93665 0.92909 0.92267 0.92030 0.91606
−0.008 −0.016 −0.027 −0.035 −0.039 −0.044
0.44542 0.49667 0.56958 0.62594 0.68148 0.76474
T = 318.15 K 0.90425 −0.054 0.89905 −0.056 0.89150 −0.057 0.88556 −0.056 0.87959 −0.054 0.87044 −0.044
0.82981 0.85611 0.90924 0.93339 0.95925
0.86313 0.86013 0.85400 0.85117 0.84812
−0.036 −0.032 −0.022 −0.016 −0.010
0.03223 0.15909 0.18418 0.25950 0.29023
0.93791 0.92642 0.92411 0.91707 0.91415
−0.005 −0.020 −0.024 −0.035 −0.038
0.33261 0.38431 0.55561 0.63658 0.74580
T = 323.15 K 0.91008 −0.043 0.90506 −0.048 0.88784 −0.056 0.87938 −0.055 0.86761 −0.045
0.84539 0.85651 0.89274 0.85112 0.95738 0.84365
−0.029 −0.020 −0.009
a similar behaviour for the excess enthalpies. For dimethyl carbonate HmE is positive and for diethyl carbonate the HmE (x) curve presents an s-shape form. The behaviour of this type of mixtures is quite different from that of (di-alkyl carbonate + alkane)(4) for which the HmE and VmE values are higher and positive. This means
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
749
TABLE 4. Parameters Ai j of equation (2), together with the standard deviation s 1−j
Ai j /cm3 · mol−1 · K 2 3
s/cm3 · mol−1
i
1
1 2 3
1.0699 −0.1322 0.0067
(1 − x)(CH3 O)2 CO + xC7 H8 0.00039 0.000110 −0.00179 0.000028 0.00394 −0.000078
1 2 3
−0.2541 −0.0599 −0.1000
(1 − x)(C2 H5 O)2 CO + xC7 H8 0.00117 −0.000011 −0.00055 0.000012 0.00353 −0.000001
0.0031
0.0008
TABLE 5. Number of contacts Ni j between groups: CHi –CH j , CHi –OCOO and OCOO–OCOO, with i, j = 2, 3. 1Ni j is the change in the number of contacts during the mixing process
Dimethyl carbonate Diethyl carbonate Hexane Dodecane
0.5 (CH3 O)2 CO + 0.5 C6 H14 + 0.5 C12 H26 0.5 (C2 H5 O)2 CO + 0.5 C6 H14 + 0.5 C12 H26
NCHi –CH j
NCHi –OCOO
NOCOO–OCOO
4.61 8.43 15.24 28.05 1NCHi –CH j
4.20 5.09
2.33 1.89
1NCHi –OCOO
1NOCOO–OCOO
−0.54 −0.70
1.09 1.40
−0.54 −0.70
−0.39 −0.51
0.78 1.02
−0.39 −0.51
that the n-π complex formation between the free electrons of the –O–CO–O group and the aromatic ring(17) is very important. Evidence of n-π interactions in (alkanone,(27) alkyl alkanoate,(28, 29) propylene carbonate,(30) or alkyl carbonate(17) + toluene) has been previously reported. The trends of HmE and VmE with the alkyl chain length of a carbonate are identical for (an organic carbonate + an alkane) and (an organic carbonate + an aromatic compound). The reason for these trends is that a pure dimethyl carbonate has more interactions between the carbonate groups than a pure ethyl carbonate. This means that during mixing the toluene or the alkane molecules can destroy a larger number of dipole–dipole interactions in the case of dimethyl carbonate, and, therefore, for the mixtures containing dimethyl carbonate the disruption of the dipolar order is higher. Thus, the excess molar enthalpies and excess molar
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0.40
–0.05
a
b
VmE /(cm3 · mol–1)
VmE /(cm3 · mol–1)
0.35
0.30
–0.06
0.25
0.20 270
290
310
330
–0.07 270
290
T /K
310
330
T /K
FIGURE 2. Temperature dependence of the excess molar a, {0.5(CH3 O)2 CO + 0.5C7 H8 }; and b, {0.5(C2 H5 O)2 CO + 0.5C7 H8 }.
volumes
VmE
for:
volumes are larger for dimethyl carbonate. This behaviour can be shown theoretically by determining the number of contacts Ni j and the increment in the number of contacts 1Ni j during mixing for (an organic carbonate + an alkane) using the Nitta–Chao model and the parameters of Garc´ıa et al.(4) The resulting values of Ni j and 1Ni j are shown in table 5. For (an alkyl carbonate + an aromatic hydrocarbon) the contact numbers cannot be obtained because there are no published parameters. Figure 2 shows how the VmE values increase with temperature for (dimethyl, or diethyl carbonate + toluene) at x = 0.5. It can be also observed that the change in VmE with the temperature is more important for (dimethyl carbonate + toluene). TEMPERATURE DEPENDENCE OF THE EXCESS VOLUMES AND PRESSURE DEPENDENCE OF THE EXCESS ENTHALPIES
The values of (∂ VmE /∂ T ) p of (dimethyl carbonate + toluene) and (diethyl carbonate + toluene) were obtained by analytical derivation of equation (2). Figures 3a and b show that (∂ VmE /∂ T ) p is positive in all cases and decreases with increase in the chain of the organic carbonate. In addition, for (dimethyl carbonate + toluene) the curves present a unique maximum although when the temperature decreases the curves’ shapes become flat. In the case of diethyl carbonate, (∂ VmE /∂ T ) p presents a double maximum. Figure 3 also shows that (∂ VmE /∂ T ) p increases when the temperature increases for (dimethyl carbonate + toluene) and when the temperature decreases in the case of (diethyl carbonate + toluene). Figure 4 shows the pressure dependence of the excess enthalpies determined from the excess volumes by using the equation: (∂ HmE /∂ p)T = VmE − T (∂ VmE /∂ T ) p .
(3)
(∂ VmE /∂ T ) p
are both positive for all
For (dimethyl carbonate + toluene)
VmE
and
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
0.5
a
2
103(∂VmE/∂T )p /(cm3 · mol–1 · K–1)
103(∂VmE/∂T )p /(cm3 · mol–1 · K–1)
2.5
T = 318.15 K
1.5
T = 308.15 K
1
T = 298.15 K
0.5
T = 288.15 K
751
b
0.4 0.3 T = 298.15 K
0.2 T = 308.15 K
0.1 T = 318.15 K
0
0 0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
x
0.6
0.8
1
x
FIGURE 3. (∂ VmE /∂ T ) p against the mole fraction x for: a, {(1 − x)(CH3 O)2 CO + xC7 H8 }; and b, {(1 − x)(C2 H5 O)2 CO + xC7 H8 } at different temperatures T . 0.2
0
a
b
E /∂p) /(J · MPa–1) (∂Hm T
E /∂p) /(J · MPa–1) (∂Hm T
T = 288.15 K
0 T = 298.15 K
T = 308.15 K
–0.2
T = 318.15 K
–0.04 T = 318.15 K
–0.08 T = 308.15 K
–0.12 T = 298.15 K
–0.4 –0.16
–0.6 0
0.2
0.6
0.4 x
0.8
1
–0.2 0
0.2
0.4
0.6
0.8
1
x
E /∂ p) against the mole fraction x for: a, {(1 − x)(CH O) CO + xC H }; and FIGURE 4. (∂ Hm 7 8 T 3 2 b, {(1 − x)(C2 H5 O)2 CO + xC7 H8 } at different temperatures T .
temperatures and of similar magnitude. As a consequence (∂ HmE /∂ p)T is small and its sign depends on the composition and temperature. This fact implies that a little change in the VmE fitting equation can cause a relatively strong variation in (∂ HmE /∂ p)T . However, for (diethyl carbonate + toluene), VmE is negative and T (∂ VmE /∂ T ) p is positive, which implies that
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1.25
a
b
x=0
1.3
x = 0.25
x=0
1.20
x = 0.25
1.2 x = 0.75 x=1
103 α /K–1
103 α /K–1
x = 0.50
1.1
1.0 280
x = 0.50
1.15
x = 0.75 x=1
1.10
290
300 310 T /K
320
330
1.05 290
300
310 T /K
320
330
FIGURE 5. Cubic expansion coefficients α for the pure liquids and for the mixtures: a, {(1 − x)(CH3 O)2 CO + xC7 H8 }; and b, {(1 − x)(C2 H5 O)2 CO + xC7 H8 } as a function of temperature T and the mole fraction x. , this work; , Sun et al.(25)
(∂ HmE /∂ p)T is negative. For both systems we conclude that the excess enthalpies change slightly with pressure within the studied temperature range. Bhattacharyya and Patterson(31) and Costas et al.(32) have suggested that the properties (∂ VmE /∂ T ) p and (∂ HmE /∂ p)T can be employed as indicators of changes of order in a solution. A destruction of order during mixing implies a negative contribution to (∂ VmE /∂ T ) p and a positive contribution to VmE , HmE and (∂ HmE /∂ p)T . In the present case for both systems (∂ VmE /∂ T ) p is positive and is larger for the system containing dimethyl carbonate. It is interesting to note that for (diethyl carbonate + toluene) all the properties, VmE , HmE , (∂ VmE /∂ T ) p and (∂ HmE /∂ p)T have very small values. This means that this system behaves as almost ideal due to a compensation of opposite effects. For (dimethyl carbonate + toluene) all these properties are higher except (∂ HmE /∂ p)T . CUBIC EXPANSION COEFFICIENTS
Figure 5 shows the cubic expansion coefficients α for the mixtures investigated at several mole fractions and temperatures. We can see that α increases with the temperature and decreases when the mole fraction of the toluene increases. Furthermore, a diminution of α is observed when the length of the organic carbonate chain increases as for HmE , and VmE . The excess cubic expansion coefficient α E , is obtained by subtracting from the observed value of α of the mixture the ideal value α id given by: α id = ϕ1 α1∗ + ϕ2 α2∗ ,
(4)
where the ∗ refers to the pure substance, and the volume fraction ϕi is given by: ∗ ϕi = xi Vm,i /Vmid ,
(5)
Molar volumes of (dimethyl carbonate, or diethyl carbonate + toluene)
753
and ∗ ∗ Vmid = x1 Vm,1 + x2 Vm,2 .
(6)
The excess cubic expansion coefficient α E is given by: α E = {(∂ VmE /∂ T ) p − VmE α id }/(Vmid + VmE ).
(7)
For (dimethyl carbonate + toluene) at T = 318.15 K, α E is positive up to 1.9·10−5 K−1 , and for (diethyl carbonate + toluene) it is also positive and an order of magnitude lower. For the first system α E increases when the temperature increases, whereas for the second the opposite occurs, and similarly for (∂ VmE /∂ T ) p . This work was carried out under the CICYT QUI98-1071-C02-01 Research Project-Spain. The authors wish to express their gratitude to Miss Silvia Miramontes for her experimental assistance. REFERENCES 1. Takahata, K.; Tanaka, M.; Hayashi, T.; Sakamoto, N. Proceedings of 1994 International Refrigeration Conference at Purdue. Purdue University, W. Lafayette, IN, USA. 1994, 141–146. 2. Hayashi, T.; Tanaka, M.; Takeuchi, K.; Takahata, K.; Sakamoto, N. Proceedings of 1996 International Refrigeration Conference at Purdue. Purdue University, W. Lafayette, IN, USA. 1996, 285–290. 3. Garc´ıa, J.; L´opez, E. R.; Fern´andez, J.; Legido, J. L. Thermochim. Acta 1996, 286, 321–332. 4. Garc´ıa, J.; Lugo, L.; Comu˜nas, M. J.; L´opez, E. R.; Fern´andez, J. J. Chem. Soc. Faraday Trans. 1998, 94, 1707–1712. 5. Dang, D.; Tassios, P. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 22–31. 6. Larsen, B. L.; Rasmussen, P.; Fredenslund, A. Ind. Eng. Chem. Res. 1987, 26, 2274–2286. 7. Gmehling, J.; Li, J.; Schiller, M. Ind. Eng. Chem. Res. 1993, 32, 178–193. 8. Nitta, T.; Turck, E. A.; Greenkorn, R. A.; Chao, K. C. AIChE. J. 1977, 23, 144–160. 9. Cocero, M. J.; Mato, F.; Garc´ıa, I.; Cobos, J. C.; Kehiaian, H. V. J. Chem. Eng. Data 1989, 34, 73–76. 10. Cocero, M. J.; Mato, F.; Garc´ıa, I.; Cobos, J. C.; Kehiaian, H. V. J. Chem. Eng. Data 1989, 34, 443–445. 11. Cocero, M. J.; Gonz´alez, J. A.; Garc´ıa, I.; Cobos, J. C.; Mato, F. Int. DATA Ser. Sel. Data Mixtures, Ser. A 1991, 112–129. 12. Negadi, L.; Blondel, A.; Mokbel, I.; Ait-Kaci, A.; Jose, J. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1993, 21, 169–194. 13. Garc´ıa, I.; Cobos, J. C.; Gonz´alez, J. A.; Casanova, C. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1987, 3, 164–173. 14. Garc´ıa, I.; Cobos, J. C.; Gonz´alez, J. A.; Casanova, C. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1987, 4, 245–253. 15. Garc´ıa, I.; Cobos, J. C.; Gonz´alez, J. A.; Casanova, C.; Cocero, M. J. J. Chem. Eng. Data 1988, 33, 423–426. 16. Garc´ıa de la Fuente, I.; Gonz´alez, J. A.; Cobos, J. C.; Casanova, C. J. Chem. Eng. Data 1992, 37, 535–537. 17. Garc´ıa de la Fuente, I.; Gonz´alez, J. A.; Cobos, J. C.; Casanova, C. J. Sol. Chem. 1995, 24, 827–835. 18. Orye, R. V.; Prausnitz, J. M. Trans. Faraday Soc. 1965, 61, 1338–1346. 19. Moumouzias, G.; Ritzoulis, G. J. Chem. Eng. Data 1992, 37, 482–483. 20. TRC Thermodynamics Tables, Texas A&M University,College Station, Table 23-2-(33.11000)d, Texas. 1994.
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21. Gamboa, I.; Tardajos, G.; D´ıaz Pe˜na, M.; Aicart, E. J. Chem. Thermodynamics 1986, 18, 885– 890. 22. Pardo, J. M.; Tovar, C. A.; Cerdeiri˜na, C. A.; Carballo, E.; Roman´ı, L. J. Chem. Thermodynamics 1999, 31, 787–796. 23. Gonzalez, J. A.; Garc´ıa, I.; Cobos, J. C.; Casanova, C. J. Chem. Eng. Data 1991, 36, 162–164. 24. Francesconi, R.; Comelli, F. J. Chem. Eng. Data 1997, 42, 45–48. 25. Sun, T. F.; Bominaar, S. A. R. C.; ten Seldam, C. A.; Biswas, S. N. Ber. Bunsen-Ges. Phys. Chem. 1991, 95, 696–704. 26. Marquardt, D. W. J. Soc. Indust. Appl. Math. 1963, 11, 431–441. 27. Shen, S.; Wang, Y.; Shi, J.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1990, 22, 387–392. 28. Grolier, J.-P. E.; Ballet, D.; Viallard, A. J. Chem. Thermodynamics 1974, 6, 895–908. 29. Jim´enez, E.; Roman´ı, L.; Wilhelm, E.; Roux-Desgranges, G.; Grolier, J.-P. E. J. Chem. Thermodynamics 1994, 26, 817–827. 30. Wilhelm, E.; Jim´enez, E.; Roux-Desgranges, G.; Grolier, J.-P. E. J. Sol. Chem. 1991, 20, 17–28. 31. Bhattacharyya, S. H.; Patterson, D. J. Chem. Soc. Faraday Trans. I 1985, 81, 375–385. 32. Costas, M.; Bhattacharyya, S. H.; Patterson, D. J. Chem. Soc. Faraday Trans. I 1985, 81, 387– 395. (Received 24 June 1999; in final form 10 December 1999)
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