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Thermodynamic properties of (an alkylbenzene + cyclohexane) at the temperature 298.15 K
M-3162 J. Chem. Thermodynamics 1995, 27, 1319–1328
Thermodynamic properties of (an alkylbenzene+ cyclohexane) at the temperature 298.15 K Shinya Fujii, Katsutoshi Tamura,a and Sachio Murakami Department of Chemistry, Faculty of Science, Osaka City University, 3-3-138 , Sugimoto, Sumiyoshi-ku, Osaka 558 Japan
(Received 6 June 1995) Excess enthalpies, excess heat capacities, densities, and speeds of sound of (ethylbenzene or propylbenzene or 1-methylethylbenzene+cyclohexane) were measured at the temperature 298.15 K. From these measurement, excess volumes, excess isentropic and isothermal compressibilities, and excess isochoric heat capacities were estimated. The excess values are compared with those for (toluene or benzene+cyclohexane). The excess enthalpies and excess volumes are positive and the excess isobaric and isochoric heat capacities are negative for all mixtures. The excess isothermal and isentropic compressibilities are positive along with positive excess volumes. Effects of excess thermal expansivities on isothermal compressibility and isochoric heat capacity are discussed. For these mixtures, the excess thermal expansivity seems to be sufficiently small to be neglected. 7 1995 Academic Press Limited
1. Introduction Alkyl substitution on benzene alters the properties of the aromatic molecule through the symmetry and the constituents on the surface of the molecule. Symmetry determines the molecular packing in the liquid, and the constituents of a molecule affect molecular interactions. Thermodynamic properties of (cyclohexane + an alkylbenzene), however, have hardly been studied except for (cyclohexane + toluene). In order to study the effects of alkyl substitution on benzene, the excess enthalpies, excess isobaric heat capacities, densities, and speeds of sound of (cyclohexane + ethylbenzene or propylbenzene or 1-methylethylbenzene) were measured at the temperature T = 298.15 K. Excess volumes, excess isentropic and isothermal compressibilities, and excess isochoric heat capacities were estimated from those measurements. The effect of excess values a E of thermal expansivity on the estimations of isothermal compressibility and isochoric heat capacity is discussed. It was, however, finally neglected, because it is as small as 10−6 K−1 for (toluene + cyclohexane) and (benzene + cyclohexane), and probably similarly small for (any other alkylbenzene+cyclohexane). a
Corresponding author.
0021–9614/95/121319+10 $12.00/0
7 1995 Academic Press Limited
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2. Experimental Alkylbenzenes and cyclohexane were fractionally distilled in a column of height 1 m or 1.2 m with ‘‘helipack’’. Mole fraction purities were q0.9995 by a g.l.c. and a Carl-Fisher method. Excess enthalpy H E was measured by a flow microcalorimeter (LKB10070). The precision is better than 20.003·H E. Excess isobaric heat capacity was measured by a home-made flow microcalorimeter. The precision is better than 20.01 J·mol−1 . Density r was measured by a vibrating-tube densimeter (Anton Paar, DMA602). The reproducibility is better than 23·10−6·r and the accuracy is restricted to 21·10−5·r as the limit of pycnometry. Speed of sound was measured by the sing-around method. The reproducibility is 20.1 m·s−1 and the accuracy better than 20.3 m·s−1 . The details of the measurements are described elsewhere.(1–4) TABLE 1. Physical properties of the component materials at T=298.15 K Property r/(g·cm−3 ) literature u/(m·s−1 ) Cp, m /(J·K−1·mol−1 ) 103·a/K−1 kS /TPa−1 kT /TPa−1 CV, m /(J·K−1·mol−1 ) a b
c-C6 H12
C6 H5C2 H5
0.77384 0.77389 a 1254.4 156.01 1.220 a 821.25 1128.6 113.6
0.86259 0.86253 a 1319.1 184.65 1.022 b 666.25 873.8 140.8
C6 H5CH2CH2CH3
C6 H5CH(CH3 )CH3
0.85771
0.85754 0.85743 a 1307.9 198.91 0.986 b 681.72 886.1 153.1
1321.0 214.19 1.02 b 668.17 871.9 164.1
Reference 5. Calculated from densities at two temperatures. TABLE 2. Excess molar enthalpies of the mixtures at T=298.15 K x
HmE J·mol−1
0.04998 0.09996 0.14994 0.19993 0.24992
118.6 224.1 313.1 387.4 446.6
0.02500 0.05000 0.10000 0.15000 0.20000
78.2 155.8 294.0 407.5 500.5
0.02500 0.05000 0.10000 0.15001 0.20001
73.9 141.5 261.7 354.3 427.1
x
HmE J·mol−1
x
HmE J·mol−1
xC6 H5C2 H5+(1−x)c-C6 H12 0.29991 491.8 0.54989 539.3 0.34990 524.5 0.59989 516.5 0.39989 545.0 0.64990 484.2 0.44989 553.8 0.69991 442.1 0.49989 551.7 0.74991 391.1 xC6 H5CH2CH2CH3+(1−x)c-C6 H12 0.25000 572.1 0.50000 688.1 0.30000 627.5 0.54996 668.4 0.35000 664.3 0.60000 637.8 0.40000 686.3 0.65000 594.1 0.45000 694.1 0.70000 539.9 xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 0.25001 477.8 0.50001 525.6 0.30001 513.3 0.55001 504.6 0.35001 533.6 0.60000 473.4 0.40001 542.4 0.65001 435.3 0.45001 539.6 0.70001 390.5
x
HmE J·mol−1
0.79993 0.84994 0.89862 0.94998 0.97499
330.2 260.9 184.8 94.5 47.4
0.75000 0.80000 0.85000 0.90000 0.95000
474.3 398.5 312.9 218.6 112.8
0.75001 0.80001 0.85001 0.97500
339.0 281.0 218.7 37.1
Properties of (an alkylbenzene+cyclohexane)
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The procedures for the estimation of excess isentropic and isothermal compressibilities and isochoric heat capacity are described elsewhere.(3)
3. Results and discussion The physical properties of the component materials are given in table 1. The properties of each component are very like one another and those of toluene except for heat capacities which correspond to molar mass. Excess molar enthalpies HmE obtained for the mixtures are given in table 2 and are plotted in figure 1 together with the curve calculated for them from the equation: X E=x(1−x)Si Ai (1−2x)i−1 ,
(1)
where X E is an excess function and x is mole fraction. The parameters Ai are estimated by a least-squares method and given in table 5. In figure 1, the smoothed curves for HmE s of (toluene+cyclohexane),(6) and (benzene+cyclohexane),(7) are also given for the sake of comparison. The substitution of an alkyl group on benzene tends to lower HmE at first and then to increase it with the chain length of the substituted alkyl group. The turning point seems to be an ethyl group. A branching effect corresponds to decrease of the chain length and thus HmE of {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 } is very close to that of {xC6 H5C2 H5 + (1−x)c-C6 H12 }. The alkyl group does not seem so much to cover over the aromatic part, even if it becomes longer.
FIGURE 1. Excess molar enthalpies at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3 + (1 − x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 }; ——, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, {xC6 H6+(1−x)c-C6 H12 }.
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FIGURE 2. Excess molar isobaric heat capacities at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3 + (1 − x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 }; ——, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, {xC6 H6+(1−x)c-C6 H12 }.
On the other hand, in the case of excess molar isobaric heat capacities Cp,E m , the substitution of an alkyl group on benzene tends to make it less negative, but alkylbenzenes are very like one another, as seen in figure 2 together with the benzene mixture reported by Tanaka(8) and the toluene one previously by us.(9) The observed values are given in table 3. Densities r and speeds of sound u observed for the mixtures are given in table 4, together with the excess volumes VmE , and excess isentropic compressibilities kSE calculated from them. The excess molar volumes of the mixtures lie in the sequence: benzene(4) q toluene(10) q ethylbenzene q propylbenzene q 1-methylethylbenzene, which are arranged along with the increase of the molar volume, as found in figure 3. The larger the molar volume is, VmE by mixing seems to be the less necessary because of excess ‘‘free volume’’ in the pure state. The ‘‘free volume’’ may be produced by the configurational contribution of a substituted chain. kSE s of the mixtures are positive and the more compressible according to the positive VmE . A branching effect corresponding to shortening of side chains is also found in figure 4. The excess isothermal compressibilities kTE and excess isochoric molar heat capacities E CV, m of the mixtures in table 4 are calculated from the isentropic compressibilities, volumes, isobaric heat capacities, and thermal expansivities of the mixtures. The thermal expansivity of a mixture is assumed to be the ideal value for the reason described below. kTE s are about 40 per cent larger than kSE s for each mixture, as shown in figure 5. The behaviour of kTE s is not essentially different from kSE s. Substitution of
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Properties of (an alkylbenzene+cyclohexane) TABLE 3. Excess molar isobaric heat capacities of the mixtures at T=298.15 K
x
Cp,E m J·K ·mol−1
0.02500 0.05000 0.09999 0.14999 0.19999 0.24998
−0.29 −0.44 −0.88 −1.28 −1.55 −1.77
0.02500 0.04999 0.09999 0.14999 0.19998 0.24998
−0.18 −0.41 −0.85 −1.19 −1.46 −1.68
0.02500 0.05000 0.09999 0.14999 0.19999
−0.21 −0.38 −0.77 −1.11 −1.28
−1
x
Cp,E m J·K ·mol−1 −1
x
Cp,E m J·K ·mol−1 −1
xC6 H5C2 H5+(1−x)c-C6 H12 0.29998 −1.95 0.59997 −2.16 0.34998 −2.08 0.64998 −2.02 0.39998 −2.19 0.69998 −1.86 0.44998 −2.23 0.74998 −1.73 0.49998 −2.23 0.79998 −1.51 0.54998 −2.19 0.84999 −1.23 xC6 H5CH2CH2CH3+(1−x)c-C6 H12 0.29998 −1.88 0.59997 −2.15 0.34997 −2.00 0.64997 −2.05 0.39998 −2.13 0.69998 −1.92 0.44997 −2.16 0.74998 −1.79 0.49997 −2.19 0.79998 −1.58 0.54997 −2.17 0.84999 −1.35 xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 0.29999 −1.70 0.54998 −2.02 0.34999 −1.81 0.59999 −1.97 0.39999 −1.93 0.64998 −1.92 0.44998 −1.99 0.69999 −1.82 0.49998 −2.03 0.74999 −1.80
x
Cp,E m J·K ·mol−1
0.89999 0.95000 0.97500
−0.87 −0.49 −0.28
0.89999 0.94999 0.97500
−1.02 −0.60 −0.38
0.79999 0.84999 0.89999 0.97500
−1.45 −1.25 −0.90 −0.29
−1
alkyl groups reduces kSE and kTE , according to restricted rotation because of a non-smooth sphere contrary to the smooth spherical benzene. The effect of chain length is large up to an ethyl group and the longer groups are similar to an ethyl group. CV,E ms are slightly less negative than the corresponding Cp,E ms, as found in figure 6. This means that any special interaction is formed in the mixtures.(11) Excess values of the thermal expansivity a E represented by a E={(1VmE /1T)p+VmE a id}/(Vmid+VmE ),
(2)
were neglected in the calculation of isothermal compressibility and isochoric molar heat capacity because they are about 10−6·K−1 (maximum: 3.9·10−6 K−1 ) for (toluene+cyclohexane)(10) which value causes only 2 TPa−1 on isothermal compressibility as seen in figure 5 and only 0.2 J·K−1·mol−1 on isochoric heat capacity as seen in figure 6. For (benzene+cyclohexane),(12) a E is also about 10−6 K−1 (maximum: 2.7·10−6 K−1 ) and its effects on isothermal compressibility and isochoric molar heat capacity is less than for (toluene+cyclohexane) in figures 5 and 6. These values are close to the experimental error though they seem large for excess values, and they hardly affect the shape and size of the excess curves. For the other alkylbenzenes, a Es are considered to be negligible (110−6 K−1 ) and using the ideal value for a of the mixture may be valid for non-polar mixtures.
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TABLE 4. Densities, speeds of sound, excess molar volumes, excess isentropic and isothermal compressibilities, and excess molar isochoric heat capacities of the mixtures at T=298.15 K x
r g·cm−3
0 0.01374 0.05019 0.09928 0.15076 0.19968 0.25089 0.30203 0.35112 0.40050 0.44261 0.55089 0.60050 0.64835 0.70408 1 0 0.50010 0.70370 0.75055 0.80037 0.85088 0.90018 0.95555 0.97498 1
0.773847 0.774965 0.777948 0.782022 0.786379 0.790606 0.795077 0.799598 0.803954 0.808380 0.812191 0.821961 0.826468 0.830821 0.835875 0.862592 0.773838 0.817322 0.835802 0.840047 0.844558 0.849144 0.853579 0.858591 0.860338 0.862583
0 0.02571 0.04226 0.10862 0.15221 0.19925 0.25086 0.30286 0.35222 0.40032 0.45061 0.49965 0.55201 0.60049 0.65024 0.69887 0.75093 0.80308 0.84910 0.89928 0.95018 1
0.783838 0.776144 0.777639 0.783591 0.787529 0.791743 0.796368 0.800990 0.805327 0.809537 0.813902 0.818078 0.822495 0.826535 0.830604 0.834546 0.838709 0.842802 0.846370 0.850200 0.854049 0.857706
u m·s−1
VmE cm3·mol−1
kSE TPa−1
xC6 H5C2 H5+(1−x)c-C6 H12 1254.33 1254.34 0.0366 1.02 1254.56 0.1276 3.44 1255.32 0.2348 6.08 1256.70 0.3264 8.05 1258.41 0.3926 9.37 1260.61 0.4467 10.24 1263.14 0.4840 10.72 1265.77 0.5093 10.98 1268.72 0.5205 10.90 1271.44 0.5186 10.62 1279.12 0.4926 9.40 1282.80 0.4642 8.76 1286.56 0.4289 8.00 1291.19 0.3815 6.95 1319.18 1254.46 1275.37 0.5161 10.14 1291.20 0.3862 6.89 1295.24 0.3401 5.94 1299.71 0.2844 4.82 1304.35 0.2192 3.69 1309.07 0.1545 2.51 1314.57 0.0696 1.08 1316.51 0.0395 0.62 1319.05 xC6 H5CH2CH2CH3+(1−x)c-C6 H12 1254.38 1254.76 0.0638 1.62 1255.08 0.1006 2.54 1257.00 0.2330 5.42 1258.74 0.2977 6.64 1260.91 0.3568 7.58 1263.67 0.4027 8.11 1266.63 0.4351 8.45 1269.74 0.4557 8.43 1272.93 0.4620 8.24 1276.40 0.4573 7.89 1279.93 0.4490 7.46 1283.81 0.4293 6.90 1287.55 0.4033 6.27 1291.39 0.3735 5.67 1295.35 0.3355 4.89 1299.65 0.2882 4.05 1304.00 0.2376 3.22 1307.93 0.1873 2.43 1312.22 0.1287 1.62 1316.67 0.0613 0.72 1320.96
kTE TPa−1
E CV, m J·K−1·mol−1
1.4 4.8 8.4 11.2 13.1 14.4 15.2 15.6 15.6 15.2 13.7 12.8 11.7 10.2
−0.11 −0.37 −0.67 −0.95 −1.17 −1.37 −1.52 −1.63 −1.72 −1.76 −1.79 −1.75 −1.68 −1.57
14.6 10.2 8.8 7.2 5.6 3.8 1.7 1.0
−1.79 −1.57 −1.44 −1.26 −1.02 −0.75 −0.37 −0.21
2.2 3.5 7.6 9.5 10.9 11.8 12.4 12.5 12.3 11.9 11.3 10.5 9.7 8.8 7.8 6.6 5.3 4.2 2.9 1.4
−0.16 −0.27 −0.67 −0.91 −1.14 −1.36 −1.53 −1.65 −1.74 −1.80 −1.82 −1.82 −1.80 −1.74 −1.67 −1.56 −1.40 −1.20 −0.92 −0.53
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Properties of (an alkylbenzene+cyclohexane) TABLE 4—continued x
r g·cm−3
0 0.02471 0.04881 0.10295 0.13898 0.19552 0.21972 0.26138 0.29963 0.35053 0.40224 0.44326 0.50129 0.55787 0.63184 0.69787 0.79894 0.84097 0.85260 0.94405 0.97503 1
0.773812 0.776058 0.778235 0.783151 0.786406 0.791482 0.793687 0.797374 0.800783 0.805260 0.809767 0.813315 0.818269 0.822992 0.829131 0.834422 0.842403 0.845618 0.846514 0.853416 0.855705 0.857537
u m·s−1
VmE cm3·mol−1
kSE TPa−1
xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 1254.44 1254.38 0.0566 1.80 1254.50 0.1092 3.31 1255.14 0.2071 6.13 1255.95 0.2622 7.46 1257.60 0.3337 9.04 1258.45 0.3524 9.48 1260.09 0.3904 10.09 1261.68 0.4109 10.48 1264.11 0.4309 10.64 1266.76 0.4392 10.57 1269.01 0.4370 10.34 1272.44 0.4249 9.76 1275.84 0.4086 9.20 1280.71 0.3625 7.95 1285.18 0.3228 6.83 1292.45 0.2312 4.72 1295.55 0.1927 3.83 1296.42 0.1793 3.57 1303.49 0.0713 1.35 1305.92 0.0327 0.60 1307.89
kTE TPa−1
E CV, m J·K−1·mol−1
2.4 4.4 8.1 10.0 12.1 12.7 13.6 14.1 14.4 14.4 14.1 13.5 12.7 11.2 9.7 6.8 5.6 5.2 2.0 0.9
−0.15 −0.28 −0.55 −0.72 −0.94 −1.02 −1.15 −1.25 −1.37 −1.46 −1.52 −1.57 −1.59 −1.57 −1.49 −1.23 −1.06 −1.01 −0.46 −0.22
FIGURE 3. Excess molar volumes at T=298.15 K. w, {xC6 H5C2 H5 + (1 − x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3 + (1 − x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 }; ——, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, {xC6 H6+(1−x)c-C6 H12 }.
TABLE 5. Parameters of equation (1) for the excess functions of the mixtures at T=298.15 K A1
HmE /(J·mol−1 ) Cp,E m/(J·K−1·mol−1 ) VmE /(cm3·mol−1 ) kSE /TPa−1 kTE /TPa−1 E −1 ·mol−1 ) CV, m/(J·K
2209.0 −8.92 2.0461 40.45 58.4 −7.17
HmE /(J·mol−1 ) Cp,E m/(J·K−1·mol−1 ) VmE /(cm3·mol−1 ) kSE /TPa−1 kTE /TPa−1 E −1 ·mol−1 ) CV, m/(J·K
2753.6 −8.73 1.7973 29.85 45.2 −7.29
HmE /(J·mol−1 ) Cp,E m/(J·K−1·mol−1 ) VmE /(cm3·mol−1 ) kSE /TPa−1 kTE /TPa−1 E −1 CV, ·mol−1 ) m/(J·K
2105.0 −8.08 1.7084 39.28 54.0 −6.29
kTE /TPa−1 (a E=0) (a E$0) a E −1 CV, ·mol−1 ) (a E=0) m/(J·K (a E$0) a
90.3 90.3 −5.03 −5.04
kTE /TPa−1 (a E=0) (a E$0) b E −1 CV, /(J·K ·mol−1 ) (a E=0) m (a E$0) b
133.8 128.1 −7.73 −7.22
a
A2
A3
A4
xC6 H5C2 H5+(1−x)c-C6 H12 295.6 82.8 −0.26 −1.59 0.5719 0.1857 21.59 11.19 5.26 30.2 14.9 0.43 −1.19 xC6 H5CH2CH2CH3+(1−x)c-C6 H12 521.8 140.8 −0.08 −2.36 2.33 0.6065 0.1850 19.87 11.25 7.19 28.4 16.1 0.48 −1.94 2.46 xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 744.5 290.8 0.95 −2.00 0.5447 0.1863 20.99 11.28 5.47 28.1 15.5 1.42 −1.44 xC6 H5CH3+(1−x)c-C6 H12 (10) 29.1 10.4 34.2 33.5 0.67 −0.65 0.22 −3.18 xC6 H6+(1−x)c-C6 H12 (4) 5.2 9.8 7.3 1.19 −0.46 0.74 −0.98
s
0.8 0.03 0.0019 0.04 0.1 0.005 1.4 0.03 0.0017 0.03 0.09 0.003 1.6 0.04 0.0020 0.04 0.1 0.004
Calculated by using values from reference 10. b Calculated by using values from reference 12.
FIGURE 4. Excess isentropic compressibilities at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3 + (1 − x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 }; ——, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, {xC6 H6+(1−x)c-C6 H12 }.
Properties of (an alkylbenzene+cyclohexane)
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FIGURE 5. Excess isothermal compressibilities at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3+(1−x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 }; ——, a E=0 and – – – –, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, a E=0 and —-—, a E$0,(12) {xC6 H6 + a E$0,(10) (1−x)c-C6 H12 }.
FIGURE 6. Excess molar isochoric heat capacities at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3+(1−x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 }; ——, a E=0 and — – —, a E$0,(10) {xC6 H5CH3+(1−x)c-C6 H12 }; — —, a E=0 and — – – —, a E$0,(12) {xC6 H6 + (1−x)c-C6 H12 }.
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Fujihara, I.; Kobayashi, M.; Murakami, S. J. Chem. Thermodynamics 1983, 15, 1. Ogawa, H.; Murakami, S. Thermochim. Acta 1985, 88, 255. Miyanaga, S.; Tamura, K.; Murakami, S. J. Chem. Thermodynamics 1992, 24, 1077. Tamura, K.; Ohmuro, K.; Murakami, S. J. Chem. Thermodynamics 1983, 15, 859. Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents, 4th edition. Wiley-Interscience: N. Y. 1986.
1328 6. 7. 8. 9. 10. 11. 12.
Properties of (an alkylbenzene+cyclohexane)
Hsu, K.-Y.; Clever, H. L. J. Chem. Thermodynamics 1975, 7, 435. Van Ness, H. C.; Abbott, M. M. Internat. DATA Series, Selec. DATA mixture Ser. A 1974 (3), 160. Tanaka, R. J. Chem. Thermodynamics 1982, 14, 259. Fujii, S.; Tamura, K.; Murakami, S. Thermochim. Acta 1995, 257, 1. Tamura, K.; Murakami, S.; Doi, S. J. Chem. Thermodynamics 1985, 17, 325. St. Romain, P. de; Tra Van, H.; Patterson, D. J. Chem. Soc., Faraday Trans. I 1979, 75, 1700 and 1708. Tamura, K.; Murakami, S. J. Chem. Thermodynamics 1984, 16, 33.
Thermodynamic properties of (an alkylbenzene+ cyclohexane) at the temperature 298.15 K Shinya Fujii, Katsutoshi Tamura,a and Sachio Murakami Department of Chemistry, Faculty of Science, Osaka City University, 3-3-138 , Sugimoto, Sumiyoshi-ku, Osaka 558 Japan
(Received 6 June 1995) Excess enthalpies, excess heat capacities, densities, and speeds of sound of (ethylbenzene or propylbenzene or 1-methylethylbenzene+cyclohexane) were measured at the temperature 298.15 K. From these measurement, excess volumes, excess isentropic and isothermal compressibilities, and excess isochoric heat capacities were estimated. The excess values are compared with those for (toluene or benzene+cyclohexane). The excess enthalpies and excess volumes are positive and the excess isobaric and isochoric heat capacities are negative for all mixtures. The excess isothermal and isentropic compressibilities are positive along with positive excess volumes. Effects of excess thermal expansivities on isothermal compressibility and isochoric heat capacity are discussed. For these mixtures, the excess thermal expansivity seems to be sufficiently small to be neglected. 7 1995 Academic Press Limited
1. Introduction Alkyl substitution on benzene alters the properties of the aromatic molecule through the symmetry and the constituents on the surface of the molecule. Symmetry determines the molecular packing in the liquid, and the constituents of a molecule affect molecular interactions. Thermodynamic properties of (cyclohexane + an alkylbenzene), however, have hardly been studied except for (cyclohexane + toluene). In order to study the effects of alkyl substitution on benzene, the excess enthalpies, excess isobaric heat capacities, densities, and speeds of sound of (cyclohexane + ethylbenzene or propylbenzene or 1-methylethylbenzene) were measured at the temperature T = 298.15 K. Excess volumes, excess isentropic and isothermal compressibilities, and excess isochoric heat capacities were estimated from those measurements. The effect of excess values a E of thermal expansivity on the estimations of isothermal compressibility and isochoric heat capacity is discussed. It was, however, finally neglected, because it is as small as 10−6 K−1 for (toluene + cyclohexane) and (benzene + cyclohexane), and probably similarly small for (any other alkylbenzene+cyclohexane). a
Corresponding author.
0021–9614/95/121319+10 $12.00/0
7 1995 Academic Press Limited
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2. Experimental Alkylbenzenes and cyclohexane were fractionally distilled in a column of height 1 m or 1.2 m with ‘‘helipack’’. Mole fraction purities were q0.9995 by a g.l.c. and a Carl-Fisher method. Excess enthalpy H E was measured by a flow microcalorimeter (LKB10070). The precision is better than 20.003·H E. Excess isobaric heat capacity was measured by a home-made flow microcalorimeter. The precision is better than 20.01 J·mol−1 . Density r was measured by a vibrating-tube densimeter (Anton Paar, DMA602). The reproducibility is better than 23·10−6·r and the accuracy is restricted to 21·10−5·r as the limit of pycnometry. Speed of sound was measured by the sing-around method. The reproducibility is 20.1 m·s−1 and the accuracy better than 20.3 m·s−1 . The details of the measurements are described elsewhere.(1–4) TABLE 1. Physical properties of the component materials at T=298.15 K Property r/(g·cm−3 ) literature u/(m·s−1 ) Cp, m /(J·K−1·mol−1 ) 103·a/K−1 kS /TPa−1 kT /TPa−1 CV, m /(J·K−1·mol−1 ) a b
c-C6 H12
C6 H5C2 H5
0.77384 0.77389 a 1254.4 156.01 1.220 a 821.25 1128.6 113.6
0.86259 0.86253 a 1319.1 184.65 1.022 b 666.25 873.8 140.8
C6 H5CH2CH2CH3
C6 H5CH(CH3 )CH3
0.85771
0.85754 0.85743 a 1307.9 198.91 0.986 b 681.72 886.1 153.1
1321.0 214.19 1.02 b 668.17 871.9 164.1
Reference 5. Calculated from densities at two temperatures. TABLE 2. Excess molar enthalpies of the mixtures at T=298.15 K x
HmE J·mol−1
0.04998 0.09996 0.14994 0.19993 0.24992
118.6 224.1 313.1 387.4 446.6
0.02500 0.05000 0.10000 0.15000 0.20000
78.2 155.8 294.0 407.5 500.5
0.02500 0.05000 0.10000 0.15001 0.20001
73.9 141.5 261.7 354.3 427.1
x
HmE J·mol−1
x
HmE J·mol−1
xC6 H5C2 H5+(1−x)c-C6 H12 0.29991 491.8 0.54989 539.3 0.34990 524.5 0.59989 516.5 0.39989 545.0 0.64990 484.2 0.44989 553.8 0.69991 442.1 0.49989 551.7 0.74991 391.1 xC6 H5CH2CH2CH3+(1−x)c-C6 H12 0.25000 572.1 0.50000 688.1 0.30000 627.5 0.54996 668.4 0.35000 664.3 0.60000 637.8 0.40000 686.3 0.65000 594.1 0.45000 694.1 0.70000 539.9 xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 0.25001 477.8 0.50001 525.6 0.30001 513.3 0.55001 504.6 0.35001 533.6 0.60000 473.4 0.40001 542.4 0.65001 435.3 0.45001 539.6 0.70001 390.5
x
HmE J·mol−1
0.79993 0.84994 0.89862 0.94998 0.97499
330.2 260.9 184.8 94.5 47.4
0.75000 0.80000 0.85000 0.90000 0.95000
474.3 398.5 312.9 218.6 112.8
0.75001 0.80001 0.85001 0.97500
339.0 281.0 218.7 37.1
Properties of (an alkylbenzene+cyclohexane)
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The procedures for the estimation of excess isentropic and isothermal compressibilities and isochoric heat capacity are described elsewhere.(3)
3. Results and discussion The physical properties of the component materials are given in table 1. The properties of each component are very like one another and those of toluene except for heat capacities which correspond to molar mass. Excess molar enthalpies HmE obtained for the mixtures are given in table 2 and are plotted in figure 1 together with the curve calculated for them from the equation: X E=x(1−x)Si Ai (1−2x)i−1 ,
(1)
where X E is an excess function and x is mole fraction. The parameters Ai are estimated by a least-squares method and given in table 5. In figure 1, the smoothed curves for HmE s of (toluene+cyclohexane),(6) and (benzene+cyclohexane),(7) are also given for the sake of comparison. The substitution of an alkyl group on benzene tends to lower HmE at first and then to increase it with the chain length of the substituted alkyl group. The turning point seems to be an ethyl group. A branching effect corresponds to decrease of the chain length and thus HmE of {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 } is very close to that of {xC6 H5C2 H5 + (1−x)c-C6 H12 }. The alkyl group does not seem so much to cover over the aromatic part, even if it becomes longer.
FIGURE 1. Excess molar enthalpies at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3 + (1 − x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 }; ——, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, {xC6 H6+(1−x)c-C6 H12 }.
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FIGURE 2. Excess molar isobaric heat capacities at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3 + (1 − x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 }; ——, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, {xC6 H6+(1−x)c-C6 H12 }.
On the other hand, in the case of excess molar isobaric heat capacities Cp,E m , the substitution of an alkyl group on benzene tends to make it less negative, but alkylbenzenes are very like one another, as seen in figure 2 together with the benzene mixture reported by Tanaka(8) and the toluene one previously by us.(9) The observed values are given in table 3. Densities r and speeds of sound u observed for the mixtures are given in table 4, together with the excess volumes VmE , and excess isentropic compressibilities kSE calculated from them. The excess molar volumes of the mixtures lie in the sequence: benzene(4) q toluene(10) q ethylbenzene q propylbenzene q 1-methylethylbenzene, which are arranged along with the increase of the molar volume, as found in figure 3. The larger the molar volume is, VmE by mixing seems to be the less necessary because of excess ‘‘free volume’’ in the pure state. The ‘‘free volume’’ may be produced by the configurational contribution of a substituted chain. kSE s of the mixtures are positive and the more compressible according to the positive VmE . A branching effect corresponding to shortening of side chains is also found in figure 4. The excess isothermal compressibilities kTE and excess isochoric molar heat capacities E CV, m of the mixtures in table 4 are calculated from the isentropic compressibilities, volumes, isobaric heat capacities, and thermal expansivities of the mixtures. The thermal expansivity of a mixture is assumed to be the ideal value for the reason described below. kTE s are about 40 per cent larger than kSE s for each mixture, as shown in figure 5. The behaviour of kTE s is not essentially different from kSE s. Substitution of
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Properties of (an alkylbenzene+cyclohexane) TABLE 3. Excess molar isobaric heat capacities of the mixtures at T=298.15 K
x
Cp,E m J·K ·mol−1
0.02500 0.05000 0.09999 0.14999 0.19999 0.24998
−0.29 −0.44 −0.88 −1.28 −1.55 −1.77
0.02500 0.04999 0.09999 0.14999 0.19998 0.24998
−0.18 −0.41 −0.85 −1.19 −1.46 −1.68
0.02500 0.05000 0.09999 0.14999 0.19999
−0.21 −0.38 −0.77 −1.11 −1.28
−1
x
Cp,E m J·K ·mol−1 −1
x
Cp,E m J·K ·mol−1 −1
xC6 H5C2 H5+(1−x)c-C6 H12 0.29998 −1.95 0.59997 −2.16 0.34998 −2.08 0.64998 −2.02 0.39998 −2.19 0.69998 −1.86 0.44998 −2.23 0.74998 −1.73 0.49998 −2.23 0.79998 −1.51 0.54998 −2.19 0.84999 −1.23 xC6 H5CH2CH2CH3+(1−x)c-C6 H12 0.29998 −1.88 0.59997 −2.15 0.34997 −2.00 0.64997 −2.05 0.39998 −2.13 0.69998 −1.92 0.44997 −2.16 0.74998 −1.79 0.49997 −2.19 0.79998 −1.58 0.54997 −2.17 0.84999 −1.35 xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 0.29999 −1.70 0.54998 −2.02 0.34999 −1.81 0.59999 −1.97 0.39999 −1.93 0.64998 −1.92 0.44998 −1.99 0.69999 −1.82 0.49998 −2.03 0.74999 −1.80
x
Cp,E m J·K ·mol−1
0.89999 0.95000 0.97500
−0.87 −0.49 −0.28
0.89999 0.94999 0.97500
−1.02 −0.60 −0.38
0.79999 0.84999 0.89999 0.97500
−1.45 −1.25 −0.90 −0.29
−1
alkyl groups reduces kSE and kTE , according to restricted rotation because of a non-smooth sphere contrary to the smooth spherical benzene. The effect of chain length is large up to an ethyl group and the longer groups are similar to an ethyl group. CV,E ms are slightly less negative than the corresponding Cp,E ms, as found in figure 6. This means that any special interaction is formed in the mixtures.(11) Excess values of the thermal expansivity a E represented by a E={(1VmE /1T)p+VmE a id}/(Vmid+VmE ),
(2)
were neglected in the calculation of isothermal compressibility and isochoric molar heat capacity because they are about 10−6·K−1 (maximum: 3.9·10−6 K−1 ) for (toluene+cyclohexane)(10) which value causes only 2 TPa−1 on isothermal compressibility as seen in figure 5 and only 0.2 J·K−1·mol−1 on isochoric heat capacity as seen in figure 6. For (benzene+cyclohexane),(12) a E is also about 10−6 K−1 (maximum: 2.7·10−6 K−1 ) and its effects on isothermal compressibility and isochoric molar heat capacity is less than for (toluene+cyclohexane) in figures 5 and 6. These values are close to the experimental error though they seem large for excess values, and they hardly affect the shape and size of the excess curves. For the other alkylbenzenes, a Es are considered to be negligible (110−6 K−1 ) and using the ideal value for a of the mixture may be valid for non-polar mixtures.
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TABLE 4. Densities, speeds of sound, excess molar volumes, excess isentropic and isothermal compressibilities, and excess molar isochoric heat capacities of the mixtures at T=298.15 K x
r g·cm−3
0 0.01374 0.05019 0.09928 0.15076 0.19968 0.25089 0.30203 0.35112 0.40050 0.44261 0.55089 0.60050 0.64835 0.70408 1 0 0.50010 0.70370 0.75055 0.80037 0.85088 0.90018 0.95555 0.97498 1
0.773847 0.774965 0.777948 0.782022 0.786379 0.790606 0.795077 0.799598 0.803954 0.808380 0.812191 0.821961 0.826468 0.830821 0.835875 0.862592 0.773838 0.817322 0.835802 0.840047 0.844558 0.849144 0.853579 0.858591 0.860338 0.862583
0 0.02571 0.04226 0.10862 0.15221 0.19925 0.25086 0.30286 0.35222 0.40032 0.45061 0.49965 0.55201 0.60049 0.65024 0.69887 0.75093 0.80308 0.84910 0.89928 0.95018 1
0.783838 0.776144 0.777639 0.783591 0.787529 0.791743 0.796368 0.800990 0.805327 0.809537 0.813902 0.818078 0.822495 0.826535 0.830604 0.834546 0.838709 0.842802 0.846370 0.850200 0.854049 0.857706
u m·s−1
VmE cm3·mol−1
kSE TPa−1
xC6 H5C2 H5+(1−x)c-C6 H12 1254.33 1254.34 0.0366 1.02 1254.56 0.1276 3.44 1255.32 0.2348 6.08 1256.70 0.3264 8.05 1258.41 0.3926 9.37 1260.61 0.4467 10.24 1263.14 0.4840 10.72 1265.77 0.5093 10.98 1268.72 0.5205 10.90 1271.44 0.5186 10.62 1279.12 0.4926 9.40 1282.80 0.4642 8.76 1286.56 0.4289 8.00 1291.19 0.3815 6.95 1319.18 1254.46 1275.37 0.5161 10.14 1291.20 0.3862 6.89 1295.24 0.3401 5.94 1299.71 0.2844 4.82 1304.35 0.2192 3.69 1309.07 0.1545 2.51 1314.57 0.0696 1.08 1316.51 0.0395 0.62 1319.05 xC6 H5CH2CH2CH3+(1−x)c-C6 H12 1254.38 1254.76 0.0638 1.62 1255.08 0.1006 2.54 1257.00 0.2330 5.42 1258.74 0.2977 6.64 1260.91 0.3568 7.58 1263.67 0.4027 8.11 1266.63 0.4351 8.45 1269.74 0.4557 8.43 1272.93 0.4620 8.24 1276.40 0.4573 7.89 1279.93 0.4490 7.46 1283.81 0.4293 6.90 1287.55 0.4033 6.27 1291.39 0.3735 5.67 1295.35 0.3355 4.89 1299.65 0.2882 4.05 1304.00 0.2376 3.22 1307.93 0.1873 2.43 1312.22 0.1287 1.62 1316.67 0.0613 0.72 1320.96
kTE TPa−1
E CV, m J·K−1·mol−1
1.4 4.8 8.4 11.2 13.1 14.4 15.2 15.6 15.6 15.2 13.7 12.8 11.7 10.2
−0.11 −0.37 −0.67 −0.95 −1.17 −1.37 −1.52 −1.63 −1.72 −1.76 −1.79 −1.75 −1.68 −1.57
14.6 10.2 8.8 7.2 5.6 3.8 1.7 1.0
−1.79 −1.57 −1.44 −1.26 −1.02 −0.75 −0.37 −0.21
2.2 3.5 7.6 9.5 10.9 11.8 12.4 12.5 12.3 11.9 11.3 10.5 9.7 8.8 7.8 6.6 5.3 4.2 2.9 1.4
−0.16 −0.27 −0.67 −0.91 −1.14 −1.36 −1.53 −1.65 −1.74 −1.80 −1.82 −1.82 −1.80 −1.74 −1.67 −1.56 −1.40 −1.20 −0.92 −0.53
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Properties of (an alkylbenzene+cyclohexane) TABLE 4—continued x
r g·cm−3
0 0.02471 0.04881 0.10295 0.13898 0.19552 0.21972 0.26138 0.29963 0.35053 0.40224 0.44326 0.50129 0.55787 0.63184 0.69787 0.79894 0.84097 0.85260 0.94405 0.97503 1
0.773812 0.776058 0.778235 0.783151 0.786406 0.791482 0.793687 0.797374 0.800783 0.805260 0.809767 0.813315 0.818269 0.822992 0.829131 0.834422 0.842403 0.845618 0.846514 0.853416 0.855705 0.857537
u m·s−1
VmE cm3·mol−1
kSE TPa−1
xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 1254.44 1254.38 0.0566 1.80 1254.50 0.1092 3.31 1255.14 0.2071 6.13 1255.95 0.2622 7.46 1257.60 0.3337 9.04 1258.45 0.3524 9.48 1260.09 0.3904 10.09 1261.68 0.4109 10.48 1264.11 0.4309 10.64 1266.76 0.4392 10.57 1269.01 0.4370 10.34 1272.44 0.4249 9.76 1275.84 0.4086 9.20 1280.71 0.3625 7.95 1285.18 0.3228 6.83 1292.45 0.2312 4.72 1295.55 0.1927 3.83 1296.42 0.1793 3.57 1303.49 0.0713 1.35 1305.92 0.0327 0.60 1307.89
kTE TPa−1
E CV, m J·K−1·mol−1
2.4 4.4 8.1 10.0 12.1 12.7 13.6 14.1 14.4 14.4 14.1 13.5 12.7 11.2 9.7 6.8 5.6 5.2 2.0 0.9
−0.15 −0.28 −0.55 −0.72 −0.94 −1.02 −1.15 −1.25 −1.37 −1.46 −1.52 −1.57 −1.59 −1.57 −1.49 −1.23 −1.06 −1.01 −0.46 −0.22
FIGURE 3. Excess molar volumes at T=298.15 K. w, {xC6 H5C2 H5 + (1 − x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3 + (1 − x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 }; ——, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, {xC6 H6+(1−x)c-C6 H12 }.
TABLE 5. Parameters of equation (1) for the excess functions of the mixtures at T=298.15 K A1
HmE /(J·mol−1 ) Cp,E m/(J·K−1·mol−1 ) VmE /(cm3·mol−1 ) kSE /TPa−1 kTE /TPa−1 E −1 ·mol−1 ) CV, m/(J·K
2209.0 −8.92 2.0461 40.45 58.4 −7.17
HmE /(J·mol−1 ) Cp,E m/(J·K−1·mol−1 ) VmE /(cm3·mol−1 ) kSE /TPa−1 kTE /TPa−1 E −1 ·mol−1 ) CV, m/(J·K
2753.6 −8.73 1.7973 29.85 45.2 −7.29
HmE /(J·mol−1 ) Cp,E m/(J·K−1·mol−1 ) VmE /(cm3·mol−1 ) kSE /TPa−1 kTE /TPa−1 E −1 CV, ·mol−1 ) m/(J·K
2105.0 −8.08 1.7084 39.28 54.0 −6.29
kTE /TPa−1 (a E=0) (a E$0) a E −1 CV, ·mol−1 ) (a E=0) m/(J·K (a E$0) a
90.3 90.3 −5.03 −5.04
kTE /TPa−1 (a E=0) (a E$0) b E −1 CV, /(J·K ·mol−1 ) (a E=0) m (a E$0) b
133.8 128.1 −7.73 −7.22
a
A2
A3
A4
xC6 H5C2 H5+(1−x)c-C6 H12 295.6 82.8 −0.26 −1.59 0.5719 0.1857 21.59 11.19 5.26 30.2 14.9 0.43 −1.19 xC6 H5CH2CH2CH3+(1−x)c-C6 H12 521.8 140.8 −0.08 −2.36 2.33 0.6065 0.1850 19.87 11.25 7.19 28.4 16.1 0.48 −1.94 2.46 xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 744.5 290.8 0.95 −2.00 0.5447 0.1863 20.99 11.28 5.47 28.1 15.5 1.42 −1.44 xC6 H5CH3+(1−x)c-C6 H12 (10) 29.1 10.4 34.2 33.5 0.67 −0.65 0.22 −3.18 xC6 H6+(1−x)c-C6 H12 (4) 5.2 9.8 7.3 1.19 −0.46 0.74 −0.98
s
0.8 0.03 0.0019 0.04 0.1 0.005 1.4 0.03 0.0017 0.03 0.09 0.003 1.6 0.04 0.0020 0.04 0.1 0.004
Calculated by using values from reference 10. b Calculated by using values from reference 12.
FIGURE 4. Excess isentropic compressibilities at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3 + (1 − x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3 + (1 − x)c-C6 H12 }; ——, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, {xC6 H6+(1−x)c-C6 H12 }.
Properties of (an alkylbenzene+cyclohexane)
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FIGURE 5. Excess isothermal compressibilities at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3+(1−x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 }; ——, a E=0 and – – – –, {xC6 H5CH3+(1−x)c-C6 H12 }; — —, a E=0 and —-—, a E$0,(12) {xC6 H6 + a E$0,(10) (1−x)c-C6 H12 }.
FIGURE 6. Excess molar isochoric heat capacities at T=298.15 K. w, {xC6 H5C2 H5+(1−x)c-C6 H12 }; q, {xC6 H5CH2CH2CH3+(1−x)c-C6 H12 }; r, {xC6 H5CH(CH3 )CH3+(1−x)c-C6 H12 }; ——, a E=0 and — – —, a E$0,(10) {xC6 H5CH3+(1−x)c-C6 H12 }; — —, a E=0 and — – – —, a E$0,(12) {xC6 H6 + (1−x)c-C6 H12 }.
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Fujihara, I.; Kobayashi, M.; Murakami, S. J. Chem. Thermodynamics 1983, 15, 1. Ogawa, H.; Murakami, S. Thermochim. Acta 1985, 88, 255. Miyanaga, S.; Tamura, K.; Murakami, S. J. Chem. Thermodynamics 1992, 24, 1077. Tamura, K.; Ohmuro, K.; Murakami, S. J. Chem. Thermodynamics 1983, 15, 859. Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents, 4th edition. Wiley-Interscience: N. Y. 1986.
1328 6. 7. 8. 9. 10. 11. 12.
Properties of (an alkylbenzene+cyclohexane)
Hsu, K.-Y.; Clever, H. L. J. Chem. Thermodynamics 1975, 7, 435. Van Ness, H. C.; Abbott, M. M. Internat. DATA Series, Selec. DATA mixture Ser. A 1974 (3), 160. Tanaka, R. J. Chem. Thermodynamics 1982, 14, 259. Fujii, S.; Tamura, K.; Murakami, S. Thermochim. Acta 1995, 257, 1. Tamura, K.; Murakami, S.; Doi, S. J. Chem. Thermodynamics 1985, 17, 325. St. Romain, P. de; Tra Van, H.; Patterson, D. J. Chem. Soc., Faraday Trans. I 1979, 75, 1700 and 1708. Tamura, K.; Murakami, S. J. Chem. Thermodynamics 1984, 16, 33.