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Ultrasonic speeds and thermodynamic properties of (benzene + nitrobenzene) under high pressures
M-1429 J.
Chem. Thermodynamics 1982, 14, 1167-l 173
Ultrasonic speeds and thermodynamic properties of (benzene + nitrobenzene) under high pressures TOSHIHARU
TAKAGI
and HIROSHI
Department of Chemistry, Kyoto Technical Matsugasaki, Kyoto 606. Japan (Received 30 March
TERANISHI University.
1982; in revised form I June 1982)
Ultrasonic speeds u in ((1 -x)C,H, + xC,H,NO,] were measured by a fixed-path pulse technique at 293.15, 303.15, and 313.15 K under pressures up to 30 or 200 MPa with an observed error of less than 0.3 per cent. Curves of u(x) change smoothly in the benzene-rich region. But near x = 0.7, u(x) apparently deviates from a smooth curve, and the apparent gap becomes progressively greater as the temperature is reduced or the pressure is raised. From the experimental values, densities, isentropic compressibilities, and expansivities were calculated at high pressures. These quantities also show unusual behavior with x similar to that of u.
1. Introduction Mixtures of (nitrobenzene + another substance) often show interesting behavior, and so are frequently used for investigations of molecular structure.t’*2’ However, unexpectedly the thermodynamic properties of binary mixtures including nitrobenzene have scarcely been reported. We have measured the ultrasonic speed in various mixtures of (benzene + another organic substance) under high pressures, and have reported the composition or pressure effect on some thermodynamic properties of the mixtures in the previous papers. 13-6’ In this paper, the ultrasonic speed in (benzene + nitrobenzene) at temperatures between 293.15 and 313.15 K and pressures up to 30 or 200 MPa were measured, and derived high-pressure thermodynamic properties are discussed. 2. Experimental Pure liquids used were reagent-grade materials supplied by Wako Pure Chemicals Industriais. The compositions of the mixtures were determined by weighing, and the accuracy of the mole fraction was better than +0.0003. The densities for mixtures thus obtained were measured with an Ostwald pyknometer (about 20 cm3) at every 5 K from 283.15 to 323.15 K, and the results were in reasonable agreements with those observed previously. (‘) The method used for measurement of ultrasonic speed was a pulse-echo technique of fixed-path type at a frequency of 1 MHz and was 0021-9614/82/121167+07
$02.00/O
0 1982 Academic Press Inc. (London) Limited
1168
T. TAKAGI
t\ND
H. TERANISHI
similar to that described previously. ‘s’ The measurements were made at pressures up to 30 MPa for temperatures of 293.15 and 313.15 K, and up to 200 MPa for 303.15 K. For lower pressures the speeds were determined at narrower pressure intervals than at higher pressures. The error of the measurements was always less than 0.3 per cent.
3. Results and discussion The experimental ultrasonic speeds u at various mole fraction x in {(l-x)C,H,+xC,H,NO,) at temperatures of 293.15, 303.15, and 313.15 K are listed in table 1. The present values for pure components at atmospheric pressure closely coincide with the results reported in the literatures, as ascertained for benzene in previous papers,‘5*6’ and for nitrobenzene as summarized in the footnotes to table 1. Figure 1 shows u(x) at constant pressure; the behavior is peculiar near x = 0.7. In particular, at 303.15 K and atmospheric pressure, as shown in figure l(b), the values increase smoothly on a convex curve in the composition range from x = 0 to about x = 0.7. But at x z 0.7 the values deviate from the smooth curve. Gabrielli and Poiani’r3’ observed the speeds in (benzene + nitrobenzene) at 298.15 K, and
TABLE
293.15
1.
0
0.2
0.4
0.6
0.8
1
303.15
0
0.2
Values
of
ultrasonic
speeds U, [Cl -x)C,H,
densities p, + xC,H,NOZ;
P
u
I’
MPa
rn.s-’
kg.rne3
and
isentropic
h’s TPa-’
.-
0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0
1321.7 1345.9 1369.9 1353.9 1374.0 1394.7 1380.9 1399.7 1417.4 1407.8 1424.0 1441.0 1439.1 1453.9 1469.4 1471.6 1486.7 1502.4
879.2 883.1 886.9 954.6 958.3 962.0 1024.2 1027.7 1031.1 1096.5. 1099.8 1103.1 1147.8 1150.9 1153.9 1203.1 1206.0 1208.9
651.1 625.1 600.8 571.5 552.7 534.4 512.0 496.7 482.7 460.2 448.4 436.6 420.7 411.0 401.4 383.8 375.1 366.5
15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0
1391.3 1411.0 1429.4 1314.3 1434.4 1452.9 1436.4 1452.6 1469.9 1457.7 1475.0 1491.0 1484.3 1499.2 1511.4 1518.4 1534.6 1551.1
890.7 894.3 897.7 965.5 969.0 972.4 1034.4 1037.7 1040.9 1106.3 1109.4 1112.4 1156.9 1159.9 1162.7 1211.7 1214.4 1217.1
580.0 561.7 545.2 517.8 501.6 487.2 468.6 456.7 444.7 425.4 414.3 404.4 392.3 383.6 376.5 358.0 349.7 341.5
0.1 5.0 10.0 15.0 20.0 0.1 5.0
1271.1 1300.4 1327.4 1347.6 1370.3 1309.0 1329.6
868.5 872.7 876.8 880.7 884.6 945.8 949.7
712.6 677.7 647.3 625.2 602.0 617.0 595.6
25.0 1390.1 30.0 1408.6 40.0 1448.6 50.0 1487.6 60.0 1524.9 30.0 1427.4 40.0 1464.9
888.3 891.8 898.6 905.0 911.1 967.6 974.0
582.6 565.1 530.3 499.3 472.0 507.2 478.4
P -
MPa 30.0
compressibilities
11 rn.s-’
I’ kg.m-3
~~
h-s TPa-’
1452.1
901.1
526.3
30.0 1470.9
975.6
473.7
30.0
1485.9
1044.0
433.9
30.0
1406.7
1115.4
394.9
30.0
1522.9
1165.5
369.9
30.0
1567.8
1219.8
333.5
70.0 1560.7 80.0 1587.6 90.0 1612.2
916.4 922.3 927.5
447.8 430.1 414.8
1002.2 1007.1
382.0 367.2
90.0 100.0
1616.2 1644.4
for
(BENZENE
+ NITROBENZENE) TABLE
T ii
-x
0.4
0.6
0.8
1
313.15 0
0.2
0.4
0.6
0.8
1
P MPa
u rn,s-’
P kg,me3
AT
HIGH
1169
PRESSURES
1 ~-continued
KS TPa-’
10.0 15.0 20.0 25.0 0.1 5.0 10.0 15.0 20.0 25.0 30.0 40.0 0.1 5.0 10.0 15.0 20.0 25.0 30.0 40.0 0.1 5.0 10.0 15.0 20.0 25.0 30.0 0.1 5.0 10.0 15.0 20.0
1351.4 1371.0 1392.9 1410.5 1342.2 1360.6 1379.4 1398.4 1413.3 1433.1 1449.2 1484.4 13444 1390.7 1407.6 1422.9 1439.7 1455.6 1471.7 1502.5 1399.3 1419.7 1436.6 1454.8 1467.0 1482.1 1493.9 1438.1 1453.8 1470.1 1486.7 1503.7
953.5 957.1 960.7 964.2 1013.9 1017.5 1021.1 1024.5 1027.9 1031.1 1034.3 1040.4 1085.7 1089.1 1092.5 1095.8 1099.1 1102.2 1105.3 1111.3 1136.9 1140.1 1143.3 1146.4 1149.4 1152.4 1155.3 1193.9 1196.9 1199.9 1202.8 1205.7
574.2 555.8 536.4 521.3 547.4 530.9 514.7 499.2 487.1 472.2 460.4 436.2 487.5 474.7 461.9 450.7 438.9 428.2 417.7 398.6 449.2 435.2 423.8 412.2 404.2 395.0 387.8 405.0 395.3 385.6 376.1 366.8
50.0 60.0 70.0 80.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 25.0 30.0 40.0 50.0 60.0
1500.7 1530.7 1560.3 1588.1 1514.6 1545.4 1574.2 1598.8 1622.7 1649.2 1675.4 1699.1 1530.9 1559.9 1585.9 1609.4 1634.8 1659.9 1680.5 1705.1 1518.0 1543.2 1570.6 1599.0 1623.6 1646.1 1667.8 1520.9 153X.4 1554.8 1581.3 1606.7
980.2 986.1 991.7 997.0 1046.3 1051.9 1057.3 1062.4 1067.4 1072.2 1076.8 1081.3 1117.0 1122.5 1127.7 1132.8 1137.7 1142.4 1147.1 1151.5 1160.9 1166.4 1171.6 1176.6 1181.5 1186.2 1190.7 1208.5 1211.2 1216.6 1221.7 1226.7
453.0 432.9 414.2 397.7 416.7 398.1 381.7 368.2 355.8 342.9 330.9 320.3 382.0 366.1 352.5 340.8 328.9 317.7 308.7 298.7 373.8 360.0 346.0 332.4 321.1 311.1 301.9 357.7 348.X 340.0 327.4 315.8
0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0
1231.0 1259.4 1281.2 1267.1 1291.6 1314.7 1297.4 1319.2 1340.7 1337.2 1356.2 1374.8 1365.3 1383.9 1400.7 1403.2 1419.1 1435.6
857.8 862.3 866.7 935.4 939.4 943.3 1004.4 1008.1 1011.8 1076.5 1080.0 1083.6 1127.9 1131.2 1134.5 1182.2 1185.3 1188.4
769.3 731.2 702.9 665.9 638.1 613.3 591.5 569.9 549.8 519.4 503.4 488.3 475.7 461.5 449.2 429.6 418.9 408.3
15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0
1305.7 1331.5 1353.4 1335.X 1356.7 1386.4 1359.8 1387.8 1397.5 1392.8 1409.9 1423.9 1416.3 1434.4 1448.5 1452.5 1469.7 1487.2
870.9 874.9 878.8 947.2 950.9 954.4 1015.4 1018.9 1022.3 1376.9 1090.3 1093.6 1137.7 1140.9 1143.9 1191.4 1194.4 1197.3
673.5 644.7 621.2 591.7 571.4 552.6 532.6 509.6 500.8 474.2 461.4 451.0 438.2 426.0 416.6 397.8 387.6 377.6
Literature values of ultrasonic speeds. u/(m s- ’ ), in C,H,NO?: 1440.“” 1476,“*1 at 313.15 K 1409,“” 1405.“L’ - 1
at 293.15
f’ kg.rnm3
P MPa
u rn.s-’
110.0 120.0 130.0 140.0 130.0 140.0 150.0 160.0 170.0 180.0 190.0 200.0 130.0 140.0 150.0 160.0 170.0 180.0 190.0 200.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 70.0 80.0 90.0 100.0
1672.7 1698.2 1721.2 1743.3 1723.0 1742.2 1763.9 1786.8 1805.1 1823.8 1842.5 1860.9 1727.9 1749.8 1767.9 1789.1 1807.1 1826.0 1844.5 1862.7 1689.9 1708.1 1709.7 1747.6 1770.1 1789.5 1807.3 1631.1 1654.4 1676.7 1697.9
1011.8 1016.4 1020.8 1025.1 1085.6 1089.X 1093.9 1097.8 1101.6 1105.3 1108.9 1112.5 1155.8 1159.9 1164.0 1168.0 1171.X 1175.5 1179.2 1182.7 1195.2 1199.5 1203.6 1207.7 1211.6 1215.5 1219.2 1231.6 1236.2 1240.8 1245.2
30.0 1373.9
882.6
600.2
30.0
1397.2
957.9
534.x
30.0 1413.9
1025.6
4x7.7
30.0 1439.5
1096.8
440.0
30.0 1466.4
1146.9
405.5
30.0 1505.1
1200.2
367.X
K 1475.‘9’
1471:“”
KS TPa i 353.2 341.1 330.6 320.9 310.3 302.3 293.X 285.3 278.5 271.9 265.6 259.5 2X9.X 281.6 274.9 267.5 261.3 255.1 249.2 244.1 292.9 285.8 284.2 271.1 263.4 256.9 251.1 305.2 295.5 2X6.1 27X.6
at 303.15
K
1170
T. TAKAGI
13-
6-4 I
0
FIGURE
(a), 293.15;
I 0.5 x
AND
H. TERANISHI
-
I 1
0
0.5 x
1
1. Composition dependence of ultrasonic speeds u in {(I -x)C6H, (b), 303.15; (c). 313.15; p/MPa: O,O.l; a. 30; 0, 60; n , 298.15
x + xC,H,NO,). K, reference 13.
T/K
their experimental values, plotted as squares in figure l(b), show a similar behavior. With rise of pressure, the plotted line of the speed for the benzene rich-region, which shows as a convex curve at atmospheric pressure, passes into a concave curve via a straight line at about 15 MPa. Further, the gaps of observed values between x = 0.6 and x = 0.8 become larger than that at atmospheric pressure. To verify the gap observed around x = 0.7 we measured again the ultrasonic speeds at x = 0.6 and x = 0.8 after re-preparing the sample of the same composition. The results thus obtained were found to reproduce well those in table 1 within experimental error: f0.06 per cent at 0.1 MPa and +0.12 per cent at 60 MPa, respectively. Moreover, the results, which were measured at 293.15 and 313.15 K to examine the temperature effects of u, were presented graphically in figures l(a) and l(c). From these results, it is found in figure l(a) that the shape of the curve in the benzene-rich region at the lowest temperature, 293.15 K, changed largely from a convex curve to a concave curve as the pressure was raised, compared with that at higher temperature, and also, the gap of speed near x = 0.7 become more remarkable with increasing pressure. A similar tendency had already been observed in u for ((1 -x)C,H,NH, (14) For these mixtures, u decreased with increasing x, and +xC,H,NO,}. whatever the curvature at x x 0.5 there grew a new curve belonging neither to that for the aniline-rich region nor to that for the nitrobenzene-rich region. In the present (benzene + nitrobenzene) it is difficult to show clearly the composition variation of u at x z 0.7, because values in the range x = 0.6 to x = 0.8 are insufficient. Thus, each curve in figure 1 was illustrated by a dotted line. When the curves for the two mixtures are compared, x in ((1 - x)&H6 + xC,H,NO,], that is in a (non-polar + polar) mixture, the value of x where the curve shows unusual behavior is found at a higher value than for { (1 -x)C6H,NH2 + xC6H,N02}, that is in a (polar + polar) mixture. It seems reasonable to consider that the irregular composition is affected largely by the polarity of the compound other than nitrobenzene.
(BENZENE
+ NITROBENZENE)
AT
HIGH
1171
PRESSURES
As the densities of (benzene + nitrobenzene) at high pressures were not available, these were calculated by the same estimation method described previously.‘3’ The values of the pressure dependence @t&),,,,, MPa of ultrasonic speed, which are required for this calculation, were determined by applying the least-squares method to the results measured at pressure intervals of about 2.5 up to 30 MPa, and the values thus obtained are listed in table 2. The densities estimated using V(p, T) for liquids or liquid (au/aP)7’,p=0.t MPa are also presented in table 1. Frequently mixtures have been represented by the Tait equation : V(p) = V(O.l MPa)[l
--.I log,,{(L+p)/(L+O.l
MPa);].
(1)
From the estimated density, the Tait equation parameters J and L were computed for each composition and temperature by a least-squares method: the values thus obtained are listed in table 2; they reproduce the estimated densities with deviations not exceeding 0.03 per cent at 303.15 K and throughout the pressure range of the present experiments. Gibson and Loeffler(15’ measured the density of pure nitrobenzene as a function of pressure. The densities at 50 MPa from the Tait parameters reported in their paper, can be evaluated as 1229.9 kg.mm3 at 293.15 K. 1221.1 kg.me3 at 303.15 K, and 1212.3 kg*m-3 at 313.15 K, respectively. These values are in close agreement with results listed in table 1 or with values derived from the Tait parameters of table 2, within 0.1 per cent. The authors reported that the densities estimated for various binary mixtures by the same method showed good agreement with experimental values reported in the literature within 0.15 to 0.35 per cent in the range of pressure up to 200 MPa. Thus, TABLE
2. Pressure
dependence (&+3p)T of ultrasonic speed. observed specific pressure, and coefficients J. L for the Tait equation
T
x
K
_ Pu MPa
”
ww, m.s-l.Mpa-l
____-
volume
J
.-
v0 at atmospheric
1. MPa
293.15
0 0.2 0.4 0.6 0.8
30.0 30.0 30.0 30.0 30.0 30.0
5.04 4.19 3.82 3.51 3.19 2.95
1137.42 1047.53 976.38 911.Y7 871.19 831.15
-____-0.21997 0.23064 0.22633 0.22377 0.22443 0.22317
303.15
0 0.2 0.4 0.6 0.8
89.6 b 168.8 b 200.0 200.0 179.8 b 107.4h
5.23 4.44 3.96 3.64 3.33 3.07
1151.43 1057.30 986.24 921.04 879.56 837.58
0.22157 0.22370 0.22214 0.22136 0.22035 0.22039
95.66 114.63 132.14 147.70 165.39 185.73
313.15
0 0.2 0.4 0.6 0.8
30.0 30.0 30.0 30.0 30.0 30.0
5.54 4.61 4.11 3.75 3.45 3.27
1165.78 1069.08 995.64 928.94 886.59 845.88
0.22074 0.22068 0.21963 0.21956 0.21740 0.21342
87 79 107.37 123.35 139.62 155.88 170.53
’ Upper
limit
of pressure.
b Freezing
pressure
102.98 124.53 140.43 156.82 177.38 198.10
1172
T. TAKAGI
AND
0
0.5 x
x FIGURE xC,H,NO,~.
2. Composition T/K: (a), 293.15;
dependence (b). 303.15;
H. TEKANISHI
I x
of isentropic compressibilities xS for ((I -x)&H, (c), 313.15; p/MPa: 0. 0.1: c), 30; 0. 60.
+
we feel confident that the densities for (benzene + nitrobenzene) estimated from the pressure dependence of the ultrasonic speed may be accurate and reliable over the present pressure range. Using the experimental ultrasonic speed u and the density p derived from the pressure dependence of u, the isentropic compressibility ICYwas determined by the Laplace equation : K~ = u- ‘p - I, The results for (benzene + nitrobenzene) at several temperatures and pressures were listed in table 1, and are plotted as a function of x in figure 2. The inaccuracy of values of K~ was less than about 2 per cent.
FIGURE 3. Composition dependence of expansivities p/MPa: 0,” O.b 0.1; @, 30; (>, 60.” I” Derived from from specific volumes reported in reference 7.)
a for {(l -x)C,H6 + xC,H,NO,I at 303.15 K. measurements at several temperatures; ‘. derived
(BENZENE
+ NITROBENZENE)
AT
HIGH
1173
PRESSURES
The expansivity a is one of the important properties for describing the state of a system. Therefore, to find out whether the abnormal behavior of u(x) persists, values of a were computed from equation (1) : a = v-l(av/aT)p = v-'[l -J
10g,,{(L+p)/(L+0.1
MPa)}](W/W),,o,
MPa
+J1/,=,, MPaCpI(~(~+p))l(d~ldT)ln10. (3) The results for benzene + nitrobenzene derived from the estimated densities for three temperatures, and for 303.15 K and various pressures, are plotted in figure 3 as a function of x, together with the values at atmospheric pressure derived from the specific volumes at every 10 K from 283.15 to 323.15 K given in the literature.“’ From this figure, it is found that the composition variation of a shows the irregular change near x = 0.7 similar to that shown by u or xs, and the magnitude of gap is distinctly more than for u. In view of the thermodynamic relation, it may be presumed from this finding that the entropy of system also shows an abnormal behavior with X. especially under high pressures. Fried and his colleagues (i6,17) observed the volumetric behavior of nitrobenzene in some solvents. According to their papers, for (benzene + nitrobenzene) the excess molar volume is negative over all compositions for which mixing is exothermic,“8’ and in addition they showed an S-curve for the nitrobenzene-rich region!i6 However, in their studies the values are treated as though they behave smoothly with composition change. Comments and suggestions from Professor T. Makita appreciated.
of Kobe University
are much
REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. IO. Il. 12. 13. 14. 15. 16. 17. 18.
Mulliken. R. S. Molecular Complex. John Wiley: New York. 1%9. Foster, R. Organic Charge-transfer Complexes. Academic Press: London. 1969. Takagi, T. J. Chem. Thermodynamics 1980, 12, 277. Takagi, T. J. Chem. Thermodynamics 1980, 12, 1183. Takagi. T. J. Chem. Thermodvnamics 1981, 13. 291. Takagi. T.; Teranishi, H. J. Chem. Thermo&zamics 1982, 14. 577. Landolt- Biirnstein, Band I, Dichrenfliissiger Sysreme. Springer-Verlag: Berlin. 1974. Takagi. T. Mem. Fat. Ind. Arts. Kyoro Tech. Univ., Sri. Tech. 1976, 25. 51. Schaaffs, W. Molekularakustik. Springer-Verlag: Berlin. 1%3. Schaaffs, W. Z. Phys. Chem. 1944, 194, 28. Nozdrev. V. F. The Use of Ultrasonics in Molecular Physics. Pergamon Press: London. 1965. Rao, K. S. ; Rao, B. R. J. Acousr. Sot. Am. 1959, 31. 439. Gabrielli, 1. ; Poiani. G. Ric. Sci. 1954, 24, 1039. Takagi. T. Rev. Phys. Chem. Jpn 1978, 48. IO. Gibson, R. E. ; Loeffer, 0. H. J. Am. Chem. Sot. 1939, 61. 2877. Fried, V.; Miller, L. P.; Wachter. H. N. Bull. Chem. Sot. Jpn 1977, 50, 497. Miller, L. P.; Wachter, H. N.; Fried, V. J. Chem. Eng. Dafa 1975, 20. 417. Landoh Biirnstein, Band ?. Mischungsund Liisungswiirmen. Springer-Verlag: Berlin. 1976.
Chem. Thermodynamics 1982, 14, 1167-l 173
Ultrasonic speeds and thermodynamic properties of (benzene + nitrobenzene) under high pressures TOSHIHARU
TAKAGI
and HIROSHI
Department of Chemistry, Kyoto Technical Matsugasaki, Kyoto 606. Japan (Received 30 March
TERANISHI University.
1982; in revised form I June 1982)
Ultrasonic speeds u in ((1 -x)C,H, + xC,H,NO,] were measured by a fixed-path pulse technique at 293.15, 303.15, and 313.15 K under pressures up to 30 or 200 MPa with an observed error of less than 0.3 per cent. Curves of u(x) change smoothly in the benzene-rich region. But near x = 0.7, u(x) apparently deviates from a smooth curve, and the apparent gap becomes progressively greater as the temperature is reduced or the pressure is raised. From the experimental values, densities, isentropic compressibilities, and expansivities were calculated at high pressures. These quantities also show unusual behavior with x similar to that of u.
1. Introduction Mixtures of (nitrobenzene + another substance) often show interesting behavior, and so are frequently used for investigations of molecular structure.t’*2’ However, unexpectedly the thermodynamic properties of binary mixtures including nitrobenzene have scarcely been reported. We have measured the ultrasonic speed in various mixtures of (benzene + another organic substance) under high pressures, and have reported the composition or pressure effect on some thermodynamic properties of the mixtures in the previous papers. 13-6’ In this paper, the ultrasonic speed in (benzene + nitrobenzene) at temperatures between 293.15 and 313.15 K and pressures up to 30 or 200 MPa were measured, and derived high-pressure thermodynamic properties are discussed. 2. Experimental Pure liquids used were reagent-grade materials supplied by Wako Pure Chemicals Industriais. The compositions of the mixtures were determined by weighing, and the accuracy of the mole fraction was better than +0.0003. The densities for mixtures thus obtained were measured with an Ostwald pyknometer (about 20 cm3) at every 5 K from 283.15 to 323.15 K, and the results were in reasonable agreements with those observed previously. (‘) The method used for measurement of ultrasonic speed was a pulse-echo technique of fixed-path type at a frequency of 1 MHz and was 0021-9614/82/121167+07
$02.00/O
0 1982 Academic Press Inc. (London) Limited
1168
T. TAKAGI
t\ND
H. TERANISHI
similar to that described previously. ‘s’ The measurements were made at pressures up to 30 MPa for temperatures of 293.15 and 313.15 K, and up to 200 MPa for 303.15 K. For lower pressures the speeds were determined at narrower pressure intervals than at higher pressures. The error of the measurements was always less than 0.3 per cent.
3. Results and discussion The experimental ultrasonic speeds u at various mole fraction x in {(l-x)C,H,+xC,H,NO,) at temperatures of 293.15, 303.15, and 313.15 K are listed in table 1. The present values for pure components at atmospheric pressure closely coincide with the results reported in the literatures, as ascertained for benzene in previous papers,‘5*6’ and for nitrobenzene as summarized in the footnotes to table 1. Figure 1 shows u(x) at constant pressure; the behavior is peculiar near x = 0.7. In particular, at 303.15 K and atmospheric pressure, as shown in figure l(b), the values increase smoothly on a convex curve in the composition range from x = 0 to about x = 0.7. But at x z 0.7 the values deviate from the smooth curve. Gabrielli and Poiani’r3’ observed the speeds in (benzene + nitrobenzene) at 298.15 K, and
TABLE
293.15
1.
0
0.2
0.4
0.6
0.8
1
303.15
0
0.2
Values
of
ultrasonic
speeds U, [Cl -x)C,H,
densities p, + xC,H,NOZ;
P
u
I’
MPa
rn.s-’
kg.rne3
and
isentropic
h’s TPa-’
.-
0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0
1321.7 1345.9 1369.9 1353.9 1374.0 1394.7 1380.9 1399.7 1417.4 1407.8 1424.0 1441.0 1439.1 1453.9 1469.4 1471.6 1486.7 1502.4
879.2 883.1 886.9 954.6 958.3 962.0 1024.2 1027.7 1031.1 1096.5. 1099.8 1103.1 1147.8 1150.9 1153.9 1203.1 1206.0 1208.9
651.1 625.1 600.8 571.5 552.7 534.4 512.0 496.7 482.7 460.2 448.4 436.6 420.7 411.0 401.4 383.8 375.1 366.5
15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0
1391.3 1411.0 1429.4 1314.3 1434.4 1452.9 1436.4 1452.6 1469.9 1457.7 1475.0 1491.0 1484.3 1499.2 1511.4 1518.4 1534.6 1551.1
890.7 894.3 897.7 965.5 969.0 972.4 1034.4 1037.7 1040.9 1106.3 1109.4 1112.4 1156.9 1159.9 1162.7 1211.7 1214.4 1217.1
580.0 561.7 545.2 517.8 501.6 487.2 468.6 456.7 444.7 425.4 414.3 404.4 392.3 383.6 376.5 358.0 349.7 341.5
0.1 5.0 10.0 15.0 20.0 0.1 5.0
1271.1 1300.4 1327.4 1347.6 1370.3 1309.0 1329.6
868.5 872.7 876.8 880.7 884.6 945.8 949.7
712.6 677.7 647.3 625.2 602.0 617.0 595.6
25.0 1390.1 30.0 1408.6 40.0 1448.6 50.0 1487.6 60.0 1524.9 30.0 1427.4 40.0 1464.9
888.3 891.8 898.6 905.0 911.1 967.6 974.0
582.6 565.1 530.3 499.3 472.0 507.2 478.4
P -
MPa 30.0
compressibilities
11 rn.s-’
I’ kg.m-3
~~
h-s TPa-’
1452.1
901.1
526.3
30.0 1470.9
975.6
473.7
30.0
1485.9
1044.0
433.9
30.0
1406.7
1115.4
394.9
30.0
1522.9
1165.5
369.9
30.0
1567.8
1219.8
333.5
70.0 1560.7 80.0 1587.6 90.0 1612.2
916.4 922.3 927.5
447.8 430.1 414.8
1002.2 1007.1
382.0 367.2
90.0 100.0
1616.2 1644.4
for
(BENZENE
+ NITROBENZENE) TABLE
T ii
-x
0.4
0.6
0.8
1
313.15 0
0.2
0.4
0.6
0.8
1
P MPa
u rn,s-’
P kg,me3
AT
HIGH
1169
PRESSURES
1 ~-continued
KS TPa-’
10.0 15.0 20.0 25.0 0.1 5.0 10.0 15.0 20.0 25.0 30.0 40.0 0.1 5.0 10.0 15.0 20.0 25.0 30.0 40.0 0.1 5.0 10.0 15.0 20.0 25.0 30.0 0.1 5.0 10.0 15.0 20.0
1351.4 1371.0 1392.9 1410.5 1342.2 1360.6 1379.4 1398.4 1413.3 1433.1 1449.2 1484.4 13444 1390.7 1407.6 1422.9 1439.7 1455.6 1471.7 1502.5 1399.3 1419.7 1436.6 1454.8 1467.0 1482.1 1493.9 1438.1 1453.8 1470.1 1486.7 1503.7
953.5 957.1 960.7 964.2 1013.9 1017.5 1021.1 1024.5 1027.9 1031.1 1034.3 1040.4 1085.7 1089.1 1092.5 1095.8 1099.1 1102.2 1105.3 1111.3 1136.9 1140.1 1143.3 1146.4 1149.4 1152.4 1155.3 1193.9 1196.9 1199.9 1202.8 1205.7
574.2 555.8 536.4 521.3 547.4 530.9 514.7 499.2 487.1 472.2 460.4 436.2 487.5 474.7 461.9 450.7 438.9 428.2 417.7 398.6 449.2 435.2 423.8 412.2 404.2 395.0 387.8 405.0 395.3 385.6 376.1 366.8
50.0 60.0 70.0 80.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 120.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 25.0 30.0 40.0 50.0 60.0
1500.7 1530.7 1560.3 1588.1 1514.6 1545.4 1574.2 1598.8 1622.7 1649.2 1675.4 1699.1 1530.9 1559.9 1585.9 1609.4 1634.8 1659.9 1680.5 1705.1 1518.0 1543.2 1570.6 1599.0 1623.6 1646.1 1667.8 1520.9 153X.4 1554.8 1581.3 1606.7
980.2 986.1 991.7 997.0 1046.3 1051.9 1057.3 1062.4 1067.4 1072.2 1076.8 1081.3 1117.0 1122.5 1127.7 1132.8 1137.7 1142.4 1147.1 1151.5 1160.9 1166.4 1171.6 1176.6 1181.5 1186.2 1190.7 1208.5 1211.2 1216.6 1221.7 1226.7
453.0 432.9 414.2 397.7 416.7 398.1 381.7 368.2 355.8 342.9 330.9 320.3 382.0 366.1 352.5 340.8 328.9 317.7 308.7 298.7 373.8 360.0 346.0 332.4 321.1 311.1 301.9 357.7 348.X 340.0 327.4 315.8
0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0 0.1 5.0 10.0
1231.0 1259.4 1281.2 1267.1 1291.6 1314.7 1297.4 1319.2 1340.7 1337.2 1356.2 1374.8 1365.3 1383.9 1400.7 1403.2 1419.1 1435.6
857.8 862.3 866.7 935.4 939.4 943.3 1004.4 1008.1 1011.8 1076.5 1080.0 1083.6 1127.9 1131.2 1134.5 1182.2 1185.3 1188.4
769.3 731.2 702.9 665.9 638.1 613.3 591.5 569.9 549.8 519.4 503.4 488.3 475.7 461.5 449.2 429.6 418.9 408.3
15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0 15.0 20.0 25.0
1305.7 1331.5 1353.4 1335.X 1356.7 1386.4 1359.8 1387.8 1397.5 1392.8 1409.9 1423.9 1416.3 1434.4 1448.5 1452.5 1469.7 1487.2
870.9 874.9 878.8 947.2 950.9 954.4 1015.4 1018.9 1022.3 1376.9 1090.3 1093.6 1137.7 1140.9 1143.9 1191.4 1194.4 1197.3
673.5 644.7 621.2 591.7 571.4 552.6 532.6 509.6 500.8 474.2 461.4 451.0 438.2 426.0 416.6 397.8 387.6 377.6
Literature values of ultrasonic speeds. u/(m s- ’ ), in C,H,NO?: 1440.“” 1476,“*1 at 313.15 K 1409,“” 1405.“L’ - 1
at 293.15
f’ kg.rnm3
P MPa
u rn.s-’
110.0 120.0 130.0 140.0 130.0 140.0 150.0 160.0 170.0 180.0 190.0 200.0 130.0 140.0 150.0 160.0 170.0 180.0 190.0 200.0 110.0 120.0 130.0 140.0 150.0 160.0 170.0 70.0 80.0 90.0 100.0
1672.7 1698.2 1721.2 1743.3 1723.0 1742.2 1763.9 1786.8 1805.1 1823.8 1842.5 1860.9 1727.9 1749.8 1767.9 1789.1 1807.1 1826.0 1844.5 1862.7 1689.9 1708.1 1709.7 1747.6 1770.1 1789.5 1807.3 1631.1 1654.4 1676.7 1697.9
1011.8 1016.4 1020.8 1025.1 1085.6 1089.X 1093.9 1097.8 1101.6 1105.3 1108.9 1112.5 1155.8 1159.9 1164.0 1168.0 1171.X 1175.5 1179.2 1182.7 1195.2 1199.5 1203.6 1207.7 1211.6 1215.5 1219.2 1231.6 1236.2 1240.8 1245.2
30.0 1373.9
882.6
600.2
30.0
1397.2
957.9
534.x
30.0 1413.9
1025.6
4x7.7
30.0 1439.5
1096.8
440.0
30.0 1466.4
1146.9
405.5
30.0 1505.1
1200.2
367.X
K 1475.‘9’
1471:“”
KS TPa i 353.2 341.1 330.6 320.9 310.3 302.3 293.X 285.3 278.5 271.9 265.6 259.5 2X9.X 281.6 274.9 267.5 261.3 255.1 249.2 244.1 292.9 285.8 284.2 271.1 263.4 256.9 251.1 305.2 295.5 2X6.1 27X.6
at 303.15
K
1170
T. TAKAGI
13-
6-4 I
0
FIGURE
(a), 293.15;
I 0.5 x
AND
H. TERANISHI
-
I 1
0
0.5 x
1
1. Composition dependence of ultrasonic speeds u in {(I -x)C6H, (b), 303.15; (c). 313.15; p/MPa: O,O.l; a. 30; 0, 60; n , 298.15
x + xC,H,NO,). K, reference 13.
T/K
their experimental values, plotted as squares in figure l(b), show a similar behavior. With rise of pressure, the plotted line of the speed for the benzene rich-region, which shows as a convex curve at atmospheric pressure, passes into a concave curve via a straight line at about 15 MPa. Further, the gaps of observed values between x = 0.6 and x = 0.8 become larger than that at atmospheric pressure. To verify the gap observed around x = 0.7 we measured again the ultrasonic speeds at x = 0.6 and x = 0.8 after re-preparing the sample of the same composition. The results thus obtained were found to reproduce well those in table 1 within experimental error: f0.06 per cent at 0.1 MPa and +0.12 per cent at 60 MPa, respectively. Moreover, the results, which were measured at 293.15 and 313.15 K to examine the temperature effects of u, were presented graphically in figures l(a) and l(c). From these results, it is found in figure l(a) that the shape of the curve in the benzene-rich region at the lowest temperature, 293.15 K, changed largely from a convex curve to a concave curve as the pressure was raised, compared with that at higher temperature, and also, the gap of speed near x = 0.7 become more remarkable with increasing pressure. A similar tendency had already been observed in u for ((1 -x)C,H,NH, (14) For these mixtures, u decreased with increasing x, and +xC,H,NO,}. whatever the curvature at x x 0.5 there grew a new curve belonging neither to that for the aniline-rich region nor to that for the nitrobenzene-rich region. In the present (benzene + nitrobenzene) it is difficult to show clearly the composition variation of u at x z 0.7, because values in the range x = 0.6 to x = 0.8 are insufficient. Thus, each curve in figure 1 was illustrated by a dotted line. When the curves for the two mixtures are compared, x in ((1 - x)&H6 + xC,H,NO,], that is in a (non-polar + polar) mixture, the value of x where the curve shows unusual behavior is found at a higher value than for { (1 -x)C6H,NH2 + xC6H,N02}, that is in a (polar + polar) mixture. It seems reasonable to consider that the irregular composition is affected largely by the polarity of the compound other than nitrobenzene.
(BENZENE
+ NITROBENZENE)
AT
HIGH
1171
PRESSURES
As the densities of (benzene + nitrobenzene) at high pressures were not available, these were calculated by the same estimation method described previously.‘3’ The values of the pressure dependence @t&),,,,, MPa of ultrasonic speed, which are required for this calculation, were determined by applying the least-squares method to the results measured at pressure intervals of about 2.5 up to 30 MPa, and the values thus obtained are listed in table 2. The densities estimated using V(p, T) for liquids or liquid (au/aP)7’,p=0.t MPa are also presented in table 1. Frequently mixtures have been represented by the Tait equation : V(p) = V(O.l MPa)[l
--.I log,,{(L+p)/(L+O.l
MPa);].
(1)
From the estimated density, the Tait equation parameters J and L were computed for each composition and temperature by a least-squares method: the values thus obtained are listed in table 2; they reproduce the estimated densities with deviations not exceeding 0.03 per cent at 303.15 K and throughout the pressure range of the present experiments. Gibson and Loeffler(15’ measured the density of pure nitrobenzene as a function of pressure. The densities at 50 MPa from the Tait parameters reported in their paper, can be evaluated as 1229.9 kg.mm3 at 293.15 K. 1221.1 kg.me3 at 303.15 K, and 1212.3 kg*m-3 at 313.15 K, respectively. These values are in close agreement with results listed in table 1 or with values derived from the Tait parameters of table 2, within 0.1 per cent. The authors reported that the densities estimated for various binary mixtures by the same method showed good agreement with experimental values reported in the literature within 0.15 to 0.35 per cent in the range of pressure up to 200 MPa. Thus, TABLE
2. Pressure
dependence (&+3p)T of ultrasonic speed. observed specific pressure, and coefficients J. L for the Tait equation
T
x
K
_ Pu MPa
”
ww, m.s-l.Mpa-l
____-
volume
J
.-
v0 at atmospheric
1. MPa
293.15
0 0.2 0.4 0.6 0.8
30.0 30.0 30.0 30.0 30.0 30.0
5.04 4.19 3.82 3.51 3.19 2.95
1137.42 1047.53 976.38 911.Y7 871.19 831.15
-____-0.21997 0.23064 0.22633 0.22377 0.22443 0.22317
303.15
0 0.2 0.4 0.6 0.8
89.6 b 168.8 b 200.0 200.0 179.8 b 107.4h
5.23 4.44 3.96 3.64 3.33 3.07
1151.43 1057.30 986.24 921.04 879.56 837.58
0.22157 0.22370 0.22214 0.22136 0.22035 0.22039
95.66 114.63 132.14 147.70 165.39 185.73
313.15
0 0.2 0.4 0.6 0.8
30.0 30.0 30.0 30.0 30.0 30.0
5.54 4.61 4.11 3.75 3.45 3.27
1165.78 1069.08 995.64 928.94 886.59 845.88
0.22074 0.22068 0.21963 0.21956 0.21740 0.21342
87 79 107.37 123.35 139.62 155.88 170.53
’ Upper
limit
of pressure.
b Freezing
pressure
102.98 124.53 140.43 156.82 177.38 198.10
1172
T. TAKAGI
AND
0
0.5 x
x FIGURE xC,H,NO,~.
2. Composition T/K: (a), 293.15;
dependence (b). 303.15;
H. TEKANISHI
I x
of isentropic compressibilities xS for ((I -x)&H, (c), 313.15; p/MPa: 0. 0.1: c), 30; 0. 60.
+
we feel confident that the densities for (benzene + nitrobenzene) estimated from the pressure dependence of the ultrasonic speed may be accurate and reliable over the present pressure range. Using the experimental ultrasonic speed u and the density p derived from the pressure dependence of u, the isentropic compressibility ICYwas determined by the Laplace equation : K~ = u- ‘p - I, The results for (benzene + nitrobenzene) at several temperatures and pressures were listed in table 1, and are plotted as a function of x in figure 2. The inaccuracy of values of K~ was less than about 2 per cent.
FIGURE 3. Composition dependence of expansivities p/MPa: 0,” O.b 0.1; @, 30; (>, 60.” I” Derived from from specific volumes reported in reference 7.)
a for {(l -x)C,H6 + xC,H,NO,I at 303.15 K. measurements at several temperatures; ‘. derived
(BENZENE
+ NITROBENZENE)
AT
HIGH
1173
PRESSURES
The expansivity a is one of the important properties for describing the state of a system. Therefore, to find out whether the abnormal behavior of u(x) persists, values of a were computed from equation (1) : a = v-l(av/aT)p = v-'[l -J
10g,,{(L+p)/(L+0.1
MPa)}](W/W),,o,
MPa
+J1/,=,, MPaCpI(~(~+p))l(d~ldT)ln10. (3) The results for benzene + nitrobenzene derived from the estimated densities for three temperatures, and for 303.15 K and various pressures, are plotted in figure 3 as a function of x, together with the values at atmospheric pressure derived from the specific volumes at every 10 K from 283.15 to 323.15 K given in the literature.“’ From this figure, it is found that the composition variation of a shows the irregular change near x = 0.7 similar to that shown by u or xs, and the magnitude of gap is distinctly more than for u. In view of the thermodynamic relation, it may be presumed from this finding that the entropy of system also shows an abnormal behavior with X. especially under high pressures. Fried and his colleagues (i6,17) observed the volumetric behavior of nitrobenzene in some solvents. According to their papers, for (benzene + nitrobenzene) the excess molar volume is negative over all compositions for which mixing is exothermic,“8’ and in addition they showed an S-curve for the nitrobenzene-rich region!i6 However, in their studies the values are treated as though they behave smoothly with composition change. Comments and suggestions from Professor T. Makita appreciated.
of Kobe University
are much
REFERENCES I. 2. 3. 4. 5. 6. 7. 8. 9. IO. Il. 12. 13. 14. 15. 16. 17. 18.
Mulliken. R. S. Molecular Complex. John Wiley: New York. 1%9. Foster, R. Organic Charge-transfer Complexes. Academic Press: London. 1969. Takagi, T. J. Chem. Thermodynamics 1980, 12, 277. Takagi, T. J. Chem. Thermodynamics 1980, 12, 1183. Takagi. T. J. Chem. Thermodvnamics 1981, 13. 291. Takagi. T.; Teranishi, H. J. Chem. Thermo&zamics 1982, 14. 577. Landolt- Biirnstein, Band I, Dichrenfliissiger Sysreme. Springer-Verlag: Berlin. 1974. Takagi. T. Mem. Fat. Ind. Arts. Kyoro Tech. Univ., Sri. Tech. 1976, 25. 51. Schaaffs, W. Molekularakustik. Springer-Verlag: Berlin. 1%3. Schaaffs, W. Z. Phys. Chem. 1944, 194, 28. Nozdrev. V. F. The Use of Ultrasonics in Molecular Physics. Pergamon Press: London. 1965. Rao, K. S. ; Rao, B. R. J. Acousr. Sot. Am. 1959, 31. 439. Gabrielli, 1. ; Poiani. G. Ric. Sci. 1954, 24, 1039. Takagi. T. Rev. Phys. Chem. Jpn 1978, 48. IO. Gibson, R. E. ; Loeffer, 0. H. J. Am. Chem. Sot. 1939, 61. 2877. Fried, V.; Miller, L. P.; Wachter. H. N. Bull. Chem. Sot. Jpn 1977, 50, 497. Miller, L. P.; Wachter, H. N.; Fried, V. J. Chem. Eng. Dafa 1975, 20. 417. Landoh Biirnstein, Band ?. Mischungsund Liisungswiirmen. Springer-Verlag: Berlin. 1976.