M-2467

.I. Chem. Thermodvnamics 1990, 22, 335-353

Fluid mixtures at high pressures

IX. Phase separation and critical phenomena in 23 (n-alkane + water) mixtures

ERWIN BRUNNER

BASF Aktiengesellschaft, D-6700 Ludwigshqfen, Federal Republic qf Germany

(Received 11 January 1990)

The p(T) projections of the critical curves and of the (liquid + liquid + gas) (Ilg) three-phase curves for 23 binary mixtures of (an n-alkane + water) with alkane-carbon numbers i = 1 to 12 and i = 14, 16, 18, 20, 24, 25, 26, 28, 30, 32, and 36 were measured. The shape of the critical curves of the mixtures changes systematically with i. All critical curves are interrupted and show (gas + gas) equilibria of the second kind. The Ilg curves are at higher pressures than the vapour pressures of the pure substances, and all end in a (liquid + gas) upper critical end point (Ig-UCEP). Up to the mixtures i = 25, along the p(T) projection of the Ilg lines up to the Ig-UCEP, the alkane-rich liquid phase is lighter than the water-rich liquid phase. The consequence is that the critical curve starting from the Ig-UCEP ends in the critical point of the alkane. As from i = 28, a barotropic phase reversal of the two liquid phases occurs on the Ilg curve before the UCEP is reached, so that, at the UCEP, the now lighter water-rich liquid phase becomes identical with the gas phase and the critical curve starting from the UCEP runs to the critical point of water. For a defined pseudo-binary mixture of (alkane mixture + water) with a fictitious alkane-carbon number between i = 26 and i = 28, this barotropic effect must occur directly at the UCEP. This means that all three phases here become simultaneously identical at the UCEP and the llg curve thus ends in a tricritical end point TCEP, a phase behaviour which has hitherto not been known. The three branches of the critical curve, oiz. the high-pressure branch I,& and the two branches I,g and lag, which start from the critical point of water or the alkane mixture, respectively, end in this tricritical end point TCEP. At TCEP the three-phase line and the three branches of the critical curve (l,l,, lig, and lag) have the same slope. The TCEP occurs in the border-line case between the two sub-classes a and b of phase- behaviour type III (classification according to van Konynenburg and Scott). In sub-class IIIa the critical curve starting at the UCEP ends at the critical point of the n-alkane and in sub-class IIIb at the critical point of water. For mixtures with i = 1 to i = 26, the high-pressure branch of the critical curve starting from the critical point of water runs first to lower temperatures and, with increasing pressures, oia a temperature minimum back to higher temperatures. For all mixtures with i = 7 to i = 26 this branch of the critical curve additionally also passes through a pressure minimum between the critical point of water and the temperature minimum. All mixtures with i 2 28 have a high-pressure high-temperature branch of the critical curve which, starting from the critical point of the alkane, first runs via a pressure maximum and pressure minimum to lower temperatures and finally, after passing through a temperature minimum, rises again. The phenomenological relations in phase behaviour on transition from type II to type III and from type IIIa to type IIIb with the characteristic intermediate stages are presented schematically with the aid of the p(T) projections of their critical curves.

CO21-9614/90/040335 + 19 $02.00/0 0 1990 Academic Press Limited

336 E. BRUNNER

1. ~ntr~u~tio~

In connection with our investigations on phase separation and critical phenomena at high pressures in binary mixtures containing polar substances, ) we measured p(T) values of the critical curves and the (liquid + liquid + gas) (Ilg) three-phase lines for 23 mixtures of (an n-alkane + water) with alkane-carbon numbers of i = 1 to 12 and i = 14, 16, 18, 20, 24, 25, 26, 28, 30, 32, and 36.

At temperatures near the critical temperature of water, fluid-phase equilibria of (an n-alkane -i- water) with i = 1 to 7 had been measured already; all these show (gas + gas) equilibria of the second type: (methane + water),8~9 (ethane + water),. I) (propane + water), 9 13) (butane + water),iO~ i . i4) (pentane + water), 5, (hexane + water),41 and (heptane + water). ( I The low-tem~rature branch of the interrupted critical curve of (hexane + water) had been measured by Scheffero8 A brief summary of the classification of phase behaviour and critical phenomena according to Scott and van Konynenburg l) was given in part VI of this series of publications.@

2. Experimental

The apparatus and measuring method for the present study were largely the same as those previously described by Brunner et uL(~~) and used for parts I to VII in this series of papers on fluid mixtures at high pressures.-) All measurements were performed in a 30 cm3 cylindrical high-pressure optical cell. The high-pressure cell previously used was fitted with a heating jacket which was connected to a thermostat circulation, so that its maximum operating temperature was limited to 600 K. To enable the measuring range to be extended to higher temperatures, a high-pressure cell fitted with bayonet heaters was built according to the same principle of construction (figure 1). The characteristics of the high-pressure optical cell are: 30 cm3 capacity; maximum operating pressure: 200 MPa at 750 K; material: Nimonic 90, a heat-resistant N&based alloy (equivalent to German standard 2.4969); eight electric heating cartridges of 500 W each; graphite as a high-pressure seal.

The precision and repeatability with which the appearance or disappearance of a phase boundary was observable is in general Ap/p < 10d3 and AT < 0.2 K. The pressures were measured by means of strain-gauge pressure transducers, which were cahbrated against a free-piston gauge before and after each series of measurements. If it is assumed that any impurities in the test substances and their thermal decomposition have no significant effect on the position of the critical or llg three- phase loci, the total error was estimated to be Ap/p < 0.004. The temperature was measured inside the cell by a 1 mm steel-sheathed thermocouple, which was checked several times over the entire temperature range of the particular tests against a calibrated platinum resistance the~ometer using a the~ostatically controlled oil and salt bath, and by measuring the vapour-pressure curve of water in the optical high-pressure cell,up to the critical point. The resolution of the device for measuring the temperature was 0.02 K, and the absolute accuracy of the temperature measurements is estimated to be as follows: 60.2 K below 373 K, ~0.3 K between

23 (n-ALKANE + WATER) MIXTURES 331

-3

50 mm

A-A

FIGURE 1. High-pressure optical cell, 30 cm3, 200 MPa, 750 K. 1, pressure-distributing ring (17-4 PH); 2, pressure screw (Nimonic 90); 3, eight bayonet heaters of 500 W each; 4, high-pressure seal ring (graphite); 5, pressure ring (Nimonic 90); 6, window (sapphire); 7, pressure vessel (Nimonic 90).

TABLE 1. Mole-fraction purity x, supplier of the test substances used, and selected literature values of the critical temperature T, and the critical pressure pE of the pure substances

Substance X Supplier T,IK p,lMPa Ref.

H,O Merck 647.14 22&x6 23 CH, 0.9995 Messer-Griesheim 190.555 4.595 24 CA, 0.9995 Messer-Griesheim 305.33 4.8714 24 Ws 0.9995 Messer-Griesheim 369.85 4.2470 24 W-I,, 0.9995 Messer-Griesheim 425.25 3.791 24 GH,, 0.9987 Merck 469.80 3.375 24 Cd,, 0.9954 Merck 507.90 3.030 24 WI,, 0.9967 Merck 540.15 2.736 24 GH,, 0.9962 Fluka 568.95 2.488 25 GH,, 0.9997 Ventron 594.65 2.281 25 CIOHH 0.9982 Merck 617.65 2.103 26 C,,H,, 0.9945 Merck 638.85 1.953 26 C,,H,, 0.9976 Ventron 658.65 1.835 26 Cd,, 0.9974 Fluka 693.15 1.622 26 C,,H,, 0.983 * Fluka 722 1.444 26 C,&JS 0.9922 Fluka 749 1.290 26 GA, 0.9970 Aldrich 771 1.200 26 Cd-ho 0.997 Fluka 809 1.020 26 C,J,, 0.994 Fluka 818 0.98 c G,H,a 0.996 Fluka 827 0.95 c G.sH,s 0.998 Fluka 843 0.89 c Go% 0.980 Fluka 857 0.83 c C,,H,, 0.987 Fhtka 871 0.79 c Cd,, 0.990 Ventron 894 0.71 c

a Pro analysi, conductivity 5 uS m-r as guaranteed by the supplier. *The impurities are isomers with nearly the same vapour pressure: x(C15H3J = 0.0012, x(C, ,Hs6) =

0.0005. Critical quantities estimated according to reference 47. Own measurement: pE = (22.060~0.010) MPa. The recommended value of 22.115 MPa from reference

27 is too high. Experimental values from Blank. .(*s) T = (674.14kO.03) K (corrected from IPTS-49 to E IPTS-68) pc = (22.045 &0.003) MPa.

338 E. BRUNNER

TABLE 2. Experimental points on the llg three-phase lines and the two branches of the interrupted critical p(T) curves of 23 (n-alkane + water) mixtures with n-alkane numbers i = 1 to 12, and i = 14, 16, 18, 20, 24, 25, 26, 28, 30, 32, and 36: temperature T, pressure p; llg, (liquid + liquid + gas) three-phase point; lg, (liquid + gas) critical point; UCEP, upper critical end point; cpl, critical point of water; cp2, critical

point of the alkane

T/K p/MPa T/K p/MPa T/K p/MPa T/K p/MPa

647.14 22.064 646.0 23.65 644.3 26.05

647.14 22.064 642.9 23.90 641.0 24.80

312.4 1.360 336.8 2.322 342.2 2.583 352.7 3.170 361.5 3.729 369.7 4.260

325.5 0.545 347.9 0.945 363.4 1.335 382.9 1.985 401.3 2.820 411.5 3.400 414.7 3.600

377.5 0.810 395.6 1.210 410.6 1.680 426.6 2.296 441.2 3.032 455.1 3.915 462.2 4.452

419.0 1.125 436.1 1.645 456.3 2.490 476.8 3.750 485.6 4.363 493.5 5.020 496.4 5.282

cpl lg

cpl k

lb

UCEP

lk

UCEP

642.4 640.3 638.6

639.3 635.6 631.4

369.85 647.14 645.8 644.9 642.5 640.8

417.8 422.1 424.1 425.25 647.14 645.3 643.0

463.8 464.7 465.7 467.5 468.6 469.4 469.80

499.0 501.6 504.4 506.4 507.90 647.14 642.2

Methane + water 28.65 636.4 38.40 31.70 634.8 41.80 34.50 633.2 45.20

Ethane + water 25.80 628.5 35.00 28.30 624.9 39.80 31.70 622.3 44.90

Propane + water 4.2470 cp2 638.5 24.88

22.064 cpl 635.5 26.20 22.39 lg 632.3 27.70 22.65 628.9 29.80 23.45 627.2 31.40 24.05 624.7 34.40

Butane + water 3.800 640.7 23.31 4.110 639.0 23.70 4.260 UCEP 636.8 24.27 3.791 cp2 634.4 24.98

22.064 cpl 631.4 26.15 22.38 Ig 628.4 27.80 22.83 626.0 29.80

Pentane + water 4.577 UCEP 647.14 22.064 cpl 4.365 lg 641.6 22.79 lg 4.220 636.6 23.65 3.878 630.6 25.32 3.608 627.4 27.20 3.440 626.2 28.50 3.375 cp2 625.3 31.00

Hexane + water 4.980 lg 640.0 22.76 4.525 636.7 23.20 3.995 633.7 23.82 3.460 631.4 24.59 3.030 cp2 629.9 25.35

22.064 cpl 627.9 27.78 22.52 Ig 627.6 31.50

Heptane + water

631.8 49.80

621 .l 49.80

623.2 37.60 621.9 43.90 621.9 48.60

623.9 33.10 623.4 36.90 623.3 38.70 623.8 42.00 624.5 45.00 626.2 49.80

625.3 34.80 626.4 38.20 628.1 42.60 630.1 47.30

629.8 36.60 632.2 40.80 634.3 43.90 636.2 47.30

414.7 0.713 Ilg 473.8 2.688 520.0 6.320 UCEP 533.1 4.36 429.5 1.028 489.7 3.659 523.8 5.89 lg 535.5 3.895 444.5 1.450 504.4 4.792 526.7 5.45 537.7 3.400 459.1 1.988 516.9 5.995 529.7 4.96 540.15 2.736 cp2

23 @-ALKANE + WATER) MIXTURES 339

TABLE 2-c~~ti~~~

T/K p/MPa T/K PlMPa T/K p/MPa T/K PIMPa

647.14 22.064 cpl 637.7 22.52 628.3 25.00 22.67 628.7 27.4 22.97 429.2 29.8 23.42 632.5 35.6 24.04 636.0 40.4

639.8 45.6 642.7 49.9

630.3 27.2 631.6 29.7 635.8 35.3 637.0 36.8 639.7 40.4 644.2 45.6

632.4 22.85 631.1 25.15 632.2 27.05 634.8 30.6 638.8 35.2 644.7 41.3 648.6 45.3 653.7 SO.8

633.3 22.44 632.0 23.14 634.8 28.28 438.7 32.18 642.9 36.10 649.1 42.07

639.0 21.73 637.6 21.73 636.2 21.78 634.5 21.94 633.4 22.45 633.3 23.70 634.2 25.05 635.7 26.60 638.4 29.15 642.9 33.25

645.2 22.13 Ii 635.9 643.2 22.20 633.7 641.7 22.27 631.5 639.9 22.36 629.7

Octane + water

643.8 22.10 641.6 22.13 639.3 22.19 637.1 22.30 634.9 22.53

CQ2 633.4 22.78 CQl 632.1 23.15 k 630.7 23.85

630.2 24.6

418.3 443.0 464.3 484.4 503.8 524.0

0.583 llg 548.6 1.087 552.0

6.525 6.030 5.250 4.663 4.112 2.488

22.064 22.09 22.10

1.755 556.6 2.668 550.0 3.868 562.9 5.552 568.95 6.750 647.14 7.410 UCEP 646.1 6.970 lg 645.0

535.1 540.0 544.8

Nonane + water

8.540

7.45

UCEP

647.14

590.3

22.064

3.345 8.26

cp1

fg 592.4

6.95

2.830 7.91

646.1

594.65

22.05

2.281

le

cp2

447.9 457.7 468.8 479.2 488.8 509.6

2.181

1.081 llg

566.9

554.0 1.350 558.9 1.745

2.652

562.8

570.8 3.960 574.2 6.44 643.8 22.03 -

5.88 642.5 22.02 5.40 640.3 22.01 4.850 638.8 22.04 4.245 636.0 22.07 3.800 634.1 22.24

523.5 5.105 577.4 539.0 6.670 580.3 545.4 7.418 583.3 548.7 7.833 586.0 553.3 8.452 588.0

Decane + water

9.330 610.4 3.923 8.880 613.6 3.224

465.8 1.473 Ilg 574.8 494.0 2.686 580.2 523.3 4.630 585.2 8.300 617.65 2.103 CQ2 543.2 6.495 590.6 7.580 647.14 22.064 co1 562.8 9.000 596.1 567.6 9.655 UCEP 600.9

6.790 644.5 22.00 1g 5.970 643.2 21.95 4.945 641.0 21.90 569.4 9.600 lg 605.9

572.9 575.5 577.8 581.9 586.7 591.0 595.8 600.8 605.5 610.1 615.1

Undecane + water

9.953 623.1 5.890 10.38 626.9 5.120 10.75 UCEP 629.8 4.420 10.67 Ig 633.0 3.590 10.45 638.85 1.953 cp2 10.20 647.14 22.064 CQl 9.780 645.8 22.03 lg 9.280 644.4 21.95 8.690 643.0 21.87 8.070 642.2 21.84 7.310 640.8 21.78

475.8 1.760 Ilg 495.2 2.597 510.5 3.470 522.3 4.305 534.4 5.310 544.5 6.300 552.2 7.150 558.2 7.873 563.0 8.500 566.8 9.040 569.8 9.476

340 E. BRUNNER

TABLE 2-continued

T/K p/MPa T/K p/MPa T/K p/MPa

519.4 4.06 Ilg 534.8 5.27 - 546.1 6.42 554.6 1.27 561.3 8.06 565.4 8.60 568.2 9.01 571.3 9.43 574.4 9.86 577.3 10.35

446.9 0.88 k 477.5 1.72 - 598.7 508.3 3.15 599.1 539.0 5.37 558.4 7.32 566.9 8.34 572.9 9.13 578.5 9.94 582.7 10.57 587.7 11.37 592.7 12.23 594.8 12.63

456.3 1.10 lb 486.9 2.08 517.9 3.72 548.4 6.14 578.4 9.65 589.6 11.34 593.3 11.95 596.8 12.56 599.9 13.12 603.2 13.17

439.4 0.730 llg 469.1 1.442 499.1 2.623 528.9 4.437 549.1 6.160 569.1 8.307 589.4 10.96 599.3 12.55 608.4 14.27 647.2 16.54 643.0 21.57 612.8 15.18 654.9 16.13 642.1 21.46

421.8 0.454 llg 509.7 451.6 0.945 540.5 479.9 1.77 570.2

Dodecane + water

580.4 10.88 654.2 2.805 583.1 11.34 658.65 1.835 cp2 584.8 594.3 597.8 608.5 617.9 629.0 638.8 646.6

597.3

604.6 608.7

11.66 UCEP 647.14 22.064 cpl 635.0 11.55 le 646.3 22.01 In 634.4

634.5 635.4

- - 11.36 645.1 21.93 10.58 644.0 21.84 9.560 642.9 21.77 7.850 641.8 21.72 6.185 640.7 21.68 4.580 639.4 21.63

Tetradecane + water

13.12 664.5 7.41 13.41 UCEP 667.9 6.66 13.48 lg 671.1 6.01 13.43 693.15 1.622 cp2 13.40 647.14 22.064 cpl

616.4 13.18 646.7 22.03 Ii 625.9 12.61 644.8 21.90 633.8 641.9 648.7 653.7 659.7

605.6 608.3 623.6 632.0 641.6 651.8

11.93 643.6 21.80 10.98 642.2 21.70 10.10 641.4 21.63

9.33 640.0 21.54 8.28 638.1 21.47

Hexadecane + water

14.27 722 1.444 cp2 14.87 UCEP 647.14 22.064 cpl 15.300 Ig 646.2 21.98 Ig 15.235 645.3 21.88 14.880 644.5 21.78 14.065 643.9 21.70

660.6 12.97 642.6 21.56 643.3 26.55 670.4 11.47 641.0 21.42 646.3 28.50 679.9 9.880 639.8 21.30 689.1 7.990 638.2 21.24

Octadecane + water

615.0 15.72 662.9 15.56 615.9 15.93 670.2 14.92 639.1 616.5 16.07 UCEP 678.6 14.05 638.5 618.4 16.30 lg 686.4 13.19 620.9 16.44 749 1.290 cp2 625.2 16.62 647.14 22.064 cpl 632.4 16.76 645.3 21.85 Ig 639.7 16.72 643.9 21.68

Eicosane + water

3.15 598.5 12.27 5.27 603.7 13.19 8.27 608.3 14.00

elMPa

638.0 636.3

636.5 639.9 643.9 647.0

636.6 21.53 635.6 22.30 636.4 23.45 639.1 25.30 642.3 27.75 645.9 30.10 649.2 32.20 652.5 34.10 655.8 36.30

637.3 636.3 636.6 637.7 638.8 640.8

650.7 31.10

640.6

637.6 637.2 637.8 639.2 640.8 643.0 651.1

613.4 14.98 617.9 15.96 622.1 17.08 UCEP

21.61 21.68 21.93 22.35 22.90 24.38 25.54 28.56 31.56 34.01

21.26 21.60 21.95 23.05 23.85 25.08

21.32 21.22 21.14 21.18 21.63 22.15 22.97 23.98 25.10 29.55

23 @-ALKANE + WATER) MIXTURES

TABLE 2-continued

341

T/K p/MPa T/K p/MPa T/K p/MPa T/K PFrPa

630.8 17.86 Ig 639.0 17.99 649.0 17.91 659.1 17.45 669.0 16.82 678.9 16.05

455.7 1.066 Ilg 484.4 1.960 513.0 3.345 533.8 4.750 554.6 6.570 682.7 20.57 643.8 21.58 573.1 8.630 692.6 19.60 642.7 21.41 594.2 Il.68 809 612.3 14.83 647.14

451.4 0.970 llg 632.9 480.7 1.825 634.9 510.7 3.233 636.0 539.7 5.265 636.4 570.7 8.385 436.9 599.4 12.38 637.4 613.3 14.78 638.1 620.8 16.24 639.4 626.9 17.56 641.9 627.3 17.67 646.7 630.3 18.36 650.4 631.9 18.77 654.4

487.5 2.10 llg 637.9 510.1 3.21 639.5 540.6 5.34 640.4 569.0 8.16 640 589.3 10.80 641.2 604.7 13.22 647.9 619.3 15.90 651.3 627.4 17.58 655.4 630.3 18.27 659.4 632.2 18.70 663.1 635.5 19.58 666.7

533.8 4.75 &3 641.2 564.1 7.57 641.0 584.3 10.07 641.1 603.6 13.03 641.6 624.0 16.93 642.0 21.28 658.4 23.05 633.9 19.23 643.0 21.41 655.4 22.84 637.3 20.19 638.1 a 20.44 639.4 20.77 640.2 21.04

689.1 14.95 639.7 21.19 771 1.200 cp2 638.6 21.18 647.14 22.064 cpl 638.3 21.34 645.5 21.85 Ig 638.5 21.86 643.8 21.62 638.8 22.07 641.0 21.33 640.5 23.00

Tetracosane + water

632.7 19.40 UCEP 646.2 21.95 fg - 651.7 20.98 Ig 645.8 21.90

662.7 21.40 645.3 21.82 472.8 21.30 644.6 21.71

1.020 cp2 641.7 21.27 22.064 cpl 640.9 21.17

Pentacosane + water

19.02 658.0 21.75 19.62 818 0.98 cP2 20.06 647.14 22.064 cpl 20.22 UCEP 646.5 21.93 Ig 20.15 Ig 645.2 21.75 20.11 643.8 21.53 20.15 643.1 21.42 20.27 642.3 21.32 20.53 641.8 21.23 20.95 641.0 21.16 21.25 641.9 21.96 21.55 643.0 22.38

Hexacosane + water

20.25 669.3 22.67 20.89 672.1 22.78 21.16 675.0 22.88

827 0.95 CP2 21.44 UCEP 647.14 22.064 cpl 21.45 lg 646.2 21.96 Ig 21.71 645.5 21.85 22.00 644.5 21.69 22.25 644.0 21.61 22.41 643.0 21.45 22.57 642.4 21.37

Oetaeosane + water

21.44 UCEP 672.2 23.78 Ig 21.35 lg 669.0 23.63 21.29 664.9 23.44 21.23 661.9 23.25

644.7 21.66 652.2 22.60 645.5 21.80 649.2 22.35 647.14 22.064 CD1 647.6 22.22 843 0.89 ep2 646.0 22.12

642.3 23.85 644.6 24.87 648.4 26.98 654.8 30.38

640.1 21.13 640.4 21.43 640.5 21.54 641.9 22.24 645.6 23.71 651.6 26.13 659.0 29.35

644.3 22.83 644.6* - 645.0 23.20 646.1 23.60 650.2 25.15 653.9 26.70 658.0 28.35 662.3 30.10 666.4 32.05

640.6 21.18 640.6 21.28 640.8 21.41 641.4 21.64 642.2 22.00 642.8 22.22 643.5 22.46 651.2 25.50 655.7 27.30 662.1 29.90

644.3 22.05 644.1 22.34 645.3 22.98 647.9 24.02 648.5 24.25 650.8 25.14 652.4 25.80 656.f 27.30

342 E. BRUNNER

TABLE 2-continued

T/K p/MPa T/K PIMPa T/K pIMPa - T/K p/MPa

502.5 2.76 Hg 637.9 532.1 4.62 638.5 562.0 7.36 639.8 590.2 11.02 641.1 609.9 14.32 641.6 629.9 18.30 641.7 635.3 19.46 642.1 635.9 19.63 642.6 636.7 19.80 643.f

499.3 2.612 llg 635 429.4 4.450 637.2 560.0 7.163 640.1 590.8 11.00 642.1 608.9 13.95 643.4 617.6 15.56 644.3 629.2 17.95 644.9 633.5 18.97 645.5

549.3 6.09 Ilg 639.4 570.3 8.30 641.6 591.4 11.08 642.4 611.9 14.40 644.5 633 - 644.7 634.2 19.00 645.1 636.7 19.62 645.8

Tricontane + water 20.09 643.9 21.63 20.27 644.8 21.73 20.63 645.6 21.87 21.03 646.3 21.96 21.35 UCEP 646.7 22.03 21.30 Ig 647.14 22.064 21.37 8.57 0.83 21.43 670.8 24.90 21.50 661.4 24.27

Dotricontane + water 646.2 21.95

19.87 646.6 22.02 20.63 647.14 22.064 21.20 UCEP 871 0.79 21.45 Ig 673.3 25.85 21.60 671.1 25.68 21.71 668.6 25.53 21.82 666.2 25.35

Hexatricontane + water 20.28 646.3 21.95 21.83 647.14 22.064 21.49 UCEP 895 0.71 21.64 lg 684.2 28.00 21.70 680.3 27.60 21.77 677.0 27.27 21.88 612.7 27.00

CPl CP2 k

CPl CP2 43

CPf CP2 k

655.6 23.95 653.0 24.13 654.5 25.25 657.8 26.85 662.1 28.75 665.3 30.20

663.7 25.22 661.0 25.28 660.0 25.66 661.7 26.85 664.8 28.55 669.1 31.02 671.9 32.45

670.5 26.87 664.6 26.55 667.6 29.00 671.3 31.46 675.0 33.50 679.5 36.05 682.9 38.05

Barotropic reversal of the two liquid phases on the Ilg three-phase line. b Barotropic reversal of the two fluid phases on the Ig-critical curve.

373 and 473 K; and ~0.5 K above 473 K. The main error in the temperature measurement by the calibrated thermocouples is to be ascribed to a time drift of the electromotive force E(t). However, this error can be significantly reduced by prolonged tempering and repeated calibration of the therm~ouples. The thermocouple was checked additionally by measuring the critical temperature for the pure substances and relating it to the critical temperature T, quoted in table 1. As a result, the relative accuracy in the vicinity of the critical temperature for both pure substances of the corresponding binary mixture has been increased to AT < 0.2 K. Systematic drifts of the measured values of pressure and temperature were observed, above all with higher alkanes, whenever the test substances were heated for a considerable time to temperatures above about 600 K. To reduce these measurement errors, which are difficult to estimate, the residence times of the test substances at high temperatures were shortened as far as possible. As a rule, these were not more than 2 to 4 h. The maximum measurement errors due to the thermal degradation of

23 @-ALKANE + WATER) MIXTURES 343

the alkanes above 600 K would in general probably not exceed values of AT = 1 K and Apfp = 0.005.

The mole-fraction purities of the substances and the suppliers are summarized in table 1, which also contains selected literature values of the critical tem~ratures and pressures of the pure substances. The purities quoted for water, methane, ethane, propane, and butane are guaranteed by the supplier. Those for alkanes with a carbon number of 4 < i < 20 were determined by capillary g.c. with different capillaries. The 25 m fused capillaries used for i > 4 were SE 54 (methylsilicone rubber with 5 per cent of phenyl and 1 per cent of vinyl) and SE 31 (methylsilicone rubber with 1 per cent of chemically bonded vinyl). A 50 m capillary with squalane was additionally used for i = 5 to 9. The alkanes for i > 19 were assayed by d.s.c. The alkanes with i > 4 and water were carefully degassed in a separate apparatus. All those having a melting temperature higher than 280 K were introduced by means of a heated screw press and heated feed lines. The substances investigated were not further purified except for hexane, which was obtained by rectification of 99 moles per cent hexane in a 50-plate column at a high reflux ratio.

TABLE 3. Prominent vatues of the Ilg three-phase line and the critical phenomena of (n-afkane + water): i, carbon number of the n-alkane; p, pressure; T, tem~ratme; ~p/~T, gradient of the critieai curve at the critical point of water, 1, upper critical end point, UCEP; 2, temperature minimum of the high-pressure branch of the critical curves; 3, pressure minimum of the high-pressure branch of the critical curve; 4, pressure maximum of the low-pressure branch of the critical curve; 5, barotropic reversal of the two

liquid phases on the Ilg three-phase line

i %PT MPa.K- T,lK

- -----__I I -1.39 - 2 -0.43 - 3 -0.24 369.1 4 -0.17 424.1 5 -0.13 463.8 6 -0.090 496.4 1 - 0.036 520.0 8 - 0.020 540.0 9 0.010 554.0

10 0.025 561.6 11 0.040 577.8 12 0.055 584.8 14 0.070 598.7 16 0.090 608.3 18 0.11 616.5 20 0.12 622.7 24 0.12 632.7 25 0.14 636.4 26 0.12 641.2 28 0.15 641.2 30 0.12 641.6 32 0.12 642.1 36 0.13 642.4

- - -

4.260 621.7 4.260 623.0 4.577 625.1 5.282 626.4 6,320 628.6 7.410 630.1 8.540 631.0 9.655 631.9

10.75 633.2 11.66 634.4 13.41 635.5 14.87 636.3 16.07 637.1 17.08 638.2 19.40 640.0 20.22 640.4 21.44 640.6 21.44 644.1 21.35 653.0 21.20 660.0 21.49 664.2

- -

- _-

46.3 38.0 32.5 29.7 27.0 26.0 25.0 24.0 23.0 22.5 22.1 21.6 21.4 21.5 21.2 21.2 21.2 22.2 24.2 25.6 26.8

- - _-.

- 640 22.00 638 21.90 638 21.70 638.0 21.60 638.0 21.46 638.0 21.23 638.2 21.13 639.0 21.13 640.2 21.10 640.6 21.13 640.8 21.1s 645.5 22.0s 653.8 23.90 662.5 25.20 665.0 26.55

- -

- -

- -

- -

- - 623.0 15.33 634.0 16.78 640 18.00 667 21.42

- -

- -

- -

640 638.1 635.9 635 633

344 E. BRUNNER

T/K

FIGURE 2. Survey of the p(T) proj~tjons of the llg three-phase fines and of the two branches of the inte~upted lg-critical curves of (n-alkane f water). indicated numbers are carbon numbers of the n-alkane; -0, vapour pressure and critical point of water; point of the n-alkane;

- - - 0, vapour pressure and critical -0, llg three-phase line and Ig-UCEP. To allow easier review, only the high-

pressure branches of the Ig-critical curve for the eight mixtures with i = 1, 3, 6, 12, 18, 24, 30, and 36, are plotted. So as not to complicate the curves, measured p(T) points have not been indicated besides the Ig-UCEPs.

3. Results aad discussion

All (n-alkane -I- water) mixtures investigated have an interrupted critical curve of type III according to the classification of Scott and Konynenburg(9-21) and, with the exception of (methane + water), an llg three-phase line that terminates at an lg-UCEP. For {methane + water) there is no common range of temperature in which both pure substances in the mixture are liquid; this means that the llg three-phase line and the lg-UCEP do not exist. The experimental p(T) values on the llg three- phase lines and on both branches of the critical curves for 23 (n-alkane f water) mixtures with carbon numbers of the n-alkanes of i = 1 to 12 and i = 14, 16, l&20, 24,25,26,28,30, 32, and 36 have been compiled in table 2. Prominent values on the critical curves are summarized in table 3. They include the slope i3pjaT of the critical curves at the critical point of water, the p(T) values of the UCEP, of the temperature minima, and of the pressure minima and maxima of the critical curves, and also of the barotropic reversal of the two liquid phases on the Ilg three-phase line. The shape

23 @-ALKANE + WATER) MIXTURES

3

3

E r

2

2

5- \

o-

s-

oi 630 640 650 660 670 680

TIK

FIGURE 3. Larger-scale section of the high-pressures branches of the critical p(T) curves for eight (n-alkane + water) mixtures with carbon numbers i = 1, 3. 6, 12, 18, 24, 30, and 36. -0, Vapour pressure and critical point of water. So as not to complicate the curves, the measured p(r) points have not been indicated.

of the llg three-phase lines and of the critical curves of the mixtures changes systematically with the carbon number i and, because of the very large differences in the polarity of alkane and water, these mixtures show a very characteristic phase behaviour.

A general review of the phase behaviour of the (n-alkane + water) family is given in figure 2. To allow easier review on the phase behaviour of the (n-alkane + water) family only for the eight mixtures with i = 1, 3, 6, 12, 18, 24, 30, and 36, the high- pressure branches of the critical curves are plotted in this figure. These high-pressure branches are presented in an enlarged scale in figure 3. To allow the shape of the high-pressure branches of critical p(T) curves to be recognized more clearly all 23 curves are plotted in figures 4a, 4b, and 4c also in an enlarged scale. In contrast to the already investigated families of (an n-alkane + pyridinef5) or acetic acid() or methanol6* I or ammoniat7) or tetrafluoromethane30* 31) or carbon dioxide(32* 33) or ethane34) and of (methane + a mixture of alkanes),35* 36) where a change of the phase behaviour from type II to type III always takes place at a corresponding change in the carbon number of the alkane, all 23 (n-alkane + water) mixtures have an interrupted critical curve with an lg-UCEP, at which the gas phase and the liquid phase of the lower density become identical. Because of the wide range of the critical temperatures, which is covered by the alkanes: T,(CH,) = 190.6 K to K(C36H74) = 894 K, the investigations cover regions of temperature, where the non-polar alkanes

346 E. BRUNNER

25

25 t

620 I

630 640 650 660 670 680

FIGURE 4. Larger-scale section of the high-pressure branches of the critical p(T) curves for all 23 (n-alkane + water) mixtures investigated. Indicated numbers are the carbon numbers of the n-alkane. -0, Vapour pressure and critical point of water. So as not to complicate the curves, the measured p(T) points have not been plotted.

have a higher volatility than water, and also regions where their volatility is lower than that of water. With increasing carbon number i, the decreasing volatility of the n-alkanes leads to the following characteristic changes in the phase behaviour of the binary mixtures. At i = 2 to i = 26, the dT) projection of the llg three-phase lines runs to an lg-UCEP. Since the water-rich liquid phase on the llg three-phase line always has a higher density than the alkane-rich liquid phase at all temperatures, the gas phase becomes identical with the alkane-rich liquid phase at the lg-UCEP. At the same time, this has the consequence that the critical curve starting from this

23 (n-ALKANE + WATER) MIXTURES 341

FIGURE 5. Dependence of the critical temperatures T(lg-UCEP) and of the temperatures Tb of the barotropic reversal of the two liquid phases of (an n-alkane + water) on the n-alkane carbon number i. 0, 1%UCEP; - - -, critical temperature of water; 0, temperatures Tb of the barotropic reversal of the two liquid phases on the Ilg three-phase lines.

lg-UCEP ends at the critical point of the corresponding alkane. With increasing carbon number of the alkane, this branch of the interrupted critical curve sweeps increasingly large temperature ranges and, for i = 26, reaches the extraordinarily high value of AT = 186 K. The second branch of the interrupted critical curve of the mixtures with i = 1 to i = 26, which starts from the critical point of water, initially passes through a temperature minimum, and rises steeply to high pressures as the temperatures rise again. For all mixtures with i = 7 to i = 26 this branch of the critical curve additionally also passes through a pressure minimum between the critical point of water and the temperature minimum.

With the carbon number i of the alkanes rising further, the temperature of the lg-UCEP rises further. Because of the very wide (liquid + liquid) miscibility gap, however, no 11-UCEP occurs with any of the mixtures. In contrast to some mixtures of (an aromatic compound + water) where, for example, an infinite miscibility was found for (naphthalene + water),37) (diphenyl + water), and (1,2,3,4- tetrahydronaphthalene + water). (45*46) the lg-critical curves remain interrupted even at high carbon numbers. When the lg-UCEP then reaches, with increasing carbon number i, temperatures which are in the range of the critical temperature of water, T,(H,O) = 647.14 K, a very characteristic change takes place in the phase behaviour, such as has hitherto not yet been found with other homologous mixtures. In the temperature region immediately below the critical temperature of water, the density

348 E. BRUNNER

(e) i = 30

25-

(f) i = 32

4

TIK TIK

FIGURE 6. Section of the Ilg three-phase lines and the two branches of the critical p(T) curves for (n-alkane + water) with the carbon numbers i = 20,24,26,28, and 30 in the region of the critical point of water. -0, Vapour pressure and critical point of water; - - - 0, Ilg three-phase line and lg-UCEP.

of the water-rich liquid phase 1, on the three-phase line decreases substantially faster with rising temperatures than that of the alkane-rich liquid phase 1, until finally the water-rich phase 1, has the lower density before the UCEP is reached. A barotropic effect with reversal of theliquid phases occurs on the l,l,g three-phase line; the consequence is that the water-rich liquid phase 1, becomes identical with the gas phase at the Ilg-UCEP. This also means that the l,g-critical curve which starts from the l,g-UCEP, now no longer ends at the critical point of the alkane cp2 but at the critical point of water cpl. The dependence of the critical temperature T(lg-UCEP) on the carbon number i together with the temperature Tb of the barotropic reversal of the two liquid phases on the 1,12g three-phase lines for i = 28, 30, 32, and 36 have been plotted in figure 5. The larger-scale section of figure 5 shows clearly the decrease of the temperature difference AT = (T(lg-UCEP)- Tb) with decreasing carbon number i. The barotropic effect was found with all mixtures with i > 28, whereas

23 @-ALKANE+ WATER) MIXTURES

T/K

349

FIGURE 7. Larger-scale section of the llg three-phase line and the critical p(r) curves for (n-alkane -t water) with i = 24, 25, 26, and 28. To have a better review the critical p(T) curves extending from the critical point of water for the mixtures with i = 24, 25, and 26 have been omitted. -0, Vapour pressure and critical point of water; - - - 0, llg-three-phase line and lg-UCEP. So as not to complicate the curves, the measured p(T) points have not been indicated.

with all mixtures with i < 26 no barotropic effect exists on the I,l,g three-phase line. With a defined quasi-binary (n-alkane + water) mixture, whose effective carbon number i lies approximately at i = 26 or a little above, AT becomes zero and the tem~rature of the UCEP and of the barotropic reversal of the two liquid phases must collapse in a (liquid 1 + liquid 2 + gas) tricritical end point l,f,g-TCEP where all three phases become simultaneously identical. When the temperature of the llg three-phase mixture with i = 26 is increased slowly, the beginning of the barotropic phase reversal of the two liquid phases makes itself conspicuous by a strong spherical rising in some parts of the interface of the two liquids shortly before the UCEP is reached.

Because the tricritical point of a ternary mixture is an invariant that exists only at a unique set of physical quantities Cp, T, x1, x2) it cannot be measured directly. For the defined quasi-binary (n-alkane + water) mixture with i x 26 this tricritical point is the end point of the three-phase line and of the three branches of the critical curve, (a) l,g, which starts from the critical point of water, (b) 12g, which starts from the critical point of the alkane mixture, and (c) 1,12, which is the ~ntinuation of the l,l,g three-phase line and which rises with increasing temperature up to high pressures. At

350 E. BRUNNER

the tricritical end point TCEP the three-phase line and the three branches of the critical curve possess the same slope. There has so far been no other example in the literature of the type of a tricritical point such as was found in the (n-alkane + water) family, where the tricritical point simultaneously is the end point of an llg three- phase line and of three branches l,l,, l,g, and 1,g of the critical curve. Tricritical points are of great thermodynamic interest, and numerous theoretical and experimental investigations have dealt with this interesting hhaviour (38-40,489 49)

phase

To show the systematic changes and the characteristic differences in phase behaviour between mixtures with i < 26 and i 2 28 sections of the llg three-phase lines and the critical p(T) curves in the region of the critical point of water are summarized for the mixtures with i = 20,24,25,26,28, and 30 in figures 6a to 6f. To give a better idea of the shape of the different curves these figures have also been simplified by omitting all measured p(T) points with the exception of those that are prominent. A larger-scale section of the region of the critical point of water for the mixtures with i = 24,25,26, and 28 is plotted in figure 7 to show in more detail these systematic changes in phase behaviour.

A further characteristic very typical of (an n-alkane + water) is the very low mutual solubility of alkane and water. (42) A consequence of this is the fact that, in the llg three-phase region, the total pressure of the mixtures is sometimes significantly higher than the sum of the vapour pressures of the individual components. This remarkable effect has already been found by Scheffer and confirmed by Roof(43 and by Tsonopoulos and Wilson. (44) It is not possible to predict quantitatively this enhancement of the vapour pressures and the effect of gas-phase non-ideality because of the inability to calculate fungacities in gaseous (alkane + water) mixtures. This is due to insufficient knowledge about intermolecular forces and volumetric properties of the mixed fluids.

4. On the topology of tricritical points

To demonstrate how tricritical points of quasi-binary mixtures occur, the two basic types of tricritical point which have so far been found in real mixtures are compared below and presented schematically in figures 8a to e and 9a to e.

TYPE II-TO-TYPE III TRANSITION

Figure 8 (a) to (f) shows in schematic p(T) projections the typical intermediate stages and border-line cases for the transition from type II to type III, as has for instance been found in (n-alkane + ammonia). () Type II (figure 8a) possesses an l,l,g three-phase line, an l,l,-UCEP, and an uninterrupted critical curve designated (1,g + l,g), to underline the connection with the other phase diagrams of figure 8. Index 1 refers to the more volatile component and index 2 to the less volatile component.

As the carbon number of the alkane rises, the (1,g + 1,g) critical curve begins to bifurcate into the two branches 1,g and 1,g. The border-line case type II/IV

73 (rr-ALKANE+ WATER) MIXTURES 351

T T T

FIGURE 8. The transition of the phase behaviour of binary mixtures from type II to type III shown as p(r) projections of the critical loci and the Ilg three-phase lines due to increasing molecular dissimilarities between the components 1 and 2, according to the classification of Scott and van Konynenburg. U, upper critical end point; L, lower critical end point; 1,12, I,g, 1~ branches of the critical curves; (l,g + t,g), uninterrupted critical curve; (I,& + llg), high-pr~sure branch of the interrupted critical curve, which starts from the critical point of component 2; p, pressure; T, temperature.

(figure 8b) is designated by the tricritical point l,l,g-TCP on the (I,g + 1,g) uninterrupted critical curve; 1,g and 1,g have the same slope at 1,&g-TCP.

Type IV (figure SC) is characterized by the interrupted three-phase line with the three critical end points Iii,-UCEP, LCEP, and l,g-UCEP and the three critical curves lil,, l,g, and 1,g.

As the carbon number of the alkane increases further and as the miscibility of the alkane and ammonia decreases, the branch of the three-phase line between LCEP and l,g-UCEP gets bigger and the gap between l,l,-UCEP and LCEP smaller, until in the border-line case of type IV/III (figure Sd) I,l,-UCEP and LCEP unite and a double-critical point DCP occurs on the three-phase line. The now united branches 1,12 and 1,g form the critical curve (lil, + l,g), which tangentially touches the three-phase line at the double-critical point.

As the miscibility of the components decreases further as a result of the increase in carbon number of the alkane, the critical curve separates from the three-phase line and phase behaviour of type III (figure 8e) is obtained with the two branches (l,l, + 1,g) and 1,g of the interrupted critical curve and an uninterrupted three-phase line with an l,g-UCEP.

The special case of the tricritical point (figure 80, in which no type IV behaviour occurs on transition from type If to type III, in other words, where the three-phase line and the (1,12 + 1,g) critical curve touch tangentialiy at l,g-UCEP, and thus the double-critical point, the tricritical end point, and the UCEP unite at a tricritical end

352 E. BRUNNER

(4 (b) Cc)

/

412

hg CD1 -

TCEP

T T T

FIGURE 9. The transition of the phase behaviour of binary mixtures from type IIIa to type IIIb with the border-line case type IIIa/IIIb. (l,l, + I,g), high-pressure branch of the interrupted critical curve, which starts from the critical point of component 1. The meaning of the other symbols is the same as in figure 8.

point l,l,g-TCEP, has so far not been found for any real fluid mixture. However, this in the realm of real probability.

TYPE IIIa-TO-TYPE IIIb TRANSITION

Figure 9 (a) to (c) shows schematically the phase behaviour of a mixture family in which only type III with an interrupted critical curve occurs as was found for the first time in (an n-alkane + water). At low alkane carbon numbers, the critical curve which starts at l,g-UCEP runs to the critical point of the n-alkane (component 2); by contrast, at high carbon numbers, it runs from lrg-UCEP to the critical point of water (component 1). The two types of phase behaviour are designated type IIIa and type IIIb, respectively.

In the border-line case IIIa/IIIb (figure 9b) the two branches of the critical curve touch the three-phase line tangentially at lg-UCEP and possess here a tricritical end point l,l,g-TCEP. The two branches 1,g and (l,l, + 1,g) which exist at low carbon numbers become the two branches 1,g and (l,l, + 1,g) which exist at high carbon numbers. A transition from type IIIa oia type IV to type IIIb analogous to the transition from type II via type IV to type III does in all probability not occur in real fluid mixtures.

REFERENCES

1. Brunner, E. J. Chem. Thermodynamics 1985, 17, 671. 2. Brunner, E. J. Chem. Thermodynamics 1985, 17, 871. 3. Brunner, E. J. Chem. Thermodynamics 1985, 17, 985. 4. Brunner, E.; Hiiltenschmidt, W.; Schlichthiirle, G. J. Chem. Thermodynamics 1987, 19, 273. 5. Brunner, E. J. Chem. Thermodynamics 1987, 19, 823. 6. Brunner, E. J. Chem. Thermodynamics 1968, 20, 273. 7. Brunner, E. J. Chem. Thermodynamics 1988, 20, 1397. 8. Welsch, H. Ph.D. Thesis, University of Karlsruhe, F.R.G. 1973. 9. Sultanov, R. G.; Skripka, V. G.; Namiot, A. Yu. Gasov. Prom. 1971, 16, 6; ibid. 1972, 17, 6.

10. Danneil, A. Ph.D. Thesis, University of Karlsruhe, F.R.G. 1966.

23 @-ALKANE + WATER) MIXTURES 353

11. Danneil, A.; Tiidheide, K.; Franck, E. U. Chem-lng.-Techn. 1967, 39, 816. 12. Sanchez, M.; Coil, R. An. Quint 1978, 74, 1329. 13. Loos, Th. W. de; Wijen, A-J. M.; Diepen, G. A. M. J. Chem. Thermodynamics 1980, 12, 193 14. Tsiklis. D. S.: Maslennikova. V. Ya. Do/cl. Akad. Nauk S.S.S.R. 1%4. 157. 417. 15. Connohy. J. F. J. Chem. Eng. Data 1966, 11, 13. 16. Peter, K. H. Diplom Thesis, University of Karlsruhe. F.R.G. 1968. 17. Briillos, K.; Peter, K. H.; Schneider. G. M. Ber. Bunsenges. Phys. Chem. 1970. 74, 682 18. Scheffer, F. E. C. Proc. Roy. Acad. Amsterdam 1913, 16. 404. 19. Konynenburg, P. H. van. Ph.D. Thesis, University of California, Los Angeles. 1968. 20. Scott, R. L.; Konynenburg, P. H. van Discuss. Furaduy Sot. 1970, 49, 87. 21. Konynenburg, P. H. van; Scott, R. L. Phil. Trans. Rov. Sot. London 1980, A 298. 495. 22. Brunner. E.; Maier, S.; Windhaber. K. J. Phys. E.: Sri. Instrum. 1984, 17, 44. 23. TRC Thermodynamic Tables: Non-Hydrocarbons. Thermodynamic Research Center: Texas A & M

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editors. Vol. 9. Academic Press: London, 1984. 40. Widom, B.; Sundar, G. Fluid Phase Equilibria 1986, 30, I. 41. Loos, Th. W. de; Penders, W. G.; Lichtenthaler, R. N. J. Chem. Thermodynamics 1982, 14, 83. 42. Shaw. D. G. Solubility Data Series. H,vdrocarbons with Water and Seawater. Vol. 37: Hvdrocarbons C,

to Cr. Vol. 38: Hydrocarbons C, to C,,. Pergamon Press: Oxford. 1989. 43. Roof, J. G. J. Chem. Eng. Dafa 1970, 15, 301. 44. Tsonopoulos, C.: Wilson, G. M. AIChE J. 1983, 29, 990. 45. Jockers, R. Ph.D. Thesis, University of Bochum. F.R.G. 1976. 46. Jockers, R.: Paas, R.; Schneider. G. M. Ber. Bunsenges. Phys. Chem. lW7, 81. 1093 47. Somayajulu. G. R. J. Chem. Eng. Datu 1989, 34, 106. 48. Meijer, P. H. E. J. Chem. Phys. 1989, 90, 448. 49. Deiters. U. K.; Pegg. 1. L. J. Chem. Phys. 1989, 90. 6632.