Experimental determination of the volume change on mixing for gaseous N2-H2, Ar-H2 and Ar-N2 between 170 and 292°K up to 100 ATM

Zandbergen,

Physica

P.

Beenakker,

33

343-365

J. J. M.

1967

EXPERIMENTAL DETERMINATION OF THE VOLUME CHANGE ON MIXING FOR GASEOUS Nz-Hz, Ar-Hz AND Ar-N2 BETWEEN 170 AND 292°K UP TO 100 ATM and J. J. M. BEENAKKER

by P. ZANDBERGEN Communication

No. 351~ from the Kamerlingh

Onnes Lahoratorium,

Leiden,

Nederland

is described

the volume

on mixing

Synopsis A direct constant Ar-N2 and

method pressure.

at several

Measurements concentrations

for measuring

were performed between

change

for the systems

170 and 292°K

N2-Hz,

and at pressures

of gases at Ar-Hz

and

between

3

100 atm.

1. I&rod&ion. In the last years considerable progress has been made in the study of the thermodynamic properties of liquid mixtures, both theoretically and experimentally. For a large number of systems, quantities like heat of mixing, volume change on mixing and excess Gibbs free energy have been measured. In this respect a good deal of attention has been paid to systems, composed of simple molecules like Hz, Dz, Nz, Ar etc. Surveys are given by Parsonage and Staveleyl), McGlashanz), and by White and Knoblers). Especially for these systems there has been important theoretical progress, based on a corresponding states treatment. Significant contributions have been reported by Prigogine4) and by Scott5). All this work is, however, virtually limited to liquid systems. Very little experimental work has been done on properties of gaseous mixtures at higher densities, not withstanding both their fundamental and technological importance. In our opinion the main reason for this lack of data is to be found in the way this problem was attacked. The classical approach to obtain thermodynamic data of gaseous mixtures is the same as the one used for pure gases, i.e. the performance of highly accurate $VT measurements. This type of work requires, as is well known, a rather complicated experimental setup, combined with a great deal of experimental skill. Furthermore these measurements are very time-consuming. The extra parameter, given by the concentration, creates in the case of gaseous mixtures a problem that is nearly unsolvable along these lines. At the moment, for most pure systems made up of simple molecules, --

343 -

344

P. ZANDBERGEN

AND

J. J. M. BEENAKKER

thermodynamic properties are reasonably well known6). In this respect we mention the outstanding experimental work, performed in the Van der Waals laboratory and the impressive data-processing program of the National Bureau of Standards. This means that the value of most thermodynamic quantities can easily be obtained for an ideal mixture, i.e. a mixture, of which the volume varies linearly with the concentration. As a consequence the only relevant information, necessary to describe the behaviour of a real mixture, is the deviation from ideality, the excess property. Hence it seems worthwile to concentrate one’s effort on a direct determination of the excess quantities, hoping that this will be the easier way to a knowledge, that enables a description of the behaviour of the real mixture. With this philosophy the Kamerlingh Onnes Laboratory group for molecular physics started a few years ago a program for the determination of the thermodynamic properties of gaseous mixtures of simple molecules. Two problems were attacked at the same time; the heat of mixing and the volume change on mixing. The reason being, that the knowledge of these two quantities makes a complete thermodynamic description possible, without having to perform the measurements with excessive accuracy. It should of course have been possible, but not practical, to determine all thermodynamic properties, starting from the volume change on mixing at constant pressure, BE, only. The accuracy needed in that case would, however, completely off-set the advantages of our direct approach. The situation in this respect is similar to the one, occurring in the study of liquid mixtures. From the point of view of theory a complete thermodynamic description is possible from a knowledge of GE (vapour pressure and composition measurements). In practice, however, it is commendable to measure directly the heat of mixing. Another reason for a study of both I?E and PE is that agreement with theory is in general more easily obtained in the case of BE than that of PE. Hence for a theoretical description of the properties of the mixtures, a knowledge of both quantities is desirable. In view of the experimental and theoretical state of affairs, the aim of our program was to measure BE and PE with an accuracy of a few percents. We started with the systems Na-Hz, Ar-Ha and Ar-Na. This choice was the result of several considerations. We wanted to start with systems that would show rather large deviations from ideality. This was expected to be the case for a mixture of two components with widely different critical temperatures, in the pre-critical region of one of its components. Furthermore we preferred to work with inexpensive gases. The technological importance of the Na-Ha mixture, combined with these arguments decided the choice in favour of this system. Ar-Hs was studied because it is expected that if nonsphericity is of little importance, this system will behave very similarly to that of Ns-Hz. This is so because the molecular interaction

EXPERIMENTAL

parameters chosen

are not too much

to study

a mixture

DETERMINATION

different of rather

in both similar

345

OF @

cases.

Finally

molecules.

Ar-N2

We studied

was the

aforementioned systems at several concentrations between 170 and 300°K and at pressures up to 100 atm. This paper will deal with the volume change on mixing. Work on heat of mixing is reported by Knoester, Taconis and Beenakker7) while a preliminary review of our program was given at the 1965 Purdue Therm ophysical Properties Symposiums). 2. Experimental method. In the past volume or pressure change on mixing measurements were only performed at pressures below 1 atma). The higher pressures and the temperature range 170-300°K create some problems, that made in our case a different setup necessary. In the systems under study PE is mostly positive, i.e. to keep the pressure on mixing constant, we have to increase the volume, or at constant volume the way from the pressure increases on mixing. The most straight-forward experimental point of view seems to be a determination of this pressure change. At pressures below 100 atm we preferred glass U-tube differential manometers, because of their simplicity combined with high sensitivity. The drawback of this method is the change in the dead volume of the U-tube of the manometer as a function of pressure-difference. To avoid this difficulty we have determined the amount of gas that has to be let out of the system to keep the pressure on mixing constant. The differential manometer serves now as a zero-point instrument. The amount of gas let out can easily be determined by using the ideal gas law from the measurement of the low pressure in a vessel of known volume at room temperature. Fig. 1 shows a schematic diagram of the apparatus, which consists of the following parts : a) The metal vessels Vr and Vs are filled with the gases to be mixed. The volumes of these vessels are calibrated by expansion of an ideal gas in a volume of known value. b) A mixing arrangement. In the vessel I’1 a smoothly fitting plunger P is placed. This plunger can be moved up and down by a connecting rod, that leaves the high pressure part of the apparatus through an O-ring seal in the room temperature section. The gases in the vessels Vi and ‘c”aare mixed by moving this plunger up and down after opening valves in the capillaries, that connect Vi and I”2 and closing valves giving access to the differential manometry. To avoid dead spaces special attention is paid to have as small as possible the volumes of the connecting capillaries and the valves, e.g. the last ones are specially constructed for this purpose in our workshop. It may be noted that the corrections for the dead space never amount to more than around 3%. c) Differential manometry and pressure reference system. To obtain an

346

P. ZANDBERGEN

Fig. 1. A schematic

AND J. J. M. BEENAKKER

diagram

of the apparatus.

accuracy of say 2% in FE it is necessary to be able to detect pressure than of the order of 1 part in 104 and this up to pressures of 100 atm. This quires not only the necessary sensitivity of the differential manometry also a high degree of stability of the pressure in the system. The sensitix of the manometry is easily obtained using oil or mercury U-tube dif ential manometers. These manometers are made of 2 mm internal I 10 mm external well annealed glass tubes. At the end of the tube a t layer of platinum is chemically deposited and subsequently it is copI electroplated. Connections with the rest of the apparatus were made soft-soldering on this copper layer. This system works very well and seld gives rise to leakage. The pressure after mixing is compared with the initial pressure i reference vessel, Va, that is in good contact with Vi and Vs. In this \ pressure variations are balanced out and no long term pressure stabi is required. d) The constant temperature bath. The vessels Vi, I’s and Vs are pla in a Dewar that is filled with liquid propane and ethylene, boiling at tl normal boiling point, to obtain respectively the temperatures 231.7 : 170.5”K. The necessary amount of stirring is obtained by a heater at bottom of the cryostat, that produces a constant stream of vapour bubl passing through the liquid. For the measurements at room temperature Dewar is replaced by a normal waterthermostat.

EXPERIMENTAL

DETERMINATION

OF PE

347

e) To bring after mixing the pressure in Vr and VZ back to the original value, gas is vented in vessel R, that is placed in a thermostated waterbath. Depending on the expected volume change we used for R volumes of about 80, 1000 or 3000 ems. The volumes are calibrated by weighing with water. The pressure of the gas in R is measured with an oil or mercury manometer. The normal procedure for a measurement is the following. The vessel Vi is filled with gas A and Vz and Va with gas B to the same pressure, as measured on the differential manometer Dr. Subsequently the valves 1, 2, 3, 4, 5 and 8 are closed the valves 6 and 7 are opened and gases A and B are mixed by moving plunger P up and down. We checked whether the mixing is complete by measuring with the manometer Dz the pressure-changes after 5, 10, 15 and 20 strokes of the piston. After 10 strokes no further pressure changes were found. To be sure of complete mixing we mix with at least 20 strokes. After the mixing is completed Ds is connected. The exact amount of gas that has to be let out to bring the pressure difference back to zero is determined by interpolation. The gas is let out in two steps, one at which the pressure difference is still slightly positive and one where this difference is slightly negative. In the very few cases studied where the pressure decreases on mixing, we obtained the volume change by extrapolation of two points with a slightly larger pressure decrease. To be able to measure at different concentrations we used in combination with Vr, two vessels, VZ and Vi, the volumes of which are half as large as the volume of VI. By interchanging the position of the gases and by replacing VZ by Vi measurements at four concentrations can be performed. In the earliest measurements at room temperature we used a slightly different setup. The slit between the plunger and the cylinder is so small (of the order of one micron), that there is practically no gas leaking through the slit, even when there is an appreciable pressure difference over the slit. Having different gases above and below the piston, V, and VI, it is possible to perform the measurements without the use of a second vessel. The gases are now mixed by forcing them through a capillary, that connects V, and Vl. The advantage of the method is that if one knows the volumes of Vu and VI as a function of the position of the piston, it is easily possible to perform measurements as a function of concentration. Damage of the plunger caused leakages along the slit and this method was abolished in favour of a separate second vessel in the later experiments at low temperatures. The values of the different volumes that are used are given in table I. The apparatus was TABLE

I

Values of the calibrated volumes in cm3

Dead space

348

I’. ZANDBERGEN

AND

J. 1. M. BEENAKKER

checked by performing a blank run with the same gases in all vessels. After going through the mixing procedure we found no pressure change. 3. Experimental results. To obtain the values of volume variation mole of the mixture we proceed in the following way. Before the mixing have in vessel VI at pressure p and temperature T, NA mole of gas A in vessel VZ, under the same condition of pressure and temperature, mole of gas B. Thus we have VI + V2 = NAP;

+ N&

per we and Nn

(1)

where Pi and P$ are the molar volumes of the pure components A and B respectively. The tilde denotes molar quantities. After mixing and reestablishment of the pressure p by letting out dN mole of the mixture in R we have VI + V2 = (NA + Ng - AN) 8, where P, is the molar volume of the mixture. tuting the mole-fractions %A and xn we find LIN NA

+

P, NB

where the excess volume,

pin

@,

is defined as Pm -

.Ap;

eqs. (3) and (4) we obtain PE

=

_

+ NBP~

eq. (2) and substi-

FE Fm

-

.nP;.

(2)

(3)

(4)

for VE

AN

NA + Ng -

Rewriting

-.nP; ------~

=

FE = Combining

-X,7;

= NAP:

AN

- (XAP;; + x&)

AN can be calculated from the pressure and the temperature of the gas in R and the volume of R. NA and Nn are calculated from the calibrated volumes of the vessels VI and T/s, the pressure p and the temperature T of gases A and B, using the known equations of state for the pure components 6). In the tables II, III and IV the results are given for the mixtures Ns-Hz, Ar-Hs and Ar-Na. As can be seen FE is not given at fixed concentrations. This is caused by the fact, that in the range of pressure and temperature where the measurements are performed, Hz, Ns and Ar are no longer behaving as a perfect gas. As a consequence the number of moles is no longer proportional to the volumes. This results in a variation of the concentration, depending on the working pressure and temperature. In our case this effect is small at room-temperature, but becomes rather large at lower temperature, as is clear from the tables II, III and IV. This is illustrated in fig. 2 and the table V for three arrangements, a, b and c, of the vessels for the mixture

EXPERIMENTAL

DETERMINATION

TABLE

I-

Results

remperaturc and

P

atm

axnbination of vessels

mole fraction HZ

mole

349

FE

II

for the mixture

NT-Q-t Nq

OF

7

Nz-HZ

PE

AN x 104 mole

BE

,

4x( 1 -x)

m3/mole

5.40

0.268

0.0373

1.050

Yz in VZ

10.05

0.264

0.0703

3.63O

VZ in VVI

14.6 25.2

0.260

0.104

0.250 0.236

0.185 0.310

0.226 0.217

0.401 0.500

79.65

0.210 0.204

0.588 0.687

382.5

139

8.36

92.1

0.198

0.807

455.5

118

7.21

3.00

0.510

0.0292

0.526

8.54

0.508

0.0488

1.485

4643 2778

a.54

5.00

8.65

8.65

9.15

0.503

0.0900

5.320

1507

9.12

9.12

12.05 16.3

0.502

0.118

9.475

9.42

0.496 0.486

0.163 0.232

17.90 39.00

1146 833

9.42 9.43

0.48 1

0.283 0.416

57.90 133.0

0.542 0.655

236.5 355.0

0.781

503.0

80.35

0.422 0.417

0.844 0.903

576.5 644.5

90.7

0.410

1.02

789.0

f =

170.5”E

40.2 50.4 60.9 69.7

I‘ =

170.5”E

H:!in VI V.2 in V2’

23.1 27.75 39.9 50.8 60.4 70.5 75.6

r = 170.5”E lz in VI \i2 in Vz

0.439 0.427

81.2” 137.0 219.O 293.”

7.36 7.26

922 517

7.29 7.62

9.38 9.35 9.48

308

8.51

10.2 11.8

238 191 161

8.61 8.93 8.71

13.1 13.2

12.3

12.9 11.4

584

9.43 10.2

10.2

480

10.2

10.2

326 250

11.0 11.6 12.1

11.0 11.7 12.2

12.2

12.4 12.3

207 174 161 150 132

12.0 11.7

12.1

11.2

11.6

7.48

0.722

0.0513

1.945

1864

14.75 25.3

0.715

0.102

7.790

0.705

0.176

23.9O

739 543

32.7

0.698 0.687

0.228

43.70

418

8.38

40.4

0.285

71.40

335

8.82

56.95

0.670

0.406

0.662

0.467

157.5 212.5

235 204

9.72

65.05

9.99

11.2

75.35 84.96

0.651 0.644 0.639

0.545 0.616 0.674

286.”

175

345.5 397.5

155 142

9.95 9.45 9.11

11.0 10.3 9.87

5.47 5.48

6.94 7.03

92.95

-

0.465 0.450

7.925 26.20

256 1 1361

zm3/mole

6.5 12.05 15.9

0.270 0.265 0.266

0.0698 0.0919

0.0374

25.7

0.26 1

0.151

39.5 55.0 75.3 91.6

0.254 0.246 0.239 0.235

0.236 0.333 0.463 0.569

7.29 7.44

9.07 9.13 9.24

7.69

9.93 10.3 11.0

0.767 2.675

2572

4.615

1046 637

5.45

6.98

12.10

5.3 1

6.09

28.15 57.20 111.5 168.5

408 289 207 169

5.08 5.20 5.26 5.30

6.70 7.00 7.23

1378

_

7.38

P. ZANDBERGEN

350

AND

TABLE

remperature and :ombination

P

atm

of vessels r = 205.7”K

II (continued)

mole fraction Hz

NN~+NEQ mole

0.724

0.0347

Ig in VI

6.1 15.1

0.720

\Jz in

24.7

0.715 0.707

0.0861 0.150

Vz

40.0 40.6

r=

231.7”K

-Iz in VZ \Tzin VI

0.228

6.14

4.91

6.02 6.13

5.08

0.699

0.316

50.00

364

5.06

6.01

75.6

0.690

0.428

224

5.33

6.23

90.7

0.686

0.513

96.35 134.5

187

5.21

6.04

9.5 14.1

0.271

0.0485

0.976

1990

4.16

5.27

0.269

0.0804

2.13”

1333

4.08

5.19

0.268

0.0804

2.700

1200

0.267

0.107 0.155

4.755

903 624 467

4.20 4.18 4.17

5.35 5.34

0.264 0.262

9.900 17.45

5.36 5.33

310 232

4.04 3.85

5.31 5.13

189

3.86

5.19

2.110

1859

5.49

5.49

4.790 8.35” 20.00 41.75

1264

5.77 5.56

5.77

598 415

5.41 5.47

5.41 5.47

71.85

315

5.45

5.45

259

5.35

202

5.35 5.30

3043 1792

4.30 4.27

5.38 5.33

1280 876

4.38 4.2 1

759 601 443

4.20 4.18

5.46 5.20 5.18 5.14 5.07

38.70

0.416

65.65 98.75

10.2

0.509

15.3

0.507

0.0735 0.108

\Tzin

20.2 31.6

0.505 0.501

0.146

45.45

0.495

0.329

59.9

0.489

0.433

72.9=

0.485

93.6

0.479

0.528 0.675

6.25 10.6

0.724 0.723

14.9 21.8 25.15

0.721 0.719

0.229

0.0317 0.0539 0.0754

104.5 168.0 0.43 1 1.235 2.48”

939

0.718 0.716

0.110 0.127 0.161

0.712 0.707

0.216 0.302

5.075 6.745 10.70 19.10 37.35

0.702

0.395

62.4O

320 244

96.2

0.699

0.476

87.35

15.0

0.253 0.248 0.248 0.246 0.247 0.244

0.046 1 0.0920 0.154 0.200 0.249 0.299

0.709 2.96” 7.92’ 13.05 20.35 26.7O

31.8 42.95 60.3 79.2

30.0 50.2 65.2 82.6 99.0

6.44

4.12

0.207 0.311

Hz in VI

292.6’K

4.96

55.6

r = 231.7”K

HP in Vi’ Nz in Vu'

6.03

1117 683 422

6.04

0.511

l-=

4.82

5.01 5.42

0.247

VZ

:m3/mole

2768

415 307

97.0

\i2 in

9.72O 26.3”

:m3/mole

PE 4x( 1 -x)

52.75

0.255 0.251

231.7”K

0.585 3.68&

:m3/mole

p

26.70

79.0

Hz in VI

mole

VP

0.232 0.313

39.9 59.6

Z-=

lo4

0.699

29.9

VZ*

4Nx

55.2

15.7 20.8

0.706

J. J. M. BEENAKKER

4.09 4.16

5.56

5.3 1

4.07

5.02 4.86

203

3.94

4.68

1598

2.46

800 479 369

2.58 2.47 2.43 2.44 2.21

3.25 3.46

296 246

3.31 3.27 3.27 3.00

EXPERIMENTAL

DETERMINATION

TABLE Temperature and

P

combination of vessels T = 292.6OK

mole

atm

-

mole

HZ

T

0.0612

19.95

0.462

Hz in VI

22.8

0.464

Nz in Vu

30.1 50.2

0.457

0.0702 0.09 17

0.457

0.153

65.1 80.6

0.454

0.198 0.243

99.0

0.453 0.452

AN x 104

NN~ + Nx2

fraction

351

FE

II (continued)

-

-i-

OF

mole

-

P#

P

:m3/mole

:m3/mole

4X(1-%)

,:ms/mole

1.72”

1205

3.39

3.4 1

2.235 3.740

1051

3.36

3.38

805

3.30

482

3.22

3.32 3.24

16.3”

373

24.50 33.25

303

3.10 3.09

3.13 3.11

249

2.83

2.86

10.15

0.296

_

PE

T = 292.6”K

15.0

0.53 1

0.0460 0.049 1

3.33

Ns in VI

30.0 50.2

0.530 0.525

1603 1501

3.15

16.0

0.899 1.090

3.14

Hz in V,

0.0913

3.66”

366

0.524 0.522

0.153

991 374

0.520

0.197 0.242

9.910 16.05

3.26 3.16

3.35 3.27

23.6O

98.9

0.519

0.295

32.50

T = 292.6”K

15.0

0.742

0.0458

Hz in V,’

30.0

0.738

0.0904

Nz in VI’

50.2

0.738

0.151

65.1

0.736

0.195

80.7

0.734 0.733

0.240

65.2 80.4

-

99.0

0.29 1

-

TABLE

and combination of vessels r =

atm

170.5’K

3.01 2.79

3.01

0.699

1607

2.46

3.21

2.815

815

2.55

3.29

7.595

487

2.46

3.18

12.05

378

2.36

3.03

17.45 24.4”

307 253

2.25 2.15

2.89 2.74

-

Ar-HZ

ANx

NEQ + Nnr

BE

10‘1

mole

mole

HZ

2.80

III

-

mole fraction

P

3.07

305 250

Results for the mixture

-

remperature

3.17

3.07

T ___.PE

4x( 1 -x)

3m3/mole

,

I

-

cm3/mole

I

4.00

0.268

0.0277

0.536

3450

6.87

8.75

Hz in VZ

5.00

0.267

0.0348

0.901

2750

7.34

4r in VI

5.15

0.267

0.0358

0.958

2675

7.38

93.8 9.43

5.2

0.267 0.265

0.036 1 0.043 1

0.265 0.259 0.255 0.25 1 0.244

0.0440 0.0923

0.994 1.405 I.450

2649 2219 2171

7.51 7.46 7.37

6.96O 11.30 17.50 33.15

1036

8.08 8.26

6.17 6.3 12.95 16.05 19.50 25.45 29.15 35.35 45.5 54.8

0.240

-

0.223 0.278 0.386 0.502 0.668 0.770

0.232 0.213 0.195 0.172

65.0 70.2 80.1 87.0 94.8

0.116 0.143 0.191

0.161 0.146

-

0.140 0.137

-

0.961 1.08 1.19

822 668 500

45.20 82.45 176.” 322.5 601.5 793.5 1255

-

1530 1545

-

9.46 10.5 10.9 11.3 12.3 12.5 15.1 18.1 21.2

8.48

429 343 247

9.05 9.10 10.8 12.1

190 142 124

13.3 14.4 14.5

98 .8 87 .9 79 .5

9.59 9.57

15.1 14.8 12.0

25.2 26.8 30.2

-

30.7 25.3

352

P. ZANDBERGEN

AND

TABLE

-

l?emperature and combination 170.5”K

3.2 in VI 4r in Vz

P

atm 3.12 10.15

36.6

0.682 0.649

83.3 95.2

170.5”K

-

0.699

dN x 104

Pmid

T

mole

c:m~/mole

0.36 1

4353

7.48

0.0699

3.795 9.005

1368

7.67

0.105 0.174

27.4O

941 548

0.26 1

73.10

365

0.373 0.466

180.” 323.”

0.565

0.629

703.0

0.547

0.711 0.821

948.5 1195.

(:m~/mole

9.40 9.43

8.40

10.3

8.98 10.8

10.7 12.4

248

12.9

14.2

205 151

15.6

16.6 19.9

19.5 21.07 20.21

134 116

21.26 20.31

2.07

0.509

0.0199

0.258

6811

9.02

9.02

0.507

0.0389

0.998

3491

9.16

9.16 9.27

5.98

0.505

0.0587

2.30°

2308

9.25

10.03

0.498

0.0994

6.98j

9.85

12.14

0.498 0.485

0.120 0.204

1365 1128

34.10

25.0

0.478 0.478

0.247 0.257

52.1° 60.1°

666 549 527

30.1 40.15

0.467 0.447

0.314 0.436

91.75 194.0

431 311

50.8

0.418

0.584

397.5

232

17.2

700.0 1225

183 144

19.5 21.8 23.6

60.2

0.388

0.740

70.0 77.8

0.352

0.941 1.11

10.50

10.1

11.6 12.0

11.6 12.1

12.8 13.2

12.9

14.8

14.9 17.7

13.3

20.5 23.9 26.7

1780

122

1.21

221”

112

25.2

28.9

0.315

1.28

2445

106

0.312

1.34

2605

101

25.3 24.5

29.3 28.6

83.0

0.329 0.321

86.6 90.3” 6.1

0.269

0.0351

0.577

2735

4.65

10.0

0.267

0.0580

1658

5.66

\r in V1

15.1 21.7 22.7

0.264 0.256

1088

6.45 5.95

0.259

0.0883 0.130 0.135

1.910 5.045

6.3 7.2 9.8

0.723 0.722

0.0360 0.0411

10.0 13.7 15.9 25.1

0.720 0.720 0.717 0.717 0.710

0.0560 0.057 1 0.0784 0.0908 0.144

r = 231.7”K

10.15

0.268

-I2 in VZ Ir in V1

15.5 25.2 30.05 34.8 45.2 57.7 76.0

0.266 0.262 0.260 0.259 0.254 0.247 0.240 0.234

0.0505 0.0776 0.127

91.85

9.85

10.1

IZ in Vz

[‘ = 2057°K 3.2 in V1 4r in Vz

4x( 1 -x)

c:m3/mole

0.0218

0.618

0.535

PE

3.98

20.1 24.15

I‘ =

0.726 0.716

-

-

pE

HZ

0.712

50.3

1r in V2’

-

fraction

15.00 24.9

60.5 75.3

l- = 170.5”K 31s in VI

III (continued)

mole

of vessels r =

J. J. M. BEENAKKER

-

0.153 0.178 0.232 0.302 0.406 0.497

to.00 12.55

-

740 713

5.91 7.24

6.92

8.3 1 7.00 9.02

0.800 0.972 1.625

2672 2342

6.16 5.74

7.68 7.15

1716

1.895 3.435 4.665 11.85

1683 1227

5.16 5.78

6.40 7.18

5.58 5.65

6.87 6.96 6.94

1.240 2.885

1842 1208

7.950 11.50 14.90 27.45 46.2” 84.95 126.5

1059 668

-

5.72 4.53

5.77 5.77

732 611 525

4.51 4.60 4.64 4.44

5.95 6.03 5.79

401 309 230 187

4.80 4.80 4.9 1 4.90

6.34 6.45 6.74 6.84

-

-

EXPERIMENTAL

DETERMINATION

TABLE

and combination

mole

P

atm

Nm+

fraction

NAP AN x

104

mole

HZ

of vessels r = 231.7”E

12.1

3.16”

15.0

0.505 0.504

0.0858

Hz in VI 4r in VZ’

0.106

20.2

0.499

0.142

4.805 8.865

25.35

0.497

0.180

29.2

0.495 0.493

0.208 0.254

0.490 0.485

0.290 0.355

59.3

0.477

69.6 80.15 92.15

35.45 40.6 49.45

353

PE

(continued)

-

-

remperaturt

III

OF

PnP

,:m3/mole

PE

PE xn3/mole

4x( 1 -x) xn3/mole

1552 1257

5.73 5.72

5.73 5.72

937 739

5.89

5.89

14.35

5.94

19.20

640

5.94 5.97

29.7O 40.35 61.2O

525 459 375

5.97 6.21

0.471

0.429 0.507

90.50 125.0

310 263

0.466

0.586

170.5

227

0.459

0.679

228.5

6.21

6.47

6.47

6.56 6.69

6.56 6.70

6.66 6.79

6.68 6.82

196

6.83

6.88

7‘ = 231.7”E

1 l.65

0.719

0.0573

1.625

1624

4.61

5.71

HZ in V1 4r in V2

20.15

0.714 0.712

0.0978

4.845

951

4.73 4.57

5.80

4.91

5.96

5.04 5.38

6.05 6.37

5.44 5.32

6.36

30.4 37.3

0.710

0.149 0.183

10.90 17.50

46.5

0.704

0.227

27.7”

59.2

0.697

0.290

47.80

70.0

0.692 0.688

0.343 0.392

67.45

321 271

0.682

0.454

85.95 115.5

237 265

79.95 92.7

623 508 409

5.57

6.19 6.16

5.35

. = 292.6”K Hz in VI’

5.0 17.9

0.255 0.249

0.0 154 0.0554

0.087 1.100

4787

2.70 2.65

3.56

1331

4r in

25.15

0.250

0.0778

2.26”

947

2.76

3.67

29.75

0.246

0.0921

3.155

800

2.75

43.7

0.246

0.136

6.540

2.6

57.2 67.8

0.242

0.179

12.35

542 412

2.87

3.92

0.213

17.15

3.86 3.85

0.236

26.7O 28.60

2.87

87.6

0.267 0.275

347 276

2.82

85.0

0.241 0.237

268

2.81

3.89 3.67 3.73

V,’

2- = 292.6”E Hz in VI Ar in Ii,

T = 292.6”p HZ in V, Ar in VI

1

0.0463

I.055

1595

3.65

0.0770

2.970

958

3.71

34.9 52.0 68.8

0.458 0.456 0.45 1 0.446 0.441

0.274

686 460 348 269

3.56

88.9

5.555 12.8O 22.35 37.35

6.6 16.5

0.528 0.529

0.0201

0.191 1.270

3667

19.5 20.0 23.9 25.8 35.9 43.0 55.1 73.3 88.6

0.527 0.527 0.528 0.526

0.0507 0.0601 0.0616 0.0737 0.0792

0.523 0.522 0.516 0.513 0.509

0.110 0.132 0.169 0.224 0.271

15.0 24.9

0.46

-

0.108 0.160 0.212

1.745 1.835 2.625 2.990 5.96” a.370 13.40 23.95 34.05

3.70 3.70 3.72

3.35

1

3.70 3.52

3.59 3.74 3.74 3.77

1454 1228

3.48 3.66

3.49 3.67

3.57

3.58

1197 1002 931 670

3.57 3.58 3.53 3.64

3.58 3.59 3.54 3.65

558 437 329 273

3.55 3.50 3.54 3.47

3.56 3.50 3.55 3.47

354

P.

ZANDBERGEN

AND

TABLE

and combination

fraction

atm

Hz in V,’

7.9 22.95

4r in VI’

24.5

T

mole

P

of vessels r = 292.6”K

III (continued)

-

remperature

HZ

-

26.9 27.9

J. J. M. BEENAKKER

AN x 104

NQ+NA~ mole

0.742

0.0241

0.741

0.0705

0.739 0.738

0.0750

mole

0.0818 0.0846

2.100 2.445

982

2.64 2.76

901 871

2.70 2.73

689

2.67

5.475

607 607

2.75 2.59

3.41 3.43 3.57 3.49

39.9

0.736

39.9 40.2

0.736

0.121 0.121

0.736

0.122

5.405

540

2.69

43.15

0.735

0.131

5.990

2.58

3.46 3.32

55.2

0.731

0.167

10.25

562 442

2.74

3.48

69.8

0.729

0.210

16.4”

0.269

2.75 2.74

3.48

0.725

351 274

-

0.116

4.885 5.145

26.65

-

P atm

of vessels

mole fraction Ns

NA~+NN~ mole

3.52 3.44 3.55 3.33

3.43

IV

Results for the mixture Temperature

170.5-K

ems/mole

2.6 1

0.737 0.736

TABLE

T =

:ms/mole 3056 1046

PE

4x( 1 -x)

38.3

89.9

and combination

t

0.206 1.770

2.645

~-

PE

Ar-Nz

AN x 104 mole

P,‘d

PE

PE

,:ms/mole

4x( 1 -x) ,:ms/mole

,:m3/mole -

-

15.2

0.268

0.112

0.07 1

855

Nz in VZ

29.4

0.263

0.232

411

Ar in VI

45.5

0.252

59.4 71.2

0.233

0.406 0.606

0.043 4.415

0.211

0.842

1.35

2.03

78.95

0.201

2.06

3.21

0.196

211.0 244.5

94.4

85.2

1.00 1.12

84.3

1.90

91.9

0.194

1.24

233 0

76.5

1.49

3.02 2.38

7.48 14.95

0.513 0.509

0.0749 0.154

39.65 51.7

0.494 0.478

0.470 0.670

60.15 69.8

0.460 0.433

0.838 1.07

76.8 83.0 88.25

0.419 0.411 0.407

1.25 1.40

1.52

93.7

0.466

1.64

10.02 35.1 49.95 57.3 69.4 74.15

0.725

0.0714

0.718 0.704 0.692 0.664 0.654

82.3 86.9

0.643 0.639 0.638

0.280 0.436 0.525 0.696 0.769 0.887 0.949

230.” 242.5

1.05

264.5

T = 170.5”K Nz in P” Ar in V?’

T = 170.5”K Na in VI Ar in Va

94.3

32.25 98.35

0.056 - 0.008

235

0.26

157 113

0.86

0.071 -0.010 0.35 1.20

1807 875

- 0.077 - 0.085

- 0.077 - 0.085

288 202

0.042 0.52

60.55 177.0

161 126

1.19 2.13

0.042 0.52 1.20 2.17

353.5

108 96.0 88.9 82.1

3.16 3.21 3.06

0.03 1 0.148 0.670 16.9”

449.0 498.5 474.0 0.034 0.139 4.36O 20.7” 86.80 130.5

3.25 3.32 3.17 2.56

2.47

1338

- 0.066

340 218 181 136 123

0.17 0.22 0.73 1.76 2.16

107 99.7 90.5

2.89 2.66

-

2.22

-0.083 0.21 0.26 0.86 1.97 2.39

-

3.15 2.88 2.40

EXPERIMENTAL

DETERMINATION

TABLE

and combination

mole

P atm

of vessels

fractior NZ

355

vE

IV (conlilzued)

-

Temperature

OF

dNx

NAP+ NN~ mole

lo4

Ym’d

mole

c:m3/mole

PE

YE

1-x) ,:m3/mole 4x(

:m3/mole

-

T = 231.7”K

17.15

0.272

0.089 1

0.097

1084

-0.123

Ns in VZ

31.0 44.85

0.269

0.384

-0.179

0.735

585 396

-0.141

0.268

0.165 0.243

-0.124

-0.158

66.2

0.263

0.371

1.615

260

-0.117

-0.151

85.0

0.260

0.487

0.979

-0.041

- 0.053

94.4

0.257

0.548

1.595

198 176

- 0.053

- 0.069

T = 231.7”K

15.05

0.484

0.110

0.117

1237

-0.134

-0.134

Nz in Vz’ Ar in VI

30.05 46.1 64.1

0.48 1

0.225 0.352

0.504

-0.139

-0.139

1.370 2.125

607 388 277

-0.155 -0.120

3.705

200

-0.155 -0.120 -0.111

-0.168

Ar in VI

-0.155

85.1

0.479 0.474 0.468

T = 231.7”K

15.0

0.724

1244

45.3

0.721

0.0776 0.242

0.080

Nz in VI Ar in VZ

0.804

398

-0.134 -0.137

69.9

0.715

0.384

1.815

251

-0.123

-0.151

92.0

0.710

0.513

I.360

la8

-0.052

- 0.063

30.8 54.85

0.253

0.096 1

0.15

767

-0.12

-0.16

Ns in VI’

0.251

0.173

- 0.22

84.95

0.247

0.271

425 272

-0.17

Ar in Vu’

0.68 1.44

-0.15

- 0.20

0.0956 0.180

0.27

772

-0.22

0.92

-0.21

-0.22 -0.21

0.267

1.73

410 276

-0.18

-0.18

0.0970 0.162

0.22 0.52

761

-0.17 -0.14

-0.17

0.164

0.54 1.72

450 274

-0.15

-0.15

-0.18

-0.18

T = 292.6OK

0.502 0.682

-0.111

-0.170

T = 292.6”K

30.7

0.463

Nz in VI Ar in Vu

57.2 84.4

0.460 0.456

T = 292.6”K

31.2

0.530

Ns in V,

51.8

Ar in VI

52.3

0.528 0.528

85.5

0.523

0.269

T = 292.6”K

30.4

0.742

0.0942

0.29

782

-0.24

-0.31

Nz in VI,’ Ar in VI’

50.4 84.2

0.740 0.737

0.157 0.263

0.68 1.11

470

-0.20

281

-0.12

- 0.26 -0.15

-

TABLE

454

-

V

The dependence of the concentration with pressures for three arrangements of the vessels for the mixture A-Hz at 170.5”K Pressure range

Concentration

-0.15

-

P.

356

ZANDBERGEN

AND

1. J. M. BEENAKKER

1

I A-H. 170.5

0.75

-

0.5

-

0.25

-

OK

*Hz I 0

I 0

9

Fig. 2 The concentration a. _4r in VI and Hz in Vs;

100

of pressure. c. Ar in Vi and Hz in PI

I

otm

50

P

Fig. 3. a. xnz = 0.268-0.137;

as a function

b. Ar in Vz and Hz in VI;

01

0

atm

so

c

PE as a function b. xn,

1

of pressure.

= 0.726-0.535;

c. xn,

= 0.509-0.312

EXPERIMENTAL

cm

DETERMINATION

OF

QE

3

mole

75 atm

“E V I 0 0 -2_

0.75

0.50

0.25

XII

Fig. 4. BE as a function

1

of concentration.

Ar-Hz at 170.5”K. In figure 3 the calculated values of PE are plotted as a function of pressure for the three combinations of vessels (curves a, b and c). Combining the graphs 2 and 3 one can obtain at round values of $, say 5, 10, 15 etc. atm values of PE at three different concentrations. Such results are plotted in fig. 4. To get the pressure dependence of BE at fixed concentrations we make cross sections in fig. 4 at the mole fractions XH, = 0.25, TABLE Smoothed

values of PE in cm3/mole for the mixture Nz-HZ

T

P

atm : !92.6”K 5 10 15 20 30 40 50 55 60 65 70 80 90 95 100

-

VI

PE for XHZ = 0.50 231.7”K

231.7”K

170.5”K

292.6” K

2.47 2.47

3.98 3.98

6.93 7.10

3.30 3.30

5.53 5.53

8.78 9.00

2.47

3.99

7.20

3.29

5.53

9.28

2.48 2.48 2.50 2.52 2.52 2.52 2.50 2.47 2.41

3.99 4.02

7.45 8.02 8.72

3.27 3.28 3.26 3.24 3.21 3.17 3.16 3.15 3.04 2.88

5.53 5.53 5.53

9.60 10.20

2.3 1 2.29 2.27

4.02 4.02

9.30

4.00 3.99 3.97 3.94 3.89 3.83

9.52 9.71 9.80 9.81 9.59 8.81

3.80

8.30

-

2.87 2.62

:

5.49 5.47 5.44 5.40 5.39 5.34 5.28 5.24

-

170.5”K

10.88 11.47 11.61 11.88 12.02 12.00 11.70 11.11 10.62

-__

PE for XHZ = 0.70

1 170.5”K

!92.6”K

231.7”K

2.75

4.54

7.52

2.75 2.71

4.54 4.52

7.60 7.67

2.68

4.50

7.76

2.64 2.60 2.55 2.53 2.51 2.51 2.50 2.40 2.34 2.32 2.30

4.44 4.38

8.08 8.50

4.32 4.29 4.26 4.23 4.19 4.19 4.08 3.94

8.92 9.06 9.03 9.07 9.09 8.76 8.10 7.60

P.

358

ZANDBERGEN

AND

TABLE Smoothed P atm

values

PE for XH% = 0.25 292.6”K

1231.7”K 1 4.33

1 170.5”K

J.

J.

M. BEENAKKER

VII

of PE in cm3/mole

for the mixture

1 PE for Xa2 = 0.50 1292.6”K 1231.7”K 1 170.5’K

Ar-HZ

BE for XHZ = 0.70 I 1292.6”K / 231.7”K 1170.5”K

5

2.69

7.2

3.67

5.71

9.3

2.95

4.84

7.9

10

2.69

4.33

7.3

3.67

5.71

9.6

2.95

4.84

8.0

15

2.72

4.37

7.8

3.67

5.75

10.3

2.95

4.84

8.2

20

2.75

4.4 1

a.3

3.67

5.80

11.4

2.95

4.84

8.55

30

2.75

4.49

9.9

3.67

6.04

13.0

2.95

4.91

9.2

40 50

2.81 2.85

4.65 4.88

12.1 14.4

3.63 3.66

6.38 6.61

14.7 16.4

2.91 2.92

5.04 5.20

10.3 11.5

60

2.90

4.91

17.0

3.63

6.73

18.3

2.90

5.29

12.5

70 75 80

2.9 1 2.91 2.91

5.00 5.05 5.09

19.6 20.8 22.0

3.60 3.60 3.60

6.79 6.78 6.77

20.4 21.6 22.4

2.90 2.89 2.88

5.3 1 5.26 5.21

13.8 14.1 14.2

a5 90

2.88 2.05

5.11 5.14

23.2 22.3

3.55 3.50

6.75 6.72

22.8 22.7

2.86 2.85

5.16 5.11

14.2 14.2

95

20.8

21.4

TABLE Smoothed P atm

values

PE for XN% = 0.20 231.7”K

1

170.5”K

VIII

of FE in cm3/mole

1 1

PE for 231.7”K

13.8

for the mixture

XN~ = 0.50

/

170S°K

/ /

Ar-Nz

BE for 231.7”K

XN~ = 0.70

1

170S”K

10 15

-0.13 -0.13

0 0

-0.14 -0.14

- 0.07 - 0.07

-0.14 -0.14

- 0.05 - 0.05

20 30

-0.13 -0.13

0 0

-0.14 -0.14

-0.07 - 0.06

-0.14 -0.14

- 0.05 - 0.05

40 45

-0.13 -0.13

0.05 0.17

-0.14 -0.14

0.10 0.25

-0.14 -0.14

0.06 0.17

50

-0.13

0.35

-0.14

0.45

-0.13

0.40

60 70

-0.14 -0.13

0.85 1.51

-0.14 -0.13

1.11 2.22

-0.11 -0.10

0.89 1.64

75

-0.10

1.81

-0.12

2.89

-0.10

2.01

80 a5

- 0.08 - 0.08

2.00 1.95

-0.11 -0.10

3.22 3.21

-0.10 - 0.08

2.43 2.43

90

- 0.07

1.66

- 0.09

2.95

- 0.06

2.22

95

1.26

2.42

1.95

0.5 and 0.7. The smoothed values of FE obtained in this way, are plotted in fig. 5. All the data given in the tables II, III and IV except the ones at 205.7”K, are treated in the same way as the Ar-Ha data at 170.5”K. The final results are given in the tables VI, VII and VIII and are plotted in figs. 5, 6 and 7. The data at 205.7”K suffer from a rather low accuracy. These measurements were performed in a bath of liquid propane at reduced pressure. Temperature control under our experimental conditions appeared to be rather difficult. This resulted in an appreciable scattering of data.

EXPERIMENTAL

0

XH,

= 0.25;

values

atm

of PE as a function

b. XH, = 0.70;

C.

359

OF vE

50

P

Fig. 5. The smoothed

a.

DETERMINATION

100

of pressure. 0.50.

xH,=

25 3

cm

mole 20

15

10

5

ii

“v’

a

I 0

292.6 OK

I

0

50

P

Fig. 6. The smoothed a. XH, = 0.25;

values

atm

of BE as a function

b. xH, = 0.70;

._ 100

of pressure.

c. XH, = 0.50.

360

P. ZANDBERGEN

AND

J. J. M. BEENAKKER

2.5

1.5

+0.5

231.7’K

ijE t I

c,b,a -0.5

I

i

I

0

atm

50

P

Fig. 7. The smoothed

values

a. XN, = 0.20;

of PE as a function

b. xNa = 0.70;

C.

xN2

=

100 of pressure. 0.50.

4. Disczcssion. As we plan to give a theoretical discussion of the results for VE in more detail in a subsequent paper, we limit ourselves here to a phenomenological analysis of the low density data. In the region where binary collisions are dominant, one can write p=

F

(1 + Ba)

(6)

Here B is the second virial coefficient and d is the molar density defined as a = 117. Denoting the second virial coefficients of the pure gases A and B and the mixture as BAA, BBB and B, we get in the limit of low densities VF = B, The second virial coefficient &

- XABAA - XBBBB.

of a binary mixture

= X~BAA

+

~XAXBBAB

can be written

-k XtBBB

(7) as (8)

where BAB is the second virial coefficient of a hypothetical gas with only A-B interactions. We define a quantity E by means of the expression E = BAB By combining

-

+(BAA+

eqs. (7), (8) and (9) one obtains a;

=

2XAXBE.

BBB).

(9)

for r:f (10)

At low densities Pn should be independent of pressure and parabolic as a function of concentration. This concentration dependence is clearly

EXPERIMENTAL

DETERMINATION

TABLE

OF

361

pE

IX

.Mixture

Nz-Hz

)

G

Observer

/

Method

170.5

a.84 6.5

3,

,>

231.7 292.6 273.1

5.40 3.28 3.95

,>

>,

i

3.47

1,

,,

323.1 373.1

2.70 2.82

>>

,> >>

203.1

6.67

223.1

5.60

This

direct

paper

Wiebe

&‘data

:.a. 10)

Bartlel;

ea.

11

12)

,,

,*

,I

248.1

4.67

273.1 293.1 298. I

3.95 4.00 4.48

ButleG Edwards

e.a. 13)

d&t

298.1

4.06

Lunbeck

e.a. 14)

direct

i

3.23

Michels This

298.

Ar-Ns

/

205.7

298.

Ar-Hz

/ 52

11)

ea.

9,

Is)

paper

PVT data direct

170.5

9.3 1

205.7

7.15

>>

,t

231.7

5.70

,,

>,

292.6 90.0

3.59 27.5

170.5

- 0.04

231.7

-0.16

292.6

- 0.20

90.0

0

Knob1.G This

e.a. l6)

paper I,

,, ,t direct ,, 1,

Knobli:

e.a. 1s)

1,

illustrated by the low pressure (5 atm.) curve in fig. 4. In the figs. 5, 6 and 7 one sees, that at room temperature TE is independent of pressure till about 50 atm and till about 35 atm at 23 1.7”K. We determine 7: from the figs. 5, 6 and 7 for all the temperatures, where measurements have been performed. The values of vt/4x( 1 - x) are generally equal within a few percents for the three concentrations of a mixture. In the figs. 8, 9 and 10 the average values of Pf/4x( 1 - x) are plotted as a function of temperature. In these graphs and also in table IX the data from literature are given la) 11) 1s) 13) 14) 15) 16) . Th ere is a rather good agreement between the results of the other authors and our experiments. For the three mixtures Ns-HZ, Ar-Hs and Ar-Nz we calculate, using eqs. (9) and (lo), B A~ as a function of temperature from the second virial coefficients of the pure gases and the values of E obtained experimentally (table X). For the B coefficients of Hs and Ar we use the data of Michels e.u.17)18)19) and for the B coefficients of Ns the data of Hoover c.u.20) Following a well known procedure, viz. plotting log[BABl versus log T and comparing this plot with the log [B*I versus log T* graph, we found that the

P. ZANDBERGEN

362

AND

J. J. M. BEENAKKER

10 3

cm

Nz-Hz

mole

5

5’ 4x0 t

0 1 5( -3

T

Vf

Fig. 8. Wiebe A Bartlett

x)

as a function

Edwards

a Michels 0 Our

e.a. 13)

30 cm3 mole

15 -

WE V0 4x(1-x) -I I 0

Fig. 9.

T

150

Vf

4x(1 A Knobler

n)

as a function

e.a. 1s)

0 Our

OK

e.a. 14) e.a. 15)

experiments

I

0

400

of temperature. D Lunbeck

e.a. lo) e.a. 11 12)

q

v

4x(1 -

OK

275

_

300

of temperature. experiments

EXPERIMENTAL

0

DETERMINATION

Y

3

I

A-N,

cm mole

363

OF @

0

0 0i

t

Fig. 10. -___ 4X(1 A Knobler

as a function

x)

e.a. 16)

Our

0

TABLE

I

The calculated

A-HZ,

-

BNZ_HZ

X

and A-N2

B A--Hz

BA--NZ

“K

cm3/mole

170

-5.04

- 10.3

180

-2.63

-

7.8

-53.5

190

-0.55

-

5.7

- 47.4

1.15 2.69

-

4.0 2.4

-42.0 -37.2

4.08 5.29 6.25

-

0.9 0.3

-32.8 - 29.0

1.5 2.5

- 25.6 -22.5

3.5 4.2

- 16.8

200 210 220 230 240 250

data are consistent

experiments.

values of BAB for the mixtures

Nz-HZ, T

of temperature.

260

7.24 a.24

270

9.07

-

cma/mole

-

with a Lennard-Jones

ems/mole -60.5

- 19.4

potential

(11) Y is the distance between the centers of the molecules A and B, EAB is the energy of the depth of the potential well and (TABis the collision diameter. B* = Bl2nNo3 and T* = kT/e are the reduced B coefficient and the reduced temperature respectively. B* as a function of T* is given in table I-B in the book of Hirschfelder, Curtiss and Birdsr). From the shifts TABLE The molecular

XI parameters

364

P. ZANDBERGEN

AND J. J. M. BEENAKKER TABLE

XII

The values of EA= and OAB from experiment and from combination rules

I

Mixtures

Nz-Hz i

Ar-Hz Ar-Ns

(E/k)=* OK 56.37 66.68 100

(El& “K

(&IP A

59.30 66.58 106.71

1

I

3.169 3.037 3.684

I (&I A

t

3.313 3.166 3.552

along the B and T axes necessary to make the theoretical and experimental graphs, we obtain CAB and OAB. In table XI we give the values of E and c of the pure gases from Hirschfelder e.u.21) and in table XII we give the experimental values of EAB and (TAB. For the purpose of comparison we note the values of EAB and CAB obtained from the usual combination rules CAB = GAB =

2/- EAAEBB

$(~AA

+

EBB).

(12)

(13)

The agreement is rather good. Note added irt proof. The results for the extrapolated values of FE agree very well with the excess second virial coefficients obtained by Brewer 22). Acknowledgements. We like to thank Prof. Dr. K. W. Taconis for his continuous advices and Dr. H. F. P. Knaap for suggestive discussions. From the technical staff of the laboratory we would like to thank particularly Mr. E. S. Prins and Mr. S. P. L. Verdegaal for constructing the apparatus. Received 28-6-66 REFERENCES

1) Parsonage, 2) McGlashan, 3) 4)

5) 6) 7)

8)

9) 10) 11) 12) 13)

N. G. and Staveley, L. A. K., Quarterly Rev. 13 (1959) 306. M. L., Ann. Rev. phys. Chem. 13 (1962) 409. White, D. and Knobler, C. M. Ann. Rev. phys. Chem. 14 (1963) 251. Prigogine, I., The molecular theory of solutions (North Holland Publishing Company, Amsterdam, 1957). Scott, R. L., J. them. Phys. 15 (1956) 193. Din, F., Thermodynamic functions of gases (Butterworths, London, 1961). Knoester, M., Taconis, K. W. and Beenakker, J. J. M., Commun. Kamerlingh Onnes Lab., Leiden No. 351~; Physica (1967) 389. M., Taconis, K. W. and ZandBeenakker, J. J. M., Van Eynsbergen, B., Knoester, bergen, P., Advances in thermophysical properties at extreme temperatures and pressures, ASME, Purdue University, Lafayette, Indiana, 1965, p. 114. Michels, A. and Boerboom, A. J. H., Bull. Sot. Chim. Belg. 8% (1953) 119. Wiebe, R. and Gaddy, V. L., J. Am. Chem. Sot. 60 (1938) 2300. Barlett, E. P., J. Am. Chem. Sot. 49 (1927) 687. Barlett,E. P.,Hetherington,H.C., Kvalnes,H.M.andTremearne,T. H., J. Am.Chem. Sot. 52 (1930) 1363. Edwards, A. E. and Roseveare, W. E., J. Am. Chem. Sot. 64 (1942) 2816.

EXPERIMENTAL

14)

Lunbeck,

15)

Michels,

A. and Wassenaar,

R. J. and Boerboom,

16)

Knobler,

C. M., Beenakker,

DETERMINATION

A. J. H., Physica T., Appl.

sci. Res. Al

J. J. M. and Knaap,

OF PE

365

17 (1951) 76. (1949) 258. H. F. P., Commun.

No. 317a;

Physica

25

1959) 909. 17)

Michels,

A., De Graaff,

W. and Ten

A., Wijker,

19) 20)

A., Levelt, J. M. and De Graaff, A. E., Canfield, F. B., Kobayashi,

Michels, Hoover, versity,

21) 22)

Hk.,

C. A., Physica

Physica

26 (1960) 393.

15 (1949) 627.

W., Physica 24 (1958) 659. R. and Leland Jr., F. W., W. M. Rice

Uni-

1963.

Hirschfelder, (John

H., and Wijker,

Seldam,

18) Michels,

Wiley,

Brewer,

J. O., Curtiss, New York,

J., J. them.

C. F. and Bird,

1954).

erg.

Data

10 (1965)

113.

R. B., Molecular

theory

of gases and liquids,