density of methanol + water between 250 k and 440 k and up to 40

Density of Methanol + Water between 250 K and 440 K and up to 40MPa and Vapor-Liquid Equilibria from 363 K to 440 K

Philippe Sentenac, Yves Bur, Evelyne Rauzy, and Charles Berro*

Departement de Chimie, Faculte des Sciences de Luminy, Universite de la Mediterranee,13288 Marseille Cedex 9, France

The density of methanol + water has been measured between 257.3 K and 442.15 K as a function ofpressure at five compositions by means of a high-pressure apparatus implementing a metal bellows as asimple cell. Bubble pressures have been determined at five temperatures between 363.15 K and 442.15K. They are compared with literature data that have been correlated by using the excess function-equation of state model.

Introduction

A knowledge of the thermodynamic properties of themethanol + water system is very important in order toimprove the prediction of phase equilibria. Numerousvapor-liquid equilibria, excess enthalpies, and excess vol-umes at atmospheric pressure have been measured attemperatures between 298.15 K and 333.15 K (McGlashanand Williamson, 1976; Benson and Kiyohara, 1980; Pateland Sandler, 1985). Few data exist above these temper-atures and under pressure. Excess volumes have beenreported by Easteal and Woolf (1985) between 278 K to323 K at pressures to 280 MPa and recently by Xiao et al.(1997) between 323 K and 573 K at two pressures of 7 MPaand 13.5 MPa. On the other hand, vapor-liquid equilibriahave been measured by Griswold and Wong (1952) at fourtemperatures between 373 K and 523 K, by Schroder (1958)at 413.15 K, and by Hirata and Suda (1967) and Hirata etal. (1975) at pressures of 0.3 MPa and 0.5 MPa.

In this work, densities are reported as a function ofpressure for methanol + water over a wide range oftemperature and composition. We have also determinedbubble pressures at five temperatures between 373 K and423 K.

Experimental Section

Materials. Methanol provided by Prolabo (Paris, France)had a stated minimum purity of 99%. It was purified byfractional distillation on a 60-plate Oldershaw type columnand was controlled by gas-chromatographic analysis (purity> 99.90%). The main impurity was water (

are carried out at given intervals of density in adjustingthe number of micrometric steps. The experiment contin-ues by decompressing the cell to the next pressure byopening and closing regulation valves (8). A measurementfor a single isotherm took 1 day.Experimental Results

Table 1 lists the density and pressure measurements ofmethanol (1) + water (2) for five compositions at ninetemperatures ranging from 257.3 K to 442.15 K. For themole fractions of methanol of 0.1061 and 0.2872, the PVTproperties have not been measured along the isotherm of257 K on account of the vicinity of melting points ofmethanol + water.

In Figure 3, the volume is plotted as a function ofpressure at constant composition (x1 ) 0.4980). The bubblepressure corresponds to the intersection of the curvesrepresenting the one-phase and two-phase regions. Thebubble pressure and composition data at five temperatures(from 363.15 K to 442.15 K) are presented in Table 2. Wehave not reported bubble pressures at lower temperaturessince the values are too small.Results and Discussion

It was difficult to compare directly our P, F, T data withthose reported in the literature since they are few innumber and are often outside the temperatures andpressures studied. Recently, Xiao et al. (1997) developeda modified corresponding-states model based on theirmeasurements and available at temperatures between 323K and 573 K and pressures between 7 MPa and 13.5 MPa.To evaluate our data, this model was used. The meanrelative deviation and the mean relative bias betweenexperimental and calculated densities defined by

are presented in Table 3. Agreement seems quite accept-able.

For vapor-liquid equilibria, the methanol + water datawere correlated using the model excess function-equationof state described previously (Peneloux et al., 1989). To

represent the properties of pure compounds a volume-translated Peng-Robinson equation of state was adopted:

The pseudo-covolume b was calculated from critical con-stants, and the dependent-temperature function a(T) isgiven by

where a(Tb) is the value of parameter a at the normalboiling temperature Tb. Parameters m1 and m2 wereadjusted in accordance with vapor pressures of purecomponents. Their values are listed in Table 4.

The excess function is defined at packing fraction ( )b/v), and the mixture equation has the following form

with

Eij denotes the binary energy parameter and varies withtemperature according to

Eij and r are two parameters adjusted using vapor-liquid equilibrium data. The isothermal VLE values be-twwen 243 K and 473 K and isobaric VLE values atatmospheric pressure reported in the literature and givenin Table 5 were selected for this evaluation. We find Eij )365.8 J cm-3 and r ) -1.823. It should be noted that wehave not taken into account our measurements in adjust-ment.

The relative mean deviation in the bubble-point pressureand absolute mean deviation in the vapor-phase composi-

Figure 1. Schematic diagram of the experimental apparatus: (1) oil tank; (2) filter; (3) piston pump; (4) shock absorber; (5) pressuregauge Heise; (6) pressure gauges; (7) breaking disk; (8) regulation valves; (9) micrometric table; (10) platinum resistance thermometer;(11) thermic regulation; (12) product introduction valve; (13) climatic fence; (14) autoclave and bellows; (15) filling cell; (16) vacuumpump.

F/F(%) )100

Ni)1

N

jFexp,i - Fcal,i

Fexp,ij (1)

r(F) )100

Ni)1

N Fexp,i - Fcal,i

Fexp,i(2)

P ) RTv - b

-a(T)

v(v + b)with ) 2(x2 + 1) (3)

a(T) ) a(Tb){1 + m1[1 - ( TTb)0.05] - m2(1 - TTb)} (4)

z )1

1 - -

i)1

p xiai

RTbiQ() +

1

2i)1

p

j)1

p b ib jxixj

i)1

p

xib i

Eij(T)

RTQ()

(5)

Q() ) 1 +

Eij ) Eij(TT )r

T ) 298.15 K (6)

Journal of Chemical and Engineering Data, Vol. 43, No. 4, 1998 593

Tab

le1.

P,G

Dat

afo

rM

eth

anol

(1)

+W

ater

(2)

atD

iffe

ren

tT

emp

erat

ure

s

P/M

Pa

F/m

oL-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF

/moL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

x 1)

0.10

61T

)27

2.46

KT

)30

2.60

KT

)33

2.55

KT

)36

3.17

KT

)38

3.57

KT

)40

3.52

KT

)42

4.05

KT

)44

3.49

K17

.355

52.3

000

40.1

4551

.451

437

.121

49.0

102

40.5

2347

.556

029

.198

45.6

890

37.8

3745

.027

028

.986

43.4

205

28.5

1942

.300

815

.863

52.2

032

38.7

4651

.354

435

.653

48.9

295

39.1

0447

.476

427

.703

45.6

076

36.3

5644

.951

727

.598

43.3

495

27.0

8142

.232

414

.346

52.1

246

37.2

6951

.279

934

.171

48.8

406

37.5

3847

.385

526

.201

45.5

273

34.8

5344

.880

626

.151

43.2

738

25.6

2742

.167

812

.905

52.0

356

35.8

1551

.190

432

.735

48.7

498

36.0

5247

.309

024

.723

45.4

574

33.3

3444

.803

224

.659

43.1

963

24.1

5242

.099

311

.482

51.9

425

34.3

4851

.107

231

.233

48.6

613

34.5

4847

.225

023

.272

45.3

919

31.8

2644

.724

723

.158

43.1

320

22.7

0142

.033

79.

949

51.8

667

32.8

2751

.024

929

.745

48.5

769

33.0

4947

.138

221

.813

45.3

292

30.3

3344

.644

521

.773

43.0

586

21.2

9341

.975

18.

476

51.7

925

31.3

3750

.937

528

.268

48.4

973

31.5

6547

.047

320

.441

45.2

438

28.9

0544

.561

620

.368

42.9

806

19.8

8841

.918

27.

021

51.7

151

29.8

4750

.840

026

.757

48.4

252

30.0

2546

.968

919

.079

45.1

697

27.4

9444

.483

518

.902

42.9

089

18.3

5841

.844

45.

601

51.6

315

28.3

9150

.744

825

.266

48.3

427

28.5

0946

.883

117

.598

45.0

952

26.1

2244

.402

417

.362

42.8

359

16.8

8441

.773

34.

077

51.5

441

27.0

4350

.664

923

.902

48.2

615

26.9

9746

.802

116

.131

45.0

165

24.6

9444

.327

315

.842

42.7

695

15.3

8141

.703

12.

596

51.4

678

25.5

1150

.590

022

.435

48.1

765

25.5

3446

.725

414

.686

44.9

455

23.1

8344

.258

914

.343

42.7

096

13.9

4441

.634

41.

128

51.3

988

24.0

2950

.498

321

.009

48.0

871

24.0

5946

.646

813

.375

44.8

743

21.7

7444

.162

612

.937

42.6

513

12.4

9441

.576

622

.501

50.4

026

19.5

0648

.004

822

.661

46.5

739

12.0

0544

.801

620

.292

44.0

865

11.4

0142

.586

610

.993

41.5

127

21.0

0950

.312

318

.055

47.9

235

21.2

4046

.495

010

.641

44.7

327

18.9

0744

.019

19.

926

42.5

177

9.51

641

.455

219

.582

50.2

236

16.5

8847

.850

419

.719

46.4

122

9.33

444

.655

617

.554

43.9

426

8.42

342

.462

68.

053

41.3

906

18.1

1950

.148

515

.230

47.7

787

18.3

2446

.335

57.

894

44.5

886

16.0

5143

.867

36.

935

42.3

993

6.65

841

.337

116

.682

50.0

708

13.7

5147

.700

016

.893

46.2

602

6.49

244

.525

014

.628

43.8

131

5.56

642

.337

05.

274

41.2

804

15.3

0249

.982

112

.323

47.6

207

15.4

1646

.187

65.

141

44.4

570

13.1

8843

.738

24.

134

42.2

759

3.86

441

.218

613

.828

49.8

892

10.9

3147

.538

513

.928

46.1

188

3.81

644

.400

511

.904

43.6

678

2.74

742

.217

52.

473

41.1

474

12.3

1149

.798

59.

598

47.4

634

12.3

9646

.054

22.

519

44.3

280

10.5

8543

.599

11.

199

40.9

851

1.34

237

.946

010

.808

49.7

160

8.11

347

.393

711

.049

45.9

800

1.25

544

.265

19.

110

43.5

257

0.78

437

.159

01.

193

33.4

167

9.36

749

.636

16.

712

47.3

218

9.69

545

.902

10.

464

41.6

114

7.73

043

.463

30.

732

33.7

583

1.16

629

.637

07.

985

49.5

624

5.26

947

.247

78.

275

45.8

338

0.42

339

.738

26.

379

43.3

917

0.70

829

.902

01.

177

26.7

206

6.64

849

.488

63.

889

47.1

728

6.81

745

.766

50.

318

33.8

429

5.08

243

.324

00.

679

26.9

269

1.17

324

.423

45.

206

49.4

055

2.56

447

.105

25.

382

45.6

896

0.28

729

.943

13.

734

43.2

580

0.68

124

.592

31.

159

22.5

790

3.77

749

.320

81.

206

47.0

266

3.99

445

.620

80.

255

26.9

359

2.41

643

.203

30.

669

22.7

125

1.15

521

.042

42.

456

49.2

504

2.62

445

.542

30.

239

24.5

851

1.12

343

.146

20.

646

21.1

582

1.11

119

.726

11.

087

49.1

642

1.17

245

.477

20.

228

22.6

978

0.64

037

.906

10.

660

19.8

057

1.13

218

.541

90.

303

44.0

695

0.24

320

.853

90.

548

33.5

597

0.68

218

.603

51.

140

17.4

350

0.25

441

.048

50.

238

19.5

241

0.46

329

.793

10.

624

17.4

884

1.10

516

.358

40.

211

35.4

289

0.23

018

.338

80.

495

26.8

609

0.65

416

.403

51.

123

15.2

750

0.16

631

.150

50.

215

17.2

248

0.47

524

.551

10.

655

15.3

170

1.09

214

.160

60.

183

27.8

672

0.23

116

.134

80.

473

22.6

819

0.64

814

.203

91.

077

13.0

241

0.15

024

.871

20.

224

15.0

163

0.44

921

.139

20.

619

13.0

596

0.15

922

.879

90.

210

13.8

605

0.43

719

.810

00.

153

21.2

366

0.20

812

.683

00.

420

18.6

181

0.19

119

.833

40.

440

17.5

121

0.10

418

.602

90.

397

16.4

346

0.12

517

.419

60.

382

15.3

565

0.10

816

.296

40.

421

14.2

456

0.10

715

.130

80.

382

13.1

053

594 Journal of Chemical and Engineering Data, Vol. 43, No. 4, 1998

Tab

le1.

(Con

tin

ued

)

P/M

Pa

F/m

oL-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF

/moL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

x 1)

0.28

72T

)27

2.36

KT

)30

2.32

KT

)33

2.81

KT

)36

3.00

KT

)38

3.52

KT

)40

3.52

KT

)42

4.29

KT

)44

2.71

K15

.193

41.8

476

27.4

4240

.985

131

.872

39.7

126

38.9

4138

.636

436

.860

37.8

328

38.8

3536

.879

538

.419

36.2

004

28.8

3135

.019

513

.663

41.7

896

25.9

7640

.922

830

.436

39.6

629

37.5

5138

.585

635

.373

37.7

823

37.2

4636

.836

536

.823

36.1

508

27.2

2034

.980

112

.207

41.7

327

24.6

1940

.806

828

.952

39.6

132

36.1

6438

.529

033

.772

37.7

319

35.6

6436

.796

335

.212

36.1

110

25.6

1734

.944

210

.736

41.6

688

23.1

1840

.747

327

.478

39.5

625

34.7

6138

.471

232

.210

37.6

796

34.1

2336

.746

233

.609

36.0

757

24.0

2934

.903

29.

232

41.6

102

21.6

4140

.692

925

.986

39.5

102

33.4

3538

.421

530

.636

37.6

331

32.5

5436

.703

432

.019

36.0

286

22.3

8434

.856

07.

776

41.5

529

20.1

2140

.625

624

.518

39.4

609

31.9

3338

.374

929

.062

37.5

788

30.9

5136

.664

330

.406

35.9

888

20.7

9534

.816

06.

350

41.4

966

18.6

8940

.588

123

.082

39.4

100

30.4

5238

.331

127

.468

37.5

256

29.4

3636

.623

528

.805

35.9

424

19.1

8834

.773

14.

877

41.4

289

17.2

8440

.530

521

.648

39.3

636

28.9

8138

.284

925

.944

37.4

716

27.9

6836

.579

827

.217

35.8

932

17.5

8434

.737

03.

501

41.3

884

15.8

5340

.474

120

.242

39.3

116

27.5

1138

.239

424

.415

37.4

260

26.4

0136

.535

925

.605

35.8

433

15.9

8634

.695

02.

114

41.3

293

14.3

8740

.423

318

.773

39.2

623

26.0

2638

.192

822

.937

37.3

874

24.8

6236

.486

924

.002

35.7

974

143.

8434

.654

71.

115

41.2

802

12.9

9340

.380

717

.287

39.2

118

24.5

5738

.145

021

.403

37.3

406

23.3

1336

.441

522

.403

35.7

543

12.7

6334

.617

711

.602

40.3

375

15.8

7639

.164

523

.080

38.0

994

19.9

4437

.289

121

.733

36.3

995

20.8

1035

.701

911

.158

34.5

818

10.1

8640

.284

314

.445

39.1

239

21.5

7938

.055

518

.401

37.2

379

20.1

6836

.353

019

.214

35.6

547

9.55

734

.542

98.

730

40.2

241

12.9

8139

.061

820

.062

38.0

077

16.8

3737

.191

018

.672

36.3

089

17.6

0635

.612

57.

940

34.5

058

7.30

640

.169

111

.503

39.0

143

18.5

7237

.961

815

.301

37.0

887

17.0

6936

.267

715

.986

35.5

683

6.30

834

.466

15.

817

40.1

209

10.0

8038

.955

417

.129

37.9

168

13.7

9737

.039

515

.488

36.2

242

14.4

1935

.527

04.

770

34.4

307

4.41

140

.070

28.

579

38.9

161

15.6

6737

.869

012

.315

36.9

894

14.0

0136

.185

112

.821

35.4

842

3.44

434

.385

63.

031

40.0

114

7.11

038

.868

714

.255

37.8

268

10.8

4136

.947

012

.426

36.1

407

11.2

1635

.437

82.

432

34.2

961

1.63

139

.958

15.

148

38.8

174

12.8

0937

.782

99.

357

36.8

991

10.9

3936

.095

19.

659

35.3

952

1.71

430

.680

01.

158

39.9

016

3.72

538

.767

311

.388

37.7

334

7.86

836

.857

59.

430

36.0

527

8.01

035

.355

71.

603

27.8

430

2.39

738

.710

39.

931

37.6

873

6.36

536

.812

57.

906

36.0

172

6.41

435

.314

71.

532

25.5

861

1.15

038

.665

08.

531

37.6

405

4.88

236

.766

36.

302

35.9

786

4.82

435

.276

91.

479

23.7

606

7.06

737

.597

63.

432

36.7

163

4.78

935

.931

23.

365

35.2

096

1.50

622

.216

25.

589

37.5

569

2.07

836

.655

23.

401

35.8

883

2.30

735

.167

71.

485

20.8

676

4.13

737

.506

40.

990

33.9

100

2.10

835

.834

51.

107

32.8

230

1.47

919

.649

22.

674

37.4

597

0.39

530

.458

00.

937

33.2

874

1.00

929

.531

11.

436

18.4

868

1.31

237

.406

80.

389

27.6

454

0.71

329

.883

60.

977

26.9

424

1.44

017

.344

60.

925

37.3

046

0.32

225

.401

40.

627

27.1

880

0.96

124

.862

21.

444

16.1

813

0.63

533

.459

70.

287

23.5

835

0.59

025

.039

10.

916

23.1

514

1.43

814

.985

80.

485

32.8

309

0.25

322

.048

60.

549

23.2

849

0.93

721

.692

51.

429

13.5

202

0.25

929

.560

00.

287

20.7

117

0.58

821

.797

30.

873

20.4

005

0.18

226

.936

70.

225

19.4

903

0.56

420

.256

50.

900

19.2

097

0.12

924

.840

70.

253

18.3

268

0.54

819

.066

80.

883

18.0

584

0.15

123

.116

70.

254

17.1

747

0.53

817

.913

50.

845

16.9

016

0.12

521

.650

90.

253

16.0

046

0.49

416

.759

70.

852

15.7

255

0.13

920

.118

30.

240

14.7

970

0.51

815

.580

90.

855

14.5

181

0.13

618

.925

20.

501

14.3

665

0.11

117

.772

30.

104

16.6

126

0.10

815

.424

60.

101

14.1

744


Tab

le1.

(Con

tin

ued

)

P/M

Pa

F/m

oL-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF

/moL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

x 1)

0.49

80T

)25

6.87

KT

)27

2.39

KT

)30

1.67

KT

)33

2.82

KT

)36

3.14

KT

)38

3.25

KT

)40

3.64

KT

)42

4.34

KT

)44

2.72

K14

.026

38.8

674

18.4

5938

.052

039

.013

37.1

646

34.1

5335

.163

839

.095

33.8

206

38.1

2832

.588

438

.223

31.6

585

34.9

5930

.660

314

.043

28.9

217

12.5

1938

.796

516

.955

37.9

798

37.6

2537

.099

332

.695

35.1

029

37.7

1633

.762

936

.775

32.5

371

36.8

5931

.604

633

.676

30.6

126

9.14

628

.732

911

.059

38.7

274

15.4

2337

.911

636

.151

37.0

413

31.1

9735

.045

836

.315

33.7

024

35.3

7232

.485

635

.446

31.5

514

32.4

1730

.565

37.

814

28.6

879

9.58

238

.663

813

.925

37.8

488

34.6

4936

.964

329

.694

34.9

800

34.9

1733

.640

833

.985

32.4

388

34.0

7731

.499

531

.136

30.5

148

6.66

328

.638

48.

049

38.5

902

12.4

5737

.780

633

.194

36.9

047

28.2

4034

.916

733

.530

33.5

839

32.6

6132

.392

532

.693

31.4

456

29.8

3930

.463

75.

353

28.5

922

6.61

438

.519

211

.021

37.7

079

31.7

9536

.845

326

.762

34.8

348

32.1

2833

.526

331

.280

32.3

444

31.2

7631

.393

028

.581

30.4

140

4.05

428

.547

05.

094

38.4

752

9.58

737

.641

130

.368

36.8

067

25.2

4934

.792

130

.690

33.4

685

29.9

2232

.299

629

.865

31.3

390

27.2

7730

.364

12.

810

28.4

974

3.73

438

.399

58.

125

37.5

677

28.8

3636

.755

723

.743

34.7

344

29.3

2633

.409

028

.520

32.2

492

28.4

9131

.290

626

.018

30.3

176

2.14

226

.816

12.

217

38.2

449

6.68

337

.499

927

.372

36.7

045

22.2

4634

.678

927

.952

33.3

488

27.1

8532

.200

327

.129

31.2

383

24.7

2330

.268

41.

881

24.4

609

5.23

037

.427

925

.940

36.5

701

20.7

6534

.619

226

.551

33.2

928

25.8

0732

.153

125

.673

31.1

875

23.4

7730

.222

91.

753

21.3

522

3.79

937

.366

224

.454

36.5

134

19.2

6134

.553

625

.172

33.2

357

24.4

0832

.104

924

.272

31.1

406

22.1

9230

.174

51.

702

18.9

826

2.36

637

.298

022

.986

36.4

423

17.7

9634

.485

523

.767

33.1

762

23.0

1932

.056

922

.894

31.0

892

20.9

1830

.130

11.

674

17.1

491

21.5

5636

.369

616

.317

34.4

238

22.4

1133

.122

121

.665

32.0

105

21.4

8731

.037

819

.650

30.0

815

1.64

315

.702

520

.104

36.2

855

14.8

1634

.361

221

.112

33.0

627

20.3

0031

.961

420

.040

30.9

907

18.3

5030

.030

71.

637

14.5

364

18.6

2536

.229

413

.319

34.3

004

19.7

1333

.007

018

.899

31.9

102

18.6

0530

.940

717

.081

29.9

833

1.63

613

.568

117

.122

36.1

654

11.8

9634

.236

618

.334

32.9

553

17.5

2031

.863

917

.208

30.8

933

15.8

3429

.935

81.

627

12.7

266

15.6

6936

.086

910

.331

34.1

786

16.9

2632

.897

316

.133

31.8

143

15.7

4330

.842

114

.599

29.8

897

1.62

211

.974

414

.199

36.0

219

8.79

934

.123

315

.539

32.8

355

14.7

2731

.771

014

.332

30.7

921

13.3

2129

.844

71.

608

11.2

704

12.7

7535

.941

97.

297

34.0

701

14.1

4832

.778

213

.349

31.7

291

12.8

9630

.746

412

.031

29.8

008

1.59

210

.583

511

.321

35.8

645

5.80

834

.010

012

.838

32.7

221

11.9

9031

.682

311

.490

30.6

988

10.7

9529

.753

71.

565

9.88

939.

842

35.7

936

4.24

533

.944

911

.443

32.6

656

10.5

8731

.636

610

.142

30.6

491

9.56

029

.705

71.

595

9.17

878.

386

35.7

277

2.86

733

.887

210

.024

32.6

064

9.29

331

.589

18.

892

30.5

996

8.29

629

.662

31.

581

8.35

846.

885

35.6

605

8.67

832

.550

27.

973

31.5

480

7.56

330

.553

27.

033

29.6

175

5.45

335

.622

57.

508

32.4

926

6.70

331

.509

56.

261

30.5

050

5.74

129

.569

54.

037

35.5

847

6.19

932

.443

65.

330

31.4

568

4.93

830

.459

84.

497

29.5

260

2.74

635

.479

74.

759

32.3

907

4.04

731

.414

43.

617

30.4

128

3.19

729

.482

33.

493

32.3

407

2.77

131

.366

22.

286

30.3

687

2.12

629

.470

52.

224

32.2

892

1.61

730

.910

11.

348

29.3

962

1.11

919

.484

61.

033

31.5

473

1.01

729

.949

51.

068

28.2

593

1.06

517

.520

40.

365

25.6

849

0.56

825

.589

10.

757

24.1

331

1.04

115

.981

00.

254

22.3

322

0.43

622

.126

70.

692

2.10

064

1.01

214

.757

20.

212

19.6

228

0.37

819

.462

30.

648

18.6

451

1.02

113

.742

80.

211

17.5

868

0.34

617

.466

00.

652

16.5

538

0.99

912

.732

10.

162

16.0

050

0.30

515

.923

60.

578

15.2

078

0.97

511

.973

40.

109

14.7

545

0.31

914

.702

40.

598

14.1

196

0.98

311

.263

10.

149

13.7

332

0.27

813

.696

60.

550

13.2

013

0.98

110

.575

40.

119

12.7

010

0.26

012

.833

20.

575

12.3

966

0.94

89.

8790

0.10

511

.929

80.

289

11.9

230

0.55

511

.661

30.

961

9.16

100.

122

11.2

172

0.27

811

.212

60.

537

10.9

647

0.94

88.

4296

0.10

710

.523

60.

276

10.5

181

0.55

110

.277

20.

109

9.68

680.

273

9.81

730.

550

9.40

030.

104

8.95

970.

265

9.09

850.

544

8.66

980.

102

8.21

970.

234

8.36

12


Tab

le1.

(Con

tin

ued

)

P/M

Pa

F/m

oL-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF

/moL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

x 1)

0.68

76T

)25

7.34

KT

)27

2.91

KT

)30

2.47

KT

)33

3.14

KT

)36

3.05

KT

)38

3.29

KT

)40

3.43

KT

)42

3.26

KT

)44

3.02

K15

.762

34.9

700

28.5

5934

.688

436

.268

33.4

872

39.6

5931

.931

438

.622

30.3

356

36.2

8129

.395

438

.996

28.6

290

38.9

3927

.855

732

.887

27.0

253

14.4

1734

.906

927

.219

34.6

306

34.9

0733

.429

438

.252

31.8

773

37.0

9130

.288

234

.687

29.3

492

37.5

4728

.586

737

.353

27.8

074

31.3

6827

.008

213

.118

34.8

471

25.8

5434

.569

833

.593

33.3

669

36.7

5731

.817

735

.568

30.2

390

33.1

2229

.301

336

.080

28.5

412

35.7

7627

.764

229

.803

26.9

544

11.8

2634

.785

224

.543

34.5

092

32.2

8333

.305

335

.269

31.7

535

34.0

8830

.188

131

.640

29.2

520

34.5

7128

.493

434

.173

27.7

152

28.2

3526

.909

110

.515

34.7

190

23.2

5334

.442

930

.958

33.2

474

33.7

0931

.703

532

.581

30.1

389

30.1

1829

.207

433

.050

28.4

487

32.5

5327

.671

726

.618

26.8

666

9.21

134

.658

221

.892

34.3

839

29.6

3533

.194

232

.254

31.6

484

31.1

1230

.087

528

.617

29.1

648

31.5

5928

.405

730

.940

27.6

239

25.0

0826

.821

37.

943

34.5

966

20.5

6734

.328

628

.328

33.1

366

30.7

8131

.588

929

.582

30.0

389

27.1

2729

.121

630

.028

28.3

661

29.3

5627

.575

823

.417

26.7

798

6.62

234

.532

619

.212

34.2

658

26.9

6333

.079

529

.367

31.5

384

28.0

3529

.994

825

.605

29.0

790

28.5

5328

.323

627

.734

27.5

290

21.8

3026

.735

55.

372

34.4

651

17.9

1034

.205

425

.641

33.0

214

27.8

9831

.481

026

.534

29.9

406

24.1

1029

.034

627

.063

28.2

795

26.0

9327

.486

520

.283

26.6

942

4.03

234

.409

916

.576

34.1

419

24.3

2132

.958

826

.367

31.4

269

25.0

7029

.901

222

.607

28.9

929

25.5

4928

.236

724

.482

27.4

429

18.6

4626

.654

32.

698

34.3

496

15.1

9934

.081

522

.980

32.9

045

24.9

0131

.374

823

.531

29.8

579

21.1

1928

.955

124

.027

28.1

954

22.8

5827

.396

417

.142

26.6

085

1.45

734

.300

713

.902

34.0

206

21.6

1632

.849

023

.377

31.3

181

22.0

2029

.804

119

.632

28.9

112

22.5

5328

.148

821

.260

27.3

533

15.5

8126

.566

412

.591

33.9

614

20.3

1232

.791

321

.887

31.2

642

20.5

4929

.755

118

.120

28.8

646

20.9

8928

.103

019

.655

27.3

067

13.9

7226

.525

611

2.88

33.8

974

18.9

8032

.731

820

.422

31.2

054

19.0

6329

.716

316

.606

28.8

186

19.4

6828

.058

618

.061

27.2

657

12.3

2726

.481

29.

820

33.8

389

17.6

2032

.675

118

.889

31.1

443

17.5

6029

.674

415

.086

28.7

718

17.9

6528

.018

116

.494

27.2

236

10.7

4026

.439

08.

466

33.7

841

16.3

1432

.614

517

.391

31.0

856

16.0

6529

.631

913

.563

28.7

262

16.5

2627

.976

814

.871

27.1

775

9.20

626

.402

17.

141

33.7

242

14.9

9032

.555

015

.913

31.0

288

14.5

2629

.593

512

.029

28.6

840

15.0

1927

.936

313

.240

27.1

400

7.47

526

.362

05.

905

33.6

610

13.6

8532

.499

714

.426

30.9

751

13.0

5229

.549

810

.526

28.6

391

13.4

8627

.892

911

.654

27.1

069

5.84

826

.323

04.

550

33.5

964

12.3

2232

.442

913

.020

30.9

214

11.5

4529

.499

29.

045

28.5

980

11.9

9927

.853

19.

975

27.0

647

4.30

026

.278

33.

264

33.5

380

10.6

7532

.386

011

.593

30.8

667

10.0

2429

.450

97.

513

28.5

532

10.5

3327

.811

08.

345

27.0

198

2.78

326

.238

81.

900

33.4

853

9.66

432

.273

410

.137

30.8

165

8.53

929

.408

85.

985

28.5

116

9.06

027

.772

06.

834

26.9

785

1.93

621

.329

41.

172

33.4

260

8.34

032

.225

58.

540

30.7

640

7.04

729

.369

64.

459

28.4

654

7.63

627

.727

05.

295

26.9

332

1.92

218

.887

67.

015

32.1

692

6.94

730

.707

95.

537

29.3

253

3.11

028

.417

46.

040

27.6

846

4.85

226

.895

61.

876

16.9

983

5.63

732

.111

65.

488

30.6

633

4.34

529

.282

81.

731

28.3

720

4.58

427

.647

22.

549

26.8

507

1.91

315

.512

44.

316

32.0

516

4.12

830

.611

52.

634

29.2

301

0.99

528

.330

93.

104

27.6

020

1.33

225

.454

51.

855

14.3

215

2.93

832

.002

72.

753

30.5

616

1.19

729

.187

10.

391

24.3

320

1.77

227

.559

51.

264

23.1

957

1.86

513

.337

91.

688

31.9

490

1.42

030

.521

21.

061

29.1

560

0.38

821

.025

70.

942

27.5

290

1.19

320

.316

31.

879

12.4

982

0.32

925

.623

70.

385

18.6

454

0.70

523

.336

31.

169

18.1

122

1.85

711

.753

50.

280

22.2

194

0.38

717

.195

80.

695

20.1

435

1.18

316

.399

91.

854

11.0

627

0.22

519

.606

20.

380

15.4

494

0.69

217

.643

11.

203

15.0

410

1.88

610

.265

50.

255

17.2

365

0.36

914

.264

80.

729

16.0

273

1.18

813

.936

81.

837

9.59

750.

209

15.7

073

0.38

113

.285

50.

698

14.7

389

1.14

713

.012

01.

859

8.91

220.

206

14.4

824

0.39

212

.448

90.

691

13.6

819

1.19

212

.212

01.

872

8.20

960.

180

13.4

720

0.34

711

.706

60.

681

12.7

947

1.16

611

.485

90.

167

12.6

137

0.37

611

.014

30.

693

12.0

167

1.18

810

.806

40.

183

11.8

534

0.35

810

.343

80.

679

11.3

079

1.16

610

.141

60.

161

11.1

552

0.32

49.

6721

0.65

910

.633

21.

145

9.46

990.

162

10.4

832

0.28

88.

9867

0.70

29.

9676

1.14

58.

7844

0.14

09.

8148

0.21

98.

2833

0.70

49.

2898

1.16

18.

0775

0.16

99.

1332

0.66

98.

5935

0.16

18.

3450

0.60

27.

8781

0.15

87.

7911


Tab

le1.

(Con

tin

ued

)

P/M

Pa

F/m

oL-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF/

mol

L-

1P

/MP

aF

/moL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

P/M

Pa

F/m

olL

-1

x 1)

0.90

61T

)25

7.51

KT

)27

2.93

KT

)30

2.40

KT

)33

2.99

KT

)36

3.27

KT

)38

3.59

KT

)40

4.03

KT

)42

4.40

KT

)44

2.56

K18

.914

30.2

487

19.0

5929

.606

328

.993

28.5

177

38.4

5927

.561

338

.268

26.2

995

39.0

9425

.551

440

.274

24.8

076

38.8

4424

.112

219

.764

22.9

994

17.4

9330

.201

617

.594

29.5

571

27.5

1628

.468

136

.978

27.5

053

36.8

4126

.249

137

.625

25.5

058

38.7

8824

.762

237

.376

24.0

690

18.3

0722

.959

216

.060

30.1

587

16.1

2329

.508

926

.062

28.4

153

35.5

3727

.452

635

.359

26.2

044

36.1

1725

.458

237

.311

24.7

193

35.8

8224

.025

016

.801

22.9

246

14.6

4830

.119

414

.635

29.4

520

24.5

9828

.358

434

.076

27.3

981

33.8

8626

.152

634

.657

25.4

145

35.7

9024

.673

634

.414

23.9

801

15.3

0722

.885

113

.225

30.0

784

13.1

5529

.404

023

.165

28.3

060

32.6

5127

.344

332

.385

26.1

079

33.2

4525

.379

234

.276

24.6

294

32.9

3923

.936

913

.776

22.8

447

11.7

8830

.025

311

.678

29.3

572

21.6

9528

.248

531

.196

27.2

954

30.9

4726

.061

131

.734

25.3

401

32.7

8824

.582

631

.417

23.8

973

12.3

0222

.808

910

.326

29.9

779

10.2

4229

.298

620

.239

28.1

926

29.7

2727

.240

829

.480

26.0

177

30.2

6925

.295

031

3.19

24.5

374

29.8

8623

.855

810

.781

22.7

747

8.85

229

.934

28.

747

29.2

417

18.7

7428

.138

128

.248

27.1

897

27.9

8125

.972

428

.798

25.2

473

29.8

5124

.494

428

.384

23.8

192

9.32

222

.737

07.

416

29.8

912

7.26

929

.187

517

.289

28.0

842

26.7

7927

.136

426

.501

25.9

228

27.2

9725

.200

928

.350

24.4

538

26.9

2323

.780

07.

781

22.6

980

6.03

229

.852

35.

817

29.1

337

15.8

1728

.038

225

.321

27.0

908

25.0

2425

.874

925

.863

25.1

573

26.8

1624

.416

225

.466

23.7

400

6.36

022

.662

14.

587

29.8

090

4.39

029

.087

414

.353

27.9

871

23.8

3027

.040

923

.562

25.8

275

24.4

0125

.112

825

.341

24.3

708

23.9

7123

.703

95.

001

22.6

290

3.22

429

.762

52.

747

28.9

781

12.8

8227

.935

122

.394

26.9

868

22.0

7825

.788

622

.942

25.0

730

23.8

4224

.326

722

.437

23.6

635

3.66

622

.598

511

.416

27.8

850

20.9

5826

.936

620

.620

25.7

472

21.4

6525

.035

322

.376

24.2

870

21.0

0923

.624

82.

411

22.5

662

9.96

027

.839

719

.456

26.8

974

19.1

1625

.709

720

.062

24.9

914

20.8

7224

.243

919

.559

23.5

865

2.28

120

.227

58.

560

27.7

918

18.0

3026

.853

217

.617

25.6

711

18.6

5524

.944

319

.364

24.2

018

18.1

3623

.548

82.

222

17.2

814

7.25

127

.748

916

.552

26.8

133

16.1

4125

.621

317

.210

24.9

003

17.8

9924

.160

916

.665

23.5

096

2.20

215

.324

55.

782

27.7

098

15.1

0026

.766

914

.639

25.5

772

15.8

6324

.858

416

.404

24.1

186

15.1

9923

.469

92.

209

13.8

082

4.41

227

.664

313

.659

26.7

167

13.1

8125

.534

014

.475

24.8

157

14.9

4924

.075

313

.715

23.4

328

2.17

512

.591

53.

066

27.6

200

12.2

0226

.672

111

.692

25.4

882

13.0

3924

.774

113

.491

24.0

321

12.2

1323

.398

92.

164

11.6

220

1.68

927

.575

910

.797

26.6

307

10.2

1525

.446

211

.683

24.7

284

12.0

1223

.992

110

.736

23.3

582

2.17

710

.816

51.

149

27.5

239

9.34

326

.591

08.

758

25.3

992

10.6

1624

.687

710

.594

23.9

512

9.28

423

.319

52.

159

10.1

322

7.86

626

.541

87.

404

25.3

558

9.28

424

.642

69.

188

23.9

116

7.87

223

.281

72.

185

9.52

196.

412

26.4

972

6.04

525

.315

57.

948

24.6

057

7.81

523

.873

76.

410

23.2

436

2.14

78.

9521

5.06

426

.456

84.

699

25.2

744

6.66

624

.564

96.

364

23.8

374

5.01

823

.203

52.

153

8.40

533.

618

26.4

181

3.34

025

.236

25.

284

24.5

226

4.96

023

.806

43.

615

23.1

644

2.15

67.

8570

2.23

626

.381

22.

035

25.1

996

3.99

924

.476

83.

685

23.7

673

2.28

323

.127

42.

131

7.29

371.

162

26.3

354

1.15

125

.135

42.

757

24.4

393

2.32

023

.730

51.

284

18.5

580

2.13

36.

7156

0.13

719

.943

31.

424

24.0

876

1.17

723

.475

41.

271

16.0

603

0.13

117

.110

41.

140

23.9

545

0.92

420

.810

71.

264

14.0

741

0.12

514

.925

30.

493

21.3

949

0.91

517

.825

21.

259

12.6

164

0.12

013

.463

20.

490

18.5

063

0.91

115

.772

11.

256

11.5

497

0.10

212

.310

70.

485

16.0

653

0.88

214

.146

31.

260

10.6

796

0.11

711

.383

20.

491

14.3

747

0.91

012

.870

61.

254

10.0

002

0.10

810

.615

50.

468

13.0

483

0.88

411

.851

21.

248

9.35

630.

120

9.95

270.

445

11.9

854

0.86

811

.012

11.

246

8.79

820.

134

9.35

130.

451

11.1

194

0.86

310

.300

91.

228

8.25

450.

120

8.79

020.

450

10.3

901

0.85

49.

6773

1.19

57.

7078

0.10

98.

2387

0.42

39.

7495

0.86

69.

1032

1.22

97.

1414

0.10

87.

6822

0.45

09.

1692

0.86

38.

5547

1.22

36.

5635

0.10

87.

1080

0.43

08.

6170

0.84

57.

9663

0.10

36.

5221

0.41

98.

0683

0.83

97.

3512

0.45

37.

5117

0.83

36.

7266

0.43

66.

9399

0.42

46.

3566


tion defined by

are given in Table 5 where NP and Ny are respectively thenumbers of determinations of bubble-point pressures andof vapor-phase compositions.

The vapor-liquid equilibrium of methanol + water hasbeen measured by Griswold and Wong (1952) between373.15 K and 523.15 K, by Schroder (1958) at 413.15 K,and by Hirata and Suda (1967) and Hirata et al. (1975)

at pressures of 0.3 MPa and 0.5 MPa. The results obtainedfrom these authors and our data are summarized in Table6. The agreement is satisfactory. Moreover, we canremark in Figure 4 that our own measurements at 424.15K agree with those of Griswold and Wong (1952) at 423.15K, the only reference temperature.

Conclusion

We have described a high-pressure apparatus designedto obtain pressure-density-temperature data of a pure-component or a mixture over the temperature range 210K-470 K and at pressures up to 70 MPa. The densities of

Figure 2. Schematic diagram of the measurement cell: (1) saphirwindows; (2) stainless steel valve; (3) fluid introduction; (4)internal iron kernel for the stirrer; (5) stirrer support; (6) stirrer;(7) external iron kernel for the stirrer; (8) copper cylinder; (9)copper column; (10) bellow; (11) chamber; (12) copper rod; (13)thermocouple; (14) column connecting the support of the externalstirrer with the micrometric table; (15) low position of the stirrer;(16) cooper mass for transferring the heating or cooling fluid tothe bottom of the bellow; (17) cooling circuit; (18) entrance tube ofthe compression fluid; (19) cooling platform; (20) entrance of liquidnitrogen.

P/P(%) )100

NPi)1

NP jPexp,i - Pcal,iPexp,i j (7)y )

1

Nyi)1

Ny

jyexp,i - ycal,ij (8)

Figure 3. Determination of bubble pressure of methanol (1) +water (2) at 363.15 K for x1 ) 0.4980: [, data in single-phaseregion (liquid); 9, data in two-phase region; 2, data in two-phaseregion not taken into account in linear regression.

Table 2. Bubble Pressures for the Methanol (1) + Water(2) System at Five Different Temperatures

P/MPa

x1 363.15 K 383.15 K 403.15 K 424.15 K 442.15 K

0.1061 0.117 0.227 0.403 0.665 1.1570.2872 0.153 0.293 0.567 0.937 1.4770.4980 0.181 0.369 0.647 1.073 1.7040.6876 0.219 0.401 0.715 1.218 1.9060.9061 0.238 0.458 0.844 1.296 2.093

Table 3. Comparison of Experimental and CalculatedLiquid-Phase Density Data at Selected Temperaturesand Pressures

T/Kpressure

range (MPa)no. ofdata F/F (%) r(F)

332.55 13.751-1.150 44 2.63 -0.30363.17 13.052-1.062 46 2.62 -1.17383.57 13.039-0.995 46 2.89 -1.75403.52 12.896-0.942 45 2.97 -1.96424.05 12.937-2.126 40 2.85 -1.81443.50 12.763-2.411 37 3.18 -1.76

Table 4. Pure Component Parameters Used in ThisStudy

compd Tc/K Pc/MPa Tb/K b/cm3mol-1 m1 m2

methanol 512.58 8.094 337.70 23.995 1.080 64 -0.170 98water 647.37 22.120 373.15 11.089 1.358 60 0.165 64

Table 5. Vapor-Liquid Equilibrium Results forMethanol + Water

type ref

temprange

(K)

pressurerange(MPa) NP P/P (%) Ny y

isothermal 1 to 13 243-474 0.00005-3.950 449 1.86 262 0.018

isobaric 14 to 39 307-421 0.026-0.507 422 2.13 387 0.011

global 871 1.99 649 0.014


the methanol + water have been measured in the single-phase and two-phase region. The VLE pressure-composi-tion data obtained from densities are in good agreementwith literature values that have been fitted to the excessfunction-equation of state model by adjusting an interactionparameter.

Literature CitedBenson, G. C.; Kiyohara, O. Thermodynamics of Aqueous Mixtures of

Non-Electrolytes. 1. Excess Volumes of Water-N-Alcohol Mixturesat Several Temperatures. J. Solution Chem. 1980, 9, 791-804.

Easteal, A. J.; Woolf, L. A. (P, Vm, T, X) Measurements for ((1-x)H2O+ xCH3OH) in the Range 278 K to 323 K and 0.1 to 280 MPA. 2.Thermodynamic Excess Properties. J. Chem. Thermodyn. 1985, 17,69-82.

Goodwin, R. D. Methanol thermodynamic properties from 176 to 673K at pressures to 700 bar. J. Phys. Chem. Ref. Data 1987, 16, 799-892.

Goodwin, R. D. Toluene thermophysical properties from 178 to 800 Kat pressures to 1000 bar. J. Phys. Chem. Ref. Data 1989, 18, 1565-1636.

Griswold, J.; Wong, S. Y. Phase-Equilibria of the Acetone-Methanol-Water System from 100 C into the Critical Region. Chem. Eng.Prog., Symp. Ser. 1952, 48, 18-25.

Hirata, M.; Suda, S. Vapor Pressure of Methanol in High-PressureRegions. Kagaku Kogaku 1967, 31, 339-341.

Hirata, M.; Ohe, S.; Nagahama, K. Computer aided data of VLE;Elsevier: Amsterdam, 1975.

Hocq, H. Ph.D. Thesis, University Aix-Marseille II, France, 1994; pp1-289.

Hocq, H.; Bur, Y.; Berro, C. Densities of liquid water, toluene, andmethanol at 240 to 450 K and up to 70 MPa and of gaseous methanolat 420 to 450 K and up to 2 MPa. ELDATA: Int. Electron. J. Phys.-Chem. Data 1995, 1, 79-86.

McGlashan, M. L.; Williamson, A. G. Isothermal Liquid-VaporEquilibria for System Methanol-Water. J. Chem. Eng. Data 1976,21, 196-199.

Patel, N. C.; Sandler, S. I. Excess Volumes of the Water/Methanol,n-Heptane/Ethyl Acetate, n-Heptane/n-Butyraldehyde, and n-Hep-tane/Isobutyraldehyde Systems. J. Chem. Eng. Data 1985, 30, 218-222.

Peneloux, A.; Abdoul, W.; Rauzy, E. Excess functions and equationsof state. Fluid Phase Equilib. 1989, 47, 115-132.

Schroder, W. Measuring vapor-liquid equilibria at elevated pressure.Chem.-Ing.-Tech. 1958, 30, 523-525.

Xiao, C.; Bianchi, H.; Tremaine, P. R. Excess molar volumes anddensities of methanol + water at temperatures between 323 K and573 K and pressures of 7.0 MPa and 13.5 MPa. J. Chem. Thermodyn.1997, 29, 261-286.

Received for review December 13, 1997. Accepted April 6, 1998.The authors acknowledge with gratitude the society TOTAL fortheir financial support through FSH and ARTEP.

JE970297P

Figure 4. Vapor-liquid equilibria of the methanol-water binarysystem at 424.15 K. Calculated curve: full line. Data: *, our work;0, Griswold and Wong at 423.15 K.

Table 6. Relative Mean Deviations in the Bubble-PointPressure for Our Data and Those Reported in theLiterature

T/K P/MPa NP P/P (%) ref

363.15 5 1.76 our work383.15 5 1.33 our work403.15 5 2.79 our work424.15 5 2.67 our work442.15 5 1.10 our work373.15 18 1.54 Griswold and Wong423.15 16 0.81 Griswold and Wong473.15 17 3.82 Griswold and Wong413.15 6 1.29 Schroeder

0.304 10 2.96 Hirata and Suda0.507 11 2.14 Hirata. and Suda0.304 26 1.78 Hirata et al.0.507 26 2.21 Hirata et al.


density of methanol + water between 250 k and 440 k and up to 40

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