Excess thermodynamic properties of binary and ternary mixtures containing methyl 1,1-dimethylethyl ether (MTBE),n-heptane, and methanol atT =  313.15 K

J. Chem. Thermodynamics 1999, 31, 1231–1246 Article No. jcht.1999.0532 Available online at http://www.idealibrary.com on

Excess thermodynamic properties of binary and ternary mixtures containing methyl 1,1-dimethylethyl ether (MTBE), n-heptane, and methanol at T = 313.15 K Jos´e J. Segovia, Mar´ıa C. Mart´ın, C´esar R. Chamorro, and ˜ ana Miguel A. Villaman´ Laboratorio de Termodin´amica, Depto. Ingenier´ıa Energ´etica y Fluidomec´anica, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, E-47071 Valladolid, Spain

(Vapour + liquid) equilibrium of {methyl 1,1-dimethylethyl ether (MTBE) + n-heptane + methanol}, {methyl 1,1-dimethylethyl ether (MTBE) + methanol}, and (methanol + n-heptane) have been measured at T = 313.15 K. The data reduction by Barker’s method provides correlations for the excess molar Gibbs energy G E m using the Margules equation for the binary systems, and the Wohl expansion for the ternary. The Wilson, NRTL, and UNIQUAC models have been applied successfully to both the binary and ternary systems E for the same ternary reported here. Using literature data of the excess molar enthalpy Hm E for mixture measured at T = 313.15 K, we have calculated the excess molar entropy Sm c 1999 Academic Press the system at the same temperature. KEYWORDS: VLE data; correlations; excess Gibbs energy; excess properties; binary mixtures; ternary mixtures

1. Introduction Methyl 1,1-dimethylethyl ether, designated by the abbreviation MTBE (methyl tert-butyl ether) is at present the most important blending agent in the formulation of gasoline because of its antiknocking effect and for being an environmentally friendly chemical, and easy to synthesize at low cost. MTBE is obtained by the catalytic reaction of methanol and isobutene. In its synthesis, the methanol/isobutene ratio is limited by the formation of an azeotrope between MTBE and the unreacted methanol. In the subsequent distillation process, it is obtained as a bottoms product in which methanol has always been found as an impurity. The third added compound, n-heptane, represents the hydrocarbons in the gasoline. a To whom correspondence should be addressed.

0021–9614/99/081231 + 16 $30.00/0

c 1999 Academic Press

1232

J. J. Segovia et al.

This work is part of a research program on the thermodynamic characterization of ternary mixtures containing oxygenated additives (ethers and alcohols), and different types of hydrocarbons (paraffins, cycloparaffins, aromatics, oleffins). In previous studies,(1–7) we have investigated binary and ternary systems containing MTBE and/or the hydrocarbons benzene, cyclohexane, n-heptane, and 1-hexene at T = 313.15 K. Here, (MTBE + nheptane + methanol), and the binary (MTBE + methanol) and (methanol + n-heptane) at T = 313.15 K form the object of the present work.

2. Experimental procedure All the chemicals used were purchased from Fluka Chemie AG and were of the highest purity available, chromatography quality reagents (of the series puriss. p.a.) with a mole fraction purity > 0.995 for MTBE and n-heptane, and a mole fraction purity > 0.998 for methanol. All liquids were degassed prior to measurements using a modified distillation method based on the technique of Van Ness and Abbott,(8) under reduced pressure generated by a double stage rotatory pump assuring p = 0.5 Pa. The mole fraction purities of the chemicals were checked by gas chromatography and were found to be: >0.999 for methyl 1,1-dimethylethyl ether and methanol, and >0.998 for n-heptane. A static {(vapour + liquid)equilibrium} (VLE) apparatus consisting of an isothermal total pressure cell has been employed for measuring the (vapour + liquid) equilibrium of the binary and ternary mixtures. The technique, developed by Van Ness and coworkers,(9, 10) has been successfully implemented by one of the present authors,(11) and is described elsewhere.(1) A diagram of the apparatus is shown in figure 1. Positive displacement pumps of 100 ml capacity (Ruska, mod. 2200-801) equipped with piston injectors were used to inject known volumes of degassed components into a cell immersed in a high-precision water bath (Hart Scientific model 6020) assuring a temperature stability of ±0.5 mK, and thermostatted at T = 313.15 K. The pump resolution is 0.01 ml, and the resulting uncertainty in the volume injected is ±0.03 ml. The cell is a cylindrical stainless steel vessel with a capacity of about 180 ml, and is provided with an externally-operated magnetic stirrer. Initially, about 50 ml of one component are injected into the evacuated cell and the vapour pressure is recorded. The second and third components are then injected in appropriate proportions so as to achieve a desired composition. The total mass injected is determined from the volume differences corresponding to the initial and final positions of the pistons, the temperature of the injectors, and the densities of the injected components. The uncertainty in the mole fraction is estimated to be less than ±5 · 10−4 . The total vapour pressure for the ternary mixture is obtained by adding a third component to a binary mixture at a fixed temperature. Six runs (dilution lines) were carried out starting with a binary mixture with the mole fraction of one component close to x = (0.3, or 0.7), and adding the third component up to a mole fraction of x = 0.5. The temperature was measured by a calibrated standard PRT-100 (SDL model 5385/100) connected to an a.c. resistance bridge (ASL model F250) with a temperature resolution of 1 mK. The estimated uncertainty of the temperature measurement is ±10 mK. The pressure was measured using a differential pressure cell provided with an indicator (Ruska

1233

23.0 ºC

5 012505

10

6

10 Pa

8

Vacuum

9

7

30

45.0 ºC

15

20

20

7

3

1

40.00 ºC

5

6 Pa

10

Vacuum

2

4

2

4

2

4

VLE of {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH}

FIGURE 1. Schematic diagram of the static VLE apparatus: 1, equilibrium cell; 2, piston injectors; 3, thermostatted bath; 4, flasks; 5, temperature indicators; 6, pressure gauge; 7, differential pressure cell; 8, variable volume pressure controller; 9, temperature controller; 10, vacuum gauge.

1234

J. J. Segovia et al.

models 2413-705 and 2416-711, respectively). When atmospheric air balances the vapour pressure of the cell, a Bourdon-fused quartz precision pressure gauge (Texas Instruments model 801) provided with a capsule indicates the pressure with an estimated uncertainty of ±5 Pa for the 125 kPa pressure range.

3. Results and correlations The use of the measuring technique described above allows a static equilibrium between the phases, assuring a true thermodynamic equilibrium. Direct sampling, particularly of the vapour phase, upsets the equilibrium, the mass of the vapour in the cell being very small; yet an appreciable mass must be withdrawn to yield an amount of condensate suitable for accurate analysis. However, as a consequence of Duhem’s theorem, sampling of the phases is, in fact, not necessary. Given a set of equilibrium (x, p) data at constant T , thermodynamics allows the calculation of the y values. Thus, the vapour phase need not be sampled, and the resulting data are thermodynamically consistent per se.(12–14) The data reduction of the binary and ternary mixtures has been performed using Barker’s method(15) according to well-established procedures.(16, 17) A developed computer program described elsewhere(1) has been used to implement the technique. The non-ideality of the vapour phase is taken into account by the virial equation of state, truncated at the second term. The second virial coefficients have been calculated by the Hayden O’Connell method(18) using the coefficients given by Dymond et al.(19) The following mixtures: {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 ) CH3 OH}, {x1 CH3 OC(CH3 )2 CH3 + (1 − x1 )CH3 OH}, and {x1 CH3 OH + (1 − x1 )CH3 (CH2 )5 CH3 } have been measured at T = 313.15 K. The data of the ternary mixture are adequately correlated by the three-parameter Wohl expansion,(20) equation (1): g123 = G Em /RT = g12 + g13 + g23 + (C0 + C1 x1 + C2 x2 )x1 x2 x3 ,

(1)

G Em

where is the excess molar Gibbs energy, R is the universal gas constant, and T is temperature, which also includes the parameters of the corresponding binaries gi j , according to equation (2). The adjustable parameters C0 , C1 , and C2 are found by regression of the ternary data. Correlations for the gi j are given by a six-parameter Margules equation(21) of the following form: gi j = G Em /RT = {A ji xi + Ai j x j − (λ ji xi + λi j x j )xi x j + (η ji xi + ηi j x j )xi2 x 2j }xi x j . (2) The binary and ternary systems have also been correlated using the Wilson,(22) NRTL,(23) and UNIQUAC(24) models, whose respective excess Gibbs energy expressions are given by the following equations: ! X X E G m /RT = − xi ln x j Ai j , (3) i

G Em /RT

=

X i

xi

j

X j

A ji G ji x j

,

X k

!

G ki xk ,

(4)

VLE of {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH}

1235

TABLE 1. Average values used for the reduction of the data for the experimental vapour pressures pis , the molar volumes ViL , and the second virial coefficients Bii and Bi j for the pure compounds investigated in this work, and corresponding literature values at T = 313.15 K CH3 OC(CH3 )2 CH3 (1)

CH3 OH (2)

CH3 (CH2 )5 CH3 (3)

pis /(kPa)

59.907

35.475

12.331

pis /(kPa)

59.830a

35.434e

12.300a

59.942b

34.982 f

12.343c

59.909c

35.445g

12.338d

59.924d

12.334h 12.335i

ViL /(cm3 · mol−1 ) Bii /(cm3 · mol−1 ) Bi j (13)/(cm3 · mol−1 ) Bi j (12)/(cm3 · mol−1 ) Bi j (23)/(cm3 · mol−1 )

122 j

41e

150i

−1426k

−1963k

−2520k

−1857k −830k

−1857k −830k −633k

−633k

a Calculated from the Antoine equation using constants reported by Reid et al.(31) b Calculated from the Antoine equation using constants reported by Ambrose et al.(32) c Reported by Lozano et al.(1) d Reported by Lozano et al.(2) e Calculated from the An-

toine equation using constants reported in TRC.(33) f Reported by Mullins et al.(25) g Reported by Toghiani et al.(26) h Reported by G´oral.(34) i Reported in TRC.(35) j Reported by Jangkamolkulchal et al.(36) k Calculated by Hayden et al.(18) from Dymond et al.(19)

G Em /RT

=

X i

xi ln(ϕi /xi ) + z/2

X i

qi xi ln(ϑi /qi ) −

X i

qi xi ln

X

!

ϑ j A ji , (5)

j

P P where G ji = exp(−α ji A ji ), ϑi = qi xi / j q j x j , ϕi = ri xi / j r j x j , and z = 10. The values of the experimental vapour pressures pis , the molar liquid volumes ViL , and the second virial coefficients (Bii , Bi j ) of the pure compounds used in the calculations are indicated in table 1. Corresponding literature values of the vapour pressures are also reported in the table for comparison purposes. Tables 2 to 4 give the experimental values of the total pressure p, and the corresponding compositions of the liquid xi and vapour phases yi as reduced by the Margules equation for the binary mixtures, and the Wohl expansion for the ternary ones. The data correlation results for the binary systems reported here are summarized in table 5, including, for convenience, those of {x1 CH3 OC(CH3 )2 CH3 + (1 − x1 )CH3 (CH2 )5 CH3 }, which have been reported previously.(5) The table also contains the values of the adjustable parameters of the various models which yield the best results by using Barker’s method, the root mean square (r.m.s.d.) of the difference between the experimental and the calculated pressure, and the maximum value of this difference (max |1p|). For the ternary system, the results of the correlation are given in table 6. In table 7, we have compared

1236

J. J. Segovia et al. TABLE 2. Total pressure p for {x1 CH3 OC(CH3 )2 CH3 + (1 − x1 )CH3 OH} at T = 313.15 K, and at various compositions of the liquid x1 and vapour phases y1 x1

y1

p/kPa

x1

y1

p/kPa

0.0000

0.0000

35.476

0.4999

0.6319

64.476

0.0551

0.2155

43.099

0.5487

0.6516

65.148

0.0991

0.3177

47.747

0.5496

0.6520

65.160

0.1474

0.3949

51.755

0.5997

0.6722

65.695

0.1940

0.4492

54.783

0.6491

0.6927

66.065

0.2458

0.4954

57.431

0.6986

0.7148

66.270

0.2971

0.5317

59.529

0.7489

0.7398

66.289

0.3477

0.5615

61.169

0.7770

0.7555

66.196

0.3985

0.5873

62.516

0.8534

0.8080

65.433

0.4046

0.5902

62.661

0.9004

0.8513

64.435

0.4491

0.6104

63.590

0.9525

0.9159

62.562

0.4493

0.6105

63.599

1.0000

1.0000

59.891

0.4993

0.6316

64.456

TABLE 3. Total pressure p for {x1 CH3 OH+ (1 − x1 )CH3 (CH2 )5 CH3 } at T = 313.15 K, and at various compositions of the liquid x1 and vapour phases y1 x1

y1

p/kPa

x1

y1

p/kPa

0.0000

0.0000

12.336

0.8756

0.7465

45.563

0.0627

0.7123

41.695

0.9007

0.7496

45.352

0.0877

0.7249

43.191

0.9205

0.7566

45.009

0.0998

0.7280

43.594

0.9405

0.7716

44.361

0.1187

0.7313

44.167

0.9509

0.7850

43.785

0.1475

0.7346

44.745

0.9606

0.8026

43.029

0.1769

0.7376

45.085

0.9710

0.8296

41.912

0.2044

0.7401

45.367

0.9816

0.8703

40.289

0.2370

0.7426

45.520

0.9906

0.9211

38.368

0.9966

0.9677

36.574

1.0000

1.0000

35.448

miscibility gap

VLE of {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH}

1237

TABLE 4. Total pressure p for {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH} at T = 313.15 K, and at various compositions of the liquid x1 and vapour phases y1 x1

x2

y1

y2

p/kPa

x1

x2

y1

y2

p/kPa

0.0000

0.0000

0.0000

0.0000

35.475

0.7060

0.0000

0.7183

0.0000

66.259

0.0271 0.0512

0.2837 0.2766

0.0465 0.0859

0.2374 0.2220

46.454 47.362

0.6875 0.6705

0.0263 0.0504

0.7007 0.6849

0.0102 0.0192

65.149 64.177

0.1012 0.1501

0.2621 0.2479

0.1610 0.2267

0.1938 0.1700

49.181 50.864

0.6241 0.5992

0.1163 0.1516

0.6426 0.6206

0.0423 0.0538

61.717 60.505

0.1999 0.2502

0.2334 0.2187

0.2865 0.3410

0.1489 0.1301

52.464 53.970

0.5629 0.5284

0.2033 0.2521

0.5892 0.5600

0.0698 0.0842

58.846 57.371

0.3044 0.3482

0.2029 0.1901

0.3942 0.4337

0.1121 0.0991

55.470 56.595

0.4936 0.4615

0.3014 0.3469

0.5310 0.5044

0.0982 0.1109

55.952 54.687

0.3998 0.4499

0.1751 0.1605

0.4772 0.5169

0.0853 0.0733

57.829 58.932

0.4239 0.3881

0.4002 0.4509

0.4732 0.4433

0.1256 0.1396

53.232 51.860

0.4997 0.0000

0.1459 1.0000

0.5544 0.0000

0.0625 1.0000

59.930 12.331

0.3526 1.0000

0.5011 0.0000

0.4133 1.0000

0.1537 0.0000

50.496 59.907

0.3023

0.6977

0.6908

0.3092

28.886

0.7008

0.2993

0.9089

0.0911

46.947

0.2728 0.2569

0.6296 0.5929

0.3525 0.3130

0.1920 0.1834

46.370 48.621

0.6849 0.6665

0.2925 0.2846

0.8328 0.7672

0.0865 0.0830

49.666 52.082

0.2416 0.2211

0.5574 0.5101

0.2894 0.2667

0.1802 0.1793

49.616 50.177

0.6304 0.5957

0.2692 0.2544

0.6811 0.6272

0.0793 0.0780

55.165 56.814

0.2118 0.1967

0.4887 0.4539

0.2580 0.2450

0.1795 0.1804

50.280 50.336

0.5606 0.5258

0.2394 0.2245

0.5883 0.5582

0.0780 0.0787

57.710 58.143

0.1817 0.1668

0.4192 0.3848

0.2328 0.2211

0.1816 0.1830

50.305 50.223

0.4916 0.4563

0.2099 0.1949

0.5338 0.5115

0.0798 0.0812

58.292 58.257

0.1512 0.0000

0.3489 0.0000

0.2089 0.0000

0.1844 0.0000

50.098 35.475

0.4221 0.3859

0.1802 0.1648

0.4914 0.4709

0.0829 0.0849

58.088 57.791

0.2960 0.2887

0.0000 0.0250

0.5310 0.4927

0.0000 0.0296

59.499 58.618

0.3508 0.0000

0.1498 1.0000

0.4509 0.0000

0.0871 1.0000

57.394 12.331

0.2818 0.2669

0.0489 0.0998

0.4616 0.4086

0.0522 0.0873

57.812 56.267

0.0269 0.0552

0.6903 0.6702

0.0340 0.0699

0.2471 0.2381

46.212 46.602

0.2520 0.2376

0.1506 0.1995

0.3675 0.3350

0.1116 0.1294

54.964 53.889

0.1005 0.1510

0.6381 0.6023

0.1264 0.1870

0.2232 0.2064

47.350 48.279

0.2227 0.2078

0.2500 0.3005

0.3057 0.2792

0.1447 0.1580

52.898 51.990

0.2011 0.2500

0.5666 0.5319

0.2443 0.2976

0.1902 0.1751

49.227 50.132

0.1933 0.1780

0.3494 0.4012

0.2552 0.2311

0.1697 0.1810

51.170 50.363

0.2999 0.3485

0.4965 0.4620

0.3500 0.3997

0.1605 0.1470

51.009 51.812

0.1633 0.1484

0.4504 0.5006

0.2093 0.1881

0.1906 0.1995

49.663 49.017

0.4004 0.4509

0.4252 0.3893

0.4517 0.5018

0.1332 0.1203

52.610 53.334

1.0000

0.0000

1.0000

0.0000

59.907

0.4999

0.3545

0.5499

0.1082

53.995

1238

J. J. Segovia et al.

Methanol (3)

60

55 50

65

45 40 MTBE (1)

30

20 Heptane (2)

FIGURE 2. Lines of constant total pressure p for {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH} at T = 313.15 K.

the results of {x1 CH3 OC(CH3 )2 CH3 + (1 − x1 )CH3 OH} with those found in the literature(25, 26) which have been reduced using a three-parameter Margules equation. E for the ternary We have also calculated the values of the excess molar entropy Sm E system using literature data for the excess molar enthalpy Hm at the same temperature of 313.15 K.(27) The resulting values are given in table 8. The miscibility gap of {x1 CH3 OH + (1 − x1 )CH3 (CH2 )5 CH3 } was predicted from (vapour + liquid) equilibria. All the miscibility limit values obtained from the different models are expressed in terms of the mole fraction of methanol in the liquid phase. They are presented in table 9, and compared with the few experimental results found in the literature.(28–30) The results for the ternary system are shown in figures 2 to 5. Constant pressure lines are shown in figure 2, constant excess molar Gibbs energy lines G Em in figure 3, and pressure and excess molar Gibbs energy surfaces in figures 4 and 5, respectively.

4. Discussion The experimental data for {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 ) CH3 OH} have been correlated using the Wohl equation which is, in fact, an extension of the Margules equation to multicomponent systems, the Wilson, NRTL, and UNIQUAC models. The minimum value of the root mean square deviation (r.m.s.d.) of 1p, obtained with the Wilson equation, is 50 Pa, and the maximum difference between the calculated and experimental pressure (max |1p|) is 145 Pa. For the Wohl equation, the r.m.s.d. of 1p is 66 Pa, and max |1p| is 175 Pa. This ternary system shows a small miscibility gap near

VLE of {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH}

1239

TABLE 5. Determined parameters of the models used for the binary subsystems of {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH} at T = 313.15 K, together with the coordinates of the azeotrope (x1 azeotrope , and pazeotrope ). The 1p term is defined as the difference between the experimental and calculated pressure, and p ∗ is the total pressure in the miscibility gap {CH3 OC(CH3 )2 CH3 (1) + CH3 (CH2 )5 CH3 (2)} Three-parameter Margules

Wilson

A12 A21

0.23992 0.25871

0.98106 0.79215

λ12 = λ21 α12

0.04026

r.m.s.d.(1p)/kPa max |1p|/kPa

NRTL 0.29870 −0.04652

UNIQUAC 1.05933 0.88423

0.3 0.022 0.045

0.029 0.054

0.030 0.055

0.030 0.055

Three-parameter Margules

Wilson

NRTL

NRTL

UNIQUAC

A13

1.20342

0.53559

0.85085

0.8186

0.24295

A31 λ13 = λ31

1.30170 0.23729

0.43375

0.68683

0.6222

1.29835

α13 r.m.s.d.(1p)/kPa

0.019

0.043

0.5862 0.023

0.47 0.071

0.180

max |1p|/kPa x1 azeotrope

0.047 0.7304

0.074 0.7295

0.070 0.7309

0.130 0.7278

0.365 0.7224

pazeotrope

66.283

66.261

66.286

66.237

66.147

Five-parameter Margules

Six-parameter Margules

NRTL

NRTL

NRTL

UNIQUAC

A32 A23

3.56423 3.45311

3.62906 3.41015

2.33306 2.17340

2.52569 2.42938

2.60057 2.55347

1.00795 0.095361

λ32 λ23

6.15996 5.33419

6.98176 4.40200

η32 η23

8.58683 8.58683

11.87196 3.26489

α23 r.m.s.d. (1p)/kPa

0.118

0.094

0.4 1.230

0.426 0.528

0.4356 0.554

2.286

max |1p|/kPa x3 azeotrope

0.197 0.7324

0.128 0.7460

3.167 0.7316

1.536 0.7427

0.860 0.7468

5.158 0.7136

pazeotrope p∗

45.775 45.621

45.434 45.621

45.833 45.621

45.639 45.621

45.349 45.621

45.554 45.621

{CH3 OC(CH3 )2 CH3 (1) + CH3 OH (3)}

{CH3 (CH2 )5 CH3 (2) + CH3 OH (3)}

1240

J. J. Segovia et al. TABLE 6. Determined parameters of the models used for {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH} at T = 313.15 K. The 1p term is defined as the difference betweeen the experimental and calculated pressure Wohl

Wilson

NRTL

UNIQUAC

A12

0.95594

0.45356

0.91499

A21

0.81554 −0.18402

1.01804

A13

0.54119

0.86017

0.23663

A31

0.42609

0.67373

1.31642

A23

0.05350

2.52627

0.10556

A32

0.04913

2.71976

1.04691

C0

2.26929

C1

2.08933

C2

1.32963

α12

0.3

α13

0.5862

α23

0.4356

r.m.s.d. (1p)/kPa

0.066

0.050

0.122

0.363

max |1p|/kPa

0.175

0.145

0.635

1.580

TABLE 7. Determined parameters for the Margules equation for {x1 CH3 OC(CH3 )2 CH3 + (1 − x1 )CH3 OH} at T = 313.15 K, together with the coordinates of the azeotrope (x1 azeotrope , and pazeotrope ), and comparison with literature data

p1s /kPa

This work

Mullins et al. (1989)(25)

Toghiani et al. (1996)(26)

59.907

60.224

60.530

p3s /kPa

35.475

34.982

34.450

A13

1.20342

1.16824

1.19362

A31

1.30170

1.16042

1.25297

λ13 = λ31 r.m.s.d.(1p)/kPa

0.23729

0.04211

0.24337

0.019

0.571

0.077

max |1p|/kPa

0.047

1.233

0.179

x1 azeotrope

0.7304

0.7283

0.7358

pazeotrope

66.283

65.287

66.310

VLE of {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH}

1241

TABLE 8. Excess thermodynamic functions for {x1 CH3 OC(CH3 )2 CH3 +x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH} at T = 313.15 K, and at various mole fractions xi . The excess molar Gibbs energy G E m is calculated by using the Wohl equation given in table 6, the excess molar E is taken from the literature,(27) and the excess molar entropy S E is calculated enthalpy Hm m E E from the thermodynamic relation G E m = Hm − T Sm x1

x2

−1 GE m /(J · mol )

E /(J · mol−1 ) Hm

E /(J · mol−1 ) T Sm

E /(J · mol−1 · K−1 ) Sm

0.6660

0.3340

141.01

332.00

190.99

0.61

0.6170 0.5718

0.3080 0.2855

449.46 670.81

585.40 699.90

135.94 29.09

0.43 0.09

0.5309 0.4935

0.2649 0.2464

829.48 942.11

746.50 764.30

−82.98 −177.81

−0.26 −0.57

0.4594 0.4280

0.2293 0.2137

1020.52 1073.24

759.90 744.70

−260.62 −328.54

−0.83 −1.05

0.3992 0.3724

0.1992 0.1859

1106.00 1123.68

725.10 702.20

−380.90 −421.48

−1.22 −1.35

0.3398 0.3032

0.1696 0.1513

1128.87 1113.76

667.50 619.40

−461.37 −494.36

−1.47 −1.58

0.2356 0.2356

0.1517 0.1175

1118.46 1027.30

552.30 512.30

−566.16 −515.00

−1.81 −1.64

0.1951 0.1602

0.0973 0.0800

937.67 836.19

439.20 372.60

−498.47 −463.59

−1.59 −1.48

0.1371 0.0970

0.0683 0.0484

754.33 585.95

323.00 237.10

−431.33 −348.85

−1.38 −1.11

0.0636 0.0352

0.0317 0.0176

414.76 245.57

160.60 91.50

−254.16 −154.07

−0.81 −0.49

0.0109 0.3000

0.0055 0.7000

80.89 129.64

25.10 296.00

−55.79 166.36

−0.18 0.53

0.2761 0.2687

0.6434 0.6260

587.36 700.98

671.70 736.50

84.34 35.52

0.27 0.11

0.2546

0.5931

887.58

810.60

−76.98

−0.25

0.2352 0.2177

0.5480 0.5073

1091.04 1229.88

850.50 860.70

−240.54 −369.18

−0.77 −1.18

0.2019 0.1874

0.4703 0.4367

1323.34 1383.91

869.60 855.10

−453.74 −528.81

−1.45 −1.69

0.1785 0.1620

0.4158 0.3776

1410.15 1437.16

838.80 811.10

−571.35 −626.06

−1.82 −2.00

0.1473 0.1219

0.3432 0.2841

1438.38 1390.79

789.20 712.50

−649.18 −678.29

−2.07 −2.17

0.1009 0.0917

0.2351 0.2136

1302.38 1248.65

642.50 613.60

−659.88 −635.05

−2.11 −2.03

0.0832 0.0680

0.1938 0.1586

1190.47 1064.55

580.60 467.60

−609.87 −596.95

−1.95 −1.91

0.0435 0.0289

0.1015 0.0674

789.06 573.40

390.60 392.30

−398.46 −181.10

−1.27 −0.58

1242

J. J. Segovia et al. TABLE 8—continued x1

x2

−1 GE m /(J · mol )

E /(J · mol·−1 ) Hm

E /(J · mol−1 ) T Sm

E /(J · mol−1 · K−1 ) Sm

0.0130

0.0301

283.46

150.90

−132.56

−0.42

0.0022

0.0053

53.17

38.90

−14.27

−0.05

0.6660

0.0000

704.33

378.00

−326.33

−1.04

0.6451

0.0323

747.03

436.70

−310.33

−0.99

0.6228

0.0658

787.31

538.40

−248.91

−0.79

0.5996

0.1005

824.15

568.30

−255.85

−0.82

0.5631

0.1553

871.70

649.00

−222.70

−0.71

0.5243

0.2135

908.38

724.50

−183.88

−0.59

0.4687

0.2969

936.74

788.60

−148.14

−0.47

0.4391

0.3413

940.59

815.30

−125.29

−0.40

0.4081

0.3878

936.48

835.40

−101.08

−0.32

0.3590

0.4615

913.12

836.00

−77.12

−0.25

0.3243

0.5135

884.58

829.50

−55.08

−0.18

0.2879

0.5681

843.48

812.60

−30.88

−0.10

0.2690

0.5964

817.78

797.20

−20.58

−0.07

0.2299

0.6552

753.35

756.80

3.45

0.01

0.1887

0.7170

670.10

692.70

22.60

0.07

0.1672

0.7491

620.35

651.20

30.85

0.10

0.1227

0.8160

497.67

552.70

55.03

0.18

0.0995

0.8508

423.69

497.20

73.51

0.23

0.0511

0.9233

242.62

345.40

102.78

0.33

0.0259

0.9611

130.58

228.00

97.42

0.31

0.3000

0.0000

646.88

180.00

−466.88

−1.49

0.2937

0.0225

735.65

238.30

−497.35

−1.59

0.2865

0.0463

821.55

325.60

−495.95

−1.58

0.2708

0.0985

985.09

467.20

−517.89

−1.65

0.2397

0.2020

1220.19

663.10

−557.09

−1.78

0.2090

0.3042

1356.53

768.10

−588.43

−1.88

0.2003

0.3332

1380.33

794.40

−585.93

−1.87

0.1814

0.3961

1411.09

824.10

−586.99

−1.87

0.1712

0.4303

1415.96

827.50

−588.46

−1.88

0.1487

0.5050

1398.37

812.40

−585.97

−1.87

0.1233

0.5896

1329.80

773.20

−556.60

−1.78

0.0943

0.6862

1184.71

707.10

−477.61

−1.53

0.0740

0.7538

1036.60

617.50

−419.10

−1.34

0.0609

0.7974

917.84

584.70

−333.14

−1.06

0.0422

0.8596

710.73

517.10

−193.63

−0.62

0.0220

0.9296

403.30

404.60

1.30

0.00

0.0134

0.9554

273.87

350.60

76.73

0.25

VLE of {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH}

1243

Methanol (3)

1600 1400 1000

1200

600 800 400 200 MTBE (1)

Heptane (2)

FIGURE 3. Lines of constant excess molar Gibbs energy GE m {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH} at T = 313.15 K. p / kPa

for

70 60 50 40 30 20 10 MTBE (1) Methanol (3)

Heptane (2) FIGURE 4. Pressure surface p for {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 ) CH3 OH} at T = 313.15 K.

1244

J. J. Segovia et al. TABLE 9. Miscibility limits x1 , and x1∗ calculated with the models used in this work, and comparison with data found in the literature for {x1 CH3 OH + (1 − x1 )CH3 (CH2 )5 CH3 } at T = 313.15 K x1

x1∗

Margules (5-parameter)

0.2263

0.8714

Margules (6-parameter)

0.2088

0.6604

NRTL (α12 = 0.4)

0.1208

0.9060

NRTL (α12 = 0.426)

0.1397

0.8920

NRTL (α12 = 0.4356)

Miscible

Miscibility

UNIQUAC

0.1153

0.8934

Tusel-Langer et al.(28)

0.2248

0.8567

Tagliavini et al.(29)

0.2536

Kiser et al.(30)

0.8486 0.8462

E /(J·mol–1) Gm

2000 1800 1600 1400 1200 1000 800 600 400

Heptane (2)

200 Methanol (3)

MTBE (1) FIGURE 5. Excess molar Gibbs energy G E m surface for {x1 CH3 OC(CH3 )2 CH3 x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH} at T = 313.15 K.

+

VLE of {x1 CH3 OC(CH3 )2 CH3 + x2 CH3 (CH2 )5 CH3 + (1 − x1 − x2 )CH3 OH}

1245

{x1 CH3 OH + (1 − x1 )CH3 (CH2 )5 CH3 } as has been determined by other authors.(28–30) We have not been able to make measurements in this region of the (vapour + liquid + liquid) equilibrium because the technique is not adequate for very low mole fractions. The pressure surface, figure 4, shows a maximum at 66.238 kPa which corresponds to the azeotrope {x1 CH3 OC(CH3 )2 CH3 + (1 − x1 )CH3 OH}, and a minimum at 12.331 kPa corresponding to the pressure of pure n-heptane. The excess molar Gibbs energy G Em of the ternary system (figures 3, and 5) shows a positive deviation from ideality, which increases always in the direction of the less ideal {x1 CH3 OH + (1 − x1 )CH3 (CH2 )5 CH3 }, and reaches a maximum value of 1672 J · mol−1 . The three-parameter Margules equation leads to the best results with a root mean square deviation of the pressure of 19 Pa for {x1 CH3 OC(CH3 )2 CH3 + (1 − x1 )CH3 OH}, and a maximum deviation of 47 Pa. The six-parameter Margules equation results in the best fit for {x1 CH3 OH + (1 − x1 )CH3 (CH2 )5 CH3 }, with an r.m.s.d. (1p) of 94 Pa, and a max |1p| of 128 Pa. The higher values found can be attributed to a large miscibility gap present in this system. Both binary systems exhibit a pronounced positive deviation from ideality. Both binary systems exhibit azeotropy. The compositions of the azeotropes as determined by the three- and six-parameter Margules equation are: x1 azeotrope = 0.7304, and pazeotrope = 66.283 kPa for {x1 CH3 OC(CH3 )2 CH3 + (1 − x1 )CH3 OH}, values close to the ones reported by Toghiani et al.,(26) namely: x1 azeotrope = 0.7358 and pazeotrope = 66.310 kPa, and x1 azeotrope = 0.74604, and pazeotrope = 45.434 kPa for {x1 CH3 OH + (1 − x1 )CH3 (CH2 )5 CH3 }. As for the prediction of the miscibility gap for {x1 CH3 OH + (1 − x1 )CH3 (CH2 )5 CH3 }, the values obtained with the five-parameter Margules equation are x1 = 0.2263, and x1∗ = 0.8714, and are close to the literature values: x1 = 0.2248, and x1∗ = 0.8567 (reported by Tusel-Langer et al.(28) ), x1 = 0.2536, and x1∗ = 0.8486 (Tagliavini et al.(29) ), and x1∗ = 0.8462 (Kiser et al.(30) ). Support for this work came from the DGICYT, Direcci´on General de Investigaci´on Cient´ıfica y T´ecnica of the Spanish Ministry of Education, Project PB95-0704, and from Junta de Castilla y Le´on (Consejer´ıa de Educaci´on y Cultura) project VA 42/96. REFERENCES 1. Lozano, L. M.; Montero, E. A.; Mart´ın, M. C.; Villama˜na´ n, M. A. Fluid Phase Equilib. 1995, 110, 219–230. 2. Lozano, L. M.; Montero, E. A.; Mart´ın, M. C.; Villama˜na´ n, M. A. Fluid Phase Equilib. 1997, 133, 155–162. 3. Segovia, J. J.; Mart´ın, M. C.; Chamorro, C. R.; Villama˜na´ n, M. A. Fluid Phase Equilib. 1997, 133, 163–172. 4. Segovia, J. J. Ph. D. Thesis, Department of Energy, University of Valladolid, Spain. 1997. 5. Segovia, J. J.; Mart´ın, M. C.; Chamorro, C. R.; Montero, E. A.; Villama˜na´ n, M. A. Fluid Phase Equilib. 1998, 152, 265–276. 6. Segovia, J. J.; Mart´ın, M. C.; Chamorro, C. R.; Villama˜na´ n, M. A. J. Chem. Eng. Data 1998, 43, 1014–1020. 7. Segovia, J. J.; Mart´ın, M. C.; Chamorro, C. R.; Villama˜na´ n, M. A. J. Chem. Eng. Data 1998, 43, 1021–1026. 8. Van Ness, H. C.; Abbott, M. M. Ind. Eng. Chem. Fundam. 1978, 17, 66–67.

1246

J. J. Segovia et al.

9. Gibbs, R. E.; Van Ness, H. C. Ind. Eng. Chem. Fundam. 1972, 11, 410–413. 10. DiElsi, D. P.; Patel, R. B.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1978, 23, 242– 245. 11. Villama˜na´ n, M. A.; Allawi, A. J.; Van Ness, H. C. J. Chem. Eng. Data 1984, 29, 293–296. 12. Van Ness, H. C.; Abbott, M. M. Classical Thermodynamics of Nonelectrolyte Solutions:with applications to phase equilibria. McGraw-Hill: New York. 1982. 13. Van Ness, H. C. J. Chem. Thermodynamics 1995, 27, 113–134. 14. Van Ness, H. C. Pure Appl. Chem. 1995, 67, 859–872. 15. Barker, J. A. Aust. J. Chem. 1953, 6, 207–210. 16. Abbott, M. M.; Van Ness, H. C. AIChE J. 1975, 21, 62–71. 17. Abbott, M. M.; Floess, J. K.; Walsh, G. E.; Van Ness, H. C. AIChE J. 1975, 21, 72–76. 18. Hayden, J. G.; O’Connell, J. P. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 209–216. 19. Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures—a critical compilation. Clarendon Press: Oxford. 1980. 20. Wohl, K. Chem. Eng. Prog. 1953, 49, 218. 21. Margules, M. Akad. Wiss. Wien, Math. Naturw. 1895, Kl. II, 104, 1243. 22. Wilson, G. M. J. Am. Chem. Soc. 1964, 86, 127–130. 23. Renon, H.; Prausnitz, J. M. AIChE J. 1968, 14, 135–144. 24. Abrams, D. S.; Prausnitz, J. M. AIChE J. 1975, 21, 116–128. 25. Mullins, S. R.; Oehert, L. A.; Wileman, K. P.; Manley, D. B. AIChE Symp. Ser. 1989, No. 271, 85, 94–99. 26. Toghiani, R. K.; Toghiani, H.; Venkateswarlu, G. Fluid Phase Equilib. 1996, 122, 157–168. 27. Tusel-Langer, E.; Lichtenthaler, R. N. Ber. Bunsenges. Phys. Chem. 1991, 2, 145–152. 28. Tusel-Langer, E.; Garc´ıa-Alonso, J. M.; Villama˜na´ n, M. A.; Lichtenthaler, R. N. J. Solution Chem. 1991, 20, 153–163. 29. Tagliavini, G.; Arich, G. Rci. Sci. 1958, 28, 1902. 30. Kiser, R. W.; Johnson, G. D.; Sheltar, M. D. J. Chem. Eng. Data 1961, 6, 338. 31. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids. Mc-Graw Hill: New York. 1987. 32. Ambrose, D.; Ellender, J. H.; Sprake, C. H. S.; Townsend, R. J. Chem. Thermodynamics 1976, 8, 165–178. 33. TRC Thermodynamic Tables—Non Hydrocarbons. Thermodynamics Research Center, The Texas A & M University System: College Station, TX. Vapour Pressures: Methanol: Table 232-1-(1.1000)-k. 1976;densities: Methanol: Table 23-2-1-(1.1000)-d. 1966. 34. G´oral, M. Fluid Phase Equilib. 1994, 102, 275–286. 35. TRC Thermodynamic Tables—Hydrocarbons. Thermodynamics Research Center, The Texas A & M University System: College Station, TX. Vapour Pressures: n-Heptane: Table 23-2(1.202)-k.1975; densities: n-Heptane: Table 23-2-(1.101)-d. 1973 36. Jangkamolkulchal, A.; Allerd, G. C.; Parrish, W. R. J. Chem. Eng. Data 1991, 36, 481–484. (Received 11 August 1998; in final form 14 April 1999)

WA 98/042