Vapour-liquid equilibrium in the quaternary system methanol-2-propanol-acetonitrile-benzene at 55 ° C

17

Fluid Phase Equilibria, 71 (1992) 17-27

Elsevier Science Publishers B.V., Amsterdam

Vapour-liquid equilibrium in the quaternary system methanol-2-propanol-acetonitrile-benzene at 55 o C Isamu Nagata ‘, Yasuo Fukushima

and Katsu Miyazaki

Department of Chemktry and Chemical Engineering, Division of Physical Sciences, Kanazawa University, Kodatsuno 2-40-20, Kanazawa 920 (Japan)

(Received July 8, 1991; accepted in final form August 23, 1991)

ABSTRACT Nagata, I., Fukushima, Y. and Miyazaki, K., 1992. Vapour-liquid equilibrium in the quaternary system methanol-2-propanol-acetonitrile-benzene at 55 o C. Fluid Phase Equilibria,71:

17-27.

The isothermal vapour-liquid equilibrium for the quaternary methanol-2-propanolacetonitrile-benzene system have been determined using a modified Boublik vapour-recirculating still at 55 o C. The experimental results are in good agreement with those calculated by the UNIQUAC associated-solution model based on binary information alone.

INTRODUCTION

As part of a series of experimental studies on quaternary mixtures containing two alcohols, acetonitrile and benzene, the present work gives results for the methanol-Zpropanol-acetonitrile-benzene system at 55 o C and experimental data are compared with those estimated from the UNIQUAC associated-solution model with only binary parameters (Nagata, 1985a, 1990a; Nagata and Ohtsubo, 1986). The binary energy parameters of the model are derived from binary vapour-liquid equilibrium (VLE) data for six systems: methanol-2-propanol at 55 o C (Gmehling and Onken, 1977); methanol-acetonitrile at 55’ C (Ohta and Nagata, 1983); methanol-benzene at 55 “C (Gmehling and Onken, 1977); 2-propanolacetonitrile at 50’ C (Nagata and Katoh, 1980); 2-propanol-benzene at 50 ’ C (Gmehling et al., 1978); acetonitrile-benzene at 45 o C (Gmehling et al., 1980). ’ Author to whom correspondence 0378-3812/92/$05.00

should be addressed.

0 1992 Elsevier Science Publishers B.V. All rights reserved

18 EXPERIMENTAL

Acetonitrile (Wako Pure Chemical Industries Ltd., guaranteed reagent grade) was used directly, methanol (first grade) was shaken with calcium oxide and distilled in 1 m glass columns with McMahon packing, and 1-propanol (first grade) was fractionally distilled after storage over anhydrous potassium carbonate. Benzene (first grade) was purified by repeated recrystallization. Densities of the chemicals used were measured with an Anton Paar densimeter DMA 40 and agreed well with literature values (Riddick et al., 1986). VLE measurements were carried out using a modified Boublik dynamic still as described previously (Nagata, 1985b). Compositions of equilibrated liquid-phase and vapour-phase samples were analyzed by combined use of a Shimadzu gas chromatograph GC-7A and a Shimadzu Chromatopac E-1B. The errors of the measured variables are: 0.16 Torr for pressure; 0.05 o C for temperature; 0.002 for liquid-phase and vapour-phase mole fractions.

RESULTS AND DATA ANALYSIS

Table 1 shows the experimental VLE data of the methanol-2propanol-acetonitrile-benzene system together with the activity coefficients y and the fugacity coefficients 4 derived from eqns. (1) and (2). P&Y, ‘I = (x,P;&

exp[ u,“(P - P;)/RT])

In 4 = (KEYJBIJ

- zy $Y,YJB,,)&

(1)

(2)

J

where the measured variables denote: P, total pressure; P”, pure-component vapour pressure; X, liquid-phase mole fraction; y, vapour-phase mole fraction; and T, absolute temperature. The pure liquid molar volume uL is estimated from a modified Rackett equation (Spencer and Danner, 1972) and the second virial coefficients B are derived from the correlation of Hayden and O’Connell (1975). According to the assumptions of the UNIQUAC associated-solution model, there are many chemical complexes in a quarternary mixture containing methanol (A), 2-propanol (B), acetonitrile (C) and benzene (D). Their general formulae are A,, Bi, (AiBj),, (B,Aj)k, AI(B,Ak)l, Bi(A,Bk)!, A,C, AiD, BiC, BiD, (A,Bj),C, (AiBj),D, (B,Aj),C, (BiAj),D, Ai(BjA,),C, A,(B,A,),D, B,(AjB,),C and Bi(AjB,),D. The equilibrium

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

No.

0.096 0.172 0.231 0.051 0.096 0.165 0.051 0.144 0.387 0.128 0.495 0.246 0.135 0.176 0.164 0.255 0.085 0.114 0.366 0.255 0.245

~1

Vapor-liquid

TABLE 1

0.134 0.218 0.262 0.280 0.160 0.248 0.283 0.245 0.127 0.136 0.272 0.265 0.183 0.174 0.254 0.222 0.398 0.130 0.141 0.229 0.236

~2

0.182 0.155 0.120 0.434 0.602 0.226 0.542 0.227 0.116 0.634 0.066 0.253 0.179 0.190 0.226 0.217 0.135 0.387 0.142 0.208 0.207

~3

0.588 0.455 0.387 0.235 0.142 0.361 0.124 0.384 0.370 0.102 0.167 0.236 0.503 0.460 0.356 0.306 0.382 0.369 0.351 0.308 0.312

~4

0.229 0.273 0.320 0.081 0.179 0.256 0.088 0.229 0.468 0.238 0.513 0.316 0.257 0.300 0.254 0.342 0.134 0.229 0.448 0.340 0.332

Y, Y3

0.171 0.147 0.121 0.378 0.451 0.206 0.475 0.208 0.099 0.477 0.081 0.231 0.166 0.165 0.206 0.190 0.158 0.300 0.121 0.184 0.187

Y2

0.115 0.140 0.143 0.237 0.141 0.153 0.245 0.159 0.055 0.119 0.114 0.147 0.129 0.112 0.154 0.118 0.257 0.104 0.064 0.122 0.126

equilibrium data for methanol (l)-Zpropanol

0.485 0.440 0.416 0.304 0.229 0.385 0.192 0.404 0.378 0.166 0.292 0.306 0.448 0.423 0.386 0.350 0.451 0.367 0.367 0.354 0.355

Y4

511.6 526.1 530.6 449.6 456.9 511.4 422.6 512.3 603.2 455.8 544.1 517.9 520.3 539.0 511.4 539.3 464.7 505.4 592.0 536.3 534.0

(Torr)

p

(2)-acetonitrile

2.414 1.647 1.447 1.416 1.688 1.564 1.448 1.608 1.427 1.678 1.104 1.308 1.955 1.810 1.562 1.421 1.451 2.005 1.418 1.405 1.423

Yl

1.879 1.442 1.235 1.636 1.730 1.347 1.577 1.421 1.105 1.714 0.968 1.225 1.567 1.479 1.324 1.220 1.289 1.729 1.138 1.216 1.214

Y2

(3kbenzene

1.557 1.613 1.730 1.261 1.097 1.502 1.192 1.513 1.651 1.098 2.156 1.518 1.559 1.508 1.502 1.516 1.771 1.257 1.617 1.525 1.551

Y3

1.290 1.557 1.747 1.799 2.293 1.675 2.040 1.654 1.889 2.318 2.934 2.071 1.418 1.518 1.703 1.897 1.681 1.548 1.899 1.895 1.868

74

0.978 0.975 0.973 0.980 0.979 0.975 0.981 0.975 0.967 0.979 0.967 0.972 0.976 0.974 0.975 0.971 0.979 0.976 0.967 0.972 0.972

dJ1

(4) system at 55 ’ C

0.967 0.964 0.963 0.971 0.971 0.965 0.974 0.965 0.956 0.971 0.959 0.963 0.965 0.963 0.965 0.962 0.970 0.966 0.957 0.962 0.962

42

0.939 0.937 0.937 0.933 0.929 0.934 0.933 0.934 0.930 0.928 0.936 0.930 0.937 0.934 0.934 0.931 0.944 0.930 0.929 0.932 0.932

43

0.982 0.983 0.984 0.993 0.999 0.986 1.001 0.986 0.985 1.003 0.991 0.991 0.983 0.984 0.986 0.988 0.984 0.989 0.986 0.987 0.987

44

20

constants for chemical complex-forming reactions are independent of the degrees of homo-association and hetero-association. The activity coefficients of methanol (A) and acetonitrile (cl are given by

@ 1

vi

i %?4

1

+qA

z

-2 q,lng+l-g@A

+LL-!L-

In yA = In Al

-ln(FeATJA)

v

(Ii - i$ ;z, K

In yc = In

qc

@c

lng+l-7

i

C

@A A

A

1

(3)

@‘c C

(4) where 2 is the coordination number set as 10, and the segment fraction Cp, the surface fraction 19,the binary adjustable parameter 7rJ related to the energy parameter a,,, the pure alcohol monomer segment fractions Q,& and @iI, and the true molar volumes of pure alcohols V’J and Vi are given by

eI

=x,%/

7 IJ =

@l

cxJqJ J

exp

=

(6)

( -aIJ/T)

[2KA + 1 - (1 + 4K,J0”]/2K;

@‘oB1 = [2K, + 1 - (1 + 4K,)‘.‘]/2K; V,o=r*/(l

-K‘@&)

vi = TB/( 1 -

Ku@;,)

The activity coeffcients of 2-propanol (B) and benzene (D) are easily derived by changing the subscript A to B in eqn. (3) and C to D in eqn. (4). The monomer segment fractions in the mixture, @*r,
21

are obtained from simultaneous

@A= Cl+ YJ*c%

solution of eqns. (12)~(15).

+ c4K4D@Dx4 + (1

rAKABSAsB -

rAr, K&SASB)*

x (2+rBK4Bs‘4(2 - T4rBGBwB)+ rAK*BsB + %I[k4KAC+ rBKBC) + ‘*rBK4BKd4(2- r*rBK~BwB) +rArBK4BKBCsBl + @DI[k4KAD + rBKBD) +r*rBK4BK4DsA(2 - r*rBGBsAsB) + r*rBKABKBDsBl) (12) r BKABSASB @B= (1+ rBKBC%I+ %3KBD@DlPB + (1- c4’*GB?4sB)* x (2+cJc4BSB(2 - ‘dBKiBWB)+ rBKAB& - r*rBKiBsAsB) +%[(r,K,c + TBKBC) + WBK4BKBCSB(2 +%rBK,B~Acx4l + @Dl[(r,K,D + TBKBD) + r.4rBKABK4DsAl) (13) +mA4BKBDsB(2 - rArBGBsAsB) mc= Qcl

1 + rc KAcSA + rc K,,S,

‘A’Bk KLEBSASB + (1 - rAr,K&SAS,)

’ rrirB

+ KAcsA + KBcSB

(14)

QD = QD1 1 + r,,KADSA + r,,KB,SB

rArBrDKh3SASB +

(1 - r,r,Ki,S,S,)

~KAD - KBJ3 rBKAB + rAKAB + KADSA + KBDSB i

where the sums, sA, s,, S, and Sa, are written as

II(15)

S,=@A,/(1-KA@Al)2

(16)

sB =%il/(1-KB@BI)2

(17)

sA=
(18)

sB = @Bl/(l-KB@Bl)

(19)

22

The true molar volume of the mixture V is given by

1 -= ’

x4

SB

rA

‘I3

-+-+

+

‘ArEi

+

+2@ YD

2 KAB

kKACSA

1 + r,K,,S,

+ rCKBC&

+ r,,K,,S,

i

+[( & +‘,jK,,+ (,t +‘,),,I(l?;;;B:;B;A The pure-component structural parameters r and q were estimated by the method of Vera et al. (1977). The association constants for alcohols at 50 o C were taken from Brandani (1983). The enthalpy of hydrogen bonding

TABLE 2 Vapour pressures, liquid molar volumes and molecular structural parameters components and second virial coefficients of the mixtures at 328.15 K Parameter

for the pure

Pure component Methanol

Vapour pressure (Torr) Molar liquid volume (cm3 mol- ‘1 Pure second virial coefficient (cm3 mol - l) r 4

2-Propanol

512.4 I 40.99

- 1438 1.15 1.12

229.5

Acetonitrile 306.6

Benzene 326.9

81.41

54.61

92.88

- 1511 2.23 1.98

- 3788 1.50 1.40

- 1157 2.56 2.05

Mixture Methanol2-propanol

Methanolacetonitrile

Methanolbenzene

2-Propanolacetonitrile

2-Propanolbenzene

Acetonitrilebenzene

- 1507 =

- 1841 a

-434 a

- 2083 a

-780 a

- 1100 a

a Cross second virial coefficient (cm3 mol-‘).

Temp. (“0

45 55 55 55 50 50

System (A-B)

Acetonitrile-benzene Methanol-acetonitrile Methanol-benzene Methanol-Zpropanol 2-Propanol-acetonitrile 2-Propanol-benzene

Binary calculated results

TABLE 3

12 13 9 20 15 15

Number of data points 0.78 1.59 0.94 1.78 0.52 0.78

0.02 0.00 0.06 0.07 0.01 0.02

6T (K)

Root-mean-square SP (Torr) 0.5 1.2 1.4 0.9 0.5 0.6

(x 103)

6X

deviations

3.6 5.3 4.7 3.8 3.7 4.1

SY (x103) - 10.54 480.17 - 71.04 - 87.96 538.50 129.75

(K)

‘AB

Parameters

258.38 - 113.15 220.25 208.01 84.11 12.72

(K>

aBA

25 24 24 26 21

45

55

55

55

II I II I II I II I II

I

Dev. a

equilibria

Number of data points

45

Temp. (“0

a I, absolute arithmetic mean; II, root-mean-square.

Methanol W-ethanol (2) -acetonitriIe (3)-benzene (4) Ethanol W-l-propanol(2) -acetonitrile (3)-benzene (4) Methanol W-l-propanol (2) -acetonitrile (3)-benzene (4) Methanol W-l-butanoI(2) -acetonitrile (3)-benzene (4) Methanol W-2-propanol(2) -acetonitrile (3)-benzene (4)

System

Prediction of isothermal quaternary vapour-liquid

TABLE 4

5.5 6.5 2.1 2.7 5.0 6.6 7.4 9.7 4.0 5.6

7.4 9.1 3.4 4.4 3.3 4.1 4.4 4.6 2.6 3.5

3.6 4.8 6.0 6.7 7.5 8.9 5.6 7.0 3.1 4.1

Vapour mole fractions

7.1 9.5 3.8 4.8 6.0 7.3 7.8 9.6 7.5 8.9

2.34 3.02 2.30 2.91 3.22 3.86 3.31 3.91 2.03 2.44

Pressure

0.71 0.93 1.01 1.20 0.72 0.86 0.79 0.97 0.41 0.50

This work

Nagata (1991)

Nagata (1990~)

Nagata (1990bI

Nagata (1990a)

Ref.

25

for alcohols was obtained as -23.2 kJ mol-’ (Stokes and Burfitt, 1973). The solvation constants at 50 “C and enthalpies of complex formation taken from previous papers (Nagata, 1985a; Nagata and Ohtsubo, 1986) are: KAB = 70 and h,, = -23.2 kJ mol-’ for methanol-Zpropanol; KAc = 30 and h,, = - 17 kJ mol-’ for methanol-acetonitrile; KAD = 4 and h = - 8.3 kJ mol-’ for methanol-benzene; K,c = 23 and hBc = - 17 kJ tr%’ for 2-propanol-acetonitrile; K,, = 2.5 and h,, = -8.3 kJ mol-’ for 2-propanol-benzene. All the h values were assumed to be independent of temperature and to fix the temperature dependence of the equilibrium constants through the van? Hoff relation. Table 2 gives the vapour pressures, liquid molar volumes and structural parameters for the pure components and second virial coefficients used in data reduction. Binary energy parameters were obtained as described by Prausnitz et al. (1980) using a computer program which minimizes the objective function (Pi - Pi*)2

5

F=

i=l

4

[

(zp+

q*)’

+

Cxli

1 (21)

+ -YE>’ --x1*i)2 (Yli

4

2 uY

where an asterisk denotes the most probable calculated value and the standard deviations of the measured variables were set as a, = 1 Tort-, ur = 0.05 K, a; = 0.001, and uy = 0.003. Table 3 summarizes the calculated binary results. Table 4 shows the deviations between the experimental and predicted values of quaternary VLE together with those for other systems (Nagata, 1990a ,b, c , 1991), indicating that agreement is very good.

LIST OF SYMBOLS

aIJ A,

B,

C,

D

A,B,C, AiBiD A,C, A,D 4,

B,C, B,D F h AB, D

hAC,

hAD,

hBC, 430

binary interaction energy parameter for the I-J pair methanol, 2-propanol, acetonitrile and benzene complexes containing i molecules of alcohol A, j molecules of alcohol B and one molecule of component C or D complexes containing i molecules of alcohol A and one molecule of component C or D second virial coefficient for the I-J pair complexes containing i molecules of alcohol B and one molecule of component C or D objective function as defined by eqn. (21) enthalpies of complex formation between unlike molecules total pressure saturated vapour pressure of pure component

I

26 41

R

r1 %, 3, S.47 SB T 4V VA07VBO XI

YI z

molecular geometric-area parameter of pure component I universal gas constant molecular geometric-size parameter of pure component I sums as defined by eqns. (16) and (17) sums as defined by eqns. (18) and (19) absolute temperature molar liquid volume of pure component I true molar volume of alcohol mixture true molar volumes of pure alcohols A and B liquid-phase mole fraction of component I vapour-phase mole fraction of component I lattice coordination number, equal to 10

Greek letters

activity coefficient of component I area fraction of component I standard deviations in pressure, temperature, liquid-phase mole fraction and vapour-phase mole fraction exp (-a,,/T) fugacity coefficient of component I at P and T fugacity coefficient of pure component I at Ps and T segment fraction of component I monomer segment fraction of component I monomer segment fractions of pure alcohols A and B Subscripts

alcohols and active non-associating components B, C, D A,, B,, C,, D, monomers of components A, B, C and D i-mers of alcohols A and B Ai, B, AB, AC, AD, binary complex BC, BD components I, J and K I, J, K i, j, k and I-mers of alcohols or indices 4 L k 1 4

REFERENCES Brandani, V., 1983. A continuous linear association model for determining the enthalpy of hydrogen-bond formation and the equilibrium association constant for pure hydrogenbond liquids. Fluid Phase Equilibria, 12: 87-104.

27 Gmehling, J. and Onken, U., 1977. Vapor-Liquid Equilibrium Data Collection, Organic Hydroxy Compounds: Alcohols, Vol. 1, Part 2a. DECHEMA Chem. Data Ser., DECHEMA, Frankfurt am Main, F.R.G., pp. 125, 217. Gmehling, J., Onken, U. and Arlt, W., 1978. Vapor-Liquid Equilibrium Data Collection, Organic Hydroxy Compounds: Alcohols and Phenols, Vol. 1, Part 2b. DECHEMA Chem. Data Ser., Frankfurt am Main, F.R.G., p. 68. Gmehling, J., Onken, U. and Arlt, W., 1980. Vapor-Liquid Equilibrium Data Collection, Aromatic Hydrocarbons, Vol. 1, Part 7. DECHEMA Chem. Data Ser., Frankfurt am Main, F.R.G., p. 122. Hayden, J.G. and O’Connell, J.P., 1975. A generalized method for predicting second virial coefficients. Ind. Eng. Chem. Process Des. Dev., 14: 209-216. Nagata, I., 1985a. On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols. Fluid Phase Equilibria, 19: 153-174. Nagata, I., 1985b. Isothermal vapor-liquid equilibria for the ternary methanol-ethanolbenzene system. J. Chem. Eng. Data, 30: 201-203. Nagata, I., 1990a. Isothermal vapour-liquid equilibrium for the methanol-ethanolacetonitrile-benzene system. Thermochim. Acta, 157: 95-104. Nagata, I., 1990b. Isothermal vapour-liquid equilibria for the ethanol + l-propanol + acetonitrile-t benzene system. Phys. Chem. Liq., 21: 137-145. Nagata, I., 1990~. Isothermal (vapour + liquid) equilibria of (methanol + propan-l-01 + acetonitrile + benzene). J. Chem. Thermodyn., 22: 501-504. Nagata, I., 1991. Isothermal (vapour + liquid) equilibria of (methanol + butan-l-01 + acetonitrile + benzene). J. Chem. Thermodyn., 23: 293-296. Nagata, I. and Katoh, K., 1980. Ternary liquid-liquid equilibria for acetonitrile-ethanolcyclohexane and acetonitrile-2-propanol-cyclohexane. Thermochim. Acta, 39: 45-62. Nagata, I. and Ohtsubo, K., 1986. Thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing two alcohols. Thermochim. Acta, 102: 185-205. Ohta, T. and Nagata, I., 1983. Vapor-liquid equilibria for the ternary systems acetonitrile2-butanone-benzene and acetonitrile-methanol-benzene at 328.15 K. J. Chem. Eng. Data, 28: 398-402. Prausnitz, J.M., Anderson, T.F., Grens, E.A., Eckert, C.A., Hsieh, R. and O’Connell, J.P., 1980. Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria. Prentice-Hall, Englewood Cliffs, NJ. Riddick, J.A., Bunger, W.B. and Sakano, T.K., 1986. Organic Solvents, 4th Edn. Wiley-Interscience, New York. Spencer, CF. and Danner, R.P., 1972. Improved equation for prediction of saturated liquid density. J. Chem. Eng. Data, 17: 236-241. Stokes, R.H. and Burfitt, C., 1973. Enthalpies of dilution and transfer of ethanol in non-polar solvents. J. Chem. Thermodyn., 5: 623-631. Vera, J.H., Sayegh, S.G. and Ratcliff, G.A., 1977. A quasi-lattice-local composition model for the excess Gibbs free energy of liquid mixtures. Fluid Phase Equilibria, 1: 113-135.