VAPOUR-LIQUID EQUILIBRIA OF THE SYSTEMS ACETONE-BENZENE, BENZENE-CYCLOHEXANE AND

ACETONE-CYCLOHEXANE AT 25°C

ALEKSANDAR TASK?, BOJAN DJORDJEVIe, DUSAN GROZDANIC, NAIM AFGANt and DRAGOMIR MALIe

Faculty of Technology and Metallurgy, Umverslty of Beograd, Yugoslavia

(Recerved 3 March 1976, accepted 15 March 1977)

Abstract-Vapour-hqmd equdtbrmm data for the binary systems acetone-benzene, benzene-cyclohexane and acetonecyclohexane have been determmed experlmentally at 25°C The reduction producers based on P - x - y as well as on P - x Isothermal data sets, which mcorporate usual thermodynamically consistent models expressmg the dependence of achvlty coefficients of hqmd composition, have been exammed for representmg the reported results Nomdeal behavlour of the both phases has been taken into account Thermodynamic consistency of the data has been shown by comparing of the experimentally obtamed vapour compositions wtth those calculated from P - x data using the best of the examined models for activity coefficients

INTRODUCTION

The use of analytical expressions which relate actimty coefficient, composltlon and temperature 1s of particular importance m the design and operation of dlstdlatlon equipment

Since the existing molecular theones are not always efficient to solve the problems of Interest, considerable effort has been lately expended m developing new concepts concerning the reduction of experimental vapour-liquid equlhbnum data, in order to obtain reliable expressions which relate activity coefficient and liquid composition[l-41 Performances of these expressions depend on the choice of the data reduction procedure, and on the spectic thermodynamic model for activity coefficients employed [S, 6] Semlempmcal models 171 of Margules, van Laar, Schatchard-Hamer, Wohl and Wdson[8] are tradltlonaily used m the calculatlonal pro- cedures when P -x - y eqmllbrlum data have to be reduced Some of these models have not been utilized previously to establish the composltlon dependences of activity coefficients from P - x data sets

In the systems reported here, spectic mteractlons oc- cur between the constltuents[9] The ObJect of the present work 1s to compare sultabrllty of the mentioned thermodynamic models and the computational proce- dures used to reduce the binary vapour-liquid equlll- brmm data of the investigated systems

EXPERIMENTAL Chemrcals and their properties Analytical grade

acetone (Merck), “Annalar” benzene (BDH), and “RP“ cyclohexane (Carlo Erba) were further purified by the methods already described [9]

Physical properties of the chemicals used for ex- perimental work are compared with the selected pu- bhshed values m Table 1 The second vn-~al coefficients, listed m the same table, for acetone and benzene were

tAlso, Boris KldrlE Institute, Beograd, Yugoslavia

estimated, respectively, by graphlcal mterpolatlon, from the data reported by Bottomley et al [lo, 111 and [12,13] The second virial coefficient for cyclohexane was ob- tamed from the data of Bottomley et al [13,14] by graphical extrapolation The second vlrlal cross- coefficients for the systems acetone-benzene and ben- zene-cyclohexane were estimated, by graphical ex- trapolation, from the data of Knoebel et al [15] and Bottomley et al [13], respectively The cross vu-& coefficient for the system acetone-cyclohexane was predicted by the method of O’Connell and Prausmtz[l6] Partial molar volumes of the components were cal- culated from the excess volumes of mixing reported by Nlgam et al 1171 for acetone-benzene, Stokes et al [lS] for benzene-cyclohexane and RadolkovlC et al [9] for acetone-cyclohexane system

Apparatus and procedure Vapour recirculation stdl as well as the experimental procedure used to obtam the vapour-liquid equlllbrlum data for the systems acetone- benzene and benzene-cyclohexane were described previously[l9] Isothermal data for the system acetone- cyclohexane were measured by a vapour and liquid reclrculatlon stall This sa and the experimental method employed were already described [20]

Equlllbrmm temperature was measured by a mercury thermometer having 0 1°C dlvlslons The temperature readings are believed accurate to f 0 02°C Equrhbnum pressure was measured by a mercury manometer and read with a precision of 0 05 mm of Hg The absolute accuracy of these measurements is probably wlthm f 0 2 mm of Hg The manometer readings were reduced to mdluneters of mercury at 0°C

Pressure m the stall was controlled by a photoelectnc amphfymg system and by a control manometer1191 Sampling of the phases at equdlbrmm was accomplished by the syrmges sunultaneously Composltlon of the samples were determined by measurmg their refractive indices at 25’C A Carl-Zeiss-Abbe refractometer, with an accuracy of 0 0001 was used Tlus corresponds to the maximum uncertainty in mole fraction of * 0 002

189

190 A TASIC et al

Table 1 Physlcal properties of components and of theu bmary mixtures at 25°C

Property Acetone Benzene Cgclohexane

Density at 25Oc, g/cm3 exper3.mental

literature

Ilefractlve index at 25OC

Vapour

Second

experimental literature

preaure at 25OC mm IIC experimental literature

molar volume at 25OC, cm3/mol

vlrlal coefflclents for 'pure components

0.7850 0.8738 0.7738 O-78501 [331 0. h73650 [if31 O-77387, [13

1.3557 1.4979 1.4231

1.35598 1331 1.49800 [331 1.4233 1351

230.40 229.55 133 231.2 [371

95.05 97.45 95.15 [34] 97.81 [3d

73. YG7 09.391 106.762

a-t 25Oc, ~m~h-101 -1901~0,liJ -1477 [12,13] -1561 [l3Jq

Cross second vlrlal acetone-benzene -1618 1151 coefflclents at benzene-cyclohexane 25Oc, cm3/mo1

-1431 1131 acetone-cyclohexane -1356+

+ Predicted value by the method of ref. 12,3]

CORRELATION OF THE DATA

The experimental vapour-liquid eqmhbrmm data were correlated by two dtierent procedures which take mto account the nomdeahty of both phases One of them 1s based on the use of P - x - y, and the other on the P - x isothermal data

The first calculational procedure was camed out through apphcatlon of eqn (1)

-e

cp,y,P = yJpo~xfzqpo’ exp g

where the fugaclty coefficient rpl of the component I m the vapour phase 1s given by eqn (2)

Incp, =tg y,B,,-lnz (2) I 1

The molar volume Y and the compresslblllty factor z of the vapour mixture were calculated using eqns (3) and (4)

E&1+;

Pv ==RT

(3)

(4)

where

The reference fugaclty for pure component I m the hqmd

phase ftq’” was obtamed from eqn (6)

f;<Po) = p,“(&a exp -;pl (6)

The fugaclty coefficient of pure saturated vapour I was calculated from the vulal equation

lnp,l=$B,,-lnz, (7)

where

Psvs B Z, ~_L-&=1+~

0, (8)

The zero pressure actlvtty coefficient Y:~‘) 1s related to the experimentally obtained actlvlty coefficient Y,(~‘, for the same hquld composltlon and temperature, by equa- tion

<P0> _ G=P YE - yJp’ exp * (9)

Various proposed and well-known integrated forms [7,8] of the Gibbs-Duhem differential equation

3, x, d In Y:~” = 0 (10)

were used to obtam the composltlon dependence of actlvlty coefficients In order to compute numerlcal values of the adjustable parameters m these expresslons, an optlmlzatlon techmque as well as an objective func-

Vapour-hqwd eqmhbna of acetonebenzene, benzen=yclohexane and acetone-cyclohexane at 25°C

thermodynamic equation tlon to be mmlmlzed were selected Problems associated with makmg these choices were considered in the literature [ 1,21-231 In the first calculatlonal procedure the objective function defined as

F=2 r:. (n-number of data pomts) (11) r-1

was used, where

r, = (Q,, - QcaJI (12)

The dlmenslonless excess Gibbs energy Q,, 1s related to the actlvlty coefficients by equation

(13)

The composltlon dependence of zero pressure actlvlty coefficients, m the expression for Q_,, was aven by equations of Margules, Van Laar, Scatchard-Hamer, Wohl[73 and W&on[8] Newton-Raphson nonhnear programmmg method[24] was used to mmlmlze the ob- Jectlve function F

It was pointed out[2-5) that the calculational proce- dure, described above, makes use of the thermodynaml- tally overspeclfied set of binary isothermal data Never- theless, It IS often practically employed Smce the ex- perimental uncertamty is, in most cases, greatest for vapour composition, different methods for the reduction of P - x data have been developed{l-51

The second calculational procedure, used m the this work, reqmres the experimental P -x data It IS simdar to the method proposed by Prausmtz[2] By mmlmlzmg the sum of squares of the differences between ex- penmental total pressure and total pressure calculated by

this method yields both parameters m the y:po’ vs xi models which satisfy the dlfferentml eqn (10) and vapour cornpositron, smce partial pressure of the component I can be expressed as product yQ The same empmcal fittmg functions for activity coefficients, used m the data reduction procedure described first, were employed m eqn (14) as well

Throughout the second calculational procedure of data reduction the objective function

(15)

and the numerical method[24], already mentioned, was used

RESULTS ANDDISCUSSION

Experimental vapour-liquid eqmhbrmm data for the systems acetone-benzene, benzene-cyclohexane and acetone-cyclohexane at 25-C, obtamed m this work, are presented m Table 2

Vapour-hqutd eqmhbnum data for the system acetone-benzene at 25°C were predicted and reported by Lltvmov[25] It can be seen from Fig 1 that the data presented here are neither III close agreement wrth the two control expenmental points of Lltvmov nor with hs predicted values Brown et al [26] reported sun&u dls- agreement, comparing their excess GBbs energies at 45”C, w&h those correspondmg to the data of Lltvmov at 25” and 35°C Kraus et al [27] reported the equdtbrmm data for this system at 30, 40 and 50°C

Table 2 Experimental vapour-hqtud eqmhbrmm data at 25°C

Acetone(l) - Benzene(2) Benzene(l) - Cyclohexane(2) Acetone(l) - Cyclohexane(2)

0.0000 0.0820 0.1850

Kg;; 0:9090 0.9320 1.0000

95.05 116.65 137.20

191.20 203.20 213.40

0.0000 0.1035 0.1750 0.2760

FEg: 0:5090

0.0000

:-i5:s2 . 0.3130 0.4015 0.4460 0.5050 0.5620 0.6505 0.7410

97.45 102.05 lca.50 K&j5 108.10

;OC&“,o .

100.60 98.15 95.05

0.0000 0.0115 0.0160 0.0250 0.0300 0.0440

EZ . 0.1125

0.6605 0.6920

:.535gz ok05

EE 0:9625 1.0000

0.0000 0.1810 0.2250 0.3cJ+O 0.3450 0.4100 0.4580 0.5330

:.a Ok325 0.6550 0.68CXl 0.69W 0.7C5C

:.;:;?i 0:72X'

:.;z: 0:8030 0.8280 0.8560

XE .

97.45 118.05 124.95

Z75.E 160:30

262.00 261.90

zg.5: 252:oo

z-z .

CES Vol 33 No 2-D

2LO -

220 --

200 -

-m I 180 - E

5 L 160 -

110 -

120 -

100

P’ NO’

A LITVI NOV (EXPI [25] A LITVINOV (CAL) [25] 0 THIS WORK

I I I

00 01 02 03 OL 05 06 07 08 09 10 X, ,Y, [ACETONE)

Fig. 1 Equlllbnum data for the system acetone(lkbenzene(2) at 25°C

Isothermal data for the system benzenecyclohexane were reported by Scatchard et al [28] at 39 99 and 69 98”C, Boubhk[29] at 10 and 60°C and Kortiim and FreterDO] at 119 3°C No data at 25°C have been found m hterature

Recently, Purr et al 1311 reported data for the system acetone-cyclohexane at 25°C Reasonably good agreement of these data with the results obtamed m the

present work IS shown m Fig 2 Pronounced steepness of P - x curve below 0 2 mole fraction of acetone caused experlmental dficulties, and hence greater uncertamty 1s associated with the presented data m this reaon

The results of two data reduction procedures pre- vlously described which are based on the mentioned fitting models for activity coefficients, are summmzed m Table 3 It can be seen from this table that the numerical

260

200

1GO

n PURl et al [31]

0 THIS WORK

00 01 02 03 OL 05 06 07 08 09 10 X,,)‘, IACETONE)

Fe 2 Equdibnum data for the system acetone(l)-cyclohexane (2) at 25°C

Tabl

e 3 P

aram

eter

s of t

he fi

ttmg m

odel

s for

syst

ems m

vest

lgat

ed at

25°

C

Para

mete

rs

from

expe

ruen

tel P-x

-y data

Pa

rame

ters

from

expe

rune

ntal

PL

x da

ta

Mode

l'

Numb

er of

para

met

ers

* B

D T&

l Al

2 82

1 A

B D

QJl

%2

“21

Marg

ul9S

van La

ar

Scat

chax

d-

HBIi

ler

Wohl

Wils

on

Marg

uleS

VenL

aar

Scat

chui

- He

Pler

Wohl

Wlls

on

Merg

ules

VanL

au

Scat

char

d-

Heme

r

wohl

Wils

on

2 3 2 3 2 3 3 4 2 2 3 2 3 2 3 3 4 2 2 3 2 3 2 3 3 4 2

0.50

73

0.44

00

0.55

66 0.

4782

0.2

067

0.51

17 0.

4402

0.

5652

0.4

712 0.

2126

0.

4955

0.4

337

0.54

57 0.

4877

0.2

253

0.51

17 0.

4402

0.

5509

0.

4830

0.2

138

0.44

98

0.49

52

0.44

24 0.4

880 -0.

0335

0.

4509

0.4

Y60

0.44

27 01

4867

-0.0

386

0.45

02 0.

4Y45

0.

4430

o&

347 -0

.035

0 0.

4423

0.

4994

0.

4722

0.5

K7 0.

7045

2.01

76 1

.739

8 2.

2052

1.

9565

0.

9777

2.

0348

1.

7423

2.

2325

1.

9227

0.

9984

1.

9171

1.

6360

2.

1205

2.~

79a 1.

1798

2.

0269

1.7

170

2.18

60 1.9

810 1.

0981

ACET

oWE(

l)-B

ENzE

NE(2

) 0.50

69

0.55

69

0.51

49

0.57

35

0.49

0s

0117

26

0.18

52

0.85

75

$544

0

1.11

10

0.w

0.65

62 0.9

064

0.42

59

0.45

68

0.42

67

0.44

97

0.42

06

0.46

78 0.1

981

0.45

27 0.1

737 0.

8705

0.62

9'7 0.9

437

EiEl

i!ix

NE(1

)-CY

CLOH

EuNE

(2)

0.45

61

0.46

10

0.45

72

0.46

49

0.45

66

0.46

01

0.84

03

0.1%

0.

8578

0.7

003

0.51

08

0.51

59

0.51

26

0.51

87

0.51

15

0.51

67 0.

0225

0.02

94

0.01

71

ACET

ONE(

l)-C

YCLO

HEXA

NE(2

) 2.

0207

2.

1572

1.68

29

1.94

70

0.9%

2.17

61 1

.902

5 0.

9105

2.09

40

0.84

76

O.YY

70

2.18

64

0.20

67 0.3

206

2.14

11 1.3

074

1.88

18 O.S

OY8 0.

9183

0.21

64 0.3

220

0.86

90 0.6

810

a Co

nver

genc

e wae no

t ac

hiev

ed

194 A TA& et al

values of parameters depend on the choice of the cal- culational procedure used for theu determination Both treatments have to produce the same values of parameters If the perfect set of P - x - y data 1s reduced usmg a sultable model for activity coefficients In ad- dition, lack-of-convergence was encountered for some of the models used in the reduction procedure of P-x data This fact 1s due to the behavlour of the oblectlve function m the parameter spece and to the nature of the muumuatlon method employed

Standard errors of estunate for vapour composltlon R,, and for total pressure Rp are presented m Table 4, mdlcatmg both the adequacy of two data reduction pro- cedures and the flexlblllty of thermodynanuc models employed

The nature of these results IS a consequence of rela- tively large dtierences m nomdeal behavlour of the mvestlgated systems Et can be seen from Table 4 that for the system acetone-benzene the reduction method, based on P -x data, provides better agreement of the experimental and calculated vapour composltlons than the other method used Significant unprovements m the same sense can be observed especially for the system acetone-cyclohexane These observations are in agreement with the conclusions of Mackay and Salvador [32] who stated that the P - x method should be used m the cases of high relative volatility and where P --x gradient 1s high The results of Table 4, cor- responding to the system benzene-cyclohexane, show that both methods of data reduction provide practically

Table 4 Comparison of experimental and calculated equflibnum data at 25°C

Standard errors of estimates and Standard errors of estrmates and mexu&l devlatlons correspondme; to the use of P-x-y data

maximal devxatlons correspondxng to the use of P-x data

Number of 91 P Yl P Ilodela parenetcrs Rb P

Yl aJl R; max Rb max y1

Q, mex R; P msx

1argllles

van Laar

Scatchard- darner

1; 0111

Uxlson

I!wles

vsii Laar

Scatchard- Hamer

I'ohl

IIllS0l-l

Fqules

van Laar

Scatchard- Hamer

"oh1

\I1ls0n

2 0.0031 -o.oogs 0.5613 1.08

3 0.0018 -0.0031 0.2950 0.76 2 0.0030 -0.0060 0.5431 l.OS 3 O.OOlG 0.0030 0.3194 0.82 2 0.0036 -0.0074 0.6340 1.02 3 0.0020 -0.0039 0.2794 0.71 3 0.0030 0.0060 0.5424 1.08 4 0.0023 0.0045 0.5366 1.17 2 0.0029 -0.0055 0.5254 1.06

2 0.0014 0.0040 0.0609 0.13 3 0.0016 -0.0036 0.0470 0.11 2 0.0014 -0.0039 0.063e 0.13 3 0.0017 0.0535 0.0539 -0.09 2 0.0014 -0.0040 0.0613 0.13

3 0.0016 -0.0037 0.0442 0.12

3 0.0016 0.0037 0.04go 0.12 4 0.0010 -0.0022 0.2614 -0.45 2 0.0014 -0.0026 0.0700 0.16

2 0.0142 0.0254 4.1184 -9.76 0.0129 0.0246

3 0.0058 -0.0113 1.8749 -3.80 0.0038 -0.0065 2 0.0133 -0.0235 3.9341 -9.57 3 0.0060 -0.0127 1.6782 -3.34 0.0032 -0.0050 2 0.0219 O.@t24 5.3432 -11.52

3 0.0076 -0.0170 2.7316 -7.83 0.0081 -0.0139 3 0.0128 0.0236 3.627a -8.17 4 0.0102 0.0193 2.5521 -4.78 0.0031 -0.004y 2 0.0059 -0.0143 0.4846 -2.55 0.0032 -0.0078

0.0029 -0.0065 0.3807 0.66 0.0018 -0.0046 0.2680 -0.59 0.0027 -0.0061 0.3881 -0.65 0.0017 -0.0036 0.2818 -0.52 0.0035 -0.0076 0.4153 -0.69 0.0023 -0.0053 0.3273 -0.69

0.0018 -0.oO.W 0.2884 -0.55 0.0026 -0.0060 0.3436 -0.62

O.OOlC o.CO40 0.0654 -0.13 0.0017 -0.0036 0.0646 -0.11 0.001y -0.0039 0.0704 -0.12 0.0018 -0.0034 0.0785 0.12 0.0020 -0.0040 0.0710 -0.13 0.0019 -0.0037 0.0702 -0.11

0.0017 -0.0037 0.0639 -0.12

3.6039 -7.84 0.6719 -1.47

0.4542 -0.86

1.9407 -4.07

0.4074 -0.69 0.36% -0.61

a lnfp form, b %1=[< (yxem- ~~~a~)z/,]~'~ , ' RP =[< (peq- Pcal)z'n] 1'2

Vapour-hquld eqmhbna of acetone-benzene, benzene<yclohexane and acetone-cyclohexane at 25°C 195

the same accuracy Mmor advantage of the method based on P -x-y data IS also m agreement with the findings of Mackay and Salvador This 1s due to the fact that the system benzene-cyclohexane has the lowest relative volatthty

It IS well known that the devlatlons between measured and predicted eqmhbrmm vanables come from both the systematic errors of the measurements and from m- adequacy of the thermodynamic mode1 employed m the reduction procedure If a spectic vapour-hqtud eqmh- bnum data set IS represented by different models, their relative surtabdlty can be mdlcated by comparmg the correspondmg devlatlons,t RY1 and Rp values for the system benzene-cyclohexane, where deviations from ldeahty are not large, mdlcate that all the models have slmfiar smtablllty Nevertheless, Margules’s equation

?A new method of checkmg the vahddy of thermodynamic models, based on the prmclple of maximum hkehhood, 1s re- cently presented by Fabnes and Renon[6]

with three parameters (P -x - y method) 1s proposed For the system acetone-benzene some differences exist m the apphcabtilty of the models It seems that three- parameter van Laar’s equation (P - x method) gves the best representation of the data The results of Table 4, for the system acetone-cyclohexane, lead to the conclusron that slgndicant vartations m flexlblllty of the models are present Wlson’s equation (P -x method) and four- parameter Wohl’s equation (P -x method) gave similar results for this system Wtison’s equation, whch uses only two adjustable parameters, seems to be shghtly better

Plots Ayl and AP vs x, for all mveseated systems and for both data reduction procedures, m which above recommended correlatmg models were mcorporated, are shown m Fe 3 Deviations presented m Ay, vs x, plots can be compared with the expenmental uncertamty m order to check the vahdlty of vapour-hqmd eqmhbrmm data One sees from Fig 3 that the mdlvldual deviations Ay, for most of the data points, correspondmg to the

ACETONE(l) - BENZENE(Z)

BENZENE(l)-CYCLOHEXANEi2) 0004 0004

O-P-x-y METHOD A- P- x MET HOD

Fig 3 Ay, and AP vs x, for the systems Investigated at 25°C

1% A TA& et al

acetonebenzene and benzene-cydohexane systems, are wlthm the range of expernnental error Proposed models for these systems gave standard errors R,, which do not exceed the range of experunental uncertamty as well, mdlcatmg that the data are thermodynamlcally consistent and that the reduction procedure 1s correct [4]

Although the W&on’s equation for the system acetonscyclohexane gave standard error R,, not much outside the range of the experlmental error, mdlvldual deviations Ay, m the acetone ddute regron are more pronounced These higher uncertamtles of the data are due to the previously mentioned experunental dlfficultles expenenced for these composltlons

Although plots AP vs x1 do not check the consistency, they mdlcate the ablltty of proposed anaIytical expres- sions for activity coefficients to fit the experunental P - x data It should be noticed from the AP vs x1 plot of Fe 3, for the system acetone-cyclohexane, that pressure measurements are not represented withm the limits of experimental uncertamty by W&on’s equation Moreover, dutnbuhon of mdlvldual AP pomts m this plot is, to some extent, characterized by nonrandom behavlour Consequently two posslbllltles can occur el- ther the lack-of-flexlbdlty of the Wdson’s equation for acetone-cyclohexane system, or some degree of mcon- slstency of the eqmhbrmm data It 1s known that these two cases cannot be strictly distinguished

Acknowledgements-The authors wsh to express then gratitude to the Sclentic Research Fund of S R Serbia, for a grant winch has made this research possible In addition, the authors are indebted to Prof D Simonovl& Faculty of Technology and Metallurgy, Beograd, for fruitful discussions durmg tlus work Also they are grateful to M AndJelkovlc who asslsted with the computer work

-4 B, 0,4,/q,, A,,, A,,

B

Bii, B,,

B,

F

L

,Li

8

; PF

NOTATION

parameters of the thermodynamic models relating activity coefficients and hquld com- position

second vlrlal coefficient defined by eqn (S), cm3/mole

second vlrlal coefficient of pure I and pure 1, cm’/mole

second VI& cross-coefficient of a binary mixture (B,, = B,,), cm3/mole

objective function defined by eqn (11)

liquid phase fugaclty of I, mm Hg reference fugaclty of pure hqmd I

at system temperature and zero pressure, mm Hg

molar excess Gibbs energy, callmole

number of data points total pressure, mm Hg saturation (vapour) pressure of

pure hqmd I at temperature T, mm Hg

Greek symbols

111 El

[3l

[4

[51 [bl 171

181 [91

Q

R

RP

RY,

z T

VE

V

-L V,

VI S

X‘

Yl Z

Z, s

&mensionless excess Gibbs energy defined by eqn (13)

umversal gas constant, cal/(mole “KS

standard error of estimate m pres- sure, mm Hg

standard error of estimate m vapour-phase mole fraction of I

dflerence defined by eqn (12) sum defined by eqn (IS) absolute temperature, “K excess molar volume of mixmg,

cm’lmole molar vapour volume of a binary

mixture, cm”lmole molar hquld volume of pure I at

temperature T, cm3/mole pmal molar liquid volume of I tn

the binary mixture of tempera- ture T, cm?mole

saturated molar volume of pure vapour I, cm3/mole

liquid-phase mole fraction of I vapour-phase mole fraction of I compresslbdlty factor compressibility factor of I at

temperature T and saturation pressure P,”

experunental isothermal liquid- phase activity coefficient of I

activity coefficient of I at tempera- ture T adjusted to zero pressure

dtierence between expenmental and calculated values

vapour-phase fugaclty coefficient of 1

fugacity coefficient of pure saturated vapour I at tempera- ture T and saturation pressure PnS

REFEREWES Barker J A, Ausb J Chem 1953 6 207 Prausmtz 1 M . Eckert C A. Orve R V and O’Connell J P , Computer ‘CalcuIatzons for Mulhcomponen! Vapour- lraurd Euurbbna Prentice-Hall, Enalewood Chffs, New Jeisey 67 Prausmtz J M , Molecular Thermodymamrcs of Fluid phase Equrlrbna Prentice-Hall, Englewood Cl& New Jersey 1969 vanNessH C,ByerS M andGlbbsR E,AIChEJ 1973 19 238 Abbot M M and van Ness H C , A ICh EJ 1975 21 62 Fabnes J F and Renon H , A I Ch E J 1975 21 735 Hala E , Pick J , Fned V and Vlllm 0 , Vapour-lrqurd Eaudrbnum Pergamon Press, London 1957 W&on G M , J Am Chem Sot 1964 86 127 RadoJkoviC N , Tasic A , Grozdamc D , DJordJevlc B and Mahc D , J Chem Thermodynamrcs 1977 9 349

Vapour-hqurd eqmhbna of acetone-benzene, benzensyclohexane and acetone-cyclohexane at 25’C 197

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Bottomley G A and Spurhng T H , Nature 1%2 1% 900 1221 Bottomley G A and Spurlmg T H , Austr J Chem 1967 20 PI 1789 r241 Bottomley G A, Proc Roy Sot 1958 A246 504 Bottomley G A and Coops I H , Nature 1962 193 268 Bottomley G A and Remmmgton T A, J Chem Sot 1958 3800 Knoebel D H and Edmlster W C , I Chem Engng Data 1968 13 312

O’Connell J P and Prausmtz J M , Ind Engng Chem Proc Des Dev 1965 6 245 Nlgam R K , Mahl B S and Smgh P P , J C’hem Ther- modynantics 1972 4 41 Stokes R H, Levien B J and March K N , J Chem Thennodynamrcs 1970 2 43

Taslc A, Dlordjevic B , Slmonovlc D , Afgan N and Mahc D, Paper presented at IV International Congress of Che- mlcal Engmeenng, Chemical Equipment Design and Au- tomation, CHISA’72 1972 Prague, Czechoslov&a Dlallc N , DlordJev:c B , Taslc A and MahC D. Pauer presented ai 2 -Internahonales Symposmm The&che Stofftrenung 1974, Dresden, DDR, Chem Techn 1974 26 497 Nagahama K , Suzuki I and Hlrata M , J Chem Engng Japan 19714 1

P51 1261 P71

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1311

1321

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Verhoeye L A, Chem Engng Set 1970 25 1903 Wtchterle I , Co11 Czechosl Chem Comm 1% 31 3821 Rosenbrock H H and Storey C , Computattonal Techntque for Chemical Engrneers Pergamon Press, Oxford 1966 Lltvmov N, D , J Phys Chem USSR 1940 14 782 Brown I and Snuth F , Austr J Chem 1957 10 423 Kraus J and Lmek J , Co11 Czechosl Chem Comm 197136 2547 Scatchard G , Wood S E and Mochel J M , J Phys Chem 1939 43 119 Boubbk T , Coil Czechosl Chem Comm 1960 25 285 Korttim G and Freter H J , Chem Ing Techn 1954 X(12) 670 Pun S P , Polak J and Ruether A J , J Chem Engng Data 1974 19 87 Mackay D and Salvador R I, Ind Engng Chem Fundl 1971 10 167 Brown I and Fock W , Austr J Chem 1957 10 417 Hermsen R W and Prausmtz J M , Chem Engng Scr 1%3 18 485 Brown I, Austr .I Scr Res 1952 A5 530 Cnuckshank A J and Cutler A J B , J Chem Engng Datu 1%7 12 326 Sassa Y , Komsb R and Katayama T , J Chem Engng Data 1974 19 44