Application of the wilson-equation to azeotropic mixtures

Fluid Phase Equilibria, 19 (1985) 201-219 Elsevier Science Publishers B.V., Amsterdam -

APPLICATION MIXTURES K. STEPHAN

201 Printed in The Netherlands

OF THE WILSON-EQUATION

TO AZEOTROPIC

and W. WAGNER

Institwt ftir Technische Thermodynamik gart, Stuttgart (W. Germany)

und Therm&he

Verfahrenstechnik,

Universitiit

Stutt-

(Received March 14, 1984; accepted in final form July 13, 1984)

ABSTRACT Stephan, K. and Wagner, W., 1985. Application mixtures. Fluid Phase Equilibria, 19: 201-219.

of the Wilson-equation

to azeotropic

The Wilson model is appropriate to describe low pressure phase equilibria. For binary mixtures only two parameters are needed. A diagram was developed, based on the Wilson model, allowing us to distinguish azeotropic from nonazeotropic binary systems. To apply this diagram the Wilson constants, and in addition the vapour pressure or boiling temperature and the molar entropy of vaporization of the pure components must be known. A few examples for the application of the method are discussed.

INTRODUCTION

The formation of a minimum or maximum boiling azeotrope is caused by the differences in the boiling points of the pure components and the molecular interaction between the pure components in the solution. Zawidzki (1900) classified binary mixtures by their deviation from Raoult’s law. He showed that mixtures with a positive deviation from Raoult’s law exhibit azeotropes with a maximum boiling point, provided that the components of such solutions do not differ too much in the vapour pressures. Mixtures with a negative deviation from Raoult’s law form azeotropes with a minimum boiling point. Owing to the polarisation the majority of interactions in a mixture are stronger than between the pure components and therefore most azeotropic mixtures exhibit minimum boiling points. Tamir and Tamir (1980) gave a qualitative approach to describe and predict the intermolecular interaction from the molecular structure. For a quantitative description of high pressure phase equilibria equations of state and for low pressure phase equilibria models based on the activity coefficient are useful. 0378-3812/85/$03.30

0 1985 Elsevier Science Publishers B.V.

202

For predicting low pressure azeotropes the activity coefficient can be calculated by the Porter equation. For a binary mixture one obtains In yi = &*(l

-xl)*,lny,=&(l

-x2)*

(1)

Yoshimoto and Mashiko (1956) developed general rules for predicting azeotropes from the parameter A. They found that azeotropes in isothermal vapour-liquid equilibria, are met when the condition

(2) is fulfilled, with the saturation pressures pls and pzs of the pure components at the temperature of the mixture. At a given pressure azeotropes occur, if we have -IAl/&

$ (T,, - G,) I

IWAS,,

(3)

where A &, , A& are the molar entropies of vaporization of the pure components and T,,, T2s are the saturation temperatures at pressurep. Eduljee and Tiwari (1976) classified mixtures according to their hydrogen bonds into different groups as proposed by Ewe11et al. (1944) and predicted the values of A in eqn. (1) wherefrom the azeotropic composition as well as the boiling point can be determined. Other rules as given by Lecat (1930), Skolnik (1948) and Denyer et al. (1949) can be derived from the condition of phase equilibrium and eqn. (l), as shown by Yoshimoto and Mashiko (1957a,b). Tamir (1981) proposed to use the Redlich-Kister equation directly to determine p(x) and T(x) of azeotropic mixtures. This model could also be applied to multicomponent mixtures, but it can also yield erroneous azeotropes caused by the polynomials, as already pointed out by Tamir. To date two or three parameter equations like Wilson’s, NRTL and UNIQUAC are available, predicting nonideal behaviour with sufficient accuracy, and an attempt seems to be promising to predict azeotropes from these parameters. This shall be done in the following. At first the basic equations for azeotropic behaviour shall be derived, provided that yi( xi, T) is known. Next these equations are applied to the Wilson model for binary mixtures. NECESSARY

AND

SUFFICIENT

CONDITION

FOR AZEOTROPES

The criterion whether an azeotrope occurs or not can be derived from the condition of phase equilibrium which reads Xl~p = YiXjpi,

i = 1,2,...,n

(4)

The Poynting correction is neglected and the gaseous phase is assumed to be

203

ideal. At the azeotropic point eqn. (4) can be written for a binary mixture as lny,=lnp/p,,

i=l,2

(5)

After eliminating the pressurep with Y~(x,, T) and ~2(+ T)

in eqn. (5) one obtains for a binary mixture (6)

ln yl - ln y2 = ln PZ~/P~~

Equation (6) is a necessary and sufficient condition for an azeotrope at constant temperature. To derive the criterion for an azeotrope at constant pressure we use the relation, e.g., Prigogine and Defay (1962), for a binary azeotropic mixture In

vi” -J TAH,i -dT-&JPAKidp Vi’

T,, RT2

i=1,2 P15

In our case the vapour phase is considered to be ideal, yl’ = 1. In addition, the molar enthalpy of vaporization AR,,, is assumed to be constant between T and q;:,. Integrating at constant pressure pis and introducing the molar entropy of vaporization

As,,+

(8) IS

one obtains from eqn. (7) RTlnyi=A,&(lTj:,-T)

i=I,2

(9)

If one assumes the activity coefficient to be independent from the temperature, then the temperature T can be eliminated in eqn. (9) and one obtains a necessary and sufficient condition for an azeotrope at constant pressure In yr For mixtures function #TM

at constant

= ln K - In y2

temperature

it is convenient

to introduce

the

(11)

We introduce furthermore JIp as the minimum value of 9 r(0 5 x1 s 1) and T” as the maximum value of #=(O 5 x1 r 1). If we have then \cI +?

I lnp2Jpr,

s G”

02)

we can find a value x1 where eqn. (6) holds and the mixture exhibits azeotropic behaviour. Similarly for mixtures at constant pressure we intro-

204

duce starting

from eqn. (10) -

+~(xI)=lny,-Klny,,K=

iFzs

(13)

02

2s

and write for the minimum value of $,(O =( x1 i 1) = $;f’” and for the maximum value of Jl,(O =(x1 $1) = I/.$“. The condition for the existence of an azeotrope derived from eqn. (10) then reads (14) The derivations above are independent from the model for coefficient. When applying the Porter model, eqn. (l), one instance the condition of azeotropes given by eqn. (2). APPLICATION

OF THE WILSON

MODEL

FOR PREDICTING

the activity obtains for

AZEOTROPES

In spite of the fact that the Wilson model (1964), is not suitable for systems with limited miscibility, it is widely known and data sources exist like those by Hirata et al. (1975) and Gmehling and Onken (1977). The significance of the Wilson constants fitted to vapour-liquid equilibrium data was investigated by Landeck and Wolff (1979). The limiting values of the activity coefficients represented by positive Wilson constants are mentioned by Pentermann (1983). Extensions of the Wilson equation to systems with limited miscibility were given by Renon and Prausnitz (1969) Hiranuma (1974, 1981) and Schulte et al. (1980). For the sake of simplicity in this paper the original Wilson equation is used In yl = 1 - ln(x,

+ x2A12) -

x1

lny,=l-ln(x,AZI+x2)-x

%A21

:tlS, 1

X2A2,

-

Xl +x242

+x2

-xAX2 2

12

1

21+x2

05) 06)

Usually the two binary constants A12, AZ1 are evaluated from vapour-liquid equilibria data. When reliable data are not available the Wilson parameters may be obtained from the activity coefficient at infinite dilution by solving the relations lnyy=

1 - In A,, - A,,

lnyr=

1 -lnA,,

-A,,

Miyahara et al. (1979) proposed to evaluate A12, A,, by means of nomographs. The limiting activity coefficients can be measured or predicted as

205

summarized in Reid et al. (1977). The composition of an azeotrope at given values of Ai2, A,, can be obtained by solving the condition of phase equilibrium eqn. (4) numerically for the composition at the azeotropic point, xl = xi’ (i = 1, 2,. . . ,n). For a binary mixture eqn. (6) or eqn. (10) may be used. A different approach was given by Eduljee (personal communication, 1984), who suggested applying the Gibbs-Konowalow conditions. From the equation for the molar excess Gibbs energy, Wilson (1964) p/RT=

-

In

xxi

i

one obtains with eqn. (9) xxilnr.=$$$

Xi(q,-

- Cx,ln

T)=

After rearranging,

the temperature

T= ~A&ixi~S/

~A%&xi

i

- CRx,

[

1

i

of the mixture is given by In

1 - xxjAji (

i

i

1 -CxjAii i

i

i

j

11

Equating dT/dx, to zero one obtains an equation relating the azeotropic composition to the Wilson constants and the pure component parameters q, and A&, which can be solved iteratively for Xi. This procedure gives the azeotropic composition 0 < xi < 1. To decide from the Wilson constants Ai2, A,, whether a mixture is an azeotrope or not the functions $r(xi) or +,(x1) shall be discussed. AZEOTROPES

AT ISOTHERMAL

VAPOUR-LIQUID

Using the function $J=( xi) temperature eqn. (6) reads +TJx,)

EQUILIBRIUM

the condition

for

an azeotrope

= lV,S/PiS

at given 07)

For monotonous increase (I) and monotonous decrease (D) of Ic/r(xi) azeotropes occur as shown in Fig. 1 if there is a value xi so that GT( xi) is equal to lnP2s/h. With the Wilson eqns. (15) and (16) we obtain for the function +=(x1) +r(x,)

=

w42, +(42 +

((A21

-

0%

+

l)W(O -

lb,

-

1)

-140

--42)x,

---42)x1

+42)

(A21

-

%‘((A21

+42)

-

lb,

+

1)

(18)

206

condition of an azeotrope was given by eqn. (12). For a monotonous increase of qLT( x1) the extreme values are +p = #=(x1 = 0) and $J?= = $&x1 = 1). With eqn. (18) we obtain the necessary and sufficient condition

The

3.20,

-2.401 0.00

0.20

0.40

0.60

1.

0.80

Xl AlZ=OB

AZl=0.3

-a40

-1.20.

-,.,,I. 0.00

0.20

0.40

0.60

0.80

Xl

Fig. 1. Azeotropes with monotonous functions &(x1).

1.1

207

of an azeotrope for this case 1 - In A,, - A,, s lnPzs/Pls s - 1 + In A,, + A,,

09)

In the case D of monotonous decrease of +r( x1) the condition of an azeotrope is - 1 + In A,, + A,, $ In p2s/pls

6

1 - In A,, - A,,

(20)

To distinguish between the values Ar2, A,, for a monotonous increase or decrease of #r(xr) the extreme values of I/J~(xJ are determined by differentiating eqn. (18) d+r(xl) dx,

o‘ x; + cxr + d

= ((1 -A,,)x,

+

42)2(G421

(21) -

1)x,

+

Q2

The coefficients are b = Af2A;r - 2A:A,, c = -Af2Ai1

.

- 2Ar,A;,

+ 2A:,A,,

+ 2A12A$

+ 4A,,A,,

+ Af2 - 2A,, + A& - 2A,, + 1

- 4A,,A,,

- 2Af2 + 4A,, - 1

d = A;, Ai1 + Af2 - 2 A,, The extreme value dJ/,(x,)/dx,

= 0 requires

bx; + cxr + d = 0

(22)

Rearranging eqn. (22) one finds for the values A21, where +r( x1) exhibits extreme values -rr,+l/r,2--4r,r, A21

(23)

2r,

=

with the constants r0 = x:Af2 - 2x:A,, + X: - 2x,A:, + 4x,A,, rl =

- 2x:Af2

+

x1 +

Af2 - 2~,,

4X,2A,, - 2x; + 2x,A;, - 4x,A,,

r2 = x:A:, - 2x:A,, + x: - xlA$

+ 2x,A,,

+ A12

A negative sign of the square root in eqn. (23) is not possible because one would then obtain negative A,,. In Fig. 2 the values Azlme plotted over A12 for different compositions between 0 I x1I 1 in stepsof x1= 0.1.The limiting curves for x1 = 1 are given by the equation

4&(X1 = 1) = 6

0 = Af2A& + A& - 2A,,

208

and for x1 = 0 by

(25) The curves in Fig. 2 intersect at Al2 = A,, = 1. Within the region limited by eqns. (24) and (25) for any given set of values of Al2 and A,, therefore only a single extreme value exists. The limiting curves given by eqns. (24) and (25) separate four regions from each other in a Azl, A,,-diagram. These regions are indicated by I, D, H, L in Fig. 3. According to eqns. (24) and (25) in the region H a maximum and in the region L a minimum of I/Jr( xl) occurs. Table 1 gives the criteria characterizing these regions. As examples of cases H, L, where \tr( x1) exhibits one extreme value the function \Lr(x1) and In pzs/pIs are plotted over x1 in Fig. 4. In the regions H, L the conditions for azeotropes eqns. (19) and (20) cannot be applied, because there are extreme values of +r ( x1) between x1 = 0 and x1 = 1. The composition of these extreme values can be obtained by solving eqn. (22) for the composition x1

=

-CdZZZ

(26)

2b

K=l

0.00 0.00

0.50

1.00

7.50

2.00

2.50

Fig. 2. Region of extreme values of 4(x,).

209 TABLE 1 Function +&x1)

in the different regions I, D, H, L d&(x,

d&(x,=0)

Region

Function $T( x1)

dx,

dx,

Monotonous increase with x1 Monotonous decrease with x, A single maximum A single minimum

>o CO CO >o

>O CO >o -=o

I D H L

=l)

In the region H the function $T(xl) exhibits a maximum. The value of this maximum $‘;“( x1& can be calculated from eqn. (18) where xIH is given by eqn. (26). The minimal value $p( x1) is GP=+&1

= 0) = 1 - In A,, - A,,

(27)

= 1) = - 1 + InA,, + A,,

(28)

or $,‘;t” = 44%

The condition for an azeotrope in this case reads +L’;“”I lnP&+s

5 ~JYYXIH)

monotonous increase

1

0.50

0.00

(29)

monotonous decrease 0.50

1m

LLM

2.00

*

2.50

XXI

12

Fig. 3. Regions I, D, H, L in the Al2 -Al,-diagram.

3.50

4

210 0.50

$1

Xl) mm. b-l( P2s/ Pls ) ’ -0.50.

-1.00.

-bM.

-2.00

_2,50 0.00

A 12 = 3.5 0.20

A2 1= 0.01 0.40

0.60

0.80

1.00

Xl

2.50

Al2 = 0.01

A21 =3.5

2.00

Fig. 4. Azeotropes with extreme values of the function &(x~)_

211

In the region L the function +T( xi) reaches a minimal value $p( xi,) which is obtained from eqn. (18), whereas xn_ is obtained from eqn. (26). The maximum value JlF”(x,) is either It/X+” = GT (xi = 0) = 1 - In A,, - A,, or a/$” = $,(x1

= 1) = -1 + InA,, +A,,

The condition for an azeotrope reads

(30) (XX ) S ln PlS/PlS 5 G” The curves separating azeotropes from nonazeotropes in the regions I, D are given by applying the eqns. (19) and (20). One obtains

+?

Rl = In pls/pzs

= -

1 + In A,, + A,,

(31)

R2 = In pls/pzs

= +

1 - In A,, - A,,

(32)

Plotting eqns. (31) and (32) for constant values of Rl = 1 and R2 = 1 and also the curves from eqns. (24) and (25) a mixture can be identified whether it is an azeotrope or not (Fig. 5). If the parameters Aiz, A,, are within the region I and D and simultaneously above the curve Rl = 1 or below the curve R2 = 1, azeotropes occur.

A 12

El

azeotropes

region H eqd29) is to use

region L nonozeotropes ml eqn(30) is to use Fig. 5. Distinction of azeotropes from nonazeotropes, constant Rl, R2.

212

With increasing values Rl and R2, which indicates an increase of the differences in the boiling points of the pure components, the region wherein azeotropes are located becomes smaller. The curves for different positive values of Rl, R2 are plotted in Fig. 6. Rl and R2 are always positive if component 1 is the one with the lower boiling point. From Fig. 6 and the parameters At2, A 21 and Rl, R2 one can decide if an azeotrope exists in the region I, D. In the region H eqn. (29) and in the region L eqn. (30) have to be considered. AZEOTROPES

AT ISOBARIC

VAPOUR-LIQUID

EQUILIBRIUM

For isobaric azeotropes the function +,(x1) according to eqn. (13) has to be analysed. With the activity coefficient from the Wilson eqns. (15) and (16)

RZ= RZ;:: R2= A12

Fig. 6. Distinction of azeotropes from nonazeotropes, variation of Rl, R2 in steps of 0.25.

213

the slope of &(x1)

is obtained as ax: + bxf + cxr + d

d&b,) dx,

= ((1 -A,*)%

+ A,*)*((A*,

(33)

- 1)x, + l)*

with the parameters a = - (1 - K)Af*A& -40

- K)A,*A*,

+ 2(1 - K)A*,

+ 2(1 - K)A:*A*, - (1 - K)A;*

- (1 - K)A& + 2(1 - K)A,*

- (1 - K)

b = (2 - K)A;*AZ,, - 2(2 - K)A:*A*, +4(2

+ 2(1 - K)A,*Asr

- K)A,*A*,

- 2(2 - K)A,*A;,

+ (3 - 2K)A;*

+ A& - 2(3 - 2K)A,*

- 2A*,

+(2-K) c = - (2 - K)A:*A;r

+ 2A;*A*,

+ 2A1*A$

- 4A,*A*,

- (3 - K)A;* + 2(3 - K)A,* - 1 d = A;*A;r

- 2A,* + A;*

For a value K = 1 in eqn. (13) +!~r(xr) becomes equal to #r(~r) and eqn. (21) identical with eqn. (33). The necessary condition for an extreme value of eqn. (33) is ax: + bxf + cxI + d = 0

(34)

Values of A,, for which eqn. (34) is fulfilled can be evaluated by rearranging eqn. (34). One finds

A21=

-

91+

\is: - 4q*qo

(35)

2q*

with the coefficients qO=$(-(1-K)A;*+2(1-K)A,*-(1-K)) +xf((3

-.2K)A,2,

- 2(3 - 2K)A,,

- (2 - K))

+x,(-(3-K)A:,+2(3-K)A,,-l)+(-2A,*+A:,) q1 = x:(2(i +x:(

- K)A;* - 4(1 - K)A,,

-2(2

- K)A& + 4(2 - K)A,,

q* = x;( - (1 - K)A;* + 2(1 - K)A,, +x:((2

+ 2(1 - K))

- K)A;,

- 2) +x,(2A:,

- (1 - K))

- 2(2 - K) A,, + 1)

+x1(-(2-K)A1,+2A,,+A3

- 4A,,)

214

A negative sign of the square root in eqn. (35) is not possible, because then one would obtain a negative A,,. Varying the composition x1 in eqn. (35) for constant values K, extreme values of +,(x1) are obtained as shown in Fig. 2. The separation lines of the regions I, D, H, L resulting from eqn. (34) at x1 = 1 and x1 = 0 are e e A,,= L ,A12= A&+1 A;,+ 1

L

which are identical to eqns. (24) and (25). The regions I, D, H, L shown in Fig. 3 are identical for isobaric and isothermal equithe Ar2, A,,-diagram librium and obey the same criteria as summarized in Table 1. Similar to the procedure for isothermal equilibrium the necessary and sufficient condition for an azeotrope at given pressure is obtained from eqn. (14). In the region I the value +,(x1) condition for an azeotrope reads 1 - In A,, - A,, $ A&,/R( In case D where #,(x1)

T,,/T,,

increases with increasing x1 and the - 1) s K( - 1 + In A,, + A,,)

is decreasing one obtains

K(-l+lnA,,+A,,)~AS,,/R(T,,/T,,-l)~l-lnA,,-AA,, For the region H #,(x1) either by $J? = I,!J~(x~= 0) =

(36)

(37)

exhibits a maximum. The minimum Z/J~ is given

1 - In A,, -A,,

(38)

or by $r

= #‘p( x1‘ = 1) = K( - 1 + In A,, + A,,)

(39)

The composition of the maximum xrn can be evaluated by solving eqn. (34). The condition for an azeotrope yields iclp s A%,,/JWi,/G,

- I) s J/&n-r)

In the region L the maximum +F” $r

W)

is given by

= +,,(xr = 0) = 1 - In A,, - A,,

or G;”

= &(x1

=l)=K(-l+lnA,,+A,,)

The composition of the minimum xn is given by eqn. (34) and the condition for an azeotrope reads

215

From eqns. (36) and (37) the curves separating azeotropes and nonazeotropes for the cases I, D in the A12, A,,-diagram are obtained. Their equations read Rl = A$,,/R(l

- T,,/T,,) = - 1 + In A,, + A,,

R2 = A&,/R( T,,/T,, - 1) = 1 - In A,, - A,,

(42) (43)

In Fig. 6 curves for different values of Rl and R2 are plotted and azeotropes can be distinguished from nonazeotropes as discussed before. EXAMPLES

In the following, with the aid of Fig. 6, a few examples will be discussed to decide whether an azeotrope exists or not. The Wilson parameters and the experimental data for these examples were taken from the book of Hirata et al. (1975). Figure 7 shows the mixture of acetone (l)-chloroform (2) which exhibits an azeotropic behaviour. The vapour pressure at the temperature T = 308.32 K of the pure components are pl, = 0.467 bar, pzS = 0.397 bar. We have then Rl = R2 = In plS/pzS= 0.163. With the Wilson constants A,, = 1.05159, A,, = 2.17465 this mixture is located in the region I above the line Rl = 0.5 in Fig. 6 and represents therefore an azeotropic mixture. The mixture chloroform (l)-benzene (2) has the Wilson constants A,, = 2.62571, A,, = 0.23694. Figure 8 shows the phase equilibrium. The saturation pressures calculated from the Antoine equation at T= 323.15 K are

0.33 0.00

CL20

COMPOSITION

am

0.40

Xl

ACETONE

Fig. 7. Phase equilibrium acetone-chloroform, T = 308.32 K.

216 pIs = 0.685 bar, pzs = 0.362 bar. In Fig. 6 this mixture is located in the region

H and the minimal value of +=(x1) is either at x1 = 0 or at x1 = 1. From eqns. (27) and (28) I/J? = -0.2023 is obtained at x1 = 0. The composition of the maximum of #r( x1) results from eqn. (26) to xIH = 0.95. Then from eqn. (18) follows $~(x,,) = 0.198. The unequality eqn. (30) now reads - 0.2023 s ln%

S

4 0.198

Owing to ln( p,,/pzs) = 0.638 eqn. (30) is not fulfilled and the mixture does not form an azeotrope at this temperature. The system ethanol (I)-water (2) has the Wilson constants A,, = 0.20022, AZ1 = 0.81564 and forms an azeotrope at the pressure p = 1.013 bar as calculated in Fig. 9. The boiling temperatures of the pure components are T,S = 351.48 K and T’S = 373.15 K. To apply Fig. 6 the constants Rl, R2 in eqns. (42) and (43) are evaluated by means of the molar heat of vaporization of the pure components taken from Reid et al. (1977), Au,, = 9260 cal mol-l, AEO, = 9717 cal mol-‘. We obtain Rl=

“;

+

-2)

X(1

-2)

=0.770

From Fig. 6 it can be seen that this mixture is located R2 = 1.0 in the region D and therefore is an azeotrope.

a321 0.m

COMPOSITION

am

a40

0.20

Xl

CHLOROFORM

Fig. 8. Phase equilibrium chloroform-benzene,

T = 323.15 K.

a80

below

1

the line

217

Figure 10 shows the T, x-diagram of the azeotropic mixture benzene (1)-cyclohexane (2). This system is described by the Wilson constants A,, = 1.00918, A,, = 0.65926. The boiling temperatures of the pure components are T,, = 353.25 IS, TzS= 353.888. The constants Rl = 0.0189, R2 = 0.0184 in eqns. (42) and (43) were calculated from AH0, = 7352 cal mol-‘, AR,,, = 7160 cal mol-‘. This mixture is located in Fig. 6 in the region D below the line R2 = 0.25 and therefore forms an azeotrope.

COMPOSITION

Xl

ETHANOL

Fig. 9. Phase equilibrium ethanol-water, p = 1.013bar.

COMPOSITION

Xl

BENZENE

Fig. 10. Phase equilibrium benzene-cyclohexane, p = 1.013bar.

218 LIST OF SYMBOLS

: Al2 b,

A21 c,

d

$X1)

AHOi K n P 90% 91, ro,

rl,

q2

r2

R

Rl, R2 Asoi T Ai;;bj X Yi

constant Porter parameter Wilson parameters constants function to describe the difference of activity coefficients molar excess Gibbs energy molar enthalpy of vaporization of pure component i constant defined by K = ( A~o,/A~o,)( T,,/T,,) number of components pressure constants constants gas constant constants molar entropy of vaporization of pure component i temperature, K molar volume change of vaporization of pure component mole fraction activity coefficient in the liquid phase of component i

i

Subscripts

0” i,j,

1, 2

P k

infinite dilution pure component components constant pressure saturated state constant temperature

Superscripts ,

I/ max min

saturated liquid phase saturated vapour phase maximum value minimum value

REFERENCES Denyer, R.L., Fidler, F.A. and Lowry, R-A., 1949. Azeotrope formation between thiols and hydrocarbons. Ind. Eng. Chem., 41: 2727. Eduljee, G.H. and Tiwari, K.K., 1976. Correlation of azeotrope data. Chem. Eng. Sci., 31: 535.

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