Correlation of azeotrope data

Chemicd Engineering Science, 1976, Vol. 31, pp. 535-540.

Pergamon Pres.

CORRELATION

Printed in Gmt Britain

OF AZEOTROPE

DATA

G. H. EDULJEEt and K. K. TIWARI Department of Chemical Technology, University of Bombay, MatungaRoad, Matunga, Bombay 400019,India (Receiued 14April 1975;accepted 29January 1976) Abstract-Yoshimoto’s correlation of azeotropic composition and boiling point has been extended to include a wide variety of mixtures on the basis of a classification which groups organic liquids according to their hydrogen bonding characteristics. The correlation highlights several features of mixture interaction and indicates the temperature span within which azeotrope formation is possible. The average standard deviation in prediction of azeotropic composition and boiling point from pure component boiling points for fourteen group combinations was 0.17and 0.03 respectively.

1.INTRODUCTION

The occurrence of constant-boiling mixtures in distillation has made the subject of azeotropy one of great importante. A number of workers have derived semiempirical relations to correlate azeotropy with the thermodynamic properties of solutions. SkolNk [ l] obtained a logarithmic relation for azeotropes involving an azeotropic agent with members of a homologous series, confining himself to hydrocarbon-hydrocarbon and alcohol-hydrocarbon solutions. Mair et al. [2] and Rossini et a1.[3] also restricted their treatment to hydrocarbon azeotropes. Meissner and Greenfield[4] presented a relation for predicting the composition and boiling temperature of azeotropes formed between a hydrocarbon or halohydrocarbon and an aldehyde, alcohol, ester, ketone or phenol. Johnson and Madonis [5] extended the MeissnerGreenfìeld correlations to include other combinations of organic liquids. The above methods do not yield much information on the theoretical aspects of azeotropy, and the equations derived are specific and complicated. Yoshimoto[6-91 analysed various aspects of azeotrope formation on theoretical considerations. In the present work Yoshimoto’s equations, which were initially proposed to correlate azeotropes formed between a fixed azeotrope agent and members of a homologous series, have been extended to include a wide variety of mixtures on the basis of the classification of Ewell et al.[lO]: this classification was also used by Johnson and Madonis [5] to extend the Meissner-Greenfield correlation. 2.THEORRTICAL CONSIDRRATIONS

Yoshimoto’s assumption is that an azeotrope mixture can be regarded as a strictly regular solution at its boiling point, thus making it amenable to Guggenheim’s quasicrystalline model [111,introducing an explicit representation for the interaction energy of the component molecules. Under isobaric conditions the following

equations are derived at azeotropic temperature T, “K [6] S,(T1- Ta) = Wx?

(1)

Sz(Tz - Ta) = wx,2.

(2)

The molecular interchange parameter W can be explicitly represented as Nz

w = -(EI, 2

+ EX- 2E12).

(3)

The azeotropic composition x2 is obtained by eliminating T, between eqns (1) and (2) and expanding into a convergent power series. Neglecting the third and higher order terms, x2 = xmls2) sz-SI

-

SI + x4SIS2) y(T1-

í-2).

(4)

Combining eqns (1) and (4), the azeotropic temperature T. is given by

In eqns (4) and (5), component 2 is chosen such that it has a larger entropy of vapourisation than component 1. Ewell et al.[lO] have pointed out that the most important single cause of deviation from ideal behaviour in liquid mixtures is hydrogen bonding. They have classified liquids into five groups according to their hydrogen bonding capabilities and have qualitatively predicted the deviation from Raoult’s law in a mixture. Table 1 summarises their classification. The mixtures discussed by Yoshimoto fa11into Classes 11-11,11-V, V-V and 111-IV. 3.CORRRLATIONOFAZROTROPICCOMPOSITlON

iPresent address, Department of Chemical Engineering, University of Birmingham, Birmingham Bl5 2TT, U.K.

Equation composition

(4) permits the prediction of azeotropic XZfrom pure component boiling points TI

G. H. EDULJEE and K. K. TIWARI

536

Table 1. Classification of organic liquids according to hydrogen bonding potentiality and deviation from Raoult’s law*

IV

V

oD1y

activa

I 8

NO bod

I

N .tOl

Ba1q.mdt.d hydmcubaw cai*C1*,at*aKIZ.*Le.

lik.

QLclJ.

I

I

I

Iplp

fordmg

capabilitfes

and Tz. A plot of (TI - TZ)against x2 for related systems should yield a straight line with slape (d(SS2)/2 W) and intercept (d - SI/& - SI). This would strictly be true for a particular class combination if the Si’s and SZ’Swere approximately the same for al1 liquid pairs (SZ not necessarily equal to SI), and if W was approximately the same in al1 cases. However, the form of eqn (4) is such that the intercept and the quantity (v’(S&)/2) in the slope remain within 210% of a mean value even when (St-SI) differs considerably, as in combinations of Class 11liquids with other groups. For example, in Class 11-V for benzene( l)nitromethane(2) SI = 20.8, SZ= 22.1, intercept = 0.492 and (~(S&)/Z) = 10.72; while for toluene(ltethanol(2), S1 = 20.8, SZ= 26.8, intercept = 0.468 and (d(S,&)/Z) = 11.81. These are wel1 within *lO% of average values of 0.465 for intercept and ll.27 for (v(S&)/2). Formic acid azeotropes of Class 11-V could also be represented by eqn (4) but were treated separately as the slope and intercept differed appreciably from those of the other azeotropes in this class combination. Liquids within Classes 111,IV and V have closely grouped S values and therefore combinations of these classes should conform to eqn (4). When SI = SZ eqn (4) reduces to: x,=;

l+$(T,-Tz)

1.

Equation (4) was applied to al1 of Ewell’s classes for which azeotropic data were available. The main source was Horsley’s compilation[l2]. Thiol-hydrocarbon data were taken from Denyer et al. [3] and Desty and Fidler [4]. Data for Class 1-1 were not available. Figures l(a)-(d) are a selection of the fourteen plots made [ 161.Scatter was most pronounced in Class 111-111,while in Class 1-11the data lay along a curve. Since the effect of the third term in eqn (4) was found to be negligible, it was concluded that Yoshimoto’s equations did not apply to this class. Linear relationships were obtained in al1 other cases, indicating that Yoshimoto’s equations could be extended on the basis of Ewell’s classification and that a single value of the

molecular interchange parameter W could be assigned to each class combination. Johnson and Madonis[5], while applying the MeissnerGreenfield correlation to Classes 11-IV and 11-V, observed that acid-hydrocarbon and acid-halohydrocarbon azeotropes could not be correlated with the remaining azeotropes of these classes. Barring formic acid azeotropes of Class 11-V, these azeotropes could be correlated by Yoshimoto’s plot with the rest of the class. Care has to be exercised in designating components 1 and 2 on the basis of their entropy values. To ascertain whether the intercept of eqn (4) as calculated from entropy data alone would be that through which the best-fit line passes, the intercept of al1 the classes plotted were calculated. For this purpose, a few representative azeotropic mixtures of each class were considered, the intercept calculated, and the average value taken as representing the whole class. Also computed was the quantity (q(SrS2)/2) in the slape, W being unknown. The calculations are detailed in Ref. [16]. An interesting feature was that the value of the intercept was within ~0.03 of 0.48 for al1classes. A line which best represented the data was drawn through a common intercept of 0.49 except for classes 11-IV and 11-V, where a value of 0.46 was used. As can be seen from the selection presented in Figs. l(a)-(d), excellent fitting was obtained. Class 1-11was not considered since eqn (4) was not obeyed. Greatest weight was placed on points within the range 0.05 < XZ< 0.95. Values of W calculated from the slope of each line are presented in Table 2. Their magnitudes can be interpreted in terms of the potential energies eii in eqn (3) and highlight several features of mixture interaction. Referring to Table 2, it can be seen that W decreases as the transition from mixtures with dissimilar molecules to those with similar molecules progresses. For example, the extent of nonideality in Class 1-V is much more pronounced than in Class V-V. This is supported by the fact that azeotropes of water with a nonpolar compound show very high activity coefficient characteristics rising as high as 60 in some cases, whereas those of nonpolar-

0.9 -

08

-

07-

06-

0.6 -

0.5 c

04-

03-

1 _. - 80

-60

I

I -40

I

I

l

-20

0

I

I 20

40

I

I 60

130

.'K

T, - T,

T,-

'K

T,.

(b)

(al

1.0 r

09

-

0.8 -

t 0.71

07-

0.61 0.6 $ 05-

0.4 -

0.3-

0.2 -

0.10 o-, -40

1 -30

1

-20

1 -10

,

I 0

, 10

I

l 20

, 30

I 40

T,-

?& ‘K (d)

Fig. 1. Plots of eqn (4). (a) Class I-V; (b) Class11-V(acid azeotropes;x = formic acid); (c) Class11-IV; (d) Class 1-111.

nonpolar mixtures rarely exceed 3. For dispersion force solutions (Class V-V) there is little interaction between the molecules, and W >O. In Class UI-IV where donor and acceptor molecules form addition compounds, E,~sE~~, EB giving W EII, giving W > 0 where component 1 is nonpolar. However, in solutions involving association in polar solvents, eZ2> elz> el1 but (eZ2- Q) > ICU- ~~~1.While W stil1 remains positive, its magnitude is not as large as in the case of polar-nonpolar solutions. This is bome out by the results for Classes 11-V and 11-11.The relative abundance of minimum azeotropes is also apparent. Of the fourteen W values obtained from various combinations of liquids,

only one is negative. The literature reports over 3000 minimum azeotropes and about 250 maximum azeotropes [121. 4.

CORRELATION OF AZEOTROPIC TEMPERATURE

According to eqn (5) a linear relationship exists between (TI - Tz) and d( Tl - 2). This was confirmed for al1 classes save Class 1-11. Figures 2(a)-(d) are a selection of the plots made. As in the case of azeotropic composition, formic acid azeotropes of Class 11-V could not be correlated with the rest of the Class. The slope and intercept of eqn (5) for the various classes were evaluated from the data in Table 2 and are presented in Table 3.

G.

538

H. EDUIJEEand K. K. TIWARI

a-

6Y

-

:*

5-

I

-

+-r 4=i 3-

0

01,

,

-60

-40

1 -60

,

I -40

,

,

,

,

-20

,

I -20

,

,

0

,

I 0

,

/

1

,

20

T,- T,.

,

40

20

/

,

40 ‘K

I

60

,

,

60

,

60

1

80

,

(

100

(dl

Fig. 2. Plots of eqn (5). (a) Class I-V; (b) Class 11-V(excluding acids); (c) Class 11-IV;(d) Class 1-111. Figures 2(a)-(d) show that the theoretical line provided a good fit to the data. On an average, the scatter of points encountered in the plot of eqn (5) was less than that observed in the plot of eqn (4). This could be due to the fact that azeotropic temperatures are generally more reliable than azeotropic compositions[l5]. Members of Class 11-IV formed maximum azeotropes, making eqn (5) in its present form inapplicable, since v[(T1 - T.)] was negative. The signs of the equation were therefore reversed and q[( 7” - Tl)] plotted against ( TZ- TI).

5. PRRDICTIONOF AZEOTROPIC COMPOSITION AND TRMPERATURR

A statistical evaluation of the predictive accuracy of eqns (4) and (5) was carried out. For this purpose the

azeotropic temperature and composition for each point plotted was calculated from these equations using the slopes and intercepts in Tables 2 and 3. The ratio [XZ(calculated)]/[x2 (observed)] = y was computed. The standard deviation was given by the formula

(6) where 7 = average y value and n is the number of data points. Standard deviations obtained in this manner are reported in Table 4, together with y values. The accuracy in predicting azeotropic temperature is greater than that of azeotropic composition.

539

Correlationof azeotropedata Table3. Slopeand interceptof eqn (5) for various classes

Table 2. Slape and intercept of eqn (4) and values of W for various classes

-ClS8

1-v 11-va x1-P

m2

ChEm

m2-61

zw

1915

0.49

0.006

0.46

0.012

0.007 0.018

0.49

585

0.019

0.49

545

1-v

0.058

4.74

II-v=

0.079

3.02

11-P

0.050

4.31

111-v

0.096

2.62

IV-v

0.098

2.52

v-v

0.135

1.04

1-IV

0.065

4.53

288

0.49

0.036

1-IV

0.007

0.49

1745

11-IV

0.012

0.46

925

x1-N

0.080

3.06

-0.124

2.33

IV-IV

0.192

1.30

I-III

0.069

4.20

1x-111

0.091

2.62

III-III

0.176

1.44

0.099

3.05

111-IV

IV-N I-III 11-111 III-III

2w

1237

0.33

IV-v

111-IV

+.e&

08.5

111-v

v-v

/

w,ca1s/mo1e

s2-sl

-0.026

0.49

-460

0.072

0.49

144

0.49

0.000

1565 670

0.49

0.017

0.49

0.060

190 1-11

1-11 11-11

1x-11

0.49

0.016

760 I-I

1-X

%xcluding fotio acid azeptroper b fo+mic acid azeotropes

b formic acid azootropes

Table4. Standarddeviationsin predictionof azeotropicparametersfor variousclasses -Cla

T

n 0 --

T-V

37

0.997

11-v

0.25

l.ooo

126

1.026

0.16

111-v N-V

1.019

45

1.062

0.30

1.009

5

0.953

0.11

l.OW

v-v

112

1.012

0.16

1.007

1-N

6

0.992

0.03

l.cOo

4b

1.051

0.19

1.005

15

1.009

0.18

1.003

11-IV III-N

3

1.055

0.36

1.001

1-111

50

1.006

0.18

0.996

11-111

45

1.017

0.12

0.999

10

1.069

0.14

1.012

1.011

0.07

1.001

N-N

111-111 1-11

24

TI-11

10

ó.AZROTROPIC RANGE

The azeotropic range is the maximum pure-component boiling point differente within which azeotrope formation is possible. For the formation of an azeotrope, XZshould lie between 0 and 1.0 and the condition for azeotrope existente as obtained from eqns (1) and (2) is

The upper and lower limits would be influenced primarily

by the magnitude of W. The larger the value of W, the greater the boiling point differente over which azeotrope formation is possible. Equation (7) was applied to al1 the classes studied using W values from Table 2. The results are presented in Table 5. For Class I-III the farthest point plotted was at (T, - T2)= 100°K (see Fig. ld) and for Class 11-11,37”K:these differ appreciably from the upper limit as calculated from eqn (7). A comparison of Figs. l(d) and 2(d) shows that the value of W cannot be improved for Class I-III since an optimum fit of eqn (5) was obtained using W = 1565, as seen in Fig. 2(d).

G. H. EDUWEEand K. K. TIWARI

540

Table 5. Azeotropic range for various classes. Lower limit (L.L.) = - W/S, from eqn (7); Upper limit (U.L.) = WIS, from eqn (7) L.I.,

OC

%

O.L.,

1-V

-71

1x-v

-31

43

11x-v

-21

28

Iv-v

93

-36

17

v-v

-14

14

1-IV

-68

80

SI-N

111-Iv N-N

NOTATION fi

number of data points N Avogadro’s number S molar entropy of vaourisation, cals/mole “K T absolute temperature, “K W interaction parameter, cals/mole azeotropic composition, mole fraction x2 Y the ratio x2(calculated)lx2(observed) Y average y value Z coordination number Greek s ym bals Eij potential energy of an i-j pair g standard deviation

-37 -21 -7

1-111

-60

11-111

-29

11x-111

-9

9

-29

29

Subscripts

1,2 refer to components a

1 and 2 refers to the azeotropic point

1-11 II-II

7. CONCLUSIONS c .* Yoshimoto’s equations have been successruuy extended to include a wide variety of azeotropic mixtures. As a predictive method, the equations are more generalised than those of Skolnik or Meissner and Greenfield. For this purpose, the components are first classified, arranged in order of increasing entropy values and the azeotropic parameters calculated from eqns (4) and (5) using the slopes and intercepts recorded in Tables 2 and 3. As with the other methods, Yoshimoto’s equations erroneously predict azeotropic behaviour in some cases. For instance, the system methanol-ethanol has a boiling point differente of 15°K and according to Table 5 falls within the region of azeotrope formation for Class II-II. However, the generality of these equations would inevitably produce some anomalies and would not be considered a drawback in their practica1 application.

REFERRNCES

[l] Skolnik H., Ind. Engng Chem. 194840 442. [2] Mair B. J., Glasgow A. R. and Rossini F. D., J. Res. Nat. Bur. Standards 194121 39. [3] Rossini F. D., Mair B. J. and Streiff A. J., Hydrocarbonsfrom Petroleum. Reinhold, New York 1952. [4] Meissner H. P. and Greenfield S. H., Ind. Engng Chem. 1948 40 438. [5] Johnson A. 1. and Madonis J. A., Can. 3. Chem. Engng 1959 3171. [6] Yoshimoto T. and Mashiko Y., Bulf. Chem. Sec. Japan 1956 29 990. [7] Yoshimoto T. and Mashiko Y., Bull. Chem. Sec. Japan 1957 30 56. [8] Yoshimoto T., Bul/. Chem. Sec. Japan 195730 505. [9] Yoshimoto T., Nippon Kagaku Zasshi 196182 530. [lO] Ewell R. H., Harrison J. M. and Berg L., Ind. Engng Chem. 1944 36 871.

[ll] Guggenheim E. A., Mixtures. Oxford 1952. 1121Horsley L. H., Azeotroaic Data. American Chemical Society, Vol. 1-1952, Vol. 2 1952. [13] Denyer R. L., Fidler F. A. and Lowry R. A., Ind. Engng Chem. 194941 2727. [14] Desty D. H. and Fidler F. A., Ind. Engng Chem. 195143 905. [15] Lessells G. A. and Corrigan T. E., Ind. Engng Chem. Data 19583 43. [16] Eduljee G. H., M.Sc. Thesis, Univeristy of Bombay, 1973.