Binary Azeotropic Systems EFFECT OF TEMPERATURE ON COMPOSITION AND PRESSURE JOSEPH JOFFE N e w a r k College of Engineering, N e w a r k , N . J .
T
H E R E exist in the literature data on azeotropic compositions of a large number of systems at a single pressure, usually atmospheric (3, I S ) . However, relatively few azeotropic compositions have been determined experimentally a t more than one pressure. Accordingly, methods for predicting azeotropic compositions a t pressures for which there are not experimental data, using data at only one pressure, are of considerable interest. Several such methods have been proposed. Among them is a method devised by Horsley ( d ) , derived from some earlier studies of Lecat (6) on azeotropic boiling points of related groups of binary systems, which involves the use of a set of charts based on data for specific classes of compounds. Another method proposed by Othmer and Ten Eyck ( I O ) is based on the integrated Clausius-Clapeyron equation and is preferably applied when data are available a t more than one pressure. Other proposed methods involve integrated forms of the GibbsDuhem equation. The simplest approach has been to assume that the activity coefficients of the components of the azeotropic system may be represented by the symmetrical two-suffix Margules equations. Based on these equations, it may be shown that ( 8 , 6,1 8 )
where 21 is the mole fraction of component 1 in the azeotrope, Pi and Pz are the vapor pressures of the pure components at the azeotropic boiling point, and P is the total pressure a t the azeotropic boiling point. Coulson and Herington further assumed that the Margules constant, A , varies inversely with the absolute temperature, T , and derived the relationship ( 2 ) (2x2
- 1)/(22i -
1) =
T log ( P l l P l ) T' log
(Pl/Pl)
where the primed quantities refer to the azeotropic composition and boiling point a t one pressure and the unprimed quantities refer to the azeotropic composition and boiling point a t another pressure. With the aid of Equation 2 Coulson and Herington have calcul,ated, based on experimental data a t atmospheric pressure, the azeotropic compositions in the ethyl acetate -ethyl alcohol system a t a series of temperatures and have found that the agreement with experimental values is of the same order of accuracy as that obtained by Carlson and Colburn, who employed a somewhat more complicated method of calculation ( 1 ) . However, comparatively few systems are satisfactorily represented by the symmetrical Margules equations, so that the use of Equations l and 2 is recommended (16)only where the azeotropic composition has not been determined a t any pressure ( I S ) . Gilliland has proposed that the two-constant Margules equations be used for predicting the effect of temperature and pressure on azeotropic composition (16). He has suggested that the Margules constants be assumed as inversely proportional to the onefourth power of the absolute temperature and has illustrated the method by applying it to the calculation of the pressure-compo-
sition relationship of the ethyl alcohol-water azeotrope. equations employed by Gilliland are: 2'1'4
log ( P / P l ) =
T1'4log ( P / P z ) T"' log (Pl/Pz) = b(221
2:
-
Z:
(b 1)
(b
+
CZZ)
+ czz + 0 . 5 ~ ) - C(1
- 321 f 1.52:)
The
(3)
(4) (5)
In Gilliland's method azeotropic data a t one temperature are employed to find constants b and c by simultaneous solution of Equations 3 and 4. These constants and the vapor pressure values a t another temperature are then substituted into Equation 5 , a quadratic equation in the composition, and Equation 5 is solved for the azeotropic composition. The total pressure a t the new temperature may then be calculated from either Equation 3 or Equation 4. Examination of the vapor-liquid equilibria of a large number of binary s y s t e m has revealed that in most cases the two-constant van Laar equations fit experimental activity coefficient data somewhat better than the two-constant Margules equations. One would therefore surmise that a method analogous to that of Gilliland, but based on the van Laar instead of the Margules equations, should yield better results. Carlson and Colburn have presented a graphical procedure ( 1 ) in which the van Laar constants are calculated from the known azeotropic composition a t a given temperature and pressure. With the aid of the van Laar equations the activity coefficient ratio is then calculated for several compositions and plotted against composition. Carlson and Colburn assume that the ratio of the activity coefficients is independent of the temperature, which is consistent with the assumption that the van Laar constants are independent of the temperature. Carlson and Colburn also plot the inverse ratio of the vapor pressures of the pure components against temperature. The azeotropic composition at any given temperature is found as the composition for which the activity coefficient ratio is equal to the inverse ratio of the vapor pressures. The method of Carlson and Colburn has the disadvantage of requiring a graphical construction, which makes it unduly lengthy when a single azeotropic composition is to be found. Moreover, Carlson and Colburn have themselves pointed out that
IF DISTILLATION I S YOUR PROBLEM you will be interested in this method for extrapolating to other pressures binary azeotropic data available for one pressure only 2533
INDUSTRIAL AND ENGINEERING CHEMISTRY
2534
systems of organic liquids tend to become more ideal as the temperature is raised. Hence, it would be logical to assume, a t least for mixtures of organic liquids, that the van Laar constants vary inversely as some power of the absolute temperature, rather than to consider them independent of temperature, as in the Carlson and Colburn plots.
I n the present study an algebraic method has been developed, based on the van Laar equations, which makes it possible to calculate azeotropic compositions as in Carlson and Colburn's graphical method, but which is not restricted to the aasumption of constant values for the van Laar constants. The required equations are derived as follows: It is convenient to start with a modified form of the van Laar equations, =
Ax: ~($21
+x 2 y
and
(T/To)" log
Bx: B
yz =
+
(xl
(7) XI>"
where 2' is the absolute temperature corresponding to the azeotropic composition, m , and To is a reference temperature at which the azeotropic composition is known. The activity coefficients, y1 and y2, and the mole fractions, x1 and z2, refer t o components 1 and 2, respectively. The van Laar equations employed by White ( 1 9 ) follow from Equations 6 and 7 if it is assumed that n = 1. On the other hand, Carlson and Colburn ( 1 ) have assumed n = 0. By analogy with Gilliland's treatment of the Margules equations ( 1 6 ) one could assume n = 0.25 in Equations 6 and 7. Subtracting Equation 6 from Equation 7, there is obtained:
(T/To)" log ( Y P / Y I ) = A B ( A 2 :
pure components a t temperature T into Equation 14. Some assumption must be made regarding the numerical value of exponent n. The pressure, P, of the azeotrope at temperature T may be found from the relations log
= AT,
+
- B z ~ ) / ( A x I Bzz)*
+ BZZ
DISCUSSION OF PROPOSED METHOD
The method developed in this paper has been tested for five systems for which azeotropic data are available over a range of temperatures and pressures. I n each case the azeotropic data a t atmospheric pressure or some pressure reasonably close to atmospheric were assumed to be given. The activity coefficients a t the azeotropic point were obtained from the relations, y1 = P / P l and y~ = P/P2, which involve the assumption of ideal gas laws for the vapor phase. The van Laar constants were found from these activity coefficient values with the aid of Equations 19 and 20 of ( I ) , and Equations 14,10, 15, and 16 were then used to calculate the azeotropic compositions and pressures a t all the other azeotropic boiling points for which experimental data were available. In order to reduce the effect on the calculations of errors in pressure-temperature measurements, where possible, vapor pressure data for the pure components were taken from the same source as azeotropic data, The results of these calculations are shown in Tables I to V. Three of the systems, methanol-benzene, carbon tetrachlorideethyl acetate, and ethyl alcohol-ethyl acetate, are mixtures of organic liquids, which should tend to become more ideal with rise in temperature. Hence, in these three cases exponent n in Equations 14 and 15 was assumed equal to 1. This is equivalent to employing the White form (19) of the van Laar equations. I n the case of two systems in which one of the components is
Table I.
(9)
Effect of Pressure on Methanol-Benzene Azeotrope
Observed (4) Mole fraction P, methanol, mm. H g 51
Total
(R
- B)/(=l - B )
Temp., t, "C.
(10)
= 1
-
( A - R)/(A- B)
200 400
124 149
6000 11000
t,
Moreover, at the azeotropic boiling point, log (PIIP2)
P 204 413
0.570 0.590
siio
o:iio
11080
XI
0.758
P 212 440
0.539 0.558
6810 12430
0.673
...
31
0:65i
Table 11. Effect of Pressure on Carbon TetrachlorideEthyl Acetate Azeotrope
Temp.,
=
.
7fin "-
0.557 0.575 n - . fiiq --" 0.748 0.807
Calculated Gilliland's Method
Proposed Method
(11)
Substituting Equations 10 and 11 into Equation 8, it follows that
log ( Y d Y l )
pressure,
26 42 57 -.
and ~2
(16)
(8)
and there are obtained the relations, XI
(15)
= (To/T)"BA'x:/R'
P = Y2P2
To eliminate 21 and 2 2 from Equation 8, let
R
y2
and
PROPOSED METHOD
(T/To)" log Yl
Vol. 47, No. 12
(13)
where PI and Pz are the vapor pressures of the pure components. Combining Equations 12 and 13, there follows:
Calculations are carried out by first determining the van Laar constants from the known azeotropic composition a t the temperature T = To ( 1 ) . The azeotropic composition at any other temperature T is then found with the aid of Equations 14 and 10 by substituting the values of vapor pressures PI and P2 of the
' C.
76.15 66.72 61.32 55.22 47.36
Observed ( 1 7 ) Total Mole pressure, fraction P, CClr, mm. Hg 21
789 584 484 385 286
Table 111.
Tepp., t, C. 0.00
38.42 60.62 71.81 79.68 91.86
0.556 0.608 0.638 0.678 0.726
P
Gilliland's Method
XI
574 475 381 287
0:597 0.612 0.655 0,717
P' 574 474 380 286
XI
O:k97 0.617 0.658 0.726
Effect o f Pressure on Ethyl AlcoholEthyl Acetate Azeotrope
Observed (7) . Total Mole pressure, fraotion P ethyl mm.'Hg alcohol, XI
27 200 500 760 1000 1500
Calculated Proposed Method
0.221 0.331 0.417 0.462 0,495 0.554
Proposed Method P
Calculated Gilliland's Method
51
25 193 496
0.185 0.328 0.419
1009 1526
0:491 0,537
...
P 24 190 493
...
1013 1540
51
0.121 0.314 0.417 0:492
0.53G
Effect of Pressure on Water-Ethyl Acetate Azeotrope
Table IV.
Obserl-ed (7) Temp., t, OC.
90.30 78.17 70,37 64,06 37,s 0.00
Total pressure, P mm.’Hg
I500 1000 760 600 200 28
Table V.
Calculated
Mole fraction water, XI
0.354 0.328 0.310 0.296 0.231 0.157
Gillilrtnd’s Proposed
.P
Method
1634 1007 ... 597 192 26
Method
21
P
51
0.345 0.321
1518 1007
0.341
0.322
0.244 0.161
598 194 26
0:ZiQ 0.253 0.180
Effect of Pressure on Water-Ethyl Alcohol
95.35 87.12 78.15 63.04 47.63 39.20 33,35
Observed (7) Total Mole pressure, fraction F, water, mm. Hg Xi
1451 1075 760 405 198 1.30
95
Table VI.
0.113 0,111 0.105
0.091 0.066 0.033 0.013
Calculated Proposed Method
Gilliland’s Method
P
P
21
3452 1075 ... 405 198 130 95
0.126 0.116
1450 1074
0.117
0:084
405 199 130 95
O:Oi3 0.079 0.073 0.069
0.059 0.046 0.039
..
51
0.112
Effect of Pressure on WaterEthyl Alcohol Azeotrope
Temp., t,
C.
9.5.35 87.12 78.15 63.04 47 63 39 20
33.35
Observed ( 7 ) Total hl ole pressure, fraction P, water, mni. Hg Xi
1451 1075 760 405 198 130 95
0.113 0.111 0.105 0.091 0.066
0.033 0.013
~
A
constants with temperature has been discussed by Mertes and Colburn (8),by Yu and Coull (do), and by Nord (9). Given experimental data on the azeotropic composition a t more than one pressure, the relation between the van Laar constants and the temperature may be expressed by means of the equations
A = (u/T)
+b
(17)
B
+d
(18)
and
, . .
0:298
Azeotrope
Temp., t , C.
2535
INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1955
Calculated Total Mole pressure, ~ s fraction ~ P, water, B mm. Hg zi
~
1.042 0.391 0.399 0.934 (0.407) (0.813) 0.423 0.590 0.440 0.344 (0.460) (0,199) 0.094 0.458
1448 1073 ..,
405 199 ... 95
0.123 0.115
:
0 083 0.054
o:Ois
water--namely, the rrater-ethyl acetate and water-ethyl alcohol systems-exponent n in Equations 14 and 15 was taken as zero. This is equivalent to employing the Carlson and Colburn form of the van Laar equations ( 1 ) . As pointed out by Carlson and Colburn ( I ) , the variation of the van Laar constants with temperature is not so simple for aqueous solutions as for mixtures of organic liquids. Tables I to V also show results calculated by Gilliland’s method (Equations 3, 4, and 5), in which the absolute temperature appears to the 0.25 power. On comparing the two sets of results, it is found that four out of the five systems are better correlated by the proposed method than by Gilliland’s method. The average deviation from experimental values of the 24 calculated mole fractions in the five systems is 0.014 by the proposed method and 0.027 by Gilliland’s method, indicating somewhat better accuracy for the proposed method. Moreover, the proposed method is more rapid than Gilliland’s procedure, which requires the solution of a quadratic equation (Equation 5). LIMITATIONS O F PROPOSED METHOD
The procedure presented in this paper is suggested for use in cases where the azeotropic composition is known a t only one pressure and temperature and it is desired to extrapolate the result to other pressures and temperatures. The assumptions used in this paper, that the van Laar constants are independent of temperature for aqueous solutions and are simple inverse functions of the absolute temperature for mixtures of organic liquids, are known t o be approximations, but are useful in the absence of experimental data. The variation of van Laar
=
(c/T)
With the aid of these relations and Equations 14 and 15 ( n would be taken aa zero) it is possible to extrapolate and interpolate for azeotropic composition as in the proposed method but with increased accuracy. Such calculations for the water-ethyl alcohol azeotrope based on data a t two pressures are shown in Table VI. It is seen by comparing Tables V and VI that azeotropic compositions in the water-ethyl alcohol system can be predicted with somewhat better consistency when the van Laar constants are calculated with Equations 17 and 18. However, there is evidence that the van Laar constants in the water-ethyl alcohol system should be correlated by different equations in the two pressure ranges above and below atmospheric (11,20). I n the case of heterogeneous systems, such as ethyl acetatewater, it is possible to use liquid-liquid solubility data instead of azeotropic compositions to evaluate the van Laar constants of Equations 6 and 7 ( 1 ) . When either solubility or azeotropic composition data a t two different temperatures and pressures are available, ~ ~ it is &possible to calculate an empirical value for n in Equations 6 and 7 so as to fit the data. This value of n may then be used in conjunction with Equations 14 and 15 to predict the azeotropic composition a t other temperatures and pressures This procedure may be used as an alternative to applying Equations 17 and 18, although with less theoretical justification. Several other methods involving less computation than the van Laar equations are available for calculation of azeotropic compositions from data a t more than one pressure (10, 12, 14, 18). LITERATURE CITED
(1) Carlson, H. C., and Colburn, A. P., IND.ENG.CHEM.,34, 581 (1942). (2) Coulson, E. A., and Herington, E. F. G., J. Chem. SOC.,1947, p. 597. (3) Horsley, L. H., Advances in Chem. Series, No. 6 (1952). (4) Horsley, L. H., Anal. Chem., 19, 603 (1947). (5) Kireev, V. A., Acta Physiochim., U.S.S.R., 14, 371 (1941). (6) Lecat, M., Ann. SOC. sci. Bruxelles, 55B,43 (1935). (7) hlerriman, R. W., J . Chem. SOC.,103, 628, 1790, 1801 (1913). (8) Mertes, T. S., and Colburn, A. P., IND.ENG.CHEM.,39, 787 (1947). (9) h-ord, M., Chem. Eng. Progr. Symposium Ser., 48, Pio. 3, 55 (1952). (10) Othmer, D. F., and Ten Eyck, E. H., Jr., IND. EXG.CHEM.,41, 2897 (1949). (11) Otsuki, H., and Williams, F. C., Chem. Eng. Progr. Symposium Ser., 49, No. 6, 55 (1953). (12) Pennington, W. A., IKD. ENG.CHEM.,44, 2397 (1952). (13) Perry, J. H., “Chemical Engineers’ Handbook,” 3rd ed., pp. 631, 633-43, McGraw-Hill, New York, 1950. (14) Pribush, A., M.S. in Ch.E. thesis, Newark College of Engineering, 1954. (15) Redlich, O., J . Chem. SOC.,1948, p. 1987. (16) Robinson, C. S., and Gilliland, E. R., “Elements of Fractional Distillation,” 4th ed., pp. 204-5, McGraw-Hill, New York, 1950. (17) Schutz, P. W., and Mallonee, R. E., J . Am. Chem. SOC.,62,1491 (1940). (18) Skolnik, H., IND.ENG.CHEM.,43, 172 (1951). (19) White, R. R., Trans. Am. Inst. Chem. Engrs., 41, 539 (1915). (20) Yu, K. T., and Coull, J., Chem. Eng. Progr. Symposium Ser., 48, KO.2, 38 (1952). RECETVED for review February 9, 1955.
ACCEPTED August 15, 1955.
