Vapor-Liquid Equilibria Data for Ternary Mixtures METHYL ETHYL KETONE-n-HEPTANE-TOLUENE
SYSTEM
HARRY H. STEINHBUSER' AND ROBERT R. WHITE University of Michigan, Ann Arbor, iMich.
vapor-liquid equilibrium data for the system methyl ethyl ketone-n-heptane-toluene a t 1 atmosphere pressure are presented. A method of determining thermodynamic consistency of the data from the Gibbs-Duhem equation
is presented and illustrated. The data are consistent to *0.002 mole fraction and *0.Zo C. and appear to be accurate to +0.004 mole fraction and * 0 . 2 " C. The data are also correlated empirically.
T
moles), provided gravitational, electrical, surface, capillary, and other effects are absent. Thus ( 7 , l j ) ,
HE development of azeotropic and extractive distillation as an important separation process of chemical industry has stimulated many investigations of the vapor-liquid equilibria of nonideal systems. While a large amount of data have been determined, correlations of such data in a generalized and conveniently usable form has proved to be an exceedingly difficult problem. It has been customary in treating nonideal equilibrium data to fit analytic functions based upon theory to the data. Unfortunately, in many systems such functions require the use of a complicated expression and the determination of many constants so that it is usually more satisfactory simply to plot the large amount of experimental data required to determine the equations on charts relating the vapor and liquid compositions rather than to evaluate the functions. The entire concept of equilibrium makes it impossible to prove whether or not experimental data do in fact represent equilibrium conditions. Reproducibility of the data by different investigators in different types of equipment is strong presumptive evidence of equilibrium but unfortunately such comparisons usually show disagreement rather than agreement between different investigators. This is particularly true in ternary and multicomponent data where the effect of experimental errors may be greatly exaggerated. One test of equilibrium data lies in the application of the GibbsDuheni relation which may be used to evaluate thermodynamic consistency. While thermodynamic consistency of experimental data does not constitute in itself a proof of equilibrium, it does constitute powerful presumptive evidence of equilibrium. IIIcorrect data may be therniodynamically consistent but thermodynamically inconsistent data cannot be correct. Thc possibility of error in e,quilibrium measurements is so large that all curves drawn through experimental data should be therniodynamically consistent even if an analytic correlation of the data is not attempted. This paper illustrates the application of the Gibbs-Duhem equation to nonideal equilibrium data determined experimentally for the ternary system methyl ethyl ketone-n-heptane-toluene and its constituent binary systems. This system was chosen because of its commercial interest in the separation of toluene from other hydrocarbons. GIBBS-DUHERl EQUATION
Since the free energy, F , is an extensive property of the phase and therefore, a homogeneous function of the f i s t degree in nL C n i d E
Present address, Rensselaer Polytechnic Institute, Troy, N. Y.
2912
=
0
(3)
Equation 3 is known as the Gibbs-Duhem equation (19). It is rigorously exact when applied to changes in composition a t constant temperature and pressure, and may be approsimately valid where only the temperature varies over a small range. Where the vapor is an ideal gas
dE
=
- S7bT + R T d I n p i
(4)
At constant temperature and pressure, since pi = P y d ,substituting ( 4 ) the expression for dF, of Equation 4 in Equation 3
Equation 5 constitutes a convenient form of the Gibbs-Duhem relation for testing the thermodynamic consirtency of isothermal and isobaiic vapor-liquid equilibrium data when the vapor phase behaves as an ideal gas. APPARATUS AND EXPERIMENTAL PROCEDURE
The e uilibrium data were obtained in an Othnier-type (18) still for ?he following systems: methyl ethyl ketonclz-heptane, methyl ethyl ketone-toluene, n-heptane-toluene, methyl ethyl ketone-benzene, and methyl ethyl ketone-n-heptane-toluene. A constant pressure of 760 mm. of mercury was maintained throughout all experimental measurements. The pressure was maintained to within ~ 0 . mm. 1 of mercury by using a pressure control system consisting of facilities for passing air through a tube connected through Drierite t o the still, the air escaping under a constant head of water In a reservoir. Temperature was measured by a thermometer easily read to 0.1 C. suspended in the still with its bulb slightly below the liquid surface, The measured temperatures were corrected for the thermometer calibration and superheat (11). The boiling temperatures of the pure components and of the azeotrope wcre observed to change over a long period even though the materials were carefully repurified in a manner identical with previous purifications. Apparently this anomaly was due to a variation of the O
For any homogeneous phase of hr components in stable equilibrium, the free energy, F , is a function of temperature, T,pressure, P, and the mass of each component present, ni (expressed as 1
and a t a given temperature and pressure
December 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY
2913
TABLE 11. EXPERIMENTAL DENSITY AND REFRACTIVE INDEX FOR METHYLETHYLK D T O N E -HEPTANE-TOLUENE ~SYSTEM Mole Ratio, MEK: Toluene
Mole Fraction n-Heptane
Density, d i J
Refractive Index, ny
0
0.0000 0.2500 0.4970 0.7447 1.0000
0.8620 0.8036 0.7556 0.7153 0.6795
1.4939 1 ,4583 1.4298 1.4060 1.3852a
0.2492
0.0000 0,2532 0.4980 0.7447 1.0000
0.8496 0.7921 0.7473 '0.7110 0.6795
1 ,4685 1.4397 1.4179s 1.3997 1,38526
0,5023
0.0000 0.2498 0.5031 0.7475 1 .oooo
0,8352 0.7805 0.7379 0,7056 0.6795
1.43996 1.4200 1I40496 1.3928 1.3852b
0.7445
0.0000 0.2480 0.6000 0.7473 1.0000
0.8189 0.7682 0.7299 0,7012 0.6795
1.4102s 1.3999b 1.3927 1.3879 1 ,3882,
1.0000
0.0000 0.2542 0.4986 Q ,7492 1.0000
0.7992 0.7521 0.7203 61.6962 0.6795
1.3762s 1.3773 I . 3793 I . 3818 1 ,38526
+
MEK
MOL
FRICTION ETHANOL IN LIQUID
Figure 1. Performance of Othmer Still on Ethyl Alcohol-Water System
0
-
Data taken w i t h Othmer still Limits of literature data
radiation effects from the heating coil. Corrections were applied to adjust the boilin points Of the mixtures to correspond to the boiling points of t%e pure components. This correction was always less than 0.2 C. MATERIALS USED
The materials used in this investigation had to be of a high degree of purity. Reagent grade materials were dried and dist,illed before being used.
TABLE I. MATERIALS USED Material
MEK Eastman Kodak reagent grade
Source
Boiling pt., C. Refractive index,
n
ss
Density dZ6 Molecul'ar weight
79.45 1.3763 0.7992 72.104
n-Heptane California Chemical Co.
Toluene Mallinckrodt reagent grade
Baker
98.3
110.62
80.2
1.3852 0.6795 100,198
1.4939 0.8620 92.134
Benzene C.P.
1.4979 0.8737 78.108
during measurements of denho,oool to o.ooo2. T~~~~~~~~~~ sity and refractive index was controlled to 10.05 C. The relation between composition, refractive index, and density for the various systems is shown by the experimental measurements presented in Tables 11,111,and IV. O
PERFORMANCE O F T H E EQUlLlBRlUM STILL
In order to test the accuracy and reliability of the equipment and experimental technique, equilibrium data were determined on the ethyl alcohol-water system and compared with the daQain the literature. This system was chosen because it has been studied more thoroughly than any other vapor-liquid system, and because it is readily analyzed by density measurements. The equilibrium data of several authors ( 1 , 3, 4, 6 , 8, 9, 10, f7) were chosen for comparison. The experimental vapor-liquid equilibrium data and temperature data are compared with the data from the literature in Figure 1 . EXPERIMENTAL DATA
The ethyl alcohol was assumed to be free of impurities except water and no attempt was made to obtain absolutely dry alcohol.
pzl, = 2.8808 log yi = log-' PiXi
PURIFICATION I
The ketone and hydrocarbons were dried by agitating with anhydrous copper sulfate (14, 16) and distilled through an &inch column packed with glass beads. The middle boiling fractions having the following boiling kanges were kept: Boilinog Range, C. Methyl ethyl ketone n-Heptane T o1ue n e Benzene
The experimental vapor-liquid equilibrium measurements are presented in Tables V to IX. The logarithm of the activity coefficients was evaluated from the formula
0.75 < 0.10 0.40 0.15
METHODS O F ANALYSIS
The binary systems methyl ethyl ketone-toluene , methyl ethyl ketone-benzene, n-heptane-benzene were analyzed by measurements of refractive index. The binary system methyl ethyl ketone-n-heptane was analyzed by measurements of density. The ternary system methyl ethyl ketonen-heptane-toluene was analyzed by measurements of both refractive index and density. Densities of the liquid samples were measured t o *0.0001 t o 0.0003 gram per ml. in pycnometers having graduated capillary arms (IS). Refractive indexes were determined by a Zeiss Abbe refractometer. The refractive index measurements were reproducible to
- log p ,
+ log 2!
(6)
Xi
TABLE111. EXPERIMENTAL REFRACTIVE INDEX FOR METHYL ETHYL KETONE-TOLUENE SYSTEM Mole Fraction MEK 0.0000 0.0482 0.0951 0.1536 0.1831 0.2533 0.3078
TABLEIV. Mole Fraction MEK
Refractive Index,
n
as
1.4939 1.4890 1.4844 1.4784 1.4754 1.4679 1.4621
Mole Fraction MEK
Refractive Index,
0.4066 0.5050 0.6029 0.7567 0.8449 1.0000
1.4511 1.4399 1.4281 1.4089 1.3974 1.3763
nV
I
EXPERIMENTAL REFRACTIVEINDEX FOR METHYL SYSTEM ETHYLKETONE-BENZENE Mole
nY
Fraction MEK
Refractive Index, n %5
1.4979 1.4910 1.4871 1.4796 1.4731 1.4664 1.4560
0.4254 0.4576 0.5016 0.6044 0.6717 0.8113 1.0000
1.4452 1.4415 1.4364 1.4239 1.4157 1,3990 1.3763
Refractive Index,
FIG. 4
N-HEPTANE-TOLUENE
SYSTEM
LOG ACTIVITY COEFFICIENT VERSUS
24
I
COMPOSITION
l
l
where p , = vapor pressure of the component ai the equilibrium temperature. The vapor pressures of thr hydrocarbons were calculr~tedfrom the following equations: 2%
!
I
I
I
6.90479 - 1268.586/(216.954
Toluene: log p ,
+ t) = 6.95334 - 1343.943,/(219.377 + t )
Benzene: log p z
=
6.89745
I I
I+.
=
%-Heptane: log p ,
,
;
:,
#
I
1
I
FIG. 3
METHYL ETHYL KETONE-TOLUENE SYSTEM LOO AOTlVlTY OOEFFICIENT VERSUS COMPOSITION
,
.
-
1206.350/(220.237
(7) (8)
4- t ) (9)
The vapor pressure of methyl ethyl ketone up to its boiling point reported in the literature ( 2 0 ) was extrapolated by plotting log p t verw6 1/7'.
.22
.zo
I
,
1 1-
1
,
I
TNERW0CYYbYICALLY CONSISTENT CURVE -_.CONSTANT
DEVIATION CURVE
.I8
- a * : '
1
9
3
1
M O L FRACTION
4
'
0
I
METHYL
8
I
ETHYL
7
' 8
I
I 9
1
KETONE IN LIQUID
Figure 5. Methyl Ethyl Ketone-Benzene System
0
INDUSTRIAL A N D ENGINEERING CHEMISTRY
December 1949
2915
TABLEV. EXPERIMENTAL VAPOR-LIQUID EQUILIBRIA FOR METHYL ETHYL KETONE+-HEPTANE SYSTEM Equilibrium Temp.,
Run NO.
0
0
10 11
12 13 14
l59 16 8
P
7 6 17 5 4 3 2 1
'
0
c.
98.3 96.1 93.7 89.4 86.4 82.25 79.95 80.05 78.35 78.2 77.45 77.0 77.15 77.0 77.25 78.1 78.70 79.05 79.45
Liquid Comp., Mole Fraction MEK 0.000
0.0033 0.027 0.074 0,122 0.230 0.354 0.369 0.475 0.507 0.6115 0.693 0.706 0.765 0.864 0.932 0.973 0.994 1.000
Vapor Comp Mol;' Fraction MEK
Activity Coefficients log Y,W log Y H
0.000
0.060 0.141 0.285 0.3755 0.495 0.572 0.578 0.632 0.645 0.691 0.727 0.736 0.7685 0.832 0.908 0.954 0.987
1.0636 0.5476 0.4613 0.3976 0.2949 0.2015 0.1866 0.1394 0.1221 0.0812 0.0553 0.0505 0.0365 0.0146 0.0076 0.0019 0.0025
1.000
0.0000
0.0000
0,0029 0.0055 0.0046 0.0100 0.0327 0.0699 0.0726 0.1176 0.1315 0.1857 0.2407 0.2427 0.2851 0.3797 0.4068 0.4982 0.5976
,.
TABLE VI. EXPERIMENTAL VAPOR-LIQUID EQUILIBRIAFOR METHYL ETHYLKETONE-TOLUENE SYSTEM Equilibrium Run No. 0
l5 17 19 l8 20 21 22 23 24 25 14 13 10 2 1 9 11 6 7 5 8 4 3 2 1 0
T%? 110.6 110.2 109.88 109.25 107.2 104.2 102.28
....
99.55 98.7 97.1 94.3 91.86 89.9 87.85 86.75 85:s 84.85 84.4 83.15 82.65 81.8 80.5 79.85 79.5 79.45
-Liquid Comp., Mole Fraction MEK
Vapor Comp., Mole Fraction MEK
0.0000
0.0000
Activity Coefficients log
YM
10%YT
0.0045 0.0085 0.0175 0.0405 0.0850 0.1190 0.1533 0.i80o 0.1981 o,2359
0.0140 0.0290 0.0555 0.1281 0.2350 0.3043 0.3536 0.3950 0.4200 ,4709
o.iio7 0.1941 0.1685 0.1876 0.1598 0.1460
0.0003 o.0011 0.0002 0.0001 0,0011 0.0031 0.0032
o.iosz
0.0oso
0.3127 0.3982 0.4682 0.5479 0.5858 0.5967 0.6420 0.6924 0.7012 0.7846 0.8015 0.8611 0.9350 0.9774 0.9939 1.0000
0.5521 0,6280 0,6854 0.7428 0,7708 0.7781 0.8027 0.8342 0.8396 0.8858 0.8955 0,9281 0.9629 0.9878 0.9954
0.0702 0.0471 0.0358 0,0249 0.0245
0.0260 0.0368 0.0449 0.0569 0,0606
o.oi34 0,0091 0.0121 0.0026 0.0048 0.0006 -0.0016 -0.0015 0.0000
0~07z5 0.0766 0.0814 0.0943 0.0986 0.1038 0.1656 0.1511 0.3015
1.0000
0.0000
0.1026 ,0934
o,0144 0.0120
..
The experimental data for the ternary system are arranged! according to isotherm temperatures. Tests are considered to belong to the same isotherm only if their temperatures differ by less1 than 0.2' C. from the average. DISCUSSION
1
BINARYSYSTEM. In correlating the results of vapor-liquid equilibrium measurements, the objective is to present the thermodynamically consistent curves which a t the same time show the smallest deviation from the experimental data, The experimental data for the binary system may be presented by thermodynamically consistent curves calculated from a modified form of Equation 3. 21 =
log
y2
=
.
LOL I R L G T W
3 d log y1 X2
TABLEVII. EXPERIMENTAL VAPOR-LIQUID EQUILIBRIA FOR HEPTANE-TOLUENE SYSTEM Run NO.
0 10 11 12 13 18 14 7 1QU 15 6
(10)
q =0
This procedure is not new (6). In the system methyl ethyl ketone-n-heptane, the activity coefficients of n-heptane were calculated from the activity coefficients of methyl ethyl ketone as evaluated from the experimental data. Similarly in the systems methyl ethyl ketone-toluene and n-heptane-toluene, the activity coefficients of toluene as evaluated from the experimental data were used to calculate the activity coefficients of methyl ethyl
IN LIQUID
ketone and %heptane, respectively. Finally, in the system methyl ethyl ketone-benzene, the activity coefficients of methyl ethyl ketone were calculated from the activity coefficients of benzene. The thermodynamically consistent relationships between activity coefficient and composition calculated from Equation fO are compared with the experimental data in Figures 2 to 5 for the four binary systems studied. The dotted curves in these figures were calculated by arbitrarily changing the liquid and vapor compositions, 0.002 mole fraction unit, and the temperature, 0.2 O from the thermodynamically consistent data in such a way as toproduce a maximum and minimum value of the calculated ac-. tivity coefficients. In virtually all cases the experimental date. fall within the dotted curves so that it may be stated that the experimental data are thermodynamically consistent to within k0.002 mole fraction unit and *0.2' C. in temperature. The thermodynamically consistent temperature-composition
21
-J
M L T H I L CTHYL UETONE
l68 17 9 5 4 3 2 1 0 G
Equilibrium Temp., C.
110.62 110.75 108.6 106.8 105.65 104.8 104.5 103.83 102.95 102.25 101,.78 101.72 101'.35 100.7 100.6 99.73 98.9 98.5 98.4 98.33 98.3
R~~ 17 of ternary,
Liquid Vapor Comp Comp Mole" Mole'' Fraction Fraction n-Heptane n-Heptane 0.000 0.000
0.025 0.062 0.129 0.185 0.235 0.260 0.286 0.354 0.412 0.448 0.455 0.497 0.568 0.580 0.692 0.843 0.940 0.975 0.994 1.000
0.048 0,lOZ
0.200 0.275 0.333 0.349 0.396 0.454 0.504 0.541 0.540 0.577 0.637 0.647 0.742 0.864 0.948 0.976 . 0.993 1.000
Activi t y Coefficients log yH log yT
....
0.1423 0.1097 0.0955 0.0806 0 0702 0.0673 0.0720 0.0496 0.0378 0.0379 0.0312 0.0262 0.0194 0.0183 0.0121 0.0031 0.0011 -0.0009 -0,0008 I
0.0000
0.0000 0.0004
0.0037
0.0080
0.0116 0,0137 0.0155 0,0129 0,0239 0.0321 0.0320 0.0393 0.0426 0.0507 0.0521 0.0621 0,0876 0.0932 0.1390 0.2245-
..
I
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2916
TABLELrIII.
EXPERIMEh-TAL VAPOR-IJQUID
EQUILIBRIA
METHYLETHYL KETONE-BESZESE SYS~M
Rur, NO. 0 13 14 15 17 18 16 19 20 21 22 23 12 10 11 9 6 7 5 8 4 3 2 1
0
Equilibrium Tzmp., C. 80.2 80.2 80.2 (9.85 79.65 z9.45 19.45 79.25 z9.15 19.05 78.8 78.45 78,55 78.35 78.35 i8,33 i8.3 78.33 78.3
Liquid Comp.. Mole Fraction MEK
Vapor Camp., Mole Fraction
MEK 0.000 0.007 0,015 0,049 0.079 0.105 0.106 0 . 131 0.151 0.177 0.222 0.290
0.338 0,419 0,462 0. 507 0.543 0.595 0.623 0,652 0.740 0.865 0.937 0.985
78.k 78.95 79.25 79.40 79.45
1 , oon
Vol. 41, No. 12
the trial and error method of drawing curves by eye through the data and checking the consistency of the curves by the GibbsDuhem relation until a satisfactory result has been attained. For this method, Equation 5 may be written:
FOR
Activity Coefficients log Y.M log y B 0.0000 ,... 0.0567 --0.0018 0.0027 0.0866 0.1165 - 0,0024 - 0.0007 0.0819 0,0767 0.0004 0,0000 0.0808 0.0707 0.0019 0.0026 0.0658 0,0576 0,0037 0,0500 0,0065 0.0386 0.0124 0.0282 0.0129 0.0215 0.0185 0.0144 0.0242 0.0123 0,0272 0.0105 0.0308 0,0077 0.0356 0.0382 0.0078
-
..I.
0.0049 0.0oon -0.0001 0.0003 0.0000
....
0.0430 0.0558 0.0548 0.0393 I . . .
relationships are shown in Figures 6 to 9. In the system n-heptaue-toluene, the temperature data of Bromiiey and Quiggle ( 2 ) appear to be &s much as 1' C. high, while those of the present investigation appear to be slightly low. In general the above procedure does not necessarily give the thermodynamically consistent curve with the smallest deviation of the experimental data from the curve and further adjustment by trial and error may prove to be advisable with poorer data. In this investigation, however, the deviation of the experimental data from the calculated curve is small and well distributed so that further adjustment is unnecessary. TERNARY M'IIXTURES.The location of the best thermodynamically consistent curves through the experimental data for ternary systems is a much more difficult task. One procedure is
M O L FRdCTlON METHYL
E T H Y L KETONE I N
LIQUID
VAPOR-LIQUID EQUILIBRIA FOR TABLE I X , EXPERIMENTAL Run No. 1
32 33 15 2 16 34 14 3 35 13 4
36
5 37 6 7 24 38 31 23 39 30 8 22 29
~ ~ ~ i ~ iLiquid , , ~Comp., i ~ ~ Mole ~ Fraction Temo.. O C . ZM ZH ZT 77.2 77.15 77.46 78.0 78.0 78.0 77.8.5 78.9 78.82 78.82 79.7 80.0 79.92 82.25 82.18 84.5 84.9 8 4 . s5 84.86 84.85 87.15 87.12 81.15
0.767 0.706 0.688 0,856 0.738 0.743 0.658 0.935 0.704 0.588 0.972 0.658 0.514 0.578 0.394 0.499 0.482 0.403 0.282 0.191 0.318 0.208 0.148 0.350 0.241 0.118 0,286 0.183 0,099 0.198 0.155 0.109 0.061 0.073 0,038 0,016 0,002 0.011 0.000
METHYL ETHYL I
