J. Chem. Eng. Data 1983, 28, 119-123
Barker method is often less sensitive to the Sham of the P vs. x , curve near the end points than is the Mixon’et 81. method. The latter reflects the shapes of the splined fits in that specific region while the former reflects the values of the G Ecorrelation constants obtained from a fit of all the data points across the entire composition range. The activity coefficient values (as well as the y, and GE values) obtained are a function also of the equation of state used to estimate the vapor-phase fugacity coefficients. Table X I shows the effect of assuming ideal gases for the acetone nitromethane system at 397.19 K where the pressure ranged from 195 to 665 kPa. The other three equations of state tested showed surprising agreement when the Tsonopoulos (7) correlation is used to estimate the B values for the virial equation.
+
Reglrtry No. Ethyl acetate. 141-78-6; acetonkrilel 75-05-8; acetonel 67-64-1; nitromethane, 75-52-5.
119
Llterature Cited (1) Khurma, J. R.; Muthu, 0.;Munjai, S.; Smith, E. D. J . Chem. Eng. Data, first of four preceding articles in this issue. (2) Khurma, J. R.; Muthu, 0.; Munjal, S.; Smith, B. D. J . Chem. Eng. Data, third of four preceding artcies In this issue. (3) Maher, P. J.; Smith, E. D.J. Chem. Eng. Data 1979, 2 4 , 16. Gumowski, E.; Carpenter, B. H. Ind. €ng. Chem. Fun(4) Mixon, F. 0.; dam. 1965, 4, 455. (5) Peng, D.-Y.; Robinson, D. E. Ind. Eng. Chem. Fundam. 1976, 4 , 455. (6) Barker, J. A. Aust. J . Chem. 1953, 6,207. (7) Tsonopouios, C. AIChE J. 1974, 20, 263. (8) Abbott, M. M.; Van Ness, H. C. AIChE J. 1975, 27, 62. (9) Gautreaux, M. F.; Coates, J. AIChE J. 1955. 7 , 496. (10) Maher, P. J.; Smith. B. D. Ind. Eng. Chem. Fundam. 1979, 78, 354. (11) Hayden, J. G.; O’Conneli, J. P. Ind. Eng. Chem. Process D e s . D e v . 1975, 74,209. (12) Haman, S.E. M.; Chung, W. K.; Eishayah, I. M.; Lu, E. C. Y. Ind. €no. Chem. Process Des. D e v . 1977, 16, 51.
Received for review July 29. 1982. AcceDted SeDtember 24. 1982. We gratefully acknowledge he financial suppoA receivd from the National Science Foundation Orant CPE-80000534 and from the Industrlai Participantsin the Thermodynamic Research Laboratory.
Total-Pressure Vapor-Liquid Equilibrium Data for Binary Systems of Nitromethane with Methanol and Ethanol Jagjit R. Khurma, 01 Muthu, Sarat MunJal, and Buford D. Smlth’
Thermodynamics Research Laboratory, Washington Universiw, St. Louis, Missouri 63130 Table I. Chemicals Used
Total-pressure vapor-liquid equlllbrlum (VLE) data are reported at approximately 298, 348, and 388 K for methanol nitromethane and at approximately 298, 348,
+
+
and 398 K for ethanol nitromethane. The experimental PTx data were reduced to yi, Y,, . . and GE values by both the Mlxon-Gumowskl-Carpenter and the Barker methods, but only the Mixon et al. results are reported In thelr entirety. Seven GE correlations were tested In the Barker data reductlon; the five-constant Redllch-Klster equation gave the best results. The effect of the equation of state choice was lnvestlgated. Introduction This paper presents total-pressure vapor-liquid equilibrium (VLE) data for nitromethane with methanol and ethanol. Previous papers have reported data for nitromethane with 1chlorobutane( I ) , with chlorobenzene ( Z ) , and with ethyl acetate, acetonitrile, and acetone (3). The apparatus and techniques used to measure all of these data have been described previously along with the defining equation for the activity coefficient and the standard states used (4). Chemicals Used
component
vendor
stated punty, %
ethanol methanol nitromethane
U.S. Industrial Chemicals Fisher Scientific Mallinckrodt
200 proof 99.9
were caught in amber bottles and back-flushed with dry nitrogen for transfer to the cell-loading operation* The stated purities Of the chemicals were verified with gas-liquid chromatography at this point. None of the compounds exhibited any degradation during the VLE measurements. The cell Dressures were stable with respect to time, and all liquids were perfectly clear when removed from the cells at the end of the last isotherm. Experimental Data Tables I I and I I I present the experimental P Tx data. The “smooth” pressure values reported are from the least-squares cubic splined fits used to provide the evenly spaced values required by the finitedifference Mixon-Gumowski-Carpenter method (5) for the reduction of PTx data. Figures 1 and 2 show the experimentaldata in terms of the pressure deviation P D from Raoult’s law P, = P - [P2’
The sources and the puritiis of the chemicals used are listed in Table I. Activated molecular sieves (either 3A or 4A) were put into the chemical containers as they were received. Just prior to being loaded into the VLE cells, each chemical was poured into a distillation flask and distilled through a Vigreux column (25” 0.d. and 470 mm long). The first and last portions of each distillate were discarded. The retained portions 0021-9568/83/1728-0119$01.50/0
99.9
+ x l ( P 1 ‘ - P*’)]
where P is the experimental mixture pressure and the f,’ values are the pure-component vapor pressures. The deviation pressure plot emphasizes the scatter more than the P vs. x 1 plot but does not show whether or not any azeotrope exists. The point symbols in Figures 1 and 2 denote the experimental data points exactly. The curves approximate-in these cases quite closely-the splined fits of those data points. For an 0 1983 American Chemical Society
.
4.775 8.623 10.779 121 902 14.202 15.301 15.963 16.394 16.799 17.140 17.313 17.435 17.434 17.305 16.973
.0003 ,0431 oao7 s 1404 e2107 -3122 ,4159 511 1 ,6154 7201 ,7355 8592 ,9053 .9545 1.0000
.ooou
n042Y
,0804
1400 ,2103 e 31 1 M e4155 51 O M ,6151 71 9Y ,7854 ,8591 ,3053 ,3549 1.0000
Table 111. Experimental P vs. x, Values for the Ethanol (1)
.oooo
a0478 e0939 ,1484 ZZOU -3051
.
.
400U
Q991 ,6063 6995 7505 .a65 1 9234 ,9618 1.0000
4.790 7.092 8.294 9.054 9.596 9.999 10.377 10.167 10.211 10.216 10.168 9.783 9.324 8.775 7.922
790 7.092 9.292 ,3.058 9.592 9.902 10.071 10.172 10.218 10.210 19.158 't
3 . a00 9.318 d 771 7 924
+ Nitromethane (2) System
.oooo
e 0477 ,0937 1483 22 0 6 3049 s 4006 4990 6062 s 6998 -7504 8651 .9235 .9618 1.0000
E T H Q N O L L11
I
N I T R O M E T H Q N E I21
+
R 2 9 8 19 6 B 3lis . 5 K C 398 . 7 K
~
C
--x, / /
/
/
- - I
10
0.20
A I
I.CO
0.60
0.40
Y Xl
+
Figure 1. Deviation from Raoult's law for the methanol (1) nitromethane (2)system. The x10' muttipiier means that the decimal point in the ordinate scale values must be moved one place to the right.
+
Figure 2. Deviation from Raoult's law for the ethanol (1) nitromethane (2)system. The x10' multiplier means that the decimal point in the ordinate scale values must be moved one place to the right.
Journal of Chemical and Engineering Data, Vol. 28, No. 1, 1983 121
Table IV. Calculated Data for the Methanol (1) L I Q U I D MOLAR VOLUMES, CC/YOL: TOTAL PRESSURE KPA x1 EXPTL. ‘k4i5 .0000 4.775 11.576 11.576 ,1000 . 2 000 14.032 14.032 15.203 15. 203 3000 15.875 15.875 4 000 16.347 16.347 5000 6000 16.743 16.743 17.081 17.081 7000 17.343 17.343 ,8000 17.439 17.439 s 9000 1.0000 16.973 16.973 L I Q U I D M3LAR VOLUMES, CC/flOL: T9TAL PRESSURE KPA x1 EXPTi CbLC. .0000 41.975 41.975 .lo00 82.576 82.577 LOO0 105.318 105.322 3000 119.157 119.162 9 000 128.251 128.254 5000 134.939 134.940 6000 140.297 140.296 144.828 7000 .so00 148.579 3000 151.412 151.411 1.0000 151.276 151.276 L I Q U I D MOLAR VOLUMES, CC/WOL:
. .
1td::fl
ESSURE KPA CdLC. 151.573 263.522 340.979 395 80 7 435.452 466.737 492.627 514.602 533.840 549.335 557.924
X1
.oooo
1000 2000 e 3000 .4000 5000 e 6000 7000 0 8000 9000 1.0000 a
0
METYRNClL 111
+
+ Nitromethane (2) System at 298.16,348.17, VL(1)
4008OrJ V L ( 2 ) =
MIXTURE FUGACITY COEFFICIENTS 1 2 ,9989 ,9980 09971 ,9953 ,9965 09943 -9962 09939 ,9960 ,9936 ,9959 .9934 ,9958 09932 09957 ,9931 09956 09930 e9956 e9930 .9957 09933 VL( 1) =
43.650
MIXTURE FUGACITY CDCFF I C I E N I S ,9438 ,9869 -9A31 09808 ,9793 -9792 ,9773 ,9765 ,9759 ,9754 09754 VL(1) =
,9684 e9775 ,9716 ,3680 ,9657 ,9640 ,9627 -9616 ,3607 ,3602 ,9606 47.000
H I X T U R E FUGACITY COEFFICIEYTS 1 2 ,9343 ,1688 09702 ,7466 .9609 .93ia ,9543 ,9215 09495 .9142 ,9459 ,9084 a9429 ,9038 -9402 ,8999 .9373 ,8967 ,9360 ,3944 ,9350 .a939
54.000
Y l
e6182 7009 7350 .7555 07722 7900 e8113 ,8416 894 1 1.0000
-
01
1 6000 1.0256 1 0945 1.2003 1 3484 1.5519 1 8320 2.2382 2.8614 3.8485 5 7062
6.6609 4 I2222 2 8995 2.1954 1.7672 1.4879 1 2988 1 1664 1e0749 1 e0235 1.0030
EXCESS
GIERS
A C T I V I TY COEFF I CIFNTS
Y1
FUNCTION JIHOLE 0.00 347.78 614.07 800.53 911.90 950.13 810.15 916.61
L
.oooo
1.0000 1.0140 1.0581 1 1304 1 2364 1 3828 1 5857 1.8739 2.3116 2 9694 4.6191
,5306 656 4 07150 -751 1 7791 804 8 8322 865 3 e9168 1.0000 VL(2)
EXCESS CIBBS FUNCTION e J/MOL E 0.00 413.46 706.90 901.63 1009.26 1037.24 989.25 866.23 664 33 379. QO 0.00
56.700
=
.
626.52 359.64 0.00
6 0 1 200
EC XI BCRE S S
Y1
‘.OOOO 04629 ~6136 6905 07391 7769 s8101 8427 8796 -9264
1.oooo
ACT1V:TY
COEFFIC!ENTS
2 8756
2.2789 1.9332 1 6735
t:x 1.2032 1.1173 1.0557 1.0147 1.0030
ETYFINCIL 1 1 1
Y I T 8 C l M E T H R N E 121
A 298.16 K B 3ua.17 K C 358.24 K
0
.
A C T I V I T Y COEFF I C f ENT S
.oooo
VL(2)
and 388.24 K
FUNCT T ON JIHOLF: 299.38 0.00
1,6000 1.0116 1.0413 1 0933 1.1724 1.2810 1e 4304 1 6420 1e 9484 2.4459 3.2349
+ NITSOMETHQNE R 29a.ia K
530.03 698.51 803.19 843.76 820.54 730.90 570.54 331.OR
0.00
[PI
B 3ua IS K
c 398 1 7
K
N
2.j
f :
0
-
w
u 9
0
m
a
0
3
3 0
N
0 0 1
0.00
I
0.20
I
I
0.60
0.40
I
0.80
0
00
X-I
Flgure 3. Activity coefficients for the methanol (1) 4- nitromethane (2) system. Curves are from Barker method; polntsare from Mixon et
al. method.
0.00
0.20
0.110
0.60
0.00
00
XI
Flgure 4. Activity coefficients for the ethanol (1) initromethane (2) system. Curves are from Barker method; points are from Mixon et al. method.
122 Journal of Chemical and Engineering Data, Vo!. 28, No. 1, 1983
Table V. Calculated Data for the Ethanol (1)
+ Nitromethane (2) System at 298.18,
L I Q U I 3 MOLAK VdLUMES, CC/M’JL:
x1
.0500
.loo0 .2000 .3000 .4300 L 5300 6000 .loo0 ,&3000 ,9000 1.0300
x1 .00c)o
.1300 .2000 3300 4003 5d03 6300
.7901)
8000 .3000 1.0000
T O T A L PRE SSURE, KPA EXPTL CALC 4,795 4.790 6.407 3.407 9.475 9.475 9.036 3.d86 10.376 13.376 10.163 10.165 10.209 10.209 10,216 10.216 13.058 113.353 9.s4a 9.542 7.922 7.322
T O T A L PRESSU2Et KPA EXPTL. CALC. 42.127 42.127 66.354 66.856 79.777 79. 703 86.943 06.947 91.376 91.379 9r.206 9 % . 207 36.J47 76.04Y 97.318 97.313 37.503 97.502 95.759 95.75d 89.300 d9.003
L I O U I D MdLAH VOLUMES, CC/MOL:
x1
0003 ,1300 .Zc)OO e 3300 .4000 5000 6000 .7300
.8000
9000
I . 0000
T O T A L PKE SSUKE KPA EXPTL CdLC. 200.329 LOO. a 2 9 290.429 290.44~ 352.303 352.614 3 96.560 396.5 74 429.1 05 429.113 S53.609 453.612 472.Q97 472.499 4i37.681 487.680 4 9 8 .O 4 1 49il.64L 504.064 504.364 438.442 4 90.4 42
VL(1) =
50.dZ’t
MIXTURE FUGACITY CJ5FF I C I E N I S a9680 ,9965 ,9961 ,9959 e9958 e9958 -9950 ,9958 ,9958 ,9960 A967
.9bL34 e9971 e9969 .?966 ,9966 ,9965 a3965 -9965 ,9965 ,9967 ,9973
MIXTURE FUCAC I S Y CUEFF ICIENTS 1 2 ,9910 .98d3 a9955 -9815 . ~ a 2 8 .9780 ,9012 e9760 -9302 ,9748 .?I96 ,9741 ,9792 e9736 ,9789 e9732 ,9769 e9732 ,3792 a9737 .3d07 ,9757
VL(1)
5
70.087
MIXTURE FUGACITY C JCFF I C IE4I.S 0’3920 ,9589 ,9499 ,9436 ,3389 $9354 e9327 ,3305 ,9289 e9281 .92d9
L
,9615 .9G65 ,9329 a9247 ,9187 ,9142 e9103 ,9001 ,9062 e9054 a9068
Table VI. Parameters for Peng-Robinson Equation‘ component
T,, K
P,, MPa
W
nitromethane ethanol methanol
588.0 516.2 5 12.6
6.313 6.383 8.096
0.3460 0.6350 0.5590
Binary interaction constant was set at 0.0 for all systems.
actual comparison of the splined-fi values and the experimental P values, see Tables I1 and 111. Both systems showed only positive deviations from Raoult’s law and those deviations increased with the temperature. The methanol system forms an azeotrope at 298.16 and 348.17 K but not at 388.24 K. The ethanol system has an azeotrope at all three temperatures. Reduced Data
The yi,Ti,and GE values selected for publication are given in Tables I V and V. Those values were obtained with the Mixon et al. data reduction method. The Peng-Robinson equation of state (6)was used to estimate the vapor-phase fugacity coefficients. The pure-compound parameters used for
348.15,
VL(2)
and 398.17 K
-
53.990 EXCESS
Y1
ACTIV!TY
COEFFIC!ENTS
.oooo
1.6000 1.0297 1 1068 1 2252 1 3915 I 6283 1 9672 2 4954 3.2874 4.6714 7.3129
,4711 e5515 5035 e6022 e 6156 ,6299 -6402 6862 7652
1 .oooo
Y l
.oL)oo
,4197 ,5461 6079 e6402 ,6790 e7072 7424 .7d17 a5 42 1.0000
.
VL(2) =
YA
* 0000
+ 3592 ,5111 ,5977 ,6579 7351 7 4 70 7904 ,8389 ,9033 1.0000
A C T I V l T Y COEFFI CIENTS 1 2 4.2653 1.0000 3.1696 1.0157 2.4531 1 SO624 1.9804 1 I408 1.6628 1.2532 1.4356 1.4134 1.2698 1e6422 1.1573 1.9510 1.0681 2 4853 1.0194 3.2613 1.oooo 4 e6878
c 100s
FUNCTION, J/HOLE 0.00 464.35 792.63 1011.52 1134.87 1170.49 1119.46 986.52 757.56 435.35 0.00
EXCESS C 108s FUNCTION, J/HOLE 0.00 374.62 659.75 a60.37 980.79 1024.15 989.18 876.47 679.72 392 3 1 0.00
61.450
AC TIV!TY 1
2.6204 2.1704 1.0544 1.6139 1.4334 1.2936 1.1857 1.1070 1.0491 1.0140 1.0000
C OEFF I C I E N T S
1 .boo0 1 0090 1.0382 1 0874 I1.1591 2608
1 4026 1 e5938 1e 3 7 4 3 2.2727 2 9609
E XCES 5 C IBBS
FUNC JH I XLE ION, 0. 00 285.62 508.23 669.56 770.07 009.1 I 786.29 698.38 542.90 313.26
0.00
the Peng-Robinson equation are in Table V I . The “experimental” pressure values tabulated in Tables I V and V are actually interpolated values from the cubic splined fits of the experimental P vs. x , values. (The fidelity with which the splined fits represent the actual experimental P values is shown in Tables I1 and 111.) The “calculated” pressure values are from the Mixon et al. data reduction method. That method can usually be made to reproduce the input P values to any desired precision. The PTx data were also reduced with the Barker method ( 7 ) using the seven GEcorrelations listed in Table V I I . As shown there for the methanol nitromethane system, the five-constant Redlich-Kister equation usually represents the experimental Pdata best with the modified Margules equation (9)a close second. The maximum percent deviation and the rootmean-squared deviation (rmsd) are defined at the bottom of Table V I I I , which gives a more complete comparison of the two data reduction methods insofar as the accuracy of the P fits is concerned. The Barker results in Table VI11 are from the five-constant Redlich-Kister GEcorrelation, and the PengRobinson equation of state was used for both data reduction methods. Usually the Mixon et al. method reproduces the experimental P values better, but for the ethanol system the
+
Journal of Chemical and Engineering Data, Vol. 28, No. 1, 1983
123
Table VII. Effect of Calculation Method on 7imValues for the Methanol (1) t Nitromethane (2) Systema calcd 7imvalues
accuracy of P fits, max % dev/rmsd 298.163 348.173
calculation method Mixon et al. Barker: absolute Van Laar Wilson NRTL modified Margules UNIQUAC Redlich-Kister, three constants Redlich-Kister, five constants Gautreaux-Coates: splined fits PD/X , x , plots a
component 1
component 2
388.24K 298.163 348.173 388.243 298.16K 348.17K 388.24K
0.1/0.0
0.1/0.0
0.1/0.1
6.876
3.821
2.869
5.600
4.459
3.107
2.811.2 0.3/0.1 0.2/0.1 0.2/0.1 1.6/0.7 0.5/0.2 0.210.1
0.9i0.5 0.3/0.1 0.3/0.1 0.3/0.1 0.5/0.3 0.3/0.1 0.2/0.1
1.0/0.3 0.5l0.2 0.3/0.1 0.310.1 0.8i0.3 0.3i0.2 0.2/0.1
6.194 7.173 7.010 7.113 6.554 6.826 7.081
3.712 3.930 3.926 3.924 3.797 3.918 3.892
2.692 2.764 2.799 2.828 2.722 2.803 2.829
4.744 5.543 5.569 5.530 5.037 5.668 5.574
3.716 3.961 3.958 4.040 3.807 3.945 4.011
2.976 3.063 3.093 3.181 3.008 3.080 3.150
6.874 6.635
3.819 3.852
2.875 2.822
5.592 5.811
4.433 4.475
3.106 3.123
Virial equation, Tsonopoulos correlation (8).
Table VIII. Comparison of the Barker and Mixon et al. Pressure Fits
rms for % devb
max % dev in P a temp, 3
Barker
Mixon
Barker
Mixon
Methanol (1) t Nitromethane (2), Peng-Robinson 298.16 0.184 0.066 0.071 0.035 348.17 0.226 0.090 0.082 0.046 388.24 0.235 0.136 0.095 0.065 Ethanol 298.18 348.15 398.17
(1) + Nitromethane (2), Peng-Robinson 0.055 0.177 0.028 0.066 0.087 0.063 0.038 0.031 0.033 0.047 0.017 0.023
.
a % dev = 100[ lPcdcd- Pexptll/Pexptl]
[cn(% d e ~ ) ~ /I /n* . ]
Table M. Effect of Equation of State Choice on -yim Values Obtained with the Mixon et al. Method for Methanol (1) t Nitromethane (2) at 388.24 K
rms for % dev =
Barker method with the five-constant Redlich-Kister equation did better for two of the three isotherms. Figures 3 and 4 show that the activity coefficient values provided by the two data reduction methods agree very well for these two systems. The points represent the Mixon et al. results while the curves approximate the Barker results. The Barker results were obtained with the five-constant RedlichKister equation. The Peng-Robinson equation of state was used by both methods. Table V I 1 illustrates how the calculated y l mvalues will vary with the GEcorrelation used by the Barker method. (Note that the numbers in Table V I 1 are based on the virial equation and the Tsonopoulos ( 8 )correlation.) The use of the GautreauxCoates (70) equations to calculate y i mvalues has been discussed in a previous paper ( 7 7). The (dP/dx,),” values needed by those equations can be obtained from the cubic splined fits or from a P,lx,x, or x,x,/P, plot ( 7 7). There is always some uncertainty in the extrapolations to x 1 = 0.0 and 1.0 on the plots, and the use of the splined-fit values is usually more reliable. The yimvalues calculated by using the splined-fit slopes agree very well with the Mixon et al. values. Even though the Mixon et al. method is based on the splined fits, the agreement of its y l mvalues with the Gautreaux-Coates values is not automatic. The finitedifference Mixon et al. method uses a quadratic fit of GEat x , = 0.0 or 1.0 plus the two adjacent GE values to “reach” the y l mvalues, and that quadratic extrapolation in general will provide different values than the Gautreaux-Coates method using the splined-fit slopes. The difference is usually small but can be sizable.
eq of state used ideal gas vinal through Bu: Tsonopoulos (8) Hayden-O’Connell(12) Redlich-Kwong: Lu modification (13) Peng-Robinson (6)
1
2
2.8139
3.5010
2.8694 3.0333 2.8778 2.8756
3.1074 3.6949 3.3397 3.2349
The ylmvalues (as well as all the y l , y,,and GE values calculated) are also functions of the equation of state used to estimate the vapor-phase fugacity coefficients. Table I X compares the Mixon resub obtained with several equations of state. The pressure ranged from 151 to 558 kPa for the methanol system at 388.24 K and at those pressure levels the variation of the calculated results with the equation of state used can be significant. Registry No. Methanol, 67-56-1; ethanol, 64-17-5; nitromethane, 7552-5.
Literature Clted (1) Khurma, J. R.; Muthu, 0.; Munjal, S.; Smlth, B. D. J. Chem. Eng. Data ., first of five preceding articles in this issue. (2) Khurma, ?. R.; Muthu, 0.; Munjai, S.; Smith, 8. D. J. Chem. Eng. Data ., third of flve preceding articles in this issue. (3) K h u r y , J. R.; Muthu, 0.; Munjai, S.; Smith, B. D. J. Chem. Eng. Data, fifth of five preceding articles in this issue. (4) Maher, P. J.; Smith, B. D. J. Chem. Eng. Data 1979, 2 4 , 18. (5) Mixon, F. 0.: Gumowski. B.; Carpenter, B. H. Ind. Ena. Chem. Fundam. 1965, 4 , 455. (6) Peng, D.-Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. I976, 4 , 455
(7) (8) (9) (10) (11) (12)
Barker, J. A. Aust. J. Chem. 1953, 6 , 207. Tsonopoulos, C. AIChE J 1974, 2 0 , 283. Abbott, M. M.; Van Ness, H. C. AIChE J. 1975, 21, 82. Gautreaux, M. F.: Coates, J. AIChE J 1955, 7, 498. Maher, P. J.; Smith, B. D. Ind. Eng. Chem. Fundam. 1979, 78,354. Hayden, J. G.: O’Connell, J. P. Ind. Ena. them. Process Des. Dev. 1975, 1 4 , 209. (13) Hamam, S. E. M.; Chung, W. K.; Eishayah, 1. M.; Lu, B. C. Y. Ind. Eng. Chem. Process D e s . D e v . 1977, 76,51. Received for review July 29, 1982. Accepted September 24, 1982. We gratefully acknowledge the financial support received from the National Science Foundation &ant CPE-80000534 and from the Industrial Participants in the Thermodynamics Research Laboratory.
