64
J. Chem. Eng. Data IQ82, 27, 64-71
and these data are included in Tables I and 11. Osmotic coefficients of the four salts are presented graphically in Figure 1.
(3) (4) (5) (Sj
Bonner. 0. D. J . Chem. Eng. Date 1981, 28, 148. Bonner, 0. D. J . chem. Thermodyn. 1879, 1 1 , 559. Robinson. R. A.: Slnclalr. D. A. J . Am. chem.Soc. 1934. 56. 1830. Robinson; R. A;: Stokes,.R. H. "Electrolyte Solutions", 2nd'ed.:'Butterworths: London, 1959; pp 483, 492.
Literature Cited (1) Esval, 0. E.; Tyree, S. Y. J . Phys. Chem. 1962, 66, 940. (2) Bonner, 0. D. J . Chem. Soc., Farsdy Trans. 1 1981, 77, 2515.
Recehred for review May 13, 1981. Accepted November 2, 1981.
Vapor-Liquid Equilibrium with Association in Both Phases. MuMkomponent Systems Containing Acetic Acid Henryk Sawlstowskl" and Peter A. Pllavakist
Department of Chemical Engineerlng and Chemical Technology, Imperial College, London S W7, England The vapor-llquld equtllbrknn behavlor of the quaternary system rnothyl acetate-mahanol-water-acetlc acld was modeled by udng the Margules equation In comblnatbn with Marok's method for the a d a t k n of acetlc acld. The constants in the Margules equation were obtained from exktlng or exp.rlmcMtally determined equHibrium composlth of the constituent M a r y and ternary mlxtwes. The final equation was experhentally verlfled on the quaternary system in the presence and the absence of the catalyst.
I ntroductlon Chemical reaction with simultaneous distillation in a column is an operation of particular interest. The practical evaluation of such a process requires the formulation of a model which describes the complete operation of the column (7). For this purpose, data on the vapor-liquid equillbria of the multicomponent system must be available. The usual equations used in process calculations for the determination of vapor-ilquid equilibrium data are the Wohi, Margules, Van b a r , Wilson, and lately the NRTL equations. Sabylin and Aristovich (2) concluded that the best predictions for multicomponent systems were given by the Wson equation, while the Wohl equation produced the worst results. The NRTL equation is superior to the Wilson equation since it can also describe systems with immiscible components. Simulation of the vapor-llquid equillbrla of systems that contain associating components is, however, difficult. Owing to the complexity of the system under investigation, Sabylln and Aristovich's conclusions do not necessarily apply, and also simulation cannot be established alone by these relationships. I n the past a model was developed by Marek and Standart (3)and used by Marek (4) to correlate data of acetic acid mlxtwes. Jenkins and Gibson-Robinson (5,6) developed a new model based on that of Marek and Standart, but they also took into account a concentrationdependent factor for the association of acetic acid in the liquid phase. These models only require the calculation of adjustable parameters as those for the integrated form of the Gibbs-Duhem equation which correlate activity coefficients to component mole fractions. They also use correction-factor expressions to include the effect of association of acetic acid. I n the present work the model developed by Marek and Standart was used (3,4). The model is applied to the quaternary system of acetic acid with water, methanol, and methyl 83, Rue des Floralies, 12OO-Brussels. Belgium.
0021-9568/82/1727-0064$01.25/0
acetate. It is, however, established that alcohols in solution (7) as well as water alone and in mixture associate to form dimers and polymers (8). This model assumes that only acetic acid forms dimers or Mgher potymers and does not take into account the association behavior of the other components but only of acetic acid. I n the case of systems containii acetic acid and methanol, there Is a further complication that the components react to form methyl acetate, aithough very slowly in the absence of the catalyst. The vapor-liquid equilibrium data for these systems were therefore obtained in a flow still in order to minimize thls complication. Thls does not, however, exclude the possibility that acetic acid does not reach the monomerdimer equilibrium mixture. Having described the complications, we studied the use of this model for these systems. Data Sets Examlned
The following vapor-liquid equilibrium data at 760 mmHg must be known: (a) methyl acetate-methanol, (b) methyl acetate-water, (c) methyl acetate-acetic acid, (d) methanolwater, (e) methand-acetic acid, (f) water-acetic acid, (9) methyl acetate-methanol-water, (h) methyl acetate-methanol-acetic acid, (i) methyl acetate-water-acetic acid, (i) methanolwater-acetic acid, and (k) methyl acetate-methanol-wateracetic acid. Existing data for systems given in the literature were considered to be correct and therefore were not repeated. System a has already been investigatedby T e s h i i et ai. (9), Crawford et ai. ( 70), Bushmakin and Kish ( 7 7), and Bredig and Bayer (72). Complete data for system b have been presented only by Teshima et ai. (9). Similarly, system d has been investigated by Fastovsklj and Petrovski] ( 73), Bennett (74), Bredlg and Bayer ( 15),Dunlop (M), Huges and Maloney ( 77), Ramalho et ai. (78), and many others; system (f) by Rivenc (79), Brown and EwaM (20), Garwin and Hutchinson (27), Othmer et ai. (22), and others;and finally system g by Crawford and Teshkna et ai. (9). Data for system et ai. (70), Kogan (23), e have been given In the literatwe by Rius et al. (24) at pressures of -706 mmHg and had to be repeated at atmospheric pressure. System f (water-acetic acid) has been presented by Rhrenc (79) in weight fraction in the liquid and vapor phases. To convert it Into mdar fractbn, we used a constant weight of monomeric acetic acid. Systems c, e, and h-k were not available and had to be experimentally determined. All of the experimentally determined vapor-liquid equilibrium data are contained in Tables I-VI. Thermodynamic relations are used extensively for the interpolation and exlrapohtbn of experimental data for systems wtth two and more components. The commonly used expressions are valid only for an ideal, or slightly nonideal, behavior of the vapor phase, but they fall completely for substances with highly
0 1982 American Chemical Society
Journal of Chemicel and Engineerlng Data, Vol. 27, No. 1, 1982 65
Table I. Vapor-Liquid Equilibrium Data for t h e Methyl
The vapor pressures of the pure components were estimated by the Antoine equation. For acetic acid the Antoine constants for the corrected vapor pressure were taken from the work of Marek (4). This corrected vapor pressure was then calculated by the expression
Acetate-Acetic Acid System E
x
p
e
r
l
m
e
n
t
a
C
l
a
l
c
u
l
a
t
e
d
,003
-.O@R ,000 -.0@3
.00!
-.003
.OlS -.c03
-.0!8
.008 .@00
log PA: = 15.6699 - 10821.l/(t
.oc>
.03@ ,077
-.@3@
,009
-.@O?
-.C2?
.
..@1? wo
000 -.011 ,008 ,005
-.toe -.00: -.00:
.co1 .CC!
-.OO! ,000
.ooc .om
.000
-.@36
.@)E
,015 ,012
-.@I: -.@I?
.@I6
-.0:i
,017
-.0>7 .O!(
-.c1: .OC!
-.00:
.@il
-.0?7
,018 .@@$
-.@!E -.0c9
.c15 .@?i
-.c:
,045
-.0Li
,056 ,032
-,@56 -.032
.O!j
-.@I:
~~
p
e
r
i
m
e
n
t
a
l
-C
si
Y2
t * O C
,071 ,088
,929
.222
110.30
.a6
.912
,259
.9@2
.27: .279
106.50
.096
106.20
.282
.I12
.866 .a57
.77a .725 .721 .677 .623 ,559 .409 .E7
107.50 105.10
.31>
.)IC
91.90
11
.lo3 ,178 .282 .305 .3:7 .466 .514 .6@@
.a22
.I18 .6?5 .603
.323
.377 .L41 .:?I .643
102.10
95.80 93.70
.532 .486 .400 .313
.797 .84C .905 .?43
.203
85.00
,156
62.10
.@?: .057
.718 .749
.282
.945
.a55
.251
.@A1
.797
.?C3
.045
70.30
.a10
.959 .955 .970 .975
78.30 74.50 73.50 72.10
.030
10.10
.022
.980
,020
69.40 68.60
.990
.00A
67.40
.687
i
.a24
i
.a41
.I90 .176 .1:g
.678
.122
y1 -
a
l
c
u
l
a
t
e
d --
Y2
Q1
.7a4 .7A1 .718 .685
.006
-a06
,016
-.016
dy2
-.0OA
.004
.@Oe
-.006
.379 .445
.621
-.002
.5:5
-.004
.0OC
.602
.398 .3t8
-.011
.@I1
,310
-.@@e
.206
.002
-.CO2
.I70
.@I4
-.@I4
.ll:
.OX
-.@20
.928
.@?2
.Old
.941
.059
.004
-.014 -.004
.952
.048
.007
-.007
.967 .971 .975 ,979 .967
,033
-.011
.632 .6?0 .I94 .830 .88:
.Oil
.@02
-.@I1 ,006
.011
.02?
.Om
.025
.003
-.003
.021
.001
-.om
,013
.009
-.0@9
.@00
nonideal vapors. Since acetic acid associates (25, 26), the system was considered nonideal. The vapor-phase nonidealities for acetic acid were handled by the correction factors of Marek and Standart (3)and of Marek ( 4 ) ,and a summary of the correlations used is presented in the Appendix. Using the Scheibel (27) correlation, we found that the correction factor for the nonldeali in the liquid phase was 1, and a value of 1 was therefore assumed throughout the calculation. The pure-component association constant K for the vapor phase was obtained from the work of Marek ( 4 ) and is as follows:
-
-log K = 9.7535
I t should be noted that the determined equilibrium data are not "true" equilibrium data since thermodynamic equilibrium in reacting systems also requires that the system be in chemical equilibrium, i.e., that the reaction has been completed. However, under such conditions it would not be possible to obtain a local concentration driving force in a packed column or its instantaneous value in a batch reboiler, and no procedures for column calculation could be established. For this reason the flash Vaporization technique was adopted, and the determined data were correlated on a nonreacting basis. No other procedure is currently available as the relevant theory on determination of vapor-liquid equilibrium data in reacting systems does not exist. Experlmental Section
Methanol-Acetic Acid System x
(2)
-.@3i
Table 11. Vapor-Liquid Equilibrium Data for t h e E
+ 698.09)
+ 0.00429 - 3166/(t + 273.2)
(1)
Note that the K is based on the vapor-phase association measurements of acetic acid by Ritter and Slmons (25) and Johnson and Nash (26). This is used for the evaluation of the correction factors which are valid only for the case of association to dimers. The dimerization constant includes the effect of the higher associations and of the slight nonideall of the various kinds of ack! molecules and hence also is a function of pressure.
The most direct and accurate method for the determination of vapor-liquid equilibria is by experimentation in a suitable still. The traditional types of equilibrium apparatuses are, however, unsatisfactory for measurement of vapor-liquid equilibrium data of a system in which a chemical reaction is taking place, since the compositions of the phases are constantly changing. I n order to avoid this difficulty, it was necessary to use a flow still. The Cathala ebulliometer (28) was selected for this purpose. I n it the reservoirs were filled with their respective liquids and the insulating envelope was heated to a temperature around the temperature of operation. The preheater and the boiler were then filled and heated. The flows of the two phases were adjusted in such a way that the desired composition was obtained. Heat exchangers were used to cool liquid and vapor samples in order to minimize losses by vaporization and suppress any chemical reaction. Generally within 15-20 mln steady-state conditions were obtained. Two samples from each phase were then taken and analyzed chromatographically. Tests of Apparatus. The apparatus was tested by using a strongly colored solution as a liquid feed (concentrated potassium bichromate solution acidified with sulfuric acid). The condensed vapor was completely colorless. I n a second test a KCI solution was employed as a feed, and condensed vapor phase failed to give any precipitate when mixed with a solution of AgNO,. This showed that the vapor was free from liquid droplets which could have been entrained. To test further the accuracy of the Cathala still, we carried out experiments for vapor-liquid equilibrium of a system which Is well documented. The system methanol-water was chosen. The agreement b e tween these resuits and existing literature data was good and confirmed the reliability of the still. Materials. Distilled water was used. Methanol was of AR q u a l i supplied by James Burrough. Methyl acetate was from BDH Chemicals. The assay (saponification) was not less than 98% . Acetic acid was glacial obtained from Hopkin and Williams with an assay of 99% minimum. Sulfuric acid (the catalyst) was of GPR quality and was supplied by Hopkin and Williams. Hydrogen (the carrier gas for the chromatograph) was pure. Anaoftkcal PrOcekKe. All of the liquid and condensed-vapor samples of the phases in equilibrium were analyzed by liquidgas chromatography for methyl acetate, methanol, water, and acetic acid with a Perkln-Elmer 452 apparatus provided with a katharometer detector (thermistors). Hydrogen was used as the carrier gas at a flow rate of 150 cm3/min and under pressure
-
66 Journal of Chemlcal 8nd Engineering DaM, Vol. 27, No. 1, 1982
TaMe 111. Vapor-Liquid Equilibrium Data for the Methyl Acetate-Methanol-Acetic Acid System E x p e r i m e n t a l
i .3343 * 3579 * 0947 .1662 -0589 .1192 .2872 SO514 -0695 *I145 .4343 -0504 .a51 .2974 .0690 -0529 -0948 .a70 .48 35 .1986 .os84 e0679 .0848 .0911 .3712 .0718 .0621 a0255 -0523 -0776
x2
x3
Y1
,0683
.5974 -4245 -7696 .3817 .3978 e 5834 .3722 .7978 .2672 .5m7 ,3868 ,4677 .le68 .6342 '.8721 * 7950 * 7178 -6744 .3376 -3199 a7552 23383 *6787 *0917 .4128 * 2904 .7@7 .e271 * 9019 -7085
-7094 .6704 .2936 -3937 .1571 *3407 ,5679 .1667 -1875 -3314 .7323 .1415 -1995 .6913 .2293 ,1738
.2176 -1357 .4521 .5433 2974 .3406 .1508 .6633 -3048 1789 -4819 .7281 ,0684 .0589 .1521 a1874 .2386 .I789 ,4815 * 1564 * 09 38 * 2365 .el72 .2160 .a78 e1772 -1474 -0458 - 2 1 39
-
-
C
y2
-2583 .7617 -4387
-1045 .2690 .2827 65468 ,7696 *4790 .3950 .3587 .7764 .4893 .2191 .7510 -7898 .lo45 .1405 .3646 .4100 ,4483 .2160 .5342
.2830
.302
.2147 .2518 .2198 .6907 -1870 -1897 ,0886 ,1909 .2312
,2307 .4463 .7360 ,2681 e7741 .3919 .3519 ,1258 .4270
.2220
.le61
80.3
70.1 ~ 4 2 3 7 94.7 -0595 71.3 ,0733 76.1 .le03 82.9 .0371 68.5 ~ 4 7 4 6 98.4 .0361 70.0 -1793 82.9 ,0486 68.2 .lo75 79.4 ,0107 65.9 ,2042 81.3 .6302 103.7 .4616 98.3 .3680 90.9 -293 88.9 .0606
.0223
65.7
,3768 e5546 ,3019
93.7 100.3 89.3 62.6 69.5 70.6 95.2 101.5 106.3 91.5
.OM2
.0412 .0389 e4234 a5595 .6833 .M18
Y1
y2
y3
.7210 .6651 2735 .3859 .1661 .3144 .5592 * 1505 .1918 .3033 .7P1 -1439 .2252 ,6833 .2117 * 1547 ,2671 ,2426 * 7503 .4281 -2540 .2034 e2372 .2352 * 6750 .I971 -1796 -0744 .1616 .2198
,0946 2447 .3030 .5345 .7331 .4776 .3710 .3617 .7626 .4896 .1922 7135 .75m .lo26 1655 .3626 * 3800 .4524 .1861 *5177 -3410 .2437 -4524 .7575 .2392 .7499 * 3952 .3735 -1378 *4319
.I844
-
a
l
c
u
l
a
Q1
-.0116 .W53
.ow2
-4235 * 0795 .loo8 .2081 .0697 .4878 -0456 .2071 -0778 .I426 .0228 .2142 ,6228 .4826 3529 .3050 .0636 -0542 4050 5529 ,3104 .0072 .0858 -0530 -4251 -5521 .TO06
-
.m99 .0243 -.0203 .0123 e0365 .0014 .0240
.0201
.W78 -.W90 ,0263 .ma7 .0162 -so043 .0281
.
-.0030 0138
-.ooo3 ,0269 a0375 -0378 .0019 -.0250
.0022
-.a24 -.0257 .a380
.0176 .019l -.0451 -0157 .0114 ,0106
e
d *3
.0002 -.0200
-.0275 -.0278 -.0326 -.0132 -.0095 -.0278 -.0292 -.0351 -.0121 -.0100
.W74 -.0210
.OW
.0151 -.0116 -.0413 -.0271
-.
.0146 -.0154 ,0157 -.0101 .0051 .0142 -0293 .0114
.0017 -.0296
.m20
-.0041 e0299 .0165 -.ooo8 -.0130 0061 -.0215 .0289
.02w .0113
.383
t
Q2
.0242
-.0033 -.0216 -.0120
-.0049
-.0282
.0017 -.0085 .0370
-e0446 0141 -.0017 .W74 -.0173 -.0065
-.
Table IV. Vapor-Liquid Equilibrium Data for the Methyl Acetate-Water-Acetic Acid System E x p e r i m e n t a l
i
=2
-2356 ,0185 -1847 -2734 .1302 * 2479 .Om8 .0522 -1494 .3901 .0196 .0252 .2851 e4332 .0035
.6172 6854 .6620 *4194 .6730 .a91 ,6805 .1718 .7280 -2331 ,6289 * 6447 -4129 .2315 .e127 ,8194 1597 e 6754 -0555 * 6950 ,4098 .2584 .4702 .4662
.0048
-0537 .0112 .a22
-
.0127 2445 .0262 -0327 .0329 .mi5 .ooo8 * 5913 .2684 .OlW 2447 * 1779 .0172 .6061 .0009 .1166 -1327 .1278 .5844 -0904
.983 * 9637
-0598 a4199 .6003 .4793 ,5172 ,6035 e1174 -9624 .7554 .6367 .6346 * 1222
.6681
x3
1472 .2961 *I533 -3072 .1968 *I430 -3107 .77a .1226 .3768 * 3515 -3301 ,3020 .3353 .le38 a1758 .7866 .3134 .3123 -2923 .3457 * 7154 e4971 .5W9 .ow2
-0355 .Ma9 * 3117 .3m7 .27@ * 3049 3793 .2765
f
.0367
.1280 .2306
.2376 * 2934 -2415
72
Yl
-8159 1942 7967 * 7524 7040 .a256 ,0922 ,2113 e7833 .e256 e1751 .238O .7768 .e310
,0710 .0679 .2165 .1289 -9174 1479 .7574 -1155 .l982 -1989 * 0467 -0478 .9087 ,7371 -1404 7330 .7339 -1359 .9082 -0515 -7153 .6863 .6829 .a943 * 6095
,1787 .6401 ,1896 .2040 .2685 .1680 .7127 * 2454 .2106 ,1300 .6221 e5856 .I923 .I309 .a097 .a234 -2335 .BO7 .0423
C
Y3
.0054 .1657 .0137 .0436 -0275 .0064 -1951 -5433 .0061 -0444
.2028 -1764 -0309 .0381 ,1193 .lo87 -5500 ,1904
t,OC
65.5 96.2 67.6 71.8 72.7 65.0 99.6 103.4 67.5 71.7 97.6 95.2 71.9 69.3 99.1 99.2 103.3 98.6
.a11
.2065 * 3523 5050 5037 .e918 .9281 .0462 .2119 .6285 2339 .2331 .6325 .0758 .9243 .2707 .2786 .2782 .0778 .3361 0
.5m .2968 .2974
.oki5 .0241 .0451 .0510 .2311 .0331
.oik -2316 .0160 .0242 .Old0
.0351 ,0389 .0279
105.1 98.8 98.6 98;9 98.8 67.8 71.9 99.2 70.6 i5.9 99.4 64.5 98.7 , ,
69.8 75.1 16.0 65.8
of 1.72 bar at the entrance of the packed column. The sample (1 mm3) was passed through a 2-m length '/,& diameter Poropak-Q column maintained at 150 OC. The accuracy of the method was assessed by analyzlng chromatographically the composition of standard test mixtues. The mean deviation between the analyzed and known component concentrations was found to be 0.5 wt %. Additional
Y1
-7781 .2046 -7529 * 7505 .6826 .78M .lo46 -1954 .7437 -8054 .1872 .2399 ,7581 .a253 .0652 .0896 .1980 .1286
.m7
.1516 * 7215 .1132 2059 -2053 so394 .0256 .8912 7464 .1701
-7420 6793 e 1570 .a857 .0287 * 7079 -6659 .6550 .a808
.5838
a
l
c
72
Y)
.203a
.om
.6228 .2251 .1891 .2755 * 1997 .6915 .2476 .2388 * 1149 5992 .5733 .1841 -1093 .e203
.BO45 -2338 .6708 ,0268 .6677 .zoo2
-3569 .4867 .4841 -9127 .9593
u
-1727 .0221
.Om3
.0418 .0170 2039 e5570 .0176 -0797 .2136 ,1868 -0578 .0654 .I145 1059 .5682 .2006 .o726 .le07 .0783 5299 * 3075 .3106 * 0479 .0151
.0288
.0800
.l910 * 5917 .2057 .2476 .6023 .0564 .9557 .2702 .2804 .2873 .0584 .3442
.0626 .2382 052 3 -0731 .2407 e0579 .0156 .0219 so537 -0577 .0608 .0720
l
a
t
Ql
.0378 -.0104 .0438 .OOl9 .0214 .0422 -.0124 *0159 -0 396 .0202 -.0121
-..0187 Wl9 .W57 "8 -.0217 .Ole5 .ooo3 .0167 -.0037 a0359 .0023 -.@377 -.0064 .m73 .0222
.0175 -.0093 -.0297 -.0090
.0546 -.0211
.0225 .0228 .0074 .0204 -0279 ,0135 .0257
e
d
Q2
-.0251 .0173 -e0355 -0149 -.0070 -.0317 .0212 -.0022 -.0282
.0151 .0229 ,0123 .0082 .0216 -.0106 .ole9
Q3 -.0127 0070 0084 -.0167 -.Old3 -.0106
-. -.
-.0088
-.0137 -.oil5 -SO353 -.0108 -.0104 -.0269 -.0273 .0048
.ooze
-.0003
-.ole2
.W99 -0155 .0134 .W63 -.0046 .0183 .0196 -.0209 -.0312 ,0174 ,0209 .0368
-.0102 -.0323
.0282
-a0145 .ow2
-0194 -.0314 .COO5 -.0018 -.009l .0194 -.m75
-.0097 -.0422 .W23
-.0107 -.0132 .0136 .mgo -.0m9 -.0116 -.W71 -.0192 -.0401 -.w91 -.0419 .0086 -.0079 -.0186 -.0188
-.0329 -.0182
details of the analytical and operational procedure are given in ref 29.
Results and Discusdon In the present work initially the Wilson and the NRTL equations were tested. In the NRTL equation 7,,and 7 ) were ad-
Journal of Chemical and Engineering Data, Vol. 27, No. 1, 1982 67 Table V. Vapor-Liquid Equilibrium Data for the Methanol-Water-Acetic Acid System E 1,
.114 8 .0344
.3555 ,0178 .3362 .I724 .3795 .1641 .4069 .0264 .1268 .1482 .0321 0399 ,0361 .4386 .1632 .I913 .0214 -4177 .0467 .3395 ,2225 .3387 .3985 .0702 .0889 .3583
x
p
e
r
i
m
e
Y,
XO
X,
.a56 6787 .5899 9141 5591 a 8097 * 5258 -7961 .5223 .3894 -5316 .SO90 .4019 ,6684 ,6818 .4855 .a165 .7880 -9098 -4968 .6815 .5184 ,5762 ,5617 .5217 5801 .6060 .5865
,2796 -2869 ,0546 .0681 * 1047 -0179 0947 -0398 .0708 .5842 .M16 .0428 ,5660 2917
-
.2821
so759 .0203
.Om7 ,0688 ,0855 .2718 .1421 .2013 -0996 ,0798 .M97 3051 .0552
-
3442 .1312 7039 -0544 7079 .5984 7237 5407 7530 -0776 3741 -5304 e0796 -1515 -1475 ,7765 -5716 ,6263 .1316 -7376 .1786 .6892 .5558 .7632 7500 ,2190 .2865 * 7309 6
n
t
a
l
C
Y-
Y,
,5361 7030 .2682 .a985 2790 * 3991
,1197 .1658 a0279 .0471 .0131 .0025 so155
.2608
* 4492
2394 ,5010 .4867 * 4587 -5083 -6897 .6972 62157 a4235 ,3697 .e273 .2506 .6782 .2676 .3869 e 2305 ,2411 .5949 * 5717 .2634
t,OC
93.4 99.6 79.0 98.3 80.6 84.1 79.4 .0101 85.3 .0076 78.6 .4214 104.6 -1392 94.3 ,0109 85.5 .4121 104.3 .1580 98.9 ~ 1 5 5 3 99.3 .a378 77.4 .0049 64.9 .0040 83.3 e0411 97.7 .on8 78.5 .1432 98.3 .0432 81.4 a0573 87.8 .0063 80.6 ,0089 78.7 .1861 97.9 .1418 95.7 .0057 78.6
justable parameters. The third parameter, ail,was estimated according to both Renon's and Prausnltz's rules as well as calculated as a third adjustable parameter. From this fit only poor agreement between the experimental and predicted y values was obtained. This was also the case obtained by Jenkins and Glbson-Robinsonwhen they t r i i to correlate data containing acetic acid with the Wilson and NRTL equations (5). Since acetic acid associates in the vapor and liquid phases, Marek's method for association of acetic acid had to be used in combination with one of the usual equations. Best results for the binary systems were obtained when Marek's method was used in combination with the Margules or NRTL equations (in the case of the NRTL equation when ail three parameters were determined). The predictions for the ternary and quaternary systems with the NRTL equation were, however, not as good as those obtained with the Margules (third-order) equation. This is explained since the Marguies equation Is a higher form of the integrated Glbbs-Duhem equation and contains ternary determined constants to correlate the complex system. For this reason the Margules equation was finally used. The most precise of the available methods to calculate the constants in the Margules equation is from the known equHlbrium compositions of the vapor and the liquid (30). This was therefore adopted for the present work. Data fits were computed for all systems. For the calculation of the binary and ternary constants, a computer program with a routine based on Powell's work (37)was used to minimize the sum of squares of the deviations of the vapor-phase mole fractions (25). For the quaternary system the quaternary Marguies equation as expressed by Marek (32)was used, and no constants needed to be determined. Calculated y values as well as deviations in the y values for all experimentally determined vapor-liquid equilibrium data are contained in Tables I-VI. The references used for the experimental points, the values calcuA 21) and ternary (C)Margules conlated for the binary (A stants, as well as the values of the root mean square deviations (rmsds) for the binary, ternary , and quaternary fits are as follows: methyl acetate-methanol ( 9 ) ,A 12 = 0.4416, A, = 0.4335, rmsd = 0.005; methyl acetate-water ( 9 ) , A,, = 1.0045, A 21 = 0.6764, rmsd = 0.023; methyl acetate-acetic acid (Table I), A = -0.1026, A = 0.61 18, rmsd = 0.020; methanol-water (13),A 12 = 0.3444, A 21 = 0.2268, rmsd =
,,,
,,
,
Y1
.3506 .1312 7040 .lo42 e6855 * 5418 7177 -5224 -7368 .0781 .3599 -4966 .0949 .1486 .I378 * 7563 .5280 -5654 .1225 .7433 * 1745 .6841 .5534 .6880 s7314 ,2256 -2839 7060
-
a
l
c
u
y3
y2 * 5204 .6903 * 2899 .e653 * 2990 e4557 -2695 .4706 .2555 .4895 .4739 * 4952 ,4937 ,6732 ,6888 e2357 -4690 -4319 * 8475 * 2465 .6669 2904 .3891 2977 * 2595 .5718 .5574 ,2881
,1290 ,1785 .0061 .0305 -0155 .0025 .0127 .W70 .W77 -4324 .1661
l
a
t
-00064
,0157 .0127
.om0
-.coo1
-.0217
-SO498 .0224 ,0566 .0060 .Ole3 .0162 -.0005 .0142
-.0566 -.0087 -.0214 -.0161 .oil5
-1585 .0255 a0575 ,0142 .0092 .2026
-1587 .0059
.OoOo
.0028
.0031 -.oOOl -.0110
-.0269 .0027 .W7 -.0194 -.0182
.0202
-.0200
-.0002
a0436 .OM9 .009l -e0057 .0041 .m51 .0024 e0752 .0186 -.0066 .0026 -0249
-.(I455 -.0622
.0019
-.0202
.0110
-.0153 .OO29 .m97
.0301 .0102
,0332 -.0200
.0128
.0012
-0041 .0113 -.0228 -.0022
.0016 -.0153 e0177 -.0002
-.0672 -.0184 ,0231 .Old3 -SO247
'
-.0079 -.COO3
-.0165 -.0169 -.o002
r
O4
-a0093 -.0127 .0218 .0166 -.0024
-.0365 .0146 .0165 .0084
-4114 ,1782 e1735 .W28
dy3
472
.03)8
.W30
d
dyl
0082
.me0
e
7
I
02t
I
I
I 0
1
02 04 06 08 10 Liquid mole fraction of methyl acetate
Figure 1. Plots of llquM vs. vapor and IiquM vs. devlatlon in vapor composltlon for the methyl acetate-methanol system.
,,
0.005; methanol-acetic acid (Table II), A = -0.0305, A 21 = 0.0098, rmsd = 0.009; water-acetic acid (9),A 12 = 0.2569, A,, = 0.2940, rmsd = 0.010; methyl acetate-methanol-water (70), C = -0.1201, rmsd = 0.035; methyl acetate-methanol-acetic acid (Table 111), C = -0.12, rmsd = 0.020; methyl acetate-water-acetic acid (Table IV), C = -0.0953, rmsd = 0.021; methanol-water-acetic acid (Table V), C = 0.3546, rmsd = 0.024; methyl acetate-methanol-water-acetic acid (Table VI), rmsd = 0.023. I n figures 1-6 all binary data points are plotted for the more volatile component showing x vs. y values as well as x vs. deviation in the y values. Experimental results proved to be in good agreement with predicted vapor compositions for the binary, ternary, and quaternary systems. Some binary systems were highly nonideal. Thus, methyl
68 Journal of C h e m i a l and Engineering Data, Vol. 27, No. 1, 1982
Table VI. Vapor-Liquid Equilibrium Data for the Methyl Acetate-Methanol-Water-Acetic Acid System zS04
E x p e r i m e n t a l
-
&
x1 .0912 .a11
,0414 .0136 ,1958 ,0373 * 0370 ,1265 .1693 * 0409 -0548 .0625 -0556 -0237 .lo65 1049 * 0570 -0277 .loo8 0245 -0570 .OM6 .0196 * 0295 .0127 e0704
-
.0244
.069 .0605 -0197 .0116 .0267 .0713 -0317 .1291
.I947 .a96
=2
*3 .5280 .la37
.09@J
.a002
.OB35 .6769 .I974 .1998 .OB27 -2173 -0585 * 3971 .2067 .03P .OM1 * 1902 .0618 .1686 .la27 .0398 e1699 * 1259 2724 SO525 -0875 e0535 .1238 .1511 .0944 * 3742 .0696 -0491
* 7967 .0083 .6396 .a24 .5223 5402 .7128 .1512 .4802 * 7569 .7474 .a45 -4971 3855 * 6579 .7116 * 7257 .2213 .4608 .8OP 5091 * 7251 -5198 .6878 * 5969 -1431 .a426 * 7249 * 5135 5194 * 7279 .6043
+
.0810
.1216 .0531 -0519
y1
e4471 .4824 * 4791 .2060 .3583 * 2998 .2667 .5754 .6161 .4011 .1702 * 3165 .5358 * 2354 .34@ .4776 .2562
f
.2382
.6482 .2611 .1963 .3876 .2409 -1855 * 1499 * 3515 .2213 ,4287 .1813 -2341 .1463 .1692 .3756 2954 .5421
-
Y2
C a l c u l a t e d Y3
.2404 .0546 .3022 .4961 .0923 .2853 -3170 ,2567 .1507 .4041 .lo77 .2743 .3600 -5276 .1776 .3153 .2848 ,3280 .2665 .3348 .2456 .2161 .5145
74.20 58.80 76.20 86.80 61.70 77.90 79.30 76.20 63.20 83.60 80.85 79.50 78.60 90.35 84.90 82.10
.3934 .1798 .6150 .26M ,1587 .2090 .2321 .1714 .1375
.3542 .3334 .0974 .4725 .5977 .4565 .3222 .4618 ,2631
81.80 80.60 81.25 86.30 92.80 92.80 83.40 88.15 78.40
I
0 0
0 0
4 0
4
o 4
0 0
4 2
4 0 0
0
2
o 0
o 0
4
o
0
o 0 0 0
0 0 0 2 2 0 0
5
0 0
.0682 .0964 .2468 .1174 .lo64 ,0884 .3686 .0813
.*93 ,0576 .0244 .1110
.W73 .1122 .0096 .lo44 .1192 .0057 .0092 .I337 .1231 .1220 -1763 .0879 -0797 .0129 .0312 .1179 ,0546 .lo79 .lo22
.lo43 .0353 .0348 .0026 .ma2 -1303 .0480 .0698
-2353 .3669 * 3765 ,0691 0 380 .3504 * 2055 *1457 .1920 .1271 .I371 -0391 .0631 .0073 .0389 1769 so475 -0057 -0725 .I726 .0798 -0715 .6252 -1575 .I736 -0775 .I383 .0423 .2020 .I930 -3976 .3928 .0998 .0962 -0137 .0646 .0454 .0469 .1164
.
.4933 .2900 .1189 -4604 .6187 .3026 ,3540 .4733 * 3472 .22M .6464 .6111 .7895 .3810 .5608 -6135 6159 .a231 .7820 .5894 a5247 .4540 .1923 .4703 .5478 * 7996 .7244 6704 e4675 .2112 .3249 .3242 .773c .7762 .a303 * 7892 .6273 .7731 .5225
.3470 .3357 -5048 .5218 .5233 .3228 ,7091 -3931 .7292 .2014 * 1905 .5282 .1226 *
5015
.0714 .5544 ,6348 .0916 .1412 .5829 ,5666 .5043 .4577 .4129 .4230 .2069 .3306 .6513 .a829 .3445 .3306 .3406 .3494 .3493 .0401 ,1266 .6715 .5413 .3768
hoc
.Pa63 .4588 .1988 .2615 .5448 .3933 .3842 .1304 .le03 .142O .6276 .3564 .0712 -1507 .3136 .1161 . 3-3-5_5 _ .4099 .06i5 -3909 ,2674 .3813 -1909
.3650 .4863 .4071 .1185 * 1095 ,4769 .la84 -2492 .1624 .27:0 .3484 .1129 -2244 .0211 -1145 ,2337 ,0785 .0373 ,2568 .2103 -1274 .lo88 .4742 .2592 .2841 .2502 .3071 .0635 .3677 .31W -4852 .4965 .2584 .2471 .0668 .2352 e0552 .1121
.2329
.2566 .1501 .Ok76 .2760 .2937 .1&5 .0968 .2869 ,1026 .2354 .4032 .2846 3931 .2343 .5942 .2016 .2569 .7599 .5511
,1964 .2629 .2962 .Ok51 .2720 .26!0 .:050 .3410 .2634 .2866 .I799 .1460 .I494 .3681 .3761 .7994 .5816 ,2290 .3255 .3227
y2
y3
-2972 .4983 * 2154 .2738 * 5910 ,3877 3926 .1342 * 2495 * 1497 .6088 .3568 ,0805 .1380 .3243 .1132 * 3247 .3969 -0733 .3918 .2721 .3818 1745 .2171 .1805 .E341 .3610 .le60 .5829 -2254 .I694 ,2065 .2299 .I493 .a857
.2215
Y1
-4521 .4416 .4294 * 1935 * 3969 * 2945 -2771 .5611 .5859 .922 * 1945 3391 * 5024 .2803 .3637 .5028 .2824 2452 .6229 .2510 .2248 * 4037 .2708
85.80
86.45 72.56 78.60 94.00 72.90 88.00
.2379 .4404 .2094 ,2887
I I
I
.1476 .la94 -3997 .3312 .6174
76.40 ,3611 72.90 .3520 66.2C .5279 81.45 ,5145 81.80 ,5809 74.20 .5383 60.70 .6689 80.95 .4074 60.60 .6800 93.8: .2276 85.30 .2228 81.3: .5873 90.90 .1133 90.20 .4730 98.iC .0832 69.00 .5255 74.80 ,6058 98.20 .lo55 89.65 .1355 67.16 1,5718 76.90 .5561 80.95 .5218 59.?6 . b 7 6 79.2c .4242 76.40 .4323 87.20 .1876 79.10 ,3057 72.50 .6351 81.80 ,3039 84.00 -3693 70.75 .3726 10.85 .3778 80.40 .3703 80.70 .3699 98.20 ,0511 90.40 .l& 73.00 .63M 79.20 .4687 83.40 .3965
I
I
I
6
.3759 .4775 .3889 ,1210
.0699 .4756 .2087 .E563 .1975 .2735 .333 .0706 .2358 .Old8 .1204 .2547 .O817 .0268
.2559 .2284 .1315 .1231 .5195 -2649 .2865 .2611 .3218 .0728 .3659 ,3250 .4767 .4716 .2461 .2405
94
-
.2273 .I313 .0493 .2625 .2907 .1420 ,1183 .2588
.1183 .2079 .388i .2843 .5969 .3001 .%96 .2090 .2666 .7745 .5601 .la98 .a505 .2556 ,0627 .2437 .2453 ,5184 .3520 .2610 .2610 .I433 .1302 .1303 .3659 .3712
.0356 .0391 .0338 .lo20 .0585 ,0442 .0042 SO775 .W42 .2910 .0547 -0579 -0540 .2121 .2368
-.0141 -.0163 -.0231 .0073 -.0576 -.0154 .0402 -.0143 -0492 -.0262 -.0323 -.0591 .W93 .0285 -.0118
.0108
.0289
.0458 .0932 -0485
-.0139 .W57
.0100
.0619 -0994 .mo2
.0673 .0360 .0330 .om5 .0305 ,0691 .1523 .0205 .0204 .0178 .0184 .OB53 .0518 .0380 .0324 .0826
4v3
4v4
.0189 -.0054 -.0418 -.0063 .OB92 -.0113 .0183 .oil5
-.0029 ,0040 .ma7 .0061
*2
*l
.0291 - . W O -.OlOg . o m .OW2 .0408 -.0395 .0497 -.0166 .3440 .0112 -5024 .0303 . O W -.0123 .0031 .W90 -.0386 -.0462 .2966 .0212 .0053 .0056 2987 .0315 -.0104 -.0084 -2452 -0595 .0143 -60038 .OW2 -.0692 * 1597 -0049 -4105 -0576 .0189 -.GO77 .Om5 -1081 -.0243 .0188 .a486 -0555 -e0226 -.0004 .3766 -0405 .0334 -.0093 .0127 5107 .0709 -.0449 .14l6 .1704 -.O229 -.0107 .2844 .0997 - . O W .0029 .2610 .1319 -.0262 .0108 .0130 * 3327 .0253 -.OD70 . 2 7 a .0271 .0253 -.0098 .3444 .0129 .0101 -.ooOg -.0047 * 2075 .a955 -.O285 .1g01 . 0 2 4 -.0161 -.0005 .0164 -5140 .0407 -.029g .4101 ,1686 -.0188 .0016 .5677 .0926 -0093 -.0115 .2911 .0787 -.OM7 .0084 .0324 * 3704 .ON7 -.0166 .3115 .0622 -.oil7 -.0062 .0863 .1215 -.0281 .0321 .0366 ,4702 .0158 -.0546 -.0013 -.0107 .5844 .0987 .4261 .1780 -.0202 .0025 .0022 * 2913 ,0792 -.0241 .0221 ~ 4 5 5 1 .0644 -.0358 .0518 2535 ,0434 -.0753
.0290
,0111
.0105 -.0175 .0401 011 3 -.0093 .0193 .0249 .0156
-.
-.0210
-.0248 -.0420 -.0372 -.om9 -.0206 -.on0 .0011
.0371 .0726 -.0197
-.mw
-.0064 .01g2 .0257 -.0166 .0169 .0360 .0309 .0238 -.0047 -.0103 -.0096 .0381
,0260 .m5 .0320 .0203 .0486 -.0162 .0219
-.0109 .00@ .0182
-.oO25 .0396 .mi3 -.om3 -.0071 -.0351 .00l5 .0146 .0423 -.0114 .0063 -.0059
.0111
.0023 .0133 -0304 00309 .0067 .OW6
-.0044
.m4 .0006 -.0220 .0480 0048 -.0136 -.GO27 -.@375 a0154 -.0024 -.0087 -.m4 -.0014 -.0053 .0w3 .0048 0094 0130 -.0149 .m5 -.0124
-.
-
-..
.0004 -. W41 -.0152 .0156 -.-.0127 0014 -.0091 .0070 -0139
-
,0293
.om
.Ol83 .0135 ,0030 .0205 -.0215 .0281
-.0042 -.0112 - e 0 1 33 -.Ole3 .0150 -.0064 .0015 -.0067 .0016
-.0157 .0275 -.0028 .0032 .0145 .0164 .0003 -.M)38 .W59 -.Of358 .0310 .OM6 -.0169 -.0005 -.0210 -.0074 -.016c -.0032 -.0097 .0180 .0105 -.0146 .0009 -.0090 .0024 -.Ole1 .0066 0004 -.0041 .0124 -.0188 -.0143 .0406 -.ma7 .0028 -.0453 .0024 -.0057 .0283 -.0114 -.0024 .0197 -.0081 -.0109 - . o w .0049 -.0147 -.0110 .0m8 -.0093 ,0024 -.0087 .0018 .0256 -.0063 -.0060 .0366 -.0057 ,0085 .0158 .0177 .ow .0191 -.0069 .0123 .0022 .006 3 .0085 .a66 .0055 .COO1 .0025 .0084 .0048 - 002 -.0037 -10192 -.0236 .0063 -.0113 -.0056 -.0557 .0095 .0252 -.0150
.
Journal of Chemkal and Engineering Data, Vol. 27, No.
I, 1982 69
E x p e r i m e n t a l
0 2
4
0 0
0 2
0
4 2
0 0
4 0 0
4
0 0 0
4 4 4
0
4 0 0 0
4
0 2 2
0 0
0 0 0
0 0 0
.1418 .0124 ,1344 -0137 .0232 .oil9 -0249 .0922 ,1971 .0241 .0615 -0424 e1752 .W97 .0084 .0114 1654 .1240 -0393 1991 1775 ,1721 ,0583 .2089 .0248 e0413 ,0183 e1379 * 2558 -0149 .a55 .0916 -0697 .1215 so974 * 2550 e0934
-0493 .(I516 .0522 .0935 .1459 .0864 .0408 ,0363 .1362 .OM5 .0436 .2805 .1116 .lo11
.0521 .6446 .0480 .2113 .0236 .3063 -2954 .1258
-
,1382
a1447 ,0591 .195 .0520 .0934 .0480 .0056 .0366 .0946 .3182 .0357 .0929 .2811 .1310 e3693
.0602
2542
.a05 .8125
6424 ,1508 *5677 .1187 -1946 ,1203 ,2238 ,6420 .6058 .2240 * 5551 * 5145 * 5257 .I378 1305 *
.a22
.6732 .6423 .a02
.7489 .7222 .5175 .7561 .7541 .7853 .4766 .7852 .7949 .8€84 .0773 .6089 .5897 .4709 .4359 e4609 .2238 .4822 -7446 .?lo9 .7416 .6062 .5158 .8124 .8292 .7211 .6081 .4007 .@79 8.5177 ,4459 .7527 e1397
-
.0727 .2102
.1201
.2878 * 3673 .2581 1547 .0622 .2014 *l384 .2102
.lo81 ,3202 ,3586 -3384
.1620
.2280
.3381 .6258 .2873 .a31 .5201 * 5224
* 5911
.1860
.6048 .3007 .4W8 .2362 * 5700 .7302 .1962 .0916 .6420 .4313 .4443
e0763 -3878 -0533 .3443 .3286 .2668 .2011
-
.3511 1451 .3445 .1242 0940 .1865 -0373 .0622 .1820
.3812
.6261
.0603
,7367 .3938 -5551 * 5046
.0885 .3820 * 2102
a4065
10
-2585 .5823 .2583 .5118 .3886 s5340 -5336 2719 .1628 .5457 .2310 .3535 .1480 .4759 .4945 .5701 .0632 .2684 .2984 .1861 .I256 .1422 .2463 ,1642 -3330 4037 .3944 .2561 .1706 .55@ * 7599 * 2719 3346 .1629 .2850 ,1643 .2027 .2310 .0713
72.50 90.60 77-40 90.50 84.50 91.20 90.30 73.50 69.95 91.30 69.00 80.00
66.60 86.40 87.35 90.30 62.50 74.60 78.10 80.45 66-20 66.50 94.20 71.15 79-40 83.50 82.50 76 * 90 64.60 89.90 98.20 73.70 80.40 68.80 14-70 64.70 72.30 69.00 66.10
.6400 .1922 .6262 ,1481 .2117 *I333 .2926 .a92 * 6409 * 2914 .4840 .4465 .5537 * 1377 .1252 .a341 .3809 .6118 .2831 .6778 *5385 * 5420 * 2299 -6414 .2663 *3833 .2118 6345 .7063 .2243 .io40 .6067
-
.460
-4476 .6015 .7063 * 4091 .478O -5392
.0786 .I899 .0846 .2759 ,3525 ,2643 .1273 ,0701 .1689 .1107 .2445 .1161 .2994 .3543 .3378 -2043 ,5824 ,0812 .4013 -0354 .3209 .31M .2703 .la95 *3531 .1505 -3509 SO833 .I131
.l756 .0266 ,0709 .1862 -3847 .0677 .1126 .3846 .2470 -3756
.2427 .5735 .2480 *4917 .3843 .5130 .5089 .2915 .1741 .5243 .2660 .do44 .I428 .4842 .5109 .5723 .0287 ,2615 .2864 .2190
-1354 .1402 .2080
.1690 -3654 .4087 -4125 02439 .1682 .5592 .7800 .2927 .3105 .I509 .2924 .la5 .1824 .2691 .0565
.0388
.W24 -.0414 ,0412 -.0585 -0843 -.0294 .0515 -.0171 ,0894 -.0130 ,0712 -.0688 ,0292 0 328 .0161 -.0351 -0737 -.0674 .0711 .m55 .0680 .0330 .OO40 -.0280 .ooo1 ,0239 ,0261 .0053 -0193 .0421 .0080 -.0428 *0454 .0140 ,0291 .0042 -0679 e0053 .0053 -.0184 .W44 -.0196 .2918 -a0439 .0200 -.0366 .0152 .0344 0575 SO175 .0248 .0244 SO645 .OS3 .0124 -0239 .0438 -.0281 .OB94 -.0124 -0297 e0353 so573 -.0147 ,0169 -.0033 .0246 ,0384 .0125 -094 .0238 -e0153 .W59 -0771 .0286 -.0346
.
-
-
.0158 -.0059 .0203 .0088 e0355 .0103 .oil9 .0201 .Old8 .0043 -.0062 .0210 -0274 -0247 -.0079 -.0196 -0325 .0113 a0277 .0214 -.OM3 -.0350 -.0080 -.0509 .02O8 .m52 . w 4 3 -.0083 .OW6 -.0164 .0237 -.0022 .m7 -0345 .0069 -e0049 -e0135 .0120 .0179 -.0329 0098 ,0234 .0020 .a152 -em35 e033 .0316 .0048 -.0020 -.0324 0050 -.@354
-.0124 .0123 .0127 0026
.0409 -.0191 .0139 .0107 -.0087 -.0042 -.0035 0074 -.0241 -.0026 -.0368 e0309
.0114 -.0072 .0167 .0218 -.W58 -.0052 -.0053 -.0098
-
-.a18 .0167 -.@353 .0139 .0182 -.0018
-.0091 .0021
.w38 .0105
.0206
-
-.0004 -.0159 0026 ,0096 .a47 .0024 .0091 .W99
-.
-.0071
-.
-.mq -.0181
-.
-. -.0020
.0122
.W24 -. 0024 -.0201 -.0208
.0241 .0120
-.0074 -.0042 .Om3
-.om
.0148
-.
.0000
.mol
-.OOx)
-.0023 -.w22 -.0110
n
-
Calculated
r
0
1
04 02 -
0
02
04
06
08
10
Liquid mole fraction of metbyl acetate
02 04 06 08 10 Liquld mole fraction of methyl acetate
0
Flgure 2. Plots of liquid vs. vapor and liquid vs. deviation in vapor composition for the methyl acetate-water system.
Flgure 3. Plots of liquld vs. vapor and liquid vs. deviation in vapor composition for the methyl acetate-acetic acid system.
acetate-water was only partially miscible (9), whereas methyl acetate-methanol exhibited an azeotrope at 0.323 mole fraction of methanol and a corresponding minimum boiling point of 54 O C (9).System c was inaccurate for vapor mole fractions of ester higher than 0.90. I t might be argued that the fit for this system could be Improved by use of the Jenkins and GibSOfFRobinsonequation which includes a liqukkphase association
factor (5). This is, however, unlikely since the inaccuracy occurs at the low acetic acid concentration end, and, in view of the wish to limit this study to the Marek equation, this t8st was outside the scope of this paper. Since dwlng operation of a reacbionld&tlllation column sulfuric acid is present as a catalyst, it was necessary to investigate the quaternary system in the presence of this catalyst. I t was
70 Journal of Chemical and Engineering Data, Vol. 27, No. 1, 1982 10
08
06 Y~
Y
,,,/,/-
O4
0
- Calculated
Calculated Fastovskij(13)
Rivenc(19)
~
,
02
-
00 -
-
I
04I-
02-
p+-050-*---r-Tr
dy 0
a-
1
02c
02 -04c
I
-04I-
6
0’2
06-
04
Liquid Tole frac:iar
08
13
10---
,
oa 06-
1
d
c4L 021
00
c
B
- Calculated 3
Experimentc
.
I
04-
-041
I
1
1
04 06 08 Liauid mole fraction of methanol
0
02
02
04
06
38
IC
Lquid mole fraction of water
Flgwe 4. Plots of liquid vs. vapor and liquid vs. deviation in vapor composition for the methanol-water system.
Y
0
oi rneti-anol
10
Flgwo 5. Plots of ilquki vs. vapor and liqukl vs. deviation in vapor
composition for the methanol-acetic acid system.
found that the same vapor-liquid equilibrium equations were valid even when the nonvolatile catalyst was present. Teshima, et al. (33)expressed the influence of sulfuric acid catalyst on vapor-liquid equilibrium of the system water-acetic acid by an equation which provided further proof that the effect of the catalyst was negligible. Hirata and Komatsu (34) investigated the same quaternary system and presented four equations to predict the vapor-lid equilibrium ratios as a function of temperatwe. Their equations were tested in the present wotk with known equilibrium data, and the resub were found to be unsatisfactory. Suruki et al. (35)also tried to simulate the system with the Margules equation modified by Marek, but they reported that their trlai failed to obtain a good relation. This is belleved to be
Flgurr 6. Plots of liquid vs. vapor and liquid vs. deviation in vapor composition for the water-acetic acid system. due to the fact that they only used quaternary experimental data to fit their constants. They then presented an equation to calculate the activity coefficients of this quaternary system. Theii equation, which consisted of 64 constants, was based on the Margules equation rearranged as a polynomial series in mole fractions of the components in the mixture. Theii equation was tested with binary, ternary, and quaternary vapor-liquid equilibrium data, and the results were also found to be unsatisfactory. Further studies of vapor-liquid relations, for quaternary systems of esterification of acetic acid with butanol and ethanol, were made by Hirata and Komatsu (36, 37). They derived some relations with graphical correlation to predict vapor-liquid equilibrium ratios as a function of temperature. Their quaternary system was, however, outside the scope of this article, and their equations were not tested. Finally, Sebastiani and Lacquaniti (38)have also taken into account the association of acetic acid in their equation to correlate acetic acid-water binary systems. They introduced a temperatwe influence on the activii coefficient and explained that this played a very important role in the thermodynamic correlation. Conslstency Testing of Blnerles All six binaries fitted a binary third-order Margules equation, in combination with Marek’s equations for associatiin of acetic acid, and were therefore considered thermodynamically consistent (39). System b presented some deviations mainly due to its strong nonideaaty, but this system satisfied Herington’s test of consistency. System c did not satisfy Herington’s test, but this was probably due to the fact that the boiling point of the components of this sytem were widely different. Furthermore, systems a and d-f satisfied Herington’s test.
Acknowledgment We express our gratitude to ICI-Europa for pemkion to use its computer. Appendlx A model was developed by Marek and Standart (3) and by Marek (4) leading to the final correlations presented here. Thus,
Journal of Chemical and Engineering Data, Vol. 27, No. 1, 1982 71
correction component i
C
(3)
i
Literature CHed
(4)
(5)
(6) The factors and which express the influence Of the vaDor-Dhase association of A, may be evaluated from a knowledge of its association constant K . The factor z B is a correction for the nonMealb in the liquid phase and may be evaluated from various generalized relations, for example, from the Scheibel correlation. The corrected vapor pressure of the associating component, PA:, and the vapor pressure of the nonassociating component PBomay be determined from the properties of the pure substances. The dependence of the activity coefficients y A and Y~ on the liquid-phase composition may be expressed by means of suitable equations. The usual empirical equations containing an adequate number of empirical constants may then be used for the correlation. constants in Margules’ binary equation constant in Margules’ ternary equation association constant corrected vapor pressure of acetic acid vapor pressure of nonassociating component temperature, O C mole fraction of component i in the liquid phase mole fraction of component i in the vapor phase factor for the influence of the vapor-phase association of A factor for the influence of the vapor-phase association of B factor for the correction of nonideality in the liquid phase activity coefficient of component i total pressure
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; 1; G2:;GG.L;
~~~~~~~~~~;
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Subscripts A B
associating component, Le., acetic acid nonassociatlng component, iae., methyl acetate, methanol, or water
Received for review July 28, 1980. Revlsed manuscript recelved November 39 1980. Accepted September 8. 1981. P.A.P. thanks the Ministry of Coordination for awarding a NATO scholarshlp wMch enabled the work to be conducted.
