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A new device for measuring isothermal vapor - liquid equilibria
Fluid Phase Equilibria,
Elsevier Scientific
6 (1981) 237-259 Publishing Company, Amsterdam
A NEW DEVICE FOR MEASURING EQUILIBRIA
ABRAHAM
TAMIR *, ALEXANDER
Department (Israel)
of Chemical
(Received
Engineering,
May 13th, 1980; accepted
237 - Printed
ISOTHERMAL
APELBLAT Ben Gurion
in The Netherlands
VAPOR - LIQUID
and MOSHE WAGNER University
in revised form November
of the Negev,
Beer Sheva
14th, 1980)
ABSRACT Tamir, A., Apelblat, A. and Wagner, M., 1981. A new device for measuring vapor-liquid equilibria. Fluid Phase Equilibria, 6: 237-259.
isothermal
A new apparatus, based on the isoteniscope, was developed for measuring vaporliquid equilibrium under isothermal conditions. In order to evaluate its performance, the following mixtures were tested: acetone-chloroform at 25’C and 35,17’C, ethanolbenzene at 45’C, and acetone-chloroform-methanol at 5O’C. The results are in excellent agreement with literature data. The advantages of the present apparatus are simplicity of construction, ease of operation, minimal consumption of chemicals, relatively quick in reaching equilibrium, the degassing process is carried out simultaneously with preparation of the samples, and the apparatus is suitable for determination of the vapor composition.
INTRODUCTION
The aim of the present work is the development of the isoteniscope, first proposed by Smith and Menzies (1910) for measuring the total pressure of pure components and mixtures, as a simple tool for determining isothermal vapor-liquid equilibria (VLE) of mixtures. Numerous experimental techniques for studying VLE at low and normal pressures have been reviewed by Haa et al. (1967). From their review, it may be concluded that dynamic methods are more common than static. This is due to difficulties in measuring accurately the total pressure and vapor composition. On the other hand, the dynamic method has the disadvantage of achieving only with difficulty steady-state boiling in an equilibrium still at very low pressure. Over the years, total pressure measurements based on the isotensiscope were improved, e.g. by McGlashan and Williamson (1961), and further development was made by Apelblat et al. (1973). In recent years, great attention has been paid to static methods which are commonly used l
To whom correspondence
037%3812/81/0000-0000/$02.50
should be addressed. @ 1981 Elsevier Scientific
Publishing
Company
238
nowadays. Gibbs and van Ness (1972) developed an apparatus providing the entire composition range measurements in a day. Ronc and Ratcliff (1976) modified the above equilibrium to increase its accuracy further. Aim (1978) emphasizes that in his static assembly design, stress was especially laid on the attainment of maximum accuracy of measurement, the related thorough degassing of pure components, and their relatively low consumption. Very recently, Maher and Smith (1979) suggested a new multicell apparatus by means of which three isotherms are measured in a typical 5-day run (including loading, degassing and isotherm measurements). The major reason for the above developments in static methods is the adequate calculating procedures which were proposed and the advent of computer facilities for the evaluation of VLE from the total pressure data at normal pressures. In particular, from the works of van Ness et al. (1973), Abbott and van Ness (1975) and Abbott et al. (1975) it may be concluded that the measurement of the vapor mole fraction, which is usually most difficult to measure, is not absolutely necessary, especially if the experimental random errors are larger than those in the liquid mole fraction. The above authors have demonstrated reliable methods to compute the vapor composition from P-X data. Accurate determination of isothermal VLE requires degassing of the liquid mixture. Reliable degassing techniques were suggested by Bell et al. (1968), Battino et al. (1971), van Ness and Abbott (1978). It should be noted that almost every serious researcher has developed his own technique for degassing, recognizing the importance of this factor in obtaining reliable data. The measurement of the vapor composition is also very complicated and the inaccuracy is caused by handling very small quantities. In addition, removal of a vapor sample may cause a marked disturbance of the equilibrium. Consequently, it is acceptable to avoid measurements of the vapor composition, as is done in all the above-mentioned techniques. However, the present authors believe that any apparatus which is proposed for measuring VLE must also provide the user with the option of an accurate technique for the determination of the vapor composition. The above-mentioned difficulties are eliminated by the present method and the total pressure and vapor composition are accurately determined. We have tested several binary and ternary mixtures for which we achieved good agreement with known data. Also, our experiments revealed that the new apparatus possessed a number of advantages, viz. simplicity of construction, ease of operation, minimal consumption of chemicals, the time of operation (including preparation of a sample and attainment of equilibrium) never exceeds one hour, and it is also possible to detect the existence of a chemical reaction, if it happens, as well as incomplete degassing, by observing the change of the pressure versus time.
239 EXPERIMENTAL
SYSTEM
The experimental system is composed of the following parts: (a) manometers and a sampling system for vapor and liquid mixtures (Fig. l), (b) a thermostatic bath, and (c) a degassing unit for liquid samples (Fig. 2). The glass sampling system for liquid and vapor mixtures and manometers The design of the sampling system shown in Fig. 1 eliminates turbance of the vapor-liquid equilibrium. It is constructed of (1) A T-type connection (G) 7-10 cm long. Two connections ling bulbs and one for the manometer. (2) Sampling bulbs, E for liquid and F for vapor, each having 40 cm3 and a stopcock, F-l. The bulb E contains a tefloncoated bar for mixing the liquid. (3) Manometer (Fig. 1). It is a modified Booth and Halbedel teniscope for measuring the vapor pressure of multicomponent
Fig. 1. Two kinds of isothermal
vapor-liquid
equilibrium
systems,
any disfor sampa volume of magnetic (1946) isomixtures.
240
Fig. 2. Degassing unit and preparation
of samples.
For measuring vapor pressures above 450 mm Hg, a differential manometer (as shown on the right-hand side of Fig. 1) is used. The manometric fluid in bulb H has a known vapor pressure which acts against pressure in the U tube (left-hand side of Fig. 1). Thermostatic bath This unit is composed .of the following components. (1) A bath (45 X 35 X 35 cm) made of Perspex with a magnetic bar on its bottom for stirring the water. (2) An FT Haake unit with a circulation pump and a temperature control unit which maintains the desired temperature within +O.Ol”C. Degassing of pure components and preparation of samples Degassing of the liquids is a crucial step needed to obtain reliable determinations of the total pressure at equilibrium. The degassing unit, shown in Fig. 2, is constructed of a horizontal manifold with inlets to the sampling bulbs, G-J, to the liquid nitrogen trap, D, and to a vacuum pump (Crompton Parkinson Doncaster a.c. Motor type). Inlet, B is introduced to avoid the oil rising in the pump after shutdown, when the magnetic valve is absent. in the vacuum system. Stopcock E enables air to enter the manifold and thus to release the bulbs after degassing and samples preparation, while inlet F is used for the connection of a Pirani gauge.
241
We prepare a binary mixture (and ternary mixtures) simultaneously by the following degassing process: two empty bulbs are weighed and each one is filled with the appropriate component having a weight corresponding approximately to the desired molar concentration. The height of the liquid in each bulb is marked and then additional amounts of the components are added (about l/3 of the original volume). The bulbs are connected to the manifold and closed. The vacuum pump is operated and the “additional l/3” is evaporated, separately from each bulb, until the original level of the components in the bulbs is reached. The closed bulbs are again weighed and connected to the manifold which is completely evacuated; stopcock C-l is closed. The bulb containing the less volatile component is immersed in liquid nitrogen and the volatile component is transferred to this bulb as a result of the temperature difference between the bulbs. In order to speed up the process, the bulb with the volatile component is heated with hot air. At the end of this step, the bulb with the known composition is once again weighed for final control of the weight and connected to the isoteniscope at the appropriate place (bulb E in Fig. 1). Also, an evacuated and weighed bulb (F) is placed in the isoteniscope for vapor sampling. Experimental
procedure
The system shown on the right-hand side of Fig. 1 (and similarly for the other one) is evacuated by connection at point A to the degassing system in Fig. 2. Stopcock B is closed and the mercury initially filling bulb C is poured into the U tube. Complete degassing is indicated by identical heights of the mercury in D, checked by means of a cathetometer (Gaertner Scientific Corporation, Chicago, U.S.A.). The accuracy in measuring the heights of the manometric fluid (mercury or silicon oil) is kO.1 mm. If the heights of the mercury vary, the degassing process must be repeated (and the mercury must be returned to bulb C). If no leaks are observed, stopcock E-l is opened and the system (Fig. 1) is immersed in the thermostatic bath. Thermal equilibrium is realized within 20 min and the height of mercury is checked several times. To obtain a vapor sample in bulb F, stopcock F-l is opened with the system still immersed in the thermostatic bath. When equilibrium is again reached, stopcock F-l is closed and the system is withdrawn from the thermostatic bath. The bulb containing liquid (E) is immersed in liquid nitrogen to condense the vapor in the system. If the mercury heights in the U tube (D) arms are identical, it indicates that no leaks have occurred; otherwise, the experiments should be repeated. When stopcock E-l is closed and stopcock B is opened, it is possible to release bulbs E and F from the isoteniscope. Accurate determination of the vapor composition is rather difficult because of the small quantities (of the order of 10 mg) accumulated in bulb F. Bulb F is immersed in liquid nitrogen and lo-15 drops of an inert solvent are added. By means of this operation, the small amounts of the condensed vapor appearing on the bulb walls are washed down and accumulate for chromatographic analysis.
242 MEASUREMENT OF VARIABLES AND ERROR ANALYSIS
Temperature
The liquid bath temperature can be maintained within ?O.Ol”C of the desired temperature and the temperature gradient from top to bottom of the bath is about +O.Ol”C. The absolute temperature was measured by means of a Hewlett Packard Quartz Thermometer Model 2801-A with a sensitivity of ~0.0001”c. Pressure
The vapor pressure of a mixture was measured by means of a U tube containing mercury. The difference in the heights of the mercury was measured by means of a cathetometer and was translated into pressure units (mm Hg at 0°C). An estimate of the error associated with the pressure measurements can be obtained as follows [for the sake of simplicity the determination of the vapor pressure of a single component is considered (for which P = PO)]. The error in a single measurement of the vapor pressure, AP, depends on accurate measuring of the bath temperature as well as that of the mercury columns, namely
(1) Considering the Antoine equation nent
for the vapor pressure of a pure compo-
log12 = Ai - & I
and that P = pgh
it results that the overall relative error in the pressure determination single measurement is given by Al’ 2.303 Bj nt + g h 7 = (t + Ci)*
(3)
of a
(4)
A typical error is, AP- t 0.2 mm Hg. Other possible sources of error in measuring P, in addition to those in t and h, might be due to incomplete degassing. As previously mentioned, a great deal of effort has been expended on the development of reliable methods for the degassing of liquids for the static VLE measurements. By considering our measurements of the vapor pressure of the pure components reported in Table 2, it may be concluded that the present method for degassing is also very efficient. As observed, our values of the vapor pressure for acetone are very slightly lower than the ones calculated
243
by eqn. (9) where, if degassing had been incomplete, the values of the vapor pressure must have been higher. Note that in comparison with our data, the data of other authors are considerably lower than the calculated ones. For chloroform, our data are slightly higher but in very good agreement with values calculated by eqn. (9).
Liquid mole fractions The liquid mole fraction is determined gravimetrically by weighing before and after each component addition with an accuracy up to AW - + 0.0001 g. Correction of the liquid mole fraction should be made taking into account vaporization into bulb F and the bent arm (Fig. 1). This is done, knowing the volume occupied by the vapor and its composition (later determined) and assuming an ideal gas behaviour. The relative error in the liquid mole fraction (XJ in a single measurement, due to errors in the weight of the fractions (W,) of a ternary mixture is (h = 1,293)
(w/z/M/z) xk = (WI/M,) + (W,/M,) + (WJMa)=
(Wk/Mk) E
(5)
3 ax Axk=C-!AWi i=laWi hence
(6) where Mk is the molecular weight. For AXZ, 1 is replaced by 2 and 2 is replaced by 1. For AX3, 1 is replaced by 3 and 3 is replaced by 1. For the ternary system, acetone-chloroform-methanol, a typical value is AXi 21 +2 x 10-4.
Vapor mole fraction This is determined by gas chromatography. The relative error in the vapor mole fraction is obtained as follows. The weight of component k in the vapor mixture is given by wk
=
zk/sk
(7)
where & is the area of component k in the chromatogram and Sk is a slope in the calibration curve of zk versus the weight Wk. Hence, the relative error of Wk or Yk reads
(8)
244
Fig. 3. Y-X diagram for the system acetone( 1)-chloroform(
2) at 25’C.
A typical value for binary and ternary mixtures is AYi 2 kO.005. Another possible errorin the determination of the vapor mole fraction might be due to the grease of the stopcock F-l (Fig. 1). The contact of the measured system with the grease may result either in dissolving of the substances in the grease or in rinsing the grease into the solvents. However, on
0.1
0.2
0.3
0.4
0.5
0.6
4
0.1
0.0
D.9
10
Fig, 4. P-X diagram for the system acetone( l)--chloroform(
2) at 25’C.
245
0
Fig. 5. Y-X
0.3
0.4
0.5
x,
06
diagram for the system
0.7
0.8
acetone(
0.9
10
1)-chloroform(
2) at 35.17OC.
the basis of the excellent agreement between our results and the measurements of others (Figs. 3-7), it is believed that the above effect is negligible. However, this effect should be carefully considered by the potential user of the proposed apparatus in the initial stages of getting acquainted with the experimental system.
Fig. 6. Y-X
diagram for the system
ethanol( 1)-benzene(2)
at 45’C.
246
Fig. 7. P-X diagram for the system ethanol( l)-benzene(
EXPERIMENTAL
DATA AND EVALUATION
2) at 45’C.
OF THE PERFORMANCE
OF THE
NEW APPARATUS
The following binary and ternary systems results were compared with known data. (1) For the acetone-chloroform system at 25”C, the data of Mueller and Kearns (1958), Campbell et al. (1966) and Zawidski (1900) at 35.17”C. (2) For the ethanol-benzene system at 45”C, the data of Brown and Smith as reported by H&la et al. (1967, p. 138). (3) For the acetone-chloroformmethanol system at 50°C the data of Severns et al. (1955). It is evident that, due to technical difficulties, the comparison was not a “point-to-point” one. The evaluation of our data and those of other authors was made by testing whether they satisfy the Gibbs-Duhem equation. This gave an indication of the reliability of each set of data separately. Afterwards, a statistical test was applied from which it was possible to determine whether two sets of data (ours and others) could be pooled together, namely, if they belong to the same population, It should be noted that for binary mixtures, the evaluation of data could be made by checking the P-X and Y-X diagrams of the pooled data. For ternary data, this approach is not possible and the statistical test proved very useful. The reliability of the vapor pressure determinations was checked by measuring the vapor pressure of pure acetone and chloroform at several temperatures. Acetone, methanol, and ethanol were purchased from Merck and chloroform and benzene from Frutarom (Haifa, Israel). Some physical constants of the chemicals are compared with literature data in Table 1.
248
TABLE 2 Vapour
pressure
of pure acetone
and chloroform
Ref.
Acetone
Chloroform
i°C)
Equation (9) Rock and Schroder (1957) Campbell et al. (1966) Mueller and Kearns (1958) This work
25
Equation (9) Zawidski (1900) This work
35.17
D% =
P (mm Hg)
IDSI
P (mm W
IDSI
230.9 229.7 226.5 226.3 230.5
0.52 1.91 1.99 0.17
196.7 196.7 197.2 197.05 198.5
0.00 0.25 0.18 1.07
351.5 344.5 351.4
1.99 0.03
298.6 292.1 299.5
2.17 0.30
- Pcalcd Obdp
P
cdcd
The various parameters appear at the end of each table. The second virial coefficients were computed on the basis of correlations suggested by Tsonopoulos (1974). The goodness of our measurements compared with data of other authors
TABLE 3 Equilibrium
data for the system
Xl
Yl
acetone( l)-chloroform
P
(mm f&z) 0.000
0.000 0.064 0.162 0.245 0.327 0.405 0.545 0.682 0.758 0.798 0.888 0.944 0.976 1.000
0.094
0.216 0.293 0.353 0.405 0.480 0.593 0.666 0.707 0.822 0.895 0.951 1.000
Bzz = -1144.0
B 11 = -2000.0 Vk = 74.05
* Azeotrope.
Vt
198.5 184.5 171.2 165.9 162.3 161.4 168.6 178.1 188.0 192.3 206.1 215.4 223.6 230.5
l
Bra = -786.2
= 80.38 cm3 mole-’
cm3 mole-’
(2) at 25’C
249 TABLE
4
Equilibrium
data for the system
acetone(
Yl
0.000
0.000
299.5
0.128 0.160 0.250 0.378 0.456 0.578 0.749 0.755 0.706 0.827 1.000
0.079 0.105 0.187 0.378 0.501 0.671 0.850 0.855 0.807 0.907 1.000
279.2 269.8 261.6 255.7 257.3 269.5 297.3 299.5 290.8 311.8 351.4
= -1660.0
Vk = 74.05 l
B22 = -1144.0
*
Blz = -707.2
cm3 mole-’
V$ = 80.38 cm3 mole-r
Azeotrope.
TABLE
5
Equilibrium Xl
data for the system Yl
0.000
0.000
0.024 0.094 0.240’ 0.320 0.373 0.377 0.420 0.546 0.665 0.737 0.847 0.976 1.000
0.125 0.265 0.345 0.356 0.376 0.372 0,378 0.415 0.451 0.485 0.585 0.910 1 .ooo
BI1 = -1229.0
VT; = 36.20 l
2) at 35.17’C
P (mm Hg)
Xl
Blr
1)-chloroform(
Azeotrope.
Bzz = -1233.0
ethanol(l)-benzene(2)
P (mm Hg) 223.5 264.2 296.3 308.5 309.7 310.1 310.1 309.4 306.0 297.2 286.0 255.0 191.8 173.0
*
Bra = -738.3
Vi = 89.33 cm3 mole-’
cm3 mole-’
at 45’C
250
was determined using a criterion suggested by Rock and Schrijder (1957). According to this criterion, isothermal data may be considered as good if I < + 42(J mole-‘)
(12)
The data can be considered
as very good if
I < + 12.6
(13)
where 1
I=RT
s 0
ln(7h2)
al
(14)
The above area test has an interesting feature. In eqn. (14), the total pressure cancels from the ratio y1/y2 = ( YI/Y2)(X2/X,)(p02/fl) and hence P has no effect on the test. Consequently, the testing done by the area test as applied to isothermal data is whether e, Xi and Yi(i = 1,2) are consistent. Usually, under isothermal conditions, Xi is measured very accurately and the values of Pi0 are known with a high accuracy. Therefore, the ratio ln(r,/yz) versus Xi will be sensitive to the scatter of Yi which is most difficult to measure and the area test made according to eqn. (14) will indicate the reliability of the vapor composition measurements. In Table 6, values of I for the binary mixtures tested in the present work and other data are compared. The major conclusion which can be drawn from Table 6 is that the present data may be considered as very good, even superior to the data of other authors. Finally, the pooled data for P-X and Y-X are presented in Figs. 3-8 which again prove the reliability of our results. A comparison with predic-
TABLE 6 Values of I [eqn. (14)] System
Temp. (“C)
I (J mole-’
Mueller and Kearns (1958) Campbell et al. (1966) This work
25
--77.4 +68.9 -8.4
Acetone-chloroform
Rock and Schroder (1957) Mueller and Kearns (1958) Kudryavtseva and Susarev (1963)
35
-34 .o -36.9 +44.2
Acetone-chloroform
Zawidski (1900) This work
35.17
Wdla et al. (1968, p. 138) This work
45
Ref.
-109.6 -12.6 12.6 -3.6
)
Acetone-chloroform Ethanol-benzene
251
Fig. 8. P-X
diagram
for the system
acetone(l)-chloroform(
tions made through the UNIFAC method shown. Vapor-liquid
2)
(Fredenslund
et al., 1977) is also
equilibria of ternary mixtures
The ternary data for acetonel:hloroform-methanol at 50°C are reported in Table 7. The data appearing in this table were tested by the McDermottEllis (1965) method in order to reject thermodynamically inconsistent points. According to this test, two experimental points a and b are thermodynamically consistent if the condition (15)
D
The local deviation,
D, is given by
m D =2
(Xi, + XA(h
where m is the number of data points. According to McDermott, the use of activity coefficients from y,p yi = x,pp
(16)
Y& - IIJ 73
computed
simply
(17)
x2
0.521 0.456 0.645 0.401 0.302 0.390 0.212 0.098 0.093 0.179 0.523 0.270 0.192 0.297 0.446 0.507
Xl
0.404 0.412 0.287 0.402 0.664 0.531 0.316 0.264 0.202 0.198 0.310 0.500 0.083 0.302 0.297 0.300
0.380 0.376 0.208 0.358 0.734 0.558 0.380 0.374 0.303 0.258 0.269 0.519 0.118 0.357 0.240 0.267
Yl
0.533 0.375 0.671 0.348 0.196 0.304 0.235 0.105 0.140 0.234 0.594 0.256 0.372 0.293 0.523 0.475
y2
0.373 0.375 0.214 0.368 0.695 0.513 0.346 0.351 0.282 0.236 0.241 0.506 0.099 0.292 0.240 0.229
Yf,calcd
0.473 0.400 0,598 0.355 0.200 0.294 0.225 0.119 0.128 0.237 0.484 0.214 0.317 0.307 0.430 0.468
P Z.calcd
Equilibriumdata foracetone(l)--chloroform(2)-methanol at 50°C
TABLE7
(15)l -0.0205 0.0478 -0.0343 0.0537 0.0241 -0.0425 0.0419 0.0192 -0.0212 -0.1300 0.0318 0.0890 -0.0690 -0.0220 0.0137 -0.0214
[ew.
505.4 528.7 535.1 539.2 545.5 547.6 546.4 549.2 548.4 549.5 549.8 550.2 552.5 552.9 555.9 561.7
D
(mm
W
P
0.0877 0.0897 0.0944 0.1035 0.0880 0.1008 0.0905 0.0806 0.0808 0.1121 0.0996 0.1117 0.0937 0.0934 0.0892 0.0979
[eqn.(2011
D max
l
0.180 0.275 0.184 0.239 0.420 0.204 0.290 0.369 0.438 0.853 0.163 0.098 0.095 0.089 0.593 0.303 0.103 0.355 0.528 0.590
0.410 0.455 0.685 0.526 0.377 0.753 0.188 0.193 0.245 0.046 0.403 0.838 0.602 0.684 0.098 0.060 0.748 0.069 0.053 0.040
0.185 0.256 0.114 0.220 0.342 0.132 0.423 0.470 0.426 0.813 0.171 0.058 0.084 0.069 0.640 0.446 0.071 0.471 0.653 0.675
By UNIFAC(Fredenslund etal.,1977).
0.354 0.443 0.615 0.491 0.299 0.723 0.193 0.223 0.251 0.093 0.337 0.783 0.487 0.586 0.191 0.071 0.713 0.101 0.089 0.085
0.391 0.437 0.639 0.492 0.242 0.747 0.181 0.184 0.191 0.046 0.371 0.823 0.549 0.633 0.116 0.062 0.741 0.079 0.049 0.042
0.177 0.231 0.124 0.187 0.040 0.122 0.347 0.400 0.434 0.779 0.161 0.054 0.076 0.061 0.568 0.439 0.060 0.465 0.577 0.605
561.3 560.2 568.7 568.8 571.1 571.1 572.9 575.0 577.6 578.1 578.3 579.0 579.0 586.6 588.9 588.0 587.9 596.4 620.0 629.2 0.0905
0.1002 0.0987 0.0924 0.1091 0.1288 0.0910 0.0900 0.1250 0.1658 0.1274 0.1172 0.0990 0.1751 0.1122 0.1946 0.1873 0.1070 0.1149
-0.0093
-0.0360 0.0417 0.0389 -0.0773 -0.0388 -0.0195 0.0114 0.0320 -0.0633 4.1111 0.0779 -0.0231 -0.0676 0.0186 0.0195 -0.0590 -0.0434 -0.0019
254
is adequate for the two-point consistency test. McDermott and Ellis (1965) recommended the use of a fixed value of 0.01 for D,, . However, as shown in eqn. (16)
An expression for D,, can be obtained by analyzing the total differential dD which contains the errors, inevitably involved, in the various measurements. From eqn. (17) dlny,=dlnP-dine The dependence final expression tions will read
+ 2 loglo
e i
+dln
Yi-dlnXi
(19)
of e on temperature is in accordance with eqn. (9). The for the local maximum deviation under isothermal condi-
(Xia
+ Xti)
A2
1
At
(20)
AX, AY, AP and At are the errors associated with the measurements of the liquid and vapor compositions, total pressure, and temperature. These were taken in the computations as +0.0002, kO.007, +O.l mm Hg and +O.Ol”C, respectively. In Table 7 are presented the ternary measurements for acetonechloroformlnethanol at 50” C. The arrangement of the data points in Table indicates that the data satisfy the 7 is in increasing order of P..D < D,, GibbsDuhem equation. is observed by testing the data of A similar behaviour, namely, D < D,,, Severns et al. (1955). However, contrary to the binary data, here it is not possible to conclude which set of data is “better”, but only that the sets are thermodynamically consistent. Predicted values of Y1 and YZ on the basis of the UNIFAC method (Fredenslund et al., 1977) are also reported in Table 7. Statistical analysis
The previous tests demonstrate the reliability of each set of data. In the following, we will test whether two sets of data, those obtained in this work and by others, can be pooled, i.e. that they belong to the same population. This has been performed by the method of testing the identity of two regression lines described by Neter and Wasserman (1974, p. 163). Let us
255
assume two regression lines of the form El = Pllfl (X) + P12f2 (X) + *a*+ &,f, Ez =P&(X)
+ P&(X)
(X)
(21)
+ . .. + P&(X)
(22)
where 0 are parameters determined on the basis of experimental data. Equation (21) corresponds to the first group of observations and eqn. (22) to the second. The choice of fi(X) should be done in such a way that the residues are homogeneous and scattered at random around the calculated curve. In order to determine whether the two regression lines are identical, we test a zero hypothesis Ho :
011 =P21,
PI2
= 022,
*-*> Plh
=
(23)
P2k
against H1 : either PI1 f pzl or PI2 f flz2 . .. or Plh f flZkor all inequalities ously
simultane-
Let us define the statistic F* as SOS(P) - SOS(E,)
F*k,mI-m2-2k
=
- SOS(E2)
SOS(Ei) + SOS(E2)
-
ml + rn2 - 2h k
1
(24)
where m ,(mJ are the number of observations (or data points) available for the determination of the parameters /3 in eqn. (21) or (ZZ), k is the number of parameters in eqns. (21) and (22), SOS(P) is the sum of squares [deviations between experimental and computed values according to eqn. (21) or (22)] based on the pooled data, namely, ml + m2 observations, SOS(E,) is the sum of squares corresponding to eqn. (21) with ml data points, and SOS(E2) corresponds to E2 with m2 observations. If F* =GF(l - a, k, ml + m2 -k)
(25)
Ho is acceptable
which means that both sets of data belong to the same population. Otherwise Ho is being rejected. (Y,the probability factor, was chosen as 0.05. The values of F are taken from tables in the book by Bennett and Franklin (1967). The above test was applied to the Y-X and P-X data where the appropriate functions satisfying the general expressions given by eqns. (21) and (22) suggested by Tamir (1981) are, for species i(=l . . . n) in a multicomponent mixture Yi
=$ Xi
+
nC1 2 k=l
XkXj[Akj,i +Bw,i(Xk-Xi)
+ C,j,i(Xk -Xi)’
+
j=k+l
where n is the number of components
and A, B, and C are parameters
*.*I(26)
256
deduced
from experimental
Y1=2x1 +X1Xz[A12,1
data. The binary form of the above equation
+B 12,l (Xl
-X*) + G*,1(& -x2j2 + ...I
is (27)
Also n-l
n
C C
P=~XiPp+
i=l
i=l
j=i+l
X~Xj[A,j+Bij(X~.-Xj)‘Cij(Xi-Xj)“...]
(28)
The statistical test was applied on the sysbems acetone--chloroform at 25°C and 35,17”C, ethanol-benzene at 45”C, a.nd acetone-chloroform-methanol at 50” C. In each case it was performed for various numbers of parameters; l-8 for binary mixtures and 3, 6, 9 and 12 for ternary mixtures.The parameters were determined from experimental data by minimizing Ci (Pobsd P calcd)f and similarly for Y. The major conclusions are (a) the zero hypothesis [eqn. (23)] was acceptable for Y-X behaviour in all cases, and (b) the zero hypothesis was clearly rejected for P-X behaviour of Zawidski (1900) data at 35.17”C compared with our data but was accepted for all other data sets which were pooled with our data. The authors of this study have sincere reservations regarding the reliability of the P-X data presented by Zawidski (1900). In Fig. 8, the P-X behaviour is demonstrated and the curve corresponding to the triangles described the data of Rock and Schroder (1957) at 35.OO”C; the other curves are at 35.17”C. It can be seen that the data of Zawidski (1900) are lower than the data of Rock and Schrijder (1957) despite the fact that they are at 35.17”C. On the other hand, as expected, our data at 35.17”C are higher than the data of Rijck and Schrader (1957). An additional element supporting our conclusion concerning Zawidski (1900) data is obtained from Table 6 where the value of I [eqn. (14)] for this data falls much under the criterion [eqn. (13)] suggested by Rock and Schrijder (1957). Our data and that of Rock and Schrijder (1957) satisfy the criterion. Azeotropic behaviour of acetone(l)-chloroform(Z)-methanol
at 50°C
For binary mixtures, it is very easy to detect directly an azeotrope from the Y-X or PX data. But for ternary mixtures it is difficult to detect the point with Xi = Yi (i = 1,2, 3). Tarnir (1981) has suggested the detection of azeotropic behaviour for multicomponent mixtures by applying the GibbsKonovalov theorem (Malesinski, 1965) to eqn. (28). For ternary mixtures, the application of 0
and
(29)
=0
=
on the ternary
form of eqn. (28) yields two equations.
The simultaneous
257
solution of these equations gives the azeotropic composition X1, XZ. In eqn. (29), XL means that P is expressed in terms of X, and XZ. The pressure at the azeotropic point is obtained by substituting the above concentration in eqn. (28). By combining the data of Severns et al. (1955) with the present work data, the prediction resulted in the saddle type azeotropic coordinates X1 = 0.387, XZ = 0.233, and P = 576.7 mm Hg compared with X1 21 0.34, X, N 0.24, and P = 565 mm Hg evaluated by Sevems et al. (1955). In eqn. (28), the parameters for its ternary form, which correspond to the above result and the combined data (Sevems and ours) are
ij l-2 1-3 2-3
Aij -388.95 302.46 632.00
Bij -62.94 -17.02 457.22
where the vapor pressure of the pure components are e = 614.5; fi = 521.5, and e = 418.0 mm Hg. The average deviation between experimental data and computed values using the above parameters was, according to eqn. (28), 2.57%. ACKNOWLEDGEMENT
We are grateful to Mr. David Azoulay who contributed substantially to the first version of the isoteniscope and to Professor Ilya Gertsbach of the Mathematics Department for helping in the statistical analysis. NOMENCLATURE
Bii Ai,Bi, Ci D, Dmax g h k
ii n IzD P PO
R SOS
virial coefficients Antoine parameters local deviation; maximum local deviation graviational acceleration height number of parameters in a series expansion number of observations molecular weight number of components index of refraction total pressure vapor pressure of pure component universal gas constant sum of squares corresponding to the difference and calculated values
between
observed
258 t T I+ x: Y P W Yi
temperature in ’ C temperature in K liquid molar volume of component i mole fraction in liquid and vapor phases density weight activity coefficient of component i
Subscripts
a, b calcd obsd
two successive experimental calculated observed
points
REFERENCES Abbot, M.M. and Van Ness, H.C., 1975. Vapor-liquid equilibrium. Part III. Data reduction with precise expression for GE. AIChE J., 21: 61-71. Abbot, M.M., Floess, J.K. and Van Ness, H.C., 1975. Vapor-liquid equilibrium. Part IV. Reduction of P-X data for ternary systems, AIChE J., 21: 72-76. Aim, K,, 1978. Measurement of vapor-liquid equilibrium in systems with components of very different volatility by the total pressure static method. Fluid Phase Equilibria, 2: 119-142. Apelblat, A., Azoulay, D. and Sahar, A., 1973. Properties of aqueous thorium nitrate solutions. J. Chem. Sot. Faraday I, 69: 1618-1624. Battino, R., Banzhof, M., Bogan, M. and Wilhelm, E., 1971. Apparatus for rapid degassing of liquids. Part III. Anal. Chem., 43: 806-807. Bell, T.N., Cussler, E.L., Harris, K.R., Pepela, C.N. and Dunlop, P.J., 1968. An apparatus for degassing liquids by vacuum sublimation. J. Phys. Chem., 72: 4693-4695. Bennett, CA. and Franklin, N.L., 1967. Statistical Analysis in Chemistry and Chemical Industry. Wiley, New York. Booth, H.S. and Halbedel, H.S., 1946. The fluorination of n-propyl trichlorosilane. J. Am. Chem. Sot., 68: 2652-2654. Campbell, A.N., Kartzmark, E.M. and Chatterjee, R.M. 1966. Excess volumes, vapor pressures and related thermodynamic properties of the system acetone-chloroformbenzene, and its component binary systems. Can. J. Chem., 44: 1183-1189. Fredenslund, A., Gmehling, J. and Rasmussen, P., 1977. Vapor-Liquid Equilibria using UNIFAC. Elsevier, Amsterdam. Gibbs, R.E. and Van Ness, H.C., 1972. Vapor-liquid equilibria from total-pressure measurements. A new apparatus. Ind. Eng. Chem. Fundam., 11: 410-413. Gmehling, J., Onken, V. and Arlt, W., 1979. Vapor-Liquid Equilibrium Data Collection Aldehydes and Ketones, Ethers. Chem. Data Series, Vol. I, Parts 3 + 4. DECHEMA, Deutsche Gesellschaft fur Chemisches Apparatewesen, Frankfurt/Main, Federal Republic of Germany, 624 pp. Hila, E., Pick, J., Frid, V. and Vilim, O., 1967. Vapor-Liquid Equilibrium. Pergamon Press, London, 599 pp. H&la, E., Wichterle, I., Polak, J. and Boublik, T., 1968. Vapor-Liquid Equilibrium Data at Normal Pressures. Pergamon Press, London, 1st edn. Kudryavtseva, L.S. and Susarev, M.P., 1963. Liquid-vapor equilibrium in systems chloroform-hexane and acetone-chloroform. Zh. Prikl. Khim.. 36: 1231-1237.
259
Maher, P.J. and Smith, B.D., 1979. A new total pressure vapor-liquid equilbrium apparatus. The ethanol + aniline system at 313.15, 350.81 and 386.67 K. J. Chem. Eng. Data, 24: 16-22. Malesinski, W., 1965. Azeotropic and Other Theoretical Problems of Vapor-Liquid Equilibrium. Interscience, New York. McDermott, C. and Ellis, S.R.M., 1965. A multicomponent consistency test. Chem. Eng. Sci., 20: 293-296. McGlashan, M.L. and Williamson, A.G., 1961. Trans. Faraday Sot., 57: 588-600. Mueller, C.R. and Kearns, E.R., 1958. Thermodynamic studies of the system acetone and chloroform. J. Phys. Chem., 62: 1441-1445. Neter, J. and Wasserman, W., 1974. Statistical Analysis in Chemistry and Chemical Industry. Wiley, New York. Riddick, J.A. and Bunger W.B., 1970. Organic solvents. In: A. Weissberger (Editor), Technical Chemistry, Vol. II, Wiley, New York. Rock, H, and Schroder, W., 1957. Vapor-liquid equilibrium measurements in the system acetone-chloroform. Z. Phys. Chem., 11: 41-55. Ronc, M. and Ratcliff, G.R., 1976. Measurement of vapor-liquid equilibria using a semicontinuous total pressure static equilibrium still. Can. J. Chem. Eng., 54: 326-332. Severns, W.H., Sesonke, A., Perry, R.H. and Pigford, R.L., 1955. Estimation of ternary vapor-liquid equilibrium. AIChE. J., 1: 401-409. Smith, A. and Menzies, A.C.W., 1910. Studies in vapor pressure. III. A static method for determining the vapor pressures of solids and liquids. J. Am. Chem. Sot., 32: 14121434. Tamir, A., 1981. Prediction of azeotropes and new correlations for fitting multicomponent vaporliquid equilibrium data. Chem. Eng. Sci., in press. Timermans, J., 1965. Physico-Chemical Constants of Pure Organic Compounds. Elsevier, Amsterdam. Tsonopoulos, C., 1974. An empirical correlation of second virial coefficients. AIChE. J., 20: 263-272. Van Ness, H.C., 1969. Classical Thermodynamics of Non-Electrolyte Solutions. Pergamon Press, Oxford, 166 pp. Van Ness, H.C. and Abbott, M.M., 1978. A Procedure for rapid degassing of liquids. Ind. Eng. Chem. Fundam., 17: 66-67. Van Ness, H.C., Stanley, M.B. and Gibbs, R.E., 1973. ‘Vapor-liquid equilibrium. Part. 1. An appraisal of data reduction methods. AIChE J., 19: 238-244. Zawidski, J.V., 1900. Uber die Dampfdrticke binarer Fliissigkeitsgemische. Z. Phys. Chem., 35: 129-203.
Elsevier Scientific
6 (1981) 237-259 Publishing Company, Amsterdam
A NEW DEVICE FOR MEASURING EQUILIBRIA
ABRAHAM
TAMIR *, ALEXANDER
Department (Israel)
of Chemical
(Received
Engineering,
May 13th, 1980; accepted
237 - Printed
ISOTHERMAL
APELBLAT Ben Gurion
in The Netherlands
VAPOR - LIQUID
and MOSHE WAGNER University
in revised form November
of the Negev,
Beer Sheva
14th, 1980)
ABSRACT Tamir, A., Apelblat, A. and Wagner, M., 1981. A new device for measuring vapor-liquid equilibria. Fluid Phase Equilibria, 6: 237-259.
isothermal
A new apparatus, based on the isoteniscope, was developed for measuring vaporliquid equilibrium under isothermal conditions. In order to evaluate its performance, the following mixtures were tested: acetone-chloroform at 25’C and 35,17’C, ethanolbenzene at 45’C, and acetone-chloroform-methanol at 5O’C. The results are in excellent agreement with literature data. The advantages of the present apparatus are simplicity of construction, ease of operation, minimal consumption of chemicals, relatively quick in reaching equilibrium, the degassing process is carried out simultaneously with preparation of the samples, and the apparatus is suitable for determination of the vapor composition.
INTRODUCTION
The aim of the present work is the development of the isoteniscope, first proposed by Smith and Menzies (1910) for measuring the total pressure of pure components and mixtures, as a simple tool for determining isothermal vapor-liquid equilibria (VLE) of mixtures. Numerous experimental techniques for studying VLE at low and normal pressures have been reviewed by Haa et al. (1967). From their review, it may be concluded that dynamic methods are more common than static. This is due to difficulties in measuring accurately the total pressure and vapor composition. On the other hand, the dynamic method has the disadvantage of achieving only with difficulty steady-state boiling in an equilibrium still at very low pressure. Over the years, total pressure measurements based on the isotensiscope were improved, e.g. by McGlashan and Williamson (1961), and further development was made by Apelblat et al. (1973). In recent years, great attention has been paid to static methods which are commonly used l
To whom correspondence
037%3812/81/0000-0000/$02.50
should be addressed. @ 1981 Elsevier Scientific
Publishing
Company
238
nowadays. Gibbs and van Ness (1972) developed an apparatus providing the entire composition range measurements in a day. Ronc and Ratcliff (1976) modified the above equilibrium to increase its accuracy further. Aim (1978) emphasizes that in his static assembly design, stress was especially laid on the attainment of maximum accuracy of measurement, the related thorough degassing of pure components, and their relatively low consumption. Very recently, Maher and Smith (1979) suggested a new multicell apparatus by means of which three isotherms are measured in a typical 5-day run (including loading, degassing and isotherm measurements). The major reason for the above developments in static methods is the adequate calculating procedures which were proposed and the advent of computer facilities for the evaluation of VLE from the total pressure data at normal pressures. In particular, from the works of van Ness et al. (1973), Abbott and van Ness (1975) and Abbott et al. (1975) it may be concluded that the measurement of the vapor mole fraction, which is usually most difficult to measure, is not absolutely necessary, especially if the experimental random errors are larger than those in the liquid mole fraction. The above authors have demonstrated reliable methods to compute the vapor composition from P-X data. Accurate determination of isothermal VLE requires degassing of the liquid mixture. Reliable degassing techniques were suggested by Bell et al. (1968), Battino et al. (1971), van Ness and Abbott (1978). It should be noted that almost every serious researcher has developed his own technique for degassing, recognizing the importance of this factor in obtaining reliable data. The measurement of the vapor composition is also very complicated and the inaccuracy is caused by handling very small quantities. In addition, removal of a vapor sample may cause a marked disturbance of the equilibrium. Consequently, it is acceptable to avoid measurements of the vapor composition, as is done in all the above-mentioned techniques. However, the present authors believe that any apparatus which is proposed for measuring VLE must also provide the user with the option of an accurate technique for the determination of the vapor composition. The above-mentioned difficulties are eliminated by the present method and the total pressure and vapor composition are accurately determined. We have tested several binary and ternary mixtures for which we achieved good agreement with known data. Also, our experiments revealed that the new apparatus possessed a number of advantages, viz. simplicity of construction, ease of operation, minimal consumption of chemicals, the time of operation (including preparation of a sample and attainment of equilibrium) never exceeds one hour, and it is also possible to detect the existence of a chemical reaction, if it happens, as well as incomplete degassing, by observing the change of the pressure versus time.
239 EXPERIMENTAL
SYSTEM
The experimental system is composed of the following parts: (a) manometers and a sampling system for vapor and liquid mixtures (Fig. l), (b) a thermostatic bath, and (c) a degassing unit for liquid samples (Fig. 2). The glass sampling system for liquid and vapor mixtures and manometers The design of the sampling system shown in Fig. 1 eliminates turbance of the vapor-liquid equilibrium. It is constructed of (1) A T-type connection (G) 7-10 cm long. Two connections ling bulbs and one for the manometer. (2) Sampling bulbs, E for liquid and F for vapor, each having 40 cm3 and a stopcock, F-l. The bulb E contains a tefloncoated bar for mixing the liquid. (3) Manometer (Fig. 1). It is a modified Booth and Halbedel teniscope for measuring the vapor pressure of multicomponent
Fig. 1. Two kinds of isothermal
vapor-liquid
equilibrium
systems,
any disfor sampa volume of magnetic (1946) isomixtures.
240
Fig. 2. Degassing unit and preparation
of samples.
For measuring vapor pressures above 450 mm Hg, a differential manometer (as shown on the right-hand side of Fig. 1) is used. The manometric fluid in bulb H has a known vapor pressure which acts against pressure in the U tube (left-hand side of Fig. 1). Thermostatic bath This unit is composed .of the following components. (1) A bath (45 X 35 X 35 cm) made of Perspex with a magnetic bar on its bottom for stirring the water. (2) An FT Haake unit with a circulation pump and a temperature control unit which maintains the desired temperature within +O.Ol”C. Degassing of pure components and preparation of samples Degassing of the liquids is a crucial step needed to obtain reliable determinations of the total pressure at equilibrium. The degassing unit, shown in Fig. 2, is constructed of a horizontal manifold with inlets to the sampling bulbs, G-J, to the liquid nitrogen trap, D, and to a vacuum pump (Crompton Parkinson Doncaster a.c. Motor type). Inlet, B is introduced to avoid the oil rising in the pump after shutdown, when the magnetic valve is absent. in the vacuum system. Stopcock E enables air to enter the manifold and thus to release the bulbs after degassing and samples preparation, while inlet F is used for the connection of a Pirani gauge.
241
We prepare a binary mixture (and ternary mixtures) simultaneously by the following degassing process: two empty bulbs are weighed and each one is filled with the appropriate component having a weight corresponding approximately to the desired molar concentration. The height of the liquid in each bulb is marked and then additional amounts of the components are added (about l/3 of the original volume). The bulbs are connected to the manifold and closed. The vacuum pump is operated and the “additional l/3” is evaporated, separately from each bulb, until the original level of the components in the bulbs is reached. The closed bulbs are again weighed and connected to the manifold which is completely evacuated; stopcock C-l is closed. The bulb containing the less volatile component is immersed in liquid nitrogen and the volatile component is transferred to this bulb as a result of the temperature difference between the bulbs. In order to speed up the process, the bulb with the volatile component is heated with hot air. At the end of this step, the bulb with the known composition is once again weighed for final control of the weight and connected to the isoteniscope at the appropriate place (bulb E in Fig. 1). Also, an evacuated and weighed bulb (F) is placed in the isoteniscope for vapor sampling. Experimental
procedure
The system shown on the right-hand side of Fig. 1 (and similarly for the other one) is evacuated by connection at point A to the degassing system in Fig. 2. Stopcock B is closed and the mercury initially filling bulb C is poured into the U tube. Complete degassing is indicated by identical heights of the mercury in D, checked by means of a cathetometer (Gaertner Scientific Corporation, Chicago, U.S.A.). The accuracy in measuring the heights of the manometric fluid (mercury or silicon oil) is kO.1 mm. If the heights of the mercury vary, the degassing process must be repeated (and the mercury must be returned to bulb C). If no leaks are observed, stopcock E-l is opened and the system (Fig. 1) is immersed in the thermostatic bath. Thermal equilibrium is realized within 20 min and the height of mercury is checked several times. To obtain a vapor sample in bulb F, stopcock F-l is opened with the system still immersed in the thermostatic bath. When equilibrium is again reached, stopcock F-l is closed and the system is withdrawn from the thermostatic bath. The bulb containing liquid (E) is immersed in liquid nitrogen to condense the vapor in the system. If the mercury heights in the U tube (D) arms are identical, it indicates that no leaks have occurred; otherwise, the experiments should be repeated. When stopcock E-l is closed and stopcock B is opened, it is possible to release bulbs E and F from the isoteniscope. Accurate determination of the vapor composition is rather difficult because of the small quantities (of the order of 10 mg) accumulated in bulb F. Bulb F is immersed in liquid nitrogen and lo-15 drops of an inert solvent are added. By means of this operation, the small amounts of the condensed vapor appearing on the bulb walls are washed down and accumulate for chromatographic analysis.
242 MEASUREMENT OF VARIABLES AND ERROR ANALYSIS
Temperature
The liquid bath temperature can be maintained within ?O.Ol”C of the desired temperature and the temperature gradient from top to bottom of the bath is about +O.Ol”C. The absolute temperature was measured by means of a Hewlett Packard Quartz Thermometer Model 2801-A with a sensitivity of ~0.0001”c. Pressure
The vapor pressure of a mixture was measured by means of a U tube containing mercury. The difference in the heights of the mercury was measured by means of a cathetometer and was translated into pressure units (mm Hg at 0°C). An estimate of the error associated with the pressure measurements can be obtained as follows [for the sake of simplicity the determination of the vapor pressure of a single component is considered (for which P = PO)]. The error in a single measurement of the vapor pressure, AP, depends on accurate measuring of the bath temperature as well as that of the mercury columns, namely
(1) Considering the Antoine equation nent
for the vapor pressure of a pure compo-
log12 = Ai - & I
and that P = pgh
it results that the overall relative error in the pressure determination single measurement is given by Al’ 2.303 Bj nt + g h 7 = (t + Ci)*
(3)
of a
(4)
A typical error is, AP- t 0.2 mm Hg. Other possible sources of error in measuring P, in addition to those in t and h, might be due to incomplete degassing. As previously mentioned, a great deal of effort has been expended on the development of reliable methods for the degassing of liquids for the static VLE measurements. By considering our measurements of the vapor pressure of the pure components reported in Table 2, it may be concluded that the present method for degassing is also very efficient. As observed, our values of the vapor pressure for acetone are very slightly lower than the ones calculated
243
by eqn. (9) where, if degassing had been incomplete, the values of the vapor pressure must have been higher. Note that in comparison with our data, the data of other authors are considerably lower than the calculated ones. For chloroform, our data are slightly higher but in very good agreement with values calculated by eqn. (9).
Liquid mole fractions The liquid mole fraction is determined gravimetrically by weighing before and after each component addition with an accuracy up to AW - + 0.0001 g. Correction of the liquid mole fraction should be made taking into account vaporization into bulb F and the bent arm (Fig. 1). This is done, knowing the volume occupied by the vapor and its composition (later determined) and assuming an ideal gas behaviour. The relative error in the liquid mole fraction (XJ in a single measurement, due to errors in the weight of the fractions (W,) of a ternary mixture is (h = 1,293)
(w/z/M/z) xk = (WI/M,) + (W,/M,) + (WJMa)=
(Wk/Mk) E
(5)
3 ax Axk=C-!AWi i=laWi hence
(6) where Mk is the molecular weight. For AXZ, 1 is replaced by 2 and 2 is replaced by 1. For AX3, 1 is replaced by 3 and 3 is replaced by 1. For the ternary system, acetone-chloroform-methanol, a typical value is AXi 21 +2 x 10-4.
Vapor mole fraction This is determined by gas chromatography. The relative error in the vapor mole fraction is obtained as follows. The weight of component k in the vapor mixture is given by wk
=
zk/sk
(7)
where & is the area of component k in the chromatogram and Sk is a slope in the calibration curve of zk versus the weight Wk. Hence, the relative error of Wk or Yk reads
(8)
244
Fig. 3. Y-X diagram for the system acetone( 1)-chloroform(
2) at 25’C.
A typical value for binary and ternary mixtures is AYi 2 kO.005. Another possible errorin the determination of the vapor mole fraction might be due to the grease of the stopcock F-l (Fig. 1). The contact of the measured system with the grease may result either in dissolving of the substances in the grease or in rinsing the grease into the solvents. However, on
0.1
0.2
0.3
0.4
0.5
0.6
4
0.1
0.0
D.9
10
Fig, 4. P-X diagram for the system acetone( l)--chloroform(
2) at 25’C.
245
0
Fig. 5. Y-X
0.3
0.4
0.5
x,
06
diagram for the system
0.7
0.8
acetone(
0.9
10
1)-chloroform(
2) at 35.17OC.
the basis of the excellent agreement between our results and the measurements of others (Figs. 3-7), it is believed that the above effect is negligible. However, this effect should be carefully considered by the potential user of the proposed apparatus in the initial stages of getting acquainted with the experimental system.
Fig. 6. Y-X
diagram for the system
ethanol( 1)-benzene(2)
at 45’C.
246
Fig. 7. P-X diagram for the system ethanol( l)-benzene(
EXPERIMENTAL
DATA AND EVALUATION
2) at 45’C.
OF THE PERFORMANCE
OF THE
NEW APPARATUS
The following binary and ternary systems results were compared with known data. (1) For the acetone-chloroform system at 25”C, the data of Mueller and Kearns (1958), Campbell et al. (1966) and Zawidski (1900) at 35.17”C. (2) For the ethanol-benzene system at 45”C, the data of Brown and Smith as reported by H&la et al. (1967, p. 138). (3) For the acetone-chloroformmethanol system at 50°C the data of Severns et al. (1955). It is evident that, due to technical difficulties, the comparison was not a “point-to-point” one. The evaluation of our data and those of other authors was made by testing whether they satisfy the Gibbs-Duhem equation. This gave an indication of the reliability of each set of data separately. Afterwards, a statistical test was applied from which it was possible to determine whether two sets of data (ours and others) could be pooled together, namely, if they belong to the same population, It should be noted that for binary mixtures, the evaluation of data could be made by checking the P-X and Y-X diagrams of the pooled data. For ternary data, this approach is not possible and the statistical test proved very useful. The reliability of the vapor pressure determinations was checked by measuring the vapor pressure of pure acetone and chloroform at several temperatures. Acetone, methanol, and ethanol were purchased from Merck and chloroform and benzene from Frutarom (Haifa, Israel). Some physical constants of the chemicals are compared with literature data in Table 1.
248
TABLE 2 Vapour
pressure
of pure acetone
and chloroform
Ref.
Acetone
Chloroform
i°C)
Equation (9) Rock and Schroder (1957) Campbell et al. (1966) Mueller and Kearns (1958) This work
25
Equation (9) Zawidski (1900) This work
35.17
D% =
P (mm Hg)
IDSI
P (mm W
IDSI
230.9 229.7 226.5 226.3 230.5
0.52 1.91 1.99 0.17
196.7 196.7 197.2 197.05 198.5
0.00 0.25 0.18 1.07
351.5 344.5 351.4
1.99 0.03
298.6 292.1 299.5
2.17 0.30
- Pcalcd Obdp
P
cdcd
The various parameters appear at the end of each table. The second virial coefficients were computed on the basis of correlations suggested by Tsonopoulos (1974). The goodness of our measurements compared with data of other authors
TABLE 3 Equilibrium
data for the system
Xl
Yl
acetone( l)-chloroform
P
(mm f&z) 0.000
0.000 0.064 0.162 0.245 0.327 0.405 0.545 0.682 0.758 0.798 0.888 0.944 0.976 1.000
0.094
0.216 0.293 0.353 0.405 0.480 0.593 0.666 0.707 0.822 0.895 0.951 1.000
Bzz = -1144.0
B 11 = -2000.0 Vk = 74.05
* Azeotrope.
Vt
198.5 184.5 171.2 165.9 162.3 161.4 168.6 178.1 188.0 192.3 206.1 215.4 223.6 230.5
l
Bra = -786.2
= 80.38 cm3 mole-’
cm3 mole-’
(2) at 25’C
249 TABLE
4
Equilibrium
data for the system
acetone(
Yl
0.000
0.000
299.5
0.128 0.160 0.250 0.378 0.456 0.578 0.749 0.755 0.706 0.827 1.000
0.079 0.105 0.187 0.378 0.501 0.671 0.850 0.855 0.807 0.907 1.000
279.2 269.8 261.6 255.7 257.3 269.5 297.3 299.5 290.8 311.8 351.4
= -1660.0
Vk = 74.05 l
B22 = -1144.0
*
Blz = -707.2
cm3 mole-’
V$ = 80.38 cm3 mole-r
Azeotrope.
TABLE
5
Equilibrium Xl
data for the system Yl
0.000
0.000
0.024 0.094 0.240’ 0.320 0.373 0.377 0.420 0.546 0.665 0.737 0.847 0.976 1.000
0.125 0.265 0.345 0.356 0.376 0.372 0,378 0.415 0.451 0.485 0.585 0.910 1 .ooo
BI1 = -1229.0
VT; = 36.20 l
2) at 35.17’C
P (mm Hg)
Xl
Blr
1)-chloroform(
Azeotrope.
Bzz = -1233.0
ethanol(l)-benzene(2)
P (mm Hg) 223.5 264.2 296.3 308.5 309.7 310.1 310.1 309.4 306.0 297.2 286.0 255.0 191.8 173.0
*
Bra = -738.3
Vi = 89.33 cm3 mole-’
cm3 mole-’
at 45’C
250
was determined using a criterion suggested by Rock and Schrijder (1957). According to this criterion, isothermal data may be considered as good if I < + 42(J mole-‘)
(12)
The data can be considered
as very good if
I < + 12.6
(13)
where 1
I=RT
s 0
ln(7h2)
al
(14)
The above area test has an interesting feature. In eqn. (14), the total pressure cancels from the ratio y1/y2 = ( YI/Y2)(X2/X,)(p02/fl) and hence P has no effect on the test. Consequently, the testing done by the area test as applied to isothermal data is whether e, Xi and Yi(i = 1,2) are consistent. Usually, under isothermal conditions, Xi is measured very accurately and the values of Pi0 are known with a high accuracy. Therefore, the ratio ln(r,/yz) versus Xi will be sensitive to the scatter of Yi which is most difficult to measure and the area test made according to eqn. (14) will indicate the reliability of the vapor composition measurements. In Table 6, values of I for the binary mixtures tested in the present work and other data are compared. The major conclusion which can be drawn from Table 6 is that the present data may be considered as very good, even superior to the data of other authors. Finally, the pooled data for P-X and Y-X are presented in Figs. 3-8 which again prove the reliability of our results. A comparison with predic-
TABLE 6 Values of I [eqn. (14)] System
Temp. (“C)
I (J mole-’
Mueller and Kearns (1958) Campbell et al. (1966) This work
25
--77.4 +68.9 -8.4
Acetone-chloroform
Rock and Schroder (1957) Mueller and Kearns (1958) Kudryavtseva and Susarev (1963)
35
-34 .o -36.9 +44.2
Acetone-chloroform
Zawidski (1900) This work
35.17
Wdla et al. (1968, p. 138) This work
45
Ref.
-109.6 -12.6 12.6 -3.6
)
Acetone-chloroform Ethanol-benzene
251
Fig. 8. P-X
diagram
for the system
acetone(l)-chloroform(
tions made through the UNIFAC method shown. Vapor-liquid
2)
(Fredenslund
et al., 1977) is also
equilibria of ternary mixtures
The ternary data for acetonel:hloroform-methanol at 50°C are reported in Table 7. The data appearing in this table were tested by the McDermottEllis (1965) method in order to reject thermodynamically inconsistent points. According to this test, two experimental points a and b are thermodynamically consistent if the condition (15)
D
The local deviation,
D, is given by
m D =2
(Xi, + XA(h
where m is the number of data points. According to McDermott, the use of activity coefficients from y,p yi = x,pp
(16)
Y& - IIJ 73
computed
simply
(17)
x2
0.521 0.456 0.645 0.401 0.302 0.390 0.212 0.098 0.093 0.179 0.523 0.270 0.192 0.297 0.446 0.507
Xl
0.404 0.412 0.287 0.402 0.664 0.531 0.316 0.264 0.202 0.198 0.310 0.500 0.083 0.302 0.297 0.300
0.380 0.376 0.208 0.358 0.734 0.558 0.380 0.374 0.303 0.258 0.269 0.519 0.118 0.357 0.240 0.267
Yl
0.533 0.375 0.671 0.348 0.196 0.304 0.235 0.105 0.140 0.234 0.594 0.256 0.372 0.293 0.523 0.475
y2
0.373 0.375 0.214 0.368 0.695 0.513 0.346 0.351 0.282 0.236 0.241 0.506 0.099 0.292 0.240 0.229
Yf,calcd
0.473 0.400 0,598 0.355 0.200 0.294 0.225 0.119 0.128 0.237 0.484 0.214 0.317 0.307 0.430 0.468
P Z.calcd
Equilibriumdata foracetone(l)--chloroform(2)-methanol at 50°C
TABLE7
(15)l -0.0205 0.0478 -0.0343 0.0537 0.0241 -0.0425 0.0419 0.0192 -0.0212 -0.1300 0.0318 0.0890 -0.0690 -0.0220 0.0137 -0.0214
[ew.
505.4 528.7 535.1 539.2 545.5 547.6 546.4 549.2 548.4 549.5 549.8 550.2 552.5 552.9 555.9 561.7
D
(mm
W
P
0.0877 0.0897 0.0944 0.1035 0.0880 0.1008 0.0905 0.0806 0.0808 0.1121 0.0996 0.1117 0.0937 0.0934 0.0892 0.0979
[eqn.(2011
D max
l
0.180 0.275 0.184 0.239 0.420 0.204 0.290 0.369 0.438 0.853 0.163 0.098 0.095 0.089 0.593 0.303 0.103 0.355 0.528 0.590
0.410 0.455 0.685 0.526 0.377 0.753 0.188 0.193 0.245 0.046 0.403 0.838 0.602 0.684 0.098 0.060 0.748 0.069 0.053 0.040
0.185 0.256 0.114 0.220 0.342 0.132 0.423 0.470 0.426 0.813 0.171 0.058 0.084 0.069 0.640 0.446 0.071 0.471 0.653 0.675
By UNIFAC(Fredenslund etal.,1977).
0.354 0.443 0.615 0.491 0.299 0.723 0.193 0.223 0.251 0.093 0.337 0.783 0.487 0.586 0.191 0.071 0.713 0.101 0.089 0.085
0.391 0.437 0.639 0.492 0.242 0.747 0.181 0.184 0.191 0.046 0.371 0.823 0.549 0.633 0.116 0.062 0.741 0.079 0.049 0.042
0.177 0.231 0.124 0.187 0.040 0.122 0.347 0.400 0.434 0.779 0.161 0.054 0.076 0.061 0.568 0.439 0.060 0.465 0.577 0.605
561.3 560.2 568.7 568.8 571.1 571.1 572.9 575.0 577.6 578.1 578.3 579.0 579.0 586.6 588.9 588.0 587.9 596.4 620.0 629.2 0.0905
0.1002 0.0987 0.0924 0.1091 0.1288 0.0910 0.0900 0.1250 0.1658 0.1274 0.1172 0.0990 0.1751 0.1122 0.1946 0.1873 0.1070 0.1149
-0.0093
-0.0360 0.0417 0.0389 -0.0773 -0.0388 -0.0195 0.0114 0.0320 -0.0633 4.1111 0.0779 -0.0231 -0.0676 0.0186 0.0195 -0.0590 -0.0434 -0.0019
254
is adequate for the two-point consistency test. McDermott and Ellis (1965) recommended the use of a fixed value of 0.01 for D,, . However, as shown in eqn. (16)
An expression for D,, can be obtained by analyzing the total differential dD which contains the errors, inevitably involved, in the various measurements. From eqn. (17) dlny,=dlnP-dine The dependence final expression tions will read
+ 2 loglo
e i
+dln
Yi-dlnXi
(19)
of e on temperature is in accordance with eqn. (9). The for the local maximum deviation under isothermal condi-
(Xia
+ Xti)
A2
1
At
(20)
AX, AY, AP and At are the errors associated with the measurements of the liquid and vapor compositions, total pressure, and temperature. These were taken in the computations as +0.0002, kO.007, +O.l mm Hg and +O.Ol”C, respectively. In Table 7 are presented the ternary measurements for acetonechloroformlnethanol at 50” C. The arrangement of the data points in Table indicates that the data satisfy the 7 is in increasing order of P..D < D,, GibbsDuhem equation. is observed by testing the data of A similar behaviour, namely, D < D,,, Severns et al. (1955). However, contrary to the binary data, here it is not possible to conclude which set of data is “better”, but only that the sets are thermodynamically consistent. Predicted values of Y1 and YZ on the basis of the UNIFAC method (Fredenslund et al., 1977) are also reported in Table 7. Statistical analysis
The previous tests demonstrate the reliability of each set of data. In the following, we will test whether two sets of data, those obtained in this work and by others, can be pooled, i.e. that they belong to the same population. This has been performed by the method of testing the identity of two regression lines described by Neter and Wasserman (1974, p. 163). Let us
255
assume two regression lines of the form El = Pllfl (X) + P12f2 (X) + *a*+ &,f, Ez =P&(X)
+ P&(X)
(X)
(21)
+ . .. + P&(X)
(22)
where 0 are parameters determined on the basis of experimental data. Equation (21) corresponds to the first group of observations and eqn. (22) to the second. The choice of fi(X) should be done in such a way that the residues are homogeneous and scattered at random around the calculated curve. In order to determine whether the two regression lines are identical, we test a zero hypothesis Ho :
011 =P21,
PI2
= 022,
*-*> Plh
=
(23)
P2k
against H1 : either PI1 f pzl or PI2 f flz2 . .. or Plh f flZkor all inequalities ously
simultane-
Let us define the statistic F* as SOS(P) - SOS(E,)
F*k,mI-m2-2k
=
- SOS(E2)
SOS(Ei) + SOS(E2)
-
ml + rn2 - 2h k
1
(24)
where m ,(mJ are the number of observations (or data points) available for the determination of the parameters /3 in eqn. (21) or (ZZ), k is the number of parameters in eqns. (21) and (22), SOS(P) is the sum of squares [deviations between experimental and computed values according to eqn. (21) or (22)] based on the pooled data, namely, ml + m2 observations, SOS(E,) is the sum of squares corresponding to eqn. (21) with ml data points, and SOS(E2) corresponds to E2 with m2 observations. If F* =GF(l - a, k, ml + m2 -k)
(25)
Ho is acceptable
which means that both sets of data belong to the same population. Otherwise Ho is being rejected. (Y,the probability factor, was chosen as 0.05. The values of F are taken from tables in the book by Bennett and Franklin (1967). The above test was applied to the Y-X and P-X data where the appropriate functions satisfying the general expressions given by eqns. (21) and (22) suggested by Tamir (1981) are, for species i(=l . . . n) in a multicomponent mixture Yi
=$ Xi
+
nC1 2 k=l
XkXj[Akj,i +Bw,i(Xk-Xi)
+ C,j,i(Xk -Xi)’
+
j=k+l
where n is the number of components
and A, B, and C are parameters
*.*I(26)
256
deduced
from experimental
Y1=2x1 +X1Xz[A12,1
data. The binary form of the above equation
+B 12,l (Xl
-X*) + G*,1(& -x2j2 + ...I
is (27)
Also n-l
n
C C
P=~XiPp+
i=l
i=l
j=i+l
X~Xj[A,j+Bij(X~.-Xj)‘Cij(Xi-Xj)“...]
(28)
The statistical test was applied on the sysbems acetone--chloroform at 25°C and 35,17”C, ethanol-benzene at 45”C, a.nd acetone-chloroform-methanol at 50” C. In each case it was performed for various numbers of parameters; l-8 for binary mixtures and 3, 6, 9 and 12 for ternary mixtures.The parameters were determined from experimental data by minimizing Ci (Pobsd P calcd)f and similarly for Y. The major conclusions are (a) the zero hypothesis [eqn. (23)] was acceptable for Y-X behaviour in all cases, and (b) the zero hypothesis was clearly rejected for P-X behaviour of Zawidski (1900) data at 35.17”C compared with our data but was accepted for all other data sets which were pooled with our data. The authors of this study have sincere reservations regarding the reliability of the P-X data presented by Zawidski (1900). In Fig. 8, the P-X behaviour is demonstrated and the curve corresponding to the triangles described the data of Rock and Schroder (1957) at 35.OO”C; the other curves are at 35.17”C. It can be seen that the data of Zawidski (1900) are lower than the data of Rock and Schrijder (1957) despite the fact that they are at 35.17”C. On the other hand, as expected, our data at 35.17”C are higher than the data of Rijck and Schrader (1957). An additional element supporting our conclusion concerning Zawidski (1900) data is obtained from Table 6 where the value of I [eqn. (14)] for this data falls much under the criterion [eqn. (13)] suggested by Rock and Schrijder (1957). Our data and that of Rock and Schrijder (1957) satisfy the criterion. Azeotropic behaviour of acetone(l)-chloroform(Z)-methanol
at 50°C
For binary mixtures, it is very easy to detect directly an azeotrope from the Y-X or PX data. But for ternary mixtures it is difficult to detect the point with Xi = Yi (i = 1,2, 3). Tarnir (1981) has suggested the detection of azeotropic behaviour for multicomponent mixtures by applying the GibbsKonovalov theorem (Malesinski, 1965) to eqn. (28). For ternary mixtures, the application of 0
and
(29)
=0
=
on the ternary
form of eqn. (28) yields two equations.
The simultaneous
257
solution of these equations gives the azeotropic composition X1, XZ. In eqn. (29), XL means that P is expressed in terms of X, and XZ. The pressure at the azeotropic point is obtained by substituting the above concentration in eqn. (28). By combining the data of Severns et al. (1955) with the present work data, the prediction resulted in the saddle type azeotropic coordinates X1 = 0.387, XZ = 0.233, and P = 576.7 mm Hg compared with X1 21 0.34, X, N 0.24, and P = 565 mm Hg evaluated by Sevems et al. (1955). In eqn. (28), the parameters for its ternary form, which correspond to the above result and the combined data (Sevems and ours) are
ij l-2 1-3 2-3
Aij -388.95 302.46 632.00
Bij -62.94 -17.02 457.22
where the vapor pressure of the pure components are e = 614.5; fi = 521.5, and e = 418.0 mm Hg. The average deviation between experimental data and computed values using the above parameters was, according to eqn. (28), 2.57%. ACKNOWLEDGEMENT
We are grateful to Mr. David Azoulay who contributed substantially to the first version of the isoteniscope and to Professor Ilya Gertsbach of the Mathematics Department for helping in the statistical analysis. NOMENCLATURE
Bii Ai,Bi, Ci D, Dmax g h k
ii n IzD P PO
R SOS
virial coefficients Antoine parameters local deviation; maximum local deviation graviational acceleration height number of parameters in a series expansion number of observations molecular weight number of components index of refraction total pressure vapor pressure of pure component universal gas constant sum of squares corresponding to the difference and calculated values
between
observed
258 t T I+ x: Y P W Yi
temperature in ’ C temperature in K liquid molar volume of component i mole fraction in liquid and vapor phases density weight activity coefficient of component i
Subscripts
a, b calcd obsd
two successive experimental calculated observed
points
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