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Vapour—liquid equilibria. IV. The ternary system carbon tetrachloride—methanol—chloroform at 293.15 K
Fluid Phase Equilibria, 44 (1988) 77-93
77
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
VAPOUR-LIQUID EQUILIBRIA. IV. THE TERNARY SYSTEM CARBON TETRACHLORIDE-METHANOL-CHLOROFORM AT 293.15 K M. GORAL, P. ORACZ and S. W A R Y C H A *
Warsaw University, Department of Chemistry, Pasteura 1, 02-093 Warsaw (Poland) (Received January 19, 1988; accepted in final form April 25, 1988)
ABSTRACT G6ral, M., Oracz, P. and Warycha, S., 1988. Vapour-liquid equilibria. IV. The ternary system carbon tetrachloride-methanol-chloroform at 293.15 K. Fluid Phase Equilibria, 44: 77-93. Total vapour pressure measurements made by the modified static method for the ternary system carbon tetrachloride-methanol-chloroform and constituent binaries at 293.15 K are presented. The different expressions for G E suitable for correlation of these data are tested. The prediction of ternary VLE from constituent binaries is studied. Our results are compared to literature data.
INTRODUCTION
Continuing our work on measurements, correlation and prediction of the ternary VLE systems of non-electrolytes, we have studied the carbon tetrachloride-methanol-chloroform system. This system, like the previous one, i.e. methanol-chloroform-acetone (G6ral et al., 1985), is very complex. The methanol-containing binaries exhibit strongly positive deviations from Raoult's law. The (G E, x) curves for these systems are highly asymmetric and the molar enthalpy of mixing ( H E) exhibits both endothermic and exothermic effects. In addition, an extremum occurs on the activity coefficients versus mole fraction curve in the methanol-chloroform system. The carbon tetrachloride-chloroform system is nearly ideal with endothermic and symmetric H E. Ternary H E data, measured by Mirzayan (1973), exhibits exothermic and endothermic areas as well as an endothermic extremum. In this paper we report the results of total vapour pressure measurements at 293.15 K.
* To whom all correspondence should be addressed. 0378-3812/88/$03.50
© 1988 Elsevier Science Publishers B.V.
78 MATERIALS
The chemicals used were o f the highest purity available from the suppliers. Carbon tetrachloride (analytical reagent grade, POCh) was threefold crystallized, fractionated on an efficient column having 80 theoretical plates and stored over 4 ,~ molecular sieves. Methanol (analytical reagent grade, POCh) was fractionated only and stored over 3 A sieves. Chloroform (analytical reagent grade, POCh) was prepared just before measurements with low pressure distillation to avoid its decomposition. The small quantity of ethanol (about 0.8%), which is added for stabilization, and a possible trace amount of water, were both removed with 5 ,~ molecular sieves. Impurities were determined chromatographically. Water content was checked using Fischer's reagent and was on the limit of detectability. All the substances has a purity of not less than 99.98%. Table 1 gives the vapour pressures of the pure substances, measured both here and by other authors, along with second virial coefficients. For methanol and chloroform, Table 1 also reports the literature and calculated enthalpies of vaporization. These
TABLE 1 V a p o u r pressure P, second virial coefficient fla~ a n d e n t h a l p y of v a p o r i z a t i o n A H v values of pure substances used Compound
P (293.15 K) (kPa) This work
Literature
Carbon tetrachloride
12.126
Methanol
13.014
12.174-T-0.013 a 12.160 T- 0,067 a 12.15 -T-0.04 c 13.028+0.020 ~ 12.996 ~: 0.012 a 13.017 b 13.020 b 13.00 -T-0.04 c 2L087-T- 0.013 a
Chloroform a b c d e f g h
21.105
- f l ~ (293.15 K) (dm3 moi-1) d
A H v (298.15 K) (kJ m o 1 - 1 ) Literature
This work
37.49 f 38.22 e
38.21 h
31.13 g 31.13 e
31.17 h
1.879
2.228
1.275
Calculated according to Boublik et al. (1973). Calculated according to Dykyj a n d R e p a l (1979) a n d Dykyj et al. (1984). Wolff a n d Hoeppel (1968). Calculated according to H a y d e n a n d O ' C o n n e l l (1975). Calculated with A n t o i n e c o n s t a n t s from Boublik et al. (1973). Rossini et al. (1952). The value r e c o m m e n d e d b y Stull et al. (1969). Calculated from our data.
79 enthalpies were determined using the Clausius-Clapeyron equation, where dP/dT was found from Antoine's equation fitted to the vapour pressures at 293.15 K (this work), 303.15 K (Oracz and Warycha, unpublished, 1987), 313.15 and 323.15 K (G6ral et al., 1985). The compressibility factor correction was estimated according to Haggenmacher (1946). We believe that the excellent agreement between enthalpies of vaporization calculated from our data and those in the literature is a valuable and independent confirmation of the high precision of our measurement technique. METHOD The vapour pressures of the mixtures were determined by a modified static method. The apparatus and experimental procedure have b e e n described previously (Janaszewski et al., 1982). During our measurements the temperature was constant to within 0.004 K and was controlled up to 0.001 K; the absolute deviation is estimated to be equal to ___0.02 K (IPTS-68). The cathetometer readings contribute < 0.004 kPa to the error of a single pressure measurement. The extended tests have shown that this is an important contribution to the error in pressure if both errors, in temperature and pressure, are treated separately. The errors in the mole fractions were < 0.0005. The ternary samples were prepared from mixtures of chloroform and methanol, to which carbon tetrachloride was added. RESULTS AND DISCUSSION The results of total vapour pressure measurements are given in Table 2 for binary mixtures and in Table 3 for ternary ones. The binary systems were correlated by various equations in the literature, e.g. Wilson (1964), N R T L (Renon and Prausnitz, 1968), U N i Q U A C (version modified by Anderson and Prausnitz (1978)), Redlich and Kister (1948), Myers and Scott (1963), van Laar extended by van Ness (1964), SSF (Rogalski and Malanowski, 1977) and pseudovolume-fraction Redlich-Kister (as suggested by Scatchard and Hamer (1935) and Asmanova and G6ral (1980)). Coefficients of these equations were obtained by a modified Barker's method (G6ral, 1977; G6ral and Janaszewski, 1977; Kolasiflska and Oracz, 1979). The values of second virial coefficients for the pure substances and for the mixtures were calculated according to Hayden and O'Connell (1975). Table 4 shows the efficiency of these equations applied to our data. For the system methanol-chloroform we used the two-parameter NRTL, since the observed global m i n i m u m of the objective function is not sensitive to change
8O TABLE 2 Liquid mole fraction x a, calculated vapour mole fraction Ya, total vapour pressure P and deviation d P values at 293.15 K. ( d P = P - Pc~c. and Ya calculated with eqn. (1)) Xa
Ya
P (kPa)
d P (kPa)
xa
ya
P (kPa)
d P (kPa)
0.4577 0.5204 0.5744 0.6975 0.7591 0.8165 0.8706 0.9333 1
0.5182 0.5254 0.5305 0.5395 0.5445 0.5510 0.5601 0.5801 1
21.442 21.470 21.457 21.378 21.300 21.180 20.937 20.372 12.126
-0.006 0.001 -0.005 -0.005 -0.004 0.012 -0.007 0.001
Carbon tetrachloride(a) + chloroform(b) 0 0 21.105 0.0383 0.0267 20.857 0.001 0.0875 0.0607 20.533 0.005 0.1600 0.1110 20.038 0.008 0.2370 0.1650 19.509 0.030 0.2802 0.1959 19.164 0.004 0.3413 0.2406 18.692 -0.002 0.4117 0.2942 18.130 -0.005 0.4671 0.3384 17.672 -0.006
0.5276 0.5839 0.6424 0.7051 0.7622 0.8220 0.8819 0.9458 1
0.3893 0~4398 0.4960 0.5616 0.6274 0.7038 0.7901 0.8960 1
17.155 16.652 16.104 15.489 14.909 14.264 13.575 12.814 12.126
-0.004 -0.002 -0.004 -0.005 0.001 0.001 -0.007 -0.000
Methanol(a) + chloroform(b) 0 0 21.105 0.0740 0.1906 24.737 0.1578 0.2279 25.319 0.2143 0.2409 25.419 0.2783 0.2557 25.415 0.3328 0.2686 25.346 0.3912 0.2829 25.195 0.4574 0.3008 24.901 0.5644 0.3397 24.039
0.6323 0.5855 0.7624 0.6956 0.7624 0.8099 0.8808 0.9385 1
0.3763 0.3498 0.4922 0.4235 0.4922 0.5564 0.6830 0.8189 1
23.133 23.781 20.342 21.950 20.337 18.981 16.781 14.927 13.014
0.005 - 0.014 0.007 0.007 0.002 - 0.012 - 0.003 0.006
Carbon tetrachloride(a) + methanol(b) 0 0 13.014 0.0417 0.2037 15.748 -0.000 0.1006 0.3427 18.224 0.000 0.1582 0.4124 19.642 -0.001 0.2173 0.4538 20.486 -0.001 0.2772 0.4798 20.972 0.001 0.3399 0.4977 21.252 0.005 0.3961 0.5090 21.384 0.005
0.000 - 0.005 0.004 - 0.004 0.001 0.007 0.003 - 0.003
of a. Therefore, a choice of the optimal value of a for this system can, within certain limits, be arbitrary. The presented results demonstrate that the expressions for G E based on the local composition concept do not provide a sufficiently accurate descript i o n o f s y s t e m s w i t h h i g h l y - s k e w e d ( G E, x ) c u r v e s ( c a r b o n t e t r a c h l o r i d e methanol) and/or systems with an extremum on the activity coefficient versus mole fraction curve (methanol-chloroform). The system carbon tetrachloride-chloroform can be described by any equation with nearly the same
81 TABLE 3 Ternary system carbon tetrachloridt(a)-metnoi(b)-chlotalofmfc) at 293.15 K: experimental liquid mole fractions x,, xb and total pressure P; vapour mole fractions y,, yb and deviations dP ( = P - PC& calculated with eqn. (3) having six ternary parameters fitted to the data
0.0831 0.1651 0.2485 0.3396 0.4143 0.0783 0.1701 0.2473 0.4962 0.5791 0.6659 0.0828 0.1641 0.3326 0.4126 0.0830 0.2439 0.3328 0.5016 OS840 0.7471 0.0821 0.1626 0.2531 0.4167 0.1716 0.3287 0.5121 0.8321 0.0835 0.2515 0.3346 0.500X 0.5780 0.7502 0.1635 0.3242 0.4162 0.0883 0.16216 0.2452 0.0834 0.1671 0.2503 0.3342 0.4136
xb
Ya
Yb
0.+063 0.0968 0.0871 0.0765 0.0679 0.1868 0.1682 0.1526 0.102l O.OS53 0.0677 0.2633 0.2400 0.1916 0.1686 0.3282 0.2706 0.2388 0.1784 0.1489 0.0905 0.3981 0.3632 0.3239 0.2530 0.4167 0.3377 0.2454 0.0845 0.5909 0.4826 0.4290 0.3219 0.2721 0.1611 0.6022 0.4865 0.4203 0.7302 0.6707 0.6045 0.8106 0.7366 0.6630 0.5888 0.5186
0.0538 0.1047 0.1550 0.2087 0.2523 0.0560 0.1165 0.1642 0.3073 0.3535 0.4031 0.0665 0.1243 0.2293 0.2747 0.0742 0.19oa 0.2442 0.3363 0.3781 0.4601 0.0834 0.1502 0.2137 0.3090 0.1740 0.2796 0.3733 0.5140 0.3.292 0.2808 0.3307 0.4&3 0.4349 0.4937 0.2448 0.3556 0.3978 0.1959 0.2854 0.3496 0.2335 0.3403 0.3997 0.4376 0.4628
0.2220 0.2283 0.2349 0.2427 0.2498 0.2473 0.2575 0.2660 0.2947 0.3053 0.3164 0.2669 0.2762 0.2960 0.3056 0.2829 0.3007 0.3112 0.3319 0.3422 0.3625 0.3006 0.3084 0.3180 0.3369 0.3262 0.3416 0.3618 0.3911 0.3731 0.3727 0.3770 0.3892 0.3954 0.4065 0.4033 0.3988 0.4015 0.4730 0.4469 0.4327 0.5548 0.4987 0.4715 0.4572 0.4498
dP (kPa) 24.733 24.241 23.778 23.185 22.717 24.991 24.525 24.126 22.747 22.225 21.711 25.014 24.603 23.699 23.281 24.914 24.103 23.643 22.807 22.411 21.404 24.693 24.367 23.889 23.153 24.063 23.379 22.603 20.961 23.309 23.141 22.903 22.391 22.138 21.534 22.683 22.593 22.403 21.198 21.893 22.175 19.638 216)rM 21.581 21.795 27.527
0,013 - 0.016 0.012 -0.028 - 0.028 - 0.017 - 0.008 0.006 0.031 0.009 0.070 0.015 0.019 - 0.008 - 0.003 0.011 0.001 - 0.012 0.002 0.029 - 0.059 - 0.008 0.029 -0.023 0.011 - 0.001 -0.012 - 0.008 - 0.063 0.001 0.001 - 0.003 0.006 - 0.003 0.013 - a.013 - 0.019 - 0.011 0.002 0.011 0.007 -0.006 0.004 0.008 0.010 0.005
82 TABLE 4 Comparison of the efficiency of different equations for binary systems at 293.15 K. Number of. parameters n, average standard error of the total vapour pressure o ( P ) a Equation
n
o(P) (kPa)
Number of sign changes b
Calculated azeotropic point Xa P (kPa)
Carbon tetrachloride-methanol Pseudovolume-Redlich-Kister Redlich-Kister Van Laar-van Ness Myers-Scott Marsh SSF UNIQUAC NRTL Wilson Athermal Mecke-Kempter
6 6 6 6 4+ 2 6 2 3 2 2
0.006 0.025 0.012 0.007 0.009 0.008 0.056 0.133 0.048 0.022
9 6 8 7 5 5 2 3 2 5
0.474 0.476 0.475 0.473 0.474 0.474 0.474 0.474 0.474
21.475 21.475 21.472 21.475 21.474 21.474 21.456 21.405 21.451
Methanol-chloroform Pseudovolume-Redlich-Kister Redlich-Kister Van Laar-van Ness Marsh SSF UNIQUAC NRTL (a = 0.2) Wilson Athermal Mecke-Kempter
6 6 4 2+ 3 6 2 2 2 2
0.007 0.007 0.007 0.007 0.013 0.222 0.117 0.262 0.276
10 6 7 6 6 4 3 4 4
0.751 0.752 0.752 0.752 0.754 0.765 0.748 0.766
25.435 25.436 25.435 25.436 25.442 25.504 25.492 25.501
Carbon tetrachloride-chloroform Pseudovolume-Redlich-Kister Redlich-Kister Van Laar-van Ness Myers-Scott SSF UNIQUAC NRTL Wilson
2 2 2 3 2 2 3 2
0.009 0.008 0.008 0.007 0.008 0.008 0.007 0.008
3 6 6 8 6 6 8 6
" o ( P ) = [Y'-(Pe×p.-Pcalc. )2//( m -- n )]1/2, where m = number of points. b If two neighbouring points lie on opposite sides of an approximation curve then one speaks of a sign change of their deviations. The points should be scattered randomly with respect to the correlating curve. An easy measure of the randomness is the number of sign changes, which should be approximately equal to m / 2 :g ( m / 2 ) 1/2.
83 accuracy. Therefore, for correlation of our binary measurements we chose the pseudovolume-fraction Redlich-Kister equation
E Ki(2Za-
GEl R T = VZa(1 -- 2a)
1) i
(1)
i=0 where
V=X,Va+ (1 -- Xa)Vb;
Za=XaVa/U
(la)
In eqn. (la) the pseudovolumes va and v b are not molar liquid volumes of corresponding pure components, but are adjustable parameters. One can observe that G E in eqn. (1) depends on the ratio of the v parameters and one of them can be set arbitrarily to one. For the other components, the v parameters evaluated with a trial-and-error method remained constant and common for all investigated binary and ternary mixtures. Values of the K~ coefficients in eqn. (1) together with their standard errors o(Ki) and the correlation coefficients qrt for pairs (Kr, Kt) are given in Table 5 for all the binary systems. The qrt values together with the standard errors o ( K i ) allow, if necessary, the estimation of standard errors of all values, which depend on K i. The coefficients A~, B i and Ci given in Table 5 may be used in eqn. (2), Ki t - Ki = A i ( ~ a - /~aa) + Bi( ~bb -- ]~bb) -{- Ci( ~ t - ~ )
(2)
to show how parameter K~ would change if the second virial coefficients flaa, flbb and 6fl = 2flab - flaa -- flbb used in this study were replaced by another set of values denoted /3a'a, flbb and ~fl'. Equation (2) clearly shows the influence of the second virial coefficients on K~ values. We can directly compare our measurements with those of Wolff and Hoeppel (1968) for the system carbon tetrachloride-methanol at 293.15 K. We compared our experimental pressure values with their data using the same reference line P+ = f ( X a , K 1 . . . , K6). The reference total pressure P+ was calculated with K1... , K 6 coefficients of the 4 / 2 - M a r s h (1977) equation fitted to Wolff and Hoeppel's data. This equation best fits their data giving a ( P ) = 0.079 kPa. Throughout all the calculations the same virial coefficients were used. The pure component vapour pressures were those reported for relevant data sets. The agreement between both sets of data is very good: results of the comparison are presented in Fig. 1. VLE data at 293.15 K for this system have been also reported by Niini (Gmehling and Onken, 1977). However, Niini's data are incorrect. Comparison of (P, x) points shows considerable and systematic differences between his data and other findings (both those of Wolff and Hoeppel and our own). The maximum deviation is 4.7 kPa (24.5%).
84 TABLE 5 Parameters ua, v b, v¢ and K i of eqn. (1) with their standard errors aKi, correlation coefficients q~j, coefficients Ai, B i and C i of eqn. (2) and cross second virial coefficients flab, fla¢, and flb~ at 293.15 K i=
0
1
2
3
Carbon tetrachloride(a) + methanol(b) /)a =1.07 o b = 2.33 flab = --0.931 d m 3 mo1-1 K i 1.3584 - 0.1481 0.2531 =
Ai= Bi = C~ =
0.0043 0.0031 0.0045
oK i = qli = q2i = q3i = q4i =
- 0.0161
0.1130
0.0026 0.0029 - 0.0032
- 0.0014 0.0004 - 0.0002
0.0059 0.0030 0.0044
0.0004 0.0001 0.0010
0.0006
0.0012
0.0020
0.0034
-0.3174 0.1766 0.6393
-0.1921 -0.6811
0.6318
-
0.0004 0.5293 -0.5969 0.6979 0.8252
4
Carbon tetrachloride(a) + chloroform(c) v a = 1.07 vc = 1 . 0 0 flac= - 1.657 d m 3 m o l - 1 Ko= 0:1745 Ao = Bo = Co = oK o =
0.0030 - 0.0037 0.0063 0.0006
Methanol(b) + chloroform(c) v b = 2.33 ~ =1.00 K i 0.9292
fl~ = -0.894 dm3mo1-1 -0.0257 0.0358
Ai = Bi = C~=
0.0038 0.0032 0.0057
0.0004 -0.0044 -0.0004
-0.0033 -0.0067 -0.0044
0.0041 0.0101 0.0071
0.0003 -0.1327 -0.4760 0.1367 0.0469
0.0011
0.0033
0.0114
0.1399 -0.6101 0.6163
-0.7206 0.5109
-0.9429
=
oK i
=
qli = q2i = q3i q4i =
=
The
binary
systems
under
0.0107
have
been
investigated
under
isobaric
as well as molar
the value of GE/RT
-
VLE
mic conditions
enthalpy
simultaneously,
each VLE
0.0009 0.0059 - 0.0023 -
consideration
authors,
this purpose
-0.1550
who have measured
sively by many
possible to compare,
-0.0763
data
various VLE
set under
at, f o r e x a m p l e ,
of mixing
comparison equimolar
(HE).
and
exten-
or isother-
Therefore,
i t is
H E sets of data. For
may
be represented
concentration,
by
henceforth
85 i
0,05
I
I
I
I
I
I
0 O
. . . . .
~D'
0 0
1
-
0
0 n _~
f
6 . . . .
•
O~ fj
o
O0 O .
0 0
qb +
0
0
i O_
O -0,05
0
-0.10
I
0
I
I
I
I
I
I
I
I
0,5
Xcct4 Fig. 1. Carbon tetrachloride-methanol, direct comparison of (P, x) data: <3, Wolff and Hoeppel (1968); e, our data. Dashed lines indicate range of error of single pressure measurement from Wolff and Hoeppel.
denoted Q0.5- The Q0.5 values calculated from various data sets were plotted against 1/T. From the Gibbs-Helmholtz equation, the slope of the resulting line should be equal to HoE s/R. Such plots for carbon tetrachloride-methanol, carbon tetrachloride-chloroform and methanol-chloroform systems are presented in Figs. 2-4. The slopes of the unbroken lines in these figures were calculated using H F data in the literature. In ranges for which H E data were not available, dashed lines have been used. For the systems with carbon tetrachloride the H E data are taken from the compilation by Belousov and Morachevskii (1970). For the methanol-chloroform system the H E at 323.15 K has been measured by Morris et al. (1975), at 308.15 K by Moelwyn-Hughes and Missen (1957) and at 298.15 K by Hirobe (Belousov and Morachevskii, 1970), Abramov et al. (1973) and recently by Nagata and Tamura (1983). In the previous work (G6ral et al., 1985) we used H E data of Morris et al. (1975) and Abramov et al. (1973). The remaining H E data at 298.15 K seemed to be inaccurate. The recent measurements of Nagata and Tamura (1983) prove that they were correct and indicate inaccuracies in the data of Abramov and his collaborators; so the data of the latter have been rejected. Scattering of points on the figures results from experimental errors in some of the literature data. The figures clearly show mutual agreement of some G E data sets as well as their consistency with H E.
86 0.55
J
o 0
/ O t 70
o/m._--e-V
• ~
/
/
0.50
A
0.45
I
I
I
I
I
I
I
3.0
35 103 / T
Fig. 2. Carbon tetrachloride-methanol; comparison of equimolar Q0.5 = GE/RT values with literature values at various temperatures; zx, Fontell (1936); D, Scatchard et al. (1946); +, Scatchard and Ticknor (1952); ~, Hipkin and Myers (1954); x, Ocon and Espantoso (1958); I, Prakash and Katti (1965); o, Wolff and Hoeppel (1968); v, Yasuda et al. (1975); o, this work. F o r the m e t h a n o l - c h l o r o f o r m system we can c o m p a r e azeotropic p o i n t s m e a s u r e d at different temperatures. T o this end we used the plot of l n ( x a ) versus 1 / T (Fig. 5). T h e series of points gives a straight line, which c o n f i r m s the internal consistency of our d a t a m e a s u r e d at different temperatures. In our opinion, all the above tests show excellent a g r e e m e n t b e t w e e n our results a n d those published in the literature, as well as internal c o n s i s t e n c y a n d consistency with m o l a r e n t h a l p y of mixing.
,
,/
0.05
/ /
0
o/ /
0.04
/
o
/
,,/
/
0
®
/
/ /
0.03
i
3.0
i
i
3.5
IO00/T
Fig. 3. Carbon tetrachloride-chloroform system; comparison of equimolar Q0.5= GElRT values with literature values at various temperatures; ~, Kaplan and Monokchow (1937); o, McGlashan et al. (1954); zx, Rulewicz et al. (1968); v, Krauze and Serwinski (1973); O, this work.
87 Q40
0.35
~ pe -
~.,e
~
o
D 0.30
l
J
i
3.0
i
I
3.2
3.4 103/T
Fig. 4. Methanol-chloroform system, comparison of equimolar Q0.5 = GElRT values with literature values at various temperatures; v, Tyrer (1912); o, Kireev and Sitnikow (1941); ×, Severns et al. (1955); e , Natradze and Novikova (1957); A, Nagata (1962); +, Abbott and van Ness (1975); v, Bushmakin and Kish (1957); zx, Tochigi et al. (1984); D, Tamir et al. (1981); o, G6ral et al. (1985); , , Oracz and Warycha (1987); e, this work.
T h e t e r n a r y s y s t e m was c o r r e l a t e d b y eqns. ( 3 ) - ( 6 ) as well as b y c o m m o n l y used e q u a t i o n s such as SSF, Wilson, N R T L a n d U N I Q U A C . E q u a tion (3) is an e x t e n s i o n o f eqn. (1) to the t e r n a r y mixture. T h e e x t e n s i o n results f r o m a n a s s u m p t i o n that the t e r n a r y m i x t u r e c a n b e t r e a t e d as a p s e u d o b i n a r y m i x t u r e o f m e t h a n o l with the m i x t u r e o f c a r b o n t e t r a c h l o r i d e - c h l o r o f o r m t r e a t e d as o n e c o m p o n e n t w i t h p r o p e r t i e s d e p e n d i n g o n c o n c e n t r a t i o n . This explains w h y in eqns. (3) a n d (4) m o l e f r a c t i o n s o f
1.3
x E i
1.1
I
I
J
3.0
J
3.5
103/T
Fig. 5. Methanol-chloroform, azeotropic mole fraction of methanol (ln values) versus temperature; n, Tochigi et al. (1984); +, Abbott and van Ness (1975);., G6ral et al. (1985); e , Oracz and Warycha (unpublished, 1987); e, this work.
88 TABLE 6 Comparison of the efficiency of different equations for the ternary system carbon tetrachloride-methanol-chloroform at 293.15 K. Average standard error of the total vapour pressure o ( P ) a, relative standard error of the total vapour pressure o ( d P / P ) b Equation
Number of parameters Binary c Ternary
o(P)
o(dP/P)
(kPa)
(%)
Pseudovolume-Redfich-Kister
(6/2/6) - 1
Eqn. (5) fl = 0 (Kohler) Eqn. (5) fl = - 1/4
5+ 1/2/6 5+ 1/2/6
SSF
6/2/6
UNIQUAC NRTL Wilson Athermal Meeke-Kempter
2/2/2 3/3/2 2/2/2 2/0/2
0.063 0.041 0.023 0.863 0.117 0.045 0.027 0.896 0.078 0.040 0.096 0.119 0.088 0.119
0.28 0.18 0.10 3.80 0.51 0.20 0.12 3.94 0.34 0.18 0.42 0.53 0.38 0.53
0 2 6 0 0 2 6 0 3 6 0 0 0 0
a o ( P ) = []](Pexp.- Pcalc.)2/( m - n)] 1/2, n = number of parameters. b o ( d P / P ) = [E[1- P~¢./Pexp.]2/(m - n)] 1/2, rn = number of points.
c Cf. Table 4.
m e t h a n o l are a s y m m e t r i c a l l y t r e a t e d with respect to two o t h e r c o m p o n e n t s . T a b l e 6 shows that eqn. (3) predicts t e r n a r y V L E d a t a b e t t e r t h a n o t h e r equations. T h e e q u a t i o n has the f o r m
G~/RT=v{[z.zbEK,(a,b ) ( 1 -
2Zb) i + z b z ~ E K , ( b ,
C)(2Zb -- 1) i
+ Z a Z ¢ K o ( a , c)] + G E ( t e r ) / R T }
(3)
where: v = XaU a q- XbU b "4- XcUc'~ Z i = XiUi/O; s u b s c r i p t b d e n o t e s m e t h a n o l a n d subscripts a a n d c d e n o t e c a r b o n t e t r a c h l o r i d e a n d c h l o r o f o r m , respectively. T h e p s e u d o v o l u m e s va, v b a n d vc are a d j u s t a b l e p a r a m e t e r s k e p t c o n s t a n t for all b i n a r y a n d t e r n a r y data; K i are c o r r e s p o n d i n g b i n a r y parameters and GZ(ter)/RT is a t e r n a r y term, a s s u m e d to b e z e r o w h e n eqn. (3) is used for p r e d i c t i o n of t e r n a r y V L E f r o m c o n s t i t u e n t binaries. T h e t e r n a r y c o n t r i b u t i o n GE(ter) has the f o r m
GE(ter) = ZaZbZc[C1 + C2fl + C3f2 + C4f(:+ C5f2 + C6flf2] w h e r e f l = 2Zb -- 1; f2 ---- (Za -- Z c ) / ( Z a + Zc)"
(4)
89 Equation (5) is the one discussed previously by Oracz (1987), to which ternary terms were added. The equation has the form 2
G E / R T = Y'~
3
~,
(x i ÷ xi)I~GE(x * ) / R T +
GE(ter)/RT
(5)
i=1 j = i + l
where x* = x J ( x i + x j). G~ is any equation suitable for the correlation of a binary mixture (i + j ) . For this reason, eqn. (5) is much more general than any other proposed in the literature. Parameter/3 is adjustable. In this work we used fl = - 1 / 4 . This value is suitable for systems with strong positive deviations from Raoult's law; for systems with strong negative deviations /3 = 1 was used by Grral et al. (1985). If/3 = 0 then eqn. (5) is equivalent to Kohler's equation. For the ternary contribution GZ(ter) in eqn. (5), we adopted the following expression:
G e ( t e r ) / R T = XaXbXc[C 1 At" C 2 ( 3 x a - 1) + C 3 ( 3 x b - 1) + C 4 ( 3 x a - 1) 2 + C5(3x b - 1) 2 + C6(3x a - 1)(3x b - 1)]
(6)
Table 6 shows the efficiency of various equations applied to the ternary data. One can see that prediction with eqn. (3) is quite good, but for description of the data with experimental accuracy ternary terms are necessary. This agrees with the conclusion of Pando et al. (1987) in a paper on the molar enthalpy of mixing in ternary mixtures. One should note the good performance of the equations based on the local composition concept in contrast to the poor performance in the constituent binaries. Results of fitting the ternary data with the eqns. (3) and (4) are given in Table 7. Apart from the correlation parameters C~, their standard errors o(C~) and the correlation coefficients qij for the pairs (C i, Cj), the coefficients a~, b~, c;, di, e~ and f~ are also given. They can be used analogously as for the binary system to recalculate the ternary parameters C~, when another set of the second virial coefficients would be used
C , ' - Ci = a,(fl~a -/3aa) -k- bi(flb b -- /3bb) + Ci(/3~c -- /3cc) "q- di( ~/3atb -- ~/3ab) + ei( 8/3~'c- 8/3ac) + g,( Sflbc -- 6flb~)
(7)
The deviations between experimental and calculated vapour pressures are presented in Table 3. To demonstrate that the reasonable use of even rough models may produce acceptable results we used the so-called athermal Mecke-Kempter model developed by Kehiaian and Treszczanowicz (1968). This model has been applied to both methanol-containing binary systems. The relevant standard deviations are given in Table 4. The relatively large standard error in the methanol-chloroform system results from the inadequacy of the
90
TABLE 7 C o e f f i c i e n t s Ct of eqn. (4) for t h e t e r n a r y p a r t of t h e e x c e s s G i b b s e n e r g y , t h e i r s t a n d a r d e r r o r s a C i, c o r r e l a t i o n c o e f f i c i e n t s qij a n d c o e f f i c i e n t s a t, b i, c i, d r, e i, gi o f e qn. (7) f o r t h e t e r n a r y s y s t e m c a r b o n t e t r a c h l o r i d e - m e t h a n o l - c h l o r o f o r m a t 293.15 K i=
1
2
3
4
5
6
- 0.3169
- 0.0431
0.1843
Ci =
0.0 570
- 0.0967
- 0.2458
ai= bt =
0.0309
0.0317
0.0036
0.0337
0.0503
0.0307
0.0009
- 0.0065
ci = di = ei = gi =
0.0 092 0.0086
0.0023 0.0199
- 0.0159 0.0208
- 0.0151 0.0034
- 0.0212 0.0268
0.0070
- 0.0022
- 0.0087
- 0.0099
- 0.0055
0.0010
0.0137
0.0141
0.0041
0.0126
- 0.0367
- 0.0396
oC t =
0.0 054
0.0130
0.0342
0.0666
0.0110
0.0368
q2t = q3i = qni = qsi q6i
0.1906 -- 0.2540 -- 0.6999 0.1491 0.0 350
- 0.2686 - 0.1538
0.5253
=
=
- -
0.2088 0.1552
0.2414
- 0.0772 - 0.1732
- 0.0856 0.0529
-0.0324
-
0.0314
0.0230
-0.0036 -
0,0140 0.0357
theory to model the behaviour of this system. Afterwards, the binary constants were used for prediction of the ternary VLE data. The ternary system was approximated by a pseudo-binary mixture, i.e. GE/RT for the ternary system was calculated from the expression for a binary system with the mole fractions equal to x* (CC14) = x(CC1,)/[x(CC14) + x(CHC13)] ; x* (CH3OH) = 1 - x* (CC14)
(8)
and the parameters linearly changing with the mole fraction of carbon tetrachloride, x * (CC14). The calculated standard deviation is given in Table 6 and, taking into account all constraints, the result is surprisingly good. ACKNOWLEDGEMENT
We appreciate the financial support provided for this work by The Polish Academy of Sciences within project PAN 3.20. LIST OF SYMBOLS
Ai,
Bi,
ai,
hi, ci,
di,
ei, gi
c,, c:,
Ci
coefficients in eqn. (2) coefficients in eqn. (7)
91
c4, c5, c6 GE
GE(ter) HE Ki P 00.5
qij
coefficients in eqns. (4) and (6) excess Gibbs energy excess Gibbs energy for the mixture i + j ternary contribution to excess Gibbs energy enthalpy of mixing Redlich-Kister parameters in eqns. (1)-(3) vapour pressure (kPa) value of G E / R T at equimolar concentration correlation coefficients between parameter pairs (K~, Kfl or
( c,, Cj)
R
gas constant T temperature (K) Va, Vb, Vc~ V adjustable pseudovolumes in eqns. (1), (3)-(4) mole fraction in liquid X mole fraction in eqns. (5) and (8) X* pseudovolume fraction in eqns. (3) Greek letters
a
N R T L parameter
aa, Bbb, fl c, /
flaa, Ebb, fl~ second virial coefficients fl exponent in eqn. (5) o standard error REFERENCES Abbott, M.M. and Van Ness, H.C., 1975. Vapor-liquid equilibrium. Part III. Data reduction with precise expressions for G E. AIChE J., 21: 62. Abramov, E.V., Mirzayan, A.S. and Devina, D.A., 1973. Heats of formation of ternary systems. 4. Izv. Akad. Nauk. Kaz. SSR. Ser. Khim., 4:42 (in Russian). Anderson, T.F. and Prausnitz, J.M., 1978. Application of the UNIQUAC equation to calculation of multicomponent phase equilibria. 1. Vapor-liquid equilibria. Ind. Eng. Chem. Process Des. Dev., 17: 552-561. Asmanova, N. and Grral, M., 1980. Vapour pressures and excess Gibbs energies in binary mixtures of hydrocarbons at 313.15 K. 1 Methylcyclohexane-benzene, - toluene, - o-xylene, -p-xylene, -ethylbenzene, and -propylbenzene. J. Chem. Eng. Data, 25: 159-161. Belousov, V.P. and Morachevskii, A.G., 1970. The Heat of Mixing of Liquids. Khimia, Leningrad (in Russian). Boublik, T., Fried, V. and Hala, E., 1973. The Vapour Pressures of Pure Substances. Elsevier, Amsterdam. Bushmakin, I.N. and Kish, I.N., 1957. Zh. Prikl. Khim., 30: 561. Dykyj, J. and RepaY, M., 1979. Tlak Nasytenej Pary Organickych Zlucenin. Veda, Bratislava. Dykyj, J., RepaY, M. and Svoboda, J., 1984. Tlak Nasytenej Pary Organickych Zlucenin. Veda, Bratislava.
92 Fontell, N., 1936. Soc. Sci. Comment. Phys.-Math., 8(15). Gmehling, J. and Onken, V., 1977. Vapor-Liquid Equilibrium Data Collection, Vol. 1-2a. Dechema, Frankfurt/Main. G6ral, M., 1977. Error analysis in Barker's method of vapour pressure isotherm data processing. Z. Phys. Chem., 258: 1040. G6ral, M. and Janaszewski, B., 1977. The problem of vapour non-ideality in Barker's method of vapour pressure isotherm data processing. Z. Phys. Chem., 258: 417-425. G6ral, M., Kolasifiska, G., Oracz, P. and Warycha, S., 1985. Vapour-liquid equilibria. II. Ternary system methanol-chloroform-acetone at 313.15 and 323.15 K. Fluid Phase Equilibria, 23: 89. Haggenmacher, J.E., 1946. The heat of vaporization as a function of pressure and temperature. J. Am. Chem. Soc., 68: 1633. Hayden, J.G. and O'Connell, J.R., 1975. A generalised method for predicting second virial coefficients. Ind. Eng. Chem. Process Des. Dev., 14: 209. Hipkin, H. and Myers, H.S., 1954. Ind. Eng. Chem., 46: 2524. Janaszewski, B., Oracz, P., G6ral, M. and Warycha, S., 1982. Vapour liquid equilibria. I. An apparatus for isothermal total vapour pressure measurements: binary mixtures of ethanol and t-butanol with n-hexane, n-heptane and n-octane at 313.15 K. Fluid Phase Equilibria, 9: 295. Kaplan, S.I. and Monokchow, Z.D., 1937. Zh. Obshch. Khim., 7: 2499. Kehiaian, H. and Treszczanowicz, A., 1968. Excess free enthalpy of athermal associated mixtures of the Mecke-Kempter type. Bull. Acad. Polon. SCi., Ser. Sci. Chim., 16: 445. Kireev, V.A. and Sitnikow, I.P., 1941. Zh. Fiz. Khim., 15: 492. Kolasifiska, G. and Oracz, P., 1979. Generalization of error analysis and problem of vapour non-ideality in Barker's method of vapour pressure isotherm data processing. Z. Phys. Chem., Leipzig, 260: 169-173. Krauze, R. and Serwinski, M., 1973. Zesz. Nauk. Politech. Lodz., 53. McGlashan, M.L., Prue, J.E. and Sainsbury, I.E.J., 1954. Equilibrium properties of mixtures of carbon tetrachloride and chloroform. Trans. Faraday Soc., 50: 1284-92. Marsh, K.N., 1977. A general method for calculating the excess Gibbs free energy from isothermal vapour-liquid equilibria. J. Chem. Thermodyn., 9: 719-724. Mirzayan, A.S., 1973. Diagrams of heat of mixing for ternary homogenous liquid systems. Ph.D., Kazakh State University, Alma-Ata (in Russian). Moelwyn-Hughes, E.A. and Missen, R.W., 1957. Thermodynamic properties of methyl alcohol-chloromethane solutions. J. Phys. Chem., 61: 518. Morris, W., Molvey, P.J., Abbott, M.M. and van Ness, H.C., 1975. Excess thermodynamic functions of ternary systems. I. Acetone-chloroform-methanol at 50 o C. J. Chem. Eng. Data, 20: 403. Myers, D.B. and Scott, R.L., 1963. Computer methods for the systematic processing of data on binary mixtures. Ind. Eng. Chem., 55: 43. Nagata, I., 1962. J. Chem. Eng. Data, 7" 367. Nagata, I. and Tamura, K., 1983. Excess enthalpies of binary and ternary mixtures of methanol with acetone, chloroform, benzene and tetrachloromethane. Fluid Phase Equilibria, 15: 67. Natradze, A.G. and Novikova, K.E., 1957. Liquid-vapor phase equilibrium in the system methanol-chloroform at pressures of 600, 500, 400 mm Hg. Zh. Fiz. Khim., 31:227 (in Russian). Ocon, J. and Espontoso, J., 1958. An. Real. Soc. Espan. Fiz. y Quim., 54B: 413.
93 Oracz, P., 1987. Vapour-liquid equilibria in complex ternary systems from binary contributions. 3rd CODATA Syrup. on Critical Evaluation and Prediction of Phase Equilibria in Multicomponent Systems, Budapest, 6-8 Sept. Pando, C., Renuncio, J.A.R., Calzan, J.A.G., Christensen, J.J. and Izatt, R.M., 1987. Correlation and prediction of ternary excess enthalpy data. J. Solution Chem., 16: 503. Prakash, O. and Katti, P.K., 1965. Indian Chem. Eng., 7: 741. Redlich, O. and Kister, A.T., 1948. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem., 40: 345-348. Renon, H. and Prausnitz, J.M., 1968. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J., 14: 135-144. Rogalski, M. and Malanowski, S., 1977. A new equation for correlation of vapour-liquid equilibrium data of strongly non-idealmixtures. Fluid Phase Equilibria, 1: 137. Rossini, F.D., Wagman, D.D., Evans, W.H., Levine, S. and Jaffe, I., 1952. Selected Values of Chemical Thermodynamic Properties (National Bureau of Standards Circular No. 500). U.S. Gov. Print. Office, Washington. Rulewicz, G., Schuberth, H. and Leibnitz, E., 1968. Untersuchungen ueber das Dampf-Fluessigkeits-Phasengleichgewicht des Systems Methytenchlorid-ChloroformTetrachlorkohlenstoff bei 45 °C mater Verwendung einer gaschromatographischen Analysenmethode. J. Prakt. Chem., 37: 122. Scatchard, G. and Hamer, W.J., 1935. The application of equations for the chemical potentials to partially miscible solutions. J. Am. Chem. Soc., 57: 1805-1909. Scatchard, G. and Ticknor, L.B., 1952. Vapor-liquid equilibrium. IX. The methanol-carbon tetrachloride-benzene system. J. Am. Chem. Soc., 74: 3724. Scatchard, G., Wood, S.E. and Mochel, J.M., 1946. Vapor-liquid equilibrium. VII. Carbon tetrachloride-methanol mixtures. J. Am. Chem. Soc., 68: 1960. Severns, W.H., Sesonske, A., Perry, R.H. and Pigford, 1LL., 1955. AIChE J., 1: 401. Stull, D.R., Westrum, E.F. and Sinke, G.C., 1969. The Chemical Thermodynamics of Organic Compounds. Wiley, New York. Tamir, A., Apelblat, A. and Wagner, M., 1981. Fluid Phase Equilibria, 6: 113. Tochigi, K., Hiaki, T. and Kojima, K., 1984. Vapor-liquid equilibria for saddle azeotropic mixture acetone-chloroform-methanol system and method for determination of ridge and valley. First CODATA Symp. on Critical Evaluation and Prediction of Phase Equilibria in Multicomponent Systems, Jachranka near Warsaw, 9-17 May. Tyrer, D., 1912. CXV. Latent heats of vaporization of mixed liquids. J. Chem. Soc., 101: 1104-1113. Van Ness, H.C., 1964. Classical Thermodynamics of Non-electrolyte Solutions. Pergamon Press, London. Wilson, G.M., 1964. Vapour-liquid equilibrium. XI. A new expression for the excess free energy of mixing. J. Am. Chem. Soc., 86: 127-130. Wolff, H. and Hoeppel, H.E., 1968. Die Assoziation von Methanol in Tetrachlorkohlenstoff (nach Dampfdruckmessungen). Bet. Bunsenges. Phys. Chem., 72: 1173-1182. Yasuda, M., Kawade, E. and Katayama, T., 1975. Kagaku Kogaku Ronbunshu, 1: 175.
77
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
VAPOUR-LIQUID EQUILIBRIA. IV. THE TERNARY SYSTEM CARBON TETRACHLORIDE-METHANOL-CHLOROFORM AT 293.15 K M. GORAL, P. ORACZ and S. W A R Y C H A *
Warsaw University, Department of Chemistry, Pasteura 1, 02-093 Warsaw (Poland) (Received January 19, 1988; accepted in final form April 25, 1988)
ABSTRACT G6ral, M., Oracz, P. and Warycha, S., 1988. Vapour-liquid equilibria. IV. The ternary system carbon tetrachloride-methanol-chloroform at 293.15 K. Fluid Phase Equilibria, 44: 77-93. Total vapour pressure measurements made by the modified static method for the ternary system carbon tetrachloride-methanol-chloroform and constituent binaries at 293.15 K are presented. The different expressions for G E suitable for correlation of these data are tested. The prediction of ternary VLE from constituent binaries is studied. Our results are compared to literature data.
INTRODUCTION
Continuing our work on measurements, correlation and prediction of the ternary VLE systems of non-electrolytes, we have studied the carbon tetrachloride-methanol-chloroform system. This system, like the previous one, i.e. methanol-chloroform-acetone (G6ral et al., 1985), is very complex. The methanol-containing binaries exhibit strongly positive deviations from Raoult's law. The (G E, x) curves for these systems are highly asymmetric and the molar enthalpy of mixing ( H E) exhibits both endothermic and exothermic effects. In addition, an extremum occurs on the activity coefficients versus mole fraction curve in the methanol-chloroform system. The carbon tetrachloride-chloroform system is nearly ideal with endothermic and symmetric H E. Ternary H E data, measured by Mirzayan (1973), exhibits exothermic and endothermic areas as well as an endothermic extremum. In this paper we report the results of total vapour pressure measurements at 293.15 K.
* To whom all correspondence should be addressed. 0378-3812/88/$03.50
© 1988 Elsevier Science Publishers B.V.
78 MATERIALS
The chemicals used were o f the highest purity available from the suppliers. Carbon tetrachloride (analytical reagent grade, POCh) was threefold crystallized, fractionated on an efficient column having 80 theoretical plates and stored over 4 ,~ molecular sieves. Methanol (analytical reagent grade, POCh) was fractionated only and stored over 3 A sieves. Chloroform (analytical reagent grade, POCh) was prepared just before measurements with low pressure distillation to avoid its decomposition. The small quantity of ethanol (about 0.8%), which is added for stabilization, and a possible trace amount of water, were both removed with 5 ,~ molecular sieves. Impurities were determined chromatographically. Water content was checked using Fischer's reagent and was on the limit of detectability. All the substances has a purity of not less than 99.98%. Table 1 gives the vapour pressures of the pure substances, measured both here and by other authors, along with second virial coefficients. For methanol and chloroform, Table 1 also reports the literature and calculated enthalpies of vaporization. These
TABLE 1 V a p o u r pressure P, second virial coefficient fla~ a n d e n t h a l p y of v a p o r i z a t i o n A H v values of pure substances used Compound
P (293.15 K) (kPa) This work
Literature
Carbon tetrachloride
12.126
Methanol
13.014
12.174-T-0.013 a 12.160 T- 0,067 a 12.15 -T-0.04 c 13.028+0.020 ~ 12.996 ~: 0.012 a 13.017 b 13.020 b 13.00 -T-0.04 c 2L087-T- 0.013 a
Chloroform a b c d e f g h
21.105
- f l ~ (293.15 K) (dm3 moi-1) d
A H v (298.15 K) (kJ m o 1 - 1 ) Literature
This work
37.49 f 38.22 e
38.21 h
31.13 g 31.13 e
31.17 h
1.879
2.228
1.275
Calculated according to Boublik et al. (1973). Calculated according to Dykyj a n d R e p a l (1979) a n d Dykyj et al. (1984). Wolff a n d Hoeppel (1968). Calculated according to H a y d e n a n d O ' C o n n e l l (1975). Calculated with A n t o i n e c o n s t a n t s from Boublik et al. (1973). Rossini et al. (1952). The value r e c o m m e n d e d b y Stull et al. (1969). Calculated from our data.
79 enthalpies were determined using the Clausius-Clapeyron equation, where dP/dT was found from Antoine's equation fitted to the vapour pressures at 293.15 K (this work), 303.15 K (Oracz and Warycha, unpublished, 1987), 313.15 and 323.15 K (G6ral et al., 1985). The compressibility factor correction was estimated according to Haggenmacher (1946). We believe that the excellent agreement between enthalpies of vaporization calculated from our data and those in the literature is a valuable and independent confirmation of the high precision of our measurement technique. METHOD The vapour pressures of the mixtures were determined by a modified static method. The apparatus and experimental procedure have b e e n described previously (Janaszewski et al., 1982). During our measurements the temperature was constant to within 0.004 K and was controlled up to 0.001 K; the absolute deviation is estimated to be equal to ___0.02 K (IPTS-68). The cathetometer readings contribute < 0.004 kPa to the error of a single pressure measurement. The extended tests have shown that this is an important contribution to the error in pressure if both errors, in temperature and pressure, are treated separately. The errors in the mole fractions were < 0.0005. The ternary samples were prepared from mixtures of chloroform and methanol, to which carbon tetrachloride was added. RESULTS AND DISCUSSION The results of total vapour pressure measurements are given in Table 2 for binary mixtures and in Table 3 for ternary ones. The binary systems were correlated by various equations in the literature, e.g. Wilson (1964), N R T L (Renon and Prausnitz, 1968), U N i Q U A C (version modified by Anderson and Prausnitz (1978)), Redlich and Kister (1948), Myers and Scott (1963), van Laar extended by van Ness (1964), SSF (Rogalski and Malanowski, 1977) and pseudovolume-fraction Redlich-Kister (as suggested by Scatchard and Hamer (1935) and Asmanova and G6ral (1980)). Coefficients of these equations were obtained by a modified Barker's method (G6ral, 1977; G6ral and Janaszewski, 1977; Kolasiflska and Oracz, 1979). The values of second virial coefficients for the pure substances and for the mixtures were calculated according to Hayden and O'Connell (1975). Table 4 shows the efficiency of these equations applied to our data. For the system methanol-chloroform we used the two-parameter NRTL, since the observed global m i n i m u m of the objective function is not sensitive to change
8O TABLE 2 Liquid mole fraction x a, calculated vapour mole fraction Ya, total vapour pressure P and deviation d P values at 293.15 K. ( d P = P - Pc~c. and Ya calculated with eqn. (1)) Xa
Ya
P (kPa)
d P (kPa)
xa
ya
P (kPa)
d P (kPa)
0.4577 0.5204 0.5744 0.6975 0.7591 0.8165 0.8706 0.9333 1
0.5182 0.5254 0.5305 0.5395 0.5445 0.5510 0.5601 0.5801 1
21.442 21.470 21.457 21.378 21.300 21.180 20.937 20.372 12.126
-0.006 0.001 -0.005 -0.005 -0.004 0.012 -0.007 0.001
Carbon tetrachloride(a) + chloroform(b) 0 0 21.105 0.0383 0.0267 20.857 0.001 0.0875 0.0607 20.533 0.005 0.1600 0.1110 20.038 0.008 0.2370 0.1650 19.509 0.030 0.2802 0.1959 19.164 0.004 0.3413 0.2406 18.692 -0.002 0.4117 0.2942 18.130 -0.005 0.4671 0.3384 17.672 -0.006
0.5276 0.5839 0.6424 0.7051 0.7622 0.8220 0.8819 0.9458 1
0.3893 0~4398 0.4960 0.5616 0.6274 0.7038 0.7901 0.8960 1
17.155 16.652 16.104 15.489 14.909 14.264 13.575 12.814 12.126
-0.004 -0.002 -0.004 -0.005 0.001 0.001 -0.007 -0.000
Methanol(a) + chloroform(b) 0 0 21.105 0.0740 0.1906 24.737 0.1578 0.2279 25.319 0.2143 0.2409 25.419 0.2783 0.2557 25.415 0.3328 0.2686 25.346 0.3912 0.2829 25.195 0.4574 0.3008 24.901 0.5644 0.3397 24.039
0.6323 0.5855 0.7624 0.6956 0.7624 0.8099 0.8808 0.9385 1
0.3763 0.3498 0.4922 0.4235 0.4922 0.5564 0.6830 0.8189 1
23.133 23.781 20.342 21.950 20.337 18.981 16.781 14.927 13.014
0.005 - 0.014 0.007 0.007 0.002 - 0.012 - 0.003 0.006
Carbon tetrachloride(a) + methanol(b) 0 0 13.014 0.0417 0.2037 15.748 -0.000 0.1006 0.3427 18.224 0.000 0.1582 0.4124 19.642 -0.001 0.2173 0.4538 20.486 -0.001 0.2772 0.4798 20.972 0.001 0.3399 0.4977 21.252 0.005 0.3961 0.5090 21.384 0.005
0.000 - 0.005 0.004 - 0.004 0.001 0.007 0.003 - 0.003
of a. Therefore, a choice of the optimal value of a for this system can, within certain limits, be arbitrary. The presented results demonstrate that the expressions for G E based on the local composition concept do not provide a sufficiently accurate descript i o n o f s y s t e m s w i t h h i g h l y - s k e w e d ( G E, x ) c u r v e s ( c a r b o n t e t r a c h l o r i d e methanol) and/or systems with an extremum on the activity coefficient versus mole fraction curve (methanol-chloroform). The system carbon tetrachloride-chloroform can be described by any equation with nearly the same
81 TABLE 3 Ternary system carbon tetrachloridt(a)-metnoi(b)-chlotalofmfc) at 293.15 K: experimental liquid mole fractions x,, xb and total pressure P; vapour mole fractions y,, yb and deviations dP ( = P - PC& calculated with eqn. (3) having six ternary parameters fitted to the data
0.0831 0.1651 0.2485 0.3396 0.4143 0.0783 0.1701 0.2473 0.4962 0.5791 0.6659 0.0828 0.1641 0.3326 0.4126 0.0830 0.2439 0.3328 0.5016 OS840 0.7471 0.0821 0.1626 0.2531 0.4167 0.1716 0.3287 0.5121 0.8321 0.0835 0.2515 0.3346 0.500X 0.5780 0.7502 0.1635 0.3242 0.4162 0.0883 0.16216 0.2452 0.0834 0.1671 0.2503 0.3342 0.4136
xb
Ya
Yb
0.+063 0.0968 0.0871 0.0765 0.0679 0.1868 0.1682 0.1526 0.102l O.OS53 0.0677 0.2633 0.2400 0.1916 0.1686 0.3282 0.2706 0.2388 0.1784 0.1489 0.0905 0.3981 0.3632 0.3239 0.2530 0.4167 0.3377 0.2454 0.0845 0.5909 0.4826 0.4290 0.3219 0.2721 0.1611 0.6022 0.4865 0.4203 0.7302 0.6707 0.6045 0.8106 0.7366 0.6630 0.5888 0.5186
0.0538 0.1047 0.1550 0.2087 0.2523 0.0560 0.1165 0.1642 0.3073 0.3535 0.4031 0.0665 0.1243 0.2293 0.2747 0.0742 0.19oa 0.2442 0.3363 0.3781 0.4601 0.0834 0.1502 0.2137 0.3090 0.1740 0.2796 0.3733 0.5140 0.3.292 0.2808 0.3307 0.4&3 0.4349 0.4937 0.2448 0.3556 0.3978 0.1959 0.2854 0.3496 0.2335 0.3403 0.3997 0.4376 0.4628
0.2220 0.2283 0.2349 0.2427 0.2498 0.2473 0.2575 0.2660 0.2947 0.3053 0.3164 0.2669 0.2762 0.2960 0.3056 0.2829 0.3007 0.3112 0.3319 0.3422 0.3625 0.3006 0.3084 0.3180 0.3369 0.3262 0.3416 0.3618 0.3911 0.3731 0.3727 0.3770 0.3892 0.3954 0.4065 0.4033 0.3988 0.4015 0.4730 0.4469 0.4327 0.5548 0.4987 0.4715 0.4572 0.4498
dP (kPa) 24.733 24.241 23.778 23.185 22.717 24.991 24.525 24.126 22.747 22.225 21.711 25.014 24.603 23.699 23.281 24.914 24.103 23.643 22.807 22.411 21.404 24.693 24.367 23.889 23.153 24.063 23.379 22.603 20.961 23.309 23.141 22.903 22.391 22.138 21.534 22.683 22.593 22.403 21.198 21.893 22.175 19.638 216)rM 21.581 21.795 27.527
0,013 - 0.016 0.012 -0.028 - 0.028 - 0.017 - 0.008 0.006 0.031 0.009 0.070 0.015 0.019 - 0.008 - 0.003 0.011 0.001 - 0.012 0.002 0.029 - 0.059 - 0.008 0.029 -0.023 0.011 - 0.001 -0.012 - 0.008 - 0.063 0.001 0.001 - 0.003 0.006 - 0.003 0.013 - a.013 - 0.019 - 0.011 0.002 0.011 0.007 -0.006 0.004 0.008 0.010 0.005
82 TABLE 4 Comparison of the efficiency of different equations for binary systems at 293.15 K. Number of. parameters n, average standard error of the total vapour pressure o ( P ) a Equation
n
o(P) (kPa)
Number of sign changes b
Calculated azeotropic point Xa P (kPa)
Carbon tetrachloride-methanol Pseudovolume-Redlich-Kister Redlich-Kister Van Laar-van Ness Myers-Scott Marsh SSF UNIQUAC NRTL Wilson Athermal Mecke-Kempter
6 6 6 6 4+ 2 6 2 3 2 2
0.006 0.025 0.012 0.007 0.009 0.008 0.056 0.133 0.048 0.022
9 6 8 7 5 5 2 3 2 5
0.474 0.476 0.475 0.473 0.474 0.474 0.474 0.474 0.474
21.475 21.475 21.472 21.475 21.474 21.474 21.456 21.405 21.451
Methanol-chloroform Pseudovolume-Redlich-Kister Redlich-Kister Van Laar-van Ness Marsh SSF UNIQUAC NRTL (a = 0.2) Wilson Athermal Mecke-Kempter
6 6 4 2+ 3 6 2 2 2 2
0.007 0.007 0.007 0.007 0.013 0.222 0.117 0.262 0.276
10 6 7 6 6 4 3 4 4
0.751 0.752 0.752 0.752 0.754 0.765 0.748 0.766
25.435 25.436 25.435 25.436 25.442 25.504 25.492 25.501
Carbon tetrachloride-chloroform Pseudovolume-Redlich-Kister Redlich-Kister Van Laar-van Ness Myers-Scott SSF UNIQUAC NRTL Wilson
2 2 2 3 2 2 3 2
0.009 0.008 0.008 0.007 0.008 0.008 0.007 0.008
3 6 6 8 6 6 8 6
" o ( P ) = [Y'-(Pe×p.-Pcalc. )2//( m -- n )]1/2, where m = number of points. b If two neighbouring points lie on opposite sides of an approximation curve then one speaks of a sign change of their deviations. The points should be scattered randomly with respect to the correlating curve. An easy measure of the randomness is the number of sign changes, which should be approximately equal to m / 2 :g ( m / 2 ) 1/2.
83 accuracy. Therefore, for correlation of our binary measurements we chose the pseudovolume-fraction Redlich-Kister equation
E Ki(2Za-
GEl R T = VZa(1 -- 2a)
1) i
(1)
i=0 where
V=X,Va+ (1 -- Xa)Vb;
Za=XaVa/U
(la)
In eqn. (la) the pseudovolumes va and v b are not molar liquid volumes of corresponding pure components, but are adjustable parameters. One can observe that G E in eqn. (1) depends on the ratio of the v parameters and one of them can be set arbitrarily to one. For the other components, the v parameters evaluated with a trial-and-error method remained constant and common for all investigated binary and ternary mixtures. Values of the K~ coefficients in eqn. (1) together with their standard errors o(Ki) and the correlation coefficients qrt for pairs (Kr, Kt) are given in Table 5 for all the binary systems. The qrt values together with the standard errors o ( K i ) allow, if necessary, the estimation of standard errors of all values, which depend on K i. The coefficients A~, B i and Ci given in Table 5 may be used in eqn. (2), Ki t - Ki = A i ( ~ a - /~aa) + Bi( ~bb -- ]~bb) -{- Ci( ~ t - ~ )
(2)
to show how parameter K~ would change if the second virial coefficients flaa, flbb and 6fl = 2flab - flaa -- flbb used in this study were replaced by another set of values denoted /3a'a, flbb and ~fl'. Equation (2) clearly shows the influence of the second virial coefficients on K~ values. We can directly compare our measurements with those of Wolff and Hoeppel (1968) for the system carbon tetrachloride-methanol at 293.15 K. We compared our experimental pressure values with their data using the same reference line P+ = f ( X a , K 1 . . . , K6). The reference total pressure P+ was calculated with K1... , K 6 coefficients of the 4 / 2 - M a r s h (1977) equation fitted to Wolff and Hoeppel's data. This equation best fits their data giving a ( P ) = 0.079 kPa. Throughout all the calculations the same virial coefficients were used. The pure component vapour pressures were those reported for relevant data sets. The agreement between both sets of data is very good: results of the comparison are presented in Fig. 1. VLE data at 293.15 K for this system have been also reported by Niini (Gmehling and Onken, 1977). However, Niini's data are incorrect. Comparison of (P, x) points shows considerable and systematic differences between his data and other findings (both those of Wolff and Hoeppel and our own). The maximum deviation is 4.7 kPa (24.5%).
84 TABLE 5 Parameters ua, v b, v¢ and K i of eqn. (1) with their standard errors aKi, correlation coefficients q~j, coefficients Ai, B i and C i of eqn. (2) and cross second virial coefficients flab, fla¢, and flb~ at 293.15 K i=
0
1
2
3
Carbon tetrachloride(a) + methanol(b) /)a =1.07 o b = 2.33 flab = --0.931 d m 3 mo1-1 K i 1.3584 - 0.1481 0.2531 =
Ai= Bi = C~ =
0.0043 0.0031 0.0045
oK i = qli = q2i = q3i = q4i =
- 0.0161
0.1130
0.0026 0.0029 - 0.0032
- 0.0014 0.0004 - 0.0002
0.0059 0.0030 0.0044
0.0004 0.0001 0.0010
0.0006
0.0012
0.0020
0.0034
-0.3174 0.1766 0.6393
-0.1921 -0.6811
0.6318
-
0.0004 0.5293 -0.5969 0.6979 0.8252
4
Carbon tetrachloride(a) + chloroform(c) v a = 1.07 vc = 1 . 0 0 flac= - 1.657 d m 3 m o l - 1 Ko= 0:1745 Ao = Bo = Co = oK o =
0.0030 - 0.0037 0.0063 0.0006
Methanol(b) + chloroform(c) v b = 2.33 ~ =1.00 K i 0.9292
fl~ = -0.894 dm3mo1-1 -0.0257 0.0358
Ai = Bi = C~=
0.0038 0.0032 0.0057
0.0004 -0.0044 -0.0004
-0.0033 -0.0067 -0.0044
0.0041 0.0101 0.0071
0.0003 -0.1327 -0.4760 0.1367 0.0469
0.0011
0.0033
0.0114
0.1399 -0.6101 0.6163
-0.7206 0.5109
-0.9429
=
oK i
=
qli = q2i = q3i q4i =
=
The
binary
systems
under
0.0107
have
been
investigated
under
isobaric
as well as molar
the value of GE/RT
-
VLE
mic conditions
enthalpy
simultaneously,
each VLE
0.0009 0.0059 - 0.0023 -
consideration
authors,
this purpose
-0.1550
who have measured
sively by many
possible to compare,
-0.0763
data
various VLE
set under
at, f o r e x a m p l e ,
of mixing
comparison equimolar
(HE).
and
exten-
or isother-
Therefore,
i t is
H E sets of data. For
may
be represented
concentration,
by
henceforth
85 i
0,05
I
I
I
I
I
I
0 O
. . . . .
~D'
0 0
1
-
0
0 n _~
f
6 . . . .
•
O~ fj
o
O0 O .
0 0
qb +
0
0
i O_
O -0,05
0
-0.10
I
0
I
I
I
I
I
I
I
I
0,5
Xcct4 Fig. 1. Carbon tetrachloride-methanol, direct comparison of (P, x) data: <3, Wolff and Hoeppel (1968); e, our data. Dashed lines indicate range of error of single pressure measurement from Wolff and Hoeppel.
denoted Q0.5- The Q0.5 values calculated from various data sets were plotted against 1/T. From the Gibbs-Helmholtz equation, the slope of the resulting line should be equal to HoE s/R. Such plots for carbon tetrachloride-methanol, carbon tetrachloride-chloroform and methanol-chloroform systems are presented in Figs. 2-4. The slopes of the unbroken lines in these figures were calculated using H F data in the literature. In ranges for which H E data were not available, dashed lines have been used. For the systems with carbon tetrachloride the H E data are taken from the compilation by Belousov and Morachevskii (1970). For the methanol-chloroform system the H E at 323.15 K has been measured by Morris et al. (1975), at 308.15 K by Moelwyn-Hughes and Missen (1957) and at 298.15 K by Hirobe (Belousov and Morachevskii, 1970), Abramov et al. (1973) and recently by Nagata and Tamura (1983). In the previous work (G6ral et al., 1985) we used H E data of Morris et al. (1975) and Abramov et al. (1973). The remaining H E data at 298.15 K seemed to be inaccurate. The recent measurements of Nagata and Tamura (1983) prove that they were correct and indicate inaccuracies in the data of Abramov and his collaborators; so the data of the latter have been rejected. Scattering of points on the figures results from experimental errors in some of the literature data. The figures clearly show mutual agreement of some G E data sets as well as their consistency with H E.
86 0.55
J
o 0
/ O t 70
o/m._--e-V
• ~
/
/
0.50
A
0.45
I
I
I
I
I
I
I
3.0
35 103 / T
Fig. 2. Carbon tetrachloride-methanol; comparison of equimolar Q0.5 = GE/RT values with literature values at various temperatures; zx, Fontell (1936); D, Scatchard et al. (1946); +, Scatchard and Ticknor (1952); ~, Hipkin and Myers (1954); x, Ocon and Espantoso (1958); I, Prakash and Katti (1965); o, Wolff and Hoeppel (1968); v, Yasuda et al. (1975); o, this work. F o r the m e t h a n o l - c h l o r o f o r m system we can c o m p a r e azeotropic p o i n t s m e a s u r e d at different temperatures. T o this end we used the plot of l n ( x a ) versus 1 / T (Fig. 5). T h e series of points gives a straight line, which c o n f i r m s the internal consistency of our d a t a m e a s u r e d at different temperatures. In our opinion, all the above tests show excellent a g r e e m e n t b e t w e e n our results a n d those published in the literature, as well as internal c o n s i s t e n c y a n d consistency with m o l a r e n t h a l p y of mixing.
,
,/
0.05
/ /
0
o/ /
0.04
/
o
/
,,/
/
0
®
/
/ /
0.03
i
3.0
i
i
3.5
IO00/T
Fig. 3. Carbon tetrachloride-chloroform system; comparison of equimolar Q0.5= GElRT values with literature values at various temperatures; ~, Kaplan and Monokchow (1937); o, McGlashan et al. (1954); zx, Rulewicz et al. (1968); v, Krauze and Serwinski (1973); O, this work.
87 Q40
0.35
~ pe -
~.,e
~
o
D 0.30
l
J
i
3.0
i
I
3.2
3.4 103/T
Fig. 4. Methanol-chloroform system, comparison of equimolar Q0.5 = GElRT values with literature values at various temperatures; v, Tyrer (1912); o, Kireev and Sitnikow (1941); ×, Severns et al. (1955); e , Natradze and Novikova (1957); A, Nagata (1962); +, Abbott and van Ness (1975); v, Bushmakin and Kish (1957); zx, Tochigi et al. (1984); D, Tamir et al. (1981); o, G6ral et al. (1985); , , Oracz and Warycha (1987); e, this work.
T h e t e r n a r y s y s t e m was c o r r e l a t e d b y eqns. ( 3 ) - ( 6 ) as well as b y c o m m o n l y used e q u a t i o n s such as SSF, Wilson, N R T L a n d U N I Q U A C . E q u a tion (3) is an e x t e n s i o n o f eqn. (1) to the t e r n a r y mixture. T h e e x t e n s i o n results f r o m a n a s s u m p t i o n that the t e r n a r y m i x t u r e c a n b e t r e a t e d as a p s e u d o b i n a r y m i x t u r e o f m e t h a n o l with the m i x t u r e o f c a r b o n t e t r a c h l o r i d e - c h l o r o f o r m t r e a t e d as o n e c o m p o n e n t w i t h p r o p e r t i e s d e p e n d i n g o n c o n c e n t r a t i o n . This explains w h y in eqns. (3) a n d (4) m o l e f r a c t i o n s o f
1.3
x E i
1.1
I
I
J
3.0
J
3.5
103/T
Fig. 5. Methanol-chloroform, azeotropic mole fraction of methanol (ln values) versus temperature; n, Tochigi et al. (1984); +, Abbott and van Ness (1975);., G6ral et al. (1985); e , Oracz and Warycha (unpublished, 1987); e, this work.
88 TABLE 6 Comparison of the efficiency of different equations for the ternary system carbon tetrachloride-methanol-chloroform at 293.15 K. Average standard error of the total vapour pressure o ( P ) a, relative standard error of the total vapour pressure o ( d P / P ) b Equation
Number of parameters Binary c Ternary
o(P)
o(dP/P)
(kPa)
(%)
Pseudovolume-Redfich-Kister
(6/2/6) - 1
Eqn. (5) fl = 0 (Kohler) Eqn. (5) fl = - 1/4
5+ 1/2/6 5+ 1/2/6
SSF
6/2/6
UNIQUAC NRTL Wilson Athermal Meeke-Kempter
2/2/2 3/3/2 2/2/2 2/0/2
0.063 0.041 0.023 0.863 0.117 0.045 0.027 0.896 0.078 0.040 0.096 0.119 0.088 0.119
0.28 0.18 0.10 3.80 0.51 0.20 0.12 3.94 0.34 0.18 0.42 0.53 0.38 0.53
0 2 6 0 0 2 6 0 3 6 0 0 0 0
a o ( P ) = []](Pexp.- Pcalc.)2/( m - n)] 1/2, n = number of parameters. b o ( d P / P ) = [E[1- P~¢./Pexp.]2/(m - n)] 1/2, rn = number of points.
c Cf. Table 4.
m e t h a n o l are a s y m m e t r i c a l l y t r e a t e d with respect to two o t h e r c o m p o n e n t s . T a b l e 6 shows that eqn. (3) predicts t e r n a r y V L E d a t a b e t t e r t h a n o t h e r equations. T h e e q u a t i o n has the f o r m
G~/RT=v{[z.zbEK,(a,b ) ( 1 -
2Zb) i + z b z ~ E K , ( b ,
C)(2Zb -- 1) i
+ Z a Z ¢ K o ( a , c)] + G E ( t e r ) / R T }
(3)
where: v = XaU a q- XbU b "4- XcUc'~ Z i = XiUi/O; s u b s c r i p t b d e n o t e s m e t h a n o l a n d subscripts a a n d c d e n o t e c a r b o n t e t r a c h l o r i d e a n d c h l o r o f o r m , respectively. T h e p s e u d o v o l u m e s va, v b a n d vc are a d j u s t a b l e p a r a m e t e r s k e p t c o n s t a n t for all b i n a r y a n d t e r n a r y data; K i are c o r r e s p o n d i n g b i n a r y parameters and GZ(ter)/RT is a t e r n a r y term, a s s u m e d to b e z e r o w h e n eqn. (3) is used for p r e d i c t i o n of t e r n a r y V L E f r o m c o n s t i t u e n t binaries. T h e t e r n a r y c o n t r i b u t i o n GE(ter) has the f o r m
GE(ter) = ZaZbZc[C1 + C2fl + C3f2 + C4f(:+ C5f2 + C6flf2] w h e r e f l = 2Zb -- 1; f2 ---- (Za -- Z c ) / ( Z a + Zc)"
(4)
89 Equation (5) is the one discussed previously by Oracz (1987), to which ternary terms were added. The equation has the form 2
G E / R T = Y'~
3
~,
(x i ÷ xi)I~GE(x * ) / R T +
GE(ter)/RT
(5)
i=1 j = i + l
where x* = x J ( x i + x j). G~ is any equation suitable for the correlation of a binary mixture (i + j ) . For this reason, eqn. (5) is much more general than any other proposed in the literature. Parameter/3 is adjustable. In this work we used fl = - 1 / 4 . This value is suitable for systems with strong positive deviations from Raoult's law; for systems with strong negative deviations /3 = 1 was used by Grral et al. (1985). If/3 = 0 then eqn. (5) is equivalent to Kohler's equation. For the ternary contribution GZ(ter) in eqn. (5), we adopted the following expression:
G e ( t e r ) / R T = XaXbXc[C 1 At" C 2 ( 3 x a - 1) + C 3 ( 3 x b - 1) + C 4 ( 3 x a - 1) 2 + C5(3x b - 1) 2 + C6(3x a - 1)(3x b - 1)]
(6)
Table 6 shows the efficiency of various equations applied to the ternary data. One can see that prediction with eqn. (3) is quite good, but for description of the data with experimental accuracy ternary terms are necessary. This agrees with the conclusion of Pando et al. (1987) in a paper on the molar enthalpy of mixing in ternary mixtures. One should note the good performance of the equations based on the local composition concept in contrast to the poor performance in the constituent binaries. Results of fitting the ternary data with the eqns. (3) and (4) are given in Table 7. Apart from the correlation parameters C~, their standard errors o(C~) and the correlation coefficients qij for the pairs (C i, Cj), the coefficients a~, b~, c;, di, e~ and f~ are also given. They can be used analogously as for the binary system to recalculate the ternary parameters C~, when another set of the second virial coefficients would be used
C , ' - Ci = a,(fl~a -/3aa) -k- bi(flb b -- /3bb) + Ci(/3~c -- /3cc) "q- di( ~/3atb -- ~/3ab) + ei( 8/3~'c- 8/3ac) + g,( Sflbc -- 6flb~)
(7)
The deviations between experimental and calculated vapour pressures are presented in Table 3. To demonstrate that the reasonable use of even rough models may produce acceptable results we used the so-called athermal Mecke-Kempter model developed by Kehiaian and Treszczanowicz (1968). This model has been applied to both methanol-containing binary systems. The relevant standard deviations are given in Table 4. The relatively large standard error in the methanol-chloroform system results from the inadequacy of the
90
TABLE 7 C o e f f i c i e n t s Ct of eqn. (4) for t h e t e r n a r y p a r t of t h e e x c e s s G i b b s e n e r g y , t h e i r s t a n d a r d e r r o r s a C i, c o r r e l a t i o n c o e f f i c i e n t s qij a n d c o e f f i c i e n t s a t, b i, c i, d r, e i, gi o f e qn. (7) f o r t h e t e r n a r y s y s t e m c a r b o n t e t r a c h l o r i d e - m e t h a n o l - c h l o r o f o r m a t 293.15 K i=
1
2
3
4
5
6
- 0.3169
- 0.0431
0.1843
Ci =
0.0 570
- 0.0967
- 0.2458
ai= bt =
0.0309
0.0317
0.0036
0.0337
0.0503
0.0307
0.0009
- 0.0065
ci = di = ei = gi =
0.0 092 0.0086
0.0023 0.0199
- 0.0159 0.0208
- 0.0151 0.0034
- 0.0212 0.0268
0.0070
- 0.0022
- 0.0087
- 0.0099
- 0.0055
0.0010
0.0137
0.0141
0.0041
0.0126
- 0.0367
- 0.0396
oC t =
0.0 054
0.0130
0.0342
0.0666
0.0110
0.0368
q2t = q3i = qni = qsi q6i
0.1906 -- 0.2540 -- 0.6999 0.1491 0.0 350
- 0.2686 - 0.1538
0.5253
=
=
- -
0.2088 0.1552
0.2414
- 0.0772 - 0.1732
- 0.0856 0.0529
-0.0324
-
0.0314
0.0230
-0.0036 -
0,0140 0.0357
theory to model the behaviour of this system. Afterwards, the binary constants were used for prediction of the ternary VLE data. The ternary system was approximated by a pseudo-binary mixture, i.e. GE/RT for the ternary system was calculated from the expression for a binary system with the mole fractions equal to x* (CC14) = x(CC1,)/[x(CC14) + x(CHC13)] ; x* (CH3OH) = 1 - x* (CC14)
(8)
and the parameters linearly changing with the mole fraction of carbon tetrachloride, x * (CC14). The calculated standard deviation is given in Table 6 and, taking into account all constraints, the result is surprisingly good. ACKNOWLEDGEMENT
We appreciate the financial support provided for this work by The Polish Academy of Sciences within project PAN 3.20. LIST OF SYMBOLS
Ai,
Bi,
ai,
hi, ci,
di,
ei, gi
c,, c:,
Ci
coefficients in eqn. (2) coefficients in eqn. (7)
91
c4, c5, c6 GE
GE(ter) HE Ki P 00.5
qij
coefficients in eqns. (4) and (6) excess Gibbs energy excess Gibbs energy for the mixture i + j ternary contribution to excess Gibbs energy enthalpy of mixing Redlich-Kister parameters in eqns. (1)-(3) vapour pressure (kPa) value of G E / R T at equimolar concentration correlation coefficients between parameter pairs (K~, Kfl or
( c,, Cj)
R
gas constant T temperature (K) Va, Vb, Vc~ V adjustable pseudovolumes in eqns. (1), (3)-(4) mole fraction in liquid X mole fraction in eqns. (5) and (8) X* pseudovolume fraction in eqns. (3) Greek letters
a
N R T L parameter
aa, Bbb, fl c, /
flaa, Ebb, fl~ second virial coefficients fl exponent in eqn. (5) o standard error REFERENCES Abbott, M.M. and Van Ness, H.C., 1975. Vapor-liquid equilibrium. Part III. Data reduction with precise expressions for G E. AIChE J., 21: 62. Abramov, E.V., Mirzayan, A.S. and Devina, D.A., 1973. Heats of formation of ternary systems. 4. Izv. Akad. Nauk. Kaz. SSR. Ser. Khim., 4:42 (in Russian). Anderson, T.F. and Prausnitz, J.M., 1978. Application of the UNIQUAC equation to calculation of multicomponent phase equilibria. 1. Vapor-liquid equilibria. Ind. Eng. Chem. Process Des. Dev., 17: 552-561. Asmanova, N. and Grral, M., 1980. Vapour pressures and excess Gibbs energies in binary mixtures of hydrocarbons at 313.15 K. 1 Methylcyclohexane-benzene, - toluene, - o-xylene, -p-xylene, -ethylbenzene, and -propylbenzene. J. Chem. Eng. Data, 25: 159-161. Belousov, V.P. and Morachevskii, A.G., 1970. The Heat of Mixing of Liquids. Khimia, Leningrad (in Russian). Boublik, T., Fried, V. and Hala, E., 1973. The Vapour Pressures of Pure Substances. Elsevier, Amsterdam. Bushmakin, I.N. and Kish, I.N., 1957. Zh. Prikl. Khim., 30: 561. Dykyj, J. and RepaY, M., 1979. Tlak Nasytenej Pary Organickych Zlucenin. Veda, Bratislava. Dykyj, J., RepaY, M. and Svoboda, J., 1984. Tlak Nasytenej Pary Organickych Zlucenin. Veda, Bratislava.
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