1162
I n d . Eng. Chem. Res. 1987, 26, 1162-1167
Domaiiska, U. Le&-Czech.-Pol. Colloq. Chem. Thermodyn. Phya Org. Chem. 2nd 1980, p 92. Domaiiska, U. Pol. J . Chem. 1981,55, 1715. Domaiiska, U. Fluid Phase Equilib. 1986, 26, 201. Domadska. LJ.; Buchowski, H.; Pietrzyk. S. Pol. J . Chem. 1982, 56, 1491. Domaiiska, LJ.; Hofman, T . J . Solution Chem. 1985, 14, 531. Fuks, G. J.; Tichonow, W. P. Kolloidn. Zh. 1976, 38, 931. Gmehling, J. G.; Anderson, T. F.; Prausnitz, J. M. Znd. Eng. Chem. Fundam. 1978, 17, 269. Goodman, D. S. J . Am. Chem. SOC.1958, 80, 3887. Gordon, L. J.; Scott, R. L. J . Am. Chem. SOC.1952, 74, 4138. Hansen, Ch. M. Ind. Eng. Chem. Prod. Res., Deu. 1969,8, 2. Harris, J. A,; Bailey, A. V.; Skau, E. L. J . Am. Oil Chem. Soc. 1968, 45, 183. Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions; Van Nostrand-Reinhold: New York, 1970; p 147. Hoerr, C. W.; Ralston, A. W. J . Org. Chem. 1944, 9, 329. Hoerr, C. W.; Sedgwick, R. S.; Ralston, A. W. J . Org. Chem. 1946, 11, 603. Hoshino, D.; Unno, Y.;Nagahama, K.; Hirata, M. Bull. Jpn. P e t . Inst. 1977, 19, 56. Kojima, J.: Tanaka, M. J . Inorg. Nucl. Chem. 1970, 32. 987. Kolb, D. K. Dissert. Abstr. 1959, 20, 82. Konstam, A. H.; Feairheller, W. R. AIChE J . 1970, 16, 837. Kowalska. T. Microchem. J . 1977, 22, 131.
Loveluck, G. J . Phys. Chem. 1960,64, 385. Madec, P. J.; Marechal, E. J . Mucromol. Sci. Chem., Ser. A 1978,12, 1091. Maryott, A.; Hobbs, M. E.; Gross, P. M. J . Am. Chem. Soc. 1949, 71, 1671. Morimi, J.; Nakanishi, K. Fluid Phase Equilib. 1977, 1, 153. Muir, R. F.; Howat, C. S., 111. Chem. Eng. 1982, 22, 89. Murata, Y.; Motomura, K.; Matuura, R. Mem. Fac. Sci. Kjnshu Uniu. 1978, l l c , 29. Pohl, H. A.; Hobbs, M. E.; Gross, P. M. J . Chem. P h y . 1941,9,408. Preckshot, G. W.; Nouri, F. J. J . Am. Oil Chem. Soc. 1957,34,151. Ralston, A. W.; Hoerr, C. W. J . Org. Chem. 1942, 7, 546. Ralston, A. W.; Hoerr, C. W. J . Org. Chem. 1945, 10, 170. Rosenbrock, H. H. Comput. J . 1960, 3, 175. Schaake, R. C. F.; Miltenburg, J. C.; van Kruif, C. G. J . Chem. Thermodyn. 1982, 14, 771. Singh, S. S. Ind. J . Chem. 1968, 6, 393. Singleton, W. S. In Fatty Acids; Markley, K. S., Ed.; Interscience: New York, 1960; Part I. p 609. Stenhagen, E.; Sydow, E. van Ark. Kemi. 1953, 6 , 309. Sliwiok, J.; Kowalska, T. Microchem. J . 1977, 22, 226. Wilson, G. M. J . Am. Chem. Soc. 1964, 86, 127.
Receiued for reuiew J u n e 13, 1985 Reuised manuscript received January 12, 1987 Accepted February 27, 1987
A Test for the Thermodynamic Consistency of VLE Data for the Systems Water-Formaldehyde and Methanol-Formaldehyde? Vincenzo Brandani,* Gabriele Di Giacomo, and Vittoria Mucciante Dipartimento di Chimica, Ingegneria Chimica e Materzali, Uniuersitii de' L'Aquila, 67100 L'Aquila, Zta1.y
Despite the appreciable amount of VLE data available for the binary systems, water-formaldehyde and methanol-formaldehyde, their thermodynamic consistency has never been tested systematically. In fact, there is no method available which is directly applicable and satisfactory for these systems even though it is known that there are several possible sources of systematic error that may be responsible for data of poor quality. As an example, there is the formation of small amounts of paraformaldehyde in some point of the equilibrium which still alters the equilibrium conditions. All the above considerations led us t o set u p a test t o determine the thermodynamic consistency of VLE data for the water-formaldehyde system and for the methanol-formaldehyde system. Application to most of the available data shows that the thermodynamic consistency of data for the system methanol-formaldehyde is usually better than that of data for water-formaldehyde. Our results may prove useful in selecting consistent data for model parametrization. The description of the VLE behavior of systems which contain water-formaldehyde or methanol-formaldehyde is of great importance for the design of separation processes in the chemical industry. In contrast to most other systems, strong chemical interactions have to be taken into account as well as physical forces both in the liquid phase and in the vapor phase. In the past, different authors have shown how to describe the VLE behavior of these complex mixtures, and many VLE experimental measurements have been published for the two binary systems, water-formaldehyde and methanol-formaldehyde. For an up-to-date survey of this subject, see Brandani and Di Giacomo (1985) and Maurer (1986). However, the thermodynamic consistency of these data has never been tested since the usual methods are not applicable in this case. In fact, Gmehling and Onken (1977, 1981, 19821, in their comprehensive collection of VLE data for binary and multicomponent mixtures a t moderate +Presented at t h e 8th Seminar on Applied Thermodynamics, Trieste, May 30-31, 1985.
pressures, do not give any consistency analysis for these systems. The only attempt to test thermodynamic consistency of water-formaldehyde VLE data was made by Brandani and Di Giacomo (1984) who applied the Gibbs-Konovalow theorems to two isobaric different sets of data at 100 kPa reported in the literature. It was possible to show that the set of data which does not present an "apparent" azeotrope does not follow the second Gibbs-Konovalow theorem, and therefore, it is not thermodynamically consistent. However, it was pointed out that the method could only be used as a rule of thumb, i.e., for rejecting data which are very wrong. In this paper, the consistency analysis is extended to most of the data reported in the literature for the two binary systems, water-formaldehyde and methanol-formaldehyde, by applying one differential and one integral test which are both based on the Gibbs-Duhem equation. Despite the peculiarity of the systems under consideration, which involve chemical reactions in both of the phases, it is worth noting that the results are not overly influenced by any assumption that we might make about the structure of the mixtures since a sufficient amount of
0888-5885/87/2626-1162$01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1163 reliable data is available to characterize independently the thermodynamic behavior of gaseous mixtures of formaldehyde both with water and with methanol.
Gaseous Mixtures, Water-Formaldehyde and Methanol-Formaldehyde Let A be the active solvent (water or methanol) and F the formaldehyde. Gaseous mixtures of an active solvent A with formaldehyde are characterized by the formation of a unnegligible quantity of associated compounds like AF. Hall and Piret (1949) were able to give a quantitative description of this phenomenon by measuring the pressure, in a constant volume, of a given quantity of a gaseous mixture of A and F for any fixed concentration and temperature. They also showed that in the range of P and T of their experimental conditions, only the associated species AF was present in the gaseous mixtures together with free molecules of A and F. By using the experimental data of Hall and Piret (1949) together with the virial equation of state truncated to the second term, Brandani and Di Giacomo (1985) calculated the apparent fugacity coefficients, @F and 4A, for the two components in the gaseous mixture. The equations found were @F
=
(uF/YF)
exp(BbP/RT)
(1)
$A
=
(UA/YA)
exp(BfAP/RT)
(2)
where UF
= 0.5yF{[(l - 23'~+ l/K$P)'
+ ~YF'/K$P]~/~ (1 - ~ Y i Fl/K$P)) (3)
UA
= (1 - 2YF)/(1 - YF) + UFYF/(1 - YF)
(4)
BfF and B i are the "free" contributions to the second virial coefficient of A and F, respectively, while K$ is the equilibrium ratio of the partial pressures for the reaction A+F=AF K$ = KA exp[(Bk + BfA - BkF)P/RT]
(5)
The parameters for calculating BfF,B i , BiF, and KAas a function of temperature are reported elsewhere (Brandani and Di Giacomo, 1985).
Experimental Values of the Activity Coefficients in the Liquid Phase Since gaseous mixtures of water or methanol and formaldehyde have already been completely characterized, it is possible to use PTxy data to obtain direct experimental information on the thermodynamic properties of liquid binary mixtures of A and F. In particular, the two independent VLE equations YFP YAP
= Y$f$aXF(1/$F)
= YAPAxA(~/$A)
exp(UF",AP/RT)
(6)
exp[uLA(P - PA)/RT + BAPA/RTl (7)
are used to find the experimental values of the activity coefficient of the active solvent, YA, and of the quantity -&@fA, the product of the activity coefficient of formaldehyde, & and its reference fugacity in the active solvent A, E;. For a given active solvent A, is only a function of the temperature of the system. Solvent molar volumes in the liquid phase, vi, and partial molar volume of formaldehyde at infinite dilution in solvent A, U;,A, together with the vapor pressure, PA,and second virial coefficient of pure A, BA, can be calculated as indicated
~ ' " ' ' ' " ' I 0 .
30t
1
e
t
0
- I
-05
y4**;
--i
-+-+
t--t
e
i
-1" -I
0
e
01
03
05
07
09
XF
Figure 1. Experimental data for the methanol-formaldehyde system at 60 "C.
by Brandani and Di Giacomo (1985). Both Y~ and can be used for a preliminary check of thermodynamic consistency of any isothermal PTxy set of data as shown in Figure 1. Here the experimental values of y;R$ obtained from eq 6, together with the experimentalvalues of TM obtained from eq 7 , are reported as a function of the apparent mole fraction of formaldehyde in the liquid phase, xF, for the methanol-formaldehyde system at 60 "C (Kogan and Ogorodnikov, 1980). Clearly, the first three values are thermodynamically inconsistent because they do not satisfy the Gibbs-Duhem equation. In fact, while the curve of YM presents a maximum, the c w e of y;R& does not present a corresponding minimum. However, from Figure 1it is not possible to say anything about the thermodynamic consistency of the remaining data. For a deeper analysis, it is necessary to know the value of #,$. For the two binary systems of interest, # c y,i obtained by observing that it is the limiting value of yFfF,A as xF goes to zero. Therefore, after correlation of experimental values of -y:fliwith the expression
-&Ri
2:
N
the value, = exp(b,), can be determined. For the water-formaldehyde system, the values of obtained by this procedure from several isothermal sets of data are practically coincident with those obtained by Brandani et al. (1980) in the range from 40 to 90 "C by using very accurate data on the total vapor pressure of the solution together with spectroscopic measurements of the concentration of anhydrous formaldehyde in aqueous solutions (Iliceto, 1954) and the cryoscopic measurements reported by Bezzi and Iliceto (1951).
Thermodynamic Consistency Test for Isothermal VLE Data Because of the difficulties in making a consistency test on binary PTxy data when the data only cover a limited concentration range, we started with a method, suggested by Fredenslund et al. (1977),which escapes this limitation. It consists of calculating y from PTx data and then comparing the calculated y's with the experimentally obtained values. As suggested by the proposers, the PTxy data set is considered consistent if the average absolute deviation between y,(exptl) and yi(calcd) is less than 0.01.
1164 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table I. Results of Fredenslund Test of Thermodynamic Consistency for the Methanol-Formaldehyde System at Three Different TemDeratures data source temp, “C AYF 60 0.029 a 70 0.035 a 80 0.046 a
~
a
as the indicator for the differential test for the thermodynamic consistency of isothermal experimental VLE data. Moreover, for the integral test of thermodynamic consistency, we evaluate the two integrals
Kogan and Ogorodnikov, 1980.
However, for the two binaries under study, we found that this test, taken alone, does not give all the required information on the thermodynamic consistency of the examined data. For example, by applying this test to the data reported in Figure 1, the absolute deviations for the three inconsistent points are found to be much less than 0.01. Furthermore, as can be seen in Table I, all three isothermal sets of data reported by Kogan and Ogorodnikov (1980) for the methanol-formaldehyde system should be considered thermodynamically inconsistent. Because of these unexpected results, we though it would be useful to try a different approach for testing the thermodynamic consistency of experimental PTxy data. This approach consists in calculating the activity coefficients of the two components from PTxy experimental data and in correlating them separately by using the highly flexible Legendre polynomials In 71 = (1 - x)2cak’(Lk - 2xDk) (9) k
In
72
= x2xak”(Lk + 2(1 - x)Dk) k
(10)
where
(k + l)Lk+l(Z) = (2k + l)zLk(z) - kLk-l(Z) (2’
- 1)Dk(z) =
(k + 1)(Lk+l(z)- zLk(z)]
Lo(z) = 1 L,(z) = 2
Do(Z) = 0 Dl(2) = 1
and
k
z=1-2x
and we set
(11)
as the indicator for the integral test for the thermodynamic consistency of isothermal experimental VLE data. To fix a criterion €or accepting consistent experimental VLE data, we have to fii limiting values for tT and cT’. For this purpose, we have selected a few isothermal binary systems from the Dechema Collection, which were found to satisfy both of the consistency tests applied by Gmehling and Onken (1977). In Table 11, the selected systems, the average value of tT, and the value of for each system are reported. It can be seen that 10.0 can be chosen as the limiting value for tT, while 3.0 can be chosen for ET’. Before eq 9 is applied to the system water-formaldehyde and to the system methanol-formaldehyde, it must be corrected according to the unsymmetric convention for the normalization of the activity coefficients In yfF = (1 - x)2Cak’(Lk- 2 d k ) - E a k ‘ (19) k
The results of the test of thermodynamic consistency on the isothermal experimental data of Kogan and Ogorodnikov (1980) for the system methanol-formaldehyde are illustrated in Table 111. The integral test is positive a t 70 and 80 “C, while the data at 60 “C are less accurate, because t T f = 2.0. If we now turn to the differential test, we see that 6 of the 9 points are consistent at 80 “C, 7 of the 10 points are consistent at 70 “C, and only 4 of the 8 points are consistent at 60 O C , Figure 2. For the water-formaldehyde system, the results of the differential thermodynamic consistency test on the isothermal experimental data of Kogan et al. (1977) are il-
Table 11. Results of Differential and Integral Tests of Thermodynamic Consistency for Selected Isothermal Systems VLE data T, no. of no. of data from Dechema “C data Dts DtS CT < 30 CT CT’ Collection” system chloroform-ethanol 16 6 60 5.4 3.2 Part 2a, p 284 ethanol-benzene 9 7 55 4.9 0.07 Part 2a, p 421 11 45 12.6 acetone-benzene 9 Parts 3 + 4, p 194 3.0 11 Part 2a, p 162 10 55 6.5 methanol-ethyl acetate 0.3 10 11 55 ethanol-ethyl acetate Part 2a, p 362 8.9 0.7 19 15 60 9.2 ethanol-ethyl acetate Part 2a, p 360 1.0 9 ethanol-ethyl acetate Part 2a, p 358 15 70 13.3 2.9 8 12 Part 2a, p 398 11.7 45 8.9 ethanol-benzene 9 10 Part 28, p 469 55 ethanol-toluene 0.3 7.5 8 Part 2a, p 401 50 9 ethanol-benzene 6.8 6.6 3.0 av 8.4 av “All from Vol. I.
Ind. Eng. Chem. Res., Vol. 26, No. 6 , 1987 1165 Table 111. Results of the Isothermal Test of Thermodynamic Consistency for the Methanol-Formaldehyde System no. of no. of data T, "C data pts pts CT C 30 t~~~ fT' 2.0 60 8 6 14.2 70 10 8 8.0 0.9 1.2 80 9 6 6.6
data source a
70
a a
Kogan and Ogorodnikov, 1980. 50
"1
p
+
L
+ 0
c 901
Lu
50
02
0
0.4
0.6
0.8 XF
Figure 3. Results of the differential thermodynamic consistency test for the water-formaldehyde system (isothermal data), from Kogan et al. (1977): (A) 90, (0) 80,(+) 70, (0)50, ( 0 )40 "C.
e
together with the available isothermal VLE data at three different temperatures. In particular, to estimate hE,eq 9 and 10 with a = a ' = a"and a = 6 a / T PIT2 have been used. Therefore, for the excess enthalpy, we obtain
e
+
0
I
A
02
04
os
06
+
I
XF
Figure 2. Results of the differential thermodynamic consistency test for the methanol-formaldehyde system (isothermal data), from Kogan and Ogorodnikov (1980): (A) 80, (0) 70, ( 0 )60 O C .
lustrated in Figure 3. It can be seen that only a few points can be considered thermodynamically consistent. Moreover, the integral test indicates that only the VLE data at 50 and 70 "C are consistent (eT' = 2.0), while the VLE data at 40,80, and 90 "C must be considered inconsistent since tT' is greater than 5.0. A possible source of experimental error during measurements of VLE for the water-formaldehyde system is the formation of small amounts of paraformaldehyde in some point of the equilibrium still, altering the equilibrium conditions. It is, however, very unlikely that the same mechanism applies in the methanol-formaldehyde system, where, as shown in the paper of Brandani and Di Giacomo (1985),the equilibria in the liquid phase move toward the formation of compounds of low molecular weight.
Isobaric VLE Data Since many isobaric VLE data are available, both for the water-formaldehyde and the methanol-formaldehyde systems, it is of practical importance that the previously described procedure be extended for application to the thermodynamic consistency test of isobaric data. Under isobaric conditions, the Gibbs-Duhem equation is
and therefore, it is necessary to know experimental excess enthalpy data. In our case, data on hE are not available, but a good estimate can be obtained by employing the thermodynamic relationship agE/RT
-= - aT
(23)
T = CAiLi i
subject to the constraints C(-l)iAi = Tbl
CAi = Tb2
i
Therefore, we obtain dT _ dx
(24)
i
- -2CAiDi i
The isobaric experimental VLE data are then used to calculate activity coefficients, which are correlated by using eq 9 and 10. Once we have obtained the two sets of parameters, ah' and ah",and parameters a],Pj, and A,, we evaluate the two contributions, A and B, as given by eq 13 and 14, respectively, and the third contribution, C, given by
C = -2x(1 - x)(C(O~,/T' + 2Pl/T3)Lj)(C,AiD,) I
(26)
and we set tp
= 100
IA
+ B + CI
IAI +
(27)
PI + IC1
as the indicator for the differential test of the thermodynamic consistency of isobaric experimental VLE data. Moreover, for the integral test of thermodynamic consistency, we analytically evaluate the two integrals, I' and I", given by eq 16 and 17 and the third integral, I,,, given by
Ih = - 0 . 2 5 x 2 ( z 2 - 1 ) ( C ( a l / T 2+ 2/3j/T3)LlJ(~A,D,J dz
hE
RT2
where j assumes the maximum value of four. The experimental T-x data are correlated by using
(21)
I
i
(28)
1166 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table IV. Results of Differential and Integral Tests of Thermodynamic Consistency for Selected Isobaric Systems no. of VLE data p, no. of data pts from Dechema system torr data pts t p < 30 +,av CP’ Collection“ page ethanol-ethyl acetate 760 9 6 13.9 14.5 354 3.9 361 760 13 5 20.4 ethanol-ethyl acetate 400 10 7 9.7 17.5 413 ethanol-benzene 14.7 av 12.0 av (I
All are Vol. I, Part 2a.
Table V. Results of the Isobaric Test of Thermodynamic Consistency for the Methanol-Formaldehyde System no. of P, no. of data pts data cp < 30 tp,., tp source torr data pts 760 6 4 8.0 6.0 a 200 6 4 18.8 18.3 a 760 6 3 18.7 45.3 b 350 6 92.6 b 200 6 100.0 b (I
Blazhin e t al., 1976. * Olevsky and Golubev, 1954.
9
100
I
+’
I
t
I
Table VI. Deviations of Predicted and Experimental Data for the Methanol-Formaldehyde System
P,
(I
1
I
02
3
A
1
04
I
1
,
06
I
06
t
1 I
by numerical integration accomplished by using a 16-point Gaussian Quadrature, and we set
as the indicator for the integral test for the thermodynamic consistency of isobaric experimental VLE data. When applied to the water-formaldehyde system and to the methanol-formaldehyde system, (1- x)Lj in eq 22 and 26 must be replaced by {(l- x)L, - 1) and ( z + l)Lj in eq 28 must be replaced by { ( z + 1)Lj - 1). In this case, the limiting values of cp and ep’ obtained from the selected system are taken as 15.0 and 12.0, respectively, according to the results reported in Table IV. In Table V and in Figure 4, we have reported the results of the application of the thermodynamic consistency test to the isobaric data of Blazhin et al. (1976) and those of Olevsky and Golubev (1954) for the methanol-formaldehyde system. We evaluated hE by using all the isothermal data of Kogan and Ogorodnikov (1980), while we interpolated g,&with = 24.33 - 7580/T
12 18
9 5
max 15 23 24 14
a
a b b b
11
‘
XF Figure 4. Results of the differential thermodynamic consistency test for the methanol-formaldehyde system (isobaric data). From 200 torr. From Olevsky and Blazhin et al. (1976): (A) 760, (0) Golubev (1954): (0)760, (+) 350, ( 0 )200 torr.
In
data source
103&F
av 9
Blazhin et al., 1976. *Olevsky and Golubev, 1954.
50
01
AT, “C av max 1.1 1.8 3.9 1.3 2.2 3.7 3.5 5.3 4.5 7.4
no. of data pts 6 6 6 6 6
torr 760 200 760 350 200
(30)
0
p
I
I
I
I
I
I
I
I
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1167 the binary systems, methanol-formaldehyde and waterformaldehyde, which in the Dechema Collection are reported without any information regarding consistency or the possibility of their correlation with any of the currently used models for the activity coefficients. The tests could prove useful in selecting consistent data for obtaining more reliable parameters for models set up for these systems. Finally, the results obtained for the water-formaldehyde system suggest the need for new experimental VLE measurements for this system, with careful and accurate controls for the absence of methanol and for the formation of paraformaldehyde in the equilibrium still.
Greek Symbols 4i= apparent fugacity coefficient of component i 7; = apparent activity coefficient of formaldehyde = apparent activity coefficient of component A y L = apparent activity coefficient of component i eT = indicator for the differential thermodynamic consistency test (isothermal) eTf = indicator for the integral thermodynamic consistency test (isothermal) ep = indicator for the differential thermodynamic consistency test (isobaric) ep’ = indicator for the integral thermodynamic consistency test (isobaric) aJ = parameters expressing the temperature dependence of the activity coefficients pJ = parameters expressing the temperature dependence of the activity coefficients
Acknowledgment
Superscripts * = unsymmetric convention in normalization of activity coefficients m = infinite dilution S = saturation A = active solvent ref = reference state E = excess properties L = liquid phase
We are indebted to the Italian Minister0 della Pubblica Istruzione for financial support.
Nomenclature ah’ = adjustable parameters in eq 9 ah’’ = adjustable parameters in eq 10 A = active solvent or the quantity defined by eq 13 Ai = adjustable parameters in eq 23 AF = methylene glycol or hemiformal bk = adjustable parameters in eq 8 B = quantity defined by eq 14 B = second virial coefficient of component A B f = “free” contribution to the second virial coefficient of component i C = quantity defined by eq 26 D = derivative of the Legendre polynomials of the kth order = reference fugacity of formaldehyde in solvent j F = formaldehyde gE = excess molar Gibbs energy hE = excess molar enthalpy I’ = integral defined by eq 16 I“ = integral defined by eq 17 Ih= integral defined by eq 28 K A = thermodynamic equilibrium constant for the reaction A + F = AF in the vapor phase K$ = equilibrium ratio of the partial pressures for the reaction A+F=AF Lk = Legendre polynomials of the kth order M = methanol N = number of data points P = total pressure P . = partial pressure of component j = vapor pressure of component A R = gas constant T = temperature Tbj= boiling point of component j u. = true mole fraction of component i in the vapor phase = molar volume of pure liquid solvent A IJ;,~ = partial molar volume of formaldehyde at infinite dilution in solvent A x = molar fraction of formaldehyde in the liquid phase x i = molar fraction of component i in the liquid phase y i = molar fraction of component i in the vapor phase z = quantity defined by eq 12
4 ui
Subscripts F, M, W = index for formaldehyde, methanol, and water, respectively A, AF = index for active solvent and methylene glycol or hemiformal, respectively b = boiling point k = order of Lagrangian polynomials P = isobaric T = isothermal Registry No. HCHO, 50-00-0; MeOH, 67-56-1.
Literature Cited Bezzi, S.; Iliceto, A. Chim. Znd. (Milan) 1951, 33, 212. Blazhin, Yu. M.; Kogan, L. V.; Vagina, L. K.; Pastor, V. E.; Morozova, A. I.; Ogorodnikov, S. K. Zh. Prikl. Khim. 1976, 49, 174. Brandani, V.; Di Giacomo, G.; Foscolo, P. U. Ind. Eng. Chem. Process Des. Deu. 1980, 19, 179. Brandani, V.; Di Giacomo, G. lnd. Eng. Chem. Fundam. 1984,23, 126. Brandani, V.; Di Giacomo, G. Fluid Phase Equilib. 1985, 24, 307. Fredenslund, A.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: Amsterdam, 1977. Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt am Main, 1977; Vol. 1, Part 1. Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt am Main, 1981; Vol. 1, Part la. Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; Dechema: Frankfurt am Main, 1982; Vol. 1, Part 2c Green, S . J.; Vener, R. E. Znd. Eng. Chem. 1955, 47, 103. Hall, M. W.; Piret, E. L. Znd. Eng. Chem. 1949, 41, 1277. Kogan, L. V.; Blazhin, Yu. M.; Ogorodnikov, S. K.; Kafarov, V. V. Zh. Prikl. Khim. 1977, 50, 2682. Kogan, L. V.; Ogorodnikov, S. K. Zh. Prikl. Khim. 1980, 53, 115. Iliceto, A. Gazz. Chim.It. 1951, 84, 536. Maurer, G. AIChE J. 1986,32, 932. Olevsky, V. M.; Golubev, I. F. Tr. Giap. Vyp. 1954, 4, 36.
Receiued for review June 19, 1985 Revised manuscript received December 10, 1986 Accepted February 27, 1987
