Vapour—liquid equilibrium in the ternary system N,N-dimethylformamide + methanol + water at 313.15 K

279

Fluid Phase Equilibria, 59 (1990) 279-290

Elsevier Science Publishers B.V., Amsterdam

VAPOUR-LIQUID EQUILIBRIUM IN THE TERNARY SYSTEM N,NDIMETHYLFORMAMIDE + METHANOL + WATER AT 313.15 K J. ZIELKIEWICZ Technical University of Gdarisk, Institute of Inorganic Chemistry, Majakowskiego 11/12, 80-952 Gdarisk (Poland)

Technology and Corrosion,

P. ORACZ Warsaw University, Department of Chemistry, Pasteura I, 02-093 Warsaw (Poland)

(Received November 20, 1989; accepted in final form March 27, 1990)

ABSTRACT Zielkiewicz, J. and Oracz, P., 1990. Vapour-liquid equilibrium in the ternary system N, N-dimethylformamide+ methanol+ water at 313.15 K. Fluid Phase Equilibria, 59: 279-290. Total vapour pressure measurements made by the modified static method for the ternary system N, N-dimethylformamide-methanol-water and constituent binaries at 313.15 K are presented. The different expressions for GE suitable for correlation of these data are tested. A prediction of ternary VLE from binary data is examined. Results for the methanol-water binary system are compared with literature data.

INTRODUCTION

The present work is the first of a series of papers containing the results of studies on ternary systems: N, N-dimethylformamide (DMF)-water-alcohol. Systems of this type exhibit a negative deviation from Raoult’s law for two out of the three binary systems under investigation (DMF-water and DMF-methanol) and in the third system (methanol-water) there is a large positive deviation. This type of ternary system has been insufficiently cited in the literature and it seems particularly interesting to examine the feasibility of predicting the behaviour of ternary systems from data for the binary systems. A negative deviation from Raoult’s law in the system DMF-water is probably caused by complex formation. A complex with the formula DMF - 2H,O is well known and its existence has been proved by many authors (Schmid and Brodbek, 1985; Godhino and Greenhow, 1985; Afanasjev et al., 1984). We assume that in a mixture of methanol-DMF 0378-3812/90/$03.50

0 1990 - Elsevier Science Publishers B.V.

280

mutual interactions of the components result in the formation of a similar complex. Vapour-liquid equilibrium (VLE) for the similar ternary systems: DMF-water-2-propanol at 353.15 K and DMF-water-ethanol at 358.15 K and 363.15 K have been described in the literature (Wu et al., 1988; Shealy et al., 1987). In this paper we present the VLE data for the binary systems methanolwater, DMF-water, DMF-methanol and the ternary system DMF-watermethanol at 313.15 K. The different expressions for GE suitable for correlation of these data are tested. A prediction of the ternary VLE from the binary data is examined. MATERIALS

Methanol (analytical reagent grade, POCh) was dried with Mg using a method described by Perrin and Armarego (1982). It was then distilled in a column 80 cm high, filled with glass rings and equipped with an automatic head for reflux regulation. The product was dried and stored over fresh 3A molecular sieves, which were changed twice. The methods of refining DMF were reviewed by Juillard (1982). In this procedure DMF (pure, POCh) was dried with anhydrous Na,CO, and CuSO,, and then distilled in vacuum (approx. 4 torr) over anhydrous CuSO, in a stream of dry nitrogen. In the second step, DMF was treated with P,O, (frequently stirred) for 2 days, then with KOH pellets for 3-4 h, and then distilled in vacuum as described above. The height of the column was 45 cm. The column was filled with glass rings and equipped with a head for reflux regulation. Distillation of DMF was carried out in the dark. The refined solvent was dried and then stored over 4A molecular sieves, in the dark, at about 278 K. The storage did not exceed 10 days. The measured conductivity of DMF was equal to 5.7 X 10v7 ohm-l cm-r. Water was distilled twice in a glass apparatus. METHOD

The vapour pressures of the mixtures were determined by a modified static method. The apparatus and the experimental procedure have been described previously (Janaszewski et al., 1982; Zielkiewicz et al., 1990). During the measurements the temperature was constant in the range of 0.002 K and was controlled to 0.001 K. The absolute error was estimated to be equal to f0.02 K (IPTS 68). The cathetometer readings contribute less than 0.004 kPa to the error of a single pressure measurement. The errors in

281

the mole fraction were less than 0.0005 for the binary and ternary samples. The binary samples with a volume of about 5-10 cm3 were prepared by weighing. The ternary samples were prepared from mixtures of DMF and water, to which methanol was added. RESULTS AND DISCUSSION

The vapour pressures and second virial coefficients of the components of the system are given in Table 1.. The results of the total vapour pressure measurements are given in Table 2 for binary mixtures and in Table 3 for the ternary mixture. The binary systems were correlated by equations such as: Redlich and Kister (1948), Van Laar extended by Van Ness (1964), Myers and Scott (1963), Marsh (1977), Wilson (1964), NRTL (Renon and Prausnitz, 1968) and UNIQUAC (Anderson and Prausnitz, 1978). Coefficients in these equations were obtained by a modification of Barker’s method (G&al, 1977; Goral and Janaszewski, 1977; Kolasihska and Oracz, 1979). The values of the 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 binary data. For all the systems investigated the two-parameter NRTL was used. Since the observed global minimum of the objective is not sensitive to a change of (Y,a value equal to 0.3 was selected. The system DMF-methanol can be described by any equation with the same accuracy, whereas for the system methanol-water the equations based on the local composition concept (Wilson, NRTL) or UNIQUAC give systematic deviations (see the number of sign changes in Table 4).

TABLE 1 Vapour pressures P and second virial coefficients B, of pure substances used Component

N, N-Dimethylformamide Methanol

Water

- B,(313.15 K) a (dm3 mol-‘)

P(313.15 K) (kPa) This work

Literature

1.221 35.443

1.333 * 0.029 35.469 rt 0.004 35.472 f 0.026 35.429&0.013 7.376 ’

7.372

a Calculated according to Hayden and O’ConneIl(l975). b Calculated according to Boublik et al. (1984). ’ CRC Handbook of Chemistry and Physics, 67th Edn., 1987.

b b b b

2.298 1.552

0.699

282 TABLE 2 Total vapour pressures, compositions, Y

P, liquid phase compositions, x, and calculated vapour phase P(kPa)

X,

Y,

P(kPa)

0.7244 0.7590 0.8116 0.8757 0.8995 0.9514 0.9802

0.2988 0.3268 0.3812 0.4806 0.5332 0.7026 0.8533

18.842 17.813 16.072 13.561 12.497 9.998 8.482

Water(a)- N, N-dimethylformamide(b), 313.15 K 0.5406 0.1999 1.472 0.0441 1.801 0.6011 0.1141 0.4058 0.6283 0.5446 2.201 0.1853 2.290 0.6349 0.2013 0.5696 0.7394 0.6536 2.607 0.2652 2.864 0.7640 0.3166 0.7073 0.7893 0.7636 3.194 0.3821 0.8286 0.4470 0.8101 3.563 0.8952 0.4492 0.8116 3.575 0.9583 0.4596 0.8183 3.632 0.4977 0.8419 3.853

0.8664 0.8972 0.9097 0.9126 0.9514 0.9585 0.9652 0.9741 0.9859 0.9946

4.130 4.514 4.707 4.753 5.543 5.736 5.922 6.239 6.713 7.125

Methanol(a)- N, N-Dimethylformamide(b), 0.5610 2.617 0.0633 0.1818 0.8232 5.595 0.8503 6.335 0.2092 0.2677 0.8922 8.054 0.9107 9.157 0.3035 0.3096 0.9135 9.347 0.3295 0.9218 9.981 0.4550 0.9576 14.302 14.963 0.4733 0.9611

0.9720 0.9837 0.9877 0.9926 0.9953 0.9959 0.9978 0.9988

17.523 21.715 23.745 27.000 29.402 30.008 32.314 33.584

Ya Water(a)-methanol(b), 0.0348 0.1050 0.2185 0.0755 0.1170 0.3298 0.1660 0.4583 0.5785 0.2161 0.2414 0.6307 0.6565 0.2553

313.15 K 32.846 30.153 27.676 24.971 22.419 21.240 20.610

Therefore, for correlation Redlich-Kister equation GE/W=

x,(1 - x,)cKj(2x, i

313.15 K 0.5415 0.6483 0.6990 0.7803 0.8407 0.8560 0.9137 0.9490

of binary measurements

- #

we have chosen the

(1)

where x, denotes the mole fraction of the first component in each binary mixture. Values of Ki coefficients in eqn. (l), together with their standard errors a( Ki) and the correlation coefficients qrt for pairs (K,; K,) are given in

283 TABLE3 Ternary system N,N-dimethylformamide(a)-methanol(b)-water(c) at 313.15 K: experimental liquid mole fractions x,, xb and total pressure P. VapOUr mole fractions y,, yb and deviations d P( = P - PC& calculated with eqn. (3)

0.0654 0.1332 0.2134 0.3081 0.4230 0.5384 0.1298 0.2066 0.2639 0.3634 0.4897 0.5913 0.0171 0.0391 0.0543 0.0651 0.0788 0.0905 0.1011 0.1963 0.2322 0.3067 0.4323 0.4782 0.0712 0.1052 0.1536 0.1853 0.2376 0.3369 0.3745 0.0324 0.0778 0.1075 0.1325 0.1588 0.2049 0.2228 0.8852 0.7301 0.6799

0.9230 0.8431 0.7487 0.6372 0.5019l 0.3661 0.8100 0.6977 0.6139 0.4683 0.2835 0.1348 0.8367 0.6268 0.4636 0.3782 0.2477 0.1363 0.0345 0.6353 0.5685 0.4301 0.1968 0.1114 0.8677 0.7363 0.6149 0.5356 0.4045 0.1555 0.0613 0.8655 0.6768 0.5534 0.4495 0.3403 0.1489 0.0744 0.0602 0.1808 0.0775

0.0016 0.0038 0.0074 0.0137 0.0262 0.0491 o.OQ37 0.0073 0.0110 0.0213 0.0490 0.1064 0.0004 0.0009 0.0015 0.0021 0.0033 0.0055 0.0105 0.0071 0.0095 0.0171 0.0487 0.0781 0.0018 0.0029 0.0051 0.0070 0.0117 0.0353 0.0628 o.OQo7 0.0020 0.0032 0.0046 0.0069 0.0157 0.0242 0.3773 0.1399 0.1800

Yb

P(kPa)

d P(kPa)

0.9946 0.9882 0.9790 0.9644 0.9374 0.8903 0.9756 0.9570 0.9394 0.8962 0.7938 0.6010 0.9493 0.8752 0.8092 0.7680 0.6783 0.5347 0.2214 0.9275 0.9080 0.8549 0.6734 0.5189 0.9779 0.9403 0.9051 0.8776 0.8200 0.5906 0.3467 0.9648 0.9073 0.8631 0.8191 0.7600 0.5619 0.3828 0.4935 0.7585 0.4616

32.755 29.869 26.357 22.161 17.142 12.370 29.145 25.285 22.350 17.284 11.127 6.565 31.416 26.269 22.870 20.284 16.582 12.715 8.396 24.010 21.848 17.331 9.781 7.082 31.370 27.820 24.269 21.913 17.923 9.925 6.701 31.788 26.871 23.639 20.844 17.744 11.568 8.788 2.907 6.320 4.573

-0.024 -0.036 -0.048 -0.043 -0.017 0.017 -0.049 -0.055 -0.059 -0.020 0.037 0.018 0.096 -0.042 0.319 -0.133 -0.150 -0.073 0.035 -0.048 -0.037 -0.010 0.012 0.024 -0.029 -0.042 -0.041 -0.034 -0.039 0.003 0.056 -0.049 -0.035 -0.052 -0.081 -0.112 -0.030 0.053 0.044 0.058 0.013

284 TABLE 4 Comparison of the efficiency of different equations for binary systems. a(P) = [C( P P&)‘/( n - m)]“2 = average standard error of the total vapour pressure, where n = number of experimental points, m = number of parameters Equation

m

u(P)(kPa)

Methanol-water Redhch-Kister Van Laar-Van Ness Myers-Scott Marsh NRTL (a = 0.3) Wilson UNIQUAC

4 3 4 2+2 2 2 2

0.009 0.011 0.009 0.011 0.156 0.173 0.173

DMF-water RedIich-Kister Van Laar-Van Ness Marsh NRTL ( OL = 0.3) Wilson UNIQUAC

5

3 2+2 2 2 2

0.011 0.013 0.012 0.060 0.054 0.054

DMF-methanol Redhch-Rister Van Laar-Van Ness NRTL (a = 0.3) Wilson UNIQUAC

2 2 2 2 2

Number of sign changes

10 6 6 2 2 2

. 0.017 0.018 0.018 0.018 0.021

Table 5 for all the binary systems. The qrt values, together with the standard errors a( Ki) allow, if necessary, the estimation of the standard errors of all values, which depend on Ki. Coefficients Aj, B,! and Ci’ given in Table 5 may be used in eqn. (2): K;-K,=A](B,‘,-B,,)+B;(B,-B,,)+C;@B’-6B)

(2)

to show how parameter Ki would change if the second virial coefficients I&, and 6B = 2B,, - B, - B,, used in this study were replaced by another set of values denoted by Bk, Bt,,. Equation (2) shows the influence of the second virial coefficient on Ki values. The system methanol-water has been investigated by many authors who have measured vapour-liquid equilibria under various P-T conditions. Therefore it is possible to compare simultaneously various VLE data. For this purpose each VLE data set under comparison may be replaced by the value of GE/RT at, say, equimolar concentration, henceforth denoted by B,,,

285 TABLE 5 Coefficients Ki(Ci) of the Redlich-Kister polynomial for the excess Gibbs energy with their standard errors a( K,)[a( C,)], correlation coefficients qij, coefficients Ai, BI and C; of eqn. (2) and cross second virial coefficients Bab, B,, Bbc at 313.15 K i=O

1

2

3

4

- 0.02002 0.01635 - 0.00084 0.00005 0.00006

-0.15167 0.02222 - 0.00066 o.OoOO5 0.00006

0.12932 0.03409 - 0.00087 0.00012 0.00014

- 0.193 - 0.557

- 0.489

- 0.12837 0.00113 - 0.00182 0.00362 - 0.00227

- 0.07272 0.00155 0.00137 - 0.00389 0.00180

0.02942 0.00297 - 0.00079 0.00198 - 0.00109

0.046 - 0.541

- 0.091

N, N-Dimethylformamide(a)-methanol(b) Bab = - 0.949 dm3 mol-’ Ki - 0.48540 0.02561 a(&) 0.00180 0.00238 A; - 0.01779 - 0.01563 B; 0.00055 0.00031 C, 0.00058 O.ooO32 4il - 0.643 N, IV-Dimethylformamide(a)-water(c) Bat = - 1.041 dm3 mol- ’ Ki - 0.26108 0.22499 a(Ki) 0.00499 0.00768 ‘4; - 0.00341 - 0.00162 B; 0.00051 0.00018 C; 0.00063 0.00022 4il - 0.624 qi2 0.044 - 0.214 4i3 - 0.449 0.031 4i4 0.435 - 0.199 Methanol(b)-water(c) B, = - 0.758 dm3 mol-’ Ki 0.57964 a(Ki) 0.00048 A; 0.00352 B; - 0.01192 Ci 0.00407 4il - 0.107 qi2 - 0.012 qi3 0.444

N, N-Dimethylformamide(a)-methanol(b)-water(c) - 0.8434 c, 0.2524 u(Ci)

Qo.s. The Qo.s values calculated from various data sets were plotted versus l/T. Such a plot for the methanol-water system is presented in Fig. 1. The full line in this figure was calculated using HE data taken from Belousov and Morachevskii (1970). Figure 2 presents the comparison between literature and experimental data obtained in the methanol-water system. In this figure, experimental pressure values are compared with corresponding refer-

286

2.6

3.0

28

3.2

3.4

lO?T

Fig. 1. Water-methanol system; comparison of equimolar value Q = GE/RT with literature data at various temperatures: e Bredig and Bayer (1927); e Bemret (1929); n Ferguson and Funnel (1929); A Uchida and Kato (1934); A Ewert (1936); 7 Othmer and Benenati (1945); D Dulitskaya (1945); 4 Griswold and Buford (1949); Q Griswold and Wong (1952); $ Green and Vener (1955); + RamaIho et al. (1961); v Kojima et al. (1968); hl Broul et al. (1969); 0 Dalager (1969); o Ratcliff and Chao, K.C. (1969); + Kato et al. (1970); 0 Kohovtova et al. (1970) and Uchida et al. (1953); X Kato et al. (1970); c) Lesteva et al. (1970); a Verhoeye and De Schepper (1973); 0 McGlashan and Williamson (1976); l this work. Note: all literature data taken from M~czyhski and Mgczyfrska (1981).

ence data using the same reference line P” =f(x,; KI . . . K,). The total reference pressure line PO was calculated on the basis of coefficients K 1". K4 of the Redlich-Kister equation determined in this paper by taking advantage of the vapour pressure values of the pure components which are

Fig. 2. Water-methanol system; comparison between correlation accuracy of Redlich-Kister equation: 0 this work; U Ferguson and Funnel (1929); + Ewert (1936); $ Ratchff and Chao (1%9); o McGlashan and Williamson (1976) - data at 308.15 K. Note: all literature data taken from M@czyhski and Mpczyfrska (1981).

287

given by authors of the quoted measuring series. This makes it possible to estimate how far the data given in the literature are compatible with the values obtained in this work, and it enables us simultaneously to avoid making a systematic error resulting from an insignificantly different measuring temperature. Since in the data cited by M~czyhski and Mgczyhska (1981) the second virial coefficients are equal to zero, the present data for the methanol-water system were recalculated in the same manner. The pure component vapour pressures are those reported for relevant data sets. McGlashan’s data at 308.15 K are also included, forwhich it is assumed that the Redlich-Kister parameters obtained at 313.15 K can be used. The ternary system was correlated by eqn. (3) as well as the commonly used Wilson and NRTL equations. Equation (3) is the one discussed by Oracz (1987), to which ternary terms were added. The equation has the form

(3) where x* = x&xi -I-xi) * G,: is any equation suitable for the correlation of a binary mixture (i +j). Parameter fl is adjustable. Among the systems investigated, two exhibit small negative deviations and the third has large positive deviations from ideality. Therefore in this work different P-values were tested. Previous investigations (G&al et al., 1988) indicate that p =

TABLE 6 Comparison of the efficiency of different equations for the ternary system N, N-dimethylformamide-methanol-water at 313.15 K. Average standard error of the total vapour pressure o(P), relative standard error of the total vapour pressure o(dP/P) Equation

Number of parameters

e(P)

e(dP/P)

Binary

Ternary

WV

m

Eqn. (3) j3 = 0 (Kohler)

2/5/4

Eqn. (3) p=-l/4 Wilson NRTL

2/5/4

0* 1 3 0* 1 0* 0*

0.269 0.075 0.071 0.237 0.071 0.193 0.229

2.83 0.49 0.44 2.62 0.45 1.04 1.65

2/2/2 2/2/2

n is the number of parameters, m is the number of points, * corresponds to Ci = 0.

288

is suitable for systems with strong positive deviations from Raoult’s law, whereas for systems with strong negative deviations /3 = 1 can be used. Finally /3 = 0 was used. For the ternary contribution GE, in eqn. (3) the following expression was tested: -l/4

G~JRT=x,x,,x;

[Cl + C,(3X,-

1) + C,(3x,

- 1) + . ..I

(4)

Table 6 shows the efficiency of equations applied to the ternary data. It has been found that only one ternary parameter, C,, is needed in the ternary contribution in eqn. (3) to describe ternary data with sufficient accuracy. Parameter C,, together with its standard error a(C,), is given in Table 5. From the data presented it follows that the best results can be obtained by applying the Redlich-Kister equation to the description of the binary data systems. In the case of the description of the ternary system the Kohler formula turned out to be the best one making use of the parameter describing the ternary effect (eqn. (3); B = 0 and eqn. (4)), which is shown in Table 6. ACKNOWLEDGEMENT

We appreciate the financial support provided for this work by the Polish Academy of Sciences within Project CPBP 01.16. LIST OF SYMBOLS

Ai, B;, C/ coefficients in eqn. (2) Baa, Bbb, Bee B& second virial coefficients B;a, Bib, C,, C,, C, coefficients in eqn. (4) GE excess Gibbs energy Kj constants in eqn. (1) P vapour pressure (kPa) QO,s value of GE/RT at equimolar concentration qrt correlation coefficients between a pair of parameters K,, K,) R gas constant T temperature (K) x mole fraction in liquid y mole fraction in vapour Greek letters

(YNRTL parameter /3 parameter in eqn. (3) u standard error

289

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290 Wu, H.S., Hagewiesche, D. and Sandler, S.I., 1988. Fluid Phase Equilibria, 43: 77. Zielkiewicz, J., Oracz, P. and Warycha, S., 1990. Total vapour pressure measurements and excess Gibbs energies for the binary systems: methanol + ethanol, ethanol+ 2-propanol, benzene + cyclohexane, benzene+ carbon tetrachloride and benzene + ethanol at 303.15 and 313.15 K. Fluid Phase Equilibria, 58: 181-189.