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Isobaric vapour-liquid equilibria of the ternary system toluene + p-xylene + 1,2-dichloroethane/Kolmiksusteemi tolueen + p-ksuleen + 1,2-dikloroetaan isobaariline auru ja vedeliku tasakaal.

INTRODUCTION

Knowledge of multicomponent vapour-liquid equilibrium (VLE) data is important in the design of equipment for separation processes. In addition, such experimental information can be used to test and develop prediction correlations. The purpose of this study was to determine VLE for the ternary system toluene + p-xylene + 1,2-dichloroethane and for three constituent binaries at four constant pressures, 26.66, 53.33, 79.99, and 101.32 kPa. A Wilson equation [1] whose main parameters ([[lambda].sub.ij] - [[lambda].sub.ii]) were assumed to be a linear function of temperature was used to obtain a fit of binary VLE data. As a continuation of our previous investigation [2], the possibility of predicting the behaviour of the ternary system from three binaries was checked. It appears that the ternary system toluene + p-xylene + 1,2-dichloroethane has not been studied earlier.

EXPERIMENTAL

All the substances used in this work were the same as in our earlier work [3]. Toluene and p-xylene ("purum" grade) were twice distilled. 1,2-Dichloroethane ("puriss" grade) was used without further purification. Densities and refractive indices of pure liquids at 298.15 K agree well with the literature values, as seen from Table 1.

The boiling temperature (T)-liquid phase composition (x) equilibrium was measured in a semi-micro ebulliometer [6]. Uncertainties of the boiling temperatures were estimated to be less than 0.05 K, and those of the mole fractions composition of the liquid mixture less than 5 x [10.sup.-4].

The T-x results for the binary systems toluene + p-xylene, toluene + 1,2-dichloroethane, and p-xylene + 1,2-dichloroethane obtained in this work are listed in Table 2.

The T-x data in binary systems were fitted with the Wilson model [1] in the form

ln [[gamma].sub.i] = -ln([x.sub.i] - [[LAMBDA].sub.ik][x.sub.k]) + [x.sub.k][[[LAMBDA].sub.ik]/[x.sub.i] + [[LAMBDA].sub.ik][x.sub.k] - [[LAMBDA].sub.ki]/[x.sub.k] + [[LAMBDA].sub.ki][x.sub.i]], (1)

where [[gamma].sub.i] is the activity coefficient of component i in the liquid phase and [[LAMBDA].sub.ik] and [[LAMBDA].sub.ki] are expressed as

[[LAMBDA].sub.ik] = exp[[a.sub.ik] + [b.sub.ik]/T], (2)

[[LAMBDA].sub.ki] = exp[[a.sub.ki] + [b.sub.ki]/T], (3)

including in the parameters [a.sub.ik] and [b.sub.ik] molar volumes of components and the gas constant [2].

The vapour pressures of pure components [P.sub.i.sup.0] needed for VLE calculation were calculated by the Antoine equation

ln([P.sub.i]/kPa) = [A.sub.i] - [B.sub.i]/T/K + [C.sub.i]. (4)

The values of the constants [A.sub.i], [B.sub.i] and [C.sub.i] are given in Table 3.

The values of the coefficients [a.sub.ik] and [b.sub.ik] of Eqs. 2 and 3, calculated by the Newton iteration method, together with the mean absolute relative error of pressure ([DELTA]P) are listed in Table 4.

VLE data for the system toluene + p-xylene were reported at a temperature of 363.15 K by Wichterle [7], at normal pressure by Schmelzer & Wolf [8] and by Sartakova et al. [9], and at 101.59 kPa by Kutsarov et al. [10]. It can be seen from Fig. 1 that the data presented here are in the best agreement with those obtained by Schmelzer & Wolf [8].

Experimental data for the system toluene + 1,2-dichloroethane have been obtained by several investigators, most of them are published also in the data collection [11, p. 109]. At normal pressure VLE data have been obtained by Jones et al. [12], Alpert & Elving [13], Rollet et al. [14], and at barostatic pressure by Sharma & Singh [15]. Ellis reported VLE data at 26.66 kPa [16], and Rivenq at 26.66, 39.99, 53.33, 79.99, and 101.32 kPa (cited in [11, p. 109]). Deviations from our results are the smallest for those of Rollet et al. [14] and the greatest for those of Jones et al. [12]. Figure 2 compares the above-mentioned experimental results with the data of this work. Rivenq's data (measured at the same pressures used in our work) deviate from our results just in the temperature determination, especially at higher 1,2-dichloroethane concentrations. This may be caused by deviations in 1,2-dichloroethane boiling temperatures (see Table 5 for values measured by different authors). Table 5 presents also the boiling point of toluene.

The boiling temperatures of 1,2-dichloroethane at four pressures measured in this work agree well with those obtained by Gutsche & Knapp [17] and Dohnal et al. [18]. The sets of Antoine constants from these publications represent boiling temperatures which differ from those of our work with an overall average absolute deviation of 0.02 K.

VLE data for p-xylene + 1,2-dichloroethane have been given in several publications [11, 15, 19, 20] at conditions which differ from those of this study. Our P vs. T data for p-xylene measured at four pressures agree well with those of Gupta & Rawat [21] with an overall average absolute deviation of 0.02 K.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

All present binary systems are nonazeotropic and weakly nonideal. As shown by us earlier [3], these systems are close to ideal also at 298.15 K, because excess molar enthalpies are only slightly negative.

The isobaric VLE data for the ternary system studied are given in Table 6.

The prediction results obtained by the modified Wilson equation are presented in Table 7. By assuming that the ideal gas law holds, calculations of VLE were made using the values of coefficients for three constituent binaries given in Table 4 and constants of the Antoine equation from Table 3. The mean absolute error for boiling temperatures at all four pressures was 0.90 K.

By assuming that the main parameters of the Wilson equation ([[lambda].sub.ij] - [[lambda].sub.ii]) vary linearly with the temperature up to 298.15 K, the ternary excess Gibbs energies [G.sup.E] vs. x.sub.i] at [x.sub.j]/[x.sub.k] = 1 are shown in Fig. 3. In the same figure the experimental [H.sup.E] data at 298.15 K obtained by us earlier [3] and the entropic term [TS.sup.E] calculated from the difference [H.sup.E] - [G.sup.E] are also plotted.

In Fig. 3a [H.sup.E] and [TS.sup.E] are s-shaped changing from positive to negative and to positive again with increasing mole fraction of 1,2-dichloroethane, [x.sub.3]. Up to [x.sup.3] about 0.2, [TS.sup.E] is larger than [H.sup.E], which results in a negative [G.sup.E]. With increasing [x.sub.3], [G.sup.E] becomes positive when [absolute value of [TS.sup.E]] > [absolute value of [H.sup.E]]. This phenomenon is valid also when aromatic hydrocarbons are added as seen in Fig. 3b and c. Presumably, the formation of charge transfer (or donor-acceptor) complexes between the aromatic hydrocarbon and 1,2-dichloroethane and their decomposition are the most important factors influencing the signs and values of excess functions in this ternary system.

[FIGURE 3 OMITTED]

ACKNOWLEDGEMENT

The authors gratefully acknowledge the Estonian Ministry of Education for financial support (project No. 0351456s00).

Received 1 April 2002, in revised form 5 September 2002

REFERENCES

[1.] Wilson, G. M. Vapor-liquid equilibrium XI. A new expression for excess free energy of mixing. J. Am. Chem. Soc., 1964, 86, 127-130.

[2.] Siimer, E., Kirss, H., Kuus, M. & Kudryavtseva, L. Isobaric vapor-liquid equilibrium in the ternary system o-xylene + nonane + cyclohexanol. J. Chem. Eng. Data, 2002, 47, 52-55.

[3.] Kuus, M., Kirss, H., Siimer, E. & Kudryavtseva, L. Excess molar enthalpies of the ternary system toluene + p-xylene + 1,2-dichloroethane at 298.15 K. Thermochim. Acta, 2002, in press.

[4.] Riddick, J. A., Bunger, W. B. & Sakano, T. K. Techniques of Chemistry. Vol. II. Organic solvents. 4th ed. John Wiley & Sons, 1986.

[5.] Konti, A., Moumouzias, G. & Ritzoulis, G. Densities, relative permittivities, and refractive indices for the binary liquid system propylene carbonate + p-xylene at 15, 20, 25, 30, and 35[degrees]C. J. Chem. Eng. Data, 1997, 42, 614-618.

[6.] Mihkelson, V., Kirss, H., Kudryavtseva, L. & Eisen, O. Vapor-liquid equilibrium T-x measurements by a semi-micro method. Fluid Phase Equilib., 1977/78, 1, 201-209.

[7.] Wichterle, I. Liquid-vapour equilibrium XXV. Vapour-liquid equilibria in system heptane-toluene-p-xylene and in systems heptane-toluene-extractive agent. Collect. Czech. Chem. Commun., 1965, 30, 3388-3398.

[8.] Schmelzer, J. & Wolf, Ch. Charakterisierung des isobaren Flussigkeit-Dampf-Gleichgewichtes des Systems Benzol-Toluol-p-Xylol. Chem. Techn., 1978, 30, 305-307.

[9.] Sartakova, O. Yu., Krutko, O. M., Khristenko, M. S. & Kormina, L. A. Synthesis of principal technological separation scheme for toluene-diglyme mixture using the additional components. Zh. prikl. khim., 1996, 69, 1077-1080 (in Russian).

[10.] Kutsarov, R. K., Ralev, I. D & Sharlapov, V. K. Study of liquid-vapor phase equilibrium for binary systems of aromatic hydrocarbons [C.sub.6]-[C.sub.8]. Zh. prikl. khim., 1993, 66, 567-573 (in Russian).

[11.] Maczynski, A., Maczynska, Z. & Rogalski, M. Thermodynamical Data for Technology. Series A. Verified Vapor-Liquid Equilibrium Data. Warszawa, 1978, Vol. 2.

[12.] Jones, C. A., Schoenborn, E. M. & Colburn, A. P. Equilibrium still for miscible liquids. Data on ethylene dichloride-toluene and ethanol-water. Ind. Eng. Chem., 1943, 35, 666-672.

[13.] Alpert, N. & Elving, P. J. Vapor-liquid equilibria in binary systems. Ind. Eng. Chem., 1951, 43, 1174-1177.

[14.] Rollet, A. P., Toledano, P., Elkaim, G. & Sonez, M. Bulliometrie des solutes volatils. Alger. Sci. Phys., 1956, 2, 403-425.

[15.] Sharma, V. K. & Singh, P. P. Liquid-vapor equilibria in some binary mixtures of nonelectrolytes. Z. phys. Chem., 1986, 267, 805-810.

[16.] Ellis, S. R. M. A new equilibrium still and binary equilibrium data. Trans. Inst. Chem. Engn., 1952, 30, 58-64.

[17.] Gutsche, B. & Knapp, H. Isothermal measurements of vapor-liquid equilibrium for three n-alkane + chloroalkane mixtures. Fluid Phase Equilib., 1982, 8, 285-300.

[18.] Dohnal, V., Blahova, D. & Holub, R. Vapor-liquid equilibrium in binary systems formed by acetonitrile, 2-butanone and 1,2-dichloroethane. Fluid Phase Equilib., 1982, 9, 187-200.

[19.] Rao, M. V. & Viswanath, D. S. Isobaric vapor-liquid equilibria of the p-xylene + 1,2-dichloroethane system. J. Chem. Eng. Data, 1982, 27, 41-44.

[20.] Siddiah, B., Rao, M. V., Ashraf, S. M. & Prasad, D. H. L. Isobaric vapor-liquid equilibria in the binary systems formed by p-xylene with 1,2-dichloroethane, 1,1,4-trichloroethane and 1,1,2,2-tetrachloroethane at 66.5 kPa. Phys. Chem. Liq., 1996, 32, 47-55.

[21.] Gupta, S. K. & Rawat, B. S. Isobaric vapor-liquid equilibria for ternary mixtures: saturated hydrocarbons, xylenes, and ethylbenzene with sulfolane at 101.325 kPa. J. Chem. Eng. Data, 1998, 43, 396-399.

Helle Kirss, Mati Kuus, Enn Siimer *, and Ludmilla Kudryavtseva

Department of Material Science, Tallinn Technical University, Akadeemia tee 15, 12618 Tallinn, Estonia

* Corresponding author, siimer@chemnet.ee
Table 1. Densities (d) and refractive indices ([n.sub.D] of
pure components at 298.15 K

Component d, kg [m.sup.-3] [n.sub.D]

 Exp. Lit. Exp. Lit.

Toluene 862.2 862.19 (a) 1.4940 1.49413 (a)
p-Xylene 856.7 856.6 (b) 1.4930 1.4931 (b)
1,2-Dichloroethane 1246.3 1246.37 (a) 1.4419 1.4421 (a)

(a)--from [4]

(b)--from [5]

Table 2. Isobaric vapour-liquid equilibria data: liquid phase mole
fraction ([x.sub.1] and boiling temperature (T) in binary systems

 P = 26.66 kPa P = 53.33 kPa

[x.sub.1] T, K [x.sub.1] T, K

Toluene (1) + p-xylene (2)

0.000 367.78 0.000 389.00
0.195 361.80 0.195 382.69
0.227 360.66 0.227 381.63
0.282 358.86 0.282 379.89
0.390 355.95 0.390 376.85
0.396 355.41 0.396 376.24
0.499 353.01 0.499 373.67
0.589 350.84 0.589 371.46
0.680 348.90 0.680 369.33
0.785 346.66 0.785 367.06
0.867 345.36 0.867 365.47
0.903 344.29 0.903 364.35
1.000 342.65 1.000 362.63

Toluene (1) + 1,2-dichloroethane (2)

0.000 319.22 0.000 337.45
0.110 320.79 0.108 339.03
0.205 322.45 0.206 340.95
0.284 323.67 0.279 342.06
0.391 325.86 0.392 344.74
0.483 327.54 0.481 346.42
0.596 330.81 0.602 350.14
0.695 333.22 0.697 352.65
0.781 336.01 0.787 355.55
1.000 342.65 1.000 362.63

p-Xylene (1) + 1,2-dichloroethane (2)

0.000 319.22 0.000 337.45
0.100 321.40 0.098 339.62
0.199 323.46 0.194 342.11
0.292 325.89 0.291 344.86
0.326 327.29 0.322 346.15
0.377 329.72 0.382 349.03
0.464 332.78 0.468 352.33
0.555 337.01 0.558 356.49
0.677 343.76 0.612 359.44
0.767 349.02 0.676 363.52
1.000 367.78 0.718 364.54
 0.767 368.98
 1.000 389.00

 P = 79.99 kPa P = 101.32 kPa

[x.sub.1] T, K [x.sub.1] T, K

Toluene (1) + p-xylene (2)

 0.000 402.85 0.000 411.49
 0.195 396.49 0.195 404.97
 0.227 395.40 0.227 404.09
 0.282 393.57 0.282 402.06
 0.390 390.46 0.390 398.91
 0.396 389.90 0.396 398.32
 0.499 387.27 0.499 395.64
 0.589 384.90 0.589 393.26
 0.680 382.68 0.680 390.97
 0.785 380.27 0.785 388.53
 0.867 378.61 0.867 386.77
 0.903 377.56 0.903 385.73
 1.000 375.66 1.000 383.76

Toluene (1) + 1,2-dichloroethane (2)

 0.000 349.29 0.000 356.63
 0.106 350.96 0.104 358.38
 0.207 352.98 0.208 360.49
 0.274 354.16 0.269 361.65
 0.393 357.03 0.394 364.58
 0.478 358.79 0.475 366.49
 0.608 362.63 0.615 370.42
 0.699 365.29 0.701 373.17
 0.793 368.31 0.799 376.27
 1.000 375.66 1.000 383.76

p-Xylene (1) + 1,2-dichloroethane (2)

 0.000 349.29 0.000 356.63
 0.095 351.54 0.093 358.95
 0.189 354.23 0.184 361.79
 0.290 357.32 0.289 365.11
 0.318 358.61 0.314 366.32
 0.387 361.63 0.392 369.48
 0.472 365.22 0.476 373.17
 0.561 369.68 0.564 377.73
 0.615 372.69 0.618 380.75
 0.675 376.75 0.674 384.98
 0.702 377.19 0.686 384.06
 0.767 382.79 0.767 391.10
 1.000 402.85 1.000 411.49

Table 3. Constants for the Antoine vapour pressure equation (Eq. 4)

Component Temperature Constants
 region, K
 [A.sub.i] [B.sub.i] [C.sub.i]

Toluene 343-384 14.08406 3148.177 -51.172
p-Xylene 368-411 13.82595 3178.599 -66.279
1,2-Dichloroethane 319-357 14.5197 3117.876 -41.736

Table 4. Fitted coefficients of the modified Wilson equation
(Eqs. 2, 3) and calculated absolute mean error ([DELTA]P of
pressure for binary systems

 System (1)+(2) [a.sub.12] [b.sub.12] [a.sub.21]

Toluene + p-xylene -0.35434 118.040 0.43197
Toluene + 1,2-dichloroethane 0.04946 -15.449 0.17245
p-Xylene + 1,2-dichloroethane -0.10223 -44.134 0.71791

 System (1)+(2) [b.sub.21] [DELTA]P, %

Toluene + p-xylene -124.937 0.32
Toluene + 1,2-dichloroethane -67.618 0.63
p-Xylene + 1,2-dichloroethane -168.002 1.35

Table 5. Boiling temperature (T ) of toluene and 1,2-dichloroethane
at different pressures

Pressure, kPa T, K

 Toluene

101.32 383.76 (a), 383.75 (b), 383.76 (c)
 79.99 375.66 (a), 375.65 (b)
 53.33 362.63 (a), 362.65 (b)
 26.66 342.65 (a), 342.65 (b), 342.65 (d)

Pressure, kPa T, K

 1,2-Dichloroethane

101.32 356.63 (a), 355.75 (b), 356.60 (c)
 79.99 349.29 (a), 348.55 (b)
 53.33 337.45 (a), 337.15 (b)
 26.66 319.22 (a), 318.85 (b), 318.85 (d)

(a)--this work

(b)--Rivenq (cited in [11, p. 109])

(c)--Rollet et al. [13]

(d)--Ellis [15]

Table 6. Isobaric vapour-liquid equilibrium data, liquid phase
mole fraction([x.sub.i], and boiling temperature (T) in the
ternary system toluene (1) + p-xylene (2) + 1,2-dichloroethane
(3) at different pressures (P, kPa)

[x.sub.1] [x.sub.2] [x.sub.3]

 0.289 0.289 0.422
 0.413 0.413 0.174
 0.177 0.177 0.646
 0.553 0.277 0.170
 0.432 0.216 0.352
 0.286 0.143 0.571
 0.222 0.444 0.334
 0.163 0.326 0.511
 0.272 0.544 0.184
 0.280 0.560 0.160
 0.332 0.336 0.332
 0.133 0.734 0.133

 T, K

P = 26.66 P = 53.33 P = 79.99 P = 101.32

 333.92 353.18 366.05 373.94
 344.30 364.26 377.35 385.65
 326.94 345.88 -- --
 343.22 362.95 375.90 384.05
 335.65 354.72 367.31 375.20
 328.07 346.62 358.68 366.15
 338.80 358.01 370.73 377.72
 331.99 351.39 364.09 371.94
 347.58 -- -- --
 349.58 369.25 381.84 390.20
 336.95 355.74 367.82 376.39
 353.36 373.60 386.65 394.83

--not determined

Table 7. Isobaric vapour-liquid equilibrium data for the ternary
system toluene (1) + p-xylene (2) + 1,2-dichloroethane (3),
predicted by the modified Wilson equation [2]

 Experimental data Predicted data

[x.sub.1] [x.sub.2] T, K [DELTA]T [y.sub.1]

P = 26.66 kPa

 0.289 0.289 333.92 -0.76 0.200
 0.413 0.413 344.30 -1.16 0.416
 0.177 0.177 326.94 -0.25 0.095
 0.553 0.277 343.22 -2.28 0.517
 0.432 0.216 335.65 -1.46 0.313
 0.286 0.143 328.07 -0.12 0.162
 0.222 0.444 338.80 -0.92 0.183
 0.163 0.326 331.99 -0.71 0.104
 0.272 0.544 347.58 -2.40 0.293
 0.280 0.560 349.58 -3.03 0.316
 0.332 0.336 336.95 -0.57 0.260
 0.133 0.734 353.36 -1.76 0.177

P = 53.33 kPa

 0.289 0.289 353.18 -0.27 0.208
 0.413 0.413 364.26 -0.64 0.422
 0.177 0.177 345.88 -0.10 0.099
 0.553 0.277 362.95 -1.78 0.526
 0.432 0.216 354.72 -0.77 0.323
 0.286 0.143 346.62 0.51 0.169
 0.222 0.444 358.01 0.10 0.188
 0.163 0.326 351.39 -0.49 0.109
 0.280 0.560 369.25 -1.93 0.319
 0.332 0.336 355.74 0.66 0.268
 0.133 0.734 373.60 -0.88 0.176

P = 79.99 kPa

 0.289 0.289 366.05 -0.30 0.212
 0.413 0.413 377.35 -0.41 0.425
 0.553 0.277 375.90 -1.57 0.530
 0.432 0.216 367.31 -0.50 0.329
 0.286 0.143 358.68 0.92 0.172
 0.222 0.444 370.73 0.54 0.192
 0.163 0.326 364.09 -0.43 0.111
 0.280 0.560 381.84 -1.00 0.320
 0.332 0.336 367.82 1.60 0.272
 0.133 0.734 386.65 -0.18 0.175

P = 101.32 kPa

 0.289 0.289 373.94 -0.20 0.214
 0.413 0.413 385.65 -0.41 0.427
 0.553 0.277 384.05 -1.52 0.532
 0.432 0.216 375.20 -0.40 0.332
 0.286 0.143 366.15 1.20 0.175
 0.222 0.444 377.72 1.72 0.193
 0.163 0.326 371.94 -0.35 0.113
 0.280 0.560 390.20 -0.94 0.320
 0.332 0.336 376.39 1.15 0.275
 0.133 0.734 394.83 0.19 0.175

 Predicted data

 [[gamma] [[gamma] [[gamma]
[y.sub.2] .sub.1] .sub.2] .sub.3] P *

P = 26.66 kPa

 0.073 0.9946 0.9811 1.0076 205.8
 0.160 0.9892 0.9813 1.0022 208.6
 0.033 1.0041 0.9896 1.0049 201.9
 0.097 0.9958 0.9703 1.0075 217.4
 0.056 0.9983 0.9706 1.0097 211.3
 0.028 1.0047 0.9792 1.0068 201.0
 0.138 0.9844 0.9881 1.0028 206.9
 0.076 0.9914 0.9895 1.0051 205.5
 0.232 0.9800 0.9895 0.9937 218.0
 0.253 0.9793 0.9899 0.9911 222.9
 0.097 0.9921 0.9806 1.0072 204.3
 0.405 0.9641 0.9967 0.9778 212.9

P = 53.33 kPa

 0.084 0.9945 0.9716 0.9986 403.6
 0.175 0.9898 0.9783 0.9851 408.3
 0.038 1.0008 0.9705 1.0013 401.4
 0.107 0.9963 0.9663 0.9928 423.6
 0.063 0.9983 0.9619 1.0005 410.3
 0.032 1.0021 0.9623 1.0027 393.1
 0.154 0.9851 0.9828 0.9898 398.8
 0.086 0.9909 0.9781 0.9974 406.6
 0.274 0.9797 0.9880 0.9721 425.0
 0.108 0.9926 0.9741 0.9959 391.4
 0.434 0.9637 0.9958 0.9556 411.1

P = 79.99 kPa

 0.087 0.9945 0.9657 0.9932 605.5
 0.184 0.9902 0.9764 0.9750 607.2
 0.112 0.9966 0.9639 0.9840 628.6
 0.067 0.9983 0.9566 0.9949 609.3
 0.034 1.0006 0.9523 1.0002 582.9
 0.163 0.9855 0.9795 0.9819 590.4
 0.091 0.9905 0.9713 0.9927 608.1
 0.286 0.9798 0.9869 0.9611 617.7
 0.114 0.9929 0.9703 0.9892 571.5
 0.451 0.9633 0.9953 0.9427 603.2

P = 101.32 kPa

 0.090 0.9945 0.9624 0.9900 764.4
 0.189 0.9904 0.9753 0.9690 768.8
 0.115 0.9968 0.9624 0.9788 793.5
 0.069 0.9983 0.9535 0.9917 768.8
 0.035 0.9998 0.9464 0.9987 733.2
 0.168 0.9856 0.9778 0.9778 723.3
 0.095 0.9903 0.9673 0.9900 767.9
 0.294 0.9799 0.9862 0.9544 780.0
 0.119 0.9931 0.9677 0.9848 735.2
 0.460 0.9631 0.9950 0.9352 756.0

* pressures calculated at experimental temperatures
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