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Vapour–liquid equilibrium at T = 308.15 K for binary systems: Dibromomethane + n-heptane, bromotrichloromethane + n-heptane, bromotrichloromethane + dibromomethane, bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane. Experimental data and modelling
Fluid Phase Equilibria 395 (2015) 1–8
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Vapour–liquid equilibrium at T = 308.15 K for binary systems: Dibromomethane + n-heptane, bromotrichloromethane + n-heptane, bromotrichloromethane + dibromomethane, bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane. Experimental data and modelling Lourdes Martínez-Baños, José Muñoz Embid, Santos Otín, Manuela Artal * Departamento de Química Física, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
A R T I C L E I N F O
A B S T R A C T
Article history: Received 26 January 2015 Received in revised form 9 March 2015 Accepted 10 March 2015 Available online 14 March 2015
In this paper, the isothermal vapour–liquid equilibrium (VLE) at T = 308.15 K have been measured for liquid binary systems dibromomethane + n-heptane, bromotrichloromethane + n-heptane, bromotrichloromethane + dibromomethane, bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane by a dynamic method. The VLE data have been reduced using the Redlich– Kister equation taking into consideration the vapour phase imperfection in terms of 2nd molar virial
Keywords: Vapour–liquid equilibrium Polyhalomethanes Modelling Peng–Robinson PC-SAFT
coefficients and molar excess Gibbs energies, GEm , have been calculated. The experimental GEm is positive for all systems presenting the greatest value for dibromomethane + n-heptane and a negligible value for dibromomethane + bromochloromethane system. From our experimental data and those reported in the literature, phase and volumetric behaviour of the binary systems containing dibromomethane, bromochloromethane, bromotrichloromethane or n-heptane have been modelled. Two equations of state, EoS, of different formulation have been used obtaining a good agreement for all systems. The mean relative deviations for the studied properties are MRD (P) = 1.57%, AAD (y) = 0.0116 and MRD (r) = 0.55% for Peng–Robinson EoS, and MRD (P) = 1.20%, AAD (y) = 0.0093 and MRD (r) = 0.38% for PC-SAFT EoS. ã 2015 Elsevier B.V. All rights reserved.
1. Introduction Classical application of polyhaloalkanes as fire extinguisher media has been restricted because their effect on the ozone layer. At present they are used mainly in various industrial processes as many organic synthesis reactions use polyalkanes similar to methane as a reaction media. Dibromomethane is one of the compounds included in the so-called Lombardo’s reagent (Zn/ Br2CH2/TiCl4) used in methylenation of ketones and ketenes [1]; it is also used as solvent of fats and resins. Bromotrichloromethane is used, for example, in chlorination reactions (Appel reactions) as an alternative of carbon tetrachloride given the high toxicity of the latter, in esterification and silylation reactions, and to prepare
* Corresponding author. Tel.: +34 876553765. E-mail address: [email protected] (M. Artal). http://dx.doi.org/10.1016/j.fluid.2015.03.023 0378-3812/ ã 2015 Elsevier B.V. All rights reserved.
Wittig reagents [2–5]. Finally, bromochloromethane is a reactant in the synthesis of biocides and chloromethylesters (N-blocked aminoacids and dipeptides) [6,7]. Also, it has been observed that bromochloromethane is an agent that reduces methane generation: increases the efficiency of the digestive process in ruminants (lower methane generation and greater milk production) [8] and inhibits the production of biogas when it is added to the piggery wastewater [9]. Then taking also into account that systems containing this type of products are not very studied in the literature [10–15] and that polyhalomethanes are used as analogues of methane derivatives with lower toxicity, it is convenient to have models that enable predicting in a simple way their behaviour under different conditions. Following our research on the halogen–halogen interactions, we report here the experimental isothermal vapour–liquid equilibrium (VLE) at T = 308.15 K for dibromomethane + n-heptane, bromotrichloromethane + n-heptane, bromotrichloromethane +
2
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dibromomethane, bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane systems.
for this equation are:
Moreover, molar excess Gibbs energies, GEm , are calculated by fitting of the experimental P x1 data with the Redlich–Kister equation. This study is completed with our previous results on the VLE of bromochloromethane + n-heptane system [11]. Finally, phase equilibria experimental data from this work along with VLE and volumetric data from literature for pure compounds and mixtures [10–18], are used to modelling the phase and volumetric behaviour of these systems with Peng–Robinson (PR) [19] and PCSAFT [20,21] equations of state.
P¼
RT aaðT r ; vÞ V b V ðV þ bÞ þ bðV bÞ
(1)
RT 2:5 RT c a ¼ 0:45724 c ; b ¼ 0:07780 Pc Pc h
aðT r ; vÞ ¼ 1 þ m 1 T 0:5 r
i2
(2)
;m
¼ 0:37464 1:54226v 0:26992v2
(3)
2. Experimental 2.1. Chemicals The specifications, density and vapour pressure of the chemicals are shown in Table 1. We compare the measured densities and vapour pressures of the products with the literature values. 2.2. Apparatus and procedure vapour–liquid equilibrium data were taken at constant temperature in a flow system as described in Muñoz Embid et al. [25] using a dynamic still designed by Berro et al. [26]. The temperature T inside the equilibrium cell was measured with a precision of 0.01 K by means of a Digitec digital thermometer (Digitec Corp.) Model 5831. The pressure P was measured by means of a Digiquartz Transmitter of Paroscientific Inc., Model 1015A, calibrated in the pressure range 0–100 kPa. The accuracy of the pressure measurements is 0.01%. Liquid and vapour mole fractions, x1 and y1, respectively, were determined by densimetric analysis using an digital density analyser Anton Paar Model DSA-5000M automatically thermostated by built-in solid state thermostat. The uncertainty of the composition measurements was estimated to be 0.0002 mole fraction.
Various modifications of the PR EoS have been proposed in literature with the aim of improving the experimental results [27]: (i) changes in the expression of the temperature-dependent function, a(Tr,v), for polar fluids; (ii) introduction of a volume correction, Dnc, which improves volume predictions without changing the VLE conditions; and (iii) the use of different mixing rules. In this work, we have used volumetric translation for polyhalomethanes and the classic one-parameter van der Waals mixing rule, where kij is the binary interaction parameter: a ¼ Si Sj xi xj aij ; b ¼ Si Sj xi xj bij
aij ¼
(4)
pffiffiffiffiffiffiffiffi 1 ai aj ð1 kij Þ; bij ¼ ðbi þ bj Þ 2
(5)
3.2. PC-SAFT EoS [20,21] This equation is based on Wertheim’s first order thermodynamic perturbation theory. It establishes a well defined model as fluid reference, hard chain reference system (spherical segments of equal size), and modelling of the actual fluid is performed by adding perturbations to the reference system. Thus, the Helmholtz ~, is written as the sum of the ideal-gas contribution, free energy, a
3. Modelling
~id , a hard-chain term, a ~hc , a contribution for the dispersive a
3.1. Peng–Robinson EoS [19]
~ , and several terms for associating, dipolar and attraction, a quadrupolar interactions. In this work:
dis
Generally, cubic equations predict reasonably well the phase behaviour of the binary systems while the correct modelling of the density requires the introduction of a correction factor; however, its simplicity makes them preferred in many engineering applications. For pure compounds, only critical point coordinates (Pc, Tc, Vc) and acentric factor value, v, are required. To mixtures a binary interaction parameter, kij, is introduced. The classical forms
~¼a ~id þ a ~hc þ a ~dis a
(6)
In this model, three parameters are needed for non-polar pure compounds: the segment number, m, the segment diameter, s , and the segment energy parameter, e. Generally, these parameters are obtained from vapour pressures and liquid densities and they
Table 1 Chemical purity, densities at T = 298.15 K and atmospheric pressure, and vapour pressures at T = 308.15 K. Chemical
Dibromomethane
Supplier
Aldrich Chemistry Bromotrichloromethane Aldrich Chemistry Bromochloromethane Aldrich Chemistry n-Heptane Fluka AG Buchs
Min. purity specified by supplier (mass%) Purification method
103 r (kg m3)
P (kPa)
Experimental Literature
Experimental Literature
>99.0
None
2.47861
>99.0
None
2.00214
2.48420 [23] 2.012 [24]
>99.0
None
>99.5
None
9.932
9.538 [18]
8.428
8.437 [18]
1.92171
1.92300 [23] 31.050
0.67960
0.67960 [22]
30.294 [18] 9.835 [22]
Standard uncertainties u for density are u(T) = 0.005 K, u(r) = 2 102 kg m3, and for pressure u(T) = 0.05 K, u(P) = 45 Pa.
9.916
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3
Table 2 Vapour–liquid equilibrium data for pressure P, liquid-phase mole fraction x1, vapour-phase mole fraction y1, activity coefficients, g1 and g 2, and molar excess Gibbs energies GEm , of the binary systems determined in this work at T = 308.15 K. y1
g1
g2
GEm (J mol1)
Dibromomethane (1) + n-heptane (2) 12.203 0.1407 13.032 0.2310 13.679 0.3402 13.997 0.4391 14.083 0.5448 14.067 0.5780 14.093 0.5796 14.049 0.6383 14.032 0.6482 13.966 0.6815 13.874 0.7227 13.614 0.7977 13.469 0.8246 13.173 0.8696 12.739 0.9124 11.755 0.9610
0.2854 0.3807 0.4616 0.5131 0.5555 0.5663 0.5676 0.5887 0.5900 0.6069 0.6175 0.6442 0.6712 0.7005 0.7433 0.8274
2.492 2.160 1.866 1.644 1.443 1.385 1.387 1.302 1.284 1.250 1.191 1.105 1.102 1.067 1.044 1.018
1.021 1.055 1.122 1.221 1.383 1.454 1.456 1.606 1.644 1.733 1.923 2.408 2.540 3.043 3.758 5.244
376 563 739 847 890 887 892 871 863 839 790 660 625 516 397 210
Bromotrichloromethane (1) + n-heptane (2) 9.999 0.1003 10.048 0.2018 10.027 0.2853 10.011 0.3934 9.949 0.4648 9.874 0.5150 9.781 0.5709 9.706 0.6080 9.715 0.6150 9.577 0.6769 9.487 0.7103 9.421 0.7289 9.256 0.7877 9.127 0.8322 8.904 0.8985
0.1067 0.2049 0.2810 0.3738 0.4347 0.4767 0.5236 0.5576 0.5610 0.6147 0.6452 0.6627 0.7208 0.7661 0.8471
1.261 1.209 1.170 1.127 1.103 1.083 1.063 1.055 1.050 1.030 1.021 1.015 1.004 0.996 0.996
1.001 1.009 1.017 1.042 1.060 1.075 1.095 1.105 1.117 1.153 1.172 1.183 1.229 1.284 1.354
62 117 146 185 196 195 190 184 187 170 157 145 121 100 69
Bromotrichloromethane (1) + dibromomethane (2) 10.076 0.0252 10.182 0.0585 10.234 0.0824 10.299 0.1494 10.330 0.2256 10.344 0.2607 10.359 0.2972 10.361 0.3263 10.336 0.3583 10.272 0.4204 10.237 0.4544 10.122 0.5279 9.982 0.593 9.731 0.6711 9.461 0.7426 9.053 0.837 8.728 0.9007
0.0445 0.0776 0.1042 0.154 0.2285 0.2615 0.2966 0.3121 0.3429 0.3927 0.4163 0.4683 0.5179 0.5778 0.653 0.7696 0.8595
2.109 1.602 1.534 1.259 1.240 1.230 1.225 1.175 1.172 1.137 1.112 1.064 1.034 0.993 0.986 0.987 0.988
0.994 1.004 1.006 1.031 1.036 1.040 1.044 1.065 1.065 1.083 1.103 1.148 1.190 1.259 1.285 1.289 1.245
34 81 104 155 195 213 232 243 250 258 260 251 232 182 139 78 28
Bromotrichloromethane (1) + bromochloromethane (2) 30.244 0.0392 29.297 0.0881 28.566 0.1245 27.202 0.1918 26.046 0.2536 24.575 0.3271 23.834 0.3664 22.784 0.4174 21.891 0.4642 21.144 0.4983 19.809 0.5625 18.923 0.6026 17.725 0.6583 17.023 0.6859 15.966 0.7318 14.862 0.7744 13.213 0.8383 11.562 0.8953 9.376 0.9694
0.0000 0.0130 0.0252 0.0399 0.0682 0.0920 0.1254 0.1448 0.1703 0.1916 0.2105 0.2497 0.2781 0.3224 0.3450 0.3896 0.4441 0.5394 0.6488
1.081 0.979 1.070 1.132 1.106 1.105 1.090 1.091 1.062 1.050 1.035 1.028 1.022 1.009 1.003 1.006 1.005 0.992 0.993
1.005 1.009 1.010 1.012 1.022 1.031 1.045 1.049 1.068 1.077 1.100 1.113 1.139 1.150 1.178 1.201 1.221 1.260 1.336
13 17 44 85 109 137 147 165 161 157 155 156 152 129 118 112 94 43 5
P (kPa)
x1
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Table 2 (Continued) P (kPa)
x1
Dibromomethane (1) + bromochloromethane (2) 29.888 0.0477 28.515 0.1026 27.411 0.1524 26.084 0.2147 25.381 0.2516 23.799 0.3318 23.041 0.3744 21.694 0.4420 20.873 0.4824 20.082 0.5205 18.858 0.5758 17.079 0.6589 16.540 0.6822 15.441 0.7368 14.738 0.7735 13.348 0.8471 12.553 0.8857 11.387 0.9412
y1
g1
g2
GEm (J mol1)
0.0136 0.0342 0.0555 0.0839 0.1040 0.1427 0.1667 0.2049 0.2343 0.2604 0.3110 0.3894 0.4203 0.4829 0.5340 0.6351 0.7059 0.8229
0.850 0.948 0.997 1.018 1.049 1.024 1.026 1.007 1.015 1.007 1.021 1.013 1.023 1.016 1.022 1.006 1.006 1.002
0.998 0.989 0.985 0.982 0.981 0.986 0.992 1.000 0.999 1.002 0.992 0.991 0.978 0.984 0.983 1.034 1.048 1.114
26 38 33 26 6 3 12 7 18 12 22 13 21 19 34 26 28 20
Standard uncertainties u are u(T) = 0.05 K, u(P) = 45 Pa, u(x1,y1) = 0.0004.
Table 3 Coefficients Ai of the Eq. (8), standard deviations in the pressure s (P), vapour-phase mole fraction s (y), and molar excess Gibbs energy values of the equimolar mixture, GEm ðx1 ¼ 0:5Þ, for the studied systems. System
A1
A2
A3
A4
Dibromomethane (1) + n-heptane (2) Bromotrichloromethane (1) + n-heptane (2) Bromotrichloromethane (1) + dibromomethane (2) Bromotrichloromethane (1) + bromochloromethane (2) Dibromomethane (1) + bromochloromethane (2)
1.3728 0.3031 0.3962 0.2779 0.0185
0.3040 0.0011 0.1200 0.0001 0.0178
0.0698 0.0788 0.1961 0.0210 0.0290
0.0523 0.0613 0.1668
0.2947 0.1270 0.1735
0.2334
0.0706
n
s ðXÞ ¼ S
N j¼1 X j;exp
Xj;cal
2
=N
o1=2
s (P) (Pa)
s (y)
GEm ðx1 ¼ 0:5Þ (J mol1)
8 9 13 21 21
0.0052 0.0062 0.0042 0.0044 0.0023
889.9 1.5 194.7 2.3 250.8 3.3 156.5 2.6 17.5 2.5
; N: total number of points and X: P or y.
provide an accurate representation for both VLE and volumetric properties. For mixtures, the Lorentz–Berthelot mixing rules are applied where the binary interaction parameter, kij, corrects the dispersion term of unlike molecules:
eij ¼
A5
pffiffiffiffiffiffiffi 1 ei ej ð1 kij Þ; s ij ¼ s i þ s j 2
Over cubic equations, PC-SAFT EoS has the advantages that their parameters have physical meaning therefore may estimate parameters within a homologous series.
(7)
[(Fig._1)TD$IG] [(Fig._2)TD$IG]
Fig. 1. Vapour–liquid equilibrium of the dibromomethane (1) + n-heptane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
Fig. 2. Vapour–liquid equilibrium of the bromotrichloromethane (1) + n-heptane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
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5
Table 4 Experimental azeotropic coordinates, Paz and x1,az, and deviations between these values and those calculated using PR and PC-SAFT EoS for studied systems in this work. System
T (K)
Paz (kPa)
x1,az
MRD (Paz) (%) PR/PC-SAFT
AAD (xaz) PR/PC-SAFT
Dibromomethane (1) + n-heptane (2) Bromotrichloromethane (1) + n-heptane (2) Bromochloromethane (1) + n-heptane (2)
308.15 308.15 298.15 313.15 308.15
14.083 10.044 19.87 [11] 37.46 [11] 10.355
0.5567 0.2584 0.924 [11] 0.934 [11] 0.2581
1.10/0.32 0.53/0.87 0.10/2.82 1.25/1.47 0.51/0.61
0.0443/0.0291 0.1590/0.0119 0.0390/0.0059 0.0380/0.0001 0.0714/0.1461
Bromotrichloromethane (1) + dibromomethane (2) MRDðPaz Þ ¼ 100j
Paz;exp Paz;EoS j; Paz;exp
AADðxaz Þ ¼ jxaz;exp xaz;EoS j.
[(Fig._3)TD$IG]
[(Fig._4)TD$IG]
Fig. 3. Vapour–liquid equilibrium of the bromochloromethane (1) + n-heptane (2) binary system. Points, experimental data [11]; solid lines, calculated data using PCSAFT EoS; dash lines, calculated data using PR EoS.
Fig. 4. Vapour–liquid equilibrium of the bromotrichloromethane (1) + dibromomethane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
[(Fig._5)TD$IG]
[(Fig._6)TD$IG]
Fig. 5. Vapour–liquid equilibrium of the bromotrichloromethane (1) + bromochloromethane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
Fig. 6. Vapour–liquid equilibrium of the dibromomethane (1) + bromochloromethane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
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[(Fig._7)TD$IG]
Fig. 7. Molar excess Gibbs energies, GEm , of the studied systems in this work. Points, experimental data; solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS. (a): dibromomethane (1) + n-heptane (2) (*), bromotrichloromethane (1) + n-heptane (2) ( [TD$INLE]), bromochloromethane (1) + n-heptane (2) at T = 298.15 K (
[TD$INLE]) [11] and T = 313.15 K (
[TD$INLE]) [11], (b): bromotrichloromethane (1) + dibromomethane (2) (
dibromomethane (1) + bromochloromethane (2) (
[TD$INLE]), bromotrichloromethane (1) + bromochloromethane (
[TD$INLE]).
4. Results and discussion 4.1. Experimental data Table 2 lists the experimental VLE data (P x1 y1), the activity coefficients (g 1, g 2), and the molar excess Gibbs energies (GEm ) for the studied systems at T = 308.15 K. GEm were calculated by fitting of the experimental P x1 data with the Redlich–Kister equation. Xn GEm ¼ A ð2x1 1Þði1Þ i¼1 i fx1 ð1 x1 ÞRTg
(8)
The values of the coefficients Ai determined by least-squares analysis, the standard deviations in the pressure, s (P), and vapour phase mole fraction, s (y), and the molar excess Gibbs energies at equimolar composition, GEm ðx1 ¼ 0:5Þ, are given in Table 3. The variation of the Gibbs energy with the pressure of the pure compounds and the vapour-phase nonideality was considered in
terms of the liquid molar volumes and the molar second virial coefficients calculated by the method of Tsonopoulos [28,29]. In order to check the thermodynamic consistence of the experimental results, the test of Van Ness and Abbott was using [30,31]: the data are consistent if the mean absolute deviation in vapour phase composition is less than 0.01. In this paper, AAD (y) = 0.0017 0.0048, showing them to be thermodynamically consistent. Moreover, the comparison with bibliography data is not possible because the studies of these type of systems in the literature are very scarce. In fact, as far as we know, the only previous experimental results on this type of systems are those of Apelblat et al. [15] corresponding at isobaric VLE (P = 760 mm Hg) of dibromomethane + bromochloromethane system. Figs. 1–3 show the experimental VLE data of the dibromomethane + n-heptane and bromotrichloromethane + n-heptane systems at 308.15 K, this work, and bromochloromethane + nheptane system at 298.15 and 313.15 K [11]. All these systems show an azeotrope (Table 4) although the form of the corresponding VLE is
Table 5 Parameters used for modelling the studied systems with PR and PC-SAFT EoS: critical properties Tc Pc Vc, and the acentric factor v, from literature; volumetric translation in PR EoS Dnc, segment number m, segment diameter s, and segment energy parameter e/kB, from literature (n-heptane) and calculated in this work (polyhalomethanes). The temperature range covered by the experimental data Trange, and the mean relative deviations MRD (X), of both vapour pressures and density data to obtain PC-SAFT parameters for pure compounds are included.
Tc (K) Pc (MPa) Vc (m3 mol1)
v Dnc PR EoS
(103 m3 kg) M (g mol1) m s (Å) e/kB (K) Trange (K) MRD (P) (%) MRD (r) (%) References
Dibromomethane
Bromotrichloromethane
Bromochloromethane
n-Heptane
583 7.1 215.5 0.3287 0.055
603 4.650 293 0.1953 0.008
558 6.399 207 0.2144 0.008
540.13 2.736 232 0.349 0
173.835 2.1268 3.5580 339.80 273–363 0.71 0.26 This work [16,32]
198.274 2.1076 3.9897 336.33 298–308 0.38 0.27 This work [18,32]
129.384 2.1995 3.4353 304.43 273–333 1.19 0.13 This work, [10,11,17,32,33]
100.202 3.4831 3.8049 238.40 182–623 0.34 2.1 [20,22]
[TD$INLE]),
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7
Table 6 Modelization for studied systems in this work using PR and PC-SAFT EoS. Binary interaction parameters kij, and deviations in phase and volumetric properties. AAD (y) PR/PC-SAFT
MRD (r) (%) PR/PC-SAFT
1.96/1.17
0.0222/0.0163
0.011/0.004 0.013/0.022 0.001/0.015
0.56/0.54 1.31/1.91 [11] 1.50/1.39
0.0068/0.0060 0.0094/0.0127 [11] 0.0107/0.0101
Bromotrichloromethane (1) + bromochloromethane (2)
0.017/0.018
1.92/0.41
0.0079/0.0039
Dibromomethane (1) + bromochloromethane (2)
0.008/0
2.19/1.78
0.86/0.32 [14] 1.06/0.36 [13] 0.47/0.50 [14] 1.02/0.35 [10] 0.38/0.53 [14] 0.30/0.44 [12] 0.32/0.48 [14] 0.27/0.49 [12] 0.27/0.12 [12]
System
kij PR/PC-SAFT
MRD (P) (%) PR/PC-SAFT
Dibromomethane (1) + n-heptane (2)
0.017/0.026
Bromotrichloromethane (1) + n-heptane (2) Bromochloromethane (1) + n-heptane (2) Bromotrichloromethane (1) + dibromomethane (2)
MRD (Tb) (%) PR/PC-SAFT
0.36/0.43 [15]
0.0125/0.0067 0.0170/0.0090 [15]
100 N X j;exp X j;EoS S j j ; X = P, Tb or r. N j¼1 X j;exp 1 N AADðyÞ ¼ Sj¼1 jyj;exp yj;EoS j ; N: total number of points. N MRDðXÞ ¼
very different. Thus, it can be seen that the dibromomethane + nheptane system, where vapour pressures for the pure compounds are very similar, presents a phase behaviour far from ideality appearing the azeotropic point near to equimolar composition. Unlike, for x1 > x1,az in the system containing bromochloromethane and for x1 < x1,az in the system with bromotrichloromethane, twophase region is reduced to a line and the mixtures behave like a pure fluid. Particularly interesting is the latter case because of the position of the azeotrope in this system. Furthermore, bromotrichloromethane + n-heptane and bromotrichloromethane + dibromomethane systems show similar phase behaviour between them (Figs. 2 and 4). VLE shape and the azeotropic coordinates (Table 4) are similar although in the haloalkane + haloalkane system a twophase region is observed at x1 < x1,az. The high ideality of bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane systems can be seen in Figs. 5 and 6, respectively. Fig. 7a and b shows the molar excess Gibbs energies for the
system, and very small for dibromomethane + bromochloromethane as expected considering the similarity between the molecules involved. Also, bromotrichloromethane + bromochloromethane system present a non-negligible value, 1
GEm ðx1 ¼ 0:5Þ ¼ 156:5Jmol
, although its phase behaviour is very
close to ideality. The sign of GEm for this system points to an important contribution to the entropic effect in the mixing process. 4.2. Modelling
studied systems. GEm is maximum for dibromomethane + n-heptane
Table 5 shows the parameters used in the PR and PC-SAFT modelling of the studied systems. The critical parameters and the acentric factor for all compounds, and the PC-SAFT parameters for n-heptane pure have been taken from the literature [22,32]. To improve the prediction of the density of the studied systems using PR EoS, a volumetric translation parameter, Dnc, for each polyhalomethane is introduced. They are calculated from the densities of the pure compounds. PC-SAFT parameters of the pure polyhalomethanes have been calculated using saturation pressures
[(Fig._8)TD$IG]
[(Fig._9)TD$IG]
Fig. 8. Deviations between the experimental (this work and [11]) and calculated (PR and PC-SAFT EoS) vapour–liquid equilibrium of polyhalomethane + n-heptane binary systems: dibromomethane (*), bromotrichloromethane ($), bromochloromethane at T = 298.15 K (~) and T = 313.15 K (!). Full symbols, PC-SAFT EoS; empty symbols, PR EoS.
Fig. 9. Deviations between the experimental (this work) and calculated (PR and PCSAFT EoS) vapour–liquid equilibrium of polyhalomethane + polyhalomethane binary systems: bromotrichloromethane (1) + dibromomethane (2) (*), bromotrichloromethane (1) + bromochloromethane (2) ($), dibromomethane (1) + bromochloromethane (2) (&). Full symbols, PC-SAFT EoS; empty symbols, PR EoS.
8
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and densities (this work and literature) so as to minimize the objective function (OF): 2 !2 !2 3 Psat Psat r ri;cal n i;exp i;exp i;cal 5 (9) OF ¼ Si¼1 4 þ ri;exp Psat i;exp
(r) = 0.55%. For PC-SAFT EoS: MRD (P) = 1.20%, AAD (y) = 0.0093 MRD (r) = 0.38%. However, the prediction of the azeotropic coordinates and the molar excess Gibbs energy values using PCSAFT are better than PR EoS. In this work, computations of different properties with PR and PC-SAFT EoS were performed using VLXE software [34].
Table 5 also includes the mean relative deviations, MRD (X), to compare experimental data (vapour pressures and density) and calculated using PC-SAFT EoS of pure compounds. To model our binary systems we have used the classical rules of mixtures. Binary interaction parameters, kij (Table 6), have been calculated by minimizing the above OF, Eq. (9), using this work and literature data [10–14]. A good agreement between experimental data and those calculated with both PR and PC-SAFT EoS for all studied systems is observed (Table 6 and Figs. 1–6). Noted that PC-SAFT EoS predicts well the thermodynamic behaviour of the dibromomethane + bromochloromethane system with a binary interaction parameter kij = 0, which agrees with the high ideality of the system and its molar excess Gibbs energy value. For this system, similar deviations between our experimental data and the isobars data published by Apelblat et al. [15] with those calculated by EoS are observed (Table 6). Therefore we can say that our data seem to be consistent with those of the literature. The mean relative deviations obtained are MRD (P) = 1.57%, AAD (y) = 0.0116 and MRD (r) = 0.55% for Peng–Robinson EoS and MRD (P) = 1.20%, AAD (y) = 0.0093 MRD (r) = 0.38% for PC-SAFT. No trends are observed in deviations of pressure with composition (Figs. 8 and 9). Nevertheless, the azeotropes and molar excess Gibbs energies modelling is better with PC-SAFT EoS especially for halomethane + halomethane systems (Table 4 and Fig. 7a and b).
Acknowledgement
5. Conclusions The isothermal vapour–liquid equilibria (VLE) at T = 308.15 K have been measured and the molar excess Gibbs energies, GEm , have been calculated for the next binary systems: dibromomethane + nheptane, bromotrichloromethane + n-heptane, bromotrichloromethane + dibromomethane, bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane. The study was completed including the bromochloromethane + n-heptane system whose VLE was determined previously by us. All systems containing n-heptane and the bromotrichloromethane + dibromomethane system exhibit azeotrope while the remaining systems present a phase behaviour near ideality. Nevertheless, the GEm values for bromotrichloromethane + bromochloromethane system indicate a significant entropic contribution. Also we performed a comprehensive bibliographic search of vapour–liquid equilibrium and densities of the pure compounds and systems included in this work. From this work and literature experimental data, phase and volumetric behaviour have been modelled. For this, we have used a cubic EoS and other EoS based on perturbation theory obtaining a good agreement for both. For Peng–Robinson EoS, the mean relative deviations for the studied properties are MRD (P) = 1.57%, AAD (y) = 0.0116 and MRD
The authors gratefully acknowledge financial support received from Gobierno de Arago’n (E32, 2011–2013). References [1] H.R. Chand, Synlett 15 (2009) 2545–2546. [2] S.G. Newman, C.S. Bryan, D. Perez, M. Lautens, Synthesis 2 (2011) 342–346. [3] Y. Al-Jasem, M. Barkhad, M. Al Khazali, H.P. Butt, N.A. El-Khwass, M. Al Azani, B. Al Hindawi, T. Thiemann, J. Chem. Res. 2 (2014) 80–84. [4] F. Cross, Synlett 14 (2010) 2204–2205. [5] J. Sun, S. Gong, Q. Sun, Adv. Mater. Res. 830 (2014) 230–233. [6] L. Muthusubramanian, R.B. Mitra, J. Soc. Leather Technol. Chem. 89 (2005) 34– 35. [7] P. Gomes, M.I. Santos, M.J. Trigo, R. Castanheiro, R. Moreira, Synth. Commun. 10 (2003) 1683–1693. [8] J. Abacia, P.G. Toral, A.I. Martín-García, G. Martínez, N.W. Tomkins, E. MolinaAlcaide, C.J. Newbold, D.R. Yañez-Ruiz, J. Dairy Sci. 95 (2012) 2027–2036. [9] J.J. Su, B.Y. Liu, Y.C. Chang, J. Environ. Sci. Health B 39 (2004) 889–902. [10] M. Artal, J. Muñoz Embid, I. Velasco, S. Otín, J. Chem. Thermodyn. 27 (1995) 475–480. [11] M. Artal, J. Muñoz Embid, I. Velasco, S. Otín, J. Solut. Chem. 26 (1997) 355–368. [12] J. Boquera, M. Artal, I. Velasco, S. Otín, J. Chem. Thermodyn. 30 (1998) 161–166. [13] A. Przybyla, M. Chorazewski, E. Zorebski, W. Marczak, Int. J. Thermophys. 32 (2011) 852–866. [14] L. Martínez-Baños, C. Rivas, J. Muñoz Embid, S. Otín, J. Chem. Eng. Data 58 (2013) 248–256. [15] A. Apelblat, J. Wisniak, A. Tamir, J. Chem. Eng. Data 26 (1981) 144–147. [16] M. Frenkel, Thermodynamics Source Database, NIST Standard Reference Database Number 69, in: P.J. Linstrom, W.G. Mallard (Eds.), National Institute of Standards and Technology, Gaithersburg, MD, 2003, pp. 20899. http:// webbook.nist.gov. [17] V. Gil-Hernández, P. García-Giménez, S. Otín, M. Artal, I. Velasco, J. Chem. Thermodyn. 37 (2005) 7–12. [18] A.P. Kudchadker, S.A. Kudchadker, R.P. Shukla, P.R. Patnaik, J. Phys. Chem. Ref. Data 8 (1979) 499–517. [19] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fund. 15 (1976) 59–64. [20] J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 40 (2001) 1244–1260. [21] J. Gross, G. Sadowski, Ind. Eng. Chem. Res. 41 (2002) 5510–5515. [22] M.L. Lemmon, REFPROP 9.0, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2010. [23] TRC Thermodynamic Tables, Thermodynamics Research Center, The Texas A&M University System, College Station, TX, 1994. [24] CRC Handbook of Chemistry and Physics, 89th ed., CRC Press/Taylor and Francis, Boca Raton, FL, 2009. [25] J. Muñoz Embid, M.A. Gallardo, J. Fernández, I. Velasco, S. Otín, An. Quím. 87 (1991) 867–872. [26] C. Berro, M. Rogalski, A. Peneloux, Fluid Phase Equilibr. 8 (1982) 55–73. [27] J.O. Valderrama, Ind. Eng. Chem. Res. 42 (2003) 1603–1618. [28] C. Tsonopoulos, AIChE J. 21 (1972) 827–829. [29] C. Tsonopoulos, AIChE J. 20 (1974) 263–272. [30] H.C. Van Ness, M.M. Abbott, Classical Thermodynamics of Non-electrolyte Solutions With Applications to Phase Equilibria, McGraw Hill, New York, 1982. [31] Aa. Fredenslund, J. Gmehling, P. Rasmussen, Vapour–Liquid Equilibria Using Unifac: A Group-Contribution Method, Elsevier, Amsterdam, 1977. [32] InfoTherm, Release 3.2, FIZ Chemie Berlin, 2013, 2015. [33] M. Chorazewski, J. Troncoso, J. Jacquemin, Ind. Eng. Chem. Res. (2015) , doi: http://dx.doi.org/10.1021/ie5038903. [34] T. Laursen, VLXE ApS, Scion-DTU, Diplomvej, Denmark, 2012.
Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Vapour–liquid equilibrium at T = 308.15 K for binary systems: Dibromomethane + n-heptane, bromotrichloromethane + n-heptane, bromotrichloromethane + dibromomethane, bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane. Experimental data and modelling Lourdes Martínez-Baños, José Muñoz Embid, Santos Otín, Manuela Artal * Departamento de Química Física, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
A R T I C L E I N F O
A B S T R A C T
Article history: Received 26 January 2015 Received in revised form 9 March 2015 Accepted 10 March 2015 Available online 14 March 2015
In this paper, the isothermal vapour–liquid equilibrium (VLE) at T = 308.15 K have been measured for liquid binary systems dibromomethane + n-heptane, bromotrichloromethane + n-heptane, bromotrichloromethane + dibromomethane, bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane by a dynamic method. The VLE data have been reduced using the Redlich– Kister equation taking into consideration the vapour phase imperfection in terms of 2nd molar virial
Keywords: Vapour–liquid equilibrium Polyhalomethanes Modelling Peng–Robinson PC-SAFT
coefficients and molar excess Gibbs energies, GEm , have been calculated. The experimental GEm is positive for all systems presenting the greatest value for dibromomethane + n-heptane and a negligible value for dibromomethane + bromochloromethane system. From our experimental data and those reported in the literature, phase and volumetric behaviour of the binary systems containing dibromomethane, bromochloromethane, bromotrichloromethane or n-heptane have been modelled. Two equations of state, EoS, of different formulation have been used obtaining a good agreement for all systems. The mean relative deviations for the studied properties are MRD (P) = 1.57%, AAD (y) = 0.0116 and MRD (r) = 0.55% for Peng–Robinson EoS, and MRD (P) = 1.20%, AAD (y) = 0.0093 and MRD (r) = 0.38% for PC-SAFT EoS. ã 2015 Elsevier B.V. All rights reserved.
1. Introduction Classical application of polyhaloalkanes as fire extinguisher media has been restricted because their effect on the ozone layer. At present they are used mainly in various industrial processes as many organic synthesis reactions use polyalkanes similar to methane as a reaction media. Dibromomethane is one of the compounds included in the so-called Lombardo’s reagent (Zn/ Br2CH2/TiCl4) used in methylenation of ketones and ketenes [1]; it is also used as solvent of fats and resins. Bromotrichloromethane is used, for example, in chlorination reactions (Appel reactions) as an alternative of carbon tetrachloride given the high toxicity of the latter, in esterification and silylation reactions, and to prepare
* Corresponding author. Tel.: +34 876553765. E-mail address: [email protected] (M. Artal). http://dx.doi.org/10.1016/j.fluid.2015.03.023 0378-3812/ ã 2015 Elsevier B.V. All rights reserved.
Wittig reagents [2–5]. Finally, bromochloromethane is a reactant in the synthesis of biocides and chloromethylesters (N-blocked aminoacids and dipeptides) [6,7]. Also, it has been observed that bromochloromethane is an agent that reduces methane generation: increases the efficiency of the digestive process in ruminants (lower methane generation and greater milk production) [8] and inhibits the production of biogas when it is added to the piggery wastewater [9]. Then taking also into account that systems containing this type of products are not very studied in the literature [10–15] and that polyhalomethanes are used as analogues of methane derivatives with lower toxicity, it is convenient to have models that enable predicting in a simple way their behaviour under different conditions. Following our research on the halogen–halogen interactions, we report here the experimental isothermal vapour–liquid equilibrium (VLE) at T = 308.15 K for dibromomethane + n-heptane, bromotrichloromethane + n-heptane, bromotrichloromethane +
2
L. Martínez-Baños et al. / Fluid Phase Equilibria 395 (2015) 1–8
dibromomethane, bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane systems.
for this equation are:
Moreover, molar excess Gibbs energies, GEm , are calculated by fitting of the experimental P x1 data with the Redlich–Kister equation. This study is completed with our previous results on the VLE of bromochloromethane + n-heptane system [11]. Finally, phase equilibria experimental data from this work along with VLE and volumetric data from literature for pure compounds and mixtures [10–18], are used to modelling the phase and volumetric behaviour of these systems with Peng–Robinson (PR) [19] and PCSAFT [20,21] equations of state.
P¼
RT aaðT r ; vÞ V b V ðV þ bÞ þ bðV bÞ
(1)
RT 2:5 RT c a ¼ 0:45724 c ; b ¼ 0:07780 Pc Pc h
aðT r ; vÞ ¼ 1 þ m 1 T 0:5 r
i2
(2)
;m
¼ 0:37464 1:54226v 0:26992v2
(3)
2. Experimental 2.1. Chemicals The specifications, density and vapour pressure of the chemicals are shown in Table 1. We compare the measured densities and vapour pressures of the products with the literature values. 2.2. Apparatus and procedure vapour–liquid equilibrium data were taken at constant temperature in a flow system as described in Muñoz Embid et al. [25] using a dynamic still designed by Berro et al. [26]. The temperature T inside the equilibrium cell was measured with a precision of 0.01 K by means of a Digitec digital thermometer (Digitec Corp.) Model 5831. The pressure P was measured by means of a Digiquartz Transmitter of Paroscientific Inc., Model 1015A, calibrated in the pressure range 0–100 kPa. The accuracy of the pressure measurements is 0.01%. Liquid and vapour mole fractions, x1 and y1, respectively, were determined by densimetric analysis using an digital density analyser Anton Paar Model DSA-5000M automatically thermostated by built-in solid state thermostat. The uncertainty of the composition measurements was estimated to be 0.0002 mole fraction.
Various modifications of the PR EoS have been proposed in literature with the aim of improving the experimental results [27]: (i) changes in the expression of the temperature-dependent function, a(Tr,v), for polar fluids; (ii) introduction of a volume correction, Dnc, which improves volume predictions without changing the VLE conditions; and (iii) the use of different mixing rules. In this work, we have used volumetric translation for polyhalomethanes and the classic one-parameter van der Waals mixing rule, where kij is the binary interaction parameter: a ¼ Si Sj xi xj aij ; b ¼ Si Sj xi xj bij
aij ¼
(4)
pffiffiffiffiffiffiffiffi 1 ai aj ð1 kij Þ; bij ¼ ðbi þ bj Þ 2
(5)
3.2. PC-SAFT EoS [20,21] This equation is based on Wertheim’s first order thermodynamic perturbation theory. It establishes a well defined model as fluid reference, hard chain reference system (spherical segments of equal size), and modelling of the actual fluid is performed by adding perturbations to the reference system. Thus, the Helmholtz ~, is written as the sum of the ideal-gas contribution, free energy, a
3. Modelling
~id , a hard-chain term, a ~hc , a contribution for the dispersive a
3.1. Peng–Robinson EoS [19]
~ , and several terms for associating, dipolar and attraction, a quadrupolar interactions. In this work:
dis
Generally, cubic equations predict reasonably well the phase behaviour of the binary systems while the correct modelling of the density requires the introduction of a correction factor; however, its simplicity makes them preferred in many engineering applications. For pure compounds, only critical point coordinates (Pc, Tc, Vc) and acentric factor value, v, are required. To mixtures a binary interaction parameter, kij, is introduced. The classical forms
~¼a ~id þ a ~hc þ a ~dis a
(6)
In this model, three parameters are needed for non-polar pure compounds: the segment number, m, the segment diameter, s , and the segment energy parameter, e. Generally, these parameters are obtained from vapour pressures and liquid densities and they
Table 1 Chemical purity, densities at T = 298.15 K and atmospheric pressure, and vapour pressures at T = 308.15 K. Chemical
Dibromomethane
Supplier
Aldrich Chemistry Bromotrichloromethane Aldrich Chemistry Bromochloromethane Aldrich Chemistry n-Heptane Fluka AG Buchs
Min. purity specified by supplier (mass%) Purification method
103 r (kg m3)
P (kPa)
Experimental Literature
Experimental Literature
>99.0
None
2.47861
>99.0
None
2.00214
2.48420 [23] 2.012 [24]
>99.0
None
>99.5
None
9.932
9.538 [18]
8.428
8.437 [18]
1.92171
1.92300 [23] 31.050
0.67960
0.67960 [22]
30.294 [18] 9.835 [22]
Standard uncertainties u for density are u(T) = 0.005 K, u(r) = 2 102 kg m3, and for pressure u(T) = 0.05 K, u(P) = 45 Pa.
9.916
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3
Table 2 Vapour–liquid equilibrium data for pressure P, liquid-phase mole fraction x1, vapour-phase mole fraction y1, activity coefficients, g1 and g 2, and molar excess Gibbs energies GEm , of the binary systems determined in this work at T = 308.15 K. y1
g1
g2
GEm (J mol1)
Dibromomethane (1) + n-heptane (2) 12.203 0.1407 13.032 0.2310 13.679 0.3402 13.997 0.4391 14.083 0.5448 14.067 0.5780 14.093 0.5796 14.049 0.6383 14.032 0.6482 13.966 0.6815 13.874 0.7227 13.614 0.7977 13.469 0.8246 13.173 0.8696 12.739 0.9124 11.755 0.9610
0.2854 0.3807 0.4616 0.5131 0.5555 0.5663 0.5676 0.5887 0.5900 0.6069 0.6175 0.6442 0.6712 0.7005 0.7433 0.8274
2.492 2.160 1.866 1.644 1.443 1.385 1.387 1.302 1.284 1.250 1.191 1.105 1.102 1.067 1.044 1.018
1.021 1.055 1.122 1.221 1.383 1.454 1.456 1.606 1.644 1.733 1.923 2.408 2.540 3.043 3.758 5.244
376 563 739 847 890 887 892 871 863 839 790 660 625 516 397 210
Bromotrichloromethane (1) + n-heptane (2) 9.999 0.1003 10.048 0.2018 10.027 0.2853 10.011 0.3934 9.949 0.4648 9.874 0.5150 9.781 0.5709 9.706 0.6080 9.715 0.6150 9.577 0.6769 9.487 0.7103 9.421 0.7289 9.256 0.7877 9.127 0.8322 8.904 0.8985
0.1067 0.2049 0.2810 0.3738 0.4347 0.4767 0.5236 0.5576 0.5610 0.6147 0.6452 0.6627 0.7208 0.7661 0.8471
1.261 1.209 1.170 1.127 1.103 1.083 1.063 1.055 1.050 1.030 1.021 1.015 1.004 0.996 0.996
1.001 1.009 1.017 1.042 1.060 1.075 1.095 1.105 1.117 1.153 1.172 1.183 1.229 1.284 1.354
62 117 146 185 196 195 190 184 187 170 157 145 121 100 69
Bromotrichloromethane (1) + dibromomethane (2) 10.076 0.0252 10.182 0.0585 10.234 0.0824 10.299 0.1494 10.330 0.2256 10.344 0.2607 10.359 0.2972 10.361 0.3263 10.336 0.3583 10.272 0.4204 10.237 0.4544 10.122 0.5279 9.982 0.593 9.731 0.6711 9.461 0.7426 9.053 0.837 8.728 0.9007
0.0445 0.0776 0.1042 0.154 0.2285 0.2615 0.2966 0.3121 0.3429 0.3927 0.4163 0.4683 0.5179 0.5778 0.653 0.7696 0.8595
2.109 1.602 1.534 1.259 1.240 1.230 1.225 1.175 1.172 1.137 1.112 1.064 1.034 0.993 0.986 0.987 0.988
0.994 1.004 1.006 1.031 1.036 1.040 1.044 1.065 1.065 1.083 1.103 1.148 1.190 1.259 1.285 1.289 1.245
34 81 104 155 195 213 232 243 250 258 260 251 232 182 139 78 28
Bromotrichloromethane (1) + bromochloromethane (2) 30.244 0.0392 29.297 0.0881 28.566 0.1245 27.202 0.1918 26.046 0.2536 24.575 0.3271 23.834 0.3664 22.784 0.4174 21.891 0.4642 21.144 0.4983 19.809 0.5625 18.923 0.6026 17.725 0.6583 17.023 0.6859 15.966 0.7318 14.862 0.7744 13.213 0.8383 11.562 0.8953 9.376 0.9694
0.0000 0.0130 0.0252 0.0399 0.0682 0.0920 0.1254 0.1448 0.1703 0.1916 0.2105 0.2497 0.2781 0.3224 0.3450 0.3896 0.4441 0.5394 0.6488
1.081 0.979 1.070 1.132 1.106 1.105 1.090 1.091 1.062 1.050 1.035 1.028 1.022 1.009 1.003 1.006 1.005 0.992 0.993
1.005 1.009 1.010 1.012 1.022 1.031 1.045 1.049 1.068 1.077 1.100 1.113 1.139 1.150 1.178 1.201 1.221 1.260 1.336
13 17 44 85 109 137 147 165 161 157 155 156 152 129 118 112 94 43 5
P (kPa)
x1
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Table 2 (Continued) P (kPa)
x1
Dibromomethane (1) + bromochloromethane (2) 29.888 0.0477 28.515 0.1026 27.411 0.1524 26.084 0.2147 25.381 0.2516 23.799 0.3318 23.041 0.3744 21.694 0.4420 20.873 0.4824 20.082 0.5205 18.858 0.5758 17.079 0.6589 16.540 0.6822 15.441 0.7368 14.738 0.7735 13.348 0.8471 12.553 0.8857 11.387 0.9412
y1
g1
g2
GEm (J mol1)
0.0136 0.0342 0.0555 0.0839 0.1040 0.1427 0.1667 0.2049 0.2343 0.2604 0.3110 0.3894 0.4203 0.4829 0.5340 0.6351 0.7059 0.8229
0.850 0.948 0.997 1.018 1.049 1.024 1.026 1.007 1.015 1.007 1.021 1.013 1.023 1.016 1.022 1.006 1.006 1.002
0.998 0.989 0.985 0.982 0.981 0.986 0.992 1.000 0.999 1.002 0.992 0.991 0.978 0.984 0.983 1.034 1.048 1.114
26 38 33 26 6 3 12 7 18 12 22 13 21 19 34 26 28 20
Standard uncertainties u are u(T) = 0.05 K, u(P) = 45 Pa, u(x1,y1) = 0.0004.
Table 3 Coefficients Ai of the Eq. (8), standard deviations in the pressure s (P), vapour-phase mole fraction s (y), and molar excess Gibbs energy values of the equimolar mixture, GEm ðx1 ¼ 0:5Þ, for the studied systems. System
A1
A2
A3
A4
Dibromomethane (1) + n-heptane (2) Bromotrichloromethane (1) + n-heptane (2) Bromotrichloromethane (1) + dibromomethane (2) Bromotrichloromethane (1) + bromochloromethane (2) Dibromomethane (1) + bromochloromethane (2)
1.3728 0.3031 0.3962 0.2779 0.0185
0.3040 0.0011 0.1200 0.0001 0.0178
0.0698 0.0788 0.1961 0.0210 0.0290
0.0523 0.0613 0.1668
0.2947 0.1270 0.1735
0.2334
0.0706
n
s ðXÞ ¼ S
N j¼1 X j;exp
Xj;cal
2
=N
o1=2
s (P) (Pa)
s (y)
GEm ðx1 ¼ 0:5Þ (J mol1)
8 9 13 21 21
0.0052 0.0062 0.0042 0.0044 0.0023
889.9 1.5 194.7 2.3 250.8 3.3 156.5 2.6 17.5 2.5
; N: total number of points and X: P or y.
provide an accurate representation for both VLE and volumetric properties. For mixtures, the Lorentz–Berthelot mixing rules are applied where the binary interaction parameter, kij, corrects the dispersion term of unlike molecules:
eij ¼
A5
pffiffiffiffiffiffiffi 1 ei ej ð1 kij Þ; s ij ¼ s i þ s j 2
Over cubic equations, PC-SAFT EoS has the advantages that their parameters have physical meaning therefore may estimate parameters within a homologous series.
(7)
[(Fig._1)TD$IG] [(Fig._2)TD$IG]
Fig. 1. Vapour–liquid equilibrium of the dibromomethane (1) + n-heptane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
Fig. 2. Vapour–liquid equilibrium of the bromotrichloromethane (1) + n-heptane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
L. Martínez-Baños et al. / Fluid Phase Equilibria 395 (2015) 1–8
5
Table 4 Experimental azeotropic coordinates, Paz and x1,az, and deviations between these values and those calculated using PR and PC-SAFT EoS for studied systems in this work. System
T (K)
Paz (kPa)
x1,az
MRD (Paz) (%) PR/PC-SAFT
AAD (xaz) PR/PC-SAFT
Dibromomethane (1) + n-heptane (2) Bromotrichloromethane (1) + n-heptane (2) Bromochloromethane (1) + n-heptane (2)
308.15 308.15 298.15 313.15 308.15
14.083 10.044 19.87 [11] 37.46 [11] 10.355
0.5567 0.2584 0.924 [11] 0.934 [11] 0.2581
1.10/0.32 0.53/0.87 0.10/2.82 1.25/1.47 0.51/0.61
0.0443/0.0291 0.1590/0.0119 0.0390/0.0059 0.0380/0.0001 0.0714/0.1461
Bromotrichloromethane (1) + dibromomethane (2) MRDðPaz Þ ¼ 100j
Paz;exp Paz;EoS j; Paz;exp
AADðxaz Þ ¼ jxaz;exp xaz;EoS j.
[(Fig._3)TD$IG]
[(Fig._4)TD$IG]
Fig. 3. Vapour–liquid equilibrium of the bromochloromethane (1) + n-heptane (2) binary system. Points, experimental data [11]; solid lines, calculated data using PCSAFT EoS; dash lines, calculated data using PR EoS.
Fig. 4. Vapour–liquid equilibrium of the bromotrichloromethane (1) + dibromomethane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
[(Fig._5)TD$IG]
[(Fig._6)TD$IG]
Fig. 5. Vapour–liquid equilibrium of the bromotrichloromethane (1) + bromochloromethane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
Fig. 6. Vapour–liquid equilibrium of the dibromomethane (1) + bromochloromethane (2) binary system at T = 308.15 K. Points, experimental data (this work); solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS.
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L. Martínez-Baños et al. / Fluid Phase Equilibria 395 (2015) 1–8
[(Fig._7)TD$IG]
Fig. 7. Molar excess Gibbs energies, GEm , of the studied systems in this work. Points, experimental data; solid lines, calculated data using PC-SAFT EoS; dash lines, calculated data using PR EoS. (a): dibromomethane (1) + n-heptane (2) (*), bromotrichloromethane (1) + n-heptane (2) ( [TD$INLE]), bromochloromethane (1) + n-heptane (2) at T = 298.15 K (
[TD$INLE]) [11] and T = 313.15 K (
[TD$INLE]) [11], (b): bromotrichloromethane (1) + dibromomethane (2) (
dibromomethane (1) + bromochloromethane (2) (
[TD$INLE]), bromotrichloromethane (1) + bromochloromethane (
[TD$INLE]).
4. Results and discussion 4.1. Experimental data Table 2 lists the experimental VLE data (P x1 y1), the activity coefficients (g 1, g 2), and the molar excess Gibbs energies (GEm ) for the studied systems at T = 308.15 K. GEm were calculated by fitting of the experimental P x1 data with the Redlich–Kister equation. Xn GEm ¼ A ð2x1 1Þði1Þ i¼1 i fx1 ð1 x1 ÞRTg
(8)
The values of the coefficients Ai determined by least-squares analysis, the standard deviations in the pressure, s (P), and vapour phase mole fraction, s (y), and the molar excess Gibbs energies at equimolar composition, GEm ðx1 ¼ 0:5Þ, are given in Table 3. The variation of the Gibbs energy with the pressure of the pure compounds and the vapour-phase nonideality was considered in
terms of the liquid molar volumes and the molar second virial coefficients calculated by the method of Tsonopoulos [28,29]. In order to check the thermodynamic consistence of the experimental results, the test of Van Ness and Abbott was using [30,31]: the data are consistent if the mean absolute deviation in vapour phase composition is less than 0.01. In this paper, AAD (y) = 0.0017 0.0048, showing them to be thermodynamically consistent. Moreover, the comparison with bibliography data is not possible because the studies of these type of systems in the literature are very scarce. In fact, as far as we know, the only previous experimental results on this type of systems are those of Apelblat et al. [15] corresponding at isobaric VLE (P = 760 mm Hg) of dibromomethane + bromochloromethane system. Figs. 1–3 show the experimental VLE data of the dibromomethane + n-heptane and bromotrichloromethane + n-heptane systems at 308.15 K, this work, and bromochloromethane + nheptane system at 298.15 and 313.15 K [11]. All these systems show an azeotrope (Table 4) although the form of the corresponding VLE is
Table 5 Parameters used for modelling the studied systems with PR and PC-SAFT EoS: critical properties Tc Pc Vc, and the acentric factor v, from literature; volumetric translation in PR EoS Dnc, segment number m, segment diameter s, and segment energy parameter e/kB, from literature (n-heptane) and calculated in this work (polyhalomethanes). The temperature range covered by the experimental data Trange, and the mean relative deviations MRD (X), of both vapour pressures and density data to obtain PC-SAFT parameters for pure compounds are included.
Tc (K) Pc (MPa) Vc (m3 mol1)
v Dnc PR EoS
(103 m3 kg) M (g mol1) m s (Å) e/kB (K) Trange (K) MRD (P) (%) MRD (r) (%) References
Dibromomethane
Bromotrichloromethane
Bromochloromethane
n-Heptane
583 7.1 215.5 0.3287 0.055
603 4.650 293 0.1953 0.008
558 6.399 207 0.2144 0.008
540.13 2.736 232 0.349 0
173.835 2.1268 3.5580 339.80 273–363 0.71 0.26 This work [16,32]
198.274 2.1076 3.9897 336.33 298–308 0.38 0.27 This work [18,32]
129.384 2.1995 3.4353 304.43 273–333 1.19 0.13 This work, [10,11,17,32,33]
100.202 3.4831 3.8049 238.40 182–623 0.34 2.1 [20,22]
[TD$INLE]),
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7
Table 6 Modelization for studied systems in this work using PR and PC-SAFT EoS. Binary interaction parameters kij, and deviations in phase and volumetric properties. AAD (y) PR/PC-SAFT
MRD (r) (%) PR/PC-SAFT
1.96/1.17
0.0222/0.0163
0.011/0.004 0.013/0.022 0.001/0.015
0.56/0.54 1.31/1.91 [11] 1.50/1.39
0.0068/0.0060 0.0094/0.0127 [11] 0.0107/0.0101
Bromotrichloromethane (1) + bromochloromethane (2)
0.017/0.018
1.92/0.41
0.0079/0.0039
Dibromomethane (1) + bromochloromethane (2)
0.008/0
2.19/1.78
0.86/0.32 [14] 1.06/0.36 [13] 0.47/0.50 [14] 1.02/0.35 [10] 0.38/0.53 [14] 0.30/0.44 [12] 0.32/0.48 [14] 0.27/0.49 [12] 0.27/0.12 [12]
System
kij PR/PC-SAFT
MRD (P) (%) PR/PC-SAFT
Dibromomethane (1) + n-heptane (2)
0.017/0.026
Bromotrichloromethane (1) + n-heptane (2) Bromochloromethane (1) + n-heptane (2) Bromotrichloromethane (1) + dibromomethane (2)
MRD (Tb) (%) PR/PC-SAFT
0.36/0.43 [15]
0.0125/0.0067 0.0170/0.0090 [15]
100 N X j;exp X j;EoS S j j ; X = P, Tb or r. N j¼1 X j;exp 1 N AADðyÞ ¼ Sj¼1 jyj;exp yj;EoS j ; N: total number of points. N MRDðXÞ ¼
very different. Thus, it can be seen that the dibromomethane + nheptane system, where vapour pressures for the pure compounds are very similar, presents a phase behaviour far from ideality appearing the azeotropic point near to equimolar composition. Unlike, for x1 > x1,az in the system containing bromochloromethane and for x1 < x1,az in the system with bromotrichloromethane, twophase region is reduced to a line and the mixtures behave like a pure fluid. Particularly interesting is the latter case because of the position of the azeotrope in this system. Furthermore, bromotrichloromethane + n-heptane and bromotrichloromethane + dibromomethane systems show similar phase behaviour between them (Figs. 2 and 4). VLE shape and the azeotropic coordinates (Table 4) are similar although in the haloalkane + haloalkane system a twophase region is observed at x1 < x1,az. The high ideality of bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane systems can be seen in Figs. 5 and 6, respectively. Fig. 7a and b shows the molar excess Gibbs energies for the
system, and very small for dibromomethane + bromochloromethane as expected considering the similarity between the molecules involved. Also, bromotrichloromethane + bromochloromethane system present a non-negligible value, 1
GEm ðx1 ¼ 0:5Þ ¼ 156:5Jmol
, although its phase behaviour is very
close to ideality. The sign of GEm for this system points to an important contribution to the entropic effect in the mixing process. 4.2. Modelling
studied systems. GEm is maximum for dibromomethane + n-heptane
Table 5 shows the parameters used in the PR and PC-SAFT modelling of the studied systems. The critical parameters and the acentric factor for all compounds, and the PC-SAFT parameters for n-heptane pure have been taken from the literature [22,32]. To improve the prediction of the density of the studied systems using PR EoS, a volumetric translation parameter, Dnc, for each polyhalomethane is introduced. They are calculated from the densities of the pure compounds. PC-SAFT parameters of the pure polyhalomethanes have been calculated using saturation pressures
[(Fig._8)TD$IG]
[(Fig._9)TD$IG]
Fig. 8. Deviations between the experimental (this work and [11]) and calculated (PR and PC-SAFT EoS) vapour–liquid equilibrium of polyhalomethane + n-heptane binary systems: dibromomethane (*), bromotrichloromethane ($), bromochloromethane at T = 298.15 K (~) and T = 313.15 K (!). Full symbols, PC-SAFT EoS; empty symbols, PR EoS.
Fig. 9. Deviations between the experimental (this work) and calculated (PR and PCSAFT EoS) vapour–liquid equilibrium of polyhalomethane + polyhalomethane binary systems: bromotrichloromethane (1) + dibromomethane (2) (*), bromotrichloromethane (1) + bromochloromethane (2) ($), dibromomethane (1) + bromochloromethane (2) (&). Full symbols, PC-SAFT EoS; empty symbols, PR EoS.
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and densities (this work and literature) so as to minimize the objective function (OF): 2 !2 !2 3 Psat Psat r ri;cal n i;exp i;exp i;cal 5 (9) OF ¼ Si¼1 4 þ ri;exp Psat i;exp
(r) = 0.55%. For PC-SAFT EoS: MRD (P) = 1.20%, AAD (y) = 0.0093 MRD (r) = 0.38%. However, the prediction of the azeotropic coordinates and the molar excess Gibbs energy values using PCSAFT are better than PR EoS. In this work, computations of different properties with PR and PC-SAFT EoS were performed using VLXE software [34].
Table 5 also includes the mean relative deviations, MRD (X), to compare experimental data (vapour pressures and density) and calculated using PC-SAFT EoS of pure compounds. To model our binary systems we have used the classical rules of mixtures. Binary interaction parameters, kij (Table 6), have been calculated by minimizing the above OF, Eq. (9), using this work and literature data [10–14]. A good agreement between experimental data and those calculated with both PR and PC-SAFT EoS for all studied systems is observed (Table 6 and Figs. 1–6). Noted that PC-SAFT EoS predicts well the thermodynamic behaviour of the dibromomethane + bromochloromethane system with a binary interaction parameter kij = 0, which agrees with the high ideality of the system and its molar excess Gibbs energy value. For this system, similar deviations between our experimental data and the isobars data published by Apelblat et al. [15] with those calculated by EoS are observed (Table 6). Therefore we can say that our data seem to be consistent with those of the literature. The mean relative deviations obtained are MRD (P) = 1.57%, AAD (y) = 0.0116 and MRD (r) = 0.55% for Peng–Robinson EoS and MRD (P) = 1.20%, AAD (y) = 0.0093 MRD (r) = 0.38% for PC-SAFT. No trends are observed in deviations of pressure with composition (Figs. 8 and 9). Nevertheless, the azeotropes and molar excess Gibbs energies modelling is better with PC-SAFT EoS especially for halomethane + halomethane systems (Table 4 and Fig. 7a and b).
Acknowledgement
5. Conclusions The isothermal vapour–liquid equilibria (VLE) at T = 308.15 K have been measured and the molar excess Gibbs energies, GEm , have been calculated for the next binary systems: dibromomethane + nheptane, bromotrichloromethane + n-heptane, bromotrichloromethane + dibromomethane, bromotrichloromethane + bromochloromethane and dibromomethane + bromochloromethane. The study was completed including the bromochloromethane + n-heptane system whose VLE was determined previously by us. All systems containing n-heptane and the bromotrichloromethane + dibromomethane system exhibit azeotrope while the remaining systems present a phase behaviour near ideality. Nevertheless, the GEm values for bromotrichloromethane + bromochloromethane system indicate a significant entropic contribution. Also we performed a comprehensive bibliographic search of vapour–liquid equilibrium and densities of the pure compounds and systems included in this work. From this work and literature experimental data, phase and volumetric behaviour have been modelled. For this, we have used a cubic EoS and other EoS based on perturbation theory obtaining a good agreement for both. For Peng–Robinson EoS, the mean relative deviations for the studied properties are MRD (P) = 1.57%, AAD (y) = 0.0116 and MRD
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