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Alkyl methanoates + benzene binary mixtures: New VLE measurements and DISQUAC analysis of thermodynamic properties
HUIDPHAS[ [OUILIBRIA ELSEVIER
Fluid Phase Equilibria 137 (1997) 173-183
Alkyl methanoates + benzene binary mixtures: New VLE measurements and DISQUAC analysis of thermodynamic properties G. Figurski a, U. E m m e r l i n g a, D. Nipprasch a, H.V. K e h i a i a n b., a Martin-Luther-Unit,ersitaet Halle-Wittenberg, lnstitutfuer Technische Chemie, D-6108 Halle, German~, b Institut de Topologie et de Dynamique des Systemes, Universite Paris VI1-CNRS, 1 rue Guy de la Brosse, F-75005 Paris, France Received 18 December 1996; accepted 6 March 1997
Abstract
Experimental vapor-liquid equilibrium (VLE) data are reported for the propyl methanoate (formate)+ benzene mixture over the entire composition range at six constant temperatures, 293.15, 303.15, 313.15,323.15, 333.15 and 343.15 K. The data were correlated with Redlich-Kister, Wilson and UNIQUAC equations for the liquid phase activity coefficients. The excess molar Gibbs energies, G E, were calculated for each temperature with vapor-phase nonidealities estimated from the virial equation of state. These experimental results along with literature data on VLE, G E and excess molar enthalpies H E of ethyl methanoates + benzene were examined on the basis of the DISQUAC group contribution model. The interaction parameters estimated by Delcros et al. [1] describe accurately the ethyl methanoate + benzene system. Revised parameters were proposed for propyl methanoate + benzene on the basis of the new VLE measurements. © 1997 Elsevier Science B.V. Keywords." Vapor-liquid equilibrium; Excess molar Gibbs energy; DISQUAC
1. Introduction
Experimental vapor-liquid equilibrium data have a great importance for the design of industrial separation processes. In continuation of our experimental investigation on vapor pressures of pure alkyl methanoates [2] and of ethyl methanoate + benzene mixtures [3], we report in this work experimental vapor-liquid equilibrium (VLE) data for propyl methanoate + benzene in the range from ca. 9 to 101 kPa, at six constant temperatures, 293.15, 303.15, 313.15, 323.15, 333.15, and 343.15 K, over the entire composition range. VLE data for this binary system are not available in literature [4,5]. These experimental results, along with our previous data on VLE of ethyl methanoate
* Corresponding author. Tel.: + 33-1-44274427; fax: + 33-1-43366844. 0378-3812/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. Pll S 0 3 7 8 - 3 8 1 2 ( 9 7 ) 0 0 0 7 1 -X
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G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173 183
+ benzene [3], are used for estimating interaction parameters in DISQUAC, an extended quasi-chemical group contribution model [6,7]. Delcros et al. [1] have published DISQUAC parameters for alkanoates + benzene or +toluene. However, part of the parameters for methanoates were only guessed, because experimental VLE data were missing.
2. Experimental 2.1. Materials"
The chemicals used (propyl methanoate, purity > 98%, density at 293.15 K, 907.3 kg m-3; refractive index at 293.15 K, 1.3770; benzene, purity > 99%, density at 293.15 K, 878.9 kg m 3; refractive index at 293.15 K, 1.5012) were obtained from Merck (Darmstadt). A check with the gas chromatograph confirmed the guaranteed purity. The substances were used without further purification. 2.2. Apparatus and procedure
The pressure-temperature ( P - T ) data have been taken at nine constant liquid phase mole fraction compositions, x i, in an all-glass dynamic equilibrium still developed by Figursld et al. [8]. The essential components are a glass flask and a heating coil, a Cottrell pump, an equilibrium chamber, a condensor for the vapor phase, and a cooler. The experimental procedure has been previously described in detail [9]. The pressure, P, was measured by means of a mercury-filled barometer (Glaswerke, Ilmenau), the reproducibility was 15 Pa. The boiling temperatures T were measured with a certified (IPT-90) Pt-resistance thermometer, the reproducibility was 0.01 K. Mixtures were prepared by mass. The final composition of the liquid-phase samples was determined refractometrically at 293.15 K, after each measurement of P, by means of an Abbe refractometer. The calibration curves were based on refractive indices of synthetically prepared mixtures. The estimated uncertainties in P, T, and x i are, respectively, o-(P) = 50 Pa, or(T) = 0.05 K and Or( X i) = 0 . 0 0 0 5 .
2.3. Results
The 19 direct experimental T - P values for pure benzene are given in Table 1, the vapor-pressure data for pure propyl methanoate at temperatures from ca. 287 to 327 K, were published earlier [2]. Experimental vapor-pressure data of the pure components have been fitted to the Antoine equation, Eq. (1), using the procedure of Hala et al. [10]: P~,lc/kPa = exp[ A - B / ( T / K
+ C)]
(1)
The Antoine parameters are: propyl methanoate: A = 14.11031, B = 2778.536, C = -60.5800; Benzene: A = 13.86193, B = 2775.679, C = - 5 2 . 9 7 6 .
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G. Figurski et al./ Fluid Phase Equilibria 137 (1997) 173-183
Table 1 Vapor pressure P of pure benzene as a function of temperature T T (K)
P (kPa)
T (K)
P (kPa)
298.31 303.73 307.74 310.99 314.27 317.79 321.27 324.58 327.59 330.77
12.783 16.323 19.443 22.274 25.505 29.373 33.670 38.177 42.724 47.919
335.11 338.96 341.39 345.20 348.44 350.56 352.43 352.89 353.40
55.906 63.845 69.260 78.514 87.122 93.232 98.718 100.196 101.815
The overall mean relative deviations in pressure, Eq. (2): (2)
A P% = (lO0/N)~[IPcalc - PI/P]
where N is the total number of experimental values, are 0.06% for propyl methanoate [2] and 0.03% for benzene. The normal boiling point of benzene calculated from this equation is 353.25 K, in agreement within 0.01 K with literature values, 353.244 [11]. The 63 experimental T - P values for propyl methanoate(1) + benzene(2) mixtures have been taken at 9 constant mole fraction compositions x~ from 0.110 to 0.910 at six constant temperatures (293.15, 303.15, 313.15, 323.15, 333.15, and 343.15 K). All the data are listed in Table 2. The experimental P - T - x data for the six isotherms of the system propyl methanoate(1)+ benzene(2) can be correlated satisfactorily by the Redlich-Kister [12], Wilson [13], and UNIQUAC [14] equations for the liquid-phase activity coefficients. The model equations are: -- the three-parameter Redlich-Kister equation G E / R T = x l x z [ a , + a z ( x I - x2) -4-a3(x I - x2) 2] --
(3)
the Wilson equation GE/RT=
- x , ( l n x, + x 2 A , 2 ) - x e ( l n x 2 +XlA2, )
(4)
- - the UNIQUAC equation ln(&l/x,)
GE/RT=xl -
"+-X 2
ln(cbz/x2) + ( z / 2 ) [ q l x
1ln(0J6,)
q , x I ln(0, + 02~-zi ) - qzX2 ln(02 + 0,T12 )
+ qaxe l n ( 0 J & e ) ] (5)
The deviation from ideal behavior of the vapor phase has been calculated from the virial equation of state, truncated after the second term, with second virial coefficients and cross virial coefficients obtained by the method of Hayden-O'Connell [15] (Table 3). The Poynting correction was calculated
176
G. Figurski et al./ Fluid Phase Equilibria 13711997) 173-183
Table 2 Experimental total pressure P data for the propyl methanoate(1)+ benzene(2) system as a function of the mole fraction x 1 of propyl methanoate in the liquid phase at different temperatures T and mole fraction y~ of propyl methanoate in the vapor phase, activity coefficients "Yi of components i and excess molar Gibbs energy G E, using the three parameter Redlich-Kister equation, Eq. (3) xl
Yl (calc)
P (kPa)
Yl (calc)
yz (calc)
G E (calc) (J m o l - l)
T = 293.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1142 0.1989 0.2877 0.4001 0.4701 0.5703 0.6783 0.7528 0.8816 1.0000
10.024 10.107 10.122 10.092 9.987 9.887 9.707 9.477 9.304 8.991 8.699
1.000 1.003 1.011 1.025 1.049 1.067 1.096 1.128 1.149 1.183 1.209
1.281 1.207 1.158 1.113 1.068 1.047 1.026 1.012 1.006 1.001 1.000
0 58 93 119 135 135 124 100 80 39 0
T = 303.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1166 0.2021 0.2919 0.4063 0.4777 0.5793 0.6872 0.7605 0.8855 1.0000
15.910 16.095 16.149 16.129 16.000 15.869 15.629 15.319 15.085 14.654 14.235
1.000 1.004 1.012 1.026 1.048 1.064 1.089 1.117 1.138 1.175 1.211
1.288 1.200 1.147 1.102 1.062 1.044 1.025 1.013 1.007 1.001 1.000
0 60 94 118 132 131 120 98 79 40 0
T = 313.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1188 0.2053 0.2961 0.4121 0.4844 0.5868 0.6945 0.7668 0.8889 1.0000
24.371 24.724 24.850 24.865 24.727 24.568 24.264 23.864 23.557 22.981 22.404
1.000 1.004 1.013 1.026 1.047 1.1)62 1.084 1.110 1.130 1.169 1.210
1.289 1.194 1.139 1.096 1.058 1.041 1.025 1.013 1.007 1.002 1.000
0 61 95 118 131 130 119 98 79 40 0
T = 323.15 K 0.000 0.110 0.200 0.300 0.430
0.0000 0.1209 0.2083 0.3002 0.4175
36.171 36.789 37.039 37.126 37.010
1.1100 1.005 1.013 1.026 1.046
1.288 1.189 1.134 1.092 1.055
0 62 96 119 131
G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173-183
177
Table 2 (continued) xl
Yl (calc)
P (kPa)
7J (calc)
72 (calc)
G E (calc) (J m o l - 1)
0.510 0.620 0.730 0.800 0.910 1.000
0.4904 0.5933 0.7006 0.7720 0.8917 1.0000
36.832 36.468 35.972 35.582 34.835 34.064
1.060 1.081 1.106 1.125 1.164 1.207
1.039 1.024 1.013 1.007 1.002 1.000
130 119 98 79 41 0
T = 333.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1227 0.2113 0.3042 0.4225 0.4959 0.5989 0.7057 0.7764 0.8941 1.0000
52.193 53.202 53.651 53.872 53.831 53.655 53.247 52.654 52.174 51.226 50.223
1.000 1.005 1.013 1.026 1.045 1.059 1.079 1.103 1.122 1.161 1.205
1.284 1.186 1.131 1.089 1.054 1.039 1.024 1.013 1.007 1.002 1.000
0 63 97 120 132 131 120 99 80 42 0
T = 343.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1244 0.2142 0.3081 0.4273 0.5009 0.6038 0.7099 0.7800 0.8962 1.0000
73.432 74.998 75.749 76.194 76.312 76.173 75.751 75.068 74.490 73.314 72.040
1.000 1.004 1.013 1.025 1.045 1.058 1.078 1.102 1.121 1.160 1.203
1.278 1.183 1.130 1.089 1.053 1.039 1.023 1.013 1.007 1.002 1.000
0 64 99 123 135 134 123 101 82 42 0
Table 3 Second virial coefficients B~I and B22, and cross virial coefficients Bj2 and liquid molar volumes V01 and Vo2 used for the VLE calculations in the system propyl methanoate(1)+benzene(2) T(K)
BI1 (mL mol - j )
B22 (mL mol - l )
Bi2 (mL mol - I )
V01 (mL tool - l )
Vo2 (mL mol - t )
293.15 303.15 313.15 323.15 333.15 343.15
-
-
-
89 90 91 92 93 94
97 98 100 101 102 103
1588 1438 1311 1202 1108 1026
2001 1818 1660 1524 1406 1301
1537 1395 1274 1170 1080 1000
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G. Figurski et a l . / Fluid Phase Equilibria 137 (1997) 173-183
Table 4 Estimated parameters of Redlich-Kister, Wilson, and UNIQUAC equations and standard deviations o ' ( P ) between experimental and correlated total pressure data for the propyl methanoate(1)+ benzene(2) system
T (K) 293.15 303.15 313.15 323.15 333.15 343.15
Redlich-Kister
Wilson
UNIQUAC
AI
A2
A3
o-(P)(kPa)
AI2
A21
cr(P)(kPa)
7.i2
721
o'(P)(kPa)
0.2224 0.2094 0.2001 0.1938 0.1899 0.1881
-0.0289 -0.0307 -0.0317 -0.0323 -0.0317 -0.0304
-0.0034 0.0129 0.0219 0.0272 0.0286 0.0272
0.04 0.06 0.07 0.08 0.09 0.10
0.6811 0.6558 0.6396 0.6311 0.6311 0.6406
1.1300 1.1745 1.2049 1.2227 1.2249 1.2160
0.04 0.05 0.07 0.08 0.1l 0.11
-717.919 -913.227 - 1039.191 - 1123.569 -1173.579 -1198.353
865.238 1130.068 1305.797 1422.345 1486.140 1510.790
0.04 0.05 0.06 0.08 0.10 0.10
Table 5 Calculated azeotropic data, temperature T,~, pressure P~,~, and mole fraction of propyl methanoate, xla ~ for the system propyl methanoate(1) + benzene(2)
T~ (K)
x l,~z
P..z (kPa)
293.15 303.15 313.15 323.15 333.15 343.15
0.193 0.225 0.260 0.260 0.333 0.377
10.175 16.211 24.929 37.148 53.830 76.080
Table 6 Excess molar Gibbs energies G E (T; x ) = 0.5) for n-alkyl methanoate(l)+benzene(2) mixtures at various temperatures T and equimolar composition. Comparison of experimental results (exp) with calculated (calc) using the coefficients t-Dis ~ s t , / and cQUaC from Table 9Table 10 st,/ n-alkyl methanoate
T (K)
G E (A- I = 0 . 5 ) (J m o l - 1 )
calc
exp
HCOOC 2 H 5
293.15 303.15 313.15 323.15
257 252 247 244
258 ~ 253 a 249 ~ 249" 247
HCOOC 3H 7
293.15 303.15 313.15 323.15 333.15 343.15
137 134 132 131 131 130
136 h 132 b 130 b 130 b 132 b 134 b
aCalculated from isothermal P - x bCalculated from isothermal P - x
Source of experimental data
Figurski and Emmerling Figurski and Emmerling Figurski and Emmerling Figurski and Emmerling Ohta and Nagata [17]
data [3], (corrected for vapor-phase nonideality). data (this work), (corrected for vapor-phase nonideality).
[3] [3] [3] [3]
G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173 183
179
Table 7 Excess molar enthalpies H E (T; x I = 0.5) for n-alkyl methanoate(l)+ benzene(2) mixtures at various temperatures T and equimolar composition. Comparison of experimental results (exp) with calculated (calc) using the coefficients c~tDl/s and C st,I QUAC from Table 9Table 10 n-alkyl methanoate
H E ( x 1 = 0.5) (J tool-1)
T (K)
calc
exp
HCOOC 2 H 5
298.15 308.15 318.15
407 383 361
402 368 344
HCOOC 3H
293.15 303.15 313.15 323.15 333.15 343.15
227 204 182 161 142 124
-------
Source of experimental data
Ohta and Nagata [17] Ohta and Nagata [17] Ohta and Nagata [17]
w i t h l i q u i d m o l a r v o l u m e s f r o m R e f . [16] ( T a b l e 3). T h e b i n a r y p a r a m e t e r s o f e a c h m o d e l h a v e b e e n obtained by nonlinear regression based on minimizing
t h e o b j e c t i v e f u n c t i o n Q:
Q --- ~ ( P c a l c - p ) 2 (6) The results indicate that the three equations correlate the data equally well (Table 4). The mole fraction y~ of propyl methanoate in the vapor phase, the activity coefficients "/i of the Table 8 Logarithm of activity coefficients at infinite dilution In ~ [ in n-alkyl methanoate(1)+benzene(2) mixtures at various temperatures T. Comparison of experimental results (exp) with calculated (calc) using the coefficients rD~S ~ s t , / and r~euAc ~st, / from Table 9Table 10 n-alkyl methanoate
HCOOC 2H 5
HCOOC3H 7
T (K)
In y~
In y~
Source of experimental data
calc
exp
calc
exp
293.15 303.15 312.96 313.15 313.48 323.15 323.67 323.86
0.514 0.486 0.461 0.460 0.460 0.438 0.437 0.437
0.383 ~ 0.405 a
0.422 a 0.396 ~ 0.104 0.370 ~
0.182
0.444 0.420 0.399 0.399 0.398 0.380 0.379 0.378
293.15 303.15 313.15 323.15 333.15 343.15
0.364 0.343 0.325 0.310 0.296 0.284
0.2488 0.2530 0.2548 0.2538 0.2508 0.246 b
0.218 0.206 0.196 0.187 0.180 0.174
0.1908 0.192 b 0.190 b 0.189 b 0.1878 0.185 b
0.405 a 0.140 0.382 a
0.343 a 0.131
Figurski and Emmerling [3] Figurski and Emmerling [3] Gon~alves and Macedo [20] Figurski and Emmerling [3] Gon~alves and Macedo [20] Figurski and Emmerling [3] Gon~alves and Macedo [20] Gon~alves and Macedo [20]
~Calculated from isothermal P-x data [3], extrapolated to x i = 0 (corrected for vapor-phase nonideality). bCalculated from isothermal P-x data (this work), extrapolated to xi = 0 (corrected for vapor-phase nonideality).
180
G. Figurski et al./Fluid Phase Equilibria 137 (1997) 173-183
components i and the excess molar Gibbs energy G E, calculated using the three-parameter RedlichKister equation, Eq. (3), are given in Table 2. The equimolar values of G E are listed in Table 6. The system propyl methanoate(1)+ benzene(2) is azeotropic in the measured P - T range. The azeotropic data were calculated from P - x data at constant temperature under application of the Wilson equation for the concentration dependence of the liquid phase activity coefficients (Table 5). From these data we obtain by extrapolation at Pdz = 101.32 kPa, Taz = 351.98 K and xl~z = 0.417. Lecat [18,19] reports T,~ = 351.65 K and xj~ = 0.440. Additionally we estimated the limiting activity coefficients y~i of the propyl methanoate(l) + benzene(2) system from the three-parameter Redlich-Kister equation (Table 8). 3. T h e o r y The DISQUAC model was applied using the same equations as reported previously [1]. The interactional terms in the thermodynamic properties G E, H E and CE contain a dispersive (DIS) and a quasi-chemical (QUAC) term which are calculated independently by the classical formulas and then simply added. 3.1. Geometrical parameters
The molecules under study, i.e. n-alkyl methanoates and benzene are regarded as possessing three types of surface s: (1) type a, (CH 3 or CH 2 groups in n-alkyl methanoates); (2) type b, (C6H6benzene); (3) type k, (CO0 group in n-alkyl methanoates). The geometrical parameters related to a group surface of type s on a molecule i, i.e. the relative volumes r i, the relative surface qi, and the surface fraction crsi (s = a, b, k), for components investigated in this work have been calculated on the basis of the group volumes VC and surfaces A6 recommended by Bondi [21], taking arbitarily the volume and surface of methane as unity. The same values have been used as previously [1]. 3.2. Estimation of the interaction parameters
The three types of surface generate three pairs of contact: (a, b), (a, k), and (b, k). The nonpolar aliphatic/benzene (a, b) interactions are represented solely by dispersive parameters t-,DIS _ which have been previously estimated [22]. The numerical values of these parameters are: ~ab.l 0.251, "~ab,2 c-DIS= 0.560, and c~D~S = --0.620. The polar aliphatic/COO (a, k) interactions are repre~ab,3 sented by both dispersive and quasi-chemical parameters which have been previously determined [23]. The numerical values of these parameters depend on the chain length of the methanoate and are listed in Table 9. The aromatic/COO (b, k) interactions are best reproduced when the corresponding -
-
Table 9 rqUAC for contacts (a, k): type a, CH 3 or CH 2 in n-alkane or Dispersive and quasi-chemical interchange coefficients, C.kD~s J , ~ak./ n-alkyl methanoate; type k, C O O in H C O O ( C H 2 ) m_ ~ECH~ m
/~DIS ~ak, I
g-,DIS ~ak,2
t-~DIS ~ak,3
t'~QUAC ~ak. I
F, QUAC ~ak.2
(-QUAC ~ak,3
1 2 >__3
1.12 1.50 1.50
1.7 3.0 3.0
0.0 0.0 0.0
4.15 3.41 3.41
5.97 4.86 4.86
1.80 1.80 1.00
G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173-183
Table 10 Dispersive interchange coefficients, ~bk,/ c-DiS for the contact (b, k): type b, C6H 6 HCOO(CH2),,, IICH3 (the quasi-chemical coefficientsare equal to zero)
181
(benzene),
?;v/
/-~DIS ~bk, 1
/'~ DIS ~bk,2
1
3.52
4.80
2.00
2 3 >4
2.98a 2.91a 2.91
3.97a 3.75 3.65
2.20 3.00 3.00
type
k,
CO0 in
/~DIS ~bk,3
~Adjusted parameter from experimental data. coefficients are taken entirely dispersive [1 ]. The numerical values of these parameters depend on the chain length of the methanoate and are listed in Table 10. Tables 6 - 8 show numerical comparisons between experimental G E, H E, and y~ data and DISQUAC calculations. Delcros et al. [1] have determined the dispersive parameters for ethyl methanoate + benzene on the basis of the experimental data of Ref. [17], G E at 323.15 K and H E at 298.15, 308.15 and 318.15 K. The parameters for the other methanoates were guessed. Our G E data on ethyl methanoate + benzene [3] are quite well represented by nearly the same parameters. However, the guessed value of the Gibbs energy parameter, ~c-D~s b k , l = 2.75 [1], yields a G E which is only 50% or less of the present G E value of propyl methanoate + benzene. A new adjustment yields r-D~S ~""bk, 1 = 2.91 (Table 10). It appears that G E is quite sensitive to the parameter value. This happens usually in mixtures of a polar + a polarizable component. The calculated G E is the sum of a small combinatorial term, a large positive dispersive term, and a large negative quasi-chemical term. Small absolute changes in the dispersive term result in large relative changes in the total G E value.
4. List of symbols Al, A2, A3 A,B,C C Cp
G H m N P q
R r
T x
Y Z
Redlich--Kister parameters, Eq. (3) parameters in the Antoine equation, Eq. (1) interchange coefficient molar heat capacity at constant pressure molar Gibbs energy molar enthalpy number of C atoms in the n-alkyl group number of experimental values pressure relative molecular surface gas constant relative molecular volume absolute temperature mole fraction in liquid phase mole fraction in vapor phase coordination number, Eq. (5)
G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173 183
182
4.1. Greek letters O/
4, Y 0 O"
A
molecular surface fraction volume fraction, Eq. (5) activity coefficient area fraction, Eq. (5) experimental uncertainty or standard deviation UNIQUAC binary parameter, Eq. (5) Wilson binary parameter, Eq. (4)
4.2. Superscripts DIS E QUAC
dispersive term excess property quasi-chemical term property at infinite dilution (x i =
o)
4.3. Subscripts a, b, k, type of contact surface: a, CH 3, C H 2 : b, C o H 6 ; k, COO az, azeotropic value i,j, type of molecule (i :/:j) l, order of interchange coefficient: 1 = 1, Gibbs energy; 1 = 2, enthalpy; l = 3, heat capacity s, t, type of contact surfaces (s va t)
References [1] S. Delcros, E. Jimenez, L. Romani, A.H. Roux, J.-P.E. Grolier, H.V. Kehiaian, Linear alkanoates+aromatic hydrocarbon binary mixtures: New excess enthalpy measurements and DISQUAC analysis of thermodynamic properties, Fluid Phase Equilibria 111 (1995) 71-88. [2] G. Figurski, U. Emmerling, Vapor pressures of pure methyl, ethyl and propyl methanoates (formates) at pressures below 102 kPa, ELDATA: Int. Electron. J. Phys. Chem. Data 2 (1996) 37-40. [3] G. Figurski, U. Emmerling, Isothermal vapor-liquid equilibria in the ethyl methanoate (ethyl formate) + benzene system at 293.15, 303.15, 313.15 and 323.15 K, ELDATA: Int. Electron. J. Phys. Chem. Data 2 (1996) 79-84. [4] I. Wichterle, J. Linek, Wagner, H.V., Kehiaian, Vapor-Liquid Equilibrium in Mixtures and Solutions: Bibliographic Database, ELDATA SARL, Montreuil, 1993, pp. 1-724. [5] I. Wichterle, J. Linek, Wagner, H.V. Kehiaian, Vapor-Liquid Equilibrium in Mixtures and Solutions: Bibliographic Database, Supplement, 3rd. ed., ELDATA SARL, Montreuil, 1995, pp. 1-180. [6] H.V. Kehiaian, Group-contribution methods for liquid mixtures: A critical review, Fluid Phase Equilibria 13 (1983) 243-252. [7] H.V. Kehiaian, Thermodynamics of binary liquid organic mixtures, Pure Appl. Chem. 57 (1985) 15-30. [8] G. Figurski, M+ Miihlenbruch, Das Dampf-Fliissigkeits-Gleichgewichteiner Reihe binaerer Gemische bei 760 Torr, Z. Phys. Chem. (Leipzig) 259 (1980) 357-362. [9] G. Figurski, Zur experimentellen Bestimmung des Dampf-Fliissigkeits-Gleichgewichts, Wiss. Z. Martin-Luther-Universitaet Halle-Wittenberg. Math.-Naturwiss. Reihe. 34 (1) (1985) 129-144. [10] E. Hala, K. Aim, T. Boublik, J. Linek, I. Wichterle, Vapor-Liquid Equilibrium at Normal and Reduced Pressures (in Czech.), Academia, Praha, 1982.
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183
[11] J.A. Riddick, W.B. Bunger, T.K. Sakano, Techniques of Chemistry, Vol. II., Organic Solvents, 4th ed., John Wiley & Son, 1986, pp. 1-1325. [12] O. Redlich, A.T. Kister, Algebraic representation of thermodynamic properties and the classification of solutions, Ind. Eng. Chem. 50 (1948) 345-348. [13] G.M. Wilson, Vapor-liquid equilibrium. XI. A new expression for the excess free energy of mixing, J. Am. Chem. Soc. 86 (1964) 127-130. [14] D.S. Abrams, J.M. Prausnitz, Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems, AIChE J. 21 (1975) 116-128. [15] J.G. Hayden, J.P. O'Connell, A generalized method for prediction second virial coefficients, Ind. Eng. Chem. Process Des. Dev. 14 (1975) 209-216. [16] J.M. Hougen, K.M. Watson, Chemical Process Principles, Part II., J. Wiley, New York, 1947. [17] T. Ohta, I. Nagata, Thermodynamic properties of four ester-hydrocarbon mixtures, J. Chem. Eng. Data 25 (1980) 283-286. [18] M. Lecat, Recl. Tray. Chim. Pays-Bas 45 (1926) 620. [19] J. Gmehling, J. Menke, J. Krafczyk, K. Fischer, Azeotropic Data, Part l, VCH, Weinheim, 1994. [20] A.S. Gon~alves, E.A. Macedo, Infinite dilution activity coefficients by comparative ebulliometry: Five systems containing ethyl formate, Fluid Phase Equilibria 85 (1993) 171-179. [21] A. Bondi, Physical Properties of Molecular Crystals, Liquid and Classes, Wiley, New York, 1968. [22] A. Ait Kaci, Ph.D. Thesis, University of Lyon, France, 1982. [23] G. Avedis, J.-P.E. Grolier, J. Fernandez, H.V. Kehiaian, Estimation of DISQUAC interaction parameters for low molecular mass analogues of polymers: Chloralkane + ester mixtures, J. Sol. Chem. 23 (1994) 135-152.
Fluid Phase Equilibria 137 (1997) 173-183
Alkyl methanoates + benzene binary mixtures: New VLE measurements and DISQUAC analysis of thermodynamic properties G. Figurski a, U. E m m e r l i n g a, D. Nipprasch a, H.V. K e h i a i a n b., a Martin-Luther-Unit,ersitaet Halle-Wittenberg, lnstitutfuer Technische Chemie, D-6108 Halle, German~, b Institut de Topologie et de Dynamique des Systemes, Universite Paris VI1-CNRS, 1 rue Guy de la Brosse, F-75005 Paris, France Received 18 December 1996; accepted 6 March 1997
Abstract
Experimental vapor-liquid equilibrium (VLE) data are reported for the propyl methanoate (formate)+ benzene mixture over the entire composition range at six constant temperatures, 293.15, 303.15, 313.15,323.15, 333.15 and 343.15 K. The data were correlated with Redlich-Kister, Wilson and UNIQUAC equations for the liquid phase activity coefficients. The excess molar Gibbs energies, G E, were calculated for each temperature with vapor-phase nonidealities estimated from the virial equation of state. These experimental results along with literature data on VLE, G E and excess molar enthalpies H E of ethyl methanoates + benzene were examined on the basis of the DISQUAC group contribution model. The interaction parameters estimated by Delcros et al. [1] describe accurately the ethyl methanoate + benzene system. Revised parameters were proposed for propyl methanoate + benzene on the basis of the new VLE measurements. © 1997 Elsevier Science B.V. Keywords." Vapor-liquid equilibrium; Excess molar Gibbs energy; DISQUAC
1. Introduction
Experimental vapor-liquid equilibrium data have a great importance for the design of industrial separation processes. In continuation of our experimental investigation on vapor pressures of pure alkyl methanoates [2] and of ethyl methanoate + benzene mixtures [3], we report in this work experimental vapor-liquid equilibrium (VLE) data for propyl methanoate + benzene in the range from ca. 9 to 101 kPa, at six constant temperatures, 293.15, 303.15, 313.15, 323.15, 333.15, and 343.15 K, over the entire composition range. VLE data for this binary system are not available in literature [4,5]. These experimental results, along with our previous data on VLE of ethyl methanoate
* Corresponding author. Tel.: + 33-1-44274427; fax: + 33-1-43366844. 0378-3812/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. Pll S 0 3 7 8 - 3 8 1 2 ( 9 7 ) 0 0 0 7 1 -X
174
G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173 183
+ benzene [3], are used for estimating interaction parameters in DISQUAC, an extended quasi-chemical group contribution model [6,7]. Delcros et al. [1] have published DISQUAC parameters for alkanoates + benzene or +toluene. However, part of the parameters for methanoates were only guessed, because experimental VLE data were missing.
2. Experimental 2.1. Materials"
The chemicals used (propyl methanoate, purity > 98%, density at 293.15 K, 907.3 kg m-3; refractive index at 293.15 K, 1.3770; benzene, purity > 99%, density at 293.15 K, 878.9 kg m 3; refractive index at 293.15 K, 1.5012) were obtained from Merck (Darmstadt). A check with the gas chromatograph confirmed the guaranteed purity. The substances were used without further purification. 2.2. Apparatus and procedure
The pressure-temperature ( P - T ) data have been taken at nine constant liquid phase mole fraction compositions, x i, in an all-glass dynamic equilibrium still developed by Figursld et al. [8]. The essential components are a glass flask and a heating coil, a Cottrell pump, an equilibrium chamber, a condensor for the vapor phase, and a cooler. The experimental procedure has been previously described in detail [9]. The pressure, P, was measured by means of a mercury-filled barometer (Glaswerke, Ilmenau), the reproducibility was 15 Pa. The boiling temperatures T were measured with a certified (IPT-90) Pt-resistance thermometer, the reproducibility was 0.01 K. Mixtures were prepared by mass. The final composition of the liquid-phase samples was determined refractometrically at 293.15 K, after each measurement of P, by means of an Abbe refractometer. The calibration curves were based on refractive indices of synthetically prepared mixtures. The estimated uncertainties in P, T, and x i are, respectively, o-(P) = 50 Pa, or(T) = 0.05 K and Or( X i) = 0 . 0 0 0 5 .
2.3. Results
The 19 direct experimental T - P values for pure benzene are given in Table 1, the vapor-pressure data for pure propyl methanoate at temperatures from ca. 287 to 327 K, were published earlier [2]. Experimental vapor-pressure data of the pure components have been fitted to the Antoine equation, Eq. (1), using the procedure of Hala et al. [10]: P~,lc/kPa = exp[ A - B / ( T / K
+ C)]
(1)
The Antoine parameters are: propyl methanoate: A = 14.11031, B = 2778.536, C = -60.5800; Benzene: A = 13.86193, B = 2775.679, C = - 5 2 . 9 7 6 .
175
G. Figurski et al./ Fluid Phase Equilibria 137 (1997) 173-183
Table 1 Vapor pressure P of pure benzene as a function of temperature T T (K)
P (kPa)
T (K)
P (kPa)
298.31 303.73 307.74 310.99 314.27 317.79 321.27 324.58 327.59 330.77
12.783 16.323 19.443 22.274 25.505 29.373 33.670 38.177 42.724 47.919
335.11 338.96 341.39 345.20 348.44 350.56 352.43 352.89 353.40
55.906 63.845 69.260 78.514 87.122 93.232 98.718 100.196 101.815
The overall mean relative deviations in pressure, Eq. (2): (2)
A P% = (lO0/N)~[IPcalc - PI/P]
where N is the total number of experimental values, are 0.06% for propyl methanoate [2] and 0.03% for benzene. The normal boiling point of benzene calculated from this equation is 353.25 K, in agreement within 0.01 K with literature values, 353.244 [11]. The 63 experimental T - P values for propyl methanoate(1) + benzene(2) mixtures have been taken at 9 constant mole fraction compositions x~ from 0.110 to 0.910 at six constant temperatures (293.15, 303.15, 313.15, 323.15, 333.15, and 343.15 K). All the data are listed in Table 2. The experimental P - T - x data for the six isotherms of the system propyl methanoate(1)+ benzene(2) can be correlated satisfactorily by the Redlich-Kister [12], Wilson [13], and UNIQUAC [14] equations for the liquid-phase activity coefficients. The model equations are: -- the three-parameter Redlich-Kister equation G E / R T = x l x z [ a , + a z ( x I - x2) -4-a3(x I - x2) 2] --
(3)
the Wilson equation GE/RT=
- x , ( l n x, + x 2 A , 2 ) - x e ( l n x 2 +XlA2, )
(4)
- - the UNIQUAC equation ln(&l/x,)
GE/RT=xl -
"+-X 2
ln(cbz/x2) + ( z / 2 ) [ q l x
1ln(0J6,)
q , x I ln(0, + 02~-zi ) - qzX2 ln(02 + 0,T12 )
+ qaxe l n ( 0 J & e ) ] (5)
The deviation from ideal behavior of the vapor phase has been calculated from the virial equation of state, truncated after the second term, with second virial coefficients and cross virial coefficients obtained by the method of Hayden-O'Connell [15] (Table 3). The Poynting correction was calculated
176
G. Figurski et al./ Fluid Phase Equilibria 13711997) 173-183
Table 2 Experimental total pressure P data for the propyl methanoate(1)+ benzene(2) system as a function of the mole fraction x 1 of propyl methanoate in the liquid phase at different temperatures T and mole fraction y~ of propyl methanoate in the vapor phase, activity coefficients "Yi of components i and excess molar Gibbs energy G E, using the three parameter Redlich-Kister equation, Eq. (3) xl
Yl (calc)
P (kPa)
Yl (calc)
yz (calc)
G E (calc) (J m o l - l)
T = 293.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1142 0.1989 0.2877 0.4001 0.4701 0.5703 0.6783 0.7528 0.8816 1.0000
10.024 10.107 10.122 10.092 9.987 9.887 9.707 9.477 9.304 8.991 8.699
1.000 1.003 1.011 1.025 1.049 1.067 1.096 1.128 1.149 1.183 1.209
1.281 1.207 1.158 1.113 1.068 1.047 1.026 1.012 1.006 1.001 1.000
0 58 93 119 135 135 124 100 80 39 0
T = 303.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1166 0.2021 0.2919 0.4063 0.4777 0.5793 0.6872 0.7605 0.8855 1.0000
15.910 16.095 16.149 16.129 16.000 15.869 15.629 15.319 15.085 14.654 14.235
1.000 1.004 1.012 1.026 1.048 1.064 1.089 1.117 1.138 1.175 1.211
1.288 1.200 1.147 1.102 1.062 1.044 1.025 1.013 1.007 1.001 1.000
0 60 94 118 132 131 120 98 79 40 0
T = 313.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1188 0.2053 0.2961 0.4121 0.4844 0.5868 0.6945 0.7668 0.8889 1.0000
24.371 24.724 24.850 24.865 24.727 24.568 24.264 23.864 23.557 22.981 22.404
1.000 1.004 1.013 1.026 1.047 1.1)62 1.084 1.110 1.130 1.169 1.210
1.289 1.194 1.139 1.096 1.058 1.041 1.025 1.013 1.007 1.002 1.000
0 61 95 118 131 130 119 98 79 40 0
T = 323.15 K 0.000 0.110 0.200 0.300 0.430
0.0000 0.1209 0.2083 0.3002 0.4175
36.171 36.789 37.039 37.126 37.010
1.1100 1.005 1.013 1.026 1.046
1.288 1.189 1.134 1.092 1.055
0 62 96 119 131
G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173-183
177
Table 2 (continued) xl
Yl (calc)
P (kPa)
7J (calc)
72 (calc)
G E (calc) (J m o l - 1)
0.510 0.620 0.730 0.800 0.910 1.000
0.4904 0.5933 0.7006 0.7720 0.8917 1.0000
36.832 36.468 35.972 35.582 34.835 34.064
1.060 1.081 1.106 1.125 1.164 1.207
1.039 1.024 1.013 1.007 1.002 1.000
130 119 98 79 41 0
T = 333.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1227 0.2113 0.3042 0.4225 0.4959 0.5989 0.7057 0.7764 0.8941 1.0000
52.193 53.202 53.651 53.872 53.831 53.655 53.247 52.654 52.174 51.226 50.223
1.000 1.005 1.013 1.026 1.045 1.059 1.079 1.103 1.122 1.161 1.205
1.284 1.186 1.131 1.089 1.054 1.039 1.024 1.013 1.007 1.002 1.000
0 63 97 120 132 131 120 99 80 42 0
T = 343.15 K 0.000 0.110 0.200 0.300 0.430 0.510 0.620 0.730 0.800 0.910 1.000
0.0000 0.1244 0.2142 0.3081 0.4273 0.5009 0.6038 0.7099 0.7800 0.8962 1.0000
73.432 74.998 75.749 76.194 76.312 76.173 75.751 75.068 74.490 73.314 72.040
1.000 1.004 1.013 1.025 1.045 1.058 1.078 1.102 1.121 1.160 1.203
1.278 1.183 1.130 1.089 1.053 1.039 1.023 1.013 1.007 1.002 1.000
0 64 99 123 135 134 123 101 82 42 0
Table 3 Second virial coefficients B~I and B22, and cross virial coefficients Bj2 and liquid molar volumes V01 and Vo2 used for the VLE calculations in the system propyl methanoate(1)+benzene(2) T(K)
BI1 (mL mol - j )
B22 (mL mol - l )
Bi2 (mL mol - I )
V01 (mL tool - l )
Vo2 (mL mol - t )
293.15 303.15 313.15 323.15 333.15 343.15
-
-
-
89 90 91 92 93 94
97 98 100 101 102 103
1588 1438 1311 1202 1108 1026
2001 1818 1660 1524 1406 1301
1537 1395 1274 1170 1080 1000
178
G. Figurski et a l . / Fluid Phase Equilibria 137 (1997) 173-183
Table 4 Estimated parameters of Redlich-Kister, Wilson, and UNIQUAC equations and standard deviations o ' ( P ) between experimental and correlated total pressure data for the propyl methanoate(1)+ benzene(2) system
T (K) 293.15 303.15 313.15 323.15 333.15 343.15
Redlich-Kister
Wilson
UNIQUAC
AI
A2
A3
o-(P)(kPa)
AI2
A21
cr(P)(kPa)
7.i2
721
o'(P)(kPa)
0.2224 0.2094 0.2001 0.1938 0.1899 0.1881
-0.0289 -0.0307 -0.0317 -0.0323 -0.0317 -0.0304
-0.0034 0.0129 0.0219 0.0272 0.0286 0.0272
0.04 0.06 0.07 0.08 0.09 0.10
0.6811 0.6558 0.6396 0.6311 0.6311 0.6406
1.1300 1.1745 1.2049 1.2227 1.2249 1.2160
0.04 0.05 0.07 0.08 0.1l 0.11
-717.919 -913.227 - 1039.191 - 1123.569 -1173.579 -1198.353
865.238 1130.068 1305.797 1422.345 1486.140 1510.790
0.04 0.05 0.06 0.08 0.10 0.10
Table 5 Calculated azeotropic data, temperature T,~, pressure P~,~, and mole fraction of propyl methanoate, xla ~ for the system propyl methanoate(1) + benzene(2)
T~ (K)
x l,~z
P..z (kPa)
293.15 303.15 313.15 323.15 333.15 343.15
0.193 0.225 0.260 0.260 0.333 0.377
10.175 16.211 24.929 37.148 53.830 76.080
Table 6 Excess molar Gibbs energies G E (T; x ) = 0.5) for n-alkyl methanoate(l)+benzene(2) mixtures at various temperatures T and equimolar composition. Comparison of experimental results (exp) with calculated (calc) using the coefficients t-Dis ~ s t , / and cQUaC from Table 9Table 10 st,/ n-alkyl methanoate
T (K)
G E (A- I = 0 . 5 ) (J m o l - 1 )
calc
exp
HCOOC 2 H 5
293.15 303.15 313.15 323.15
257 252 247 244
258 ~ 253 a 249 ~ 249" 247
HCOOC 3H 7
293.15 303.15 313.15 323.15 333.15 343.15
137 134 132 131 131 130
136 h 132 b 130 b 130 b 132 b 134 b
aCalculated from isothermal P - x bCalculated from isothermal P - x
Source of experimental data
Figurski and Emmerling Figurski and Emmerling Figurski and Emmerling Figurski and Emmerling Ohta and Nagata [17]
data [3], (corrected for vapor-phase nonideality). data (this work), (corrected for vapor-phase nonideality).
[3] [3] [3] [3]
G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173 183
179
Table 7 Excess molar enthalpies H E (T; x I = 0.5) for n-alkyl methanoate(l)+ benzene(2) mixtures at various temperatures T and equimolar composition. Comparison of experimental results (exp) with calculated (calc) using the coefficients c~tDl/s and C st,I QUAC from Table 9Table 10 n-alkyl methanoate
H E ( x 1 = 0.5) (J tool-1)
T (K)
calc
exp
HCOOC 2 H 5
298.15 308.15 318.15
407 383 361
402 368 344
HCOOC 3H
293.15 303.15 313.15 323.15 333.15 343.15
227 204 182 161 142 124
-------
Source of experimental data
Ohta and Nagata [17] Ohta and Nagata [17] Ohta and Nagata [17]
w i t h l i q u i d m o l a r v o l u m e s f r o m R e f . [16] ( T a b l e 3). T h e b i n a r y p a r a m e t e r s o f e a c h m o d e l h a v e b e e n obtained by nonlinear regression based on minimizing
t h e o b j e c t i v e f u n c t i o n Q:
Q --- ~ ( P c a l c - p ) 2 (6) The results indicate that the three equations correlate the data equally well (Table 4). The mole fraction y~ of propyl methanoate in the vapor phase, the activity coefficients "/i of the Table 8 Logarithm of activity coefficients at infinite dilution In ~ [ in n-alkyl methanoate(1)+benzene(2) mixtures at various temperatures T. Comparison of experimental results (exp) with calculated (calc) using the coefficients rD~S ~ s t , / and r~euAc ~st, / from Table 9Table 10 n-alkyl methanoate
HCOOC 2H 5
HCOOC3H 7
T (K)
In y~
In y~
Source of experimental data
calc
exp
calc
exp
293.15 303.15 312.96 313.15 313.48 323.15 323.67 323.86
0.514 0.486 0.461 0.460 0.460 0.438 0.437 0.437
0.383 ~ 0.405 a
0.422 a 0.396 ~ 0.104 0.370 ~
0.182
0.444 0.420 0.399 0.399 0.398 0.380 0.379 0.378
293.15 303.15 313.15 323.15 333.15 343.15
0.364 0.343 0.325 0.310 0.296 0.284
0.2488 0.2530 0.2548 0.2538 0.2508 0.246 b
0.218 0.206 0.196 0.187 0.180 0.174
0.1908 0.192 b 0.190 b 0.189 b 0.1878 0.185 b
0.405 a 0.140 0.382 a
0.343 a 0.131
Figurski and Emmerling [3] Figurski and Emmerling [3] Gon~alves and Macedo [20] Figurski and Emmerling [3] Gon~alves and Macedo [20] Figurski and Emmerling [3] Gon~alves and Macedo [20] Gon~alves and Macedo [20]
~Calculated from isothermal P-x data [3], extrapolated to x i = 0 (corrected for vapor-phase nonideality). bCalculated from isothermal P-x data (this work), extrapolated to xi = 0 (corrected for vapor-phase nonideality).
180
G. Figurski et al./Fluid Phase Equilibria 137 (1997) 173-183
components i and the excess molar Gibbs energy G E, calculated using the three-parameter RedlichKister equation, Eq. (3), are given in Table 2. The equimolar values of G E are listed in Table 6. The system propyl methanoate(1)+ benzene(2) is azeotropic in the measured P - T range. The azeotropic data were calculated from P - x data at constant temperature under application of the Wilson equation for the concentration dependence of the liquid phase activity coefficients (Table 5). From these data we obtain by extrapolation at Pdz = 101.32 kPa, Taz = 351.98 K and xl~z = 0.417. Lecat [18,19] reports T,~ = 351.65 K and xj~ = 0.440. Additionally we estimated the limiting activity coefficients y~i of the propyl methanoate(l) + benzene(2) system from the three-parameter Redlich-Kister equation (Table 8). 3. T h e o r y The DISQUAC model was applied using the same equations as reported previously [1]. The interactional terms in the thermodynamic properties G E, H E and CE contain a dispersive (DIS) and a quasi-chemical (QUAC) term which are calculated independently by the classical formulas and then simply added. 3.1. Geometrical parameters
The molecules under study, i.e. n-alkyl methanoates and benzene are regarded as possessing three types of surface s: (1) type a, (CH 3 or CH 2 groups in n-alkyl methanoates); (2) type b, (C6H6benzene); (3) type k, (CO0 group in n-alkyl methanoates). The geometrical parameters related to a group surface of type s on a molecule i, i.e. the relative volumes r i, the relative surface qi, and the surface fraction crsi (s = a, b, k), for components investigated in this work have been calculated on the basis of the group volumes VC and surfaces A6 recommended by Bondi [21], taking arbitarily the volume and surface of methane as unity. The same values have been used as previously [1]. 3.2. Estimation of the interaction parameters
The three types of surface generate three pairs of contact: (a, b), (a, k), and (b, k). The nonpolar aliphatic/benzene (a, b) interactions are represented solely by dispersive parameters t-,DIS _ which have been previously estimated [22]. The numerical values of these parameters are: ~ab.l 0.251, "~ab,2 c-DIS= 0.560, and c~D~S = --0.620. The polar aliphatic/COO (a, k) interactions are repre~ab,3 sented by both dispersive and quasi-chemical parameters which have been previously determined [23]. The numerical values of these parameters depend on the chain length of the methanoate and are listed in Table 9. The aromatic/COO (b, k) interactions are best reproduced when the corresponding -
-
Table 9 rqUAC for contacts (a, k): type a, CH 3 or CH 2 in n-alkane or Dispersive and quasi-chemical interchange coefficients, C.kD~s J , ~ak./ n-alkyl methanoate; type k, C O O in H C O O ( C H 2 ) m_ ~ECH~ m
/~DIS ~ak, I
g-,DIS ~ak,2
t-~DIS ~ak,3
t'~QUAC ~ak. I
F, QUAC ~ak.2
(-QUAC ~ak,3
1 2 >__3
1.12 1.50 1.50
1.7 3.0 3.0
0.0 0.0 0.0
4.15 3.41 3.41
5.97 4.86 4.86
1.80 1.80 1.00
G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173-183
Table 10 Dispersive interchange coefficients, ~bk,/ c-DiS for the contact (b, k): type b, C6H 6 HCOO(CH2),,, IICH3 (the quasi-chemical coefficientsare equal to zero)
181
(benzene),
?;v/
/-~DIS ~bk, 1
/'~ DIS ~bk,2
1
3.52
4.80
2.00
2 3 >4
2.98a 2.91a 2.91
3.97a 3.75 3.65
2.20 3.00 3.00
type
k,
CO0 in
/~DIS ~bk,3
~Adjusted parameter from experimental data. coefficients are taken entirely dispersive [1 ]. The numerical values of these parameters depend on the chain length of the methanoate and are listed in Table 10. Tables 6 - 8 show numerical comparisons between experimental G E, H E, and y~ data and DISQUAC calculations. Delcros et al. [1] have determined the dispersive parameters for ethyl methanoate + benzene on the basis of the experimental data of Ref. [17], G E at 323.15 K and H E at 298.15, 308.15 and 318.15 K. The parameters for the other methanoates were guessed. Our G E data on ethyl methanoate + benzene [3] are quite well represented by nearly the same parameters. However, the guessed value of the Gibbs energy parameter, ~c-D~s b k , l = 2.75 [1], yields a G E which is only 50% or less of the present G E value of propyl methanoate + benzene. A new adjustment yields r-D~S ~""bk, 1 = 2.91 (Table 10). It appears that G E is quite sensitive to the parameter value. This happens usually in mixtures of a polar + a polarizable component. The calculated G E is the sum of a small combinatorial term, a large positive dispersive term, and a large negative quasi-chemical term. Small absolute changes in the dispersive term result in large relative changes in the total G E value.
4. List of symbols Al, A2, A3 A,B,C C Cp
G H m N P q
R r
T x
Y Z
Redlich--Kister parameters, Eq. (3) parameters in the Antoine equation, Eq. (1) interchange coefficient molar heat capacity at constant pressure molar Gibbs energy molar enthalpy number of C atoms in the n-alkyl group number of experimental values pressure relative molecular surface gas constant relative molecular volume absolute temperature mole fraction in liquid phase mole fraction in vapor phase coordination number, Eq. (5)
G. Figurski et al. / Fluid Phase Equilibria 137 (1997) 173 183
182
4.1. Greek letters O/
4, Y 0 O"
A
molecular surface fraction volume fraction, Eq. (5) activity coefficient area fraction, Eq. (5) experimental uncertainty or standard deviation UNIQUAC binary parameter, Eq. (5) Wilson binary parameter, Eq. (4)
4.2. Superscripts DIS E QUAC
dispersive term excess property quasi-chemical term property at infinite dilution (x i =
o)
4.3. Subscripts a, b, k, type of contact surface: a, CH 3, C H 2 : b, C o H 6 ; k, COO az, azeotropic value i,j, type of molecule (i :/:j) l, order of interchange coefficient: 1 = 1, Gibbs energy; 1 = 2, enthalpy; l = 3, heat capacity s, t, type of contact surfaces (s va t)
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