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Isothermal vapour-liquid equilibrium data of the benzene-propylene system at 25°C
Fluid Phase Equilibria, 46 (1989) 53-58 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
53
I S O T H E R M A L V A P O U R - L I Q U I D E Q U I L I B R I U M DATA OF THE B E N Z E N E - P R O P Y L E N E S Y S T E M AT 25 °C HIROFUSA YAMAMOTO, KAZUNARI OHGAKI and TAKASHI KATAYAMA Department of Chemical Engineerin& Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560 (Japan) (Received May 17, 1988; accepted in final form September 7, 1988)
ABSTRACT Yamamoto, H., Ohgaki, K. and Katayama, T., 1989. Isothermal vapour-liquid equilibrium data of the benzene-propylene system at 25 o C. Fluid Phase Equilibria, 46: 53-58. The vapour-liquid equilibria ( p - x - y relation) and the liquid molar volumes (Vlm-X relation) of the benzene-propylene system were measured at 25 o C using a swing method and a weighing method, respectively. The equilibrium properties (p-x-y-Vim relation) are correlated very well by the Soave-Redlich-Kwong equation of state with a binary parameter (k U = 0.0157).
INTRODUCTION Phase equilibrium properties at elevated pressures are essential not only in practical problems b u t also in thermodynamic studies on equations of state. It would be interesting to investigate the applicability of an equation of state to p - x - y relations and volumetric properties simultaneously. In the present study, isothermal v a p o u r - l i q u i d equilibria ( p - x - y relation) and saturated molar volumes ( V ~ - x relation) of the b e n z e n e - p r o pylene system were measured at 25 ° C b y means of a swing method and a weighing method (Ohgaki et al., 1988), respectively. N o equilibrium properties of the system have been reported in the literature. The S o a v e - R e d l i c h K w o n g (SRK) equation of state (Soave, 1972) was used to correlate the experimental p-Vlm-X-y data and fugacity coefficients. EXPERIMENTAL DETAILS As the experimental apparatus and procedure used in this study are essentially the same as described in a previous paper (Ohgaki et al., 1988), the details are not mentioned here. 0378-3812/89/$03.50
© 1989 Elsevier Science Publishers B.V.
54 The phase equilibria ( p - x - y relation) were measured by means of a static method, the so-called swing method. The apparatus had two equilibrium cells. Both the vapour and liquid phases of each cell were connected by flexible tubes. The liquid contents of the cell were "swung" from one cell to another through the flexible tube as one of the cells was moved up and down. A small amount of sample of each phase, which was drawn out from a sampling port in the flexible tube without disturbing the phase equilibrium, was expanded in a Pyrex flask. The composition of each sample was analysed using gas chromatography. Another apparatus, using the weighing method, was used for measuring the saturated molar volume of the liquid phase (Vl-x relation). The cell volume having a small pressure dependence was calibrated utilizing pure saturated benzene and propylene, the properties of which are available in the literature (Angus et al., 1976; Reid et al., 1977). The equilibrium pressure was measured using a quartz-Bourdon gauge calibrated against an air piston gauge with an accuracy of 100 Pa. The equilibrium temperature was measured by a platinum wire resistance thermometer bridge within an accuracy of _ 0.01 ° C.
Materials The propylene used in this study was specially supplied by Sumitomo Chem. Co., Ltd., and had a specified minimum purity of 99.96 mol.%. The benzene, obtained from the Merk Co., was Spectro-grade with a specified minimum purity of 99.7 mol.%. Both chemicals were used without further purification. RESULTS AND DISCUSSION The saturated molar volumes of the liquid phase are listed in Table 1 and shown in Fig. 1. The Vlm--X curve has a minimum where the mole fraction of propylene is about 0.8. Such behaviour has not been observed in four other systems containing propylene (Ohgaki et al, 1988). The Vtm--X data were correlated using the Redlich-Kister-type equation presented in Table 1. Vapour-liquid equilibrium data are shown in Fig. 2. As the mole fraction of propylene in the vapour phase is nearly equal to 1.0, the Lewis rule can apply to the propylene in the vapour phase. The fugacity coefficients of propylene in each phase are Ot = @~*
(1)
~1 = q~g2Yz/Xz
(2)
55 TABLE 1 Saturated molar volume of liquid phase for the benzene(1)-propylene(2) system at 25 o C Composition X2
Molar volume V1 (cm 3 mo1-1)
0.0 0.1325 0.2918 0.4407 0.5764 0.6868 0.8212 0.9195 1.0
89.18 a 86.97 85.21 83.51 82.10 80.95 80.18 80.95 83.39 b
Vm1 = g mI* l X 1 + gd~2x 2 - (2.0232 + 32.394x2)xlx 2 a From Reid et al. (1977). b From Angus et al. (1976).
where x 2 and Y2 are the mole fractions of propylene in the liquid and vapour phases respectively. The fugacity coefficient ~2g* of pure propylene was obtained from the IUPAC-recommended value (Angus et al., 1976). The value of Ol2 was calculated from eqns. (1) and (2). The activity coefficient ~t2 of propylene in the liquid phase is expressed as
o" exp [[ j:~' F21 dp]} -1 V2 =q,~2y2p(x2f2 , : ~--~
(3)
where p is total pressure and fo* is the fugacity of pure liquid propylene at the standard state (p =p0). ~21 is the partial molar volume of propylene in 90 \
0
expl.
C
"6 85 E v
75 0-0
0~5
1-0
x2 [--]
Fig. 1. Saturated molar volume of liquid phase for the system benzene(1)-propylene(2) at 25°C.
56 1.5
i
0 expi. --
"'0 1.0 13. ~r
5RKeq.
~p~/ li
0.5
vapor
pt~as~
0
015 x2, Y2[-J
1.0
Fig. 2. Vapour-liquid equilibria for the system benzene(1)-propylene(2) at 25 o C.
the liquid phase. By using the Redlich-Kister equation (Redlich et al., 1952), the activity coefficient "/1 of benzene is evaluated under the isothermal and isobaric Gibbs-Duhem conditions. Then the fugacity coefficient ~1~ of benzene in the vapour phase is obtained from eqn. (4). ~lXl f ? * dP~=~l p
exp[f~po(Vl/RZ) dP] P --1
(4)
where subscript 1 denotes benzene. Finally, the fugacity coefficient of benzene in the liquid phase is obtained from eqn. (5).
q;
q)~yl/xl
=
(5)
The partial molar volumes in eqns. (3) and (4) were calculated from the differentiation of the Redlich-Kister-type equation for the V l - x data. The p - x - y data and the fugacity coefficients obtained are presented in Table 2. The SRK equation was applied to the p - x - y data obtained by using a binary parameter, kij. The parameters f~a and fib in the SRK equation were evaluated from the saturated pressure and liquid density data for each component (flal = 0.3933, ~ b l = 0.07881, f~2 = 0.40736 and f~b2= 0.08117). The critical properties and acentric factor of each substance were obtained from the "Property Data Bank" (Reid et al., 1977). As Fig. 2 shows, the p - x - y relation is satisfactorily correlated with the value of k u = 0.0157. The fugacity coefficients of both components evaluated from eqns. (1)-(5) are also compared in Fig. 3 with those of the SRK equation (kij = 0.0157). Furthermore, the Vtm--Xrelation is expressed very well by the SRK equation (kij 0.0157), except for the minimum value of V~ as shown in Fig. 1. However, two different values of k~j must be introduced in the correlations =
57
4 ~ 2
O' expl. --
snt~ eq.
\
-2
-40
0.6 p EMPo~
1.2
Fig. 3. F u g a c i t y c o e f f i c i e n t s for t h e s y s t e m b e n z e n e ( 1 ) - p r o p y l e n e ( 2 ) at 25 ° C.
TABLE 2
p-x-y
r e l a t i o n a n d f u g a c i t y c o e f f i c i e n t s for t h e b e n z e n e ( 1 ) - p r o p y l e n e ( 2 )
Pressure
Composition
Fugacity coefficients
p (MPa)
x2
Y2
111 ~
In ~
0.01269 a 0.1477 0.2321 0.3538 0.4660 0.5690 0.6827 0.7870 0.8830 0.9523 1.0428 1.0948 1.1566 b
0.0 0.0773 0.1367 0.2231 0.3161 0.4252 0.5379 0.6432 0.7444 0.8265 0.9073 0.9509 1.0
0.0 0.9101 0.9435 0.9632 0.9746 0.9801 0.9852 0.9890 0.9917 0.9940 0.9966 0.9981 1.0
- 0.0103 - 0.1270 - 0.1695 - 0.2434 - 0.2404 - 0.3166 - 0.3490 - 0.3678 - 0.4325 - 0.4701 - 0.5009 - 0.5300 -- 0.663 c
--
s y s t e m a t 25 ° C
In ~
0.0103 2.4556 2.8960 3.2932 3.5335 3.6799 3.7902 3.8471 3.8598 3.8346 3.8065 3.7820 3.797 c
- --
In ~12
0.0202 0.0315 0.0475 0.0621 0.0751 0.0893 0.1020 0.1135 0.1216 0.1321 0.1380 0.1449
2.4557 1.9003 1.4151 1.0639 0.7600 0.5159 0.3282 0.1733 0.0629 - 0.0382 - 0.0896 -- 0 . 1 4 4 9
a F r o m R e i d et al. (1977). b F r o m A n g u s et al. (1976). c E x t r a p o l a t e d value.
of p-x-y reported
and
Vl-x
previously
relations (Ohgaki
for
other
four
systems
containing
propylene
et al., 1988).
ACKNOWLEDGMENTS The the
authors
experimental
are grateful
to Youki
measurements,
and
Gohda to the
for his assistance Sumitomo
Chem.
in performing Co.,
Ltd.,
for
58
supplying the propylene. This work was largely supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan. LIST OF SYMBOLS
f
k P
R T
Vm x
Y Y +
f~a, f~b
fugacity (MPa) binary parameter in SRK equation pressure (MPa) gas constant (J K -a mo1-1) temperature (K) molar volume (cm3 mol-1) mole fraction of liquid phase mole fraction of vapor phase activity coefficient fugacity coefficient parameter in SRK equation
Subscripts sat 1 2
saturated property benzene propylene
Superscripts g
1 0
gas phase liquid phase standard state (p = 0 Pa) partial molar quantity pure component
REFERENCES Angus, S., Armstrong, B. and de Reuck, K.M., 1976. Propylene. International Thermodynamic Tables of Fluid State. Pergamon Press, Oxford. Ohgaki, K., Takata, H., Washida, T. and Katayama, T., 1988. Phase equilibria for four binary systems containing propylene. Fluid Phase Equilibria, 43: 105-113. Redlich, O., Kister, T. and Turnquist, C.E., 1952. Thermodynamics of solutions. Analysis of vapor-liquid equilibria. Chem. Eng. Progr. Syrup. Ser., 48: 49-61. Reid, R.C., Prausnitz, J.M. and Sherwood, T.K., 1977. The properties of gases and liquids. Property Data Bank. McGraw-Hill, New York, 3rd edn., pp. 629-666. Soave, G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27: 1197-1203.
53
I S O T H E R M A L V A P O U R - L I Q U I D E Q U I L I B R I U M DATA OF THE B E N Z E N E - P R O P Y L E N E S Y S T E M AT 25 °C HIROFUSA YAMAMOTO, KAZUNARI OHGAKI and TAKASHI KATAYAMA Department of Chemical Engineerin& Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560 (Japan) (Received May 17, 1988; accepted in final form September 7, 1988)
ABSTRACT Yamamoto, H., Ohgaki, K. and Katayama, T., 1989. Isothermal vapour-liquid equilibrium data of the benzene-propylene system at 25 o C. Fluid Phase Equilibria, 46: 53-58. The vapour-liquid equilibria ( p - x - y relation) and the liquid molar volumes (Vlm-X relation) of the benzene-propylene system were measured at 25 o C using a swing method and a weighing method, respectively. The equilibrium properties (p-x-y-Vim relation) are correlated very well by the Soave-Redlich-Kwong equation of state with a binary parameter (k U = 0.0157).
INTRODUCTION Phase equilibrium properties at elevated pressures are essential not only in practical problems b u t also in thermodynamic studies on equations of state. It would be interesting to investigate the applicability of an equation of state to p - x - y relations and volumetric properties simultaneously. In the present study, isothermal v a p o u r - l i q u i d equilibria ( p - x - y relation) and saturated molar volumes ( V ~ - x relation) of the b e n z e n e - p r o pylene system were measured at 25 ° C b y means of a swing method and a weighing method (Ohgaki et al., 1988), respectively. N o equilibrium properties of the system have been reported in the literature. The S o a v e - R e d l i c h K w o n g (SRK) equation of state (Soave, 1972) was used to correlate the experimental p-Vlm-X-y data and fugacity coefficients. EXPERIMENTAL DETAILS As the experimental apparatus and procedure used in this study are essentially the same as described in a previous paper (Ohgaki et al., 1988), the details are not mentioned here. 0378-3812/89/$03.50
© 1989 Elsevier Science Publishers B.V.
54 The phase equilibria ( p - x - y relation) were measured by means of a static method, the so-called swing method. The apparatus had two equilibrium cells. Both the vapour and liquid phases of each cell were connected by flexible tubes. The liquid contents of the cell were "swung" from one cell to another through the flexible tube as one of the cells was moved up and down. A small amount of sample of each phase, which was drawn out from a sampling port in the flexible tube without disturbing the phase equilibrium, was expanded in a Pyrex flask. The composition of each sample was analysed using gas chromatography. Another apparatus, using the weighing method, was used for measuring the saturated molar volume of the liquid phase (Vl-x relation). The cell volume having a small pressure dependence was calibrated utilizing pure saturated benzene and propylene, the properties of which are available in the literature (Angus et al., 1976; Reid et al., 1977). The equilibrium pressure was measured using a quartz-Bourdon gauge calibrated against an air piston gauge with an accuracy of 100 Pa. The equilibrium temperature was measured by a platinum wire resistance thermometer bridge within an accuracy of _ 0.01 ° C.
Materials The propylene used in this study was specially supplied by Sumitomo Chem. Co., Ltd., and had a specified minimum purity of 99.96 mol.%. The benzene, obtained from the Merk Co., was Spectro-grade with a specified minimum purity of 99.7 mol.%. Both chemicals were used without further purification. RESULTS AND DISCUSSION The saturated molar volumes of the liquid phase are listed in Table 1 and shown in Fig. 1. The Vlm--X curve has a minimum where the mole fraction of propylene is about 0.8. Such behaviour has not been observed in four other systems containing propylene (Ohgaki et al, 1988). The Vtm--X data were correlated using the Redlich-Kister-type equation presented in Table 1. Vapour-liquid equilibrium data are shown in Fig. 2. As the mole fraction of propylene in the vapour phase is nearly equal to 1.0, the Lewis rule can apply to the propylene in the vapour phase. The fugacity coefficients of propylene in each phase are Ot = @~*
(1)
~1 = q~g2Yz/Xz
(2)
55 TABLE 1 Saturated molar volume of liquid phase for the benzene(1)-propylene(2) system at 25 o C Composition X2
Molar volume V1 (cm 3 mo1-1)
0.0 0.1325 0.2918 0.4407 0.5764 0.6868 0.8212 0.9195 1.0
89.18 a 86.97 85.21 83.51 82.10 80.95 80.18 80.95 83.39 b
Vm1 = g mI* l X 1 + gd~2x 2 - (2.0232 + 32.394x2)xlx 2 a From Reid et al. (1977). b From Angus et al. (1976).
where x 2 and Y2 are the mole fractions of propylene in the liquid and vapour phases respectively. The fugacity coefficient ~2g* of pure propylene was obtained from the IUPAC-recommended value (Angus et al., 1976). The value of Ol2 was calculated from eqns. (1) and (2). The activity coefficient ~t2 of propylene in the liquid phase is expressed as
o" exp [[ j:~' F21 dp]} -1 V2 =q,~2y2p(x2f2 , : ~--~
(3)
where p is total pressure and fo* is the fugacity of pure liquid propylene at the standard state (p =p0). ~21 is the partial molar volume of propylene in 90 \
0
expl.
C
"6 85 E v
75 0-0
0~5
1-0
x2 [--]
Fig. 1. Saturated molar volume of liquid phase for the system benzene(1)-propylene(2) at 25°C.
56 1.5
i
0 expi. --
"'0 1.0 13. ~r
5RKeq.
~p~/ li
0.5
vapor
pt~as~
0
015 x2, Y2[-J
1.0
Fig. 2. Vapour-liquid equilibria for the system benzene(1)-propylene(2) at 25 o C.
the liquid phase. By using the Redlich-Kister equation (Redlich et al., 1952), the activity coefficient "/1 of benzene is evaluated under the isothermal and isobaric Gibbs-Duhem conditions. Then the fugacity coefficient ~1~ of benzene in the vapour phase is obtained from eqn. (4). ~lXl f ? * dP~=~l p
exp[f~po(Vl/RZ) dP] P --1
(4)
where subscript 1 denotes benzene. Finally, the fugacity coefficient of benzene in the liquid phase is obtained from eqn. (5).
q;
q)~yl/xl
=
(5)
The partial molar volumes in eqns. (3) and (4) were calculated from the differentiation of the Redlich-Kister-type equation for the V l - x data. The p - x - y data and the fugacity coefficients obtained are presented in Table 2. The SRK equation was applied to the p - x - y data obtained by using a binary parameter, kij. The parameters f~a and fib in the SRK equation were evaluated from the saturated pressure and liquid density data for each component (flal = 0.3933, ~ b l = 0.07881, f~2 = 0.40736 and f~b2= 0.08117). The critical properties and acentric factor of each substance were obtained from the "Property Data Bank" (Reid et al., 1977). As Fig. 2 shows, the p - x - y relation is satisfactorily correlated with the value of k u = 0.0157. The fugacity coefficients of both components evaluated from eqns. (1)-(5) are also compared in Fig. 3 with those of the SRK equation (kij = 0.0157). Furthermore, the Vtm--Xrelation is expressed very well by the SRK equation (kij 0.0157), except for the minimum value of V~ as shown in Fig. 1. However, two different values of k~j must be introduced in the correlations =
57
4 ~ 2
O' expl. --
snt~ eq.
\
-2
-40
0.6 p EMPo~
1.2
Fig. 3. F u g a c i t y c o e f f i c i e n t s for t h e s y s t e m b e n z e n e ( 1 ) - p r o p y l e n e ( 2 ) at 25 ° C.
TABLE 2
p-x-y
r e l a t i o n a n d f u g a c i t y c o e f f i c i e n t s for t h e b e n z e n e ( 1 ) - p r o p y l e n e ( 2 )
Pressure
Composition
Fugacity coefficients
p (MPa)
x2
Y2
111 ~
In ~
0.01269 a 0.1477 0.2321 0.3538 0.4660 0.5690 0.6827 0.7870 0.8830 0.9523 1.0428 1.0948 1.1566 b
0.0 0.0773 0.1367 0.2231 0.3161 0.4252 0.5379 0.6432 0.7444 0.8265 0.9073 0.9509 1.0
0.0 0.9101 0.9435 0.9632 0.9746 0.9801 0.9852 0.9890 0.9917 0.9940 0.9966 0.9981 1.0
- 0.0103 - 0.1270 - 0.1695 - 0.2434 - 0.2404 - 0.3166 - 0.3490 - 0.3678 - 0.4325 - 0.4701 - 0.5009 - 0.5300 -- 0.663 c
--
s y s t e m a t 25 ° C
In ~
0.0103 2.4556 2.8960 3.2932 3.5335 3.6799 3.7902 3.8471 3.8598 3.8346 3.8065 3.7820 3.797 c
- --
In ~12
0.0202 0.0315 0.0475 0.0621 0.0751 0.0893 0.1020 0.1135 0.1216 0.1321 0.1380 0.1449
2.4557 1.9003 1.4151 1.0639 0.7600 0.5159 0.3282 0.1733 0.0629 - 0.0382 - 0.0896 -- 0 . 1 4 4 9
a F r o m R e i d et al. (1977). b F r o m A n g u s et al. (1976). c E x t r a p o l a t e d value.
of p-x-y reported
and
Vl-x
previously
relations (Ohgaki
for
other
four
systems
containing
propylene
et al., 1988).
ACKNOWLEDGMENTS The the
authors
experimental
are grateful
to Youki
measurements,
and
Gohda to the
for his assistance Sumitomo
Chem.
in performing Co.,
Ltd.,
for
58
supplying the propylene. This work was largely supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture, Japan. LIST OF SYMBOLS
f
k P
R T
Vm x
Y Y +
f~a, f~b
fugacity (MPa) binary parameter in SRK equation pressure (MPa) gas constant (J K -a mo1-1) temperature (K) molar volume (cm3 mol-1) mole fraction of liquid phase mole fraction of vapor phase activity coefficient fugacity coefficient parameter in SRK equation
Subscripts sat 1 2
saturated property benzene propylene
Superscripts g
1 0
gas phase liquid phase standard state (p = 0 Pa) partial molar quantity pure component
REFERENCES Angus, S., Armstrong, B. and de Reuck, K.M., 1976. Propylene. International Thermodynamic Tables of Fluid State. Pergamon Press, Oxford. Ohgaki, K., Takata, H., Washida, T. and Katayama, T., 1988. Phase equilibria for four binary systems containing propylene. Fluid Phase Equilibria, 43: 105-113. Redlich, O., Kister, T. and Turnquist, C.E., 1952. Thermodynamics of solutions. Analysis of vapor-liquid equilibria. Chem. Eng. Progr. Syrup. Ser., 48: 49-61. Reid, R.C., Prausnitz, J.M. and Sherwood, T.K., 1977. The properties of gases and liquids. Property Data Bank. McGraw-Hill, New York, 3rd edn., pp. 629-666. Soave, G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27: 1197-1203.