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Henry’s constants and infinite dilution activity coefficients of propane, propene, butane, isobutene, 1-butene, isobutane, trans-2-butene and 1,3-butadiene in 1-propanol at T=(260 to 340) K
J. Chem. Thermodynamics 36 (2004) 101–106 www.elsevier.com/locate/jct
HenryÕs constants and infinite dilution activity coefficients of propane, propene, butane, isobutene, 1-butene, isobutane, trans-2-butene and 1,3-butadiene in 1-propanol at T ¼ (260 to 340) K Yoshimori Miyano
*
Department of Chemistry and Bioscience, Kurashiki University of Science and the Arts, 2640 Nishinoura, Tsurajimacho, Kurashiki 712-8505, Japan Received 2 April 2003; accepted 21 August 2003
Abstract The HenryÕs constants and the infinite dilution activity coefficients of propane, propene, butane, isobutane, 1-butene, isobutene, trans-2-butene and 1,3-butadiene in 1-propanol at T ¼ (260 to 340) K are measured by a gas stripping method. The rigorous formula for evaluating the HenryÕs constants from the gas stripping measurements is used for these highly volatile mixtures. The accuracy of the measurements is about 2% for HenryÕs constants and 3% for the estimated infinite dilution activity coefficients. In the evaluations for the infinite dilution activity coefficients, the nonideality of solute is not negligible especially at higher temperatures and the estimated uncertainty in the infinite dilution activity coefficients include 1% for nonideality. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Data; Mixture; HenryÕs constant; Activity coefficient; 1-propanol; Gas stripping
1. Introduction A systematic study of gas solubilities, like HenryÕs constants, is useful in providing design data for absorption processes, as well as, indirectly, in aiding the analysis of molecular interactions in solutions. Butane gas is highly soluble in nonpolar, nonassociating solvents. Solubilities of nonreacting gases in nonpolar, nonassociating solvents generally follow an order of increasing solubility with increase in the normal boiling point temperature of liquefied gas. As the boiling point temperature of butane is higher than that of isobutane, it is expected that the solubilities of butane are greater than that of isobutane which means that the HenryÕs constant of butane are smaller than those of isobutane. Similarly, it is expected that the HenryÕs constants of 1butene are smaller than those of isobutene. While this approximate relationship exists, it is not sufficiently consistent to permit the prediction of gas solubility even for simple solutions. In polar and associating solvents, *
Tel.: +81-86-440-1069; fax: +81-86-440-1062. E-mail address: [email protected] (Y. Miyano).
0021-9614/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2003.08.018
the degree of association in the solvent has a most profound effect on the solubility [1]. Although a large number of {alkane + alcohol} and {alkene + alcohol} solubility data have been published, few data are available for binary mixtures of butane, or 1-butene, and their isomers with alcohol. The solubility data will be used to develop predictive methods. For group contribution methods, it may be necessary to take into account the differences between isomers. To develope molecular theory, an accurate intermolecular potential is necessary. The HenryÕs constant is directly related to the residual chemical potential of solute at infinite dilution, which is evaluated from the intermolecular potential between a solute molecule and a solvent molecule. Therefore, the HenryÕs constant is a suitable macroscopic property for testing the intermolecular potential between different kinds of molecules. The gas stripping method, proposed by Leroi et al. [2], has been used to measure the activity coefficients at infinite dilution of solutes in nonvolatile solvents, when the vapor pressures of the solutes were negligibly small [3,4]. In the previous work [5], the HenryÕs constants for binary mixtures of butane, or isobutane, or 1-butene or
102
Y. Miyano / J. Chem. Thermodynamics 36 (2004) 101–106
isobutene in methanol were measured with this method. For these volatile solutes and solvents, rigorous expression were derived for data reduction. In this work, the HenryÕs constants of binary mixtures propane, or propene, or butane, or isobutane, or 1butene, or isobutene, or trans-2-butene or 1,3-butadiene in 1-propanol are reported at T ¼ (260 to 340) K as measured by the gas stripping method.
2. Theory The gas stripping method, originally proposed by Leroi et al. [2], is based on the variation of vapor phase composition when the highly diluted solute of the liquid mixture is stripped from the solution by a constant flow of inert gas (helium). They derived an approximate equation to express the relationship between the solute peak area, S, detected by a gas chromatography, which is proportional to the vapor phase composition stripped from the solution, and the total volume of helium, Dt , flowing out of an equilibrium cell at time t as follows: ! c1 pglg S p pslg Dt : ð1Þ ln ¼ 1 ln 1 S0 pslg p pslg ns;0 RT In equation (1) S0 is the peak area of solute at time t ¼ 0, c1 the infinite dilution activity coefficient of solute, pglg the saturated vapor pressure of pure solute, pslg the saturated vapor pressure of pure solvent, p the system pressure, ns;0 the number of moles of solvent in the cell at t ¼ 0, R the gas constant, T the absolute temperature, D the flow rate of helium, and t the experimental time. From the equation (1), the activity coefficient of the solute at infinite dilution can be obtained. When the dry gas volume of helium, Dt , is used, it is not possible to solve the equation, which are based on the material balance and the thermodynamic relationships at equilibrium. Equation (1), which was derived under some assumptions, may not be used for highly volatile mixtures. When the volume, V , of the saturated gas flowing out of the equilibrium cell is used, we obtain [5] ! S Hg uVs ln ¼ 1 S0 uVg ð1 þ aÞfsL;o auVs Hg ! ð1 þ aÞfsL;o =uVs aHg =uVg V ; ð2Þ ln 1 ZRTnLs;0 þ Hg VGP;0 =uVg where Hg is the HenryÕs constant of solute, fsL;o the fugacity of pure solvent at the reference state (pure liquid at system temperature and pressure), Z the compressibility factor of the saturated vapor in the cell, uVg and uVs the fugacity coefficients of solute(g) and solvent(s) in vapor phase, respectively. The superscripts V and L are vapor and liquid phase, respectively. The nLs;0 is the
number of moles of solvent in the liquid phase in the cell at t ¼ 0 which is equivalent to V ¼ 0. The VGP;0 is the initial volume of the vapor phase in the cell. The volume of vapor phase in the cell at time t, VGP , is slightly depends on the gas volume withdrawn from the cell and it is expressed as pslg mL;lg s ; ð3Þ ZRT where mL;lg is the liquid molar volume of solvent at sats uration. At infinite dilution of solute, the solvent can be treated as a pure substance and the following relationship can be used: VGP ¼ VGP;0 þ aV ;
a¼
fsL;o ¼ pslg : uVs Equation (2) can be recast as 0 1 V H =u g g S 1A ln ¼ @ S0 ð1 þ aÞpslg a Hg =uVg 1 0 ð1 þ aÞpslg a Hg =uVg V A: ln @1 ZRTnLs;0 þ VGP;0 ðHg =uVg Þ
ð4Þ
ð5Þ
The infinite dilution activity coefficient of solute, c1 , can be obtained from lg 1 Hg ¼ fgL;0 c1 ¼ fglg kc1 ¼ ulg g pg kc ;
ð6Þ
and c1 ¼
Hg ; lg lg ug pg k
ð7Þ
where k is the Poynting correction factor, and may be approximated by 0 1 p pglg mL;lg g A: ð8Þ k exp @ RT The vapor pressures for pure substances were obtained from the literature [6]. The saturated liquid densities for pure substances were obtained from [7]. The thermodynamic properties appear in above equations, were calculated from the virial equation of state truncated after the second virial coefficient. The details of the calculation method was described elsewhere [5]. However, for propane and propene the pressure was sufficiently high, at higher temperatures, that the virial equation of state was truncated after the third virial coefficient. The fugacity coefficient of solute at saturation is given by 2 !2 3 lg lg 2 Bp p C B g g 4 5; ulg þ ð9Þ g ¼ exp RT 2 RT where B and C are the second and the third virial coefficients of solute, respectively. The third virial coefficients
Y. Miyano / J. Chem. Thermodynamics 36 (2004) 101–106
for propane and propene obtained from [8]. For other gases, we used C ¼ 0. The second virial coefficients were obtained from Van Ness and Abbott [9] and Tsonopoulos [10] as described in our previous paper [5]. The volume of the saturated gas flowing out of the equilibrium cell, V , can be evaluated from h i S0 p pslg V þ ð1 C2 V ÞC1 þ1 1 ¼ ZRTnHe ; KC2 ðC1 þ 1Þ ð10Þ
103
where nHe is the number of moles of helium flowing out of the cell and it was measured by a mass flow meter. The K is the proportional constant between the peak area of solute detected by a gas chromatography and its partial pressure. The values of K for all solutes were determined by using pure solutes.
the cell, the temperatures of the bath and the total moles of helium, nHe , which could be obtained from the integration of the flow rate, were also measured every 1 h. The pressure in the cell was assumed equal to atmospheric pressure and measured by a pressure transducer (Paroscientific, Inc., Digiquartz Pressure Transducer Model 215A and Tsukasa Sokken Co. Ltd., Digiquartz Pressure Computer Model 600S) with an accuracy of 10 Pa. The accuracy of HenryÕs constants obtained was 2%, and mostly depended on the accuracy of the mass flow meter. The butane, isobutane, 1-butene and isobutene were supplied by Takachiho Kagaku Kogyo at specified minimum mass fraction purities of 0.998, 0.99, 0.99 and 0.99, respectively. The propane and propene were supplied by Japan Fine Products at specified minimum mass fraction purities of 0.995 and 0.995, respectively. The trans-2-butene and 1,3-butadiene were supplied by Aldrich Chemicals at specific minimum mass fraction purities of 0.99 and 0.99, respectively. The 1-propanol was supplied by Wako Pure Chemical Ind., with a specified minimum mass fraction purity of 0.999.
3. Experimental
4. Results and discussion
An apparatus described previously [5] was used to measure HenryÕs constants. About 43 cm3 of the solvent (1-propanol) was introduced into the equilibrium cell, of volume about 44 cm3 , and the actual quantity determined by mass. The equilibrium cell was immersed in a constant-temperature bath [filled with {ethylene glycol + water}] and connected to a supply of solute gas and helium. The temperature was controlled within 0.02 K, and measured by a quartz thermometer (Hewlett Packard Co., Model 2804A) with accuracy of 0.01 K. After evacuating the connecting lines, the lines were pressurized with a solute gas at an arbitrary pressure, and then the solute gas was introduced into the equilibrium cell. The amount of the solute gas introduced into the cell was adjusted to keep the mole fraction lower than 3 104 in solution. After evacuating the connecting lines, helium began to flow into the equilibrium cell at a flow rate of about 2 cm3 min1 , which was measured by a mass flow meter (Koflok Co., Model 3300), with a maximum flow rate of 2 cm3 min1 and accuracy of 1%. The flow rate was controlled by a fine metering valve (double needles, Swagelok Co., SS2-D). The gas flowing out of the equilibrium cell was kept at a higher temperature than that of the bath, to avoid condensation, and introduced to a gas chromatograph (Hitachi Ltd., Model G-3000, with double flame ionization detector) to measure the solute peak area, S. Sampling, for the gas chromatography, was performed every 1 h and continued for about 15 h. The pressure in
Figure 1 shows the temperature dependency of the HenryÕs constants of propane, propene, butane,
and C1 ¼
Hg =uVg ð1 þ aÞpslg aHg =uVg
;
ð1 þ aÞpslg aHg =uVg C2 ¼ ; ZRTnLs;0 þ VGP;0 Hg =uVg
ð11Þ
FIGURE 1. HenryÕs constants of propane, propene, butane, isobutane, 1-butene, isobutene, trans-2-butene and 1,3-butadiene in 1-propanol at T ¼ (260 to 340) K (s, propane; m, propene; , butane; r, isobutane; d, 1-butene; n, isobutene; j, trans-2-butene; }, 1,3-butadiene; , propane, Exp. [14]; , propene, Exp. [14]; , propene, Exp. [13]; , propene, Exp. [11]; , butane, Exp. [12]; +, isobutene, Exp. [11]).
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Y. Miyano / J. Chem. Thermodynamics 36 (2004) 101–106
isobutane, 1-butene, isobutene, trans-2-butene and 1,3butadiene in 1-propanol at temperature from (260 to 340) K. Few data for propane, propene, butane and isobutene could be found in literatures. Narasimhan et al. [11] measured the gas solubilities of propene and isobutene at T ¼ 293:15 K and p ¼ 101:3 kPa. Miyano and Hayduk [12] measured the butane solubility at T ¼ (283.15 to 313.15) K and p ¼ 101:3 kPa. Konobeev and Lyapin [13] measured lg equilibria for (propene + 1propanol) at T ¼ (293.15 to 333.15) K and p ¼ (107.4 to 774.1) kPa. Nagahama et al. [14] measured the lg equilibria for (propane + 1-propanol) and (propene + 1-propanol) at T ¼ 293:05 K and p ¼ (143 to 960) kPa. In general, it is difficult to estimate the HenryÕs constants from gas solubility data at atmospheric pressure or lg equilibrium (VLE) data. The VLE and gas solubility data are usually measured at intermediate concentration and the smoothed data are obtained from the correlation with an activity coefficient equation. HenryÕs constants can be obtained from the extrapolation of the equation to infinite dilution. The HenryÕs constants so obtained will depend strongly on the equation. For comparative purposes, however, this figure contains the extrapolated values which had been estimated with Margules equation [15]. Figure 2 shows the temperature dependency of the infinite dilution activity coefficients for the same systems. As shown in figure 2, the infinite dilution activity coefficients between butane and isobutane show similar temperature dependencies and the differences in the values are small, about 7%, and the activity coefficients of butane are lower than that of the isomer. The similar phenomenon can be observed among 1-butene, isobutene and trans-2-butene. The differences in the infinite dilution activity coefficients among these gases are about 3%. But the infinite dilution activity coefficients of 1butene are greater than that of isobutene and smaller than that of trans-2-butene. The HenryÕs constants and the infinite dilution activity coefficients obtained in this work are listed in table 1 with some other predicted properties. As all experiments were obtained under atmospheric pressure, the estimated fugacity coefficients of solute in vapor phase and the compressibility factors of vapor were around to be unity (uV g ¼ 1, Z ¼ 1) for all systems. On the other hand, for evaluation of the infinite dilution activity coefficients, the nonideality of gases at saturation is not negligible. For highly volatile solutes like propene, the vapor pressure at T ¼ 340 K is about p ¼ 2900 kPa and the nonideality should be evaluated. As described in the previous section the nonideality of solute was calculated by the virial equation of state. To examine the viability of the virial equation of state at these high pressures, the Soave equation of state [16] was used for comparative purposes for calculating the fugacity coefficients of solute at saturation. The calcu-
FIGURE 2. The infinite dilution activity coefficients of propane, propene, butane, isobutane, 1-butene, isobutene, trans-2-butene and 1,3-butadiene in 1-propanol at T ¼ (260 to 340) K (s, propane; m, propene; , butane; r, isobutane; d, 1-butene; n, isobutene; j, trans2-butene; }, 1,3-butadiene; , propane, Exp. [14]; , propene, Exp. [14]; , propene, Exp. [13]; , propene, Exp. [11]; , butane, Exp. [12]; +, isobutene, Exp. [11]).
lated results from the virial equation of state truncated after the third virial coefficients agree with that calculated from the Soave equation of state within 1%. This means that the evaluated activity coefficients slightly depend on the estimation method for the nonideality. Therefore, it is considered that the accuracies of the obtained infinite dilution activity coefficients in table 1 may be no more than 3%. A group contribution method like UNIFAC [17] is widely used for the correlation of activity coefficients in industrial designs. In these methods, the fugacity of solute at saturation is approximated with the vapor pressure and the effective activity coefficient, c1 eff , is obtained from equation (7) as follows: lg c1 eff ¼ Hg =pg :
ð12Þ
This effective activity coefficient does not depend on the nonideality of solute and the accuracy of it is 2%. The values of the effective activity coefficients at infinite dilution are also listed in table 1. The comparison of c1 and c1 eff shows that the difference between them is very large at high temperatures and the temperature dependency of c1 is smaller than that of c1 eff .
Y. Miyano / J. Chem. Thermodynamics 36 (2004) 101–106
105
TABLE 1 HenryÕs constants and infinite dilution activity coefficients of solutes in 1-propanol T/K
Hg /kPa
c1
c1 eff
pslg /kPa
pglg /kPa
ulg g
k
311.3 582.5 998.8 1602.4 2431.9
0.920 0.881 0.836 0.791 0.747
0.992 0.983 0.968 0.947 0.915
259.98 279.96 299.96 320.03 339.95
1305 2330 3746 5535 7584
4.60 4.62 4.64 4.61 4.56
4.19 4.00 3.75 3.45 3.12
Solute ¼ propane 0.2 0.8 3.2 10.3 28.3
259.92 279.94 300.03 320.02 340.10
1246 2205 3546 5160 7042
3.58 3.61 3.66 3.64 3.64
3.24 3.10 2.94 2.69 2.43
Solute ¼ propene 0.2 0.8 3.2 10.3 28.5
384.7 710.6 1207.5 1916.7 2898.5
0.914 0.877 0.834 0.788 0.739
0.990 0.980 0.963 0.940 0.904
260.05 280.05 299.99 320.05 340.04
309 642 1194 1970 2985
5.17 5.06 5.03 4.88 4.74
5.03 4.81 4.62 4.30 3.95
Solute ¼ butane 0.2 0.8 3.2 10.3 28.4
61.3 133.4 258.2 458.1 755.0
0.971 0.952 0.926 0.894 0.857
1.002 0.999 0.994 0.986 0.974
259.98 279.94 300.16 320.00 339.92
502 988 1732 2750 4051
5.48 5.37 5.24 5.14 5.05
5.26 5.01 4.69 4.37 4.02
Solute ¼ isobutane 0.2 0.8 3.2 10.3 28.2
95.3 197.3 369.6 629.5 1006.6
0.960 0.936 0.904 0.868 0.828
1.000 0.996 0.989 0.978 0.963
260.03 280.04 299.98 320.03 340.00
308 641 1177 1938 2951
4.13 4.12 4.11 4.05 4.01
4.01 3.89 3.75 3.52 3.29
Solute ¼ 1-butene 0.2 0.8 3.2 10.3 28.4
76.9 164.7 314.2 550.1 896.2
0.968 0.946 0.919 0.885 0.847
1.001 0.998 0.992 0.983 0.971
259.91 279.95 299.94 320.06 340.16
308 641 1173 1946 2956
4.09 4.08 4.04 4.00 3.94
3.96 3.85 3.68 3.48 3.23
Solute ¼ isobutene 0.2 0.8 3.2 10.3 28.6
77.7 166.7 318.7 559.5 914.8
0.968 0.946 0.918 0.884 0.845
1.001 0.997 0.992 0.983 0.970
260.02 280.03 299.99 320.09 340.06
236 501 936 1586 2441
4.20 4.15 4.10 4.06 3.98
4.10 3.96 3.79 3.61 3.36
Solute ¼ trans-2-butene 0.2 0.8 3.2 10.3 28.4
57.5 126.6 246.8 439.9 725.5
0.973 0.955 0.930 0.900 0.865
1.002 0.999 0.995 0.988 0.978
259.99 280.05 300.01 320.04 339.99
235 496 924 1546 2366
3.39 3.37 3.37 3.34 3.29
3.29 3.20 3.10 2.94 2.75
Solute ¼ 1,3-butadiene 0.2 0.8 3.2 10.3 28.3
71.5 155.1 298.4 525.9 861.6
0.971 0.951 0.925 0.893 0.857
1.001 0.998 0.993 0.985 0.974
5. Conclusion The HenryÕs constants and the infinite dilution activity coefficients have been obtained from the gas stripping measurements at temperatures from (260 to 340) K. In evaluating the HenryÕs constants from the gas stripping measurements, the HenryÕs constant did not depend on the nonideality of solute and solvent so
much. The activity coefficients, on the other hand, strongly depended on the nonideality of solute at the reference state. The accuracy of HenryÕs constants measured by this work is within 2% at the entire temperature range. The accuracy of the infinite dilution activity coefficients, on the other hand, is within 3% which is worse than that for the HenryÕs constants because of the inaccuracy of the
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Y. Miyano / J. Chem. Thermodynamics 36 (2004) 101–106
estimated nonideality of gases, especially highly volatile gases like propane and propene.
Acknowledgements This paper reports part of the work supported by Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science (13650820), which is gratefully acknowledged.
References [1] W. Hayduk, H. Laudie, AIChE J. 19 (1973) 1233–1238. [2] J.-C. Leroi, J.-C. Masson, H. Renon, J.-F. Fabries, H. Sannier, Ind. Eng. Chem., Process. Des. Dev. 16 (1977) 139–144. [3] K. Fukuchi, K. Miyoshi, T. Watanabe, S. Yonezawa, Y. Arai, Fluid Phase Equilibr. 182 (2001) 257–263. [4] K. Fukuchi, K. Miyoshi, T. Watanabe, S. Yonezawa, Y. Arai, Fluid Phase Equilibr. 194–197 (2002) 937–945.
[5] Y. Miyano, K. Nakanishi, K. Fukuchi, Fluid Phase Equilibr. 208 (2003) 223–238. [6] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, McGraw-Hill, New York, 1987. [7] B.D. Smith, R. Srivastava, Thermodynamic Data for Pure Compounds: Part A and Part B, Elsevier, Amsterdam, 1986. [8] J.H. Dymond, E.B. Smith, The Virial Coefficients of Pure Gases and Mixtures, Clarendon Press, Oxford, 1980. [9] H.C. Van Ness, M.M. Abbott, Classical Thermodynamics of Nonelectrolyte Solutions, McGraw-Hill, New York, 1982. [10] C. Tsonopoulos, AIChE J. 21 (1975) 827–829. [11] S. Narasimhan, G.S. Natarajan, G.D. Nageshwar, Indian J. Technol. 19 (1981) 298–299. [12] Y. Miyano, W. Hayduk, J. Chem. Eng. Data 31 (1986) 77–80. [13] B.I. Konobeev, V.V. Lyapin, Khim. Promst. Moscow 43 (1967) 114–116. [14] K. Nagahama, S. Suda, T. Hakuta, M. Hirata, Sekiyu Gakkai Shi 14 (1971) 252–256. [15] M. Margules, Sitzgsber Acad. Wiss. Wien 104 (1985) 1243. [16] G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203. [17] A. Fredenslund, J. Gmehling, P. Rasmussen, Vapor–Liquid Equilibria Using UNIFAC, Elsevier, Amsterdam, 1977.
JCT 03/042
HenryÕs constants and infinite dilution activity coefficients of propane, propene, butane, isobutene, 1-butene, isobutane, trans-2-butene and 1,3-butadiene in 1-propanol at T ¼ (260 to 340) K Yoshimori Miyano
*
Department of Chemistry and Bioscience, Kurashiki University of Science and the Arts, 2640 Nishinoura, Tsurajimacho, Kurashiki 712-8505, Japan Received 2 April 2003; accepted 21 August 2003
Abstract The HenryÕs constants and the infinite dilution activity coefficients of propane, propene, butane, isobutane, 1-butene, isobutene, trans-2-butene and 1,3-butadiene in 1-propanol at T ¼ (260 to 340) K are measured by a gas stripping method. The rigorous formula for evaluating the HenryÕs constants from the gas stripping measurements is used for these highly volatile mixtures. The accuracy of the measurements is about 2% for HenryÕs constants and 3% for the estimated infinite dilution activity coefficients. In the evaluations for the infinite dilution activity coefficients, the nonideality of solute is not negligible especially at higher temperatures and the estimated uncertainty in the infinite dilution activity coefficients include 1% for nonideality. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Data; Mixture; HenryÕs constant; Activity coefficient; 1-propanol; Gas stripping
1. Introduction A systematic study of gas solubilities, like HenryÕs constants, is useful in providing design data for absorption processes, as well as, indirectly, in aiding the analysis of molecular interactions in solutions. Butane gas is highly soluble in nonpolar, nonassociating solvents. Solubilities of nonreacting gases in nonpolar, nonassociating solvents generally follow an order of increasing solubility with increase in the normal boiling point temperature of liquefied gas. As the boiling point temperature of butane is higher than that of isobutane, it is expected that the solubilities of butane are greater than that of isobutane which means that the HenryÕs constant of butane are smaller than those of isobutane. Similarly, it is expected that the HenryÕs constants of 1butene are smaller than those of isobutene. While this approximate relationship exists, it is not sufficiently consistent to permit the prediction of gas solubility even for simple solutions. In polar and associating solvents, *
Tel.: +81-86-440-1069; fax: +81-86-440-1062. E-mail address: [email protected] (Y. Miyano).
0021-9614/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2003.08.018
the degree of association in the solvent has a most profound effect on the solubility [1]. Although a large number of {alkane + alcohol} and {alkene + alcohol} solubility data have been published, few data are available for binary mixtures of butane, or 1-butene, and their isomers with alcohol. The solubility data will be used to develop predictive methods. For group contribution methods, it may be necessary to take into account the differences between isomers. To develope molecular theory, an accurate intermolecular potential is necessary. The HenryÕs constant is directly related to the residual chemical potential of solute at infinite dilution, which is evaluated from the intermolecular potential between a solute molecule and a solvent molecule. Therefore, the HenryÕs constant is a suitable macroscopic property for testing the intermolecular potential between different kinds of molecules. The gas stripping method, proposed by Leroi et al. [2], has been used to measure the activity coefficients at infinite dilution of solutes in nonvolatile solvents, when the vapor pressures of the solutes were negligibly small [3,4]. In the previous work [5], the HenryÕs constants for binary mixtures of butane, or isobutane, or 1-butene or
102
Y. Miyano / J. Chem. Thermodynamics 36 (2004) 101–106
isobutene in methanol were measured with this method. For these volatile solutes and solvents, rigorous expression were derived for data reduction. In this work, the HenryÕs constants of binary mixtures propane, or propene, or butane, or isobutane, or 1butene, or isobutene, or trans-2-butene or 1,3-butadiene in 1-propanol are reported at T ¼ (260 to 340) K as measured by the gas stripping method.
2. Theory The gas stripping method, originally proposed by Leroi et al. [2], is based on the variation of vapor phase composition when the highly diluted solute of the liquid mixture is stripped from the solution by a constant flow of inert gas (helium). They derived an approximate equation to express the relationship between the solute peak area, S, detected by a gas chromatography, which is proportional to the vapor phase composition stripped from the solution, and the total volume of helium, Dt , flowing out of an equilibrium cell at time t as follows: ! c1 pglg S p pslg Dt : ð1Þ ln ¼ 1 ln 1 S0 pslg p pslg ns;0 RT In equation (1) S0 is the peak area of solute at time t ¼ 0, c1 the infinite dilution activity coefficient of solute, pglg the saturated vapor pressure of pure solute, pslg the saturated vapor pressure of pure solvent, p the system pressure, ns;0 the number of moles of solvent in the cell at t ¼ 0, R the gas constant, T the absolute temperature, D the flow rate of helium, and t the experimental time. From the equation (1), the activity coefficient of the solute at infinite dilution can be obtained. When the dry gas volume of helium, Dt , is used, it is not possible to solve the equation, which are based on the material balance and the thermodynamic relationships at equilibrium. Equation (1), which was derived under some assumptions, may not be used for highly volatile mixtures. When the volume, V , of the saturated gas flowing out of the equilibrium cell is used, we obtain [5] ! S Hg uVs ln ¼ 1 S0 uVg ð1 þ aÞfsL;o auVs Hg ! ð1 þ aÞfsL;o =uVs aHg =uVg V ; ð2Þ ln 1 ZRTnLs;0 þ Hg VGP;0 =uVg where Hg is the HenryÕs constant of solute, fsL;o the fugacity of pure solvent at the reference state (pure liquid at system temperature and pressure), Z the compressibility factor of the saturated vapor in the cell, uVg and uVs the fugacity coefficients of solute(g) and solvent(s) in vapor phase, respectively. The superscripts V and L are vapor and liquid phase, respectively. The nLs;0 is the
number of moles of solvent in the liquid phase in the cell at t ¼ 0 which is equivalent to V ¼ 0. The VGP;0 is the initial volume of the vapor phase in the cell. The volume of vapor phase in the cell at time t, VGP , is slightly depends on the gas volume withdrawn from the cell and it is expressed as pslg mL;lg s ; ð3Þ ZRT where mL;lg is the liquid molar volume of solvent at sats uration. At infinite dilution of solute, the solvent can be treated as a pure substance and the following relationship can be used: VGP ¼ VGP;0 þ aV ;
a¼
fsL;o ¼ pslg : uVs Equation (2) can be recast as 0 1 V H =u g g S 1A ln ¼ @ S0 ð1 þ aÞpslg a Hg =uVg 1 0 ð1 þ aÞpslg a Hg =uVg V A: ln @1 ZRTnLs;0 þ VGP;0 ðHg =uVg Þ
ð4Þ
ð5Þ
The infinite dilution activity coefficient of solute, c1 , can be obtained from lg 1 Hg ¼ fgL;0 c1 ¼ fglg kc1 ¼ ulg g pg kc ;
ð6Þ
and c1 ¼
Hg ; lg lg ug pg k
ð7Þ
where k is the Poynting correction factor, and may be approximated by 0 1 p pglg mL;lg g A: ð8Þ k exp @ RT The vapor pressures for pure substances were obtained from the literature [6]. The saturated liquid densities for pure substances were obtained from [7]. The thermodynamic properties appear in above equations, were calculated from the virial equation of state truncated after the second virial coefficient. The details of the calculation method was described elsewhere [5]. However, for propane and propene the pressure was sufficiently high, at higher temperatures, that the virial equation of state was truncated after the third virial coefficient. The fugacity coefficient of solute at saturation is given by 2 !2 3 lg lg 2 Bp p C B g g 4 5; ulg þ ð9Þ g ¼ exp RT 2 RT where B and C are the second and the third virial coefficients of solute, respectively. The third virial coefficients
Y. Miyano / J. Chem. Thermodynamics 36 (2004) 101–106
for propane and propene obtained from [8]. For other gases, we used C ¼ 0. The second virial coefficients were obtained from Van Ness and Abbott [9] and Tsonopoulos [10] as described in our previous paper [5]. The volume of the saturated gas flowing out of the equilibrium cell, V , can be evaluated from h i S0 p pslg V þ ð1 C2 V ÞC1 þ1 1 ¼ ZRTnHe ; KC2 ðC1 þ 1Þ ð10Þ
103
where nHe is the number of moles of helium flowing out of the cell and it was measured by a mass flow meter. The K is the proportional constant between the peak area of solute detected by a gas chromatography and its partial pressure. The values of K for all solutes were determined by using pure solutes.
the cell, the temperatures of the bath and the total moles of helium, nHe , which could be obtained from the integration of the flow rate, were also measured every 1 h. The pressure in the cell was assumed equal to atmospheric pressure and measured by a pressure transducer (Paroscientific, Inc., Digiquartz Pressure Transducer Model 215A and Tsukasa Sokken Co. Ltd., Digiquartz Pressure Computer Model 600S) with an accuracy of 10 Pa. The accuracy of HenryÕs constants obtained was 2%, and mostly depended on the accuracy of the mass flow meter. The butane, isobutane, 1-butene and isobutene were supplied by Takachiho Kagaku Kogyo at specified minimum mass fraction purities of 0.998, 0.99, 0.99 and 0.99, respectively. The propane and propene were supplied by Japan Fine Products at specified minimum mass fraction purities of 0.995 and 0.995, respectively. The trans-2-butene and 1,3-butadiene were supplied by Aldrich Chemicals at specific minimum mass fraction purities of 0.99 and 0.99, respectively. The 1-propanol was supplied by Wako Pure Chemical Ind., with a specified minimum mass fraction purity of 0.999.
3. Experimental
4. Results and discussion
An apparatus described previously [5] was used to measure HenryÕs constants. About 43 cm3 of the solvent (1-propanol) was introduced into the equilibrium cell, of volume about 44 cm3 , and the actual quantity determined by mass. The equilibrium cell was immersed in a constant-temperature bath [filled with {ethylene glycol + water}] and connected to a supply of solute gas and helium. The temperature was controlled within 0.02 K, and measured by a quartz thermometer (Hewlett Packard Co., Model 2804A) with accuracy of 0.01 K. After evacuating the connecting lines, the lines were pressurized with a solute gas at an arbitrary pressure, and then the solute gas was introduced into the equilibrium cell. The amount of the solute gas introduced into the cell was adjusted to keep the mole fraction lower than 3 104 in solution. After evacuating the connecting lines, helium began to flow into the equilibrium cell at a flow rate of about 2 cm3 min1 , which was measured by a mass flow meter (Koflok Co., Model 3300), with a maximum flow rate of 2 cm3 min1 and accuracy of 1%. The flow rate was controlled by a fine metering valve (double needles, Swagelok Co., SS2-D). The gas flowing out of the equilibrium cell was kept at a higher temperature than that of the bath, to avoid condensation, and introduced to a gas chromatograph (Hitachi Ltd., Model G-3000, with double flame ionization detector) to measure the solute peak area, S. Sampling, for the gas chromatography, was performed every 1 h and continued for about 15 h. The pressure in
Figure 1 shows the temperature dependency of the HenryÕs constants of propane, propene, butane,
and C1 ¼
Hg =uVg ð1 þ aÞpslg aHg =uVg
;
ð1 þ aÞpslg aHg =uVg C2 ¼ ; ZRTnLs;0 þ VGP;0 Hg =uVg
ð11Þ
FIGURE 1. HenryÕs constants of propane, propene, butane, isobutane, 1-butene, isobutene, trans-2-butene and 1,3-butadiene in 1-propanol at T ¼ (260 to 340) K (s, propane; m, propene; , butane; r, isobutane; d, 1-butene; n, isobutene; j, trans-2-butene; }, 1,3-butadiene; , propane, Exp. [14]; , propene, Exp. [14]; , propene, Exp. [13]; , propene, Exp. [11]; , butane, Exp. [12]; +, isobutene, Exp. [11]).
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Y. Miyano / J. Chem. Thermodynamics 36 (2004) 101–106
isobutane, 1-butene, isobutene, trans-2-butene and 1,3butadiene in 1-propanol at temperature from (260 to 340) K. Few data for propane, propene, butane and isobutene could be found in literatures. Narasimhan et al. [11] measured the gas solubilities of propene and isobutene at T ¼ 293:15 K and p ¼ 101:3 kPa. Miyano and Hayduk [12] measured the butane solubility at T ¼ (283.15 to 313.15) K and p ¼ 101:3 kPa. Konobeev and Lyapin [13] measured lg equilibria for (propene + 1propanol) at T ¼ (293.15 to 333.15) K and p ¼ (107.4 to 774.1) kPa. Nagahama et al. [14] measured the lg equilibria for (propane + 1-propanol) and (propene + 1-propanol) at T ¼ 293:05 K and p ¼ (143 to 960) kPa. In general, it is difficult to estimate the HenryÕs constants from gas solubility data at atmospheric pressure or lg equilibrium (VLE) data. The VLE and gas solubility data are usually measured at intermediate concentration and the smoothed data are obtained from the correlation with an activity coefficient equation. HenryÕs constants can be obtained from the extrapolation of the equation to infinite dilution. The HenryÕs constants so obtained will depend strongly on the equation. For comparative purposes, however, this figure contains the extrapolated values which had been estimated with Margules equation [15]. Figure 2 shows the temperature dependency of the infinite dilution activity coefficients for the same systems. As shown in figure 2, the infinite dilution activity coefficients between butane and isobutane show similar temperature dependencies and the differences in the values are small, about 7%, and the activity coefficients of butane are lower than that of the isomer. The similar phenomenon can be observed among 1-butene, isobutene and trans-2-butene. The differences in the infinite dilution activity coefficients among these gases are about 3%. But the infinite dilution activity coefficients of 1butene are greater than that of isobutene and smaller than that of trans-2-butene. The HenryÕs constants and the infinite dilution activity coefficients obtained in this work are listed in table 1 with some other predicted properties. As all experiments were obtained under atmospheric pressure, the estimated fugacity coefficients of solute in vapor phase and the compressibility factors of vapor were around to be unity (uV g ¼ 1, Z ¼ 1) for all systems. On the other hand, for evaluation of the infinite dilution activity coefficients, the nonideality of gases at saturation is not negligible. For highly volatile solutes like propene, the vapor pressure at T ¼ 340 K is about p ¼ 2900 kPa and the nonideality should be evaluated. As described in the previous section the nonideality of solute was calculated by the virial equation of state. To examine the viability of the virial equation of state at these high pressures, the Soave equation of state [16] was used for comparative purposes for calculating the fugacity coefficients of solute at saturation. The calcu-
FIGURE 2. The infinite dilution activity coefficients of propane, propene, butane, isobutane, 1-butene, isobutene, trans-2-butene and 1,3-butadiene in 1-propanol at T ¼ (260 to 340) K (s, propane; m, propene; , butane; r, isobutane; d, 1-butene; n, isobutene; j, trans2-butene; }, 1,3-butadiene; , propane, Exp. [14]; , propene, Exp. [14]; , propene, Exp. [13]; , propene, Exp. [11]; , butane, Exp. [12]; +, isobutene, Exp. [11]).
lated results from the virial equation of state truncated after the third virial coefficients agree with that calculated from the Soave equation of state within 1%. This means that the evaluated activity coefficients slightly depend on the estimation method for the nonideality. Therefore, it is considered that the accuracies of the obtained infinite dilution activity coefficients in table 1 may be no more than 3%. A group contribution method like UNIFAC [17] is widely used for the correlation of activity coefficients in industrial designs. In these methods, the fugacity of solute at saturation is approximated with the vapor pressure and the effective activity coefficient, c1 eff , is obtained from equation (7) as follows: lg c1 eff ¼ Hg =pg :
ð12Þ
This effective activity coefficient does not depend on the nonideality of solute and the accuracy of it is 2%. The values of the effective activity coefficients at infinite dilution are also listed in table 1. The comparison of c1 and c1 eff shows that the difference between them is very large at high temperatures and the temperature dependency of c1 is smaller than that of c1 eff .
Y. Miyano / J. Chem. Thermodynamics 36 (2004) 101–106
105
TABLE 1 HenryÕs constants and infinite dilution activity coefficients of solutes in 1-propanol T/K
Hg /kPa
c1
c1 eff
pslg /kPa
pglg /kPa
ulg g
k
311.3 582.5 998.8 1602.4 2431.9
0.920 0.881 0.836 0.791 0.747
0.992 0.983 0.968 0.947 0.915
259.98 279.96 299.96 320.03 339.95
1305 2330 3746 5535 7584
4.60 4.62 4.64 4.61 4.56
4.19 4.00 3.75 3.45 3.12
Solute ¼ propane 0.2 0.8 3.2 10.3 28.3
259.92 279.94 300.03 320.02 340.10
1246 2205 3546 5160 7042
3.58 3.61 3.66 3.64 3.64
3.24 3.10 2.94 2.69 2.43
Solute ¼ propene 0.2 0.8 3.2 10.3 28.5
384.7 710.6 1207.5 1916.7 2898.5
0.914 0.877 0.834 0.788 0.739
0.990 0.980 0.963 0.940 0.904
260.05 280.05 299.99 320.05 340.04
309 642 1194 1970 2985
5.17 5.06 5.03 4.88 4.74
5.03 4.81 4.62 4.30 3.95
Solute ¼ butane 0.2 0.8 3.2 10.3 28.4
61.3 133.4 258.2 458.1 755.0
0.971 0.952 0.926 0.894 0.857
1.002 0.999 0.994 0.986 0.974
259.98 279.94 300.16 320.00 339.92
502 988 1732 2750 4051
5.48 5.37 5.24 5.14 5.05
5.26 5.01 4.69 4.37 4.02
Solute ¼ isobutane 0.2 0.8 3.2 10.3 28.2
95.3 197.3 369.6 629.5 1006.6
0.960 0.936 0.904 0.868 0.828
1.000 0.996 0.989 0.978 0.963
260.03 280.04 299.98 320.03 340.00
308 641 1177 1938 2951
4.13 4.12 4.11 4.05 4.01
4.01 3.89 3.75 3.52 3.29
Solute ¼ 1-butene 0.2 0.8 3.2 10.3 28.4
76.9 164.7 314.2 550.1 896.2
0.968 0.946 0.919 0.885 0.847
1.001 0.998 0.992 0.983 0.971
259.91 279.95 299.94 320.06 340.16
308 641 1173 1946 2956
4.09 4.08 4.04 4.00 3.94
3.96 3.85 3.68 3.48 3.23
Solute ¼ isobutene 0.2 0.8 3.2 10.3 28.6
77.7 166.7 318.7 559.5 914.8
0.968 0.946 0.918 0.884 0.845
1.001 0.997 0.992 0.983 0.970
260.02 280.03 299.99 320.09 340.06
236 501 936 1586 2441
4.20 4.15 4.10 4.06 3.98
4.10 3.96 3.79 3.61 3.36
Solute ¼ trans-2-butene 0.2 0.8 3.2 10.3 28.4
57.5 126.6 246.8 439.9 725.5
0.973 0.955 0.930 0.900 0.865
1.002 0.999 0.995 0.988 0.978
259.99 280.05 300.01 320.04 339.99
235 496 924 1546 2366
3.39 3.37 3.37 3.34 3.29
3.29 3.20 3.10 2.94 2.75
Solute ¼ 1,3-butadiene 0.2 0.8 3.2 10.3 28.3
71.5 155.1 298.4 525.9 861.6
0.971 0.951 0.925 0.893 0.857
1.001 0.998 0.993 0.985 0.974
5. Conclusion The HenryÕs constants and the infinite dilution activity coefficients have been obtained from the gas stripping measurements at temperatures from (260 to 340) K. In evaluating the HenryÕs constants from the gas stripping measurements, the HenryÕs constant did not depend on the nonideality of solute and solvent so
much. The activity coefficients, on the other hand, strongly depended on the nonideality of solute at the reference state. The accuracy of HenryÕs constants measured by this work is within 2% at the entire temperature range. The accuracy of the infinite dilution activity coefficients, on the other hand, is within 3% which is worse than that for the HenryÕs constants because of the inaccuracy of the
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estimated nonideality of gases, especially highly volatile gases like propane and propene.
Acknowledgements This paper reports part of the work supported by Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science (13650820), which is gratefully acknowledged.
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JCT 03/042