Znd. Eng. Chem. Res. 1993,32, 2193-2198
2193
Prediction of Gas Solubilities in Pure and Mixed Solvents Using a Group Contribution Method Marianne CattB, Christian Achard, Claude-Gilles Dussap, and Jean-Bernard Gros* Laboratoire de Gdnie Chirnique Biologique, Universitd Blaise Pascal, 631 77 Aubiere cedex, France
A new and simple model for predicting gas solubilities in pure and mixed solvents at low pressure and temperature is proposed. A method for predicting Henry’s constants of single gases in mixed solvents from the corresponding binary data and introducing the volume fraction of molecules is presented. An extrapolation to pure solvents using a group contribution method is developed for N2, HZ, CO, C02, CHI, C2H4). Good results are obtained in a wide variety of solvents seven gases (02, and solvent mixtures (alkanes, alcohols, ketones, esters, ethers, aromatic compounds, cyclic compounds and water). This new model gives better results than the MHVB, GC-EOS, and Sander’s models, with fewer adjustable parameters.
Introduction
Fundamental Equation
The importance of gas solubility in the chemical and biochemical industries and the scantness of experimental data (Fogg and Gerrard, 1991) have prompted the development of several methods for the estimation of Henry’s constants in pure and mixed solvents. Most of these are based on modified UNIFAC models or group contribution equations of state. Unfortunately, no method has been available that will successfully predict solubility of gases at atmospheric pressure and low temperature in pure and mixed solvents involving nonpolar and polar components, including aqueous mixtures. The purpose of this work was to develop anew group contribution method to predict gas solubility in such conditions. Group contribution techniques, especially the UNIFAC model (Fredenslundet al., 19751,have beenvery successful for the phase equilibrium predictions of mixtures of subcritical components for which little or no experimental information is available. Several authors have tried to predict gas solubility with modified UNIFAC models. When a symmetric activity coefficient is correlated, the authors used the correlation of Prausnitz and Shair (1961) to determine the hypothetical liquid fugacity of the dissolved gas at the temperature and pressure of the system. Antunes and Tassios (1983) and Nocon et al. (1983) incorporated free volume effects into the UNIFAC model. The model of Sander et al. (1983) uses the unsymmetric activity coefficient approach to describe phase equilibria. This model, which required cumbersome estimation of solvent-solvent, gas-solvent, and gas-group interaction parameters, enables the prediction of solubility in pure and mixed solvents. Group contribution equations of state have been used to correlate gas solubilities in pure and mixed solvents over wide ranges of temperature and pressure. Using a procedure originally introduced by Huron and Vidal (1979), several authors have derived mixing rules from the UNIFAC excess Gibbs energy model. The UNIWAALS model (Gani et al., 1989) is based on the extension of Larsen et al. (1987) of the UNIFAC model; it is applied to three gas-solvent systems. The MHVl and MHVP models (Michelsen, 1990a,b) incorporate mixing rules derived from Larsen’s model in the SoaveRedlich-Kwong equation of state (Dah1 et al., 1991; Holderbaum and Gmehling, 1991). Similarly, the group contribution equation of state (GC-EOS model) uses a van der Waals type equation of state with mixing rules based on an NRTL-like expression for Helmholtz energy (Skjold-Jorgensen, 1984, 1988; Wolff et al., 1992).
The fundamental equation for the prediction of gas solubilities using a group contribution technique is obtained from an adequate representation of gas solubilities in mixed solvents. If the mixture of solvents is considered as ideal (the mixtures of the dissolved gas with pure solvents are assumed to follow Henry’slaw), differentiation of the excess Gibbsenergy expression for a multicomponent mixture (Prausnitz et al., 1986) yields the well-known Krischevsky equation:
As noted by Puri and Ruether (19741, this expression unexpectedly affords a reasonable approximation, but for more accurate estimates the nature of the solvent mixture has to be taken into account. The model proposed here uses a somewhat more realistic, but still simplified assumption. From the van Laar model, the molar excess Gibbs energy is given by (Prausnitz et al., 1986) r2r3
.E
RT =
2r2a12x1x2
+ 2r3a13X1X3 + 2--a23x$3 rl r2 r3 x1 -x2 -x3
+ rl + 71
(2)
where aij parameters are characteristic constants of interactions between molecules i and molecules j . On differentiation, the activity coefficient of component 1 is
As the molar fraction of dissolved gas (subscript 1) remains small, the activity coefficient of the gas in the pure solvent i is calculated by In 71”)= 2rl~li. Assuming the interactions between solvent molecules do not affect the gas solubility, eq 3 can be simplified considering a23 = 0
0888-5885/93/2632-2193$04.00/00 1993 American Chemical Society
2194 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993 Table I. Constants for Calculation of JU I Parameters. i CH3
CHz CH
C &Ha C-CH
Nz 5.705 232.234 5.455 373.323 8.737 -804.005 6.482
02
6.455 -22.683 5.942 33.509 6.703 -747.595 O.OO0 O.OO0 6.277 140.292 3.820
O.OO0
5.877 383.985 13.741 O.OO0 6.066 492.318 8.670 O.OO0 8.740 -50.948 6.855 363.059 8.365 236.618 6.686 357.843 9.052 -558.851 7.991 62.853 164.982 -8432.8 -21.56 -8.436 X 103
O.OO0
ACH AC
6.476 190.880 5.649 O.OO0
OH CHaCO C-CH2CO CHaCOO CHzO CHsOH HzO
8.867 -258.203 6.895 175.266 7.559 295.051 6.551 231.340 6.201 7.840 8.248 -137.628 144.396 -7775.1 -18.397 -9.44 x 1 w
co 6.602 O.OO0 6.252 O.OO0 1.818 O.OO0 na na 6.596 95.563 5.141 O.OO0
6.428 263.208 7.107 O.OO0 9.720 -311.022 6.615 249.022 na na 6.509 232.861 6.293 -67.630 na na 171.764 -8296.9 -23.3376 O.OO0
Hz 5.346 491.336 5.930 446.759 6.687 O.OO0 10.616 O.OO0 6.205 472.860 na na 5.574 800.472 9.193 O.OO0
7.687 421.515 6.376 694.646 6.301 966.024 6.318 689.891 5.040 897.273 7.3644 408.380 125.939 -5528.45 -16.8893 O.OO0
coz
CH4 5.744 O.OO0 6.903 -573.769 nab na na na 5.714 na 9.530 na 6.669 -148.027 6.466 na 9.151 -568.082 7.625 -315.012 9.769 -619.636 7.388 -275.875 8.880 -1154.067 8.5246 -440.0
183.768 -9111.71 -25.038 1.434 X lo-‘
2.861 540.334 7.929 -1098.127 4.655 O.OO0 na na 4.929 na na na 8.455 -1 121.785 6.719 -1121.785 13.872 -2557.739 14.329 -3220.795 na na na na 1.590 na 9.502 -1285.86 159.854 -8741.68 -21.6694 1.1026 X 1V
C& 6.063 -410.307 11.554 -2419.949 2.358 O.OO0 na na na na na na 8.788 -1311.87 1.556 na 11.670 -1825.672 9.235 -1441.415 na na 8.752 -1313.154 na na 5.4680 na 152.923 -7959.78 -20.511 O.OO0
a First row gives Aij; second row gives Bij; third row and fourth row for H2O give Cij and Di,. na: no reliable data available. c Solubility at 298.15 K.
(4)
where and a3 are the effective volume fractions of the solvents. The above equation is generalized in terms of Henry’s constants, to predict the solubility of a gas in a solvent mixture:
Importantly, though the mixture of solvents is considered to present no binary interactions, the size parameters of the pure solvents are not assumed to be identical, which improves the basic Krischevsky equation (eq 1). In practice, the volume fraction of component i, ai, is calculated using the expression derived by Kikic et al. (1980):
a; =
xirizl3
Exjrj2’3 I
where ri is the volume parameter of molecule i as defined in the UNIFAC model (Fredenslund et al., 1975). Equation 5 for representing gas solubility in mixed solvents is then extended as a group contribution method for predicting gas solubility in pure solvents:
where Xi and Ri are respectively the mole fraction in solution and the volume parameter of group i. hij is a pseudo Henry’s constant for gas solubility in a solution containing only groups of type i, having the same units as H (atm). The temperature dependency of hij is given by the following function: In hij = A ,
+3 T + CijIn T + DijT
This equation has the same structure as the correlation of Wilhelm et al. (1977) for the solubility of gases in water, considered here as a group. We use only the first two terms for the other groups, given the lack of temperaturedependent experimental data and the small solubility dependency on temperature for other solvents. Accordingly, the correlation will not describe maximum gas solubilities. Estimation of Parameters. The temperature-dependent parameters hij determined in this work for 7 gases and 15modified UNIFAC groups are given in Table I. For each gas j the parameters are estimated simultaneously from all the available pure solvent solubility data, by minimizing the following function: (10)
The summation extends over all groups as defined in the UNIFAC model present in the solvent solution. +i is the volume fraction of group i given by
where n is the number of data points, and subscripts exp and calc refer respectively to experimental and calculated Henry’s constants. References for all the experimental data used in this study are listed in the Appendix.
Ind. Eng. Chem. Res., Vol. 32, No. 9,1993 2195 Table 11. Speoification of Experimental Information: Number of Different Systems for Which Experimental Data Were Used in the Estimation of Parameters; Mean Absolute Deviation, Average Percentage Error, and Maximal Obnerved Deviation 02 Nz CO H2 CH4 COz C2H4 CHa CHz CH C c-CH~ C-CH ACH AC OH CHsCO C-CH2CO CHgCOO CHzO
23 19 3 1 5 2 4 3 7 3 2 1 2
M.A.Dev(atm) A.P.Err(%) maxdev (5%)
23.6 2.4 9.3
0
26 21 23 22 17 19 3 1 2 1 na 1 3 2 2 1 1 na 2 2 2 1 1 1 1 0 9 1 1 1 1 1 1 na 1 2 3 2 2 1 2 1 22.7 1.3 6.5
8.5 0.9 5.8
14.9 0.6 4.2
17 14
20
6 5 6 1
2 1 8 1
na na n a 1 1
3.0 1.1 9.5
n
a
2.9 3.0 9.5
2.7 2.9 12.5
na: not available.
Table 111. Volume Parameters of Groups (Larsen et al., 1987)
CHs CHz CH C c-CH~ C-CH ACH AC
group CHsCO c-CH~CO CHsCOO CH2O CHsOH HzO OH
0.9011 0.6744 0.4469 0.2195 0.6744 0.4469 0.5313 0.3652
a Reeetimatad
o
l
I
L"
zz
Y E
0
6
16 NUMBER OF CARBON RTOMS
Figure 1. Experimental and calculated Henry's constants in n-alkanes as a function of carbon number at 298.15 K. ( 0 )Oxygen; (0) nitrogen; (A)hydrogen; (A)carbon monoxide; (m) methane; ( 0 ) carbon dioxide.
4i 5 c
c v
R
BrOUP
o
15
18 11 n a a 1 1 na na na 3 2 n a 1 na na 2 1 8 1 1 1
z
)
-
2,.
R 1.6724 1.4457 1.9031 0.9183 1.oooO 0.9200 3.3642a
Lo
z -
P -
O
from pure solvent data (original value = 1.oooO).
Published gas solubility data often display wide deviations and discrepancies. Accordingly, all data were carefully checked, and any which appeared unreliable were excluded at the outset. The experimental data cover a temperature range from 273.15 to 323.15 K. The actual number of optimized coefficients depends on the amount and the reliability of the available experimental information. Only one or two seta of data are available for the determination ) . cases it is of some parameters (e.g., h c ~ f l . ~In~ these uncertain how good the predictions will be for other systems of the same type. The numbers of different mixtures for which experimental data were used in the estimation of parameters are given in Table 11,except for water and methanol. In these two cases the molecules are groups and the hij parameters are not true group contribution parameters but pure solvent coefficients (Wilhelm et al., 1977;Foggand Gerrard, 1991;Wilhelm andBattino, 1973). Table I1 also gives the mean absolute deviation M.A.Dev, the average percentage error A.P.Err, and the maximal observed deviation max dev. n
Figure 2. Experimental and calculated Henry's constants in n-alcohols as a function of carbon number at 298.15 K. ( 0 )Oxygen; (0) nitrogen; (A)hydrogen; (W) methane.
The average percentage error, all solvents included, ranges from 0.6 % for hydrogen to 3.0 % for carbon dioxide. The maximal observed deviation, all systems included, is 12.5%. The group volume parameters Ri are those of Larsen et al. (1987). However, it was not possible to describe the solubility of some gases in pure alcohols using the value for ROH. This parameter was reestimated with all the experimental data at 298.15 K. The volume parameters used in this work are given in Table 111. A distinction is made between CH3, CH2, CH, and C groups to account for the variation in the solubility of a gas in a series of linear and branched alkanes. In the same way, to account for the variation in the solubility of a gas in linear and cyclic alkanes, the groups CH2 and cyclic CH2 (CH and cyclic CH) are distinguished. It is of note that this method will not differentiate between two solvents containing the same combination of groups in terms of group molar fractions (e.g., cyclohexane and cyclooctane).
Predicted Results and Comparison with Other Models n
Ewe,A.P.Err =
HdclKxp
a=l
n
x 100
(12)
In Pure Solvents. The accuracyof the proposed method in describing gas solubility in pure solventa is illustrated in Figures 1-4. Figures 1 and 2 show experimental and calculated solubilities for some gases in the series of linear n-alkanes and n-alcohols at 298.15 K. Figures 3 and 4 show solubilities as a function of temperature for some gases in 2-methyl-1-propanol, ethanol, methyl acetate, and pentylbenzene. The calculated Henry's constants are in close agreement with experimental values. The proposed
2196 Ind. Eng. Chem. Res., Vol. 32, No. 9,1993 4500
I
* z q , LL
Y
-
L
0
273.15
I
323.15
TESPERATURE, K
Figure 4. Experimental and calculated Henry’s constanta as a function of temperature. (0)Methane in ethanol; (m) ethylene in 2-propanol; (u)carbon dioxide in pentyl benzene.
method was compared with the MHVB model (Dah1et al., 1991),with the GC-EOS model (Skjold-Jorgensen, 1988), and with the model of Sander et al. (1983). Importantly, the new model is computationally faster than all these models. Results presented in Table IV are given as the average percentage error (A.P.Err) and the maximal observed deviation (max dev). Sander’s and GC-EOS models will only predict gas solubilities in water, alkanes, alcohols, ketones, and simple aromatic compounds, and so no result is available for the hydrogen-methyl acetate system. As shown in Table IV, the new method is able to predict solubility in more pure solvents than Sander’s model and with similar agreement with experimentaldata. Also, fewer adjustable parameters are required. MHVB
and GC-EOSresults are not always in very close agreement with experiment, and the number of parameters required is far greater than for the other two models. It is noteworthy that these models, which also require pure component parameters (Pc, Tc, ...), were originally developed for high-pressure and high-temperature gas solubilities, which lie outside the scope of the proposed model. In Solvent Mixtures. With the use of the results obtained by the proposed group contribution method to calculate the solubilities in pure solvents, eqs 5 and 6 with the volume parameters of Larsen et al. (1987)are compared with ternary experimental data. The results are presented for four ternary systems in TableV, which shows the results from calculations with MHV2, GC-EOS, and Sander’s models and with the ideal mixture approximation given by eq 1. In all cases the deviationsfor the proposed method are below 10.5 % . Figures 5, 6, and 7 respectively show experimental and calculated Henry’s constants in the oxygen-watel-ethanol system at 313.15 K, in the nitrogenwater-ethanol system at 293.15 K, and in the oxygenwater-methanol system at 313.15 K. For aqueous alcohol mixtures Henry’s constants are represented far better with the proposed method than with Sander’s model: the volume effects of molecules are not allowed for with the UNIFAC model, and so rather large deviations may be expected with Sander’s model for strongly nonideal mixtures such as aqueous alcohol systems. The proposed model performs slightly better than GC-EOS and MHV2 models for the Nz-water-ethanol system; by contrast, it is much more accurate in representing the ternaries including oxygen. Interestingly, the new model slightly improves the predictions compared with the ideal mix approximation for the water-methanol system (Table V). This is because the volume parameters of water and methanol are nearly identical (0.92 and 1.00, respectively), and so volume fractions approximate molar fractions. The improvement is much more significant for water-ethanol systems. The new model is also able to predict solubility in nonaqueous mixtures, as well as Sander’s model (Table V). Figure 8 shows the results for the nitrogen-ethanolbenzene system at 298.15 K. As stated, the number of parameters required by the new model is, for solvent mixtures too, smaller than in Sander’s, MHV2, and GCEOS models. In all the cases studied the results of the proposed method are better than those of the other models, showing that valuable predictions of gas solubilities in mixed solvents can be simply obtained provided pure solvent Henry’s constants are known.
Table IV. Solubility Results for Binary - Systems -
T (K)
system Ozethanol
273-323
C&-propanol-2
273-323
Orpropanone-2
273-323
Hrmethyl acetate
273-313
model new model MHVB Sander GC-EOS new model MHV2 Sander GC-EOS new model MHVB Sander GC-EOS new model MHV2 Sander GC-EOS
no. of params useda 6 14 7 12 6 14 7 12 4 14 6 12 4
14
m a dev ( % ) 2.3 12.3 1.0 28.4 5.0 6.6 2.4 11.3 3.2 55.6 5.4 5.3 0.2 33.8
A.P.Err ( % ) 1.0 11.7 0.7 25.5 2.7 5.7 1.3 7.6 1.7 30.5 2.8 3.0 0.1
15.8
* Adjustable parameters only, excluding pure component parameters for MHVB and GC-EOS models.
ref data, no. of data points Battino et al. (1983). . ..7
Sahgal et al. (1978), 3
Battino et al. (1983), 7
Horiuti (1931), 6
Ind. Eng. Chem. Res., Vol. 32, No. 9,1993 2197 Table V. Solubility Results for Ternary Systems system T (K) model no. of params used“ Orwater-ethanol 313.15 new model 10 MHVB
Orwater-methanol
313.15
Sander GC-EOS ideal mixb new model MHV2
Nrwater-ethanol
293.15
Sander GC-EOS ideal mixb new model MHV2
Nethanol-benzene
298.15
Sander GC-EOS ideal mixb new model MHVB
Sander GC-EOS ideal mixb a
A.P.Err (%)
mar dev (%)
6.5 27.6 19.6 13.7 33.3 10.5 39.3 20.2 18.0 13.5 9.8 12.3 19.8 11.8 22.1 1.1 39.8 1.0 10.0 1.2
17.3 110.3 40.6 24.8 65.3 19.6 110.0 36.9 30.9 23.4 24.8 30.8 43.3 22.8 55.6 2.3 53.9 2.2 24.9 2.9
30 12 24 6 14 11 12 10 30 12 24 8 30 11 24
ref data, no. of data points Tokuneaa (1975). - . . . 12
Tokunaga (1975), 12
Tokunaga (1976),16
Nitta et al. (1978),11
Adjusted parameters from binary data. Calculated from eq 1. 601
60
L
w L
s
$ h 8
E
E
E
8
0
0 0
MOLE FRACTION ETHANOL
u.0
1.0
Figure 5. Experimentaland calculated Henry’s constants of oxygen in water-ethanol mixtures at 313.15 K as a function of composition. ( 0 )Tokunaga et al., 1975. (0) Wilhelm et al., 1977.
HOLE FRACTION HETHWOL
..o
Figure 7. Experimentaland calculated Henry’sconstants of oxygen in water-methanol mixtures at 313.15 K as a functionof composition. Wilhelm et al., 1977. ( 0 )Tokunaga et al., 1975. (0) 30(
c
1 s
c
0 0 MOLE FRACTION ETHANOL
Figure 6. Experimentaland calculated Henry’sconstantsof nitrogen in water-ethanol mixtures at 293.15 K as a function of composition. ( 0 )Tokunaga et al., 1975. (0)Wilhelm et al., 1977.
Conclusion This simple semiempirical group contribution method
can be applied to predict the solubility of seven gases (02, Nz,CO, H2, C02, CH4, CzH4) in pure solvents and in solvent mixtures comprising polar and nonpolar components, a t low pressure and temperature. The overall performance of this model is better than that of MHV2, GC-EOS, and Sander’s models, with fewer adjustable parameters, for pressure and temperature ranges well below critical conditions of the solvents. On the basis of the results presented, the influence of the nonideality of the solvent
0.0
MOLE FRIlCTION BENZENE
,o
Figure 8. Experimental and calculated Henry’sconstantaof nitrogen in ethanol-benzene mixturea at 298.15 K aa a function of composition. ( 0 )Nitta et al., 1978. mixture on gas solubility may thus be ascribed to combinational or size effecta rather than specific interactions.
Nomenclature Aij, Bij, Cij, Dij
= temperature parameters
H = Henry’s constant, atm
Hi = Henry’s constant in pure solvent i, atm hij = pseudo Henry’s constant, atm Hmk= Henry’s constant in mixed solvent, atm Ri = volume parameter of group i rj = size or volume parameter of molecule i T = temperature, K
2198 Ind. Eng. Chem. Res., Vol. 32, No. 9, 1993
Xi = mole fraction of group i xi
= mole fraction of molecule i
= volume fraction of molecule i di = volume fraction of group i Qii
Appendix. Pure Solvent Data References Battino, R.; Evans, F. D.; Danforth, W. F.; Wilhelm, E. The solubility of gases in liquids 2 the solubility of He, Ne, Ar, Kr, N2,02, CO and C02 in 2-methyl-1-propanol (1to 55 “C). J. Chem. Thermodyn. 1971,3, 743-751. Battino, R.; Rettich, T. R.; Tominaga, T. The solubility of oxygen and ozone in liquids. J.Phys. Chem. Ref.Data 1983,12,163-178. Battino, R.; Rettich, T. R.; Tominaga, T. The solubility of nitrogen and air in liquids. J. Phys. Chem. Ref. Data 1984,13,563-600. Boyer, F. L.; Bircher, L. J. The solubility of nitrogen, argon, methane, ethylene and ethane in normal primary alcohols. J.Phys. Chem. 1960,64,1330-1331. Fogg, P. G. T.; Gerrard, W. Solubility of gases in liquids. A critical evaluation of gaslliquid systems in theory and practise; Wiley: New York, 1991. Gallardo, M. A.; Lopez, M. C.; Urieta, J. S.; Gutierrez Losa, C. Solubility of He, Ne, Ar, Kr, Xe, H2, D2, N2,02, CH,, C2I4, C2&, CF,, SF6 and C02 in cycloheptanone. Fluid Phase Equilib. 1989, 58,159-172. Gallardo, M. A.; Lopez, M. C.; Urieta, J. S.; Gutierrez Losa, C. Solubility of He, Ne, Ar, Kr, Xe, H2, D2, N2,02, CH,, C&&,c2H6, CFd, SF6 and CO2 in cyclopentanone from 273.15 K to 303.15 K and gas partial pressure of 101.33kPa. Fluid Phase Equilib. 1989, 50, 223-233. Gironi,F.; Lavecchia,R. Solubilitiesof carbon dioxide in alkylaromatic solvents at low pressure. Fluid Phase Equilib. 1992,78,335-344. Hale, J. M. Oxygen measurements in non-aqueous fluids. Orbisphere Technical News; Orbisphere Laboratoires Geneve: Geneva, 1988. Hayduk, W.; Walter, E. B.; Simpson, P. Solubility of propane and C02 in heptane, dodecane and hexadecane. J. Chem. Eng. Data 1972, 17, 59-61. Horiuti, J. On the solubility of gas and coefficient of dilatation by absorption. Sci. Pap. Zmt. Phys. Chem. Res. 1931,17,125-256. Jadot, R. Chromatographic determination of Henry’s constants. J. Chin. Phys. Physicochimbiol. 1972,69, 1036-1040. Katayama, T.; Nitta, T. Solubilities of hydrogen and nitrogen in alcohols and n-hexane. J. Chem. Eng. Data 1976,21, 194-196. Kobatake, Y.; Hildebrand, J. H. Solubility and entropy of solution of He, N2, Ar, 0 2 , CHI, C2&, C02 and SFa in various solvents. Regularity of gas solubility. J. Phys. Chem. 1961,65, 331-334. Lenoir, J. Y.; Renault, P.; Renon, H. Gas chromatographic determination of Henry’s constants of 12 gases in 19 solvents. J. Chem. Eng. Data 1971, 16,340-342. Lin, P. J.; Parcher, J. F. Direct gas chromatographic determination of the solubility of light gases in liquids. Henry’s law constants for eleven gases in n-hexadecane, n-octacosane and n-hexatriacontane. J. Chromatogr. Sci. 1982,20,33-38. Narasimhan, S.; Natarajan, G. S.; Nageshwar, G. D. Solubilities of ethene, propene and 2-methylpropene in normal alcohols. Indian J. Technol. 1981,19,298-299. Sahgal, A.; La, H. M.; Hayduk, W. Solubility of ethylene in several polar and non-polar solvents. Can. J. Chem. Eng. 1978,56,354357. Schaffer, S. K.; Prausnitz, J. M. Correlation of hydrogen solubilities in non-polar solvents based on scaled-particle theory. AIChE J. 1981,27,844-848. Tremper, K. K.; Prausnitz, J. M. Solubility of inorganic gases in high boiling hydrocarbon solvents. J. Chem.Eng. Data 1976,21,295299. Waters, J. A.; Mortimer, G. A.; Clements, H. E. Solubility of some light hydrocarbons and hydrogen in some organic solvents. J. Chem. Eng. Data 1970,15, 174-176. Wilcock, R. J.; Battino, R. Solubilities of gases in liquids 2 The solubilities of He, Ne, Ar, Kr, 0 2 , N2, CO,(202,C&, CFh and SF6 in n-octane, 1-octanol, n-decane and 1-decanol. J. Chem. Thermodyn. 1978,10,817-822. Wilhelm, E.; Battino, R. The solubility of gases in liquids 4: calculations on gas solubilities in hexafluorobenzene and benzene. J. Chem. Thermodyn. 1971,3, 761-768. Wilhelm, E.; Battino, R. Thermodynamic functions of the solubilities of gases in liquids at 25 OC. Chem. Rev. 1973, 73, 1-9.
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* Abstract published in Advance ACS Abstracts, August 16, 1993.
