Styrene Hydroformylation in Supercritical Carbon Dioxide: Rate and

Publication Date (Web): January 12, 2001 .... Earl L. V. Goetheer , Arjan W. Verkerk , Elwin de Wolf , Berth-Jan Deelman , Gerard van Koten , Jos T. F...
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Ind. Eng. Chem. Res. 2001, 40, 1113-1118

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Styrene Hydroformylation in Supercritical Carbon Dioxide: Rate and Selectivity Control Bin Lin and Aydin Akgerman* Chemical Engineering Department, Texas A&M University, College Station, Texas 77843-3122

Supercritical fluids have the unique characteristic of density-tuned physicochemical properties that can affect reaction rates and selectivities. We have studied homogeneously catalyzed styrene hydroformylation in supercritical carbon dioxide (scCO2) and have shown that the reaction rate and the regioselectivity can be varied by changes in pressure at constant temperature. This rate and selectivity change is explained in terms of the transition state theory. We have determined the partial molar volumes of the reaction products based on the Peng-Robinson equation of state for an infinite-dilution solution model, a real solution model, and a real solution model with regressed interaction coefficients. Then, the estimated partial molar volumes were used to predict the experimentally observed selectivity behavior. Through these simulations, an understanding of the reaction rate and selectivity control by adjustment of the pressure was developed. Introduction The unique characteristic of supercritical fluids (SCFs) is density-tuned physicochemical properties, which can affect reaction rates and selectivities. This has been the subject of many recent studies.1-3 Hydroformylation of olefins is the largest-scale homogeneously catalyzed industrial process. The reaction is typically represented by the overall reaction

The regioselectivity is defined as the ratio of branched aldehyde to linear aldehyde in this study, and normally one or the other isomer is the desired product. When the reaction is carried out in conventional solvents, the selectivity can only be affected by temperature for a given solvent at fixed concentrations of the reactants. However, when the reaction is carried out in a SCF, the selectivity can also be affected by pressure at the optimum reaction temperature. Cobalt- and rhodiumbased catalysts are commercially utilized for hydroformylation. Compared to cobalt, rhodium is more stable and has higher activity and better selectivity, resulting in milder reaction conditions. In this study we report on styrene hydroformylation, where the branched aldehyde is the desired isomer. In addition, styrene hydroformylation is an asymmetric reaction. Its branched product, 2-phenylpropionaldehyde, is a chiral molecule, and enantioselectivity is also important. A number of studies have been reported on olefin hydroformylation in SCFs.2,4-7 In 1995, the first study of asymmetric * To whom correspondence should be addressed. Tel: 409845-3375. Fax: 409-845-6446. E-mail: [email protected].

catalysis in supercritical media was reported by Burk et al.8 Their preliminary studies effectively show the feasibility of conducting a highly enantioselective hydrogenation reaction in supercritical carbon dioxide (scCO2). More importantly, their data indicated that higher enantioselectivities may be achieved in scCO2 compared to organic solvents. Recently, Leitner’s group reported on rhodium-catalyzed asymmetric styrene hydroformylation in the presence of compressed carbon dioxide.9 A rhodium complex [(acac)Rh(CO2)] and the chiral ligand (R,S)-BINAPHOS were used as catalysts. The authors observed phase separation during the reaction and concluded that the asymmetric reaction takes place only in the CO2-rich liquid phase consisting of styrene and product aldehydes, because the ligandmodified rhodium catalyst only dissolved in the liquid phase. They followed this work with studies on using a rhodium complex of perfluoroalkyl-substituted ligand (R,S)-3-H2F6-BINAPHOS and achieved high regioselectivity and enantioselectivity in scCO2.10 These are the first studies reporting on the asymmetric styrene hydroformylation in high-pressure carbon dioxide; however, there were no reports on either the kinetics or an explanation on the change in rates and selectivities. Experimental Section The phase behavior of the reaction mixture is a major concern in reactions in SCFs. A reasonable solubility of the catalyst as well as appropriate reaction temperature, pressure, and concentration must be sustained to ensure that the reaction is carried out in the singlephase supercritical region. To observe the phase behavior of the reaction mixture under the reaction conditions, a small reactor cell with sight windows was fabricated. The windows allowed the reactor interior to be monitored visually and enabled us to confirm that the reaction mixture was in the single-phase supercritical region. The cell was placed on a small stir plate and agitated by a stir bar. The cell was heated externally with a heating tape. This reactor was used only for phase observations, and no kinetic determinations were made.

10.1021/ie000312a CCC: $20.00 © 2001 American Chemical Society Published on Web 01/12/2001

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Figure 2. Structure DuPHOS)]+BARF-.

of

the

catalyst

{[(COD)Rh(Et-

Results and Discussion

Figure 1. Experimental assembly.

A schematic diagram of the experimental setup used to study the reaction is shown in Figure 1. The main part of the system consisted of a 300 mL vessel with a magnetic drive stirrer by Autoclave Engineers. The temperature control system provided a stable temperature control within (1 °C. The kinetic studies were performed in this batch reactor system. The reactor was cleaned thoroughly before the start of each experiment. Carbon dioxide was used to flush the whole system of air. The desired amount of catalyst was loaded in the reactor in a glass ampule, and the reactor was sealed and flushed by carbon dioxide followed by syngas (1:1 ratio of H2/CO). Then the desired amount of styrene was weighed and injected into the vessel via a syringe, and the vessel was sealed immediately, followed by introduction of syngas. The reactor was then pressurized by carbon dioxide and heated to the desired temperature. When the temperature was ∼20 °C less than the set reaction temperature, additional liquid CO2 was added by a minipump. The final pressure adjustment was made when the set reaction temperature was reached. The Magnedrive stirrer was then switched on and the glass ampule broken, introducing the catalyst to the reaction mixture. The stirrer speed was 1250 rpm for each run. Samples were taken by a double-valve sampling system. Opening and then closing valve 4 trapped the SCF samples in the tubing line between V4 and V5, which was preheated by a heating type to the reaction temperature. The pressure was then released slowly through V5, and the effluent was bubbled through tetrahydrofuran (THF) in an ice bath to trap the products and unreacted reactants. The sample line was then washed with THF to collect any precipitated products during supercritical phase expansion and with low-pressure carbon dioxide to dry the loop for the next sample. The samples were analyzed using a HP 5890 GC with a flame ionization detector. The amounts of unreacted styrene and the products 2-phenylpropionaldehyde and 3-phenylpropionaldehyde were determined, and the reaction conversion and regioselectivity were calculated. The product samples were also analyzed by GC/MS with a B-DM ChiralDex capillary column to determine the enantioselectivity. The analysis for enantioselectivity was also conducted by 1H NMR to confirm the results.

It is well-known that the critical loci of the reaction mixture would be very much different from the critical point of carbon dioxide, although carbon dioxide constitutes 95+% of the reaction mixture. The rhodium catalyst {[(COD)Rh(Et-DuPHOS)]+BARF- has the fluorinated anion BARF to increase the catalyst solubility in scCO2. The catalyst structure is shown in Figure 2. The solubility of the catalyst in pure carbon dioxide was less than 0.05 mM; however, its solubility in the reaction mixture was higher, which was determined in the view cell reactor. The desired amount of reactants, such as styrene, carbon monoxide, and hydrogen, was added to the cell to observe the catalyst solubility in the reaction mixture in the supercritical region. After initial experiments indicating the acceptable solubility of the catalyst in the supercritical phase, experiments were designed to determine the approximate critical point of the reaction mixture at different concentrations. A group contribution method11 was used to obtain a rough estimate of the critical properties of reaction mixtures. Then, the cell with the sight window was used to run the experiments at the vicinity of these conditions to experimentally determine the critical point. It should be noted that this technique does not give the critical loci, but rather it yields the conditions above which the reaction mixture is in a single supercritical phase. At all experimental conditions, we kept the ratio of styrene to catalyst at 1000:1. At the reaction concentrations of our interest, only at temperatures >55 °C and pressures >130 bar was the catalyst sufficiently soluble and were the reaction mixtures in the supercritical phase region. Therefore, reaction temperatures were selected at 65 and 80 °C for styrene hydroformylation, and the reactions were carried out in the pressure range 144.4-200 bar. These conditions ensure operation in the supercritical region. The initial concentration for styrene was varied from 0.096 to 0.167 mol/L. The partial pressure of CO and H2 was 17.2 bar each in all experiments. This corresponds to about 1.2 mol/L of equimolar CO/H2 concentration (∼0.6 mol/L of each), which was about 3.6-6.3 times the molar excess of the amount needed for each for complete conversion. Only a trace amount of ethylbenzene was detected in some experiments, which indicates that the hydrogenation reaction was not significant. There were no alcohols detected. The products were 2-phenypropionaldehyde and 3-phenylpropionaldehyde. We have determined that at all reaction conditions there was no enantiometric excess; hence, there was no enantioselectivity. The possible explanation for the lack of enantioselectivity is presented elsewhere.12

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001 1115

Figure 3. Styrene conversion at 80 °C and different pressures; styrene mole fraction xstyrene ) 0.01 at all conditions.

Figure 4. Regioselectivity at different pressures for reaction conditions in Figure 4.

To evaluate the pressure effect on the reaction rate, the reactions should be carried at constant temperature and composition. Because the reactor was a batch reactor where the pressure was adjusted by the amount of CO2 in the reactor, different amounts of styrene were used depending on the pressure in order to maintain a constant styrene mole fraction in all runs. A constant initial mole fraction implies that at low pressures the amount of styrene added to the reactor (hence, its concentration is in moles per volume) is smaller. Figure 3 shows styrene conversion profiles at 80 °C and a constant initial styrene mole fraction of 0.01 at 144.8, 172.3, and 200 bar pressure. We have also made runs at a constant styrene concentration for all runs but varying initial mole fraction. The same trend was observed, but the differences in the rate and selectivity were larger.12 The lines in the figures are visual aides and are not specific fits or predictions unless otherwise specified. The conversion increases with pressure at high reaction times, but it looks like there is an induction period at 200 atm (also at 65 °C, Figure 5). We do not have an explanation for that observation, but it may be due to analytical limitations in measuring low conversion (difference of two large numbers). The increase in conversion with pressure is not just due to the higher concentrations at higher pressures, as explained below. Figure 4 shows the regioselectivity as a function of pressure at 80 °C; the regioselectivity decreases with pressure. The results show that both the reaction rate and the reaction selectivity are affected by pressure at constant temperature. Because the selectivity control is our major interest, a detailed investigation of the pressure-selectivity relation was conducted and transi-

Figure 5. Styrene conversion at 65 °C and different pressures; styrene mole fraction xstyrene ) 0.01 at all conditions.

Figure 6. Regioselectivity at different pressures for reaction conditions in Figure 6.

tion-state theory was used to explain this phenomenon.13 Phase behavior study indicated that the critical temperature of the reaction mixture is about 55 °C; actually, it is between 50 and 60 °C at our reactant compositions. Therefore, a more significant pressure effect on the reaction rate and selectivity would be expected at the temperature that is closer to 60 °C. Hence, experiments were carried out at 65 °C at pressures of 144.8 and 200 bar. The mole fraction of styrene was kept constant at 0.01, and the catalyst-tostyrene ratio was kept constant at 1:1000. As can be seen from the styrene conversion profiles in Figure 5, at a given reaction time, the conversion is increased with pressure at higher reaction times. Figure 6 shows the regioselectivity of the reactions at 65 °C. The regioselectivity again decreases with pressure, which shows the same trend as that at 80 °C; however, there are two differences between the data obtained at 65 and 80 °C. First, the regioselectivity at 65 °C is higher than the regioselectivity at 80 °C when the reactions were carried out at the same pressure; second, a larger regioselectivity change with pressure was observed at 65 °C, while the pressure changed from 144.8 to 200 bar at both temperatures. The reaction rate is obviously decreased when the reaction was carried at a lower temperature. The most significant observation obtained from the experimental study is that the reaction rate and selectivity can be varied by pressure at constant temperature. To explain this change of the rate and selectivity with pressure at constant temperature, transition-state theory is employed. Based on the transition-state theory, the pressure dependence of the reaction rate constant is related to the partial molar volume as given in eq 1,

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(

)

∂ ln kx ∂P

)-

T,x

∆V h vj M* - vj A - vj B ) RT RT

(1)

where ∆V h is the activation volume, or the difference between the partial molar volume of the activated complex M* and the partial molar volumes of the reactants A and B and vj M*, vj A, and vj B are the partial molar volumes of the transition state and reactants A and B, respectively. It should be noted that this equation is valid for rate constants measured at constant mole fraction kx; hence, that was the reason for the concentration adjustment at different pressures to obtain constant mole fraction at each experimental condition. Equation 1 is strictly valid for an elementary reaction, and hydroformulation is a multistep reaction network. However, eq 1 also applies to the rate-determining step in a reaction network, and if all other reactions are in pseudoequilibrium, eq 1 will yield the pressure dependency of the overall reaction as well. If the reaction is a parallel reaction giving two products (branched and linear aldehydes for example), then

-RT

(

)

∂ ln(kB/kL) ∂P

T,x

( )

) RT

∂ ln S ∂P

T

) vj M*,B - vj M*,L (2)

where S is the regioselectivity defined as the ratio of rate constant kB of the reaction forming the branched aldehyde to rate constant kL of the reaction forming the linear aldehyde and vjM*,B and vjM*,L are the partial molar volumes of two transition states. Therefore, the partial molar volume difference of the two transition states will determine how the regioselectivity would vary with pressure. If the difference is positive, then the regioselectivity will decrease with pressure, whereas if the difference is negative, then the regioselectivity will increase with pressure. It is the unique property of the SCFs that the partial molar volumes of the components become very large negative numbers in the vicinity of the critical point. Therefore, their difference could be a large positive or a large negative value. In any case, the reaction regioselectivity could be varied significantly by pressure, when it is run at conditions in the vicinity of the critical point. Again, eq 2 is strictly valid for the elementary steps, and the two products are formed from two different intermediates. The reaction network consists of hydrogen insertion followed by rearrangement and styrene insertion, which forms the two different intermediates. Each intermediate goes through rearrangement and CO insertion, which upon further rearrangement forms the two final intermediates, and we have shown that their dissociations forming the product aldehydes and regenerating the catalyst are the ratedetermining steps.12 Hence, eq 2 is then valid for the overall reaction as well because all other steps are then in equilibrium. Our data indicate that the regioselectivity decreases with pressure, which implies a positive difference of the partial molar volumes (branched - linear). If the partial molar volumes of the transition states can be estimated, not only can they be used to confirm our experimental results but more importantly they can be used to predict a priori whether there would be any change in regioselectivity with pressure using eq 2. Unfortunately, the partial molar volume of the transition state is very difficult to estimate without knowing the structure of the transition state. However, the partial molar volume of the products can be estimated. One approach is as a

first approximation to assume that the partial molar difference for the transition states will not be much different from the partial molar difference of the product aldehydes. There are a number of theoretical calculation methods to estimate partial molar volumes.14-16 We used the Peng-Robinson equation of state.17 The Peng-Robinson equation of state along with van der Waals mixing rules has been found to be successful in describing the phase equilibrium of mixtures including SCFs and is widely used in the literature.18,19 Given an equation of state, the partial molar volume of a solute in a solvent can be determined from the standard thermodynamic relation (species 1 ) solvent and species 2 ) solute)

vj 2 )

( ) ∂VT ∂n2

) vmKTn

T,P,n1

( ) ∂P ∂n2

(3)

T,n1

where KT is the isothermal compressibility of the mixture. When the Peng-Robinson equation of state is employed, this equation yields vj 2 ) vmKT

[

vm - bm + b2 (vm - bm)2

RT -

]

(vm2 + 2vmbm - bm2)(2x1a12 + 2x2a22) - 2amb2(vm - bm) (vm2 + 2vmbm - bm2)2

(4) where vm and KT are the molar volume and isothermal compressibility of the mixture, respectively, am, a12, a22, and bm are parameters of the Peng-Robinson equation of state, and x1 and x2 are mole fractions of the solute and solvent, respectively. If infinite dilution of the solute is assumed, the expression becomes

vj ∞2 ) v1KT,1

[

v1 - b1 + b2 (v1 - b1)2

RT -

]

(v12 + 2v1b1 - b12)(2a12) - 2a12 - 2a11b2(v1 - b1) (v12 + 2v1b1 - b12)2

(5) where vj ∞2 is the partial molar volume of a solute at infinite-dilution solution, v1 is the molar volume of the solvent, and KT,1 is the isothermal compressibility of the solvent. We used eq 4 or eq 5 to determine the partial molar volumes of the reaction products of styrene hydroformylation. The first set of simulations were carried out by assuming infinite dilution and using eq 5. It was further assumed that the interaction coefficients are zero because the interaction coefficient kij is an experimentally determined parameter and no data are available currently. The partial molar volume prediction and the regioselectivity prediction are shown in Figures 7 and 8, respectively. Because eq 2 gives the change in selectivity rather than the absolute selectivity, the data point at 144.8 bar was chosen as the starting point. As can be seen from Figure 7, both partial molar volumes become large negative values in the supercritical region. Because the partial molar volume of the linear aldehyde is a larger negative value than that of the branched aldehyde, their difference (branched - linear) is posi-

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Figure 7. Infinite-dilution partial molar volumes of 2-phenylpropionaldehyde (branched) and 3-phenylpropionaldehyde (linear) in scCO2 as a function of pressure at T ) 80 °C.

Figure 9. Partial molar volume difference of branched and linear aldehydes (B - L) in the infinite-dilution solution and in the real mixture solution at T ) 80 °C.

Figure 8. Prediction of the pressure dependency of the B/L ratio for styrene hydroformylation products at 80 °C.

Figure 10. Prediction of the pressure dependence of the B/L ratio for styrene hydroformylation products at 65 °C.

tive. The prediction of the change in regioselectivity with pressure at 80 °C is shown in Figure 8 as the P-R fit, infinite-dilution solution. As can be seen from the figure, the prediction shows the same trend as the experimental data: the regioselectivity decreases with pressure at constant temperature. The simulation indicates that the infinite-dilution assumption yields a qualitative prediction of the trend in the change in regioselectivity with pressure. The second set of simulations was carried out using the real mixture solution model, where eq 4 is applied. In eq 4, the isothermal compressibility of the mixture, KT, is needed in order to calculate the partial molar volume of solute 2 in the mixture. While the isothermal compressibility of pure CO2 is easy to estimate, the mixture’s isothermal compressibility, KT, is not available in the literature. Considering the definition of isothermal compressibility, an assumption is made as given by eq 6.

Table 1. Binary Interaction Coefficients between CO2 and Aldehydes

KT ) -

( )

1 ∂VT VT ∂P

T,n1,n2

)-

( )

1 ∂vm vm ∂P

T,n1,n2

(6)

Using the Peng-Robinson equation of state, one can obtain how the mixture molar volume vm varies with pressure at constant temperature and composition. From that, the isothermal compressibility of the mixture can be calculated. Interaction coefficients were again assumed to be zero for the calculation of the partial molar volumes. Results of simulations indicated that the partial molar volumes of both the branched aldehyde and the linear aldehyde became larger negative values in the real mixture compared to the values in infinite-

temp, °C

compound

kij

80 80

2-phenylpropionaldehyde (branched product) 3-phenylpropionaldehyde (linear product)

-0.11 -0.14

dilution solution. As a result, the difference of the partial molar volume in the real mixture solution is larger than the value in infinite-dilution solution, which can be seen from Figure 9. However, at the reaction pressures of 140-200 bar, this difference in the partial molar volumes of the two aldehydes is almost identical with the values obtained from infinite-dilute solution assumption. The prediction of the change of regioselectivity with pressure using the real solution approach is also given in Figure 8 as the P-R fit, the real mixture solution, without kij. The prediction shows the same trend with experimental data: the regioselectivity is decreased with pressure at constant temperature; however, the prediction is still more qualitative than quantitative. In the final set of simulations, we have relaxed the assumption of zero interaction coefficients. The regioselectivities at different reaction conditions have been determined experimentally; using the data at 80 °C, the best fit binary interaction coefficients were regressed from eq 2 and are given in Table 1. The predictions of the regioselectivity changes with pressure at 80 °C using the regressed interaction coefficients are also shown in Figure 8 as the P-R fit, the real mixture solution, with kij. As expected, the regioselectivity can be precisely predicted at 80 °C. We used the interaction coefficients

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regressed at 80 °C to estimate the partial molar volumes in scCO2 at 65 °C and calculated the change of regioselectivity with pressure. The predictions are shown in Figure 10. The prediction is also significantly improved at 65 °C when the interaction coefficients are included. Because the lack of data in the literature, the interaction coefficients used in this study were regressed from the experimental regioselectivity data. Without the interaction coefficients, the prediction of the change of regioselectivity with pressure is only qualitative, but it has the same trend, indicating that the regioselectivity can be controlled with pressure. More importantly, the potential advantage of this approach is that it could be used as a general a priori prediction technique. It can be used to search the regions in temperature and pressure where the largest change in selectivity is expected, and experiments can be performed in that region. Especially, if the interaction coefficients are available, the approach discussed in this study will be proven particularly useful for the prediction of the pressure dependence of regioselectivity of the reactions in the supercritical region. Acknowledgment This project has been funded by Grants 028TAM2640 and 118TAM3640 in part with Federal Funds as part of the program of the Gulf Coast Hazardous Substance Research Center which is supported under cooperative agreement R815197 with the United States Environmental Protection Agency and in part with funds from the State of Texas as part of the program of the Texas Hazardous Waste Research Center. The contents do not necessarily reflect the views and policies of the U.S. EPA or the State of Texas, nor does the mention of trade names or commercial product constitute endorsement or recommendation for use. Literature Cited (1) Clifford, A. A.; Pople, K.; Gaskill, W. J.; Bartle, K. D.; Rayner, C. M. Potential Tuning and Reaction Control in the DielsAlder Reaction Between Cyclopentadiene and Methyl Acrylate in Supercritical Carbon Dioxide. J. Chem. Soc., Faraday Trans. 1998, 94, 1451-1456. (2) Guo, Y.; Akgerman, A. Determination of Selectivity for Parallel Reactions in Supercritical Fluids. J. Supercrit. Fluids 1999, 15, 63. (3) Lin, B.; Akgerman, A. Isoprene/Methyl Acrylate DielsAlder Reaction in Supercritical Carbon Dioxide. Ind. Eng. Chem. Res. 1999, 38, 4525-4530.

(4) Rathke, J. W.; Klingler, R. J.; Krause, T. R. Propylene Hydroformylation in Supercritical Carbon Dioxide. Organometallics 1991, 10, 1350. (5) Koch, D.; Leitner, W. Rhodium-Catalyzed Hydroformylation in Supercritical Carbon Dioxide. J. Am. Chem. Soc. 1998, 120, 13398-13404. (6) Palo, D. R.; Erkey, C. Homogeneous Catalytic Hydroformylation of 1-Octene in Supercritical Carbon Dioxide Using a Novel Rhodium Catalyst with Fluorinated Arylphosphine Ligands. Ind. Eng. Chem. Res. 1998, 37, 4203-4206. (7) Palo, D. R.; Erkey, C. Homogeneous Hydroformylation of 1-Octene in Supercritical Carbon Dioxide with [RhH(CO)(P(pCF3C6H4)3)3]. Ind. Eng. Chem. Res. 1999, 38, 2163-2165. (8) Burk, M. J.; Feng, S.; Gross, M. F.; Tumas, W. Asymmetric Catalytic Hydrogenation Reactions in Supercritical Carbon Dioxide. J. Am. Chem. Soc. 1995, 117, 8277-8278. (9) Kainz, S.; Leitner, W. Catalytic Asymmetric Hydroformylation in the Presence of Compressed Carbon Dioxide. Catal. Lett. 1998, 55, 223-225. (10) Francio, G.; Leitner, W. Highly Regio- and EnantioSelective Rhodium Catalyzed Asymmetric Hydroformylation without Organic Solvents. Chem. Commun. 1999, 1663-1664. (11) Li, L.; Kiran, E. Estimation of Critical Properties of Binary Mixtures Using Group Contribution Methods. Chem. Eng. Commun. 1990, 94, 131-141. (12) Lin, B. Environmentally Friendly Organic Synthesis in Supercritical Carbon Dioxide. Ph.D. Dissertation, Texas A&M University, 2000. (13) Evans, M. G.; Polanyi, M. Some Applications of the Transition State Methods to the Calculation of Reaction Velocities, Especially in Solution. Trans. Faraday Soc. 1935, 31, 875. (14) Liu, H.; Macedo, E. A. A Study on the Models for Infinite Dilution Partial Volumes of Solutes in Supercritical Fluids. Ind. Eng. Chem. Res. 1995, 34, 2029-2037. (15) Eckert, C. A.; Ziger, D. H. Statistical Mechanics and Thermodynamics-Solute Partial Molar Volumes in Supercritical Fluids. J. Phys. Chem. 1986, 90, 2738-2946. (16) Wasen, U. V.; Schnelder, G. M. Partial Molar Volumes of Naphthalene and Fluorene at Infinite Dilution in Carbon Dioxide near Its Critical Point. J. Phys. Chem. 1980, 84, 229-230. (17) Peng, D.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem., Fundam. 1976, 15, 59-64. (18) Anderko, A. Equation-of-State Methods for the Modeling of Phase Equilibria. Fluid Phase Equilib. 1990, 61, 145-225. (19) Johnston, K. P.; Peck, D. G.; Kim, S. Modeling Supercritical Mixtures: How Predictive Is It? Ind. Eng. Chem. Res. 1989, 28, 1115-1125.

Received for review March 10, 2000 Revised manuscript received November 9, 2000 Accepted November 28, 2000 IE000312A