Carbon Dioxide

diffusion coefficients at infinite dilution.1,2 .... diagram of the ethanol/H2O/CO2 mixture. .... 0.39) mixtures at 170 atm: (+) 0, (9) 20, (2) 30, an...
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Anal. Chem. 1998, 70, 2783-2788

Molecular Diffusion Coefficients in Ethanol/Water/ Carbon Dioxide Mixtures Isabelle Souvignet and Susan V. Olesik*

Department of Chemistry, The Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210

Supercritical and liquid mixtures of ethanol/H2O/CO2 are increasingly used to extract solutes from solid or semisolid matrixes when nontoxic solvents and fast extraction kinetics are desired. Accordingly, to better understand the mass transport capabilities of these mixtures, the diffusion coefficients of benzene, anthracene, m-cresol, and p-nitrophenol in enhanced-fluidity liquid mixtures of ethanol/H2O/CO2 were studied. The effect of mixture composition and temperature variation on the measured diffusion coefficients was studied. In a mixture containing 0.61/0.39 mole ratio ethanol/H2O, the diffusion coefficients of the four solutes increased comparably either by adding 30 mol % CO2 or by changing the temperature of the mixture from 25 to 60 °C. The experimental data were compared to that predicted by the Stokes-Einstein and the Wilke-Chang relations. Often, the experimental diffusion coefficients were greater than those predicted by these mass transport relations. However, the Eyring relationship was useful in describing the variation of diffusion coefficients as a function of temperature change for all of the ethanol/H2O/CO2 mixtures tested. An understanding of the diffusion process in high-pressure liquid mixtures is required if such mixtures are to be used either as mobile phases in chromatography or as extraction fluids. Often, mass transfer in the mobile phase controls efficiency in chromatography. Therefore, information on molecular diffusion coefficients of solutes is useful for the optimization of a chromatographic system. Mass transport properties are primarily investigated through the analyses of self-diffusion or binary diffusion coefficients at infinite dilution.1,2 Previous studies included the investigation of binary or ternary molecular diffusion coefficients in supercritical fluids.3-7 Sassiat et al. briefly analyzed the effect of the methanol content on the molecular diffusion of benzene in methanol/carbon dioxide mixtures in the subcritical state5 and Lee and Olesik investigated the effect of the temperature increase on the diffusion coefficient for mixtures of methanol/ H2O/CO2.8 (1) Robb, W. L.; Drickamer, H. G. J. Chem. Phys. 1951, 19, 1504. (2) Timmerhaus, K. D.; Drickamer, H. G. J. Phys. Chem. 1952, 20, 981. (3) Springston, S. R.; Novotny, M. V. Anal. Chem. 1984, 56, 1762. (4) Lauer, H. H.; McManigill, D.; Board, R. D. Anal. Chem. 1983, 55, 1370. (5) Sassiat, P. R.; Mourier, P.; Caude, M. H.; Rosset, R. H. Anal. Chem. 1987, 59, 1164. (6) Sun, C. K. J.; Chen, S. H. AIChE J. 1985, 31, 1904. (7) Olesik, S. V.; Woodruff, J. L. Anal. Chem. 1991, 63, 670. (8) Lee, S. T.; Olesik, S. V. Anal. Chem. 1994, 66, 4498. S0003-2700(97)01263-8 CCC: $15.00 Published on Web 06/04/1998

© 1998 American Chemical Society

Analytical equations can be used to predict the mass transport properties of a solute in a given medium. These estimations are not always sufficiently accurate for molecular diffusion coefficient of solutes in ternary fluid mixtures at high pressure. The paucity of experimental data, as well as the limited accuracy of the available analytical equations for their estimations leads to a need in their experimental determinations. The present study describes the experimental determination of the molecular diffusion coefficients for polar (m-cresol, 3-nitrophenol) as well as nonpolar (benzene, anthracene) solutes in ternary liquid mixtures of ethanol/H2O/CO2. Ethanol/CO2 and ethanol/H2O/CO2 mixtures are often used for the extraction of solutes when nontoxic solvents are required.9 The effect of both the mixture composition and temperature was studied. The applicability of mass transport equations that are commonly used to describe the diffusion in liquid mixtures was also investigated. EXPERIMENTAL SECTION Materials. All chemicals were used as received. Ethanol and acetone were HPLC grade obtained from Fischer Scientific (Pittsburgh, PA). The water was laboratory distilled. CO2 was SFC/SFE grade (99.997% pure) from Air Products (Allentown, PA). Anthracene and benzene were Baker grade obtained from J. T Baker Chemical Co. (Phillipsburg, NJ); 3-nitrophenol (99% pure) and m-cresol (99% pure) were obtained from Aldrich Chemical Co., Inc. (Milwaukee, WI). Benzene and m-cresol were used as neat solutes whereas anthracene and 3-nitrophenol were diluted in a mixture of ethanol/H2O. The concentrations of 3-nitrophenol and anthracene in the mixtures of ethanol/water were 0.4 × 10-3 and 2 × 10-3 M, respectively. Mixture Preparation. The ternary mobile phases were prepared according to the following procedure. Ethanol and H2O were mixed and transferred in an ISCO 260-D syringe pump (isco, Lincoln, NE). Liquid CO2 was then delivered to the pump at room temperature at 204 atm. The mixture was allowed to equilibrate overnight at 170 atm. Chromatographic System. The connection from the syringe pump to the injector was ∼60 cm of stainless steel tubing placed in the oven in order to preheat the mobile phase. The fluid mixture was delivered to 17 m fused-silica capillary tubing (Polymicro Technologies, Phoenix, AZ) with 247-µm i.d. The fused-silica tube was coiled in a 9-cm radius. A Valco W-series high-pressure injection valve (Valco Instruments Co. Inc., Houston, (9) Montanari, L.; King, J. W.; List, G. R.; Rennick, K. A. J. Food Sci. 1996, 61, 1230.

Analytical Chemistry, Vol. 70, No. 14, July 15, 1998 2783

TX) with a 200-nL injection volume was used. The oven was an HP-SFC (Hewlett-Packard Co., Avondale, PA). The detector was a Spectra 100 UV-visible detector (Spectra-Physics Analytical, Fremont, CA). The detector excitation was set at 254 nm, and the time constant was 0.3 s. The detection was done on-column by removing the polyimide coating from the capillary fused-silica tubing. To maintain the pressure in the chromatographic system, an appropriate length of 30-µm fused silica was used as a postdetector restrictor. The chromatographic data were analyzed using Peakfit (Peakfit Analysis Software, Jandel Scientific, San Rafael, CA). All measures were replicated five times. The errors reported for each point are the standard deviations at the 95% confidence level. RESULTS AND DISCUSSION The properties of the enhanced-fluidity liquid mixtures of ethanol/H2O/CO2 depend on the mixture composition as well as on pressure and temperature. In this study, mixtures containing either 0.61/0.39 or 0.50/0.50 mole ratio of ethanol/H2O were combined with varying proportions of CO2. Over the temperature range investigated, the maximum proportion of CO2 that can be added to the ethanol/H2O mixtures is determined by the phase diagram of the ethanol/H2O/CO2 mixture. Ethanol/H2O/CO2 Phase Diagram. The phase diagram for ethanol/H2O/CO2 is available for a large range of pressures and temperatures (68-205 atm and 25-60 °C).10,11 For the temperature range of 25-60 °C, multiple phases occur for pressures below 136 atm. For a starting liquid mixture with 0.61/0.39 mole ratio ethanol/H2O, the maximum mole fraction of CO2 to be added is 0.455 at 170 atm (2500 psi) and for 25 °C < T < 65 °C.11 The addition of up to 60 mol % CO2 requires a pressure greater than 205 atm over the same temperature range in order to remain in the one-phase region. In the case of a starting liquid mixture of ethanol/H2O with a higher proportion of water, i.e., 0.50/0.50 mole fraction ethanol/H2O, the maximum amount of liquid CO2 is limited to a mole fraction of 0.20 at 170 atm. For a mixture with a lower proportion of H2O, i.e., 0.78/0.22 mole fraction ethanol/ H2O, a liquid phase with 80 mol % of CO2 is achieved at a pressure of only 136 atm. If such ternary phases are to be used as mobile phases in reversed chromatography and the extraction of polar solutes, the proportion of H2O should be significant. Band-Broadening Technique. Experimental diffusion coefficients, Dm, were determined using the chromatographic band dispersion technique.12-14 The broadening of the chromatographic peak as expressed by its variance (σ2) is a function of the characteristics of the column and the mass-transfer properties of the solute (Dm). With a laminar flow profile, the analyte that was introduced into the capillary tube is eluted as a Gaussian peak whose variance is described by13

σ2 )

2DmL dcLu + u 96Dm

(1)

where L, u, and dc are the column length, the linear velocity, and (10) Gilbert, M. L.; Paulaitis, M. E. J. Chem. Eng. Data 1986, 31, 296. (11) Baker, L. C. W.; Anderson, T. F. J. Am. Chem. Soc. 1957, 79, 2071. (12) Taylor, G. Proc. R. Soc. London, Ser. A 1953, 219, 186. (13) Aris, R. Proc. R. Soc. London, Ser. A 1956, 235, 67. (14) Giddings, J. C.; Seager, S. L. Ind. Eng. Chem. Fundam. 1962, 1, 277.

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Table 1. Comparison of Experimental Diffusivities of Solutes in CO2 (40 °C, 160 atm) with Data from the Literature solute

solvent

Asa

benzene neat 0.99 naphthalene hexane 0.99 acetone neat 1.00

Dmb (×105, cm2 s-1) 13.6 ( 0.13 10.9 ( 0.012 13.5 ( 0.064

lit.c

lit.d

14.5 ( 0.8 12.6 11.6 ( 0.8 12.2 14.7 ( 0.4

a The average asymmetry factor (A ) was calculated at 10% of the s peak height. b Average value of five replicates. c From ref 5. d From ref 4. The overall precision stated was 2.9 ( 0.6%.

the diameter of the column, respectively. The peak variance, σ2, is also expressed as

σ2 ) LH

(2)

where H is the chromatographic plate height. Diffusivities of the solute in both the axial and the radial directions contribute to the overall chromatographic band broadening. The first and second terms of eq 1 account for the diffusion in the axial and radial directions, respectively. The contribution of the axial diffusion can be neglected if the linear velocity is described by the following equation:5

u > 140Dm/d

(3)

This condition was met in our experiments. Another source of error that is frequently encountered in the case of a coiled capillary tube is the onset of secondary flow. To eliminate the possibility of secondary flow, the aspect ratio (ratio of coil diameter to tube i.d.) must be as high as possible. The aspect ratio in these experiments was 729, and the range of linear velocities was 2-3 cm s-1. Secondary flow will not contribute to band dispersion under these conditions.15 Validation of Method. The performance of the experimental setup was estimated by the determination of the binary molecular diffusion of m-cresol, benzene, and acetone in supercritical carbon dioxide. Table 1 is a comparison of the experimental diffusion coefficients of the solutes in supercritical CO2 with literature values. The data agree well with the published values. Effect of Temperature and Mixture Composition on the Diffusion of Solutes. Figures 1 and 2 illustrate the effect of temperature and fluid composition on the binary diffusion coefficient for anthracene and 3-nitrophenol. Similar data for benzene and m-cresol are available as part of the Supporting Information. The mobile-phase composition was varied by adding different amounts of liquefied CO2 to a 0.61/0.39 mole ratio ethanol/H2O mixture; the resultant ternary mixtures contained between 0 and 0.40 mole fraction of CO2. The temperature was varied from 25 to 60 °C. The molecular diffusion coefficients of the solutes were increased by an increase in the temperature and/or an increase in the mole percent of CO2 in the mixture. For all four solutes, the observed increase in diffusion coefficient with 30% CO2 was comparable to that observed when the temperature was increased to 60 °C with no added CO2. By adding 40 mol % CO2 to the (15) Tijssen, R. Anal. Chim. Acta 1980, 114, 71.

Figure 1. Effect of temperature and mole fraction of CO2 on the molecular diffusion coefficient of anthracene in ethanol/H2O (0.61/ 0.39) mixtures at 170 atm: (+) 0, (9) 20, (2) 30, and (b) 40 mol % CO2.

Figure 2. Effect of temperature and mole fraction of CO2 on the molecular diffusion coefficient of 3-nitrophenol in ethanol/H2O (0.61/ 0.39) mixtures at 170 atm: (+) 0, (9) 20, (2) 30, and (b) 40 mol % CO2.

0.61/0.39 mole fraction ethanol/H2O mixture at 25 °C, the diffusion coefficients of all of the solutes increased by at least 200%. Of course, the greatest increase in the diffusion coefficients was observed when both the temperature and the proportion of CO2 were increased. Gains of ∼450% were observed for all solutes when the mobile-phase composition was increased from 0 to 40% CO2 and the temperature was increased from 25 to 60 °C. The overall increase in molecular diffusion coefficient also depends on the nature of the solute. The nonpolar compounds, such as benzene and anthracene, have higher diffusion coefficients than m-cresol and 3-nitrophenol in the ethanol/H2O/CO2 mixtures. m-Cresol and 3-nitrophenol can form hydrogen bonds with water or ethanol in the mixture. The solvation spheres of the polar solutes are expected to be larger than those of benzene and anthracene. The increase in the “apparent volume” leads to a decrease in the diffusivities of these compounds in the ethanol/ water/CO2 mixtures. The initial composition of the ethanol/H2O also significantly affects the changes in the diffusivity with added temperature and increased proportion of CO2. Figures 3 and 4 show the variation in the diffusion coefficients of anthracene and 3-nitrophenol over the same temperature range using an initial mixture of 0.50/0.50 mole fraction ethanol/H2O. Due to phase boundary limitations, the maximum amount of liquefied CO2 added was 20 mol %. The addition of 20 mol % CO2 at 25 °C increases the diffusion

Figure 3. Effect of temperature and mole fraction of CO2 on the molecular diffusion coefficient of anthracene in ethanol (0.50/0.50) mixtures at 170 atm: (+) 0 and (9) 20 mol % CO2.

Figure 4. Effect of temperature and mole fraction of CO2 on the molecular diffusion coefficient of 3-nitrophenol in ethanol/H2O (0.50/ 0.50) mixtures at 170 atm: (+) 0 and (9) 20 mol % CO2.

coefficients of the analytes by ∼100%. The combination of 20 mol % added CO2 and an increase in temperature of 60 °C increased the diffusion coefficients by 325-380%. Small proportions of added CO2 affect the diffusion coefficients of solutes in this ethanol/ H2O composition substantially. Lee and Olesik8 studied the effect of temperature and mobilephase composition on the molecular diffusion coefficients of anthracene and benzene in mixtures of methanol/H2O/CO2. The methanol/H2O mole ratio was held constant at 70/30. The effect of the temperature change is similar for the ethanol/H2O and methanol/H2O mixtures. For the ethanol/H2O (61/39) and the methanol/H2O mixtures, an increase in the temperature from 25 to 60 °C provides a ∼100% increase in the molecular diffusion coefficient of anthracene or benzene. The addition of liquid CO2 had a markedly different effect on the solute diffusion coefficients in the two systems (ethanol/H2O, methanol/H2O). Over the same temperature range (25-60 °C), and mole fraction of CO2, the diffusion coefficients of benzene and anthracene increase ∼700% for the methanol/H2O/CO2 mixture compared to 450% for the ethanol/H2O/CO2 mixtures. The addition of CO2 must have markedly different effects on the hydrogen bond interactions in the two systems. Estimation of Viscosity. Calculations were undertaken to estimate the variation in viscosity with temperature for the mixtures of ethanol/H2O/CO2. The variation in viscosity with temperature for the mixtures of ethanol/water (0.61/0.39 mole Analytical Chemistry, Vol. 70, No. 14, July 15, 1998

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Figure 5. Temperature effect on the viscosity of ethanol/H2O (0.61/ 0.39) mixture with various amount of CO2: (+) 25, (9) 30, (0) 40, (b) 50, and (]) 60 °C.

fraction) was determined from the interpolation of experimental data published in the literature.16 In the case of mixtures with low isothermal compressibility (i.e., 10-4 atm-1) such as ethanol/ water mixtures, the effect of pressure on the viscosity is negligible.17 The viscosities of the ethanol/H2O/CO2 mixtures over the temperature range of 25-60 °C and at a pressure of 172.3 atm were estimated using the method developed by Chung et al.18 This method applies a one-fluid approximation to correlate the properties of the components to those of the mixture. The accuracy of the method is typically of the order of 8-9% for both nonpolar and polar dense fluid mixtures. The densities of the liquid mixtures were estimated according to the modified Hankinson-Brobst equation.18 The viscosities of liquefied CO2 at 170 atm for different temperatures were calculated according to the following equation:19

ln(η105) ) 3.3882 +

1.3423F 1.909 - F

(4)

η and F are the viscosity (P) and density (g cm-3), respectively. The density of CO2 was taken from the databank SFC Solver (Isco). The accuracy of this equation is expected to be on the order of (3%19. Figure 5 illustrates the predicted effect of temperature and composition on the viscosity of mixtures containing 0.61/0.39 mole fraction ethanol/H2O to which various amounts of liquefied CO2 were added. The viscosities of the mixtures containing 0.61/0.39 mole ratio ethanol/H2O (without CO2) were taken from the literature.16 The decrease in the viscosity achieved by an increase in the temperature up to 60 °C could be easily obtained by the addition of 0.2-0.3 (depending of mixture composition) mole fraction of the low-viscosity fluid, i.e., CO2 under isothermal conditions. The effect of the temperature on the viscosity is larger for the fluid mixtures with a smaller proportion of CO2 as (16) Bingham, E. C.; Hatfield, J. E.; Jackson, R. F. Bur. Stand. J. Res. Sci. 1917, 298. (17) Abaszade, A.; Agaev, N. A.; Kerimov, A. M. Russ. J. Phys. Chem. 1971, 45, 1517. (18) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987; Chapters 9, 11. (19) Herreman, H.; Grevendonk, W.; De Bock, A. J. Chem. Phys. 1970, 53, 185.

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compared to those with a larger proportion. This result is expected since the viscosity depends on the extent of the hydrogen bonds. As the mole fraction of CO2 in the ethanol/ H2O mixture increases, the fraction of hydrogen bonds between alcohol and H2O molecules decreases. The breakdown of the hydrogen bonds by an increase in the temperature is then more noticeable for a mixture with a small proportion of CO2. Stokes-Einstein Equation. Often the hydrodynamic StokesEinstein (S-E) equation serves as a basis for the prediction of the molecular diffusion coefficients of solutes in liquids. The theory was originally developed for the diffusion of solute molecules that are larger than the solvent molecules. It assumes that the solute is diffusing into a continuous medium and that only macroscopic properties, such as viscosity, temperature, and the hydrodynamic radius of the diffusing solute control the diffusion coefficient as shown in eq 5, where

Dm ) kT/Cπηr

(5)

k is the Boltzmann constant, T is the absolute temperature, C is a constant, η is the viscosity, and r is the hydrodynamic radius of the solute. The value of the constant C can be either 6 or 4. If the solvent is treated as a continuous fluid, it is assumed to stick to the surface of the diffusing particle. This condition corresponds to the “stick” boundary condition of fluid flow and the value of C is 6. When the fluid slips over the surface of the diffusing particle, C ) 4 is used. Self-diffusion in compressed benzene and tetramethylsilane was successfully described by the StokesEinstein equation.20 The relationship holds also for hydrogenbonded liquids, such as methanol, using the slip boundary limit C ) 4.21 However, the Stokes-Einstein equation often overestimates the diffusion coefficients of solutes in supercritical fluids.7,22 The Stokes-Einstein equation was tested against the experimental diffusion coefficients determined in the present study. The hydrodynamic radii of the solutes were approximated by their Lennard-Jones radii.18 Values of 2.89 and 2.56 Å were chosen for m-cresol and benzene as their hydrodynamic radii, respectively.18,20 The radius of anthracene (4.60 Å) was estimated using the molecular modeling software HyperChem (Autodesk, Inc., Sausalito, CA). The slip boundary condition was most compatible with the experimental data. Therefore C ) 4 was used. Figures 6 and 7 show plots of the experimental diffusion coefficients and those predicted using the Stokes-Einstein equation versus the reciprocal viscosity under isothermal conditions, for anthracene and m-cresol, respectively. Changes in viscosity of the fluid mixtures were achieved by adding various amounts of liquefied CO2 to a 0.61/0.39 mole fraction ethanol/water mixture. The Stokes-Einstein equation underestimated the molecular diffusion coefficients for benzene and anthracene (Figure 6); it approximates the diffusion coefficients for m-cresol reasonably well except for the lowest viscosity conditions studied. The deviation of the experimental data from the Stokes-Einstein equation is illustrated by the nonlinearity as well as the lack of zero point intercept of these plots. Moreover, the plots tend to deviate much more from the S-E prediction at (20) Parkhurst, H. J., Jr.; Jonas, J. J. Chem. Phys. 1975, 63, 2705. (21) Jonas, J.; Akai, A. J. Chem. Phys. 1977, 66, 4946. (22) Debenedetti, P. G.; Reid R. C. AIChE J. 1986, 32, 2024.

Dm ) 7.4 × 10-8(ΦM)0.5T/ηVA0.6

(6)

where Φ, M, T, η, and VA are the association factor, the molecular weight of the solvent, the temperature, the viscosity, and the molal volume of the solute at its normal boiling point, respectively. The molal volumes of the solutes at their normal boiling point were calculated according to the Lebas additive volume method (see Table 2).18 The association factor, Φ, was 2.6 for water, 1.5 for ethanol, and 1 for carbon dioxide.24 The diffusion in multicomponent liquid mixture introduces a modification of the “ΦM” term according to the following equation: Figure 6. Stokes-Einstein equation applied to the molecular diffusion coefficient of anthracene in ethanol/H2O (0.61/0.39) mixtures with various amount of CO2 at 170 atm: Experimental data: (0) 25, (O) 30, (4) 40, and (3) 50 °C, (]) 60 °C. Stokes-Einstein: (9) 25, (b) 30, (2) 40, (1) 50, and ([) 60 °C.

Figure 7. Stokes-Einstein equation applied to the molecular diffusion coefficient of m-cresol in ethanol/H2O (0.61/0.39) mixtures with various amount of CO2 at 170 atm. Experimental data: (0) 25, (O) 30, (4) 40, (3) 50, and (]) 60 °C. Stokes-Einstein: (9) 25, (b) 30, (2) 40, (1) 50, and ([) 60 °C.

low value of the viscosity, i.e., for mixtures with the highest proportion of CO2. Previous results show that, under isobaric conditions, the extent of solvent clustering in an enhanced-fluidity liquid is larger for mixtures with a high mole fraction of CO2.23 The radius of the diffusing species is then expected to be larger in mixtures of ethanol/H2O for the 0.4 mole fraction of CO2 compared to a mixture with a smaller amount of CO2 dissolved in it. This variable solute hydrodynamic volume would not improve the fit of the Stokes-Einstein equation for the anthracene and benzene diffusion coefficients because the necessary volumes would be smaller than the physical dimensions of the molecule. Wilke-Chang Equation. The Wilke-Chang (W-C) equation is a formula derived from the Stokes-Einstein theory and modified in order to fit the diffusion of organic solutes into water and other polar solvents.24 This empirical relationship is defined according to (accuracy ∼10%)

(23) Souvignet, I.; Olesik, S. V. J. Chem. Phys. 1995, 99, 16800. (24) Wilke, C. R.; Chang, P. AIChE J. 1955, 1, 264.

Φm )

∑(x Φ M ) i

i

i

(7)

i

where xi is the mole fraction of the ith component in the mixture. The association parameter is the effective molecular weight of the solvent with respect to the diffusing process. The WilkeChang equation is expected to provide a better fit of the experimental data since the association parameter, ΦM, accounts for the association between solvent-solvent molecules. A good estimation of the diffusivities of organic compounds into water was found using the Wilke-Chang equation.25 Figures 8 and 9 show the experimental diffusion coefficients of anthracene and 3-nitrophenol, respectively, in the ethanol/H2O/ CO2 mixtures (starting with a 0.61/0.39 ethanol/H2O mixture) plotted against the values calculated with the Wilke-Chang equation. Results obtained using the Wilke-Chang equation were similar to those with the Stokes-Einstein in that the WilkeChang underestimates the diffusivities of anthracene and benzene. However, the Wilke-Chang equation provided estimates that were fairly close to the experimental values for the more polar solutes, m-cresol and 3-nitrophenol. Eyring Rate Theory. In a liquid mixture (including hydrogenbonded liquids), the effect of the temperature on the solute diffusion coefficients is often described by the Eyring rate theory (eq 8),26-28 where

ln Dm ) A -Ea/RT

(8)

A is the preexponential constant, Ea is activation energy of diffusion, T is the absolute temperature, and R is the gas constant. Figures 10 and 11 are representative plots of ln Dm versus the reciprocal of temperature for anthracene and m-cresol. The Eyring rate expression fit the data well for all solutes with r g 0.98 for all solutes. Table 3 shows a comparison of the activation energies for diffusion for all four solutes. The activation energy decreases substantially in each case after the addition of CO2. This large decrease with added CO2 was also observed for the methanol/H2O/CO2 mixtures.8 However, for the methanol/H2O/ CO2 liquid mixtures, the decrease was so great that the decrease in the ln Dm was not a linear function to 1/T. The activation (25) Olander, D. R. AIChE J. 1961, 7, 175. (26) Glasstone, S.; Laidler, K.; Eyring, H. The Theory of Rate Processes; McGrawHill: New York; 1941. (27) Durou, C.; Hot, J. P. J. Chem. Eng. Data 1977, 22, 123. (28) Chen, S. H.; Davis, H. T.; Evans, D. F. J. Chem. Phys. 1982, 77, 2540.

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Table 2. Calculation of the Molal Volume of the Solute at Its Boiling Point by the LeBas Method17 solute

VA (cm3 mol)

benzene anthracene m-cresol 3-nitrophenol

96.0 196.7 125.6 114.5

Figure 10. Plot of Ln Dm versus 1/T for anthracene: (0) 0, (b) 20, (4) 30, and (1) 40 mol % CO2 (experimental).

Figure 8. Wilke-Chang equation applied to the molecular diffusion coefficient of anthracene in ethanol/H2O (0.61/0.39) mixtures with various amount of CO2 at 170 atm. Experimental data: (0) 0, (O) 20, (4) 30, and (]) 40 mol % CO2. Wilke-Chang: (9) 0, (b) 20, (2) 30, and ([) 40 mol % CO2.

Figure 11. Plot of Ln Dm versus 1/T for m-cresol: (0) 0, (b) 20, (4) 30, and (1) 40 mol % CO2 (experimental). Table 3. Variation of Activiation Energy (Ea) for Diffusion of Four Solutes as a Function of Ethanol/H2O/ CO2 Mixture Composition Eaa (kJ/mol)

Figure 9. Wilke-Chang equation applied to the molecular diffusion coefficient of 3-nitrophenol in ethanol/H2O (0.61/0.39) mixtures with various amount of CO2 at 170 atm. Experimental data: (0) 0, (O) 20, (4) 30, and (]) 40 mol % CO2. Wilke-Chang: (9) 0, (b) 20, (2) 30, and ([) 40 mol % CO2.

energies determined for the ethanol/H2O/CO2 mixtures were similar in magnitude to those found in other highly associated solvent systems29 and lower than those observed for weaker associated enhanced-fluidity mixtures, such as tetrahydrofuran/ CO2.30

CO2 (%)

anthracene

benzene

m-cresol

p-nitrophenol

0 20 30 40

1.9 1.5 1.4 1.5

1.7 1.4 1.4 1.4

1.9 1.6 1.8 1.6

1.9 2.1 1.5 1.6

a

For mixtures containing 0.61/0.39 mole ratio ethanol/H2O.

SUPPORTING INFORMATION AVAILABLE Figures illustrating the effect of temperature and mole fraction of CO2 on the molecular diffusion coefficient of benzene and m-cresol in ethanol/H2O (0.61/0.39) and ethanol/H2O (0.50/0.50) mixtures at 170 atm (4 pages). Ordering information is given on a current masthead page.

ACKNOWLEDGMENT This work was supported by the NSF with Grant CHE-9503284. (29) Sanchez, V.; Oftadeh, H.; Durou, C.; Hot, J.-P. J. Chem. Eng. Data 1977, 22, 123. (30) Yuan, H.; Olesik, S. V. J. Chromatogr. A 1997, 785, 35.

2788 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998

Received for review November 18, 1997. Accepted April 14, 1998. AC971263N