Article pubs.acs.org/jced
Solubility of Benzoic Acid in Mixtures of CO2 + Hexane Janette Mendez-Santiago† and Amyn S. Teja* School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, United States ABSTRACT: The solubilities of solid benzoic acid in mixtures of CO2 + hexane have been measured at temperatures ranging from (308 to 338) K, pressures ranging from (10 to 35) MPa, and cosolvent concentrations ranging from (0 to 7) mol % hexane. The consistency of the data was verified via plots of the enhancement factor versus the density as suggested by dilute solution theory. The dilute solution theory was also used to correlate and extrapolate the data using three parameters that are independent of temperature, pressure, and cosolvent concentration.
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INTRODUCTION The presence of a cosolvent or a cosolute generally results in an increase in the solubility of a solid in a supercritical fluid,1−7 although a decrease in the solubility is also known to occur.8−10 As a result of these opposite trends, it has proved difficult to generalize the effect of cosolvents on solubility in a supercritical fluid. Attempts at generalization have also proved difficult because of the limited availability of data on ternary and higher systems at supercritical conditions. There is therefore a need for more data and models to provide an understanding of the behavior of supercritical solid + solvent + cosolvent systems. Although many empirical11−13 and semiempirical14,15 models have been proposed for this purpose, they generally rely on the availability of good data for the evaluation of model parameters. We have shown previously16,17 that an extended theory of dilute solutions based on the work of Harvey and others18−20 provides a simple test for the consistency of solid-supercritical fluid solubility data. The dilute solution model was also extended to multiple solute systems by us.17 In the present work, we apply this model to validate new measurements of the solubility of benzoic acid in mixtures of carbon dioxide and hexane. We show that the addition of hexane leads to an increase in the solubility of benzoic acid and that the ternary data can be correlated using the extended dilute solution theory with adjustable parameters that do not depend on temperature, pressure, or cosolvent concentration.
Figure 1. Schematic of the apparatus for solubility measurements.
frits) were placed at each end of the cartridge to minimize carry-over of the solid. The packed cartridge was weighed on a Mettler digital balance (model G 245) to 0.0001 g before placing it in the extractor chamber. The apparatus could be operated between ambient conditions and a maximum temperature and pressure of 423 K and 69 MPa, respectively. The temperature of the extractor chamber was maintained constant within ± 1 K. A solvent−cosolvent mixture was prepared by adding a known amount of cosolvent to the syringe pump and filling the pump with the solvent (carbon dioxide). The mixture was allowed to sit for about 16 h, with the pressure being cycled several times to ensure complete mixing. A pressure setting was then selected and the outlet valve of the syringe pump was opened to allow the solvent-cosolvent mixture to flow into the density meter and pressure gauge. The inlet valve to the extractor was closed at this point to allow the density of the
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EXPERIMENTAL SECTION A schematic diagram of the apparatus used in this work is shown in Figure 1. The apparatus consists of an Isco syringe pump (model 260D), an Anton Paar density meter (DMA 512), a Heise pressure gauge (model 710A), an Isco extractor (SF2-10), a sample collection vessel, and a Precision Scientific wet test meter (model 63111). The Isco extractor cartridge had an internal volume of 10 mL and was packed with about 3 g of solid and two layers of glass beads. Two filters (2 μm porosity © 2012 American Chemical Society
Received: May 29, 2012 Accepted: October 24, 2012 Published: November 1, 2012 3438
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determined to have an uncertainty of u(ρ) = 2 × 10−6 mol·mL−1. The wet test meter (Precision Scientific, model 63111) was factory calibrated and further calibrated by comparing mass flows of carbon dioxide obtained from pump readings with those from the wet test meter. It should be added that the amount of carbon dioxide displaced by the pump could be calculated because the syringe pump was kept at constant temperature and pressure. The relative uncertainty in the solubility data was determined to be ur(x) = 0.05.
mixture to be measured at the extraction temperature and pressure. The density meter was maintained at the extraction temperature by recirculating water with a Exocal bath circulator (model EX-100 UHP), and the temperature was monitored with a type K thermocouple connected to a multimeter (Fluke 8840A). The multimeter was calibrated against a Hart Scientific Standard Platinum Resistance Thermometer (SPRT, model 2560). The inlet valve to the extractor was then opened and the cartridge was pressurized with the solvent and allowed to equilibrate for at least 5 min. Initial readings (extractor temperature, pressure, wet test meter, pump volume and pressure, density meter period, and temperature) were recorded, followed by slow opening of the outlet valve to allow the saturated supercritical fluid to exit the extractor. The flow rate was manually controlled (approximately 0.2 mL/min at the syringe pump) and the outlet valve was heated with heating tape to about 353 K to compensate for the JouleThompson effect and to minimize precipitation of the solid in the valve. The temperature of the depressurization valve was recorded with a thermocouple. Upon depressurization, the solute and cosolvent dropped out of solution and were collected in a test tube immersed in a dry ice/ethanol cold trap. The test tube was connected to the depressurization valve with a small piece of stainless steel tubing and was initially loaded with about 10 mL of butanol to trap the solid and cosolvent. The depressurized solvent flowed through a rotameter and then into the wet test meter where its total volume was determined. The system was leak tested before and after each experiment, and each run lasted until at least 0.1 ft3 of solvent or 0.1 g of solute were collected. Intermediate measurements were taken every 5 min to ensure that the conditions were stable at the desired set points. At the end of each run, the cartridge was depressurized by opening an outlet valve connected to a vent line. The solute and cosolvent that dropped out of solution during this step were also collected. The cartridge was then removed and weighed (after drying). The depressurization valves and the tubing connecting the extractor to both collection vessels were then cleaned with a solvent and analyzed for solute content. The amount of solute in each collection vessel was determined by analyzing the contents by HPLC (Thermo Separation Products) consisting of a membrane degasser (model A-1170), a gradient pump (model P4000), a photodiode array detector (SpectroMonitor 5000), and a sample injector (Precision Sampling, model LC-241). A phthalic acid internal standard was used to calibrate the instrument. The amount of solute obtained by HPLC was compared with that obtained from measurements of the weight loss of the cartridge. This ensured that all solid in the depressurization valve and connecting lines had been collected. For most experiments, at least 95% of the solid was recovered. Any data point with less than 90% solid recovery was discarded. The amount of cosolvent in the collection vessel was determined by analyzing the contents using a gas chromatograph (Hewlett-Packard 6894) equipped with a flame ionization detector. Methanol or hexane was used as an internal standard depending on the mixture being analyzed. The pressure gauge (Heise 710A) was calibrated against a Budenberg dead-weight pressure tester with a manufacturer certified relative uncertainty ur(p) = 0.0005 (under standard conditions). The relative uncertainty in the measured pressure was ur(p) = 0.001 at pressures below 414 bar. The density meter was calibrated with two fluids (water and carbon dioxide) and experimental densities were
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VALIDATION OF EXPERIMENTAL TECHNIQUE The solubility of benzoic acid in pure carbon dioxide at 308 K was measured to validate the experimental technique. The source and purity of the materials are listed in Table 1, and Table 1. Source and Purity of Materials compound CO2 methanol hexane benzoic acid
purity 99.99 99.99 >99 >99.5
% % % %
source Air Products Fisher Scientific Fisher Scientific Fisher Scientific
Table 2. Experimental Mole Fraction Solubility y2 of Benzoic Acid in CO2 at Temperature T and Pressure pa T/K
p/bar
y2
308.15 308.15 308.15 308.15 308.15 308.15
101.2 151.7 202.2 252.7 303.2 353.7
0.00100 0.00166 0.00221 0.00268 0.00286 0.00274
a
Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 bar, and ur(y2) = 0.05.
results are listed in Table 2. Our data, together with the data of Dobbs et al.21 and Schmitt and Reid,22 are plotted in Figure 2. The three sets of data show reasonably good agreement with each other. Solubility data for benzoic acid in (96.5% carbon dioxide +3.5 mol % methanol) and (97% carbon dioxide +3%
Figure 2. Comparison of the experimental solubility of benzoic acid in CO2. The points represent data from this work (●), Schmitt and Reid22 (■), and Dobbs21 (▲). 3439
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Table 5. Experimental Solubility y2 of Benzoic Acid in {97.2 % CO2 (1) + 2.8 % Hexane (3)}, the Experimental Density ρ1 of CO2, and the Experimental Density ρ1+3 of the {97.2 % CO2 (1) + 2.8 % Hexane (3)} Mixture at Temperature T and Pressure pa
methanol) were also measured, and the results are included in Table 3. These data were found to lie between the data for benzoic acid in pure carbon dioxide and in pure methanol, as expected. Table 3. Experimental Mole Fraction Solubility y2 of Benzoic Acid in Mixtures of {(1 − x3)CO2 + x3CH3OH} at Temperature T and Pressure pa T/K
p/bar
x3
y2
318.15 318.15 318.15 318.15 318.15 308.15 308.15 308.15 308.15 308.15
101.2 151.9 202.5 253.1 303.9 101.2 151.8 202.6 253.2 303.8
0.035 0.035 0.035 0.035 0.035 0.030 0.030 0.030 0.030 0.030
0.00593 0.01084 0.01005 0.01032 0.01038 0.00671 0.00726 0.00777 0.00770 0.00775
p/bar
ρ1+3/mol·mL−1
ρ1/mol·mL−1
y2
308.15 308.15 308.15 308.15 318.15 318.15 318.15 318.15 328.15 328.15 328.15 328.15
202.5 253.1 303.7 355.7 202.6 253.4 303.2 354.9 202.2 253.1 303.4 354.4
0.01898 0.01973 0.02030 0.02081 0.01803 0.01876 0.01945 0.02004 0.01689 0.01788 0.01868 0.01924
0.01973 0.02054 0.02117 0.02171 0.01854 0.01955 0.02029 0.02091 0.01723 0.01850 0.01938 0.02009
0.00351 0.00395 0.00429 0.00415 0.00453 0.00546 0.00605 0.00659 0.00582 0.00733 0.00790 0.00884
a
Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 bar, u(ρ) = 0.000002 mol·mL−1, and ur(y2) = 0.05.
a
Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 bar, u(x3) = 0.001, and ur(y2) = 0.05.
Table 6. Experimental Solubility y2 of Benzoic Acid in {96.9 % CO2 (1) + 3.1 % Hexane (3)}, the Experimental Density ρ1 of CO2, and the Experimental Density ρ1+3 of the {96.9 % CO2 (1) + 3.1 % Hexane (3)} Mixture at Temperature T and Pressure pa
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DATA AND CORRELATION The solubility of benzoic acid in carbon dioxide + hexane was measured at several temperatures, pressures, and hexane concentrations. The data are listed in Tables 4−8 and plotted Table 4. Experimental Solubility y2 of Benzoic Acid in {97.8 % CO2 (1) + 2.2 % hexane (3)}, the Experimental Density ρ1 of CO2, and the Experimental Density ρ1+3 of the {97.8 % CO2 (1) + 2.2 % Hexane (3)} Mixture at Temperature T and Pressure pa T/K
p/bar
ρ1+3/mol·mL−1
ρ1/mol·mL−1
y2
308.15 308.15 308.15 308.15 318.15 318.15 318.15 318.15 328.15 328.15
202.9 253.1 303.9 354.9 203.0 253.0 303.7 354.6 303.9 354.1
0.01914 0.01978 0.02037 0.02094 0.01811 0.01891 0.01957 0.02010 0.01872 0.01936
0.01974 0.02054 0.02117 0.02170 0.01855 0.01954 0.02030 0.02091 0.01939 0.02009
0.00329 0.00311 0.00342 0.00389 0.00401 0.00420 0.00518 0.00568 0.00619 0.00796
T/K
p/bar
ρ1+3/mol·mL−1
ρ1/mol·mL−1
y2
308.15 308.15 308.15 308.15 308.15 318.15 318.15 318.15 318.15 328.18 328.15 328.15 328.15
152.1 202.6 253.0 304.6 354.6 151.5 253.1 303.5 354.4 202.5 253.4 303.7 355.3
0.01801 0.01882 0.01950 0.02007 0.02058 0.01676 0.01864 0.01923 0.01980 0.01680 0.01775 0.01849 0.01906
0.01859 0.01973 0.02054 0.02118 0.02170 0.01695 0.01954 0.02029 0.02091 0.01724 0.01850 0.01939 0.02010
0.00323 0.00373 0.00409 0.00457 0.00441 0.00429 0.00593 0.00638 0.00642 0.00655 0.00774 0.00833 0.01012
a Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 bar, u(ρ) = 0.000002 mol·mL−1, and ur(y2) = 0.05.
other thermodynamic properties of the mixture. We have shown previously that eq 1 is able to fit solubility data for a large number of solids within experimental uncertainty. Since A and B do not depend on the temperature or pressure, eq 1 can also be used to predict the solubility at other conditions. When a cosolvent is used, we can extend the model to ternary systems as follows:
a
Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 bar, u(ρ) = 0.000002 mol·mL−1, and ur(y2) = 0.05.
in Figure 3 and 4. The solubility of benzoic acid increases with increasing cosolvent concentration, with the highest solubility being observed at the highest cosolvent concentration, temperature and pressure measured in this work (7 % hexane, 338 K and 354.4 bar). The data were correlated using the theory of dilute solutions16,17 which gives the following expression for binary systems: T ln E = A + Bρ1
T/K
T ln E = G′ + H′ρ1 + J ′x3
(2)
where E is the enhancement factor for solute 2 in the ternary mixture, ρ1 is the pure solvent density (cosolvent and solute free), and x3 is the cosolvent mole fraction (solute free). Also, G′, H′, and J′ are constants. Equation 2 was used to correlate the solubility data measured in this work. It proved possible to correlate the benzoic acid solubility in CO2 + hexane with an average absolute deviation between correlated and experimental values of 6.22 %, which compares well with the experimental uncertainty. Values of the constants in eq 2 were found to be as
(1)
y2p/ps2
where E = and is the enhancement factor, y2 is the mole fraction of the solute in the mixture, p is the pressure, ps2 is the sublimation pressure of the solute, T is the temperature, ρ1 is the density of the solvent, and A and B are constants related to 3440
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Table 7. Experimental Solubility y2 of Benzoic Acid in {95 % CO2 (1) + 5 % Hexane (3)}, the Experimental Density ρ1 of CO2, and the Experimental Density ρ1+3 of the {95 % CO2 (1) + 5 % Hexane (3)} Mixture at Temperature T and Pressure pa T/K
p/bar
ρ1+3/mol·mL−1
ρ1/mol·mL−1
y2
308.15 308.15 308.15 308.15 308.15 318.15 318.15 318.15 318.15 318.15 328.15 328.15 328.15 328.15 328.15
152.1 202.6 252.6 304.1 355.0 151.5 202.8 252.9 303.9 355.4 151.6 202.5 253.8 303.9 355.1
0.01757 0.01836 0.01898 0.01953 0.02007 0.01646 0.01746 0.01823 0.01879 0.01926 0.01521 0.01656 0.01742 0.01805 0.01859
0.01859 0.01973 0.02053 0.02118 0.02170 0.01695 0.01855 0.01954 0.02030 0.02092 0.01500 0.01725 0.01851 0.01939 0.02010
0.00369 0.00432 0.00473 0.00512 0.00500 0.00445 0.00593 0.00670 0.00786 0.00818 0.00531 0.00742 0.00947 0.01124 0.01198
Figure 3. Solubility of benzoic acid in CO2 + hexane mixtures. The points represent measurements at 308.15 K (■), 318.15 K (●), 328.15 K (⧫), and 338.15 K (▲). The lines represent calculations for hexane concentrations of 7 % (solid line); 5 % (dotted line), and 2.2 % (dashed line).
a Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 bar, u(ρ) = 0.000002 mol·mL−1, and ur(y2) = 0.05.
Table 8. Experimental Solubility y2 of Benzoic Acid in {93 % CO2 (1) + 7 % Hexane (3)}, the Experimental Density ρ1 of CO2, and the Experimental Density ρ1+3 of the {93 % CO2 (1) + 7 % Hexane (3)} Mixture at Temperature T and Pressure pa T/K
p/bar
ρ1+3/mol·mL−1
ρ1/mol·mL−1
y2
318.15 318.15 318.15 318.15 318.15 328.15 328.15 328.15 328.15 328.15 338.15 338.15 338.15 338.15 338.15
151.7 202.4 253.2 303.7 355.4 151.5 202.9 253.0 303.8 354.6 151.8 202.3 252.6 303.7 354.4
0.01621 0.01706 0.01771 0.01824 0.01869 0.01514 0.01621 0.01698 0.01754 0.01804 0.01380 0.01528 0.01619 0.01684 0.01741
0.01696 0.01854 0.01955 0.02030 0.02092 0.01500 0.01726 0.01850 0.01939 0.02009 0.01280 0.01584 0.01739 0.01846 0.01926
0.00591 0.00726 0.00788 0.00860 0.00976 0.00725 0.00989 0.01255 0.01396 0.01496 0.00834 0.01207 0.01710 0.02025 0.02262
Figure 4. Solubility of benzoic acid in 93 % CO2 + 7 % hexane. Lines represent calculations using eq 2 and the points represent measurements at 338.15 K (▲), 328.15 K (●), and 318.15 K (⧫).
and (0 to 7) % hexane. The data were correlated using an extended dilute solution theory. The three regressed constants in the dilute solution expression were found to be independent of temperature, pressure, and hexane concentration, suggesting that the expression may be used to extrapolate/predict data at conditions that have not been measured.
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a
Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.1 bar, u(ρ) = 0.000002 mol·mL−1, and ur(y2) = 0.05.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: 1-404-894-3098. Fax: 1-404-894-2866.
follows: G′ = 1500 K, H′ = 108154 mL·K·mol−1, and J′ = 39.91 K. Figure 4 illustrates the results of the regression for a cosolvent concentration of 7 % hexane. Note that the ln y2 is plotted against solvent density ρ1 in this figure, so that the fit is not as good as for ln E vs ρ1. Nevertheless, it should be added that the three parameters of eq 2 are independent of the conditions, and therefore data at any temperature, pressure and cosolvent concentration can be calculated using the values of G′, H′, and J′ reported above.
Present Address †
ExxonMobil Canada East, 100 New Gower St., Suite 1000, St. John’s, Newfoundland, Canada A1C 6K3. Notes
The authors declare no competing financial interest.
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REFERENCES
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CONCLUSIONS New data for the solubility of solid benzoic acid in mixtures of CO2 + hexane are reported at (308 to 338) K, (10 to 35) MPa, 3441
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