Measurement and Modeling of the Solubility of Anthracene and

Article pubs.acs.org/jced

Measurement and Modeling of the Solubility of Anthracene and Carbazole in Compressed Isobutane Fabiola Martínez, Alicia Martín, and Jesusa Rincón* Department of Chemical Engineering, Faculty of Environmental Sciences and Biochemistry, Universidad de Castilla-La Mancha, Avda. Carlos III, s/n, 45071 Toledo, Spain ABSTRACT: The solubilities of anthracene and carbazole in liquid and supercritical isobutane have been experimentally determined in a static view cell, at temperatures from (367 to 418 K) and pressures from (3.2 to 8.6) MPa. The solubilities of anthracene varied from (7.3 to 51.8) mg of solute per gram of isobutane, whereas those of carbazole were from (1.4 to 9.9) mg of solute per gram of isobutane within the experimental range studied. These differences in solute solubilities have been explained attending to the higher vapor pressures of anthracene and its smaller dipole moment (and so stronger affinity to isobutane). The experimental solubilities have been compared to those of these solutes in propane and CO2. At similar reduced temperature and pressure conditions, it has been found that solute mole fractions are higher in isobutane than in the other two fluids (3 to 15 times and 160 to 270 times higher than in propane and CO2, respectively). Anthracene and carbazole solubilities in isobutane have been modeled by the Peng−Robinson equation of state. Good fit of the experimental results has been obtained (APD values of 6.7 % for anthracene and 9.7 % for carbazole). cosolvents13,18−20 or other alternative supercritical solvents have been proposed in the literature.9−12,21 Considering that any evaluation of the extraction process must be tied closely to the knowledge of the solute solubility in the appropriate fluid, in earlier works we investigated the solubility of several PAHs in sub- and supercritical propane and compared it to that in CO2.22−25 For all PAHs investigated we found that propane was a better solvent and that the magnitude of the solubility differences in both fluids was PAH dependent. In this work, we go one step further, and the solubility in isobutane of two PAHs, anthracene and carbazole, is studied at pressures from (3.2 to 8.6) MPa and temperatures from (367 to 418) K. The use of isobutane is investigated because nonpolar hydrocarbons such as propane and isobutane may dissolve PAHs more easily than CO2 due to their higher polarizability.19 Consequently, isobutane may be a better choice for some particular environmental applications. Furthermore, iso-butane rather than n-butane has been used because, at constant molecular weight of the hydrocarbon solvent, it has been reported in the literature that solvents having a tertiary carbon perform better than those without that atom in the extraction of carbonaceous material from porous matrices.26 In this paper, apart from experimentally determining the solubility of anthracene and carbazole in isobutane, we have compared them to those found in the bibliography for propane and CO2.22,23,27,28 Moreover, the experimental solubility data of both PAHs in isobutane are modeled by the Peng−Robinson

1. INTRODUCTION Polycyclic aromatic hydrocarbons (PAHs) are usually formed during incomplete combustion of organic material. Taking this into account, and also the wide distribution of organic matter (coal, wood, fossil fuels, food waste, etc.) and organic matter combustion processes, PAHs are amply scattered in the environment. Besides, they tend to coalesce and dissolve in the fatty substances of particles and easily originate long-lived micropollutants, being their environmental sinks air, soil, water, and vegetation.1 Nonetheless, soil has been reported to be their major repository.2,3 An interesting technology to clean PAH-contaminated soils (and other PAH-contaminated matrices, such as exhaust cracking catalysts) is supercritical fluid extraction. Over the years it has been successfully used at commercial scale in the pharmaceutical and food processing industries, but new applications have emerged more recently, such as soil cleaning and waste recycling.4−13 Compared to classical extraction with liquid solvents its main advantages are that both extraction of materials and phases separation occur faster. Likewise, it should be noticed that the solvent is easily recovered due to the special mass transfer characteristics of supercritical fluids (liquid-like density and gas-like viscosity, diffusivity, and surface tension).14 Carbon dioxide, being inexpensive, nonexplosive, readily available, and easily separated from the extracted products, has been typically used in the supercritical extraction of contaminated matrices5,15−17 but, unfortunately, it cannot quantitatively extract organic compounds of high molecular weight, like PAHs, because of their relatively low solubility in supercritical CO2.14 To overcome this problem the use of © 2012 American Chemical Society

Received: March 6, 2012 Accepted: September 26, 2012 Published: October 3, 2012 2928

dx.doi.org/10.1021/je300430d | J. Chem. Eng. Data 2012, 57, 2928−2935

Journal of Chemical & Engineering Data

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Figure 1. Layout of the experimental setup.

equation with two sets of mixing rules using one or two fitting parameters.

planning the experimental conditions, so working temperatures close to the above limit were avoided. The pressure transducer measures with an accuracy of 0.01 MPa, and the accuracy of the thermocouple in the measurement of the temperature is 0.1 K. On the other hand, a pressure variation of ± 0.2 MPa and a temperature variation of ± 3 K are allowed by the equipment’s control system. These pressure and temperature variations (± 0.2 MPa and ± 3 K) were considered to evaluate the uncertainties in isobutane density, isobutane mass, and solute mole fraction, as indicated below. The amount of solute (anthracene or carbazole) used in the experiments was weighted in an ED224S balance supplied by Sartorius (Germany), whose accuracy is 0.1 mg. 2.2. Experimental Procedure. A solubility experiment was started by placing a given amount of solute in the view cell. “After that, the cell was closed and heated up to a given temperature by means of the embedded heaters and the temperature controller”.25 The mixer was connected after the set temperature was attained. The system pressure was increased in the constant-volume cell by pumping in more solvent. “To determine the solute solubility, the pressure was increased (at isothermal conditions) in short intervals of (0.2 to 0.4) MPa until the point at which only one phase was observed through the sapphire window. Between intervals, the pressure was held for about 5 minutes before the next increase. The experiments were recorded in the PC connected to the camera. This allowed the subsequent viewing of the phase equilibrium images with their corresponding real-time pressure and temperature data”.25 The amounts of solute and solvent in the cell at the moment at which only one phase was observed were used to calculate the experimental solubility. The amount of isobutane in the cell when the solute just disappears was determined from the volume of the cell (0.1 L) and the density of isobutane at the conditions of the test (obtained from NIST29), according to misobutane = ρ·V, in which ρ and V are the isobutane density and the cell volume, respectively.

2. EXPERIMENTAL SECTION The experimental details of this work (Materials and Experimental Setup and Experimental Procedure) have been thoroughly described in previous works of our group.22−25 In this paper, quotation marks (with sentences copied from a previous work25) have been used to avoid self-plagiarism. 2.1. Materials and Experimental Setup. In this work isobutane (methylpropane, mass fraction 0.9995, Abelló Linde) was employed as solvent, and anthracene (mass fraction 0.990, Aldrich) and carbazole (mass fraction 0.980, Aldrich) were employed as solutes. An experimental apparatus (Thar Technology, Inc., Pittsburgh, PA), model R100CW was used to determine the solubilities of anthracene and carbazole in isobutane. “It is schematically shown in Figure 1 and consists of a cylindrical view cell (volume 0.1 L) with two sapphire windows mounted 90° apart for the observation and recording of the phase behaviour inside the cell using a camera and an illumination source. It is equipped with a pressure transducer, a temperature controller (with embedded heaters), a high pressure motordriven mixer, and a high pressure pump (P-50, Thar Technology)”.25 Isobutane was cooled down and then pumped to the view cell. “The camera, which was connected to a PC, allowed the observation and recording of the phase behaviour inside the cell under all of the pressure and temperature conditions tested. For decompressing the system, a metering valve (MV) with a heating device was used. A filter protected the metering valve against potential blockage due to solidification of the solutes during decompression”.25 The maximum working temperature allowed in the cell is 423 K (due to the temperature limitation given by the use of the motor-driven mixer). This fact was taken into account in 2929



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“Finally, it should be mentioned that according to the manufacturer’s specifications of the equipment, the standard uncertainty in the cell volume was 1 mL”,25 and pressure and temperature variations allowed by the control system in the cell were ± 0.2 MPa and ± 3 K. In addition, the uncertainty associated with the isobutane density (1.1 %) was estimated according to previous works of our group,23−25 taking into account that the uncertainty in the reference data for the isobutane density is below 0.5 %.30 The influence of pressure and temperature variations on the density was also considered. Consequently, and taking into account that misobutane = ρ·V, the relative combined standard uncertainty in the isobutane mass in the cell, ur(misobutane), was 0.015 [i.e., ur(misobutane) = Δmisobutane/ misobutane = 0.015]. The uncertainty in the mass of solute was 2 mg, according to experiments performed to determine the amount of solid that could be visually detected in the equilibrium cell. The standard uncertainties in the molar masses31 were 0.00189 g·mol−1 for isobutane, 0.00648 g·mol−1 for anthracene, and 0.00556 g·mol−1 for carbazole. As a result, the uncertainties in the anthracene and carbazole mole fractions were determined according to these uncertainty data by an error propagation analysis.32,33 Tables 1 and 2 show

the relative uncertainties in the mole fractions of anthracene, ur(yAN), and carbazole, ur(yCA), respectively, which are lower than or equal to 0.016 for anthracene [i.e., ur(yAN) = ΔyAN/yAN ≤ 0.016] and lower than or equal to 0.034 for carbazole. These values agree with those found from repeatability tests that allowed estimating the uncertainty derived from the variability in execution of the solubility experiments. The repeatability was determined from the relative standard deviation of the arithmetic mean of four replicates of a solubility experiment, as this parameter is widely used to express the precision and repeatability of an assay.31 Specifically, the conditions of these repeatability tests were 408 K and 6.3 MPa. The relative standard deviation of the arithmetic mean was found to be around 1.5 % for both solutes analyzed, anthracene and carbazole.

3. RESULTS AND DISCUSSION The solubilities of anthracene and carbazole in isobutane, expressed as solute mole fraction, are shown in Tables 1 and 2. It can be seen that in the pressure and temperature range analyzed the anthracene mole fractions vary from 2.4·10−3 to 1.7·10−2 in the experimental range studied, which is equivalent to (7.3 and 51.8) mg of solute per gram of isobutane. In the case of carbazole, solute mole fractions are between 5.0·10−4 and 3.4·10−3, which correspond to (1.4 and 9.9) mg of solute per gram of isobutane. 3.1. Physicochemical Properties of Solvent and Solutes. To interpret and model the experimental solubility data of the two PAHs in isobutane, the physicochemical properties of solvent and solutes should be taken into account. Thus, the most relevant physicochemical properties of anthracene, carbazole, and isobutane are shown in Table 3. Regarding the vapor pressure of anthracene (PvapAN) and carbazole (PvapCA), they have been calculated from eqs 1 and 2, according to the literature.47,48

Table 1. Experimental Results of Anthracene Solubility in Isobutanea uncertaintyc T/K 367

408

413

P/MPa 4.9 6.2 7.6 4.5 5.1 6.4 7.4 8.6 6.1 6.8 7.5

yANb −3

2.4·10 2.9·10−3 3.4·10−3 8.3·10−3 9.7·10−3 1.4·10−2 1.5·10−2 1.5·10−2 1.0·10−2 1.4·10−2 1.7·10−2

ΔyAN·yAN−1 1.6·10−2 1.6·10−2 1.5·10−2 1.5·10−2 1.5·10−2 1.5·10−2 1.5·10−2 1.5·10−2 1.5·10−2 1.5·10−2 1.5·10−2

Table 3. Molar Mass (M), Normal Boiling Temperature (Tbp), Melting Temperature (Tmp), Critical Temperature (Tc), Critical Pressure (Pc), Acentric Factor (ω), Ground State Dipole Moment (μg), and Polarizability (α) of Anthracene, Carbazole, Isobutane, Propane, and CO2

a

T and P standard uncertainties u: u(T) = 3 K, u(P) = 0.2 MPa. bMole fraction of anthracene (AN) in isobutane. cRelative combined standard uncertainty of AN mole fraction.

Table 2. Experimental Results of Carbazole Solubility in Isobutanea uncertaintyc T/K

P/MPa

yCAb

367

3.2 3.7 6.3 7.2 4.8 6.2 7.0 7.8 6.1 6.8 7.1

5.0·10−4 5.7·10−4 8.3·10−4 1.3·10−3 2.3·10−3 2.9·10−3 3.4·10−3 3.4·10−3 2.8·10−3 3.0·10−3 3.1·10−3

408

413

ΔyCA·yCA−1 3.4·10−2 3.1·10−2 2.3·10−2 1.9·10−2 1.7·10−2 1.6·10−2 1.6·10−2 1.6·10−2 1.6·10−2 1.6·10−2 1.6·10−2

a Value taken from ref 31. bValue taken from ref 34. cValue taken from ref 35. dValue taken from ref 29. eValue taken from ref 27. Other values are reported for ωanthracene in ref 39 and 46. fValue taken from ref 36: gValue taken from ref 37: hValue taken from ref 38: iValue taken from ref 39: jValue taken from ref 40: kValue taken from ref 41: lValue taken from ref 42: mValue taken from ref 43: nValue taken from ref 44: oValue taken from ref 45:

a

T and P standard uncertainties u: u(T) = 3 K, u(P) = 0.2 MPa. bMole fraction of carbazole (CA) in isobutane. cRelative combined standard uncertainty of CA mole fraction.

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Journal of Chemical & Engineering Data vap ln(PAN /Pa) = 31.620 −

11378 T /K

vap log10(PCA /Pa) = 14.04 −

5288.4 T /K

Article

than that of carbazole. This observation may be imputed to the fact that the solute vapor pressure is one of the main parameters influencing the solubility and, in the experimental range analyzed, at a given temperature the anthracene vapor pressure (and therefore the anthracene solubility) is always higher than that of carbazole.47,48 In addition, it is widely known14 that the solubility of the solutes also depends on the solute−solvent interactions which, in turn, highly depend on their polarity. Isobutane can be considered a nonpolar solvent (its ground state dipole moment, μg, is 0.13 D), and therefore its affinity for nonpolar solutes is higher than for polar ones. Thus, according to the solute and solvent polarity (dipole moment) the affinity of isobutane for anthracene (μg = 0.6 D) must be higher than that for carbazole (μg = 1.0 D). Therefore, the larger solubility of anthracene in isobutane, compared to carbazole, can be attributed to both its higher vapor pressure and smaller polarity. 3.3. Comparing the Solubility of Anthracene and Carbazole in Isobutane, Propane, and CO2. In previous works of this group22,23 the solubilities of anthracene and carbazole in propane were compared to those in carbon dioxide, the most widely used solvent at the supercritical state. It was reported that, at similar reduced conditions of temperature and pressure, the solubilities of carbazole and anthracene were, respectively, 1 and 2 orders of magnitude larger in propane. These findings were illustrative of the very good characteristics of compressed propane in relation to CO2 for the extraction of PAHs.22,23 In the present work, the solubility of these solutes in isobutane is compared to that previously reported using propane as solvent. To prevent the effect of the closeness to the critical point of the solvent (isobutane: Tc, 407.8 K, Pc, 3.63 MPa; propane: Tc, 369.8 K, Pc, 4.25 MPa) the comparison of the data has been performed considering the reduced pressure (Pr) and temperature (Tr) of the solvents (Tr = T/Tc; Pr = P/Pc). Figure 2 shows the comparison of anthracene solubility in isobutane and propane at Tr values of 0.9 and 1.0 at different values of Pr. It may be seen that the solubility of anthracene is

(1)

(2)

“The calculation of the dipole moments of the solutes has been carried out using the HyperChem computational chemistry package.42 Geometry optimization of the molecules was performed using Molecular Mechanics with Amber2 force field. The molecular structure that represents the potential minimum energy for each molecule was obtained using the Polak-Ribiere conjugate gradient method (with default values of parameters: RMS energy gradient 0.1 ((kcal)·(Å·mol)−1). Subsequently, the dipole moment of the molecules was obtained (performing single point calculation) after application of AM1 semiempirical method with unrestricted Hartre-Fock (UHF) Method”.25 3.2. Effect of Temperature and Pressure on the Solutes Solubility in Isobutane. The effect of pressure on the solubility of both solutes is analogous: increases of pressure at isothermal conditions lead to increases in the solute solubility. Nevertheless, increases of temperature at isobaric conditions produce different effects on the solubility of these solutes. For anthracene, isobaric increases of temperature below 7 MPa show that a solubility maximum is reached at the critical temperature of isobutane (408 K), whereas at higher pressure, increases of temperature produce increases in the solubility. In the case of carbazole, at all pressures investigated, maximum values of the solubility were obtained at 408 K. These results are closely related to the effect of pressure and temperature on solvent density and solutes vapor pressure, which are the main parameters affecting the solutes solubility.14,49 Specifically, as the solvent density increases, its solvent power increases, and consequently, the solute solubility is also increased; on the other hand, the solute solubility increases as the solute vapor pressure becomes larger. As a consequence, pressure increases lead to solubility increases of the solutes in isobutane in the pressure−temperature region studied in this work, because of the higher isobutane density. However, increases of temperature cause contrary effects: decreases in the solvent power (and therefore in the solute solubility) due to the decrease of isobutane density and increases in anthracene and carbazole solubility due to the higher solutes vapor pressure. Thus, considering the experimental observations it may be inferred that, in the case of anthracene and for temperature values below the critical temperature, the effect of the solute vapor pressure dominates over that of the solvent density, so temperature increases lead to higher solubilities. However, above the critical temperature and pressures below 7 MPa, the abrupt decrease of isobutane density by increasing the temperature produces the decrease of anthracene solubility. In the case of carbazole, the same reasoning can be applied to explain the effect of temperature on the solubility in the entire pressure range studied (the effect of the solute vapor pressure dominates for temperatures below the critical temperature, and above this value the solvent density effect is stronger). Regarding the comparison of the solubility of both solutes (anthracene and carbazole) in isobutane, it is shown that anthracene presents larger solubilities in the entire experimental range studied. For similar pressures and temperatures, anthracene solubility is around 1 order of magnitude higher

Figure 2. Comparison of anthracene solubility in isobutane and propane at (a) Tr = 0.90 and (b) Tr = 1.0. Solvent: ⧫, isobutane; □, propane. 2931



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3.4. Modeling of the Solubility of Anthracene and Carbazole in Isobutane. The experimental values of the solubility obtained have been correlated to find mathematical expressions that allow the prediction of anthracene and carbazole solubility in isobutane at different operating conditions. The Peng−Robinson equation (eq 3) has been used to this end.50 Parameters a(T) and b are defined by eq 4 and 5.

around 2.8 times larger in isobutane than in propane at Tr 0.9 (and similar values of Pr). Likewise, it is between 4 and 10 times higher at Tr of 1.0. The solubilities of carbazole in isobutane and propane at Tr values of 0.9 and 1.0 are presented in Figure 3. As shown, the solubilities of carbazole in isobutane are between 10 and 15 times larger than those of carbazole in propane for similar reduced temperatures and pressures.

P=

a(T ) R·T − υ−b υ·(υ + b) + b·(υ − b)

ai(T ) = 0.45724·

R2·TC,2 i PC, i

(3)

·

⎛ ⎜1 + (0.37464 + 1.54226·ω − 0.26992·ω 2)· i i ⎜ ⎝ ⎛ ⎜1 − ⎜ ⎝

2 ⎞⎞ T ⎟⎟ TC, i ⎟⎠⎟⎠

(4)

bi = 0.07780·

R ·TC, i PC, i

(5)

For multicomponent systems, mixture parameters aM and bM are estimated by the expressions given in eq 6. In these equations aij and bij represent the interaction parameters whose calculation is via mixing rules which there are different sets reported in the literature.22,28,50,51

Figure 3. Comparison of carbazole solubility in isobutane and propane at (a) Tr = 0.90 and (b) Tr = 1.0. Solvent: ⧫, isobutane; □, propane.

aM =

Considering that at the Tr values studied in the comparison (0.9 and 1.0) the densities of both solvents are practically coincident at similar reduced conditions (that of isobutane been only around 3 % higher), to understand the solubility results it is required to consider the affinity of the solvents for these solutes. Thus, bearing in mind that the ground state dipole moment of both solvents (isobutane, μg = 0.13 D; propane, μg = 0.08 D)29,43 and their polarizabilities (isobutane, α = 8.1 Å3; propane, α = 6.3 Å3)44,45 are higher for isobutane, it can also be expected a higher solubility of both PAHs in isobutane. It is so because of the dipole−dipole and dipole− dipole induced interactions between both PAHs and isobutane, more polar and polarizable than propane, are larger in the case of isobutane and, as a consequence, anthracene and carbazole solubilities are larger in isobutane. This explanation agrees with the experimental evidence that the solubility enhancement of carbazole in isobutane, relative to propane, is higher than in the case of anthracene. Definitely, these results highlight the excellent behavior of isobutane as a solvent of PAHs, a behavior that is even better than that of propane and CO2,22,23 following the PAH solubility in these solvents of the order: isobutane > propane > CO2. This experimental finding was somewhat expected since isobutane has an extra C group, compared to propane, and polarizability scales with the solvent molecule volume (therefore increasing as one goes from propane to isobutane). Consequently, from these results one may extrapolate that lighter solvent hydrocarbons with molecular weight higher than butane, like pentane, hexane, and so forth may dissolve PAHs even better than those analyzed in this work. This is a hypothesis to be confirmed in future works.

∑ ∑ yi ·yj ·aij i

bM =

∑ ∑ yi ·yj ·bij

j

i

j

(6)

The set of mixing rules used by Peng and Robinson50 to estimate interaction parameters (aij and bij) was the one-fluid van der Waals set of rules, which is defined by eqs 7 (where kij = kji, kii = 0). This set of mixing rules, labeled S1 in this work, implies the use of the fitting parameter kij. S1: aij =

ai ·aj ·(1 − kij)

bij = (b1 + b2)/2

(7)

Likewise, a set of mixing rules with two fitting parameters (kij and δij) has been used. It is labeled S2 and defined by eq 8 (where kij = kji, kii = 0, δij = δ ji, δii = 0). This set has been used by our group in previous works yielding good correlation of the experimental results.22−25 S2: aij =

ai ·aj ·(1 − kij)

bij =

bi ·bj ·(1 − δij) (8)

To find the optimal values of the fitting parameters, the Newton method has been used to minimize the average percentage deviation (APD), the objective function represented by eq 9, that compares the experimental (y2) and calculated (y2cal) solubility expressed as solute mole fraction (where subscript 2 corresponds to the solute, which are anthracene or carbazole in this work). ⎛ n |y − y cal | ⎞ 2, i 2, i ⎟ (100%) APD = ⎜⎜∑ ⎟· n y 2, i ⎝ i=1 ⎠

(9)

For each compound, the best values of the fitting parameters of the Peng−Robinson equation using mixing rules sets S1 and 2932



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S2, together with the APD values, are shown in Table 4. It can be appreciated that the modeling of the solubility of anthracene Table 4. Results Obtained in the Correlation of the Solubility of Anthracene and Carbazole in Isobutane Using the Peng−Robinson Equation of State parameter solute anthracene carbazole

set of mixing rules

no. parameters

k12

S1 S2 S1 S2

1 2 1 2

0.0976 0.1390 0.1605 0.2798

δ12 −0.0082 0.2113

APD/% 7.76 6.73 14.09 9.66

in isobutane by Peng−Robinson gives good fitting of the experimental results with the two sets of mixing rules tested, with APD below 8 % in all cases, even with the set of mixing rules involving one fitting parameter. The S2 set of mixing rules allows attaining the best fitting results (APD = 6.7 %). The prediction of the carbazole solubility in isobutane by Peng− Robinson yields slightly worse results than those of anthracene, with APD of 9.7 % for the best fitting with set of mixing rules S2, and 14.1 % for the worse one, attained by the set S1 with one parameter. As expected, in both cases (anthracene and carbazole) the best fitting results were attained when using the set of mixing rules with two fitting parameters, although satisfactory results were also obtained with one parameter. Finally, in Figure 4 the Peng−Robinson predicted data (using the S2 set of mixing rules) are compared against the experimental ones for both solutes. The model would ideally describe the system if all points laid over the line y2cal = y2 (represented by a gray line in Figure 4). It may be observed that experimental and estimated solubility data for both solutes studied show a high degree of agreement.

Figure 4. Comparison of the experimental solubility data (y2) with calculated values (y2cal) obtained from the Peng−Robinson equation of state: ⧫, 367 K; ■, 408 K; ▲, 413 K. (a) Solubility of anthracene modeled using set of mixing rules S2. (b) Solubility of carbazole modeled using set of mixing rules S2.

percentage deviations (APD) from the experimental results of 6.7 % for anthracene and 9.7 % for carbazole, for the best fitting. These results indicate that the Peng−Robinson expression with the proposed mixing rules set may predict accurately the solubility of anthracene and carbazole in near critical and supercritical isobutane.

■

4. CONCLUSIONS Anthracene and carbazole solubilities in compressed isobutane have been experimentally determined in a static view cell at temperature values of (367, 408, and 413) K and pressure ranges of (4.5 to 8.6) MPa for anthracene and (3.2 to 7.3) for carbazole. The values of anthracene mole fraction in the experimental range studied vary from 2.4·10−3 to 1.7·10−2, whereas for carbazole, the mole fractions in isobutane are between 5.0·10−4 and 3.4·10−3. The higher solubilities of anthracene in isobutane have been explained by its higher vapor pressures and smaller polarity compared to carbazole. These solubilities in isobutane have been compared to those of these solutes in propane and CO2 at similar reduced conditions. The anthracene mole fractions in isobutane are between 2.5 and 10 times higher than those in propane and between 180 and 270 times higher than those in CO2. Solubilities of carbazole in isobutane are more than 1 order of magnitude larger than in propane and around 170 times higher than in CO2. These results stand out the extraordinary properties of isobutane as solvent for the supercritical extraction of PAHs, which are even better than those of propane and CO2. The solubility data obtained have been modeled by the Peng−Robinson equation employing two different sets of mixing rules (with one or two fitting parameters). For both solutes, slightly better fitting results were obtained by the mixing rules set with two fitting parameters. Experimental and Peng−Robinson modeled solubility data showed a good agreement, with average

AUTHOR INFORMATION

Corresponding Author

*Tel.: +34 902204100. Fax: +34 925268840. E-mail address: [email protected]. Funding

The authors gratefully acknowledge the support to this work through projects 096/2006/3-11.3, A141/2007/2-11.3, and CMT 2006-10105 financed by the Spanish Ministries of Environment and Science and Technology. Likewise, financial support through the PAI08-0195-3614 project by the Junta de Comunidades de Castilla-La Mancha is acknowledged. Notes

The authors declare no competing financial interest.

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