measurement and modeling of the solubility of anthracene and carbazole in compressed isobutane

Measurement and Modeling of the Solubility of Anthracene andCarbazole in Compressed IsobutaneFabiola Martínez, Alicia Martín, and Jesusa Rincon*

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 inliquid and supercritical isobutane have been experimentallydetermined in a static view cell, at temperatures from (367 to418 K) and pressures from (3.2 to 8.6) MPa. The solubilitiesof anthracene varied from (7.3 to 51.8) mg of solute per gramof isobutane, whereas those of carbazole were from (1.4 to 9.9)mg of solute per gram of isobutane within the experimentalrange studied. These differences in solute solubilities havebeen explained attending to the higher vapor pressures ofanthracene and its smaller dipole moment (and so strongeraffinity to isobutane). The experimental solubilities have been compared to those of these solutes in propane and CO2. At similarreduced temperature and pressure conditions, it has been found that solute mole fractions are higher in isobutane than in theother two fluids (3 to 15 times and 160 to 270 times higher than in propane and CO2, respectively). Anthracene and carbazolesolubilities in isobutane have been modeled by the Peng−Robinson equation of state. Good fit of the experimental results hasbeen obtained (APD values of 6.7 % for anthracene and 9.7 % for carbazole).

1. INTRODUCTION

Polycyclic aromatic hydrocarbons (PAHs) are usually formedduring incomplete combustion of organic material. Taking thisinto account, and also the wide distribution of organic matter(coal, wood, fossil fuels, food waste, etc.) and organic mattercombustion processes, PAHs are amply scattered in theenvironment. Besides, they tend to coalesce and dissolve inthe fatty substances of particles and easily originate long-livedmicropollutants, being their environmental sinks air, soil, water,and vegetation.1 Nonetheless, soil has been reported to be theirmajor repository.2,3

An interesting technology to clean PAH-contaminated soils(and other PAH-contaminated matrices, such as exhaustcracking catalysts) is supercritical fluid extraction. Over theyears it has been successfully used at commercial scale in thepharmaceutical and food processing industries, but newapplications have emerged more recently, such as soil cleaningand waste recycling.4−13 Compared to classical extraction withliquid solvents its main advantages are that both extraction ofmaterials and phases separation occur faster. Likewise, it shouldbe noticed that the solvent is easily recovered due to the specialmass transfer characteristics of supercritical fluids (liquid-likedensity and gas-like viscosity, diffusivity, and surface tension).14

Carbon dioxide, being inexpensive, nonexplosive, readilyavailable, and easily separated from the extracted products, hasbeen typically used in the supercritical extraction ofcontaminated matrices5,15−17 but, unfortunately, it cannotquantitatively extract organic compounds of high molecularweight, like PAHs, because of their relatively low solubility insupercritical CO2.

14 To overcome this problem the use of

cosolvents13,18−20 or other alternative supercritical solventshave been proposed in the literature.9−12,21

Considering that any evaluation of the extraction processmust be tied closely to the knowledge of the solute solubility inthe appropriate fluid, in earlier works we investigated thesolubility of several PAHs in sub- and supercritical propane andcompared it to that in CO2.

22−25 For all PAHs investigated wefound that propane was a better solvent and that the magnitudeof 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 atpressures from (3.2 to 8.6) MPa and temperatures from (367 to418) K. The use of isobutane is investigated because nonpolarhydrocarbons such as propane and isobutane may dissolvePAHs more easily than CO2 due to their higher polarizability.

19

Consequently, isobutane may be a better choice for someparticular environmental applications. Furthermore, iso-butanerather than n-butane has been used because, at constantmolecular weight of the hydrocarbon solvent, it has beenreported in the literature that solvents having a tertiary carbonperform better than those without that atom in the extractionof carbonaceous material from porous matrices.26 In this paper,apart from experimentally determining the solubility ofanthracene and carbazole in isobutane, we have comparedthem to those found in the bibliography for propane andCO2.

22,23,27,28 Moreover, the experimental solubility data ofboth PAHs in isobutane are modeled by the Peng−Robinson

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

Article

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

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equation with two sets of mixing rules using one or two fittingparameters.

2. EXPERIMENTAL SECTION

The experimental details of this work (Materials andExperimental Setup and Experimental Procedure) have beenthoroughly described in previous works of our group.22−25 Inthis paper, quotation marks (with sentences copied from aprevious work25) have been used to avoid self-plagiarism.2.1. Materials and Experimental Setup. In this work

isobutane (methylpropane, mass fraction 0.9995, Abello Linde)was employed as solvent, and anthracene (mass fraction 0.990,Aldrich) and carbazole (mass fraction 0.980, Aldrich) wereemployed as solutes.An experimental apparatus (Thar Technology, Inc.,

Pittsburgh, PA), model R100CW was used to determine thesolubilities of anthracene and carbazole in isobutane. “It isschematically shown in Figure 1 and consists of a cylindricalview cell (volume 0.1 L) with two sapphire windows mounted90° apart for the observation and recording of the phasebehaviour inside the cell using a camera and an illuminationsource. It is equipped with a pressure transducer, a temperaturecontroller (with embedded heaters), a high pressure motor-driven mixer, and a high pressure pump (P-50, TharTechnology)”.25 Isobutane was cooled down and then pumpedto the view cell. “The camera, which was connected to a PC,allowed the observation and recording of the phase behaviourinside the cell under all of the pressure and temperatureconditions tested. For decompressing the system, a meteringvalve (MV) with a heating device was used. A filter protectedthe metering valve against potential blockage due to solid-ification of the solutes during decompression”.25

The maximum working temperature allowed in the cell is423 K (due to the temperature limitation given by the use ofthe motor-driven mixer). This fact was taken into account in

planning the experimental conditions, so working temperaturesclose 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 measure-ment of the temperature is 0.1 K. On the other hand, a pressurevariation of ± 0.2 MPa and a temperature variation of ± 3 K areallowed by the equipment’s control system. These pressure andtemperature variations (± 0.2 MPa and ± 3 K) were consideredto evaluate the uncertainties in isobutane density, isobutanemass, 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 bySartorius (Germany), whose accuracy is 0.1 mg.

2.2. Experimental Procedure. A solubility experiment wasstarted by placing a given amount of solute in the view cell.“After that, the cell was closed and heated up to a giventemperature by means of the embedded heaters and thetemperature controller”.25 The mixer was connected after theset temperature was attained. The system pressure wasincreased in the constant-volume cell by pumping in moresolvent. “To determine the solute solubility, the pressure wasincreased (at isothermal conditions) in short intervals of (0.2 to0.4) MPa until the point at which only one phase was observedthrough the sapphire window. Between intervals, the pressurewas held for about 5 minutes before the next increase. Theexperiments were recorded in the PC connected to the camera.This allowed the subsequent viewing of the phase equilibriumimages with their corresponding real-time pressure andtemperature data”.25 The amounts of solute and solvent inthe cell at the moment at which only one phase was observedwere used to calculate the experimental solubility. The amountof isobutane in the cell when the solute just disappears wasdetermined from the volume of the cell (0.1 L) and the densityof isobutane at the conditions of the test (obtained fromNIST29), according to misobutane = ρ·V, in which ρ and V are theisobutane density and the cell volume, respectively.

Figure 1. Layout of the experimental setup.

Journal of Chemical & Engineering Data Article

dx.doi.org/10.1021/je300430d | J. Chem. Eng. Data 2012, 57, 2928−29352929

“Finally, it should be mentioned that according to themanufacturer’s specifications of the equipment, the standarduncertainty in the cell volume was 1 mL”,25 and pressure andtemperature variations allowed by the control system in the cellwere ± 0.2 MPa and ± 3 K. In addition, the uncertaintyassociated with the isobutane density (1.1 %) was estimatedaccording to previous works of our group,23−25 taking intoaccount that the uncertainty in the reference data for theisobutane density is below 0.5 %.30 The influence of pressureand temperature variations on the density was also considered.Consequently, and taking into account that misobutane = ρ·V, therelative combined standard uncertainty in the isobutane mass inthe cell, ur(misobutane), was 0.015 [i.e., ur(misobutane) = Δmisobutane/misobutane = 0.015]. The uncertainty in the mass of solute was 2mg, according to experiments performed to determine theamount of solid that could be visually detected in theequilibrium cell. The standard uncertainties in the molarmasses31 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 uncertaintydata 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 lowerthan 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. Thesevalues agree with those found from repeatability tests thatallowed estimating the uncertainty derived from the variabilityin execution of the solubility experiments. The repeatability wasdetermined from the relative standard deviation of thearithmetic mean of four replicates of a solubility experiment,as this parameter is widely used to express the precision andrepeatability of an assay.31 Specifically, the conditions of theserepeatability tests were 408 K and 6.3 MPa. The relativestandard deviation of the arithmetic mean was found to bearound 1.5 % for both solutes analyzed, anthracene andcarbazole.

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 rangeanalyzed the anthracene mole fractions vary from 2.4·10−3 to1.7·10−2 in the experimental range studied, which is equivalentto (7.3 and 51.8) mg of solute per gram of isobutane. In thecase 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 soluteper gram of isobutane.

3.1. Physicochemical Properties of Solvent andSolutes. To interpret and model the experimental solubilitydata of the two PAHs in isobutane, the physicochemicalproperties of solvent and solutes should be taken into account.Thus, the most relevant physicochemical properties ofanthracene, carbazole, and isobutane are shown in Table 3.Regarding the vapor pressure of anthracene (PvapAN) andcarbazole (PvapCA), they have been calculated from eqs 1 and 2,according to the literature.47,48

Table 1. Experimental Results of Anthracene Solubility inIsobutanea

uncertaintyc

T/K P/MPa yANb ΔyAN·yAN−1

367 4.9 2.4·10−3 1.6·10−2

6.2 2.9·10−3 1.6·10−2

7.6 3.4·10−3 1.5·10−2

408 4.5 8.3·10−3 1.5·10−2

5.1 9.7·10−3 1.5·10−2

6.4 1.4·10−2 1.5·10−2

7.4 1.5·10−2 1.5·10−2

8.6 1.5·10−2 1.5·10−2

413 6.1 1.0·10−2 1.5·10−2

6.8 1.4·10−2 1.5·10−2

7.5 1.7·10−2 1.5·10−2

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

Table 2. Experimental Results of Carbazole Solubility inIsobutanea

uncertaintyc

T/K P/MPa yCAb ΔyCA·yCA−1

367 3.2 5.0·10−4 3.4·10−2

3.7 5.7·10−4 3.1·10−2

6.3 8.3·10−4 2.3·10−2

7.2 1.3·10−3 1.9·10−2

408 4.8 2.3·10−3 1.7·10−2

6.2 2.9·10−3 1.6·10−2

7.0 3.4·10−3 1.6·10−2

7.8 3.4·10−3 1.6·10−2

413 6.1 2.8·10−3 1.6·10−2

6.8 3.0·10−3 1.6·10−2

7.1 3.1·10−3 1.6·10−2

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

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

aValue taken from ref 31. bValue taken from ref 34. cValue taken fromref 35. dValue taken from ref 29. eValue taken from ref 27. Othervalues are reported for ωanthracene in ref 39 and 46.

fValue taken from ref36: gValue taken from ref 37: hValue taken from ref 38: iValue takenfrom ref 39: jValue taken from ref 40: kValue taken from ref 41: lValuetaken from ref 42: mValue taken from ref 43: nValue taken from ref44: oValue taken from ref 45:



= −PT

ln( /Pa) 31.62011378

/KANvap

(1)

= −PT

log ( /Pa) 14.045288.4

/K10 CAvap

(2)

“The calculation of the dipole moments of the solutes hasbeen carried out using the HyperChem computationalchemistry package.42 Geometry optimization of the moleculeswas performed using Molecular Mechanics with Amber2 forcefield. The molecular structure that represents the potentialminimum energy for each molecule was obtained using thePolak-Ribiere conjugate gradient method (with default values ofparameters: RMS energy gradient 0.1 ((kcal)·(Å·mol)−1).Subsequently, the dipole moment of the molecules wasobtained (performing single point calculation) after applicationof AM1 semiempirical method with unrestricted Hartre-Fock(UHF) Method”.25

3.2. Effect of Temperature and Pressure on theSolutes Solubility in Isobutane. The effect of pressure onthe solubility of both solutes is analogous: increases of pressureat isothermal conditions lead to increases in the solutesolubility. Nevertheless, increases of temperature at isobaricconditions produce different effects on the solubility of thesesolutes. For anthracene, isobaric increases of temperature below7 MPa show that a solubility maximum is reached at the criticaltemperature of isobutane (408 K), whereas at higher pressure,increases of temperature produce increases in the solubility. Inthe case of carbazole, at all pressures investigated, maximumvalues 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 solutessolubility.14,49 Specifically, as the solvent density increases, itssolvent power increases, and consequently, the solute solubilityis also increased; on the other hand, the solute solubilityincreases as the solute vapor pressure becomes larger. As aconsequence, pressure increases lead to solubility increases ofthe solutes in isobutane in the pressure−temperature regionstudied 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 solutesolubility) due to the decrease of isobutane density andincreases in anthracene and carbazole solubility due to thehigher solutes vapor pressure.Thus, considering the experimental observations it may be

inferred that, in the case of anthracene and for temperaturevalues below the critical temperature, the effect of the solutevapor pressure dominates over that of the solvent density, sotemperature increases lead to higher solubilities. However,above the critical temperature and pressures below 7 MPa, theabrupt decrease of isobutane density by increasing thetemperature produces the decrease of anthracene solubility.In the case of carbazole, the same reasoning can be applied toexplain the effect of temperature on the solubility in the entirepressure range studied (the effect of the solute vapor pressuredominates for temperatures below the critical temperature, andabove 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 thatanthracene presents larger solubilities in the entire experimentalrange studied. For similar pressures and temperatures,anthracene solubility is around 1 order of magnitude higher

than that of carbazole. This observation may be imputed to thefact that the solute vapor pressure is one of the mainparameters influencing the solubility and, in the experimentalrange analyzed, at a given temperature the anthracene vaporpressure (and therefore the anthracene solubility) is alwayshigher than that of carbazole.47,48 In addition, it is widelyknown14 that the solubility of the solutes also depends on thesolute−solvent interactions which, in turn, highly depend ontheir polarity. Isobutane can be considered a nonpolar solvent(its ground state dipole moment, μg, is 0.13 D), and thereforeits affinity for nonpolar solutes is higher than for polar ones.Thus, according to the solute and solvent polarity (dipolemoment) 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 tocarbazole, can be attributed to both its higher vapor pressureand smaller polarity.

3.3. Comparing the Solubility of Anthracene andCarbazole in Isobutane, Propane, and CO2. In previousworks of this group22,23 the solubilities of anthracene andcarbazole in propane were compared to those in carbondioxide, the most widely used solvent at the supercritical state.It was reported that, at similar reduced conditions oftemperature and pressure, the solubilities of carbazole andanthracene were, respectively, 1 and 2 orders of magnitudelarger in propane. These findings were illustrative of the verygood characteristics of compressed propane in relation to CO2for the extraction of PAHs.22,23 In the present work, thesolubility of these solutes in isobutane is compared to thatpreviously reported using propane as solvent. To prevent theeffect 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 performedconsidering the reduced pressure (Pr) and temperature (Tr) ofthe 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 differentvalues of Pr. It may be seen that the solubility of anthracene is

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



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 timeshigher at Tr of 1.0. The solubilities of carbazole in isobutaneand propane at Tr values of 0.9 and 1.0 are presented in Figure3. As shown, the solubilities of carbazole in isobutane arebetween 10 and 15 times larger than those of carbazole inpropane for similar reduced temperatures and pressures.

Considering that at the Tr values studied in the comparison(0.9 and 1.0) the densities of both solvents are practicallycoincident at similar reduced conditions (that of isobutanebeen only around 3 % higher), to understand the solubilityresults it is required to consider the affinity of the solvents forthese solutes. Thus, bearing in mind that the ground statedipole 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, itcan also be expected a higher solubility of both PAHs inisobutane. 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 caseof isobutane and, as a consequence, anthracene and carbazolesolubilities are larger in isobutane. This explanation agrees withthe experimental evidence that the solubility enhancement ofcarbazole in isobutane, relative to propane, is higher than in thecase of anthracene.Definitely, these results highlight the excellent behavior of

isobutane as a solvent of PAHs, a behavior that is even betterthan that of propane and CO2,

22,23 following the PAH solubilityin these solvents of the order: isobutane > propane > CO2. Thisexperimental finding was somewhat expected since isobutanehas an extra C group, compared to propane, and polarizabilityscales with the solvent molecule volume (therefore increasingas one goes from propane to isobutane). Consequently, fromthese results one may extrapolate that lighter solventhydrocarbons with molecular weight higher than butane, likepentane, hexane, and so forth may dissolve PAHs even betterthan those analyzed in this work. This is a hypothesis to beconfirmed in future works.

3.4. Modeling of the Solubility of Anthracene andCarbazole in Isobutane. The experimental values of thesolubility obtained have been correlated to find mathematicalexpressions that allow the prediction of anthracene andcarbazole solubility in isobutane at different operatingconditions. The Peng−Robinson equation (eq 3) has beenused to this end.50 Parameters a(T) and b are defined by eq 4and 5.

υ υ υ υ= ·

−−

· + + · −P

R Tb

a Tb b b

( )( ) ( ) (3)

ω ω

= ··

·

+ + · − · ·

−

⎛⎝⎜⎜⎛⎝⎜⎜

⎞⎠⎟⎟⎞⎠⎟⎟

a TR T

P

TT

( ) 0.45724

1 (0.37464 1.54226 0.26992 )

1

ii

i

i i

i

2C,2

C,

2

C,

2

(4)

= ··

bR T

P0.07780i

i

i

C,

C, (5)

For multicomponent systems, mixture parameters aM and bMare estimated by the expressions given in eq 6. In theseequations aij and bij represent the interaction parameters whosecalculation is via mixing rules which there are different setsreported in the literature.22,28,50,51

∑ ∑ ∑ ∑= · · = · ·a y y a b y y bi j

i j iji j

j ijM M i(6)

The set of mixing rules used by Peng and Robinson50 toestimate interaction parameters (aij and bij) was the one-fluidvan 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.

= · · − = +a a a k b b bS1: (1 ) ( )/2ij i j ij ij 1 2 (7)

Likewise, a set of mixing rules with two fitting parameters (kijand 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 usedby our group in previous works yielding good correlation of theexperimental results.22−25

δ= · · − = · · −a a a k b b bS2: (1 ) (1 )ij i j ij ij i j ij

(8)

To find the optimal values of the fitting parameters, theNewton method has been used to minimize the averagepercentage deviation (APD), the objective function representedby eq 9, that compares the experimental (y2) and calculated(y2

cal) solubility expressed as solute mole fraction (wheresubscript 2 corresponds to the solute, which are anthracene orcarbazole in this work).

∑=| − |

·=

⎛

⎝⎜⎜

⎞

⎠⎟⎟

y y

y nAPD

(100%)

i

ni i

i1

2, 2,cal

2, (9)

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

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



S2, together with the APD values, are shown in Table 4. It canbe appreciated that the modeling of the solubility of anthracene

in isobutane by Peng−Robinson gives good fitting of theexperimental results with the two sets of mixing rules tested,with APD below 8 % in all cases, even with the set of mixingrules involving one fitting parameter. The S2 set of mixing rulesallows attaining the best fitting results (APD = 6.7 %). Theprediction 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 rulesS2, and 14.1 % for the worse one, attained by the set S1 withone parameter. As expected, in both cases (anthracene andcarbazole) the best fitting results were attained when using theset of mixing rules with two fitting parameters, althoughsatisfactory results were also obtained with one parameter.Finally, in Figure 4 the Peng−Robinson predicted data (usingthe S2 set of mixing rules) are compared against theexperimental ones for both solutes. The model would ideallydescribe the system if all points laid over the line y2

cal = y2(represented by a gray line in Figure 4). It may be observedthat experimental and estimated solubility data for both solutesstudied show a high degree of agreement.

4. CONCLUSIONSAnthracene and carbazole solubilities in compressed isobutanehave been experimentally determined in a static view cell attemperature values of (367, 408, and 413) K and pressureranges of (4.5 to 8.6) MPa for anthracene and (3.2 to 7.3) forcarbazole. The values of anthracene mole fraction in theexperimental range studied vary from 2.4·10−3 to 1.7·10−2,whereas for carbazole, the mole fractions in isobutane arebetween 5.0·10−4 and 3.4·10−3. The higher solubilities ofanthracene in isobutane have been explained by its higher vaporpressures and smaller polarity compared to carbazole. Thesesolubilities in isobutane have been compared to those of thesesolutes in propane and CO2 at similar reduced conditions. Theanthracene mole fractions in isobutane are between 2.5 and 10times higher than those in propane and between 180 and 270times higher than those in CO2. Solubilities of carbazole inisobutane are more than 1 order of magnitude larger than inpropane and around 170 times higher than in CO2. Theseresults stand out the extraordinary properties of isobutane assolvent for the supercritical extraction of PAHs, which are evenbetter than those of propane and CO2. The solubility dataobtained have been modeled by the Peng−Robinson equationemploying two different sets of mixing rules (with one or twofitting parameters). For both solutes, slightly better fittingresults were obtained by the mixing rules set with two fittingparameters. Experimental and Peng−Robinson modeledsolubility data showed a good agreement, with average

percentage deviations (APD) from the experimental results of6.7 % for anthracene and 9.7 % for carbazole, for the bestfitting. These results indicate that the Peng−Robinsonexpression with the proposed mixing rules set may predictaccurately the solubility of anthracene and carbazole in nearcritical and supercritical isobutane.

■ AUTHOR INFORMATIONCorresponding Author*Tel.: +34 902204100. Fax: +34 925268840. E-mail address:[email protected] authors gratefully acknowledge the support to this workthrough projects 096/2006/3-11.3, A141/2007/2-11.3, andCMT 2006-10105 financed by the Spanish Ministries ofEnvironment and Science and Technology. Likewise, financialsupport through the PAI08-0195-3614 project by the Junta deComunidades de Castilla-La Mancha is acknowledged.NotesThe authors declare no competing financial interest.

■ REFERENCES(1) Mumtaz, M.; George, J. Toxicological Profile for Polycyclic AromaticHydrocarbons; U.S. Department of Health and Human Services,Agency for Toxic Substances and Disease Registry: Washington, DC,1995.(2) Wild, S. R.; Jones, K. C. Polynuclear aromatic hydrocarbons inthe United Kingdom environment: a preliminary source inventory andbudget. Environ. Pollut. 1995, 88, 91−108.(3) Chung, M. K.; Hu, R.; Cheung, K. C.; Wong, M. H. Pollutants inHong Kong soils: polycyclic aromatic hydrocarbons. Chemosphere2006, 67, 464−473.(4) Gan, S.; Lau, E. V.; Ng, H. K. Remediation of soils contaminatedwith polycyclic aromatic hydrocarbons (PAHs). J. Hazard. Mater.2009, 172, 532−549.

Table 4. Results Obtained in the Correlation of theSolubility of Anthracene and Carbazole in Isobutane Usingthe Peng−Robinson Equation of State

parameter

soluteset of mixing

rulesno.

parameters k12 δ12 APD/%

anthracene S1 1 0.0976 7.76S2 2 0.1390 −0.0082 6.73

carbazole S1 1 0.1605 14.09S2 2 0.2798 0.2113 9.66

Figure 4. Comparison of the experimental solubility data (y2) withcalculated values (y2

cal) obtained from the Peng−Robinson equation ofstate: ⧫, 367 K; ■, 408 K; ▲, 413 K. (a) Solubility of anthracenemodeled using set of mixing rules S2. (b) Solubility of carbazolemodeled using set of mixing rules S2.



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measurement and modeling of the solubility of anthracene and carbazole in compressed isobutane

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