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Ind. Eng. Chem. Res. 2006, 45, 4454-4460
Solubility of Solid Polycyclic Aromatic Hydrocarbons in Pressurized Hot Water: Correlation with Pure Component Properties Pavel Kara´ sek, Josef Planeta, and Michal Roth* Institute of Analytical Chemistry, Academy of Sciences of the Czech Republic, VeVerˇ´ı 97, 61142 Brno, Czech Republic
A semiempirical relationship was developed to correlate solubility of solid polycyclic aromatic hydrocarbons (PAHs) in pressurized hot water using only pure-component properties. The required properties of water include cohesive energy density, internal pressure, and relative permittivity (dielectric constant), all at the particular temperature and pressure. The required properties of PAHs include triple-point temperature, enthalpy of fusion, the molar volume of the subcooled liquid, and the molar volume of the solid. The correlation was developed from experimental solubility data of eight 2- to 5-ring PAHs at temperatures within 313-498 K, with the solubility (equilibrium mole fraction) ranging within 10-11 to 10-3. Considering the wide range of the source data, the extreme nonideality of water-PAH systems, and the absence of any water-PAH interaction parameters, the correlation provides an adequate reproduction of the source data. Further, the correlation yields a relatively reasonable prediction of PAH solubilities outside the range of the source data, namely, at environmentally relevant conditions of 298.15 K and 0.1 MPa. In addition to the correlation, new data on aqueous solubilities of fluorene and fluoranthene are also reported. 1. Introduction The growing emphasis on sustainable development leads to increasing use of “green” solvents, with water taking an important position. The physical properties of water that are decisive for the solvating abilities, i.e., the relative permittivity (dielectric constant), the cohesive energy density, and the ion product, can be tuned within very wide limits through changes in temperature and pressure.1,2 Liquid water at temperatures between the normal boiling point and the critical point, often referred to as pressurized hot water (PHW), has recently seen some interesting applications in sample treatment procedures for analytical chemistry,3-9 extractions of plant materials,10-13 and environmental remediation processes.14-19 Despite the growing number of applications of PHW, there is a relative lack of fundamental studies of solubility in PHW for some classes of important solutes, and predictive correlations of solubility of heavy organic nonelectrolytes in PHW within a wide range of temperature and pressure are virtually absent. Solubility measurements of organic solids in PHW have been concentrated on polycyclic aromatic hydrocarbons (PAHs).20-24 The previous attempts to correlate the aqueous solubilities of PAHs at elevated temperature and pressure were limited to simple relations describing the temperature dependence of the solubilities of individual PAHs,22,23 and the need for a more general correlation has already been recognized several years ago.22 This paper presents a semiempirical correlation of aqueous solubility of solid PAHs in a wide range of temperature and pressure. To provide the correlation with some predictive ability, it has been constructed in pure-component properties only, i.e., no water-PAH interaction parameters are involved. The aim is to develop a rapid estimation tool for process design purposes using readily available data on pure PAHs and well-established * To whom correspondence should be addressed. E-mail: roth@ iach.cz. Phone: +420-532-290-171. Fax: +420-541-212-113.
formulations for pure-component properties of water. Naturally, the treatment has no ambition to describe the complex liquidgas and liquid-liquid critical curves and three-phase liquidliquid-gas lines in water-PAH binaries.25 2. Experimental Section To extend the range of data available for testing the predictive ability of the correlation, the aqueous solubilities of fluorene and fluoranthene were measured at temperatures within 313 K to the PAH melting point and at a pressure of 5 MPa. Fluorene (>99 mol %) and fluoranthene (99 mol %) were purchased from Sigma-Aldrich (Prague, Czech Republic) and used as received. The method, the apparatus, and the procedure were the same as those employed recently by Kara´sek et al.24 The resultant solubilities (equilibrium mole fractions, x2) are listed in Table 1. The data from Table 1 were fitted with the aid of the equation
ln x2 ) pT + q
(1)
where the coefficients p and q are given in Table 2. 3. Development of the Correlation At phase equilibrium in a binary system containing water (1) and a solid PAH (2), the fugacities of the PAH in both phases are equal. Assuming that the solid phase is pure PAH, the source relationship for modeling the mole fraction solubility of the solute, x2, is
x2 )
f s20 γ2 f l20
(2)
where f s20 and f l20 are the fugacities of the pure solid solute and the pure subcooled liquid solute, respectively, and γ2 is the Raoult-law activity coefficient of the solute referred to the pure
10.1021/ie0514509 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/09/2006
Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4455 Table 1. Aqueous Solubilities of Fluorene and Fluoranthene at 5.0 MPa solute fluorene
fluoranthene
T/ K
109x2a
109 SDb
313.2 333.2 353.2 373.2 378.2 383.2 313.2 333.2 353.2 373.2 378.2
382 1150 3270 9420 11700 15800 39.9 132 414 1360 1890
9.31 29.5 113 211 216 432 1.20 5.42 5.19 24.8 44.5
a Mean values from five determinations at each condition. b Standard deviations (SD) are based on five determinations at each condition.
Table 2. Least-Squares Estimates of the Coefficients of Equation 1 and Standard Deviations of the Estimates solute
fluorene
fluoranthene
Tmin/K Tmax/K p/K-1 SD (p/K-1) q SD q
313.2 383.2 5.281 × 10-2 3.86 × 10-4 -31.29 0.138
313.2 378.2 5.899 × 10-2 3.76 × 10-4 -35.51 0.132
subcooled liquid solute at the particular T and P. The puresolute fugacity ratio in eq 2 can be obtained from the thermochemical cycle described by Prausnitz et al.26 The effects of elevated pressure on the pure-solute fugacities f s20 and f l20 should be taken into account through the respective Poynting corrections. In the present application, the triple-point pressure of the PAH solute can always be considered negligible with respect to the total pressure. For example, the triple-point pressure of naphthalene is only 993.5 Pa.27 Further, assuming that both the solid solute and the subcooled liquid solute are incompressible, the pure-solute fugacity ratio can be expressed by
ln
() f s20
f l20
)
(
)
(
)
∆hfus Tt2 ∆CP2 Tt2 ∆CP2 Tt2 2 1+ -1 ln + RTt2 T R T R T (Vs20 - Vl20)P (3) RT
where R is the molar gas constant, T is the temperature, Tt2 is the triple-point temperature of the solute, ∆hfus 2 is the molar enthalpy of fusion of the solute at Tt2, ∆CP2 is the difference between the molar isobaric heat capacities of the pure subcooled s0 s0 liquid solute and the pure solid solute ()Cl0 P2 - CP2), and V2 l0 and V2 are the molar volumes of the pure solid solute and the pure subcooled liquid solute, respectively. Highly nonideal binary systems of water and an aromatic hydrocarbon have attracted attention for a long time. Thermodynamic approaches used for modeling these systems included, e.g., group contribution concepts,28-30 Margules equations,31 modified regular solution theory combined with cubic equation of state,32 or a fluctuation theory-based treatment.33 Most of these approaches, however, were concentrated on modeling the systems at environmentally relevant conditions near 298 K and 0.1 MPa. Although group contribution models of thermodynamic properties in binary aqueous systems at high temperature and pressure are available,34,35 the models are largely focused on electrolytes or small organic nonelectrolyte molecules. In the present contribution, only a few types of functional groups are involved, and emphasis is on the description of the
temperature and pressure effects on solubility rather than on modeling the activity coefficients of a large variety of mixtures at a fixed temperature and pressure. Therefore, a group contribution method is not used here, and the model has to take account of the variation of solvent properties of water within a wide range of temperature and pressure. According to the regular solution theory,36 the Raoult-law activity coefficient of a liquid solute 2 in a binary mixture with solvent 1 is given by
ln γ2 ) Vl20Φ12(c11/2 - c21/2)2/(RT)
(4)
where c1 and c2 are the cohesive energy densities of the solvent and the solute, respectively, and Φ1 is the volume fraction of the solvent in the mixture. Since it starts from the presumption that dispersion interactions are the only kind of intermolecular forces in the mixture, the regular solution theory is inadequate for mixtures with hydrogen bonding between unlike or like molecules. Nearly 40 years ago, Wiehe and Bagley37 proposed that the product of the molar volume and the internal pressure was a measure of the dispersion interaction energy in liquids regardless of the presence of other intermolecular forces. According to this approximate approach, the cohesive energy density reflects the energy needed to break all intermolecular interactions, whereas the internal pressure only reflects breaking nonspecific interactions, with hydrogen bonds left intact. As the different kinds of intermolecular interactions acquire varying importance within the temperature and pressure domain of PHW, we have considered both the cohesive energy density, c1, and the internal pressure, Pint 1 , of water as suitable parameters for correlating the PAH activity coefficient γ2 within a wide range of temperature and pressure. Adding the relative permittivity, r1, of water as another correlating parameter, we attempted to model γ2 using several functional forms of empirical nature. Finally, we selected the following relationship,
1 ln γ2 ) Ac1 + BPint 1 + C(r1 - 1) Vl20
(5)
Therefore, the complete expression used to correlate the solubilities of solid PAHs in PHW was
ln x2 ) ln
() f s20
f
l0 2
- Vl20[Ac1 + BPint 1 + C(r1 - 1)]
(6)
The source data to obtain the coefficients A, B, and C were the experimental values of x2 for eight 2- to 5-ring PAHs measured by dynamic saturation method at temperatures within 313-498 K and pressures within 0.1-40 MPa. The data sources are specified in Table 3, and more details are available in the Supporting Information. Briefly, the individual experimental solubilities x2 were converted to the activity coefficients γ2, and the coefficients A, B, and C of eqs 5 and 6 were estimated by least-squares regression of the (1/Vl0 2 ) ln γ2 values on the water properties, c1, Pint 1 , and r1 - 1, at the corresponding values of T and P. The sources of the individual properties of water and PAHs are described below. At this point, a note should only be made of the correct limiting behavior of the correlation. In a hypothetical liquid solvent 1 with ideal gas-like properties, c1 ) 0, Pint 1 ) 0, and r1 ) 1, so that eq 5 predicts ln γ2 ) 0 and eq 6 yields the ideal solubility of a solid solute 2 in solvent 1 l0 ()f s0 2 /f 2 ).
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Table 3. Source Data for the Correlation PAH
T/K
naphthalene anthracene pyrene chrysene 1,2-benzanthracene triphenylene perylene p-terphenyl a
P/MPa
313-348 313-483 298-413 298-498 313-423 313-468 298-473 333-483
0.1-7.0 0.1-7.7 0.1-40 0.1-6.2 4.9-5.2 5.0-6.4 0.1-5.0 4.9-6.7
γ2a
x2 10-6
10-5
4.50 × to 4.35 × 7.40 × 10-9 to 2.20 × 10-4 1.07 × 10-8 to 5.40 × 10-6 1.60 × 10-10 to 7.58 × 10-5 3.37 × 10-9 to 2.96 × 10-6 1.82 × 10-9 to 2.83 × 10-5 3.00 × 10-11 to 5.00 × 10-6 8.49 × 10-10 to 3.93 × 10-5
ref for x2
2.03 × to 6.67 × 3.63 × 103 to 1.43 × 106 1.49 × 105 to 1.08 × 107 8.92 × 103 to 6.29 × 107 2.97 × 105 to 3.09 × 107 3.24 × 104 to 2.18 × 107 6.12 × 104 to 8.04 × 107 2.30 × 104 to 2.06 × 107 104
104
21, 24 22-24 22, 23 22 24 24 22 24
γ2 calculated via eq 2 using experimental values21-24 of x2 and f s20/f l20 values obtained from eq 10. Table 4. PAH Properties Used to Obtain the Fugacity Ratio f s20/f l20
4. Water Property Sources 4.1. Internal Pressure. At a particular temperature and pressure, the density and the other required properties of water were calculated from the wide-range thermodynamic formulation of Wagner and Pruss38 using the software (a DLL library that can be called from an Excel spreadsheet) provided by the authors of the equation. As the software provides a function to calculate the thermal pressure coefficient, (∂P/∂T)V, the internal pressure of water is readily obtained from
Pint 1 ) T(∂P/∂T)V - P
(7)
4.2. Cohesive Energy Density. Calculation of the cohesive energy density of water, c1, requires the residual (cohesive) energy, uc1, and the molar volume, Vl0 1,
c1 ) uc1/Vl10
(8)
In their thermodynamic formulation, Wagner and Pruss have used liquid water at the triple point as the reference state for internal energy. Therefore, a correction is needed to convert the Wagner-Pruss value of molar internal energy calculated by the software, uWP1, into the cohesive energy, uc1, referred to the ideal-gas state of water at the particular temperature. The relationship between uc1 and uWP1 is
uc1 ) uWP1 + RT - hT0 t1 -
∫TT CP10 dT
(9)
t1
where hT0 t1 is the molar enthalpy of water in the ideal-gas state at the triple-point temperature of water, Tt1, and C0P1 is the isobaric molar heat capacity of water in the ideal-gas state. With the reference state used by Wagner and Pruss, hT0 t1 ) 45 064.319 57 J‚mol-1. The integral in eq 9 can be evaluated using eq 5.6 and Table 6.1 in the original paper of Wagner and Pruss.38 4.3. Relative Permittivity. Relative permittivity of water, r1, was obtained from the correlation developed by Ferna´ndez et al.39 employing the density of water calculated for the particular T and P from the thermodynamic formulation of Wagner and Pruss. The calculation of r1 does not require any additional computational effort; once the density of water at the particular T and P is known, the calculation of r1 is straightforward.39 5. PAH Property Sources 5.1. Fugacity Ratio. In calculating the fugacity ratio f s20/ the terms with ∆CP2 in eq 3 were invariably neglected, f leading to the simplified expression l0 2 ,
(
)
Tt2 (Vs20 - Vl20)P f s20 ∆hfus 2 1+ ln l 0 ≈ RTt2 T RT f2
(10)
PAH
-1 ∆hfus 2 /(J‚mol )
ref.
Tt2/K
ref.
naphthalene biphenyl acenaphthene fluorene anthracene phenanthrene pyrene fluoranthene chrysene 1,2-benzanthracene 2,3-benzanthracene triphenylene benzo[a]pyrene dibenz[a,h]anthracene perylene benzo[g,h,i]perylene coronene
19 100 18 576 21 460 19 580 29 370 18 000 17 360 18 728 26 150 21 380 31 800b 24 740 17 320 31 160 32 580 17 370 19 200
42 43 44 44 44 47 44 48 49 42
353.39 342.09 366.56 387.94 488.93 372.38 423.81 383.36 531.4a 430.05a 630.15a 471.01 449.55a 543.15a 550.15 554.2a 710.5a
41 43 45 45 46 45 48 48 49 50 50 48 50 50 52 49 53
44 42 42 51 42 42
a Normal melting point temperature. b Estimated from the normal melting point temperature and the average entropy of fusion for the other C18H12 PAH isomers.
One reason for the simplification was the lack of ∆CP2 data for a large part of PAHs included in this study. Another reason was that, in a recent work on correlation and prediction of ∆CP2, Pappa et al.40 concluded that the presumption ∆CP2 ) 0 was relatively the best approximation in the prediction of ideal solubility of solid PAHs (as compared to approximating ∆CP2 by the entropy of fusion and to the use of group contribution s0 methods to predict Cl0 P2 and CP2). Nevertheless, it is clear that, in a particular water (1)-PAH (2) system, the approximation ∆CP2 ) 0 becomes more and more problematic with the decreasing temperature because the resultant relatiVe error in the estimated solubility x2 is proportional to (Tt2 - T). 5.2. Enthalpy of Fusion and the Triple-Point Temperature. The ∆hfus 2 and Tt2 data were selected among those included in the NIST Chemistry WebBook.41 Wherever the Tt2 value was not available, it was substituted by the normal melting point temperature of the PAH concerned. The values and the original sources42-53 of the ∆hfus 2 and Tt2 data are listed in Table 4. 5.3. Molar Volume of the Subcooled Liquid. This quantity is needed in the working equations of the correlation (eqs 5 and 6) as well as in the Poynting correction of the fugacity ratio (eqs 3 and 10). The subcooled liquid molar volume, Vl0 2 , was estimated from the modified Rackett equation54 using the critical properties estimated from the Joback method55 with the parameters tabulated by Poling et al.56 The parameter ZRA of the modified Rackett equation was approximated by the critical compressibility factor obtained from the calculated critical properties. Although experimental values of the critical properties are available for some of the PAHs included in this study, we used the Joback estimations for all PAHs to retain consistency in the procedure. When calculating the critical temperature from the Joback correlation, we used the experimental value of the normal boiling point temperature wherever
Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4457 Table 5. Coefficients of Equations 5 and 6 coefficient
least-squares estimate
standard deviation in the coefficient estimate
A/(mol‚J-1) B/(mol‚J-1) C/(mol‚m-3)
384.4 -313.1 -9587
65.1 55.7 1815
available;41 otherwise, the normal boiling point temperature was estimated using the Joback method. 5.4. Molar Volume of the Solid. The molar volume of the solid PAH is needed in the Poynting correction of the fugacity ratio f s20/f l20 (eqs 3 and 10). At a particular temperature, the quantity Vs0 2 was estimated from the subcooled liquid molar 57 volume Vl0 2 with the aid of the correlation of Goodman et al. 6. Results and Discussion 6.1. Source Data: Fitted vs Experimental Solubilities. Table 5 contains the coefficients A-C (eqs 5 and 6) obtained by the least-squares fitting described above. Although the correlation has some physical basis in the regular solution theory (eq 4) and in the interpretation of internal pressure by Wiehe and Bagley,37 the three coefficients should be regarded as strictly empirical parameters. In eq 5, the largest contribution (in absolute magnitude) to (1/Vl0 2 )ln γ2 is always that of the Ac1 term. The contributions of the BPint 1 and the C(r1 - 1) terms are negative, and C(r1 - 1) is the more important term of the two. At first glance, the negative signs of the B and C coefficients may appear unphysical. However, when judging the magnitude and sign of the coefficients, it is important to note that pure-water properties c1, Pint 1 , and r1 cannot be changed independently of each other. Instead, the relationship among c1, Pint 1 , and r1 is a complicated function of temperature and pressure, and that is why the resultant coefficients are of an empirical nature. Experimental solubility data together with other relevant properties are detailed in the Supporting Information file. The file also illustrates the extent of variation of c1, Pint 1 , and r1 within the temperature and pressure range of the source data. In any of the coefficients A-C, the ratio of the coefficient estimate to the standard deviation in the coefficient estimate always exceeds 5.25 (in the absolute value). This number can be used to assess the statistical significance of the coefficient estimates. Comparing this number with the critical values of the Student’s t distribution58 for 79 degrees of freedom ()82 source data points - 3 coefficients), one concludes that, in all three coefficients, the hypothesis “the coefficient equals zero” can be rejected at a confidence level exceeding 99%. Figure 1 shows a comparison of the experimental solubilities with the values calculated from the correlation using the fitted coefficients A-C. Considering the wide range of the source data, the extreme nonideality of water-PAH systems, and the absence of any water-PAH interaction parameters, the correlation provides an adequate reproduction of the source data, with the expt mean value of 100|xcalc - xexpt equal to 44% and the 2 2 |/x2 median value equal to 26% (see Supporting Information). 6.2. Predictive Power of the Correlation. It is difficult to test the predictive ability of the correlation in the temperature and pressure region characteristic of PHW because nearly all experimental data available for that region have been utilized in the development. The solubilities of fluorene and fluoranthene reported in this work were not used to obtain the coefficients A-C in eqs 5 and 6 and can therefore be employed to compare the experimental data with the x2 values calculated from eq 6. The comparison is included in Figure 1, showing that the
Figure 1. Experimental solubilities vs calculations from eq 6. Source data used to develop the correlation: O, naphthalene;21,24 ], anthracene;22-24 0, pyrene;22,23 2, chrysene;22 4, 1,2-benzanthracene;24 3, triphenylene;24 1, perylene;22 /, p-terphenyl.24 Fluorene (+) and fluoranthene (×) solubilities were not included in the source data.
Figure 2. Aqueous solubilities50,59 of PAHs at 298.15 K and 0.1 MPa vs predictions from eq 6: b, biphenyl;50 0, acenaphthene;50 [, fluorene;50 ], phenanthrene;50 9, fluoranthene;50 4, 1,2-benzanthracene;50 L, 2,3benzanthracene;59 3, triphenylene;50 /, benzo[a]pyrene;50 x, dibenz[a,h]anthracene;50 +, benzo[g,h,i]perylene;59 X, coronene.59 The small dots indicate the cumulated source data (see Figure 1).
deviations of the calculated solubilities from the experimental data for fluorene and fluoranthene are comparable to those of the source solutes. In fluorene, this result is somewhat surprising as a larger deviation would be expected because of the presence of the methylene group in the fluorene molecule. Although the correlation has been intended for the solubility of solid PAHs in PHW, it can also be tested against the aqueous solubilities of PAHs at 298.15 K and 0.1 MPa. Because of their environmental relevance, the data on PAH solubilities in water at these conditions are relatively plentiful. In fact, the solubilities at 298.15 K and 0.1 MPa of naphthalene, anthracene, pyrene, chrysene, and perylene, quoted by Miller et al.,21,22 were included in the source data (see Supporting Information). Figure 2 shows a comparison of the predicted vs experimental data at 298.15 K and 0.1 MPa together with a cumulative presentation of the source data used to develop the correlation. The experimental solubilities at 298.15 K and 0.1 MPa are the values recommended by Shiu and Ma50 except for the solubilities of 2,3-benzanthracene, benzo[g,h,i]perylene, and coronene that were taken from Mackay and Shiu.59 Considering the wide range of solubilities (over 7 decadic orders of magnitude) and the absence of binary or higher interaction parameters, the performance of the correlation appears to be relatively reasonable.
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Overall, the scattering of the data points around the perfectmatch line is larger in the left half of the plot, i.e., the deviations of the calculated values from the corresponding experimental solubilities increase with decreasing experimental solubility. There are several reasons for that. The most obvious reason is that, with decreasing solubility and decreasing temperature, a particular water-PAH system becomes more nonideal (see γ2 values in Supporting Information) and, consequently, more difficult to describe by any model. Another reason is the omission of the ∆CP2 terms from the expression for the fugacity ratio f s20/f l20 (eqs 3 and 10) because the induced error becomes more serious with decreasing temperature and, therefore, with decreasing solubility. Yet another reason is that the uncertainty in the experimental values also increases with decreasing solubility. For example, while the solubility data recommended by Shiu and Ma50 indicate that xtriphenylene > x1,2-benzanthracene at 2 2 298.15 K, the results reported by May et al.60 suggest the opposite. 7. Conclusion Solubilities of solid PAHs in PHW were correlated using only pure-component properties of PAHs and well-established, IAPWS-recommended61 formulations for thermodynamic properties38 and relative permittivity39 of water (IAPWS ) The International Association for the Properties of Water and Steam). Thereby, rapid estimations of aqueous solubilities of solid PAHs are made possible without the need for iterative calculations of phase equilibria. Obviously, the relative success of this approximate approach results largely from the narrow scope of the correlation and, to a lesser extent, from the possibility to treat the solid phase as a pure PAH. Extension of the scope and/or modeling of the interactions between water and a liquid PAH would certainly require some form of explicit inclusion of solute-solvent interactions, e.g., through an equation-of-state model, through an excess Gibbs energy model, or through a combination of both.62,63 Acknowledgment We thank Prof. Dr.-Ing. Wolfgang Wagner (Institute of Thermo- and Fluid Dynamics, Faculty of Mechanical Engineering, University of Bochum, Germany) and Prof. Dr.-Ing. Roland Span (Chair of Thermodynamics and Energy Technology, Institute for Energy and Process Technology, University of Paderborn, Germany) for the software package based on the wide-range thermodynamic formulation for water38 and for a copy of ref 38. We gratefully acknowledge the financial support of this work by the Czech Science Foundation (Project No. GA203/03/0859 and Project No. GA203/05/2106), by the Grant Agency of the Academy of Sciences of the Czech Republic (Project No. A4031301 and Project No. B400310504), and by the Academy of Sciences of the Czech Republic through Institutional Research Plan No. Z40310501. Supporting Information Available: Table showing the experimental solubility data, xexpt 2 , used to develop the correlaint tion, the corresponding values of f s20/f l20, γ2, Vl0 2 , c1, P1 , and calc r1 - 1, and the calculated solubilities, x2 . This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature A ) coefficient in eqs 5 and 6 (mol‚J-1) B ) coefficient in eqs 5 and 6 (mol‚J-1) C ) coefficient in eqs 5 and 6 (mol‚m-3)
c ) cohesive energy density (MPa) CP ) molar isobaric heat capacity (J‚mol-1‚K-1) f ) fugacity (MPa) h ) molar enthalpy (J‚mol-1) p ) coefficient in eq 1 (K-1) P ) pressure (MPa) q ) coefficient in eq 1 R ) molar gas constant (J‚mol-1‚K-1) T ) temperature (K) u ) molar internal energy (J‚mol-1) V ) molar volume (m3‚mol-1) x ) mole fraction Subscripts 1 ) solvent (water) property 2 ) solute (PAH) property c ) cohesive (energy) t ) triple-point property V ) constant volume WP ) Wagner-Pruss (molar internal energy) Superscripts 0 ) pure component calc ) calculated value expt ) experimental value fus ) fusion (enthalpy of) int ) internal (pressure) l ) subcooled liquid s ) solid Greek Symbols γ ) activity coefficient r ) relative permittivity Φ ) volume fraction AbbreViations PAH ) polycyclic aromatic hydrocarbon PHW ) pressurized hot water Literature Cited (1) Harvey, A. H.; Friend, D. G. Physical Properties of Water. In Aqueous Systems at EleVated Temperatures and Pressures. Physical Chemistry in Water, Steam and Hydrothermal Solutions; Palmer, D. A., Ferna´ndez-Prini, R., Harvey, A. H., Eds.; Elsevier-Academic Press: London, U.K., 2004; Chapter 1, pp 1-27. (2) Weinga¨rtner, H.; Franck, E. U. Supercritical Water as a Solvent. Angew. Chem., Int. Ed. 2005, 44, 2672-2692. (3) Hawthorne, S. B.; Yang, Y.; Miller, D. J. Extraction of Organic Pollutants from Environmental Solids with Sub- and Supercritical Water. Anal. Chem. 1994, 66, 2912-2920. (4) Pawlowski, T. M.; Poole, C. F. Extraction of Thiabendazole and Carbendazim from Foods Using Pressurized Hot (Subcritical) Water for Extraction: A Feasibility Study. J. Agric. Food Chem. 1998, 46, 31243132. (5) van Bavel, B.; Hartonen, K.; Rappe, C.; Riekkola, M.-L. Pressurised Hot Water/Steam Extraction of Polychlorinated Dibenzofurans and Naphthalenes from Industrial Soil. Analyst 1999, 124, 1351-1354. (6) Hyo¨tyla¨inen, T.; Andersson, T.; Hartonen, K.; Kuosmanen, K.; Riekkola, M.-L. Pressurized Hot Water Extraction Coupled On-line with LC-GC: Determination of Polyaromatic Hydrocarbons in Sediment. Anal. Chem. 2000, 72, 3070-3076. (7) Ramos, L.; Kristenson, E. M.; Brinkman, U. A. T. Current Use of Pressurised Liquid Extraction and Subcritical Water Extraction in Environmental Analysis. J. Chromatogr., A 2002, 975, 3-29. (8) Smith, R. M. Extractions with Superheated Water. J. Chromatogr., A 2002, 975, 31-46.
Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006 4459 (9) Carabias-Martı´nez, R.; Rodrı´guez-Gonzalo, E.; Revilla-Ruiz, P.; Herna´ndez-Me´ndez, J. Pressurized Liquid Extraction in the Analysis of Food and Biological Samples. J. Chromatogr., A 2005, 1089, 1-17. (10) Basile, A.; Jime´nez-Carmona, M. M.; Clifford, A. A. Extraction of Rosemary by Superheated Water. J. Agric. Food Chem. 1998, 46, 52055209. (11) Rovio, S.; Hartonen, K.; Holm, Y.; Hiltunen, R.; Riekkola, M.-L. Extraction of Clove Using Pressurized Hot Water. FlaVour Fragrance J. 1999, 14, 399-404. (12) Kuba´tova´, A.; Lagadec, A. J. M.; Miller, D. J.; Hawthorne, S. B. Selective Extraction of Oxygenates from Savory and Peppermint Using Subcritical Water. FlaVour Fragrance J. 2001, 16, 64-73. (13) Shotipruk, A.; Kiatsongserm, J.; Pavasant, P.; Goto, M.; Sasaki, M. Pressurized Hot Water Extraction of Anthraquinones from the Roots of Morinda citrifolia. Biotechnol. Prog. 2004, 20, 1872-1875. (14) Lagadec, A. J. M.; Miller, D. J.; Lilke, A. V.; Hawthorne, S. B. Pilot-Scale Subcritical Water Remediation of Polycyclic Aromatic Hydrocarbon- and Pesticide-Contaminated Soil. EnViron. Sci. Technol. 2000, 34, 1542-1548. (15) Kuba´tova´, A.; Lagadec, A. J. M.; Hawthorne, S. B. Dechlorination of Lindane, Dieldrin, Tetrachloroethane, Trichloroethene, and PVC in Subcritical Water. EnViron. Sci. Technol. 2002, 36, 1337-1343. (16) Kronholm, J.; Desbands, B.; Hartonen, K.; Riekkola, M.-L. Environmentally Friendly Laboratory-Scale Remediation of PAHContaminated Soil by Using Pressurized Hot Water Extraction Coupled with Pressurized Hot Water Oxidation. Green Chem. 2002, 4, 213-219. (17) Kronholm, J.; Kalpala, J.; Hartonen, K.; Riekkola, M.-L. Pressurized Hot Water Extraction Coupled with Supercritical Water Oxidation in Remediation of Sand and Soil Containing PAHs. J. Supercrit. Fluids 2002, 23, 123-134. (18) Kuba´tova´, A.; Herman, J.; Steckler, T. S.; de Veij, M.; Miller, D. J.; Klunder, E. B.; Wai, C. M.; Hawthorne, S. B. Subcritical (Hot/Liquid) Water Dechlorination of PCBs (Aroclor 1254) with Metal Additives and in Waste Paint. EnViron. Sci. Technol. 2003, 37, 5757-5762. (19) Kronholm, J.; Kuosmanen, T.; Hartonen, K.; Riekkola, M.-L. Destruction of PAHs from Soil by Using Pressurized Hot Water Extraction Coupled with Supercritical Water Oxidation. Waste Manage. (Oxford) 2003, 23, 253-260. (20) Ro¨ssling, G. L.; Franck, E. U. Solubility of Anthracene in Dense Gases and Liquids to 200 °C and 2000 bar. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 882-890. (21) Miller, D. J.; Hawthorne, S. B. Method for Determining the Solubilities of Hydrophobic Organics in Subcritical Water. Anal. Chem. 1998, 70, 1618-1621. (22) Miller, D. J.; Hawthorne, S. B.; Gizir, A. M.; Clifford A. A. Solubility of Polycyclic Aromatic Hydrocarbons in Subcritical Water from 298 K to 498 K. J. Chem. Eng. Data 1998, 43, 1043-1047. (23) Andersson, T. A.; Hartonen, K. M.; Riekkola, M.-L. Solubility of Acenaphthene, Anthracene, and Pyrene in Water at 50 °C to 300 °C. J. Chem. Eng. Data 2005, 50, 1177-1183. (24) Kara´sek, P.; Planeta, J.; Roth, M. Solubility of Solid Polycyclic Aromatic Hydrocarbons in Pressurized Hot Water at Temperatures from 313 K to the Melting Point. J. Chem. Eng. Data 2006, 51, 616-622. (25) Brunner, E.; Thies, M. C.; Schneider, G. M. Fluid Mixtures at High Pressures: Phase Behavior and Critical Phenomena for Binary Mixtures of Water with Aromatic Hydrocarbons. J. Supercrit. Fluids, in press. (26) Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-Phase Equilibria; Prentice Hall: Upper Saddle River, NJ, 1999; Chapter 11, pp 638-641. (27) Ru˚zˇicˇka, K.; Fulem, M.; Ru˚zˇicˇka, V. Recommended Vapor Pressure of Solid Naphthalene. J. Chem. Eng. Data 2005, 50, 1956-1970. (28) Tsonopoulos, C.; Prausnitz, J. M. Activity Coefficients of Aromatic Solutes in Dilute Aqueous Solutions. Ind. Eng. Chem. Fundam. 1971, 10, 593-600. (29) Amidon, G. L.; Anik, S. T. Application of the Surface Area Approach to the Correlation and Estimation of Aqueous Solubility and Vapor Pressure. Alkyl Aromatic Hydrocarbons. J. Chem. Eng. Data 1981, 26, 2833. (30) Kan, A. T.; Tomson, M. B. UNIFAC Prediction of Aqueous and Nonaqueous Solubilities of Chemicals with Environmental Interest. EnViron. Sci. Technol. 1996, 30, 1369-1376. (31) Fan, C. H.; Jafvert, C. T. Margules Equations Applied to PAH Solubilities in Alcohol-Water Mixtures. EnViron. Sci. Technol. 1997, 31, 3516-3522. (32) Bader, M. S. H.; Gasem, K. A. M. Modeling Infinite Dilution Activity Coefficients of Organic-Aqueous Systems Using a Modified Regular Solution Equation and Cubic Equations-of-State. Can. J. Chem. Eng. 1998, 76, 94-103.
(33) Ruckenstein, E.; Shulgin, I. Solubility of Hydrophobic Organic Pollutants in Binary and Multicomponent Aqueous Solvents. EnViron. Sci. Technol. 2005, 39, 1623-1631. (34) Yezdimer, E. M.; Sedlbauer, J.; Wood, R. H. Predictions of Thermodynamic Properties at Infinite Dilution of Aqueous Organic Species at High Temperatures via Functional Group Additivity. Chem. Geol. 2000, 164, 259-280. (35) Sedlbauer, J.; Bergin, G.; Majer, V. Group Contribution Method for Henry’s Law Constant of Aqueous Hydrocarbons. AIChE J. 2002, 48, 2936-2959. (36) Reference 25, Chapter 7, pp 313-326. (37) Wiehe, I. A.; Bagley, E. B. Estimation of Dispersion and Hydrogen Bonding Energies in Liquids. AIChE J. 1967, 13, 836-838. (38) Wagner, W.; Pruss, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387-535. (39) Ferna´ndez, D. P.; Goodwin, A. R. H.; Lemmon, E. W.; Levelt Sengers, J. M. H.; Williams, R. C. A Formulation for the Static Permittivity of Water and Steam at Temperatures from 238 K to 873 K at Pressures up to 1200 MPa, Including Derivatives and Debye-Hu¨ckel Coefficients. J. Phys. Chem. Ref. Data 1997, 26, 1125-1166. (40) Pappa, G. D.; Voutsas, E. C.; Magoulas, K.; Tassios, D. P. Estimation of the Differential Molar Heat Capacities of Organic Compounds at Their Melting Point. Ind. Eng. Chem. Res. 2005, 44, 3799-3806. (41) NIST Chemistry WebBook; NIST Standard Reference Database Number 69; Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards and Technology: Gaithersburg, MD, 2003; http:// webbook.nist.gov/ chemistry. (42) Acree, W. E. Thermodynamic Properties of Organic Compounds: Enthalpy of Fusion and Melting Point Temperature Compilation. Thermochim. Acta 1991, 189, 37-56. (43) Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A.; Steele, W. V. The Thermodynamic Properties of Biphenyl. J. Chem. Thermodyn. 1989, 21, 1307-1331. (44) Domalski, E. S.; Hearing, E. D. Heat Capacities and Entropies of Organic Compounds in the Condensed Phase, Vol. 3. J. Phys. Chem. Ref. Data 1996, 25, 1-525. (45) Finke, H. L.; Messerly, J. F.; Lee, S. H.; Osborn, A. G.; Douslin, D. R. Comprehensive Thermodynamic Studies of Seven Aromatic Hydrocarbons. J. Chem. Thermodyn. 1977, 9, 937-956. (46) Goursot, P.; Girdhar, H. L.; Westrum, E. F. Thermodynamics of Polynuclear Aromatic Molecules. III. Heat Capacities and Enthalpies of Fusion of Anthracene. J. Phys. Chem. 1970, 74, 2538-2541. (47) Rastogi, R. P.; Bassi, P. S. Mechanism of Eutectic Crystallization. J. Phys. Chem. 1964, 68, 2398-2406. (48) Wong, W.-K.; Westrum, E. F. Thermodynamics of Polynuclear Aromatic Molecules. 1. Heat Capacities and Enthalpies of Fusion of Pyrene, Fluoranthene, and Triphenylene. J. Chem. Thermodyn. 1971, 3, 105-124. (49) Casellato, F.; Vecchi, C.; Girelli, A.; Casu, B. Differential Calorimetric Study of Polycyclic Aromatic Hydrocarbons. Thermochim. Acta 1973, 6, 361-368. (50) Shiu, W.-Y.; Ma, K.-C. Temperature Dependence of PhysicalChemical Properties of Selected Chemicals of Environmental Interest. I. Mononuclear and Polynuclear Aromatic Hydrocarbons. J. Phys. Chem. Ref. Data 2000, 29, 41-130. (51) Sabbah, R.; El Watik, L. New Reference Materials for the Calibration (Temperature and Energy) of Differential Thermal Analysers and Scanning Calorimeters. J. Therm. Anal. 1992, 38, 855-863. (52) Wong, W.-K.; Westrum, E. F. Thermodynamics of Polynuclear Aromatic Molecules. II. Low-Temperature Thermal Properties of Perylene, Coronene, and Naphthacene. Mol. Cryst. Liq. Cryst. 1980, 61, 207-228. (53) Smith, G. W. Phase Behavior of Some Condensed Polycyclic Aromatics. Mol. Cryst. Liq. Cryst. 1980, 64, 15-17. (54) Spencer, C. F.; Adler, S. B. A Critical Review of Equations for Predicting Saturated Liquid Density. J. Chem. Eng. Data 1978, 23, 8289. (55) Joback, K. G.; Reid, R. C. Estimation of Pure-Component Properties from Group-Contributions. Chem. Eng. Commun. 1987, 57, 233-243. (56) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2001; pp C.1-C.4. (57) Goodman, B. T.; Wilding, W. V.; Oscarson, J. L.; Rowley, R. L.: A Note on the Relationship between Organic Solid Density and Liquid Density at the Triple Point. J. Chem. Eng. Data 2004, 49, 1512-1514. (58) Electronic Statistics Textbook; StatSoft, Inc.: Tulsa, OK, 1999; http://www.statsoft.com/textbook/stathome.html. (59) Mackay, D.; Shiu, W. Y. Aqueous Solubility of Polynuclear Aromatic Hydrocarbons. J. Chem. Eng. Data 1977, 22, 399-402.
4460
Ind. Eng. Chem. Res., Vol. 45, No. 12, 2006
(60) May, W. E.; Wasik, S. P.; Miller, M. M.; Tewari, Y. B.; BrownThomas, J. M.; Goldberg, R. N. Solution Thermodynamics of Some Slightly Soluble Hydrocarbons in Water. J. Chem. Eng. Data 1983, 28, 197-200. (61) IAPWS Releases, Guidelines and Other Documents; http:// www.iapws.org/release.htm. (62) Orbey, H.; Sandler, S. Modeling Vapor-Liquid Equilibria. Cubic Equations of State and Their Mixing Rules; Cambridge University Press: New York, 1998; pp 44-93. (63) Anderko, A. Cubic and Generalized van der Waals Equations. In Equations of State for Fluids and Fluid Mixtures; Experimental Thermo-
dynamics Series; Sengers, J. V., Kayser, R. F., Peters, C. J., White H. J., Jr., Eds.; Elsevier: Amsterdam, 2000; Vol. 5, Ch. 4, Part I, pp 75-126.
ReceiVed for reView December 29, 2005 ReVised manuscript receiVed April 6, 2006 Accepted April 11, 2006 IE0514509
