Prediction of Vaour Pressures of Dioxin Congeners Xian-Wei Li, 1 Etsuro Shibata, 2 Eiki Kasai, 2 Takashi Nakamura 2 1 R & D Center, Baoshan Iron & Steel Co., Ltd., Fujin Rd., Baoshan District, Shanghai 201900, China 2 Institute of Multidiscilinary Research for Advanced Material, Tohoku University, 1,1 Katahira, 2-Chome, Aobaku, Sendai 980-8577, Jaan Abstract: The vaour ressures and thermal roerties of non-measured olychlorinated dibenzo--dioxins and furans (PCDDs/PCDFs) are redicted by using a correlation method based on the exerimental vaor ressures obtained by the Knudsen effusion method. The vaor ressures of all the 59 PCDDs and 131 PCDFs redicted here are more or less higher than the data redicted by Rordorf, although the calculation method is the same. For the most toxic 2,3,7,8-TeCDD, the vaour ressure at 298 K redicted in this study is 6.2 10-6 Pa, 31 times higher than the value rovided by Rordorf. Keywords: PCDDs/PCDFs, Dioxins, Vaour ressure 1 Introduction Vaour ressures are fundamental roerties of ersistent organic ollutants and are imortant in determining their distributions and results in the environment. Due to large number of dioxin congeners and of other POPs, exerimental measurements can only cover a minor fraction of them, so that the rediction of vaour ressures of dioxin congeners by semi emirical correlations is useful and necessary. Prediction methods thus lay an imortant role in environmental research, roviding data otherwise inaccessible, and those more doubtful in testing. Numerous equations and correlations for estimating vaour ressure are resented in literature. Most methods are emirical and the derived results are very rough. [1-4] Rordorf [5-7] suggested a good correlation method to redict vaour ressure, which derives from thermodynamic theory. Based on exerimental vaour 1.
ressure data, this method gives not only the enthaly and entroy of sublimation but also the enthaly of melting and boiling oint. Based on our exerimental data reorted in the recently aer [8], this research emloys the correlation method to redict the vaour ressure of all PCDDs/PCDFs. Correlation methods are of articular imortance when dealing with dioxin congeners since there are thousands of ossible homologues and isomers. Correlation methods also allow testing of exerimental data set for self-consistency. Calculation of related substance roerties (i.e. boiling oints and enthalies of fusion) is ossible starting from vaour ressure data. 2 Prediction methods Equations that relate vaour ressure to temerature are commonly derived by integration of the Clausius-Claeyron equation: [1] d ln /dt= H v /( Z R T 2 ) (I) where is the vaour ressure, H v is the heat of vaorization, R is the gas constant, T is the temerature, and Z is a comressibility factor, given by Z = V/(R T) (II) where V is the volume difference between vaour and liquid. The correlation method uses the liquid hase as a reference state, as has been the case for most redictive vaour ressure methods. Suersaturated liquid hases are usually defined at the temerature of interest. A full use is made of the measured temerature deendence of the vaour ressure of the solid. The data are extraolated to the melting oint and the liquid hase is brought in at this oint. Enthalies ( H m ) and entroies of fusion ( S m ) are defined for the melting temerature (T m ) and unknown temerature deendencies of these functions are not involved. The two arameters are determined for the different comounds and are found to vary significantly between these comounds. The redicted method is not limited by assumtion of either temerature or substance indeendence of the entroies of fusion. Entroies of fusion are affected by symmetry relations between molecule and crystal lattice. Figure 1 illustrates the calculation rocedure of vaour ressure correlation method suggested by Rordorf. 2.
These correlations ermit the estimation of boiling oints and enthalies of evaoration for dioxins and the solid-state vaour ressures can be redicted by the equations of Fig 1 for dioxin congeners of known melting oints. ln (/Pa) T b (T b )=101,325 Pa Liquid T b = boiling oint G = molar Gibbs energy T m = melting oint T m liqud = solid H = molar enthaly S = molar entroy Subcooled liquid C = molar heat caacity R = gaas constant Solid (T) = vaour ressure at T Subscrit s : sublimation Subscrit v : vaorization K/T Subscrit m : fusion At the boiling oint: H v (T b ) = T b K F (36.61+R ln T b ) (1) where K F =1.01 S v (T b ) = H v (T b )/T b + R ln (2) where =101,325 Pa In the liquid hase: H ( T v 2 ) = H v ( T ) + C 1 T2 T1 gas liq. dt gives after integration for T 1 =T b and T 2 =T: H v (T) = H v (T b ) [1 + K ( 1 T/T b )] (4) with K = -T b C gas-liq. / H v (T b ) (5) Setting formula (4) into the Clausius-Claeyron equation, d ln ( T ) = T b T H v ( T b )[1 + K(1 T / T b (3) 2 )]/ RT dt gives after integration from the melting to boiling oint: ln (T m ) = ln - ( H v (T b )/R T b )[(1+K)(T b /T m -1)-K ln(t b /T m ) (7) At the melting oint: From G s = G m + G v (8) H m = H s - H v (9) and G = H - T S (10) follows S m = S s - S v (11) For T=T m : G m (T m )= 0 (12) and S m (T m ) = H m (T m )/ T m (13) From G v = - RT ln liq. = H v - T S v (14) follows for T = T m : S v (T m ) = R ln liq (T m ). + H v (T m )/T m (15) From equation (4), for T=T m : H v (T m ) = H v (T b ) [1 + K ( 1 T m /T b )] (4) In the solid hase: G s (T) = -RT ln solid (T) = H s (T) T S s (T) (16) R ln solid ( T ) = [ S s ( T m ) + T Tm C g s / TdT ] [ H R ln solid (T) = S s (T m ) - H s (T m )/T (18) s ( T m ) / T + Fig 1 The calculation rocedure of correlation method suggested by Rordorf [5]. (Relationshi between the vaour ressures of the solid and the liquid hase) (6) T Tm C g s dt ] (17) 3.
3 Predicted vaour ressure results for PCDDs/PCDFs Enthalies and entroies of sublimation of the 22 PCDDs/PCDFs were obtained by linear regression of the exerimental vaour ressures over the indicated temerature intervals in the aer ublished recently [8]. They hold for the mid temerature, T mid =2(T max T min )/(T max + T min ), of the investigated temerature ranges, and are recalculated for the melting oints and room temerature by means of bracket exressions of equation (17). The melting oint (T m ) data come from literature [9]. The boiling oint (T b ) aears in several exressions and is determined in an iterative rocedure. EXCEL is used for the solution of the equations shown in Fig 1 by an iterative rocedure. Figures 2 and 3 show that the enthaly of sublimation and derived boiling oint of PCDDs and PCDFs correlate well with the substitution number of chlorine, while the melting oint and entroy of sublimation show a great deal of scatter. 160 150 PCDDs 350 PCDDs 140 330 H sub(298k), kj/mol 130 120 110 S sub, J/mol/K 310 290 100 90 y = 6.5821x + 95.907 R 2 = 0.9174 270 y = 2.3454x + 297.57 R 2 = 0.1676 80 250 (a) (b) 160 350 150 PCDFs PCDFs 140 330 H sub(298k), kj/mol 130 120 110 S sub(298k), J/mol/K 310 290 100 90 y = 7.3232x + 88.561 R 2 = 0.9444 80 4. 270 y = 4.8032x + 281.83 R 2 = 0.6587 250
(c) (d) Fig 2 Chlorine correlations of thermal roerties, (a) enthaly of sublimation of PCDDs, (b) entroy of sublimation of PCDDs, (c) enthaly of sublimation of PCDFs, (d) entroy of sublimation of PCDFs 850 850 800 PCDDs 800 PCDFs 750 750 Tb (K) 700 650 Tb (K) 700 650 600 600 550 y = 29.105x + 564.001 R 2 = 0.949 550 y = 34.452x + 554.597 R 2 = 0.998 500 (a) 500 Cl substituion number (b) Fig 3 Chlorine correlations of boiling oint of PCDDs and PCDFs The determined boiling oints are then set for correct rediction of the vaour ressures ( liquid (T m )= solid (T m )) at the melting oints. The determined boiling oints and enthalies of fusion of the dioxin congeners are also correlated with the degree of chlorine substitution. Figures 3 and 4 show the correlations of the redicted boiling oints and enthalies of fusion with the degree of chlorination (x). The relation is as the following. For PCDDs: T b = 29.10 x + 564.00 ( K) H m (T m ) = 3.808x + 22.105 ( kj mol -1 ) For PCDFs: T b = 34.45 x + 554.60 (K) H m (T m ) = 3.553x + 20.801 (kj mol -1 ) Using these formulas, boiling oints and enthalies of fusion are redicted for unknown dioxin congeners, and then the solid-state vaour ressures are calculated by the equations of Fig 1. 5.
The thermal roerties and vaour ressures for 59 PCDDs and 131 PCDFs are redicted. 100 PCDDs 100 PCDFs 80 80 H (T m), kj/mol 60 40 H (T m), kj/mol 60 40 20 Hv(Tm) Hm(Tm) 0 20 Hv(Tm) Hm(Tm) 0 (a) (b) Fig 4 Chlorine correlations of enthalies of evaoration and fusion of PCDDs and PCDFs at melting oint All the vaour ressures of PCDDs/PCDFs redicted here are more or less higher than the data redicted by Rordorf [7] for the same comounds. Figure 5 shows the vaour ressure differences between Rordorf s study and this study for the toxic congeners, which are all substituted at the ositions 2, 3, 7, and 8. For the most toxic 2,3,7,8-TeCDD, the redicted vaour ressure at 25 by this study is 6.2 10-6 Pa, which is 31 times higher than the value given by Rordorf. Therefore, the concentration of air saturated with 2,3,7,8-TeCDD at 25 can arrive at 805 ng/m 3. 6.
0-2 -5-7 ln ( /Pa) -10 ln ( /Pa) -12-15 2,3,7,8-TeCDD,This study 2,3,7,8-TeCDD, Rordorf 1,2,3,7,8-PeCDD,This study 1,2,3,7,8-PeCDD, Rordorf 1,2,3,4,7,8-HxCDD,This study 1,2,3,4,7,8-HxCDD, Rordorf -20 2.4 2.6 2.8 3 3.2 3.4 1000 (K/T ) 1,2,3,7,8,9-HxCDD,This study -17 1,2,3,7,8,9-HxCDD, Rordorf 1,2,3,6,7,8-HxCDD,This study 1,2,3,6,7,8-HxCDD, Rordorf 1,2,3,4,6,7,8-HCDD,This study 1,2,3,4,6,7,8-HCDD, Rordorf -22 2.4 2.6 2.8 3 3.2 3.4 1000 (K/T ) (a) (b) 0 0-5 -5 ln ( /Pa) -10 ln ( /Pa) -10-15 2,3,7,8-TeCDF, This study 2,3,7,8-TeCDF, Rordorf 1,2,3,7,8-PeCDF, This study 1,2,3,7,8-PeCDF, Rordorf 1,2,3,4,7,8-HxCDF, This study 1,2,3,4,7,8-HxCDF, Rordorf -20 2.4 2.6 2.8 3 3.2 3.4-15 2,3,4,7,8-PeCDF, This study 2,3,4,7,8-PeCDF, Rordorf 2,3,4,6,7,8-HxCDF, This study 2,3,4,6,7,8-HxCDF, Rordorf 1,2,3,4,7,8,9-HCDF, This study 1,2,3,4,7,8,9-HCDF, Rordorf -20 2.4 2.6 2.8 3 3.2 3.4 1000 (K/T ) 1000 (K/T ) (c) (d) Fig 5 Comarison of vaour ressure of high chlorinated PCDDs/PCDFs redicted by Rordorf s study and this study 4 Conclusions Based on our measured vaour ressure data set of a number of dioxin congeners, the vaour ressure and thermal roerties of non-measured PCDDs/PCDFs are redicted by using a correlation method. The enthaly of 7.
sublimation and calculated boiling oint correlate well with the degree of chlorination, while the melting oint and entroy of sublimation show a great deal of scatter. All vaour ressures of the 59 PCDDs and 131 PCDFs redicted here are more or less higher than the data redicted by Rordorf, although the calculated method is the same. For the most toxic 2,3,7,8-TeCDD, the vaour ressure at 25 redicted by this study is 6.2 10-6 Pa, which is 31 times higher than the value given by Rordorf. The concentration of air saturated with 2,3,7,8-TeCDD at 25 can hence attain 805 ng/m 3. References 1 Lyman WJ, Reehl WF, Rosenblatt DH. Handbook of Chemical Proerty Estimation Methods, American Chemical Society, Washington, DC, 1990. 2 Miller DG. Estimating vaor ressures a comarison of equations. Ind. Eng. Chem., 56 (1964), 46. 3 Miller DG. Derivation of two equations for the estimation of vaor ressures, J. Phys. Chem., 68 (1964), 1399. 4 Partington JR. An Advanced Treatise on Physical Chemistry( Vol. 2). Longmans, Green and Co., London, 1951. 5 Rordorf BF. Thermal roerties of dioxins, furans and related comounds. Chemoshere, 15 (1986), 1325 1332. 6 Rordorf BF. Prediction of vaor ressures, boiling oints and enthalies of fusion for twenty-nine halogenated dibenzo--dioxines. Thermochim. Acta, 112 (1987), 117 122. 7 Rordorf BF. Prediction of vaour ressures, boiling oints and enthalies of fusion for twenty-nine halogenated dibenzo--dioxins and fifty-five dibenzofurans by a vaor ressure correlation method. Chemoshere, 18 8.
(1989), 783 788. 8 Li X-W, Shibata E, Kasai E, and Nakamura T.. Vaor ressures and enthalies of sublimation of 17 olychlorinated dibenzo--dioxins and 5 olychlorinated dibenzofurans. Environmental Toxicology and Chemistry,23 (2004), 348-354. 9 Shiu W-Y, Ma K-C. Temerature deendence of hysical-chemical roerties of selected chemicals of environmental interest. II. Chlorobenzenes, olychlorinated bihenyls, olychlorinated dibenzo--dioxins, and dibenzofurans. J. Phys. Chem. Ref. Data,29 (2000) 387-462. 9.