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3.2 Prediction Methods
CHAPTER 3 Prediction of vapour pressures of dio血congeners
3.I Introduction
VapotF Pressures are fundamentalproperties of persistent organic pollutantsandare important in
detemmmgtheir dis廿ibution and fate inthe envirorLnent･ Due tothere is a large number of dioxin
congeners and other Pops,the experinentalmeastqements call Cover Only aminorfraction of them, the pr,.ediction of vapotq pressures of dioxin congeners by correlation relationships is usdlland necessary.
Predicdon methods phyanimportant role inthe enviromcntalresearch.
Ntnerotw equationsand correlationsfor estinatlng Vapour preSSureare PreSentedinthc literattJre.
Most of the methodsare empiriCalandthe derived resultsare very rough. [14】
Rordorf l517】 suggested a good c0‑lation method to predict vapour presstwe, which derivedfromthe
thernodynamiCthcory. Based on experinentalvapour pressure data,血s methodgives not onlythe
enthalpy and entropy of sublimation but alsothe enthalpy of meltingand boiling point. Based onthe
experimentaldata of a part of dioxin congeners neastFe in Chapter 2,血s research enploycdthe
comlation method to predictthe vapotu pressure ofall PCDDsnCDFsand PBDDsnBDFs.
Correlation ncthods are of particular importance when dealingwith dioxin congeners sincethereare thousands of homologuesand isomeqs. Correlation methodsallow testing of the experimentaldata set for
self‑consistency. Calculation of relぬd substance Properties (i.e. boiling points and enthalpies offusion
from vapour pressure data) is possible.
and AZ is a compressibilityfactor,given by
AZ‑p AV!(R I) (Ⅱ)
where AV isthe volume difference between vapourand liquid.
The correhtion method uses the liquid phases as reference statesandthis has been the case for most
pre‑dictive vapourpresstwe methods･ Supersaturated liquid phasesare tuually defined atthe temperature of interest. Afuller use is made here of the measured temperature dependence of the vapotrr pressures of
the solid. The data are extrapolated tothe melting pointsand the liquid phases are broughtinatthis point･
Enthalpies (AHm)and entropies offusion (ASn)are definedforthe melting temperattFe (T‑)and unknowntenperature dependencies of these functions are not involved･ The two parameters are deterninedforthe different compounds andarefound to vary significantly between compounds･ The predicted method is not limited by assumptions of temperature or substance independence of entropleS Of
fusion. Symeby relations between moleculeand crystallattice affectthe entropies effusion.
Figure 3. I illustrates the procedurewf vapour pressure correlation method suggested by Rordorf･
Relative substance independenceand therefore easy predictabilityof entropies of evaporation atthe boihng point (Tb) arethe basis of the present correlation method･ Fishtine's formula lS] has been used to predictedthe entropies of evaporationforthe dice‑t compounds at Tb, (see formulas (1) and (2))･
AHv(Tb) = Tb KF (36.61+R ln Tb) ASP(Tb) = AHv(Tb)/Tb + Rlmpo
At the boiling POint:
KF‑1.OI po=101,325 Pa
IJI the liqtLid phase:
AHv (,2 ) ‑ AHv (T. ) I g AC, gas‑LLq'dT
(3)′
glVeS曲r integration for Tl‑Tband T2‑T:
AHv(I) ‑ AHvCrb) ll +K( I ‑ I;!Tb)
K = ‑Tb AC,gaSlliq･/帆(Tb)
Se血gfo‑ula (4)intothe Clausius‑Clapqyron equation,
Ippodlnp(T) = LTD AHv (Tb )ll ･ K(1 ‑T/Tb)]/RT2dT
glVeS曲r integradonfromthe melting to boiling pomt:
hp(Tm) = hpo ‑ (AHv(Tb)瓜Tb)[(1+K)(I;JTn‑1)‑K h(帆)
At the mcltiAg point:
AGs = AGm + AGv AHn ‑ AHs ‑ AHv AG=AH‑ TAS ASTn‑ ASTs ‑ ASv AGn (Tm)‑ 0
ASTm(Tn) ‑ AHn(Tm)/ Tm
AGv ‑ ‑ RTlmpliq. ‑ AHv ‑ TAR, AS(Tm) ‑ R h pllq(Tm). + AHv(Tm)/Tm
From equadon (4), AHv(Tn) ‑ AHvCrb) ll +K ( 1 ‑ I:mb)
h the solid phase:
AGs(I) ‑ ‑RTlnps｡lid(I) ‑ AHs(I) ‑ TASs(T)
R hp･oLLd(T) ‑ 〔ASS (T‑ ). ￡ ACpg S /Td'HAHB (Tm )/, I ￡ ACpg‑BdT]
Rlmps｡lid(I) ‑ Ass(Tm) ‑ AHs(Tn)〟
(6)
(7)
(8)
(9)
(10)
(ll)
(12)
(13)
(14)
(15)
Ⅹ/T
Fig 3･ 1 ne calculation procedure of correlation method suggested by Rordorf l5]･
(Relationship betweenthe vapotq pressures of the solidandthe liquid phase･) (KF‑ I.01,p0 ‑ 101,325 Pa)
Tb = boiling polnt, Tm ‑ melting point, H ‑ molarenthalpy, S = molar entropy, G ‑ molar Gibbs energy,
C, ‑ molar heat capacity, R = gaas constant, p(I) = vapour pressure at T, Subscript s‥ sublimation,
Subscript v: vaporizadon, Subscript m:fusion.
The ctxrvatttres of the liquid phase vapour presstJre CtmeS SteJnfromthe temperature dependence of
the enthalpies of evaporation. The enthalpies of evaporation canbe determined as a hction of
temperature if the differences of the hea(capacities of the gasand liquid phasesareknown(fomula (3)).htegration of formula (3) leads to formulae (4)and (5). Setting formula (4) intothc clausius･Chpeyron
equation･ The heat capacities ofgasesand liquids were estimated bythe group comibution methods l2･3]
The temperattqe dependences of the change of heat capacides were neglected. Mackay l4】 has shown
thatthe Clausius‑Clapeyron equation canbeanalytically integrated to (7) if the enthalpy of evaporation is
brought into the form of equation (6). Vapour pressures of liquids ofknownfreezingand boiling points
can be predicted by equation (7). Equation (7) Canalso be used to estimate boiling points if the melting
pointsand vapour presst汀eS at Tmare known forgiven compounds.
The enthalpies of fusion need to beknownforthe projection of solid vapotq presstqe cuⅣesfrom
bredicted) liquid vapotw presst汀e data. The Gibbs Bee energiesand enthalpies of sublimation equalthe
stn of the corresponding血nctions offusion plus melting (see equations (8)and (9)).
Equ血on (ll), which is obtained from equations (8), (9)and (10), statesthat similar sums hold for
the entropleS. The entropleS Offusion at Tn equalthe enthalpies offusion divided by the melting temperatures (equatiot1 13) asthe Gibbs Bee energies of fusionare zero at Tm. The enthalpies of evaporation can be estimated by equation (4) forthe melting points. Expression (15), which is obtained from equation (14), pmits the calculation of the entropy of evaporadon at Tn ill COmbiJlationwith
eqtl血ons (4) and (7).
Enthalpiesand entropleS Offusion can be predicted for Tmfron experinentalenthalpiesand entropies of sublimation (at Tn) by equations (4), (9) (ll)and (15). A correlation of the evaluated enthalpies offusionwiththe degee of chlorine substitution (Fig 3. 1) enablethe estimation of enthalpies
(and entropies by equation (13)) offusion f♭r A‑chlorinated dioxins. Equations (9)and (ll)allowthe
conversion of predicted enthalpiesand entropleS Of evaporation to enthalpiesand entropies of sublimation.
Solid state vapor pressure curve can now be predicted by equation (17) which is obtainedfron equation (16).
The differences of the heat capacities of the gas andthe solid phases equalthc rotationalaAd the
translationalheat capacides of the gasesminusthe lattice‑mode heat capacities : Cpgas･solid= 4R ‑ Cl弧ice･
Thc lattice parts can be estimated bythe rule of Dulong and Petit and approach 6R at ambient temperatures for crystals composed of moleculeswiththree nonzero moments of inedia･ Solid to gas heat changes of 116.6 J･ mo1‑1･ K‑I werether/efore assumed. Equation (17) Canbe appFOXimated by equadon
( 1 S) to calculate vapour pressures over a narrow temperature range.
These correlations permitthe estimation of boiling pomtsand enthalpies of evaporadon for dioxins andthe solid state vapour pressures canbe predicted bythc equations ofFig 3.1for dioxin congeners of known melting polntS.
3.3 Predicted Vapour Pressure Results for PCDDsnCDFs
Enthalpies and entropleS Of sublimation of the 22 PCDDsノPCDFs w耶Obtained by linear
regressions of the expenmentalvapour pressures overtheindicated temperattqe intemalSinChapter 2･
They holdforthemid temperattqe, Tmid‑2(Tnax TJ/(Tmax + Tmin), Of the investigated temperature ranges,
and recalculated fTorthe melting polntSand room temperattqe by means of bracket expressions of equation
(17). The results weqe shown in Table 3.1. The neldng point (㌔) data come komtheliterature (see Table
1.2 in Chapter I).
The boiling point (Tb) appears in severalexpressions and was determined in an iterative procedure.
EXCEL was used for the solution of the equations shownin Fig 3. I by iterative procedure. The calculated boiling pouts of the 22 PCDDs/PCDFs were hstedinTable 3.2.
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subl血ation of PCDDs, (C) enthalpy of sublinadon of PCDFs, (d) entropy of sublinadon of PCDFs.
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0 0
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Figures 312and 3･3 showthat the enthalpy of sublinadon ad derived boiling point of PCDDsand PCDFs correlate wellwiththe substitution number of chlorine, while the melting polntand entropy of
sublimation show a great dealof scatter.
′
The determined boiling polntS Werethen set for correct prediction of the vapour pressures
(恥quid(Tn)=psoud(Tn)) at the melting points. The detemied boiling points and enthalpies offusion of the
dioxin congeners were correlatedwiththe degree of chlo血e substitution. Figures 3.3 and 3.4 showthe
correlations of the predicted boiling pointsand enthalpies of fusionwiththe degree of chlorination (X).
The reladon is asthe following.
ForPCDDs: Tb‑29.lox+564.00 K
AHm(Tm)‑3.808Ⅹ+22.105 kJ･mo1‑I
ForPCDFs: Tb‑34.45X+554.60 K
AHn(㌔) ‑3.553Ⅹ+20.801 kJ･mol l
Boiling polntS and enthalpies offusiomare predicted forunknown dioxin congem耶uSingthese
formulas,andth飢the solid state vapour pressures were calculated bythe equadons of Fig 3. 1.
The predictedthermalproperties and vapour pressures for 59 PCDDsand 13 I PCDFsare listed in Tables
33 and 3.4, respectively.
Allthe vapour pressures of PCDDsnCDFs predicted here are more or less higherthanthe data
predicted by Rordorf l7]forthe sane compoundsI Figtqe 3･5 shows the vapour presstqe differences between Rordorf's studyand this studyforthe toxic congeners, which subsdtuted at positions 2, 3, 7,and 8.
Forthe most toxic 2,3,7,8･TeCDD,the predicted vapour presstqe at 25 ℃ by dds study is 6.2×10 6
Pa, and is 31times higherthanthe value given by Rordorf. TherefTore,the concentration of air saturated
with2,3,7,8‑TeCDD at 25 ℃ Canarrive at 805 ng/n3.
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