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Calculation of the Thermodynamic Properties of Polycyclic Aromatic Hydrocarbons by an Incremental Procedure.

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[6] The assignment of the configuration of 2 is based on the (1,r) relative configuration of the 2, 3, and 3' centers determined by H,H-NOESY (see ref. [9]), and
on chemical correlation with enantiomerically pure (2R)-phycocyanobilin
dimethyl ester. This latter compound was obtained by chromatographic separation of the enantiomers of the ring-D methyliminoester (see ref. [8b]) on
triacetylcellulose, and subsequent hydrolysis. The (2R) configuration was determined by comparison of the CD spectra: J. E. Bishop, J. 0. Nagy, J. F.
O'Connell, H. Rapoport, J. Am. Chem. Soc. 1991, f13.8024-8035.
[7] a) J.-H. Fuhrhop, P. Kriiger, W. S. Sheldrick, Justus Liebigs Ann. Chem. 1977,
339-359; b) J.-H. Fuhrhop, P. Kriiger, ibid. 1977, 360-370.
[XI a) J. Iturraspe, A. Gossaner, Photochem. Photobiol. 1991, 54, 43-49; b) R.
Micura. K. Grubmayr, Bioorg. Med. Chem. Lett. 1994, 21, 2517-2522.
[9] Cross peaks in the H,H-NOESY spectra of 2 and 3 that are relevant to the
2-3-3";
5-7'; 8'*10++12; 13'++15*17'.
configuration: 3-5-3';
I
Am. Chem. Soc. 1975, 97, 1949-1954; b) ibid.
[lo] a) G. Wagniere, G. Blauer, .
1976, 98, 7806-7810; c) H. Falk, The Chemistry of Linear Oligopyrroles and
Bile Pigments, Springer, Vienna - New York, 1989, p. 426.
[I 11 The (1 5 2 -15E) photoisomerization requires thiol catalysis: a) F. Thiimmler,
W. Riidiger, Tetrahedron 1983, 39, 1943-1951; b) H. Falk, N. Muller, T.
Schlederer, Monatsh. Chem. 1980, iff, 159-175. The (15E -152) photoisomerization does not require addition of thiol.
Calculation of the Thermodynamic Properties
of Polycyclic Aromatic Hydrocarbons
by an Incremental Procedure**
Karen Nass, Dieter Lenoir," and Antonius Kettrup
Dedicated to Professor Paul von Rag& Schleyer
on the occasion of his 65th birtkduy
Uniform substances are characterized by both their thermodynamic and their molecular properties."] After the triumphs of
quantum chemistry,121it has been possible in the past decade to
calculate the inherent molecular properties of compounds in the
gas phase.[31Certain thermodynamic properties of substances,
like the melting and boiling point, the vapor pressure, and the
corresponding energy values of the phase transitions, are ensemble properties of molecules and thus not accessible with
these methods.[41Apart from group theoretical procedures, several empirical methods are used for the prediction of these properties.L5]The vapor pressure and the enthalpy of sublimation of
synthetic compounds (xenobiotics) are important properties
relevant for the environment,f6I and a relationship between
structure and these thermodynamic quantities can be used in
model calculations for otherwise unknown values.
We studied the group of polycyclic aromatic hydrocarbons
and found a general relationship between structure and vapor
pressure, and between structure and enthalpy of sublimation.
The results are based on the data from thirty polycyclic aromatic hydrocarbons containing five- and six-membered rings that
are found in the environment.
The vapor pressure of several substances are known, but the
quoted values vary mostly by an order of magnitude. We further
developed the gas saturation method of vapor pressure determil
nation and measured the vapor pressures and en-thalpies of sublimation of the selected compounds.[g1This method can be used
[*I Prof. Dr. D. Lenoir, Dr. K. Nass, Prof. Dr. A. Katrup
Institnt fur Okologische Chemie, GSF-Forschungszentrum fur Umwelt und
Gesundheit GmbH
lngolstiidter Landstrasse 1, D-85758 Oberschleissheim (Germany)
Telefax: Int. code + (89)3187-3371
e-mail: lenoir@gsf.de
[**I We thank Prof. Cammenga, Brdunschweig, and Dr. Utschick, GSF, for vdhable suggestions.
Angew. Chem Int. Ed. Engl. 1995, 34, No 16
0 VCH
to measure vapor pressue over a wide range as well as in mixtures. The results of the experiments are collated in Table 1. In
all cases the temperature range of between 40 and 180 "C lay well
below the critical temperature for each substance. The logarithm of the value of the measured vapor pressure was plotted
against the reciprocal temperature. For a linear relation this
corresponds to the intergration of the Clausius-Clapeyron
equation in which the temperature dependence of the enthalpy
can be neglected if the measurements are made well below the
critical temperature. The enthalpy of the relevant phase transition was determined from the slope of the lines.
Table 1. Vapor pressure and enthalpy of sublimation for 30 polycyclic aromatic
hydrocarbons measured in the temperature range 40-180°C in 5°C steps; the
average of three experimental values were determined at each temperature step.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Substance
P (25 oc),,,,a,,lat.d
[Pal
AS"bHrn
[kJ mol - '1
naphthalene
biphenyl
biphenylene
acenaphthene
acenaphthylene
flnorene
anthracene
dihydroanthracene
phenanthrene
1-phenylnaphthalene
fluoran thene
4,s-dimethylphenanthrene
benzo[a]fluorene
benzo[b]fluorene
triphenylene
tetracene
pyrene
chrysene
benzanthracene
9-phenyldnthracene
binaphthalene
benzo[b]fluoranthene
dibenz[a,c]anthracene
dibenz[a,h]antliracene
benzo[a]pyrene
benzo[e]pyrene
perylene
benzo[g,h,i]perylene
9,lO-diphenylanthracene
coronene
10.86
1.56
3.75 x l o - '
3.97 x 10-1
1.26 x lo-'
1.10 x 10-1
1.21 10-3
3.28 x lo-'
2.57 x lo-'
3.20 10-3
1.60 x lo-'
1.23 x lo-'
1.11 x 10-4
3.12~
lo-"
2.80 x
2 . 2 0 ~lo-'
7.60 x 10-4
1.36 x
2.12x 10-6
4.50~
2.17 x lo-'
1.00 x 10-6
5.65 10-9
4.93 x lo-'
5.30 x lo-'
7.89 x lo-'
5 . 5 4 ~lo-'
1.01 x 10-8
1.88 x 10-8
3.56 x lo-''
71.7
81.8
82.7
83 2
77.2
84.9
99.7
93.9
88.9
88.6
98.3
85.9
105.4
111.2
114.5
126.5
97.9
118.8
115.5
118.7
138.3
119.2
135.0
134.1
122.5
117.9
123.2
129.9
137.5
143.2
The magnitude of the vapor pressure and the enthalpy of
sublimation of these compounds can be derived from the structure. If naphthalene or fluorene is the reference compound, each
higher homologue can be developed through the following
structural features: [''I
Structural feature
Structural feature
Structural feature
Structural feature
1 : linear ortho annelation
2: angular ortho annelation
3 : angular peri annelation
4: phenyl group substitution
Each annelation step contributes a fixed increment to the magnitude of the vapor pressure and enthalpy of sublimation. The
vapor pressure p at 25 "C and the enthalpy of sublimation
AsubHm
of the homologous series of polycyclic aromatic hydrocarbons can be described by Equations (a) and (b).
AsubHm
=B
+ n,Y, + n,Y, + n,Y, + n,Y,
Verlagsgesellschajt mbH. 0-69451 Weinheim. 1995
OS70-0833/95/1616-1735iT 10.00+ .2SjO
1735
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In the Equations (a) and (b), I ? , , fz2, n 3 , and n4 are the
number of structural features 1, 2, 3, and 4; A =10.86 Pa.
B = 71.7 kJmol-' for the reference substance naphthalene;
A =1.1 x l o - ' Pa, B = 84.9 kJmol-' for the reference substance fluorene; and X , and Y, are constants having the values
shown in Table 2.
Table 2 Valucs of the constants from Equations (a) and (b)
m
X",
y,
[kJ mol1.29 x lo-"
1.81 x 10-3
2.22 x 10-2
3 . 5 0 ~10-3
'1
27.7
17.7
10.2
18.3
quantitative detcrmination i5 po55ible. All the substances under investigation were
commercially available compounds with a purity of 99.9% or greater.
The overall error of the method includes the error in calibration and the in the
temperature measurement. If this error is taken into account for the linear regression of the vapvr pressure curve accoi-ding to y = 0 + hx, an error of i O . 5 Yo is
inherent in the constant i i and k 1 "/o in the constant h. The error in the extrapolation
of the vapor pressure to 25 'C and in the calculation of the enthalpy of sublimation
thus depcnd on the values u and hand are therefore different for each substance. Use
of thi? error calculation with the reference substance anthracene gives a maximum
error of about XIYO for the extrapolated vapor pressure and about 1 % for the
enthalpy of sublimation. In contrast, the studies on the reproducibility for 15 measurements of anthracene yielded a standard deviation of2.5 "A. The vapor pressurc
of anthracene therefore is 1.21 x lo-' Pa +7.4% with a statistical reliability of
99%, while the etitlialpy of sublimation is 99.8 kJinol-' ~ 1 . 2 % .
Received: October 4, 1994
Revised: March 17. 1995 [Z7373IE]
Gei-man versioii: Aiigrw. C/icnr. 1995, i07,1865-1866
Keywords: polycyclic arenes . vapor pressure
The method of calculation will be demonstrated for the example of coronene (Pig. 1). The vapor pressure p at 25 "C for
coronene is given as 3.58 x lo-* and 2.01 x lo-'' Pa;[']
the published enthalpy of sublimation is 112.05 and
138.02 kJmol-I. The calculation according to Equations (a)
and (b) yield a vapor pressure value of 3.4 x lo-'' Pa and an
enthalpy of sublimation of 140.2 kJmol-'.
I
[ l ] a) See textbooks of physical chemistry such a s G. M. Barrow, PIr.
Cheinre. 8th cd., Vieweg, Braunschweig, 1990; b) Landoldt-Bornstei
werte uwd Funktionen uus Physik, Chemie, Astronomic, Gcqihysik uiid Tcdinik,
6th ed., Springer. Berlin. 1980: c) Ilunrlhuch of C'hemisrrv and Physics, 75th Ed.
(Ed.: D. L. Lide). CRC Press, Boca Raton, FL, USA. 1994.
[2] a) H. Prima,, Ch~iiir~try,
Quunrum mechrmrcr uwd R~~ductioili,vni.
Springer,
Berlin, 1981 ; b) H. Primas in Der Puuli-.lung-Dia/og und .xrine Bedeulnngfur die
moderne Wissensc/?uj'f(Ed.: H. Atmanspacher), Springer, Berlin, 1995.
[3] a) T. Clark. A Hundhook of Computations/ Chw~i,strj,
Wiley. New York, 1985;
b) W. J. Helm. L. Radom, P. von R. Schleyer, J. A. Pople. Ah inifio Molecu/ur
Orhital T/zeory, Wilcy, New York, 1986; c) see papers on calculated moleculs
in Chemical Abstracts.
[4] H. Primas, C/i?iii. C'nsrrer Zeit 1985, 1 Y . 109-119: ihid. 19, 160 167.
[S] W. J. Lymaiin. W. F. Reehl. D. H. Rosenblatt, Hundhuok of Chfdmiral Propcrfj,
Esriinution Methods, American Chemical Society. Mc Graw Hill, 1990.
[6] a) R. P. Schwarsenbach. P. M . Gschwend, D. M. Iinboden. Enivironmcnta/ Orgunir Cheinrslry, Wilcy, New York. 1993. S. 56 75; b) K . Ballschmiter. Ai~griv.
C'liem. 1992, 104. 501-528; A n g e x CIrem. Inf. E d Eng/. 1992. 31, 487 -515.
lic Aronzutir H,~rlrocurhons(Ed.: A.
171 G . Grimmer in Hundlx~ok of Pol
Bjorseth), Dekker, New York. 1983, S. 149-1132,
[ 8 ] M. Stephenson, S. Malanowski, Hund/iook of tlic Thcrmod~rrniiii~~s
of Orguiirc
Compounds, Else\ ier, Amsterdam, 1987.
[9] a) K. XaR. Dissertation. TU Munchen. 1994: bhe\iew on vanor oressurc mcasurements : W Hessler. Wissmxhufiliche Zeitsrhriff der Wilhelrn-Pieck-Uniwrsitiit Rostork, Mathcmutisch-Nnturii i.s.senschuffl/~chrRerhe 1976, 10 1047 1066; ihid. 1977. 7, 75% 784; c) F. Wania. W. Y Shin, D. Mackay, J. Chem.
Eng. Data 1994, 35 (3). 572-577.
10 principle, the relation can be derived from the parent compound benrene.
The vapor pressure data for this compound is, however. inaccurate for technical reasons connected with the gas saturation method.
a) A relation has been defined for the vapor prcssurc of n-alkanes: every CH,
group contributes an increment to the vapor pressure: K. Ruiifka, V. Majer,
J. Phys. Cherir. Ref: Dutu 1994, 23, 1-39; b) a relation has been described for
the enthalpy of sublimation of aliphatic hydrocarbons: J. S. Chikos. R. Annuziata, L. 11. Hadon. A. S. Hyman, J. F. Liebinan, .I Org. C/rem. 1986. 5f.
431 1-4314: c) a relation between vapor pressure and the number of chlorine
atoms in the compound can be derived for certain chloroarenes' B F. Rordorf,
Therinochim. Acru 1985, 85. 435--438; K. Liu. R. M. Dickhut. C'iicmospherc
1994,29, 5x1 -589.
a) N. B Chapman. J. Shorter, Advances in Linear Free Enrrg1 Krlafioii.shii,.s,
Plenum Prcys, London, 1972: b) C. Hansch. A w . Clieir?. Res. 1993. 26,
147- 153.
S. W. Benson, Thrrmochemita/ Kinetics, Wiley. New York. 1976.
, .
Fig. 1. Representation of the method of calculation of the vapor pressure and the
enthalpy of sublimation of coronene with naphthalene as reference on the basis of
Equations (a) and (b).
The results show that within a class of substances a relationship between structure and vapor pressure, and structure and
enthalpy of sublimation exists.["] To our knowledge no relationship could previously be derived for these thermodynamic
parameters. The relations (a) a'nd (b) have the mathematical
form of a linear free energy relationship (LFER) somewhat like
the Hammett or Hammett-Taft equation." Additive relations
have been derived by Benson for certain molecular properThus we have shown that a relationship exists between the
ensemble property or molecules and the structural elements.
Through the relation between vapor pressure or enthalpy of
sublimation and other thermodynamic parameters like melting
and boiling points, a general derivation of thermodynamic
parameters is possible.
Experimental Procedure
The measurements were performed with the VPA 434 instrument of the company
Netrsch-Geritehau, based on the gas saturation method [9a], in which a stream of
inert gas flows ovci- the sample. The saturated stream of gas i s passed over a n
adsorption segment and after a predetermined time diverted into a gas chromatograph while heating the segment to relcase adsorbed substances. In this way a
1736
J', VCH C ~ i - l c i ~ ~ s g e s f ~ l l .mhH,
s c h ~ ~0-65451
l
U'einhcmi,
1595
0570-0833/95134/7-173~
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Angew Ckem. I n / . Ed. Eiigl. 1995. 34. No. 17
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