Experimental and theoretical study of the enthalpy of formation of 3,6-diphenyl-1,2,4,5-tetroxane molecule.

Abstract

We report the results obtained for the experimental determination and the theoretical calculation of the enthalpy of formation of 3,6-diphenyl-1,2,4,5-tetroxane molecule. The experimental work was performed using a macrocalorimeter to measure the combustion heat, and the sublimation enthalpy was determined via the measurement of the vapor pressure at equilibrium with the vapor phase at different temperatures resorting to the Clapeyron-Claussius equation. Theoretical calculations were performed using semiempirical AM1 and PM3 methods as well as ab initio techniques at the 3-21, 6-31G(d,p), and 6-311G(d,p) basis set levels.

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Short Communication
TheScientificWorldJOURNAL (2002) 2, 455–460
ISSN 1537-744X; DOI 10.1100/tsw.2002.126


*Corresponding author. Email: castro@dalton.quimica.unlp.edu.ar
©2002 with author.

455
Experimental and Theoretical Study of the
Enthalpy of Formation of 3,6-Diphenyl-1,2,4,5-
Tetroxane Molecule
N.L. Jorge1, L.C.A. Leiva1, M.G. Castellanos1, M.E. Gómez Vara1, L.F R.
Cafferata2, and E.A. Castro3,*
1Área de Fisicoquímica, FACENA, Universidad Nacional del Nordeste, Avda. Libertad
5300, 3400 Corrientes, Argentina; 2LADECOR, Departamento de Química, Facultad de
Ciencias Exactas, Universidad, Nacional de La Plata, Calles 47 y 115, La Plata 1900,
Argentina; 3CEQUINOR, Departamento de Química, Facultad de Ciencias Exactas,
Universidad, Nacional de La Plata, Calles 47 y 115, C.C. 962, La Plata 1900, Argentina
E-mail: castro@dalton.quimica.unlp.edu.ar


Received November 15, 2001; Revised January 7, 2002; Accepted January 9, 2002; Published February 15,
2002


We report the results obtained for the experimental determination and the
theoretical calculation of the enthalpy of formation of 3,6-diphenyl-1,2,4,5-
tetroxane molecule. The experimental
macrocalorimeter to measure the combustion heat, and the sublimation enthalpy
was determined via the measurement of the vapor pressure at equilibrium with the
vapor phase at different temperatures resorting to the Clapeyron-Claussius
equation. Theoretical calculations were performed using semiempirical AM1 and
PM3 methods as well as ab initio techniques at the 3-21, 6-31G(d,p), and 6-
311G(d,p) basis set levels.
work was performed using a
KEY WORDS: 3,6-diphenyl-1,2,4,5,-tetroxane, experimental, enthalpy of formation,
semiempirical calculation, ab initio calculation
DOMAINS: analytical chemistry, modeling

INTRODUCTION
Peroxides are widely used in several chemistry areas due to their high reactivity with organic and
inorganic substrates[1]. Their specific properties as free radicals reaction initiators are amply
employed in synthetic chemistry[2], especially in polymerization processes. Unfortunately,
several members of these kind of compounds are very unstable and just a small number are easy
to manipulate with a sensible degree of security and are available as commercial products.
Among these peroxides is a large number of peroxyacids and peroxyesters[3]. Although the
importance of these compounds is well known in the chemistry area, several structural aspects
and reactivity modeling need to be precisely defined[4]. Chemical reactivity of these molecules,

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in thermal decomposition or induced by metals through an electronic-transfer process
decomposition, probably involves an homolytic breakdown of the O–O bond with free radicals
formation as a critical reaction step[5,6]. These chemical species, or their decomposition
products, are normally involved in quick reactions with several substrates[2]. Therefore, it is
necessary to know the tentative schema of the reactivity models of peroxyacids and peroxyesters
as well as the energies associated with the homolytic rupture of these molecules and their
corresponding radicals. These parameters represent basic information about the chemical
reactivity of these molecules, although the subsequent reactions involving the radicals (usually
with very large rate constants) could determine the reaction paths. Energies of the homolytic
breakdown (dissociation) are known for a small number of peroxides and standard literature
registers just a rather limited number of confident information for radicals[7,8]. These values are
known with an accuracy of c.a. ±1 kcal/mol due to experimental difficulties[9,10].
The dissociation enthalpy ∆H can be calculated via the enthalpy of formation ∆Hf of the
molecules involved, using Eq. 1:

∆H(R – R) = ∆Hf(R) + ∆Hf(R) – ∆Hf(R – R)

The enthalpy of formation for molecules appearing in Eq. 1 is known.
The aim of this paper is to report the experimental enthalpy of formation of the 3,3,6,6-
tetramethyl 3,6-diphenyl-1,2,4,5-tetroxane molecule (DPhTOx), as well as the results calculated
through theoretical, semiempirical, and ab initio methods.
(1)
EXPERIMENTAL METHOD
A macrocalorimeter has been used to measure the combustion heat[11]. Substance was located in
a gelatine capsule and was burnt in an oxygen atmosphere at P = 25 atm. The necessary current
for ignition is 2 amperes (amp). The water equivalent E of the calorimeter was determined with a
reference substance (benzoic acid) and the experimental average value is E = 670.0 ± 1.5
cal/grade.
A summary information of the auxiliary quantities for the combustion heat experiments and
complementary details are given in Table 1, where we have included the standard deviations for
each experimental result. Combustion enthalpies and formation heats are given in Table 2.
Sublimation enthalpy of DPhTOx was determined via the vapor pressure at equilibrium with
the vapor phase at different temperatures resorting to the Claussius-Clapeyron equation.
Measurements were made with the mercury manometer through a Bodestein differential
equipment. For each temperature of the substance we determined the equilibrium vapor pressure.
Experimental values are displayed in Table 3.
RESULTS
Thermochemical Measurements
The determination of the combustion heat was made in a macrocalorimeter (Malher adiabatic
calorimetric bomb)[11]. Substance was burnt in an oxygen atmosphere at P = 25 atm. Ignition
current was 2 amperes. The equivalent energy of the calorimeter E was determined with a
standard reference sample of benzoic acid and the measured E was 670.0 ± 1.9 cal/K, for every
experiment. The crystalline compound under study was pressed in a gelatine capsule. The
isothermal process at the bomb and the corresponding correction to the standard normal state was
made following the procedure described by Groth[12] (Table 2). Results obtained in each
experimental experience are listed in Table 1. The specific combustion heats (∆Uc) obtained in

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TABLE 1
Typical Results of the Combustion Experiences


1 2 3 4 5 6
MDFT/g
0.0820 0.0894 0.0800 0.0851 0.0325 0.0444
mgel/g
0.3562 0.2786 0.3428 0.3567 0.1280 0.1282
mFe/g
0.0428 0.0429 0.0447 0.0428 0.0385 0.0341
∆T/K
0.66043 0.57478 0.63960 0.66765 0.25475 0.27831
(magua+E) ∆T/cala
2222.65 1937.01 2155.45 2249.98 858.51 937.91
mgel ∆Ugel/calb
1568.70 1226.95 1509.69 1570.91 563.71 564.59
mFe ∆UFe/calc
68.48 68.64 71.52 68.48 61.66 54.57
∆Uc/cal/g
7176.39 7174.66 7178.01 7175.01 7175.25 7179.10
∆Hc/cal/mol
-1750.45 -1750.02 -1750.84

-1750.11 -1750.17 -1751.11

TABLE 2
Specific Combustion Energies (∆Uc) Resulting from the Combustion Experiences
in (cal/grade) and Normal Combustion Enthalpies (∆Ho
c) in kcal/mol

Experiment #
∆Uc(c) ∆Ho
c(c)
1
7176.39 -1750.45
2
7174.66 -1750.02
3
7178.01 -1750.84
4
7175.01 -1750.11
5
7175.25 -1750.17
6
7179.10 -1751.11
Mean
7176.40 -1750.45
SDa
±2.0

±0.3
every combustion determination are given in Table 2. Normal enthalpies of combustion (∆Hc) and
the normal heat of formation (∆Hf) calculated from the previous data are presented in Table 3.
In order to reduce data to the normal conditions, we employed the conventional procedures.
We have also calculated the sublimation heat of DPhTOx from the vapor pressure equilibrium
with the vapor phase at different temperatures (Table 4) using the Claussius-Clapeyron equation.
Measurements were performed resorting to a Bodestein differential manometer.
Typical results for the experimental combustion determinations of diperoxide in study are
given in Table 1. Individual values of combustion energies (∆Uc), together with the average value
of experimental determinations and its standard deviation are displayed in Table 2. In order to
obtain the normal enthalpies of formation (∆Ho
we used the following molar enthalpies of formation[12]: H2O(l) = – (68.38 ± 0.04) kcal/mol,
CO2(g) = – (94.14 ± 0.13) kcal/mol.
In Table 3 we list the normal molar enthalpies of combustion and normal molar enthalpies of
formation in the gas and solid states. The normal deviations of the average values include the
f)from the normal combustion enthalpies (∆Hoc)

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TABLE 3
Molar Enthalpies of DPhTOx (kcal/mol)

Experiment #
∆Hc
0
(c)
∆Hf
0
(c)
∆Hf
0
(g)a
1
-1750.45 23.82 15.62
2
-1750.02 23.39 15.19
3
-1750.84 24.21 16.01
4
-1750.11 23.48 15.28
5
-1750.17 23.54 15.34
6
-1751.11 24.48 16.28
Mean
-1750.45 23.82 15.62
SD
±0.3
±0.3
±0.3
a Standard enthalpies of formation in gas the phase obtained from the sublimation enthalpies (∆Η s =
8.2 kcal/mol) determined from the vapor pressure measurements shown in Table 4.


TABLE 4
Vapor Pressure of DPhTOx at Different Temperatures,
Measured via a Bodestein Differential Manometer

T(C) p(mmHg)
18.0 12.0
29.0 2.0
34.8 2.0
41.7 36.6
50.2 50.0
58.6 68.0


calibration uncertainties and those associated to the combustion energies of the auxiliary
materials. Finally, we determine the thermochemical properties of DPhTOx.
Theoretical Calculations
One of the main purposes of the calorimetric studies is to find the energies of the substituted
compounds. Thermochemical relationships are important since in some cases the formation
enthalpy, for example those corresponding to hydrocarbons, are know with great accuracy, but
enthalpies of formation of substituted compounds usually are known with low degree of accuracy,
or they are doubtful or even completely inaccessible. A way to know the energetic effects when
substituents are introduced is to employ theoretical methods.

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METHODOLOGY
In order to make the theoretical calculation of the enthalpy of formation, it is necessary to find out
a suitable isodesmic chemical reaction to optimize the corresponding molecular structures and to
perform the vibrational frequencies (using the optimized geometries), applying the method to
obtain the total molecular electronic energy at 298 K.
We used the Gaussian 94 package to perform the calculations[13]. When one tries to optimize
molecular geometries, it is necessary to locate the absolute minimum point over the potential
energy hypersurface which gives the corresponding equilibrium structure. The optimization is
complete when the numerical process converges, i.e., when forces are zero. The convergence
criteria employed in the Gaussian 94 package are:

•
Forces are practically zero.
•
The average square root of forces must be zero.
•
The shift calculation for the next step must be small.
•
Second derivative of the shift must be zero.
RESULTS AND DISCUSSION
The isodesmic reaction to calculate the heat of formation is:
CH3
+ 2 CH3OOCH3
2
H
H
O
O
O
O
4 CH3 +

We made a geometric optimization procedure for each compound involved in the chemical
reaction using semiempirical methods (AM1 and PM3, respectively) and ab initio techniques: at
the 3-21G, 6-31G(d,p) and 6-311G(d,p) basis set levels. In Table 5 we show the energy values for
each of them.

TABLE 5
Calculated Energies of Formation (in Hartree Units) and Heat of Reaction (in Hartree Units)
AM1 PM3 RHF 3-21G RHF 6-31G(d,p) RHF 6-3111G(d,p)
PhCH3
0.159098 0.155271 –268.095478 –269.611640 –269.658609
CH4
0.034185 0.028432 –39.925088 –40.150502 –40158264
CH3OOCH3
0.047722 0.032618 –227.484385 –228.742221 –228.699771
DFT
0.298213 0.262975 –831.503374 –836.139541 –836.310114
∆Hr
0.021313 0.000925 –0.044000 –0.033827 –0.030850
∆Hf(kcal/mol)


48.70 34.90 7.87 14.25 16.12

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TABLE 6
Normal Energy of Formation in kcal/mol


AM1 PM3 RHF 3-21G RHF 6-31G(d;p) RHF 6-311G(d;p)
DFT 48.70 34.90 7.87 14.25 16.12


In Table 6 we give the values obtained from the normal energies of formation of DFT,
employing the data corresponding to each molecule of the reaction scheme.
CONCLUSION
The experimental determination of heats of formation by means of the combustion heat data is a
rather exact method, and it is relatively easy to perform it in a laboratory. The theoretical
procedure based on using the isodesmic chemical reaction allows one to obtain theoretical data,
which usually are very close to experimental data.
Theoretical calculations made at the ab initio level with a 6-311G(d,p) basis set is quite
similar to the experimental determination. Geometrical parameters of the DFT molecule derived
from this calculation reproduce quite well the crystallographic data reported by the literature[12].

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This article should be referenced as follows:

Jorge, N.L., Leiva, L.C.A., Castellanos, M.G., Gómez Vara, M.E., Cafferata, L.F.R., and Castro, E.A. (2002)
Experimental and theoretical study of the enthalpy of formation of 3,6-diphenyl-1,2,4,5-tetroxane molecule.
TheScientificWorldJOURNAL 2, 455–460.

Handling Editor:

C. Robinson, Principal Editor for Analytical Chemistry — a domain of TheScientificWorldJOURNAL.