Enthalpies of formation and strain of chlorobenzoic acids from thermochemical measurements and from ab initio calculations.

Abstract

Molar enthalpies of sublimation of 2-chloro-, 3-chloro-, and 4-chlorobenzoic acids were obtained from the temperature dependence of the vapor pressure measured by the transpiration method. Thermochemical investigations of chlorobenzoic acids available in the literature were collected and combined with own experimental results to obtain their reliable standard molar enthalpies of formation at T = 298.15 K in the gaseous state. Ab initio calculations of chlorobenzoic acids have been performed using the G3(MP2) theory, and results from the homodesmic reactions are in excellent agreement with experiment. New results help us to resolve the uncertainty in the available thermochemical data on chlorobenzoic acids. The strain enthalpies of chlorobenzoic acids have been assessed using an isodesmic reaction procedure.

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Enthalpies of Formation and Strain of Chlorobenzoic Acids from Thermochemical
Measurements and from ab Initio Calculations
Vladimir N. Emel’yanenko, Agata Strutynska,†and Sergey P. Verevkin*
Department of Physical Chemistry, UniVersity of Rostock, Hermannstr. 14, 18051 Rostock, Germany
ReceiVed: September 14, 2004; In Final Form: March 24, 2005
Molar enthalpies of sublimation of 2-chloro-, 3-chloro-, and 4-chlorobenzoic acids were obtained from the
temperature dependence of the vapor pressure measured by the transpiration method. Thermochemical
investigations of chlorobenzoic acids available in the literature were collected and combined with own
experimental results to obtain their reliable standard molar enthalpies of formation at T ) 298.15 K in the
gaseous state. Ab initio calculations of chlorobenzoic acids have been performed using the G3(MP2) theory,
and results from the homodesmic reactions are in excellent agreement with experiment. New results help us
to resolve the uncertainty in the available thermochemical data on chlorobenzoic acids. The strain enthalpies
of chlorobenzoic acids have been assessed using an isodesmic reaction procedure.
Introduction
Derivatives of benzoic acid are compounds of considerable
industrial and environmental significance. However, thermo-
chemical data on substituted benzoic acids are apparently in a
state of disarray.1Although experimental values of the enthalpies
of formation in the crystalline state, ∆fH°m(cr), of 2-chloro-,
3-chloro-, and 4-chlorobenzoic acids, available from the
literature,2-4,7are in close agreement with each other, the range
of enthalpy values of sublimation, ∆cr
compounds differ over 20.0 kJ mol-1(see Table 1). Thus,
additional experiments on chlorobenzoic acids are necessary in
order to validate available experimental data on sublima-
tion enthalpies and to obtain reliable enthalpies of formation
∆fH°m(g) ) ∆fH°m(cr) + ∆cr
measurement of ∆cr
transpiration method have been made, and these are comple-
mented with high level ab initio calculations.
gHm, for each of these
gHm. It is for this reason that
gHm of three chlorobenzoic acids using
Experimental Section
The 2-chloro-, 3-chloro-, and 4-chlorobenzoic acids and
4-tert-butylbenzoic acid supplied by Aldrich and Fluka with a
mass-fraction purity of about 0.99 were further purified by
repeated sublimation in a vacuum. GLC analysis of the samples
used for vapor pressure measurements on a capillary column,
SE-30 of 25 m length, failed to show the presence of any
impurities (greater than 0.01 mass percent).
Vapor pressures and enthalpies of sublimation, ∆cr
substituted benzoic acids were determined using the method of
transference in a saturated stream of nitrogen. The method has
been described in detail before12,13and has proven to give results
in agreement with other established techniques. The temperature
dependence of the vapor pressures was used to determine the
enthalpies of vaporization of the pure substances. A sample of
approximately 0.5 g of the sample was mixed with glass beads
gHm, of
and placed in a thermostated U-tube of length 10 cm and
diameter 0.5 cm. Preheated nitrogen stream was passed through
the U-tube at constant temperature ((0.1 K). The flow rate of
the nitrogen stream was measured using a soap film bubble flow
meter ((0.2-0.3%) and optimized in order to reach the
saturation equilibrium of the transporting gas at each temperature
under study. We tested our apparatus at different flow rates of
the carrier gas in order to check the lower boundary of the flow,
below which, the contribution of the vapor condensed in the
trap by diffusion becomes comparable to the transpired one. In
our apparatus the contribution due to diffusion was negligible
at flow rates down to 0.5 dm3‚h-1. The upper limit for our
apparatus was a flow rate of 7.5 dm3‚h-1. Thus, we carried out
the experiments in the using flow rates ranging from 4 to 5
dm3‚h-1which ensured that transporting gas was in saturated
equilibrium with the coexisting solid phase in the saturation
tube. The material transported was condensed in a cold trap.
The amount of condensed product was determined by weighing
((0.0001 g).
The saturated vapor pressure pi
calculated from the amount of product collected within a definite
period of time. Assuming that Dalton’s law of partial pressures
when applied to the nitrogen stream saturated with the substance
i of interest is valid, values of pi
satat each temperature Tiwas
satwere calculated:
where R ) 8.31447 J‚K-1‚mol-1; mi is the mass of the
transported compound, Miis the molar mass of the compound,
and Viis its volume contribution to the gaseous phase. VN2is
the volume of transporting gas and Tais the temperature of the
soap film bubble flow meter. The volume of transporting gas
VN2was determined from the flow rate and time measurements.
Ab Initio Calculations. Standard ab initio molecular orbital
calculations were performed with the Gaussian 03 Rev.04 series
of programs.14Energies were obtained at the G3(MP2) level of
theory. G3 theory is a procedure for calculating energies of
molecules containing atoms of the first and second row of the
periodic chart based on ab initio molecular orbital theory. A
modification of G3 theory that uses reduced orders of Møller-
* Towhom correspondenceshouldbeaddressed.E-mail:
sergey.verevkin@uni-rostock.de. Fax: ++49 381 498 6502. Telephone:
++49 381 498 6508.
†Socrates-Erasmus student from the Faculty of Chemistry, Warsaw
University of Technology, Poland.
pi
sat) miRTa/VMi;
V ) VN2+ Vi
(VN2. Vi)(1)
10.1021/jp045852q CCC: $30.25 © xxxx American Chemical Society
Published on Web 00/00/0000PAGE EST: 5.8

Page 2

Plesset perturbation theory is G3(MP2) theory.15,16This method
saves considerable computational time compared to G3 theory
with limited loss in accuracy, but it is much more accurate that
G2(MP2) theory. G3(MP2) theory uses geometries from second-
order perturbation theory and scaled zero-point energies from
Hartree-Fock theory followed by a series of single-point energy
calculations at the MP2(Full)/6-31G(d), QCISD(T)/6-31G(d) and
MP2/GTMP2Large levels of theory (for details see ref 15). The
enthalpy value of studied compounds at T ) 298 K was
evaluated according to standard thermodynamic procedures.17
Results and Discussion
Vapor Pressure Measurements. Experimental vapor pres-
sures of alkyl carbamides have been measured by using the
transpiration method in the broad temperature range over 50
K. In each case the measurements have been performed possibly
close to the reference temperature 298.15 K. The following
equation
was fitted to the experimental p, T data using a and b as
adjustable parameters. T0 appearing in eq 2 is an arbitrarily
chosen reference temperature (which in this case is 298.15 K).
Consequently, from eq 2 the expression for the vaporization
enthalpy at temperature T is
Values of ∆cr
isobaric molar heat capacities of solid chlorobenzoic acids,18
Cp
zoic acids, Cp
Supporting Information). Experimental results and parameters
a and b are listed in Table 2.
To establish the validity of the transpiration method for
benzoic acid derivatives, the admittedly reliable enthalpy of
sublimation of 4-tert-butylbenzoic acid6was measured in this
work. The vapor pressures and enthalpy of sublimation ∆cr
from this work were in a very good agreement with the literature
data6(see Table 1).
gCp have been derived from the experimental
cr, and isobaric molar heat capacities of gaseous chloroben-
g, were calculated using ab initio methods (see
gHm
Enthalpies of Sublimation. ∆cr
pendencies of vapor pressures of chlorobenzoic acids have been
reported in the literature recently.29Also enthalpies of sublima-
tion for these compounds were measured at elevated tempera-
tures with the help of a Tian-Cavet calorimeter equipped with
the Knudsen effusion cell11or by using the “drop-method” (a
sample was dropped into the hot zone of the calorimeter)9and
have been reported. The authors of these works adjusted their
measured values of ∆cr
298.15 K, by different and ill-defined methods. It is for this
reason that in this work the original published experimental
results9,11were readjusted to the reference temperature T )
298.15 K in the same manner as our own results (using the
experimental isobaric molar heat capacities of solid chloroben-
zoic acids,18Cp
ab initio calculations), and new ∆cr
calculated in order to make a more reliable comparison with
results from this work (see Table 1).
The value of ∆cr
obtained in this work is in very good agreement with those from
Adedeji et al.9as well as those from Sabbah and Hirtz.11
However, it should be noted that Adedeji et al.9measured the
vaporization enthalpy ∆l
sublimation enthalpy, ∆cr
enthalpy of fusion, ∆cr
is required. The experimental enthalpy of fusion, ∆cr
) 26.29(0.28 kJ‚mol-1of 2-chlorobenzoic acid was measured
at a melting temperature of 414.10 K,11and due to the deviation
of the melting temperature from T ) 298.15 the observed value
of the enthalpy of fusion of 2-chlorobenzoic acid had to be
adjusted to the reference temperature of 298.15 K. The adjust-
ment was calculated using the equation19,20
gHm. The temperature de-
gHmto the reference temperature, T )
cr, and gaseous isobaric heat capacities, Cp
gHm(298.15 K) values were
g, from
gHm(298.15 K) for 2-chlorobenzoic acid
gHmfor this compound. To calculate
gHm(298.15 K), the value of the
lHm(298.15 K), for 2-chlorobenzoic acid
lHm(Tfus)
where the value of ∆cr
molar heat capacities of liquid chlorobenzoic acids, Cp
236.0 J‚mol-1.K-1calculated according to procedure developed
by Chickos.21The isobaric molar heat capacities of the solid
lCphas been derived from the isobaric
l)
TABLE 1: Compilation of Data on Enthalpies of Sublimation ∆cr
techniquea
p-tert-butylbenzoic acid
gHmof Benzoic Acids Derivatives
temp range/K
325.4-342.8
373.0-402.5
333.2
413
>414
323.1
320.2-339.2
338.1-402.6
328.2
414
323.1
320.1-340.1
348.5-404.1
333.2
413
363.1
333.2-356.1
358.4-398.3
∆cr
gHm(T)/kJ‚mol-1
103.8 ( 0.4
102.1 ( 0.7
79.5 ( 1.7
72.4c
90.7 ( 0.5c
100.0 ( 0.5
105.1 ( 0.4
99.91 ( 0.36
80.8 ( 1.7
99.6
100.5 ( 0.4
101.2 ( 0.4
98.8 ( 0.8
87.9 ( 1.7
101.9
99.3 ( 0.4
103.3 ( 0.5
105.7 ( 0.8
∆cr
gHm(298 K)b/kJ‚mol-1
105.2 ( 0.4
105.4 ( 0.7
80.4 ( 1.7
101.5
119.9 ( 0.6
100.6 ( 0.5
105.8 ( 0.4
101.5 ( 0.4
81.6 ( 1.7
102.2
101.1 ( 0.4
101.9 ( 0.4
100.6 ( 0.8
88.8 ( 1.7
105.0
101.0 ( 0.4
104.5 ( 0.5
107.9 ( 0.8
ref
K
T
TE
DC
DSC
C
K
T
TE
DC
C
K
T
TE
DC
C
K
T
6
this work
8
9
10
11
29
this work
8
9
11
29
this work
8
9
11
29
this work
2-chlorobenzoic acid
3-chlorobenzoic acid
4-chlorobenzoic acid
aTechniques: T ) transpiration; K ) mass loss Knudsen method; C ) Calvet calorimetry with Knudsen cell; DC ) drop Calvet microcalorimetry;
TE ) torsion-effusion method. DSC ) differential scanning calorimetry.bOriginal vapor pressure available in the literature were treated using eqs
2 and 3 in order to evaluate enthalpy of sublimation at 298.15 K in the same way as our own results in Table 2.cEnthalpy of vaporization.
R ln pi
sat) a +b
T+ ∆cr
gCpln(
T
T0)
(2)
∆cr
gHm(T) ) -b + ∆cr
gCpT
(3)
{∆cr
lHm(Tfus/K) - ∆cr
{(0.75 + 0.15Cp
lH°m(298.15 K)}/(J‚mol-1) )
cr)[(Tfus/K) - 298.15]} -
{(10.58 + 0.26Cp
l) [(Tfus/K) - 298.15]} (4)
B
J. Phys. Chem. A
Emel’yanenko et al.

Page 3

chlorobenzoic acids, Cp
standard enthalpy of fusion at T ) 298.15 K, ∆cr
) 20.87 ( 0.28 kJ‚mol-1was calculated (see Table 3) with
this adjustment (the uncertainty of the correlation was not taken
into account). The latter value was used to calculate the enthalpy
of sublimation, ∆cr
acid from the data in ref 9 (see Table 1). The vaporization
enthalpy of 2-chlorobenzoic acid measured by Holdiness10has
also been adjusted to the reference temperature in the same way,
cr, were sourced from ref 18. The
lHm(298.15 K)
gHm(298.15 K), of the solid 2-chlorobenzoic
but his value of sublimation enthalpy is about 20 kJ‚mol-1large
than other values, and we have no explanation for this
discrepancy because of the lack of detail in the experimental
procedure reported in the original publication.10Thus, for
2-chlorobenzoic acid we now have three consistent values of
sublimation enthalpy which are all are very close to a value of
101 kJ‚mol-1(see Table 1). Recently, new data on the vapor
pressures of a series of chlorobenzoic acids have been measured
using the Knudsen method.29Surprisingly, this recent result for
TABLE 2: Results from Measurements of the Vapor Pressure p of Benzoic Acid Derivatives Using the Transpiration Method
Ta/K
mb/mg
VN2c/dm3
4-tert-Butylbenzoic acid; ∆cr
ln(p/Pa) )337.64
gas flow/(dm3/h)
pd/Pa(pexpt- pcalcd)/Pa
∆cr
gHm/kJ‚mol-1
gHm(298.15 K) ) (105.40 ( 0.69)kJ.mol-1
Rln(
4.79
4.7917.63
4.7925.79
4.79 38.46
4.7956.58
4.79 84.08
2-Chlorobenzoic acid; ∆crgHm(298.15 K) ) (101.50 ( 0.36)kJ.mol-1
R
-116576.59
R(T, K)
-37.5
T, K
298.15)
373.0
383.0
387.9
392.6
397.6
402.5
35.0
13.1
12.5
13.2
8.7
28.7
65.76
10.39
6.79
4.79
2.16
4.79
7.49 0.1
0.1
102.59
102.22
102.03
101.86
101.67
101.48
-0.6
0.0
-0.4
1.3
ln(p/Pa) )321.2
R
-108153.2
R(T, K)
-22.3
Rln(
0.85
1.50
2.26
3.80
9.59
18.15
30.95
52.89
81.76
112.7
170.6
258.1
246.4
T, K
298.15)
338.1
344.0
348.0
352.9
362.8
369.9
376.1
382.8
387.8
392.7
397.7
402.6
402.6
13.2
8.0
14.0
18.7
11.9
13.2
13.2
12.7
27.9
14.0
20.1
129.5
26.3
249.83
85.84
98.81
78.75
19.72
11.55
6.77
3.83
5.43
1.97
1.88
7.96
1.70
5.37
5.37
5.37
5.35
5.38
5.41
5.41
5.35
5.35
5.37
5.37
5.37
4.85
0.0
0.0
0.0
0.1
0.1
0.2
0.3
100.71
100.56
100.46
100.33
100.08
99.91
99.75
99.58
99.45
99.33
99.20
99.08
99.08
-0.6
1.7
-5.4
-1.9
8.6
-2.2
3-Chlorobenzoic acid; ∆cr
ln(p/Pa) )318.5
gHm(298.15 K) ) (100.58 ( 0.78)kJ‚mol-1
Rln(
5.14
5.14
5.14
5.14 15.30
5.14 24.46
5.1439.02
5.14 54.81
5.1476.10
5.14 119.1
5.14174.3
5.14257.7
R
-107316.8
R(T, K)
-22.6
T, K
298.15)
348.5
353.6
363.6
368.7
374.1
379.1
384.1
389.1
394.1
399.1
404.1
15.8
16.4
5.0
13.4
18.8
26.7
17.8
12.4
16.7
14.2
21.0
111.35
66.60
8.57
13.80
12.17
10.80
5.14
2.57
2.23
1.29
1.29
2.25
3.91
9.23
-0.1
0.1
-0.4
0.2
0.4
2.5
-0.1
-5.5
-1.1
-0.7
5.3
99.51
99.38
99.13
99.00
98.87
98.74
98.61
98.49
98.36
98.23
98.11
4-Chlorobenzoic acid; ∆cr
ln(p/Pa) )329.4
gHm(298.15 K) ) (107.87 ( 0.80)kJ‚mol-1
Rln(
5.46
5.52
5.46
5.50
5.05
5.05
5.05 11.19
5.50 12.48
5.5017.96
5.5025.88
5.5039.93
5.5038.69
R
-115891.6
R(T, K)
-26.9
T, K
298.15)
358.4
363.2
367.7
368.2
373.2
378.3
382.5
384.3
388.3
393.3
398.1
398.3
24.2
13.4
22.9
14.4
19.6
13.3
14.2
11.3
12.9
11.9
11.5
12.8
334.21
116.77
135.51
77.09
68.12
29.69
20.18
14.29
11.46
7.33
4.58
5.22
1.15
1.82
2.67
3.00
4.61
7.12
0.02
0.01
-0.12
0.07
-0.04
-0.27
0.54
-0.02
0.47
-0.59
0.89
-0.98
106.23
106.11
105.99
105.98
105.85
105.71
105.61
105.56
105.46
105.33
105.20
105.20
aTemperature of saturation.bMass of transferred sample, condensed at T ) 299 K.cVolume of nitrogen, used to transfer mass m of sample.
dVapor pressure at temperature T, calculated from m and the residual vapor pressure at the cooling temperature T ) 299 K.
Enthalpies of Formation and Strain
J. Phys. Chem. A C

Page 4

2-chlorobenzoic acid ∆cr
kJ‚mol-1(see Table 1) is in substantial disagreement with the
average of 101 kJ‚mol-1discussed above. We compared the
data for the temperature dependence of vapor pressure derived
in this work with those measured in ref 29. High-temperature
ranges of the both studies are almost overlapping, and the vapor
pressures in this region are in very good agreement. However,
the vapor pressures at lower temperatures from ref 29 have a
different trend, which is the cause of the disagreement in the
sublimation enthalpies. Taking into account, that vapor mea-
surements from this work covers temperature range which is
three times larger than that in ref 29, our value of ∆cr
(298.15 K) for 2-chlorobenzoic acid seems to be more reliable.
Furthermore, the measurements in this work are in good
agreement with the two other values reported in the literature.9,11
The value of ∆cr
obtained in this work is in good agreement with those from
Adedeji et al.9and those from Sabbah and Hirtz,11and Ribeiro
da Silva et al.29(see Table 1).
The values of ∆cr
not in very good agreement with the data reported by Adedeji
et al.9and Ribeiro da Silva et al.29but are still within acceptable
limits. The disagreement of our result with those from Sabbah
and Hirtz11is over 5 kJ‚mol-1and cannot be explained.
Experimental measurement of the sublimation enthalpies of
the three isomeric chlorobenzoic acids are reported by Wolf
and Weghofer8from the torsion-effusion method. As can be
seen in Table 1, their values are generally 20 kJ‚mol-1lower
than data from other sources. This method is considered the
most reliable for vapor pressure measurements, hence we
postulate that in fact the vaporization enthalpies of chlorobenzoic
acids were measured in the work of Wolf and Weghofer and
are erroneously denoted sublimation enthalpies. If this sugges-
tion is indeed true, then the values reported by Wolf and
Weghofer8are in good agreement with the vaporization enthal-
pies of chlorobenzoic acids reported in this work (Table 3,
column 6).
Enthalpies of Vaporization. ∆lgHm. The scatter of the
available experimental results on sublimation enthalpies for 2-
and 4-chlorobenzoic acids, described above, has made it
necessary to analyze the vaporization enthalpies of these
compounds in order to further validate results obtained in this
work. Indeed, experimental values of sublimation enthalpies,
∆cr
comparison, because each enthalpy of sublimation consists from
two contributions: the enthalpy of vaporization, ∆l
enthalpy of fusion, ∆cr
tion, in most cases readily obey the additive rules,22or are able
to demonstrate some general regularities, especially for ortho-,
meta-, and para-substituted benzenes.23,24Thus, a valuable test
of the consistency of the experimental data presented in this
gHm(298.15 K) ) ) 105.8 ( 0.4
gHm-
gHm (298.15 K) for 3-chlorobenzoic acid
gHm(298.15 K) for 4-chlorobenzoic acid is
gHm, hardly lend themselves for further interpretation or
gHm, and
lHm. In contrast, enthalpies of vaporiza-
work on sublimation enthalpies of chlorobenzoic acids, is the
comparison of their vaporization enthalpies. The latter values
were calculated from difference ∆cr
in Table 3. We used the experimental enthalpies of fusion
∆cr
consistent with the earlier measurements reported in the ref 18)
and adjusted them to T ) 298.15 K according to eq 4.
It is obvious, from Table 3, that the vaporization enthalpies
of 3- and 4-chlorobenzoic acids are indistinguishable within the
boundaries of their experimental uncertainties. Such behavior
is typical for most of meta- and para-substituted benzenes.23
The vaporization enthalpy of o-chlorobenzoic acid is about
5 kJ‚mol-1lower than those of meta- and para-isomers, and
this diminishment is quite apparent because of the lower packing
order in the liquids due to the steric hindrance caused by the
repulsion between chloro and carboxylic groups. A similar
pattern is exhibited by methyl derivatives of benzoic acids,
which can be seen from the highly reliable thermodynamic data
reported in Table 3.5Indeed, the spatial requirements of chloro-
and methyl-group are very similar, following enthalpies of
vaporization of ortho-, meta-, and para-isomers of chlorobenzoic
acids and methylbenzoic acids should be very close. The data
on vaporization enthalpies of these benzoic acid derivatives
presented in Table 3 validate this hypothesis. Thus, the values
for the vaporization enthalpies of benzoic acid derivatives
taken for comparison possess internal consistency, subsequently
the values of the sublimation enthalpies of chlorobenzoic acids
measured in this work (see Table 2) could be used further
for the calculation of the standard enthalpies of formation,
∆fH°m(g), of these compounds.
Calculation of the Gaseous Enthalpies of Formation.
Combustion enthalpies of the chlorobenzoic acids have been
reported by numerous investigators.2-4,7Most measurements
have been performed on 4-chlorobenzoic acid, which is now
accepted as a suitable reference compound for the combustion
enthalpies of chloro-containing compounds.4,7The enthalpies
of formation, ∆fH°m(cr) at 298.15 K, derived from the combus-
tion results are very consistent and we selected the following
recently published values for the calculation of the gaseous
enthalpy of formation: 2-chlorobenzoic acid11∆fH°m(cr) )
(-405.1 ( 0.5) kJ‚mol-1; 3-chlorobenzoic acid11∆fHm°(cr) )
(-423.2 ( 0.8) kJ‚mol-1; and 4-chlorobenzoic acid4∆fHm°(cr)
) (-429.9 ( 2.2) kJ‚mol-1. Furthermore, for the estimation
of the gaseous enthalpy of formation of chlorobenzoic acids,
we used values ∆cr
that are listed in Table 2. The calculated values of the standard
molar enthalpies of formation ∆fH°m(g) of chlorobenzoic acids
are given in the last column in Table 5.
Quantum Chemical Calculations for Chlorobenzoic Acids.
Results of ab initio molecular orbital methods for calculation
of the enthalpy of formation of chlorobenzoic acids have not
gH°m- ∆cr
lHmand presented
lHmavailable in the literature11(these values are generally
gHm(298.15 K) derived in the present study
TABLE 3: Compilation of Experimental Data on Enthalpies of Fusion ∆cr
∆cr
∆cr
Tfus/kJ‚mol-1
2-methylbenzoic acid20.1718
3-methylbenzoic acid15.7318
4-methylbenzoic acid 22.7218
2-chlorobenzoic acid26.29 ( 0.2811
3-chlorobenzoic acid 22.00 ( 0.3311
4-chlorobenzoic acid34.26 ( 0.1711
lHm, Enthalpies of Sublimation
gHm, and Calculated Enthalpies of Vaporization ∆l
gHmof Methyl- and Chlorobenzoic Acids
compound
lHmat
Tfus/K
376.9
381.9
452.8
414.10
427.83
513.53
∆crlHmaat
298.15 K/kJ‚mol-1
16.55
11.73
15.47
20.87 ( 0.28
15.95 ( 0.33
24.35 ( 0.17
∆cr
gHmat
298.15 K/kJ‚mol-1
95.9 ( 0.15
97.0 ( 0.35
98.8 ( 0.35
101.5 ( 0.4
100.6 ( 0.8
107.9 ( 0.8
∆l
gHmbat
298.15 K/kJ‚mol-1
79.3 ( 0.1
85.3 ( 0.3
83.3 ( 0.3
80.6 ( 0.5
84.7 ( 0.8
83.6 ( 0.8
aThe experimental enthalpies of fusion ∆cr
calculated as the difference ∆cr
lHm measured at Tfus and adjusted to 298.15 K (see text).bThe enthalpy of vaporization ∆l
gHm(from column 5) and ∆cr
gHm,
lHm(from column 4).
D
J. Phys. Chem. A
Emel’yanenko et al.

Page 5

been yet reported in the literature. In standard Gaussian-n
theories, theoretical enthalpies of formation are calculated
through atomization reactions.25Raghavachari et al.,26have
proposed the use of a set of isodesmic reactions, the “bond
separation reactions”, to derive theoretical enthalpies of forma-
tion. Isodesmic reactions conserve the number of types of bonds
and should thus be an improvement on simple atomization
reactions. Further enhancement in the calculation of enthalpies
of formation should be provided by homodesmic reactions,
which, in addition to the types of bonds, also conserve the
hybridization of the atoms in the bond. We have calculated the
enthalpies of formation of chlorobenzoic acids with help from
both standard atomization reactions as well as homodesmic
reactions. For the latter method, we have chosen the following
three reactions:
Using enthalpies of these reactions calculated by G3(MP2) and
enthalpies of formation ∆fH°m(g), for benzene, chlorobenzene,
and benzoic acid recommended by Pedley et al.24enthalpies of
formation of all three isomeric chlorobenzoic acids have been
calculated (see Table 5) and they are in excellent agreement
with the experimental values derived in this work. Enthalpies
of formation of chlorobenzoic acids derived with help of the
atomization procedure are systematically (about 10 kJ‚mol-1)
more negative than the experimental results.
Strain in Chlorobenzoic acids. Conventional strain-enthal-
pies could be derived as the differences between the observed
enthalpies of formation in the gaseous state and values calculated
by application of group-additivity schemes.27,28However,
especially for the benzene derivatives their strain is more
convenient to determine as the enthalpy of a distribution reaction
which is in general the same as reactions 5-7 mentioned above.
In this case, a sum of bricks (or additive groups) on the left
and on the right side of reaction remains constant and the
enthalpy of such a reaction expresses only the mutual interaction
of substituents on the benzene ring. For instance, from the
enthalpy of reaction 5, one can distinguish the strain of
2-chlorobenzoic acid in comparison with benzene, chloroben-
zene, and benzoic acid, or in other words, this strain is caused
by steric interactions of the chloro and carboxylic substituents.
As can be seen in Figure 1, the carboxylic group in 2-chlo-
robenzoic acid is forced to take a position out of the plane of
the benzene ring with a distance of 3.01 Å between chlorine
and oxygen atoms. This distance would be only 2.85 Å if there
was coplanar positioning of the carboxylic relative to the
benzene ring, but during geometry optimization procedures the
carboxylic group prefers the out-of plane position in order to
avoid steric repulsions. In contrast, (see Figures 2 and 3) the
carboxylic group in 3- and 4-chlorobenzoic acid is coplanar with
the benzene ring, and such a position is more preferable for the
conjugation of π-electrons of benzene ring with electrons of
carboxylic group and these two molecules, in the absence of
the steric effects, are expected to exhibit only weak destabiliza-
tion. We calculated the strain in chlorobenzoic acids with help
of reactions 5-7 and using experimental enthalpies of formation,
∆fH°m(g), of the reaction participants. These calculations (see
Table 6) reveal that 2-chlorobenzoic acid is profoundly desta-
bilized by about 20 kJ‚mol-1due to steric reasons. A weak
destabilization of about 2 kJ‚mol-1in 3- and 4-chlorobenzoic
acid is apparently due to the electron redistribution in the
benzene ring on substitution.
A substantial advantage of ab initio calculations toward
benzene derivatives is that this method allows for the calcula-
tions of such interactions (or strain) directly from enthal-
TABLE 4: G3(MP2) Total Energies at 0 K and Enthalpies
at 298.15 K (in hartree) of the Molecules Studied in This
Work
G3(MP2)
compounds
2-chlorobenzoic acid
3-chlorobenzoic acid
4-chlorobenzoic acid
benzoic acid
chlorobenzene
benzene
-E0
-H298
879.346429
879.353033
879.353741
420.192542
690.986059
231.824309
879.355008
879.362481
879.363190
420.200783
690.992623
231.829758
TABLE 5: Results of Calculation of the Standard Enthalpy
of Formation ∆fH°m(g) for ChloroBenzoic Acids in the
Gaseous Phase at 298.15 K in KJ‚mol-1
G3(MP2)
homodesmic
-303.9
-321.3
-323.2
compounds
2-chlorobenzoic acid
3-chlorobenzoic acid
4-chlorobenzoic acid
atomization
-314.6
-331.9
-333.8
experimental
-303.6 ( 0.6
-322.6 ( 1.1
-322.0 ( 2.3
2-chlorobenzoic acid + benzene f
benzoic acid + chlorobenzene (5)
3-chlorobenzoic acid + benzene f
benzoic acid + chlorobenzene (6)
4-chlorobenzoic acid + benzene f
benzoic acid + chlorobenzene (7)
Figure 1. Optimimized structure of 2-chlorobenzoic acid.
Figure 2. Optimimized structure of 3-chlorobenzoic acid.
Figure 3. Optimimized structure of 4-chlorobenzoic acid.
Enthalpies of Formation and Strain
J. Phys. Chem. A E