Thermochemical study of the liquid phase equilibrium reaction of dihalomethanes by NMR spectroscopy

Article abstract of DOI:10.1016/j.cplett.2005.05.016

The liquid phase equilibrium reaction of dihalomethanes (2CH₂BrI ? CH₂Br₂ + CH₂I₂) has been investigated by NMR spectroscopy, as a function of the temperature and initial concentration of the reactants. The equilibrium constants have been experimentally determined for this reaction from the profile of the NMR spectra. Heat capacity measurements were carried out in the temperature range from 293.15 to 353.15 K by differential scanning calorimetry. The results relate the heats of formation of the three compounds and confirm the recently determined heat of formation of CH₂I₂ of 107.5 kJ mol^-1.

Full text of DOI:10.1016/j.cplett.2005.05.016

Chemical Physics Letters 409 (2005) 230–234
www.elsevier.com/locate/cplett
Thermochemical study of the liquid phase equilibrium reaction of
dihalomethanes by NMR spectroscopy
a,b
J.Z. D a´ valos , A.F. Lago a,*, Tomas Baer a
a
Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, USA
b
Instituto de Quimica-Fisica ꢀRocasolanoꢁ, CSIC, Serrano 119, 28006 Madrid, Spain
Received 15 April 2005; in final form 3 May 2005
Available online 3 June 2005
Abstract
The liquid phase equilibrium reaction of dihalomethanes (2CH
2
2 2 2 2
BrI ¢ CH Br + CH I ) has been investigated by NMR spec-
troscopy, as a function of the temperature and initial concentration of the reactants. The equilibrium constants have been experi-
mentally determined for this reaction from the profile of the NMR spectra. Heat capacity measurements were carried out in the
temperature range from 293.15 to 353.15 K by differential scanning calorimetry. The results relate the heats of formation of the three
ꢀ
1
compounds and confirm the recently determined heat of formation of CH
2005 Elsevier B.V. All rights reserved.
2 2
I of 107.5 kJ mol .
ꢀ
1
. Introduction
ous literature values were 117.6 ± 8.3 [6] and
ꢀ
1
19.5 ± 2.2 kJ mol [7].
The present work was undertaking to check the self
1
The investigation of the thermochemistry of haloge-
nated compounds have recently attracted increasing
interest. Halomethane compounds have been found in
different environmental media, and are now known to
represent an important source of reactive halogens in
the oceans as well as in the atmosphere [1–3].
consistency of the TPEPICO study by investigating
the equilibrium of the disproportionation reaction
(2CH BrI ¢ CH Br + CH I ). This was carried out
2
2
2
2 2
by equilibrating initial concentration mixtures in solu-
tion at various temperatures and analyzing the concen-
trations by NMR spectroscopy as a function of the
reaction time. In order to determine the standard enthal-
Very limited experimental results on the thermochem-
istry of halomethanes in solution are available in the lit-
erature, due in part to the difficulty in obtaining
accurate heats of formation for these compounds via
standard calorimetric techniques. The gas phase thermo-
chemistry of halomethanes, on the other hand, has been
the object of recent experimental [4] and theoretical [5]
investigations. The experimental study by threshold
photoelectron photoion coincidence (TPEPICO) spec-
troscopy [4] suggested that the heat of formation of
0
py of reaction (T = 298.15 K) we have also employed
differential scanning calorimetry (d.s.c) experiments to
measure reliable solution phase heat capacities for each
species in a range of temperatures.
2. Experimental
ꢀ
1
CH I should be reduced to 107.5 ± 2.9 kJ mol . Previ-
2
2.1. Materials
2
The high purity (>98%) dihalomethane reactants
(CH Br , CH I , CH BrI), (CH ) NI as catalyst, and
*
Corresponding author. Fax: +1 919 962 2388.
E-mail address: lago@email.unc.edu (A.F. Lago).
2
2
2 2
2
3 4
NMR-grade solvent, acetonitrile-d3 (CD CN), were
3
0
009-2614/$ - see front matter ꢀ 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2005.05.016

J.Z. D a´ valos et al. / Chemical Physics Letters 409 (2005) 230–234
231
purchased from Sigma–Aldrich and used without fur-
ther purification.
2
.2. Reaction of equilibrium monitoring by NMR
1
The H NMR spectroscopy was employed in the
investigation of the liquid phase equilibrium reaction
of diluted (ꢁ5%) dihalomethanes in CD CN solvent,
3
and (CH ) NI as catalyst, over the temperature range
3
4
from 338 to 353 K. A Bruker Avance 400 MHz wide
bore magnet QNP instrument was used for obtaining
1
H NMR spectra. The error affecting the areas of the
NMR peaks is estimated to be less than 1% [8].
Two mixtures of liquid solutions were prepared and
placed into sealed NMR Pyrex cells in approximately
1
Fig. 1. H NMR spectra for CH
CD
2
Br
2
(1), CH
2
I
2
(2), CH BrI (3) in
2
3
CN solution at t = 0 h (a) at non-equilibrium condition, and at
t = 56 h (b) after reaching equilibrium at T = 338.15 K.
1
:3:1 and 2:3:3 (CH Br , CH BrI, and CH2I2, respec-
2
2
2
tively) concentration ratios. The cells were placed in a
glycerin bath and maintained at temperatures constant
to within ±0.2 K. The cells were removed from bath
and quenched in cooled water for several minutes before
each NMR measurement. Measurements were per-
formed at different temperatures, T = 338.15, 343.15,
0.7
T = 338.15 K
Keq = 0.449
0.6
0.5
0.4
0.3
3
48.15 and 353.15 K. This temperature range was dic-
tated by the very slow rate of halogen atom exchange
at low temperatures, and the boiling point of the solu-
tion at high temperatures.
cr
A differential scanning calorimeter (d.s.c.), Perkin–
Elmer DSC-2C, was used to determine the heat capacity
values in the range from 293.15 to 353.15 K, using a
ꢀ
1
0.2
heating rate of 0.17 K s , and with a sensitivity of
.008 W at full scale. The accuracy of the molar heat
capacities was estimated between 1% and 2% [9].
0
0.1
0
5
10
15
20
25
30
35
40
45
50
55
60
t, h
3
. Results and discussion
Fig. 2. Evolution of concentration ratio (cr) of reaction (1) at
T = 338.15 K.
The equilibrium reaction for these dihalomethanes in
solution is described in Eq. (1). The corresponding equi-
The concentration of each species was taken as pro-
portional to the intensity of its corresponding NMR
peak area (I , x = 1[CH Br ], 2[CH I ], 3[CH BrI]),
librium constant (K ) have been determined in the usual
eq
way (Eq. (2)). This reaction takes place in a dilute and
homogeneous liquid medium, so that the solution has
properties that resemble those obtained for infinitely di-
lute solutions.
x
2
2
2 2
2
which in turn is proportional to the number of the cor-
responding protons (i.e., protons with same NMR
chemical environments) in the solution [10]. Fig. 1 shows
1
typical H NMR spectra for the dihalomethanes studied
in CD CN solution.
2
CH
2
BrI ¢ CH
2
Br
2
þ CH
2
I
2
K
eq; D
r
H
m
ðlÞ
ð1Þ
ð2Þ
3
½
CH
2
Br
2
ꢂ ꢃ ½CH
2
I
2
ꢂ
I
1
ꢃ I
2
The evolution of the concentration ratio (cr) of
I ꢃI
K
eq
¼
¼
.
2
2
3
1
2
½
CH
2
BrIꢂ
I
reaction (1), given by: cr ¼
2
3
, was examined for two
I
Table 1
Average value of Keq obtained from the cr curves for each temperature studied
T (K)
338.15
343.15
348.15
353.15
K
eq
0.449 (0.006)
0.444 (0.005)
0.441 (0.006)
0.438 (0.005)
Values between parentheses correspond to the uncertainties obtained from fit cr-curves.

232
J.Z. D a´ valos et al. / Chemical Physics Letters 409 (2005) 230–234
-5.8
-6.0
-6.2
-6.4
-6.6
-6.8
145
140
135
130
125
slope = 1.6
=0.14)
(
ε
CH2I2
2
r =0.99, sd=0.55
K
-7.0
-7.2
CH BrI
2
ln
120
R
2
r =0.918, sd=0.35
<
T>=345.65 K
115
-
7.4
7.6
CH Br
2
2
-
110
105
2
r =0.986, sd=0.16
2.80 2.82 2.84 2.86 2.88 2.90 2.92 2.94 2.96 2.98
3
290
300
310
320
330
340
350
360
1
0 /(T/K)
T(K)
3
Fig. 3. Plot of R Æ ln Keq versus 10 /T.
Fig. 4. Experimental heat capacities for each dihalomethane in liquid
phase, Cp,m(l,T) fitted to polynomial functions.
different mixtures of halomethanes, starting with ratios
of approximately cr = 0.1 and 0.7. A typical example
of such study is presented in Fig. 2. It is clear from
Fig. 2 that the same equilibrium concentration is
reached in both cases after about 60 h of reaction. Fur-
thermore, these experiments provide Keq as the limiting
value for the fitting of the cr curves (fitted with
r > 0.98). The experimental data are presented in Table
1, where the average values of Keq have been obtained at
different temperatures.
experimental range of temperatures is D H
=
m,345.65
r
ꢀ
1
(
ꢀ1.6 ± 0.3) kJ mol . It has been calculated from the
corresponding slope taken from the linear fitting of the
data. The uncertainty assigned to the D H value
r
m,345.65 K
was calculated from the error e of the corresponding
slope. The constant term in the linear fit equation can be
considered as the entropy at the mean tempera-
2
ꢀ1
ꢀ1
ture DSr,345.65 K = ꢀ11.4 J K mol , which matches
with the expected statistical entropy term, R Æ ln(0.25) =
ꢀ
1
11.53 kJ mol , for this exchange reaction. The origin
ꢀ
The molar Gibbs energy (D G ) and molar enthalpy
r
m
of this term lies in the rotational symmetry numbers of
reactants and products, which are 2 for the di-bromo
and di-iodo methanes, but only 1 for the mixed
compound.
(D H ), for reaction (1), can be calculated by using the
r m
well-known thermodynamic relations
D
r
G
m;T ¼ ꢀR ꢃ T ꢃ ln Keq
;
ð3Þ
ð4Þ
and
The value for the enthalpy of reaction (1) at the stan-
0
dard temperature (T = 298.15 K) was computed from
d ln Keq
dð1=TÞ
D H
¼ ꢀR ꢃ
.
Kirchoffꢁs Eq. (5) [11]
r
m;T
Z
2
98.15 K
3
0
m
The plot of R Æ ln Keq versus 10 /T values is represen-
ted in Fig. 3. The linear fitting is represented by equation:
R Æ ln Keq = 1.6 Æ (10 /T)ꢀ11.4 (J K mol ) (r = 0.986,
s.d. = 0.013). The molar enthalpy for reaction (1) ob-
tained at the mean temperature (ÆTæ = 345.65 K) of the
D H ðlÞ ¼ D H
þ
DCp;mðl; TÞdT; ð5Þ
r
r
m;345.65 K
3
45
.
65 K
3
ꢀ1
ꢀ1
2
where Cp,m(l,T) corresponds to the experimental heat
capacity curves obtained from the d.s.c. measurements
(Fig. 4).
Table 2
Parameters of polynomial-fit functions for the heat capacities
2
ꢀ1 ꢀ1
0
p;m
a
ꢀ1
ꢀ1Þ
Dihalomethane
C
p,m(l,T) = a + b Æ T + c Æ T (J mol
K
)
C
ðlÞ ðJ mol
K
(
293.15 6 T 6 353.15) K
a
b
c
This work
From NIST Database [12]
ꢀ
ꢀ
ꢀ
3
3
4
b
104.1 ± 0.2 105.3
c
CH
2
2
2
Br
2
235.04
273.77
109.23
ꢀ0.865
ꢀ1.188
ꢀ0.029
1.45 · 10
2.3 · 10
1.46 · 10
106.0 ± 2.1
123.7 ± 2.5
113.3 ± 2.3
b
112.8 ± 0.2 133.8
d
CH
I
2
CH
BrI
–
a
b
c
Experimental value at T = 298.15 K.
Shehatta [13] determined these values using a micro drop heat-capacity calorimeter.
Harrison and Moelwyn-Hughes [14].
Carson et al. [15] reported this value as specific heat capacity.
d

J.Z. D a´ valos et al. / Chemical Physics Letters 409 (2005) 230–234
233
The experimental values of Cp,m(l,T) were fitted by
quadratic polynomial functions using the least-squares
method. Table 2 shows the parameters from those fit-
in agreement within the uncertainty limits. In addition,
the results obtained in this work also confirm the consis-
0
tency of the gas phase D
et al. [4]. The only condensed phase heat of formation
value found in the thermochemical tables from the liter-
f
H ðgÞ values reported by Lago
m
tings and also the available experimental standard
0
p;m
C
ðlÞ values. It is noteworthy to mention that the
0
Cp,m(l,T) values for CH BrI were not available in the lit-
2
ature is the one for CH I , D
f
H ðlÞ ¼ 68.5 ꢄ 0.8 [7].
2 2
m
erature, and were determined for the first time in the
present work. In addition, we also should point out that
the measured heat capacities for CH I at T = 298.15 K
This can be compared to a value obtained by subtracting
the heat of vaporization from Lagoꢁs. [4] gas phase value
of 107.5 kJ/mol. Depending on the value of the vapori-
zation energy used (see Table 3), we obtain 55.3 and
61.9 kJ/mol. Both of these values are lower than the
68.5 kJ/mol, but the experimental heat of vaporization
gives a better agreement.
2
2
is significantly different from those found in the litera-
ture (see Table 2). On the other hand, the literature
value of Cp,m(l,T) for the CH Br is in agreement with
2
2
our measured value. The contribution of the last term
in Eq. (5) was evaluated, and found to be
ꢀ
1
ꢀ
0.34 kJ mol . Thus, the value of enthalpy of reaction
1) in solution, determined using this procedure is,
(
4. Conclusions
0
ꢀ1
D H ðlÞ ¼ ꢀ1.9 ꢄ 0.3 kJ mol .
r
m
By taking into account the equilibrium constant K
eq
The equilibrium reaction (2CH BrI ¢ CH Br +
2
2
2
or the molar Gibbs energy and enthalpy values for reac-
tion (1), we conclude that in this reaction the negative
entropy terms dominates over the negative enthalpy
term.
CH I ) has been studied by using NMR spectroscopy
2
2
to determine the equilibrium concentrations. Equilib-
rium constants have been obtained from the profile of
the NMR spectra and the heat capacities were deter-
mined for each dihalomethanes from d.s.c. experiments.
The calculation of the reaction enthalpy in the gas
0
0
m
phase, D H ðgÞ from D H ðlÞ requires a knowledge of
r
m
r
The heat capacity of CH BrI has been experimentally
2
0
m
the enthalpy of vaporization ðD H Þ for each species.
v
measured for the first time in this work. The results
for the equilibrium constant Keq (ꢁ0.44) and the molar
Gibbs energy suggest that the reaction among dihalome-
thanes (2CH BrI ¢ CH Br + CH I ) is dominated by
We list both experimental and estimated values in Table
0
3
. In order to estimate D
v
H
we have used the Wadso¨
m
0
equation [16]: D
v
H
¼ 20.92 þ 0.172 ꢃ ðT bp ꢀ 273Þ (in
m
2
2
2
2 2
ꢀ
1
kJ mol ), where Tbp is the normal boiling point. We
also used the following literature values for
Tbp = 370.15, 412.15 and 455.15 K for CH Br , CH BrI
entropy effects. The heats of vaporization of the three
compounds are such that the solution phase heat of
reaction should be equal to the gas phase heat of reac-
tion. The heat of reaction derived in the present work,
2
2
2
and CH I , respectively. It is found that the total contri-
2
2
0
m
0
m
ꢀ
1
bution of D H to the change in the enthalpy of the
v
D H ¼ ꢀ1.9 ꢄ 0.9 kJ mol , agrees within experimen-
r
0
m
ꢀ1
ꢀ1
reaction studied is DðD
v
H Þ ¼ 0 ꢄ 0.8 kJ mol . Thus,
tal error to the value derived from the measured gas
phase heats of formation in a recent PEPICO experi-
ment, D H ¼ 0.7 ꢄ 3.7 kJ molꢀ [4].
0
m
the value of D
r
H ðgÞ is ꢀ1.9 ± 0.9 kJ mol . The
0
m
0
1
derived D
r
H ðgÞ can be compared to the value obtained
r
m
0
from the standard enthalpy of formation D
f
H ðgÞ for
m
each species (shown in Table 3), recently obtained by
Lago et al. [4] from gas phase dissociative photoioniza-
tion experiments. The value obtained by this way is
Acknowledgements
0
ꢀ1
D H ðgÞ ¼ 0.7 ꢄ 3.7 kJ mol . These results show that
r
m
The authors thank the US Department of Energy for
support this work and also the Thermochemistry group
from IQFR (Madrid) for d.s.c. measurements. A.F.
Lago gratefully acknowledges the post-doctoral fellow-
ship from CNPq-Brazil, and J.Z. D a´ valos acknowledges
the Ministerio de Educaci o´ n, Cultura y Deporte of
Spain for the PR2004-0031 Grant.
0
the values of D
r
H
determined by the two methods are
m
Table 3
0
m
Standard molar enthalpies of formation D
f
H ðgÞ and vaporization
0
m
D
v
H
for dihalomethanes
CH
2
Br
2
CH
2
BrI
2 2
CH I
0
m
0
a
b
b
b
d
Df H ðgÞ
3.2 ± 3.4
c
55.0 ± 3.4
c
107.5 ± 4.5
c
52.2
45.6 ± 0.6
a
DvH
37.6
6.97 ± 0.10
44.9
41.2
m
d
e
3
a
ꢀ1
.
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In kJ mol
b
c
Values taken from [4].
Value estimated from Wads o¨ ꢁs equation [16].
Experimental values taken from NIST Standard Reference Data-
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2
2
2 2
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