Precise equilibrium constants from spectrophotometric data: BrCl in Br2/Cl2 gas mixtures

Article abstract of DOI:10.1021/jp027227w

The equilibrium constant for the reaction, Br₂(g) + Cl₂(g), ? BrCl(g). is estimated using the classic spectrophotometric method with precise data and a multispectrum fitting approach. Analysis of spectra for 18 Cl₂:Br₂ mixing ratios yields K° = 9/1 at 22°C, with a nominal statistical error (1 σ) of 0.04. This error translates into a remarkable precision of 0.4 cm^-1 in the dissociation energy of BrCl, easily beating that for the current best spectroscopic estimate (±5 cm^-1). However, a sensitivity analysis shows that K° is susceptible to small systematic errors and minor changes in the least-squares fit model, leading to a more conservative estimate of 2% error. The derived K° is consistent with statistical mechanical estimates that employ the current value for the BrCl dissociation energy, but it differs considerably from some recently measured and used values, which range from 6.4 to 10.4. The revised estimate of the BrCl dissociation energy is D_e = 18 248 ± 2 cm^-1.

Full text of DOI:10.1021/jp027227w

J. Phys. Chem. A 2003, 107, 753-757
753
Precise Equilibrium Constants from Spectrophotometric Data: BrCl in Br2/Cl2
Gas Mixtures
Joel Tellinghuisen
Department of Chemistry, Vanderbilt UniVersity, NashVille, Tennessee 37235
ReceiVed: October 16, 2002; In Final Form: NoVember 15, 2002
The equilibrium constant for the reaction, Br2(g) + Cl2(g) a BrCl(g), is estimated using the classic
spectrophotometric method with precise data and a multispectrum fitting approach. Analysis of spectra for
18 Cl2:Br2 mixing ratios yields K° ) 9.1 at 22 °C, with a nominal statistical error (1 σ) of 0.04. This error
translates into a remarkable precision of 0.4 cm-1 in the dissociation energy of BrCl, easily beating that for
the current best spectroscopic estimate ((5 cm-1). However, a sensitivity analysis shows that K° is susceptible
to small systematic errors and minor changes in the least-squares fit model, leading to a more conservative
estimate of 2% error. The derived K° is consistent with statistical mechanical estimates that employ the current
value for the BrCl dissociation energy, but it differs considerably from some recently measured and used
values, which range from 6.4 to 10.4. The revised estimate of the BrCl dissociation energy is De ) 18 248
( 2 cm-1.
Introduction
sociation in I2 and Br2;10 while this is highly likely, it is not
certain. (ii) A preliminary attempt to reanalyze the data of Maric
The diatomic interhalogens are formed readily in the gas
phase reaction
et al.1 by a multispectrum fitting method suggested that such
an approach should be capable of yielding K° with a precision
better than 1%.11 This corresponds to an uncertainty of <1 cm-1
in De, which rivals direct spectroscopic methods and constitutes
a remarkable testament to the power of modern data analysis
methods in what is essentially a thermochemical determination.
(iii) At the same time, the least-squares (LS) analysis was highly
sensitive to small changes in assumptions, including changes
in the weighting algorithm for the different spectra. If the full
potential of such an approach is to be realized, a better
understanding of the role of systematic errors is desirable.
The present study was undertaken to address these issues.
Absorption spectra of Cl2/Br2 gas mixtures have been recorded
with high precision at room temperature, over the spectral region
of 190-650 nm. The data have been analyzed by a nonlinear
LS multispectrum fitting model, which has been varied exten-
sively in trial-and-error fashion to examine the model error. The
results support the statistical mechanical estimate of K°, confirm
the great potential precision of the method, and characterize
quantitatively the sensitivity to a number of possible systematic
errors.
X2(g) + Y2(g) a 2 XY(g)
(1)
In all cases, this reaction favors the product interhalogen, but
the tendency is weakest for BrCl, where K° is only ∼10. Thus,
appreciable amounts of Br2 and/or Cl2 are always present along
with BrCl for any mixing ratio of the parent gases. Because all
three species absorb light in the UV-visible spectral region,
spectrophotometry has been the method of choice for determin-
ing K° and the absorption cross-section of BrCl(g). In a modern
reexamination of this problem, Maric et al.1 recorded spectra
at a dozen different Cl2:Br2 mixing rations, from 1:4 to 31:1,
and obtained K° ) 10.1 ( 1.1 at 25 °C. They also reviewed
earlier work in detail and, noting that their K° value was the
largest yet obtained, suggested that further work was desirable.
At least two subsequent determinations have appeared, but they
have hardly settled the issue: Cooper et al.2 obtained 7.0 ( 0.3
and Bartlett and Margerum3 estimated 10.4 ( 0.4. For reference,
two widely used tabulations of thermodynamics data yield 6.864
and 7.695 for K° at 25 °C.
Recently, I pointed out that the accuracy and precision of K°
are limited by a single uncertain spectroscopic parameter, the
dissociation energy of BrCl.6 Using the most recent assessment
of this quantity (De ) 18 247 ( 5 cm-1),7 from analysis of
predissociation data8 for υ ) 6 in the B state of BrCl, I obtained
K° ) 8.95 ( 0.5. The 6% uncertainty in K° comes entirely from
the uncertainty in De, which resulted from the need to estimate
a large centrifugal barrier in the predissociating state. Other
predissociation data, for υ′ ) 7,8,9 limit De to a maximum value
of 18 253 cm-1 and K° to values <9.6.
While the spectroscopic data might seem to settle this issue,
there are reasons why further pursuit of the spectrophotometric
approach is worthwhile: (i) The determination of De in ref 7
rested on the assumption that the predissociating state was the
1Π analogue of the states responsible for spontaneous predis-
Experiment Section
Absorption spectra of Cl2, Br2, and mixtures of the two
ranging from 8:1 to 1:3 Cl2:Br2 were recorded at a resolution
and interval of 1 nm on a Shimadzu UV-2101PC UV-visible
spectrophotometer, using a 1.0 cm quartz cuvette and a 9.71
cm ((0.01 cm) quartz cell equipped with Suprasil windows.
No check was made of the photometric accuracy, which is stated
as (0.004 at A ) 1 by the manufacturer. The cells were attached
to a vacuum line (∼1 mTorr minimum pressures1 Torr ≈ 133
Pa) for direct pressure measurement with a quartz bourdon gauge
(Texas Instruments), which was calibrated against a mercury
manometer. The sensitivity and precision of the pressure
measurements was ∼0.01 Torr, and the absolute accuracy (from
the calibration) was estimated to be ∼0.1% for P > 10 Torr.
10.1021/jp027227w CCC: $25.00 © 2003 American Chemical Society
Published on Web 01/14/2003

754 J. Phys. Chem. A, Vol. 107, No. 5, 2003
Tellinghuisen
TABLE 1: Cl2/Br2 Mixtures and Pressures for Recorded
Spectra
minute initially. On further expansion into the cuvette (which
involved another 20% drop in P), the rate of decline dropped
sharply. This behavior is tentatively attributed to adsorption of
the gas on the walls of the system (including the bourdon gage).
Similar behavior was observed for pure Br2 but not for Cl2,
and it seemed stronger for the Br-rich mixtures. Thus, it is
possible that this adsorption involves Br2 (and perhaps BrCl)
preferentially, which makes it a potential source of systematic
error. The effect on the mixing ratios is at most ∼1%; however,
the LS analysis fails to substantiate this problem (see below).
Absorption spectra of gases at low P deviate negatively from
Beer’s law in regions of discrete (line) absorption. For the
present study, the main problem in this respect is the Br2
absorption, which shows such deviations for λ > 510 nm.12 For
the determination of the equilibrium constant K°, only data for
λ < 510 nm were used. To obtain reliable low-resolution spectra
for BrCl in the region λ > 510 nm, spectra of Br2 and of several
of the mixtures were recorded with admixture of ∼700 Torr
N2, using the long path cell (where the halogen concentrations
were low).
Spectral Fitting Method. Because reaction 1 conserves
molecules, the molar absorptivity ꢀλ for any mixture can be
obtained as a function of wavelength from the measured
absorbance Aλ using the Beer’s law definition, Aλ ) ꢀλcl, where
c is the concentration and l is the path length. The absorbance
is the usual base 10 logarithm of the reciprocal transmittance,
A ) log (I0/I). For any mixture at any wavelength, the
absorptivity of the mix can be represented as a weighted average
of the contributions from the three species:
P range
P range
no.a
rb
(Torrc)
no.a
rb
(Torrc)
1
2
3
4
5
6
7
8
9
2.194
1.472
0.619
8.27
111
48-127
74
140
133
59-72
72-155
106
10
11
12
13
14
15
16
17
18
1.174
0.4124
1.0021
2.23
112
73
98
120
15-39
27
14
3.32
2.23
0.369
5.377
1.784
0.4679
1.0014
0.4645
4.033
0.3355
25-32
21-32
61
a 1.0 cm cuvette used for 1-13; 9.71 cm cell used for 14-18.
b Mixing ratio, [Cl2]0/[Br2]0. c 1.00 Torr ≈ 1/750 bar.
The experiments were conducted at room temperature (22.0 (
0.5 °C). Although subsequent (static) checks showed that the
instrument’s cell compartment could warm by as much as 3 °C
over the course of a day, the consistency among the data
themselves in the LS analysis was ∼0.3%, indicating that
temperature variations were limited to 1 °C.
Bromine (Fisher, reagent grade) was stored in a bulb on the
vacuum system following trap-to-trap distillation at 0 °C and
differential evaporation designed to minimize the more volatile
(Cl2) and less volatile (water) impurities. Chlorine (Matheson,
high purity) was admitted to the system directly from a lecture
bottle. Spectra of both pure gases were taken on a number of
days, for both the short and the long path length cells. The
system was always rinsed with at least one portion of each pure
gas prior to its use for obtaining these spectra. A similar
procedure was used to prepare the mixtures, in the course of
which the spectrum of the Cl2 was normally taken as a check
against possible contamination with residual Br2.
ꢀλ(mix) ) fBr ꢀλ(Br2) + fCl ꢀλ(Cl2) + fBrClꢀλ(BrCl) (2)
2
2
The equilibrium fractions fi of the three components are related
to the initial mixing ratio, r ) [Cl2]0/[Br2]0, through the
equilibrium constant K°:
The relevant volumes of the vacuum system were calibrated
using air at low pressures. The ideal gas law was used at all
times in these calibrations and in converting pressures to
concentrations for the analysis of the absorption data.
fBrCl ) Y(1 - Z1/2)
(3)
The mixtures were prepared by using liquid nitrogen to freeze
measured pressures of each gas together in a mixing bulb. The
mixtures were then exposed to light and heat from a quartz
halogen lamp for at least 10 min to facilitate mixing and
equilibration. After it was cooled back to room temperature,
each mixture was first expanded into the main vacuum manifold
and then after several minutes, into the absorption cell. Spectra
were recorded after a further wait of several minutes for thermal
and pressure stabilization. Then, the mix was recondensed in
the mixing bulb and the procedure was repeated at least once.
In this way, spectra were obtained 2-4 times for each mixture,
often at two or more total pressures, and typically over a total
time period of 3 h. There was never any indication from these
multiple spectra that chemical equilibration was incomplete: The
greatest disparity observed in the estimated molar absorptivity
for a single mixture was 0.8% and was essentially constant
across the spectrum. The estimated absorptivity ꢀλ was usually
taken as a simple average of the several spectra for a given
mix, although in a few cases outlier spectra were excluded.
Results were obtained for 13 mixtures in the short cell and five
in the long, as summarized in Table 1.
where Y ≡ K°/(K° - 4) and Z ≡ 1 - (4/Y)r(1 + r)-2. The
other fractions are then
fBr ) (1 + r)-1 - fBrCl/2
(4)
2
and fCl ) 1 - fBrCl - fBr . Through these relations, all of the
2
2
mixture spectra contain information about K° and the spectra
of all three components.
The LS model developed to analyze the data contained no
assumptions beyond these. In addition, I measured the absorption
for the pure parent gases under the same conditions as used for
the mixtures and treated ꢀλ(Br2) and ꢀλ(Cl2) as known (although
uncertain in some computations). Thus, the fit model processed
the spectral data for all mixtures (or specified subsets) in terms
of a single K° and a single value of ꢀ(BrCl) at each wavelength.
The data were typically analyzed in this fashion for every third
to fifth λ value, over a specified λ range, giving K° and 50-90
ꢀλ(BrCl) values for up to 1600 total ꢀλ values.
The precision of spectrophotometric data depends inherently
on the specific instrument and on the wavelength and strength
of the absorption. To assign weights to the data, I started with
a statistical error calibration for the Shimadzu instrument13 and
added a percentage uncertainty for each spectrum, with the latter
based on observations from the multiple spectra for a given mix.
The scaled contribution was taken to be 0.3-0.4% in different
calculations; this exceeded the instrumental value except for
very weak absorption, so the statistical error at each wavelength
The spectra recorded using the 1 cm cuvette involved
mixtures at typical pressures of ∼100 Torr and yielded peak
absorbances of ∼0.5. Pressures a factor of five lower were used
for the 10 cm cell, yielding peak A ≈ 1. Because of the
expansion methods used, the initial pressures in the mixing bulb
were a factor of five larger. After the gas was expanded into
the manifold, the pressure typically declined by ∼0.2 Torr per

BrCl in Br2/Cl2 Gas Mixtures
J. Phys. Chem. A, Vol. 107, No. 5, 2003 755
Figure 2. Absorption spectra (molar absorptivity) for Cl2, Br2, and
several Cl2/Br2 mixtures at 22 °C. From top to bottom at 400 nm, the
spectra are for pure Br2 (indicated), r ) 0.336, 0.619, 1.00, 3.32, 8.27,
and ∞ (Cl2, indicated).
Figure 1. Differences (other, this work) in molar absorptivity (L mol-1
cm-1) of Cl2(g) at room temperature, from Seery and Britton (b),17
Burkholder and Bair (O),18 Hubinger and Nee (×),19 Ganske et al. (0),20
and Maric et al. (dashed).21 From the present work, the peak absorptivity
at 22 °C is 68.3 L mol-1 cm-1 at 330 nm, and the standard error near
adjusted peak absorptivity is 170.1 L mol-1 cm-1. The spectra
of Cl2 and Br2 are illustrated in Figure 2, along with representa-
tive spectra for the mixtures.
the peak (from an average of 10 spectra) is 0.12 L mol-1 cm-1
.
LS Analysis. Because of concerns about the reliability of
the Cl2 and Br2 spectra, their transferability from long to short
path spectra, the possibility of preferential adsorption of Br2
on the walls of the vacuum system, temperature and path length
uncertainties, and proper weighting of the various spectra,
considerable trial-and-error LS fitting was carried out on the
data. In course, the LS model was altered to incorporate
correction factors (i) to scale the Br2 and/or Cl2 spectra, for
either or both of the cells, (ii) to scale the mixture spectra for
either the short or the long path cell, and (iii) to adjust the mixing
ratio for selected spectra or for all spectra. Further, the weighting
algorithm was varied, and the effects of selective deletion of
data subsets and wavelength ranges were examined. The primary
results of these computations may be summarized as follows:
(i) With all data in the range of 250-510 nm included in the
fit, the nominal precision (1 σ) of K° is 0.04, which corresponds
to a remarkably small uncertainty of 0.4 cm-1 in De for BrCl.
(ii) However, the results are highly sensitive to small
systematic errors of the type mentioned, so that it is difficult to
realize this precision. My best estimate of K° is 9.1 ( 0.2. This
value is consistent with the spectroscopy/statistical mechanical-
based estimate and is more precise by a factor 2.5, corresponding
to an uncertainty of 2 cm-1 in De for BrCl.
Of all the possible correction parameters discussed above,
one was clearly indicated and was incorporated in the final
fitting: a scale factor for all of the measured ꢀλ values obtained
with the 1 cm cuvette. The actual value varied slightly depending
on the wavelength range included in the analysis, but a typical
value was 0.9934(4). This is close to the previously mentioned
correction factor for the Br2 spectra obtained with this same
cuvette, suggesting that it is largely a path length adjustment.
Without this correction, the fit ø2 was 38% larger, and K° was
smaller by 0.25.
was taken as a combination of the A ) 0 instrumental value
(converted to ꢀ) and the percentage error. Weights were then
defined in the usual way, as wi ) σλi-2. A percentage error of
0.4% yielded reduced ø2 values near unity for the fits, supporting
the reasonability of this assessment.14
The nonlinear fit algorithm employed fairly standard
methods,14-16 with all partial derivatives obtained numerically,
by finite difference, using part in 105 changes in the parameters.
Results and Discussion
Experimental Spectra. Reliable spectra for the pure parent
gases are essential, so ꢀλ was obtained for each parent gas by
averaging 5-10 spectra recorded at different pressures, in both
absorption cells. On most days, further checks were made of
the pure gases to guard against contamination in the preparation
of the mixtures. These checks nearly always agreed with the
reference spectra within ∼0.3% at peak absorption (330 nm for
Cl2, 416 nm for Br2).
Results for Cl2 are compared with other determinations in
Figure 1. The present values agree most closely with the spectra
of Burkholder and Bair18 but still deviate in some regions by
as much as 0.7%. Differences are larger and more systematic
in the comparisons with other results and are greatest for the
most recently published results from Hubinger and Nee.19 From
the standpoint of the present analysis, the differences are quite
significant in the region of strongest absorption. For example,
two different determinations two years apart, each involving
an average of eight or more spectra, agreed in peak absorptivity
within 0.1 L mol-1 cm-1, and the weakest single spectrum
(deemed an outlier) recorded for either the short or the long
path cell was only 1 L mol-1 cm-1 weaker near the peak.
The Br2 spectra recorded on this system were compared
previously with other results, in conjunction with a quantum
reanalysis of the absorption transitions in this molecule.12
However, the Br2 spectra obtained using the long cell at low
pressures in the present work are weaker by ∼1% than those
recorded at higher pressures in the short cuvette, an effect that
I have attributed mainly to possible path length errors for the 1
cm cuvette and deviations from ideal gas behavior22 at the
relatively high Ps involved (29-107 Torr). A reanalysis of the
absorption data in ref 12 with inclusion of a scaling parameter
for my spectra yields a better fit and a value of 0.9937(6) for
this parameter,23 which mainly just adjusts my spectra into
optimal agreement with the older data of Passchier et al.24 The
At the Br2 pressures used in many of the mixtures, ꢀλ for Br2
is P-dependent below 250 nm, due to formation of dimers.22
Thus, the fitting was restricted to λ > 250 nm. As was already
noted, the maximum wavelength was taken as 510 nm. In one
of the sensitivity tests, data were fitted in the range λs - 510
nm. As λs was increased from 250 to 360 nm, K° dropped by
1%.
Other factors examined in the sensitivity analysis had similar
effects on the LS value of K°. Selective deletion of individual
data sets increased or decreased K° by as much as 1%.
Reasonable changes in the weighting algorithm had a compa-
rable impact. These included varying the proportional error
factor from its final value of 0.004, increasing and decreasing

756 J. Phys. Chem. A, Vol. 107, No. 5, 2003
Tellinghuisen
Figure 3. Derived spectrum (molar absorptivity, L mol-1 cm-1) of
BrCl at 22 °C and statistical error (top, scale to right).
the base (ꢀ ) 0) uncertainty, and treating the Br2 and Cl2 spectra
and the r values as statistically uncertain.
The correction parameter that yielded the greatest change in
K° was the hypothetical Br2 adsorption adjustment. This was
taken as a single scale factor for all of the r values, and although
it differed only slightly from unity [0.9920(12)], including it
reduced the ø2 of the fit by over 4% and increased K° by 3%.
Although it seems likely that some such effects did occur in
the experiments, the justification for this correction is less clear-
cut than that for the 1 cm data, especially since the direction is
wrong for preferential adsorption of Br2. It is conceivable that
this parameter is compensating for some other systematic effect
in the preparation of the mixtures. In partial deference to it, I
have adjusted my final recommended value for K° upward from
9.0 to 9.1. The uncertainty of 2% loosely encompasses the larger
value of K° that is obtained when this parameter is included in
the model.
The value of K° ) 9.1 at 22 °C corresponds to 9.03 at 25 °C.
This is consistent with the statistical mechanical value, and it
implies a dissociation energy for BrCl, De ) 18 248(2) cm-1
.
BrCl Spectra. The low-resolution molar absorptivity of BrCl
obtained from this analysis is illustrated together with its
statistical error in Figure 3. For the region 250-510 nm, these
spectra were obtained directly from the LS fit, with K° ) 9.1;
and the displayed error in Figure 3 is the directly obtained
statistical error. The regions λ < 250 nm and λ > 510 nm were
obtained from a smaller data set of seven spectra all having
Figure 4. Comparison of present BrCl spectrum with other determina-
tions: Seery and Britton (b),17 Hubinger and Nee (O),19 and Maric et
al. (dashed).1
The experimentally measured and derived spectra for Cl2 and
BrCl are presented at 10 nm intervals in Table 2. Cubic spline
fits to these spectra reproduce the omitted values (at 1 nm
intervals) with rms and maximum errors of 0.06 and 0.3 L mol-1
cm-1, respectively.
large r (hence small PBr ). These results were compared with
2
those from a smaller data set involving only the lower P spectra
from the 9.7 cm cell and found to be consistent. Also,
comparisons of pressurized and unpressurized spectra for these
Cl2-rich mixtures showed no significant differences for λ > 510
nm. A pressurized Br2 spectrum was used in the analysis.
The plotted statistical error in Figure 3 ignores the possible
systematic effects. However, a 1% change in K° alters ꢀλ by at
most 0.12 L mol-1 cm-1, which amounts to only 0.1% change
in ꢀλ near the main peak. Incorporation of the r scaling factor
in the analysis has a comparable impact, for each percent change
in K°.
The present BrCl spectrum is compared with other determi-
nations in Figure 4. The new spectrum agrees most closely with
that of Maric et al.,1 except in the vicinity of the strongest peak
(Figure 4B), where it agrees better with the early determination
of Seery and Britton.
Conclusion
The equilibrium constant for the formation of BrCl(g) from
Cl2(g) + Br2(g) has been estimated from a multispectrum
nonlinear LS analysis of spectrophometric data. A fit of spectra
for 18 different mixing ratios of Cl2 and Br2 yields K° with a
remarkable statistical precision of 0.4%, which translates into
an uncertainty for the dissociation energy of BrCl that is an
order of magnitude smaller than the current (5 cm-1 from
spectroscopic data. However, the LS analysis is quite sensitive
to possible systematic errors in the data and to minor changes
in the fit model, including assumptions about the weights of
the data and the wavelength region chosen for analysis. The
estimate of K° is particularly sensitive to systematic errors in
the mixing ratio: A decrease by 0.8% for all r values led to a
3% increase in K°.
A significant contribution to the BrCl absorption in the main
peak comes from the B r X transition, which is also responsible
for discrete absorption in other halogens.8-10,25 The role of other
transitions in the spectrum has been the topic of several recent
studies1,2,19,26,27 but is not a primary concern in the present work
and so will not be considered further.
The K° value from this study is in complete accord with the
statistical mechanical estimate, which relied upon an interpreta-
tion of predissociation data for the BrCl dissociation energy.
This interpretation involved the assumption that the predisso-

BrCl in Br2/Cl2 Gas Mixtures
J. Phys. Chem. A, Vol. 107, No. 5, 2003 757
TABLE 2: Experimental Spectra for Gaseous Cl2 and BrCl
estimates for BrCl are more understandable, since these are tied
to the determination of K°. In this regard, it should be noted
that the BrCl absorption cross-sections presented in Table 56
of ref 28 are not computed from the recommended equation
(from ref 1) but are the measured values from ref 19, which
are arguably in poorest accord with other determinations.
at 22 °C
λ
λcor
ꢀλ
ꢀλ
λ
λcor
ꢀλ
ꢀλ
(nm)a (nm)b (Cl2)c (BrCl)c (nm)a (nm)b (Cl2)c (BrCl)c
200 200.14
210 210.07
220 220.13
230 230.08
240 240.13
250 250.07
260 260.14
270 270.06
280 280.14
290 290.05 16.39
300 300.14 31.28
310 310.06 48.80
320 320.13 63.10
330 330.07 68.32
340 340.13 62.98
350 350.07 50.41
360 360.13 35.38
0.17
0.05
0.04
0.06
0.04
0.12
0.60
2.22
6.88
7.28
11.58
15.59
17.15
15.01
10.73
6.47
3.33
1.46
0.70
1.01
410 410.06 3.49
420 420.15 2.61
430 430.08 1.98
440 440.14 1.49
450 450.09 1.05
460 460.15 0.73
470 470.09 0.47
480 480.16 0.30
490 490.08 0.20
500 500.17 0.12
510 510.09 0.07
520 520.18 0.03
530 530.10 0.04
540 540.18 0.01
550 550.12 0.03
560 560.18 0.03
570 570.13 0.03
580 580.19 0.03
590 590.13 0.02
600 600.21 0.02
59.99
46.95
38.59
33.28
29.40
25.61
21.59
17.25
13.18
9.46
6.53
4.32
2.75
1.72
1.01
0.57
0.33
0.20
0.14
0.09
Acknowledgment. I thank Dubravko Maric for valuable
correspondence on this problem and for providing the absorption
data from refs 1 and 20, which provided an early impetus for
the work.
References and Notes
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A: Chem. 1994, 83, 179.
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(3) Bartlett, W. P.; Margerum, D. W. EnViron. Sci. Technol. 1999, 33,
3410.
(4) Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic
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York, 1989.
(5) Chase, M. W., Jr. NIST-JANAF Thermochemical Tables, 4th ed.;
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(6) Tellinghuisen, J. J. Chem. Phys. In press.
3.48
10.13
23.26
44.45
69.82
93.09
370 370.06 22.45 106.37
380 380.14 13.32 106.06
390 390.06
400 400.15
7.95
5.04
94.32
76.85
a Fiducial wavelength. b Corrected standard air wavelength, from ref
(7) Tellinghuisen, J. J. Chem. Phys. 1988, 89, 6150.
(8) Clyne, M. A. A.; McDermid, I. S. Faraday Discuss. Chem. Soc.
1979, 67, 316.
13. c Molar absorptivity, units L mol-1 cm-1
.
(9) Clyne, M. A. A.; McDermid, I. S. J. Chem. Soc., Faraday II 1978,
74, 798.
(10) Heaven, M. C. Chem. Soc. ReV. 1986, 16, 405.
(11) Tellinghuisen, J. Unpublished work, 1995.
1
ciating state was the same C Π state that is responsible for
spontaneous predissociation in I2 and Br2. While this attribution
seemed highly likely, the present agreement provides corrobora-
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There is little doubt that K° values derived from experimental
spectrophotometric data should agree with the ideal gas values
from statistical mechanics. It is true that the current measure-
ments for the 1 cm cuvette involved higher pressures than have
been used in such experiments in the past. At the highest Br2
pressures (60 Torr), ideal gas deviations for this species are
almost 0.4%, and absorption by Br2 dimers below 250 nm is
evident.22 However, there was no indication, from residuals
analysis, of absorption by any species other than Cl2, Br2, and
BrCl in the 250-510 nm region employed for the analysis. This
result is consistent with more extensive checks for deviation
from Beer’s law by others.1 The LS reduced ø2 of ∼1 for the
assumed 0.4% uncertainty in the mixture spectra confirms that
this is a reasonable assessment of the uncertainties associated
with temperature and mixture preparation in the present study.
The halogen spectra under investigation here have become
of importance to atmospheric modeling in recent years.1,21,28
While the differences between the present absorptivities and
those recommended in ref 28 are not likely to be significant in
such applications, it is still surprising that recent estimates of
ꢀλ for a continuous absorption band in a molecule as simple as
Cl2 vary by >1% near the peak (Figure 1). Variations in the