Complex equilibria in unsaturated vapor over AlBr3

Article abstract of DOI:10.1134/S0036024408110022

Unsaturated AlBr 3 vapor pressure was measured over the temperature and pressure ranges 560-845 K and 54-145 torr by the static method using a quartz diaphragm pressure gauge with increased sensitivity (the confidence interval of pressure, including thermal drift of zero pressure gauge point, was 0.3 torr, and that of temperature, 0.3 K). Two equilibrium models were considered, one including AlBr₃ and Al₂Br₆ and the other, AlBr₃, Al₂Br₆, and Al₃Br ₉. The molecular constants of all vapor constituents were determined using density functional theory at the B3LYP/6-31G(d,p) level. The thermodynamic functions of all bromides were calculated in the rigid rotator-harmonic oscillator approximation. The enthalpies of independent equilibria for each model were determined by minimizing the residual sum of the squares of pressure discrepancies. According to the first model, 0.5Al₂Br₆ = AlBr₃, ΔH^o(298.15) = 13629.1 ± 9 cal/mol. According to the second model, 0.5Al₂Br₆ = AlBr ₃, ΔH^o(298.15) = 13638.8 ± 8 cal/mol, and 1.5Al₂Br₆ = Al₃Br₉, ΔH ^o(298.15) = -8528 ± 800 cal/mol. The second model, for which the variance of pressure differs insignificantly from the experimental variance of pressure, should be given preference.

Full text of DOI:10.1134/S0036024408110022

ISSN 0036-0244, Russian Journal of Physical Chemistry A, 2008, Vol. 82, No. 11, pp. 1801–1807. © Pleiades Publishing, Ltd., 2008.
Original Russian Text © A.D. Rusin, L.A. Nisel’son, 2008, published in Zhurnal Fizicheskoi Khimii, 2008, Vol. 82, No. 11, pp. 2011–2017.
CHEMICAL THERMODYNAMICS
AND THERMOCHEMISTRY
Complex Equilibria in Unsaturated Vapor over AlBr3
A. D. Rusina and L. A. Nisel’sonb
a Faculty of Chemistry, Moscow State University, Moscow, 119992 Russia
b VGUP “GIREDMET,” Moscow, Russia
e-mail: rusin@phys.chem.msu.ru
Received June 28, 2007
Abstract—Unsaturated AlBr3 vapor pressure was measured over the temperature and pressure ranges 560–
845 K and 54–145 torr by the static method using a quartz diaphragm pressure gauge with increased sensitivity
(the confidence interval of pressure, including thermal drift of zero pressure gauge point, was 0.3 torr, and that
of temperature, 0.3 K). Two equilibrium models were considered, one including AlBr3 and Al2Br6 and the other,
AlBr3, Al2Br6, and Al3Br9. The molecular constants of all vapor constituents were determined using density
functional theory at the B3LYP/6-31G(d,p) level. The thermodynamic functions of all bromides were calculated
in the rigid rotator–harmonic oscillator approximation. The enthalpies of independent equilibria for each model
were determined by minimizing the residual sum of the squares of pressure discrepancies. According to the first
model, 0.5Al2Br6 = AlBr3, ∆H°(298.15) = 13629.1 9 cal/mol. According to the second model, 0.5Al2Br6 =
AlBr3, ∆H°(298.15) = 13638.8 8 cal/mol, and 1.5Al2Br6 = Al3Br9, ∆H°(298.15) = –8528 800 cal/mol. The
second model, for which the variance of pressure differs insignificantly from the experimental variance of pres-
sure, should be given preference.
DOI: 10.1134/S0036024408110022
INTRODUCTION
major component content no less than 99.9% was sub-
jected to additional deep purification by rectification on
a high-performance column. The product, AlBr3, was
also subjected to deep purification by rectification on a
plate column with slit perforation and overflow pipes.
In experiments, the purest middle AlBr3 fraction was
used. A mass spectrometric analysis of purified AlBr3
transformed into Al2O3 showed that the content of
impurities most characteristic and difficult to remove
(Fe, Ni, Cr, Cu, Ca, Mg, Ti, Ga, Na, K, and other so-
called metallic impurities) did not exceed 1–0.1 ppm
(1 ppm = 10–4 wt %). With respect to the impurities
specified, AlBr3 used in experiments was no less than
99.9995% pure. AlBr3 is one of the most hygroscopic
compounds. It is easily hydrolyzed and oxidized (even
with air oxygen at comparatively low temperatures).
All operations with it were therefore performed taking
special precautions. Ampules were opened and filled in
special boxes in the atmosphere of dry nitrogen from
Dewar flasks with liquid nitrogen.
Unsaturated AlBr3 vapor pressure was measured in
[1]. In that work and in [2–5], it was found that equilib-
ria Al2Hal6 = 2AlHal3 took place in vapors of Group III
metal halides. It was, however, shown in [6] that errors
in vapor pressures measured in these works could be
substantial. In addition, there was a significant temper-
ature gradient along the reaction vessel in [1], which
was not duly taken into account. In all the preceding
works, the influence of the thermal drift of the zero
point of diaphragm pressure gauges on the results of
vapor pressure measurements was ignored. In any
event, there are no numerical thermal drift data in the
literature, except one of the earliest works [7]. It was
shown in [8] that the thermal drift of the zero pint of
quartz diaphragm pressure gauges was the main source
of errors in vapor pressure measurements. A new tech-
nique for performing tensimetric experiments and ana-
lyzing experimental data with corrections for thermal
zero point drift was suggested in [9, 10]. In [10], a
model experiment was performed with inert gas pres-
sure measurements over the temperature range 300–
1000 K. It was of interest to perform similar measure-
ments for a real object. In this work, unsaturated AlBr3
vapor pressure was measured.
A scheme of the experimental unit is shown in Fig. 1.
A reaction vessel with a crescent-shaped quartz
manometer was rigidly fixed on a steel bench. A three-
section furnace with a 70 mm inside diameter was
mounted on a stand and could be moved in the vertical
direction. Each furnace section was fed from a separate
VRT-3 temperature controller. An equalizing block
made of stainless steel with walls 5 mm thick was
inserted into the furnace. Temperature was measured by
two Pt/Pt–10% Rh thermocouples, mobile and immo-
EXPERIMENTAL
The synthesis of AlBr3 from the elements was per-
formed in a doubly fused quartz reactor. Aluminum was
of A 9999 grade. Bromine of ch. (pure) grade with the bile, calibrated against a gas thermometer, which was a
1801

1802
RUSIN, NISEL’SON
14
15
8
7
11
12
6
18
17
5
10
16
4
13
9
3
2
1
Fig. 1. Scheme of experimental unit: 1, furnace; 2, equalizing block; 3, reaction vessel; 4, entry for immobile thermocouple; 5, dia-
phragm; 6, chamotte insert; 7, asbestos cap; 8, mobile thermocouple; 9, cylinder with dry argon; 10, glass–metal junction; 11, damp-
ing volume (5 l); 12, PMT-2 vacuum gauge; 13, mercury manometer; 14, LGN-2 laser; 15, screen; 16 and 17, fine adjustment valves;
and 18, vacuum valve.
reaction vessel with a diaphragm of sensitivity variance was made by the thermal drift of the zero pint
45 mm/torr. The error in temperature measurements of the diaphragm pressure gauge (~89%). The unit was
was 0.3 K. The position of the mobile thermocouple always either evacuated (fore vacuum) or filled with dry
along the vessel was measured on a millimeter scale. argon. The diaphragm rod position was determined
No rubber or silicon pipe connections were used. Com- using an optical system. Light from a source (an LGN-2
pensation pressure was measured with a KM-10 cathe- laser) passed through a lens and was reflected from the
tometer and a mercury manometer with tubes with an rod mirror and focused on a screen of a scaled chart
inside diameter of 18 mm. Movable meniscus illumina- paper. The diameter of the light spot on the screen was
tors made them clearly seen in the field of vision of ~1 mm. In addition, two more light spots were always
KM-10. One manometer arm was evacuated with a fore present on the screen because of laser beam reflection
pump.
Argon preliminarily held for no less than two weeks
in a cylinder with granulated KOH at a pressure of 10–
12 atm was used as a compensating gas. The error in
compensation pressure measurements was 0.03 torr.
Here and throughout, all errors correspond to a 0.95
from the outside and inside optical window planes. The
coordinates of the rod mirror and one of the spots from
the optical window are denoted below by y1 and y3,
respectively. The y3 coordinate characterized the posi-
tion of the reaction vessel as a whole.
Before measurements, manometer sensitivity and
confidence probability. The total pressure variance was zero point thermal drift were measured. To determine
s2(p) = 0.0222147 torr2, the confidence interval of pres- sensitivity, the diaphragm chamber was filled with
sure was 0.3 torr. The major contribution to the pressure argon to a pressure of ~60 torr. The position of the zero
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 82 No. 11 2008

COMPLEX EQUILIBRIA IN UNSATURATED VAPOR OVER AlBr3
1803
point y01 was fixed. Next, pressure drop ∆p ( ~2 torr)
∆y, mm
120
was sequentially created between the reaction and com-
pensation volumes and y1 was measured. The results of
18 y01 , ∆p, and y1 measurements were processed by the
80
1.0 torr
method of least squares according to the equation
40
∆y = α∆p,
where ∆y = y01 – y1. This gave α = 20.16 0.3 torr. The
0
thermal drift of the zero point was measured in a vac-
uum. According to [8], corrections (~0.1 torr) were
introduced into vapor pressure measurements for zero
point shift at pressure p with respect to the vacuum.
Thermal drift measurements were performed during
one month. The thermal drift curve is shown in Fig. 2,
where the electromotive force (EMF) of the mobile
thermocouple E1 measured at the center of the dia-
phragm is plotted on the abscissa axis. On the axis of
ordinates, the
–40
–80
0
2
4
6
E, mV
Fig. 2. Zero point thermal drift of a diaphragm pressure
gauge.
∆y• = (y1• – y3• ) – (y10 – y03)
values are plotted. Here, y•1 and y3• are measured at
EMF E1, and y01 , and y30 are the room-temperature val-
ues determined before thermal drift measurements. The
furnace was heated to the required temperature, and y•1 ,
y•3 , and temperature field along the reaction vessel were
measured (y01 and y03 are the zero point and optical win-
ing a day, measurements at several temperatures were
taken. After this, the vessel was cooled to room temper-
ature, and the absence of residual pressure was
checked. Sometimes, the furnace was not switched off
during night, which allowed conclusions to be drawn
concerning the establishment of thermodynamic equi-
librium in vapor and pressure gauge zero point shifts.
During heating, the mean temperature under thermal
equilibrium conditions decreased, and during cooling,
it increased. This was related to the special features of
VRT-3 temperature controller operation.
During temperature field measurements, the mean
diaphragm chamber temperature changed by 0.02–
0.4 K. Because of the high diaphragm pressure gauge
sensitivity, we observed how pressure changed in paral-
lel with E2. For this reason, for each pressure measured,
we calculated the temperature field as described in [10].
It was assumed that the rate of temperature variations at
dow coordinates). The temperature gradient along the
reaction vessel was 0.5–3 K. Pressure was determined
by the equation
p0 = p + [(y•1 – y3• ) – (y1 – y3)]/α,
where p0 and p are the pressure in the diaphragm cham-
ber and the compensation pressure, respectively, and y1
and y3 are the corresponding coordinates at the com-
pensation pressure. The p0 pressure differed from p by
0.1–0.3 torr.
After thermal drift measurements, the furnace was
lowered, the ampule with AlBr3 was broken, placed into
the diaphragm chamber, and carefully sealed off under
continuous evacuation. The furnace was raised, and the
balancing block was closed with chamotte inserts and
an asbestos cap, as is shown in Fig. 1.
Table 1. Molecular constants of Al2Br6 and Al3Br9 in the
ground electronic state X1A(px = 1)
Molecule
Al2Br6
Al3Br9
Symmetry
C2v
C3v
The furnace was heated to the required temperature.
During heating and subsequent cooling, compensation
pressure was maintained using fine adjustment needle
valves 16 and 17 (Fig. 1). The compensation pressure
differed from the pressure inside the diaphragm cham-
ber by tenths of a torr. Thermal equilibrium in the fur-
nace was established in 1–2 h. Next, the temperature
field and pressure were determined. The temperature
field was measured during ~30 min at eight points
along the vessel. During these ~30 min, the mean tem-
perature changed at a rate of 0.01–0.02 K/min accord-
ing to immobile thermocouple EMF E2 readings. Dur-
Symmetry
2
3
number σ
IAIBIC × 10117
,
0.84648208+08
0.86965731+09
g3 cm6
ν, cm–1
A1: 505, 408.8, 203.3, A1: 515.3, 394, 183.5,
134.2, 100.8, 58.3, 132.2, 92.7, 71.7, 40;
21.7;
A2: 243.5, 119.6, 43.9
A2: 210.5, 111.7, 42.8; E:497.3,371.9,318.6,
B1: 339.7, 96.9, 70.1; 200.5, 107.2, 105.1,
B2: 495, 366.1,
194.5, 87, 68.7
69, 58.1, 48.3, 30.5
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 82 No. 11 2008

1804
RUSIN, NISEL’SON
Table 2. Temperature and vapor pressure (p, torr) measurements
T, K
p
δp
T, K
p
δp
T, K
p
δp
561.87
561.86
561.83
561.79
561.76
561.75
561.75
561.75
560.66
560.54
560.47
560.35
560.26
560.19
560.14
560.09
560.04
560.00
574.61
574.60
574.61
574.65
574.70
574.70
574.70
574.71
574.54
574.53
574.52
574.55
574.57
574.57
574.57
574.55
586.05
585.96
585.92
585.85
585.77
585.70
585.66
605.76
605.78
605.82
605.84
605.82
605.82
605.82
605.82
621.19
621.11
54.77
54.78
54.75
54.75
54.74
54.74
54.72
54.72
54.46
54.46
54.41
54.40
54.41
54.42
54.40
54.35
54.34
54.37
56.87
56.86
56.90
56.91
56.87
56.89
56.89
56.90
56.85
56.82
56.83
56.84
56.84
56.83
56.86
56.87
58.97
59.00
59.00
58.98
59.00
58.95
58.96
63.11
63.08
63.03
63.11
63.13
63.07
63.09
63.08
66.72
66.72
0.082
0.089
0.071
0.073
0.068
0.067
0.049
0.048
–0.033
–0.011
–0.053
–0.046
–0.018
0.005
–0.009
–0.050
–0.049
–0.019
0.001
–0.003
0.035
0.040
–0.011
0.010
0.008
621.06
621.03
620.98
620.91
620.84
620.79
640.61
640.65
640.66
640.65
640.64
640.64
640.64
640.65
655.64
655.64
655.70
655.72
655.61
655.55
655.38
675.02
675.08
675.11
675.14
675.16
675.17
675.16
675.15
690.91
690.87
690.85
690.83
690.80
690.77
690.74
690.71
724.57
724.66
724.69
724.71
724.72
724.76
724.79
724.82
725.06
725.03
725.00
724.95
724.91
724.86
66.72
66.68
66.69
66.67
66.66
66.64
72.09
72.10
72.13
72.11
72.13
72.12
72.11
72.09
76.54
76.51
76.51
76.54
76.52
76.51
76.45
83.13
83.14
83.14
83.14
83.15
83.15
83.15
83.15
88.76
88.74
88.73
88.73
88.70
88.66
88.65
88.63
101.81
101.79
101.81
101.84
101.87
101.86
101.85
101.87
102.20
102.19
102.20
102.15
102.17
102.17
–0.049
–0.084
–0.064
–0.063
–0.059
–0.062
0.046
0.043
0.064
0.046
0.070
724.83
724.79
742.75
742.78
742.81
742.86
742.90
742.93
742.96
742.99
743.12
743.12
743.13
743.17
743.17
743.13
743.15
743.19
758.38
758.33
758.29
758.24
758.22
758.20
758.19
758.18
779.70
779.76
779.82
779.85
779.85
779.81
779.70
779.59
801.75
801.71
801.68
801.65
801.64
801.63
801.61
801.60
844.66
844.59
844.56
844.53
844.49
844.46
844.44
844.42
102.12
102.09
109.52
109.52
109.53
109.55
109.56
109.59
109.61
109.63
109.59
109.60
109.63
109.64
109.63
109.63
109.64
109.64
115.32
115.25
115.27
115.24
115.25
115.25
115.23
115.22
124.09
124.08
124.12
124.10
124.09
124.15
124.14
124.07
131.64
131.60
131.59
131.61
131.59
131.57
131.58
131.56
146.07
146.06
146.04
146.07
146.05
146.04
146.02
146.05
0.086
0.063
0.236
0.216
0.218
0.218
0.211
0.229
0.241
0.242
0.155
0.165
0.191
0.183
0.177
0.186
0.195
0.169
–0.255
–0.303
–0.270
–0.275
–0.260
–0.251
–0.271
–0.273
0.196
0.163
0.178
0.150
0.139
0.211
0.247
0.220
–0.346
–0.379
–0.372
–0.348
–0.356
–0.375
–0.356
–0.374
0.137
0.149
0.140
0.175
0.167
0.169
0.152
0.185
0.065
0.053
0.031
–0.043
–0.074
–0.096
–0.071
–0.062
–0.044
–0.057
0.087
0.074
0.064
0.056
0.054
0.014
0.000
0.055
0.061
0.061
–0.028
–0.024
–0.021
–0.018
–0.026
–0.005
0.012
–0.031
0.015
0.027
–0.027
–0.038
–0.038
–0.030
–0.048
–0.078
–0.075
–0.080
–0.125
–0.173
–0.174
–0.147
–0.126
–0.146
–0.172
–0.163
0.069
0.014
0.060
0.014
0.037
–0.010
–0.046
–0.104
–0.035
–0.010
–0.068
–0.050
–0.056
–0.082
–0.067
0.072
0.090
0.069
0.099
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 82 No. 11 2008

COMPLEX EQUILIBRIA IN UNSATURATED VAPOR OVER AlBr3
Table 3. Vapor pressure optimizations in terms of various equilibrium models
1805
Equilibrium model
∆H2(298.15), cal/mol ∆H3(298.15), cal/mol
s2, torr2
β, torr/K
1
2
1
1
2
13629.1
13638.8
9
8
–
–8528.5
–
0.0272382
0.0194113
3.531755
6.082971
3.878664
0.1837
0.18408
0.1886
–
13740.9 100
13658.8 80
13638.4
–
–10143
–
all vessel points equaled that where the immobile ther- D2h symmetry. According to density functional theory
mocouple was fixed. This assumption was justified calculations (B3LYP/6-31G(d,p), Gaussian 03 package
because the main vessel volume was in the zone of the [13]), the D2h structure is a transition state, and a non-
main furnace section, whereas the remaining volume planar configuration of C2v symmetry corresponds to
(diaphragm) was ~2%, and the temperature gradient the potential energy minimum. This method was used
was very small. A method for taking into account the for preliminary calculations of the molecular constants
temperature gradient in a vessel in the presence of com- and thermodynamic functions of AlBr3, which were in
plex equilibria in the system was suggested in [11]. close agreement with the functions calculated using the
Calculations performed in this work showed that, molecular constants from [12]. The molecular con-
because of the low temperature gradient, the mean tem- stants of aluminum bromides are listed in Table 1.
perature of the vessel could be calculated on the These constants were used in thermodynamic function
assumption of equal vapor densities over the whole ves- calculations in the harmonic oscillator–rigid rotator
sel. Temperature field and pressure measurements were approximation. The theoretical vibrational frequencies
performed at 19 temperatures (ten during heating and were scaled with a factor of 0.9611 [13].
nine during cooling) in four days. At two temperatures,
For each equilibrium model, the optimum β and
seven pressure measurements were made, at one tem-
∆H2 (model 1) and β, ∆H2, and ∆H3 (model 2) values
perature, 10 measurements, and, at other temperatures,
eight pressure measurements at each temperature.
were calculated by the method suggested in [14], that
is, by the minimization of the residual sum of the
squares of pressure discrepancies
where pi denotes the experimental pressures and p•i ,
i = 1, m (pi – p•i )2 ,
∑
RESULTS AND DISCUSSION
Two equilibrium models were considered:
model 1
the vapor pressures calculated according to the model
used; m = 152.
The experimental vapor pressures and vapor pres-
sures calculated for both models are listed in Table 2.
The table contains mean temperatures (K), experimen-
tal pressures (pexpt), and the differences δp = pexpt – p*,
where p* is the pressure calculated according to
model 2. At the beginning and at the end of each exper-
iment, vapor pressures were measured at approximately
equal temperatures. The δp values allow us to draw
conclusions about the reproducibility of vapor pressure
measurements. Table 3 contains the results of vapor
pressure optimization according to different equilib-
rium models. The fourth column of the table contains
the sample variances of vapor pressures s2 (torr2), and
the last column, the optimum β values (torr/K).
A comparison of the Fisher test values for the mod-
els (the first and second rows in Table 3) shows that the
difference between models 1 and 2 is significant,
although the concentration of the trimers was only
1.2%. This was related to fairly high accuracy of vapor
pressure measurements. For model 1, the error in ∆H2
is specified for a 0.95 confidence probability. For model
0.5AlBr6 = AlBr3 + ∆H2(298.15),
model 2
1.5Al2Br6 = Al3Br9 + ∆H3(298.15),
0.5AlBr6 = AlBr3 + ∆H2(298.15).
The parameters to be determined were ∆H2 for
model 1 and ∆H2 and ∆H3 for model 2. In addition, one
more variable in both models was the β = nAlBr R/V
3
value, the vapor density in the diaphragm chamber on
the assumption that sample vapors consisted of AlBr3.
The β value was calculated from the sample weight
(0.04771 g) and the diaphragm chamber volume
(59.6 ml), β = 0.1872 torr/K. The error in β was deter-
mined by the accuracy of diaphragm chamber volume
measurements, which was estimated at 0.1–0.2 ml.
The real β value was, however, smaller. After the
ampule with the sample was opened, an uncontrolled
amount of the substance was removed during subse-
quent evacuation.
The thermodynamic functions of the dimer and 2, the confidence region for ∆H2 and ∆H3 was con-
monomer were reported in [12]. The functions of the structed (Fig. 3). The response surface in the ∆H2, ∆H3
dimer were calculated in [12] for a planar structure of coordinates was a narrow slit with steep slopes. The
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 82 No. 11 2008

1806
–∆H3, kcal/mol
RUSIN, NISEL’SON
–∆H3, kcal/mol
4
7
8
9
6
8
10
12
13560
13600
13640
13680 13720
∆H2, cal/mol
13630
13635
13640
13645
∆H2, cal/mol
Fig. 3. Confidence region of the enthalpies of equilibria (1)
and (2).
Fig. 4. Confidence region of ∆H and ∆H according to cal-
2 3
culations based on the experimental data from [1].
boundaries of the confidence region were used as errors pressure variance value (the bottom of the ravine) was
in the enthalpies. For ∆H2, these boundaries are identi- 6.67 torr2. The lower ∆H3 limit was –11510 cal/mol.
cal (they are listed in Table 3), whereas, for ∆H3, the
For all models and also without taking zero point
upper boundary is ~1700 cal/mol, and the lower bound-
thermal drift into account, close enthalpies of predom-
ary is 640 cal/mol. The β values found for both models
inant equilibrium (1) were obtained. It follows that,
are in agreement with the experimental β value, consid-
even under the conditions of an insufficiently high
ering errors in reaction vessel volume values and possi-
accuracy of pressure and temperature measurements,
ble AlBr3 weight loss before measurements.
reasonable enthalpy values can be obtained for the pre-
dominant equilibrium. An increase in the accuracy of
We already mentioned that due attention to the zero
pressure and temperature measurements allows equilib-
point thermal drift was not paid in the literature. It
ria with the participation of products present in compar-
would be interesting to learn to what extent the neglect
atively small concentrations to be revealed and their
of thermal drift influences the results of vapor pressure
thermodynamic characteristics determined. The statis-
optimization. For comparison, we also performed cal-
tical method cannot by itself unambiguously identify
culations using pressure values obtained without ther-
the presence of certain products in vapor, but, in com-
mal drift corrections. The results are listed in the third
bination with other methods, for instance, spectro-
row of Table 3 (model 1). Vapor pressure measurements
scopic, such information can be obtained.
without thermal drift corrections give sharply incorrect
results. At low temperatures, pressures are underesti-
mated by ~2.5 torr, and, at high temperatures, they are
ACKNOWLEDGMENTS
exaggerated by ~3.5 torr. The confidence interval for
The authors thank O.V. Dorofeeva for the calcula-
tions of the molecular constants and thermodynamic
functions of aluminum bromides.
∆H2 increases by an order of magnitude, and the pres-
sure variance, by two orders of magnitude. Calculations
by model 2 could not be performed because of the
divergence of iterative minimization of the residual
sum of the squares of pressure discrepancies.
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Similar results can be expected for other vapor pres-
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the side of large ∆H3 values. The boundary pressure
variance value for a 0.95 confidence probability was
12.33 torr2, and, at ∆H3 = –5000 cal/mol, the minimum
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