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The neglected halogen dimer bands: The neglected halogen dimer bands: Dimerization equilibrium constants Dimerization equilibrium constants
from spectrophotometric datafrom spectrophotometric data
Joel Tellinghuisen
Department of ChemistryVanderbilt UniversityNashville, TN 37235
An old problem:
Br2(g) Evans, JCP 23, 1426 (1955).
Ogryzlo & Sanctuary, JPC 69, 4422 (1965).
Passchier, Christian, & Gregory, JPC 71, 937 (1967).
Wen & Noyes, JPC 76, 1017 (1972).
I2(g) Tamres, Duerksen, & Goodenow, JPC 72, 966 (1968).
Passchier & Gregory, JPC 72, 2697 (1968).
I2(soln) Keefer & Allen, JCP 25, 1059 (1956).
de Maine, et al., JCP 24, 1091; Can. JC 35, 573 (1957); JMS 4, 271 (1960).
Consider Br2(g) …*
*J.Phys.Chem.A. 2008 (ASAP).
0
2
4
6
8
10
200 220 240 260 280 300
6 Torr
27 Torr
52 Torr
72 Torr
119 Torr
(cm
Š1
L m
olŠ
1 )
nm
Treat as sum of contributions:
A = b (1 [Br2] + 2 Kc[Br2]2 )
b (1 c + 2 Kc c2 )
Ideal gas: c = P/RT = c1 + c2
c1 = (2 Kc)–1 [(1 + 4 Kc c)1/2 – 1]
Feasibility of analysis depends on extent to which c1 ≠ c; if c2 is too small, can estimate only 1 and 2 Kc.
Analyze 18 spectra using simplified scheme
0
1
2
3
200 220 240 260 280 300
(cm
Š1 L
mo
lŠ1 )
nm
0
400
800
1200
Kc 2
(cm
–1 L
2 m
ol–
2)
dimer
monomer
Passchier, Christian, & Gregory
Wen & Noyes
Hubinger & Nee, (1995)
Present — dimer slighty stronger, monomer weaker
23°C
For multispectrum analysis, need to weight data, because short- much less precise. Use preliminary analysis to estimate 2(l).
-18
-17
-16
-15
-14
-13
-12
-11
200 220 240 260 280 300
ln(s
2 )
nm
Examine results from 4-parameter model at selected wavelength. (Parameters include constant A0.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007
A
c (mol/L)
0
0.004
0.008
0.012
0.016
0 0.0002 0.0004 0.0006
Differences between 3- and 4-parameter models appear only on blowup — suggests baseline important.
205 nm
Another question: Given subtle differences, are parameters and errors returned by 4-parameter model realistic? Address w/ Monte Carlo calculations.
Key Results:
• Parameters not significantly biased and errors reasonable.
• 2 is ~35% smaller for 4-parameter model, when justified.
• Parameters Kc, 1, A0 near-normal; 2 grossly nonnormal — manifested as divergences in MC runs; none when 4th parameter defined as 2Kc.
Examine baseline by accumulating statistics on multiple scans. [Baseline is set by an instrumental routine run w/ solvent in sample cell.]
Error bars = standard errors.
Blue and red recorded for same baseline function; yellow after resetting.
Conclusion: Need baseline data; include as zero-c spectra.
-0.002
-0.001
0.000
0.001
0.002
0.003
0.004
200 220 240 260 280 300
me
an
ba
selin
e
nm
3
Global analysis — Fit to 3 A0 parameters, 1, and 2 at each , plus Kc valid at all —18 spectra + 6 baseline scans.
Examine dependence of Kc on data selection …
0
1
2
3
4
5
6
190 200 210 220 230
Kc
(L/m
ol)
average wavelength (nm)
From such considerations, Kc = 2.5(4) L/mol.
Results from analyzing 4 adjacent (1 nm) wavelengths at a time.
van’t Hoff plot for comparison with previous — present Kc more than factor 2 larger.
-5.2
-4.4
-3.6
-2.8
-2.0
2.2 2.4 2.6 2.8 3.0 3.2 3.4
ln KP
103/T(K)
Lasater, et al., JACS, 1950.
Kokovin, Russ. J. Inorg. C., 1965.
(Both from ideal gas model of PVT deviations; correction for excluded V is in right direction but too small to resolve discrepancies.)
Discrete structure in spectra? Examine residuals.
Statistically significant excursions attributed to subtle correlation effects.
-4
-2
0
2
4
6
200 220 240 260 280 300
no
rma
lize
d r
esi
du
al
nm
monomerdimer
• Although Kc is >2 times previous estimate, it, H° (–9.5 kJ/mol), and S° (–51 J mol–1 K–1) are commensurate with results for I2(g) (more below).
• Maximum [Br4] < 2% at 23°C and 119 Torr; dimers should become much more prominent at lower T, e.g., in properly designed free-jet expansions.
• Dimer bands long attributed to charge-transfer transitions; nothing new there from this study.
• Monomer band factor of 4 weaker than weakest of well-known UV-visible bands, A X. Factor of 7 weaker than corresponding band for I2 (270 nm, below).
• For the dimer, 2Kc is a factor of 2 weaker than the same in I2.
So, on to I2 (soln) …
0
10
20
30
40
50
60
70
80
300 400 500 600 700 800
3.2 mM 6.5 9.7 13.1 16.2
nm
I2 in CCl4
ap
p (L
mo
l–1 c
m–
1)
4
5
6
7
8
9
10
11
360 370 380 390 400 410nm
ap
p (L
mo
l–1 c
m–
1)
0
1
2
3
4
5
6
7
800 810 820 830 840 850nm
A different baseline problem — cell replacement error.
Position and strength of monomer band depend strongly on medium; current CCl4 results suggest more than one transition.
0
10
20
30
40
50
60
70
80
250 300 350 400
Present, CCl4, 22°C
de Maine, 22°C, CCl4 " chloroformTamres, 140°C, vaporPasschier,150°C, vapor
(L
mo
l–1 c
m–
1)
nm
I2I2
Quantitative consensus lacking, but T dependence does yield consistent estimates of H° for dimerization. Prominent medium wavelength shift. Shape again suggests multiple transitions.
0
500
1000
1500
2000
2500
3000
3500
250 300 350 400
Present, CCl4, 22°
de Maine, CCl4, 22°
" 45°C
K
c (c
m–
1)
nm
I4
T (g), 140°
P (g), 150°
270°
I4
These dimerization equilibria are notoriously problematic, so it is reassuring to consider a related “slam dunk” — the BrCl formation reaction.*
0
40
80
120
160
200 250 300 350 400 450 500 550 600
Br2Cl2r = 8.27 3.32 1.0014 0.619 0.3355
nm
* J. Phys. Chem. A. 107, 753 (2003).
Analysis yields K = 9.1, with a nominal of 0.04. This translates into a remarkable ±0.4 cm–1 in De for BrCl — a precision that rivals spectroscopic methods from essentially a thermochemical method. Consideration of possible model error leads to a more conservative ±0.2, and De = 18 248 ± 2 cm–1.
0
20
40
60
80
100
120
0
0.1
0.2
200 250 300 350 400 450 500 550 600
nm