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