A Kinetic Study of the Recombination Reaction Na + SO₂ + Ar Page: 1,656
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1656 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
TABLE I: Summary of Rate Constant Measurements for Na + SO2
+ Ar
kp2 * ekp2,
[M] [Ar], [Na]0, [S02]max, 10-12 cm3
P, kPa 10' cm-3 rm, s 10" cm-3 i0'l cm-3 molecule' s-'1.67
2.33
2.36
3.60
6.00
9.84
9.84
12.3
20.0
25.7
25.9
25.9
32.7
33.3
33.9
40.0
46.7
46.7
47.3
53.6
66.7
80.010
Ul)
0
E
C7
E8
6
4
20
1.53
2.15
2.17
3.31
5.52
9.05
9.05
11.3
18.4
23.7
23.8
23.8
30.1
30.7
31.2
36.8
42.9
42.9
43.6
49.3
61.3
73.60
0.5
0.3
0.6
2.0
1.6
0.7
0.7
1.7
1.8
1.8
1.8
7.0
1.8
0.9
0.9
1.8
1.6
1.6
6.4
1.8
2.3
2.22.2
1.4
1.7
2.2
1.9
1.5
3.0
2.2
1.6
1.9
1.7
3.8
1.5
1.9
1.0
1.6
1.0
1.7
1.8
1.1
1.6
1.12 4
14
13
25
22
17
8.8
8.8
4.8
20
10
6.3
15
7.5
3.7
3.9
6.5
1.4
3.0
7.2
6.6
2.9
2.73.32 t 0.10
4.24 + 0.17
5.31 0.22
7.85 0.40
12.2 0.7
20.5 0.5
18.8 0.7
20.3 0.8
33.3 1.4
37.3 1.2
32.9 0.5
30.5 1.3
47.5 1.8
54.6 2.6
61.4 2.6
51.8 3.5
39.4 2.4
53.0 3.8
48.2 2.1
63.0 5.8
69.5 6.0
84.1 8.56 8
[Ar]/1018 cm-3
Figure 3. Plot of pseudo-second-order rate constant for Na + SO2
against [Ar]. The straight line corresponds to a linear least-squares fit
to the first eight points.
varied from 1.0 X 10l to 3.8 X 10" cm3, which was always much
less than [SO2] to ensure pseudo-first-order conditions. There
was no significant influence of [Na]o on the kp,2 values which
demonstrates that neither photolysis nor reaction products affected
the observed kinetics. Reaction 1 was therefore isolated from any
interfering processes. NaBr was also tried as a photolytic precursor
for Na but, despite a literature value for its absorption cross section
at 308 nm similar to Na!,15 no Na was detected even at higher
temperatures. There was no consistent variation of kp,2 with r,
which was varied by a factor of about 10, an observation which
shows that thermal decomposition of the SO2 was insignificant.
For a given actinic intensity [Na]0 increased with Tres which
indicates that the heated gas did not reach equilibrium with the
solid Nal. The vapor pressure of NaI at 787 K corresponds to
1.2 X 1012 cm-3,t6 which is therefore an upper limit to the [NaT]
actually employed.
Preliminary experiments showed that even at very large [Na]0,
not used for kinetic measurements, about 30% of the resonance
light was transmitted. Presumably it passed around the photolysis
region in the reactor. A correction was therefore subtracted from
I and I4 before analysis, the effect of which was to increase kps1,
slightly (by less than 5%).
(15) Davidovits, P.; Brodhead, D. C. J. Chem. Phys. 1967, 46, 2968.
(16) Cogin, G. E.; Kimball, G. E. J. Chem. Phys. 1948, 16, 1035.Shi and Marshall
4
0
E
E2
' 1
00 1 2 3 4 5 6 7
[Ar]1/10-18 cm3
Figure 4. Lindemann plot of reciprocal pseudo-second-order rate con-
stant for Na + SO2 against reciprocal [Ar].
Figure 3 is a plot of k,,2 versus [M]. At [M] < 1018 cm-3
third-order behavior is observed, where k,2 cc [M]. Figure 3 also
shows the best weighted linear fit to the first eight points. The
intercept is (1.7 3.4) X 10-13 cm3 molecule-' s-' (statistical
uncertainties in fitted parameters are quoted as 1c), which is
therefore insignificantly different from zero. The lack of any
significant true bimolecular reaction between Na and SO2 is
consistent with the thermochemistry: the channel Na + SO2 --
NaO + SO is endothermic by 276 42 kJ mol- at 0 K.'7 At
[M] > 1018 cm-3 a linear extrapolation of the low-pressure data
lies above the measured k 2 values, which shows that these
measurements are in the falloff region.
These observations can be interpreted in terms of a simple
Lindemann mechanism.18 An initial excited adduct is formed,
which can either decompose back to reactants or be stabilized by
collision with the bath gas:Na + SO2 m NaSO2*
NaSO2* + M -+ NaSO2 + M(5)
(6)In the low-pressure limit, process 6 is rate-limiting and third-order
kinetics are predicted (k0 is the third-order rate constant):ks,2,0 = ko[M] = k5k6[M]/k-5
(7)
At the high-pressure limit, second-order kinetics are expected:
k = k. = k
(8)
The observed pseudo bimolecular rate constant for Na con-
sumption according to this mechanism iskp,2(Lindemann) = k0[M]/tl + k0[M]/klj
(9)
Equation 9 is fitted to our data by plotting 1/k,2 versus 1/[M],
and the results are shown in Figure 4. There is a good fit to our
observations, with k0 = (2.4 * 0.2) X 10-29 cm6 molecule-2 s-I
and k. = (1.2 t 0.2) X 100 cm3 molecule-1 s-1.
The Lindemann mechanism is known to predict too sharp a
falloff of kp,2 with [M],'8 and a more realistic empirical expression
for k,,2 used in the NASA rate constant compilations19 is also
tested here:
k,,2(NASA) = k,2(Lindemann) x 0.61+(o ko[M/k-)t' (10)
This expression is based on an RRKM analysis where the energy
(17) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.;
McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed.;
J. Phys. Chem. Ref. Data 1985, 14 (Suppl. No. 1).
(-) Robinson, P. J.; Holbrook, K. A. Lnimolecular Reactions; Wiley-
Interscience: London, 1972; Chapter 1.
(19) DeMore, W. B.; Molina, M. J.; Sander, S. P.; Golden, D. M.;
Hampson, R. F.; Kurylo, R. F.; Howard, C. J.; Ravishankara, A. R. Chemical
Kinetics and Photochemical Data for Use in Stratospheric Modeling. Eval-
uation Number 8.; JPL Publication 87-41; Jet Propulsion Laboratory: Pas-
adena, 1987.-"
1 1
I r0
* -
* S
0
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Shi, Youchun & Marshall, Paul. A Kinetic Study of the Recombination Reaction Na + SO₂ + Ar, article, February 1, 1991; [Washington, D.C.]. (https://digital.library.unt.edu/ark:/67531/metadc503254/m1/3/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.