Thermal rate constants over thirty orders of magnitude for the I+H2 reaction

Article abstract of DOI:10.1016/S0009-2614(00)00072-5

I-atom atomic resonance absorption spectrometry has been used to measure thermal rate constants for the I+H₂ → HI+H reaction between 1755 and 2605 K in reflected shock waves. Measured rate constants can then be expressed by k₁=(3.92±

Full text of DOI:10.1016/S0009-2614(00)00072-5

10 March 2000
Ž
.
Chemical Physics Letters 319 2000 99–106
www.elsevier.nlrlocatercplett
Thermal rate constants over thirty orders of magnitude for the
IqH2 reaction
J.V. Michael , S.S. Kumaran , M.-C. Su , K.P. Lim
Chemistry DiÕision, Argonne National Laboratory, D-193, Bldg. 200, Argonne, IL 60439, USA
Received 5 November 1999; in final form 6 December 1999
)
1
2
Abstract
I-atom atomic resonance absorption spectrometry has been used to measure thermal rate constants for the IqH2
HI
qH reaction between 1755 and 2605 K in reflected shock waves. Measured rate constants can then be expressed by
y
9
3
y1
k1s 3.92"1.15 =10 exp y21 398"658 KrT cm molecule sy1. Combining these results with earlier values, the
Ž
.
Ž
.
y
10
Ž
.
Ž
exp y17 070"
rate behavior over the combined temperature range, 230 K(T(2605 K, is: k1s 4.52"0.34 =10
34 KrT cm moleculey1 sy1. This result holds over ;30 orders of magnitude and is discussed in terms of bimolecular
3
.
rate theory. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction
tures. However, at higher temperatures, the fraction
of the bound complex mechanism to the total reac-
tion rate decreased. Above 600–700 K, an atomic
chain mechanism eventually dominates, and the reac-
tion between I-atoms and H2 ,
Chemical kinetics investigations on the H2rI2
reaction system 105 years ago were the first gas-phase
chemical dynamics studies ever reported 1 . Boden-
w x
stein suggested several mechanisms; however, a di-
rect bimolecular reaction through a four-center inter-
mediate was eventually considered to be the most
probable pathway. Anderson has recently reviewed
IqH2
HIqH ,
1
Ž .
then becomes important. Rate constants were mea-
sured at five temperatures between 667 and 800 K,
and the temperature dependence was:
w x
previous work on this system 2 . In a series of
w
x
papers 3–7 , Sullivan determined that the direct
four-center reaction was negligible and that a bound
complex mechanism dominated at lower tempera-
k s 5.89"0.96 =10y12 T 0.5 exp y16 507
Ž
.
Ž
1
"250 KrT cm3 moleculey1 sy1
.
2
Ž .
.
)
Corresponding author. Fax: q1-630-252-4470; e-mail:
michael@anlchm.chm.anl.gov
w
x
This work 3–7 was carried out with extraordinary
care; however, the analysis of results was quite
complicated. Work on the reverse reaction at lower
temperatures, HqHI, is much more extensive, and
three relatively direct measurements have been re-
1 Present address: Cabot, 700 E. US Highway 36, Tuscola, IL
61953, USA.
2 Faculty Research Participant, Department of Educational Pro-
grams, Argonne. Permanent address: Department of Chemistry,
Butler University, Indianapolis, IN 46208, USA.
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
Ž
.
PII: S0009-2614 00 00072-5

(
)
100
J.V. Michael et al.rChemical Physics Letters 319 2000 99–106
w
x
ported 8–10 . Even though these reported rate con-
stants can be transformed to k1 through equilibrium
constants, the combined temperature range of all
previous studies is then only 230–800 K. In order to
theoretically understand this reaction, higher-temper-
ature values of the rate constant are needed in a
completely analogous way as in the ClqH2rD2
2.2. Gases
Ž
.
Kr Scientific Grade, 99.999% used as the dilu-
ent in the experimental mixtures was obtained from
MG Industries and used without further purification.
Ž
.
Purified Grade He 99.995% from Airco Industries
was used as the driver gas and as the diluent in the
I-atom resonance lamp. H2 Scientific Grade,
w
x
reaction case 11,12 . This realization supplies the
main motivation for the present work.
Ž
.
99.9999% was obtained from MG Industries and
Ž
.
used without further purification. CF3I 99% , ob-
tained from Aldrich Chemical, was further purified
by bulb-to-bulb distillation with the middle third
being retained for mixture preparation. Gas mixtures
were stored in an all glass vacuum line, and the
pressures were accurately measured with a Baratron
capacitance manometer.
2. Experimental
The kinetics studies were performed by observing
using the I-atom atomic resonance absorption
spectrometric ARAS detection technique 13–15
in reflected shock wave experiments. Since the shock
w x
I
t
Ž
.
w
x
tube and associated equipment have been described
Žw
x
w
x
.
elsewhere 16 ; see Ref. 17 for original references ,
only a few additional comments are necessary.
3. Results
2.1. Apparatus
In the present work, the thermal decomposition of
Ž
.
The circular shock tube 9.74 cm i.d. used in this
study is 7 m in length, and is separated from the
w
x
CF3I 13 was used as the source of I-atoms for
Ž .
studying reaction 1 . The conditions of the experi-
Ž
driver chamber by a thin aluminum diaphragm 4 mil
unscored 1100-H18 . The tube was routinely pumped
ments are shown in Table 1. Thirteen experiments
were carried out between 1755 and 2605 K. Mea-
sured time-dependent absorbance was converted to
.
to -10y8 Torr between experiments by an Edwards
Vacuum Products model CR100P mechanicalrdiffu-
sion pump combination system. All experiments in
this work were performed in the reflected wave
regime. Shock velocities were measured with eight
w x
absolute I using the curve-of-growth yielding abso-
lute I-atom profiles, two of which are shown in Fig.
t
1. Note that there is substantial noise due to the low
Ž
.
quantum efficiency ;3% of the photomultiplier at
Ž
equally spaced pressure transducers PCB Piezotron-
ics, model 113A21 . Reflected shock wave thermo-
dynamic properties were calculated from measured
Nicolet 4094C digital oscilloscope incident veloci-
ties with appropriate boundary layer corrections 18–
20 .
The I-atom ARAS photometer system has been
w
x
l0165 nm 13 . The signal to noise ratio is ;10,
and, therefore, the estimated accuracy of absolute I
is typically "10%. CF3I decomposition 13 is so
fast at the temperatures of the present experiment
.
w x
w
x
Ž
.
w
w
x
w x
that CF3I s I is a good approximation. Hence,
0
0
x
w x
the initial decrease in I is due exclusively to reac-
Ž .
tion 1 ; i.e., the initial kinetics follow the rate law,
Ž
previously described, and the curve-of-growth the
w x.
w x w x
ln I r I
syk1st t ,
.
3a
Ž
.
Ž
.
Ž
.
Ž
plot of absorbance, ABS 'yln ItrI0 , against I
t
0
12
w
x
w x
has been determined 13–15 . For I (3=10
0
w x
w
x
where I s CF3I . Approximate bimolecular rate
atoms cmy3, the curve is linear; however, deviations
0
0
Ž .
constants for reaction 1 can then be determined
from,
w x
from linearity occur at higher I . In the present
0
work, the linear relationship was mostly used except
in a few instances where I exceeded 3=1012
w x
0
w
x
k1 fk1str H2
,
3b
Ž
.
0
atoms cmy3. Above this concentration a polynomial
w x
w
x
fit to the curve-of-growth was used to convert mea-
since I < H2 0, i.e., almost no H2 is initially
0
w x
w x
sured absorbance to absolute I .
destroyed in the reaction. As seen in Fig. 1, I
t

(
)
J.V. Michael et al.rChemical Physics Letters 319 2000 99–106
101
Table 1
Ž
Ž .
6
HqIqKr
the thermal decomposition of HI reaction
in
High-temperature rate data for IqH2
.
Table 2 . To our knowledge, HIqKr
has never been studied, and therefore, classical colli-
sion theory was used to estimate the rate constant
from kskZ E0rRT exp yE0rRT rs!, where s
is one-half number of internal degrees of freedom
XCF I s1.0169=10y6 , XH s1.0690=10y2
3
2
a
b
b
c
d
P1
Ms
r5
Ž
T5
k1
Ž
K12
Torr
10 cmy3
cm sy1
18
3
Ž
.
.
Ž
K
.
.
s
Ž
.
Ž
.
e
Ž
Ž
Ž
Ž
Ž
Ž
Ž
Ž
Ž
Ž
Ž
Ž
.
Ž
.
.
.
.
.
.
.
.
.
.
.
.
.
15.95 2.683 3.271
15.91 2.804 3.380
15.96 2.903 3.492
15.95 2.960 3.538
15.67 2.920 3.442
15.96 3.044 3.609
16.00 3.337 3.828
15.98 2.860 3.458
15.99 2.737 3.345
11.02 3.136 2.588
10.99 3.108 2.565
11.00 2.980 2.489
11.01 2.911 2.447
1755 1.8 y14
1.95 y4
.
.
.
.
.
.
.
.
.
.
.
.
Ž
3.48 y4
1901 4.8 y14
Ž
.
Ž
i.e., 1.5 , E0 is the bond energy of HI 70.425 kcal
Ž
6.93 y4
2019 9.0 y14
moly1 , Z is the collision rate constant, and k is the
.
Ž
1.06 y3
2091 1.3 y13
Ž
9.26 y4
w x
2039 1.4 y13
collision efficiency 24 . By analogy with most di-
atomic dissociations, the value for k is taken to be
;0.04. Combining all factors, the expression for HI
dissociation shown in the table was derived. The
contribution from reactions 6 – 8 in Table 2 was
-5% under all conditions and was therefore negligi-
Ž
2.14 y3
2201 2.0 y13
Ž
7.09 y3
2605 1.0 y12
Ž
7.16 y4
1964 8.2 y14
Ž
4.11 y4
1814 3.0 y14
Ž . Ž .
Ž
3.36 y3
2352 4.5 y13
Ž
3.11 y3
2313 3.9 y13
Ž
1.70 y3
2138 2.0 y13
w x
ble since the absolute accuracy in I is "10%.
Hence, fitting of profiles really involves adjustment
t
Ž
Ž
1.20 y3
2046 1.1 y13
a The error in measuring the Mach number, Ms, is typically
0.5–1.0% at the one standard deviation level.
b Quantities with the subscript 5 refer to the thermodynamic
state of the gas in the reflected shock region.
c Rate constants for reaction
mechanism in Table 2.
1
from fitting
Ž .
w x
I using the
t
d K12 is the fitted equilibrium constant for reaction
Ž .
1 with
k2 sk1 rK12
.
e Parentheses denote the power of 10.
decreases to a minimum value and then slowly in-
w x
creases to give back I at higher temperatures. This
0
w
x
behavior is similar to ClqH2 11 and indicates that
the reaction moves toward equilibrium. I-atoms are
Ž
.
then released, through reaction y1 , to values ap-
w x
w x
proaching I due to increasing H at longer times.
The reversible reaction is partially driven by H-atom
0
formation through the reactions, CF3 qH2
CF3H
qH, both of which have been recently studied in
w
x
our laboratory 21 . However, the long time recovery
w x
back to I is due to additional H-atom formation
0
from the H2 thermal dissociation. The reaction sys-
tem is therefore complex, and chemical modeling is
required. Initial values for k1 can, however, be deter-
Ž
.
Ž .
mined from initial profiles using Eqs. 3a and 3b .
The Arrhenius expression that best described the
thirteen approximate values was k1 f 3.87 =
10y9 exp y21410 KrT cm3 moleculey1 sy1. The
individual values for the experiments were then used
as starting values in chemical simulations using the
mechanism of Table 2.
Ž
.
Fig. 1. Two typical I-atom ARAS profiles for IqH2 experiments.
Top panel: T5 s2352 K, r5 s2.588=1018 cmy3
,
CF3I 0 s
and H2 0 s2.766=1016 cmy3
w x
, . Bottom
w
x
2.631=1012 cmy3
panel: T5 s1901 K, r5 s3.380=1018 cmy3
w x
, CF3I 0 s3.437=
1012 cmy3, and H2 0 s3.613=1016 cmy3. The solid lines are
Most of the rate constants given in Table 2 have
w
x
w
x
been previously measured 23 with the exception of
fits using the mechanism of Table 2.

(
)
102
J.V. Michael et al.rChemical Physics Letters 319 2000 99–106
Table 2
Mechanism used for fitting I profiles from the IqH2 reactiona
w x
b
0
CF3IqKr
IqH2
HqHI
CF3 qIqKr
HIqH
H2 qI
CF3HqH
CF3 qH2
HqHqKr
HqIqKr
HqI2
IqHI
k0 s3.24=10y9 exp y17286 KrT
Ž .
Ž
.
Ž .
1
k1 sfitted
k2 sfitted
Ž
Ž .
2
c
3
CF3 qH2
CF3HqH
H2 qKr
HIqKr
IqHI
k3 s1.244=10y24 T 3.702 exp y3283 KrT
Ž .
.
4
k4 sk3rK3d4
k5 sfitted
Ž .
Ž .
5
6
k6 s1.474=10y6 Ty1 exp y35440 KrT
e
Ž .
Ž
.
f
k7 s1.33=10y9 exp y18685 KrT
Ž .
7
Ž
Ž
.
f
HqI2
k8 s6.6=10y10 exp y20 KrT
Ž .
8
.
a All rate constants are in cm3 moleculey1 sy1
.
b
w
x
Ref. 13 .
c
w
x
Ž .
Ref. 21 , Eq. 12 .
d
Ž .
Ž .
w
x
w x
K34 is the equilibrium constant for 3 and 4 , evaluated from Ref. 22 as described in Ref. 21 .
e Estimated, as described in the text.
f
w
x
Ref. 23 .
Ž . Ž .
in k1, k2 , and k5 of Table 2. However, initial values
for the experiments are already available from the
imally perturbed by reactions 2 – 8 in Table 2.
Hence, k1 is effectively determined under isolated
chemical kinetics conditions.
Ž
.
Ž .
initial profile analysis based on Eqs. 3a and 3b .
For given k1’s, values for the equilibrium constants
Equilibrium constants, K12 , have also been calcu-
Ž .
Ž .
w x
between
1
and
2
were adjusted giving k2 s
lated from the Janaf tables 22 giving,
k1rKeq. Simultaneously k5 was also varied until the
simulation matched experiment within "10%. In-
spection of the mechanism shows that the minimum
K12 s4.863 exp y17 011 KrT ,
5
Ž
.
Ž .
Ž .
between 1700 and 2600 K. Eq. 5 is plotted in Fig.
3 along with the values inferred from the fits to the
mechanism and listed in Table 1. Lastly, the fitted
w x
values for I and the times at which they occur are
dependent on the mutual choice of k2 and k5, i.e.,
the values are strongly correlated. On the other hand,
the values for k1 are minimally affected by the other
two choices, particularly in the initial profile region
of a given experiment. In order to fit all experiments
to within "10% over the time range of 0 to 2 ms,
we found that few additional adjustments in k1 from
the initial slope analysis were necessary to give the
best fits. Two typical fits are shown in Fig. 1 as solid
lines. The final values for both k1 and the equilib-
rium constant are given in Table 1.
An Arrhenius plot of the results given in Table 1
Ž .
for reaction 1 is shown in Fig. 2 along with the
linear least-squares line,
k s 3.92"1.50 =10y9 exp y21 398
Ž
.
Ž
1
"658 KrT cm3 moleculey1 sy1
.
4
Ž .
.
Ž .
Eq. 4 is almost identical to the result obtained from
the initial slope analysis, reinforcing the points that:
Fig. 2. Arrhenius plot for IqH2 over the temperature range,
Ž .
Ž .
a I-atom formation from reaction 0 in Table 2 is
1755–2605 K. The points are listed in Table 1, and the line is the
Ž .
Ž .
instantaneous; and b initial I-atom profiles are min-
linear least-squares description, Eq. 4 .

(
)
J.V. Michael et al.rChemical Physics Letters 319 2000 99–106
103
w
x
determination from Du and Hessler 25 and is calcu-
lated from k5 s8.86=10y10 exp y48 321 KrT
Ž
.
cm3 moleculey1 sy1. As mentioned above, the mu-
tual values, k2 and k5, are strongly correlated.
Therefore, the final values shown in Figs. 3 and 4
are not considered to be determinations. Rather, we
view these results as being consistent with accepted
values for K12 and measured values for k5.
4. Discussion
Ž .
The present results for reaction 1 are the first to
be reported in the temperature range, 1755–2605 K.
In a lower temperature regime, Sullivan has summa-
w x
rized the results for I-atoms with both H2 and D2
and has discussed these in terms of transition state
6
theory. For H2 , k1 is: 6.51=10y22, 2.77=10y21
,
Fig. 3. Van ’t Hoff plot of K12 inferred from profile fitting using
the mechanism of Table 2. The line is calculated from the Janaf
1.22=10y20, 3.02=10y20, and 1.84=10y19 cm3
moleculey1 sy1 at 630, 667, 710, 738, and 800 K,
respectively. These results are plotted in Arrhenius
form along with the present values in Fig. 5.
Ž .
tabulation, Eq. 5 .
Ž
.
Ž
HqHqKr re-
values not listed for H2 qKr
Ž .
.
action 5 in Table 2 are plotted as filled squares in
Fig. 4. The solid line in this figure is an experimental
Fig. 5. Arrhenius plot for IqH2 over the temperature range,
Ž
.
220–2700 K. The points are from: Table 1 B ; Sullivan, see text
Ž
.
Ž
.
Ž .
I ; Lorenz et al., see text ' ; Umemoto et al., see text v ;
and Vasileiadis and Benson, see text l . The line is calculated
Ž
.
Ž .
Fig. 4. Arrhenius plot of inferred rate constants B from profile
fits for H2 qKr HqHqKr. The line is from the experiments
of Du and Hessler see text .
from the linear least-squares representation of the data as given in
Ž .
Eq. 6 .
Ž
.

(
)
104
J.V. Michael et al.rChemical Physics Letters 319 2000 99–106
w x
Results for the reverse reaction come from three
the H2 andror D2rI2 systems 6 . Garrett and Truh-
lar studied several H-atom transfer reactions, includ-
ing the title reaction, by combining the bond en-
w
x
previous studies 8–10 . Vasileiadis and Benson have
reviewed this earlier work and have evaluated k2 to
be 6.2=10y11 exp y327"35 KrT cm3 mole-
Ž
.
Ž
.
ergy–bond order BEBO method with variational
transition state theory 26 . Baer and Last used a
modified diatomics in molecules DIM method to
determine potential energy surfaces for both abstrac-
culey1 sy1 over the temperature range, 230–373 K.
w
x
w
x
Ž
.
Using Janaf equilibrium constants 22 , we have
transformed the individual values from these studies
to k1. From Lorenz et al. 8 , k1 is: 1.41=10y39
,
w x
w
x
tion and exchange reactions 27 . Umemoto et al.
used an extended London–Eyring–Polanyi–Sato
7.06=10y35, and 6.81=10y30 cm3 moleculey1 sy1
Ž
.
at 250, 298, and 373 K, respectively. From Umem-
LEPS method to evaluate transition state configura-
oto et al. 9 , k1 is: 2.46=10y42, 1.16=10y40
,
w x
tion, force field, and energetics for the title reaction
and isotopic variations thereof. They then applied
both conventional and variational transition state the-
ory to calculate absolute rate constants and isotope
6.23=10y39, 1.73=10y37, and 4.05=10y35 cm3
moleculey1 sy1 at 230, 242, 257, 270, and 297 K,
respectively. The 298 K value from Vasileiadis and
Benson gives k1 s7.06=10y35 cm3 moleculey1
sy1. These values are also included in the Arrhenius
plot shown in Fig. 5.
w x
effects 9 . With an extended basis set, Anderson
w
x
2,28 performed ab initio electronic structure calcu-
lations using the Gaussian method.
The line in Fig. 5 is a linear least-squares repre-
sentation of the entire database and is given by,
In this study, the BEBO method has been applied
along with conventional transition state theory
Ž
.
CTST to estimate rate constants for IqH2. The
log k1rcm3 moleculey1 sy1
linear transition state was found to be very near to
.
˚
˚
.
Ž
products RH – H s1.755 A and RH – I s1.609 A at
E10 s34.387 kcal moly1. Since D E00 s32.840, E20
s1.547 kcal moly1. The vibration frequencies at the
sy 9.345"0.031 y 7413"14K rT ,
6
Ž .
Ž
.
Ž
.
Ž .
over the range, 230–2605 K. The points are within
"24.6% of the line at the one standard deviation
level with the largest absolute difference between the
saddle point are: ns s2231, n b s225 2 , and ni s
307i cmy1. CTST calculations with Eckart tunneling
give predictions that do not agree with experiment.
Ž
w x
points and line being y54% i.e., the point at 2605
The LEPS surface of Umemoto et al. 6 was then
Ž .
K where Eq. 6 gives 6.5 whereas the experiment is
used. The transition state configuration has RH – H
s
10=10y13 cm3 moleculey1 sy1 . Within these er-
0
˚
˚
.
1.62 A and RH – I s1.62 A with E1 s33.595 and
E20 s0.755 kcal moly1. The vibration frequencies
Ž .
ror ranges, Eq. 6 is applicable over ;30 orders of
y1
Ž .
magnitude. We know of no other property of any-
thing in any branch of science that is describable by
a linear relationship over this large dynamic range.
Hence, the IqH2 reaction system is unique for at
are: ns s2129, n b s307 2 , and ni s1934i cm
.
Again, applying Eckart tunneling, the calculations do
not agree with experiment, principally because the
bending frequencies are so low that too much curva-
ture is predicted in the Arrhenius plot. As in the
Ž .
least two reasons: a as mentioned above, it was part
w
x
of the consideration of Bodenstein in the first gas-
ClqH2 reaction 11 , the bending frequencies have
to be substantially increased in order to reconcile
theory and experiment. Therefore, we have modified
the LEPS surface of Umemoto et al. by adjusting E10
w x
Ž .
phase dynamics study ever performed 1 ; and b the
linear description of its rate behavior is applicable
over more orders of magnitude than any other prop-
erty in the entire field of science.
to 33.490 kcal moly1 so that E20 s0.650 kcal moly1
the evaluated value of Vasileiadis and Benson 10 .
The lowest standard deviation between experimental
,
Ž .
w x
Theoretical calculations on reaction 1 and its
reverse have already been made; however, these
calculations are not sophisticated simply because the
potential energy surface has not been determined
with high-level ab initio electronic structure theory.
Sullivan used transition state theory methods and
measured isotope effects to try to rationalize data in
Ž .
and predicted values is obtained with n b s486 2
cmy1. Eckart tunneling factors were included even
though they are small and only increase the predic-
tion at 230 K by less than a factor of two. To within
-5% over the range, 230–2605 K, a three-parame-

(
)
J.V. Michael et al.rChemical Physics Letters 319 2000 99–106
105
Ž
.
ter non-linear least-squares fit to the Eckart calcula-
tion is,
procedure might yield higher or perhaps lower
effective bending frequencies, but it may in turn then
reconcile the present and past discrepancies between
theory and experiment.
k1th s4.092=10y16 T1.812
=exp y16 056 KrT cm3 moleculey1 sy1
.
7
Ž
.
Ž .
Ž .
Acknowledgements
The data points are within "33.0% of Eq. 7 at the
one standard deviation level with the largest absolute
Ž .
difference being q80% at 373 K where Eq.
7
The authors want to thank Drs. A.F. Wagner and
L.B. Harding for useful discussions. This work was
supported by the US Department of Energy, Office
of Basic Energy Sciences, Division of Chemical
Sciences, under Contract No. W-31-109-Eng-38.
gives 3.78 whereas the experiment is 6.81=10y30
cm3 moleculey1 sy1. Hence, the adjusted theoretical
fit, Eq. 7 , is substantially worse than the linear
expression, Eq. 6 . The ‘best’ theoretical fit requires
both energy and bending frequency scaling. We have
found that mutual optimization of both quantities
Ž .
Ž .
with Wigner tunneling gives predictions that are
0
Ž .
close to that from Eq. 6 , i.e., "25.4% with E1 s
References
34.027 kcal moly1 implying E20 s 1.187 kcal
Ž
moly1 and n b s520 2 cmy1. Mutual optimization
using Eckart tunneling always gives a worse compar-
ison with the data. The Wigner calculation gives the
largest absolute difference at 230 K, y44%, where
the calculation gives 4.36 whereas the experiment is
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