Kinetics and mechanism of the gas phase oxidation of sulfur dioxide

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Kinetics and mechanism of the gas phase oxidation of sulfur dioxide
Nold, Charles Robert
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117 leaves : illustrations ; 29 cm


Subjects / Keywords:
Sulfur dioxide -- Oxidation ( lcsh )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )


Includes bibliographical references (leaves 108-109).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Chemistry
Statement of Responsibility:
by Charles Robert Nold.

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Source Institution:
|University of Colorado Denver
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|Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
20960254 ( OCLC )
LD1190.L46 1989m .N64 ( lcc )

Full Text
Charles Robert Nold
B.A., University of Colorado at Denver, 1986
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Chemistry

This Thesis for the Master of Science Degree by
Charles Robert Nold
has been approved for the
Department of
z8y ns*?

Nold, Charles Robert (M.S., Chemistry)
Kinetics and Mechanism of the Gas Phase Oxidation
of Sulfur Dioxide
Thesis directed by Professor Larry G.Anderson
The initial step in the gas phase oxidation
of sulfur dioxide is the production of the H0S02
radical by the reaction OH + S02 H0S02.
Airshed models used to predict sulfuric
acid concentrations treat the next step in the
mechanism as a lumped process such as: OH + S02^-~
H2S04. This erroneously neglects elementary
reactions of the bisulfite radical, reactions which
may act as a sink for the radical thus ultimately
affecting the H2S04 concentrations.
Airshed models which do not treat the gas
phase oxidation of sulfur dioxide by a lumped
mechanism as mentioned above may have incorrect
mechanistic information regarding the elementary
reactions of the bisulfite radical. Some models
treat the reaction of H0S02 with 02 as an addition
reaction, the 02 adds to the H0S02 and others
treat the process as a hydrogen abstraction
mechanism, H02 allows regeneration of OH, and S03
is formed as a result of the reaction.

This work supports the hydrogen abstraction
reaction and report rate constants for the
bisulfite reactions with 02 and NO. The rate
constant for the H0S02 reaction with 02 is
(4 i 2) x 1013 cm3/molecule sec. The rate
constant for the H0S02 reaction with NO is (2 1 1)
x 10-12 cm3/molecule sec.
The H0S02 + 02 reaction rate constant is
large enough to affect the mechanistic pathway
of S02 conversion to H2S04. This step in the
process will proceed by a hydrogen abstraction
reaction, with the regeneration of a hydroxyl
radical. Airshed models using this mechanistic
and kinetic information should predict a more
linear relationship between S02 emissions and
H2S04 deposition, resulting in more accurate
model results.
The H0S02 + NO reaction rate constant is
not large enough to be a significant factor in
reducing the H0S02 concentration in the
atmosphere, given the concentration of NO in
polluted air.
These studies indicate that a H0S02
complex with water either does not exist and/or
that it does not significantly affect the

kinetics or mechanism of the H0S02 reaction with
02. Hense, water vapor complexation with H0S02,
if it occurs, does not affect the atmospheric
oxidation of S02 by hydroxyl radicals.
The form and content of this abstract are approved.
I recommend its publication.

The author wishes to thank first and
foremost Dr. Larry G. Anderson for his support
in all areas of this research.
Juan Bonilla was very helpful during
many stages of this project and his help is
appreciated. Other students who assisted in
areas of this project and whose assistance is
appreciated are Paul Gates and Grant Underwood.

I. INTRODUCTION.............................. 12
The Chemistry of Interest............... 16
II. EXPERIMENTAL............................ 2 9
Discharge-flow Apparatus................ 31
Hardware................................ 34
Flow Tube............................ 35
Flow controllers................... 39
Pressure measurement............. 4 0
Calibration............................. 41
Detector................................ 48
Software................................ 51
Experiment Design....................... 54
OH Radical Production................ 55
Titrations........................... 56
H0S02 Production..................... 59
Pre-Titration Experiments............ 60
N02 titration...................... 60
N02 baseline signal count.......... 60
S02 baseline signal count.......... 61

NO baseline signal count......... 61
02 baseline signal count......... 62
02 titrations....................... 63
NO titrations....................... 65
III. RESULTS and DATA ANALYSIS................. 67
Chemical Model.......................... 69
Rate Constants of Interest.............. 74
Data Analysis Theory.................... 75
02 titration: NO close.............. 78
02 titration: NO far................ 88
NO titration: NO far................ 95
H20 experiments...................... 101
Conclusions............................ 104
Bibliography................................... . 108
A. System Hardware.......................... 110

1. N02 Base Results....................... 61
2. Reaction Mechanism..................... 76
3. Values for kg..........................105
4. Values for k10.........................106
5. Features of the Lab Master Board.......112
6. Flow Controller Logic..................116

1. Flow tube for H0S02 reaction with 02 & NO.32
2. Flow tube for H0S02 reaction with H20......3 6
3. Calibration of N02 flow controller, WTM...43
4. Calibration of N02 flow controller, bulb..43
5. Calibration of N02 flow controller, bubbl.45
6. Calibration of N02 flow controller, bubbl.45
7. Linear Regression Bulb, WTM and Bubble ...46
8. Residual plot of linear regression.........46
9. Polynomial regression Bulb, WTM and Bubbl.47
10. Residual plot of polynomial regression....47
11. Resonance-Fluorescence detector............49
12. N02 titration results......................57
13. N02 titration analysis.....................58
14. N02 titration model results................72
15. [OH] vs [H] model result curve.............73
16. 02 titration, NO close to PMT, Low OH.....79
17. 02 titration, NO close to PMT, High OH....80
18. Model 02 titration, NO close, Low OH......82
19. Model 02 titration, NO close,High OH......83
20. Model 02 titr.,NO close, vary k8. .......84

FIGURES (cont.)
21. Model 02 titr.,NO close, vary k10..........86
22. Model 02 titr.,NO close, vary H02..........87
23. 02 titration, NO far from PMT, Low OH 89
24. 02 titration, NO far from PMT, High OH....90
25. Model 02 titration, NO far, Low OH.........91
26. Model 02 titration, NO far, High OH........92
27. Model 02 titr, NO far, increase k8.........93
28. Model 02 titr, NO far, decrease k10........94
29. NO titration, NO far from PMT, Low OH 96
30. NO titration, NO far from PMT, High OH....97
31. Model NO titr., NO far, Low OH.............98
32. Model NO titr., NO far, High OH............99
33. Model NO titr., NO far, increase k8.......100
34. Model NO titr., NO far, decrease k10......102

Acid deposition control strategy as
presently implemented by the National Acid
Precipitation Assessment Program uses chemical
kinetic computer submodels of airshed and
long-range transport models to describe the fate of
sulfur dioxide and nitrogen oxides and their
reaction products in the natural and polluted
troposphere (1).
There are three major submodels which
combine to form an airshed model (1). First is the
submodel for emissions of the primary pollutants,
including their chemical nature, locations, and
temporal variations. Second is the submodel for
meteorological and topographical features of the
region, including such parameters as temperature,
relative humidity, wind speed and direction,
atmospheric stability, inversion height, surface
elevation, and other terrain features. The third
submodel is the chemistry of the pollutants,
including both the kinetics and mechanisms of the

reactions converting the primary pollutants into
secondary pollutants.
The phenomenon of acid rain has generally
been assumed to result from the long range
transport (LRT) of pollutants. In the United
States for example, LRT from the Midwest and South
has been suggested as a major cause of acid
precipitation in the northeastern states. Because
of the complex meteorology involved in such LRT,
early computer models for acid rain which
incorporated the emissions, meteorology, and
chemistry only included simple chemical submodels.
Prior to 1980 the chemistry of S02 in these models
was often treated in terms of only one lumped
reaction, Reaction [1].
S02 + OH --- H2S04 [1]
The value of k-^ was calculated somewhat arbitrarily
based on field observations and chemical intuition
The first attempt to incorporate S02
chemistry into a LRT model was done by Rodhe,
Crutzen and Vanderpol in 1981 (2), using the lumped
mechanism of Reaction [1] to represent H2S04
formation. They calculated the deposition of

sulfuric acid at various points downwind under
conditions they judged to be representative of
those in northern Europe in 1955 and 1975. At
downwind travel times of 10 h, for example, the
concentration of sulfuric acid was predicted to
increase by 30% over this 20 year period,
despite an increase in S02 emissions ofa70%. In
fact, most of the calculated 30% increase in H2S04
is due to an assumed increase in the direct rate of
emission of H2S04. If this direct emission of acid
had been assumed to remain constant, the model
predictions after 10 h would show a net decrease in
H2S04 formation despite the large increase in S02.
The term "non-linearity" refers to a non-
linear relationship between sulfur dioxide
emissions and H2S04 deposition. Although the amount
of H2S04 produced increases as S02 increases, it
does not do so in direct proportion to the S02
increase (3). "Nonlinearity" arises from the
assumed removal of one OH radical for each S02
oxidized, (Reaction [1]), since OH is the limiting
reagent. As S02 is increased, if the oxidation is
by Reaction [1], the OH radical concentration will
decrease. The Rodhe model calculates that
reductions in the deposition of H2S04 are predicted

not to be directly proportional to reductions in
S02 emissions, thus there is a non-linearity
between sulfur dioxide emissions and H2S04
Rodhe and co-workers emphasized that the
chemistry itself was simplified. This first
attempt at incorporating S02 chemistry into an LRT
model illustrated the importance of including
detailed chemistry in these models. Since then a
number of comprehensive research programs
directed toward developing LRT models that
incorporate detailed chemistry in both the gas and
liquid phases have been initiated in laboratories
around the world. Models are currently being
developed in the United States by the National
Center for Atmospheric Research (the RADM model
1985), by Environmental Research and Technology
(4), and by Systems Application Inc. (5,6).
Paramount to the success of a useful
model is the correct kinetic and mechanistic
information for reactions of atmospheric
significance. Such input can only be obtained piece
by piece, usually involving complicated, time
intensive research of the elementary reactions that
contribute to the overall process of interest. The

subject of this work is just that, a small, but
vital piece of the overall picture.
The Chemistry of Interest
There are serious social and economic
implications derived from the application of kinetic
data in computer models that assess the impact of
anthropogenic chemicals in the troposphere and
stratosphere. This situation has increased the
concern for reliable and accurate rate and
mechanistic data for a wide range of atmospheric
This work addresses the gas phase oxidation
of sulfur dioxide to sulfuric acid. Reliable
studies must be performed to elucidate the
mechanistic pathway of S02 conversion to H2S04.
These studies concern the gas phase elementary
reactions which are responsible for sulfuric acid
The goal of this work is to correctly
identify the kinetic and mechanistic pathways of
the gas phase oxidation of sulfur dioxide. With
this information, hopefully the National Acid
Precipitation Assessment Programs' models can
function correctly. Given correct source input

of sulfur dioxide and other pertinent information,
the model should be able to correctly predict
quantities of acid deposition. The discussion
below indicates the importance of correct rate
and mechanistic input to insure the correct
output of the model.
Possible side reactions of the bisulfite
radical which are examined in this study are its
reaction with NO, 02 and H20. Rate and mechanistic
data are determined for these reactions.
Sulfuric acid formation begins with an
ozone molecule which photolytically decomposes to
electronically excited oxygen atoms, 0(1D), with
sunlight absorption at the short-wavelength region
of the spectrum by Reaction [2]. The O^D) species
formed in Reaction [2] is much more reactive than
the groundstate 0 atoms 0(3P), often symbolized by
0. 0 (-^D) reacts efficiently when it collides with
a water molecule by Reaction [3] to form a highly
important transient in atmospheric chemistry, the
hydroxyl radical, [OH].
03 + hv(290-350nm) --- 0(1D) + 02 [2]
0 (1D) + H20 ---
2 OH

The hydroxyl radical, unlike many other
radicals, is unreactive toward oxygen. It
survives to react with most atmospheric impurities
(pollutants) such as the hydrocarbons, aldehydes,
NO, NO2, SO2 and CO.
In the presence of sulfur dioxide and
oxygen, the hydroxyl radical will, form sulfur
trioxide by a multistep process involving the
bisulfite radical (not shown in Reaction [4]).
Reaction [4] is only a general schematic
equation of the oxidation process, and not
meant to depict elementary reactions. Sulfur
trioxide will react with water to make sulfuric
acid, Reaction [5] (7).
OH + S02 + 02 ---- S03 [4]
S03 + H20 --- H2S04 [5]
Though there are many possible oxidation
processes for S02, the major rate-controlling step
in the gas-phase oxidation of SO2 in the
troposphere is generally accepted by atmospheric
scientists to be Reaction [6]. Reaction [6] is
important in tropospheric chemistry since it is the
first step in the conversion of S02 into sulfuric

acid. M is any species which can serve to
deenergize the excited H0S02 radical and stabilize
the H0S02 radical.
OH + S02 + M ------H0S02 + M [6]
At atmospheric pressure, Reaction [6] is in
the falloff region between third and second order.
The effective bimolecular rate constant recommended
for 1 atm and 25C is k6(bi) = 9 x 1013
cm3/molecule sec (8) with an uncertainty of
approximately 150%. For an average OH concentration
of 1 x 106 molecules/cm3, the natural lifetime of
S02 with respect to this one gas phase process will
be 13 days.
Reaction [6] has been extensively studied
(10,16,17). The rate constant for this reaction,
k6 has been measured by flash photolysis
resonance fluorescence technique at pressures
ranging from 13 Torr to 1 atm with various third
bodies (He, Ar, N2, SFg) and at temperatures up to
424 K. Results of experiments at pressures below
10 Torr carried out by using the discharge flow-
resonance fluorescence techniques have been reported
(9) (p=l-4 Torr, T=298 K, M=Ar,N2).

Until very recently computer airshed
models have treated the gas-phase oxidation with a
lumped mechanism as shown in Reaction [1] ignoring
the formation and the possible side reactions of
the bisulfite radical (7) The problem with this
lumped mechanistic treatment is that if the
bisulfite radical reacts with any atmospheric
constituent at a significant rate, the bisulfite
radical concentration will decrease, ultimately
changing the H2S04 concentration that the model
predicts. It is paramount that computer airshed
models used to predict sulfuric acid concentrations
have as their input the correct kinetic and
mechanistic input.
A large number of reactions involving H0S02
have been suggested. These reactions pass the
first test often applied: the potential candidate
reactions must have the thermodynamic potential to
occur. This can be measured qualitatively by the
sign of the enthalpy change (AH) for the overall
reaction. If it is negative, or exothermic (heat
is released as the reaction occurs at constant
pressure), this could indicate a low activation
energy barrier and a reasonably fast reaction. If
AH is highly positive for a given reaction, the

activation energy may be large and the reaction
then would be slow.
Another thermodynamic consideration for the
determination of the spontaneity of a reaction is
the entropy change. A significant increase in
entropy between reactants and products may be
sufficient to overcome a slightly positive AH.
These points will be brought to bear later in the
discussion of the bisulfite radicals possible
reaction with H20.
Equilibrium thermodynamics, however tells
us nothing about the rates of chemical processes,
and the rate of the reaction must be fast enough
to make the reaction significant. Thus,
elementary rate constants for these reactions must
be determined. These data, coupled with
estimates of the concentrations of the transients
in the atmosphere, allow us to evaluate the
significance of each reactant in oxidizing S02 in
the atmosphere (15).
It has been proposed that the bisulfite
radical would react with oxygen in an addition
reaction forming the peroxybisulfite radical,
H0S0202 (16), Reaction [7]. M is any species which
can serve to deenergize the excited H0S0202 radical
and stabilize this radical.

H0S02 + 02 + M----H0S0202 + M [7]
The H0S0202 would eventually produce H2S04
by an unknown mechanism. This reaction is
exothermic by 67 kJ/mol and the prevalence of
oxygen among the atmospheric gases would suggest
that may be a major pathway.
There is probably not much H0S02 in the
atmosphere due to its rapid reaction with 02 (kg =
4 x 10-13 cm3/molecule second) (11). Reaction [8],
H0S02 + 02 --- H02 + S03 [8]
the H0S02 reaction with 02, is probably the
predominant fate of the bisulfite radical because
of the high concentrations of 02 in the atmosphere.
A possible observation of atmospheric H0S02 has
been reported by Arnold et al. (12) from in situ
stratospheric ion composition measurements. They
identified a series of negative ion clusters
HS04(H2S04)nHS03, n=l-3, containing an H0S02
ligand. Using their composition measurements and a
model of ion and neutral chemistry, they were able
to infer [H0S02]= 3 x 105 molecule cm-3 at 40.8 km.
It should be noted that their mass resolution was
1 amu so they could not distinguish between S03
and H0S02. A reevaluation of the data led to

the conclusion that the experiment did not estimate
H0S02 or S03 concentrations in the atmosphere (13).
Another possible observation of this
radical comes from the work of Hashimoto et
al. (14) who have reported a tentative
identification of H0S02 trapped in an Ar matrix
at 11 K using FTIR spectroscopy.
There appears to be good evidence that
H0S02 is formed in Reaction [6] and it ultimately
leads to the generation of sulfuric acid aerosol.
However, H0S02 is a free radical that is probably
highly reactive toward several atmospheric
compounds and it is not now clear what elementary
reaction pathways are important in the conversion
to H2S04.
Although Reaction [8] is endothermic by 25
kJ/mol, Stockwell and Calvert (7) have found some
evidence for its occurrence. This result has been
confirmed by Margitan (17) in a flash photolysis
study of the S02 + OH reaction, in which OH was
regenerated in the system through Reaction [8]
and Reaction [9].
H02 + NO-----t- N02 + OH [ 9 ]
Margitan reported a rate constant k8 =(4 i 2) x

10-13 cm3 molecule-1 s-1 using a computer simulation
of the reaction mechanism. Schmidt et al. also
reported the regeneration of OH from a photolysis
study of the OH + S02 reaction in 1 atm of
synthetic air and in the presence of NO (18).
Whether the H0S02 + 02 reaction proceeds by
an addition mechanism or by a hydrogen abstraction
has an important effect on the models used to
describe atmospheric S02 oxidation. If the
addition reaction, (Reaction [7]) were the dominant
channel, each S02 oxidized removes at least one OH
radical from the atmosphere thus S02 will deplete
the atmosphere of OH. The atmospheric depletion of
the hydroxyl radical occurs because the H0S02
radical cannot participate in Reactions [8] and [9]
to regenerate the hydroxyl radical. Since the
source of OH, Reaction [3], is weak, the atmosphere
can become depleted of OH when the S02
concentration is high, as in a power plant or
smelter plume.
If Reaction [8] were the dominant channel,
the H02 product may react with NO, Reaction [9], to
regenerate OH. In this case, S02 will not deplete
the atmosphere of OH. We will give evidence for a
mechanistic route involving Reaction [8]._

Additional evidence for the hydrogen
abstraction channel was given by McKeen et al.(19)
who modeled the stratospheric effects of the 1982
El Chichon volcano plume. If Reaction [7] were the
dominant channel, volcanic S02 would reduce the
stratospheric [OH], and the plume should show the
effects of this reduced OH concentration, e.g.,
increased [O3]. The [03] would increase for the
following reason. The anthropogenic source of 03
is a two step process that begins with the
photolysis of N02 to make NO and 0 atoms. The 0
atoms react with 02 to make 03. If [OH] decreases,
less OH will react with the N02 and thereby leaving
more N02 to produce 03, thus increasing the 03
concentration. Experimental observations of the El
Chichon plume showed no [03] increase (19) and
Burnett et al. (20) observed an increase in the
total column [OH].
To summarize the above discussion, we want
to perform mechanistic studies on the bisulfite
radical's reaction with 02. We will show that the
hydrogen abstraction mechanism is the correct
pathway, Reaction [8], as opposed to the addition
mechanism, Reaction [7].

Other proposed reactions of H0S02 and
H0S0202 include reactions with NO, N02, H20,
hydrocarbons, and surface absorption
Where there are regions of high S02 and OH
concentrations, there is likely to be considerable
NO concentrations. If Reaction [10] is happening
at a significant rate, it could act as a sink for
the bisulfite radical. Thus Reaction [10] should be
studied to determine it's atmospheric significance.
H0S02 + NO ---PRODUCT [10]
Reaction [10] is studied using a
discharge flow resonance fluorescence system
and a rate constant determined for this process.
With a rate constant and atmospheric concentrations
of NO we can determine the importance of this
process and whether or not Reaction [10] will act
as a sink for the bisulfite radical, thus affecting
the overall S02 oxidation mechanism.
Another possible fate of the H0S02 radical
is its association with H20 by Reaction [11].
H0S02 + H20 .H0S02H20 [11]

Friend proposes this elementary reaction to
rationalize their observed rates of aerosol
nucleation in the S02 oxidation by OH radicals
(22). A major point in favor of Reaction [11] is
that H20 will complex and/or react with S03 which
is structurally similar to H0S02 (9,10,24), so
H20*H0S02 formation is possible. However, Chen
and Plummer suggest that the S03*H20 complex may
dissociate back to reactants with about the same
probability as it rearanges to sulfuric acid (24).
The large entropy decrease that accompanies
the association of the bisulfite radical and water
molecules must be overcome by a significant energy
release or the complex will be unimportant. Calvert
and Stockwell illustrate this point using reasonable
estimates of the thermodynamic quantities
associated with Reaction [11] (25).
If at 298 K, AH-L^-SOkJ/mol and aS31
=-37.3 eu at 1 atm standard state (this aH estimate
was taken as one-half the enthalpy change for the
reaction H20 + S03 H2S04; the AS was taken as equal
to that for this same reaction), then at 50%
relative humidity and 298 K the ratio of the
concentration of the H0S02*H20 complex to that for
the uncomplexed H0S02 radical at equilibrium would

be only approximately 4xl0-3. However the stability
of the complex is very sensitive to the magnitude
of For example if aH-^ is approx. -68
kJ/mol then the ratio of complex to uncomplexed
radical at equilibrium would be 100:1 at 50%
relative humidity and 298 K.
Calvert and Stockwell (25) do not believe
that AH^ is less than -50 kJ/mol and favor the
abstraction of H by S02, Reaction [8], as the
dominant fate of the bisulfite radical in the
troposphere. The above arguments of Calvert and
Stockwell (25) are based largely on chemical
intuition and should be questioned. The best way to
determine whether H20 has an effect on the S02
oxidation mechanism is to go into the laboratory
and perform experiments designed to look for
effects, as we have done.
We have studied the bisulfite
radical's mechanistic pathway on its way to
sulfuric acid aerosol and provided evidence for the
hydrogen abstraction mechanism. In addition, the
rate of Reaction [10] was studied and a rate
constant determined to see if this reaction is of
atmospheric significance. The reaction of the
bisulfite radical with H20 is studied to determine
if thisxwill affect the S02 oxidation mechanism.

Chapter II
The experimental system chosen to study the
bisulfite chemistry is known as a discharge
flow-resonance fluorescence system. The "discharge
flow" refers to the physical flow tube and radical
production and the "resonance fluorescence" refers
to the detector used on the system. In this
method, the time dependences of concentrations are
determined by measurement at different distances
along the axis of a tube, usually cylindrical.
Atoms are rapidly pumped along the length of the
flow tube under steady state conditions. In the
case of a velocity of gas flow which is constant
with respect to both axial and radial displacement
(plug flow), distance along the tube axis and
reaction time are in direct proportion.
The discharge flow technique dates from
around 1958. This date marked the establishment of
the first simple, specific and reliable method for
the determination of atom concentrations, the
measurement of oxygen atom concentrations by

titration with N02 (26).
The flow tube technique has been the most
prolific source of kinetic data near 300 K. There
are several advantages of this technique over some
others. One of the major advantages of the flow
tube technique is the immense variety of methods
that can be used to detect the reactants and
products. This advantage is derived from the
steady-state nature of the flow system in which the
progress of the reaction is frozen at any fixed
observation point along the tube. Since the
concentrations of the reactants are constant at
that point the detector can sample in real time.
The second major advantage of the flow tube method
is the great versatility it provides for working
with a wide variety of reactants. With the flow
tube method it is possible to generate two
different labile reactants in isolation and to
study their reactions under carefully controlled
conditions. Titration reactions, which will be
described later, play an important role in the
reactant versatility of the flow tube, since they
make it possible to produce accurately known
concentrations of labile reactants.

There are other advantages to using the
flow tube for gas phase kinetic studies. One is
expense. By using a simple detection scheme such as
chemiluminescence or resonance fluorescence, a flow
tube kinetic system can be assembled at low cost.
Another advantage is that the complex chemistry can
be simplified by introducing reactants at different
positions along the flow tube axis.
Discharge-flow Apparatus
A typical discharge flow apparatus consists
of four types of interconnected systems; (a) the
discharge tube and the flow tube; (b) apparatus for
the measurement of atom and radical concentrations;
(c) a system of flowmeters and vacuum valves; and
(d) an independent conventional high vacuum line
for gas handling, Figure 1.
The mode of operation is as follows.
Partially dissociated gas from the discharge is
pumped rapidly into the flow tube, where reactants
may be added and measurements obtained. For
measurements of the rates of reaction of atoms and
radicals, the flow tube is conveniently a
cylindrical or rectangular cross section glass or
silica tube of some 20-50 mm i.d., and 10-200 cm in

He-carrier gas
r \
Inj ection

Microwave Discharge


Excitation Ports
\ t /
Fluorescence Viewing Ports
Figure 1. Flow Tube for NO and 02 Experiments

length. In the experimental system used in these
studies a typical flow velocity was between 600 to
900 cm s-1, resulting in total reaction times
of .13 to 0.2 s.
The dimensions (particularly the diameter)
of the flow tube are restricted to those given
above by the requirements for plug flow. Plug flow
assumes that the velocity of gas flow is constant
with respect to both axial and radial displacement.
The range of total pressures over which reactions
may be studied is then similarly restricted (about
0.5-10 Torr).
The main variables other than time of
reaction in a kinetic study using the discharge
flow method are the partial pressures of reagents,
p^, including that of any third body M. These
partial pressures are simply related to the
corresponding flow rates of reagents F^, to the
total pressure p, and to the total flow rate, TF,
if all components approximated as ideal gases: p^ =
pFj/TF. (Note the distinction between flow rates
(mol s-1) and flow velocity (cm s-1). p is
measured directly with pressure gauges attached to
the flow tube.

A system of flow controllers is necessary
for the control and measurement of gases. The
accurate calibration of these flow meters is
essential to the measurement of rate constants free
from systematic errors, and a number of
discrepancies reported in the literature are
probably due to errors in flow meter calibrations.
The most common methods of calibration are based on
measurements of rates of pressure increase in a
calibrated volume. Calibration techniques are
discussed later.
This discussion of hardware will include
the flow tube and all associated hardware used in
the experiments.
Two computers were used for data
acquisition and control in these experiments, an
IBM XT Personal Computer model #5160 and a Zenith
Data Systems Personal Computer model #ZF 148-52.
The IBM has a hard disk, a 360K disk drive and 64OK
of memory. The Zenith has two 36OK disk drives and
640K of memory. There is a slight difference
between the data acquisition hardware on the two
computers. Because the digital to analog converter

(DAC) board has only two digital to analog (D/A)
channels a second board was added to the IBM with
an additional 4 channels. The Zenith has a
different board, a Data Translation DT2815 DAC
board that has 8 D/A channels, in addition to the 2
already provided by the Lab Master Board. This
provides for a total of 10 D/A channels.
Flow Tube
There were two different flow tubes used in
these experiments. Figure 1 shows a diagram of the
flow tube used in the NO and 02 experiments and
Figure 2 shows a diagram of the flow tube used in
the H20 experiments. The flow tubes are
constructed in pieces and held together by O-ring
joints and Thomas pinch clamps.
Both flow tubes are glass and were
constructed by the Rocky Mountain Scientific
Glassblowing Company. The inside walls are coated
with a halocarbon wax series #1500, batch no.
84-253 provided by Halocarbon Products Corporation.
The wax is a blend of completely halogenated
chlorofluorocarbons and is completely inert to all
acids, alkalis and oxidizing agents, wet or dry (as
claimed by the company). This coating has been

He-carrier gas
N02 H20/He

found to be very efficient in reducing the wall
reactions (27).
Flow tube lf used for the NO and 02
experiments, had an inside diameter of 30 mm. The
halocarbon wax wall coating was measured to be
0.5mm so the effective inside diameter for
calculation purposes was 29.0 mm. Flow tube 2,
used for the H20 experiments was manufactured with
an inside diameter of 25.0 mm. Using the same wall
coating of 0.5 mm, the effective diameter of flow
tube 2 was 24.0 mm.
The outside of the flow tubes was wrapped
with black felt to prevent light from entering the
detector through the flow tubes. There was no
temperature control of the flow tubes. All
experiments were run at ambient temperature. The
reaction kinetics should not be affected by the
narrow shift in ambient temperature during
experimental runs, though no sensitivity
calculations were performed to demonstrate this.
The entry ports of the different gases are
indicated in Figure 1. A H2/He mixture is passed
through a microwave discharge cavity which is
powered by an Opthos microwave power supply. The
forward power was maintained at 50 watts and the

reflected power was tuned for a minimum, usually no
higher than 0.5 watts. The H atoms were diluted
with He 13 cm from the discharge. He is the major
gas in the flow tube and thus serves to define the
physical properties of the gas stream e.g.,
pressure, flow velocity, heat capacity, thermal
conductivity, viscosity, etc. Helium is a common
choice as a carrier gas because of its inertness,
high thermal conductivity, and excellent diffusion
coefficients (28).
N02 enters the main flow tube axis 21 cm
from the microwave cavity. The N02 will rapidly
(1.3 x 10-10 cm3/molecule sec) react with the H
atoms to make hydroxyl radicals by Reaction [12].
H + N02 OH + NO [12]
There are 9.5 cm from the N02 entry point
and the NO port. Between the NO port and the S02
ports and the each of the next three consecutive
ports there are 10.7 cm. Continuing along the flow
tube axis there is a side arm with two ports. One
is capped and the other is an NO port which is
located 22.5 cm from the detector.

Flow controllers. Gases are controlled by
calibrated Unit Instruments mass flow controllers
model UFC-1000. These flow controllers require 15
VDC power input and a 0-5 VDC input voltage for
complete operation. A thermal flow sensor develops
a linear output signal from 0-5 VDC over the
selected flow range. The operator programs the
computer to supply an input voltage which is the
"set point" voltage. The controller will maintain
preset mass flow rate to within 0.2% of setting
when the pressure differential across the flow
controller is between 10-50 psi. The flow
controller accuracy is 1% of full scale.
Flow controller operation is as follows.
The software asks for a flow for a particular gas
in units of standard cubic centimeters per minute
(seem). The software inputs that flow (seem) into
a subroutine containing calibration curve
information for that flow controller. The voltage
needed to set the flow controller is calculated and
sent to the digital to analog converter for
conversion and output to the flow controller. The
flow controller will also measure,the amount of gas
that is actually flowing and output a voltage to

the analog to digital converters for input to the
computer. This output voltage is used in gas
concentration calculations.
The flow controller valves may be closed
regardless of whether or not there is a set voltage
applied to the flow controller.
Pressure measurement. Total pressure was
monitored by a calibrated MKS baratron 0-10 Torr
pressure gauge. The MKS baratron Type 122A
Absolute Pressure Transducer is inherently
temperature stable at zero pressure and capable of
withstanding high overpressure conditions and is
self compensating with temperature changes at other
pressures. It is accurate to lo.5 % and pressure
measurements are totally independent of the gas
type or composition. It is powered by ll5 VDC and
outputs 0 to 10 VDC over the 0-10 Torr pressure
range. The MKS is a capacitance manometer which
consists of a flexible metal diaphragm placed
between two fixed electrodes. When different
pressures are applied to each side of the diaphragm
it causes a deflection which results in a change in
capacitance between the electrodes, thus a change
in output voltage. One side of the diaphragm is
vacuum sealed to less than 107 Torr and the other

side receives the pressure which causes the
The pressure port is located at the center
of the reaction zone to minimize errors and
corrections due to the pressure gradient in the
flow tube. The pressure port is smooth and oriented
at right angles to the gas flow in order to measure
only the static pressure in the flow tube. The MKS
baratron output is read by a Dana Digital Voltmeter
model 4470 and the analog signal is also sent to
the analog to digital convertor so that the
computer may also read and process the current
In order to be able to relate the counted
fluorescence photons "signal" to something
meaningful such as concentrations of OH radicals
used in experiments, it is necessary to accurately
know the flows of gases into the system.
Therefore, the Unit Instruments Mass flow
controllers are subjected to a rigorous calibration

Three different calibration methods are
used for the flow controllers. Particular
attention was paid to the N02 flow controller
because it is fundamental to the understanding of
the quantity of OH in the system. To calibrate the
N02 flow controller the three methods used are the
wet test meter (WTM), the bubble meter and the
calibrated bulb method. The wet test meter simply
records the amount of flow during a given amount of
time and this rate is plotted versus the output
voltage from the flow controller. This curve is
shown in Figure 3.
Another calibration method employs a bulb
of known volume, which we call the bulb method.
This methods entails measuring the pressure rise in
an evacuated bulb as a function of time. The slope
from each pressure vs time plot is plotted versus
the output voltage for the corresponding curve. A
calibration curve of flow vs output voltage is
generated as shown in Figure 4. This task is
simplified using software developed in this
A third calibration method is the bubble
method. Using this method, one watches the motion
of a soap bubble being pushed by a flow from the

4 3
Figure 3. N02 flow controller calibration, WTM
Figure 4. N02 flow controller calibration

flow controller up an incremented tube. The rise
in a given amount of time is measured and this rise
is converted to volume. Thus, the flow during a
measured amount of time is plotted against the
output voltage from the flow controller, Figure 5
and Figure 6. These calibrations are done quite
easily using the software developed in this
Figure 7. shows a curve combining the
results of all three calibration methods for the
N02 flow controller. The curve appears to be
linear. A plot of the residuals, Figure 8.,
displays a nonrandom pattern indicating there may
be some sort of systematic error inherent in the
calibration methods. There appears to be a
nonrandom pattern to all three methods, and this
source of error cannot be identified. The
agreement between the three methods however, is
good. The WTM and the Bulb method agree within
0.5% and the Bubble method agrees within 5% of both
of those methods.
The data combining all three methods were
then subjected to a fourth order polynomial fit and
the results are shown in Figure 9. Figure 10, a
plot of the residuals still displays some sort of


Figure 8.
Residuals of Linear Regression
Bubble A WTM Q ,Bulb/

Figure 10. Residuals of Polynomial Regression
Bubble A WTMQ ,Bulb/

systematic error. The linear regression line
resulting from the combination of all three methods,
Figure 7., was used for the NO and 02 titration
experiments. In the future, and for the H20
experiments the fourth order polynomial line is
A diagram of the detector is shown in
Figure 11. A He/H20 mixture flows through a quartz
tube passing through a microwave cavity. The
outlet of the quartz tube is connected to a vacuum
pump and the system is maintained at a pressure of
approximately 10 Torr. The mixture of H20 and He
was obtained by passing the He through a vessel
containing H20.
The high energy microwaves split the water
into excited hydroxyl radicals and H atoms. The
excited hydroxyl radicals fluoresce giving off
light of 306 nm, forming a resonance lamp. The
light travels down a 20mm diameter tube (coated
with carbon black soot on the inside to absorb
stray light). The light passes through a focusing
lens designed to focus the light into the center of

Figure 11. Resonance Fluorescence
Detection System

the tube, then travels into the flow tube.
Hydroxyl radicals in the flow tube are excited by
the 306 nm light from the resonance lamp. These OH
radicals in the flow tube fluoresce, emitting light
in the 306 nm range isotropically.
A photomultiplier tube sitting 90 degrees
to the flow tube is used to detect fluorescence by
counting photons. The Woods horn is in position to
absorb any stray light which is not absorbed by the
OH radicals. This prevents light from bouncing off
of the opposite walls of the flow tube and into the
photomultiplier tube.
There is a narrow bandpass filter in front
of the photomultiplier transmitting light in the
304-310 nm range. The photomultiplier pulses are
then amplified and discriminated against with a
threshold level set to eliminate noise. The
amplifier/discriminator also converts ECL pulses
into TTL pulses and sends them to the counter on
the computer for counting and storage.
The signal is typically counted for 25 one
second periods, then a mean and a standard
deviation of the mean are calculated. If the
standard deviation of the mean is above a preset
fraction of the mean, typically 2 percent, the

current data are rejected and the counting process
begins again.
Software for control of experiments was
written in BASIC. Software written prior to my
entry into the graduate program was written by Juan
Bonilla and Paul Gates. Some calibration software
was written by Neil Anderson.
There are two data acquisition and control
programs used in these experiments. They are
identical except for the digital to analog
conversion subroutines. The IBM and the Zenith PCs
had different digital to analog boards. The
subroutine to set the analog voltages is different
and specific to each computer. The following
outline describes the program flow. After
completing one experiment another would begin if
the software had been programmed to do so.
I. Program the experimental parameters
A. Name the experiments.
B. Program the file 'OPERATE"
1. Calibration information for
each flow controller

2. Gas and concentration for
each flow controller
3. Number of experiments
4. Statistical stabilization
5. Counting period
(time interval)
6. Number of cycles of
counting period
7. "OPERATE" is stored to disk
C. Program gas flows
1. Gas flow in standard cubic
centimeters per minute (seem)
2. Amount of incrementation of
a gas if a titration is
being done
3. Number of repetitions for
this particular experiment
II. Data acquisition
A. Flow controller subroutines
1. D/D signal output to open
flow controllers
2. D/A signal output to set
flow controller valves.

3. A/D signal input from output
voltage from flow controllers
and pressure gauges
4. subroutine to average output
voltages and compare std.
dev. of mean to preset
statistical criteria and
either accept or reject data.
5. Counter counts TTL pulses
from amp/discriminator.
6. Subroutine to average
pulse counts and either
accept or reject based on
preset statistical criteria
and the std. dev. of the
7. repeat the above six
procedures for each
repetition in an exp.
B. Computational task
1. Gas concentrations are
calculated from input

2. Total flow in seem is
calculated from input
3. system velocity is
III. Output
A. Hard copy of all the above
B. All data stored to floppy
Experiment Design
The study of the kinetics and mechanism of
the bisulfite radical are complicated by the number
and variety of possible reactions. It is with this
in mind that we have attempted to design
experiments which will be very specific to the
chemistry we are interested in studying at that
The discharge flow tube, by virtue of its
construction and design affords the chemist the
opportunity to study very specific gas phase
processes. This can be done easily by varying the
entrance port and the concentration of reactant

OH Radical Production
The hydroxyl radical is produced in the
flow tube by passing a hydrogen-helium mixture
through a microwave discharge which produces H
atoms. The H atoms are reacted with nitrogen
dioxide according to Reaction [12].
The importance of titration reactions
cannot be overemphasized because they provide the
foundation for nearly all kinetic measurements in
flow systems. They are fast stoichiometric
reactions that provide clean and quantitative
methods of preparing labile species. Primary to
understanding data from the discharge flow system
used in these experiments is the determination of
the correct hydroxyl radical concentration.
To determine the hydroxyl radical
concentration, a gas phase titration was performed
before and after each set of experiments. H atoms
were titrated with N02 according to Reaction [12].
The titrations would generally proceed through 20
"repetitions". With each successive addition of
N02, the OH fluorescence signal will increase until
the titration reaches an endpoint, at which point
any further addition of N02 will not result in an

increase in the OH fluorescence signal, Figure 12.
If the N02 is increased even further there is a
decrease in the OH concentration due to the OH +
N02 reaction to make HN03.
The titration provides hydroxyl radical
concentration information (discussed in the
following paragraph) as well as information
regarding the optimum amount of N02 needed to react
with the H atoms. We want to add enough N02 so that
the H + N02 reaction rapidly goes to completion,
but not so much that we destroy OH by it's reaction
with excess N02 to make HN03.
A tangent is drawn by hand to two portions
of the curve as shown in Figure 13. A
perpendicular to the X axis is drawn from the
intersection of the two tangent lines to the X
axis. The resultant N02 concentration is the
endpoint of the titration. Because of Reaction
[12] stoichiometry the initial H atom concentration
equals the N02 concentration at the endpoint. The
H atom concentration is linearly related to the OH
radical concentration using a numerical model. The
OH concentration at the detector that is determined
is correlated with the OH fluorescence signal count
at the endpoint in the titration. This results in

Figure 12. N02 Titration Results

Figure 13.
NC>2 Titration Analysis

a "sensitivity factor", in units of (molecules/cm3
OH/OH fluorescence counts).
H0S02 Production
The bisulfite radical is produced by
reacting the hydroxyl radical with sulfur dioxide
according to Reaction [6]. Enough S02 is added,
approximately 1 x 1015 molecules/cm3, to assure
complete conversion of hydroxyl radical to H0S02
within the allowed reaction time of 20 msec.
The rate of a reaction is a function of
reactant concentration and a rate constant. Hence,
information about the reaction can be gained by
varying the concentration of one reactant while
keeping the other reactant concentrations the same
which is essentially a titration. To study the
bisulfite radicals' reactions with 02 and NO a
series of gas phase titrations were performed. The
bisulfite radical was titrated with either oxygen
or nitric oxide. These titrations were designed to
be done several different ways so that we could
look at very specific processes while making other
reactions occurring in the flow tube unimportant.

Pre-Titration Experiments
Prior to doing gas phase titrations, a
series of experiments were always performed so that
we understood what chemistry was going on in the
flow tube. The following experiments are an
example of an experimental sequence:
1. N02 titration
2. N02 base
3. S02 base
4. NO base
5. 02 titration
6. N02 titration
NOo titration. The N02 titration
experiment was performed before and after each
series of experiments to ensure a good
understanding of the OH concentration.
N02 base. The N02 base experiments
determine the OH fluorescence signal. The
concentration of N02 was typically 3.0 x 1012, H2
was 4 x 1011, He was 9 x 1016 molecules/cm3. Gas
flows were typically 30 standard cubic centimeters
per minute (seem) of 0.22% N02 in He, 1.25 or 2.5
seem of 0.2 % H2/He mixture, and 900 seem of He
diluent or carrier gas. The OH fluorescence signal
was very consistent and had a low standard
deviation, Table 1.

Table 1. N02 Base Results
Repetition OH Signal(counts) std. dev.
1 22,494 211
2 21,989 199
3 22,375 201
4 22,532 220
SOo base. Approximately 1-2 X 1015
molecules/cm3 of sulfur dioxide were added to the
system with the flows used during an N02 base.
This concentration of S02 corresponds to a flow of
about 9 seem. It was necessary to determine what
quantity of the signal would be lost by the sulfur
dioxide's reaction with OH to make H0S02. The S02
was always added at the same port shown on the flow
tube diagram, Figure 1.
NO base. To observe the effect of adding
NO to the system before the 02 was added, an NO
base experiment was done by adding NO to the flow
system at concentrations of 1 x 1014 molecules/cm3.
The other gases present were N02, H2 and S02. The
signal was expected to go down due to the NO
reaction with OH to make HONO, and this decrease
needed to be quantified. This experiment was also
done so that the effect of Reaction [9] could be

observed, the regeneration of the hydroxyl radical
after the 02 was added to create the hydroperoxyl
radjlcal. It was neccessary to see how much OH
was regenerated when the 02 was added, and the
NO base provided a bottom level to the OH
fluorescence signal, and additional signal could
be attributed to adding 02 to the system.
NO + H02 ---- OH + N02 [9]
The hydroperoxyl radical, H02, is formed when the
bisulfite radical reacts with 02.
The NO is added experimentally to the flow
system at two different locations depending on
which reaction being studied. The locations where
the NO is added are shown on the flow tube diagram,
Figure 1. NO is added either before or after the
H0S02 + 02 reaction has completed. This permits the
observation of the chemical competition of the NO
and the 02 for the H0S02 radical.
02 base. An 02 base experiment was run
during NO titration experiments only.
Approximately 2 x 1015 molecules/cm3 of oxygen were
added to the system. Other gases present in the
above mentioned concentrations were N02, H2/He,
S02, He. The effect of oxygen on the OH

fluorescence signal before titrating the bisulfite
radical with NO was quantified by this experiment.
Oi titrations. In order to study the
bisulfite's reaction with 02 a series of 02
titrations were performed. The oxygen was always
added at the same port, which is labeled on the
flow tube diagram, Figure 1. This reaction
distance provided adequate time for the H0S02 to
react with 02 before reaching the detector.
Several types of 02 titrations were
performed. They involve adding a constant
concentration of NO to the system at either of the
two NO ports shown on the flow tube diagram, Figure
1. Experiments where NO was added closer to the
detector, or the photomultiplier (PMT) are known as
"NO close". Experiments where the NO was added
farther from the PMT with respect to the other NO
port are known as "NO far". 02 titrations where NO
was added both close and far from the PMT, were
performed at different OH concentrations.
Different OH concentrations were obtained by
varying the H2/He flow through the microwave

After performing the essential experiments
described above an 02 titration would be performed.
All gases are flowing in the concentrations
described above and oxygen starts at zero and
increases to 2.0 x 1015 molecules/cm3.
Experiments were designed to be specific to
important processes. If NO is added far from the
photomultiplier, kinetic and mechanistic
information is obtained about both the H0SO2
reaction with NO and 02 at the same time.
Essentially NO and 02 are competing with each other
for the bisulfite radical. The H0S02 + NO reaction
will proceed at the same rate during the entire
experiment because the concentration of NO is not
changing. The rate of the H0S02 + 02 reaction will
change as a function of added oxygen.
When the NO is added to the flow system
close to the PMT during an 02 titration we are
looking at essentially only the H0S02 + 02
reaction. H0S02 will react with 02 to make H02 and
S03 long before the H0S02 radical makes it down the
flow tube to react with the NO. At high 02
concentrations there will be no H0S02 left to react
with the NO. This experiment was also important in
that it allowed us to study the H02 wall loss rate.

Titrations done at different initial OH
concentrations, "low OH", about 5 x 1011
molecules/cm3 and "high OH", about 1 x 1012
molecules/cm3 of OH. There should be no difference
in the data due just to working at different OH
concentrations, except higher signal.
NO titrations. NO titrations were
performed by titrating the bisulfite radical with
NO at concentrations from 0 to 2.5 x 1014
molecules/cm3. The titrations were done with the
following gases in the system: 02, N02, H2/He, He,
NO. NO was added to the system at two different
ports, one close to the PMT and one far from the
By titrating with NO far from the PMT the
H0S02 reaction with NO can be studied along with
the H0S02 + 02 reaction as the NO and 02 compete
for the bisulfite radical. Analogous but opposite
to the 02 titration the rate of the H0S02 + 02
reaction will remain constant, because 02 is not
changing. The H0S02 + NO rate will change as a
function of added nitric oxide.
Titrating with NO added close to the PMT
provides an indication of the rate of H02 wall
loss. Essentially all the H0S02 has reacted with

the 02 by the time the reactants make it to the
"far" NO port. NO cannot react with H0S02, but
reacts with H02.

Chapter III
The detection system on the discharge-
flow resonance fluorescence system only measures
photons. Since the experimentor is interested in
knowing what the hydroxyl radical concentration is,
the photon counts or signal, must be related
reliably to the hydroxyl radical concentration.
This task is effectively accomplished by using N02
titrations, discussed earlier in the experimental
A N02 titration data file will consist of a
list of the N02 concentrations entering the flow
tube and the corresponding OH signal. In order to
correlate each OH signal with an OH concentration
each N02 titration was subjected to the following
1. The program inputs a N02 data file
that was written to disk at the time
the experiment was performed.
2. The OH resonance fluorescence signal
that is produced by photon counting

is taken from the file and printed,
one OH signal corresponding to a par-
ticular N02 concentration, with the
N02 concentration continuously
increasing throughout the experiment
for a given number of repetitions,
usually 20.
3. The titrations were always started
with zero N02 flow but there were ap-
proximately 200 counts of measured OH
fluorescence signal due to background
light. Where there was no N02
but there was signal, this "back-
ground" signal was subtracted
from the total counts.
4. The graphical endpoint of the N02
titration in terms of the N02
concentration was entered in the
computer: This is necessary
because of the stoichiometry of
Reaction [12] the N02 concentration
should equal the H atom concentration.

5. To calculate the H atom concentration
in units of molecules/cm3, the flow
of N02 in units of seem must be con-
verted to molecules/cm3.
6. The program calculates:
1) The H atom concentration at the
endpoint in the N02 titration
2) The model OH concentration at
endpoint in the N02 titration
3) A sensitivity factor which
relates the measured
OH fluorescence signal to the OH
concentration. This factor was in
units of (OH concentration in
ppb)/OH measured fluorescence
Chemical Model
The above procedure refers to a model
during the analysis procedure. The N02 titration
data analysis is the studies first use of the Gear,
model (29) numerical algorithm which solves a
system of linear differential equations.
The chemistry occurring inside the flow
tube is extremely complicated. We have estimated
that there are 21 major reactions occurring at any

given time, depending on what gas has been
introduced into the system. The only measureable
chemical is the hydroxyl radical.
A rate equation can be written for all 21
reactions occurring inside the flow tube. The rate
constants for all but a few (the few being the ones
that we are studying) of the reactions are well
known and reported in the literature. With the
correct input, the model should predict correctly
what is happening inside the flow tube. All the
model has to do is solve the system of differential
Many differential equations that arise in
science cannot be solved analytically. Therefore
they must be solved by numerical methods. Solving
a differential equation numerically involves
calculating the behavior of the solution function
one step at at time and thus building up a
representation of the solution function in tabular
form. The solution is obtained as a set of points
that lie close to the solution function.
The Gear "model" is the numerical algorithm
used to solve the rate equations pertinent to our
flow system. The model matches the N02 titration
experiment very well, as it should since this is

the simplest of the experiments we do. Figure 14
shows a N02 titration experiment and the predicted
model result. Since the only rate constants that
we are unsure of at this point are ones involving
some species with sulfur in it, and there is no
sulfur in the reaction system or the model at this
point, those rate constants are insignificant.
The input into the N02 titration model
consists of the measured N02 concentration and the
initial hydrogen atom concentration in ppb. The
model output is the OH concentration at the PMT.
The model is run using the same N02 input
concentration, which was 135 ppb. This was the
experimental concentration of N02 used in the base
experiments. The N02 would be in excess and assure
complete conversion of the H atoms into OH. Ten
different model runs were done, each with a
different input H atom concentration. A linear
relationship is established between input H
concentration and output OH concentration, Figure
It is significant to note that the hydrogen
atom concentration is determined experimentally by
performing an N02 titration. The H atom

Figure 14. N02 Titration Model Results
Data O
Model A

0 5 10 15 20 25 30
Hydrogen Concentration (ppb)
Figure 15. Linear Regression
[OH] = .2162*[H] + .7664

concentration is equal to the N02 concentration at
the endpoint.
The OH concentration at the photomultiplier
for a base experiment is found by using Figure 15
with the appropriate H atom concentration. The OH
concentration is correlated with the signal counts
at the endpoint to arrive at a sensitivity factor
which is then used for the experiments following
the N02 titration. N02 titrations were done with a
high degree of frequency, always before and after
any set of experiments were to be performed,
usually every 2-6 hours.
Rate Constants of Interest
We are interested in determining rate and
mechanistic data for several processes. They are
reiterated below.
hoso2 + 2 H.02 + S03 [8]
hoso2 + NO PRODUCT [10]
hoso2 + h20 - hoso2*h2o [11]
The rate constants for [8] and [10] were
input into the model, then compared to experimental
results. The rate constants were adjusted in

such a fashion that the model fit the data. This
sounds like a simple task for one set of data and
one model, but there were eight different sets of
experiments, each at a high and low concentration
of initial OH concentration. So there were
essentially sixteen different experiments that the
model was to mimic. All experiments were run from
4-20 times with weeks separating some of them.
Reproducibility was excellent, demonstrated by
the small error bars on the data, which resulted
from averaging data for the same experiment run
weeks apart.
Data Analysis Theory
Some experiments were better than others
for looking at a particular process. The reason
for this is that some processes, either Reaction
[8] or [10], had no effect on the chemistry inside
the flow tube. I will describe the general method
used to derive rate constant data for reaction [8]
and [10] and then treat each type of experiment
individually. The complete mechanism input into
the model in its final form is shown in Table 2.

Table 2. Reaction Mechanism
Reaction Rate Constant
1. H + N02 OH + NO 1.1 E-10
2. OH + S02 hoso2 1.2 E-14
3. OH + OH h2o + 0 1.9E-12
4. OH + H0S02 h2o + so3 7.5 E-ll
*5. OH wall 10 s-1
6. OH + NO HONO 3.57 E-14
7. OH + N02 hono2 8.6 E-14
8. hoso2 + o2 &03 + ho2 4 E-13
9. H02 + NO H- + N02 8.3 E-12
10. H0S02 + NO Products 2 E-12
11. 0 + OH H + o2 3.3 E-ll
12. 0 + no2 NO + 02 9.3 E-12
13. ho2 + no2 ho2no2 1.76 E-14
14. 0 + ho2 OH + 02 5.9 E-ll
15. OH + H02 H20 + 02 7 E-ll
16. ho2 + ho2 h22 + 2 1.7 E-12
*17. hoso2 wall 17.5 s"1
*18. ho2 wall 25 s_1
19. OH + OH h2o2 6.06 E-14
20. 0 + NO * no2 8.36 E-15
21. 0 + no2 NO + 02 8.29 E-15
* units are listed for first order rate constants

In order to study Reaction [8], pertinent
experiments would be the titration of the bisulfite
radical with 02 and adding NO close to the PMT as
well adding far NO away from the PMT. Titrating the
bisulfite radical with NO and adding the NO far
from the PMT will also provide information. All
three experiments were done at high and low OH
concentrations. The rate parameters for Reaction
[8] were varied until a best fit of the model to
the data was obtained for all three experiments.
However, in order to gain information
regarding the rate constant for Reaction [10] the
most important experiments to model are the 02
titrations while adding a constant amount of NO far
from the PMT and also an NO titration adding the NO
far from the PMT. Both of these experiments are
also important to model Reaction [8], so the
modeling efforts must be done in tandom, fitting
one set of parameters to one experiment then
checking the same model against another experiment.
An analysis of the deviation of the model from
experiment, high or low, and whether the shape of

the curve was correct or not, suggests which rate
constants whould be increased or decreased.
Having fit the above set of experiments
satisfactorily my model parameters were tested
against the rest of the data to insure a "best
fit". Rate constants were varied when modeling each
set of data in order to gain an appreciation for
the important processes occurring in each type of
experiment, as well as, to determine the
sensitivity of the model to each process.
C>2 titration: NO close. Figures 16 and 17
show the experimental results of titrating the
bisulfite radical with 02 while adding a constant
flow of NO close to the PMT. The error bars
represent standard deviations from all of the
averaged concentrations taken from different
When there is no 02 in the system, the
initial OH concentration is low. As 02 is added
the bisulfite radical reacts with the 02 making the
hydroperoxyl radical by Reaction [8]. The
hydroperoxyl radical regenerates the OH radical by
Reaction [9]. There is an excess of NO present in
the system. As the concentration of 02 flowing
into the flowtube increases, the [OH] increases.

. 02 Titration, NO close to PMT
Low OH
Figure 16

Figure 17
0, Titration, NO close to PMT
High OH

H0S02 + 02---- H02 + SO3 [8]
H02 + NO ---- OH + N02 [ 9 ]
These experiments, like all other
experiments, were done at two different initial OH
concentrations. If the model fits at one OH
concentration it should work for both. By
comparing Figures 18 and 19, it is apparent that the
model doesn't fit either of them perfectly.
Working at only one OH concentration would give a
better fit to the data, but this may introduce a
systematic error. Although neither model fits the
data perfectly, the model is still with in the
error bars of the data.
These experiments were useful for studying
the kinetics of Reaction [8]. These experiments
also allowed one to evaluate the wall loss of
hydroperoxyl radical. This is because the bisulfite
radical will react with the 02 forming the H02
radical, which must travel the length of the flow
tube until it reacts with the NO close to the PMT.
Figures 18 and 19 show the best fit of the
model to the data. Figure 20 shows the sensitivity
of the model to k8. In Figure 20, the rate constant
k8 was decreased from a best fit of 4 x 10-1^ to 1

Figure 18. Model Result, 02 Titration
NO close to PMT, Low OH
k8 = 4 x 10~13 cm3/molecule sec
k10 = 2 x 10-12 "

Figure 19. Model Result, 02 Titration
NO close to PMT, High OH
k8 = 4 x 10-13 cnr/molecule
k10 = 2 x 10-12 "

Figure 20. Model Result, 02 Titration
NO close to PMT, Low OH
Top: kQ = 4 x 10-13 cm3/molecule sec
Bottom: k8 = 1 x 10-13
kiQ = 2 x 10-12 cm3/molecule sec

x 10-13 cm3/molecule sec. The model clearly shows
that as Reaction [8] slows down, there is less
regeneration of the OH radical.
Figure 21 demonstrates the sensitivity of
the model to variations in k10* k10 was increased
from a best fit of 2 x 10-12 to 3 x 10-12
cm3/molecule sec. Increasing Reaction [10], H0S02
+ NO Products, depletes the system of HOS02
without regenerating the OH radical. However, it
is useful to note that the model predicts that at
high 02 concentrations the two curves approach each
other, as one would expect. This is because the
concentration of 02 has become sufficiently high so
that the rate of the bisulfite reaction with 02 is
much faster than it's reaction with NO. This type
of comparison is useful in determining the
sensitivity of the model to rate constant
Figure 22 shows the sensitivity of the
model to varying the H02 wall loss. By decreasing
the H02 wall loss rate constant in the model from
25 s-1 to 22.5 s1 we see a dramatic increase in
the OH concentration predicted by the model. This
is due to less H02 lost to the flow tube walls,
permitting more OH regeneration by Reaction [9].

Figure 21. Model Result, 02 Titration
NO close to PMT, Low OH
Top: k10 = 2 x 10-;}-2 cm3/molecule sec
Bottom: k10 = 1 x 1012
k8 = 4 x 10-13 cm3/molecule sec

8 7
Figure 22. Model Result, 02 Titration
NO close to PMT, Low OH
H02 wall loss variation
Top: H02 wall loss =22.5 s-1
Bottom: H02 wall loss =25.0 s-1
k8 = 4 x 1013 cm3/molecule sec
k10 = 2 x 1012 '

02 titration: NO far. Figure 23 and 24
show the results of titrating the bisulfite radical
with O2 while adding the NO far from the PMT. The
maximum hydroxyl radical concentration observed
during these titrations is less than that observed
when NO was added close to the PMT. The reactions
of 02 and NO with the bisulfite radical are in
direct competition, Reaction [8] and [10].
Figure 25 and 26 show the model results for
these two experiments. These experiments were
useful in determining rate constants for Reactions
[8] and [10].
Increasing k8 produces more H02 which will
regenerate more OH and we see a corresponding signal
increase, Figure 27.
If k10 is decreased the rate of Reaction [10]
slows and NO will not be an effective sink for the
bisulfite radical. Hence, the bisulfite radical
reaction with oxygen will become more important,
increasing the hydroxyl radical concentration and
the signal, Figure 28.
Although the model does not fit the data as
well as one would like, it can be seen by Figure 27
and 28 that this experiment is sensitive to the two

Figure 23. o2 Titration, NO far from PMT
Low OH


Figure 24. On Titration, NO far from PMT
High OH

Figure 25. Model Result. 02 Titration
NO far from PMT, Low OH
ko = 4 x 10-13 cm3/molecule sec
k10 = 2 x 1012 "

Model Result, 02 Titration
NO far from PMT, High OH
k8 = 4 x 10-13 cm3/molecule sec
k10 = 2 x 1012 '
Figure 26.

Figure 27. Model Result, 02 Titration
NO far from PMT, High OH
Top; kg = 7 x 10-13 cm3/molecule sec
Bottom: k8 = 4 x 1013 "
k10 = 2 x 10~12 cm3/molecule sec

Figure 28. Model Result, 02 Titration
NO far from PMT, High OH
Top: k10 = 1 x 10-3-2 cm3/molecule sec
Bottom: k10 = 2 x 1012 "
k8 = 4 x 10-13 cm3/molecule sec

processes of interest and therefore valid in
elucidating rate constants for these reactions.
NO titration: NO close: Experiments were
performed where the bisulfite radical was titrated
with NO while keeping the 02 constant. These
experiments were performed at high and low OH
concentrations. Because of the nature of these
experiments (ie, they really don't tell us anything
about the chemistry of interest) only a couple of
these experiments were performed and their analysis
will not be discussed.
NO titration: NO far. Figure 29 and 30
show the result of titrating the bisulfite radical
with NO while adding a constant concentration of
02. These experiments allowed us to study the
competing Reactions [8] and [10]. The OH
concentration goes up dramatically with the
addition of a small quantity of NO to the system.
As more and more NO is added to the system, the
rate of Reaction [10] increases and NO acts as a
sink for the bisulfite radical. This leads to a
steady decrease in the OH concentration.
Figures 31 and 32 show the best fit of the
model to the experimental results for both high and
low OH concentrations. Figure 33 shows the effect

2. 4
1. 8
1. 2
. 6
0 5 10 15 20 25
Figure 29. NO Titration, NO far from PMT
Low OH

Figure 30. NO Titration, NO far from PMT
High OH

Figure 31. Model Result, NO Titration
NO far from PMT, Low OH

Figure 32. Model Result, NO Titration
NO far from PMT, High OH

0 5 10 15 20 25
Figure 33. Model Result, NO Titration
NO far from PMT, Low OH
Top: k8 = 7 x lO-J-3 cm3/molecule sec
Bottom: k8 = 4 x 1013
kio = 2 x 10-12 cm3/molecule sec