investigation of the pressure dependence of so3 formation./67531/metadc4403/m2/1/high... · sulfur...

APPROVED: Paul Marshall, Major Professor Angela Wilson, Committee Member Ruthanne Thomas, Chair of the Department of

Chemistry Sandra L. Terrell, Interim Dean of the Robert B.

Toulouse School of Graduate Studies

KINETIC STUDY OF THE PRESSURE DEPENDENCE OF SO3 FORMATION

Jacinth Naidoo, BSc (Honors)

Thesis Prepared for the Degree of

MASTER OF SCIENCE

UNIVERSITY OF NORTH TEXAS

December 2003

Naidoo, Jacinth, Investigation of the Pressure Dependence of SO3 Formation.

Master of Science (Chemistry), December 2003, 85 pp., 7 tables, 25 illustrations,

references, 120 titles.

The kinetics of the pressure dependent O + SO2 + Ar reaction have been

investigated using laser photolysis resonance fluorescence at temperatures of 289 K, 399

K, 581 K, 699 K, 842 K and 1040 K and at pressures from 30-665 torr. Falloff was

observed for the first time in the pressure dependence. Application of Lindemann theory

yielded an Arrhenius expression of k(T) = 3.3 x 10-32exp(-992/T) cm6 molecule-1 s-1 for

the low pressure limit and k(T) = 8.47 x 10-14exp(-468/T) cm3 molecule-1 s-1 for the high

pressure limit at temperatures between 289 and 842 K. The reaction is unusual as it

possesses a positive activation energy at low temperature, yet at higher temperatures the

activation energy is negative, illustrating a reaction barrier.

ii

ACKNOWLEDGEMENTS

I would sincerely like to thank my advisor Dr. Paul Marshall for so freely and

interestingly sharing his wealth of knowledge, his interest and enthusiasm about gas

phase kinetics with me.

I would also like to thank Dr. A Goumri and Dr. L.R Peebles for their mentoring and

assistance.

I am grateful for the support, encouragement and advice of my dear husband Derrick, and

my parents Elaine and Meg Govender.

I would like to acknowledge financial assistance from the educational fund of Murial and

Harold Onishi.

Finally I would like to thank the Robert. A Welch Foundation and the National Science

Foundation for their financial support of this work.

iii

TABLE OF CONTENTS

LIST OF TABLES…. ………………………………………….………… v

LIST OF ILLUSTRATIONS.......….......………………………………… vi

Chapter

1. INTRODUCTION

1.1 Coal and its combustion products ............................................. 6

1.2 Fuel desulphurization................................................................. 10

1.3 Flue gas desulphurization

1.3.1 Limestone-based method...................................... 11

1.3.2 Magnesium based method………………….…... 12

1.3.3 Ammonium sulfate based method……………… 13

1.3.4 Dry injection method…………………………… 14

1.4 Relevance of SO2 to flame combustion………………………. 15

1.5 SO3 formation………………………………………………… 17

1.6 The effect of sulfur on NOx emission………………………… 19

2. EXPERIMENTAL METHODS

2.1 Flash Photolysis Resonance Fluorescence (FP-RF) technique… 21

2.2 Kinetic experimental procedure……………………………….. 24

2.3 Materials……………………………………………………….. 26

2.4 Data analysis…………………………………………………… 27

2.5 SO2 absorption cross-section determination…………………... 29

3. RESULTS AND DISCUSSION

3.1 Results…………………………………………………………... 33

3.2 Discussion………………………………………….…………… 33

iv

3.3 Background to Lindemann theory…………………………………. 35

3.4 Third body contribution to the third order rate…………………….. 47

3.5 Comparison of rate constant with those from prior determinations. 40

3.6 Spin considerations…………………………………………….…. 43

3.7 Statistical analysis of O + SO2 + Ar reaction……………………… 45

4. CONCLUSION………………………………………………………… 48

APPENDIX A………………………………………………………….. 50

APPENDIX B…………………………………………………………. 53

REFERENCES………………………………………………………… 76

v

LIST OF TABLES

Table Page

1. Summary of rate constant for the low and high pressure limits

for the O + SO2 + Ar reaction.……………………………… 39

2. Summary of rate constant measurements for O + SO2 + Ar .

at 289 K ……………….…………………………………. 54

3. Summary of rate constant measurements for O + SO2 + Ar

at 399 K…………………………………………………… 58


at 581 K…………………………………………………… 60


at 699 K…………………………………………………… 63


at 842 K…………………………………………………… 64


at 1040 K………………………………………………… 67

8. Summary of the rate constants available for the SO2+O +Ar

reaction................................................................................ 41

vi

LIST OF ILLUSTRATIONS

Figure Page

1. Plot of estimated sulfur emission from biomass burning,

biogenic and non-biogenic sources…………………… 5

2. Plot of estimated global emission of sulfur in 1980…… 9

3. Illustration of a flash- photolysis resonance setup………. 23

4. Plot of fluorescence intensity including background of

SO2+ O + Ar at 297 torr and 1047 K……………………. 28

5.Plot of pseudo first order rate constant for the loss of O radicals

at 297 torr and 1047 K........................................................ 29

6. Beer-Lambert plot of SO2 at room temperature………… 51



9. Plot of temperature dependence of SO2 cross section absorption 32

10. Plot of first order rate constant vs. pressure at 289 K…… 57



13. Plot of first order rate constant vs. pressure at 699 K……. 63

14. Plot of first order rate constant vs. pressure at 841 K…….. 65

15. Plot of first order rate constant vs. pressure at 1040 K…….. 72

vii

16. Lindemann plot at 289 K…………………………………. 73

17. Lindemann plot at 399 K………………………………… 73




21. Lindemann plot at 1040 K………………………………. 75

22. Plot of low- pressure limit for O + SO2 + Ar vs. T……… 38

23. Arrhenius plot of extrapolated kinf for

O + SO2 + Ar recombination…………………………….. 38

24. Comparative plot of rate constant of reaction 3.1 obtained from

various experimental studies…………………………..… 42

25. A simple energy diagram for the reaction mechanism

as suggested by Davis………………………………………….. 44


as suggested by Westenberg and deHaas……..………………… 43


as suggested by Troe et al……..………………………..……… 47

1

CHAPTER 1

INTRODUCTION

Sulfur compounds such as SO2, SO3, H2S, COS, CS2, C4H4S, CH3SCH3 and CH3SH are

emitted into the atmosphere from non-biogenic, biogenic and anthropogenic sources.

Estimates of total sulfur emissions have varied widely.1-4 Identified as a major pollutant,

sulfur dioxide, SO2 is the central focus of this study. In flame chemistry there is a direct

relationship between sulfur compounds and radical reactions. SO2 is believed to be a sink

for radicals such as O, H and OH. There is also evidence to suggest that SO2 may

influence NOx chemistry in flames and flue gases.5-13

Emissions of sulfur compounds into the atmosphere have non-biogenic, biogenic and

anthropogenic sources. Vegetation, marine algae, soils, wetlands, and sulfur reducing

bacteria are the major biogenic sources of sulfur compounds released into the

atmosphere.14-16 Vegetation contains on average 0.25% dry weight sulfur.17 Sulfur

compounds may be released from living plant leaves17 and decaying leaves,18 although

sulfur emission rates from decaying leaves are 10 to 100 times higher than emissions

from living leaves of the same species.18 In addition, many fungi and bacteria are known

to release sulfur compounds during plant decomposition. H2S is emitted from some

plants.19-23 Emission rates of H2S have varied between 0.006 to 0.25 g S m-2 yr-1,22 from

several lawns and a pine forest on aerobic soil in France, to 0.24 to 2.4 g S m-2 yr-1 from

2

humid forests in the Ivory Coast, West Africa.23 Other sulfur compounds known to be

emitted from plants are dimethyl sulfide, DMS,24,25 carbonyl sulfide, COS,20 carbon

disulfide, CS2,24-29 and possibly ethyl mercaptan.28,29 H2S and DMS are the major sulfur

species emitted from crops such as corn, soybeans, oats and alfalfa.28,30,31

Another biogenic source of sulfur is wetlands. The major compounds emitted are H2S and

DMS. Emission of DMS is dependent on temperature,32 and on the bacterial species S.

alterniflora.33 Emission of H2S is estimated to be 5.3 x 10-4 to 52.6 g m-2 yr-1 and is

closely associated with tidal cycling.32,34-38 Biogenic sulfur emissions originate also from

soil. The major sulfur species emitted are H2S, OCS, CS2, DMS and DMDS. Soil surface

temperature,31 soil nitrogen content,39 soil type and moisture content, are factors

determining the flux of sulfur gases from soils, which range from 1.2 to 23.4 mg S m-2yr-1

for temperatures between 20 and 30 0C.31,40,41 Global emission of sulfur from the

terrestrial biosphere is approximated at 0.91 Tg S yr-1.4 This includes 0.86 Tg S yr-1 from

vegetation and 0.05 Tg S yr-1 from soils.

The marine biosphere is the leading source of biogenic sulfur emissions. DMS, CS2,

CH3SH and CH3SSCH3 gases are produced biologically and H2S and OCS is produced

photochemically.42 DMS, the most abundant compound emitted,42,43 was first reported in

1972 in oceanic waters,18,43 before being measured throughout the Pacific, Atlantic and

southern seas. DMS concentrations are in the range of 0.5 to 5 nmol/L in open ocean

3

surface seawater, although the concentration varies depending on the region and season.

Dimethyl -sulfoniopropionate (DMSP), a precursor to DMS, has been identified in

marine algae, P. fastigiata,44 and phytoplankton,45 and is enzymatically cleaved to yield

DMS and acrylic acid. The initial investigation of global DMS flux was based on

observations in the Atlantic and eastern tropical Pacific and a value of 32 Tg S yr-1 was

proposed.42,46,47 When seasonal variations of DMS concentration were accounted for, the

estimate of global DMS flux was revised to 16 ± 11 Tg S yr-1.48 CS2 and OCS are also

present in surface open ocean waters at concentrations of 16 ± 8 pmol/L and 10 to 100

pmol/L respectively.49-54 The fluxes of OCS and CS2 were approximated at 1.2 % of the

flux of DMS.20,50,52,53 CH3SH and CH3SSCH3 are volatile sulfur species suspected of

being present in marine sediments, and decomposing algal mats. Recent evidence

however suggests that these compounds are produced as an artifact of sampling if

plankton undergoes anaerobic decomposition.55

Geothermal emissions, such as sulfur springs and volcanoes, are non-biogenic sources of

SO2. Including emissions from lava, volcanoes are estimated to contribute 3.9 Tg of

emitted S per year.56 Erupting and non-erupting degassing volcanoes emit sulfur

compounds into the stratosphere, although erupting volcanoes account for the majority of

sulfur emitted.57 While SO2 is the major specie emitted, SO42- and H2S comprise less than

1%,58 and OCS less than 0.1% of the total sulfur emission.59,60 SO2 emissions from

volcanoes are periodic and vary with eruption activity. Remote sensing correlation

4

spectrometry was used to measure SO2 emissions from eruptions in Japan,61 Central

America,62 Hawaii 63 and Italy.64,65 The volcanic contribution to atmospheric SO2

emission was estimated at 5 Tg S yr-1 by extrapolation to cover all of the earth’s surface

and excluding the big eruptions.62

Sea spray is a more important source of atmospheric sulfur. The amount of sulfur emitted

depends on the sulfur concentration in seawater, which is roughly constant at 0.27%, and

the extent to which sulfur ions are enriched relative to Na+ and Cl- ions by fractionation

during spray formation. About 7-10 % of spray generated sulfate is deposited on land

surfaces.66,67 The total emission of sulfur from sea spray is accepted as 44 Tg S yr-1.

Classification of biomass burning as a source of atmospheric sulfur has varied in previous

studies of global sulfur emissions, from not treated,2 to a source separate from man made

sources,3,4 to a natural source of sulfur.1 Since about 95 % of biomass burning is human

initiated,68 it is considered an anthropogenic source of sulfur here. Biomass burning is a

significant source of sulfur, with SO2 the major compound emitted. An estimated 50 to 60

% of global emissions are derived from savannah fires.69 Total sulfur emissions from

biomass burning was calculated at 1.44 to 2.94 Tg Syr-1.1

5

0

20

40

60

80

100

120

biomassburning

volcanoes marine bios. terrestrialbios.

man-made

Tg

S pe

r ye

ar

Spiro et al for 1980

Bates et al for 1990

Cullis and Hirschlerfor 1980

Figure 1: Estimates of sulfur emission from biomass burning, biogenic and non-biogenic

sources and anthropogenic sources.

Large differences in estimates of sulfur emission from biomass burning, and the marine

and terrestrial biosphere may be attributed to varying models and emission factors used in

the three studies.1,2,4 Bates et al1also reported limited resolution and few specific source

types in their global estimate of sulfur emission. Differences in global sulfur emission

from biomass burning, biogenic and non-biogenic sources were also introduced in

different seasonal and latitudinal considerations.

6

Copper extraction, and to a much lesser extent, lead and zinc extraction are

anthropogenic contributors to sulfur emissions in the smelting of non-ferrous metals.

Sulfur emissions from smelting have been on the decline and in 1976 these emissions

were estimated at 21.4 Tg SO2 (10.7 Tg S), of which 18.8 Tg SO2 (9.4 Tg S) was emitted

during the production of copper. For the year 1980, sulfur emission from the smelting of

copper, lead and zinc was estimated to be 6.8 Tg S yr-1. Countries leading sulfur

emissions from smelting of ores are Chile, Peru, Zaire and Zambia. A small contributor

to total atmospheric sulfur is the manufacture of sulfuric acid and the total annual

emission was calculated to be 1.25 Tg S in 1976.2 In the year 2000, an estimated 1 Tg S

was emitted globally from lead and zinc smelting, and sulfuric acid production.

Petroleum refinery and petroleum products are the second major source of anthropogenic

atmospheric sulfur with an average refinery in 1965 emitting 25 tons of S per 100,000

barrels of petroleum.70 In 1974, an estimated 29.15 Tg S was emitted from petroleum

products,2 while in 2000 the estimate was reduced to 23 Tg S produced from oil refining

processes.3

1.1 Coal and its combustion products

Combustion of coal and petroleum, petroleum refining and smelting of non-ferrous ores

are the main industrial sources of atmospheric sulfur. During the combustion of coal SO2

is evolved through the oxidation of sulfur resulting in flue gas concentrations of 500-

2000 ppmv. Total sulfur emission from coal was calculated to be 61.9 Tg S in 1976.2 A

7

dramatic increase is observed in the total sulfur emitted into the atmosphere over the last

hundred years. Over 1990-1999, US coal consumption increased by 16.7%, reaching

1,039 million tons in 1999.71 About 90.5% of domestic consumption in 1999 was by the

electric power sector. Accurate estimations of emissions from coal combustion require

the knowledge of the magnitude of coal consumption as well as the sulfur content of the

coal, which is highly variable between 0.2–10 % sulfur by weight.72,73

Sulfur compounds present in coal are classed into organic and inorganic sulfur containing

compounds. Almost all inorganic sulfur is pyrite sulfur. The ratio of inorganic: organic

sulfur is approximately 2:1,74 although the ratio may vary from 4:1 to 1:3.75 Most bound

sulfur was determined to be in the form of thiophenic, aromatic and aliphatic structures.75

Total yield of sulfur compounds from coal depends on the rank of the coal and the

temperature. The carbon content of a coal determines its rank. Coals with the least to the

most carbon content are: - lignite, sub-bituminous, bituminous and anthracite. Anthracite

yields about 5% of sulfur compounds while highly volatile lignite may yield a maximum

of 50% of gaseous sulfur compounds.76

The coal combustion process involves the ignition and burning of crushed and pulverized

coal in a combustion chamber. Fine particles (fly ash) are suspended in the flue gas.

Course particles settle at the bottom of the chamber and have two components: bottom

ash and boiler slag. The fourth product of coal combustion is coal ash, which is derived

8

from inorganic impurities, and either remains in the combustion zone or is carried in the

flue gas stream.

In an attempt to control sulfur emissions from coal combustion, the US government

implemented the Clean Air Acts Amendments in 1990, which took effect in two phases.

The first phase began in 1995 and limited the 110 power plants built before 1978 to 2.5

pounds of SO2 per million British thermal units (BTU) of energy generated. The second

phase took effect in 2001 and limits emissions by all power plants to 1.2 pounds of SO2

per million BTU of energy generated.

9

0

10

20

30

40

50

Hard co

al co

mbusti

on

cokin

g of c

oal

lignit

e com

busti

on

petro

leum us

es

wood f

uel c

ombu

stion

copp

er sm

elting

lead s

melting

zinc s

melting

other

Tg S

Spiro etalCullis & Hirschler

Figure 2: Global emission of sulfur in 1980

Various techniques have been implemented to limit SO2 emissions from coal-fired plants.

While some methods are based on the removal of sulfur from the coal (fuel

desulphurization), other methods are based on extracting SO2 gas from the flue gas (flue

gas desulphurization).

10

1.2 Fuel desulphurization

Sulfur is commonly removed from coal by cleaning. Traditional methods of coal cleaning

are based on the reduction of ash-forming materials. The physical coal cleaning processes

such as crushing and separation mainly removes inorganic sulfur. However, these well-

established techniques do not completely remove pyrites from coal, thereby reducing SO2

emission by less than 30%. It is hoped that the advanced yet underdeveloped physical

cleaning methods such as flotation, agglomeration and flocculation will remove more of

the inorganic SO2.24,77

1.3 Flue gas desulphurization (FGD)

The general trend in reduction of SO2 emissions from flue gas has been the switch to low

sulfur containing coal or the blending of low sulfur containing coal with high sulfur

containing coal. The plant may also be co-fired with natural gas. Alternatively flue gas

desulphurization equipment may be installed. Although 200 FGD methods have been

identified, only four of these methods are economically and technically feasible. The four

listed FGD methods are classified into two categories: wet and dry processes.

- Lime-limestone based method

- Magnesium based method

- Ammonium sulfate based method

- Dry injection method

The first three of these methods are wet processes and the fourth method is a dry process.

11

1.3.1. Lime- limestone based method

In the lime process, lime is slaked on site to form calcium hydroxide slurry, which reacts

with sulfur gases to form a calcium sulfite (CaSO3) and calcium sulfate (CaSO4) as

illustrated by the following reactions:

SO2 (aq) + Ca (OH) 2 (aq) CaSO3· ½ H2O (s) + ½ H2O (1.1)

SO2 (aq) + ½ O2 (aq)+ Ca (OH) 2 (aq)+ H2O CaSO4· 2 H2O (s) (1.2)

where (aq): slurry or solution; (s):solid and (g):gas.

In the process utilizing limestone, similar chemistry is observed, although CO2 is

generated. The process is described by the following reactions:

SO2 (aq) + CaCO3 (aq) + ½ H2O CaSO3·½ H2O (s) + CO2 (g) (1.3)

SO2 (aq) + ½ O2 + CaCO3 (aq) + 2 H2O CaSO4·2 H2O (s) + CO2 (g) (1.4)

The limestone reacts with the gaseous SO2 to form calcium sulfate (CaSO4) or gypsum

under oxidizing conditions. The formation of gypsum sometimes poses a problem with

sludge disposal, although gypsum has been used for gypsum binders, plasters, and

plasterboard manufacture and as additives in Portland cement production.78 It has been

found that sulfation in reaction 1.4 causes fouling in boilers firing high sulfur fuels.79-81

Fouling in boilers has been attributed to insufficient seed crystals in the slurry when a

supersaturated state has been reached. Almost pure deposits of CaSO4, meters in length,

have been found on the walls of the upper furnace, in the cyclone and on the super

heaters. It was thought that these solid deposits are derived from various fuel ash species

12

within the system, but detailed investigation of the solid demonstrated that fouling was

linked to an agglomeration mechanism.82 Often the lime or limestone is recirculated in a

scrubber. Although calcined limestone is useful in reacting with SO2 enabling reduction

of SO2 emissions, it is an active catalyst for CO oxidation83 and the oxidation of nitrogen

containing compounds, leading to the formation of NO and N2O.84

1.3.2. Magnesium based method

In this regenerative process, SO2 is captured by formation of magnesium sulfite. Reactive

MgO is slaked, forming Mg(OH)2 slurry, which becomes the absorber. SO2 and SO3

react with MgO forming MgSO2 and MgSO3 respectively. The process is illustrated by

the following reactions:

Mg(OH)2 + 5 H2O + SO2 MgSO3·6 H2O (1.5)

Mg(OH)2 + 2 H2O + SO2 MgSO3·3 H2O (1.6)

Mg(OH)2 + 6 H2O + SO3 MgSO4·7 H2O (1.7)

SO2 + MgSO3·6 H2O Mg(HSO3)2 + 5 H2O (1.8)

SO2 + MgSO3·3 H2O Mg(HSO3)2 + 2 H2O (1.9)

Mg(HSO3)2 + MgO + 11H2O 2 MgSO3·6 H2O (1.10)

Mg(HSO3)2 + MgO 5 H2O 2 MgSO3·3 H2O (1.11)

The aqueous sorbent slurry containing MgO, MgSO3 and MgSO4 is concentrated in a

clarifier and then fed into a continuous centrifuge. MgSO3·6 H2O, MgSO3·3 H2O and

13

MgSO4·7 H2O and unreacted MgO crystals are contained in this “wet cake”. The

supernatant is returned to the main recirculation stream. The “wet cake” is dried at a

temperature of 176-232 0C. The dry mixture is then calcined at 800-1000 0C. This

calcining regenerates MgO and releases SO2, which is used in the production of H2SO4 or

elemental sulfur. Typically an excess of 95% of sulfur gas is removed by this method

during operation at a pH of 5.5-6.5.

1.3.3. Ammonium sulfate based method

This popular European method uses ammonia as sorbent. Fly ash and other particulates

are removed from the flue gas by being passed through a spray drier and an electrostatic

precipitator. The following chemistry is observed upon entry of the flue gas into the

scrubber that contains ammonia:

SO2 + 2 NH3 + H2O (NH3) 2SO3 (aq) (1.12)

CO2 + 2 NH3 + H2O (NH3) 2CO3 (aq) (1.13)

(NH3) 2SO3 + ½O 2 (NH3) 2SO4 (aq) (1.14)

Injection of oxidized liquor, containing ammonium sulfite and smaller concentrations of

ammonium carbonate and ammonium sulfate, into a spray drier decomposes the sulfite

and carbonate fractions. Ammonium sulfate remains and is used as sulfur blending stock

in chemical fertilizer formulations. A second washing of the clean flue gas leaving the

scrubber prevents scaling in this FGD unit. This method is highly advantageous as there

is direct reaction of ammonia with SO3, leading to the formation of ammonium sulfate.

14

This is helpful in eliminating corrosion related problems in the reactor. Efficiencies in

sulfur removal with this process are reported to be about 95%.

1.3.4. Dry injection method

This method is one of the dry processes, of which there are three types: spray drying, dry

injection and simultaneous combustion of fuel sorbent mixtures. The method is based on

sulfur oxides reacting with reagent in the duct and on the surface of filter bags.

Commonly used reagents are Nahcolite and trona, which closely commercially resemble

sodium hydrogen carbonate. The reaction chamber is heated to the temperature at which

the sorbent decomposes. Nahcolite and trona decompose at 1350C and 93 0C,

respectively. Decomposition of the sorbent increases porosity, reaction surface and the

reaction rate.

Decomposition of sorbent is described by the following reactions:

2NaHCO3 NaCO3 + CO2(g) + H2O(g) (1.15)

2(Na2CO3)·NaHCO3·2H2O 3 Na2CO3 + CO2(g) + H2O(g) (1.16)

Reaction of SO2 with the sorbent is described by the following reaction:

Na2CO3 + SO2 + ½O 2 Na2 SO4 + CO2(g) (1.17)

Dry methods have an advantage over wet lime-limestone based methods, as their end

products are solid and can be treated by fly ash handling systems. This eliminates the

handling of wet sludge, however, sodium based byproducts must be properly disposed of,

to prevent the rise of potential environmental problems from the leaching of highly

15

soluble sodium based FGD byproducts. Dry methods however require a higher ratio of

sorbent to sulfur than wet methods, as gas-solid reactions proceed slower than gas-liquid

reactions.

As part of their Clean Coal Technology program, the Department of Energy instituted a

new process called the Integrated Gasification Combined Cycle (IGCC), where coal is

not burned directly but converted to gas, then combusted in a combined-cycle gas

turbine. Gasification of coal occurs in an enclosed pressurized reactor under reducing

conditions. Synthesis gas or syn gas is a mixture of CO and H2, and is produced from

gasification. The syn gas is cleaned before it is burned in air or oxygen and combustion

products are generated at high temperature and pressure. Under reducing conditions,

sulfur is present mainly as H2S and some COS. H2S is more easily removed than SO2.

Sulfur is produced in elemental form as a by-product in most units.

This method uses a combined cycle format where a combusted syn gas drives a gas

turbine. Heat exchange between hot exhaust gas and water and or team is used to

generate superheated steam, which drives a steam turbine. This has reduced SO2

emissions by 98%, and increased plant efficiency by 40%.

1.4 Relevance of SO2 to flame combustion

In a flame, radicals are generated by sequences of elementary reactions such as:

H + O2 OH + O (1.18)

16

H + O2 HO2 (1.19)

OH + H2 H2O + H (1.20)

O + H2 OH + H (1.21)

The rate of overall combustion is determined in large part by the elementary reaction

between H atoms and O2 molecules. The higher the temperature the larger the

contribution of reaction 1.18 relative to reaction 1.19.

Interest in SO2 lies in its ability to affect basic flame chemistry, as the coupling of sulfur

chemistry with radical chemistry has been evident. Recombination of radicals is

catalyzed by SO2 through the following mechanism:85,86

X + SO2 + M X SO2 + M (1.22)

Y + X SO2 XY + SO2 (1.23)

where X and Y may be O, H or OH radicals. These reactions have been found to

influence flame behavior and explosion limits.87 Three mechanisms have been identified

depending on which radical initially attacked SO2: the “H cycle”, “the O cycle” and “the

OH cycle”. This study focused on reaction 1.22 with X being O radicals. The “O-cycle”

in a lean flame is comprised of the following reaction sequence.

O + SO2 + M SO3 + M (1.24)

O + SO3 SO2 + O2 (1.25)

17

Reaction 1.24 is considered to be one of the elementary steps in aerosol formation. (Refer

to section 1.5 for more information on aerosol formation). Formation of SO3 through the

recombination of SO2 and O atoms (reaction 1.24) is spin forbidden when the ground

states of O (3P), SO2 (1A1) and SO3 (1A1') are involved. Several experimental studies of

reaction 1.24 have illustrated positive activation energies at low temperature,88 while at

higher temperatures the reaction rate decreased with temperature.89,90

Although both reactants are present in the atmosphere, reaction 1.24 is of little

consequence there. In the atmosphere the ratio of molecular oxygen to SO2 molecules is

so high that the following reaction with atomic oxygen radicals, produced from the

photolysis of NO2 or O3, is ensured.

O + O2 O3 (1.26)

Photodissociation of SO2 into SO molecules and O atoms require 565 kJ/mol,91 which is

impossible energetically for wavelengths of light greater than 218 nm. Solar radiation

reaching the lower atmosphere is of wavelength greater than 290 nm; thus only molecular

reactions involving the ground and electronically excited states of SO2 can occur at the

300-400 nm wavelength.

1.5 SO3 formation

Reaction 1.24 has been determined to be the only major homogenous source of SO3 in

flames,92 which is highly corrosive and contributes to aerosol formation. While

18

consumption of SO3 is not well characterized, competition between reaction 1.24 and

reaction 1.25 yields the net SO3 formed. The catalytic effects of surface deposits also

contribute to SO3 formation. When the vanadium content of a fuel is high, especially in

large oil fired units, SO3 formation becomes very important, as vanadium catalyzes

reaction 1.24. SO3 is not readily removed from exhaust gases by conventional flue gas

desulphurization methods. SO3 readily reacts with water to form sulfuric acid. The

reaction is so exergonic that a fine aerosol of H2SO4 is formed that passes through

scrubbers. SO3 emissions may be reduced by addition of methanol, CH3OH, or hydrogen

peroxide (H2O2), which lead to HO2 formation. Hydrogen peroxide reacts directly with

SO3 to produce the HO2 radical as illustrated by the following reactions:

SO3 + H2O2 HSO3 + HO2 (1.27)

HSO3 + M OH + SO2 + M (1.28)

Methanol reacts with hydroxyl radicals in a flame to produce the HO2 radical as

illustrated by the following reactions:

CH3OH + OH CH2OH + H2O (1.29)

CH2OH + O2 CH2O + HO2 (1.30)

HO2 formation in a combustion system is desirable as this radical is the active specie that

converts NO to NO2 and SO3 to SO2 by the following pathways:

NO + HO2 NO2 + OH (1.31)

SO3 + HO2 HSO3 + O2 (1.32)

HSO3 + M SO2 + HO + M (1.33)

19

1.6 The effect of sulfur on NOx emission

NOx is the collective term for the oxides of nitrogen NO and NO2. NOx gases are a major

contributor to acid rain and photochemical smog. NOx gases in combustion systems are

derived from nitrogen contained in combustion air and from nitrogen contained in fuel,

such as coal or heavy oil. Nitric oxide, NO, is formed when N2 reacts with O2 in air

during combustion at high temperature and during oxidation of fuel nitrogen.

N + O2 NO + O (1.34)

NO2 is produced from the further oxidation of NO:

NO + O2 NO2 + O (1.35)

In a cyclic set of reactions, NO is formed from the reactions of NO2 with O, H and OH:

NO2 + O NO + O2 (1.36)

NO2 + H NO +HO (1.37)

NO2 + OH NO + HO2 (1.38)

The interest in sulfur combustion products lies in their potential to influence NOx

chemistry in flames and exhaust gases. Sulfur can either reduce or enhance NOx

concentration in flames, depending on the conditions.5,6,8-13Fuel sulfur-nitrogen

interactions in exhaust gases are of particular interest, as they may shift the balance

between NO2 and SO2, and the less desirable NO and SO3. NO is relatively inert which

makes removal difficult. NO2 even though undesirable is efficiently removed by SO2

scrubbers, which cannot remove highly corrosive SO3.93 For efficient SOx and NOx

20

removal, conversion of NO to NO2 and SO3 to SO2 is required. In an experiment

simulating flue gas, 90% NO-to-NO2 and SO3-to-SO2 conversion was achieved by

injection of methanol into gas.94

Chief strategies utilized in NOx reduction in combustion are minimizing the excess air

supply, reducing the optimum combustion temperature, and staging of the combustion

process. A successful fuel staging method for NOx control has been reburning, which

exploits the sequence of combustion stages. About 80-90% of fuel is burned in the main

combustion zone in a fuel lean environment, forming NOx. More fuel is injected into the

secondary combustion zone at 1400- 1700 K, establishing a fuel-rich environment, where

NOx removing reactions occur. At optimum conditions, NOx emissions may be reduced

by 50-70%.

Although many kinetic investigation of reaction 1.24 have been performed,89,90,95-104 the

rate constant of the reaction has not been determined with certainty. Most kinetic

determinations have been performed at low temperatures (300-500 K). At high

temperatures (1700-2500 K) the rate of reaction 1.24 has been estimated using the reverse

dissociation rate constant for SO3. In the intermediate temperature range, no experimental

measurements are available. The mechanism of the reaction has also not been clearly

established as evidenced by discussions on the state of the reaction product, SO3.90,99,105

21

CHAPTER 2

EXPERIMENTAL METHOD

2.1 Flash (Laser) Photolysis/ Resonance Fluorescence (FP-RF) Technique

In 1967 Norrish and Porter received the Nobel Prize for the development of the flash

photolysis technique, which was designed to overcome the shortcomings of other

contemporary kinetic techniques. The basis of the technique is the pulsed photolysis of a

precursor compound with light (UV or visible), which creates a reactive specie. The light

source is either a flashlamp or a laser. The latter was used in these experiments. The pulse

of light should have a shorter duration than the reaction being studied.

The radicals generated by the flash are excited by absorption of continuous radiation, in

resonance with a higher electronic state, from the resonance lamp. Decay of radicals to

the ground state produces fluorescence radiation, which is detected as photons by the

photomultiplier tube (PMT), which is situated perpendicular to the laser and the

resonance lamp. The PMT is connected to a multichannel scaler with photon counting

electronics to interpret the fluorescence detected by the PMT. Fluorescence radiation is

monitored as a function of time. Since fluorescence is proportional to radical

concentration, the relative radical concentration as a function of time is obtained.

An excimer laser operating at 193 nm was used as a light source for flash photolysis in

these experiments. A laser has a short pulse duration, a precisely defined wavelength

22

range and a well-defined spatial profile, which makes it a good light source. Refer to

figure 3 for the flash photolysis-resonance fluorescence apparatus.

O (3P) radicals are generated by pulsed photolysis of sulfur dioxide (SO2) diluted in argon

(Ar) bath gas, by 193 nm radiation from an excimer laser (PSX-100, MCB). The

radiation passed through a suprasil quartz window transmitting light at λ > 165 nm. The

energy of the laser was varied between 0.014 – 0.20 mJ, by adjusting the number of

filters (copper mesh and steel micro fiber sheets) between the laser and the reactor. When

the energy output of the laser was too low for experimental operation, the laser was

evacuated and filled with a fresh F2, Ar, and Ne gas mixture.

The concentration of the reaction product, atomic O (3P), was monitored during the

course of the reaction by time resolved resonance fluorescence at a wavelength of 130-

131 nm (O (3s) 3S O (2p) 3P2,1,0).106 Resonance radiation was generated by a

microwave discharge lamp through which a mixture of 0.9% O2 in Ar gas at a pressure of

300 mtorr was passed. Fluorescence was detected by a solar-blind PMT (Thorn EMI,

9423 B), situated orthogonal to the resonance lamp and the laser. The fluorescence is

passed through a multichannel scaler (EG & G Ortec ACE) with photon counting

electronics. A digital delay-pulse generator (model DG535, Stanford Research Systems

Inc.) triggered the laser. The delay pulse generator also provided trigger pulses to a

computer controlled multichannel scaler.

23

Figure 3: flash-photolysis resonance fluorescence apparatus.

Kinetic measurements of O radicals were investigated as a function of temperature and

pressure. Experiments were performed at ambient temperature, 399 K, 581 K, 699 K, 842

K, and 1040 K and at pressures from 25- 660 torr. For the experiments at 399 K, 581 K,

699K, 842 K, and 1040 K, the temperature was measured before and after each

experiment by inserting a movable thermocouple into the reaction zone. The

thermocouple (Omega, type K, chrome (+) vs. alumel (-)) was corrected for radiation

24

errors, which occur from loss of heat out of the reaction zone through the windows of the

reactor.107

2.2 Kinetic Experimental Procedure

A stainless steel reactor was employed in this kinetic study. This type of reactor can

successfully be employed at temperatures up to about 1100 K. The reactor has a window

cooling system, which prevents overheating of the rubber vacuum seals, especially during

operation at higher temperatures. Acetone was used in routine cleaning of the reactor.

The reactor and the gas handling system were evacuated overnight using a mechanical

pump. In preparation for an experiment, the gas handling system was vacuumed to ≤ 4

mtorr, using a combination of a mechanical pump and a diffusion pump. The system was

evacuated to similar vacuum levels before gas mixtures were made up or diluted.

At the beginning of the project, the flow meters were calibrated using soapsuds, Ar gas

and calibrated cylinders. The actual flow rate was calculated from how long the suds took

to reach a given volume. At least five flow rates within the operation range of each flow

meter were tested and each volume tested timed several times (with a 0.1 s difference).

Flow meter readouts were always zeroed when no gas was flowing. Pressure in the

reactor was adjusted using a needle valve, which is connected to the outlet port of the

reactor. The needle valve is also connected to a stopcock, which opens to the vacuum

pump and the gas handling system. During an experiment the flows of SO2 and Ar were

25

complementary to some total volume flow rate so as to prevent fluctuations in reactor

pressure.

A steady slow flow of reactant in bath gas was allowed to flow into the reactor for at least

20 minutes to saturate the reactor walls with reactant. The effect of secondary chemistry

was investigated using different laser energies; at least a doubling of the lower energy, at

a single pressure at each temperature that the reaction was investigated at. A large

difference in the pseudo-first rate constants would indicate a large effect of secondary

reactions.

The gas residence time is the average time a sample of gas spends from entry into the

reactor until reaching the center of the reaction zone. Varying the flow rates and the

pressure varied the residence time of the gas, which is useful in detection of systematic

error, arising for example from thermal decomposition. Pulses of light at a wavelength of

193 nm from the laser passed into the reactor through a suprasil quartz window.

Fluorescence from the resonance lamp is focused into the reactor through a CaF2 window

transmitting at λ >125 nm. Radical detection in the reactor is achieved by detection of

fluorescence at 130.2 nm and is focused through a CaF2 lens before the PMT. In the

reactor, Ar sweeper gas passes around the windows to prevent adsorption onto the optics,

especially at higher temperatures.

26

For each set of experiments, the pseudo-first-order rate constants for at least five different

concentrations of reactant were determined. The maximum SO2 concentration in a given

experiment was at least 1.0 x 1016 molecules/cm3. Higher SO2 concentrations were

permitted by a good signal and small uncertainty of the pseudo-first-order rate constant.

Lower and higher flows were alternated for easy detection of systematic errors.

2.3 Materials

Ar (99.9999%, Air Liquide) and N2 (industrial grade, Air Liquide) were used directly

from the cylinder. SO2 (99.98%, MG Industries) was purified by distillation from a trap

first cooled by liquid N2. The SO2 gas was then subjected to several freeze, pump and

thaw cycles using a trap cooled to about 175 K by a liquid N2 /methanol slush. Cold

methanol at 263 K was used in the distillation of impurities from SO2 at atmospheric

pressure. An SO2 gas mixture was prepared by firstly pumping on the pure SO2, frozen

by liquid N2. The liquid N2 was replaced by cold methanol at 223 K to thaw the solid SO2

to vapor slowly. SO2 gas mixtures were prepared by filling a bulb with a few torr of pure

SO2 vapor which is diluted with Ar to some total pressure at about 1000 torr. Once

pressure of the gas mixture had fallen to a few hundred torr, the gas mixture was often

diluted, depending on the dilution. O2 (99.999%, Air Liquide) was stored in a bulb and a

few percent of pure O2 was diluted with Ar and stored in a separate bulb. Gas mixtures

were prepared the day before commencement of an experiment to ensure good mixing

and proper distribution of gas molecules.

27

2.4 Data Analysis

Following generation, atomic oxygen is mainly lost in two process:

O + SO2 SO3 (2.1)

O wall loss (2.2)

-d [O]/dt = k1 [O][ SO2] + kw [O] (2.3)

Since [SO2]0 >> [O]0, then the [SO2] remains approximately constant and the rate law is

ln ([O]/[O]0) = - (kw + k1 [ SO2] )t = -kps1t (2.4)

[O] = [O]0 exp (-kps1t) (2.5)

where the pseudo-first-order rate constant, kps1, consists of two terms: kw and k1[SO2],

which is the rate of decay of [O] in reaction (2.1). The second term, kw, is the rate of

decay of O radicals in the absence of SO2, due to its diffusion out of the reaction zone

and its slow reaction with impurities in the bath gas. In many of the lowest pressure

experiments kw was large compared to a change in the pseudo-first-order rate. These

experiments were excluded from the analyses. The pseudo-first-order rate is determined

from a non-linear least squares fit to fluorescence decay of O radicals, although

background from scattered light must be considered in the analysis algorithm to account

for the observed fluorescence signal I. This is achieved by modifying equation 2.5 above:

I = A exp (-kps1t) + B (2.6)

where A and B are constants and B represents the background.( Refer to figure 4 for the

plot of fluorescence decay of O atoms with time). The second order rate constant, k1 was

28

then obtained from the gradient of a linear plot of kps1 versus SO2 as illustrated in figure

5.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350

200

400

600

800

1000

1200

Fluo

resc

ence

Inte

nsity

Time/s

Figure 4: Plot of fluorescence intensity including background of SO2+O+Ar at 297 torr

and 1047 K with an SO2 concentration of 7.9 x 1015 molecules cm-3

29

0 2 4 6 8 10 12 14 160

50

100

150

200

250

300

K ps1 /s

-1

[SO2]/1015 cm3 molecule-1

Figure 5: Plot of pseudo-first-order rate constant (kps1) for the loss of O radicals at 297

torr and 1047 K. Open symbol corresponds to decay in figure 4.

2.5 SO2 Absorption Cross-Section (σ) Determination

The ultraviolet absorption cross-section of SO2 is required to calculate the concentration

of SO2 photolyzed, hence the concentration of O radicals produced. Calculating O

radicals produced involves the Beer-Lambert law:

Itrans = I0 exp (-σ cl) (2.7)

Itrans and I0 represent the intensity of transmitted and incident light respectively. σ is the

molecular absorption cross coefficient with units of cm2 molecule-1, c is the concentration

of the absorbing specie in molecules cm-3 and l is the path length in cm. The cross section

may also be measured in terms of ε, which is the molar absorption coefficient with units

of cm2 mole-1.

30

Although the absorption coefficients in the vacuum ultraviolet region have been

published,108-111 fine structure around 193.3 nm leads to varying estimations of the cross

section at the laser photolysis wavelength. The absolute cross-section of SO2 at room

temperature was determined in a set of three experiments using an excimer laser source

and a flowing gas cell. Mixtures of slightly less than 1 % SO2 in Ar gas were passed

through the cell. Complete saturation of the cell was attained usually after two hours of

constant flow before attenuated light was measured with a pulse energy meter (Molectron

detector Inc, model J25LP). Saturation of the cell was determined by the consistency of

the absorbance at a constant SO2 flow. The attenuated signal was averaged by a digital

oscilloscope (Tektronix Inc., model 2440). The SO2 concentration in the cell was

changed by altering the gas pressure in the cell.

Error limits generated from the determination of absolute absorbance at room

temperature were obtained from the flowmeter corrections and the limits of the digital

temperature and pressure readouts. Statistical errors of the constrained fit Beer-Lambert

plots (figures 6-8 in Appendix A) were 2.1 %, 1.9 % and 1.7 %. With a path length of 35

cm the absorption coefficients derived from these plots are 7.40 x 10-18, 7.44 x 10-18 and

7.40 x 10-18 cm2 molecule-1. The mean absorption coefficient is (7.4 ± 0.4) x 10-18 cm2

molecule-1. Error limits of the mean absorption coefficient of SO2 were generated from

error limits of the SO2 concentration of each Beer-Lambert plot. Deviation from the best

fit Beer-Lambert plot were obtained from a best fit to the edges of the error limits of the

31

SO2 concentration, yielding closely symmetrical positive and negative deviation from the

best fit. The best fits were constrained to pass through the origin.

The absorption coefficient of SO2 has been estimated by Fockenberg and Preses,113 from

prior literature,108,109 to be 6 x 10-18 cm2 molecule-1 at room temperature At 193 nm, the

absorption cross of SO2 has been measured to be 8.24 x 10-18 cm2 molecule-1 at 300 K.112

The temperature dependence of the absorption cross section of SO2 has been investigated

at 345 and 925 K at 193 nm,113 and between 293 and 1070 K at 200 – 350 nm.114

Fockenberg and Preses reported a 40 % decrease in the SO2 absorption cross-section

between 345 and 925 K, which fixes the SO2 absorption cross section at 925 K relative to

the cross section at 345 K. SO2 absorption cross sections at 873 and 1073 K were

determined relative to the cross section at room temperature, assuming that relative

absorption cross sections remained the same for 200 and 193 nm. The temperature

dependence of the SO2 absorption cross-section can then be estimated at other

temperatures from a linear interpolation illustrated on the following page:

32

200 400 600 800 1000 1200

0.6

0.7

0.8

0.9

1.0

Rel

ativ

e Ab

sorb

ance

T, K

Figure 9: Temperature dependence of cross section absorption of SO2. The equation of

the above interpolation is: Rel. abs. = (1.16 ± 0.11)T – (5.24 x 10-4 ± 1.29 x 10-4)

33

CHAPTER 3

RESULTS AND DISCUSSION

3.1. Results

SO2 + O + (M) SO3 + (M) (3.1)

Second order rate constants for reaction 3.1 at 289 K, 399 K, 581 K, 699 K, 840 K and

1040 K were obtained under different conditions and are listed in tables 1-6 in appendix

B. The rate constants have statistical errors of 1σ. Results are independent of the laser

energy, verifying the isolation of the reaction 3.1 from any secondary chemistry.

3.2 Discussion

Previous studies of reaction 3.1 have been limited by temperature and pressure

considerations. In this study the kinetics of reaction 3.1 have been assessed at pressures

between 30 torr and pressures close to atmospheric pressure (660 torr) and at

temperatures between ambient and 1040 K.

Lifting of previous temperature and pressure restrictions allows for the study of the

pressure dependence of reaction 3.1. The reaction is found to be in the falloff region at

temperatures studied here, which is a new observation. Unlike with other temperatures of

this study, the plot of first order rate constant vs. pressure at 1040 K does not yield a y

intercept of zero, but 5 x 10-15 cm3molecule-1s-1. The y intercept reflects some overall rate

and since the y intercept increased from 0 to 5 x 10-15 cm3molecule-1s-1, there might be a

34

shift in the chemistry at this temperature. It was initially speculated that the abstraction

reaction

SO2 + O → SO + O2 (3.2)

might be a competing reaction at this temperature. If so, the rate of reaction obtained at

1040 K from a log k vs. temperature plot for reaction 3.2 is the contribution to the

observed rate of reaction 3.1

The study of the reverse rate of reaction 3.2 was carried out over a temperature range of

450-585 K at a total pressure of 20 torr by Garland.115 Incorporating data from literature

together with the measured rates, she derived the rate expression at 250-3500 K:

k(T)= 1.5 x 10-13 T1.4exp(-1868/T) cm3 s-1.

The rate of the forward and reverse reactions are related by the equilibrium constant:

Keq = kforward/kreverse (3.3)

The equilibrium constant of the forward reaction 3.2 was determined from the following

relationship:

-RT ln Keq = ∆reactionG0 (3.4)

where ∆reactionG0 is the Gibbs free energy of the forward reaction in kJ/mol and calculated

from thermodynamic tables.116 R is the universal gas constant and T is the temperature in

K. At 1040 K the derived rate of the forward reaction 3.2 is 7 x 10-16 cm3molecule-1s-1,

which is a small contribution to the y intercept of rate vs. pressure for reaction 3.1 at

1040 K. The origin of the non-zero intercept is therefore unknown.

35

To analyze the pressure dependence of the reaction 3.1, the Lindemann-Hinshelwood

theory was implemented.117,118

3.3. Background to Lindemann theory

In 1922 Frederick Lindemann suggested a reaction sequence to account for the observed

first order kinetics of spontaneous unimolecular reactions, such as isomerizations and

decompositions, instead of implied second order kinetics. The sequence for the reverse of

bond decomposition, i.e., recombination of radicals is:

A + B C* (3.5)

C* A +B (3.6)

C* + M C +M (3.7)

C* is an energized molecule of C, which has sufficient energy to isomerizes or

decompose. C* is formed by the transferal of kinetic energy of M. C* is either de-

energized to C by the transferal of energy to M, or C* can be transformed to products A

or B when it has the extra vibrational energy to disrupt the necessary bond. Reaction 3.6

is favored at lower pressure while at higher pressures reaction 3.7 is the dominant

pathway. The reaction rate is:

ν = d[C]/dt = -d[A]/dt = krec[A][B] (3.8)

d[A]/dt =-ka[A][B] + kb[C*] (3.9)

where a, b and c represent the rate constants of reactions 3.5, 3.6 and 3.7 respectively.

36

Applying the steady state approximation to C* yields:

d[C*]/dt = -kb[C*]+ ka[A][B] –kc[C*][M] = 0 (3.10)

Substitution into equation 3.10 into equation 3.9 yields a rate constant of:

krec =(-kakc[M]/(kb+ kc [M]) (3.11)

There are two limiting cases in determining the rate constant k. The first case, when kc

[M] >> kb, is favored at higher pressure and the rate constant,

k∞ = ka (3.12)

Equation (3.12) is the high-pressure limit. The high-pressure rate law is second order.

The second case, when kc [M] << kb, occurs at lower pressure, where the rate determining

step is stabilization by collision and the rate constant,

k0= kakc[M]/kb (3.13)

Equation (3.13) is the low-pressure limit and the low-pressure rate law is third order.

Application of Lindemann-Hinshelwood theory to reaction 3.1 yields the following:

SO2+O SO3* (3.14)

SO3* O + SO2 (3.15)

SO3*+ M SO3+ M (3.16)

The reaction rate for reaction 3.1 is:

ν = d[SO3]/dt= -d[O]/dt = krec[O][SO2] (3.17)

If k1, k2 and k3 represent the rate constants of reactions 3.14, 3.15 and 3.16 respectively,

then

37

d[O]/dt =-k1[O][SO2] + k2[SO3*] (3.18)

d[SO3*]/dt = k1[O][SO2] – k2 [SO3*] –k3 [SO3*][M] (3.19)

From the steady state approximation

[SO3*] = k1[O][SO2]/(k2+k3[M]) (3.20)

Substituting equation 3.20 into equation 3.18 yields:

d[O]/dt =k1[O][SO2] + k2k1[O][SO2]/(k2+k3[M]) (3.21)

d[O]/dt = [O][SO2] (-k1+ k2k1/(k2+k3[M])) (3.22)

krec = (k1k3[M]/(k2 + k3[M])) (3.23)

1/krec = 1/k1+ (k2/k3k1)(1/[M]) (3.24)

A plot of 1/krec vs. 1/[M] therefore yields k1-1 as the y intercept and (k2/k3k1) as the slope.

Therefore the rate constant k1 and the ratio of k2 to k3k1 may be determined from a plot of

1/krec vs. 1/[M].

When [M] is small:

krec,0= k1k3[M]/k2 (3.25)

and when [M] is large:

krec,∞= k1 (3.26)

See figures 15-20 in Appendix B for data fit to Lindemann-Hinshelwood theory. Rate

constants at the low and high pressure limits, calculated from the Lindemann-

Hinshelwood plots, were then plotted as a function of temperature. See figures 22 and 23

for plots of the rate constants at the low and high pressure limits. See table 1 for a

summary of these rate constants.

38

200 300 400 500 600 700 800 900

1x10-33

1x10-32

k o, c

m6 m

olec

ule-2

s-1

Tem perature, K

Figure 22: Plot of low-pressure limit for O + SO2 + Ar vs. T. The interpolated curve is a

quadratic fit of the form log k(T) = [(-6.3 ± 2.6) x 10-6]T2 + [(8.6 ± 3.0) x 10-3]T + (-35.0

± 0.8) cm6 molecule-1s-1.

1.0 1.5 2.0 2.5 3.0 3.5

2.0x10-14

4.0x10-14

6.0x10-14

1000K/ T

k inf, m

olec

ule-1

cm

3 s-1

Figure 23: Arrhenius plot of extrapolated k∞ for O + SO2 + Ar recombination. A linear fit

is shown and has the form k(T) = 8.5 x 10-14exp(-468/T) cm3 molecule-1 s-1.

39

Table 1: Summary of rate constants at the low and high pressure limits.

Temperature, K k0 k∞

293 8.0 x 10-34 1.8 x 10-14

399 4.6 x 10-33 2.2 x 10-14

581 6.3 x 10-33 4.0 x 10-14

699 9.2 x 10-33 3.4 x 10-14

842 7.3 x 10-33 5.5 x 10-14

3.4 Third body contribution to the third order rate

Since reaction 3.1 is slow, relatively large concentrations of SO2 were used in this kinetic

study. It is therefore necessary to evaluate the ratio of the contribution of SO2 to Ar as a

third body in the determination of the rate constant. The overall rate of reaction 3.1 is a

function of a third order rate and O, SO2 and Ar concentrations.

d[O]/dt = -kIII[O][ SO2][M] (3.27)

kIII [M] = kIII,SO2[SO2] + kIII,Ar[M] (3.28)

The third order rate constant kIII is the sum of the product of the third order rate of each

third body and its concentration. At room temperature,102

kIII,SO2 = (9.5 ± 3.0) x 10-33 cm6 molecule-2 s-1

kIII,Ar = (1.05 ± 0.21) x 10-33 cm6 molecule-2 s-1

40

SO2 is about 9 times more efficient than Ar as a third body and therefore at low total

pressures (low [Ar]) SO2 could potentially interfere with determination of kIII,Ar. Data

reflecting a third body contribution from SO2 greater than 11 % of Ar third body

contribution were eliminated from the analysis.

3.5 Comparison of rate constants with those from prior determinations

At room temperature, the value of the rate constant falls between the rate constants

quoted by Davis,103 and Atkinson and Pitts.102 The value obtained in this study lie closely

outside the statistical error limits quoted in the Atkinson paper. Unfortunately no

statistical error limits are available from the Davis paper. The rate constant quoted by

Halstead and Thrush96 is about an order of magnitude greater than the rate determined in

this study at room temperature. The rate constant of 2.8 x 10-33 cm6 molecule-1

s-1 obtained by Mulcahy et al using afterglow detection121 has been preferred over their

previous determinations of 3.9 x 10-33 cm6 molecule-1 s-1 and 6.6 x 10-32 cm6 molecule-1 s-

1 by ESR detection,99 because of the greater sensitivity of the afterglow method.121 At 399

K, the rate constants obtained in this study are about a factor of two larger than those

quoted by Atkinson and Pitts. Study of the reaction over the other temperatures, cover a

range which has not been previously explored, hence no prior kinetic data are available

for the 580 – 1040 K region.

41

Table 7: Summary the rate constants available for the SO2+O +Ar reaction including

results from this study.

Experimental Method Temperature, K k0, cm6 molecule-2 s-1 Reference

SO2 afterglow 299

2.8 x 10-33 121

SO2 afterglow 300

1.3 x 10-32 96

FP-RF 353-220

3.4 x 10-32exp(-1120/T) 103

FP-NO2 chem. 299-440

3.1 x 10-32exp(-2000/RT) 102

Shock wave 1700-2500

2.9 x 10-35exp(7870/T) 90

LP-RP 289-1040

3.3 x 10-32exp(-992/T) this study ESR, electron spin resonance spectroscopy; FP, flash photolysis; LP, laser photolysis

RF,Resonance fluorescence; FP-NO2 chem, flash photolysis NO2 chemiluminescence

All of the tabulated kinetic studies of reaction 3.1 have employed Ar as a bath gas, while

other kinetic determinations of reaction 3.1 have employed various bath gases such as N2,

He, O2, SO2 and N2O.99-103 The different collisional efficiencies of these bath gases have

resulted in rate constants varying as much as a factor of 40 at room temperature.101

Estimations of the third body relative efficiencies have also varied. Collisional

efficiencies are principally a function of molecular complexity and mass. In Davis’ study

of reaction 3.1, several bath gases including Ar were used. A conversion factor of 0.87

was adopted there in the conversion from N2 to Ar efficiency.

42

0.000 0.001 0.002 0.003 0.004 0.00510-34

1x10-33

1x10-32

k 0,

cm6 m

olec

ule-2

s-1

1/Temperature, K-1

Figure 24: Comparative plot of rate constant of reaction 3.1 obtained from various

experimental studies, including this.

(—— reference 90; - - - reference 103, ▲ reference 102 , ■ this study ,○ reference 96,

reference 99, - . - reference 89.)

43

3.6. Spin Considerations

The reaction of SO2 with oxygen atoms violates spin conservation rules when the ground

states of O (3P), SO2 (1A1) and SO3 (1A1') are concerned. Referring to Figure 24 it is

evident that at low temperature reaction 3.1 has a positive activation energy (from the

slope of the plot) which is suggestive of a barrier to reaction 3.1. At high temperature the

rate of the reaction 3.1 was determined from the reverse dissociation reaction and the

equilibrium constant and shows a negative activation energy.

Davis103 accounts for the positive temperature dependence of reaction 3.1 in a two step

mechanism, the first of which is the formation of a spin-allowed triplet SO3 molecule.

The second step involves intersystem crossing between triplet and singlet ground state

SO3. Intersystem crossing is often associated with spin-orbit coupling, which arises when

a heavy atom such as S is present. Formation of singlet SO3 violates the spin conservation

rule, and may account for the energy barrier of reaction 3.1.

44

Figure 25: A simple energy diagram for the mechanism of reaction3.1 as suggested by

Davis.103 ISC represents intersystem-crossing.

Westenberg and deHaas101 suggest that the positive temperature dependence of reaction

3.1 occurs when the positive energy of the excitation process of :

SO3(1A)→SO3*(3A) excitation energy = E3

*

is greater than the heat of enthalpy for reaction 3.1 (∆rxnH). So a positive temperature

dependence is observed when E3*>|∆rxnH|. A negative temperature dependence of

reaction 3.1 at high temperature can then be explained in terms of E1*< |∆rxnH|, where E1

*

is the energy of SO3*(1A) formation after intersystem crossing. This mechanistic theory

may be verified by quantum mechanical calculations of the triplet and singlet state

energies of SO3.

45

Figure 26: A simple energy diagram for the proposed intermediates in the mechanism of

reaction 3.1 as suggested by Westenberg and deHaas.101 ISC represents intersystem-

crossing.

3.7 Statistical Analysis of O + SO2+Ar

Troe has suggested a broadening factor, which when incorporated with the Lindemann

scheme gives a better estimation of the high pressure limit.119 In the Lindemann-

Hinshelwood model, a fall-off curve is described by:

k/k∞ = (k0/k∞)/(1 + k0/k∞) ≡ FLH(k0/k∞) (3.29)

The broadening of the falloff curve is accounted for in a collision broadening factor

k/k∞ = FLH(k0/k∞)FBF(k0/k∞) (3.30)

46

where FLH and FBF represent the Lindemann-Hinshelwood and broadening factor

functions. Detailed analysis of FBF in terms of Troe’s statistical adiabatic channel model

may be found elsewhere.120,121

Troe applied this kind of theoretical analysis to reaction 3.1.89,90 The dash-dot curve of

figure 24 is a fit of this analysis. Troe calculated the barrier of reaction 3.1 as the

difference between the threshold energy, which was best fit to experimental data, and the

heat of enthalpy for the reverse dissociation reaction 3.1. The estimated barrier at 0 K is

13.8 ± 4 kJ/mol.

The rate constant at the high-pressure limit at room temperature obtained from Troe’s

theoretical analysis89 is k∞= P x (2.16 x 10-13) cm3 molecule-1 s-1 where P represents the

triplet-singlet transition probability. Troe’s rate constant compares favorably with the rate

constant of k∞= 1.8 x 10-14 cm3 molecule-1 s-1 calculated in this study for the high pressure

limit. The implied value of P is ~ 0.1, which is consistent with Troe’s lower limit of 0.03.

47

Figure 27: A simple energy diagram for the proposed intermediates in the mechanism of

reaction 3.1 as suggested by Troe et al.90 ISC represents intersystem-crossing.

48

CHAPTER 4

CONCLUSION

The rate constant for the O + SO2 +(Ar) reaction has been measured between 289 and

1040 K by the laser photolysis resonance fluorescence technique. The reaction is spin

forbidden and slow, so large concentrations of SO2 were used in this kinetic study.

Conditions were selected to make the contribution of SO2 to the third order reaction

minor to the contribution from M = Ar. The rate obtained in this study illustrates a barrier

to the reaction because at low temperature the reaction has a positive activation energy

while at higher temperature it possesses a negative activation energy.

For the first time fall-off behavior was observed in O + SO2 recombination. The rate

expression for the O + SO2 +(Ar) reaction over the temperature range of 289 to 842 K is:

log k(T) = [(-6.3 ± 2.6) x 10-6]T2 + [(8.6 ± 3.0) x 10-3]T + (-35.0 ± 0.8) cm6 molecule-1 s-1

for the low pressure limit and k(T) = 8.5 x 10-14exp(-468/T) cm3 molecule-1 s-1 for the

high pressure limit. The kinetic study at 1040 K may be revisited, as concerns over

possible side reactions have arisen due to a non-zero first order rate at zero pressure at

this temperature.

The temperature dependence of the absorption coefficient of SO2 was estimated relative

to the absorption coefficient at room temperature, which was measured at

49

(7.4 ± 0.4) x10-18 cm2 molecule-1.

50

APPENDIX A: Spectroscopic data

51

0 . 0 5 . 0 x 1 0 1 4 1 . 0 x 1 0 1 5 1 . 5 x 1 0 1 5 2 . 0 x 1 0 1 5 2 . 5 x 1 0 1 5 3 . 0 x 1 0 1 5 3 . 5 x 1 0 1 50 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

Ln(I 0/I)

[ S O 2 ] m o l e c u l e s / c m 3

Figure 6: Beer-Lambert plot of SO2 at room temperature. (Temperature = 295 K,

I0 = 0.047 mJ, τres = 4.4-10.0 s, average τres = 6. 7 s, laser repetition rate =2 Hz)

0 1 x 1 0 1 5 2 x 1 0 1 5 3 x 1 0 1 50 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6

0 . 7

0 . 8

0 . 9

[ S O 2 ] m o l e c u l e s / c m 3

Ln(I 0/I)


I0 = 0.040 mJ, τres = 7.6-17.7 s, average τres = 11.2 s, laser repetition rate =10 Hz)

52

0 .0 5 .0 x 1 0 1 4 1 .0 x 1 0 1 5 1 .5 x 1 0 1 5 2 .0 x 1 0 1 5 2 .5 x 1 0 1 5 3 .0 x 1 0 1 50 .0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 .7

0 .8

[S O 2 ]m o le c u le s /c m 3

Ln(I 0/I)


I0 = 0.051 mJ, τres = 9.6-20.5 s, average τres = 12.7 s, laser repetition rate =10 Hz)

53

APPENDIX B: Kinetic Data

Codes:

A: datum included in analysis

B: datum excluded in analysis due to SO2 contributing more than 11 % to the third body

efficiency than Ar.

C: datum excluded from analysis due to non-linearity in the kps1 vs. [SO2] plot.

D: datum excluded from analysis due to a large uncertainty of the rate derived from the

kps1 vs. [SO2] plot.

E: conditioning of the reactor questionable; datum excluded in analysis

F: percentage ratio of [SO2] to [Ar] contribution as a third body

Int: y intercept

54

Table 2: Rate constant measurements for O + SO2 + Ar at 289 K

Temp P τres I0 [O]0,min [O]0,max [SO2]0,min

σ [SO2]0,min [SO2]0,max

σ [SO2]0,max F [Ar] k σk Int. σ Code

K torr s µJ 1012 molec.cm-3

1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1

1016 molec. cm-3 s-1

287 202 3.5 15.8 7.5 15.0 1.93 0.09 4.95 0.10 6.6 6.80 3.5 0.4 -5 12.0 A

287 201 3.5 85.0 30.6 81.2 1.41 0.09 4.85 0.10 6.5 6.77 3.6 0.1 3 2.1 A

287 200 3.5 34.6 9.1 33.6 0.99 0.09 4.80 0.10 6.5 6.73 3.5 0.03 1 1.0 A

286 122 4.4 13.8 5.4 13.3 1.54 0.12 4.89 0.13 10.7 4.12 2.6 0.1 -2 2.4 A

287 77 2.9 13.8 6.8 11.5 2.02 0.08 3.97 0.09 13.9 2.59 1.5 0.1 10 2.8 B

287 650 14 13.8 4.1 10.8 0.42 0.11 3.65 0.12 1.5 21.88 7.4 0.1 6 1.7 A

287 652 14 17.8 6.8 14.0 0.42 0.11 4.81 0.12 2.0 21.95 7.7 0.3 20 8.1 A

287 522 11 17.8 1.7 16.2 0.33 0.09 4.52 0.10 2.3 17.57 7.1 0.2 11 4.4 A

288 404 10 11.9 3.7 11.0 0.32 0.09 4.63 0.10 3.1 13.55 6.7 0.4 11 10.1 A

288 406 11 17.8 1.6 16.6 0.32 0.08 4.67 0.10 3.1 13.62 8.6 0.2 22 6.8 C

294 300 13 16.8 4.2 13.8 0.28 0.10 3.88 0.11 3.6 9.86 5.9 0.4 15 7.0 A

294 302 13 32.6 8.2 26.5 0.28 0.10 3.84 0.11 3.5 9.92 6.1 0.2 17 3.3 A

293 664 28 15.8 1.3 13.0 0.30 0.07 3.88 0.08 1.6 21.89 9.5 0.3 28 4.9 A

55

Table 1 continued: Rate constant measurements for O + SO2 + Ar at 289 K





1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


293 664 28 33.6 2.8 27.6 0.30 0.07 3.88 0.08 1.6 21.89 9.8 0.4 45 7.6 A

294 452 19 27.7 1.4 22.3 0.18 0.05 3.77 0.06 2.3 14.85 8.2 0.4 24 7.5 C

292 651 12 15.8 2.6 16.9 0.61 0.15 5.83 0.16 2.4 21.54 7.8 0.3 37 7.9 A

292 651 12 31.6 5.3 33.9 0.61 0.15 5.83 0.16 2.4 21.54 7.9 0.5 52 16.8 C

292 548 12 11.9 1.9 12.2 0.60 0.15 5.46 0.15 2.7 18.13 7.5 0.1 15 3.0 A

292 548 12 19.8 3.2 20.4 0.60 0.15 5.46 0.15 2.7 18.13 7.4 0.1 26 4.0 A

293 375 9.6 11.9 1.8 12.4 0.56 0.12 5.57 0.13 4.1 12.36 6.1 0.0 10 1.0 A

293 650 17 11.9 1.8 12.2 0.56 0.10 5.44 0.11 2.3 21.43 8.7 0.1 20 2.6 A

293 650 17 19.8 3.0 20.3 0.56 0.10 5.44 0.11 2.3 21.43 8.8 0.2 29 5.9 A

294 450 15 18.6 3.2 19.1 0.64 0.09 5.44 0.10 3.3 14.79 7.3 0.1 17 1.8 A

293 300 9.6 11.9 0.7 8.3 0.23 0.06 3.14 0.06 2.9 9.89 5.9 0.2 9 3.1 A

293 300 9.6 25.7 1.7 18.0 0.23 0.06 3.14 0.06 2.9 9.89 6.6 0.2 13 2.9 A

296 607 15.3 32.1 6.6 35.8 0.76 0.09 4.64 0.09 2.1 19.81 8.8 0.3 41 6.4 A

56






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


296 507 15.8 32.1 6.9 40.9 0.81 0.09 8.02 0.11 4.4 16.55 7.9 0.3 33 7.5 A

296 204 12.8 29.6 5.3 24.4 0.66 0.07 3.89 0.10 5.3 6.66 4.9 0.1 18 0.6 A

296 31 3.78 29.6 3.3 16.2 0.40 0.03 2.31 0.09 20.7 1.01 1.8 0.2 31 1.2 B

297 657 13.8 54.2 7.8 73.3 0.53 0.14 9.20 0.16 3.9 21.37 8.9 0.7 82 25.2 A

297 657 13.7 17.8 2.6 24.1 0.53 0.14 9.18 0.16 3.9 21.37 8.6 0.3 33 11.4 A

297 30 1.86 17.8 1.4 9.2 0.29 0.02 2.14 0.06 19.8 0.98 1.4 0.1 40 0.8 B

297 248 7.73 16.2 8.7 19.8 1.19 0.08 5.20 0.10 5.8 8.07 5.3 0.03 18 0.7 A

57

0 100 200 300 400 500 600 7000

1

2

3

4

5

6

7

8

9

10

11

Rat

e C

onst

ant,

10-1

5 cm

3 mol

ecul

e-1 s

-1

P re s s u re , to rr

Figure 10: Plot of first order rate constant vs. pressure at 289 K

58






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


398 663 20 65.2 3.3 18.3 0.19 0.05 1.13 0.05 0.6 16.09 16.3 0.4 19 2.7 A

399 528 19 65.2 2.4 19.2 0.14 0.05 1.19 0.05 0.8 12.78 16.5 0.2 12 1.7 A

399 300 9.2 88.9 2.5 31.2 0.10 0.02 1.45 0.03 1.8 7.26 12.8 0.1 9 0.8 A

399 100 6 88.9 1.5 30.7 0.06 0.02 1.42 0.04 5.3 2.42 6.4 0.2 14 1.0 A

399 75 5.6 53.4 1.1 18.8 0.08 0.02 1.46 0.04 7.3 1.82 5.1 0.2 18 0.9 A

396 30 2.9 53.4 1.6 18.0 0.11 0.03 1.38 0.06 17.1 0.73 2.3 0.2 44 1.0 B

395 200 7.5 53.4 3.0 18.9 0.21 0.09 1.46 0.09 2.7 4.89 8.5 0.1 15 1.3 A

59

0 100 200 300 400 500 600 7000

2

4

6

8

10

12

14

16

18

Rat

e C

onst

ant,

10-1

5 cm

3 mol

ecul

e-1 s

-1



60






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


581 30 1.9 52.0 1.1 15.7 0.09 0.04 1.36 0.05 24.7 0.50 3.8 0.3 87 1.3 B

581 225 5.7 118.6 3.6 32.4 0.13 0.06 1.22 0.06 3.0 3.74 13.6 0.2 14 1.6 A

581 101 3.2 118.6 2.0 32.4 0.07 0.03 1.05 0.04 5.7 1.68 8.0 0.1 29 0.6 A

582 654 14 126.0 3.6 30.6 0.18 0.03 1.07 0.03 0.9 10.86 25.6 0.7 6 4.2 A

582 654 14 46.4 1.3 11.3 0.11 0.03 1.07 0.03 0.9 10.86 26.1 0.5 4 3.1 A

581 520 12 126.0 3.0 30.3 0.10 0.03 1.07 0.03 1.1 8.65 23.7 0.4 4 2.3 A

580 363 12 62.2 1.9 15.1 0.13 0.03 1.07 0.03 1.6 6.05 18.8 0.4 6 2.1 A

61

0 100 200 300 400 500 600 7000

2

4

6

8

10

12

14

16

18

20

22

24

26

28

Rat

e C

onst

ant,

10-1

5 cm

3 mol

ecul

e-1 s

-1



62






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


696 255 8.9 133.4 3.4 29.4 0.11 0.02 1.04 0.03 2.7 3.54 15.90 0.50 3 2.4 A

696 255 9.1 51.38 1.3 9.0 0.11 0.02 0.82 0.03 2.1 3.54 14.60 0.90 7 3.4 A

696 75 3.9 133.4 3.3 19.5 0.11 0.01 0.68 0.02 5.9 1.04 6.00 0.20 41 0.7 A

692 655 8.8 128.5 5.1 32.8 0.18 0.07 1.22 0.08 1.2 9.14 25.80 1.00 8 7.1 A

700 518 9.2 128.5 4.9 30.8 0.17 0.08 1.15 0.08 1.5 7.15 24.50 0.90 -1 6.5 A

699 601 8 98.8 3.6 23.3 0.16 0.07 1.12 0.07 1.2 8.31 25.10 0.50 14 3.1 A

699 401 6.1 98.8 3.1 23.9 0.14 0.05 1.15 0.05 1.9 5.54 20.10 0.10 10 1.0 A

699 175 4.7 98.8 2.9 22.7 0.13 0.04 1.09 0.04 4.1 2.42 11.80 0.10 15 0.9 A

699 30 1.6 98.8 1.2 18.8 0.05 0.01 0.89 0.04 19.4 0.41 2.30 0.30 108 0.9 B

63

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 00

5

1 0

1 5

2 0

2 5

3 0

Rat

e C

onst

ant,

10-1

5 cm

3 mol

ecul

e-1 s

-1



64






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


844 403 4 60 1.4 11.7 0.12 0.03 1.01 0.03 2.0 4.61 19.3 0.7 21 3.7 A

844 253 7.5 69.2 1.4 9.7 0.10 0.05 0.71 0.05 2.2 2.90 15.4 0.7 13 2.9 A

843 50 1.5 33.6 0.2 5.4 0.05 0.01 0.83 0.02 13.1 0.57 3.8 0.4 94 0.9 B

841 561 5 25 0.9 5.2 0.18 0.05 1.09 0.05 1.5 6.44 24.3 1.2 15 8.7 A

842 125 3.7 25 0.6 5.2 0.12 0.04 1.08 0.04 6.8 1.43 8.2 0.3 35 1.8 A

842 200 6 109 3.5 20.7 0.16 0.06 0.98 0.06 3.9 2.29 13.4 0.7 14 3.7 A

841 25 1.1 109 2.3 12.0 0.11 0.01 0.56 0.02 17.6 0.29 2.7 0.9 185 2.6 B

843 660 7.4 91 2.1 18.3 0.11 0.04 1.04 0.04 1.2 7.56 28 0.7 14 4.0 A

842 25 1.1 61 0.8 9.2 0.07 0.01 0.78 0.03 24.6 0.29 3.1 1.3 188 3.3 B

65

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 00

5

1 0

1 5

2 0

2 5

3 0

Rat

e C

onst

ant,

10-1

5 cm

3 mol

ecul

e-1 s

-1



66






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


1031 200 1.4 123.5 1.1 4.6 0.052 0.002 0.22 0.00 1.0 1.87 31.6 0.9 106 1.1 E

1032 200 1.3 133.4 1.5 6.1 0.066 0.002 0.26 0.00 1.3 1.87 30.4 2.2 98 3.7 D

1044 200 2 133.4 1.7 8.9 0.073 0.004 0.39 0.01 1.9 1.85 10.9 1.2 108 2.4 D

1045 200 1.1 123.5 0.2 3.6 0.011 0.002 0.17 0.00 0.8 1.85 9.9 1.4 92 1.6 D

1045 101 0.8 123.5 0.6 5.7 0.026 0.003 0.27 0.00 2.6 0.93 8.1 4.2 134 7.1 D

1031 102 0.8 31.6 0.1 0.8 0.020 0.001 0.15 0.00 1.4 0.96 10.2 1.1 127 1.0 D

1046 198 2.3 59.3 1.5 6.9 0.220 0.015 0.82 0.02 4.1 1.83 9.1 0.9 117 3.6 D

1046 198 2.4 197.6 4.9 27.3 0.220 0.015 0.82 0.02 4.1 1.83 9.1 0.3 115 1.5 A

1043 201 1.2 123.5 1.5 17.7 0.071 0.008 0.85 0.01 4.1 1.86 9.3 0.2 91 0.7 A

1043 201 1.2 31.6 0.4 4.5 0.071 0.008 0.85 0.01 4.1 1.86 9.8 0.2 89 0.7 C

1046 99 1.2 128.5 2.7 20.4 0.044 0.034 0.95 0.04 9.4 0.91 6.3 0.8 130 3.0 C

1047 499 3 59.3 1.5 17.9 0.140 0.085 1.88 0.09 3.7 4.60 14.9 0.4 96 3.1 C

1047 50 0.6 98.8 1.5 7.7 0.088 0.017 0.46 0.02 9.0 0.46 3.8 0.5 182 1.2 C

67






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


1048 300 3.6 98.8 2.3 17.9 0.130 0.100 1.15 0.10 3.8 2.77 11.9 0.5 117 2.7 A

1047 601 3.1 128.5 9.2 29.5 0.250 0.069 1.41 0.07 2.3 5.55 18.3 0.4 82 3.3 A

1048 25 0.3 128.5 0.5 18.4 0.074 0.007 1.12 0.03 44.0 0.23 3.1 0.7 307 2.9 B

1047 351 3.6 108.5 1.6 19.6 0.082 0.064 1.09 0.08 3.0 3.24 12.6 0.4 105 2.4 A

1046 351 1.8 98.8 2.5 29.3 0.150 0.040 1.86 0.04 5.2 3.24 13.4 1.3 86 10.9 A

1048 650 3.6 187.7 2.8 28.7 0.087 0.037 0.91 0.04 1.4 5.99 21.8 0.6 69 2.8 A

1049 550 4 187.7 2.9 28.7 0.088 0.037 0.89 0.04 1.6 5.06 20.0 0.3 64 1.6 A

1049 425 4.4 187.7 2.7 34.8 0.082 0.041 1.12 0.04 2.6 3.91 17.2 0.3 72 1.8 A

1049 251 3.1 138.3 2.4 22.2 0.099 0.029 0.96 0.03 3.8 2.31 12.1 1.1 79 3.7 A

1048 151 2.8 98.8 1.4 12.2 0.080 0.026 0.73 0.03 4.7 1.39 9.3 1.8 96 4.7 A

1047 75 1.8 88.9 1.5 9.8 0.099 0.017 0.65 0.02 8.5 0.69 8.0 1.1 123 2.8 C

1047 30 0.55 88.9 0.4 5.2 0.028 0.006 0.34 0.01 11.1 0.28 3.1 1.0 242 2.1 B

1047 30 0.56 79.1 0.3 4.7 0.025 0.008 0.35 0.01 11.4 0.28 3.2 2.0 247 3.5 B

68






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


1047 60 1.1 79.1 0.4 10.6 0.032 0.015 0.80 0.02 13.1 0.55 5.9 0.7 142 1.7 B

1045 402 3.6 79.1 1.3 10.4 0.093 0.043 0.78 0.04 1.9 3.72 24.3 3.5 76 14.3 D

1044 655 12 55.3 1.6 5.1 0.17 0.085 0.55 0.09 0.8 6.06 28.4 1.2 89 4.8 D

1037 655 4 55.3 0.9 6.9 0.093 0.028 0.74 0.03 1.1 6.10 23.8 0.2 57 0.9 A

1043 520 3.1 55.3 0.6 7.2 0.066 0.022 0.60 0.02 1.1 4.82 20.1 0.5 53 2.2 A

1043 80 1.9 79.0 0.8 10.9 0.055 0.014 0.81 0.02 9.9 0.74 6.6 1.4 107 3.8 D

1042 249 2.2 79.0 0.0 11.2 0.059 0.016 0.88 0.02 3.4 2.31 12.5 0.1 51 0.5 A

1043 152 1.6 55.3 3.5 3.8 0.12 0.01 0.39 0.01 2.5 1.41 8.9 0.6 118 1.2 A

1042 660 3.4 23.9 20.2 4.5 0.11 0.029 1.08 0.03 1.6 6.12 23.1 0.3 99 1.7 A

1042 660 3.4 92.9 20.2 17.3 0.11 0.029 1.08 0.03 1.6 6.12 23.9 0.4 95 2.1 A

1043 76 1.3 81.2 6.5 9.8 0.084 0.012 1.03 0.02 13.2 0.70 6.10 1.00 146 3.0 B

1044 31 1.1 81.2 15.3 14.6 0.053 0.01 0.69 0.03 21.8 0.29 4.80 1.20 250 3.2 B

1043 550 3.3 118.6 3.1 23.8 0.091 0.025 1.01 0.03 1.8 5.09 32.20 2.10 48 12.6 D

69






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


1045 450 3.6 118.6 16.3 20.9 0.15 0.027 1.15 0.03 2.5 4.16 21.00 0.80 68 5.5 C/D

1049 433 2.58 62.0 2.0 13.3 0.19 0.021 1.31 0.02 3.0 3.99 41.6 1.5 166 9.8 D/E

1048 656 3.9 62.0 1.8 17.9 0.17 0.031 1.80 0.03 2.7 6.05 39.6 1.1 131 7.4 D/E

1050 200 1.54 62.0 0.5 14.6 0.045 0.012 1.45 0.02 7.1 1.84 26.5 1.3 110 5.4 D

1049 646 4.75 48.0 1.1 11.3 0.13 0.015 1.44 0.02 2.2 5.95 33.1 5.0 116 20.7 D

1050 330 4.65 64.0 1.4 13.2 0.13 0.017 1.25 0.02 3.7 3.04 31.1 1.6 94 7.0 D

1049 649 3.85 74.0 1.4 24.1 0.11 0.038 2.06 0.04 3.1 5.98 23.1 0.6 90 4.3 A

1049 313 3.7 68.0 1.5 16.0 0.13 0.036 1.45 0.04 4.6 2.88 17.9 1.4 105 9.2 C

1048 104 1.82 71.0 0.9 13.0 0.075 0.01 1.11 0.02 10.5 0.96 20.3 1.3 110 4.1 D

1048 428 6.1 61.0 1.0 9.4 0.092 0.025 0.93 0.04 2.1 3.95 17.0 0.9 114 3.7 A

1048 203 5.3 49.0 1.0 5.8 0.12 0.033 0.70 0.04 3.4 1.87 13.3 0.9 124 2.9 A

1048 210 3.75 70.0 1.1 14.3 0.089 0.041 1.24 0.05 5.8 1.94 17.7 0.8 90 4.3 E

1047 208 1.23 70.0 2.9 25.9 0.24 0.017 2.38 0.02 11.2 1.92 11.0 0.6 78 4.2 A

70






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


1047 109 3.83 98.8 1.9 14.8 0.11 0.042 0.90 0.05 8.1 1.01 14.4 2.9 116 12.0 E

1047 111 1.39 98.8 0.9 24.4 0.051 0.014 1.52 0.02 13.4 1.02 7.0 0.6 102 3.1 B

1046 52 1.2 98.8 2.0 19.1 0.12 0.013 1.18 0.03 22.2 0.48 7.4 0.8 159 3.2 B

1047 30 0.35 73.0 0.4 8.6 0.035 0.004 0.69 0.02 22.6 0.28 9.4 2.4 261 9.9 B

1046 32 1.11 67.0 1.3 9.6 0.11 0.013 0.86 0.03 26.3 0.30 4.0 3.3 249 10.3 B

1046 47 0.82 67.0 2.9 12.7 0.084 0.01 1.16 0.03 24.2 0.43 7.3 2.8 183 10.7 B

1047 301 3.6 63.2 1.6 12.8 0.15 0.04 1.23 0.04 4.0 2.78 13.0 0.8 92 4.6 C

1047 297 1.76 63.2 2.0 14.7 0.18 0.02 1.43 0.02 7.1 1.82 12.3 0.1 72 0.8 A

1047 547 3.9 56.1 1.9 9.4 0.08 0.022 1.01 0.02 1.8 5.05 40.2 6.8 56 29.5 C

1047 547 3.9 125.0 4.3 36.1 0.08 0.022 1.80 0.03 3.2 5.05 26.1 2.1 77 12.3 C

1047 102 1.43 56.1 0.8 9.6 0.08 0.0083 1.04 0.02 10.0 0.94 8.0 0.6 105 2.1 A

1046 551 3.91 70.2 2.1 23.5 0.17 0.047 2.12 0.05 3.8 5.09 22.1 2.6 113 18.0 C/E

1046 551 3.91 148.2 4.3 49.6 0.17 0.047 2.12 0.05 3.8 5.09 24.3 2.1 84 18.2 C

71






1012 molec.cm-3

1016 molec.cm-3

1016 molec. cm-3

1016 molec. cm-3

1016 molec. cm-3 %

1018 molec.cm-3

10-15

cm-1. molec-1.s-1


1046 33 0.77 71.9 1.2 11.7 0.10 0.0112 0.98 0.03 29.1 0.30 7.2 0.9 241 2.8 B

72

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 00

2

4

6

8

1 0

1 2

1 4

1 6

1 8

2 0

2 2

2 4

2 6

Rat

e C

onst

ant,

10-1

5 cm

3 mol

ecul

e-1 s

-1

P r e s s u r e , t o r r


73

0.0 5.0x10-20 1.0x10-19 1.5x10-19 2.0x10-19 2.5x10-19 3.0x10-190.0

5.0x1013

1.0x1014

1.5x1014

2.0x1014

2.5x1014

3.0x1014

3.5x1014

4.0x1014

1/R

ate

cons

tant

, cm

-3 m

olec

ule

s

1/[Ar]

Figure 16: Lindemann plot at 289 K

0.0 2.0x10-19 4.0x10-19 6.0x10-19 8.0x10-190.0

2.0x1013

4.0x1013

6.0x1013

8.0x1013

1.0x1014

1.2x1014

1.4x1014

1.6x1014

1.8x1014

2.0x1014

1/R

ate

cons

tant

, cm

-3 m

olec

ule

s

1/[Ar]


74

0.0 1.0x10-192.0x10-193.0x10-194.0x10-195.0x10-196.0x10-197.0x10-190.0

2.0x1013

4.0x1013

6.0x1013

8.0x1013

1.0x1014

1.2x1014

1.4x1014

1/R

ate

cons

tant

, cm

-3 m

olec

ule

s

1/[Ar]


0.00 2.50x10-19 5.00x10-19 7.50x10-19 1.00x10-18 1.25x10-180.0

2.0x1013

4.0x1013

6.0x1013

8.0x1013

1.0x1014

1.2x1014

1.4x1014

1.6x1014

1.8x1014

1/R

ate

cons

tant

, cm

-3 m

olec

ule

s

1 /[Ar]


75

0.0 2.0x10-19 4.0x10-19 6.0x10-19 8.0x10-190.0

2.0x1013

4.0x1013

6.0x1013

8.0x1013

1.0x1014

1.2x1014

1/R

ate

cons

tant

, cm

-3 m

olec

ule

s

1 /[Ar]


0.0 5.0x10-19 1.0x10-18 1.5x10-180.0

2.0x1013

4.0x1013

6.0x1013

8.0x1013

1.0x1014

1.2x1014

1.4x1014

1.6x1014

1/R

ate

cons

tant

, cm

-3 m

olec

ule

s

1/[Ar]


76

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