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Gas Phase Reaction Kinetics

Of Neutral Oxygen Species

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UNITED STATES DEPARTMENT OF COMMERCE

C. R. Smith, Secretary,

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Gas Phase Reaction Kinetics of

Neutral Oxygen Species

Harold S. Johnston

University of California, Berkeley, California 94720

This research was supported by the

Advanced Research Projects Agency

of the Department of Defense under

Project DEFENDER

NSRDS-NBS 20

S • National Standard Reference Data Series —

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Issued September 1968

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C., 20102 • Price 45 cents

Foreword

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in
Preface

Now that chemical kinetics is approaching a certain level of maturity, with some of the field

passing from frontline research to established applied science, its quantitative data should be

tabulated in handbooks. Decisions must be made as to what to tabulate; suggestions have in- cluded: Empirical rate constants with defined order and regardless of mechanism, parameters

of the Arrhenius equation or parameters of activated-complex theory, nothing but molecular

transition probabilities or cross sections for identified changes of quantum states. The position

taken in this review is that we should tabulate individual rate constants for elementary chemical

reactions. I oppose basing handbooks on the other proposals listed above for the following reasons: Empirical rate data for an unanalyzed complex reaction are analogous to empirical thermodynamic

data for an impure unanalyzed substance; the data may be useful for the case in hand but of no

general interest. The bare reporting of parameters of the Arrhenius equation or activated-complex

theory equation conceals the source of the numbers, the probable error, the relationship to other

investigations. In tables of data of this sort one entry may represent an average of several hundred

observed points as obtained by a dozen different investigators over a wide temperature range, and

another entry may be a wild guess by an amateur in the field or the unsupported prediction of a crude theory. A refusal to tabulate any kinetic data except fundamental, quantum-state transitions

is analogous to a refusal to tabulate any thermodynamic data until they are obtained by statistical

mechanics from molecular parameters.

The idea of elementary chemical reactions, as opposed to complex reactions on the one hand

and elementary chemical-physical reactions or elementary physical reactions on the other hand,

is the main topic of section 1. A detailed discussion of each of three complex reaction systems

(decomposition of O2, decomposition of O3, and isotopic exchange between oxygen species) is the subject matter of the next three sections. The fifth section gives a discussion of a theoretical

problem raised by these data. The strictly handbook elements of this report are given by the

tables, summarized further in tables 15, 17, and 28 and in section 6. Nonkineticists are inclined

to expect greater precision from kinetic data than is really there; as a step toward correcting this

misapprehension, all data are presented in figures, where the experimental scatter and range of

observations are readily seen.

IV
Acknowledgment

An extensive set of reprints supplied by the Chemical Kinetics Information Center, National

Bureau of Standards, permitted this study to get off to a fast start. This set of reprints was checked

for completeness and supplemented by a literature search carried out by Frank Kotlier. During

the summer of 1966 the first draft of this report was prepared. A major gap in the study was filled by the detailed results of Benson and Axworthy’s review of the ozone data, and S. W. Benson let us borrow and copy A. E. Axworthy’s thesis. Axworthy’s thesis contains an outstanding review

of ozone kinetics before 1955. The thesis (like the journal article) does not list the individual rate constants, k\ and kj , but only the Arrhenius parameters from the set as a whole. We wanted to display individual rate constants to get a qualitative impression of the precision of the data and

to compare the results with those of other workers in the field. Edward Valenzuela set up a computer program to recompute rate constants for individual runs from the detailed data as assembled

in Axworthy’s thesis.

Undergraduate students bring a keen critical approach and fresh viewpoint to research or re- view problems. The content of this report including peripheral topics was divided into over 30

parts, and each part was assigned as a term paper in a senior course in inorganic chemistry.

In some cases the students discovered references I had overlooked, provided more extensive

calculations than I had made, or provided new insights into the problem. In all cases these term

papers provided valuable checks on previous work, especially relative to literature coverage,

reading of data points from graphs in journal articles, and probing for side reactions that might

distort reported rate constants.

The decomposition and recombination of molecular oxygen was reviewed by Richard Scheps

and Harvey Janszen. The excited electronic states of O and of O2 and the effect of electrical

discharges on O2 were reviewed by Robert Crooks, Miss Margaret Arner, and Gary Silver. Equilibrium constants for various reactions in O, O2, and O3 systems plus reactions involving these

species with oxides of nitrogen were recomputed and tabulated by David Hsu and Joseph Wong.

Various aspects of the thermal and photochemical decomposition of ozone were studied by William L. Bigbee, John E. Corn, Samuel Bader, and Edward Valenzuela. The literature on isotopic

exchange between O, O2, and O3 was reviewed by Richard F. Reichelderfer.

Unless one takes elaborate precautions, gaseous oxygen will contain traces of water, or organic

material, or N2 , which is converted to oxides of nitrogen in an electrical discharge. These impurities

interact with O, O2, and O3 in a large number of side reactions; the literature was reviewed for

quantitative data in these systems by N. L. Ackley, Alan Brattesani, P. Y. Chan, Miss Lainee Chen,

David Cohen, Marshall Coopersmith, Charles Crews, Miss Deborah Doyle, David Freeman, Kaynan

Gokturk, Nick Hornberger, Michael B. Johnson, Gill Keith, Miss Teresa Leung, Alan Levy, Herbert Moore, David Payne, Brian Plankey, Bill Power, Art Pritchard, James Reynolds, Miss Irene

Sun, Alan Teranishi, Larry White, and H. S. Wong.

During the summer of 1967, all quantitative data in the O, O2 and O3 systems were checked

and organized by a computer program carried out by Charles Crews. The preparation of figures

and typing of the manuscript were done by Mrs. Nancy Monroe.

I am grateful to all who have helped in the preparation of this review.

Harold S. Johnston

Berkeley, California

October, 1967

V
Contents

Page Foreword Ill Preface IV Acknowledgment V

1. Complex processes and elementary reactions 1

1.1. Neutral oxygen species 1 1.2. Complex chemical systems 1

a. Shock tube experiments 2

b. Thermal decompositions of ozone in static systems 2

c. Photolysis of ozone 3

d. Electrical discharges 4

e. Surface reactions of oxygen atoms and of ozone 4

f. Production of oxygen atoms by other methods 5

g. Isotopic exchange 5

1.3. Elementary physical reactions 5

1.4. Elementary chemical-physical reactions 5

1.5. Elementary chemical reactions 5

a. Definition 5

b. List of cases considered in this review 6

c. Side reactions 7

1.6. Purpose of this review 8

2. Decomposition of oxygen molecules and recombination of oxygen atoms 8

2.1. Decomposition of molecular oxygen 8

2.2. Recombination of atomic oxygen 9

2.3. Equilibrium constants and rate constants 11

2.4. Recommended values of rate factors 12

3. Decomposition of ozone 21

3.1. Mechanisms 21

a. Other reviews 21

b. Jahn mechanism 21

c. Bimolecular mechanism 22

d. Unimolecular mechanism 22

e. Benson and Axworthy mechanism 23

f. Energy chains 25

g. Photolysis in red light 25

3.2. Observed data 26

a. Relative efficiency of foreign gases 26

b. Rate constants for Reaction 1 26

c. Jahn’s rate constant and the ratio k2 lk3 26

d. Rate constants for Reaction 2 28

e. Rate constants for Reaction 3 28

3.3. Interpretation of observed data 29

a. Equilibrium constants from kinetic data 29

b. Extended values of k\ and k3 31

c. Self-consistent set of elementary rate constants 33

4. Isotopic exchange between oxygen species 42

5. Discussion 44

5.1. Why does Ki = k\jk2 at the low-pressure limit of a unimolecular reaction? 44

a. Mathematical models 45

b. Physical model as derived from rate of exchange 45

6. Summary 46

7. References 47

VI
Gas Phase Reaction Kinetics of Neutral Oxygen Species

Harold S. Johnston

The available data for reactions among neutral oxygen species, oxygen atoms, oxygen molecules

and ozone, have been reviewed. Selected data have been reanalyzed and used to establish values for the rates of these reactions: O) + M —

0 + 0 + M (M = 02 , Ar)

O + O + M —> 0> + M (M = 02) 03 + M —> O + 6, + M (M = 02 , 03 , He, Ar, N,, CO.)

0 + 0. + M-^03 + M (M = 02 , 03 , He, Ar, N,, C02 ) O + 03 —

02 + 02 O + 02 —> O + 02 (isotopic exchange)

Key words: Chemical kinetics, dissociation, isotopic exchange, oxygen atom, oxygen molecule,

ozone, recombination, review.

1. Complex Processes and Elementary Reactions

1.1. Neutral Oxygen Species

Neutral oxygen species are oxygen atoms, O,

oxygen molecules, O2, and ozone, O3. However, each

of these species has relatively long-lived electronic

or vibrational states, which in one sense of the

word constitute separate species. The electronic

states of atomic oxygen include 0(3 P), 0('D), and

OpS). The first few electronic states of molecular

oxygen are 02 ( 3Sy ), 02 pA9), 02 PXg), 02(3Sj), and

02 (3 £i7)- The ground electronic state of ozone is expressed as O3PA). Certain spectroscopic constants of O, O2, and O3 are given in tables 1, 2,

and 3. In this review, reactions will be classified as in

the author’s book. Gas Phase Reaction Rate Theory [59] 1

: Complex chemical systems, elementary

physical reactions, elementary chemical-physical

reactions, and elementary chemical reactions. For

definitions of these cases, the reader is referred to

1 Figures in brackets indicate the literature references at the end of this paper.

the book; examples of each case of importance to

this review are presented below.

1.2. Complex Chemical Systems

A laboratory operation that carries out a chemical

reaction is typically “complex” in that it involves

a number of elementary chemical steps. Certain

experimental methods and chemical reactions in- volving neutral oxygen species are given here.

TABLE 1. Properties of the first few electronic

states of oxygen atoms [19, 55, 57]

Atomic states Energy relative to lowest state AHI

kcal/mole eV kcal/mole

0(3 P) 0 0 59.2

OPD) 45.4 1.967 104.6

OPS) 96.6 4.188 155.8

Table 2. Properties offirst few electronic states of oxygen molecules

Molecular

state Relative

energy (T0 ) Bond

length

Vibrational

frequency

D°0 Dissociation

products .

02 ( 3S-)

kcal/mole

0

A

1.207

cm~x 1580kcal/mole

118.3 3 P + 3 P

o2 (

i a!/ ) 22.5 1.216 1509 95.7 3P + 3P

02 02*) 37.5 1.227 1433 80.6 3 P + 3 P

02 (*X +

U ) 102.1 1.42 819 15.1 3 P + 3 P

02 ( 3X7) 141.1 1.60 700 21.3 'D + 3P

298-126 0- 68—2 1
Table 3. Molecular and thermodynamic properties of ozone [57]

Moments of inertia, gram cm2

Ix = 7.875 X 10-40 Iy = 62.844 X 10-40 h= 70.888 x 10-40

Vibration frequencies, cm 1

o»i = 705

a)9 = 1043

0) 3=1110

Thermodynamic properties

A///998 =34.1 kcal/mole

OaOA) -^02 ( 3S-)+0(3 P)

A

r

^/298 =25. 46 ±.4 kcal/mole 3 A,//o = 24.25 ± .4 kcal/mole 3

3 See discussion of error on p. 29.

a. Shock Tube Experiments [125, 62]

In a shock-tube experiment, a high-pressure gas

is suddenly thrust into a low-pressure gas by breaking a plastic or a metal diaphragm. The low-pres- sure gas is compressed adiabatically and thereby

heated (in a time much less than 1 p, s) from room

temperature to a much higher temperature, determined by pressure ratios between high- and lowpressure regions and by the thermodynamic properties of the gases. Temperature rises of hundreds

or even thousands of degrees centigrade are obtainable this way. The compressed gas has a steady, high-temperature state for a few milli- seconds. The temperature can be calculated from

observed shock-wave velocities. Kinetic processes

are observed by fast recording of some appropriate

property of the system, such as absorption of x rays by dense carrier gases (krypton), absorption

of vacuum ultraviolet radiation by the molecule

O2 , or absorption of ultraviolet by the molecule O3 . Ozone decomposes with a millisecond lifetime

around 700-900 K, and it decomposes in times

much shorter than lp.s to produce excess oxygen

atoms above 1500 K. Oxygen molecules decompose

at a rate convenient for shock tube study between

4000 and 8000 K, although rate measurements

have been carried out as low as 3000 K and as high

as 17,000 K.

At low temperatures, processes involving dif- ferent sized energy jumps tend to occur at widely

different rates; reactions with low-energy barriers

occur much faster than reactions with high-energy

barriers. At high temperatures, energy differences

become relatively unimportant, and many processes occur simultaneously at comparable rates. The

Boltzmann factor, exp( —

A

E/RT), for an energy

difference of one electron volt, or about 23 kcal/

mole, is 10-17 at room temperature but only 0.1

at 5000 K. Considerations such as products with

high density of states, or high multiplicity, or high

entropy become as important as energy differences

at high temperatures.

In shock-tube experiments, the short observation times and the limited number of monochromatic photons that can be put through narrow slits lead to an irreducible error from “shot noise” in

the measuring light beam. Under a typical set of

conditions, this error turns out to be about 1 percent in measurement of concentration and about

10 percent in measurement of rate (calculated from

1012 photons per second at 10 A band pass, 10~

6

second observation limit, 10 percent absorption

of light by the chemical of interest, and square

root of 9 X 105 is 1 percent). There are other random

errors associated with shock tubes, such as irregularities in membrane rupture and errors associated

with velocity measurements. There are possible

systematic errors associated with shock tubes,

such as boundary layer cooling with adiabatic

expansion of shocked gas into a cooled boundary

layer and nonideality of shocked gas especially

for nonmonatomic gases. Errors in the interpretation of data arise when one thinks one is measuring the rate of a given chemical reaction but another

process of about the same rate is interfering. For

example, the vibration-translational relaxation

time of O2 becomes the same order of magnitude

as the dissociation lifetime at about 8000 to 10,000

K. When all errors are considered in shock-tube

work, rate constants have somewhat greater scat- ter (factor of two to four in a single measured rate constant) than gas-kinetic data obtained by conventional, “slow” methods. Thus comparable pre- cision is to be expected between fast shock experiments and ordinary slow experiments only if the

shock-tube points are 4 to 16 times as numerous. Whereas shock tube experiments are subject to systematic errors (as mentioned above), conventional gas kinetics is also susceptible to systematic

errors, such as competing surface reactions and

thermal gradients in the reacting gas. Provided

the investigator with the shock tube takes a large

number of data points, the shock tube can be

equally as valid as any other method in producing

quantitative kinetic data.

b. Thermal Decomposition of Ozone in Static

Systems

The overall reaction (2 Oa = 3 O2 ) produces a pressure increase as it occurs. The extent of re- action can be found from the initial pressure and

composition and from the pressure at any time.

2
Alternatively the extent of reaction can be cal- culated from pressure at any time and final pres- sure when all the ozone has decomposed. Ozone

attacks mercury manometers, and its decomposition is catalyzed by most metals, so the problem of pressure measurement requires care in selection of method. Sulfuric acid manometers

have been widely used for this purpose. Most

measurements of the decomposition of ozone at temperatures between 300 and 500 K have been

carried out in this way, although pressure measure- ments have been supplemented or replaced by

other physical or chemical methods in some cases. Data developed by this technique are reviewed

in some detail in section 3 and will not be discussed

in detail here.

Hydroxyl radicals catalyze the decomposition of ozone in a chain reaction: 2

HO + 03 HO, + OaHO2 + O2

HO + 2 02 Chain (1-7)

net 2 O3 -» 3 O2.

When ozone is photolyzed by ultraviolet radiation

in the presence of water vapor, quantum yields

greater than 100 are readily observed. Dry ozone

photolyzed at 2537 A has been observed by Norrish and Wayne [91] to give quantum yields up

to 16, and this high quantum yield is explained in terms of a “thermal chain” carried by excited vi- brational states of the product oxygen molecule:

c. Photolysis of Ozone

Ozone weakly absorbs red light [26] around

6000 A to give the forbidden transition,

03 + hv (6000 A) -> 02 (

3

^) + 0(3 P). (1-1)

The upper limit to the observed quantum yield in

wet or dry ozone is two:

O('D) + O3 * 02 + Of (high v) Of(y> 17)+03 -> 2 O2 + OOD)

net 2 O3 —> 3 02 .

Chain (1-8)

At 2537 A the primary decomposition of ozone produces O2 in excited electronic state or states or 'Ag), which also decomposes ozone [5, 70,

82, 85, 91]:

k3 0(3P)+ 03 > 2 Os. (1-2)

O2OX+ or ^T-Oa -^2 O2 + O. (1-9)

Quantum yields less than two are explained by

competition from the back reaction,

With added inert gases, N2 or CO2, the quantum

yield is reduced.

A'2 0(3 P) + 02 + M » 03 + M. (1-3)

Studies of this system give quantitative values of

the rate constant ratio, A2/A3, and the mechanism

will be analyzed in detail in the chapter on ozone. Ozone strongly absorbs ultraviolet radiation to produce singlet oxygen molecules and singlet oxygen atoms [91, 15, 52]

O3 + hv (A 3130 A) -» 02 (

1 Ag) + OPD),

(1-4)

03 + hv (A 2680 A) -> O2PX+ or >Ay) + O(’D). (1-5)

03 + hv-+ O2PX+ or l Ag) +OQD) (1-10)

OPD) +N2 ^0(3 P) + N2 . (1-11)

With added oxygen molecules the quantum yield

of dry ozone decomposition approaches zero, be- cause of the great speed of the reaction:

OPD) + 02 + M —> 03 + M. (1-12)

This complicated mechanism of the photolysis

of ozone by ultraviolet light is fairly well understood on a qualitative basis, but there are relatively few data that give quantitative estimates

of rate constants.

Although ground-state triplet oxygen atoms do not

react with water vapor, singlet oxygen atoms rapidly

react with water vapor [92], to produce hydroxyl

radicals, which have been directly observed by

the method of flash spectroscopy

0(1 D) + H2 0 —» 2HO. (1-6)

2 The reaction (a), HO + 0;t —* HO2 + O2 , is known not to be very fast, and the reaction

(b), HO2 + O3—HO+ 2 O2, is expected to be even slower [64]. At high radical concentration, such as that produced by flash photolysis or microwave discharge, the

fast [64] radical-radical termination reaction (c), HO + H02 H,0 + 0», would quench

this chain reaction. However, in photochemical reactions at moderate light intensity, such as direct sunlight or steady arc lamps, a long chain reaction is possible. The

chain length is given by A a [03 ]/Av[H02] . The value of kc is about 10“ n cm 3/particle-s. At 30 mm of 0;> and light absorption rate of 10 13 photons/cm3

-s, the steady-state con- centration of HO2 is about 10 12 per cm3

. The chain length, under these conditions, exceeds unity as k„ exceeds 10 -17 cm3 /particle-s. The existence of long chains in ozone

photolysis implies a rate constant of about 10~ ,e or larger for A„.

3
d. Electrical Discharges

In typical, recent, quantitative studies, oxygen

flows rapidly through an electrical discharge (usually a microwave cavity) and through long observation tubes. In some cases other substances are added to oxygen before the electrical discharge,

and in some cases other gases are mixed with the

flowing gas stream after it passed through the discharge. Oxygen atom concentration as a function

of position in the steady-flow tube gives oxygen

atom concentration as a function of time. The

oxygen atom concentration can be measured by a number of physical and chemical methods [67, 72].

In the limit of absolutely pure oxygen, few or no oxygen atoms are produced in an electric discharge, but 10 to 20 percent of excited OA'A^)

molecules are formed. Addition of traces of N2 , N2 0, NO, H2 , or H2 0 markedly catalyze the for- mation of oxygen atoms. The measured catalytic

efficiency of trace gases is as follows:

Added

gas

O Atoms produced per molecule of

added gas

Ref. [21] Ref. [68]

n2 80-100 80-90

n2 o 80-90

NO 40-45

h2 150-195 160-120

h2 o 90-130

He s=0.2

Ar 0.2

C02 =s0.2

(1-13)

Kaufman [68a] believes the effect must be due

to large changes in surface recombination efficiency

within the active discharge region.

On the other hand, when argon is a carrier gas

in great excess over oxygen, there is a fairly clean

production of oxygen atoms, presumably by col- lision of 02 with electronically excited Ar.

In a number of cases 02 (

1 A,/ ) and 02 (‘Sy) react

with notably different rates than does 02 ( 3£“).

The unsuspected presence of large concentrations

of metastable 02 species and also the effects of

impurities in these systems caused systematic

errors in the observed rate constants for a number

of studies. All studies of oxygen atoms produced

from electrical discharges in oxygen should be

examined very critically. Since the bond dissociation energy of ozone is approximately equal

to the electronic excitation energy of 02 ('A(y ) and

O^’Xj), the study of ozone kinetics is particularly

sensitive to the presence of electronically excited

oxygen molecules. Virtually all studies of ozone

kinetics in electrical discharges before 1964 are not suitable for quantitative values of rate constants.

e. Surface Reactions of Oxygen Atoms and

of Ozone

The overall recombination of oxygen atoms on

a surface,

0 + 0 + W —

>

02 + W, ( 1 —14)

occurs by way of two successive collisions, with one atom being more or less loosely held by the surface

until the other arrives. The subject was reviewed

in detail by Kaufman [67]. Results are expressed

in terms of the coefficient, y, the fraction of col- lisions of oxygen atoms with the surface that leads

to recombination. Results are not very reproducible.

A given investigator may find variations of up to a factor of five for a given surface, and different

investigators may differ by a factor of 102 or more. A sample of the internally consistent room-temperature results of Linnett [76] and co-workers is as follows:

Surface y

Ag 0.24.

other metals 0.003 to 0.17.

halides around 10~3

. Pyrex (3. 1-4.5) X lO"5

. silica (0.7-1. 6) X 10-4

. other oxides 10-4 to 10-2

.

(1-15)

On glass or silica the recombination coefficient, y, increases slowly with an increase in temperature.

The thermal decomposition of ozone (2 0:} = 3 02 ) is extremely sensitive to surface catalysts. Perman and Greaves [96] studied the effect of various

solid substances placed at the bottom of a 350 ml

flask, and Axworthy [3] reinterpreted the data in terms of actual rate relative to homogeneous rate of decomposition of ozone. Results are as follows:

T°C Solid surface Rate/homogeneous

rate

100 clay pipe 2.6 to 244.

100 CuO powder 6.5 to 110.

100 Platinum black 5.0 to 6.6. 100 Platinum foil 1.0. 100 Nickel foil 1.1 to 1.3. 60 Pb02 powder 21 to 25.

40 CuO powder 4.2 X 103 to 9.5 X 104

. 40 MgO powder 2.5 X 105 to 4.3 X 10b

. 40 Mn02 9.7 X 104 to 4.8 X IOC

15 Mn02 2.9 X 106 to 2.2 X 10H

.

(1-16)

4
f. Production of Oxygen Atoms by Other

Methods

Absorption and emission of radiation often represent elementary physical reactions:

Photolysis (17) of NO2 between 3000 and 4000 A

gives NO plus 0(3 P). The mercury sensitized photolysis of N2 0 also gives 3 P oxygen atoms and the

relatively unreactive N2 . Photolysis [84] of C02 in

the vacuum ultraviolet gives 0(X D) and CO. Photolysis of 02 in the vacuum ultraviolet gives

0( x D) + 0(3 P).

A special method of preparing oxygen atoms in

large yields in a flow reactor and in an environment

free of molecular oxygen is to dissociate N2 to atoms

in an electric discharge and then titrate the nitrogen atoms with nitric oxide [90]:

N + NO^N2 + 0. d-17)

The thermal decomposition of ozone in a shock

tube is an excellent method of producing a large excess of ground state oxygen atoms [125, 71].

The thermal decomposition of ozone at low pres- sure in a fast-flow system is a clean source of 0(3P),

whose reactions have been studied by fast mixing

with other gases [70].

g. Isotopic Exchange

02 ( 3lg)+hv -» 02 (

x A9), (1-22)

03 (yi, v2 , vz) + hv —> 03 (i>i, v2 , v'z). (1-23)

1.4. Elementary Chemical-Physical

Reactions

In any chemical reaction the set of atoms that

constitute the products are arranged in a different

structure from the same set of atoms that were the

reactants; the change in structure as opposed to a mere change in quantum number inside a given

structure is the essence of a chemical process.

The ideal elementary chemical-physical reaction

is a chemical reaction that occurs as a result of a single collision in which the quantum state (translational, rotational, vibrational, and electronic) of

every reactant and product is known, for example,

0(3 P)+ 03 (

1 A, Vi, V2, Vz, J, Ka , Kb)

relative velocity 1 02 (3Ss , V, J) + 02 (

1 A9 , V, J)

(1-24)

The isotopic composition (masses 16 and 18,

usually) of 02 and 03 can be determined by highresolution mass spectrometers; and the rate of

isotopic exchange between 02 + 02 , 02 + 03 , and

03 + 03 has been studied, although these reactions

are slow except under special circumstances.

1.3. Elementary Physical Reactions

An elementary physical reaction is a process

that changes the quantum state, but not the structure, of a molecule. Important examples in this

review are translational-vibrational energy transfer:

02 (i/) + M

, (1-18)

relative velocity 2

03 (t>[ , v'2 , *4') + m

. (1-19)

relative velocity 2

Also translational-electronic energy transfer is important in these systems:

02 (u) + M

relative velocity 1

03(^ 1 , V2, lfr)+M_

relative velocity 1

relative velocity 2

Although every reactive collision is an elementary

chemical-physical reaction, so far, no laboratory

experiment has been so well controlled that all states of all reactants and products were known

when a rate was measured. (In principle, a velocityselected crossed molecular beam with field-selected

internal states of reactants and products could be

used to observe and measure the reaction cross

section for an ideal elementary chemical physical

reaction.) In the absence of methods of observing

ideal chemical-physical processes, the definition

of an elementary chemical-physical reaction is extended to include a chemical reaction that occurs

in one collision where the change of quantum state of at least one sort of energy is known:

O3 + hv (3000 A) 02 (‘Aff) + 0( X D)

O + O + M —* 02 (v = 19) + M (1—25)

0(1 D) + 03(

1 A)-> OzOA^ + OaOS^).

1.5. Elementary Chemical Reactions

02 (

1 As) + M

relative velocity 1

Q2 (%-+M

•> relative velocity 2

( 1 -20)

0( x D) + M

relative velocity 1

0(3 P) + M

relative velocity 2

( 1 -21 )

a. Definition

A system undergoing no net chemical reaction

and at thermal equilibrium with its surroundings

will have a uniform temperature, and the molecules

in the system will be distributed over translational

and internal quantum states according to the Boltzmann distribution function. The molecules have an

5
equilibrium distribution over states. A system

undergoing a chemical reaction may have a uniform translational temperature in equilibrium with

surroundings, but the internal states of the molecule,

especially electronic or vibrational, may be far

from the equilibrium distribution characterized

by the translational temperature. The unimolecular

decomposition of a polyatomic molecule is a wellunderstood example of this effect:

O-i O3 + M —» 05 + M,

b,

(1-26)

03* + M - > O3 + M,

Ci

d-27)

03*- > 02 + 0, (1-28)

where the asterisk indicates vibrational energy in ozone greater than the critical energy for its dissociation. The steady-state concentration of vi- brationally excited ozone in a particular energy

level, i, is

[Q:f],_ q f [M]

[03 ] 6,-[M]+c,

(1-29)

At sufficiently high pressure, deactivation b occurs

very fast compared to decomposition c so that the

actual distribution function approaches the equilibrium value, even though reaction is occurring:

T7pf sTr =iPi) ^ (1_30)

ITJ3 J bi

At low pressures, the unimolecular reaction, a, is so fast that deactivation, 6; , essentially never

occurs; every molecule that reaches the critical

level of energy eventually decomposes; the steadystate distribution function takes the limiting form:

[Of]*

[O3]

oi[Ml = (pt )°

s Ci (1-31)

The equilibrium distribution function (P,)eqis determined by one macroscopic variable, the temperature T. The steady-state distribution function

(Pi)ss is determined by two macroscopic variables,

temperature T and total effective gas concentration [M] . The two-parameter steady-state distri- bution function is as reproducible and well defined

as the more familiar one-parameter equilibrium distribution function.

The definition of an elementary chemical reaction

is the total effect of an elementary chemical-physical

reaction where the reactants are distributed ac- cording to a steady distribution function, fixed

by a small number of macroscopic variables (no

restriction is made on the distribution of reaction

products).

b. List of Cases Considered in this Review

The elementary chemical reactions of importance

in this review are listed here for convenience of

reference:

D. O2 + M —* O + O +

M

R. O + O + M —* O2 + M

1 . O3 + M —* O2 + O + M

2. O + O2 + M -» 03 + M (1-32)

3. O + 03 -> 2 02

4. 2 O2 * O + O3

5. O + 02 —* 02 + O (exchange)

Rate constants are written with “lower case” k and

subscripts: AD , AR , ku A2 , A3, k4 , and k5 . Equilibrium

constants are written with “upper case” A and

subscripts: Kp , Ai, A3 (A« = A51

, A2 = Ay1

. A4 —A3 1 ). The rate constant of an elementary reaction is constant throughout the course of reaction at one

temperature, but it usually varies with temperature.

In tables and figures we report observed rate constants and temperatures; and it is desirable to express these empirical data in an appropriate

functional form. Most theories of elementary reaction rates indicate that the rate constant varies with

temperature as k oc f(T) exp ( — E/RT), where

f{T) depends weakly on temperature and exp

(—E/RT) is a strong function of temperature.

Under limiting conditions, especially at high temperature, the weak f(T) usually takes the form of Tm . Thus, the manner with which gas phase reactionrate theory predicts the rate constant to vary with

temperature may be expressed in an approximate

general form as BTm exp ( — E/RT). In the theoretical models, the parameter A usually has the physical

interpretation of an energy barrier, and the parameters B and m have physical interpretations.

Chemical kinetic data usually possess so much

experimental error and scatter that they are totally

unable to support the three-parameter relation. A

least-squares fit of the three-parameter relation to scattered experimental data usually gives physically

ridiculous values to the parameters B, m, and A: and

values of the parameters are quite unstable with

respect to addition or removal of small blocks of

data. Thus, experimental data are usually interpreted in terms of a two-parameter equation:

(1) m is set to zero (Arrhenius equation), (2) A is set to zero, (3) m is assigned some theoretical value

with B and A fitted to the data, (4) or A is assigned its theoretical value with B and m fitted to the data. As

a part of this review, all rate constants were fitted

by each of the following relations by the method

of least squares:

k = A exp( — E/RT), (1-33)

k = BTm exp( —E'/RT)

,

(1-34)

II a (1-35)

6
and in some cases either m or E' of eq (1-34) was

assigned a theoretical value. The form of the final

recommended equation differs for the various

elementary reactions.

The activation energy is a measure of how the

rate constants change with temperature:

(4) Hydrogenous material giving H, HO, HO2 free

radicals (readily produced from some organic

materials):

0 + 0H^02 + H

H + 02 + M H02 + M

O + H02 -> HO + 02

chain 0-43)

ea =-r d In k

d(l/T)

(1-36) net O + O —» 02 .

The activation energy for each of the equations for

k given above is Ea = E,

Ea = E

'

+ mRT,

Ea = nR T.

Decomposition of ozone 2 03 = 3 02 (1) Heterogeneous decomposition of ozone (see

section 1.2e above).

(2) Oxides of nitrogen produced from N2 as im-

(1-44)

(1-37) purity in ozonizer:

(1-38)

N2 O5 ?± no2 +no31 NO2 + o3 —* no3 + 02 chain

2N03 - 2no2 + 02

(1-39)

net 2 O3 = 3 02 . For the Arrhenius equation, the activation energy

does not change with temperature; for the other two

relations the activation energy is temperature

dependent.

(3)

Hydrogenous material giving H, HO, or H02 free radicals (readily produced from some

organic materials):

c. Side Reactions

Either the forward or the reverse reaction of each

elementary reaction above can be imitated by complex, side reactions; and these reactions have been

a major source of error in many would-be quantitative studies. Examples of complex mechanisms

that imitate other chemical reactions are:

Reaction R 0 + 0 + M-^02 + M

(1)

Heterogeneous reactions on surfaces W:

O + W^O . . . W

o . . . w+o-»o2 + w

net O + O —» 02 . (1-40)

(2)

Homogeneous catalysis by oxides of nitrogen:

O + NO + M —> N02 + M"

O + NO2 -» NO + O2

chain (1-41)

net O + O + M—» 02 + M.

(3)

The ozone mechanism:

O + 02 + M -> 0;! + M

O + 03 -> 2 02

chain (1-42)

H + O2 + M

HO + 03 HO2 + MHO2 + O2 H02 + 03 -> HO + 2 O2

chain (1-45)

net 2 03 = 3 02 .

(4)

Excited states of 02 and O:

+ 03 * 2 O2 + O

O2OA0) + 03 —

>

2 O2 + O . ^ O* (vibrations) + 03 —> 2 O2 + O

Of'Di + HiO —» 2HO (followed by 1-45).

Reaction 2 0 + 02 + M-^03 + M

(1) All side reactions that imitate reaction R and

reaction R itself act to speed the removal of

oxygen atoms. If the progress of reaction is followed in terms of disappearance of oxygen

atoms, the observed rate is faster than that

of reaction 2.

(2) All side reactions that destroy ozone (heterogeneous and homogeneous) make reaction

2 appear too slow if the reaction is followed

in terms of formation of ozone.

(3) Homogeneous decomposition of ozone by ex- cited states of 02 (see above) both destroys

03 and regenerates O. Thus reaction 2 appears to go too slowly.

(4) Hydrogen-containing free radicals regenerate O atoms to make reaction 2 appear too slow:

net O + O + M —

>

02 T M. 2HO —> H2 0 + O. (1-47)

7
Reaction 3 O + O3 —» 2 O2

(1) Hydrogen-containing free radicals:

O + HO 02 + H

H + 03 -> HO + 02

net O + O3 —* 2 02 .

chain (1-48)

(2) Oxides of nitrogen (N2O5 in presence of ozone):

O + n2 o5 NO, + O3

no2 +no3 ->

02 + 2NO,

NO3 + O2

N2O5

• chain (1-49)

net O + O3 = 2 O2.

(3) Excited electronic states of O:

0(1 D) + 03 —* 2 02 . (1-50)

(4) All other processes listed above that remove

O or decompose ozone would introduce error

into a measured value of k3 . Almost all side

reactions have the net effect of increasing the

apparent rate of reaction 3.

1.6. Purpose of This Review

In section 1.2 above, we briefly discussed many

different experimental systems where rates were measured involving some combination of O, 02 , and 03 . In all cases oxygen atoms are involved

as reactants, products, or intermediates. In section 1.5 above we listed seven elementary chemical

reactions of interest plus a substantial number of

side reactions involving surfaces, hydrogen-containing free radicals, oxides of nitrogen and excited

electronic species of O and 02 . Each elementary

reaction involves oxygen atoms as either reactant

or product. In principle every laboratory reaction

involves all seven elementary reactions. Formally,

the problem may be expressed in terms of a matrix

of laboratory reactions and elementary reactions

(see table below).

Experimental measurements give laboratory

reactions as an unknown function of seven elementary reactions plus X elementary side reactions.

What we desire may be formally expressed as the

Laboratory

reactions

Elementary reactions X side

reac- D R 1 2 3 4 5

tions

1 . O,, shock tube ID 1R 11 12 13 14 15 IX

2 . O3 , shock tube 2D 2R 21 22 23 24 25 2X

3. O2 , photolysis 3D 3R 31 32 33 34 35 3X

4. O3, photolysis 4D 4R 41 42 43 44 45 4X

5. 03 , heated 5D 5R 51 52 53 54 55 5X

6. 02 , electrical discharge 6D 6R 61 62 63 64 65 6X

7. Photolysis of NO2 , N2 0. etc. 7D 7R 71 72 73 74 75 7X

8. Electrical discharge

in N2 , etc. 8D 8R 81 82 83 84 85 8X

Y. Other studies YD YR Y1 Y2 Y3 Y4 Y5 YX

inversion of these relations or the inversion of the

matrix indicated above. We want to eliminate the

effect of side reactions (either physically or by

subtraction of their known effect), and evaluate

the rate constants of the seven elementary reactions

from observations of laboratory systems. By control of concentrations, temperature, light intensity,

etc., we can set large numbers of entries in the

matrix to zero. By combining two or more laboratory

studies, we can sometimes evaluate two or more

elementary reactions, formally analogous to reduction of a matrix to its irreducible blocks.

The object of this report is to go to the original

literature and, insofar as possible, to reinterpret

the published data of quantitative studies that contribute to the separation and evaluation of the seven elementary rate constants. The results of different

investigators are combined. Isolated quantitative

studies that do not lead to evaluation of the ele- mentary rate constants are not utilized. Older

studies (pre-1933) of ozone decomposition and early

(pre-1964) studies involving electrical discharges

in oxygen contain much larger experimental error (section 1.5c above) than recent studies, and usually

these are omitted. Thus the object of this review is not to produce an exhaustive bibliography, nor to prepare exhaustive tables of observed data, but

rather it is to get the best estimate of the seven elementary rate constants and to tabulate the quantitative experimental data used to get these best

estimates.

2. Decomposition of Oxygen Molecules and Recombination of

Oxygen Atoms

2.1. Decomposition of Molecular

Oxygen

The equilibrium constants for the reaction

02 = 0 + 0 ( 2- 1 ) Kd = [0] 2 /[02 ], particles/cm3

has been taken from the JANAF tables [57], and are given between 100 and 6000 K in table 4. 3 Above

3000 K oxygen is significantly dissociated to atoms,

and the rate of the thermal decomposition of oxygen,

3 Table 4 and all subsequent numbered tables, as well as all figures, will be found

at the end of the section in which they are first mentioned.

8
02 + M^ 0 + 0 + M (2-2)

d[02 ]_ , [02] [M], particles/cm3 -s, ~~dr~ k"

has been studied in shock tubes between 3000 and

17,000 K. Several investigators used argon as the

shock-tube “fluid”, with approximately 1 percent

oxygen. Under these conditions the shock tube

performs relatively closely to ideal theory, and the

temperature of the gas can be accurately calculated from measured shock wave velocities. Other

investigators used pure oxygen as the shocked gas,

and in these cases there is ambiguity about the

temperature-time relationship as translational

energy is taken up by molecular vibrations, and the

shock waves are more likely to give nonideal

behavior. Limited studies have been made with

krypton or xenon as foreign gas, M. This review

gives especial emphasis to the extensive series

of runs made with argon and with oxygen.

In the evaluation of rate constants from observed

rates, it is usually necessary to consider the re- verse reaction as well as the forward reaction:

kn

O + O + M * 02 + M

-^i=i»[°2] [M]-A:fi [0] 2[M] = MO.][M] - (UK,,) [0] 2 [M]. (2-3)

Some investigators published tables of rate constants k[) at each observed temperature, and these

data are reproduced in tables 8 and 9. Other authors

published only graphs showing data points in an

Arrhenius plot of log ko versus T~ l

. In these cases we have read the points from the graphs and en- tered the data in tables 5, 6 , and 7. In other cases

the authors did not present the data as either

tables or graphs, but rather they gave only the

Arrhenius equation and temperature range. Such

data are essentially lost, but table 10 summarizes

the little information that is available from three

such studies. We feel that authors should insist

(to editors of journals) that both tables of data and

graphs should be published for the rate constants

of elementary chemical reactions.

For the decomposition of oxygen with excess

argon as carrier gas, there are four sets of quantitative data, presented as tables 5, 6, 7, and 8, and all of the points of the four investigations are

also given in figure 1 A. The agreement between

different studies and the scatter of points in each

study is readily seen in figure 1. The data from each

investigation were treated by the method of least

squares for the two-parameter Arrhenius equation,

(1-33), and by the three-parameter equation,

(1-34). The parameters, E, m, and E' , so obtained,

are given for each of the four studies as the first four lines of table 11. The scatter of the points is so great that the data cannot support a threeparameter, least-squares fit; the values of m and

E' are in violent disagreement from one author

to another and are physically absurd. The scatter

of points is such that even the two parameters of

the Arrhenius equation are given only with a large

standard deviation, and reference [108] seems to have some systematic, temperature-dependent error. The data of all four studies were combined, and

the least-squares parameters, E, m, and E' , are given as the fifth entry in table 11. The last four

entries in table 11 were obtained by use of all data

except that for a given study. These last five entries show that even all the data taken together

are not enough to establish a three-parameter relation, but the two parameters of the Arrhenius equation are fairly well established. The activation

energy is about 105 kcal/mole, whereas the dissociation energy of oxygen is 118 kcal/mole. This computed activation energy is about the same whether

all four sets of data are used or any three sets are employed. The curve shown in figure 1 was obtained

in a way to be described later. The data observed for the dissociation of pure

oxygen are given in tables 9 and 10 and plotted

in figure IB. The line labeled Ay in figure IB is the reverse of the reaction obtained in the decomposition of ozone:

A-3 0:i +0-^02 + 02 , (2-4)

A-4 02 + 02 —* 0.3 + o

,

Kz = Ay/Ay and Ay = k:i jKs.

From the observed value of A 3 (section 3) and the

value of K3 calculated from JANAF tables, the

value of Ay was found (table 26). It is clear from

figure IB that the decomposition of oxygen at high

temperatures does not go by way of the ozone mechanism: Ay, Ay.

2.2. Recombination of Atomic

Oxygen

The recombination of oxygen atoms has been

studied in a variety of different ways. At room temperature a nonequilibrium excess of oxygen atoms

has been formed by electrical discharges in oxygen,

by reaction of nitrogen atoms with nitric oxide

(N + NO —» N2 + O), by ultraviolet photolysis of

oxygen, and by other photochemical methods. At

temperatures above 1000 K, large concentrations

of oxygen atoms have been formed by the thermal

decomposition of ozone (O3 + M —* 02 + O + M) in a shock tube. Also shock tubes have been used to dissociate 02 at high temperatures, and then the

shocked gas was cooled by expansion, and atom

recombination was observed at a lower temperature.

The data are given in table 12.

298-126 0-68—3 9
T 0 0 0 0 O rO 0 0 0 0 O ro 0 0 o_ o_ rO 0“ o’ 00" m" fO

CM

Figure 1 . Observed second-order

rate constants k D (cm3

/particle-s)

for the thermal dissociation of

oxygen.

O2 + M —* O + O + M

(A) M is Ar

OWray [125] Schexnayder and Evans [108] ACamac and Vaughn [23] Anderson [1] Curve is calculated from

log &«== — 5.37 — log T- 25.95 (1000/7’).

(B) M is O2 Schexnayder and Evans [108] Curve M: Function A'd as reported by

Matthews [88] Curve R.K.D.: Function An as reported

by Rink, Knight, and Duff [103]. Curve A4 : Rate constant for the reaction 02 + 02 * 03 + O as deduced from

ozone kinetics (Table 28).

A considerable complication in the study of the

recombination of oxygen atoms is the large number

of alternate paths to reaction R, which give the

same overall reaction (see section 1, 1.5c).

When oxygen atoms are produced by electrical or photochemical dissociation of 02 , there is

always a large excess of 02 ; and at low temperatures

the ozone mechanism predominates. Except for

reference [90], where O was produced from the

titration of N and NO. all room temperature studies

require corrections both for surface reactions and

for the ozone mechanism. Such corrections have

10
been made (by the original authors except where

noted otherwise) for the room-temperature rate constants entered in table 12. The observed rate constants for recombination

of oxygen atoms are listed in table 12 and plotted

in figure 2. Certain parameters of the Arrhenius

equation from the data are given in table 13, and

also the data are treated by means of the twoparameter equation (1-35). The scatter in the data

is so great that neither E nor n can be reliably

obtained, although a value of about — 1 is indicated

for n from the argon data.

As an energy-transfer agent, O2 is much more

effective than argon, although various authors

give widely different estimates of the relative

efficiency (Camac and Vaughn 3; Schexnayder

and Evans 9; and Wray 18). The relative effi- ciencies of various foreign gases for the dissociation

and recombination of oxygen are given in table 14. The relative efficiency of O atoms to O2 molecules

is obtained by the authors’ detailed interpretation

of their data during the course of individual runs. The various authors are in considerable disagreement with each other concerning relative efficiency

of M gases. However, there is a concensus that

O2 is about an order of magnitude more efficient

than Ar, and O is about three times as efficient as O2 .

2.3. Equilibrium Constants and Rate

Constants

It should be emphasized that tables 4 to 14 contain observed kinetics data. No use has been made

of the relation between rate constants and equilibrium constants, which is valid at chemical

equilibrium,

Kt)=ki)/k/{ , (2—5)

although the individual authors made minor use

of this relation in correcting their observed dissociation rate for back reaction. At the short times and

fast rates observed in a shock tube, several authors

have questioned whether the above relation is applicable. In Gas Phase Reaction Rate Theory,

we showed that a sufficient criterion for a rate constant having its equilibrium value is that

reactants have an equilibrium distribution over

states. The reactants for the recombination reaction

are atoms, and the only important energy states are translational; translational energy states are equilibrated within a few collisions. The reactants

for the dissociation are oxygen molecules, with

translational, rotational, vibrational, and low-lying

electronic energy levels. Vibrational relaxation

FIGURE 2. Observed third-drder rate constants kR {cm?Iparticle2 -s) for recombination

of oxygen atoms.

20 + M -> 02 + M. •M = Ar

M = 02 with corrections at room temperature for surface recombination of atoms and for contribution of ozone-mechanism (O + 02 + M —

O3 + M, O3 + O * 202).

11
times have been measured and are about the same

magnitude as dissociation times [125] above 8000 K,

and thus, it is fairly certain that the reactant O2 does not have an equilibrium distribution over

vibrational states. With kR having its equilibrium

value (that is, the elementary physical and chemicalphysical rate functions are averaged over an equilibrium distribution of states of O and of M) and

with kp being an average over the nonequilibrium

distribution function, the relation K= ko!

k

R is not

expected to be literally true. But the question

remains whether the departure of ko from its equilibrium value is a small effect (1 percent or less) or a large effect (a factor of 10 or more).

As a test of the magnitude of this effect, kp is calculated from kR Kp. All the points where M

is O2 are plotted on figure 3, along with a bar showing the range of observed kp. The high temperature

kR point by Wilson [123] (where a shock wave was

cooled by expansion), and the high temperature

points of Kiefer and Lutz [71] (where ozone was

decomposed in a shock wave) join smoothly on the

extenuation of the observed rate constants for

decomposition. The low temperature rate constants for recombination give values of kp = kR Kp

that lie on the same curve as the observed function

kp. For the runs with argon and with oxygen, the

other test of K=kD/kR is given by figure 4, where

kf

{

is calculated from kp/Kp and plotted on the same

graph with observed values of kR . The scatter of

the observed kp in figure 3 is plus or minus a factor

of two, and the scatter in values of kR is even larger,

about a factor of 5. Figures 3 and 4 show that the

relation Kp — kp/kR is obeyed within this (rather

large) range of experimental scatter. Thus it is

concluded that the effect of nonequilibrium distribution of O2 during reaction is smaller than

experimental error, and full use of the relation

Kp=kp/kR should be made in the interpretation

of data.

2.4. Recommended Values of Rate

Factors

The observed activation energy from 3000 to 17,000 K is between 100 and 110 kcal/mole, table 11,

whereas the dissociation energy is 118 kcal/mole.

Although the Arrhenius equation k = A exp (-E/RT)

is widely used in kinetics, theories of kinetics

indicate that A is a weak function of temperature.

Especially at high temperatures, simple theories

of reaction rates indicate that the rate constant

should have the form of eq (1-34), k = BTm exp

(— E'/RT). However, we have already shown that

the data contain so much scatter that they cannot

support a least-squares fit to a three-parameter

relation. The procedure followed is that all data were examined together and judgment was used to pick the parameter m, and then the method of

least squares was applied to all the data to fix B

and E'. The arguments and methods used are discussed below.

The activation energy is a measure of how the

rate constants change with temperature, eq (1-36).

Any relation of activation energy to barrier height

or other model follows from some theory, not from

the definition of activation energy. If the rate constant has the form (1-34), the activation energy

is E = E' + mRT [eq. (1-38)]. If E' represents some

T°K 000 000

if) m oj

O

oo

O

o

id o

o

FIGURE 3. Comparison of

function fitted to observed

dissociation rate constant,

kD , to that calculated from

kp — kRKD where M is O2 . Range of kD observed given

by figure 1.

W. Wilson [123] K.L. Kiefer and Lutz [71] G.M. Golden and Myerson [48] K.K. Kaufman and Kelso [69] Solid curve is calculated from log kD = - 4.34 - log T- 25.95 ( 1000IT). Dashed curve is kj from ozone

kinetics (CL + CL —> O3 + O).

12
T

o O O o O O o

o O O o O O o

ro CD (D CD o o

CM to o'— o'

CM

Figure 4. Comparison of observed third-order rate constants kR with values

calculated from kR =kD/KD. ®M=Ar, kft observed

OM = Ar, A r = kol

K

d AM= 02 , kR observed

AM. = O 2, kn = ko/Kp

Line segment R.K.D. is range of data covered by Rink, Knight, and Duff [103]. Data by Schexnayder

and Evans are not included. Curves are given by:

log A«(0>) = — 29.42 -log T- 0.0745 (1000)/r

log kR (Ar) = - 30.45 -log T- 0.0745 (1000)/7’

barrier height, the observed activation energy

will he greater than the barrier height if m is positive or less than the barrier height if m is negative. In

13

this case the observed activation energy is less

than the bond dissociation energy, so m must be

negative. The observed activation energy as a
function of temperature varies with m as follows

(keal/mole):

The mid-range of observation is about 5,000 to 10,000 K; the observed activation energy (“all data,”

in table 11) is 105 ±3 kcal/mole.4 Thus m seems to be closer to —1 than to —0.5 or to —1.5.

Where argon is the catalyst, all data for observed

Ad and for Ad = A«/Ad were combined and fitted to the three-parameter equation by least squares.

The result was

log b = — 5.06

m = — 1.085 (2-7)

E' = 118.06 kcal/mole.

Note that the indicated value of m is about minus

one.Inspection of figure 4 shows that the best slope

through the points, plotted as log A versus log T, is slightly less than one in magnitude, about —0.9.

With three lines of argument leading to a value

of about minus one for the parameter m, it was

decided to take minus one as its value, and the

other terms B and E' are found from least squares

and the data. The resulting recommended rate- constant functions for Ad are given in table 15. This function gives the curve plotted in figure 1. The equilibrium constant Kn is given in table 4

and it is almost equally well approximated by the

two parameter equation,

log Kd = 25.0799 - 25.8745 (1000/7”) , (2-8)

as by the three-parameter equation,

4 The estimated error is twice the standard deviation.

log = 25.4254 -25.8959 (1000/T)

-0.0977 log T. (2-9)

The recombination rate constant is calculated from

the function for Ad (table 15),

log A0(Ar) = - 5.37 -25.95 (1000/7

7 ) — log T, (2-10)

and the two-parameter equation for Kd to give

log kR ( Ar) - - 30.45 — log T— 0.0745 ( 1000/T)

.

( 2-11 )

This curve is plotted through the argon data in

figure 4, and within experimental error the curve

passes more or less through the center of the data

at low and at high temperatures.

It was assumed that when M is O2 the rate functions Ad and kR have the same form as when M

is Ar. The constant B was adjusted (leaving m and

E' at the same values as for Ar) to give agreement

with the O2 data at high temperature, and the

calculated curve for Ad(C>2 ) is given in table 15 and

plotted in figure 3. On this plot the agreement between observed data and fitted function seems quite

satisfactory. However, the data for kR{Oo) present

more of a problem. The function is taken as Ad/Ad,

is written out in table 15, and is plotted with the

data in figure 4. The agreement between the function A/dCB) and the data above 1000 K is very good,

but below 1000 K the experimental data, which

have been heavily corrected for the ozone mechanism, lie far below the caleulated^curve. Figure 3

shows the ozone function (O2 + 02 03 + O) over

a wide range of temperature. Below 1000 K, the ozone mechanism (A4 ) is faster than the direct

decomposition (Ai); and as a usual thing the recombination by way of ozone will be faster than direct

recombination. Thus, either the reported rate constants [69, 48] have been overly corrected for

the ozone mechanism, or the AftfCb) function behaves

very much differently from the A«(Ar) function

below 1000 K. Table 15 gives recommended values

for Ao(Ar) and A«(Ar) between 300 and 15.000 K,

but the corresponding functions for oxygen are recommended only between 1.000 and 8,000 K.

These recommended values are also given in section 6.

14
Table 4. Equilibrium constants from JANAF

tables [57] for the reaction 02 = 0 + 0 ( units of

particles!cm 3

)

log Kn = 2 log K„ -RT+ log jVAvob .

T °K 1000IT log Kd

100 10.000 -233.594

200 5.000 -104.421

300 3.333 -61.281

400 2.500 -39.682

500 2.000 -26.713

600 1.667 -18.060

700 1.429 -11.879

800 1.250 -7.241

900 1.111 -3.631

1000 1.000 -0.750

1200 0.8333 3.577

1400 .7143 6.674

1600 .6250 8.978

1800 .5556 10.776

2000 .5000 12.209

2200 .4545 13.381

2400 .4167 14.360

2600 .3846 15.179

2800 .3571 15.882

3000 .3333 16.489

3200 .3125 17.021

3400 .2941 17.488

3600 .2778 17.899

3800 .2632 18.272

4000 .2500 18.602

4200 .2381 18.902

4400 .2273 19.172

4600 .2174 19.419

4800 .2083 19.644

5000 .2000 19.853

5200 .1923 20.042

5400 .1852 20.217

5600 .1786 20.382

5800 .1724 20.532

6000 .1667 20.672

The equilibrium constant can be approximated

by either of the following least-squares expressions:

Log Kn = 25.0799 — 25.8745 (1000/T)

Log Kp = 25.4254 — 25.8959 (1000/7’) - 0.0977 log T.

These expressions were obtained by fitting the

JANAF data at 100° intervals over the range

100-6000K.

TABLE 5. Observed rate constants kD [cm*Iparticle

-

5) M = Ar

(Wray [125])

T lOOO/T log k

5076. 0.1970 - 14.400

5141. .1945 -14.190

5263. .1900 - 14.200

5319. .1880 -14.120

5376. .1860 - 14.020

5731. .1745 - 13.900

5780. .1730 -13.960

5830. .1715 -13.890

5952. .1680 -13.680

6060. .1650 -13.510

6172. .1620 -13.600

6172. .1620 -13.550

6250. .1600 -13.520

6289. .1590 -13.390

6410. .1560 -13.410

6493. .1540 -13.400

6514. .1535 -13.380

6803. .1470 -13.210

7067. .1415 -13.020

7576. .1320 -12.770

7692. .1300 -12.660

7751. .1290 - 12.740

7782. .1285 -12.430

7812. .1280 -12.540

8196. .1220 -12.430

9090. .1100 -12.200

9174. .1090 -12.230

9345. .1070 -12.090

9523. .1050 -12.000

9803. .1020 -11.890

9842. .1016 -12.050

9852. .1015 -12.000

9901. .1010 -11.960

10101. .0990 -11.920

10152. .0985 -11.850

10256. .0975 -11.720

10309. .0970 -11.800

10416. .0960 -11.740

10638. .0940 -11.760

10638. .0940 -11.700

10695. .0935 -11.620

10752. .0930 -11.770

11050. .0905 - 11.740

11111. .0900 -11.700

11299. .0885 -11.680

15
Table 5. Observed rate constants k D ( cm 3

/particle

s) M= Ar —Continued

(Wray [125])

Table 6. Observed rate constants kD (cm3

/particles) M= Ar — Continued

(Camac and Vaughan [23])

T 1000/7" log k

11363. .0880 -11.510

12658. .0790 -11.480

13157. .0760 -11.380

14184. .0705 -11.220

14285. .0700 -11.320

15037. .0665 -11.370

15384. .0650 -11.220

16129. .0620 -11.090

17241. .0580 -11.170

Data read from graph: O2 mostly 0.5 or 2 percent

with 7 points at 4 percent; U.V. absorption.

TABLE 6. Observed rate constants kD ( cm 3 /particle

s). M = Ar

(Camac and Vaughan [23])

T 1000/r log k

3450. 0.2900 -16.210

3460. .2889 -16.180

3565. .2800 -16.000

3695. .2705 -15.670

4070. .2455 -15.100

4170. .2398 -14.920

4180. .2390 -15.020

4225. .2367 -14.780

4230. .2365 -14.760

4300. .2325 -14.730

4310. .2320 -14.850

4425. .2260 - 14.460

4580. .2180 -14.470

4690. .2130 -14.390

4930. .2030 -14.020

T 1000/r log k

4930. .2030 -14.180

4930. .2030 - 14.330

4950. .2020 -14.280

4980. .2005 -14.110

5020. .1995 -14.170

5020. .1995 - 14.090

5020. .1995 -13.970

5140. .1945 -14.120

5140. .1945 -13.920

5140. .1945 -13.850

5180. .1930 -14.090

5195. .1925 - 14.000

5360. .1865 -13.720

5390. .1855 -13.710

5390. .1855 -13.850

5570. .1795 - 13.660

5890. .1700 -13.290

5940. .1685 -13.310

5970. .1675 -13.330

5970. .1675 -13.250

6020. .1660 - 13.240

6030. .1655 -13.280

6130. .1630 -13.300

6270. .1595 -13.090

6270. .1595 - 13.090

6290. .1590 -13.040

6410. .1560 -13.050

6540. .1530 - 12.960

6840. .1462 -12.850

7520. .1330 - 12.490

7550. .1325 -12.440

Data read from graph; O? from 0.25 to 1 percent:

U.V. absorption.

16
Table 7. Observed rate constants kD {cm*Iparticle

-

5 ) M = Ar.

(Anderson [ 1 ])

T 1000/T log k

4130. 0.2421 -15.660

4250. .2353 -15.420

4300. .2326 -15.290

4300. .2326 -15.240

4450. .2247 -15.000

4560. .2193 -14.740

4590. .2179 - 14.820

4600. .2174 -15.060

4650. .2151 - 14.800

4650. .2151 - 14.640

4650. .2151 -14.550

4670. .2141 -14.770

4750. .2105 - 14.890

4810. .2079 -14.700

4850. .2062 - 14.700

5010. .1996 -14.440

5090. .1965 -14.950

5090. .1965 -14.520

5090. .1965 -14.270

5150. .1942 -14.180

5320. .1880 -14.010

5340. .1873 -14.280

5340. .1873 -14.170

5440. .1838 -14.070

5440. .1838 -13.890

5750. .1739 -13.920

5750. .1739 -13.820

5950. .1681 - 13.680

5950. .1681 -13.520

6050. .1653 -13.510

6100. .1639 -13.520

6200. .1613 -13.440

Data read from graph; O2 from 2.8 to 8.3 percent;

U.V. absorption.

Table 8. Observed rate constants kD {cm*Iparticle- 5) M = Ar (9/1 Ar/02) k based on equivalent Ar

(Schexnayder and Evans [ 108])

T 1000/T log k

5000. 0.200 a - 13.940

5095. .196 -13.740

5316. .188 -13.860

5500. .182 a - 13.470

5603. .178 -13.390

5710. .175 -13.470

5960. .168 -13.080

6000. .167 a - 13.560

6364. .157 -12.890

6629. .151 - 12.880

7000. .143 a - 12.760

7081. .141 -12.620

7762. .129 -12.350

7935. .126 -12.500

8000. .125 a - 12.540

8540. .117 -12.340

8760. .114 -12.530

9000. .111 a - 12.420

9188. .109 -12.410

9426. .106 -12.250

9428. .106 -12.110

10204. .098 -12.350

a Calculated from data by “method of isothermal

line,” which is an alternate method of evaluating

rate constants from experimental data.

298-126 0- 68—4 17
Table 9. Observed rate constants kD (cm 3

/particle

s) M = 02

(Schexnayder and Evans [108])

T 1000/r log k

3500. 0.286 a - 14.170

3805. .263 - 14.050

4000. .250 a - 13.720

4238. .236 -13.730

4412. .227 -13.380

4500. .222 a - 13.440

4745. .211 -13.270

4749. .211 -13.260

5000. .200 a - 13.240

5500. .182 a - 13.030

5542. .180 -12.760

5985. .167 -12.580

6000. .167 a - 12.850

6553. .153 -12.290

7000. .143 a - 12.460

7150. .140 -11.920

7162. .140 -12.230

7387. .135 -12.060

7885. .127 -11.670

8122. .123 -11.920

8988. .111 -11.680

Table 10. kD at extremes of fitted Arrhenius

function M is O2

T 1000/r log kD References

3000

5000

0.333

.200

-16.03

-13.17

Matthews [88].

3500 .286 -15.20 Rink, Knight, and

6000 .167 -12.47 Duff [103].

2800

5000

.343

.200

-16.93

-13.22

Byron [22].

a

2600 .385 -16.95 Generalov and

7000 .143 -11.71 Losev [43a]. b

Data presented only as function, neither as graphs nor tables.

a Rates observed, but reported in a form such

that rate constants cannot be recalculated. The

results above are from a recalculation by Wray

[125],

b Although this article contains data points,

presented graphically, it became available to us

too late to be included in the detailed study. Only

the end points are included here.

a Calculated from data by “method of isothermal

line,” which is an alternate method of evaluating

rate constants from experimental data.

Table 11 . Least squares parameters for the dissociation of oxygen in presence of excess argon

References No. of 771000

Least-squares parameters

points

E (kcal) m E' (kcal)

Wray [125] 54 5.1-17 1 14 ± 3

a -2.2 150±18 a Anderson [1] 32 4.1 —6.2 1 16 ±11 3.6 80 ±209

Camac and Vaughn [23] 46 3. 5-7.6 106 ±3 0.8 98 ±27

Schexnayder and Evans [108] 22 5.0-10 78 ±10 -10 220 ±98

All data 154 3.5-17 105 + 3 -0.2 108+16

All except Wray 100 3.5-10 105 ±5 -2.4 131 ±35

All except Anderson 122 3.5-17 100± 3 -0.1 101 ±13

All except C and V 108 4.1-17 111 ±4 -1.7 136 ±21

All except S and E 132 3.5-17 106 ±3 0.3 102 ±15

a Twice the standard deviation.

o2 + m-^o + o + m

k = A exp (-E/RT)

k = BTm exp (- E'/RT). 18
TABLE 12. Observed data, recombination of oxygen atoms

a As recalculated (for surface reactions) by

Morgan and Schiff.

b 0-2 /Ar = 50/50, but corrected to equivalent Oj.

c 0-i/Kr = 41/59, but corrected to equivalent O2 .

19
Table 13. Least-squares parameters for recombination of oxygen atoms

References

No. of

points T M

Least-squares

parameters

E kcal n

Kiefer and Lutz [71] 8 1486 - 2822 O, and Ar — 5 4 — 1 4

7 1799-2571 CL and Kr 0.52 0.12

15 1486-2822 o2 -3.6 -1.0

Wray [125] 15 1350 — 2950 Ar -0 79 — 0 17

All 0, data a 18 300-2822 02 — 0 30 — 0 24

All Ar data b 18 293 - 2950 o2 -1.54 -1.06

k = A exp (—E/RT) or k=CTn. a Refs [71, 69, 48, 123] (compare table 12).

b Refs [125, 90, 101] (compare table 12).

Table 14. Relative efficiencies of various foreign gases for dissociation and recombination of oxygen

O'2 + Mi^O + O + M

R /

References k T M/M' k/k'

Camac and Vaughn [23] kp 6000-7000 Ar/02 1/3

5000-7500 Ar/O 1/25

Schexnayder and Evans [108] kv 5000-9000 Ar/02 1/9

Wray [125] ki> 5000 Ar/O, 1/18

Ar/O 1/50

Rink [102] ko 3500 - 5000 Ar/Kr 1/2

Ar/Xe 1/6

Rink, Knight, and Duff [103] kp 3500 o,/o 1/3

0,/Xe 3.4/1

Morgan and Schiff [90] kv 29-3 Ar/N, 0.3

He/N, 0.3

N,0/N, 1.4

co2 /n. 3.0

SFh/N2 3.0

Morgan and Schiff [90] plus kv 293 o2 /n. 1/1

Kaufman and Kelso [69],

20
Table 15. Recommended rate constants for dissociation kD and recombination kR of oxygen

log /fo(Ar) = — 5.37 — log T- 25.95 (1000IT)

log kD(02 ) = -4.34 -log T- 25.95 (1000/D

MAr)/M02 )= 1/10.8

log A = 25.08 -25.8745 (1000/D

log A'«(Ar) = — 30.45 — log T- 0.0745 (1000/D

log M02 ) = - 29.42 -log T- 0.0745 (1000/7)

A-d(02 ) = 4.57x 10-5 7

1 exp (- 118.7/AD cm3

/ particle-s

Icr( 02) = 3.80 X 10_307

_1 exp ( — 0.34/AD cm6

/ particle2 -s MAr)/M02 )= 1/10.8

These relations apply 300-15,000 for Ar as M

1000-8000 for 02 as M.

3. Decomposition of Ozone

3.1. Mechanisms

a. Other Reviews

An early effort to make a quantitative study of the

thermal decomposition of ozone was carried out

by Jahn [56] in 1906. Between then and about 1930,

several studies were made. In general, the authors

encountered trends they could not explain and

apparently erratic results, and they disagreed with one another. This situation was reviewed by Wulf

and Tolman [128] in 1927 and by H. J. Schumacher

[112] in 1930. The troubles were ascribed to impurities, and a series of investigations under Schumacher [113] made a major effort to eliminate

impurities. The culmination of this effort was a study by Glissman and Schumacher [47]. The results

had good precision, but there still were unexplained

trends in the nonconstant second-order rate “constants”. The real problem was that the investigators

in the 1930’s did not understand the nature of unimolecular reactions at the low-pressure limit. Here

was a case where the experimentalist was unable to explain his data until the theory of the process was

clarified.

The existence and nature of the low-pressure

limit of unimolecular reactions [89] was established

in the early 1950’s, and the mechanism of the ozone

decomposition was established by Benson and

Axworthy [11] in 1957, largely by reinterpreting

the data of Glissman and Schumacher. A detailed

review of all the older data is to be found in Axworthy’s Ph. D. thesis [3]. Another review covering

data through 1959 is given by Campbell and Nudelman [24], These authors reported that the only

quantitative data in the literature before 1959 was

that of Glissman and Schumacher. Between 1959

and 1967, several careful quantitative studies have

made (see tables of data in this review), both on the

direct decomposition of ozone and on related studies

of oxygen atoms and molecules. In the literature a number of different mechanisms have been proposed and used. The so-called “Jahn mechanism,”

“unimolecular mechanism,” and “bimolecular

mechanism” are all special cases of the single

mechanism as assembled by Benson and Axworthy

[11]. The differential and integrated rate equations

for each of the special “mechanisms” will be summarized in the following sections.

b. Jahn Mechanism

The overall reaction is

20:i = 302 . (3-1)

The general definition of “the rate of reaction”

then is

1 4O3] _i 4

0

2] 2 dt 3 dt

(3-2)

Jahn proposed that ozone is in thermal equilibrium

with atomic and molecular oxygen, and the atomic

oxygen irreversibly attacks ozone as a rate determining step:

O3 ^O-2 + O, A’i — k\/k2 (3—3)

O3 + O —* 02 + 02 , A3. (3—4)

The rate expression from the mechanism is d[03 ] dt

2k,[0:d [O]. (3-5)

21
The concentration of atomic oxygen is given by the

equilibrium constant.

Ki = [0][0*]/[03]. (3-6)

The defined rate in terms of Jahn’s mechanism is R=- 1 4O3 ] 2 dt

K,ks

[Osf

[ 02 ] kj

[O3 ?

[ 02 ]’ (3-7)

where Jahn’s constant, kj, is the product of the

equilibrium constant and rate constant,

kj — K\ks — AiA3 /A2 . (3—8)

Stoichiometry provides a relation between ozone and oxygen, at any stage of reaction:

[O2] = [O2 ] 0+| ([03]o-[03]) = [02L-| [03], (3-9)

where [ 02]o is oxygen at zero time, [CX]* is oxygen

at infinite time.

[02 L = [02]o+|[03 ] 0, (3-10)

and [

O

3 ] 0 is initial ozone. With the stoichiometric

relation, the differential rate expression can be

expressed in terms of one variable, [03]:

c^C>3]_o7 [O3]

2

7 — 2kj o [o2 l-|[o3 ]

(3-11)

This equation is readily integrated to give

[O2L /[Oalo

[03 ]o\[03]

[Q3]o

[03] 2kjt. (3-12)

It is convenient to define the ratio of final oxygen

to initial ozone as A and the ratio of initial ozone

to ozone at any time as x: A=[02 ]J[Os]o, x = [03 ] 0/[03 ]. (3-13)

With these definitions the integrated equation for

Jahn’s mechanism is

A(x— 1) — |In x = 2 kjt. (3-14)

If one starts with dilute ozone (a few percent or less)

in oxygen, data are described fairly well by this rate expression.

c. Bimolecular Mechanism

Some authors have interpreted their data in

terms of a bimolecular mechanism.

kfl .

For this mechanism the differential and integral

equations are the simple, standard forms:

403]

dt

2Ab[03 ]

2

, J 1_

[ 03 ] [ 03 ] 0

2A'st. (3-16)

In terms of the quantity, x, defined above, the

integrated equation is

[03 ] 0 (x— 1) —2kB t. (3-17)

If one starts with pure ozone, the expression fits the data moderately well at early times, but the

calculated “constant” increases throughout the course of a given run. This drift, unexplained in

the 1930’s, was one of the major problems faced by

workers on this reaction at that time, and it is a feature of relative efficiency of 03 and 3/2 02 as an energy-transfer catalyst in the unimolecular

decomposition of ozone.

d. Unimolecular Mechanism

The unimolecular mechanism takes the rate- determining step to be the elementary unimolecular

decomposition of ozone at its low-pressure limit,

followed by reaction 3 as a fast following reaction:

03 + M * 02 + M,

o3 + o —* 02 + 02 ,

k\ (slow),

A3 (fast).

(3-18)

The rate in terms of ozone is

d[0-,]

dt

2Ai[03 ] [M],

Actually, M is not one thing, but at least two (03 and 02 ), and perhaps more if foreign gases. X, are added. The efficiency with which oxygen or a foreign gas, X, excites the vibrational states of ozone is different from that for ozone itself. Thus

the rate expression should be written: -|

^= Ai[03] [03] + MOJ [02 ] + A-. x[03] [X]

= i,[03

] {[03] + ^[0.] + ^[X]}

= Ai[03 ]{[03] + a[0,J + jS[X]} (3-19)

where a = kn/ki is the relative efficiency of oxygen

and ozone, and /3 = Ai X/Ai is the relative efficiency

of the foreign gas, X, and ozone. It is convenient

to define the “equivalent concentration of ozone”

as [M],

[M] = [03 ] + a[02 ] + /3[X]. (3-20)

03 + 03 —* 302 (3-15)

22

However, since 2 ozone molecules are not equivalent to 3 oxygen molecules, the value of [M] changes
throughout the course of reaction. The differential

equation in one variable, [O3], including the stoi- chiometric relation and the definition of [M], is 4O3

elementary unimolecular reaction at the lowpressure limit. The scheme is:

dt

O3 + M —

02 + O + M ki. - 2A4O3 ] [M]

0*2 + O + M —> O3 -T M k-i , (3-26)

2*. (l-|«) [O3]2 + 2A: 1 (4O2] 00 +)8[X])[O3].

03 + O * 02 + 02 A: 3 .

(3-21) The steady-state condition applied to oxygen atoms

The integrated equation is

1 , f[03 ]o [M]

[ML

ln

l[03] [M]„j

2k,t ' (3 22)

where [M] has been defined above, and the limits on [M] are

gives

[O] iitOsHM]

A:2 [02 ] [M] + A:3[03 ] As in other mechanisms, stoichiometry gives

[02] = [0i-|[03],

(3-27)

[M] 0 — [03 ]o + a[02 ]o + /8[X]

(3—23)

[M]x = a[02 ] x + /3[X],

If a new variable y is defined as the ratio of initial M to M at any time,

y— [M] 0/[M], (3-24)

the integrated equation takes the simple form of

In x/y=2[M]x

kit. (3-25)

This rate expression is applicable at moderately

high temperatures, perhaps 750-1100 K. At still higher temperatures, above 1500 K, reaction 1 is so much faster than reaction 3 that reaction 3 may

be neglected entirely. In this case the above rate expressions still apply if the factor of two in front

of k, is dropped. At low temperatures reaction 3

gives a factor of two increase over reaction 1 alone,

at high temperatures reaction 3 does not occur to a

significant degree, and at intermediate temperatures

the rate of reaction 3 may be directly and separately

observed [62].

e. Benson and Axworthy Mechanism [11]

The mechanism proposed by Jahn was applied

in most of the early work on ozone decomposition

in excess oxygen. A complex mechanism was proposed by Glissman and Schumacher for the decomposition of concentrated ozone [47]. This included

Jahn’s two reactions (3-3 and 3-4). With the passage

of time the requirement of equilibrium in reaction

(3-3) was removed and a steady-state condition

applied to the concentration of oxygen atoms in

all the mechanisms [47, 74a]. In 1957 Benson and

Axworthy [11] showed that the steady-state adaptation of Jahn’s mechanism could explain the

results obtained both for concentrated and dilute ozone. Their formulation considers reaction 1 an

and the definition of M is

[M] = [03] + a[02 ] + /3[X] = (l-f <*) [03]+a[Oi + /3[X],

In terms of the defined rate R the differential

equation is

p 1 403] A1A4O3HM]

2 dt A2[M] [02 ] + &3 [03]

’

Benson and Axworthy interpreted experimental

data directly in terms of the differential equation,

by constructing the functions [O3] [M]//? and

[02 ] [M]/[03]:

[O3] [M] _ 1 k2 [M][02 ] 1 1 [M][Q2 ] R k\ A1A4O3] A'i kj [O3]

(3-29)

Between successive experimental points (actually

a graphical smoothing procedure was used) the

instantaneous rate, R, is computed, and a plot of

experimental [O3] [M]//? against experimental

[M] [02]/[03] should be a straight line of intercept

A7 1 and of slope kj 1. To carry out this procedure one must first know the relative efficiencies, a and /3, especially a. Benson and Axworthy [11] deduced

these constants from Glissman and Schumacher’s

[47] experimental data and also from some data

obtained by Axworthy [3] but never published.

Also other experimental studies (to be discussed

later) give these relative efficiencies. At this point

we tabulate the relative efficiencies, a and (3. for

various gases as found by various workers and as used and recommended in this review, table 17. Benson and Axworthy used Glissman and Schumacher’s data both to evaluate relative efficiency

of M gases and as a test of mechanism. This procedure adds up to fitting a large number of param23
eters to the data: the confirmation of Benson and

Axworthy’s values by completely independent

experimental methods [26, 70, 62] and systems gives

strong support to this mechanism for the homogeneous thermal decomposition of ozone in the

temperature range 300 to at least 1000 K, since

the high temperature mechanism given above is a special case of the Benson and Axworthy

mechanism.

Benson and Axworthy interpreted Glissman and

Schumacher’s data by the differential equation

derived from their mechanism. Their published

article did not list the individual values of Ay and

Ay but only the parameters of the Arrhenius equation fitted to these quantities. From Axworthy’s

thesis we recomputed Ay and Ay by this method, and

the values for individual runs are listed in table 18

for Ai and table 22 for kj.

The differential equation from Benson and Axworthy’s mechanism can be expressed in terms of one variable [O3] and integrated. The differential

equation is

40a] 2Ai^[Q3]-{(l-3/2a)[0:,]+q[02], + /3[X]}

d‘ fa ([O-i-f [O3])

{

(l -f a) [03] + a[02] M + /3[X]

J + £3[03]

The integrated equation is

1 [Q.3]q[M] [OyG /[O3J0 -I \ _3 1 [Oslo

[Q3][M]q A2 [Oslo V[0.3] ) 2

in

[03 ] 2[M]J

1 Ay 21

(3-30)

(3-31)

In terms of A, x, and y defined above, the integrated

equation is

, ,

. A(x — 1)— - In x

In x/y _ _Ay 3

2[MU 1 As 21 (3-32)

The observable function on the left-hand side may

be defined as /j, and the observable function on

the right-hand side may be defined as/), since these

functions give Ay and Ay if one has respectively the

unimolecular mechanism and Jahn’s mechanism.

The integrated equation may be written in several

different forms for different purposes. For a run

with a series of observed concentrations of ozone

as a function of time, a plot of f\ against fj gives

Ay as intercept and A2/A3 as slope:

A2 /i = Ai— -/}. (3-33)

"3

approaches completion the Jahn mechanism

makes an important contribution to the rate. Starting with ozonized oxygen, typically about

3 percent ozone, one starts the run with both

unimolecular mechanism and Jahn mechanism

contributing to the rate; but as the reaction progresses, the unimolecular mechanism (with its sensitivity to M gases) fades to zero, and the

reaction fully follows the Jahn mechanism.

If an experimenter reported initial conditions

and the reactant concentration at only one time,

it would appear that we have two unknowns, k\

and Ay, and only one datum, so that the data are useless for any quantitative reinterpretation.

However, if conditions are close to the Jahn re- gion, we can correct for the effect of the unimolecular term by using literature values of Ay as a cor- rection on Ay:

kj

fj

I-/1/A,’

(3-35)

The integrated equation may be written as

+ (3-34)

A1 A./

Once we have an estimate of Ay and A.y, as from

Benson and Axworthy’s study [11], we can test a given set of experimental conditions to see if it is clearly in the unimolecular mechanism

(fj/kj<l), clearly in Jahn's region (/i/Ay 1), or in the intermediate region where the full Benson-Axworthy mechanism must be used. One

of the confusions in the older literature is that

usually both mechanisms operated at once, but

with different weights over the course of a run. Starting with pure ozone, one is fully within the

unimolecular region at first, but as the reaction

where fj and f\ are obtained from the experimental

data, Ai is obtained from Benson and Axworthy,

and the corrected Jahn constant, kj, is then found

from the experimental data. The data of Garvin

[43] and table 3 of Pshezhetskii et al. [99] were

corrected in this way. Similarly, data close to the

unimolecular limit may be corrected for the Jahn

term by the relation

kl=z

i-fj/ky (3_36)

Some of Garvin's data [43] and table 1 of Pshezhetskii et al. [99] were corrected in this way.

A considerable body of the older literature [3] contains data with such experimental scatter and

uncertainty that the data cannot be used to obtain

24
values of rate constants. However, we can test to see if the observations generally fall within the

range of the present interpretation and assignment

of constants or if the observations contain some

quite different trends or some real unsuspected

feature. A consistency test between current interpretation and older data is to write the integrated

equation as

3 _ In x/y

| A(x~l) —-~2 In x

2[M]x

Ar, 2k

j

• (3-37)

The experimental points are plotted as

* = [03 ]o/[Os] against time t. The currently as- signed values of the constants Ay and kj are used in

the above equation to solve for time t as a functin of x.

f. Energy Chains

The energetics of the three steps in the Benson-Axworthy mechanism,

03 -*02 + 0 A£0 = 24.2

02 + 0-^03 A£0 = — 24.2

0( 3 P)+03 (

] A)-^202 ( 3S7) A£0 = — 94.2,

(3-38)

have led many investigators to assign a large part

of AEs as vibrational energy to one or both products,

O*. This excited vibrational species is assumed to decompose an ozone molecule:

O* + 03 —

>

02 + 02 + O, A'£. (3-39)

posing ozone, Jones and Davidson [62 j observed ozone disappearance with a time resolution of

about 5 /x s, such that at early times all reaction was from reaction 1 and at later times reaction 3

built up to give a doubling of the overall rate. If the energy chain played a predominant role, the

rate when reaction 3 was fully developed would

be much more than twice as great as the rate where

reaction 3 was totally inoperable. The errors and

uncertainties of the shock-tube experiments set a 20-percent limit on any conclusion that can be made,

and thus the upper length on the energy chain at 800 K is assigned to be 1.2. Energy chains do not

seem to be important in the overall kinetics of the

thermal decomposition of ozone. It must be con- cluded that ozone deactivates an excited oxygen

molecule (with i><17) more rapidly than it is dissociated by it: 0*{v > 6) +03 —> 202 + 0(3 P), slow

O* (v > 1 7 ) + 03 —» 202 + O ( ’ D )

.

fast

g. Photolysis in Red Light [26]

With radiation around 6000 A, ozone weakly

absorbs light to give the forbidden transition,

03 + /^^02 ( 3 £-) + 0( 3 P).

Let / represent the rate of light absorption in units

of photons cm_3

s

_1

. This reaction is followed by

steps 2 and 3: 02 + O + M * 03 + M, k-2, 03 + 0 * 02 + 02 , A'3 . The combination of reactions E and 3 gives a chain

reaction, where vibrational excitation of the product is one carrier of the chain and an oxygen

atom is the other chain carrier. There has been

direct spectroscopic observation of oxygen molecules in vibration levels up to v=l7 in both flash

photolysis of ozone [78] and in its thermal decomposition [62] at moderately high temperatures,

700-900 K. It has been demonstrated by direct

experiment that highly vibrationally excited

nitrogen N* can decompose ozone [97], and as discussed in section 1 Q* from OLDJ+Os decomposes ozone to give OLD). Thus it is extremely

plausible that reaction E does occur. However,

there are experimental studies that indicate

that the “chain length” may be very short, less

than 1.05 at room temperature [26], and less than

1.2 at 800 K [22].

These experimental studies and the related ar- guments are as follows: In the photolysis of ozone

by red light (see below), reaction 2 and 3 occur,

and any contribution by step E would give a quantum yield greater than two; the quantum yield

extrapolated to pure ozone was precisely two with

uncertainty less than 5 percent; thus the strong

upper limit of 1.05 for “chain length” at room

temperature. In the shock-tube study of decomWith the steady-state assumption for intermediate

oxygen atoms, one obtains the rate expression for ozone disappearance,

403 ] _ 2/A-3 [03 ] dt “A-2 [02 ][M] + A-3 [03

]’ (3-40)

The definition of quantum yield, 4>, is the number

of molecules that react per photon absorbed:

d[03\/dt

(3-41)

From the mechanism, the quantum yield is $

2A'3 [03 ]

A' 2 [02 ][M] + A-3 [03 ]- (3-42)

It is useful to solve this relation in terms of reciprocal quantum yield, with some rearrangement of

terms, to give

J_/2 \ faM

[02 ]\cp V M03 ]

Aj> ak-2 [02 ] /3k2 [X]

h A-3 [03] h [03

]‘ (3-43)

25
By omitting foreign gases, X, this system gives

A2/A3 as an intercept and oikz/ks as the slope of a

plot of the observable function [02]

_1 (2/<h — 1) against the ratio [O2] [O3]. The ratio of slope

to intercept gives a the relative efficiency of oxygen to ozone in energy-transfer to ozone. The method

gives the best and most direct measure of relative

efficiencies of various gases in this role. By flooding ozone with a great excess of foreign gas, X, its relative efficiency, /3 , can also be found. Values of

these relative efficiencies as energy transfer

agents are given in table 17, and values of A2/A3 di- rectly observed this way are listed in table 25.

3.2. Observed Data

a. Relative Efficiency of Foreign Gases

The relative efficiency of a foreign gas, M, in

energy transfer to ozone can be found by relative rate measurements of either reaction 1 or reaction 2:

O3 + O3 —» O + 03 O3 + X-+O + X

O2 + O + O3 —> O3 "T O3

O2 + O + X —

>

O3 -T X

Ay

A'ix,

k2 Ei\. (3—44)

Since oxygen is the product of reaction, it is present

in all runs, and its relative efficiency in either reaction 1 or reaction 2 is defined as

ot — Ay ( O2 ) / Ay — A'2 ( O2 ) / Ay. (3—45)

The relative efficiency of added gas, X, is defined as — kix/ki = k-zx/kz. (3—46)

Observed values for relative efficiencies of various

gases is given in table 17. Three different authors

find this important factor for oxygen to lie between

0.42 and 0.44, and the value 0.44 is adopted here.

Unlike the case for oxygen molecules (table 14),

the relative efficiencies of X gases in the dissociation of ozone are well and reproducibly characterized. These factors for O2 and for Ar are probably

accurate to 10 percent or better. The ratio, Ayi,/Ar.v2 , is essentially the same at 291 K and around 800 K

(last entry in table 17), and based on this fact, one assumes the relative efficiency of foreign gases

for ozone not to change significantly with temperature. In subsequent tables of Ay and Ay, the relative

efficiencies of table 17 have been used to put all rate constants on the basis of equivalent ozone:

[M] = [03 ] + a[02 ] + /3[X]. (3-47)

b. Rate Constants for Reaction 1

The observed rate constants for reaction 1, Ar lx , have been corrected for relative efficiency of

foreign gases and entered as log Ay as a function of

T and lOOO/T in table 18. All sets of data judged to be free of large systematic errors are included.

The temperature range is 343 to 910 K, although no one author covered all of this range. Axworthy

[3] made a series of runs with various added gases,

such as H2 0 and H2O2, and with ozone produced

in various ways: these data were never published

except in the Ph. D. thesis, but they are included

in table 18. One run was made at 303 K. In most

later interpretations of data, we do not use Axworthy’s data, although his values of Ay agree

quite well with those of other authors. The observed values of Ay including Axworthy’s point at 303 K are plotted in figure 5. The various authors

are in satisfactory agreement with each other.

The data of each author in table 18 were fitted

by the method of least squares to three empirical

equations (1-33) to (1-35). In general, the data of

any one investigation had so much scatter that the

three-parameter equation gave ridiculous results

to the least squares treatment. Most interpretation

of the data is based on the two-parameter Arrhenius

equation, and these parameters for each author

are reported as log A and E in table 19. The activation energies, E, reported by the various authors

varied between 21.4 and 25.2 kcal/mole — with no

apparent trend with temperature (note that this is much better than the results on the dissociation

of oxygen, kn, table 11). All data by all authors were

pooled, and the Arrhenius parameters are reported

in table 20. Also each author was omitted from the

total, and A and E found. The activation energies,

omitting given authors, vary between 22.8 and 23.5

kcal. The interpretation of ozone kinetics by Benson

and Axworthy was based on the data of Glissman

and Schumacher. From table 20 we see that all data excluding Glissman and Schumacher give

essentially the same Arrhenius parameters as all data by all authors including Glissman and Schumacher. However, the combined data of all authors

with their wide range of temperature give significantly different results from those obtained by

Benson and Axworthy from Glissman and Schumacher alone.

The observed rate constants. Ay, are so numerous

that it is difficult to get all of the points on one

graph. In order to display certain functions more

clearly, the rate constants. Ay, are averaged in groups of approximately constant temperature in table 21 and plotted in figure 12. The good agreement between various authors,

figure 5, and the stability of the Arrhenius parameters to omission of any set of data, table 20. indicate

that the rate constant function for reaction 1 is very well characterized.

c. Jahn’s Rate Constant and the Ratio k-Jka

The rate constant, Ar./, has been observed over a much more narrow temperature range than Ay. The experimental points as found for various

workers are given in table 22 and plotted in figure 6.

26
T°K

Figure 5. Observed values

of ki. O3 + M —» O2 + 0 + M, where M is equivalent ozone. Units

are cm3

1particle-s.

Jones and Davidson [62] Garvin [43], data recalculated with integrated equation A Pshezhetskii et al. [99] 0 Zaslowsky et al. [131] OGlissman and Schumacher

[47], data recalculated by

method of Benson and

Axworthy [11] Axworthy’s room temperature point [3] The line is given by:

log &i=—8.783—4.965 (1000/D.

o O O o o

o O O o o

CD CD m ro

1000/T

FIGURE 6. Observed values

of John’s constant

kj = Kik3 .

Units are s

_1

.

Symbols are the same as in figure

5, except # is value observed

by Jahn [56] in 1906. Line cal- culated from log kj= 14.855 — 6.471 (1000/D (not least- squares fit to the data).

T °K

27
The ratio of rate constants, kz/k3 , is directly

observed in photolysis of ozone by red light, and

it is obtained by interpreting detailed sets of data

by the integrated equation. In the latter case

values of kz/k3 and of k,j are obtained from the same

data. Observed values of A 2 /A 3 are given in table 23

and figure 7.

d. Rate Constants for Reaction 2

Many investigators have attempted to measure

the rate of reaction 2 (O + O2 + M —» O3 + M).

Oxygen atoms are typically produced by an electrical

discharge through oxygen. For many years results were especially irreproducible between different

investigators. The side reactions that caused the

trouble are discussed in section 1 , 1.5c. About

1964 the nature of the difficulty was recognized,

and quantitative studies have since been made, in one case over a wide temperature range and in

the other case over a wide range of foreign gases, M.

These results are listed in tables 24 and 25; and the

data are plotted in figure 8 according to k> = C2 T

n

, and in figure 11 according to the Arrhenius equation.

The data still show moderately severe scatter and

agreement between different workers is only fairly

good. An error of about 50 percent is indicated.

e. Rate Constants for Reaction 3

Only in the shock-tube work of Jones and David- son [62] was it possible to measure directly the rate

of reaction 3 (O + 03 —» 2O2 ). In other cases one

always measures the ratio of reaction 2 to reaction 3

or some other complex quantity. The directly observed rate constants, A:3 , are given in table 25.

The scatter of the data is such and the range of

1000/

T

is so small that these 11 observations really

constitute only one point (log k3 = — 11.9 with a range of ±0.3) at one temperature, about 850 K.

At other temperatures we have observed values

of kz/ka and observed values of kz over the same

temperature range. The data in figure 8 were fitted

by least squares to the function kz — C2 Tn

. For an observed value of A2/A3 at a particular temperature

T, we evaluate k2 from the least-squares function

at that temperature, and k3 is calculated from k2 (function)/(/f2 /A:3 )obServed- The values of k3 deduced

from kinetic data in this way are listed in table 23.

These rate constants plus those directly observed,

table 25, are plotted together in figure 9A. The

points fall into three groups: Jones and Davidson’s

shock-tube points at high temperature, Glissman

and Schumacher’s data around 100 °C from the

decomposition of ozone, and Castellano and

Figure 7. Observed values of kzlk3 .

#Gastellano and Schumacher [25, 26] Mathias and Schiff [87] O Glissman and Schumacher [47] Line not based on least-squares fit to these data but from

the ratio of separately fitted and A 3 .

log A2/A3 = — 23.638+ 1.506 (1000ID.

28
Figure 8. Observed values of

k2 ( cm6

/particle2 -s ). OExperimental points [28] Least-squares line given by

log k2 = ~ 24.0768 -3.4683 log T. Data of Kaufman and Kelso [70

1

indicated by are not included in least-squares fit to the line.

Schumacher’s points at room temperature from the

photolysis of ozone in red light. It is to be noted

that Glissman and Schumacher’s data around 373 K

show just as much scatter as Jones and Davidson’s

shock-tube data. We believe that if Castellano and

Schumacher had obtained more points, their re- sults too would show a fairly high scatter, since

the activation energy indicated by Castellano and

Schumacher is far less than that indicated by all three sets of data, covering a wide temperature

range. The Arrhenius parameters for k%, as shown

in figure 9A, are given in table 27. The observed

value of &3 and the value of A3 calculated from the

JANAF tables were used to obtain the rate constant, k\ , for the reverse reaction (table 26).

3.3. Interpretation of Observed Data

a. Equilibrium Constants from Kinetic Data

It should be emphasized that all figures from 5

through 9A contain only observed rate constants;

these constants were deduced from the experimental data by means of the Benson-Axworthy

mechanism. No use has been made of the presumed

relation between rate constants and equilibrium

constant,

Kx = kdk2 h=kj!K1 . (3-48)

We have refrained from assuming these relationships for two reasons: Some doubt has been ex- pressed about the heat of formation of ozone (it may be in error by as much as 0.4 kcal), and some

doubt has been expressed as to whether the relation

is valid for a unimolecular reaction at its lowpressure limit.

The JANAF value for the heat of formation of ozone is based on two calorimetric experiments

[50, 63] on the overall reaction,

o3 (g0 -* 3/2 o2 (g).

The paper [50] by Guenther, Wassmuth, and

Schryver (1932) contains extensive error analysis

and detailed description of the equipment; they

report data from which one calculates 5

A/H£98 = 33.89 ± 0.36 kcal/mole.

A previous paper [63] by Kailan and Jahn (1910),

which reports less experimental detail and gives

less basis for estimation of error, gives data from

which one estimates

A/H298 = 34.3 ± 0.6 kcal/mole.

The JANAF tables accept the average of these

two values with an overall error limit,

A/H298 = 34. 1 ± 0.4 kcal/ mole.

In this review the JANAF value is used, but we

feel that the value, 33.9 of Guenther, Wassmuth.

and Schryver is to be preferred.

Let us review the arguments why some people

fear that ATi = A i/A 2 might not be valid in the present

case. At total chemical equilibrium between 02 ,

5 The estimates of error in the next three expressions were made by the authors

of the JANAF tables.

29
0 0 0 0 O O

0 0 0 0 O O

00 N u> rO

Figure 9. (A) Observed values

of k 3 . A Directly observed by Jones and David- son [62], Computed from Ar2/A3 . Castellano and Schumacher [26] Mathias and Schiff [87] QGlissman and Schumacher [47]

Figure 9. (B) Observed values of

k 3 (cm3

1particle-s) including ex- tended values from kj/Ki.

A Directly observed by Jones and Davidson

[62]. Computed from A'>/£ 3 , and k3 . •Castellano and Schumacher [26] • Mathias and Schiff [87] Computed from kj/Ki.

Glissman and Schumacher [47] O Garvin [43] Jahn [56] Line calculated from least-squares fit to the data, log *3 = - 10.697-1.047 (1000/7').

1000/ T

O, and 03 , all states of reactants, products, and

intermediate collision complexes have the equilibrium distribution characterized by the temperature T. The rate constant, ki, for example, is an

average of molecular rate constants (elementary

chemical physical rate constants) over the definite

equilibrium distribution function. If there are no

products of reaction, the forward reaction will

proceed under conditions where reactants and

products are not at equilibrium. If the reactants

have a distribution over states essentially the same

as at equilibrium, then any average taken over this

30
distribution function should be essentially the same

as an average taken at true chemical equilibrium.

In particular the average of the molecular rate constants that give k\ at equilibrium would give

the same average value of k\ under conditions of

unbalanced chemical reaction. If the reactants have

a nonequilibrium distribution over molecular

states, then the averaging of molecular transition

probabilities that gives k\ would not be expected

to be the same as at equilibrium. For a unimolecular

reaction at its low-pressure limit, the reactants have

a profoundly nonequilibrium distribution over

vibrational states, and this change in distribution

function gives an average rate constant lower than

the equilibrium value, easily a factor of 1000. The

reactant of reaction 1 is O3 with a strong nonequilibrium distribution over vibrational states. The

reactants of reaction 2 are O and O2 with an essentially equilibrium distribution over translational

states. With O3 having a nonequilibrium distribution

function and with 02 and O having an equilibrium

distribution over their states, one may fear that A: 2 will have its equilibrium value, k\ will have its nonequilibrium value, and Ki = kilk2 would fail (see, however, section 5). For ozone kinetics we have precisely observed

values of ki over a wide temperature range and the

data are well described by an Arrhenius function,

k\ (/) =Ai exp (— EJRT),

where A\ and E\ have been fitted to experimental

data, table 20. Also we have fairly precise values

of A2 over a more restricted temperature range.

Each value of observed k-> divided by the functional

k\ calculated for the same temperature gives a

strictly kinetic estimate of the equilibrium constant,

K[ = k\ (function)/

A

2 (observed). (3-49)

This ratio is entered for each observed hi in table

24A to give a set of K' from 188 to 373 K. Another

method of estimating the equilibrium constant

by a strictly kinetic method is from observed values

of k.j divided by functional (fig. 9A) A:3 : K”—kj (observed)/^ (function). (3-50)

This ratio is given for each observed kj in table 22 . The thermodynamic equilibrium constant K\ is given in table 16, and is plotted as the smooth

curve in figure 10. Points for the kinetic-constant

ratio K[ are plotted circles or as a triangle in

figure 10 , and points for K" are plotted as squares.

The kinetic constants K' and K” overlap each other

quite well. The equilibrium constants deduced

from kinetics generally lie slightly below the

thermodynamic equilibrium constant. Agreement

between the kinetic K and thermodynamic K would

be improved if the heat of formation of ozone is reduced a few tenths of a kilocalorie. The discrepancy between K' and K at low temperature

depends critically on the activation energy assigned

to k\. The points in table 24A and the circles in

figure 10 were calculated, using 23.06 kcal as the

activation energy for reaction 1. If this activation

energy is decreased to about 22.7 or 22.8, the

kinetic K' and thermodynamic K come into agreement within the scatter of the kinetic data. It must

be admitted that the scatter in the kinetic data is such that no strong case can be made for changing

the heat of formation of ozone, and figure 10 cannot

be interpreted as giving a measurable demonstration

of failure of K\ = ki/k2 .

b. Extended Values of k\ and k3

Since the relation, Ai = A'i/A;2 , appears to be at least as valid as the observed function, ki, this

relation can be used to extend the temperature

range of the rate constant, k\. The extended set of

these rate constants is

ki (extended) is Ai (obs) and k2 (obs) Ai(thermo).

(3-51)

The values of k\ (extended) as found from k2 are given as the last column in table 24A. The full data of ki (extended) are shown in figure 12 with

the least-squares line.

Likewise the function, A3 , can be extended as

follows by adding the terms, kj/Ki, to the observed

values of A3 :

A3 (extended) is k3 (obs) and kj/Ki (thermo). (3-52)

The additional values of k3 as deduced from kj are given as the last column in table 22. The observed

values of k3 , the values obtained from red-light

photolysis, A2/(A2/A3 ), and the values extended

from kj are plotted in figure 9B with the leastsquares line.

The rate constant functions, kx , k\ (extended), kj , k2 /k3 , A2 , and k3 were each fitted to the three functions, A exp ( —E/RT), BTm exp (— E'/RT ), and

CTn. The parameters. A, E, B, m, E', C, and n for

each of these six functions are listed in table 27.

Even with the extended data for Ai, the threeparameter function gives physically unreasonable

parameters, and the parameters are unstable with

respect to omission or inclusion of small sets of

data. For the other rate constants, note particularly

kj , the data are totally unable to support the threeparameter function. In some cases the empirical

function C gave about as good a fit to the scattered

data as the Arrhenius equation. However, the

general picture is that the data, including A2 , are best described by the two-parameter Arrhenius

equation. Unlike the case with the dissociation of

oxygen, there is nothing about the data that gives

compelling evidence for equation B.

31
log

k

p

log

K

T

FIGURE 10. Comparison ofequilibrium constant calculated

from kinetic data and that

found from thermodynamics.

•A' = Ai/A-2 with A'2 from reference [28] .A K' with A2 from Kaufman and Kelso

[70] DA — kjl A3 Line is K from JANAF Thermodynamic

Tables.

T°K

O

rO o

O

OJ

Figure 11. Observed values of k2 with line calculated from k> = ki/Ki ( compare Fig. 8). log k 2 = - 34.335 + 0.459 (1000/7").

3.5 4.0

1000/ T

32
T°K

o o o o o O

o o o o o O

O 00 If) rO <M

1000/T

Figure 12. The extended function ki.

Observed values of k\ averaged in groups, # ; and values of k\ calculated from reverse reaction and equilibrium constant, ki = k2 Ku O . The line is given by

log A, = -8.783 -4.965 (1000/T)

Ai = 1.65X 10-9 exp ( — 22.72IRT) cm3/particle-s.

c. Self-Consistent Set of Elementary Rate

Constants

This reviewer has at his disposal substantially more quantitative data than that available to Benson

and Axworthy about 10 years ago. Some quantitative differences in finally recommended rate factors

will appear, and yet the same qualitative conclusions

are reached: (1) The mechanism is adequately

given by that of Benson and Axworthy; (2) the

functions, Ay, A2 , Ay, Ay, and K\ are adequately

described by the Arrhenius equation, A exp (-E/

RT); and (3) we should demand self-consistency

between the rate constants and the equilibrium

constant:

Ki = ki / Ay = Ay/ Ay. (3—53)

The various observed rate constants and rate constant ratios, Ay, Ay, Ay/Ay, Ay, Ay, cover different

ranges of temperature and represent the work

of various sets of investigators. The least-squares

parameters fitted to the individual observed functions are not completely self-consistent, and it is desirable to find a self-consistent set for the recom- mended rate factors. Out of the six observable quan33
tities, ki, k2 , k3 , A' 2 /^3 , kj, and Ki, only three are independent. Benson and Axworthy took ki, kj, and K\

as their independent set, and derived k2 and A3 . With the quantitative data now available, kj covers

a relatively narrow temperature range and parameters based on it have a high error of estimate. We

take as our three independent sets of data: ( 1 ) the

extended k\ (figure 12 ), (2 ) the equilibrium constant

Ki (table 16), and (3) the extended A3 (figure 9B).

The least-squares parameters for the Arrhenius

equation of these functions are given in table 28,

and the fines in figures 9B and 12 are based on these

parameters. The function A2 was calculated from

k2 — kilKi, and the observed data are compared

to this function in figure 11. The function follows

Thrush’s [28] trend with temperature, and it falls between the somewhat different room-temperature

values as given by Thrush [28] and by Kaufman [70]. If the observed values of k2 are regarded as having

random errors of ±25 percent, there is satisfactory

agreement between the recommended function,

k2 = k1 IKi, and observed k2 . For extrapolation to other temperatures, we recommend k2 = ki/K\,

not the observed k2 function itself. The function,

kj, was calculated from kj — Kik3 , and this is the

function plotted through the data points in figure 6. The fine plotted through the data of A:2 /A 3 in figure 7

is based on the recommended values of A3 and k2 . The recommended values for the elementary

rate constants in the decomposition of ozone are

fisted in table 28 and repeated in the summary,

section 6.

Table 16. Equilibrium constant Ki for the reaction

O3 = O2 + O (particles/cm 3

) from JANAF tables

T 1000/T log Ki

200 5.000 -1.548

300 3.333 7.484

400 2.500 11.921

500 2.000 14.658

600 1.667 16.546

700 1.429 17.830

800 1.250 18.788

900 1.111 19.529

Table 17. Relative efficiencies for various foreign

gases in activating ozone at its low-pressure

limit

Approximate equations for calculation of Ki.

log A, = 25.5524 -5.4243 (1000IT)

log Ki = 24.2129 - 5.3520 ( 1000/T)

+ 0.4357 log T.

34
TABLE 18. Observed, values of ki {cm^jparticle-s), corrected to equivalent ozone

T iooo/r

---

log k i

- - ' J M Ref. T 1000/7

1 log k\ M Ref.

769. 1.300 -15.19 Ar [62]. 403. 2.480 -21.05

778. 1.286 -15.09 403. 2.480 -21.04

779. 1.284 -15.05 403. 2.480 -21.06

787. 1.270 -15.00 416. 2.404 -20.85 a [43].

792. 1.262 -15.09 425. 2.353 -20.69

812. 1.230 -14.93 425. 2.353 -20.49

824. 1.213 -14.81 429. 2.331 -20.60

825. 1.211 -14.85 473. 2.114 -19.26

827. 1.209 -14.76 473. 2.114 -19.36

828. 1.208 -14.76 477. 2.096 -19.09

840. 1.190 -14.72 483. 2.070 -19.08

840. 1.190 -14.67 488. 2.049 -18.83

841. 1.188 -14.70 488. 2.049 -18.89

846. 1.181 -14.54 488. 2.049 -18.96

871. 1.148 -14.41 488. 2.049 -18.84

876. 1.140 -14.43 507. 1.972 -18.24

881. 1.133 -14.44 507. 1.972 -18.35

890. 1.122 -14.35 514. 1.946 -18.26

910. 1.098 -14.24 516. 1.938 -18.31

910. 1.098 -14.18 557. 1.795 -17.77

689. 1.452 -15.94 n2 559. 1.789 -17.52

694. 1.440 -15.89 559. 1.789 -17.52

788. 1.269 -15.04 343. 2.915 -23.47 [47].

831. 1.202 -14.71 343. 2.915 -23.41

837. 1.193 -14.72 353. 2.833 -22.96

855. 1.169 -14.60 353. 2.833 -22.96

863. 1.158 -14.56 353. 2.833 -22.96

344. 2.910 -23.26 [99]. 363. 2.755 -22.68

354. 2.825 -22.90 Table 1. 363. 2.755 -22.68

373. 2.680 -22.27 363. 2.755 -22.58

392. 2.550 -21.60 363. 2.755 -22.57

420. 2.380 -20.80 363. 2.755 -22.55

388. 2.580 -21.58 [131]. 363. 2.755 -22.55

388. 2.580 -21.58 363. 2.755 -22.55

393. 2.542 -21.36 363. 2.755 -22.55

393. 2.542 -21.37 363. 2.755 -22.54

393. 2.542 -21.34 363. 2.755 -22.54

393. 2.542 -21.37 363. 2.755 -22.52

393. 2.542 -21.34 363. 2.755 -22.52

393. 2.542 -21.36 363. 2.755 -22.52

393. 2.542 -21.35 363. 2.755 -22.52

393. 2.542 -21.36 363. 2.755 -22.51

393. 2.542 -21.35 363. 2.755 -22.49

398. 2.512 -21.22 363. 2.755 -22.49

398. 2.512 -21.20 363. 2.755 -22.48

a As reinterpreted by use of integrated equation.

35
Table 18. Observed values of ki (cm3

/particle-s), corrected to equivalent ozone — Continued

T 1000/T log k\ M Ref.

363. 2.755 -22.47 344. 2.907 -23.00

373. 2.681 -22.19 344. 2.907 -23.08

373. 2.681 -22.19 344. 2.907 -23.17

373. 2.681 -22.15 352. 2.841 -23.04

373. 2.681 -22.14 362. 2.762 -22.57

373. 2.681 -22.10 362. 2.762 -22.60

383. 2.611 -21.89 363. 2.755 b - 22.43

383. 2.611 -21.80 363. 2.755 -22.48

383. 2.611 -21.80 363. 2.755 c - 22.48

353. 2.833 -22.96 363. 2.755 -22.44

353. 2.833 -22.96 363. 2.755 -22.55

353. 2.833 -22.96 363. 2.755 -22.52

363. 2.755 -22.55 363. 2.755 -22.51

363. 2.755 -22.54 363. 2.755 -22.43

363. 2.755 -22.54 363. 2.755 -22.17

363. 2.755 -22.52 364. 2.747 c - 22.06

373. 2.681 -22.19 364. 2.747 c - 22.47

373. 2.681 -22.14 364. 2.747 c - 22.48

373. 2.681 -22.14 364. 2.747 c — 22.35

353. 2.833 -23.00 364. 2.747 -22.51

353. 2.833 -22.96 364. 2.747 -22.51

363. 2.755 -22.57 364. 2.747 -22.49

363. 2.755 -22.55 373. 2.681 -22.00

363. 2.755 -22.55 373. 2.681 -22.14

353. 2.833 -23.00 374. 2.674 -22.09

374. 2.674 -21.92

353. 2.833 -22.96

363. 2.755 -22.55

363. 2.755 -22.55

363. 2.755 -22.55

303. 3.300 -25.26 [3].

b Added H2 02 . c Added H2 0.
Table 19. Least-squares jit of ki to Arrhenius equation for the various authors

References T Range K M

Intercept

log A,

Ex kcal/mole

Jones and Davidson [62] 769-910 Ar -8.99 21.8

Jones and Davidson [62] 689-863 n2 -9.02 21.8

Garvin [43] 416-559 02 -7.66 25.1

Pshezhetskii et al. [99] 34T-420 03 -9.70 21.4

Zaslowsky et al. [131] 388-403 03 - 8.21 23.6

Glissman and Schumacher [47] 343-383 O3 - 8.02 24.1

353-373 n2 -7.98 24.2

353-363 He -7.60 24.8

353-363 C02 -7.36 25.2

Axworthy [3] 303-374 03 - 8.68 22.9

log k\ = log A\ — Ei/2.303 RT.

A is Am converted to equivalent ozone.

Table 20. Least-squares fit of ki to Arrhenius equation for all data excluding authors one by one

All data

excluding references T range

Intercept

log dlj

E! kcal/mole

Jones and Davidson [62] 303-559 -8.39 23.5

Garvin [43] 303-910 -8.70 22.9

Pshezhetskii et al. [93] 303-910 -8.67 23.0

Zaslowsky et al. [131] 303-910 -8.67 23.0

Glissman and Schumacher [47] 303-910 -8.73 22.8

Axworthy [3] 343-910 -8.64 23.1

All data 303-910 - 8.68 23.0

Table 21. Observed values of ki averaged in groups for plotting in figure 12

Authors 1000/7" log k\ Authors 1000IT log k\

Jones and Davidson [62]

Zaslowsky et al [131] — Con.

1.11 -14.21 2.54 -21.35

1.135 -14.40 2.58 -21.58

1.185 -14.63

1.22 -14.85

' Pshezhetskii et al. [99] 2.38 -20.80

1.28 -15.10 2.55 -21.60

1.445 -15.92 2.68 -22.27

2.82 -22.90

Garvin [43] 1.79 -17.64 2.91 -23.26

1.955 -18.30

2.05 -18.90 Glissman and Shumacher [47].. 2.61 -21.85

2.10 -19.22 2.68 -22.15

2.34 -20.59 2.76 -22.58

2.40 -20.85 2.83 -22.96

2.92 -23.44

Zaslowsky et al. [131] 2.48 -21.05

2.51 - 21.20 Axworthy [3] 3.30 -25.26

37
Table 22. Observed values of kj, s

1 and other quantities deduced from kj

T iooo/r log kj log K'[ M log k3 (calc)

Ref. T 1000/r log kj log K'[ M log k 3 (calc)

Ref.

416. 2.404 -0.80 12.31 -13.29 a [431 363. 2.755 -3.10 10.35 -13.68

425. 2.353 -.55 12.51 -13.32 363. 2.755 -3.08 10.37 -13.66

425. 2.353 -.44 12.62 -13.20 363. .2.755 -3.07 10.38 -13.65

429. 2.331 -.40 12.64 -13.28 363. 2.755 -3.06 10.39 -13.64

473. 2.114 .95 13.79 -13.11 363. 2.755 -3.03 10.42 -13.61

473. 2.114 1.38 14.22 - 12.68 363. 2.755 -3.02 10.43 -13.60

477. 2.096 1.32 14.14 -12.84 363. 2.755 -3.02 10.43 -13.60

483. 2.070 1.30 14.09 -13.00 363. 2.755 -3.00 10.45 -13.58

488. 2.049 1.56 14.33 - 12.86 363. 2.755 -3.00 10.45 -13.58

488. 2.049 1.61 14.38 -12.81 363. 2.755 -3.00 10.45 -13.58

488. 2.049 1.64 14.41 -12.78 363. 2.755 -2.96 10.49 -13.54

488. 2.049 1.66 14.43 -12.76 373. 2.681 -2.89 10.49 -13.88

488. 2.049 1.73 14.50 -12.69 373. 2.681 -2.70 10.68 -13.68

488. 2.049 1.73 14.50 -12.69 373. 2.681 - 2.66 10.72 -13.64

507. 1.972 2.34 15.04 -12.50 373. 2.681 -2.57 10.81 -13.56

507. 1.972 2.43 15.13 -12.41 373. 2.681 -2.57 10.81 -13.56

514. 1.946 2.44 15.12 -12.54 383. 2.611 -2.32 10.99 -13.47

516. 1.938 2.63 15.30 -12.39 383. 2.611 - 2.11 11.20 -13.68

557. 1.795 3.28 15.81 -12.52 383. 2.611 -2.04 11.27 -13.40

559. 1.789 3.41 15.94 -12.42 353. 2.833 -3.62 9.90 n2

559. 1.789 3.41 15.94 -12.42 353. 2.833 -3.59 9.93

393. 2.545 - 1.88 11.37 -13.60 [99] 353. 2.833 -3.57 9.95

403. 2.481 -1.48 11.70 -13.55 363. 2.755 -3.18 10.27

413. 2.421 -1.17 11.96 -13.56 363. 2.755 -3.14 10.31

423. 2.364 -0.96 12.11 -13.66 363. 2.755 -3.08 10.37

423. 2.364 -.91 12.16 -13.62 363. 2.755 -3.02 10.43

423. 2.364 -.89 12.18 -13.60 373. 2.681 -2.70 10.68

423. 2.364 -.89 12.18 -13.60 373. 2.681 - 2.66 10.72

423. 2.364 -.83 12.24 -13.54 373. 2.681 -2.59 10.79

433. 2.309 -.60 12.42 -13.60 353. 2.833 -3.60 9.92 He

343. 2.915 -4.17 9.43 -13.75 [47] 353. 2.833 -3.55 9.97

343. 2.915 -4.03 9.57 -13.89 363. 2.755 -3.14 10.31

353. 2.833 -3.74 9.78 -13.90 363. 2.755 -3.00 10.45

353. 2.833 -3.59 9.93 -13.75 363. 2.755 -3.00 10.45

353. 2.833 -3.55 9.97 -13.71 353. 2.833 -3.52 10.00 C02

363. 2.755 -3.33 10.12 -13.91 353. 2.833 -3.51 10.01

363. 2.755 -3.24 10.21 -13.82 363. 2.755 -3.10 10.35

363. 2.755 -3.24 10.21 -13.82 363. 2.755 -3.09 10.36

363. 2.755 -3.21 10.24 -13.79 363. 2.755 -3.06 10.39

363. 2.755 -3.20 10.25 -13.78 373. 2.681 -2.60 10.78 -13.58 [28]

363. 2.755 -3.19 10.26 -13.77 373. 2.681 -2.51 10.87 -13.50

363. 2.755 -3.18 10.27 -13.76 400. 2.500 -1.50 11.70 -13.47 [56]

363. 2.755 -3.17 10.28 -13.75

a Reinterpreted by use of integrated equation.

K[' = kj (observed)/

A

3 (function),

log k3 (function) = — 10.8215 — 0.9526 ( 1000/7

1 )

A' 3 (calc) = Av(observed)//^i (thermodynamic).

38
Table 23. Observed values of k2 /k2 , cnriffp article, and value of k;i deduced from this ratio and observed k2 (where ranges of temperature overlap). The ratio k2 /k3 is corrected to equivalent ozone

T 1 000/7" log k2 /k3 M log A'3 Ref. T looo/r log k2 /k3 M log k3

278. 3.595 -18.53 -14.02 [26] 373. 2.681 -19.27 -13.73

291. 3.434 -18.68 -13.94 373. 2.681 -19.62 -13.38

298. 3.353 -18.77 -13.89 373. 2.681 -19.44 -13.56

298. 3.353 -19.09 [87] 373. 2.681 -19.46 -13.54

298. 3.353 -18.72 -13.94 373. 2.681 -19.62 -13.38

343. 2.915 -19.24 -13.63 [47] 383. 2.611 -19.47

343. 2.915 -19.42 -13.45 383. 2.611 -19.68

353. 2.833 -19.21 -13.70 383. 2.611 - 19.85

353. 2.833 -19.38 -13.53 353. 2.833 -19.38 n2 353. 2.833 -19.39 -13.52 353. 2.833 -19.41

363. 2.755 -19.57 -13.39 353. 2.833 -19.35

363. 2.755 -19.34 -13.62 363. 2.755 -19.47

363. 2.755 -19.38 -13.58 363. 2.755 -19.35

363. 2.755 -19.51 -13.45 363. 2.755 -19.52

363. 2.755 -19.46 -13.50 363. 2.755 -19.39

363. 2.755 -19.41 -13.55 373. 2.681 -19.43

363. 2.755 -19.58 -13.38 373. 2.681 -19.48

363. 2.755 -19.70 -13.26 373. 2.681 -19.58

363. 2.755 -19.68 -13.28 353. 2.833 -19.42 He

363. 2.755 -19.34 -13.62 353. 2.833 -19.38

363. 2.755 -19.31 -13.65 363. 2.755 -19.42

363. 2.755 -19.25 -13.71 363. 2.755 -19.55

363. 2.755 -19.44 -13.52 363. 2.755 -19.57

363. 2.755 -19.24 -13.72 353. 2.833 -19.46 C02 363. 2.755 -19.33 -13.63 353. 2.833 -19.48

363. 2.755 -19.19 -13.77 363. 2.755 -19.46

363. 2.755 -19.46 -13.50 363. 2.755 -19.48

363. 2.755 -19.55 -13.41 363. 2.755 -19.47

363. 2.755 -19.54 -13.42

363. 2.755 -19.44 -13.52

39
TABLE 24A. Observed values of k2 , cm^lparticle 2 s, in the presence of Ar corrected to equivalent ozone and other quantities derived from k2 .

1000/7

1 log k-2 (obs)

log K[ log Ay

(calc)

188. 5.319 -32.15 -3.30 -35.41

189. 5.291 -31.79 -3.52 -34.90

194. 5.155 -32.11 -2.51 -34.49

202. 4.950 -31.99 -1.60 -33.26

205. 4.878 -32.01 -1.22 -32.90

210. 4.762 -32.15 -0.49 -32.41

215. 4.651 -32.16 0.08 -31.82

220. 4.545 -32.21 0.66 -31.30

228. 4.386 -32.24 1.49 -30.47

235. 4.255 -32.31 2.22 -29.84

242. 4.132 -32.32 2.85 -29.18

247. 4.048 -32.34 3.30 -28.75

254. 3.937 -32.33 3.85 -28.14

262. 3.817 -32.76 4.88 -27.92

273. 3.663 -32.36 5.26 -26.69

273. 3.663 -32.31 5.21 -26.64

275. 3.636 -32.58 5.61 -26.76

276. 3.623 -32.74 5.84 -26.85

290. 3.448 -32.65 6.63 -25.82

296. 3.378 -32.68 7.01 -25.47

304. 3.289 -32.72 7.50 -25.03

307. 3.257 -32.73 7.67 -24.86

311. 3.215 -32.71 7.87 -24.62

315. 3.175 -32.75 8.11 -24.44

321. 3.115 -32.81 8.47 -24.18

328. 3.049 -32.82 8.81 -23.83

335. 2.985 -32.85 9.16 -23.51

343. 2.915 -32.85 9.52 -23.13

344. 2.907 -32.82 9.53 -23.06

348. 2.874 -32.89 9.76 -22.95

353. 2.833 -32.86 9.94 -22.70

358. 2.793 -32.89 10.17 -22.51

363. 2.755 -32.94 10.41 -22.36

368. 2.717 -32.97 10.63 -22.18

373. 2.681 -33.04 10.89 -22.06

K[ = ki (function)/A2 (observed).

log Aj (function) = — 8.6430 — 5.0394 (1000/jP).

Ay (calc) = Ay (observed) K\ (thermodynamic).

40
TABLE 24B. Observed values ofk>, cm 6

/particle 2 -s, in the presence of various foreign gases

T 1000/7" log T log k2 (obs)

log A

- 2 (eq 0.0

M Ref.

300. 3.333 2.477 -33.36 -32.89 He [70]

300. 3.333 2.477 -33.40 -32.83 Ar

300. 3.333 2.477 -33.19 -32.83 O2

300. 3.333 2.477 -33.25 -32.86 N,

300. 3.333 2.477 -32.82 -32.80 C02

300. 3.333 2.477 -32.82 -32.80 N,0

300. 3.333 2.477 -32.80 -32.81 cf4 300. 3.333 2.477 -32.47 -32.81 SF<; 300. 3.333 2.477 -32.22 -32.80 H2 0

Table 25. Observed values of k 3 cm:l s

1 Table 26. Equilibrium constant K;J for the reacT K 1000/7" M log A’

3

Rel.

769 1.300 Ar -11.98 [62]

812 1.230 -12.19

827 1.209 -11.89

840 1.190 -12.16

846 1.181 -11.85

876 1.140 -11.62

910 1.098 -11.74

788 1.269 n2 -11.90 [62|

831 1.202 -11.80

837 1.193 -11.87

863 1 . 158 -11.82

k tion o + o3 ^o2 + 0-2 From JANAF tables and

k

4 the calculated function for the reverse reaction k 4

T 1000/7" log K3 Ref.

3500. 0.286 5.96 [57]

4000. .250 5.21

4500. .222 4.63

5000. .200 4.16

5500. .182 3.78

6000. .167 3.47

log K:i = - 0.0254 + 20.941 ( 1000/7’)

.

log kz = - 10.697- 1.047 (1000/7").

log k4 = - 10.672 -21.988 (1000/7").

Table 27. Summary of least-squares parameters for ozone kinetics

Equation Parameter k 1 k\ (ex) k.j A2/A-3 A-2 A'

3

A log A -8.68 -8.78 ’15.25 -22.52 -34.00 -10.82

E, kcal 23.0 22.7 30.5 -5.1 -1.8 4.4

B log B 2.86 -10.1 -67.2 -37.4 -25.4 -26.4

m -3.61 0.44 26.9 5.0 3.0 4.9

E' 26.8 22.4 7.9 -8.4 -0.25 -0.44

C log C -77.6 -90.4 -96.0 0.49 -24.1 -25.1

n 21.6 26.3 36.3 -7.8 -3.47 4.48

Equations:

A k — A exp ( —E/RT) B k = B T

m exp {—E'/RT)

C k = CT«

k\(ex)= k\ (obs) and k2K\.

k3 = k:i { obs) and A 2 / ( A2/A3)

-

41
Table 28. Recommended values of constants

(200-900 K)a

Self-consistency between Ay, Ay, Ay, Ay, and Kx in

terms of Arrhenius equations.

E

,

keal/mole

log Ay = — 8.783 — 4.965 (1000/D 22.72

based on all observed Ay and Ay/Ci.

log Kx = 25.552 - 5.424 ( 1000/7

1 ) 24.82

based on JANAF tables,

log Ay = log Ay — log Kx = -34.335 + 0.459 (lOOO/T) -2.10

log Ay = - 10.697- 1.047 (1000/7

1 ) 4.79

based on observed Ay, kj/Kx, and

Ay/(Ay/Ay).

log Ay = log K i +log Ay = 14.855-6.471 (lOOO/T) 29.60

log Ay = - 10.672-21.988 (1000/7

1 ) 100.6

based on observed Ay and K3 from

JANAF tables.

Ay = 1.65 X 10" 9 exp (—22.72/RT) cm3 /particle-s

Ay = 4.63 X 10 -35 exp (2.10/RT) cm6/particle 2 -s Ay = 2.00 X 10~ n exp (—4.79/RT) cm3 /particle-s

Ay = 7.16 X 10 14 exp (-29.60/RT ) s" 1 Ai = 3.56xl025 exp (— 24.82//?7

1 ) particle/cm 3 Ay = 2.12 X 10 _u exp (—100.6/RT) cm3 /particle-s

a The reactions are:

1 . 0.3 + M —* O + 02 + M

2. O + 02 + M —> O3 + M

3. O + O3 * 02 + 02 4. 02 + 02 ^ O + O3

Kx is the equilibrium constant for reactions 1 and 2.

k.i is the Jahn mechanism rate constant for ozone

decomposition in excess oxygen, see eq (3-8).

4. Isotopic Exchange Between Oxygen Species

Molecular oxygen is readily obtained highly

enriched in the isotope of mass number 18. Exchange reactions can be followed by analysis

with mass spectrometers. Unperturbed molecular

oxygen can be stored indefinitely at room temperature without measurable exchange:

16 02 + 18 02 16 018 0 + 16018 0 (slow). (4-1)

Similarly, direct exchange between molecular ozone and molecular oxygen is slow:

and direct exchange between molecular ozone with

itself is slow:

,8 03 +,6 03 -> 18 0,6 02 + 18 02

,fi 0 (slow). (4-3)

However, the exchange between oxygen molecules

occurs very rapidly if oxygen atoms are produced

in or added to the system. The elementary exchange

reaction appears to be

k5 0 + 02 ^ 02 + O, 18 02 + ,6 0.3

18 018 016 0 + 16 02 (slow), (4-2)

42

(4-4)
which is measurable by virtue of exchange of iso- topic species:

160 + 18 02 -> 16 018 0 + 18 01 . 18 0 + 16 02 -> 16 018 0 + 16 OJ

chain (4-5)

net 18 02 +

1602 —» 216 018 0.

When ozone was photolyzed in the presence of

18 02 and 16 02 , the quantum yield for exchange

between the oxygen species was 125 at room

temperature [61]. Results of four different investigations giving quantitative values of k-0 are summarized in table 29.

The value of the rate constant is

k5 — 1.0 X 10-12 cm3/particle-s

Table 29. Observed values of isotopic exchange

reactions in oxygen species

0 + 02 — ; 02 + 0

T log h

(cm3 /particle-s)

References

272 -11.8 Ogg and Sutphen

[93, 94].

273 -11.77 Brennen and JNiki

[18].

298-402 — 11.19 — 239/7’ Jaffe and Klein [55a].

300 -12.0 Herron and Klein

[53].

at 273 K, which is a moderately large bimolecular

rate constant, and little or no activation energy is indicated for this reaction. In any system of O, 02 , and O3, several fast reactions will occur simultaneously; the most rapid reactions at low temperature are: O + 02 02 + O (4-6)

O + 02 + M 03 + M

O + O3 02 + 02 .

The ratio of rate 5 to rate 2, at room temperature,

depends only on the concentration of gas M:

Rate 5 _ k5 Rate 2 &2 [M]

(4-7)

and this ratio is plotted as a function of total pres- sure in figure 13. The exchange rate is faster than ozone formation at all pressures below 40 atm.

Between 0.02 and 0.2 atm the exchange reaction occurs 1000 to 100 times as often as the formation

of ozone. The ratio of rate 5 to rate 3 depends on

temperature and the ratio of ozone to oxygen:

Rate 5 _ £5 [Q2 ] . _R

Rate 3 A- 3 [03 ]

' j

This ratio of rates is plotted in figure 14 as an

Arrhenius plot for various values of the ratio

[03 ] / [02 ] . Under most conditions rate 5 is faster

than rate 3. At room temperature rate 5 exceeds

rate 3 if the ozone is less than 99 percent.

273, adopted value, log k$, — 12.0.

log M /atm

V Figure 13. Relative rate of oxygen exchange

(O + 02 02 + O) to ozone formation

(O + 02 + M ^

O3 + M) as a function of equivalent ozone M pressure in atmospheres; room

temperature, but these ratios are not expected

to vary rapidly with temperature.

43
T°K

o o o o o o

o o o o o o

CO N CD LO ro

1000/

T

FIGURE 14. Relative rate of oxygen exchange

(0 + 02^02 + 0) to oxygen atom reaction

with ozone (0 + 03-^02 + O2 ) as function

of the ratio of ozone to oxygen [Osj/fC^] and

temperature (on the assumption that ks

does not change with temperature ).

5. Discussion

5.1. Why Does K\ = k\lk<i at the LowPressure Limit of a Unimolecular

Reaction?

At the low-pressure limit of a unimolecular reaction, the reactant has an extraordinarily nonequilibrium distribution over vibrational state, which gives

large measurable consequences (easily a factor of

1000 in observed rate). At the low-pressure limit of

a bimolecular association the reactants still have an

essentially equilibrium distribution over states. At the molecular level, the elementary chemical

dissociation is the flying apart of an excited polyatomic molecule: for a bimolecular association it is the stabilization by collision of an excited molecule.

One may well ask, how can the average of a molecular transition function over a nonequilibrium

distribution function possibly be equal to the aver- age of an energy transfer function over an essentially

equilibrium distribution function? In terms of ozone

kinetics, one asks, how can K\ possibly equal A 1 /A 2 at the nonequilibrium, low-pressure limit of the

unimolecular reaction?

The activation energy for the dissociation of O2 is less than the bond dissociation energy. Also, the

activation energy of the decomposition of ozone is less than the bond dissociation energy. This effect can be formally explained in terms of a rate-constant

expression that has the form

k = BTm exp (-D/RT), (5-1)

where D is the dissociation energy and m is some

constant. The activation energy, as given by

eq (1-38), is EA = D + mRT. (5-2)

If m is negative, the observed activation energy is less than the bond dissociation energy. For lowpressure dissociations, mRT represents the thermal

excitation of the internal coordinates of the molecule

above the zero-point vibrational energy. The average

energy of a harmonic oscillator above the zero-point

energy is

44
The energy term mRT is a classical-mechanical,

upper-limit estimate of the quantum mechanical

average energy as given by eq (5-3). For 02 at 5000 K the average vibrational energy of the molecule is 8 kcal, and at 10,000 K the average vibrational energy of the molecule is 18 kcal. Thus the

empirical value of m= — 1 as deduced in section 2

is largely ascribable to average vibrational excitation of the 02 molecule (compare relation 2—6). For

ozone at 300 K, the three vibrational energies are:

Frequency (cm *) Average energy (kcal)

705 0.08

1043 .02

1110 .02

Total 0.12

The bond dissociation energy of ozone at absolute

zero is 24.2 kcal/mole; the minimum activation

energy in terms of the oscillators is thus 24.1 kcal/

mole; but the observed activation energy is 22.7

kcal/mole. If we invoke three degrees of rotational

energy of reactant with only two degrees of rotational energy of dissociating fragments, another

2 RT or 0.3 kcal can be found. However, it remains a

fact that the observed activation energy for the ozone dissociation is substantially less than can be

explained by the existing simple theories (Rice,

Ramsperger, Kassel, Marcus, etc.).

Thus we have two interesting facts to discuss:

(1) Why do the ratios of nonequilibrium rate constants give the correct equilibrium constant, and

(2) Why is the activation energy for ozone so much

less than the bond dissociation energy?

dissociation relaxation time actually observed.

The rate constant, ki, for ozone represents the

low-pressure (second-order) limit of a unimolecular

decomposition, and ko represents a bimolecular

recombination at its low-pressure (third-order)

limit. The extended theory of Rice and of Widom

predicts that even for these extreme cases the ratio

of observed rate constants should give the thermodynamic equilibrium constant. In this review we

have been careful to keep separate what experiments actually show and what theory actually

predicts. In the present instance there is satisfactory agreement between theory and experiment on

this score.

b. Physical Model as Derived From Rate of

Exchange

The reaction of hydrogen atom, H, with hydrogen

molecule, H2 , occurs over an energy barrier, the H3 collision complex [59]. The interaction of atomic

oxygen with molecular oxygen does not occur over

a potential barrier but rather over a potentialenergy well, namely, ozone. The exchange reaction 5

is probably of the “compound nucleus” type with an intermediate complex lasting about 10-11

s, as opposed to the H3 complex which lasts only for a period of about one vibration:

0 + 02 4 03*

Of —

>

02 + O (5-4)

Of + M 03 + M.

With this simplified scheme the rate constants for

reactions 5 and 2 are identified:

a. Mathematical Models

General aspects of this question have been

discussed recently by Widom [121a] and by Rice

[101a]. In terms of general arguments Rice con- cluded that if unambiguous reaction rate constants can be measured experimentally, then the quotient

of the experimentally determined constants will

give the equilibrium constant. Widom illustrated

and enlarged on this theorem with a detailed treat- ment of a very simple example, a reversible isomerization. The theory of Rice is logical and persuasive,

but not rigorous. The example given by Widom is rigorous; but the case is special, forward and

reverse reactions being first order; and one is not

convinced as to its generality.

The experimental data for both the decomposition

of oxygen and for the decomposition of ozone indi- cate that the ratio of forward to reverse rate constant agree very well with the chemical equilibrium

constant. These examples represent extreme conditions. At the high temperature of observation, the

vibrational relaxation time of 02 approaches the

k5 — d/2

ko = b{d[c)

.

(5-5)

(The factor 1/2 comes from the equal probability of

excited 16 016 018 0 breaking up as

1(i 0+ lfi 018 0 and

180 + 160160.) The ratio of rate 5 to rate 2 is given by figure 13,

and it is generally much larger than one. The principle of microscopic reversibility states that at equilibrium every molecular process and its exact reverse occurs at the same average rate. Conversely,

if a molecular process and its exact reverse occur

at the same average rate, the reactants and products

are at equilibrium. If the molecular process d

occurs at approximately the same rate as its inverse

c (b is a rare event, figure 13), then the highly excited

vibrational states of ozone (Of above the critical

energy) are in equilibrium with 02 and O and

therefore in a distribution with respect to ozone

the same as that at chemical equilibrium. The

population distribution among many of the lowlying vibrational states of ozone must be that

45
corresponding to equilibrium. If ozone was at equilibrium with all of its vibrational states up to the critical energy, then the rate of reaction 1 would

necessarily have its high-pressure limiting value

since O2 + O sets up an equilibrium distribution of

0| above the critical energy. Thus the nonequilibrium distribution that gives rise to the “fall-off”

with pressure of a unimolecular reaction must

apply primarily to states just below the critical

energy. For such a band of states, activation to the

high-density states above the critical energy is faster than deactivation to the low-density states well below the critical energy. The “rate determining step” in ozone decomposition is activation up

to a band of states a few kilocalories per mole

below the critical energy (hence the activation

energy of 22.7 kcal whereas the bond energy is

24.2 kcal). Within this band further activation to dense upper states and dissociation to O2 and O

are faster than deactivation to relatively nondense

lower vibrational states. For the bimolecular association, the reactants O and O2 associate and fly

apart many times before they are deactivated below

the critical energy, and even that is not enough

since re-dissociation is more rapid than further

deactivation. The “rate determining step” is further

deactivation to get across the “nonequilibrium

band” of states. Thus, the observed rate of exchange gives a

clear, qualitative, physical picture of why the

activation energy is less than the bond-dissociation

energy and why the ratio of rate constants at the

low-pressure, nonequilibrium limit of unimolecular

reactions, still gives the equilibrium constant.

6. Summary

Thermal, homogeneous reactions of O3, O2, and

O are well accounted for by a set of seven elementary chemical reactions:

D. O2 + M —» 0 + O + M

R. O + O + M —

O2 + M

1. O3 + M —* O + O2 T M

2.0 + O2 + M —* O3 + M

3. O + O3 * O2 + O2

4. O2 + O2 —* O + O3

5. O + O2 —* O2 + O (exchange)

The experimental data obtained by many different investigations have been combined to obtain

rate constants as a function of temperature for each

of the first six elementary reactions and to obtain

the rate constant of reaction 5 at room temperature.

The recommended rate constants for the seven

elementary reactions are (where energies in the

exponent are kilocalories/mole):

Ad(02 ) = 4.57 X 10_5 r

_1 exp (-118.7/RT)

cm3/particle-s

*«(O2 ) = 3.80x lO-30^-1 exp ( — 0.34/R7

7 ) cm6/particle2 -s

kp(02)lko(Ar) — 10.8 (and A-«(02 )/^(Ar) 10.8)

T: 300 to 15,000 °K for Ar as M

1000 to 8000 °K for 02 as M

A1 (03 )=1.65x 10- 9 exp (-22.72/RT)

cm3/particle-s

A2 (03 ) = 4.63 X IO-35 exp (2.10/R7

1 ) cm6/particle2 -s

A3 = 2.00 X 10-11 exp ( — 4.79/RT)

cm

3

/particle-s

*4 = 2.12 X 10- 11 exp (-100.6/RT)

cm3 /particle-s

*5 = 1.7 X 10-12 cm3/particle-s

T: 200 to 1000 °K

Relative efficiencies of various M gases for reactions 1 and 2 are given in table 17. As an aid to the reader in forming his own

estimate of the magnitude of error in these functions, we have presented graphs of actual experimental data for the first five elementary rate constants, together with a curve representing the

recommended function:

Ad figures 1A and IB

A"/? figure 4

Ay figures 5 and 12

A2 figure 11

A3 figure 9B

Over the actual range of observations we present

the following estimates 6 of the uncertainty in the

logarithm of A:

log Ad ± 0.3

log kR ± 0.3

log Ay ±0.1

log k-i ± 0.2

log A3 ±0.2

6 These error estimates are subjective and personal. Consideration is given to the

scatter of points for given authors (see the figures in this report), the agreement be- tween different authors, the stability of the overall picture to inclusion or omission

of any one author, possible systematic errors especially under extreme conditions, and conformation of the experimental data to gas-phase reaction-rate theory. Within

the temperature ranges of the experimental data, we feel that a 95 percent confidence can be placed on the rate constants plus or minus the error interval given here.

46
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49

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