Reaction rate coefficients for flame calculations

COMBUSTION A N D F L A M E 32, 1-34 (1978)

Reaction Rate Coefficients for Flame Calculations D. E. JENSEN and G. A. JONES Mlnurrv of Defence. Propellants. Explosives and Rocker Motor Establishment. Westcorr. A yletbury. Bucks. England

A list of recommended rate coefficients for chemical reactions occurring in flames is given Rate coefficients, expressed as functions of temperature for the range IOOO • T • 3000 K, are either taken from experiments described in the scientific literature or estimated by comparison with rate coefficients for analogous reactions. Brief notes on the origins of recommended coefficients are included and rough uncertainties are attached to the listed values. A table showing reaction equilibrium constants a~ function~ of temperature is also provided

INTRODUCTION This article contains a list of chemical reaction rate coefficients compiled for use in calculations of flame structures. In many respects it is an updated version of a previous report ! , published in 1971, although the number of reactions considered is greatly increased. Many of the rate coefficient expressions recommended in 1971 are substantially revised in the light of work published during the past six years. A ma)or specific application of the data given in this article at PERME Westcott is to the calculation of electromagnetic properties (e.g. infrared and visible radiation emissions, free electron content) of rocket exhaust flames, as illustrated in [2]. This accounts for the emphasis on reactions of metal derivatives, including charged species, for which no previous compilation of evaluated rate data is available in the literature. Although this application was uppermost in the authors' minds when the list of recommendations was drawn up. the values given should be useful in a wide range of other combustion contexts, including those of MHD power generation, industrial burners, fire inhibition, combustion driven lasers and turbine engines. The reactions for which rate coefficients are listed in no sense constitute a reaction mechanism for any particular calculation: the reactions incorporated in the scheme for such a calculation Copyr~ht ~ 1978 by The Combustion Institute Published by El~vlE,r North-Holland, Inc.

must always be selected in the light of the particular characteristics of the combustion system under consideration and the Name structure properties required. Thus, although selections from the reactions of this article should be found to account for most of the required properties of rocket exhausts (which are turbulent diffusion flames), the listing is clearly incomplete in other combustion contexts; it does not include, for example, reactions involving sulphur or soot, omits many reactions involving nitrogen and (except for sodium and potassium atoms) does not consider reactions of particular internal energy states of atoms or molecules. Rate coefficients listed are defined in the manner usually adopted in descriptions of chemical rate processes. For example, the rate coefficient k of the reaction a,4 + b B + c C .... a'A' + b'B' + c'C' ...

is defined by

k=-

1

alAl

a[AI°[B]b[C] ~-..

at

I

alIBI

b i A l ° l B I b l C 1 <...

dt

....

0OI 0-2180/78IOO32-OOOI $O135

D. E. JENSEN and G. A. JONES The rate coefficient for the reverse reaction is similarly defined by I

k, = _

dl,4'l

a'IA'I°'IB'Ib'ICI~'.., I

dr dla']

b'lA'l°'l¢lb'lC'l~'-., dt

At equilibrium (when the reaction is balanced) the net rate of change of [A 1, [ a l . [61 "'" is zero. For species A, then

=k'i,4'l =' IB,I b' ICI c' ... - =I¢IAI=IBIblCl

~ .... O.

(Similar expressions arise from consideration of the net rates of change of [B], [C] "" .) Hence,

k k'

IA'I°'IB'I

b'lC'lc' ...

1,41 ° lal b 161c

' "

where K is the equilibrium constant. TermolecuIar rate coefficients are expressed in units of ml 2 molecule - a s- ) and bimolecular rate coefficients in ml molecule - ) s- ) . All temperatures are expressed in Kelvins. The rate coefficients given are based, wherever possible, on experimental measurements. Where no measurements are available (as applies to a large number of reactions), coefficients are estimated by comparison with those for similar reactions, allowances being made in the light of collision and transition state theories for probable steric, reduced mass and cross section differences. Although recent progress on theoretical calculations of unmeasured rate coefficients has been encouraging, such handicaps as the lack of accurate molecular configurations and potential energy surfaces for transition states make it difficult to justify a more rigorous approach at present. It is urged that under no circumstances should the reader make use of a rate coefficient given in this article without considering the comment indicating the source of the value.

The rate coefficients are intended for use in calculations on combustion systems at temperatures between I000 and 3000 K. Extrapolations outside this temperature region, especially to lower temperatures, should be made only with extreme caution. The "Arrhenius" forms in which k and K are expressed merely provide convenient empirical fits for the specified temperature range. In nearly all cases, however, the experimental data are not accurate enough to warrant a more complicated form of expre~on for this range. The uncertainty factor UF given for each rate coefficient is such that k X UF and k/UF provide probable approximate upper and lower bounds respectively to k at that temperature within the range 1000-30OO Kelvins for which the rate coefficient is least accurately known. Such uncertainty factors take account of the random errors quoted by authors, of possible systematic errors and of th,: need to extrapolate available results into temperature ranges often widely different from those of the experiments themselves, and are consequently somewhat subjective. Their principal purpose is to give the nonspecialist user an opportunity to assess the likely maximum error introduced into his calculation of a particular flame structure feature by uncertainty in a given rate coefficient. Uncertainty factors of I0 or I00 appear frequently, as do those of 30; this last value is intended to convey nothing more precise than that UF is greater than I0 but less than I00. Large uncertainty bounds associated with the rate coefficient of a given reaction do not necessarily imply that there may be substantial errors in calculations involving this reaction. On the one hand, a reaction with large uncertainty limits in its rate coefficient may in any case be so fast that it is close to chemical equilibrium; on the other, a different reaction, also with large rate uncertainties, may in any case be so dow that its contributions are overwhelmed by those of concomitant mixing processes. Two particularly difficult points in the description of chemical kinetics arise in the case of the reactions involving "third bodies" or "collision partners" M (e.g. those in groups A and G). The first is that different third bodies have different (and sometimes unknown) efficiencies in these

RATE COEFFICIENTS FOR FLAME CALCULATIONS

reactions. Here an attempt is made to give rate coefficients averaged for the more effective third bodies (e.g. CO a, HaO, N a) in a typical flame. The concentration [M] is then taken as the sum of concentrations of all gas phase species present. The deficiencies of this approach are clear: our defence of its use is that the errors which it introduces into practical flame calculations are usually (although not always) small by comparison with possible errors in rate coefficients for individual third bodies. The attention of the reader with strong interests in relative efficiencies of different M is directed to more detailed and specialist-oriented reviews (e.g. Refs. [3-51, 180). A second difficulty is that the third body reactions (and their reverse reactions) actually take place via stepwise processes involving excited molecular or atomic states, vibrational and electronic. Consequently the reverse reactions often have overall rate coefficients much higher than the **collision frequency". One should really take account of individual reactions of these states rather than choose. as here, overall rate coefficients for overall-and, in a sense, artificial-reactions. Fundamental data currently available are insufficient for dealing with this problem. Alternative formal descriptions of the chemical rate processes occurring in flames (e.g. those in terms of cross sections expressed as functions of molecular energy rather than in terms of rate coefficients expressed as functions of temperature), which in the future may resolve this difficulty, lead at present to even greater problems. The "collision frequencies" to which kineticists often refer rate coefficients are generally those calculated on the assumption that all chemical species are in ground electronic, vibrational and rotational states, although this common usage is sometimes rather misleading. The simplest collision theory expression fi~r a bimolecular rate coefficient k is k -- p n o Z ( 8 K T / r r # ) t / 2 exp (-E/KT)

where p is a "steric" or "probability" factor, no ~ the collision cross section. K the Boltzmann constant,/J the reduced mass and E the activation energy. The product pnoa(8tcT/ntJ) l l a is termed the pre-exponential factor, and ~ o a ( 8 K T / n p ) t l a is

(loosely) called the collision frequency, even though p and no 2 are experimentally inseparable. For a typical reaction with reduced mass 2.5 X I0 - ~ 3 g and collision cross section 3 X I0 - 1 9 m z at 1600K, thecoflision frequency is 5 X 10- 1 o nd molecule- 1 sec- l Thus a preexponential factor of 5 X 10- 1 ° nd molecule- I sec- l would, in this ternunology, imply a steric

factor of unity. The values of rate coefficients given are considered to be the best that can be gleaned from the literature published up to the end of 1976. although a few later references are given. The notes on sources of data are brief and the list of references far from complete: much valuable kinetic work is not acknowledged or discussed in order that the report should remain relatively short.

The rate quotient law (which states that the ratio of the rate coefficient k~ of the forward reaction to the rate coefficient k_~ of the backward reaction is equal to the equilibrium constant K,. and apparent deviations from which arise only from inadequate descriptions of rate processes) is assumed to hold for all reactions. Occasional difficulties, the source of which is noted above, result from this assumption for the overall reactions of type A + B + M ,e A B + M. but these difficulties must be accepted at present. The equilibrium constants listed are deliberately set in a form that makes it easy to determine the implied pre-exponential factor and activation energy in k_, from the tabulated value of ki. This form introduces some small errors in Ki at the extremes of the temperature range considered (up to ahnost a factor of 2 in some cases), but the uncertainty factors in both k~ and k_, are almost always much larger than the errors so incurred. The method of numbering reactions is retained from Ref. [ I ]. It keeps arbitrarily related reactions in groups and enables one to add reactions conveniently as new data become available. LIST OF RATE COEFFICIENTS Bimoleculaf rate coefficients are in units of mi molecule-t sec-I ; termolecular rate coefficients

in ml 2 molecule - 2 sec - l .

D. E. J E N S E N a n d G. A. J O N E S Reactton

Number

Rate Coefficient

Uncertainty Factor

O+O+M-O2*M

AI

3 x 1 0 - 3 4 e x p (+900/1")

O+H+M~OH+M

A2

I x 10-29T -!

I0 30

H+H+M~H2+M

A3

3 x 10-3OT-I

30

H+OH+M-

H20+M

A4

I x 10-25T -2

I0

CO+O*M

~ ('O2 + M

A5

7 X 10 - 0 3 e x p l - 2 2 0 0 / T )

30

OH+H2+

H20+H

BI

1.9 x 10 - 1 5 T l ' 3 e x P ( - 1 8 2 5 / T )

2

O + H2 + O I I + H

B2

3 . 0 x 10- 1 4 T e x p l - 4 4 8 0 / T )

1.5

H+O2+OH+O

B3

CO + O H + C O 2 + H

B4

2 4 x I0- I O exp ( - 8 2 5 0 / T ) 2 8 x 10 - 1 7 T t . 3 e x p ( 3 3 0 / T )

3

OH+OH+

H20+O

B5

I x 10 - 1 1 exp(-SS0/'l')

3

CO + 0 2 ~ CO 2 + O

B6

4.2 x 10- 1 2 exp(--24000/T)

3

1.5

H *CI2 ~ HCI + CI

CI

1,4 x I0 - I O exp (-580/'T)

I0

C1+ H 2 ~ H C I * H

('2

!,4 x I0 - 1 ! e x p ( - 2 1 3 0 / T )

5

H20*CI~

C3

1,6x I0 - I O e x p ( - 9 1 O O / T )

I0

C4

4 x 10- 1 2 e x p ( - 2 5 0 0 / T )

30 30

HCI+OH

OH + ( 1 ~ H C I + O H2 + F

('5

H + F2 ~ HI+'+ F

C6

7 x 10- l l exp (--1650OFT) I x IO-I°exp(-.700/T)

Li+HCI-

LiCI+H

DI

2 x 10- t O c x p ( - 5 o o / ' r )

30

Na+HCI-

NaCI+H

D2

2 x io- i °

exp(-4000/T)

30

exp(-2500[T)

30

H+HF~

10

D3

3 x 10- l °

Li * 1120~ LiOH + H

D4

6 X 10 - 1 1 e x p ( - I l O O O / ' r )

30

Na+H20~

D5

8 × I0 - l i

expl-22000/"D

30

I)6

I x I0 - 1 0 exp(--20000/T)

30

K + I I B O 2 - * K B O2 + H

D7

2 x I0 - I O e x p ( - 4 2 0 0 / T ~

30

K + H2WO, t ~ KHWO 4 * H

D8

2 x I0 - t O exp(-5OO/'T)

30

K+H2MoO 4~

D9

2 x 10- t O exp(-5OOFl')

30

N a + H B O 2 ~ NIBO 2 + H Li + HBO2 - t.iBO2 + H

DIO

I x I0 - I O e x p ( - 5 0 0 O F r )

30

DII

I x I0 - I O exp ( - 1000/T)

30

Cs + H 2 0 - C ~ ) H + H

DI2

2 x I0 - I O exp(-18OOO/T)

30

H+CI+M-

El E2

4 x 10"-2s T - 2

I00

2 x IO- 3 3 exp (900/T) 3 × 10- 2 9 T - !

30

3 x 10- 3 0 T - ! ' 5

I00

3 x 10- 2 8 T - I 5 x 10--28 T - i

30

1:2 13

6 x 10- 2 8 T - !

30

LI+CI+M • LiCI+M

1:4

2 x 10-28 T-I

30

Na+CI+M

1.5

3 x I0 - 2 8 T - 1 5 × I0 -.28 T - I

30 30

K+HCI-

KCI+H

K +H20~

NaOH+H KOH+H

KHMoO 4 + H

HCI+M

CI+CI + M ~ C I 2 + M t1+1 + M ~

HF+M

I +F+M-

F2+M

L3 I-.4

Li+OH*M

* LiOH+M

FI

Na+OH+M~ K+OH+M-*

K*CI+M~

NaOII+M KOH+M • NaCI+M KCI*M

1:6

30

30

RATE COEFFICIENTS FOR FLAME CALCULATIONS Reaction Li*÷ e- t M~

Number

Lit M

Rate Coefficient

Uncertainty Factor

GI

4 X 10-24T ''1

Na ÷ ÷ e-- • M ~ Na • M

G2

4 X I0 -24 T -!

5

K°÷e-

G3

4X

5

Cs÷÷e - +M-*Cs+M

G4

4 X 10 - 2 4 T - 1

5

In*÷c-

G5

6 X 10 - 2 1 T - 2

10

t M-',K÷

M

tM~In+M

10-24 T-!

5

Li * • CI - "~ L, + CI

HI

7.6 X 10 - 8 T - ° . •

10

N a * • C I - -.* Na • CI

112

2.2 X 10- 8 T -°.~'

l0

K * + C I - --, K ÷ CI

H3

17 X 10- ~ T - ° . 5

I0

L i * • O H - ~ L i t OII

H4

I X 10 -41 T -'O.~'

I00

Na ÷ ÷ O H -

H5

I X 10 - 8 T - ° . 5

100

K÷ + O H - .-,, K ÷ OH

H6

I X 10 -41 T - ° - 5

I00

Li ÷+ CI - ÷ M --~ LiCI + M

117

1.2 X 10 - 1 5 T - 3 . 5 exp (- 300/-r)

i0

Na ÷ • C I - + M

"-~Na ÷ OH

~NaCI•M

H8

5.5 X 10 - 1 6 T - 3 . S e x p ( - ? 5 0 / T )

10

K * ÷ C I - • M " KCI+ M

119

1.6 X 10- I S T - 3 . 5 exp ( - 2400/ '! ')

10

OIl•e-÷M

Jt

3 x 10 - 3 !

I00

J2

I x 10- 3 2 exp (3000IT)

30

HCI•e--CI-÷H

J3

1.4 x 10- 7 exp ( - 7600/-r)

i0

HBO2+e--

J4

x 10-41 exp ( - I IO00/T)

100

CI+e-+

"OHM -CI-

÷M

÷ M

BO 2 - + H ~HMoO 4-÷H

J5

x 10- 8 e x p ( - 1 5 0 0 / T )

I00

H 2 W O 4 ÷ ¢ - - HWO 4 - • :1

J6

x 10 - 8 e x p ( - IO00/T)

I00

H20 + e-

J7

x 10- 8 e x p ( - 3 5 0 0 0 / T )

100

J8

x 10- 9

30

J9

x 10 - 9

30

JlO

x I0 - a o

30

H2MoO 4 • e -

-OH-

• H

MoOa -

HMoO 4- • H ~

HWO a - • H O2•e-

• H20

wo O-*H20

•M-O2-•M

LI

2 x 10- 7 e x p ( - 2 3 0 0 0 / ' r )

I00

L2

3 x 10- T e x p i - I S O O O / T )

I00

KH20* * M - K ÷t H20+ M

L3

I x 10 - 7 exp(-IOOOO/'r)

I00

LiH20*÷e-

-Li÷H20

L4

I x 10 - 7

30

Nit

L5

I x 10 - 7

30

L6

I x 10 - 7

30

L,H20 ÷•CI--Li÷CI÷H20

L7

4 x 10 - 8

100

N a H 2 0 * • ( ' 1 - -- Na + CI • 1120

LB

4 x 10 - 8

I00

KH20*•CI-

L9

4 x i0 -8

I00

LiH~O ÷ t M - L i * t NaH20÷ t M -

Na't

NaH~O++e -KH20* • e-

H2Ot M H20+ M

H20

~ K ÷ H20

~K*CI•H20

LIO

4 × 10 - 8

100

N a H 2 0 * • O H - - Na • OH • H 2 0

LI I

4 × 10 - 8

100

KII20* • OH-

LI2

4 x 10 ' - s

I00

MI

I x 10- 2 9 T - t

I00

M2

2 x 10- t O e x p ( - I S 0 0 / T )

100

N a t CIO ~ NaCI + O

M3

3 × 10 - I O exp ( - I500/T)

100

K+CIO-KCI+O

M4

3 x I0 -I Oexp(-I SOO/ T)

I00

L i H 2 0 ÷ • OH - -

CI+O÷M~ L|tCIO

LI•OH

• H20

- K • OH • H 2 0

CIO÷M

~ bCItO

D. E. JENSEN and G. A. JONES Reaction

Number

Rate Coefficient

Uncertainty Factor

C10+ H ~ HCI+O

M5

I x 10 - t O ¢ x p ( - 5 0 0 / T )

30

C10÷O~O+02

M6

I I x 10 - t O © x p ( - 2 2 0 / T )

5

CIO ÷ OH - C I ÷ HO2

M7

1.3 x I0 - ! !

30

Lt÷O2÷M

~

Na÷02 + M-

exp(-1380/T)

LIO2 + M

NI

I x 10--30T -1

100

NaO2 ÷ M

N2

I x 10 - 3 0 T - - I

10

N3

I x 10 - 3 O T - I

10

LIO 2 + CI ~ LtCI ÷ 0 2

N4

I x 10-1Oexp(-IOOO/T)

30

Na02

N5

I x 10 - l O e x p ( 1 0 0 0 / T )

30

N6

I x 10 - 1 0

30

K÷02+M~

K02

K02+M

÷ CI ~ NaCI + 0 2 + CI~

KCI ÷ 0 2

¢xp(-1000/T)

N7

3 x 10 - 1 2 e x p ( - I O O O O / T )

100

N8

3 x 10 - 1 2 exp ( - IO000/T)

100

Nq

3 x 10 - 1 2 e x p ( - 1 0 0 0 0 / l ' )

I00

NIO

2 x 10 - I !

30

NaO 2 + O H ~ N a O H + O 2

NII

2 x I0 - 1 1

30

KO 2 + O H ~

NI2

2 x 10 - l l

30

N a ( 2 S I I 2 ) + H + OH ~ Na ( 2 P l / 2 ) + H 2 0

NI3

I x 10 -'~1

30

Na(2Sll2 ) + H + OH ~ Na(2P312) + 1120

NI4

I x 10 - 3 1

30

Na(2SI/2) + H + H ~ Na(2Pl/2) ÷ H2

NI5

I x I0 -''31

30

N a ( 2 S l l 2 ) + H + II ~ Na(2P3/2) ÷ H 2

NI6

I x 10 --'11

30

Na(2Sll2 ) ÷ O ÷ O ~ Na(2Pll2 ) + 02

NIT

5 x 10 - 3 0

100

Na(2S! 12) + 0 ÷ 0 -- Na(2P3t2) + 0 2

NI8

5 x 10 - ' 1 0

100

Na(2SI/2)+M~

NI9

1.2 x 10 - I 1 T O ' b e x p l - 2 4 4 0 0 / ' r )

5

L i 0 2 + H 2 ~ L i O H + OH NaOII • OH

NaO 2 + H 2 ~

K02÷H2

- KOH+OH

LiO 2 • O H -

LIOH+O 2

KOH+O 2

Na(2Pll2)+M

N a ( 2 S l l 2 ) + M - Na(2P312) + M

N20

2.4 X 10 - l l

N a ( 2 P I / 2 ) + M -- Na(2P312) + M

N24

3 x 10 - I O

5

K(2S112) + It * OH ~ K(2Pl12 ) ÷ H 2 0

N25

I x 10 --31

100

K(25112) + H * OII ~ K(2P312) ÷ H 2 0

N26

I x 10 - 3 1

I00

K(2S!12) + H + H ~ K(2Pl12) + H 2

N27

I x 10 - 3 1

100

K(~'J1;2) ÷ H * H - K(2P3/2) ÷ H 2

N28

I x 10- 31

100

K(351/2) ÷ O ÷ O ~ K ( 2 P I / 2 ) ÷ O2

N29

5 x 10 - 3 0

100

K(~II2)

N30

5 x 10 - 3 0

N31

1.2 X I0 - l l

.]-0.5 cxp (- 18690/T)

5

K ( 2 S t / 2 ) + M ~ K(2Pa/2) + M K(ZI'I/=) + M - K ( ~ / 2 ) +M

N32

2 4 x 10 - ! !

I ..0.5 ¢xp ( 1 8 8 2 0 / T )

5

N35

3 x 10 - l O e x p i - 2 0 0 / T )

10

Na÷H02~

N38

I X I0 - l l

exp(-1000/T)

30

N41

I x I0 - 1 1 e x p ( - 1 0 0 0 / T )

30 10

÷ O * O ~ K(2P312) ÷ 0 2

K(2SI/2)÷M

K÷HO2

• K(2PII2)+M

Na02 ÷H ~ K02÷H

"1`0.5 exp ( - 2 4 4 0 0 / T )

5

I00

H÷O2÷M~HO2÷M

PI

2 x 10 - 3 2 cxp (500/'1")

CI + H O 2 ~ HCI + 0 2

P2

1.2 x 1 0 - 1 ° e x p ( - 4 8 0 / T )

10

H + HO 2 ~ OH + OH

P3

4x

10-1°exp(-950/-r)

5

H + HO 2 ~ H a ÷ 0 2

P4

4x

10 - l l e x p ( - 3 5 0 / T )

5

H 2+HO2-H20+OH

P5

I x 10-12expi-9400/T)

CO + H O 2 ~ CO 2 ÷ OH

P6

2.5 x I O - I O e x p ( 1 1 9 0 0 / T )

I0

O * HO 2 ~ OII * 0 2

P7 P8

8x

30 30

OH+HO 2--H20÷O

2

10 - I 1 e x p ( - 5 0 0 / T ) 5 × 10 - 1 1

I0

RATE COEFFICIENTS FOR FLAME CALCULATIONS Reaction

Numbez

Rate Coell'~ient

Uncertainty I.actor

CHO ÷ O ~ CO + OH

OI

3 x 10 - 1 1 exp ( - 2500/T)

100

CHO÷OH~CO

÷H20

02

I x I0 - 1 1

100

CO÷H•M~CHO+M

03

2x 10--33exp(-gS0/T)

100

CHO ÷ H ~ CO • H2

04

2 x 10 - t O exp ( - 2500/'1")

30

CH4 • !t - CH3 + H2

Q5

7 x I 0 - 1 ° exp I - 7500/T)

30

CH4 • O ~ C H 3

Q6

5 x 10 - ! 1 cxp ( - 4 5 0 0 / T )

5

Ctl 4 • OII ~ CH 3 • H 2 0

Q7

5 x 10 - I i

5

C H 2 0 + OH ~ CHO + H 2 0

Q8

I x i 0 - 1 0 exp ( - 5 0 0 / T )

100

CH20• H -CHO÷

(,,)9

5 x 1 0 - t i exp ( - 2 1 0 0 / T )

30

C H 2 0 + O - CHO ÷ OH

QI0

2 x 1 0 - 1 0 exp ( - 2 2 0 0 / T )

30

CH 3 • OH - C H 2 0 ÷ H 2

OI I

7 x 10 - 1 2

100

CII 3 • 0 2 - C H 2 0 • OH

QI2

5 × 10 - 1 3 exp 1 - 5 5 0 0 / T )

100

CH 3 • O ~ C H 2 0 + H

QI3

I x I 0 - 1 0 exp 1 - 5 0 0 / T )

100

CII 3 • H • M ~ C H

QI4

2 x 1 0 - 2 ! T--3

I00

CH 3 • CH 3 ~ C2H e

QI5

l x 1 0 - 1 1 exp ( 5 0 0 f r )

30

c2116 ÷ H ~ C2H 5 • H 2

QI6

5 × 10"-17 T 2 e~p ( - 3 5 0 0 / T )

10

C2H3+H~C2H 4•tl 2

QI?

8 x i0 - I !

100

C2H 4 • H ~ C2H 3 • H 2

QIg

3 x 10-11 exp ( 3 5 0 0 / 1 " )

10

C2H 3 ÷ H ~ C 2 H 2 + H

QI9

7 x 10-12

30 1000

•OH

H2

4•M

2

exp i--2500flr)

C2H 2 + H ~ C2H • H 2

Q20

3 x 10 - l O e x p (-9500/1")

C21!+tl ~C 2•112

Q21

4 x IO-llexp(-Ig000/T)

100

C21| 4 + H ~ C2H 5

Q22

4 x 10 - 1 2 exp ( - 5 0 0 f r )

30

C2H 2 • H ÷ M ~ C2H 3 + M

Q23

I x 10 - 3 3 exp (4800/T)

100

C2 • I | • M ~ C 2 H ÷ M

024

I x 10 - 2 8 ~ 1

100

CHO • 0 2 ~ CO ÷ HO 2

025

2 x 10 - 1 0 exp 1-2000/1")

30

CH 3 • O ~ CH * H 2 0

Q26

5 x 10 - ! 1 exp ( - 1000FI')

100

CI•OH*M

~ HOCI• M

RI

I x 10-29"1 "-1

100

HOCI÷It ~CIO+H 2

R2

I x 10 - ! 1

100

IIOCI ÷ OH ~ CIO ÷ H20

R3

3 × 10 - 1 2

100

HOCI • O ~ CIO • OH

R4

2 x 10 - ! 1

100

CaOH* + e -

SI

0.5 T - 2

5

$2

4 × 10 - ! 1 ¢xp (3680/'1")

30

CaOII+H~Ca+H20

$3

4 x 10 - 1 2 e x p ( 6 0 0 / T )

30

Ca • HC! - CaCI ÷ H

$4

3 x 10 - I O ¢xp ( 5 0 0 0 / 1 " )

30

CaCI 2 + H ~ CaCI + HCI

$5

I x 10-1Oexp (-5000/T)

30

Ca(OH) 2 + H ~ C a O H + H 2 0

$6

3 x I0 - I I

30

CaO•H20~

$7

6 x I0 - t O

30

CaOH* • e - ~ CaO ÷ H

$8

0.5 T - 2

5

CaOH++H~Ca÷+H20

S9

I x IO-l°exp(

BaOII•H ~ Ba+H20

$21

4 x 10 - 1 2 e x p ( - S 0 0 / T )

30

BaO+ H 2 0 ~

$22

3 x 10 - 1 2

30

~ C a ÷ OH

CaOH + H - C a O ÷

H2

Ca(OH) 2

Ba(OH) 2

expl-600/T)

1000/T)

30

8

D. E. J E N S E N a n d G. A. J O N E S

Number

React!on

Rale Coelfictenl

$23

3 x 10 - i t

BI(Oll) 2 • H ~ BaOH + H20

$24

I x IO-IOexp(300/T)

B a O H * 4. e -

BaOH • H -

BaO 4. H 2

cxp(-E00/T)

Uncertainly Factor I0 30

S25

I x 10 - 7

10

BaOH ÷•e--BaO•H

$26

I x IO - 7

IO

B a O H * + H ~ Ba ÷ 4. H 2 0

$27

I x 10 - I O exp ( - 1000/3")

30

CH+O~

I00

- Ba • O H

CHO*+e-

T3

5 × 10-gT -I

CHO* + H 2 0 ~ H3 O÷ • CO

T4

I x 10 - 8

I0

H30* 4. Li ~ Li* 4. H 2 0 + I!

T5

1.7 × 1 0 - S T - !

5

H 3 0 * 4 . N a - Na ÷ • H 2 0 •

T6

4 x 10 - 2 1- - 2

5

T7

4 5 × 10 - 2 "I- - 2

5

II

H30* + K - K* 4. 1120 4. tt H30*

• In ~ In" 4. H 2 0 4. H

H30'*" • C I -

-H20

• H • CI

exp(-17OO/T)

T8

I x 10 - 8

I0

T9

7 × 10 - 5 T - I

I0

H30'*'•OH-

~ 114.OH+H20

TI0

8 x 10 - g

30

H30*•e-~

H4.H4.OII

TI I

6 x 10 - 4 T - !

5

NO4. NO ~ N 2 0 + O

UI

2.2 x 1 0 - 1 2 e x p ( - 3 2 1 0 0 / T )

5

N 2 0 • H ~ N 24"OH

U2

1.3 x I O - l ° e x p ( 7 6 0 0 / T )

3

N O ' * ' H 4 . M - HNO4.M

t'3

5 × 10 - a 2 exp (300/T)

10

HNO+H-

U4

8 x 10 - 1 2

I0

HNO • OH ~ NO 4. H 2 0

U5

6 x 10 - i l

5

N2+O~NO+N

U6

13 × 10 - t O e x p ( 3 8 0 0 0 / T )

5

N•O 2 ~NO*O

U7

I I x 10-14Texp(3150/T)

3

Fe + H 2 0 - F e O H + It

VI

1.3 x I O l O e x p l -

30

FeOll + 11 ~ FcO + H 2

V2

5 x I0 -I !

FeO + !120 - Fe(OH)2 Fc(OII) 2 • H ~ FeOH • H 2 0

NO4.H 2

16700/T)

exp(-8OO/T)

30

V3

9 x 10 - 1 2

I0

V4

I.I x 1 0 - 1 0 e x p i - 3 0 0 / T )

I0

VII

I.I x 10-1Oexp(-1400/"r)

I0

MoO 3 • H 2 0 ~ H2MoO 4

VI2

I x I0 -! 1

30

H2MoO 4 • H - llMoO 8 + H 2 0

VI3

I 4 x IO-IOexp(_3OO/T)

30

HWO 3 • H

V21

I.I x 1 0 - 1 O e x p i - 1 0 0 0 / T i

10

WO 3 • H 2 0 ~ H2WO 4

V22

I x IO - I O

30

H2WO 4 . II • FIWO3 + H 2 0

V23

3 x IO - 1 0 cxp ( - IO00/T)

30

Co•OH

V31

I x 10--1Oexp(-IO00/-I)

30

CoOH + H ~ CoO 4. It 2

V32

2 x I0 - ! 0 exp ( - 8 0 0 / T )

I00

CoO • H 2 0 ~ Co4OH) 2

V33

3 x 10- 1 3

30

Co(OH) 2 • H ~ CoOH • H 2 0

V34

4 x 10 - I O exp (-300/'1")

I00

H • H(+C/) ~ H2(4.Cr)

V41

2 x 10 - 2 " /

I00

H 4. H(4-SnO) ~ H2(4.SnO)

V42

5 x 10 2 g

100

IIMoO 3 • H

-MoO 3+H 2

-'WO 3+H 2

~CoO•H

RATE C O E F F I C I E N T S FOR FLAME CALCULATIONS

9

NOTES ON RATE COEFFICIENTS AI

A2 A3

A4

A5

B1 B2 B3 134 B5 136 CI

C2

C3

Baulch, Drysdale, Duxbury and Grant [3l recommend k ^ s = 5.2 × 10- i s exp (000/7") ml a molecule - a s - l a n d k _ * ! = 3.0 X I0 - s T - t exp(-Sg380/TJmlmolecule - s s - l . b o t h f o r M - ~ A r , ln combination with our value for the equilibrium constant K A I , the latter expression yields kAz = 2 X I0 - a t T - t exp (200/T)ml a molecule - a s- z , agreeing with the recommendation 5 X 10- 3 5 exp (qOO/T) ml a molecule - a s- t to better than a factor of 2 throughout the temperature range of interest. For M - such other flame molecules as N a, CO a and H a, values of kA! are typically some .3 to I0 times higher [,3]. The listed value O f k A t appears to be a reasonable selection for use in flame calculations. Baulch, Drysdale. Home and Uoyd [4] decline to make a recommendation for/c A a because of the lack of experimental data. The estimate of Ref. [ I ] is retained here. A great deal of experimental work has been done on this reaction, hut the results are scattered and appear to show substantial third-body variations4 . i s ° . Baulch, Drysdale, Home and Uoyd [4] suggest kAa = 8.3 × IO- a s ml a molecule - a s- t at 300 K for M - H a and k _ x a = 3.'7 X I0 - t ° exp 1-48300/'/'1 ml molecule - t s- t for M - Ar. Dixon-Lewis and Williams l l 8 0 ] give kA3 = " 8 X I0 - a o T - ! for M - N a or At, 2.5 X IO - a t T -o.6 for M - H a and 1.7 × 10 - a s T - t . a s for M - HaO, all in ml a molecule - a s- t . The listed value is a compromise selected for use in practical flame calculations. A thorough review for different M. directed towards the specialist reader, is given in Ref. [ 1801. Baulch, DTysdale, Home and U o y d [4] r e c o m m e n d / c ^ 4 = 3.9 X 10 - a S T - a ml a molecule -~' s- t for M - HaO, and suggest that other third bodies are somewhat less effective in inducing recombination than is HaO. Dixon-Lewis and Williams [ 180] give kA4 = 4.4 × I0 - a 0 T - a ml a molecule - a s- t for a general third body. A value o f I × I0 - a S 7" - a ml a molecule - a s- ! is listed here for practical flame calculations: this agrees reasonably well with measurements on the reverse reaction [ 4 1 Baulch, D~ysdale, Duxbury and Grant [3] suggest k,~ 5 = 6.5 × I0 - a a exp (-2184/7") ml a molecule - a s- t for M - CO. In the light of the scattered results for other third bodies [ 3 ] , this is a reasonable value to adopt for flame calculations. It agrees well with Dixon-Lewis and Williams' recommendation I 1801 kA.~ = I .i × I0 - a a exp ( - 2300/T) ml a molecule - a s- t for "50-800 K The listed value is taken from Ref. [180]. The listed value is taken from Refs. [4] and [ I 80]. The listed value is taken from Ref. [ 180]. This rate coefficient is selected to fit data collected in Ref. [3]. The listed value is taken from Ref [4]. It agrees well with that of Ref. [ 1 8 0 ] The listed value is taken from Ref. [3]. The values of k c l to be found in the literature (e.g. Refs. [6-12] ) vary widely. That listed weights heavily the recent results of Bemand and Clyne [10] and Wagner, Welzbacher and Zellner [12], which agree well with one another. Ambidge, Bradley and Whytock [13] give/c_ca = 8 × I O - t a exp(-16OO/T) ml molecule - I s- t These authors also account for a previous apparent discrepancy [ 14] between measurements of the rate coefficients for the forward and backward steps of this reaction. The value of Ref. [13] is adopted. It is in reasonable agreement with previous work. Takacs and Glass [ 15], Anderson, Zahniser and Kaufman [ 16] and Smith and Zellner [ 17] all find k _ c a to be about 7 X 10 - l a rnl molecule - t s - t at 295 K. Wilson, O'Donovan and Frtstrom [18] give/C_ca -- 1.3 × 10 - i t ml molecule - t s - t at 1930K. The listed rate coefficient, which correspends to /C_ca = 2 × 10 - i t exp ( IO00/T) ml molecule - t s - ! . tits all these determinations.

10

C4

C5

C6

D! D2

D3 134 D5 136 D7 D8 DO

D.E. JENSEN and G. A. JONES although the selected activation energy for the reaction ( - C 3 ) is larger than those given in Refs [16] and [17], and the listed expression would not be the best to use close to room temperature. Balaknin, Egorov and Intezarova [19] give k - c 4 = 2 X 10- ) 2 exp (-230OIT) ml molecule - ) s- ) for 295 <~ T <: 371 K, Wong and Belles [20] give k_c4 = 2 X 10- ) I exp (-3600/:/') ml molecule - l s- ) for 356 <: T <: 628 K and Brown and Smith [21] give k - c ( -- 2.5 x I0 - l ~ exp (-2970/7") ml molecule - ) s- ) for 293 <~ T <~ 440 K. At 360 K, these expressions yield 3.4 X I0 - 1 5 rnl molecule - ) s- l , 9 X I0 - 1 6 ml molecule - ) s- ) and 6.5 X 10 -16 ml molecule - ) s- I respectively and are therefore not in good agreement. We have selected /c-c4 = 5 X I0 - l a exp (--300017") rnl molecule - ) s- ) as a compromise, converting this to the listed value of/cc4. Directly measured values of/Cc5 do not agree well with one another: Jacobs, Giedt and Cohen [22] give /cc5 = 2 X 10 - l ) exp ( - 1 7 6 0 0 / T ) rnl molecule - l s- ) but Biauer [23] gives /cc5 = 3 X IO--l~ exp ( - 17500/T) ml molecule - ) s- ! ; Kondratiev [32] summarizes measurements o f / c - c 5 suggesting a pre-exponential factor in /cc5 of about 4 X 10 - l ) ml molecule - ) s- ) . Values obtained for / c - c 5 at 300 K include 2.5 X 10 - ) ) (Ref. [24]), 1.8 X 10 - ) ) (Ref. [25]), 6.3 X 10- ) 1 (Ref. [26]), 7 X 10 - ) 2 (Ref. [27]) and 3 X 10 - ) ) (Ref. [28]) ml molecule - l s - l . a n d are, thus, also rather scattered. We have selected/c-c6 = 5.5 X 10 - ) t exp (-300/T) ml molecule - ) s- ) (2 X 10 - ! 1 ml molecule - l s- ) at 300 K) as a compromise and converted this to/cc5 = 7 X i 0 - ) l exp ( - 1 6 5 0 0 / T ) ml molecule - 1 s- ) . Further work on this reaction is clearly needed. Albright, Dodonov. Lavrovskaya, Morosov and Tal'rose [9] f'md/ccs = ' X 10 - ) ° exp ( - 1 2 0 0 / / ) mi molecule- ) s - l for 294 < T ~ 565 K. This expression gives k c 6 = 4 X ! 0 - ) 2 ml molecule- ) s- ) at 300 K. Rabideau, Hecht and Lewis [27] give/Ccs = 4 X 10 - 1 2 ml molecule - ) s- l at 30OK. but Clyne, McKenney and Walker [24] give/ccs = 2.5 X 10 - ! ) ml molecule - t s- ) at this same temperature. We list /ccs = I X 10- ) o exp ( - 7 0 0 / T ) ml molecule - l s- ) (I X 10- ) ! ml molecule - ) s - ) at 300 K) as a compromise. This rate coefficient is estimated by comparison with those given for reactions D2 and D3 below. The listed value is based on measurements made by Polanyi [29] as long ago as 1932; no recent measurements have been reported. However, Kondratiev [30] discusses results of Taylor and Datz [31] which suggest that the rate coefficient of the reaction K + HBr -" KBr + H is given by/C = 3 X 10 - 1 2 T ° . s exp ( - 1 7 0 0 / T ) ml molecule - l s- l , or, at around 1600 K. by/C -- 1.2 X 10 - ) o exp ( - 1 7 0 0 / T ) ml molecule - ! s- ) . Other early results for this and other reactions reviewed by Kondratiev [32] suggest pre-exponential factors close to collision frequencies but activation energies which, in conjunction with the best modern values for the standard enthalpy changes of reaction D2 a . d others, imply unlikely negative activation energies for such reactions as the reverse of D2. The listed value for/CD2 is a reasonable compromise. Taylor and Datz [31 ] used a molecular beam technique on a clean experimental system, but the early work suffers from uncertainties concerning the possible effects of condensed particles [29]. This rate coefficient, like k o 2 ' is based on the work of Polanyi [29] and the review and discussion of Kondratiev [ 3 0 . 3 2 ] . The listed value is estimated in a manner similar to that in which/Cos was obtained.~ The listed value is estimated in a manner similar to that in which kO8 WaS obtained. This rate coefficient is estimated on the basis of the general discussions of reactions of this type given by Jensen [33] and Sugden [34] and the experimental evidence of Jensen and Padley [35]. The activation energy in ko,~ is arbitrarily taken to be about 4 kJ mole ! higher than the endothermiclty [36]. The pre-exponential factor is estimated by analogy with those in/coa a n d / c o s . The listed value is estimated in a manner similar to that in which/co't was obtained, thermochemical data stemming from Refs. [36 and [37]. The listed value is estimated in a manner similar to that in which/co't was obtained, thermochemical data stemming from Refs. [36] and [38].

RATE COEFFICIENTS FOR F L A M E CALCULATIONS

DIO DI I DI 2 El

The The The The

listed value is estimated in a manner similar to that in listed value is estimated in a manner similar to that in listed value is estimated in a manner similar to that in following results have been obtained from shock tube

Reference 39

E3

1.1 x l0 - l t

exp ( - 3 5 0 0 0 / T )

which kO. I was obtained. which kD7 was obtained. which kD6 was obtained. measurements o f k - E ) :

k _ E ! at 3500K

k _ E 1 at

5 x 10 - 1 6

8 x 10 - 2 2

1500 K

40

7 x 10 - l l e x p ( - 4 1 0 O O f r )

6 x 10 - 1 6

41

8 x lo--tl exp(-416OO/T)

6 x 10 - 1 6

9 x tO - a a 7 × 10 - 2 3

8 x lO - 1 6

9 x IO - 2 2

42

E2

k _ E i , ml molecule - ! s- I

It

3.2 x 1 0 - 1 3 T ° . b e x p ( - 3 5 1 0 0 / ' r )

All the above values are o f M - Ar; considerable disagreement exists concerning the relative efficiencies o f Ar and HC! as M [ 4 1 , 4 3 ] . The remits agree remarkably well at t e m p e r a t u r e s ( ~ 3500 K) typical o f the experiments but extrapolate to values in much less satisfactory agreement with one other at temperatures more typical o f flames. Combined with the equilibrium constant, the results of Refs. [39] and [42] give kt, l ~ 7 X I0 - a 6 exp ( + 1 7 2 0 0 / T ) m l a molecule - a s- l , while those of Refs. [40] and [41] give k E l ~ 5 X 10 - a 6 exp ( + I 0 8 0 0 / T ) m l a molecule - a s- t . The surprisingly steep temperature dependences of these values o f kEt may imply significant contributions from finite rate populations o f vibrational levels o f HCI, the kinetic importance o f which might be lessened in the presence of molecular (as distinct from atomic) M. The absolute magnitude o f k E l at 3500 K impfied by the remits (I X I0 - a a ml a molecule - a s- ! for M - Art appears reasonable: that at i S00 K (~> I X 10- a t ml a molecule - a s- t ) less so. As an arbitrary compromise, we have selected kEx = 4 X I0 - a e T - a mi a molecule - a s- t for a typical flame third body. Further work on this reaction remains necessary. Lloyd [ 4 4 ] , on the basis of data from several sources, recommends kE2 = 6 X I0 - a 4 exp (900/7") ml a molecule- 2 s- t for M - Ar and 200 <~ T < 500 K. With the equilibrium constant given by K~ 2 = 3 X I0 - a S exp (28,600/73 ml molecule - l , this would correspond approximately to k_E2 = 2 X 10 - 9 exp ( - 2 7 7 0 0 / 7 3 ml molecule - t s- t ( k _ g a = 2 X 10- 2 4 ml molecule - t s- t at 800 K and 1.9 X I0 - 1 5 ml molecule - ) s- l at 2000 K). Such values of k - E a do not agree particularly well with direct measurements. Jacobs and Giedt [451 and Carabetta and Palmer [461, for example, give k - E 2 = 1.5 X I0 - t ° exp ( - 2 4 2 0 0 / 7 3 ml molecule - t s - t ( I . I X I0 - a a ml molecule - t s- t at 800 K; 8.3 X I0 - t 6 ml molecule - t s - t at 2000 K); tttraoka and ltardwick [471 give k - a 2 -1.5 X !0 - a T - I . s exp ( - 2 8 , 600173 ml molecule - t s - t (1.9 X 10 - a s ml molecule - 1 s - I at 800 K; l.O X I0 - t 4 ml m o l e c u l e - t s - t at 2000 K). Because of the scatter in the direct measurements o f k - E a and the fact that the kE2 value of Lloyd [44] implies one o f k _ a 2 which lies between the direct values o f the latter at 2000 K, we have accepted kg2 = 6 X I0 - a 4 exp (900/73 ml 2 molecule - 2 s - l for M = Ar and arbitrarily raised this through a factor of 3 to allow for the fact that typical flame collision partners M are probably among the more effective for both forward and backward steps of reaction E2. For M - Ar, Jacobs. Giedt and Cohen [22] give k _ , , a = 1.9 X I0 - 5 T - I exp ( -6-/, 500/T) ml molecule - I s - t and Blauer [23] gives k - g a = 8 X 10 - 6 T - t exp ( - 6 7 . 5 0 0 / 7 3 ml molecule - i s - t . These data suggest kEa ~ I X I0 - 2 ~ T - I ml 2 molecule - 2 s - t . Making allowance for the presence in flames of collision partners more efficient in inducing recombination than Ar. we suggest kEa = 3 X 10 - 2 9 T - t ml 2 molecule - a s- I . The measured values of k _ g a agree well with predictions o f k E a based on the theory of Benton and Fueno [48].

12 E4

FI

F2 F3 F4 F5

F6 GI

G2 G3 G4 G5

HI

D. E. JENSEN and G. A. JONES Lloyd J44J recommends k_z4 = 8 X 10 - 1 2 exp ( - 1 4 . 300/7") ml molecule - I s- I for M - Ar. weighting the work of Britton, Johnson and Seery J49. 50J more heavily than that of Diesen [51, 521 . In combination with the equilibrium constant, this gives k~: 4 = 1 X I0 - a 6 exp (4000/7") m] 2 molecule - 2 s- I . o r /cE4 -- 1.4 X I0 -aS ml 2 molecule - 2 s- i at I. 500 K. Breshears and Bird 1531 f i n d k _ E 4 = 6 X tO - I I exp( 17,470/T) mlmolecule - I s- I f o r M - A r ( c o r r e s p o n d i n g t o k z 4 = 8 X I0 - a s exp (850/T) ml 2 molecule - 2 s - t , o r 1.4 X I0 - 3 s ml 2 molecule - 2 s- I at 1500 K ) a n d k - z 4 = 1.6 X I0 - I ° exp ( 17, 520/7") ml molecule - I s- l for M - F 2 ( k z 4 -- 2.1 X tO - a s exp (800IT) ml 2 molecule-2 s - t , or 3.6 X I0 - 3 s ml 2 molecule - 2 s - t at 1500 K). These results contrast rather sharply with LJoyd's suggestion {441 o f k z 4 ~ 3 X I0 - a 4 ml 2 molecule - 2 s I for I000 < T < 2000 K, based upon the direct measurements of k - z 4 and the theoretsca] estimates of kz4 made by Bensen and Fueno [481 : the discrepancy may reflect deviations front the rate quotient law and uncertainties in the formulation of the equilibrium constant at high temperatures 1441. Ganguli and Kaufman 1541 have reported kE4 = 8 X 10 -:ss ml 2 molecule - 2 s- t at 295 K for M Ar and Ultree [551 has fognd/cE4 = 6 X 10- 3 4 ml ~ molecule - 2 s- t at room temperature for M He. We suggest kE4 = I X I0 - a ° T - t . s ml 2 molecule - 2 s- t (1.9 X 10 - a 4 m] 2 molecule - 2 s - t at 300 K; 1.7 X I0 - a s ml 2 molecule - 2 s- t at 1500 KI for use with M - A t , and convert this to kE4 -- 3 X l 0 - a ° T - t.s ml 2 molecule-2 s - ! for a general flame third body. The theoretical arguments of Refs. 1331 and 1341 and the experimental results of Bulewicz and Sugden [56] are a source of approximate values o f k r t and k - F t . This work suggests that the proexponential factor in the rate coefficient of the reaction CuOH + M -" Cu + OH + M cannot be much smaller than 0 X 10 - 4 7"-1 ml molecule - t s - t and. by analogy, the pro-exponential factor in k - F t is probably not much less than this. If the activation energy in k - F t is set equal to the endothermicity [36], k _ v t Kt~ t = k t~! becomes not much less than 8 X ! O-2S 7"- I m12 m o l e c u l e - 2 s - 1 . A value of 3 X 10 - 2 s 7" - I is suggested for use in flame calculations. This rate c o e f f i c i e n t greater than k^4, but by no means the largest rate coefficient for a termolecular recombination of small neutral species ever suggested (cf. Ref. [57] }-carries an uncertainty factor of one to two orders of magnitude. It is unlikely that the reaction is bimolecular rather than termolecular under flame conditions. The listed value is estimated in a manner similar to that in which k~- t was obtained. The listed value is estimated in a manner similar to that in which k F t was obtained. The value o f kF4, like that of kt~s, is based on the review of Troe and Wagner [ 179]. TroeandWagner[179]suggestk_F:,~SX 1 0 - g e x p l - 4 6 , 0 O O / 7 " ) m l m o l e c u l e - t s- t f o r M - ~ A r at around T = 3000 K, corresponding to kt~s ~ 2 × 10 - 3 2 exp (2500/7") ml 2 molecule - 2 s - t . The value listed for a typical flame M seems reasonable by comparison. The value of k~- 6, like that of k F s . is based on the review of Troe and Wagner [I 70]. Results of a number o f flame determinations o f k o t are gathered together in Ref. [58J. Recombination rate coefficients for Me* + e - + M -," Me + M all fit the expression k = 4 × 10 - 2 4 7' - t ml 2 molecule - 2 s - t whatever the identity of the alkali metal atom Me, for any typical set of collision partners M. This recommendation is adopted as acceptably accurate for flame calculations. The listed value, like k G l . is based on the recommendation of Ref. [58]. The listed value, like kc; t, is based on the recommendation of Ref. [58]. The listed value, like k o 1, is based on the recommendation of Ref. [58]. Rate coefficients for k o s and k _ G 5 have been measured by Kelly and Padley [157]. Their results suggest a value for k(~, at 2440 K of about I X 10 - 2 7 ml 2 molecule - 2 s - t and a 7`-2 temperature dependence for this rate coefficient. The listed value is based on this work. This value is taken from the recent work of Burdett and Hayhurst [59]. It stems from measurements made on atmospheric pressure flames of H 2 + 0 2 + N 2 to which controlled amounts of lithium and

RATE COEFFICIENTS FOR FLAME CALCULATIONS

H2

H3 H4

H5 116 H7

!!8

13

chlorine are added. A mass spectrometric sampling method was used for flame temperatures between 1800 and 2400 K. This value is taken from the recent work of Burdett and Hayhurst [5c~]. It stems from measurements made on atmospheric pressure H a + 0 2 4- N2 flames to which controlled amounts of sodium and chlorine are added. A mass spectrometric sampling method was used for flame temperatures between 1800 and 2400 K. The listed value is taken from Ref. 1601. This rate coefficient is estimated by comparison with k H 1, RH 2 and k a 3. The suggested value carries the implication that the potential energy curves for the different LiOH states are not unfavourably placed with respect to one another. The possible error bounds are consequently large. The preexponential factor in k_H4 implied is about 3 X 10- t t ml molecule - t s - t at 2000 K. This rate coefficient is estimated in a manner similar to that in which kH4 was obtained. This rate coefficient is estimated in a manner similar to that in which ku4 was obtained. Burdett and Hayhurst [59], from their mass spectrometric study of atmospheric pressure H 2 + 0 2 + N 2 flames to which lithium and chlorine are added, find R_H,Z = 4 X 10.7 T - 3 . s exp ( 7 7 , 5 0 0 / T ) ml molecule-t s - t . This corresponds to kH-z -- 1.2 X 1 0 - t ~, T - 3 . s exp (- 300/T)ml 2 molecule-2 s - t , which agrees satisfactorily with calculations made on the basis of the theory of Bates and Flannery [61 ]. See also the notes on reactions H8 and Hg. From the theory of Ref. [61 ] and polarisability and collision data of Ref. [62J, the following values of RH a for different collision partners M may be calculated:

kHa, ml 2 molecule--2 $--1

M

1000 K

2000 K

3000 K

N2

3.6 x 10 -2.7

5 5 x 10 - 2 8

1.9 x 10 - 2 8

H20

7.8 × 10 -2"7

7 5 x 10 - 2 8

2.0 x 10 - 2 8 2.4 x 10 - 2 8

HCI

6.5 x 10 - 2 . /

7.5 x 10 - 2 8

CO

3.9 x 10 -2.7

6 8 × 10 - 2 8

1.9 x 10 -211

CO 2

4.7 x 10 -2.7

7 2 x 10 - 2 8

2.5 x 10 - 2 8

02

3.5 x 10 -2.7

5.4 x 10 - 2 8

I 9 x 10 - 2 8

From their mass spectrometric measurements on atmospheric pressure flames at temperatures between 1800 and 2400 K to which sodium and chlorine are added, Burdett and Hayhurst [59] find k_Ha = I.I X I0 "r T - a - s e x p ( -66,750/T)mlmolecule - I s- l . T r a n s l a t e d i n t o k H s -- 5.5 X 10-t 7"-3,s exp (-750/7"1 ml 2 molecule - 2 s- ! , this gives kHa = 8.2 X 10- 2 7 ml 2 molecule - 2 s- I at 1000 K, 1.07 X 10 -27 ml 2 molecule - 2 s- I at 2000 K and 2.9 X 10- 2 8 ml 2 molecule - 2 s- I at 3000 K. This agreement between theory and experiment is good. The value of Ref. 59 is adopted for flame calculations. It is noteworthy that the theory [61 ] predicts approximately the same values for the rate coefficients of Cs* + F - + M ," CsF + M as are measured in shock tube experiments [ 6 3 ] , although the theoretical and experimental temperature dependences differ for this reaction. See also the note on reaction Hr.

HQ

From the theory of Ref. [61 ] and the polarisability and collision data of Ref. [62l. the following values of kH9 for different collision partners M may be calculated:

D. E. JENSEN and G. A. JONES

14

kHg. ml 2 molecule--2 $--!

JI J2

J3

J4

M

I000 K

2000 K

N2 H20 HCI CO CO 2 O2

4.2 x 10 -2.7 1.0 x 10- 2 6 4.5 x 10-2.7 4.5 x 10-2.7 5.3 x 10-2.7 4.1 x 10 - 2 ` /

5.6 x 10- 2 8 8.4 x 10- 2 8 8.1 x 10-28 5.9 x 10-28 7.4 x 10- 2 5 5.5 x 10-26

3000 K 1.6 2.5 2.4 1.9 2.4 1.8

x 10- 2 8 x 10- 2 8 x 10-28 x 10-21l

x 10- 2 8 x 10-28

Burdett and Hayhurst [00] find k_H9 = 2.2 X 10.7 T -a.5 exp ( - 6 0 8 0 0 / T ) m l m o l e c u l e - n s- n , corresponding to kH9 = 1.6 X 10- 1 5 T - s . 5 exp ( - 2 4 0 0 / 7 ) ml a molecule - 2 s- 1 (4.6 X 10-a'~ 1.3 X 10 - 2 7 and 4.9 X 10 - 2 8 ml 2 molecule - 2 s- 1 at 1000, 2000 and 3000 K respectively, and in good agreement with the theory). This value is adopted. The recommended values o f k _ r 4 , k _ F s , k_F6 and k_H.7, k_Ha and k_H9 are broadly in line with the relative probabilities for collisional dissociation of the alkali halides AB into A ÷ + 13- and A + B respectively discussed in Ref. II 79l. See also the notes on reaction H8. This rate coefficient is estimated by comparison with ka2 and kal o, no experimental measurements of k j l being available. Mand] I~1 has measured k _ j a in shock tube experiments for the temperature range 3500-5500 K. He finds that k_a2 = I X 10- 1 ° exp ( - 4 2 , 0 0 0 / 7 ) ml molecule - 1 s- t for M -= Ar or N a. This corresponds to a value for kj2 ~ I X 10 - 3 2 exp ( 3 0 0 0 / 7 ) m l 2 molecule - 2 s- ! , which is adopted. Measurements of this rate coefficient have produced widely scattered results (cf. Refs [65-721). Fehsenfeld, Ferguson and Schmeltekopf 168, 69] and Howard, Fehsenfeld and McFarland [65] have measured k _ j 3 as 1.0 × 10- 9 ml molecule - n s- ! at around room temperature. This would suggest a value of k_a3 of at least I X 10- n ° ml molecule - t s- ! at flame temperatures ~ " 0 0 0 K [73] and imply a pre-exponential factor in ka3 well in excess o f l 0 - a ml molecule - I s - 1 . The preliminary results of Buchelnikova [71], on the other hand, are interpreted by Calcote and Jensen [70] as implying a pre-exponential factor in kj3 orders of magnitude lower. In an attempt to resolve this discrepancy, Burdett and Hayhurst [66, 67] have studied the reaction in the gases sampled from H a + 0 2 + N z flames containing C I - . They conclude that reaction J3 is balanced at atmospheric pressure in flames of temperatures 1800-2800 K0 but interpret their results in terms of relaxation of the equilibrium within the mass spectrometric sampling cone used, finding k_j3 = 7 × 10-1 o ml molecule - n s - 1 . This agrees with the values o f Refs [65], [68] and [691 . In contrast, Calcote [72] reports that Miller and Gould find k j 3 = 3 X 1 0 - 1 0 exp ( - 1 3 , 0 0 0 / 7 ) ml molecule - t s - t ' these authors also sampled atmospheric pressure H 2 + N 2 -~ O 2 flames containing C I - with a mass spectrometer, but interpreted their results in terms of non-equilibrium in the flame itself. Miller and Gould's value for kj3 corresponds to k - j a ~- 10 - n s m l molecule - n s - t . a result more consnstent with that of Buchelnikova [71 ]. Because Burdelt and Hayhurst [67] explain how sampled profiles o f [CI- ] in flames might falsely suggest that reaction J3 is not balanced in the flames themselves, wc accept their value as the best currently available, but recommend that still further work on the reaction is needed. The k - j 3 value o f 7 × IO- l ° ml molecule-n s - n (independent o f temperature for 1800 < T < 2800 K) corresponds to k j a = 1.4 X IO - 7 exp ( - 7 6 0 0 / 7 ) ml molecule - n s - n . Miller and Gould [74] have made measurements on dissociative attachment o f electrons to HBO a in H 2 + O 2 ÷ N 2 flames at temperatures between 1730 and 2250 K and pressures of 13 to 101 kN m - 2 (O.13-1 atmosphere). They interpret their results in terms o f a value for k) 4 of 3 × l 0 - n ° exp ( - I 1,000/7") ml m o l e c u l e - l s - t the pre-exponential factor in k j4 being similar to that in k j 3

RATE COEFFICIENTS FOR FLAME CALCULATIONS

J5 J6 J7

J8 J9 JlO LI

L2

1_3

1.4

L5

15

found by the same workers [72]. it is possible, however, that these results might alternatively be interpreted in terms o f reaction J4 being balanced in the flame gases but unbalanced to varying extents in the mass spectrometer sampling system used (cf. Ref. [67]). Following the arguments o f Ref. [67], we suggest using ka4 = I X I0 - s exp ( - i l , 0 0 0 / 7 " ) ml molecule - t s - t for the present. Such a value carries wide error bounds, and further study of this reaction is necessary. This rate coefficient is estimated by comparison with kja, kj4 and ka~ (see the notes on these rate coefficients). The uncertainty factor is consequently large. This rate coefficient is estimated in a manner similar to that in which ka5 was obtained. The rate coefficient k-j7 has been measured at around room temperature by Ferguson, Fehsenfeid and Schmeltekopf [69] as about I X I0 - a ml molecule - t s-1" The temperature dependence of k_j~ is probably slight, but might be expected to decrease this value of k-aT to not less than I0 - t ° mi molecule - t s- 1 at typical flame temperatures [73]. With JANAF data [36] for O H - , this leads to a value of ka7 of about I X 10 - 7 exp (-35,000/:7) mi molecule - t s- ! , i.e., to a preexponential factor in ka7 of similar magnitude to that found in k j s by Burdett and Hayhurst [66, 67]. Ca/cote and Jensen [70], on the other hand, interpret the preliminary results of Buchelnikova [71 ] as indicating a pre-exponential factor in kj7 of not more that I0 - ! ° ml molecule - t s- ! . The listed value is a compromise which weights the results of Ref. [69] more strongly than those of Ref. [711. This rate coefficient is estimated by comparison with other ion/molecule reaction rate coefficients given in, e.g., Ref. [75]. Thermochemical data for the reaction stem from Ref. [38]. This rate coefficient is estimated by comparison with other ion/molecule reaction rate coefficients given in, e.g., Ref. [75]. Thermochemical data for the reactions stern from Ref. [37]. This value is based on the work of Pack and Phelps [76, 77]. It should be within a factor of 30 of the true value under flame conditions. This rate coefficient is estimated by comparison with k~. a and kL3. The endothennicity measured by Hayhurst [78] is preferred to that given by Dzidic and Kebarle [79] because the latter is based upon a rather inaccurate extrapolation of results for higher hydrates of Li ÷. Johnsen, Brown and Biondi [80] find that, at 30OK, k - L a = 1 X I0 - a s and 4.7 X IO- ~ ° ml 2 molecule-2 s - t for M -- HaO and He respectively. If k _ L z is assumed to vary as 7"- t (a reasonable but arbitrary and uncertain assumption), these values may be converted to 1.5 X 10 - 2 0 ml z molecule - a s- t (HaO) and 7 X I0 - a t ml a molecule - 2 s- t (He) at 2000 K. In combination with the equilibrium constant, these results yield k,. 2 = 1.5 X I0 - s exp ( - 1 5 , 0 0 0 / T ) and 7 X I0 - s exp ( - 1 5 , 0 0 0 / T ) ml molecule - l s - l respectively. We suggest adopting k,. 2 = 3 X !0 -~ exp (-15,000/T) for use in flame calculations. For reactions LI-1..3, the possibility of deviations from the rate quotient law, and perhaps even contributions from bimolecular hydration under some conditions, add to the uncertainties involved. Johnsen, Brown and Biondi [80] give k--L3 -- 4.5 X I0 - a s ml ~ molecule - z s- t for M = H 2 0 and k_,. a = 2.6 X I0 - 3 ° ml 2 molecule - 2 s -~ for M = He at 300 K. With k_,. a arbitrarily assumed to vary as T - t , these values convert to 7 X 10 - a ° ml 2 molecule - 2 s- ! (H20) and 4 X I0 - 3 1 ml 2 molecule-2 s - l (He) at 2000 K, and, combined with the equilibrium constant, give kL3 = 3 X I0 - 7 exp (-IO,OOO/T) rni molecule - l s - l and kL3 = 2 X I0 - a exp (-IO,O00/T) rnl molecule - I s - ! respectively. We suggest adopting kLs = I X 10 - 7 exp ( - 10,000/7) rnl molecule - l s - ! for use in flame calculations. (See also the note on reaction L2). This rate coefficient is estimated by comparison with coefficients for other dissociative recombinations of positive ions with electrons, including the fairly reliable values for k T ! I, ks ! and ks z.~ (see Refs. 82-88). It is emphasized that the products of such dissociative recombinations are rarely identified, and one must be wary of the apparent implications of a given dissociative recombination rate coefficient for the reverse (chemiionization) step. (See also the note on reaction LI .) This rate coefficient is estimated in a manner similar to that in which kL4 was obtained.

16 1.6 L7

D. E. JENSEN and G. A. JONES This rate coefficient is estimated in a manner similar to that in which kL4 was obtained.

Burdett, Hayhurst and Morley Iggl have obtained a value for the rate coefficient of HsO ÷ + C I - --" HaO + HC! o f about 4 X I0 - a ml molecule - t s - l in the temperature range 1800-2600 K. The reaction products were not identified, it seems reasonable to assign a similar value to kL'l. The enthalpy change o f reaction L7 implied by the work of Hayhurst [78]is preferred to that corresponding to the work o f Dzidic and Kebarle [79] for the reason given in the notes on reaction LI. Great caution must be exercised in considering the implications of kL.~ for the reverse (chemiionization) step because the products of the reaction are uncertain. I..8 This rate coefficient is estimated in a manner similar to that in which kL'1 was obtained. This rate coefficient is estimated in a manner similar to that in which kL7 was obtained. L9 LIO This rate coefficient is estimated in a manner similar to that in which kL7 was obtained. L l l This rate coefficient is estimated in a manner similar to that in which k L7 was obtained. L i 2 This rate coefficient is esturnated in a manner similar to that in which kc7 was obtained. M! We are aware of no experimental measurements of k M t. The listed value is estimated by comparison with three body recombination rate coefficients for which data are available, including k A Z and

kK2. The pre-exponentia] factor in kMa is thought likely to be close to the collision frequency. An arbitrary activation energy of 12 kJ mole - l is inserted into the listed expression for kM2 as a result of comparison of reaction M3 with other, formally similar, bimolecular reactions. M3 This rate coefficient is estimated in a manner similar to that in which kM 2 was obtained. M4 This rate coefficient is estimated in a manner similar to that in which k u 2 was obtained. M5 C]yne and Walker [90] have obtained a lower limit for k~45 at 300 K of I X I0 - I t ml molecule- t s- t . The listed rate coefficient is consistent with this and appears reasonable by comparison with rate coefficients in groups B and C. Note, however, that the reaction CIO + H~ ~ HCI + OH is apparently very slow at room temperature [91]. M6 Watson [92] recommends kMs = 5 × IO- 1 1 ml molecule - t s - I at 300 K, implying that the activation energy cannot be large. Clyne and Nip [93] have recently reported kM6 = I . l × i0 - 1 ° exp ( - 2 2 0 / 1 3 ml molecule - t s - ) , with a very low activation energy indeed. Clyne and Nip's value is adopted. M7 Cox and Derwent [94] argue that k_M7 must be lower than kp2 at 306 K; for kpa they give a value of 3.5 × I0 - I t ml molecule - ) s - ! at this temperature. We have listed kp2 = 1.2 × IO- l ° exp ( - - 4 8 0 / T ) ml molecule - l s - l . If k _ M . ~, in line with Cox and Derwent's argument, is set equal to I × l 0 - 1 ° exp ( - I O 0 0 / T ) ml molecule - ! s- I (4 × IO- l a ml molecule - 1 s- 1 at 306 K ) , k M . t becomes 1.3 × IO - ) ) exp ( - 1 3 8 0 / T ) ml molecule - I s- ! , the listed value. This rate coefficient is estimated by comparison with kN,, and kNs. We are not aware of any NI experimental data, kinetic or thermochemical, for this reaction. This value stems from the work of Carabetta and Kaskan [95, q6J. The T - ! temperature N2 dependence is arbitrarily inserted: Carabetta and Kaskan observed little variation of kr¢2 with temperature. The enthalpy change for the reaction is given by McEwan and Phillips [97]. This rate coefficient is based on the work of Carabetta and Kaskan [95, 96]. (See also the note to N3 reaction N2.) The equilibrium constant is estimated on the basis of results given in Ref. [97]. N4 This rate coefficient is estimated by comparison with kp4. (See also the note on reaction NI .) N5 This rate coefficient is estimated by compartson with kp4. This rate coefficient is estimated by compartson with kt,,t. (See also the note on reaction N3.) N6 This rate coefficient is estimated by comparison with k p s . (See also the note on reaction NI .) N7 N8 This rate coefficient is estimated by comparison with k p s . This rate coefficient is estimated by comparison with kt,~,. (See also the note on reaction N3.) N9 NIO The listed rate coefficient is estimated by comparison with k p s , which is itself an estimated value. (See also the note on reaction NI ). M2

17

RATE COEFFICIENTS FOR FLAME CALCULATIONS Nil NI2

This rate coefficient is estimated in a manner similar to that in which k s ! o was obtained. This rate coefficient is estimated in a manner similar to that in which k s no was obtained. See also the note on reaction N3. N I 3 Padley and Sugden [98l given k s n 3 = 6 X 10- - 3 2 m] 2 molecule - a s- n at flame temperatures ~2000 K. If the improved quenching data recommended by Jenkins [99] are used to reinterpret these results, a slightly higher value o f k s n a is obtained. That selected is as good an estimate as is currently available. N I 4 This rate coefficient is based on the work o f Refs. 1981 and 1991. (See also the note on reaction NI3.) N I 5 Padley and Sugden 198] give kNn5 = 2 x 10 - a 2 ml 2 molecule- 2 s- n at flame temperatures 2000 K. With improved quenching data [99], this is converted to k s n s = 6 X I 0 - 3 2 ml 2 molecule - 2 s- n . Carabetta and Kaskan 11001 find k s | 6 = 4 X 10- a n ml 2 molecule - 2 s- I . which Jenkins [99] suggests may be a little too high. The selected value seems a reasonable compromise. N I 6 This rate coefficient is based on the work described in Refs. [ 9 8 - 1 0 0 ] . (See also the note on reaction N 15.) NIT This value is based on the work o f Carabetta and Kaskan [100 I, corrected for the improved quenching cross sections given by Jenkins 1991. N I 8 This value is based on the work o f Carabetta and Kaskan [100 I, corrected for the improved quenching cross sections given by Jenkins [99]. N I 9 Quenching cross sections for the Na ZPl/2 and 2Pa/2 states in collisions w,th different molecules (o 2, not Ire 2) are given by Jenkins [ 1011 as follows:

N20 N24

N25 N26 N27 N28 N29 N30 N31

Molecule

Cross icctlon ( I 0 - n6 cm 2)

H2 N2 02 CO 2 H20 CO

2.87 6.95 12.30 I 7.00 0.50 I 1.90

These results are reasonably consistent with previous values [ I01 ]. For a typical flame molecule of molecular weight 25 ainu and reduced mass 2 X IO - 2 a g, it is reasonable to take a quenching cross section 02 of I0 X I0 - l e cm 2. The value of k _ N s 9 is then 1.2 X lO - l l T e's mlmolecule - l s- I ; this translates into the value OfkN! 9 listed. This rate coefficient was obtained in the same way as kN he. Jenkins [ 102], Burhop and Massey [ 103] and Krause [ IO4] all consider the cross section of reactlon N24 to be large and the value of kN24 to be close to the collision frequency. The value listed should not be greatly in error. This rate coefficient is set equal to that of the analogous reaction for sodium, N ] 3. This rate coefficient is set equal to that of the analogous reaction for sodium, N 14. This rate coefficient is set equal to that of the analogous reaction for sodium, N 15. This rate coefficient is set equal to that of the analogous reaction for sodium. N I6. This rate coefficient is set equal to that of the analogous reaction for sodium, N 17. This rate coefficient is set equal to that of the analogous reaction for sodium, N I8. Quenching cross sections for the K aPl/2 and 2Pa/2 states with different molecules (02. not no2t are given by Jenkins [ 105] as follows:

18

D. E. JENSEN and G. A. JONES Moiccul©

Cross section (10 - t 6 cm 2)

H2 CO 2 H20

1.03 2140 0.90

N2 02 CO

5 60 15.50 12.40

For a typical flame molecule, it is reasonable to take a cross section o 2 o f 10 × I 0 - t s cm 2 for a reduced mass o f 2.5 X I 0 - a 3 g. The deactivation rate coefficient is then 1.2 X i 0 - i t 7 .0.5 ml molecule - 1 s- I . This implies a value for kNa t o f 1.2 X i 0 - I t T °'b exp (-18,690/7") ml molecule - t s - t

N32 N35 N38 N41 PI

P2

P3 P4 P5

P6

P7

This rate coefficient is obtained in the same way as kN3t. This rate coefficient is estimated in a manner similar to that in which kN24 was obtained. This rate coefficient is estimated by comparison with rate coefficients o f group P reactions. This rate coefficient is estimated by comparison with those of group P reactions. Baulch, Drysdale, Home and Lloyd 14] discuss this reaction in detail and recommend k p l = 4.1 X l 0 - 3 a exp (500/7") ml 2 molecule - 2 s - t for M - He or At, in reasonable agreement with the recent assessment o f Slack [ 181]. For an "'average" third body other than H 2 0 , it would seem reasonable to write k p t = I X 10 - 3 2 exp (500/7") ml a molecule - a s - I (see data for relative efficiencies of H a. CO a, O a. N a and inert gases summarized in Refs. [4, 180, 181] ). F o r M - HaO, however, the results collected in Ref. 4 suggest a value for kp t as high as I × I0 - a l exp (500/7") ml z molecule - 2 s - t . Under conditions where this reaction plays an important part, it might therefore be wise to describe reaction PI in terms o f two separate rates, one for M - HaO and one for M - any other flame m o l e c u l e The listed value is intended for use in applications when both water and other molecules are present. The rather wide uncertainty limits thus do not do justice to the accuracy of the experimental data, as they stem largely from the fact that allowance is made for variations o f H 2 0 mole fractions from one flame to another. Cox and Derwent [q41 give a value for ke2 o f 2 . 5 X I0 - t l ml molecule - t s - t at 306 K. The activation energy must therefore be small. We have arbitrarily inserted an activation energy of 4 kJ m o l e - t obtaining the listed value of kp2. This recommendation is based on Refs. [ 4 , 1 0 6 and 180l. This recommendation is based on Refs. 14, 106 and 180l. Baulch, Drysdale, Home and Lloyd [4] and U o y d [1061 recommend a rate coefficient of 1.2 X 10- t I exp (-9400/7") ml m o l e c u l e - t s - t for the reaction H z + HO2 -" H202 + It, the products of this reaction being preferred to H i O + OH [41. In flame calculations, however, the main interest in such a reaction is usually in its rate o f removal of HO l rather than in its products. We disregard HaO l as a result of its relative unimportance as a reaction intermediate in high temperature flames. Reaction P5 as written should account adequately for removal of HO l by H i in these flames. The value listed is that suggested by Bauich, Drysdale, Duxbury and Grant [3]. It differs substantially from that of Ref. [I ] at the lower temperatures o f interest; this reaction has attracted a good deal of attention since 1971, partly because it is thought to play an important part in removing CO from polluted air [3 l- The listed value agrees quite well with that of Dixon-Lewis and Williams I 180]. Lloyd [IO61 estimates kt,~ = 8 X tO - t t exp(-5OO/T) mlmolecule - t s - t . w h i c h is rather higher than Dixon-Lewis and Williams' upper limit [180] of 3 X IO- t l ml molecule - t s - l but seems a reasonable value to use for high-temperature flame calculations.

RATE COEFFICIENTS FOR FLAME CALCULATIONS P8

19

Hochanadel, Ghormley and Ogren 110"71 and DeMore and Tschuikow-Roux [1081 suggest kra = 2 X lO - l ° ml molecule -= s-1 at 300 K, implying a very small activation energy. Uoyd [1061 lists k r , = 8 X I0 - ! 1 exp (-500/7) ml molecule - i s- t and Dixon-l.~wis and Williams [180] 1.3 X I0 - I t ml molecule - l s -1 at 15OO K. Clearly large uncertainties remain. We suggest using a temperature-independent value of 5 X I0 T M ml molecule - I s- I for flame calculations as a compromise. QI Baulch, Drysdale, Duxbury and Grant 131 decline to make a recommendation for kQt because no experimental measurements are available. The listed value is estimated by comparison with kQ4, consistent with the result of Mack and Thrush l IOO] that kQz ~ 0.14 kQ4 at 300 K. Q2 Baulch, l:~'ysdale, Duxbury and Grant [3] decline to make a recommendation for kQ2 because no experimental measurements are available. The rough estimate of Ref. [ I I is retained. Q3 Baulch, Drysdale, Duxbury and Grant 131 and Dixon-Lewis and Williams [1801 suggest/cQ3= 2 x I0 - 3 a exp ( - 8 5 0 / 7 ) and 1.4 X I0 - a a exp ( - 7 5 5 / 7 ) ml a molecule - 2 s - n respectively for M - Ii 2 a! 300-800 K. We adopt the former expression for use in flames for all M. The large uncertainty bounds reflect doubts concerning the temperature-dependence of kQa and its possible variation with the nature of M. Q4 Baulch, Drysdale, Duxhury and Grant [31 decline to make a recommendation for kQ4 because of the lack of experimental data. Brennen, Gay, Glass and Niki [I IOI consider kQ4 to be greater than kQ0. The listed estimate is consistent with this view. Q5 Although there has been a good deal of work on this reaction, it is not easy to select a best value for the rate coefficient. Schofield [ l l l l and Kondratiev [32] recommend kQs = 7 X IO- I s exp ( - 5 8 0 0 / 7 ) and 9 X I O - i ) exp ( - 6 4 5 0 / 7 ) ml molecule - 1 s - l respectively, but Fristrom and Westenberg [6], taking a different view of the relative reliabilities of the same experimental data, give kQs = 8 X IO- l ° exp ( - 6750/7) ml molecule - ! s - ) . More recently, a theoretical analysis by Clark and Dove [112l has suggested kQ~ = 3.7 X lO - 2 ° T a exp ( - 4 4 0 0 / 7 ) ml molecule - 1 s- I . We suggest k ~ s = 7 X tO - ) ° exp ( - 7 5 0 0 / 7 ) ml molecule- t s - i as a compromise for use in flame calculations. Q6 Schofield [ l l l l , Kondratiev [32l and Herron and Huie I l l 3 ] recommend k(~ s = 5 X IO- I 1 exp ( - 4 0 0 0 / 7 ) , 8 X IO- I I exp (-4500/7") and 3.5 X IO- ! 1 exp ( - 4 5 5 0 / 7 ) ml molecule - ! s - I respectively, on the basis of data from several sources. The listed value agrees well with these recommendations, although rather less well with Brabbs and Brokaw's determination [I 141 of kQe = 3 X ! 0 - !o exp (-59OO/7) ml molecule - i s - l, for the temperature range of interest. Q7 This rate coefficient is based on the recommendation of Wilson and Westenberg [1151 . It agrees well with the expressions kQ~ = 1.2 X l0 - I ° exp ( - 3 0 0 0 / 7 ) m l molecule - ) s - ! and k(~7 = 1.3 X I0 - l ° exp (-2900/7)ml molecule - 1 s - ) suggested by Schofield [ l l l l and Kondratiev [321 respectively and with other results summarized in Ref. [i IO I . Q8 Morris and Niki [1171 find kQs = 1.4X I O - | l m l m o l e c u l e - | s - ! at 300 K. Wilson Ill81 suggests k~a = 8 X lO - l l ml molecule - I s - ! for 300 < T < 1600 K. Peelers and Mahnen [ l l g ] give kQB = 3.8 X IO- I ! ml molecule - I s - I for 1400 < T < 1800 K, while Kondratiev [32l tentatively suggests kQs = I X IO- I ° ml molecule - ! s - ! for 770 < T < 1500 K. All these valuesare much higher than the early value of Avramenko and Lorentzo [120]. The listed value is a compromise. Q9 Schofield [ l l l l gJvesavalue f o r k Q g o f l X I O - l ° e x p ( 2300/T) mlmolecule - l s - I . K o n d r a t i e v [32] suggests the similar expression kQ9 = 5 X IO - l l exp ( 2 1 0 0 / 7 ) ml molecule - i s - I . The latter expression is adopted. QIO Kondratiev [321 suggests k q l o = 2 X IO- I ° exp ( - 1 7 0 0 / 7 ) ml molecule - I s - ~ . The value listed differs only slightly from this expression, but agrees better with results reported by Mack and Thrush [ 1091. Q l l Fenimore [1211 suggests a bimolecular rate coefficient of 7 X IO- 1 2 ml molecule -~ s -~ at ic)70 21¢0 K for the reaction of CH a with OH. The products of reaction are uncertain, but may well be

20

D. E. JENSEN and G. A. JONES

C H 2 0 + H. This value is listed, but must be applied with caution. The steps leading to production of C H 2 0 from CHa in combustion processes are not well understood, and it is difficult to envisage the transition complex if reaction QI I occurs as a single step. (See also the notes on reaction QI 3.) QI 2 Fristrom and Westenberg [6] argue that reaction Q I 2 , with a rate coefficient ~ 1 0 --I a ml molecule - I s - I, can be used to describe one path of conversion o f CHs to C H 2 0 in combustion systems (see the notes on reaction QI 3). Work on numerical matching o f shock tube concentration profiles suggests k Q 12 = 2 X 1 0 - 1 2 exp ( - 6 2 6 0 / 1 3 ml m o l e c u l e - 1 s - i (Ref. [ 122] ) and kQ 12 = 3.3 × ! O- 14 ml m o l e c u l e - ! s i at 1350 K (Ref. [ 1231 ). Similar analysis o f shock-initiated methane oxidation [1241 results in k Q ! 2 = 2 X I0 - l a exp ( - 5 0 0 0 / T ) m l m o l e c u l e - l s - ! at 1900-2400 K This last expression gives kQi z = 5 × IO - I s ml molecule - I s- I at 1350 K and therefore does not agree well with the results o f Refs. [122] and [123]. Brabbs and Brokaw [I 14] argue against the occurlence o f reaction Ol 2 in similar combustion regimes, suggesting instead CH 3 + O 2 -, CHsO + O followed by CHsO + M -. C H 2 0 + H + M or CHsO + CO -- CO2 + CHa. Clearly this reaction is a controversial one. For the present, we suggest a compromise between the values o f Refs. [ 122] and [ 124 ], 5 × 1 0 - I s exp ( - 5500/13 ml m o l e c u l e - ! s - i , with wide uncertainty bounds. Q I 3 Fenimore and Jones [125~ suggest reaction Q13 as a means of converting CHs to C H 2 0 in combustion systems, assigning kQ I a a value of 3 X I O - ! I ml m o l e c u l e - ! s - ! for 1200 <~ T , ( 10OO K. Several other workers have also interpreted their results in terms of this reaction. Bowman [I 24] gives kQl:~ = 1.7 X 10 - I ° ml molecule - I s - I at 1900-2400 K. Biordi, Lazzara and Papp [126] give k o ! 3 -- 1.8 × 10 - I ° ml molecule - 1 s - ! at 1550-1725 K. Izod, Kistiakowski and Matsuda [ 122] report Re l a = 6 X 10 - i I exp (- 1600/1") ml m o l e c u l e - i s - l and Clark, izod and Matsuda [123] give k Q l a = 4 X IO - j l ml molecule - I s - I at 1350 K. All these results are obtained via fitting of concentration profiles to rather complicated mechanisms, however, and Dixon-Lewis and Williams [I 27] argue that the results of Baldwin, Jackson, Walker and Webster [I 28l rule out significant contributions from reaction Q I 3 in premixed flames containing methane. Nevertheless, it seems probable (although not certain) that there is a rapid direct step from CH s to C H 2 0 which occurs in high temperature methane oxidation, and reaction Q I 3 is arbitrarily chosen as one means of accomplishing this conversion for the present. The value selected for the rate coefficient, ! × I 0 - !o exp ( - 5OO/T) ml m o l e c u l e - 1 s - l , is a compromise among the results of Refs. 122-126, and is in reasonable agreement with other values collected together in Ref. [116]. The retention o f reaction QI 3 is thus analogous to that of reactions QI I and QI 2. objections to these last two reactions also having been raised (see, for example, Refs. [I 15. 125,127] ). Q I 4 Dean and Kistiakowski [129] find that at IO kPa pressure in shock tubes the decomposition CIt4(+M) -" CHs + H(+M) follows bimolecular kinetics, and for M - Ar give k - Q 1 4 = 2.7 × 10 - s exp ( - 5 1 , 500/1") ml molecule - I s - ! . The work of Ref. [130] gives k _ Q i 4 = 4 × 10 - 1 ° exp (-32500/1") ml molecule - l s - I for M =- inert gas, the activation energy in which is startlingly low. Bowman [ 124] gives k - Q i • = 2.3 X IO- 7 exp ( - 4 4 , 5 0 0 / 1 3 ml molecule - ! s- t , also for inert gas M. These three expressions yield:

Ref. 129

Ref. 130

Ref. 124

k _ Q t 4, m l mole~.'ule - !

,~-I, 1500 K

3 x IO - 2 1

2 x 10 - 1 9

3 × 10 - 2 0

k _ Q l 4. m l m o l e c u l e - !

s-1 . 2000 K

2 x 10 - 1 7

4 × 10 - 1 7

5 x 10 - 1 7

k _ Q ! 4. m l m o l e c u l e - !

s- ! . 2 5 0 0 K

3 × I0 -tb

9x

4 x 10 - 1 6

10 - 1 6

RATE COEFFICIENTS FOR F L A M E C A L C U L A T I O N S

QI5

QI6

21

The rate coefficients thus agree fairly well for the typical experimental temperatures 2000-2500 K, but imply quite discordant values outside this temperature range. Direct measurements of k Q ) • (e.g. Ref. [I 311 ) give values ==3 X I0 - 2 ° ml 2 molecule - 2 s- n at about 300 K, wlth only a slight dependence on temperature. We suggest kQt • = 8 X 10 - 2 2 T - a ml 2 molecule - 2 s- n for I000 < T < 3000 K for M -= Ar (3 X I0 - 2 0 ml 2 molecule - 2 s- t at 300 K; IX I0 -an ml 2 molecule - 2 s- ) at 2000 g). In the temperature range of interest, this corresponds to k _ Q t 4 -- 2 X 105 7`-3 exp ( - 5 4 , 60017) ml molecule - ) s- ) , giving/c_Qn • = 3.5 X IO - ) ~ ml molecule - ) s- l at 2000 K and A _ Q t 4 = 4 X I0 - n 5 ml molecule - n s- I at 2500 K. For M --- a typical flame molecule, we suggest the listed value of 2 X I0 - 2 n 7"-a ml 2 molecule - 2 s- n . The discrepancies among the room temperature and shock tube measurements are both marked and unaccounted for, and the listed error bounds are therefore wide. The form of the equilibrium constant for reaction Q I 4 listed is particularly unsuitable for extrapolation to temperatures below I000 K; quite different expressions for both this constant and k(~ t • would be selected at low temperatures. Be)son and O'Neal 11321 recommend k _ Q l 5 = 5.6 X 10 )6 exp ( 4 5 , 0 7 0 / 7 " ) s- l , which corresponds to /(Qt5 = 5 X I0 - l ) exp ( - I 19017') ml molecule - ) s- l , At 2q.~ K, however, this gives kQ t 5 = q X I 0 - t s ml molecule- l s- t, which is considerably lower than has been measured directly (James and Simons [1331. for example, give k e t 5 = 5.6 X I0 - ) ) ml molecule - ) s- ) at 293 K: Parkes, Paul and Quinn 11341 give/cQl5 = 4 x I 0 - ) ) ml molecule - l s- ) for 250<: T < 4 5 0 K). We suggest using kQl ~ = I X I0 - l ) exp (50017) ml molecule - ) s- ) . This fits the low temperature results reasonably well, agrees adequately with the results reported in Ref. 11351 for 1120 < T < 1400 K, and yields an expression f o r / ( - - Q l ~ , I.I X 10 )6 exp ( - 4 3 , 380/71 s- ) , which is not too discordant with the collected, rather scattered, results summarized by Benson and O'Neal I1321 or with more recent work (e.g. Ref. l 136] ). The error bounds remain rather wide at the higher temPeratures of flame interest.

Schofield [I I I I and Kondratiev [ 3 2 ] , on the basis of data from several sources, suggest k Q t s = 2.2 X 10 - ) ° exp ( - 5 2 0 0 / T ) and kQ! 6 = 1.7 X I0 - 1 ° exp ( - 4 8 0 0 / T ) m l molecule - I s- I respectively. Clarke and Dove [I 12], however, suggest kQl s = 9 X 10 - 2 2 T 3"s exp ( - ' ~ 6 2 0 / T ) ml molecule - ) s- ) as being more acceptable on theoretical grounds. These three expressions agree reasonably well for the temperatures of 5 0 0 - I 0 0 0 K at which most of the experimental measurements have been made, but the recommendation of Clarke and Dove [ ] 121 gives markedly greater values at higher temperatures. We suggest using kQt 6 = 5 X ]0 - l ~ T 2 exp ( .3500/T1 ml molecule - 1 s- ) for the temperature range of interest. Q I 7 Halstead, Leathard, Marshall and Purnell 113.71 suites)/cQ)7 = 8 x 10- ) ) ml molecule - I s- l on the basis of their measurements at 2c~0 K and 8 - 1 6 tort. The products of reaction here are in some doubt, and may be C l l a + CH a rather than C2H 4 + H a. The activation energy is likely to be small, and a temperature-independent value of 8 X 10 - ) ) ml molecule - I s- I is listed, with wide error bounds. QI 8 The suggestion of Schofield [ I I I ] that/(Q) a = 2.0 X 10- t t exp ( - 3 4 6 0 / T ) ml molecule- t s- 1 Is adopted. QI c) Benson and Haugen {1381 suggest k(~)o = "7 X I0 - 1 2 ml molecule - I s- ! at I'~O0 < T < 1"700 K This value is adopted, it is consistent with the lower limit of about 2 X 10 - 1 2 ml molecule - I s-1 given by Volpi and Zocchi [1391 for T m 310 K. Q20 Michael and Weston [1401 suggest kQ2 o = 6 X I0 - i s ml molecule - ! s - ! at room temperature. Browne. Porter. Verlin and Clarke [14l I interpret their work on the computer fitting of concentration profiles in flames as indicating the quite inconsistent value o f k Q 2 o = 3 X I0 - ) ° exp ( - 9 5 0 0 / T) ml m o l e c u l e - ) s - t . but the uncertainties inherent in such a matching process are large. We list /cQ 2o = 5 X i 0 - ) o exp ( - 2 0 0 0 / T ) ml m o l e c u l e - ) s - ) ; the possible error bounds are wide indeed. O21 We are aware of no experimental work on this reaction. The pre-exponential factor in /¢Q21 is set

22

Q22

Q23

Q24 Q25

Q26

RI

R2 R3 R4 SI

$2

$3

D. F. JENSEN and G. A. JONES equal to thai in the rate coefficient of the formally similar reaction P4. The activation energy is obtained via arbitrary addition of 12 kJ mole- t to the endothermicity. Measurements ofkQaa at room temperature (e.g. Refs. I142. 143, 1371 ) result in a median value of about 7 X I0 - I s ml molecule - l s- l . The activation energy is small 11421 (~=4 kJ mole - l ). With kQ22 = 4 X I0 - 1 2 exp ( - 5 0 0 / T ) ml molecule - I s- l and an equilibrium constant of I . I X 10 - 2 4 exp (+I7.000/T) ml molecule - l . a value of 4 X I012 exp ( - 1 7 , 5 0 0 / T ) s- l for k - Q a 2 results. This agrees adequately with the rather scattered measurements of k _ Q a = at 6 0 0 - 8 0 0 K summarized by Benson and O'Neal [132l. Benson and Haugen [ 138,1441 glve k-Q2a = 1.2 x 10-9 exp ( - 15,BOO~T) ml molecule- t s- t for conditions in which M is probably Ar. This corresponds to k~2_~ = 3.4 X l 0 - a 4 exp (4800/T) ml ~' molecule - a s- I . For a typical flame molecule, this may reasonably be converted to the listed value ofkQ2 a, the uncertainty bounds in which are large. It appears that no experimental work has been done on this reaction. The listed value is estimated by comparison with other three-body recombination rate coefficients, including kpt and kA4. Baulch, Drysdaie, Duxbury and Grant 131 decline to make a recommendation for kQ2 s because of the paucity of experimental data. Peelers and Mahnen I110l suggest kQas = 5 X I0 -11 m] mole. cule - t s- r at 1400 < T < 1800 K. The activation energy is probably small [3]. The listed value is consistent with both suggestions and with the estimate of Demerjian, Kerr and Calvert [145l that kQ2 s ~ 1.7 X 10 - l a ml molecule - t s - t at about 300 K. Westenberg and de Haas [146] tentatively suggest this reaction as a possible step in methane oxidation, with no associated rate coefficient given but in conjunction with the view that the reaction is fast by comparison with Q6. The listed rate coefficient is consistent with this view. It is estimated by comparison with other group Q rate coefficients, and in the light of the mechanistic as well as the kinetic uncertainties involved carries wide error bounds. The advantage of including this reaction in calculations is that it affords, in combination with other reactions from groups Q and T, a formally complete interim description of the production of ions from a hydrocarbon in a flame. Such a description remains to be tested against results of the many experimental studies of hydrocarbon flame ionization, however. In the absence of any available experimental data for this reaction, the listed value of k R t is estimated by comparison with those of rate coefficients for termolecular reactions on which measurements have been made. No experimental data are available for this reaction. The listed value is estimated by comparison with measured values for rate coefficients o f formally similar bimolecuiar reactions. This rate coefficient is estimated in a manner similar to that in which kR2 was obtained. This rate coefficient is estimated in a manner similar to that in which kR= was obtained. This rate coefficient was measured by Hayhurst and Kittelson [881 . The implied pre-exponential factor in k - s t is higher than that sugggested in Ref. [i 471 , but the absolute value of k _ s t remains roughly the same as a result of a change in the formulation of the equilibrium constant K s t . Cotton and Jenkins 11481 have measured ks= at 1570 K and 1800 K, finding ks= = 4.5 × 10 - t 2 ml m o l e c u l e - t s - l at both temperatures. The listed value o f ks2 gives 3.8 X 1 0 - ! = ml m o l e c u l e - t s - t at 1570 K and 5.2 X I0 - t = m l m o l e c u l e - t s - t at 1800 K. It corresponds t o k _ s = = 1.5X 10 - 1 ° exp ( - 5 0 0 / T ) ml molecule - t s - t , with a small activation energy rather than the value decreasing with increasing temperature implied by the results o f Ref. 1148[ used directly. Reaction $2. together with the other group S reactions influencing radical concentrations in flames, is worthy of further study. The formally similar reactions LiOH + H --. Li + H=O. NaOH + H -" Na + HaO. KOH + H --" K + H=O and CsOH + H --- Cs + H=O have been assigned values o f 4.3 × 10 - I = exp ( - 9 5 0 / T ) . 3.5 × IO- I = exp (- I100/T). 3.6 X 10 - l a exp (- IO00/T) and 4.5 × 10 - t = e x p ( - 700/T) ml molecule - t s - i

RATE COEFFICIENTS FOR FLAME CALCULATIONS

23

respectively (see the notes on reactions D4-D6 and DI 2 and the equilibrium constants for these reactions}. The listed value of ks3 is estimated similarly. $4 This rate coefficient is estimated by comparison with kD2 and kD3. $5 The equilibrium constant for this reaction is approximately given by Ks~, = 0.8 exp ( 4 4 4 0 / T ) . The activation energy in the listed value for ks5 is therefore sufficient to give the backward step of reaclion $5 an activation energy of about 5 kJ mole - t . which appears reasonable. The preexponential factor in ks5 is estimated by comparison with that in R_D3; the collision cross section in ks5 might be expected to be somewhat larger, but the probability factor somewhat smaller, than the corresponding quantities in k _ o 3 . $6 The listed rate coefficient is estimated by comparison with those for the reverse steps of group D reactions and with kv 4. $7 Cotton and Jenkins [148] interpret their measurements of catalysed radical recombination rates in flames as indicating a value for k s ./ at 1570-1800 K of about 3 X 10-t 2 ml molecule-t s-1. This interpretation, however, is not based upon the best current value for the equilibrium constant of reaction $2, on which the value obtained for k s ./ depends. Use of Ks2 = 0.27 exp (-318017), in direct combination with the other data of Cotton and Jenkins [148[,leads to ks. / ~ 6 X lO - 1 ° ml molecule - 1 s - t . This rate coefficient seems rather large for a bimolecular recombination reaction, but is nevertheless listed as the best at present available for use in flame calculations. Further work on this reaction is needed. $8 This rate coefficient, like k s t , is taken from the work of Hayhurst and Kittelson [88]. No positive identification of the products of dissociative recombination of CaOH* with e - has yet been made. $9 On the basis of comparison with other ion-molecule reaction rate coefficients (e.g. Ref. [75] l, one might expect kse to be at least I × IO- t ° exp (-IOOO/T)ml molecule - I s- t . Combined with Ks0 = 0.024 exp (7100/T), this gives a value for k_s9 of 4 × IO- ~ exp (--8100/7")ml molecule-t s - t , which appears reasonable. The listed value of ks9 should not be in error by more than a factor of 30. S21 This rate coefficient is estimated in a manner similar to that in which k _ n 6 , k _ u s and k_ o4 were obtained. $22 This rate coefficient is based on the work of Cotton and Jenkins [148]. reinterpreted tn the light of more recent values for the enthalpies and entropies of formation of BaO and BaOH [ 14c~[. See also the notes on reactions $2 and $7. $23 This rate coefficient is taken from the work of Cotton and Jenkins [148]. $24 This rate coefficient is estimated by comparison with kv,t and other formally similar reactions. $25 Jensen [147] estimates a value ~lO-./ ml molecule - t s - I for ks25 at 2000-2500 K. Similar values are obtained for the rate coefficients of dissociative recombination between CaOH ÷ and e - and between SrOtP and e - by Hayhurst and Kittelson [88]. The products of the reaction between BaOH ÷ and e - have not been identified, and may be Ba + OH or BaO + H. ¢See also the notes on reaction S2O

$27 T3

SI .) Jensen [147[ estimatesavalueofabout I0-./ ml molecule -t s-t for ks26 a! 2000°2500 K. Similar values are obtained for the rate coefficients of dissociative recombination between C a O H * and eand between SrOH* and e- by Hayhurst and Kitlelson [88[. The products of the reaction between B a O H ° and e- have not been identified, and m a y be Ba + O H or B a O + H. (See also the notes on reaction SI .) This tale coefficient is estimated in a manner similar to thal in which ks9 was oblalned. The several rough estimates of this rate coefficient at flame temperatures ~ 2 0 0 0 K include 3 × IO- t 2 ml molecule -l s-t (Ref. [1501). -~ X lO -12 ml molecule -t s-I (Ref. [1511)and 3 X I0 -la ml molecule- t s- t (Ref. [ 152 [ ).The equilibrium constant of the reaction is approximately 1.2 X lO- s exp (- 1700/7). so that a value for k.ra of I X lO -12 at 2000 K corresponds to k_.ra = 2 × I0-./

24

D. E. JENSEN and G. A. JONES ml molecule - I s - l . Such a value for a dissociative recombination rate coefficient appears reason-

able by comparison with, for example,/Cst,/Cs2 s and/C,rl I. We suggest k - , r 3 = 4 X 10- 4 T - ! ml m o l e c u l e - i s - ! and hence k,r3 = 5 X 1 0 - 9 T - I exp ( - 1700/7") ml molecule - ! s - ! T4 Calcote and Jensen ['/0] use results from several sources in estimating kT4 ~ ! X 1 0 - 8 ml molecule - ! s - l at about 2000 K. Peeters and Van Tiggelen [151] find k'r4 -- 7 X 10- 9 ml molecule - ! s - t at similar temperatures. Both values are in reasonable agreement with theoretical estimates for this type o f positive ion-molecule reaction (cf. Ref. {I 53] ), and the listed value should be reasonably realistic for the temperature range o f interest. TS This rate coefficient is based upon the experimental work o f Hayhurst and Telford [154, 155[. T6 This rate coefficient is based upon the experimental work of Hayhurst and Telford [154, 155J. T7 This rate coefficient is based upon the experimental work o f Hayhurst and Telford [154, 155]. T8 This rate coefficient is estimated by comparison with/cTS,/CTe and/CT-~. rq The value listed for k.rs is based upon the work of Burdett, Hayhurst and Morley [Sq], who find /C'rg/k'r ! I -- 0.1 I at 1800-2600 K. The products o f this dissociative recombination were not identitied by these authors and are in some doubt. TIO The preliminary value listed for this rate coefficient is based upon unpublished work o f Calcote and Kurzius [ 156]. TI I Several experimental determinations of the rate coefficient of dissociative recombination between H 3 0 + and e - have been reported (e.g. Refs. [ 8 2 - 8 7 ] ) . The temperature dependence o f the rate coefficient is not reliably established, but a T - i dependence seems likely to be roughly correct. The experimental measurements then fit the expression k,rl t = 6 X 1 0 - 4 T - t ml molecule - t s - ! reasonably well. This expression gives k,ri i -- 3 X I0 - ' t ml molecule - 1 s- I at 2000 K. Hayhurst and Telford [82l find a value for/C_,rl ! of 6 X I0 - 3 e e x p ( - 1 4 , 0 O O / T ) ml 2 molecule - 2 s - ! at ,,2000-2450 K. With the equilibrium constant K,rl i given by 6.5 X !028 exp ( 1 4 , 9 0 0 / 7 ) m o l e c u l e ml - l . this translates into k , r l l = 4 × I0 - ' t exp (qOO/T') ml molecule - I s- I , or 6 × I0 - ~ ml molecule - t s - I at 2000 K. The agreement with the direct measurements of kT! l is good, in the light of the various sources o f possible experimental error, and supports the contention that the products of dissociative recombination are indeed H ÷ H + OH. The recommended value o f 6 × 1 0 - 4 T - ! ml molecule - I s - ! should be accurate to within a factor o f 5 for typical flame conditions. UI The listed value is taken from Ref. [SJ. It agrees well with the recommended value o f k _ u l given by Dixon-Lewis and Williams [ 180l. U2 The listed value, taken from Ref. [5J, agrees well with the recommendation of Dixon-Lewis and Williams [ 180l. U3 Baulch, Drysdale, Home and Lloyd [5] give k u 3 -- 1.5 × 1 0 - 32 exp (300/7") ml 2 molecule - 2 s- l for M ~- H 2 in the temperature range 230 <~ T <~ 700 K, suggesting error bounds o f ±50 per cent for this range. Dixon-Lewis and Williams [180] accept this value, but also give/cu3 -- 2.8 × 10- 3 2 and 1.9 X 10 - 3 t ml 2 molecule - 2 s - l for M - Ar and H 2 0 respectively. These results are consistent with the recent experiments of Oka, Singleton and Cvetanovic [ 158J. The listed value takes all this work into account, a compromise of 5 X 10 - 3 2 exp ( 3 0 0 / 7 ) m l 2 molecule - 2 s - I being suggested for use with a general flame third body. U4 Baulch, Drysdale, Home and Lloyd [5] suggest A:u4 = 8 × 10 - r 2 ml molecule - l s - ! at 2000 K. Bulewicz and Sugden [159] find k u 4 to be approximately I × 1 0 - I I ml molecule - ! s- ! at temperatures between 16OO and 2000 K. Koshi, Ando, Oya and Asaba [160] give a value for A - v 4 of 6.7 × IO - I t e x p ( - 2 9 . 0 O O / T ) mlmolecule - i s - t , w h i c h may be translated into k u 4 - 9 × I0 - t l exp ( - I 100/7") ml molecule - I s- i . A temperature-independent value for k u 4 of 8 × I0 - t z ml molecule - t s - I should be accurate to within a factor of IO for the temperature range of major interest in a flame context. U5 Baulch, Drysdale. Home and Lloyd (5] lean heavily on the work of Halstead and Jenkins [ 161J in recommending a value for k u ~ of 6 × IO - ! I ml molecule - ! s - I at 2000 K. Within the limits of

25

RATE COEFFICIENTS FOR FLAME CALCULATIONS

U6 U7 VI V2

V3 V4 VII

VI2 VI3 V21 V22 V23 V31 V32

V33 V34 V41

V42

experimental error, this agrees with the work of Bulewicz and Sugden [1591. The listed value should be accurate to within a factor of 5 at flame termperatures. The listed value is that recommended in Ref. [50. The listed value is that recommended in Ref. [5]. This estimate is taken from Ref. ll621. (See also the note to reaction V2.) The listed value is taken from Ref. [1621. Reactions V I-V4 are intended to account for catalysis of radical recombination in H a + 0 2 + N 2 flames by iron, and the probable errors involved in using the set of rate coefficients and equilibrium constants given in Ref. I 1621 for calculations on other flames would be substantially smaller than the individual rate coefficient uncertainties suggest. The listed value is taken from Ref. 11621. (See also the note to reaction V2.) The listed value is taken from Ref. [162l. (See also the note to reaction V2.) The listed value is taken from Ref. [1631 . Reactions VI i - V I 3 and V a I - V 2 3 are intended to account for catalysis of radical recombination in H 2 + 0 2 + N 2 flames by molybdenum and tungsten respeclively. The probable errors involved in using either set of rate coefficients and equilibrium constants for calculations on other flames would be substantially smaller than the individual rate coefficient uncertainties suggest. The listed value is taken from Ref. [1631 . (See also the note to reaction V1 I.) The listed value is taken from Ref. [163]. (See also the note to reaction V1 I.) The listed value is taken from Ref. [1630. (See also the note to reaction V! i.) The listed value is taken from Ref. [1631. (See also the note to reaction VI 1.) The listed value is taken from Ref. [ 1 6 3 ] (See also the note to reaction V I l . ) The listed value is an estimate taken from Ref. [164]. (See also the note on reaction V32.) The listed value is taken from Ref. [164]. Reactions V31-V34 are intended to account for catalysis of radical recombination in H 2 + O s + N 2 flames by cobalt, and the probable errors involved in using the set of rate coefficients and equilibrium constants given in Ref. [ 164] for calculations on other flames would be substantially smaller than the individual rate coefficient uncertainties suggest. The listed value is taken from Ref. [1641 . (See also the note on reaction V32.) The listed value is taken from Ref. [164]. (See also the hole on reaction V32.) This artificial overall rate coefficient is suggested by Jensen and Webb [1651 as a means of describing the catalysis of radical recombination in flames by chromium observed by Bulewicz and Padley [166, 167]. When it is used, the concentration of chromium is set equal to the total concentration of this metal in the flame, irrespective of what chromium compounds are formed therein. This artificial overall rate coefficient is suggested on the basis of the work of Bulewicz and Padley [166,168l and Jensen and Jones [163[ as a means of describing the catalysis of radical recombination in flames by tin. When it is used, the concentration of tin oxide is set equal 1o the total concentration of tin in the flame, irrespective of what other tin-containing species may be present.

Equilibrium Constanls as Function of Temperature a Reaction

O+ O+M ~ O 2+M O+H+M ~OH÷M H + H + M ~ H2÷M H + O H + M ~ H20+M C O + O + M ~CO 2+M

Number

AI A2 A3 A4 A5

Equilibrium Constant

7.1 8.8 3.8 8.9 8.5

o Units of molecule m1-1 for concentrations u.~d throulzhout

× x x x x

10-26exp(59580/'l") 10-25 exp (51610/1") 10-25 exp (52650/1") 10-26exp160180/T) 10"-27expt62470/T)

Source Reference

36 36 36 36 36

D. E. J E N S E N a n d G. A. J O N E S

26 Reaction

Number

Equilibrium Constant

Source Reference

OH + H a - H20 + H

BI

0.23 exp (7530/T)

36

O + Ha - O H + H

B2

2.26 exp (- 1040/T)

36 36

H + Oa - ' O H + O

B3

12.4 exp ( - 7 9 7 0 / T )

C O + OH " ' C O I l ÷ H

B4

9.6 × 10- 3 exp (10860/T)

36

OH + OH - H 2 0 + O

B5

0.102 exp (8570/'T')

36

CO + 0 2 --" CO 2 ÷ O

B6

0.12 exp ( 2 8 9 0 / T )

36

H + CI a - HCI * CI CI + H a - HCI + H

CI

2.26 exp (23510/T)

36

C2

1.73 exp ( - 5 3 0 / T )

36

H=O + CI -- HC! + OH

C3

7.4 exp ( - 8050/T)

36

OH + CI -. HCI + O

C4

0.75 exp (510/T)

36

H ÷ HF --H 2 + F

C5

1.37 exp ( - 16200/T)

36

H + F 2 ~ HF + F

C6

2.1 exp (50530/1")

36

Li + HCI - LiC1 + H.

DI

4.2 exp (4610/T)

36

Na + HC1 --" NaC! + H

D2

6.6 exp ( - 3610/T)

36

K ÷ H O ~ KC'I + H

D3

9.5 exp ( - 1960/T)

36

Li ÷ H=O - LiOH ÷ H

134

13.9 exp ( - 10050/T)

36

Na + H=O ~ NuOH + H

D5

23 exp ( - 2 0 9 0 0 [ T )

36

K + H20 ~KOH ÷ H

136

28 exp ( - 19000/'1")

36

K + HBO a -- KBO 2 + H

D7

60 exp ( - 3700/T)

36

K + HaWO 4 -- KHWO4 ÷ H

D8

4.0 exp (2900/T) 3.6 exp (3500/'1")

36, 37 36, 38

K + H:IMoO 4 ~ KHMoO4 + H

D9

Na + HBO a - NaBO 2 ÷ H

DIO

37 exp ( - 4 5 0 0 f r )

36

Li + HBO:I -- LiBO a ÷ H

DI I

46 exp (1680/T)

36

Cs + HaO - CsOH + H

DI 2

44 exp ( - 17300/T)

36

H + C1 + M ~ HCI + M C! ÷ CI ÷ M ~ 0 2 + M

El

6.4 x 10 - 2 6 exp ($2120:T)

36

E2

3.0 x 10- 2 6 exp (28610/'I")

36

H + F + M ~ HF + M

E3

2.8 x 10 - 2 8 exp (68680/!")

36

F+F÷M

E4

1.30x !~ 25exp(18320/T)

36

-F 2+M

L.i + O H + M -. LiOH ÷ M

FI

1.20 x 10 - 2 4 exp (50130[T)

36

Na+OH+M

F2

2.0 x I0 "'24 exp (39300/T)

36

K÷OH+M-KOH+M

F3

2.5 x 10- 2,1 exp (41200/T)

36

Li + CI + M -. LiC'I + M

F4

2.7 x I0 --24 exp (56740/T)

36

Na+CI÷M

~ N~-'I + M

K÷CI÷M

-KCI÷

F5 F6

4.4 x 10- 2 4 expf48510fl') 6.3 x 10 - 2 4 exp($OI70rT)

36 36

Li* ÷ e - +

M - Li*M

GI G2 G3 G4 G5

1.18 x 10 -21exp(65350/T)

36

1.18 x 10 -21 exp(62410/'T)

36

1.18 x 10 -21 exp($3130/T)

36

1.18 x 10 -21expK47200/T)

36

1.18 x 10 ''21 exp (69900/'r)

36, 169

~NaOH+M

Nt++e-+M-K++e-+M

M

Na+M -.K*M

Cs* * e - - + M -,Cs* M In*+e--+M~ln+M

RATE COEFFICIENTS FOR FLAME CALCULATIONS

27

Reaction

Number

Li÷ + CI-" --- Li + CI

HI

11.3 exp (20420/T)

36

Na ÷ + C I - -- Na ÷ O

H2

1 !.3 exp (I 7480/T)

36

~ K + CI

Equilibrium Constant

Source Reference

H3

I 1.4 exp ( 8 2 O O / T )

36

Li ÷ + O H - ~ Li + OH

H4

7.9 exp (41280/'I")

36

Na ÷ + OH-- - Na + OH

H5

7.9 exp (38340/1")

36

K + + O H - - K + OH

H6

7.9 exp (29060/T)

36

Li + + C I - + M ~ LiCI + M

H7

3.0 x 1 0 - 23 exp (77200/T)

36

Na++ CI-- ÷ M ~ NaCI + M

H8

5.0 x 10- 2 3 exp (66000/1")

36

K + + C I - ÷ M -- KCI + M

H9

7.1 x 10- 2 3 exp (58400/'1")

36

OH+e-÷M+ O H - - + M CI+e-+ M-CI-÷ M

JI

1.5 x 10- 2 2 exp (24030/1")

36

J2

I.I x 10- 2 2 exp (44860/T)

36

HO+e--.CI-+H

J3

195 exp (-7600/I")

36

J4

660 exp ( -8160/1")

36

J$

24 exp ( 5 0 ( 0 )

38

J6

25 exp (I 300/T)

37

J7

1600 exp ( - 36060/T)

36

K ÷ ÷ O-

-BO 2 - ÷ H

HBO 2 ÷ ¢ -

H2MoO 4 ÷ e - ~ H M o O 4 - + H

H2WO 4 ÷ e -

~HWO 4 - * H

HaO + e - - OFU ÷ H HMoO 4 - * H ~ M o O 3 - * HaO

J8

0.85 exp (10400/T)

38

HWO4-

J9 JlO

0.87 exp (5700/'i") 1.3 x 10- 2 ) exp(7400/T)

37 36

÷ H-

WOs-

O2+e-÷M-O2--+

+ HaO M

LI

2.2 x 1023 exp (-23000/'I')

78.81

NaHaO ÷ ÷ M - N a

÷+HaO+M KHaO ÷ + M ~ K÷+Ha{)+M

L2 L3

1.0x 10z 3 e x p ( - 1 5 0 0 0 / T ) 3.6 x 1022 exp ( - 10000/1")

78.79.81 78.79, 81

Litl20 ÷ + M ~

Lt÷ ÷ H 2 0 ÷ M

LiHaO ÷ + e - ~ Li ÷ HaO

1,4

260 exp (42350/T)

36. ?8.81

NallaO-- * e - -. Na ÷ H20

L5

120exp (47410/I")

36.78.79. 81

KHaO ÷ + e - -'* K + H 2 0 L i H a O ÷ ÷ C I - ~ Li + CI + H 2 0

L6 L7

43 exp (43130/'T) 2.5x 1 0 2 4 e x p ( - 2 5 1 0 / T )

36.78.79.81 36.78. 81

N a H 2 0 ÷ ÷ C I - - Na + CI + HaO

L8

1.1 x 1024 exp (255Of'F)

36, 78.79. 81

KHaO ÷ ÷ C I - ~ K + C I + H 2 0

L9

4.0 x IO 2a exp ( - 1730/T)

36, 78, 79.81

L i H a O " ÷ OH-- - Li ÷ OH ÷ HaO

LIO

I.? x 1024 e x p ( I B 3 1 0 f l ' )

36,78, 81

NaHaO ÷ + O H - ~ Na * OH + H 2 0

LII

7.9 x I02~1 exp (23380[I')

36, 78, 79, 81

KHaO ÷

LI2

2.8 x IO 23 exp (191OO/T)

36, 78, 79, 81

O+CI+

+

OH-- - K ÷ OH

M-

CIO+ M

+

H20

MI

9.5 x IO- 2 0 exp (314OO/T)

M2

3.6 exp (24930/T)

Na + CIO - NaC1 ÷ O

M3

5 . ' / e x p (167OO[T)

36

K ÷CIO - KCI÷ O

M4

8.3 exp (! 8360/T)

36 36

Li * CIO - LiCI ÷ O

H ÷CIO ~ HCI+O

M$

O÷CIO ~ Oa+CI

M6

0.87 exp (20320/'1") 9.4 x 10- 2 exp (27780/T)

OH +CIO ~ HO a + CI

M?

0.125 cxp (-376/T)

Na+Oa+M ~NaO2+M K÷Oa+M- K O a ÷ M

N2

1.36 X 10- 2 4 exp (30950/1") 1.5 x 10- 2 4 exp (327oo/r)

N3

36 36

36 36 97 97

D. E. JENSEN and G. A. JONES

28 Reaction

Number

Equilib.um Constant

Source Referenc(

NaO 2 • CI ~ NaCI + O 2

N5

3.2 exp (17560/T)

36, 97

KO 2 + C I ~ K C I + O

N6

4.2 exp (17500/1")

36, 97

NaO 2 + H 2 ~ NaOH + O H

N8

42 cxp (-680/1")

36, 97

KO 2 • H 2 -

N9

46 exp (-520/'!")

36, 97

NIl

1.5 exp 18300/'1")

36, 97

NI2 NI 3

1.7 exp 18500/T) 8.9 x 10 - 2 6 exp(35770/T)

36, 97 36

NaO 2 • O H

2

KOH•OH -NaOH+O 2

KO 2 • O H ~ K O H + O 2 Na(SSI/2) • H • OH ~ Na(2Pl/2) • HsO N a ( 2 S I / 2 ) • H • OH ~ NaiSP3/2) • HsO

NI4

1.78 x 10- 2 5 ¢ x p ( 3 5 7 5 0 / T )

36

Na(SSI/2) • H • H - Na(SPI/2) • H 2

N15

3 8 x 10 -SG exp (28240/T)

36

Na(2P$/2) • H 2

NI6

7.6 x 10- 2 5 exp 128220/T)

36

Na(SSI/2 ) • O • O ~ Na(:IPII2 ) • 0 2

NIT

71 x 10- 2 6 exp (35170/T)

36

N a ( 2 S I / 2 ) • O • O ~ Na(SP312 ) • O 2

NI8

1.42 x 10- 2 ~ exp 135150/'1")

36

Na(SSI/2) + M ~ Na(SPl/2) • M

NI9

1.00 ¢xp ( - 24410/T)

36

Na(SSI/2) + M ~ Na(2P312) ÷ M

N20

2.00 exp 1 24430/3")

36

Na(SPll2) • M ~ Na(;IP312) • M K(2S1/2) • H • OH ~ K(2P1/2) • HsO

N24 N25

2 0 0 exp ( - 25/"1")

36

8.9 x I0 -~A~ ¢xp 141490/1")

36

K(2Sl12) • H • OH ~ K(2P312) • HsO K(2S1/2) • H • H ~ K(SPI/2 ) • H 2

N26 N27

1.78x 10- 2 5 ¢ x p ( 4 1 4 1 0 / T )

36

x 10-26¢xp(33960/T)

36

K(SSl12 ) • !1 • H ~ K(2P312) • H 2 K(2S!/2 ) • O • O ~ K(SPI/2 ) • 0 2

N28 N29

7.6 x 10 - 2 ~ exp 133880/T)

36

7.1 x 10- 2 6 ¢xp 140890/T)

36

K ( S S I / 2 ) + O • O ~ K(SP~IIS) • O 2

N30

1.42 x I0 -SG ¢xp 140810/'r)

36

K(2S!12 ) • M ~ K(2Pl/2) • M

N31

1.00exp(

36

K ( 2 S I / 2 ) + M ~ K(2P3/2 ) • M

N32

2 0 0 exp ( - 18770/T)

36

K(SPII2 ) • M ~ K(SP312) • M

N35

2.00 exp ( - 83/T)

36

Na+HO 2-

N38

1.20 cxp 17490/T)

36, 97

N41

1.35 ¢xp 19230/T)

36, 97

Na(SSllS) • H •

H ~

NaO 2 + H

K • HO 2 ~ KO 2 • H H•02•M CI•HO

2~

3.8

18690/T)

- HO2•M

P]

1.18× 10- 2 4 c x p ( 2 3 4 6 0 / T )

36

HCI•O

P2

0.56 cxp 128670/T)

36

2

H • tiO 2 - OH + OH

P3

9.3 exp 120180/T)

36

H • HO 2 ~ H 2 • 0 2

P4

0 3 3 exp 129200/T)

36

H 2 • HO2-.. H 2 0 + O I I

P5

2.2 exp (27710/T)

36

CO+HO 2 ~

I)6

0.090 exp (31050/T)

36

P7

0.75 exp (28160/T)

36

OH+HO 2~H20+O 2

P8

0.076 exp 136730/T)

36

CHO+O ~ CO+OIl

Ol

0.34 exp 144400/'1")

36

C H O + OH ~ CO + HsO

02

CO*tl*M-CHO+Id

Q3

0034 exp (53070/T) 2.7 x 10- 2 4 c x p 1 7 1 0 0 / ! " )

36 36

O

CO 2 • O H

• HO 2 ~ O 2 •

OH

Q4

O, 145 exp (45520/"r)

36

Q5

23

36

~CH 3+OH CH 4 • O H ~ C H 3•H~D

Q6 Q7

58 exp ( - 1 IO01T) 5.8 ¢xp (7530/T)

36 36

CHsO + OH ~ CHO • H 2 0

Q8

CH20•H~

Q9

2.8 exp ( 15160IT) I 1.9 exp (7610/T)

36 36

CHO•H~CO+H CH 4 + H

2

~CH$+H 2

CH 4 • O

CHO•H 2

RATE COEFFICIENTS FOR FLAME CALCULATIONS Reaction

Number

29 Equilibrium C o n s t a n t

Source Reference

CH~/~t. O - CHO • OH

QI0

27 exp (6530/T)

CH 3 • OH - C H 2 0 • H,j

QI I

0.034 exp (36040/1")

36

CH,~ • O 2 - C H 2 0 + OH

QI 2

0.95 exp (26970/'I")

36

CH 3 • O - C H 2 0 • H

QI 3

0.079 exp (34960/'!")

36

CH 3 • H • M

QI4

4x

36

CH 3 • CH$ ~ C21~

QI5

8.8 x 10 -211 e x p (43880/T)

C2H e • H -

C2H 5 • H 2

QI6

21.7 exp (I 140/T)

36, I./0-173

C2H 5 • H ~ C2H 4 • H 2

QI7

0.35 exp (35700/13

36, 170-1./3

C2H 4 • H - C2H $ • H 2

QI8

6.3 exp ( - 5 9 0 / T )

36, I./0-173

C2H 3 • H ~ C 2 H 2 • H 2

QI9

1.35 exp ( 3 2 3 0 0 / T )

36, I./0-173

C2H 2 + H ~ C2H + H~

Q20

4.5 e x p ( - 2600/T)

36

C2H + H ~ C 2 + H 2

Q21

2.3 exp ( - 16580/'I")

36

C2H 4 • H - C2H 5

Q22

I.I x 10 - ~ t exp ( I ? 0 0 0 / T )

36, 170-1./3

C 2 H 2 + H • M ~ C21~j • M

Q23

2.8 x 10- 2 5 exp (20400/'!")

36. 170-1"/3

C 2 • H • M ~ C2H • M

Q24

1.65 x 10 - 2 6 exp (69200/'I")

C H O + 0 2 - CO • HO 2

Q25

0.44 exp (16330/T)

36

CH 3 • O ~ CH • H 2 0

Q26

3.5 exp (5940/'1")

36

CI • OH + M - HOCI + M

RI

1.9 x 10 -2f~ exp (29600/T)

36

HOCI • H - CIO • H 2

R2

1.8 exp (3250/T)

36

HOC1 • OH ~ CIO * H 2 0

R3

0.41 exp (10780/'!")

36

HOCI • O ~ CIO • OH

R4

4.0 exp 12210/T)

36

CaOH ÷ + e-- - Ca + OH

SI

84 ©xp (20'~20/T)

CaOH•H

52

0.27 exp ( - 3180/T)

CaOH•H -Ca•H20 Ca•HCI~CaCI•H

53

0.018 exp (9320/'1")

$4

22.4 exp (-4200/'1")

36

CaCI~ • H ~ CaCI • HCI

$5

0.80 exp ( - 4 4 4 0 / ' r )

36

Ca(OH) 2 * H ~ CaOH • H 2 0

$6

0.24 exp (+ 10600/'r)

CaO * H 2 0 ~ Ca(OH)2

$7

6.0 x 10 - 2 4 exp (45250/1")

36, 148, 149, 175.1 ./7

CaOH ÷ • e - ~ C a O • H

$8

290 exp (15500/'1")

36. 147, 149, 174-176

CaOH ÷ • H

$9

0.024 exp (./100/T)

3 6 , 1 4 7 . 174

BaOII • H ~ Ba • H 2 0

$21

0.0144 exp (4230/'T)

BaO • H 2 0 ~ Ba(OH) 2

$22

1.32 x 10 - 2 3 e x p ( 3 0 2 9 0 / ' l )

BaOH • H - BaO • H 2

$23

0.12 exp (10840/'r)

Ba(OH)2 * H - BiOH • H 2 0

$24

0.24 exp (11520/I")

BaOH + • e -

~CH 4•M

~CaO•!12

~ Ca + • H 2 0

-Ba•OH

10 - 2 " l e x p ( 5 4 6 0 0 / 1 3

36

36. 170-1 ./3

36

36, 147, 174 36, 149, ] ./5, 176 36, 149

3 6 , 1 4 8 . 149, 177

149 148, 149, 36, 177 36,

$25

66 e x p (7400/1")

14./

BaOH + • ¢ - - B a O • H

$26

126 exp (21540/T)

36, 147

BaOH ÷ • H ~

$27

0.019 exp (4440/T)

Ba + • H 2 0

36, 169, 147

CH + O - C H O + + e -

T3

1.24 x 10- 5 r x p ( - 16"/oFr)

36

CHO* + H 2 0 - H s O * + CO

T4

0.2"/exp (15250/T)

36

H30 ÷*Lt-Li

÷•H20•H

149

36, 148, 149, 177

T5

4.9 x 1024 exp (9780/'1")

36

H 3 0 ÷ + Na - Na + + H 2 0 • H

T6

4.9 x 1024 exp (12700/T)

36

H 3 0 ÷ + K ~ K+ + H 2 0 + H

T7

4.9 x 1024 exp (22000/'13

36

I). E. JENSEN and G. A. JONES

30 Reaction

Equilibrium Constant

Number

Source Reference

HsO ÷ • In - In ÷ • H 2 0 • M

T8

H30 ֥CI-

T9

5.5 x 102*. exp (30200fr)

36

TI0 TI I

4.0 x 102.. exp (51020fr) 6.5 x 10211exp (14900/'T)

36 36

Ui U2 U3 U4 U5 u6 u7

0.026 exp ( - 19100/'!") 19 exp (33200/T) 3.1 x 10 - 2 . . exp (24640/'1") 1.30 exp (27900/'T) 0.31 exp (35450fr) 4.6 exp ( - 3 7 9 0 0 f r ) 4.7 exp (16120/T)

36 36 36 36 36 36 36

VI V2 V3 V4 VII VI2 VI 3 V21 V22

66exp(-16100/T) 0.044 exp (5400/T) 9.0 x 10-aS exp (35500/T) I 0 exp ( I 1700/T) 0.037 exp (I 9600f1") 4.3 x 10- 2 3 exp (24700/'1) 0.23 exp (8350/T) 0.037 exp (9000fr) 1.4 x 10-211 exp (39500/'I")

HaWO 4 • H ~ HWO s • HaO Co+OH~CoO•H

V23

0.73 exp (4150/'I")

163

V31

0.45 exp (I 200/'i")

164

CoOH • H -. COO • H 2 COO + H20 ~Co{OH) 2 Co(OH) a • H ~ CoOH • H20 H + H(+Cr) ~ H2(+Cr) H • H(+SnO) ~ Ha(+SnO)

V32 V33 V34 V41 V42

0.25 exp (I 7TOO/T)

164

~HaO•H•CI

H$O ÷ • O H - - ~ H ~ I O • H • O H H$O ÷ • e-- ~ H • H ÷ OH

NO+ NO-

NzO÷O

N20•H~

N 2•OH

NO+H+M~

HNO+M

HNO•

H ~ NO ÷ H2

HNO•

OH - N O • H 2 0

N2+O N+O

~NO+N 2 ~NO•O

Fe+HaO-

FeOH+H

FeOH+H~

FeO+H a

FeO + H 2 0 ~ Fe(OH) 2 Fe(OH) 2 + H ~ FeOH + H 2 0 HMoO 3 + H

~MoO 3•H 2

MoO a • H a O ~ H 2 M o O 4 H 2 M o O 4 • H ~ H M o O 3 • H20

HWOs ÷ H ~ WOa • Ha WO 3 + H,,)O ~ HaWO 4

The authors thank Dr. M. A. A Clyne (Queen Mary College. London}, Dr. D. L. Baulch (University o f Leeds), Dr. R. F. Hampson (NationaI Bureau o f Standards, Washington, D. C. ) and Dr. G. DixonLewis (Leeds University) for helpful discussions and comments. They are particularly grateful to Dr. Dixon-Lewis and to Dr. D. J. Williams for an opportunity to see a comprehensive review article ( R e f [ 180]) on hydrogen and carbon monoxide oxidation prior to publication. © Controller. Her Ma/esty's Stationery Office. London, ! 9 7 7.

4.9 x 1024 exp (5180fr)

2.7 x 10- ' ) 4 exp (24950/T) 0.56 exp ( i o o o o f r ) 3.8 X 10 -a*. exp (52650fr) 3.8 × 10-a*. exp (52650/T)

36. 169

36, 162, 178 36, 162. 178 36, 162, 178 36. 162. 178 163 36 163 163 36

164 164 36 36

REFERENCES I. 2.

3.

Jeruml, D. E. and Jonek G. A., RPE Tech. Report 71/9, 1971 Jerome, D. E. and Wlb(m, A. $. Comlmst. Flame 25,43 (1975). h u l c h , D. L., DryKhble, D. D., Dmcbuq, J. mid

Gflmt, S. J., Evaluated Kinetic Data for High Temperature Reactions. Vol. 3, Buttcrworths, London, 4.

1976. k u k : h , D. L., DqryMak, D. D., Home, D. G. and

Uoyd, A. C., E~aluated Kinetic Data for High Temperature Reactto~ts, Vol. l. Butterwozths. London. 1972

31

RATE COEFFICIENTS FOR FLAME C A L C U L A T I O N S 5. h n l d l , D. L., Dffultle, D. D., Home, D. G. and Lloyd, A. C., Evaluated Kinetic Data [or High Temperature Reactions. Vol. 2. Butterworths, 6 7. 8 9.

I0. II 12. 13 14. 15. 16 17. 18.

19.

20 21. 22. 23.

24 25.

26 27 28.

29.

London. 1973. F ~ t m m , E. M. and Wutenbeql, A. A., Flame Structure. McGraw-Hill. New York 1965. Klein, F. S. and Wolftbeql, M., J. Chem. Phys. 34, 1494 (1961). Jacobs, T. A., Cdedt, R. R. and Cohen, N., J. Chem. Phyt 49, 1271 (1968). Albdght, R. G., Dodemov, A. F., Lavmvdumyu, G. K., Momto% I. I. and Tat'role, V. L., J. Chem. Phys. 50, 3632 (1969). Bemand, P. P. and Clyne, M. A. A., J C S. Fara. day !! 73, 394 (1977). Ambidle , P. F., Bi~lley, J. N. and Whytock, D. A. J C S. Faraday ! 72, 1157 (1976). Wqpwr, H. G~, Webbacher, U. and 7.,dries, R., Ber. Bunsenges. Phys. Chem. 80, 902 (1976). AmbldM, P. F., Ikudley, J. N. end Whyto(k, D. A., J C S. Faraday ! 72, 2143 (1976), Wettenbeqi, A. A. and de I-lau, N.,J. Chem. Phys. 48, 4405 (1968). Takact, G. A. and Glat~ G. P., J. Phys. Chem. 77, 1948 (1973). Zahn/mr, Z., Kaufman, F. and Andenon, J. G., Chem. Phys. Left. 27,507 (1974). Smith, L W. M. and Zellner, R., J. C. S. Faraday H 70, 1045 (1974). Wilson, S. E., O'Donovun, J. T. and F m t m m , R. M., rweifh Symposium (International) on Combustion. The Combustion Institute. Pittsburgh. 1969, p. 929. Balalmia, V. P., F.41orov, V. I. and Intezatova, E. I., Kinetic and Catalysis 12, 258 (1971) (Translation from Kinetika i Kataliz 1971, 12(2). 299). Wonlk E. L. and Belles, F. E., NASA TN D-6495 (1971). Brown, R. D. H. and Smith, I. W. M., lnt. J. Chem. Kin. 7, 301 (1975). Jacoh~ T. A., Giedt, R. R. and Cohen, N., J Chem. Phys. 43, 3688 (1965). Bhmer, J. A., J. Phys. Chem. 72, 79 (1968). (]yne, M. A. A., McKenney, D. J. und Walker, R. F., Can. J. Chem. 51, 3596 (1973). Homann, K. H., Solomon, W. G., Wamatz, J., Wqlaer, H. El. and 7.,eew.h, F., Bet Bunsenges. Phys. Chem. 74,585 (1970). Kompt, K. L. and WanMr, J., Chem. Phyt Lett 12,560 (1972). Rabidean, S. W., Hecht, H. G. and Lewla, W. B., J. Magn. Resonance 6, 384 (1972). Dodoaov, A. F., Lavm~Imya, G. K., Mommy, I. I. n d Td'rme, V. L., Dokl. ANad. NouN. (SSSR) 198,622 (1971). Pol,anyi, M., Atomic Reactions. Williams and Norp t e . London, 1932.

30.

Koadrttlev, V. N., Chemical Kinetics o[ Gas Reactions. Pergamon. New York 1964. p. 90 31. T|ylot, E. H. and DItz, S., .I. Chem. Phys. 23,

32.

33. 34. 35. 36.

37. 38.

39. 40.

1711 (1955). Kondrutiev, V. N., Rate Constants o[ (;as Phase Reoctions. Science Publishing House. Moscow 1970. Jenaen, D. E., Combust. Flame 18, 217 (1972L Stqgden, T. M., Trans. Faraday Soc. 52, 1465 (1956). Jenaen, D. E. and Pudley, P. J., Trans Faraday Soc 62, 2140 (1966) J A N A F Thermochemwal Tables (D. R. Stall and H. Prophet, Eds.)NBS-NSRDS No. 37. 1971. Supplement J A N A F Thermochemical Tables. 1974 Supplement. M. W. Chase. J. L. Curnutt. A T. Hu, H. Prophet, A. N. Syverud and L. C. Walker. J Phys. Chem. Ref. Data 3, 311 (1974). Supplement J A N A F Thermochemicol Tables. 1975 Supplement; M. W. Chase, J. L. Cumutt, H. Prophet. R. A. McDonald and A. N. Syverud, J. Phys. Chem. Re[ Data4, I (1975). Jemmn, D. E. and Miller, W. J., J. Chem. Phys. 53, 3287 (1970). Jemen, D. E. and Millet, W. J., Thirteenth Symposium (International) on Combustion, The Combustion Institute. Pittsburgh, 1971. p. 363. Jtcoht, T. A., Giedt, R. R. and Cohen, N., J Chem. Phys. 46, 1958 (1967). Seery, D. J. and Bowman, C. T., J. Chem PhFs. 48,

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D. E. JENSEN and G. A JONES

32 56. 57 58. 59. 60. 61. 62.

63. 64. 65. 66. 67.

68. 69

70. 71. 72.

73. 74. 75. 76.

77 78. 79.

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RATE COEFFICIENTS FOR FLAME CALCULATIONS 110. II! 112. I 13. 114.

115

116.

117 118 119.

120. 12 !

122 123 124.

125 126.

127

128.

129 130

131

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132 133 134. 135 136. 137

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142. 143. 144. 145. 146. 147 I48 149. 150

151.

152.

153 154. 155 156. 157.

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34 158. 159. 160.

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Received I July 1977: revised !0 October 1977