AERONOMICA ACTA

I N S T I T U T D - A E R O N O M I E S P A T I A L E D E B E L G I Q U E 3 - Avenue Circulaire

B - 1180 BRUXELLES

A E R O N O M I C A A C T A

A - N° 2 6 1 - 1 9 8 3

Modeling of stratospheric ions : a first attempt

by

G. BRASSEUR and A. CHATEL

B E L G I S C H I N S T I T U U T V O O R R U I M T E - A E R 0 N 0 M I E

3 - Ringlaan

B - 1180 B R U S S E L

FOREWORD

T h i s paper has been presented at the 9th Annual meeting of the European Geophysical Society held in Leeds (Great-Britain), A u g u s t 1982. It will appear in the Annales Geophysicae.

A V A N T - P R O P O S

Cet article résume une communication présentée à la 9e réunion annuelle de la Société Européenne de Géophysique qui s'est tenue à Leeds (Grande Bretagne) en août i y 8 2 . Il sera publié dans Annales Geophysicae.

VOORWOORD

Dit artikel is een samenvatting van een mededeling die gedaan werd op de 9e Algemene Vergadering van de "European Geophysical Society" die plaats vond in Leeds (Groot-Brittanië) in augustus 1982.

Het zal gepubliceerd worden in Annales Geophysicae.

VORWORT

Dieser Aufsatz stellt die Zusammenfassung einer Mitteilung

während der 9. Allgemeinen Tagung der Europäischen Geophysicalischen

Gesellschaft in Leeds (Gross-Britannien) im August 1982 da. Er wird

veröffentlicht in den Annales Geophysicae.

M O D E L I N G O F S T R A T O S P H E R I C IONS : A F I R S T A T T E M P T

by

G. B R A S S E U R ( * ) and A . C H A T E L ( * * )

A b s t r a c t

'Several observations of positive and negative ions around 35 km have shown the complexity of the ion chemistry in the strato- sphere. T h e presence of cluster ions s u c h as H

+

X

n

( H 2 0 )

m

(with probably X = C H ^ C N ) has been detected. Negative ions s u c h as N 0

3

( H N 0

3

)

n

and HSO~ ( H

2

S 0

4

)

n

( H N 0

3

)

m

are also present. T h e chemical kinetics of these ions is still poorly known. T h e purpose of the paper is to present and d i s c u s s preliminary results obtained with a model which simulates the behavior of stratospheric ions.

Résumé

Des observations effectuées aux environs de 35 km d'altitude ont montré la complexité de la chimie des ions dans la stratosphère. La présence d'agrégats du type

^{H + x n}

(

^H

2 ° )

^{m X e s t}

Probablement C H ^ C N ) a été détectée. Des ions négatifs du type N 0

³

( H N 0

³

>

ⁿ

et H S O " ( H _ S O . ) ( H N O _ ) sont également présents. La cinétique chimique

4 b 4 n <5 lïl

des ions n'est pas encore bien connue. Un modèle décrivant le comportement des ions stratosphériques a cependant été établi, s u r base de certaines hypothèses. Les résultats préliminaires sont discutés dans cet article.

( * ) A s p i r a n t au Fonds National de la Recherche Scientifique.

(**) Now at the Cliniques Universitaires de B r u x e l l e s - Hôpital Erasme.

Samenvatting

Waarnemingen v e r r i c h t op hoogtes rond 35 km hebben de complexiteit van de ionen-chemie in de stratosfeer aangetoond. Clusters

van het type H

+

X ( H „ 0 ) (met X waarschijnlijk gelijk aan C H _ C N ) n d. m ^ werden gedetecteerd. Negative ionen van het type NO^CHNOg^ en

HSO~(H„SO,) werden eveneens gevonden. De kinetische chemie van de 4 2 4 n

ionen is nog onvoldoende gekend. Op basis van bepaalde hypotheken werd nochtans een model ontwikkeld dat het gedrag van de strato- sferische ionen weergeeft. In dit artikel worden de preliminaire resultaten besproken.

Zussammenfassung

Beobachtungen auf einer Höhe von ungefähr 35 km zeigten eine sehr grosse komplexität der stratosphärischen Ionen-Chemie.

Aggregate des T y p e s

H + x n

(

H

2 ° ^

n w u r d e n

identifiziert wobei X sehr wahrscheinlich CHgCN ählich ist. Negative Ionen des T y p e s NC>

3

(HN0

3

)

n

und

H S 0

4 ( H 2

S C

V n

s i n d e b e n f a l l s

identifiziert. Obwohl die kinetische Theorie de Ionen-Chemie noch nicht genügend gekannt ist, ist ebenwohl, dank bestimmten Hypothesen, ein Modell entwickelt worden, das das Benehmen der stratosphärischen Ionen T a t w i r k l i c h beschreibt.

In dieser Aufsatz werden die vorhergehenden Ergebnisse besprochen.

- 2 -

1. I N T R O D U C T I O N

T h e identification of ions in the stratosphere has become technically possible only in the recent years after the development of balloon borne mass spectrometers. T h e available measurements of positive ion composition have to be attributed to A r n o l d et al (1977;

1978; 1982) and Arijs et al (1978; 1980; 1982). The observations made in the altitude range of 33-37 km reveal the presence of two distinct families of ion species with more or less the same abundance : (1) the proton hydrates ( P H ) which are clusters in the form of H

3

0

+

( H

2

0 )

n

and ( 2 ) the non-proton hydrates ( N P H ) whose chemical structure can be written as H

+

X

0

( H _ O ) , X being a molecule with a proton affinity exceeding that of water vapor. Arijs ct al (1980) have derived unambigously from their high resolution spectra that the mass of the X molecule should be equal to 41 amu and that the most likely candidate for this molecule is acetonitrile ( C H ^ C N ) as s u g g e s t e d b y A r n o l d et al (1978). The proton affinity of C H ^ C N is 187.4 kcal whereas that of water vapor . is 168.9 kcal only. T h e atmospheric b u d g e t of acetonitrile as well as its stratospheric concentration is not yet known. C H ^ C N is frequently used as an industrial solvent and it could also be produced by combustion processes.

The chemical composition of negative ions has also been derived from mass spectrometric observations ( A r n o l d and Henschen, 1978; Arijs et al, 1981; 1982; Mc C r u m b and A r n o l d , 1981; A r n o l d et al, 1981; 1982; V i g g i a n o and A r n o l d , 1981). These in situ measurements indicate that the major ions are probably clusters belonging to two different families, namely H S 0

4

(

H 2 S

° 4 ^ ^

H N

° 3 ^ m

a n d

NO~ ( H N 0

3

)

n

- T h i s underlines the important role played b y sulfuric and nitric acid in the formation of stratospheric negative ions and the expected relation with the aerosol layers.

- 3 -

I

Up to now, due to t h e limited knowledge of t h e chemical processes involving s t r a t o s p h e r i c ions, no detailed model of t h e ionic composition below 50 km has been established. O n l y p a r t i a l calculations have been presented to explain some o b s e r v a t i o n s . T h e purpose of this paper is to attempt to produce a global model of t h e ions in t h e s t r a t o - s p h e r e . Because of t h e large amount of u n c e r t a i n t i e s in t h e chemical d a t a , such a model remains p r e l i m i n a r y . Many assumptions have still to be made and f o r example t h e values of some rate constants have been

"tuned" until t h e calculated and observed ion concentration were in good agreement. T h e i n t e r e s t of such a model however is to show t h a t , with reasonable assumptions, t h e adopted chemical scheme can explain t h e available o b s e r v a t i o n s . An other objective is to analyze t h e r e l a t i v e

importance of t h e d i f f e r e n t reaction paths and to determine which p a r a - meters have t h e largest influence on t h e concentration v a l u e s .

2 . T H E ION SCHEME

T h e ionization in t h e s t r a t o s p h e r e is due to t h e action of galactic cosmic r a y s . T h e corresponding rate of i o n - p a i r formation can be calculated from t h e expression suggested by Heaps ( 1 9 7 8 ) . When applied to a geomagnetic latitude of 4 6 ° , corresponding to t h e site of A i r e sur I'Adour where most observation are made, t h e Heaps formula becomes

Q = 7 . 1 x 1 0 "

1 8

[M] ( 1 )

above t h e altitude of 30 km and

- 4 -

Q = 1.7 x 10"

2 0

[M]

1

'

1 5

(2)

between 18 and 30 km. In these expressions, [M] is the total concentra- -3 -3 -1 tion expressed in cm and Q the ionization rate given in cm s .

T h e main loss process of the ions is the recombination between positive and negative c h a r g e s . T h e corresponding recombination coefficient a can be deduced either from observational data (Gringel et al, 1978; Rosen and Hofman, 1981) or from laboratory work (Smith and C h u r c h , 1977; Smith and Adams, 1982). Its value can also be established from theoretical considerations ( B a t e s , 1982). In the present model, we have adopted the expression

a(cm

³

s "

¹

) = 6 x 10"

⁸

( 3 0 0 / T )

⁰

-

⁵

+ 2 x 10~

^{2 6}

[M] (300/T)

⁴

(3)

which provides values lying between those suggested by Bates (1982) and Smith and Adams (1982). In this formula, T is the temperature expressed in K . Introducing the electro-neutrality condition, one can immediatly derive that the total concentration of positive and negative ions is given by

n

⁺

= n~ = (Q/c0

^{1 / 2}

(*>

- -3 -3 and is equal to 6000 cm at 20 km, 4400 cm at 30 km, 2800 cm at

40 km and 1500 cm"

³

at 50 km, if the temperature profile of the US Standard atmosphere (1966) is used.

- 5 -

2.1. Positive ions

Since the primary ion N* exchanges its electrical charge instantaneously with O^, one can consider that each ionization leads to the formation of an ioni2ed oxygen molecule. The subsequent chemistry has been described in several papers and in particular by Ferguson (1979) and Arnold (1980). O* reacts with O to form O* which can be

hydrated to produce O^.H^O and subsequently other hydrates with higher orders are obtained by supplementary hydrations

H 0

+

(H 0) + H O + M — H 0

+

(H 0) + M (n £ 0) (5) 3 2 n 2 3 2 n + l

which are characterized by a forward reaction rate k^ and a reversed rate constant k associated to the thermal dissociation. The ratio

r

[HgO ( H

2

0 )

n + 1

]/[H

3

0 (

H 2

° )

n

l

i s

proportional to the equilibrium constant K = k V k which varies intensively with the temperature.

n+1, n f r

The values of these parameters reactions k

1 2

to k^g in table 1 are taken from the recent paper by Lau et al (1982).

The non-proton hydrates H^O*

x

g (

H 2 0

)

n a r e f o r m e d b

V' reactions of PH with an X molecule and subsequent conversions between X and H

2

0 . Different candidates have been suggested for X (e.g.

Na OH by Ferguson, 1978) but since the mass of this molecule is unambigously equal to 41 a . m . u . , according to Arijs et al (1980), the most likely candidate for X seems to be acetonitrile (CH^CN). Other non-proton hydrates, namely H

3

0

+ Y

£ (

H 2 0

) n '

a

P P

e a r i n t h e s

P

e c t r a

obtained by Henschen and Arnold (1981) and Arnold and Henschen (1982), where Y is a molecule with mass 32 ± 1. This molecule has been tentatively identified as methanol (CH_OH) by Henschen and Arnold (1981). The proton affinity of CH^OH (182 kcal mole ) is larger than

- 1

that of water vapor but smaller than that of acetonitrile. Therefore H 0

+

Y ( H „ 0 ) should react with C H . C N . Since the stratospheric budget

3 2 n -3

- 6 -

T A B L E 1 : Chemical scheme for the positive ions in the stratosphere and adopted rate constants (X = CHgCN).

3 -1 Reaction Rate constant (in cm s for

2-body reactions and in cm^ s * for 3-body reactions)

° 2

+

° 2

+ M

""

+ M + M -»• 0 * + 02 + M

V °3 °2

°5

+

°2 " \

+

°3 o

+

H

2

o o ,H

²

0 + n

3

°4

+ H

2° °2-

H

|°

+

°2

o H

2

O + o

2

- o

4 + +

H

2

O

0 . H20 + H20 - H30+ + O H + 02

O2. H2O + H2O H3O+. O H + O2

H30+. 0 H + H20 •*• H30+. H20 + O H H3O+ + N2O5 N O * H2O + H N O3

H30+ + H N 03 -*• N 02. H20 + H20

N 02- H20 + H20 + M N 02( H20 )2 + M N 02( H20 )2 + H20 - H3O+. H2O + H N O3

H30+ + H20 + M •*• H ^ 0+. H20 + M H30+. H20 + M -»• H30 + H20 + M

H30+. H20 + H20 + H -> H30+( H20 )2 + M H30+( H20 )2 + M » H3O+. H2O + H2O + M H3O+( H2O )2 + H2O + M -»• H3O+( H2O )3 + M H3O+( H2O )3 + M H30+( H20 ) ^ + H20 + M H30+( H20 )3 + H2O + M H3O ( H204) + M H3O+( H2O )4 + M -»• H3O +( H20 ) + H2O + M H3O+( H2O) + x H30+( H 0 ) X + H20 H3O+. H2O . X + H2O H3O ( H20 )2 + X

-30 3 2 k = 2.6 x 10 (300/T)

k = 2.4 x 10"

6

(300/T) e -

4 9 0 0 / T

1 x I«"

10

k

2 b

= k

2

/2 x 10

4

k^ = 1.2 x 10 k = 1.5 x 10"

9

,.-10 -2300/T k., = 2 x 10 e

, -10 k

5

= 2.4 x 10

k, = 1.2 x 10~

9

6

-9

k

?

= 1.4 x 10 k

0

= 1.3 x 10~

9

k = 1.6 x 10 -9 k = 2 x 10 -27

- 1 0

k = 2 x 10

-17 -4 k = 2.5 x 10 T

k

Wb =

3

'

7 7 X 1 0 1 0 T _ 5 e

'

1 5 9 1 0 / T

k , = 2.8 x 10'

8

-

1

T"

7

-

5

11/ i n

1 8 9

T~

8

-

5

"9819/T k, = 1.14 x 10 T e

l 4 b

- 7 - 8 1 k = 2.9 x 10 T *

, o /, ,«21 -9.1 -9013/T k,.,, = 3.44 x 10 T e

1 7 b

7 - 1 4

k = 1.52 x 10' T

U I M 3 4 T "1 5 E - 6 3 9 4 / T

k

10_1HD

, = 1.51 x 10 T _q k

2Q

= 3.6 x 10

20b 0 (case 1)

3.5 x 10"

16

(case 2)

- 7 -

H / . L O . X + H O • + M H 0

+

X ( H O ) + M k = k

+ + _oR 7 2 S 2 / T H

³

0 . X ( H

²

0 )

²

+ M H O X H

²

0 + H

²

0 + M k

^{4 b}

= k

^{2 1}

/ ( 8 . 4 x 10 T e )

H

3

0

+

( H

2

0 )

3

+ . X - H3O X ( H

2

0 )

2

+ H

2

0 k

2 2

= 3 . 3 x î o "

9 v

H

³

0

⁺

X ( H

²

0 )

²

+ H

²

0 H

³

0

⁺

( H

²

0 )

³

+ X k

^{2 2 b}

= 0 ( c a s e 1)

= 5 x 1 0 ~

1 4

( c a s é 2 ) H

³

0

⁺

X ( H

²

0 )

^{2 +}

H

²

O

⁺

M - H

³

0

⁺

X ( H

²

0 )

^{3 +}

M k

^{2 3}

= k

^{1 8}

H

³

0 X ( H

²

0 )

³

+ M + H

³

0 X ( H

²

0 )

²

+ H

²

0 + M k

^{2 3 b}

= K

^{2 3}

/ ( 8 . 4 x 10 T E

³

) H

³

O

⁺

( H

²

O )

a

+ x -»• H

³

O

⁺

X C H

²

O )

³

+ H

²

O k

2 4

= 3. 0 x 1 0 "

⁹

H

³

0

⁺

X ( H

²

0 )

³

+ H

²

0 -> H

³

0

⁺

( H

²

0 )

⁴

+ X k

^{2 4 b}

= 0 ( c a s e 1)

= 4 . 3 x 1 0 "

1 2

( c a s e 2 ) H

³

0

⁺

X H

²

0 + X H

³

0

⁺

X

²

+ H

²

0 k

^{2 7}

= k

^{2 0}

/ 5

H

3

0

+

X

2

+ H

2

0 - H

3

0

+

X H^O + X k

2 7 b

= k

2 0 b

x 10 H „ 0

+

X „ + H O + M -> H O X H O + M k = k

•^4. + - 2 8 6 8 4 3 / T H

3

0 X

2

H

2

0 + M -»• H

3

0 X

2

+ H

2

0 + M k

2 g b

= k

2 g

/ ( 8 . 4 x 10 T e ) H

³

O

⁺

X ( H

²

O )

2

+ x - H

³

O

⁺

X

²

H

²

O + H

²

O K

^{2 9}

= K

^{2 2}

H

³

0

⁺

X

²

H

²

0 + H

²

0 - H

³

0

⁺

X ( H ^ 0 )

²

+ X k

^{2 9 b}

= k

^{2 2 b}

x 1 . 8 H 0

⁺

X „ H - 0 + H - 0 + M H

^o

0 X „ ( H

^o

0 )

^o

+ M k . = k .

3 7 2 2 " 2 . 3 2 2 2 30 23 _

2 g 5

3 7

9

/

T H

3 °

X

2

( H

2

0 )

2

+ M

* f

X

2

H

2 °

+ H

2 °

+ M k

3 0 b

= k

3 0

/ ( 8

"

4 X 1 0 T 6 }

H

³

O

⁺

X

²

H

²

O + x ^ H ^O x

3

+ H

2

O k

3 4

= k

2 9

H

³

O

⁺

X

^{3 +}

H

²

O - H

³

O X

^{2 +}

H

²

O

⁺

x k

3 4 b

= k

2 9 b

H

³

O

⁺

X ( H

²

O )

3

x H

³

O

⁺

X

²

( H

²

O )

²

k

^{3 1}

= k

^{2 4}

H

³

0

⁺

X

²

( H

²

0 )

^{2 +}

H

²

O H

³

0

⁺

X ( H

²

0 )

³ +

x k

^{3 1 b}

= k

^{2 4 b}

- 8 -

of methanol is n o t y e t k n o w n , t h e possible e f f e c t of a Y molecule has not been c o n s i d e r e d in t h e model. T h e g e n e r a l PH to N P H c o n v e r s i o n will t h e r e f o r e be w r i t t e n

H

3

0

+

( C H

3

C N )

£

( H

2

0 )

n

+ CH

3

CN ^ H

3

0

+

( C H

3

C N )

£ + 1

( H

2

0 )

n

j + H

2

0 ( 6 )

f o r S, i 0 a n d n £ 1. Smith e t al ( 1 9 8 1 ) h a v e m e a s u r e d t h e r a t e of such r e a c t i o n s f o r & = 0 . T h e y o b t a i n r a t h e r h i g h v a l u e s s h o w i n g t h a t , e v e n w i t h a small a m b i e n t c o n c e n t r a t i o n of a c e t o n i t r i l e , t h e c o n v e r s i o n f r o m PH to NPH could be v e r y e f f i c i e n t . I n p r i n c i p l e , h o w e v e r , t h i s p r o c e s s could be limited b y a r e c o n v e r s i o n of N P H to PH whose a m p l i t u d e d e p e n d s on t h e c o r r e s p o n d i n g r e v e r s e r e a c t i o n s r a t e s . S i n c e t h e v a l u e of t h e s e l a t t e r c o n s t a n t s is not k n o w n , t w o e x t r e m e cases h a v e been c o n s i d e r e d in t h e c a l c u l a t i o n : case 1 assumes t h a t t h e r e v e r s e r a t e c o n s t a n t is equal to z e r o f o r r e a c t i o n s 2 0 , 2 2 , 2 4 , 2 7 , 2 9 , 31 a n d 34 - see t a b l e 1 a n d f i g . 1 . I n case 2 , r e v e r s e r e a c t i o n s a r e assumed t o be e f f i c i e n t w i t h t h e c o r r e s p o n d i n g r a t e s as g i v e n in t a b l e 1 . I n o r d e r to f i t t h e o b s e r v a t i o n a t 35 k m , t h e model r e q u i r e s in each case a d i f f e r e n t a c e t o n i t r i l e p r o f i l e . T h e c o n c e n t r a t i o n v a l u e as assumed in case 1 is u n i f o r m l y m u l t i p l i e d b y 50 w h e n case 2 is c o n s i d e r e d ( f i g . 2 ) . T h e s h a p e of t h e s e p r o f i l e s is based on an a n a l y s i s , b y H e n s c h e n a n d A r n o l d ( 1 9 8 1 ) . Reactions f o r SL > 0 h a v e n e v e r been m e a s u r e d a n d it is t h e r e f o r e assumed t h a t k

2 7

= k ^ / S ; k

3 4

= k

2 Q

= k

2 2

; k

3 1

= k

2 4

.

H y d r a t i o n of t h e NPH ions must also be c o n s i d e r e d . S e v e r a l e q u i l i b r i u m c o n s t a n t s of t h e f o l l o w i n g r e a c t i o n s

H

3

0

+

( C H

3

C N )

£

( H

2

0 )

n

+ H

2

0 + M ^ H

3

0

+

( C H

3

C N )

£

( H

2

0 )

n + 1

+ M , ( 7 )

- 9 -

131-

cosmic rays

o;

2

.M © M 0 HjO ©

O2. H2O

NO2 ,H2O

10)

NQ2 ,(H20)2

n,O

5

® HNOJ ®

^H3O

<5

°2 °3 (D

©

H30 . OH

© M (12

^H

3O . H2O

© H,0

M C\£i

POSITIVE IONS STRATOSPHERE

X = C H J C N

H3O .(H,0)2

HJO . M (17) M

^H

3O.(H2O).

. X

H30 X H2O

@ ^{21 M}

(18) M

H3O X(H20)2

H3O X2

@ M

23 M

H3O X2H2O

H3O X3

H30 (H20)4 (NPH) X

©

^H;0

H30 X(H20)3 (A) X

®

^H2O

H3O X2(H20)2 (B)

(C)

Fig. 1.- Chemical scheme adopted for the positive ions in the stratosphere.

VOLUME MIXING RAT IC

Fig. 2.- Vertical distributions of the acetonitrile mixing ratio adopted in the

model.

have been measured b y Böhringen and A r n o l d ( 1 9 8 1 ) at t h e specific t e m p e r a t u r e of 227 K. Since t h e value of these constants depends crucially on t h e local t e m p e r a t u r e , and in o r d e r to introduce in t h e model such a dependence, it has been assumed t h a t t h e AS value

- 1 - 1

corresponding to these reactions is equal to - 24 cal K mol . In f a c t , this parameter does not change considerably from one reaction to another and f o r example in the processes considered by Lau et al

- 1 - 1

( 1 9 8 2 ) , AS varies only from - 2 1 . 7 to - 2 8 . 4 cal K mol .

Using t h e measured K value at 227 K and the assumed AS eq v a l u e , t h e equilibrium constant is d e r i v e d from t h e formulae

K ( a t » "

¹

) = e ^ e * ( 8 )

eq

K (cm

3

) = 1.367 x 1 0 "

2 2

T K ( a t m "

1

) ( 8 b i s ) eq

where R is t h e gas constant, AH and AS t h e d i f f e r e n c e of e n t h a l p y and e n t r o p y f o r t h e reaction which is considered. T h e determination of t h e thermodynamical parameters r e q u i r e s detailed laboratory work as recently s t a r t e d b y A r n o l d and B o h r i n g e r ( p r i v a t e communication). In t h e expectation of measured values of f o r w a r d reaction rates f o r processes ( 7 ) t h e following w o r k i n g values are introduced in t h e model (see table 1) : k

2 g

= k

2 1

= k

1 ?

and k

3 Q

= k

2 3

= k

1 g

. Such an assumption is quite acceptable since t h e concentration values depend essentially on t h e specified equilibrium constants and not on t h e individual f o r w a r d and r e v e r s e reaction r a t e s .

T h e numerous rate constants used in t h e model will not be discussed in this p a p e r . Most values listed in table 1 are t a k e n from t h e paper by A l b r i t t o n ( 1 9 7 8 ) in which t h e most important references are q u o t e d . In some cases when t h e reaction rate or its t e m p e r a t u r e

- 1 2 -

d e p e n d e n c e is not k n o w n t h e v a l u e i n d i c a t e d in t h e t a b l e r e f e r s to t h e a s s u m p t i o n w h i c h is m a d e .

2 . 2 . N e g a t i v e ions

T h e n e g a t i v e ion scheme w h i c h a p p l i e s to t h e s t r a t o s p h e r e is v e r y c o m p l i c a t e d . T h e s t a r t i n g p o i n t is t h e a t t a c h m e n t of a f r e e e l e c t r o n on an o x y g e n molecule. O^ is s u b s e q u e n t l y t r a n s f o r m e d into CO~ t h r o u g h d i f f e r e n t p a t h s ( s e e F e r g u s o n , 1 9 7 9 ) a n d C 0

3

is t h e n c o n v e r t e d into N O ~ . T h i s l a t t e r ion is p a r t i c u l a r l y s t a b l e since its e l e c t r o n a f f i n i t y is one of t h e h i g h e s t of all k n o w n ions. C l u s t e r i n g r e a c t i o n s a r e h o w e v e r p o s s i b l e , e s s e n t i a l l y w i t h w a t e r v a p o r a n d n i t r i c a c i d , l e a d i n g to h e a v y ions such as N 0 ~ ( H N 0

3

)

£

(

H 2

0 )

n w i t h £ a n d

n ^ O . S i n c e t h e s e ions r e a c t r a p i d l y w i t h s u l f u r i c acid ( V j g g i a n o e t a l , 1 9 8 0 ) , c l u s t e r s of t y p e H S O ~ ( H N C >

3

)

£

( H

2

S C >

4

)

m

( H

2

0 )

n

a r e e x p e c t e d to a p p e a r a n d can be i d e n t i f i e d f r o m mass s p e c t r o s c o p i c o b s e r v a t i o n s ( s e e e . g . t h e l a t e s t p a p e r s b y A r i j s e t al ( 1 9 8 2 ) a n d A r n o l d e t al ( 1 9 8 2 ) ) . F i g u r e 3 shows a possible r e a c t i o n scheme s u g g e s t e d b y A r i j s et al ( 1 9 8 1 ) to e x p l a i n his o b s e r v a t i o n a l d a t a . Most of t h e c o r r e s p o n d i n g k i n e t i c s is u n k n o w n e x c e p t r e a c t i o n r a t e s k

4 g

, k

g 0

a n d k

g 4

( s e e t a b l e 2 ) w h i c h h a v e been r e c e n t l y m e a s u r e d b y V i g g i a n o e t al ( 1 9 8 2 ) . In most c a s e s , w o r k i n g v a l u e s h a v e t h u s been a d o p t e d . For r e a c t i o n s of t y p e

n o ~ ( h n o

³

)

^£

+ h n o

³

+ m ^ n o

³

( h n o

³

)

^{£ + 1}

+ M , ( 9 )

no r a t e c o n s t a n t is a v a i l a b l e e x c e p t f o r £ = 0 , w h e r e F e h s e n f e l d e t al - 2 6 6 - 1

i n d i c a t e a v a l u e s l i g h t l y l a r g e r t h a n 1 x 10 cm s . T h e r e f o r e , a - 2 6 6 - i

f o r w a r d r a t e c o n s t a n t of 1 x 10" cm s has been a p p l i e d f o r all v a l u e s of Z w i t h an e q u i l i b r i u m c o n s t a n t t a k e n f r o m t h e s t u d y b y

D a v i d s o n et al ( 1 9 7 7 ) a n d Wlodek e t al ( 1 9 8 0 ) . T h e h y d r a t i o n

- 1 3 -

F i g . 3.- C h e m i c a l s c h e m e r e l a t e d to t h e m o s t a b u n d a n t n e g a t i v e i o n s i n t h e s t r a t o s p h e r e ( A d a p t e d f r o m A r i j s e t a l , 1 9 8 1 ) .

-14-

T A B L E 2 Chemical scheme f o r t h e n e g a t i v e ion in t h e s t r a t o s p h e r e a n d a d o p t e d r a t e c o n s t a n t s .

R e a c t i o n 3 - 1

Rate c o n s t a n t ( i n cm s f o r 2-body r e a c t i o n s and

i n cm^ s * f o r 3-body r e a c t i o n s )

e + 0

2

+ M - » 0

2

+ M

° 2

+

° 3

+

° 2

° 3

+ C

° 2 "

C

° 3

+

° 2 co"

+

o

2

- o ;

+

c o

2

0~ + 0

?

+ M 0~ + M OT + M 0~ + 0

o

+ M 4 2 2

° 4

+ C 0 2

-

C 0

4

+

° 2

C

° 4

+

° 2 * ° 4

+ C

° 2

C 0

4

+

° 3 - ° 3

+ C

° 2

+

° 2 co^ + h

2

o -»• o

2

. h

2

o + co

2

O

2

.H

2

O -> CO"

+

H

2

O

0~ + H

2

0 + M -> 0

2

. H

2

0 + M O

2

.H

2

O + M ^ O

2

+ H

2

O + M O".H

2

O + NO

2

-> NO" + o

2

+ H

2

O 0

2

. H

2

0 + H

2

0 + M -»• 0

2

- 2 H

2

0 + M 0 " . 2 H

2

0 + M O " . H

2

0 + H

2

0 + M

° 2

H

2 °

+

° 3 * ° 3 -

H

2 °

+

° 2 O

2

. H

2

O + HNO

3

•+ NO".H

2

O + HO

2

O

2

.H

2

O + N

2

O

5

-»• NO^.H

2

O + NO

2

+ o

2

0

3

+ e" -»• o" + 0

2

o" + 0

2

-»• 0

3

+ e"

+

° 3 " ° 3

+

°

0~ + H

2

0 + M

0

" -

H

2

0 + M

0 " . H

2

0 + HN0

3

N 0

3

. H

2

0 + OH 0 " . H

2

0 + N

2

0

5

•* N 0

3

. H

2

0 + HN0

2

- 3 0

- 1 0 - 1 0

- 1 5 31 - 1 4

- 1 4 k j = 2 x 10

k

2

= 6 x 10 k

3

= 5 . 3 x 10 k = 3 . 9 x 10

3b

k , = 3 . 4 x 10'

u

k

4 b

= 2 . 7 x 10 k = 4 . 3 x 1 0

_ 1

°

- 1 3 k_, = 2 x 10

5 b - 1 0

k , = 1 . 3 x 10

6

- 9

k = 1 . 3 x 10

- 1 0

k_, = 5 . 8 x 10

7 - 2 8

k

g

= 2 . 2 x 10

k

9 b

= k

9

/ 1 0 X 1 0 - 1 0

k = 9 . 0 x 10

- 2 8

k = 6 . 0 x 10

•=

k

n /

3 x 1 0~1 6

l l b 1 1 - 1 0

k = 2 . 3 x 10 k , . = 1 . 0 x 10 - 9

1 4

- 9

k = 1 . 0 x 10

k ^ = 9 . 1 x 1 0

_ 1 2

( T / 3 0 0 )

1 4 6

1 6

- 1 2

k . , , = 1 . 0 x 10

1 6 b

- 1 0

k = 8 . 0 x 10

- 2 8

k

1 9

= 1 . 3 x 10 k = 1 . 0 x 1 0 "

9

k

2 1

= 1 . 0 x 10 - 9

- 1 5 -

O . H

2

0 + H

2

0 -*• OH . H

2

0 + OH 0 H ~ . H

2

0 + HN0

3

N 0 g . H

2

0 + H

2

0 0 H ~ . H

2

0 + N

2

0

5

N 0 ~ . H

2

0 + HN0

3

OH".H O + H O + M -*• 0H~.2H O + M

z z z

•11

OH . 2 H

2

0 + M OH

•

H

2°

+ H

2 °

+ M

OH . 2 H

2

0 + HN0

3

N 0

3

- 2 H

2

0 + H

2

0 OH . 2 H

2

0 + N

2

0

5

N 0

3

- 2 H

2

0 + HN0

3

° 3

+ H

2 °

+ M

"" ° 3

H

2 °

+ M

0

3

- H

2

0 + M -> 0

3

+ H

2

0 + M o

3

. h

2

o + co

2

- c o

3

+ o

2

+ h

2

o 0

3

- H

2

0 + H

2

0 + M -> 0

3

- 2 H

2

0 + M 0

3

. 2 H

2

0 + M -»• 0

3

- H

2

0 + H

2

0 + M O

3

. H

2

O + hno

3

N 0

3

- H

2

0 + oh + 0

2

O

3

. H

2

O + N

2

O

5

n o

3

. H

2

O + NO

3

+ o

2

0

3

- 2 H

2

0 + HN0

3

N 0

3

- 2 H

2

0 + OH + 0

2

0

3

- 2 H

2

0 + N

2

0

5

N 0

3

. 2 H

2

0 + N0

3

+ 0

2

C0

3

+ H

2

0 + M + C 0

3

- H

2

0 + M C0~.H

2

0 + M CO~ + H

2

0 + M

C 0

3

- H

2

0 + HN0

3

-> N 0

3

- H

2

0 + OH + co

2

c o

3

. h

2

o + n

2

o

5

n o

3

. h

2

o + no

3

+ c o

2

C 0

3

- H

2

0 + H

2

0 + M C 0

3

. 2 H

2

0 + M C 0

3

- 2 H

2

0 + M C 0

3

. H

2

0 + H

2

0 + M C 0

3

- 2 H

2

0 + HN0

3

N 0

3

- 2 H

2

0 + OH + C0

2

C 0

3

- 2 H

2

0 + N

2

0

5

-»• N 0

3

- 2 H

2

0 + N0

3

+ CO, N0

2

+ e" -*• NO~

HNÓ

3

+ e" -> N0

2

+ OH N

2

0

5

+ e" N0

2

+ N0

3

no

2 +

o

3

n o

3 +

o

3

N0

2

+ H

2

0 + M N 0

2

. H

2

0 + M N 0

2

. H

2

0 + M •»• N0

2

+ H

2

0 + M N0~ + H

2

0 + H N 0

3

. H

2

0 + M NO".H

2

O + M -> N0

3

+ H

2

0 + M NO" + H-SO. -» HSOT + HNO

3 2 4 4 3

k

2 2

= 1 . 0 X ¹⁰ k = 1 . 0 X 1 0 "

9

k „ = 1 . 0 X 10 - 9

2 4 - 2 8

k = 3 . 5 X 10 k25b =

k 2 5

/

1 0

"

1 4

- 9 - 9

• 2 8

k „ , = 1 . 0 ₂₆ X ¹⁰ k

2 7

= 1 . 0 X ¹⁰ k = 2 . 7 X ^10'

2 8

- 1 4

k

2 8 b

= k

2 8

/ 1 0 1 0

k = 3 . 5 X 10

- 2 8

k

3 1

= 5 0 X 1 0 k

3 1 b =

k

3 1

/ 1 0

" ^ k

3 3

= 1 . 0 x 10

k

3 4 =

1 0

*

1 0

k

3 5

= 1 . 0 x 10 k „ , = 1 . 0 x 10-9

3D

- 2 8

- 1 4

- 9

- 2 8

k

3 7

= 1 x 10

k

3 7 b =

3 3 X 1 0

k

3 g

= 1 . 0 x 10 k

3 g

= 1 . 0 x 10 k . „ = 5 . 0 x 10

40

k

4 0 b =

k

4 0

/ 6

° "

1 0

k . , = 1 . 0 x 10

4 1

- 9

k

/ 0

= 1 . 0 x 10

4 2 - 8

k . „ = 5 . 0 x 10

3 - 8

k = 5 . 0 x 10 k . _ = 5 . 0 x 10

- 8

4 5

- 1 0

k

/ £

= 1 . 2 x 10

4 6

- 2 8

k , . , = 1 . 6 x 10

4 7

- 1 5

k,-,^ = 5 . 0 x 10

4 7 b

- 2 8

k

4 8

= 1 . 6 x 10

k

4 8 b =

k

4 8

/ 4

-

4

*

1 0

k . „ = 2 . 6 x 10 49

- 1 7

- 1 5

- 1 6 -

t

N 0

2

. H

2

0 + H

2

0 + M -*• N 0

2

. 2 H

2

0 + M N 0

2

. 2 H

2

0 + M N 0 ~ . H

2

0 + H

2

0 + M n o

2

. h

2

o + h n o

3

-»• n o " . h

2

o + h n o

2

n o

2

. h

2

o + n

2

o

5

n o ^ . h

2

o + 2 N 0

2

N 0

2

. 2 H

2

0 + H N 0

3

-*• N 0 ~ . 2 H

2

0 + H N 0

2

N 0

2

- 2 H

2

0 + N

2

0

5

- N 0 ~ . 2 H

2

0 + 2 N 0

2

N 0

3

- H

2

0 + H

2

0 + M -»• N 0 ~ . 2 H

2

0 + M N 0 ~ . 2 H

2

0 + M N O ' . ^ O + H

2

0 + M N O

³

. H

²

O + h n o

³

N O

3

. h n o

3

+ H

2

O N 0

³

. H N 0

³

+ H

²

0 -»• N 0

³

. H

²

0 + H N 0

³

N 0

³

- 2 H

²

0 + H N 0

³

-*• N 0

³

. H N 0

³

. H

²

0 + H

²

0 N 0

³

. H N 0

³

- H

²

0 + H

²

0 N 0 ~ . 2 H

²

0 + H N 0

³

N 0 ~ . H N 0

³

+ H

²

0 + M N 0

³

. H N 0

³

- H

²

0 + M N 0

³

. H N 0

³

. H

²

0 + M N 0

³

. H N 0

³

+ H

²

0 + M n o

³

. h n o

³

+ h

²

s o

⁴

H S O . . H N O + H N O

4 3 3 N 0

³

- H N 0

³

+ H N 0

³

+ M N 0

³

- 2 H N 0

³

+ M N O ~ . 2 H N 0

³

+ M -»• N 0

³

- H N 0

³

+ H N 0

³

+ M

N O

³

. H N O

³

. H

²

O + H N O

³

N O

³

. 2 H N O

³

+ H

²

O N 0 ~ . 2 H N 0

³

+ H

²

0 N 0

³

. H N 0

³

. H

²

0 + H N O g N O ~ . 2 H N 0

³

+ H

²

0 + M -»• N 0

³

. 2 H N 0

³

. H

²

0 + M N 0 ~ . 2 H N 0

³

. H

²

0 + M

N 0

3

- 2 H N 0

3

+ H

2

S 0

4

N O

3

. 2 h n o

3

. H

2

O + H

2

S O

4

N 0

³

. 2 H N 0

³

+ H

²

0 + M H S 0 T . 2 H N 0 „ + H N 0

o

4 3 3 H S 0

⁴

. 2 H N 0

³

- H

²

0 + H N O , H S O , .

4 H N 0

³

+ H N 0

³

+ M •* H S 0

⁴

- 2 H N 0

³

+ M h s o T .

4 2 H N 0

3

+ M -*• H S 0 ~ . H N 0

3

+ H N 0

3

+ M h s o T .

4 H N O

³

+ H

²

S O

⁴

H S O

⁴

. H

²

S O

⁴

+ H N O

³

h s o T .

4 H N O » + H O + M -*• H S 0 T . H N 0

o

. H

o

0 +

3 2 4 3 2 M

h s o T .

4 H N O

³

. H

²

O + M -»• h s o

⁴

. H N O

³

+ H

²

O + M h s o T .

4 2 H N 0

3

+ H

2

0 + M -*• H S 0 " . 2 H N 0

3

. H

2

0 + M h s o

⁴

. 2 H N 0 . H 0 + M -»• H S Q - . 2 H N 0 + H

²

0 + M H S O ^ . 2 H N O . + H S O . -»• H S O T . H S O . . H N O + H N O -

3 2 4 4 2 4 3 3

h s o T .

4 2 H N 0

o

. H

o

0 + H S O . H S O T . H . S O . . H N O . . H . O

3 2 2 4 4 2 4 3 2

+

h n o

³

_ o o k = 1 . 6 X 1 0

k

5 1 b = k

5 1

/ 8 . 0 X 1 0 "

k

5 2

= 1 . 0 x l O k = 1 . 0 x 1 0

^{- 9}

k _ . = 1 . 0 x 1 0 - 9

5 4

- 9

k = 1 . 0 x 1 0 _OQ

= 1 . 6 x 1 0 5 o

K ^ = k . , / 1 . 9 6 x 1 0 5 Ô D 5 6

k

^{5 7}

= 3 . 0 x 1 0

k

5 7 b =

k

5 7

/ 6

- ° ?

1 0 5

k = 1 . 0 x 1 0

k

5 8 b =

k

5 8

/ 2

' ° »

1 0 5

k

5 9

= 3 x 1 0

k

5 9 b =

6 0 X 1 0

"

1 5

k ,

n

= 2 . 3 x 1 0 k

6

= 1 . 0 x 1 0 26

k

6 1 b = W

¹

-

^{9 4 X 1 0}

e x p ( 9 2 4 0 / T ) k

^{6 2}

= 1 . 0 x 1 0

^{- 9}

k

6 2 b =

^k

6 2

^{/ 2}

°

^{X 1 0 5}

L , = 3 . 0 x 1 0

6 3

- 1 5

k , - , : 3 . 0 x l O

6 3 b

_ o

k , „ = 1 . 1 x 1 0

6 4

- 1 0

k , _ = 4 . 0 x 1 0

6 5

- 2 6 k , , = 1 . 0 x 1 0

- 1 8 k , , , = 5 . 0 x 1 0

6 6 b

k , _ = 5 . 0 x 1 0 - 2 8 k , _ = 3 . 0 x 1 0

6 8

- 1 5

k

6 8 b =

⁶ 0 X 1 0 2 8

k ,

ⁿ

= 3 . 0 x 10

6 9

- 1 5

k ,

q h

= 3 . 0 x 1 0 .

6 9 b _

^{1 0}

k = 5 . 0 x 1 0 k

^{? 1}

= 1 . 0 x 1 0 -9

-17-

H S 0

4

. H N 0

3

. H

2

0 + «Nog -> HS0

4

-2HN0

3

+ H

2

0 HS0~.2HN0

3

+ H

2

0 -»• H S 0 ^ . H N 0

3

. H

2

0 + HN0

3

HS07.H

o

S0. + HNO„ •> HSOT.H-SO. .HNO„ + M 4 2 4 3 4 2 4 3 H S 0 ^ . H

2

S 0

4

. H N 0

3

+ M -* H S 0

4

. H

2

S 0

4

+ HN0

3

+ M H S 0 ~ H

o

S 0 . + H„SO. + M -»• HS07.2H

o

S0. + M

4 2 4 2 4 4 2 4

HSO7.2H„SO. + M -> HS07.H„S0. + H„SO. + M

4 2 4 4 2 4 2 4

H S 0

4

. H

2

S 0

4

+ H

2

0 + M H S 0

4

. H

2

S 0

4

. H

2

0 + M H S 0 ~ . H

2

S 0

4

. H

2

0 + M H S 0

4

. H

2

S 0

4

+ H

2

0 + M

HS07.H„S0..HN0

o

+ H

o

0 + M H S 0 7 . H „ S 0 . . H N 0

o

. H „ 0 4 2 4 3 2 4 2 4 3 2

+ M

H S 0 7 . H

o

S 0 . . H N 0

o

. H

o

0 + M HSOT.H

o

S0..HN0

o

+ H

o

0 4 2 4 3 2 4 2 4 3 2

+ M

HSOT.H.SO..HNO. + H.SO. HSOT>2H_SO. + m m

4 2 4 3 2 4 4 2 4 3

HS07.H_S0. .H-O + HNO -*• HSOT.H-SO. .HN0

o

+ H„0 4 2 4 2 3 4 2 4 3 2 HS07.H„S0. .HN0

o

+ H„0 •> HS07.H

o

S0. .H O + HNO

4 2 4 3 2 4 2 4 2 3

HS07.H„S0. .H„0 + H „SO. HS07.2H„S0, + H

o

0

4 2 4 2 2 4 4 2 4 2

H S 0

4

. 2 H

2

S 0

4

+ H

2

S 0

4

+ M -»• H S 0

4

. 3 H

2

S 0

4

+ M HS07.3H„S0. + M -» HS07.2H

o

S0. + H.SO. + M

4 2 4 4 2 4 2 4

0

2

. 2 H

2

0 + HN0

3

N0

3

-2H

2

0 + H0

2

0

2

. 2 H

2

0 + N

2

0

5

-»• N 0

3

. 2 H

2

0 + N0

2

+ 0

2

0

2

. 2 H

2

0 + 0

3

- 0

3

. 2 H

2

0 + 0

2

N 0

2

. 2 H

2

0 + 0

3

-»• N 0

3

. 2 H

2

0 + 0

2

NO

2

.H

2

O + o

3

NO

3

.H

2

O + o

2

N0~ + HN0

3

NO~ + HN0

2

C0~ + HN0

3

-» NO~ + HC0

3 C 0

3

+ N

2 ° 5 *

N 0

3

+ N 0

3

+ C 0

2 NO~ + N

2

0

5

NO" + 2N0

2

O" + H

2

S0H4 ~ + OH

NO~ + HN0

3

+ M -> N0~.HN0

3

+ M N0

3

-HN0

3

+ M N0

3

+ HN0

3

+ M

co

3

+ n o

2

n o

3

+ co

2

o

3

+ n o

2

-»• NO

2

.H

2

O + H

2

9 + o

2

k

? 2

= 1 . 0 X 10~

9

k _ _ , = 2 . 5 X 1 0 "

1 5

72b

k = 1 . 0 X 10

7 4

-17

k . = 1 . 5 X 10

7 4 b

k = 1 . 0 X 10

- 2 0

k = 3 . 0 X 10

7 5 b -7R

k_,, = 3 . 0 X 10

7 6

-15

k , = 6 . 0 X 10

7 6 b

-?R

k = 3 . 0 X 10

k = 3 . 0 X 10 / /D

•15

k = 5 . 0 X 10 /O

k = 1 . 0 X 10 -9 -9

79b

k

8 0

k

81

k

81b

k

8 2

k

83

k

84

k

8 6

k

87

k

8 8

k

89

k

90

k

91

= 2 . 5 X 10 -15

= 1 . 0 X 10

= 1 . 0 X 10 -9 - 2 6

= 7 . 0 X 10

^{- 2 1}

= 1 . 0 X 10

= 1 . 0 X 10

= 2 . 6 X 10

= 1 . 0 X 10

= 1 . 0 X 10

= 1 . 6 X 10

= 8 . 0 X 10

= 2 . 8 X 10

= 7 . 0 X 10 -9 -9

- 1 0 - 1 0

- 1 0

-9

- 1 0 - 1 0 - 1 0

95

<96

= 1 . 5 4 X 10 -9

= 9 . 0 X 10 -25

k

96b =

k

9 6

/ 5

-

6 X 1 0

-27 T exp (13130/T)

- 1 0

97 '98

= 2 . 0 x 10

= 9 . 0 x 10

^{• 1 0}

- 1 8 -

O

2

. 2 H

2

O + NO

2

-»• N O

2

. H

2

O + H

2

O + o

2

N 0 ~ . H N 0

3

. H

2

0 + H

2

S 0

4

H S 0 " . H N 0

3

. H

2

0 + HN0

3

HSOT .HNO„ .H^O + H„SOT H S o 7 . H „ S O . . H

^o

0 + HNO 3 2

o " + c o

2

+ o

2

O " . H

2

O + o

2

4 2 4 2 CO3

⁺

O

²

° 3

+ H

2 °

° 4

H

2 ° ° 2

H

2 °

+

° 2

HSOT + H

o

S 0 . + M -*• H S 0 T . H

o

S 0 . + M 4 2 4 4 2 4 HS0T.H

o

S0. + M -»• HSOT + H . S O , + M

4 2 4 4 2 4 HSOT + HNO + M -»• HSOT.HNO- + M

4 3 4 3 HS07.HN0

o

+ M HSOT + HNO + M

4 3 4 3 N0

3

-2HN0

3

+ HN0

3

+ M N0

3

-3HN0

3

+ H N 0

3

. 2 H N 0

3

+ M •*• N0

3

-2HN0

3

+ HN0

3

+ M

N0~.3HN0

3

+ HN0

3

+ M -*• N0

3

-4HN0

3

+ M NO~.4HNO + M -> N 0

3

. 3 H N 0

3

+ HN0

3

+ M

: 9 . 0 X i o "

1 0

= 1 . 0 X 10-

9

= 1 . 0 X 10-

9

= 3 . 1 X 1 0 "

2 8

= 1 . 0 X 1 0 "

1 1

= 1 . 0 X 1 0 "

1 0

= 3 . 0 X 1 0 -

2 6

99

k

i o o

k

1 0 1

k

1 0 2

k

1 0 3

k

1 0 6

k

1 5 0

k

1 5 0 b

= 1 0 X 1 0

151 = 2 . 0 X 10

k

1 5 1 b

= L O x l

°

= 1 . 0 X 10

- 2 1

I 26

- 2 1

26 152

' l 5 2 b

•29

153

C

153b

= k

1 5 2

/ 6 . 2 6 10 T e x p ( 7 0 7 0 / T )

= 1 . 0 X Î O "

2 6

= k

1 5 3

/ 5 . 9 1 X 10- T e x p ( 4 6 9 6 / T )

-19-

NO

3

(HNO

3

)

£

+ H

2

O + M ^ NO

3

(HNO

3

)

£

H

2

O + M (10)

- 2 8 6 has been assumed to be slower with a rate constant of 3 x 10 cm s . Since t h e e q u i l i b r i u m constant related to this process is u n k n o w n , an adjustment of this parameter has been made. T h e e r r o r in relation to t h i s u n c e r t a i n t y is small since most of t h e calculated concentrations a r e not v e r y sensitive to these reactions.

T h e r a t e constants of t h e following t w o - b o d y reactions, namely

HS0-(H

2

S0

4

)

m

( H N 0

3

)

£

+ H

2

S 0

4 -

H S

V

H

2

S

V

m +

l

( H N

°

3

V l

+ m

3

( 1 1 )

H S O ^ S O ^ (HN0

3

)

£

( H

2

0 )

n

+ HN0

3

- H S

0

; ( H

2

S 0

4

)

m

( H N 0

3

)

£ + 1

( H

2

0 )

n

_

1

+ ( 1 2 )

- 9 3 - 1

have been p u t equal to 1 x 10 cm s . T h e same value has been used f o r t h e rates r e f e r r i n g to all reactions of HNC>

3

and N

2

C>

5

with negative cluster ions. All other rate constants have been t a k e n from t h e compilation b y A l b r i t t o n ( 1 9 7 8 ) o r , in certain cases when no data is available, have been estimated r a t h e r a r b i t r a r i l y or adjusted to f i t t h e observation at 35 km. T h e adopted values are given in table 2 .

3. MODEL D E S C R I P T I O N

Since t h e lifetime of all ions is v e r y s h o r t , equilibrium conditions are reached almost instantaneously. T h e r e f o r e t h e system

- 2 0 -

d e s c r i b i n g the balance of each ionic species is p u r e l y a l g e b r i c a n d can be written f o r the p o s i t i v e a n d the n e g a t i v e ions r e s p e c t i v e l y b y the equation

A X = B (13)

when X is a column v e c t o r r e p r e s e n t i n g the concentration v a l u e s x. (j = 1 to N , where N is the n u m b e r of s p e c i e s ) , B with elements b. (i = 1 to N ) r e p r e s e n t s the external s o u r c e s of ionization a n d d e p e n d s t h e r e f o r e on the v a l u e of Q a n d A is a N x N s q u a r e matrix whose elements a., take into a c c o u n t all chemical p r o c e s s e s . T h e s e f a c t o r s w h i c h r e p r e s e n t the i n v e r s e of the time c o n s t a n t a s s o c i a t e d to reaction from ion j to ion i, are a f u n c t i o n of the chemical rate c o n s t a n t s a n d of the neutral species c o n c e n t r a t i o n s . In the case of the diagonal elements a., w h i c h r e p r e s e n t the loss term of ion i, a term a c c o u n t i n g f o r the recombina- tion between p o s i t i v e a n d n e g a t i v e c h a r g e s a p p e a r s . A s s u m i n g t h a t the v a l u e of the recombination rates are identical f o r all ions ( e q . 3 ) a n d i n t r o d u c i n g the electroneutrality c o n d i t i o n , the a., coefficients f o r the positive ions become i n d e p e n d e n t of the concentration of the n e g a t i v e ions a n d vice v e r s a b u t d e p e n d e n t on the Q v a l u e t h r o u g h equation (4 ).

T h e two decoupled a l g e b r i c s y s t e m s are them s o l v e d b y a classical i n v e r s i o n method. For the p o s i t i v e c h a r g e s , the model t a k e s

" into a c c o u n t 25 d i f f e r e n t species a n d 44 chemical reactions while f o r the n e g a t i v e c h a r g e s 38 d i f f e r e n t species a n d 134 chemical reactions are c o n s i d e r e d . T h é concentration v a l u e s of the neutral t r a c e species are taken from the 1 - D model d e s c r i b e d b y B r a s s e u r et al (1982) e x c e p t f o r s u l f u r i c acid whose vertical profile is similar to t h a t g i v e n b y the model of T u r c o et al (1979). T h e vertical d i s t r i b u t i o n of the t e m p e r a t u r e is taken from the U S S t a n d a r d A t m o s p h e r e (1966).

- 2 1 -

4 . M O D E L R E S U L T S

4 . 1 . P o s i t i v e ions

When t h e c o n c e n t r a t i o n v a l u e s o r t h e r e l a t i v e a b u n d a n c e of t h e p o s i t i v e ions p r o v i d e d b y t h e model a r e a n a l y z e d , it immediately a p p e a r s t h a t t h e c o n d i t i o n s a r e r a p i d l y c h a n g i n g w i t h t h e a l t i t u d e l e v e l . T h i s has to be a t t r i b u t e d to t h e s t r o n g d e p e n d e n c e of t h e e q u i l i b r i u m v a l u e s to t h e local t e m p e r a t u r e . T h e a n a l y s i s of a n y o b s e r v a t i o n a l d a t a t h e r e f o r e r e q u i r e s a v e r y a c c u r a t e k n o w l e d g e of t h e t e m p e r a t u r e in a d d i t i o n to t h e w a t e r v a p o r c o n c e n t r a t i o n . T h e amount of C H g C N w h i c h is p r e s e n t is also an i m p o r t a n t p a r a m e t e r b u t no o b s e r v a t i o n is y e t a v a i l a b l e . From t h e model c a l c u l a t i o n , it can h o w e v e r be d e d u c e d , w h e n case 1 ( l o w C H C N a n d no NPH to PH r e c o n v e r s i o n ) is compared to case 2 ( h i g h C H ^ C N a n d an e f f i c i e n t N P H to PH r e c o n v e r s i o n ) t h a t t h e o b s e r v a t i o n s a t all a l t i t u d e a r e much b e t t e r f i t t e d w h e n case 1 is a d o p t e d . I n o t h e r w o r d s , as s u g g e s t e d b y f i g u r e 4 , t h e r e a c t i o n s c o n v e r t i n g p r o t o n h y d r a t e s i n t o n o n - p r o t o n h y d r a t e s s h o u l d be v e r y e f f i c i e n t e v e n a t low level w h e r e t h e w a t e r v a p o r c o n c e n t r a t i o n is r e l a t i v e l y h i g h . T h e r e v e r s e mechanism can t h e r e f o r e p r o b a b l y be n e g l e c t e d in t h e whole s t r a t o s p h e r e .

?

One can show e a s i l y t h a t t h e r e c o n v e r s i o n of NPH to PH will o c c u r o n l y if t h e r e v e r s e r e a c t i o n r a t e becomes of t h e o r d e r of a [ n " ] / [ H

2

0 ] w h e r e a is t h e r e c o m b i n a t i o n c o e f f i c i e n t , [ n ] t h e t o t a l ion c o n c e n t r a t i o n a n d [ H g O ] t h e w a t e r v a p o r c o n c e n t r a t i o n . When t h e p a r a m e t e r s , t e m p e r a t u r e a n d c o n c e n t r a t i o n s v a l u e s a d o p t e d in t h e p r e s e n t model a r e u s e d , t h e r e c o n v e r s i o n r e a c t i o n becomes e f f i c i e n t f o r

- 1 6 +3 - 1 a r a t e l a r g e r t h a n 1 x 10 cm s

A r n o l d et al ( 1 9 8 1 a ) h a v e d i v i d e d t h e N P H ions into t h r e e c a t e g o r i e s called A , B a n d C . A r e f e r s to ions w i t h H X c o r e s , B to

- 2 2 -

20 40 60 80 RELATIVE AMOUNT ( p e r c e n t )

F i g . 4.- R e l a t i v e a m o u n t of t h e p r o t o n h y d r a t e s and t h e n o n p r o t o n h y d r a t e s c a l c u l a t e d for two d i f f e r e n t c o n d i t i o n s (cases 1 and 2 ) .

- 2 3 -