Implications of Data on the Gas Phase Decomposition of Ozone

Implications of Data on the Gas Phase Decomposition of Ozone SIDNEY W. BENSON and ARTHUR E.

AXWORTHY,

1

Jr.

Department of Chemistry, University of Southern California, Los Angeles 7, Calif.

Downloaded by CORNELL UNIV on August 21, 2016 | http://pubs.acs.org Publication Date: January 1, 1959 | doi: 10.1021/ba-1959-0021.ch053

The kinetic data on the decomposition of ozone via oxygen atoms are considered in terms of their implications for the possible existence of direct bimolecular reactions of ozone molecules a n d energy chains carried by excited oxygen. A direct bimolecular reaction of ozone to form oxygen if it exists at all, must have an activation energy of between 17 a n d 21 kcal., but not higher. Energy chains carried by excited oxygen are unlikely on several theoretical considerations, in accord with the limits estimated for the rate of such reactions from the data. The anomalies in the rate constants for the reactions O + M O + O + M are understandable in terms of the theory of unimolecular reactions. In the case of ozone it is essentially a unimolecular reaction at its low pressure limit. Finally, the processes occurring in a n electric discharge through oxygen are considered. O x y g e n atoms are a very rapid catalyst for the synthesis of ozone a n d the limiting yields are probably fixed by the local temperatures a n d the processes causing direct dissociation of ozone rather than oxygen atom attack. 3

2

T h e d e c o m p o s i t i o n of ozone, p e r h a p s one of t h e s i m p l e s t possible s y s t e m s f r o m a c h e m i c a l v i e w p o i n t , h a s been a n e x t r e m e l y c o m p l e x a n d d i f f i c u l t s t u d y k i n e t i c a l l y . T h e r e a c t i o n i s e n o r m o u s l y s e n s i t i v e t o h o m o g e n e o u s c a t a l y s i s b y t r a c e s of halogens, l i g h t , oxides of n i t r o g e n , h y d r o c a r b o n s , p e r o x i d e s , a n d m e r c u r y v a p o r , a n d t o h e t e r o geneous c a t a l y s i s b y m e t a l s a n d m e t a l oxides. B e c a u s e ozone i s p r o d u c e d b y p a s s i n g e l e c t r i c discharges t h r o u g h o x y g e n , t h e p r o b l e m of e l i m i n a t i n g these t r a c e c a t a l y s t s is one of o b t a i n i n g o x y g e n free f r o m t r a c e s of n i t r o g e n , o x i d e s o f n i t r o g e n , a n d h y d r o g e n - c o n t a i n i n g c o m p o u n d s s u c h as w a t e r , because u n d e r t h e influence of t h e d i s c h a r g e a l l w i l l p r o d u c e o n e o r a n o t h e r of t h e a b o v e - m e n t i o n e d c a t a l y s t s . T h e k i n e t i c s t u d y is f u r t h e r c o m p l i c a t e d b y t h e fact t h a t t h e reaction is s t r o n g l y exo t h e r m i c (34.5 k c a l . p e r m o l e of o z o n e ) , so t h a t t e m p e r a t u r e g r a d i e n t s of m e a s u r a b l e m a g n i t u d e a r e q u i c k l y e s t a b l i s h e d i n a flask c o n t a i n i n g d e c o m p o s i n g ozone gas. T h i s s e l f - h e a t i n g i n f a c t i m p o s e s severe l i m i t s o n t h e r a n g e of e x p e r i m e n t a l c o n d i 1

Present address, S h e l l O i l C o . , M a r t i n e z , C a l i f . 398

OZONE CHEMISTRY AND TECHNOLOGY Advances in Chemistry; American Chemical Society: Washington, DC, 1959.

BENSON A N D A X W O R T H Y - G A S

399

PHASE DECOMPOSITION

tions i n which the decomposition m a y be studied, because the limits of the thermal explosion are reached at partial pressures well below 1 a t m . M e c h a n i s m of Pyrolysis Despite these complexities, or eccentricities, it appears that the homogeneous, thermal, gas phase decomposition of ozone can be described b y a very simple mecha nism, which is a modification of the one first proposed b y Jahn (8) : M + 0

^ 0

3

+ 0 + M - 2 4 . 6 kcal.

2

(1, 2)

2

Ο + 0 Λ

2 0 + 93 kcal.

(3)

2

3

where M represents a suitably weighted sum of all the substances (including ozone) present i n the gas phase. It has recently been shown (1,4) that * ° f work on dilute ozone (5, 12), most of it not very quantitative, and the more precise and very extensive work on concentrated ozone b y Glissmann and Schumacher (6) can be fitted to the above mechanism with the results (1, 4):


a u

fci(M

= 0 )

= 4.61 X 10

3

t

n

e

exp (-24,000/i2T) liter/mole-sec.

12

fc,(M = 0 ) = 6.00 X 10 exp (+600/#T) liter /mole -sec. h = 2.96 X 10 exp ( - 6 , 0 0 0 / β Τ ) liter/mole-sec. 7

3

2

10

(4)

2

7

T h e effects of various "foreign" gases are represented b y : M = 0 + 0.44 0 + 0.41 N , + 1.06 C 0 3

2

2

+ 0.34 He

(5)

where the coefficients represent the efficiency of the respective gas (relative to ozone) in both activation and deactivation of ozone. If a stationary state for oxygen atoms is assumed, the above mechanism gives:

(

fe(0,)(M)

U

+ *,(0,)

w

and for the rate of decomposition of ozone:

= 2fe(0) (0 ) B8

3

2huo y

.

3

w

n

J ,

°

fc2( 2)

L

1 +

(

()

, fa(Q») Ί fe(â)(M)j

w h i c h differs f r o m t h e o r i g i n a l J a h n (8) r e s u l t b y t h e b r a c k e t e d t e r m i n t h e d e n o m i n a t o r o f E q u a t i o n 7. I n t w o e x t r e m e cases w h i c h a r e n e v e r q u i t e r e a l i z e d i n l a b o r a t o r y p r a c t i c e , t h e r a t e e x p r e s s i o n reduces t o : A . C o n c e n t r a t e d Oo [fc.(0,) » /c (0 )(M)] 2

2

2fc (0,)(M) 1

-> 2A^(0 ) (if M=Oa)

2

3

B. Dilute 0

(8) (9)

3

[*,((),) « * (0 )(M)] -=igp - -ψ g | 2

2

2

(10)

F r o m t h e a b o v e d a t a , / b / / b = 493 e x p ( - 6 6 0 0 / 2 2 Γ ) m o l e / l i t e r , w h i c h h a s t h e v a l u e 0.187 a t m . a t 3 0 ° C . a n d 2.04 a t m . a t 100° C . C a s e A i s t h u s 9 0 % r e a l i z e d a t 30° C . o n l y i n m i x t u r e s c o n t a i n i n g less t h a n 15 m m . of o x y g e n a n d m o r e t h a n 9 0 m m . of ozone. A t 100° C , C a s e A i s 9 0 % a c h i e v e d i n m i x t u r e s w i t h less t h a n 100 m m . o f 3

2


400

A D V A N C E S IN

CHEMISTRY SERIES

o x y g e n i f 0 > 100 m m . C a s e Β is e a s i l y a c h i e v e d a t 30° C , b u t o n l y w i t h d i f f i c u l t y a t 100° C — i . e . , a t 1 a t m . of o x y g e n o n l y i f 0 < 0.02 a t m . T h e s e cases i l l u s t r a t e some of t h e o b s e r v e d p a r a d o x e s of t h e ozone d e c o m p o s i t i o n . P u r e ozone decomposes at a s e c o n d - o r d e r r a t e w i t h a n a p p a r e n t a c t i v a t i o n e n e r g y w h i c h changes as t h e r e a c t i o n proceeds, f r o m 24 k c a l . (k^ t o a b o u t 30 k c a l . (k k /k ). A d d i n g o x y g e n to p u r e ozone accelerates its r a t e of d e c o m p o s i t i o n , w h i l e a d d i n g o x y g e n t o d i l u t e ozone i n h i b i t s i t s r a t e of d e c o m p o s i t i o n . (Compare Equation 8 with M = 0 + 0 . 4 4 0 a g a i n s t E q u a t i o n 10. A d d i t i o n of f o r e i g n gases to p u r e ozone—e.g., N , C 0 — a c c e l e r a t e s t h e r a t e , w h i l e t h e i r a d d i t i o n t o d i l u t e ozone has no effect.) This results i n the w e l l k n o w n b e h a v i o r , o b s e r v e d d u r i n g single r u n s w i t h c o n c e n t r a t e d ozone, t h a t t h e a p p a r e n t s e c o n d - o r d e r r a t e c o n s t a n t c o n t i n u e s to increase o v e r t h e course of the reaction. 3

3

1

3

2

2

2

2

G l i s s m a n n a n d S c h u m a c h e r (6) i n t e r p r e t e d t h e i r d a t a i n t e r m s of a m i x e d m e c h a nism including a direct bimolecular reaction 2 0 ® 3 0 . I n t h e r e i n t e r p r e t a t i o n of these d a t a , B e n s o n a n d A x w o r t h y (4) d e c i d e d t h a t t h e r e w a s n o evidence f o r s u c h a reaction. [ A r e a p p r a i s a l of t h e m o r e recent w o r k of O g g a n d S u t p h e n (9) s i m i l a r l y shows t h a t t h e i r d a t a do n o t r e q u i r e the i n t r o d u c t i o n of s u c h a d i r e c t b i m o l e c u l a r reaction.] F o r s u c h a r e a c t i o n t o c o n t r i b u t e , let us s a y 1 0 % t o the scheme p r o p o s e d , k w o u l d h a v e t o be a b o u t 0.2 k ( E q u a t i o n 9) o v e r the p r e s s u r e a n d t e m p e r a t u r e range s t u d i e d . T h e f r e q u e n c y f a c t o r of R e a c t i o n Β w o u l d be e x p e c t e d t o be a b o u t 1 0 to 10 t i m e s t h e f r e q u e n c y of collisions w h i c h w o u l d be a b o u t 2 Χ 1 0 liter/mole-sec. I f k = 0.2 k is set a t 100° C , E m u s t be b e t w e e n 18 a n d 21.5 k c a l . p e r m o l e , d e p e n d i n g o n t h e steric f a c t o r u s e d . T h e o b s e r v e d r a t e of d e c o m p o s i t i o n of c o n c e n t r a t e d ozone (1) a t l o w t e m p e r a t u r e s , w h e r e s u c h a r e a c t i o n has t h e best chance of b e i n g o b s e r v e d , verifies these f r e q u e n c y f a c t o r s a n d a c t i v a t i o n energies as u p p e r a n d lower limits, respectively, for such a proposed bimolecular p a t h . 3


3

B

2

r

- 1

- 3

B

1 1

1

B

I t is v e r y d i f f i c u l t as w e l l as tedious t o o b t a i n r e p r o d u c i b l e r a t e c o n s t a n t s u n d e r these c o n d i t i o n s , because t h e slowness of t h e d e c o m p o s i t i o n is s u c h t h a t e v e n s l i g h t a m o u n t s of c a t a l y s i s c a n t h r o w t h e results off b y a c o n s i d e r a b l e a m o u n t . Energy Chains and

Thermal

Gradients

B e c a u s e R e a c t i o n 3 is e x o t h e r m i c b y 93 k c a l . , a n d r e q u i r e s 6 k c a l . p e r m o l e a c t i v a t i o n e n e r g y , the p r o d u c t o x y g e n molecules share b e t w e e n t h e m 99 k c a l . of excess e n e r g y . I f t h i s is p r e s e n t as t r a n s l a t i o n a l e n e r g y , e a c h o x y g e n p r o d u c t m o l e c u l e w i l l h a v e 49.5 k c a l . of excess t r a n s l a t i o n a l e n e r g y w h i c h is n o t e x p e c t e d t o be effective i n e x c i t i n g ozone molecules t o d i s s o c i a t i o n . B e c a u s e of the r e q u i r e m e n t s for m o m e n t u m c o n s e r v a t i o n , o n l y 3 / 5 of t h i s e n e r g y is a c t u a l l y a v a i l a b l e f o r c o n v e r s i o n to i n t e r n a l ex c i t a t i o n i n a c o l l i s i o n w i t h a n o r m a l ozone, w h i c h w o u l d be a b o u t 20 k c a l . T h i s is sufficient f o r d i s s o c i a t i o n of ozone. B u t excess t r a n s l a t i o n a l e n e r g y is a l w a y s v e r y q u i c k l y d e g r a d e d , so t h a t t r a n s l a t i o n a l l y e x c i t e d o x y g e n m o l e c u l e s w i l l n o t be e x p e c t e d t o be efficient as e n e r g y c h a i n c a r r i e r s . T h e a v a i l a b l e e n e r g y is n o t sufficient t o excite a n y b u t the l o w - l y i n g , m e t a s t a b l e , singlet, e l e c t r o n i c states of o x y g e n ( 7 ) . O n g r o u n d s of s p i n c o n s e r v a t i o n n o t m o r e t h a n one s u c h state s h o u l d be e x p e c t e d , so t h a t t h e r e m a i n i n g e n e r g y of f r o m 61 t o 76 k c a l . w o u l d be p r e s e n t as v i b r a t i o n p l u s r o t a t i o n of the t w o o x y g e n p r o d u c t m o l e c u l e s . O f t h e t w o e l e c t r o n i c states, t h e l o w e r ( Δς) has insufficient e n e r g y (22.5 k c a l . ) t o dissociate ozone. T h e u p p e r state (^g) has e n o u g h e n e r g y (37.6 k c a l . ) , b u t t h e c o l l i s i o n a l t r a n s f e r to ozone v i o l a t e s s p i n c o n s e r v a t i o n a n d w o u l d be e x p e c t e d t o be v e r y inefficient. τ

V e r y l i t t l e is k n o w n a b o u t t h e t r a n s f e r of v i b r a t i o n a l e n e r g y f r o m one m o l e c u l e t o a n o t h e r , b u t f o r d i s s i m i l a r species s u c h as o x y g e n a n d ozone i t w o u l d be e x p e c t e d t o be v e r y i n e f f i c i e n t l y t r a n s f e r r e d i n s u c h l a r g e a m o u n t s as w o u l d be r e q u i r e d f o r a n e n e r g y c h a i n . I t seems m u c h m o r e reasonable t o expect v i b r a t i o n a l l y e x c i t e d o x y g e n m o l e c u l e s t o lose t h e i r e n e r g y p r e f e r e n t i a l l y i n c o l l i s i o n w i t h o t h e r o x y g e n molecules


BENSON A N D

401

A X W O R T H Y - G A S PHASE DECOMPOSITION

a n d i n steps of 1 o r 2 q u a n t a a t a t i m e . T h u s the a priori evidence w o u l d o p p o s e t h e existence of e n e r g y c h a i n s i n t h i s s y s t e m . T h e k i n e t i c evidence a g a i n s t e n e r g y c h a i n s has b e e n e x a m i n e d b y B e n s o n a n d A x w o r t h y (1,4). I f we l o o k a t t h e m e c h a n i s m f o r e n e r g y c h a i n s , t h e o r i g i n a l scheme becomes : 0

3

+ M ^

2

0

+ 0 +

2

M

Ο + 0 i > 20 * 3

0 * + 0 2

3

X

0

0 * + M ' i o


2

[

2

+ 0

2

2

2

+ O)

(chain)

(11)

+ M (deactivation)

w h e r e M ' is w r i t t e n t o p o i n t o u t t h e different possible efficiencies of v a r i o u s gases i n t h i s r e a c t i o n as o p p o s e d t o R e a c t i o n s 1 a n d 2. A p p l y i n g t h e s t a t i o n a r y s t a t e t r e a t m e n t to b o t h Ο a n d 0 * leads t o : 2

d(Q,)

2fetfc,(M)(Q,)»

( 1 2 )

2fc,(0 )

( U

2

.

(0 ). 8

w h i c h differs f r o m the p r e v i o u s e x p r e s s i o n , E q u a t i o n 7, b y t h e t e r m i n b r a c k e t s , i n v o l v i n g t h e r a t i o k (M')/k (0 ). T h e m a x i m u m e x p e c t e d v a l u e of t h i s r a t i o w o u l d be ^ 1 i n p u r e ozone—i.e., M ' = 0 — w h i c h w o u l d i m p l y e q u a l chances of e x c i t a t i o n o r d e a c t i v a t i o n o n c o l l i s i o n of 0 * w i t h ozone. B e c a u s e a v a l u e of 1 w o u l d i m p l y e x p l o s i o n of p u r e ozone, i t is c e r t a i n t h a t t h e t r u e v a l u e is c o n s i d e r a b l y less t h a n 1. 5

4

3

3

2

T h i s has the net effect of i n c r e a s i n g the s t a t i o n a r y state of o x y g e n a t o m s a b o v e t h e t h e r m o d y n a m i c a l l y e x p e c t e d l i m i t a n d t h u s e n h a n c i n g t h e r a t e . H o w e v e r (1, 4)> s u c h e n h a n c e m e n t w o u l d be e x p e c t e d t o d e p e n d s o l e l y o n the r a t i o of ( 0 ) / ( M ) a n d t o be i n d e p e n d e n t of t e m p e r a t u r e . B e n s o n a n d A x w o r t h y h a v e s h o w n t h a t t h e r e is no evidence t o s u p p o r t s u c h a n effect a n d t h a t the e n h a n c e m e n t s o b s e r v e d are e x p l i c a b l e o n g r o u n d s of t h e t e m p e r a t u r e g r a d i e n t s p r o d u c e d b y t h e d e c o m p o s i t i o n . I n terms of a v a i l a b l e d a t a , t h e p r e c i s i o n is sufficient t o c o n c l u d e t h a t k /k ^ 15, w h i c h w o u l d s u p p o r t the p r e v i o u s l y stated speculations on energy transfer. 3

5

Unimolecular

4

Features

T h e r a t e c o n s t a n t s f o u n d f o r t h e i n d i v i d u a l steps 1 a n d 2 s h o w a n u m b e r of a n o m a l i e s . I n t h e first p l a c e , t h e a c t i v a t i o n e n e r g y f o r R e a c t i o n 1 is less t h a n t h e e n e r g y change f o r t h e process, w h i c h leads t o t h e c o r o l l a r y a n o m a l y t h a t t h e a c t i v a t i o n e n e r g y of 2 is n e g a t i v e . L a s t l y , t h e f r e q u e n c y f a c t o r of 1 is g r e a t e r t h a n c o l l i s i o n frequencies b y a f a c t o r of a b o u t 20. R e a c t i o n 3, aside f r o m i t s g r e a t e x o t h e r m i c i t y , h a s a n o r m a l f r e q u e n c y f a c t o r f o r s u c h a r e a c t i o n a n d p r e s e n t s no s t r a n g e f e a t u r e s . The steric f a c t o r is a b o u t 0.1, w h i c h is j u s t a b o u t w h a t one w o u l d c a l c u l a t e f r o m t r a n s i t i o n state theories. T h e s e a n o m a l i e s a p p e a r u n d e r s t a n d a b l e , h o w e v e r , w h e n t h e d e c o m p o s i t i o n of ozone is l o o k e d u p o n f r o m t h e p o i n t of v i e w of a u n i m o l e c u l a r r e a c t i o n a t i t s l o w p r e s s u r e l i m i t . W i t h t h r e e i n t e r n a l v i b r a t i o n s a n d a m a x i m u m of t w o a c t i v e r o t a t i o n s , t h e m e a n l i f e t i m e of t h e a v e r a g e ozone m o l e c u l e u n d e r g o i n g d e c o m p o s i t i o n is e x p e c t e d to be v e r y s h o r t (2) c o m p a r e d t o c o l l i s i o n t i m e s , e v e n a t 1 - a t m . p r e s s u r e . I n c o n sequence, t h e s t a t i o n a r y s t a t e c o n c e n t r a t i o n s of c r i t i c a l l y e n e r g i z e d 0 * m o l e c u l e s , w h i c h c o n t r i b u t e t o t h e o v e r - a l l d e c o m p o s i t i o n , are f a r b e l o w the c o n c e n t r a t i o n s c a l c u l a t e d a t e q u i l i b r i u m a n d t h e s l o w step i n t h e r e a c t i o n becomes the r a t e of a c t i v a t i o n of ozone. 3

If

we

designate

by

( 0 ) $ * the s t a t i o n a r y state 3

concentration

of

ozone


mole-

402

ADVANCES

IN CHEMISTRY SERIES

cules h a v i n g i n t e r n a l e n e r g y E^£E* = Δ # ι ° , i n excess o f t h a t r e q u i r e d f o r d e c o m p o s i t i o n , t h e d e t a i l e d m e c h a n i s m c a n be w r i t t e n as : M + 0 1 ± (0,)»* + M 3

bi

(Ο,),* ^ 0 + Ο

(13)

2

Ο + 0

Λ

3

20-2

I f w e n o w a p p l y s t a t i o n a r y state m e t h o d s t o ( 0 ) $ * a n d 0 w e f i n d :


-

" δ,·(Μ) +

t U i ; s s

-

C i

*

3

W

+

M

O

O

( I 4 )

b,(M) + a

+

(

L

b

>

where, o n substitution a n d rearrangement : ( Μ ) ( 0 ) Σ (,-—-) ) aw

[d(O0 + *»(0,)]

3

2c*(O0* =

(

M

>^)

2

(16)

χ

(w^)

+

f

e

(

a

)

[ I t i s a s s u m e d here t h a t o x y g e n a t o m s a r e a t t h e r m a l e q u i l i b r i u m . T h i s i s v a l i d , because t h e y a r e i n v o l v e d o n l y i n s e c o n d - o r d e r o r h i g h e r r e a c t i o n s (3). T h e s u m s i n these expressions a r e o v e r - a l l i n t e r n a l e n e r g y states whose t o t a l energies a r e i n excess of Δ ^ Λ ] T h i s gives f i n a l l y , f o r t h e r a t e o f d e c o m p o s i t i o n of o z o n e :

(17)

A t h i g h pressures w h e r e 6 ^ M > c f o r a l l e n e r g y states of ( 0 ) * c o n t r i b u t i n g s i g n i f i c a n t l y t o t h e r e a c t i o n , t h i s reduces t o : t

3

2 =*m dt

. M^OO

4

^Kf)

(18)

d(O ) + h(O ) t

t

T h e densities n e e d e d f o r s u c h a c o n d i t i o n t o b e f u l f i l l e d a r e satisfied v i r t u a l l y o n l y i n s o l u t i o n , n o t i n t h e gas p h a s e . A t l o w pressures, o n t h e other h a n d , where t h e b u l k of ( 0 ) * w h i c h a r e i m p o r t a n t decompose m u c h faster t h a n they collide (the condition actually m e t w i t h i n t h e gas phase r e a c t i o n ) : 8

-d(O ) dt M -

4

2Α;,(Μ)(0,)»(Σα,·)

t

>° (M)(0 ) ( Σ ^ ) 2

(19)

+λ; (0 ) 3

3

If this is compared w i t h the previous expression ( E q u a t i o n 7) w e c a n m a k e t h e following identifications : hi = Σα* = ΣΚώί k

2

(20)

= X ^ d

w h e r e K — a /b = t h e e q u i l i b r i u m c o n s t a n t f o r t h e c o n c e n t r a t i o n of ( 0 3 ) 1 * . I f now it i s a s s u m e d t h a t bi m a y b e r e p l a c e d b y \Z = λχ2χ 1 0 liter/mole-sec. where Ζ t

i

i

1 1


BENSON AND

403

A X W O R T H Y - G A S PHASE DECOMPOSITION

is t h e c o l l i s i o n f r e q u e n c y of 0 * a n d 0 ( a s s u m e d t o be 2 Χ 1 0 ) a n d λ i s t h e p r o b a b i l i t y of d e a c t i v a t i o n of 0 * o n c o l l i s i o n , K c a n be e s t i m a t e d as f o l l o w s . T h e e x p e r i m e n t a l a c t i v a t i o n e n e r g y gives us t h e difference b e t w e e n t h e a v e r a g e e n e r g y of t h e states t h a t c o n t r i b u t e t o r e a c t i o n , ( 0 ) ^ * , a n d n o r m a l o z o n e . A t 100° C . t h i s gives 25.3 k c a l . of i n t e r n a l e n e r g y f o r t h e a v e r a g e ( 0 ) * t h a t is r e s p o n s i b l e f o r r e a c t i o n . T h e v i b r a t i o n frequencies of W i l s o n a n d B a d g e r (11) a r e u s e d h e r e (705, 1043, a n d 1110 c m . ) ; 1.3 k c a l . of the a b o v e e n e r g y a r e i n r o t a t i o n . I f w e n o w c o m p u t e t h e n u m b e r of w a y s of d i s t r i b u t i n g t h i s e n e r g y a m o n g t h e i n t e r n a l m o d e s of ozone, w e find a p p r o x i m a t e l y 65 v i b r a t i o n a l states, a s s u m i n g t h a t s m a l l d i s c r e p a n c i e s m a y be t a k e n u p i n r o t a t i o n a n d b y a n h a r m o n i c i t i e s . F r o m a s t a t i s t i c a l p o i n t of v i e w w e c a n a p p r o x i m a t e K — ^ ο~ ^Ι w h e r e g ^ 65 a n d 3

1 1

2

t

3

3

3

4

- 1

t

{

Έ

ητ

t

= Kct. = 24 k c a l . I f t h e m o m e n t s of i n e r t i a h a v e c h a n g e d t h i s s h o u l d be i n c l u d e d i n g as s h o u l d a n y s i g n i f i c a n t changes i n f r e q u e n c y a n d c o n t r i b u t i o n s f r o m a n h a r m o n i c i t y . T h i s finally y i e l d s f o r A t h e ρ r e - e x p o n e n t i a l f a c t o r of k t h e v a l u e 1.3 λ Χ 1 0 l i t e r / m o l e - s e c , w h i c h o n c o m p a r i s o n w i t h t h e e x p e r i m e n t a l v a l u e of k ( f o r M = 0 ) , gives λ ο w h i c h seems of reasonable o r d e r of m a g n i t u d e . B e n s o n a n d A x w o r t h y (4) h a v e s h o w n b y a s i m i l a r c a l c u l a t i o n t h a t λ ο ^ 1/50, a n d f r o m efficiencies of t r i p l e collisions t h a t λ ο ^ 1 / 1 4 0 . T h e t r u e v a l u e is p r o b a b l y s o m e w h e r e n e a r 1 / 5 0 , w h i c h is also c o n s i s t e n t w i t h o u r d e d u c t i o n o n t h e efficiency of e n e r g y c h a i n s .


i}

1 3

ly

1}

t

2

2

2

2

T h e h i g h p r e - e x p o n e n t i a l f a c t o r of R e a c t i o n 1 is t h u s d u e t o a v e r y l a r g e e n t r o p y of a c t i v a t i o n f o r 0 * . S u c h l a r g e f a c t o r s are g e n e r a l l y n o t m e t w i t h i n b i m o l e c u l a r r e a c t i o n s . T h e y do o c c u r i n t h i s s p e c i a l t y p e of b i m o l e c u l a r r e a c t i o n , h o w e v e r , w h i c h i n v o l v e s e n e r g y t r a n s f e r . R i c e (10) has discussed s i m i l a r effects i n t h e c l o s e l y r e l a t e d r e a c t i o n s M + X -» M + 2X, w h i c h h a v e e v e n h i g h e r f r e q u e n c y f a c t o r s . 3

2

Competitive Reactions Involving O x y g e n

Atoms

The Ozonizer. T h e d a t a o b t a i n e d p e r m i t us t o a n s w e r some q u e s t i o n s c o n c e r n i n g c o m p e t i t i v e r e a c t i o n s of o x y g e n a t o m s a n d i n p a r t i c u l a r t h e r e a c t i o n s g o i n g o n i n a n o z o n i z e r , w h i c h are r e s p o n s i b l e f o r ozone p r o d u c t i o n . T h e r e a r e t h r e e p r i n c i p a l p a t h s f o r t h e p r o d u c t i o n of ozone f r o m o x y g e n i n a n o z o n i z e r . T h e s e i n v o l v e s y n t h e s i s f r o m a t o m s , f r o m m e t a t h e t i c a l r e a c t i o n s of m e t a s t a b l e m o l e c u l e s , a n d finally f r o m d i s s o c i a t i v e r e c o m b i n a t i o n s of i o n s . I l l u s t r a t i v e e x a m p l e s of e a c h m i g h t be :

Ο +0

+ M -> 0

2

0 *( Σ„+) - f 0 3

2

Or + 0

2

0

Λ

+

Λ

2

+

3

M 0

Ο +

(21) 3

+ Ο + energy

3

C o m p e t i n g w i t h these processes f o r t h e d e s t r u c t i o n of b o t h o x y g e n a t o m s a n d ozone is:

Ο + 0 -> 2 0 Ο + Ο + ΜΛΟ + Μ 3

2

(22)

2

F r o m t h e p o i n t of v i e w of o z o n e p r o d u c t i o n , i t c a n be s h o w n f r o m t h e d a t a t h a t R e a c t i o n 3 w i l l not compete seriously w i t h the synthetic R e a c t i o n 2 under conditions u s u a l i n o z o n i z e r s . T h u s R /R = k (0 ) ( M ) / f t = 5.3 ( M ) ( 0 ) / ( 0 ) a t 3 0 ° C . a n d 0 . 2 ( M ) ( 0 ) / ( 0 ) a t 100° C . W h e n M = 1 a t m . , t h i s gives f o r t h e l i m i t i n g s t a t i o n a r y c o n c e n t r a t i o n s of ( 0 ) w h e n R = R ; ( 0 ) / ( 0 ) = 5.3 a t 3 0 ° C . a n d 0.2 a t 100° C . B o t h v a l u e s a r e i n excess of ozone y i e l d s a c t u a l l y a c h i e v e d i n o z o n i z e r s . I f w e a s s u m e t h a t R e a c t i o n 9 p r o c e e d s a t e v e r y t e r m o l e c u l a r c o l l i s i o n , we c a n s h o w t h a t i t w i l l be f a s t e r t h a n R e a c t i o n 2 as l o n g as t h e r a t i o 0 / 0 < 1 / 1 0 0 . 2

2

s

2

2

8

2

3

3

3

2

3

3

2

2


404

A D V A N C E S IN CHEMISTRY SERIES

It thus appears that a possible and fast mechanism for the production of ozone is b y way of oxygen atoms which act as catalysts

for the conversion of 0 - * 0 . 2

3

Because oxygen atoms are essentially slow i n destruction of ozone, the limiting sta tionary process must be the destruction of ozone via the same type of process which is responsible for oxygen destruction—e.g., electron bombardment—or else the increase in temperature of the discharge which would finally provoke the thermal decomposition of ozone and make Reaction 3 a limiting process. This can be rather serious, because the chief mode of removal of oxygen atoms if their concentration is 1% of oxygen

or greater, is b y the exothermic

producing 119 kcal. per mole of oxygen. (0

2

= 1 atm.)

Reaction 9,

Because the half life under these conditions

will be of the order of 1 to 5 microseconds, rather high instantaneous

temperatures can be produced, heat diffusion being relatively slow compared to these times. A n alternative mode of reaction, which is not so fast and which could lead i n


principle at least to the establishment

of high ozone concentrations, might be v i a

the generation of large concentrations of metastable

0 ( 2 +). 2

3

M

Their long lifetime

with respect to radiative processes and collision processes could lead to delayed produc tion of ozone (Reaction 7) outside of the discharge zone and hence to inherently greater yields.

Unfortunately, nothing appears to be known concerning their reaction.

Literature (1)

Cited

Axworthy, A. E., J r . , Benson, S. W., ADVANCES IN CHEM. SER., N o . 23, 388 ( 1 9 5 9 ) .

(2) Benson, S. W., J. Chem. Phys. 20, 1064 (1952). (3) Benson, S. W., Axworthy, A. E., Jr., Ibid., 21, 428 (1953). (4)

(5) (6) (7) (8) (9) (10) (11) (12)

Ibid., 26, 1718 ( 1 9 5 7 ) .

Garvin, D., J. Am. Chem. Soc. 76, 1523 (1954). Glissmann, Α., Schumacher, H. J., Z. phys. Chem. 21B, 323 (1933). Herzberg, G., "Spectra of Diatomic Molecules," Van Nostrand, New York, 1950. Jahn, S., Z. anorg. Chem. 48, 260 (1906). Ogg and Sutphen, thesis, Stanford University, 1955. Rice, Ο. K., J. Chem. Phys. 8, 727 (1940). Wilson, M. K., Badger, R. M., Ibid., 16, 741 (1948). Wulf, O. R., Tolman, R. C., J. Am. Chem. Soc. 49, 1183, 1202 (1927).

RECEIVED for review June 19, 1957. Accepted June 19, 1957. Work supported by the Office of Ordnance Research under Contract N o . D A - 0 4 - 4 9 5 Ord-345 with the University of Southern California. Taken in part from the thesis of A. E. Axworthy, Jr., presented to the Graduate School, University of Southern California, in partial fulfillment of the requirements for the Ph.D. in chemistry.


Implications of Data on the Gas Phase Decomposition of Ozone

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