Kinetic Considerations of Efficiency of Ozone Production in Gas

Kinetic Considerations of Efficiency of Ozone Production in Gas Discharges SIDNEY W. BENSON

Downloaded by AUBURN UNIV on September 12, 2017 | http://pubs.acs.org Publication Date: January 1, 1959 | doi: 10.1021/ba-1959-0021.ch054

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

Various schemes for the production of ozone from oxygen in an electric discharge are considered. There are a number of low energy paths available through O-1 ions a n d at least one excited state of O. Despite the availability of these paths, the efficiency of the discharge is very low, partly because of the slow thermal dissipation of energy in the dis charge itself. The remainder results from the rela tively high gas temperature occurring in the dis charge, which causes thermal decomposition of the ozone. 2

T h e s y n t h e s i s of a m e t a s t a b l e m a t e r i a l f r o m i t s elements presents c o n f l i c t i n g aspects of k i n e t i c , t h e r m o d y n a m i c , a n d p r a c t i c a l i n t e r e s t . O z o n e p r o d u c t i o n f r o m o x y g e n i s t y p i c a l of m a n y s u c h s y n t h e s e s , b u t i t is e x t r e m e . T h e e n t h a l p y change i s v e r y l a r g e , ΔΗ (1 a t m . ) = + 3 4 k c a l . p e r m o l e , a t t h e same t i m e t h a t t h e e n t r o p y change is b o t h f a i r l y l a r g e a n d u n f a v o r a b l e , AS° (1 a t m . ) = —16.7 c a l . p e r m o l e ° C . (6). T h u s , t h e r e is n o reasonable set of t e m p e r a t u r e s a n d pressures a t w h i c h t h e e q u i l i b r i u m c o n s t a n t w o u l d be s u f f i c i e n t l y l a r g e t o m a k e t h e use of c a t a l y s t s feasible, i f s u c h existed. T h e r e v e r s i b l e o x i d a t i o n of o x y g e n i n a n e l e c t r o c h e m i c a l c e l l m i g h t b e t h e m o s t efficient m e t h o d of p r o d u c t i o n , a n d i t s e x p e n d i t u r e of e n e r g y m i g h t b e closest t o t h e t h e o r e t i c a l , AF° = + 3 9 k c a l . p e r m o l e . H o w e v e r , e l e c t r o c h e m i c a l m e t h o d s h a v e n o t succeeded i n c o m p e t i n g w i t h gas d i s c h a r g e m e t h o d s . T h e reaction, Ό

68 kcal. + 3 0

20

2

(1)

3

s h o u l d t a k e p l a c e efficiently i n t h e gas p h a s e , b u t t h e r e q u i r e m e n t s a r e r a t h e r severe. B e c a u s e of t h e u n f a v o r a b l e free e n e r g y c h a r g e , t h e e n e r g y i n p u t of 68 k c a l . c a n n o t be m a d e a v a i l a b l e t h e r m a l l y . I t m u s t b e p r o v i d e d i n t h e f o r m of e x c i t e d states o r a t o m s of 0 , w h i c h r e a c t t o f o r m 0 p r e d o m i n a n t l y . T h u s , t h e s y s t e m m u s t b e c o n v e r t e d t o one whose free e n e r g y is h i g h e r t h a n 0 , so t h a t t h e c o n v e r s i o n t o 0 w i l l b e spontaneous. I f 0 m o l e c u l e s c o u l d be e x c i t e d t o a m e t a s t a b l e s t a t e , 0 * , possessing a b o u t 34 k c a l . p e r m o l e , t h e n t h e r e a c t i o n 3

3

3

2

2

20 * + 0 -> 2 0 2

2

(2)

3

c o u l d o c c u r as a t h e r m o n e u t r a l t e r m o l e c u l a r ( o r t w o c o n s e c u t i v e b i m o l e c u l a r ) process at a reasonable r a t e . T h e m e t h o d of e x c i t a t i o n m u s t n o t d e s t r o y 0 , a n d t h e c o m p e t i n g s e c o n d - o r d e r process of c o l l i s i o n a l d e - e x c i t a t i o n of 0 * m u s t b e s l o w c o m p a r e d t o R e a c t i o n 2. T h e r e is a m e t a s t a b l e state of 0 , ( S ) , w h i c h i s 37.5 k c a l . p e r m o l e 3

2

2

1

i ?

+

405

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

A D V A N C E S IN CHEMISTRY SERIES

40ό

a b o v e t h e g r o u n d s t a t e of 0 . T h i s s h o u l d f u l f i l l t h e r e q u i r e m e n t s , b u t t h e r e i s n o evidence t h a t i t c a n participate i n such a reaction. Theoretically, R e a c t i o n 2 is n o t f a v o r e d , as i t i n v o l v e s a change i n s p i n m u l t i p l i c i t y . I t is also i n conflict w i t h d a t a o n t h e d e c o m p o s i t i o n o f ozone. I f R e a c t i o n 2 were a t a l l m e a s u r a b l e , i t s reverse r e a c t i o n s h o u l d b e e x t r e m e l y f a s t . B e n s o n a n d A x w o r t h y {1, 2) h a v e s h o w n , h o w e v e r , t h a t t h e reverse of R e a c t i o n 2 m u s t h a v e a n a c t i v a t i o n e n e r g y i n excess of 2 0 k c a l . i f i t s p r e exponential factor is 2 Χ 1 0 liters/mole-sec. T h u s , k w i l l be too s m a l l f o r R e a c t i o n 2 e v e r t o b e f a s t i n t h e r a n g e f r o m 0 ° t o 100° C . H i g h e r t e m p e r a t u r e s c a n n o t b e c o n s i d e r e d , because o f t h e i n c r e a s i n g r a t e of d e c o m p o s i t i o n of 0 w i t h t e m p e r a t u r e b y a n Ο a t o m m e c h a n s i m . A n y such l o w energy p a t h w o u l d be i n c o m p a t i b l e w i t h t h e exist ence of 0 a t r o o m t e m p e r a t u r e . I n c a l c u l a t i n g t h e efficiency of s u c h a process, t h e mode of excitation m u s t be considered. T h e p r o d u c t i o n o f p h o t o n s i s v e r y inefficient energetically, a n d t h e absorption intensities w o u l d be extremely s m a l l f o r t h e p r o d u c t i o n of s u c h m e t a s t a b l e states. 2

9

2

3


3

T h e first k n o w n m e t a s t a b l e s t a t e , c o m p a t i b l e w i t h t h e d a t a o n 0 decomposition, w h i c h could lead t o 0 formation is 2 a t 103 k c a l . a b o v e t h e g r o u n d s t a t e . T h i s state c o u l d produce 0 b y : 3

3

3

w

+

3

0 ( Σ , + ) + 0 —> 0 3

2

2

0 + 0

2

3

+ Ο + 10 kcal.

(3)

+ M—>0 + M

(4)

3

w h i c h s h o u l d b e r e a s o n a b l y fast a t r o o m t e m p e r a t u r e (1, 2). S u c h a s c h e m e c o u l d p r o d u c e 0 a t a cost of 51.5 k c a l . p e r m o l e , n e g l e c t i n g t h e inefficiency o f p r o d u c i n g 3 + the 2 w a n d t h e losses b y d e a c t i v a t i o n . T h e r e is v e r y l i t t l e i n f o r m a t i o n o n t h e c h e m i c a l r e a c t i o n s of t h i s s t a t e . T h e p h o t o c h e m i c a l s y n t h e s i s (7) of 0 a t 2537 Α . , Ρ ~ 1300 a t m . a n d Φ ( 0 ) ^ 1.14, c a n b e e x p l a i n e d b y i t . T h e state p r o d u c e d i s t h e 3

3

3

3

5

+ w

b y a forbidden absorption.

I n t h e gas d i s c h a r g e m e t h o d , ozone i s p r o d u c e d f r o m Ο a t o m s , w h i c h were p r o d u c e d b y dissociating 0 b y inelastic collisions of electrons. T h e o v e r - a l l reaction is: 2

10, + e- -> e" + Ο - 59 k c a l . 1

1

Μ + 0 +0 ^4θ + Μ 2

3

N e g l e c t i n g t h e e n e r g y o f p r o d u c i n g e x c i t a t i o n electrons, t h e cost i s 59 k c a l . p e r m o l e . C u r r e n t figures (8) of a b o u t 4 1 0 k c a l . p e r m o l e h a v e b e e n g i v e n f o r l a r g e scale c o m m e r c i a l o z o n i z e r s . T h e t h r e s h o l d e n e r g y f o r these e l e c t r o n s i s 118 k c a l . p e r m o l e (5.09 e . v . ) . L o w e r e n e r g y processes i n v o l v i n g t h e a b u n d a n t n e g a t i v e i o n s , O and 0 , s h o u l d b e possible i n a gas d i s c h a r g e i n 0 . A p r o b a b l e i n i t i a t i o n process r e q u i r i n g o n l y 3.6-e.v. t h r e s h o l d e l e c t r o n s is d i s sociative attachment, -

2

_

1

1

2

e

+ 0 —> Ο + Ο

- 1

2

- 1

- 83 kcal.

(6)

u s i n g t h e recent v a l u e s f o r t h e e l e c t r o n affinities o f O a n d O 2 " of 1.5 e.v. (8) a n d 1 e.v. ( 5 ) , r e s p e c t i v e l y . I f t h i s i s f o l l o w e d b y R e a c t i o n 4 p l u s -

O"

1

+ 0 -> 0 2

3

+ e" -

1

1

10 kcal.

1

(7)

w h i c h s h o u l d b e r e l a t i v e l y fast e v e n a t 2 5 ° C , t h e t o t a l cost f o r 0 w i l l b e o n l y 4 1 . 5 k c a l . p e r m o l e . A n e x o t h e r m i c process, c o m p e t i n g w i t h R e a c t i o n 7 a t 1 a t m . , w i t h v e r y l o w a c t i v a t i o n energy is 3

Ο"

1

+ 0

2

+ 0 -> 0 2

3

+ O2- + 13 kcal.

(8)

1

T h i s m a y b e f a s t e r t h a n R e a c t i o n 7, b u t i t i s e s s e n t i a l l y w a s t e f u l . t u r e m u s t b e s u f f i c i e n t l y h i g h so t h a t t h e e q u i l i b r i u m

T h e tempera

(9)


407

B E N S O N - P R O D U C T I O N IN G A S DISCHARGES

lies l a r g e l y t o t h e l e f t ; o t h e r w i s e t h e e l e c t r o n is l o s t . T h i s i s p r o b a b l y t h e case a t 2 5 ° C . a n d t h e l o w e l e c t r o n densities p r e v a l e n t i n gas d i s c h a r g e s . R e a c t i o n 9 a n d i t s reverse a r e l i k e l y t o b e v e r y s l o w a t r o o m t e m p e r a t u r e because t h e y w i l l b e c o l l i s i o n c o n t r o l l e d — i . e . , M + 0 + e- -» ( V " + M . T h e f o l l o w i n g t e r m o l e c u l a r process i s t h e o n l y one i n t h e d i s c h a r g e w h i c h does n o t use 0 a t o m s t o m a k e 0 : 1

1

2

3

e- + 0

+ 0 -> 0

1

2

2

+ Ο"

1

- 60 kcal.

(10)

I t w o u l d r e q u i r e a t h r e s h o l d e l e c t r o n e n e r g y n e a r 2.6 e.v. I f t h i s r e a c t i o n i s f o l l o w e d b y R e a c t i o n 7 o r 8, i t w o u l d cost o n l y 3 0 k c a l . p e r m o l e , o r less t h a n t h e p r e v i o u s m i n i m u m t h e o r e t i c a l e s t i m a t e . T h i s c a n o c c u r o n l y because t h e cost o f p r o d u c i n g t h e 2.6-e.v. e l e c t r o n s , w h i c h i s n o t s m a l l , i s n e g l e c t e d . T h i s process w o u l d n o t b e p r o b a b l e unless t h e r e w e r e a n e x c i t e d state of 0 a b o u t 4.1 e.v. a b o v e t h e g r o u n d s t a t e , w h i c h does n o t a p p e a r l i k e l y (δ). I n a l l these i o n i c processes, Ο and e are 0 destroyers. T h e equilibria for the following reactions l i e f a r to t h e right : -

2


3

-

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1

1

-

+ 0 -^l 0

1

3

e' + 0 1

3

™0

1

3

2

+ 0 2 " + 82 kcal.

(11)

2

+ O " + 10 kcal.

(12)

1

1

T h e s e r e a c t i o n s p r o b a b l y r e q u i r e n o a c t i v a t i o n e n e r g y a n d so a r e v e r y f a s t . A l t h o u g h these r e l a t i v e l y r a p i d , k i n e t i c processes p r o d u c e 0 a t a cost of f r o m 3 0 t o 59 k c a l . p e r m o l e , m o s t i n d u s t r i a l a n d l a b o r a t o r y processes h a v e efficiencies s o m e 1 0 - f o l d l o w e r (8). A l l t h e p o s t u l a t e d m e c h a n i s m s i n v o l v e e l e c t r o n s of f a i r l y h i g h energies. T h e r e is a c o n s i d e r a b l e e n e r g y cost i n m a i n t a i n i n g s u c h a h i g h t e m p e r a t u r e e l e c t r o n gas i n a d i s c h a r g e . E v e n f o r a p h o t o c h e m i c a l s y n t h e s i s , t h e e n e r g y cost i s h i g h f o r p r o d u c i n g p h o t o n s of t h e r e q u i r e d w a v e l e n g t h . A l s o , c h e m i c a l processes i n the discharge dissipate energy t h e r m a l l y . F o r every mole of 0 produced b y R e a c t i o n 4, 24.5 k c a l . of h e a t w i l l b e l i b e r a t e d . S i m i l a r l y , 0 is a t t a c k e d b y O , b y O " " , a n d b y e . T h e r e a c t i o n of 0 + 0 - » 2 0 l i b e r a t e s 9 3 k c a l . of h e a t , O ( R e a c t i o n 11) l i b e r a t e s 8 2 k c a l . , a n d e ( R e a c t i o n 12) l i b e r a t e s 10 k c a l . I n a d d i t i o n , e x c i t a t i o n a n d i o n i z a t i o n of 0 a r e c o n s i d e r e d e n e r g y - w a s t i n g processes. 3

3

1

3

- 1

3

_

-

2

1

1

2

B e c a u s e a l l h e a t d i s s i p a t e d i n t h e gas m u s t e v e n t u a l l y b e c o n d u c t e d t o t h e w a l l s , t h e m a i n t e n a n c e of a l o w t e m p e r a t u r e i n t h e d i s c h a r g e r e q u i r e s a n a r r o w g a p ( w a l l s close t o g e t h e r ) , l o w c u r r e n t s , a n d l o w space v e l o c i t i e s ( l o w specific r a t e s o f 0 production). These requirements are opposite to the conditions w h i c h w o u l d be suggested b y t h e k n o w n s e n s i t i v i t y o f o z o n e t o w a l l c a t a l y s i s a n d t h e e n h a n c e d r a t e of d e s t r u c t i o n o f s u c h c a r r i e r s as Ο , O , a n d ea t w a l l s . A l l of these c o n t r i b u t e t o l o w efficiency 0 p r o d u c t i o n . T o t h e e x t e n t t h a t h e a t i s n o t s u c c e s s f u l l y d i s s i p a t e d , t h e m e a n t e m p e r a t u r e rises a n d t h e t h e r m a l d e c o m p o s i t i o n of 0 b e c o m e s i n c r e a s i n g l y important. 3

-

1

1

3

3

A s i m p l i f i e d s c h e m e r e p r e s e n t s m o s t o f t h e i m p o r t a n t processes i n p r o d u c i n g a n d d e s t r o y i n g 0 i n a t y p i c a l gas d i s c h a r g e : 3

e"

+ 0

1

2

- ^ 2 0

-f-e"

1

Eq. 4

Ο + 0 + M --!-> 0 + M 2

(15)

3

E q . 13

Ο + 0 ——» 2 0 8

e

-i + 0

3

— ^ 0

2

2

+ 0 + e~i)

Processes i n v o l v i n g O2"" a n d O are m i n o r i n comparison, a n d their features are e s s e n t i a l l y t h e s a m e . P r o b a b l y h a l f o r m o r e of t h e 0 p r o d u c e d c o m e s f r o m R e a c t i o n 1

-

1

3

4.


408

A D V A N C E S IN CHEMISTRY SERIES

T h e r e a c t i o n s Ο + w a l l -> % 0 a n d 0 - f O + M - » 0 + M m a y be i g n o r e d , because t h e y w i l l n o t b e i m p o r t a n t u n t i l 0 / 0 > 0.01, a n u n l i k e l y r a t i o a t 1 a t m . of 0 . T h e reverse of R e a c t i o n 4 m a y be i n c l u d e d , i n p r i n c i p l e , i n P r o c e s s 14. As Ο a t o m s h a v e a h a l f l i f e a t 1 a t m . of 0 of a b o u t 1 0 - s e c o n d (1, 2) b y R e a c t i o n 4, s t a t i o n a r y states a r e q u i c k l y e s t a b l i s h e d i n t h e d i s c h a r g e e v e n a t v e r y h i g h flow velocities. I f t h e u s u a l s t a t i o n a r y state conditions are a p p l i e d to Ο a n d 0 , t h e m a x i m u m possible c o n c e n t r a t i o n of 0 is g i v e n b y i t s s t a t i o n a r y s t a t e : 2

2

2

2

5

2

3

3

T w o l i m i t s a r e possible f o r t h e r a t i o 0 / 0 , v e r y large or s m a l l :


3

(OA

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2

depending

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(

1

7

)

kj ki3

4/CH «

W i t h t h e u s u a l h i g h v o l t a g e a r c , t h e e l e c t r o n t e m p e r a t u r e is of t h e o r d e r of 20 t o 50 e.v. F o r t h e b u l k of t h e electrons, k s h o u l d n o t b e t o o different f r o m k , a l t h o u g h p e r h a p s l a r g e r b y a f a c t o r of a b o u t 3 t o 10. T h e r a t i o w i l l b e i n d e p e n d e n t of gas t e m p e r a t u r e . T h e r a t i o & ( M ) / & c a n be readily calculated f r o m t h e d a t a of B e n s o n a n d A x w o r t h y (1, 2) a n d , a t M = 1 a t m . of 0 , h a s t h e v a l u e s 2 . 3 ( 2 7 ° C ) , 0 . 2 0 ( 1 0 0 ° C ) , 0 . 0 6 3 ( 1 5 0 ° C ) , 0 . 0 2 4 ( 2 0 0 ° C ) , a n d 0 . 0 0 6 ( 3 0 0 ° C ) . E v e n i f k /k 100, m a x i m u m y i e l d s of 0 of t h e o r d e r o f 1 5 % a t 2 7 ° C . a n d 4 . 5 % a t 100° C . s h o u l d be o b t a i n e d . H o w e v e r , t h e y i e l d s a r e s t r o n g l y d e p e n d e n t o n t h e gas t e m p e r a t u r e . s

4

14

1 3

2

lé

j

=

3

T h e temperature equation i n a n ozonizer is

â

v

2

r

è

+

0

=

f

( 1 8 )

w h e r e Κ = t h e r m a l c o n d u c t i v i t y , d = d e n s i t y , C = specific h e a t a t c o n s t a n t p r e s s u r e , Τ = t e m p e r a t u r e , t = t i m e , a n d Q = specific r a t e of h e a t p r o d u c t i o n i n t h e g a s . I f t h i s i s i d e a l i z e d as a t h i n l a y e r of gas flowing b e t w e e n i n f i n i t e p l a t e s of s e p a r a t i o n 2x c m . , t h e p r o b l e m s i m p l i f i e s t o a o n e - d i m e n s i o n a l flow. T h e s t a t i o n a r y s t a t e t e m p e r a t u r e d i s t r i b u t i o n i s , a s s u m i n g Κ = oo a t t h e w a l l s a n d T = w a l l t e m p e r a t u r e , p

0

w

Τ — T

= W [-

(19)

x

w

w h e r e χ is m e a s u r e d f r o m a p l a n e h a l f w a y b e t w e e n t h e w a l l s . T h e s o l u t i o n of t h e t i m e - d e p e n d e n t p r o b l e m f o r a n i n i t i a l u n i f o r m t e m p e r a t u r e d i s t r i b u t i o n i s k n o w n (4). C o n s t a n t d e n s i t y is a s s u m e d , b u t t h e c o r r e c t i o n i s n o t i m p o r t a n t except for large gradients. T h e m e a n time required to establish this d i s t r i b u t i o n is given b y Ι

ι

/

2

^ 2 ψ

0

ρ

( 2 0 )

F o r 0 a t 1 a t m . , 2 5 ° C , a n d 2x = 0.3 c m . , ty ^ 0.25 s e c o n d . F o r m u c h s h o r t e r r e a c t i o n t i m e s , c o n d u c t i o n i s ineffective a n d t h e r e a c t i o n c a n b e c o n s i d e r e d a d i a b a t i c . A s t e m p e r a t u r e s m a y b e e x t r e m e l y h i g h , t h i s p r o v i d e s a s h a r p l i m i t o n t h e r a t e of p r o d u c t i o n . One solution m i g h t be pulse operation i n w h i c h Ο atoms are produced i n less t h a n 10 ju,sec. a n d t h e n r e a c t t o f o r m 0 . U n f o r t u n a t e l y , t h e h e a t l i b e r a t e d i n t h i s process w o u l d p r o d u c e c a t a s t r o p h i c t e m p e r a t u r e s , because i t w o u l d b e p r o d u c e d i n t h e n e x t 10 jmsec. 2

0

2

3


BENSON—PRODUCTION IN

GAS

409

DISCHARGES

T h e a v e r a g e t e m p e r a t u r e s , T, are o b t a i n e d b y i n t e g r a t i n g E q u a t i o n 19 the walls. τ

φ

-

Τ

μ

'

T

between

"

(21)

where T is t h e m a x i m u m s t a t i o n a r y t e m p e r a t u r e w h i c h o c c u r s a t t h e c e n t e r of t h e vessel ( E q u a t i o n 1 9 ) . I f 5 % p r o d u c t i o n of 0 f r o m p u r e 0 is a s s u m e d i n a residence t i m e of 1 s e c o n d a t a n a v e r a g e e n e r g y d i s s i p a t i o n of 350 k c a l . p e r m o l e of 0 , t h e n M~T = 150° C , a n d f - T = 50° C . A l t h o u g h t h e c o n d i t i o n s a r e close t o those of u s u a l o p e r a t i o n s , t h e t e m p e r a t u r e s are r a t h e r h i g h a n d p r o v i d e a s h a r p l i m i t on the m a x i m u m possible 0 c o n c e n t r a t i o n s . L o n g e r residence t i m e s s h o u l d r e d u c e these t e m p e r a t u r e s . I n p r a c t i c e , t h e r e w o u l d be a m o r e w a s t e f u l d i s s i p a t i o n of h e a t i n m a i n t a i n i n g the discharge over large periods. M

3

2

3

T

W

W


3

Literature (1)

Cited

Benson, S. W., Axworthy, A. E., Jr.,

ADVANCES

IN

CHEM.

SER.

No.

21,

398

(1958).

(2) Benson, S. W., Axworthy, A. E., Jr., J. Chem. Phys. 26, 1718 (1957). (3) Branscomb, L. M., Smith, S. J., Ibid., 25, 598 (1956). (4) Margenau, H., Murphy, G. M., " T h e Mathematics of Physics and Chemistry," Van Nostrand, New York, 1956. (5) Massey, H. S. W., Burhop, E. H. S., "Electronic and Ionic Impact Phenomena," Clarendon Press, Oxford, 1952. (6) Natl. Bur. Standards (U. S.), Circ. 500 (1952). (7) Warburg, Ε., Z. Elektrochem. 27, 133 (1921). (8) Welsbach Corp., Philadelphia, Pa., communication, 1956. RECEIVED for review June 19, 1957. Accepted June 19, 1957. Work supported by the Office of Ordnance Research, U. S. Army, under Contract No. DA-04-495-Ord-345 with the University of Southern California.


Kinetic Considerations of Efficiency of Ozone Production in Gas

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