Aqueous-Phase Reactions in Clouds

Chapter 8

Aqueous-Phase Reactions in Clouds Stephen E. Schwartz

Downloaded by CORNELL UNIV on September 5, 2016 | http://pubs.acs.org Publication Date: September 3, 1987 | doi: 10.1021/bk-1987-0349.ch008

Environmental Chemistry Division, Brookhaven National Laboratory, Upton, NY 11973

R e a c t i o n of d i s s o l v e d gases i n c l o u d s o c c u r s by the sequence gas-phase diffusion, interfacial mass t r a n s p o r t , and c o n c u r r e n t aqueous-phase d i f f u s i o n and reaction. I n f o r m a t i o n r e q u i r e d f o r e v a l u a t i o n of r a t e s of such r e a c t i o n s i n c l u d e s fundamental data such as e q u i l i b r i u m c o n s t a n t s , gas solubilities, kinetic r a t e laws, i n c l u d i n g dependence on pH and c a t a l y s t s or inhibitors, diffusion coefficients, and mass-accommodation coefficients, and situational data such as pH and c o n c e n t r a t i o n s of r e a g e n t s and o t h e r species i n f l u e n c i n g r e a c t i o n r a t e s , l i q u i d - w a t e r cont e n t , drop s i z e distribution, insolation, temperature, etc. Rate e v a l u a t i o n s i n d i c a t e that aqueousphase o x i d a t i o n of S(IV) by H 2 O 2 and O3 can be important for representative c o n d i t i o n s . No import a n t aqueous-phase r e a c t i o n s of n i t r o g e n s p e c i e s have been identified. E x a m i n a t i o n of m i c r o s c a l e masst r a n s p o r t r a t e s i n d i c a t e s t h a t mass t r a n s p o r t o n l y rarely l i m i t s the r a t e of i n - c l o u d r e a c t i o n f o r representative conditions. F i e l d measurements and s t u d i e s of r e a c t i o n kinetics in authentic precipitat i o n samples are c o n s i s t e n t w i t h r a t e e v a l u a t i o n s .

The c o m p o s i t i o n of l i q u i d - w a t e r c l o u d s and p r o c e s s e s r e s p o n s i b l e f o r t h i s c o m p o s i t i o n are of obvious c u r r e n t i n t e r e s t i n c o n j u n c t i o n w i t h the s o - c a l l e d a c i d p r e c i p i t a t i o n phenomenon s i n c e c l o u d s cons t i t u t e the immediate p r e c u r s o r o f p r e c i p i t a t i o n . A d d i t i o n a l l y , c l o u d c o m p o s i t i o n i s of i n t e r e s t because i m p a c t i o n of c l o u d d r o p l e t s on s u r f a c e s may d i r e c t l y d e l i v e r d i s s o l v e d s u b s t a n c e s onto n a t u r a l or a r t i f i c i a l m a t e r i a l s . I n - c l o u d processes a l s o influence c l e a r - a i r c o m p o s i t i o n s i n c e d i s s o l v e d s u b s t a n c e s r e s u l t i n g from such r e a c t i o n s are r e l e a s e d i n t o c l e a r a i r as gases or a e r o s o l p a r t i c l e s upon c l o u d e v a p o r a t i o n . I t i s thus d e s i r e d to g a i n enhanced d e s c r i p t i o n of the c o m p o s i t i o n of c l o u d s and the mecha-

0097-6156/87/0349-0093$06.00/0 © 1987 American Chemical Society

Johnson et al.; The Chemistry of Acid Rain ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

THE CHEMISTRY OF ACID RAIN

94

nisms whereby c l o u d s a t t a i n t h a t c o m p o s i t i o n . T h i s paper o u t l i n e s methods of d e s c r i b i n g aqueous-phase r e a c t i o n s i n l i q u i d - w a t e r c l o u d s , w i t h emphasis on p r o c e s s e s i n v o l v i n g d i s s o l u t i o n and r e a c t i o n of s u l f u r and n i t r o g e n o x i d e s to form s u l f u r i c and n i t r i c acids.


Acid Incorporation

Mechanisms

The p r o c e s s e s by which c l o u d s i n c o r p o r a t e s u l f u r i c and n i t r i c a c i d s are c o n v e n i e n t l y d i s t i n g u i s h e d i n t o two c a t e g o r i e s depending upon whether o x i d a t i o n takes p l a c e i n the gas phase or i n the aqueous phase, as i l l u s t r a t e d s c h e m a t i c a l l y i n F i g u r e 1. F o r an examinat i o n of gas-phase a t m o s p h e r i c o x i d a t i o n of S O 2 and N O 2 see (_1,2^). P r o d u c t s of t h i s o x i d a t i o n , a e r o s o l s u l f u r i c a c i d and s u l f a t e and n i t r a t e s a l t s , and gas-phase n i t r i c a c i d , are e x p e c t e d to be r a p i d l y and to g r e a t e x t e n t i n c o r p o r a t e d i n t o c l o u d d r o p l e t s upon c l o u d formation (3,4). L i q u i d - w a t e r c l o u d s (5) r e p r e s e n t a p o t e n t i a l l y i m p o r t a n t medium f o r a t m o s p h e r i c c h e m i c a l r e a c t i o n s i n view of t h e i r h i g h l i q u i d water c o n t e n t [10^ to 1 0 times t h a t a s s o c i a t e d w i t h c l e a r a i r a e r o s o l (6)] and h i g h s t a t e of d i s p e r s i o n ( t y p i c a l drop r a d i u s ~10 ym). Clouds a r e q u i t e p r e v a l e n t i n the atmosphere ( f r a c t i o n a l g l o b a l coverage ~50%) and p e r s i s t e n t ( l i f e t i m e s of a few tenths of an hour to s e v e r a l h o u r s ) . The presence of l i q u i d water a l s o cont r i b u t e s to thermochemical d r i v i n g f o r c e f o r p r o d u c t i o n of the h i g h l y s o l u b l e s u l f u r i c and n i t r i c a c i d s . A t a m i c r o s c o p i c l e v e l , the uptake and r e a c t i o n of a gas i n a c l o u d d r o p l e t c o n s i s t s of the f o l l o w i n g s t e p s , as i l l u s t r a t e d i n F i g u r e 2: (1) d i f f u s i o n from the b u l k gas phase to the a i r - w a t e r i n t e r f a c e , (2) t r a n s f e r a c r o s s the i n t e r f a c e , (3) e s t a b l i s h m e n t of any r a p i d aqueous-phase e q u i l i b r i a , and (4) aqueous-phase d i f f u s i o n c o n c u r r e n t w i t h (5) aqueous-phase r e a c t i o n . These steps d e f i n e the i n f o r m a t i o n n e c e s s a r y to e v a l u a t e the r a t e s of such r e a c t i o n s . Fundamental d a t a , which must be determined by l a b o r a t o r y e x p e r i ments, i n c l u d e e q u i l i b r i u m c o n s t a n t s , gas s o l u b i l i t i e s , k i n e t i c r a t e laws, i n c l u d i n g any dependence on pH and c o n c e n t r a t i o n s of other reagents c a t a l y s t s , or i n h i b i t o r s , gaseous and aqueous d i f f u s i o n c o e f f i c i e n t s , and mass-accommodation c o e f f i c i e n t s . The mass-accommodation c o e f f i c i e n t i s the f r a c t i o n of gas k i n e t i c c o l l i s i o n s of a gaseous s p e c i e s upon an i n t e r f a c e r e s u l t i n g i n t r a n s f e r of the s p e c i e s a c r o s s the i n t e r f a c e , and i s expected to depend on the i d e n t i t y of the s o l u t e gas and s o l v e n t , and the presence, i f any, o f s u r f a c e a c t i v e m a t e r i a l s . S i t u a t i o n a l d a t a , which must be measured i n the f i e l d or e l s e modeled or assumed, i n c l u d e pH and c o n c e n t r a t i o n s of r e a g e n t s and o t h e r s p e c i e s i n f l u e n c i n g r e a c t i o n r a t e s , l i q u i d - w a t e r c o n t e n t , drop s i z e d i s t r i b u t i o n , i n s o l a t i o n , temperature, e t c . T h i s paper takes the approach of e v a l u a t i n g r e a c t i o n r a t e s f o r assumed r e p r e s e n t a t i v e v a l u e s of these parameters. I n f e r e n c e s drawn from such e v a l u a t i o n s can be examined f o r c o n s i s t e n c y w i t h f i e l d measurements. 5

O x i d a n t s p r e s e n t i n the atmosphere t h e r m o c h e m i c a l l y capable of o x i d i z i n g S 0 o r N 0 i n c l u d e n o t o n l y m o l e c u l a r O 2 but a l s o the t r a c e , h i g h l y r e a c t i v e c o n s t i t u e n t s O 3 and H 0 t h a t are the prod u c t s of secondary a t m o s p h e r i c p h o t o c h e m i c a l r e a c t i o n s . Despite 2

2

2

2



SCHWARTZ

Aqueous-Phase Reactions in Clouds

F i g u r e 1. S c h e m a t i c r e p r e s e n t a t i o n o f pathways f o r a t m o s p h e r i c f o r m a t i o n o f s u l f u r i c and n i t r i c a c i d s and t h e i r s a l t s . (Reproduced w i t h p e r m i s s i o n from R e f . 28. C o p y r i g h t 1986 Lewis P u b l i s h e r s , Inc.)

CLOUD GAS

1

Ρα(°°)

DROPLET

PHASE

2, » Ρ (ο)-^Ά(α)

r

Α

4
). The pH independence r e s u l t s from the d e c r e a s i n g s o l u b i l i t y of S O 2 w i t h d e c r e a s i n g pH ( F i g u r e 3 ) i n c o n j u n c t i o n w i t h the a c i d c a t a l y z e d r e a c t i o n ( F i g u r e 4 ) . W h i l e the i n s t a n t a n e ous r e a c t i o n r a t e i s q u i t e h i g h , the e x t e n t o f r e a c t i o n may be l i m i t e d by a v a i l a b i l i t y o f H 2 Û 2 > s i n c e the few a v a i l a b l e measurements to date of H 2 O 2 c o n c e n t r a t i o n s i n c l e a r a i r ( 1 2 - 1 4 ) and i n c l o u d w a t e r (15) suggest t h a t the c o n c e n t r a t i o n o f t h i s s p e c i e s r a r e l y i f ever exceeds a few p a r t s p e r b i l l i o n (gas-phase volume f r a c t i o n ) and i s o f t e n l e s s . The importance o f t h e H 2 0 - S ( I V ) r e a c t i o n suggested by these e v a l u a t i o n s and the l i m i t e d a v a i l a b i l i t y o f H C>2 emphasize the need f o r enhanced u n d e r s t a n d i n g o f the s o u r c e s o f H 2 O 2 , i n c l u d i n g gas-phase f r e e - r a d i c a l r e a c t i o n s and


2

2

2

2

2

2

2

2


SCHWARTZ

Aqueous-Phase Reactions in Clouds 1

~ I0

1

1

HN0

3

-

1 0

_

N

H

3

^

\


-

HCOOH^^

H 0 2

CH3COOH — H0

H CO 2

--

2

^so

1

2

2

1

1

4

5

+ OH CH3CHO PAN

pH ^

N0 NO

2

F i g u r e 3 . pH-Dependence o f the e f f e c t i v e Henry's law c o e f f i c i e n t f o r gases w h i c h undergo r a p i d a c i d - b a s e d i s s o c i a t i o n r e a c t i o n s i n aqueous s o l u t i o n , as a f u n c t i o n of s o l u t i o n pH. B u f f e r c a p a c i t y of s o l u t i o n i s assumed to g r e a t l y exceed i n c r e mental c o n c e n t r a t i o n from uptake o f i n d i c a t e d gas. A l s o i n d i cated a t the r i g h t o f the f i g u r e a r e Henry's law c o e f f i c i e n t s f o r n o n - d i s s o c i a t i v e gases. F o r r e f e r e n c e s see ( 2 8 ) . I0 i

1

6

1

1

1

1

|

1

Γ

pH

F i g u r e 4. Second-order r a t e c o n s t a n t k(2) f o r o x i d a t i o n of s u l f u r ( l V ) by hydrogen p e r o x i d e d e f i n e d a c c o r d i n g to d [ S ( V I ) ] / d t = k ( 2 ) [ H 0 2 ] [ S ( l V ) ] , as a f u n c t i o n of s o l u t i o n pH. S o l i d curve i s f i t to data by Overton ( 2 9 ) . Dashed l i n e s (slope = - 1 corresponding to H catalyzed o x i d a t i o n of H S O 3 " i n pH range 3 to 6 ) a r e a r b i t r a r i l y p l a c e d t o encompass most o f the d a t a . Temperature 25°C except as i n d i c a t e d . F o r r e f e r ences see ( 2 9 ) . 2

+


98


p o s s i b l e aqueous-phase r e a c t i o n s i n v o l v i n g O 3 and/or f r e e r a d i c a l s . The 0 3 - S ( l V ) r e a c t i o n e x h i b i t s a very s t r o n g pH dependence t h a t i s due t o t h e S O 2 s o l u b i l i t y ( F i g u r e 3) and r a t e c o n s t a n t ( F i g u r e 5) b o t h d e c r e a s i n g w i t h d e c r e a s i n g pH. T h i s r e a c t i o n ( f o r assumed O 3 c o n c e n t r a t i o n o f 30 ppb) i s important o n l y a t h i g h pH (>5) and, i n view of the f o r m a t i o n of s t r o n g a c i d by t h i s r e a c t i o n , i s s e l f quenched. The r i g h t - h a n d o r d i n a t e o f F i g u r e 6 expresses the r e a c t i o n r a t e as p e r c e n t of gas-phase S O 2 o x i d i z e d p e r hour, p e r u n i t l i q u i d water c o n t e n t o f the c l o u d . O x i d a t i o n r a t e s i n these u n i t s may be compared to c l e a r - a i r o x i d a t i o n r a t e s ( o f o r d e r 1% h " ) , a l t h o u g h t h i s comparison should be tempered by the s m a l l f r a c t i o n of the boundary l a y e r t h a t i s occupied by c l o u d s . Downloaded by CORNELL UNIV on September 5, 2016 | http://pubs.acs.org Publication Date: September 3, 1987 | doi: 10.1021/bk-1987-0349.ch008

1

A u t h e n t i c P r e c i p i t a t i o n K i n e t i c S t u d i e s . A r e c e n t study (JL6) has examined the c h e m i c a l k i n e t i c s of the H202~S(IV) r e a c t i o n i n r a i n water and m e l t water of snow c o l l e c t e d a t our l a b o r a t o r y to a s c e r t a i n whether the r a t e e x p r e s s i o n f o r t h i s r e a c t i o n determined w i t h n o m i n a l l y "pure" water a p p l i e s to such a u t h e n t i c p r e c i p i t a t i o n samples, and by e x t e n s i o n , to c l o u d w a t e r . K i n e t i c s t u d i e s were c a r r i e d o u t on more than 300 p r e c i p i t a t i o n samples o b t a i n e d over a two-year p e r i o d ; sample c o l l e c t i o n was t y p i c a l l y 30 min, and k i n e t i c runs were u s u a l l y made w i t h i n the n e x t 30 min. Reaction was i n i t i a t e d by adding t y p i c a l l y no more than 4 μΜ of H 2 O 2 , HS03~, or b o t h , as n e c e s s a r y to a sample a l i q u o t . V a l u e s of the e f f e c t i v e second-order r a t e c o n s t a n t determined i n these samples a r e shown i n F i g u r e 7. A l t h o u g h the data e x h i b i t c o n s i d e r a b l e s c a t t e r , they f a l l c l o s e to the "pure water" data f o r t h i s r e a c t i o n . Much of the s c a t t e r was a t t r i b u t e d to u n c e r t a i n t y i n pH; i n f l u e n c e o f i o n i c s t r e n g t h o r o f formaldehyde was excluded. We thus g a i n from t h i s study c o n s i d e r a b l e c o n f i d e n c e i n the a p p l i c a b i l i t y o f l a b o r a t o r y s t u d i e s of the k i n e t i c s of the H 2 0 - S ( I V ) r e a c t i o n to e v a l u a t i o n s i n cloudwater. S i m i l a r s t u d i e s o f o t h e r r e a c t i o n s , however, a r e l a c k i n g and should be undertaken. 2

M a s s - T r a n s p o r t K i n e t i c s . The past s e v e r a l y e a r s have seen con s i d e r a b l e p r o g r e s s i n examining the problem o f coupled mass t r a n s p o r t and aqueous-phase c h e m i c a l r e a c t i o n a p p l i e d to c l o u d d r o p l e t s . The q u e s t i o n t h a t must be addressed i s whether m a s s - t r a n s p o r t c o u p l i n g the b u l k ( l a r g e d i s t a n c e from drop) gas-phase c o n c e n t r a t i o n t o , a c r o s s , and w i t h i n the drop s u r f a c e i s s u f f i c i e n t l y r a p i d to m a i n t a i n the Henry's law c o n c e n t r a t i o n of the d i s s o l v e d reagent gas ( r e l a t i v e to the b u l k gas phase) i n the face of aqueous-phase r e a c t i o n t h a t serves as a s i n k f o r t h i s s p e c i e s . H y p o t h e t i c a l reagent c o n c e n t r a t i o n p r o f i l e s i n the v i c i n i t y of a drop a r e i l l u s t r a t e d i n F i g u r e 8. I f m a s s - t r a n s p o r t i n one o r more o f the r e g i o n s (gas-phase, i n t e r f a c e , aqueous-phase) i s n o t s u f f i c i e n t l y r a p i d to m a i n t a i n a n e a r l y u n i f o r m c o n c e n t r a t i o n p r o f i l e , then the d i m i n i s h e d aqueous-phase reagent c o n c e n t r a t i o n w i l l r e s u l t i n a d i m i n i s h e d r e a c t i o n r a t e compared to t h a t f o r assumed Henry's law e q u i l i b r i u m a t the b u l k gas-phase c o n c e n t r a t i o n . T h i s s i t u a t i o n would r e q u i r e t h a t models e v a l u a t i n g gas-aqueous r e a c t i o n s i n c l o u d s t r e a t d i f f e r e n t drop s i z e s s e p a r a t e l y , r e f l e c t i n g d i f f e r i n g r e a c t i o n r a t e s and r e s u l t a n t d i f f e r i n g c o n c e n t r a t i o n s . Techniques


SCHWARTZ


-

-

ι χ

ι E r i c k s o n et a l . ,

ο

P e n k e t t et αϊ., 1 9 7 9

ι 1977

• δ

Maahs,l983 Martin,l984

ν

H o i g n è " et a l . , 1985

ι

• •

1

1

•

—

X

—

9f

-


w

1

\

1

1

F i g u r e 5. Second-order r a t e c o n s t a n t k ( 2 ) f o r o x i d a t i o n of s u l f u r ( l V ) by ozone d e f i n e d a c c o r d i n g to d [ S ( V l ) ] / d t = k ( ) [ 0 ( a q ) ] [ S ( l V ) ] , as a f u n c t i o n of s o l u t i o n pH a t 2 5 ° C Curve r e p r e s e n t s a three-component ( S O 2 , H S O 3 " , S O 3 - ) r a t e e x p r e s s i o n due to Hoigné ( 3 0 ) . F o r r e f e r e n c e s see (30,31). 2

3

1000

100

0.01

0.001

F i g u r e 6. Rate of aqueous-phase o x i d a t i o n of S ( I V ) by O 3 (30 ppb) and H 2 O 2 (1 ppb), as a f u n c t i o n of s o l u t i o n pH. Gasaqueous e q u i l i b r i a a r e assumed f o r a l l r e a g e n t s . R/ps0o r e p r e s e n t s aqueous r e a c t i o n r a t e per ppb o f gas-phase S O 2 . P/L r e p r e s e n t s r a t e of r e a c t i o n r e f e r r e d to gas-phase S O 2 p a r t i a l p r e s s u r e per cm3-m~3 l i q u i d water volume f r a c t i o n . Temperature 2 5 ° C M o d i f i e d from R e f . ( 1 0 ) .


THE CHEMISTRY OF ACID RAIN HYDROGEN P E R O X I D E - S U L F U R ( IV)

KINETICS

IN AUTHENTIC PRECIPITATION S A M P L E S Brookhaven National Laboratory, 1983-1985 Lee et al., 1986

I0

4


10*

PH 2

F i g u r e 7. Second-order r a t e c o n s t a n t k ( ) o f H2Û2-S(IV) r e a c t i o n determined i n f r e s h l y c o l l e c t e d r a i n w a t e r samples. The s o l i d l i n e i s a r e g r e s s i o n l i n e c o n s t r a i n e d to s l o p e o f -1. Dashed l i n e s , t r a n s f e r r e d from F i g u r e 4, r e p r e s e n t envelope o f r e s u l t s from s t u d i e s i n p u r i f i e d water i n v a r i o u s l a b o r a t o r i e s . Data from Ref. ( 1 6 ) . AQUEOUS PHASE

GAS PHASE

j

I

Ί y

A*

-iCpSSio) A(a) Â S S

Nay 0

λ

j 1

1

1

1

3

2

//

' co

F i g u r e 8. H y p o t h e t i c a l c o n c e n t r a t i o n p r o f i l e s i n gas and aqueous phases i n d i c a t i n g g r a d i e n t i n reagent c o n c e n t r a t i o n due to f l u x o f m a t e r i a l i n t o and w i t h i n drop. C o n c e n t r a t i o n s c a l e s of aqueous-phase ( r < a) l e f t o r d i n a t e and gas-phase ( r > a) r i g h t o r d i n a t e a r e chosen so t h a t the same c o o r d i n a t e on each s c a l e r e p r e s e n t s the c o n d i t i o n o f phase e q u i l i b r i u m . D e p a r t u r e from the u n i f o r m p r o f i l e a t the "bulk' ( r =oo) v a l u e r e p r e s e n t s the i n a b i l i t y o f mass t r a n s p o r t to m a i n t a i n the reagent concen t r a t i o n as the reagent i s consumed by aqueous-phase r e a c t i o n . (Reproduced w i t h p e r m i s s i o n from Ref. 28. C o p y r i g h t 1986 Lewis P u b l i s h e r s , I n c . ) 1



8.

SCHWARTZ


101

f o r such treatment are o u t l i n e d i n Ref. (Γ7). Alternatively, i f m a s s - t r a n s p o r t l i m i t a t i o n i s a b s e n t , model e v a l u a t i o n s would be greatly simplified. From the above o u t l i n e , the m a s s - t r a n s p o r t problem i s seen to c o n s i s t of c o u p l e d boundary v a l u e problems ( i n gas and aqueous phase) w i t h an i n t e r f a c i a l boundary c o n d i t i o n . C l o u d d r o p l e t s are s u f f i c i e n t l y s p a r s e ( t y p i c a l s e p a r a t i o n i s of o r d e r 100 drop r a d i i ) t h a t drops may be t r e a t e d as independent. For c l o u d d r o p l e t s ( d i a m e t e r ~5 ym t o ~40 \im) both gas- and aqueous-phase masst r a n s p o r t are dominated by m o l e c u l a r d i f f u s i o n . The f l u x a c r o s s the i n t e r f a c e i s g i v e n by the m o l e c u l a r c o l l i s i o n r a t e times an accommodation c o e f f i c i e n t (a < 1) t h a t r e p r e s e n t s the f r a c t i o n of c o l l i s i o n s l e a d i n g to t r a n s f e r of m a t e r i a l a c r o s s the i n t e r f a c e . Magnitudes of mass-accommodation c o e f f i c i e n t s a r e n o t w e l l known g e n e r a l l y and t h i s h o l d s e s p e c i a l l y i n the case of s o l u t e gases upon aqueous s o l u t i o n s . For t h i s reason α i s t r e a t e d as an a d j u s t a b l e parameter, and we examine the v a l u e s of α f o r which i n t e r f a c i a l mass-transport l i m i t a t i o n i s s i g n i f i c a n t . Values of α i n the range 10~6 to 1 have been assumed i n r e c e n t s t u d i e s ( e . g . , 18). As noted below, r e c e n t e x p e r i m e n t a l s t u d i e s have y i e l d e d measurements of t h i s i m p o r t a n t q u a n t i t y f o r systems of i n t e r e s t i n cloud chemistry. S o l u t i o n of the coupled m a s s - t r a n s p o r t and r e a c t i o n problem f o r a r b i t r a r y c h e m i c a l k i n e t i c r a t e laws i s p o s s i b l e o n l y by numer i c a l methods. The problem i s g r e a t l y s i m p l i f i e d by d e c o u p l i n g the time dependence of m a s s - t r a n s p o r t from t h a t of c h e m i c a l k i n e t i c s ; the m a s s - t r a n s p o r t s o l u t i o n s r a p i d l y r e l a x to a pseudo steady s t a t e i n view of the s m a l l dimensions of the system ( 1 9 ) . The gas-phase d i f f u s i o n problem may be s o l v e d p a r a m e t r i c a l l y i n terms of the net f l u x i n t o the drop. I n the case of f i r s t - o r d e r or p s e u d o - f i r s t o r d e r c h e m i c a l k i n e t i c s an a n a l y t i c a l s o l u t i o n to the problem of coupled aqueous-phase d i f f u s i o n and r e a c t i o n i s a v a i l a b l e ( 1 9 ) . These s o l u t i o n s , t o g e t h e r w i t h the i n t e r f a c i a l boundary c o n d i t i o n , s p e c i f y the c o n c e n t r a t i o n p r o f i l e of the reagent gas. I n t u r n the e x t e n t of d e p a r t u r e of the r e a c t i o n r a t e from t h a t c o r r e s p o n d i n g to s a t u r a t i o n may be determined. F i n a l l y c r i t e r i a have been developed (17,19) by which i t may be a s c e r t a i n e d whether or not there i s a p p r e c i a b l e ( e . g . , 10%) l i m i t a t i o n to the r a t e of r e a c t i o n as a consequence of the f i n i t e r a t e of mass t r a n s p o r t . These c r i t e r i a are l i s t e d i n T a b l e 1. E x a m i n a t i o n of Mass-Transport L i m i t a t i o n . The a v a i l a b i l i t y of c r i t e r i a f o r m a s s - t r a n s p o r t l i m i t a t i o n a l l o w s e x a m i n a t i o n of the importance of such l i m i t a t i o n In r e p r e s e n t a t i v e s i t u a t i o n s . This i s c o n v e n i e n t l y a c h i e v e d by means of graphs, as shown i n F i g u r e s 9 and 10 f o r the S ( l V ) - 0 3 S(IV)-H202 r e a c t i o n s , r e s p e c t i v e l y . Here the i n e q u a l i t i e s i n T a b l e 1 are r e p r e s e n t e d as l i n e s i n a plane whose c o o r d i n a t e s are l o g k d ) and l o g H ( o r l o g H*). Each of the s e v e r a l c r i t e r i a thus appears as a s t r a i g h t l i n e i n t h i s p l a n e . The sense of the f i g u r e i s t h a t m a s s - t r a n s p o r t l i m i t a t i o n i s absent ( i . e . , 1 0 " " 3 , l i t t l e o r no m a s s - t r a n s p o r t l i m i t a t i o n i s i n d i c a t e d f o r most c o n d i t i o n s . Accommodation C o e f f i c i e n t Measurements. R e c e n t l y Lee and Tang ( 2 0 ) have p r e s e n t e d measurements o f the accommodation c o e f f i c i e n t s o f 0 ^ and S O 2 on aqueous s o l u t i o n . I n the case of O 3 a v a l u e of 5 χ 1 0 " ^ i s r e p o r t e d . I t i s seen by e x a m i n a t i o n o f F i g u r e 9 t h a t an accom modation c o e f f i c i e n t of t h i s magnitude i s w e l l above the v a l u e t h a t would l e a d t o i n t e r f a c i a l m a s s - t r a n s p o r t l i m i t a t i o n under c i r c u m s t a n c e s of i n t e r e s t , i n t e r s e c t i n g the O 3 l i n e o n l y a t pH > 6 , w e l l


8.


SCHWARTZ

105


beyond the onset of aqueous-phase m a s s - t r a n s p o r t l i m i t a t i o n . For S O 2 o n l y a lower l i m i t to the accommodation c o e f f i c i e n t has been d e t e r m i n e d , v i z . , α ^ 2 χ 10"3. However even t h i s v a l u e i s s u f f i c i e n t l y g r e a t to r u l e out m a s s - t r a n s p o r t l i m i t a t i o n under most c i r c u m s t a n c e s of i n t e r e s t . Thus, the S(IV) curve i n F i g u r e 9 ( O 3 r e a c t i o n ) c r o s s e s the α = 2 χ 10"3 i n t e r f a c i a l bound o n l y a t pH 5.7, and i n F i g u r e 10 ( H 2 O 2 r e a c t i o n ) l i e s e n t i r e l y below t h i s bound. E v i d e n t l y no i n f o r m a t i o n i s a v a i l a b l e p e r t i n e n t to the massaccommodation c o e f f i c i e n t of H 2 O 2 on aqueous s o l u t i o n t h a t would p e r m i t assessment of the r o l e of i n t e r f a c i a l m a s s - t r a n s p o r t l i m i t a t i o n of t h i s important r e a c t i o n . N i t r o g e n Oxide R e a c t i o n s . E x a m i n a t i o n of p o s s i b l e aqueous-phase r e a c t i o n s of n i t r o g e n d i o x i d e and p e r o x y a c e t y l n i t r a t e has r e v e a l e d no r e a c t i o n s of importance to c l o u d c h e m i s t r y (21,22). This s i t u a t i o n i s a consequence of the low s o l u b i l i t i e s and/or low r e a c t i v i t i e s of these gases w i t h substances expected to be p r e s e n t i n c l o u d w a t e r , a l t h o u g h s t u d i e s w i t h a c t u a l p r e c i p i t a t i o n samples would be v a l u a b l e i n c o n f i r m i n g t h i s s u p p o s i t i o n . NO2 has been shown (23) to r e a c t w i t h d i s s o l v e d S ( I V ) , but the d e t a i l s of the mechanism and r a t e of t h i s r e a c t i o n remain to be e l u c i d a t e d . An i n - c l o u d r e a c t i o n of importance a t n i g h t and p o s s i b l e a l s o d u r i n g the day i s the uptake of n i t r i c a c i d by gas-phase r e a c t i o n s NO2

+

NO3

O3 +

—> NO2

NO3 —>

+

O2

N2O5

f o l l o w e d by uptake of N 2 O 5 and/or N O 3 by c l o u d w a t e r and aqueousphase r e a c t i o n (24, 25). Q u a n t i t a t i v e e v a l u a t i o n of the r a t e of t h i s p r o c e s s a w a i t s d e t e r m i n a t i o n of the s o l u b i l i t y and r e a c t i v i t y o f N O 3 and N 2 O 5 as w e l l as d e t e r m i n a t i o n of mass-accommodation coefficients. F i e l d Measurements F i e l d measurements, i n a d d i t i o n to p r o v i d i n g c o n c e n t r a t i o n s and o t h e r s i t u a t i o n a l data n e c e s s a r y f o r k i n e t i c e v a l u a t i o n s , a l s o a l l o w i n f e r e n c e s to be drawn about the o c c u r r e n c e of chemical r e a c tions i n clouds. Such i n f e r e n c e s i n c l u d e the f o l l o w i n g : 1. G r e a t e r a c i d i t y of cloudwater (measured by the r a t i o [ H ] / ( [ N 0 - ] + 2 [ S 0 4 ] ) or [H+]/[NH +]) than i n c o r r e s p o n d i n g c l e a r - a i r (26) i s i n d i c a t i v e of the o c c u r r e n c e of a c i d forma t i o n by i n - c l o u d r e a c t i o n . 2. G r e a t e r f r a c t i o n a l c o n v e r s i o n of S O 2 to c l o u d w a t e r s u l f a t e than o f N O 2 to c l o u d w a t e r n i t r a t e (27) i s i n d i c a t i v e of more e x t e n s i v e i n - c l o u d o x i d a t i o n of S O 2 than of N O 2 . 3. An apparent mutual e x c l u s i v i t y of gas-phase S O 2 and aqueous H 2 O 2 observed i n n o n - p r e c i p i t a t i n g l i q u i d - w a t e r s t r a t i f o r m c l o u d s , i . e . , one or the o t h e r s p e c i e s p r e s e n t but never b o t h a t a p p r e c i a b l e c o n c e n t r a t i o n s ( 2 7 ) , i s c o n s i s t e n t w i t h the H202~S(IV) r e a c t i o n proceeding to c o m p l e t i o n i n such c l o u d s . These i n f e r e n c e s from f i e l d measurements p r o v i d e support f o r the a p p l i c a b i l i t y of e v a l u a t i o n s of c l o u d c h e m i s t r y based upon l a b o r a tory studies. +

=

3

4


106


Conclusions Techniques a r e a t hand to e v a l u a t e the r a t e s of aqueous-phase a c i d formation reactions i n clouds. Such e v a l u a t i o n s i n d i c a t e t h a t o x i d a t i o n of S O 2 by H 2 O 2 and O 3 can be i m p o r t a n t i n - c l o u d r e a c t i o n s f o r assumed r e p r e s e n t a t i v e reagent c o n c e n t r a t i o n s and o t h e r c o n d i t i o n s . R a p i d aqueous-phase r e a c t i o n s do n o t appear to be i n d i c a t e d f o r o x i d a t i o n o f n i t r o g e n o x i d e s to n i t r i c a c i d .


Acknowledgments T h i s work was supported by the N a t i o n a l A c i d P r e c i p i t a t i o n Assess ment program through the PRECP p r o j e c t funded by the U.S. Depart ment o f Energy and was performed under the a u s p i c e s of the U n i t e d S t a t e s Department of Energy under C o n t r a c t No. DE-AC02-76CH00016.

Literature Cited 1. Calvert, J . G.; Stockwell, W. R. Acid generation in the tro posphere by gas-phase chemistry. Environ. Sci. Technol. 1983, 17, 428A-442A. 2. Calvert, J. G.; Stockwell, W. R. Mechanism and rates of the gas-phase oxidations of sulfur dioxide and nitrogen oxides in the atmosphere. In SO2, NO and NO2 Oxidation Mechanisms: Atmo spheric Considerations; Calvert, J . G., Ed.; Butterworth: Boston, 1984; pp. 1-62. 3. Twomey, S. Atmospheric Aerosols; Elsevier: Amsterdam, 1977; pp. 143-164. 4. Levine, S. Z.; Schwartz, S. E. In-cloud and below-cloud scavenging of nitric acid vapor. Atmos. Environ. 1982, 16, 1725-1734. 5. For a discussion of cloud microphysical properties see e.g. Pruppacher, H. R. and Klett, J . D. Microphysics of Clouds and Precipitation; D. Reidel: Dordrecht, 1978. 6. Ho, W. W.; Hidy, G. M.; Govan, R. M. Microwave measurements of the liquid water content of atmospheric aerosols. In Advances in Environmental Science and Technology; Hidy, G. M. et al., Eds.; Wiley: New York, 1980; Vol. 9, pp. 215-236. 7. Schwartz, S. E.; White, W. H. Kinetics of reactive dissolu tion of nitrogen oxides into aqueous solution. In Advances in Environmental Science and Technology; Schwartz, S. Ε., Ed.; Wiley: New York, 1983: Vol. 12, pp. 1-116. 8. Penkett, S. Α.; Jones, B. M. R.; Brice, Κ. Α.; Eggleton, A. E. J. The importance of atmospheric ozone and hydrogen per oxide in oxidising sulphur dioxide in cloud and rainwater. Atmos. Environ. 1979, 13, 123-137. 9. Erickson, R. E.; Yates, L. M.; Clark, R. L.; McEwen, D. The reaction of sulfur dioxide with ozone in water and its possi ble atmospheric significance. Atmos. Environ. 1977 , 11, 813-817. 10. Schwartz, S. E. Gas-Aqueous Reactions of Sulfur and Nitrogen Oxides in Liquid-Water Clouds. In SO , NO and NO2 Oxidation Mechanisms: Atmospheric Considerations; Calvert, J . G., Ed.; Butterworth: Boston, 1984; pp. 173-208. 2


8.

SCHWARTZ

11.

12.

13.


14.

15. 16.

17.

18. 19.

20.

21. 22.

23.

24.


107

For a recent review see Calvert, J . G.; Lazrus, Α.; Kok, G. L.; Heikes, B. G.; Walega, J. G.; Lind, J . ; Cantrell, C. A. Chemical mechanisms of acid generation in the troposphere. Nature 1985, 317, 27-38. Kok, G. L.; Heikes B. G.; Lazrus, A. L. Gas and aqueous phase measurements of hydrogen peroxide. Symposium on Acid Rain; I. Sources and Atmospheric Processes, Division of Petroleum Chemistry, Inc.; American Chemical Society, preprints, 1986, Vol. 31, No. 2, pp. 541-544. Heikes, B. G.; Kok, G. L.; Lazrus, A. L.; Walega, J. G. Η2Ο2, O3 and SO2 measurements in the lower troposphere over the eastern U.S.A. during fall. J. Geophys. Res. 1987, in press. Tanner, R. L . ; Markovits, G. Y.; Ferreri, Ε. M.; Kelly, T. J. Sampling and determination of gas-phase hydrogen peroxide fol lowing removal of ozone by gas-phase reaction with nitric oxide. Anal. Chem. 1986, 58 1857-1865. Kelly, T. J.; Daum, P. H.; Schwartz, S. E. Measurements of peroxides in cloudwater and rain. J. Geophys. Res. 1985, 90, 7861-7871. Lee, Y.-N.; Shen, J.; Klotz, P. J . ; Schwartz, S. E.; Newman, L. Kinetics of the hydrogen peroxide-sulfur(IV) reaction in rainwater collected at a northeastern U.S. site. J. Geophys. Res. 1986, 91, 13264-13274. Schwartz, S. E. Mass-transport considerations pertinent to aqueous-phase reactions of gases in liquid-water clouds. In Chemistry of Multiphase Atmospheric Systems; Jaeschke, W., Ed.; Springer: Heidelberg, 1985; pp. 415-471. Chameides, W. L. The photochemistry of a remote marine stratiform cloud. J . Geophys. Res. 1984, 89, 4739-4755. Schwartz, S. E. and Freiberg, J. E. "Mass-transport limita tion to the rate of reaction of gases in liquid droplets: Application to oxidation of SO2 in aqueous solutions. Atmos. Environ. 1981, L5, 1129-1144. Tang, I. N.; Lee, J. H. Accommodation coefficients of ozone and sulfur dioxide: Their implications on SO2 oxidation in cloud water. American Chemical Society Symposium Series, 1987; this volume. Lee, Y.-N.; Schwartz, S. E. Evaluation of the rate of uptake of nitrogen dioxide by atmospheric and surface liquid water. J. Geophys. Res. 1981, 86, 11971-11983. Lee, Y.-N. Atmospheric aqueous-phase reactions of nitrogen species; Kinetics of some aqueous-phase reactions of peroxyacetyl nitrate. Conference on Gas-Liquid Chemistry of Natural Waters; Brookhaven National Laboratory, 1984; BNL 51757, Papers 20, 21. Lee, Y.-N.; Schwartz, S. E. Kinetics of oxidation of aqueous sulfur(lV) by nitrogen dioxide. In Precipitation Scavenging, Dry Deposition, and Resuspension; Pruppacher, H. R., Semonin, R. G., Slinn, W. G. Ν., Eds.; Elsevier: New York, 1983; pp. 453-470. Heikes, B. G.; Thompson, A. M. Effects of heterogeneous pro cesses on NO3, HONO, and HNO3 chemistry in the troposphere. J. Geophys. Res. 1983, 88, 10883-10895.



108


25.

Chameides, W. L. The possible role of NO3 in the nighttime chemistry of a cloud. J . Geophys. Res. 1985, 91, 5331-5337. 26. Daum, P. H.; Schwartz, S. E.; Newman, L. Acidic and related constituents in liquid water stratiform clouds. J. Geophys. Res. 1984, 89, 1447-1458. 27. Daum, P. H.; Kelly, T. J.; Schwartz, S. E.; Newman, L. Measurements of the chemical composition of stratiform clouds. Atmos. Environ. 1984, 18, 2671-2684. 28. Schwartz, S. E. Chemical conversions in clouds. Aerosols: Research, Risk Assessment and Control Strategies; Lee, S. D., Schneider, T., Grant, L. D., Verkerk, P. J., Eds.; Lewis: Chelsea, MI, 1986; pp. 349-375. 29. Overton, J. Η., Jr. Validation of the Hoffmann and Edwards' S(IV)-H202 Mechanism. Atmos. Environ. 1985, 19, 687-690. 30. Hoigné, J.; Bader, H.; Haag, W. R.; Staehelin, J . Rate con stants of reactions of ozone with organic and inorganic com pounds in water-III. Water Res. 1985, 19, pp. 993-1004. 31. Martin, L. R. Kinetic studies of sulfite oxidation in aqueous solution. In SO2, NO and NO2 Oxidation Mechanisms: Atmo spheric Considerations; Calvert, J. G., Ed.; Butterworth: Boston, 1984; pp. 63-100. RECEIVED May 15, 1987


Aqueous-Phase Reactions in Clouds

Recommend Documents