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1Chemical Equilibrium in SeawaterR. M. PYTKOWICZ, E. ATLAS, and C. H. CULBERSONSchool of Oceanography, Oregon State University, Corvallis, Ore. 97331
The concept of chemical equilibrium can be applied to theoceans in three ways; it enters the study of the geochemical control of the oceanic composition, for fast reactions equilibriumconstants are used to calculate the concentrations of speciespresent in seawater, and for slow reactions departures fromequilibrium are useful for kinetic studies.Seawater differs from the solutions that are usuallyexamined by chemists because of the large number of solutesand , at times, of suspended particles that are present in theoceans. Also, one must consider the concurrent effects ofpurely chemical, hydrographic, biological, and geologicalprocesses upon the composition of seawater. One must consider as well the gravitational field and pressure, temperature,and compositional gradients that result from the extent anddepth of the oceans.
The study of the equilibrium chemistry of the oceans isfacilitated because the major ions are present in almost constantproportions. This makes seawater an ionic mediumwhich canbe characterized by one compositional parameter, the chlorinityor the salinity. The constancy of the relative composition is notalways present in estuaries because river water, which mixeswith seawater, has its major ions in proportions which differfrom those in seawater. Still, it will be shown that equilibriumdata obtained for seawater can often be applied to estuarinewaters.
In this work we will first examine briefly the compositionof seawater. Then, we will outline some major aspects ofequilibria as applied to the oceans. Next, we will consider towhat extent these equilibrium considerations are relevant toestuaries and finally, we will examine some topics on the control of the oceanic composition. Wewill not attempt a compre-
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In Marine Chemistry in the Coastal Environment; Church, T.;ACS Symposium Series; American Chemical Society: Washington, DC, 1975.
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2 M A R I N E C H E M I S T R Y
h e n s i v e c o v e r a g e o f t h e s u b j e c t b u t w i l l e m p h a s i z e b a s i c c o n c e p t s a n d m e t h o d s .
T h e C o m p o s i t i o n o f S e a w a t e rA l l t h e n a t u r a l l y o c c u r r i n g e l e m e n t s a n d m a n y o f t h e i r
c o m p o u n d s f i n d t h e i r w a y i n t o t h e o c e a n s t h r o u g h r i v e r s , g r o u n dw a t e r s , a e r i a l t r a n s p o r t , a n d s u b m a r i n e v o l c a n i s m . A fewm a j o r c o n s t i t u e n t s , s h o w n i n T a b l e I , a c c o u n t f o r o v e r 90% b Yw e i g h t o f t h e s o l u t e s p r e s e n t i n s e a w a t e r ( 1 ) .
T a b l e I . M a j o r C o n s t i t u e n t s o f S e a w a t e r o f 34. 3%oS a l i n i t y (19%o C h l o r i n i t y )
C o n s t i t u e n t p p mo n s t i t u e n t p p m C o n s t i t u e n t p p m2+C l " 18,971 C a 403.9
N a + 10,555 K + 391s o 4 2 " 2,657 H C O ~ 142M g 1,268 B r " 65.9
B ( O H ) 25. 6S r 2 + 7 .7F " 1. 3
T h e s e m a j o r c o n s t i t u e n t s a r e p r e s e n t i n a l m o s t c o n s t a n tp r o p o r t i o n s i n t h e o c e a n s (1_,2) i n d i c a t i n g t h a t t h e m i x i n g t i m e o ft h e o c e a n s , w h i c h i s o f t h e o r d e r of 1,000 y e a r s , i s f a s t r e l a t i v et o t h e i n p u t r a t e s a n d t o t h e r e a c t i v i t y o f t h e c o n s t i t u e n t s (3.-5).T h e c o n s t a n t r e l a t i v e c o m p o s i t i o n a l s o l e d t o t h e d e f i n i t i o n s o fc h l o r i n i t y a n d s a l i n i t y w h i c h a r e p r e s e n t e d i n s t a n d a r d o c e a n o -g r a p h i c t e x t s , e. g. , R i l e y a n d C h e s t e r (6). It i s i m p o r t a n t t or e a l i z e t h a t t h e c h l o r i n i t y c a n be u s e d t o r e p r e s e n t t h e e x t e n t o fm i x i n g o f r i v e r w a t e r w i t h s e a w a t e r i n a n e s t u a r y . T h e d e f i n e ds a l i n i t y l o s e s i t s m e a n i n g , h o w e v e r , w h e n t h e o c e a n i c p r o p o r t i o n s o f t h e m a j o r i o n s a r e a l t e r e d i n e s t u a r i n e w a t e r s o r i n t h ep o r e w a t e r s o f s u b m a r i n e s e d i m e n t s .
T h e m i n o r e l e m e n t s v a r y g r e a t l y i n t i m e a n d s p a c e (1_) a n da r e i n g e n e r a l q u i t e i m p o r t a n t b e c a u s e o f t h e i r p a r t i c i p a t i o n i nc h e m i c a l , b i o l o g i c a l , a n d g e o l o g i c a l p r o c e s s e s . T h e s e e l e m e n t sa r e e x a m i n e d e l s e w h e r e i n t h i s v o l u m e .
T h e g e n e r a l g e o c h e m i c a l c o n t r o l o f t h e c h e m i c a l c o m p o s i t i o n o f t h e o c e a n s i n t e r m s o f e q u i l i b r i a , s t e a d y s t a t e s , a n df l u x e s b et w e e n n a t u r a l r e s e r v o i r s i s a v i t a l t o p i c . I t s s t u d y
y i e l d s i n s i g h t s i n t o t h e c h e m i c a l h i s t o r y o f s e a w a t e r a n d h e l p su s u n d e r s t a n d t h e p o t e n t i a l i m p a c t o f m a n - m a d e p e r t u r b a t i o n s
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In Marine Chemistry in the Coastal Environment; Church, T.;ACS Symposium Series; American Chemical Society: Washington, DC, 1975.
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1. P Y T K O W I C Z E T A L . C h e m i c a l E q u i l i b r i u m i n Seawater 3
u p o n t h e e n v i r o n m e n t ( 5 , 7 - 1 1 ) . T h i s s u b j e c t w i l l b e e x a m i n e db r i e f l y a t t h e e n d o f t h i s w o r k , a f t e r a c r i t i c a l r e v i e w o f t h em a i n r e a c t i o n s w h i c h i n f l u e n c e t h e l o c a l d i s t r i b u t i o n s o f c h e m i c a l s p e c i e s i n s e a w a t e r . T h e f i r s t t o p i c r e l a t e d t o l o c a l e q u i l i b r i a w i l l b e t h e d i s s o c i a t i o n o f w e a k a c i d s .
D i s s o c i a t i o n o f W e a k A c i d s
T h e d i s s o c i a t i o n c o n s t a n t s o f w e a k a c i d s a n d b a s e s c a n b eu s e d f o r t h e c a l c u l a t i o n o f t h e c o n c e n t r a t i o n s o f m o l e c u l e s a n di o n s o f o c e a n o g r a p h i c i n t e r e s t b e c a u s e t h e d i s s o c i a t i o n r e a c t i o n sa r e f a s t r e l a t i v e t o c o m p e t i n g b i o l o g i c a l a n d g e o l o g i c a l p r o c e s s e s a n d r e a c h e q u i l i b r i u m . C a r b o n i c a c i d i s a n e s p e c i a l l yi m p o r t a n t w e a k e l e c t r o l y t e b e c a u s e o f t h e r o l e s i t p l a y s i n l i f ea n d i n t h e f o r m a t i o n o f l i m e s t o n e s a n d d o l o m i t e s . A l s o , i ts e r v e s a s a m o d e l s y s t e m f o r t h e s t u d y o f o t h e r e l e c t r o l y t e sw h i c h a r e p r e s e n t i n t h e o c e a n s .
T h e u s e o f t h e r m o d y n a m i c d i s s o c i a t i o n c o n s t a n t s i s n o tr e c o m m e n d e d f o r c a r e f u l w o r k i n s e a w a t e r b e c a u s e i t r e q u i r e st h e e s t i m a t e o f t h e t o t a l a c t i v i t y c o e f f i c i e n t s o f s i n g l e i o n s ( 1 2 ) .T h e s e c o e f f i c i e n t s a r e c o n v e n t i o n a l q u a n t i t i e s a n d , t h e r e f o r e ,t h e i r a c c u r a c y i s u n k n o w n . S t i l l , t h e r m o d y n a m i c c o n s t a n t s m a yb e a n d a r e o f t e n u s e d f o r f a s t l o w a c c u r a c y e s t i m a t e s b y m a r i n eg e o c h e m i s t s w h e n c o n s t a n t s m e a s u r e d i n a c t u a l s e a w a t e r a r e n o ta v a i l a b l e .
B u c h e t a l . ( 1 3 ) i n t r o d u c e d t o o c e a n o g r a p h y t h e s o - c a l l e da p p a r e n t d i s s o c i a t i o n c o n s t a n t s m e a s u r e d d i r e c t l y i n s e a w a t e r .I n t h e i r p r e s e n t f o r m , f o r a g e n e r i c a c i d H A , t h e s e c o n s t a n t sa r e d e f i n e d b y ( 1 4 )
P a r e n t h e s e s r e p r e s e n t c o n c e n t r a t i o n s a n d T r e f e r s t o t o t a l ( f r e ep l u s i o n - p a i r e d ) q u a n t i t i e s , a p j i s t h e c o n v e n t i o n a l h y d r o g e n i o na c t i v i t y d e f i n e d , f o r e x a m p l e , o n t h e N B S s c a l e , k i s a c o n s t a n t ,w i t h i n t h e r e p r o d u c i b i l i t y o f p H d a t a , w h i c h i s c a n c e l l e d o u tb e t w e e n t h e d e t e r m i n a t i o n a n d t h e a p p l i c a t i o n o f K ' ( 1 4 ) . T h u s ,k d o e s n o t a f f e c t t h e a c c u r a c y w i t h w h i c h (A")^ a n d H A c a n b ed e t e r m i n e d . A p p a r e n t c o n s t a n t s h a v e b e e n s h o w n t o b e i n v a r i a n tf o r m a n y p r o c e s s e s o f o c e a n o g r a p h i c i n t e r e s t ( 1 4 ) .
A n o t h e r d e f i n i t i o n o f d i s s o c i a t i o n c o n s t a n t s , w h i c h d i f f e r sf r o m K ' o n l y i n t h a t ( H + ) T i s u s e d i n s t e a d o f k a ^ , w a s p r o p o s e d
K = k aR ( A ) T( H A ) ( 1 )D
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b y H a n s s o n (15) . ( H + ) T c a n b e d e t e r m i n e d e i t h e r w i t h t r i sb u f f e r s p r e p a r e d i n s e a w a t e r (16) or w i t h c o n v e n t i o n a l N B Sb u f f e r s (17). We w i l l r e t u r n t o a l t e r n a t e d e f i n i t i o n s o f t h e p Hl a t e r .
T h e a p p a r e n t d i s s o c i a t i o n c o n s t a n t s a n d t h e c o n s t a n t sd e f i n e d b y H a n s s o n fo r c a r b o n i c a c i d a n d fo r b o r i c a c i d w e r ed e t e r m i n e d i n s e a w a t e r a t a t m o s p h e r i c p r e s s u r e b y s e v e r a lw o r k e r s ( 1 3 , 1 5 , 1 8 - 2 0 ) . D i s t e c h e a n d D i s t e c h e (21) , C u l b e r s o ne t a l . ( 22 ), a n d C u l b e r s o n a n d P y t k o w i c z (23) e x t e n d e d t h e m e a s u r e m e n t s t o t h e h i g h p r e s s u r e s w h i c h a r e e n c o u n t e r e d i n t h ed e e p o c e a n s . C u l b e r s o n a n d P y t k o w i c z (23) p r o d u c e d c o r r e c t i o nt a b l e s f o r t h e i n c r e a s e i n p H t h a t o c c u r s w h e n d e e p s e a w a t e rs a m p l e s a r e b r o u g h t t o s h i p b o a r d .
T h e c a r b o n d i o x i d e s y s t e m i n s e a w a t e r c a n b e d e s c r i b e d b yf o u r e q u a t i o n s i n s i x u n k n o w n s o n c e t h e a p p a r e n t d i s s o c i a t i o nc o n s t a n t s a r e k n o w n a n d t h e b o r a t e c o n t r i b u t i o n i s s u b t r a c t e df r o m t h e a l k a l i n i t y (2 4). O n e c a n , t h e r e f o r e , c o m p l e t e l y s p e c i f yt h e s y s t e m b y m e a n s o f a n y t w o r e l e v a n t m e a s u r e m e n t s . T h i sh a s l e d t o a p r o l i f e r a t i o n o f m e t h o d s , e a c h w i t h i t s o w n a d v a n t a g e s a n d d r a w b a c k s . O n e c a n m e a s u r e t h e p H a n d t h e t i t r a t i o na l k a l i n i t y w h i c h c a n be o b t a i n e d a c c u r a t e l y b y a s i n g l e a c i d a d d i t i o n (17). A l t e r n a t i v e l y o n e c a n d e t e r m i n e t h e t i t r a t i o n a l k a l i n i t ya n d t h e t o t a l C 0 2 b y a G r a n t i t r a t i o n (25) , t h e p C 0 2 a n d t h e t o t a lC 0 2 g a s o m e t r i c a l l y , a n d s o o n . T h e c h o i c e o f a m e t h o d d e p e n d su p o n t h e q u a n t i t y o f p r i m a r y i n t e r e s t .
I n s i t u p H p r o b e s , s u c h a s t h o s e d e v e l o p e d b y M a n h e i m(26) a n d b y G r a s s h o f f ( 27 ), a r e o f s p e c i a l i n t e r e s t f o r t i m es e r i e s m e a s u r e m e n t s i n e s t u a r i e s . T h e y a r e a d a p t a b l e f o rp r o b i n g p o r e w a t e r s o f s e d i m e n t s . T h i s e l i m i n a t e s p o s s i b l es h i f t s i n m i n e r a l - s e a w a t e r e q u i l i b r i a t h a t m a y o c c u r w h e n s e d i m e n t s a r e b r o u g h t t o d i f f e r e n t t e m p e r a t u r e s a n d p r e s s u r e s i n t h el a b o r a t o r y .
T h e a p p a r e n t d i s s o c i a t i o n c o n s t a n t s o f p h o s p h o r i c a c i d i ns e a w a t e r , n e e d e d f o r t h e s t u d y o f t h e f o r m a t i o n o f a p a t i t e s a n dp h o s p h o r i t e s , w e r e d e t e r m i n e d b y K e s t e r a n d P y t k o w i c z (28) .K ' j f o r h y d r o g e n s u l f i d e w a s m e a s u r e d b y G o l d h a b e r (29). C u l b e r s o n e t a l . (1 7) d e t e r m i n e d t h e d i s s o c i a t i o n c o n s t a n t s o f h y d r o f l u o r i c a c i d a n d o f b i s u l f a t e i o n s . C u l b e r s o n a n d P y t k o w i c z (30)m e a s u r e d t h e i o n i z a t i o n o f w a t e r i n s e a w a t e r .
I t s h o u l d b e e m p h a s i z e d t h a t t o t a l a c t i v i t y c o e f f i c i e n t s a n d ,t h e r e f o r e , a p p a r e n t c o n s t a n t s , w h i c h a r e r e l a t e d t o t h e r m o d y n a m i c o n e s b y t h e s e c o e f f i c i e n t s , d e p e n d u p o n t h e m a j o r i o nc o m p o s i t i o n o f t h e m e d i u m . T h u s , o n e s h o u l d u s e t h e s e q u a n t i t i e s w i t h c a r e i n e s t u a r i e s a n d i n t h e p o r e w a t e r s o f s e d i m e n t s
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In Marine Chemistry in the Coastal Environment; Church, T.;ACS Symposium Series; American Chemical Society: Washington, DC, 1975.
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1. P Y T K O W I C Z E T A L . C h e m i ca l E q u i l i b r i u m i n Seawater 5
b e c a u s e t h e m a j o r i o n c o m p o s i t i o n o f t h e s e m e d i a m a y d i f f e rf r o m t h a t o f o c e a n i c w a t e r s .
p H o f S e a w a t e r
I t w a s m e n t i o n e d e a r l i e r t h a t t h e N B S b u f f e r s c a l e , w h e na p p l i e d t o s e a w a t e r , y i e l d s a q u a n t i t y k a ^ j a n d t h a t k i s c a n c e l l e do u t i n p r a c t i c e , w i t h i n t h e r e p r o d u c i b i l i t y o f p H d a t a . T h u s , i ti s t h e r e p r o d u c i b i l i t y r a t h e r t h a n t h e a c c u r a c y o f p H d a t a w h i c hi s r e l e v a n t t o o c e a n o g r a p h i c m e a s u r e m e n t s . W e f o u n d i n o u rl a b o r a t o r y t h a t c a r e f u l p H m e a s u r e m e n t s i n s e a w a t e r a r e r e p r o d u c i b l e t o w i t h i n 0 . 0 1 p H u n i t s b e t w e e n d i f f e r e n t e l e c t r o d e s a n dt h a t t h e r e p r o d u c i b i l i t y a p p e a r s t o b e l i m i t e d b y t h e l i q u i d j u n c t i o n p o t e n t i a l s .
H a n s s o n ( 1 6 ) p r o p o s e d a p m H - p s c a l e b a s e d u p o n b u f f e r sp r e p a r e d i n s e a w a t e r . B a t e s a n d M a c a s k i l l ( 3 1 ) a l s o u s e d s u c hb u f f e r s b u t d e t e r m i n e d p m H j r i n s t e a d o f p m H - p . ( H + ) ,p a n d ( H + ) pw h e r e t h e s u b s c r i p t s F a n d T r e f e r t o t h e f r e e a n d t o t h e t o t a lc o n c e n t r a t i o n s , a r e r e l a t e d b y ( 1 7 )
( H + ) T = ( H + ) F + ( H S 0 4 ~ ) + ( H F ) ( 2 )
T h e N B S , t h e p m H T , a n d t h e p m H - p s c a l e s c a n b e r e l a t e d b ym e a n s o f t h e d a t a p r e s e n t e d b y C u l b e r s o n e t a l . ( 1 7 ) .
I t i s p o s s i b l e t h a t t h e u s e o f b u f f e r s p r e p a r e d i n s e a w a t e r ,m a y r e d u c e t h e l i q u i d j u n c t i o n p o t e n t i a l a n d , t h e r e f o r e , i n c r e a s et h e r e p r o d u c i b i l i t y o f p H d a t a . O n t h e o t h e r h a n d , t h e p r e p a r a t i o n o f s e a w a t e r b u f f e r s a n d o f r e f e r e n c e e l e c t r o d e s b y i n d i v i d u a li n v e s t i g a t o r s m a y i n t r o d u c e s y s t e m a t i c e r r o r s .
W i t h r e g a r d t o t h e g e n e r a l c o n t r o l o f t h e o c e a n i c p H , S i l l e n( 7 ) s u g g e s t e d t h a t c l a y - s e a w a t e r i n t e r a c t i o n s e x e r t a p r i m a r yp H - s t a t t i n g r o l e . P y t k o w i c z ( 5 J c o n c l u d e d , h o w e v e r , t h a t t h ec a r b o n d i o x i d e s y s t e m i s t h e m a j o r p H b u f f e r i n g a g e n t i n t h ep r e s e n t o c e a n s .
S o l u b i l i t i e s o f M i n e r a l s
T h e m o s t i n t e n s e l y s t u d i e d s a l t i n s e a w a t e r h a s b e e n c a l c i u m c a r b o n a t e b e c a u s e o f i t s b i o l o g i c a l a n d g e o l o g i c a l i m p o r t a n c e .I n a d d i t i o n , w o r k o n c a r b o n a t e s h a s y i e l d e d c o n c e p t s a n d t e c h n i q u e s w h i c h a r e a p p l i c a b l e t o t h e i n t e r a c t i o n s o f o t h e r s a l t s a n do f s o l i d s i n g e n e r a l w i t h s e a w a t e r .
W a t t e n b e r g { 32 ) f i r s t d e t e r m i n e d t h e s o l u b i l i t y o f c a l c i t e i n
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6 M A R I N E C H E M I S T R Y
s e a w a t e r a t a t m o s p h e r i c p r e s s u r e . H e u s e d t h e s t o i c h i o m e t r i cs o l u b i l i t y p r o d u c t
w h e r e t h e s u b s c r i p t S r e f e r s t o t h e c o n c e n t r a t i o n a t s a t u r a t i o n .T h e u s e o f s t o i c h i o m e t r i c s o l u b i l i t y p r o d u c t s o b v i a t e s t h e n e e d t oe s t i m a t e t h e a c t i v i t y c o e f f i c i e n t s o f s i n g l e i o n s . T h e s e p r o d u c t sr e m a i n e s s e n t i a l l y c o n s t a n t a t a g i v e n s a l i n i t y f o r p r o c e s s e s ,s u c h a s t h e d i s s o l u t i o n a n d t h e p r e c i p i t a t i o n o f c a r b o n a t e s i n t h eo c e a n s , w h i c h h a v e o n l y a s l i g h t e f f e c t u p o n t h e m a j o r i o n c o m p o s i t i o n o f s e a w a t e r . T h e r e h a v e b e e n m a n y m e a s u r e m e n t s o ft h e s o l u b i l i t y o f c a r b o n a t e s i n s e a w a t e r a t a t m o s p h e r i c p r e s s u r es i n c e W a t t e n b e r g ( 3 2 ) , t h e m o s t r e c e n t o n e s b e i n g t h o s e o fM c l n t i r e (3 3) a n d o f I n g l e e t a l . (3 4) .
P y t k o w i c z a n d c o - w o r k e r s (35 -39 ) e x t e n d e d t h e r e s u l t s o nc a r b o n a t e s t o h i g h p r e s s u r e s b y m e a n s o f p o t e n t i o m e t r i c m e a s u r e m e n t s w h i l e B e r n e r (40) , M i l l e r o a n d B e r n e r ( 41 ), a n dD u e d a l l (42) u s e d t h e p a r t i a l m o l a l v o l u m e a p p r o a c h .
S e v e r a l i n t e r e s t i n g f e a t u r e s e m e r g e d f r o m t h e s t u d y o f t h es o l u b i l i t y o f c a l c i u m c a r b o n a t e i n s e a w a t e r , w h i c h m a y b e r e l e v a n t t o o t h e r s o l i d s . S o m e o f t h e s e f e a t u r e s a r e ; t h e m e t a s t a b l es u p e r s a t u r a t i o n o f n e a r - s u r f a c e w a t e r s , t h e h y s t e r e s i s a n d l a c ko f r e p r o d u c i b i l i t y o f s o l u b i l i t y d a t a f o r c a l c i t e , t h e f a c t o r s t h a tc o n t r o l t h e c r y s t a l f o r m t h a t p r e c i p i t a t e s f r o m s e a w a t e r a n d t h ed i a g e n e t i c a l t e r a t i o n o f s e d i m e n t s , t h e k i n e t i c b e h a v i o r o f c a r b o n a t e m a t e r i a l s a t d e p t h , t h e c y c l i n g o f c a r b o n a t e s i n n a t u r e ,t h e p H b u f f e r i n g o f s e a w a t e r , a n d t h e d i s t r i b u t i o n a n d f l u x e s o ft h e c a r b o n d i o x i d e s y s t e m i n n a t u r e .
T h e m e t a s t a b i l i t y o f t h e c a l c i u m c a r b o n a t e s u p e r s a t u r a t i o ni n n e a r - s u r f a c e w a t e r s r e s u l t s f r o m t h e i n h i b i t i o n o f n u c l e a t i o na n d g r o w t h b y m a g n e s i u m i o n s , o r g a n i c m a t t e r , a n d p h o s p h a t ei o n s ( 4 3 - 4 6 ) . T h e r e s u l t s o f P y t k o w i c z (43_,45) s h o w e d t h a t t h ei n o r g a n i c p r e c i p i t a t i o n o f c a r b o n a t e s i n t h e o c e a n s c a n o n l y o c c u ri n a f e w s p e c i a l e n v i r o n m e n t s a n d t h a t t h e r e m o v a l o f c a r b o n a t e sf r o m s e a w a t e r i s p r i m a r i l y b i o g e n i c .
W e y l (47) o b s e r v e d t h a t t h e s o l u b i l i t y o f c a l c i t e i n s e a w a t e ru n d e r g o e s h y s t e r e s i s - t y p e e f f e c t s w h i c h w e r e n o t o b s e r v e d t oa n y s i g n i f i c a n t e x t e n t f o r a r a g o n i t e . H e a t t r i b u t e d h i s r e s u l t s t ot h e a d s o r p t i o n o f m a g n e s i u m i n s u r f a c e c o a t i n g s . H y s t e r e s i s d u et o s u r f a c e c o a t i n g s m a y b e t h e c a u s e o f t h e p o o r r e p r o d u c i b i l i t yo b s e r v e d i n c a l c i t e s o l u b i l i t y d a t a . T h e p r e s e n c e o f h y d r a t e dp h a s e s , w h i c h m a y a f f e c t t h e s o l u b i l i t y b e h a v i o r o f c a l c i t e , h a s
K ' S P (3)
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1. P Y T K O W I C Z E T A L . C h e m i c a l E q u i l i b r iu m in Seawater 7
r e c e n t l y b e e n p r o p o s e d (48).T h e o r g a n i c a n d i n o r g a n i c f a c t o r s t h a t c o n t r o l t h e c r y s t a l
f o r m o f c a l c i u m c a r b o n a t e t h a t i s p r e c i p i t a t e d i n o r g a n i c a l l y f r o ms e a w a t e r w e r e s t u d i e d b y K i t a n o (4 9) a n d K i t a n o e t a l . ( 50 ).A l t h o u g h m o s t o f t h e c a r b o n a t e s e d i m e n t a t i o n i n s e a w a t e r i s b i o g e n i c ( 4 3 , 4 5 ) , t h e s e r e s e a r c h e s m a y l e a d t o i n s i g h t s i n t o p r o c e s s e s w i t h i n t h e b o d y f l u i d s o f o r g a n i s m s . T h e f o r m o f c a l c i u mc a r b o n a t e t h a t p r e c i p i t a t e s f r o m n o r m a l s e a w a t e r , t o w h i c h a s o l -u l b e c a r b o n a t e s a l t h a s b e e n , a d d e d t o s u p e r s a t u r a t e i t , i s a r a g o -
n i t e C a l c a r e o u s o r g a n i s m s p r o d u c e p r i m a r i l y a s e r i e s o f m a g n e s -i a n c a l c i t e s a l t h o u g h s o m e a r a g o n i t e i s a l s o f o r m e d . T h e m e c h a n i s m s w h i c h c o n t r o l t h e c r y s t a l f o r m s o f c a l c i u m c a r b o n a t e i nt h e s h e l l s o f c a l c a r e o u s o r g a n i s m s h a v e n o t y e t b e e n e l u c i d a t e d .
A r a g o n i t e i n s e d i m e n t s i s c o n v e r t e d g r a d u a l l y t o t h e m o r es t a b l e c a l c i t e (5 1) a n d m a g n e s i a n c a l c i t e s t e n d t o b e d i a g e n e t i c a l -l y a l t e r e d t o p u r e r c a l c i t e s a n d t o d o l o m i t e (52, 53). C h a v e e t a l .(54) f o u n d t h a t t h e s t a b i l i t y o f c a r b o n a t e s i n s e a w a t e r i n c r e a s e si n t h e o r d e r ; h i g h m a g n e s i a n c a l c i t e , a r a g o n i t e , l o w m a g n e s i a nc a l c i t e , p u r e c a l c i t e , d o l o m i t e , b u t B e r n e r (46) r e c e n t l y c o n c l u d e d t h a t c a l c i t e s w i t h 2 - 7 % m o l e - f r a c t i o n o f M g C O ^ a r et h e r m o d y n a m i c a l l y s t a b l e i n s e a w a t e r .
I n t e r m e d i a t e o c e a n i c w a t e r s a r e u n d e r s a t u r a t e d i n t h eN o r t h P a c i f i c O c e a n . T h i s i s t h e r e s u l t o f t h e h i g h c o n c e n t r a t i o no f c a r b o n d i o x i d e p r e s e n t t h e r e b e c a u s e t h e w a t e r s a r e o l d a n de x t e n s i v e o x i d a t i o n o f o r g a n i c m a t t e r h a s t a k e n p l a c e i n t h e m .A l l d e e p o c e a n i c w a t e r s a r e u n d e r s a t u r a t e d a s t h e r e s u l t o f t h ee f f e c t s o f h i g h p r e s s u r e s a n d l o w t e m p e r a t u r e s u p o n t h e s o l u b i l i t y o f c a l c i u m c a r b o n a t e (36-39 , 55) .
D e g r e e o f s a t u r a t i o n d a t a i n d i c a t e t h a t c a r b o n a t e s e d i m e n t sc a n p e r s i s t u n t i l b u r i a l w h i l e e x p o s e d t o u n d e r s a t u r a t e d w a t e r s(5 5 ,5 6 ) . T h i s c o n c l u s i o n i s c o n f i r m e d b y t h e f a c t t h a t t h e l y s o -c l i n e , t h e d e p t h a t w h i c h c a l c a r e o u s t e s t s f i r s t s h o w s i g n s o f d i s s o l u t i o n , i s w e l l a b o v e t h e c a r b o n a t e c o m p e n s a t i o n d e p t h , w h i c hm a r k s a s u d d e n d e c r e a s e i n t h e c a r b o n a t e c o n t e n t o f s e d i m e n t s(57 , 58). M o r s e a n d B e r n e r (59) c o n c l u d e d f r o m t h e i r k i n e t i cr e s u l t s t h a t t h e l a r g e i n c r e a s e i n d i s s o l u t i o n r a t e a t t h e c o m p e n s a t i o n d e p t h c o r r e s p o n d s t o a c h a n g e i n t h e m e c h a n i s m o fs o l u t i o n .
D i s s o l u t i o n o f c a r b o n a t e s a t d e p t h l e d t o s t u d i e s o f t h e c a r b o n d i o x i d e - c a r b o n a t e c y c l e s w i t h i n a n d t h r o u g h t h e o c e a n s a sw e l l a s t o s t u d i e s o f t h e f a c t o r s w h i c h c o n t r o l t h e c a r b o n d i o x i d ec o m p o n e n t s a n d t h e p H ( 5 , 8 , 9 , 6 0 ) .
O t h e r m i n e r a l s w i t h s o l u b i l i t i e s t h a t h a v e b e e n d e t e r m i n e di n s e a w a t e r a r e c a l c i u m p h o s p h a t e s (61) , s i l i c a (62, 63) , th e l e a s t
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8 M A R I N E C H E M I S T R Ys o l u b l e c o m p o u n d s o f a s e r i e s o f t r a c e m e t a l s ( 6 4 ) , a n d c l a y s( 6 5 ) .
I n s o l u b i l i t y w o r k a s w e l l a s i n t h e c a s e o f d i s s o c i a t i o nc o n s t a n t s i t i s i m p o r t a n t , b e f o r e a p p l y i n g e q u i l i b r i u m d a t a o b t a i n e d i n s e a w a t e r t o e s t u a r i e s a n d t o p o r e w a t e r s t o a s c e r t a i nt h a t t h e r e h a v e b e e n n o l a r g e c h a n g e s i n t h e m a j o r i o n p r o p o r t i o n s .
I o n A s s o c i a t i o n
T h i s i s a n i m p o r t a n t t o p i c b e c a u s e t h e f o r m a t i o n o f i o n -p a i r s , b y a f f e c t i n g t h e d i s t r i b u t i o n s o f s o l u t e s i z e s a n d c h a r g e s ,m o d i f i e s m o s t p h y s i c o - c h e m i c a l p r o p e r t i e s o f s e a w a t e r , i n c l u d i n g s o l u b i l i t y e q u i l i b r i a .
G a r r e l s a n d T h o m p s o n ( 6 6 ) p i o n e e r e d w o r k o n t h e f o r m a t i o n o f i o n - p a i r s i n s e a w a t e r . T h e y w e r e f o r c e d t o m a k e a l a r g en u m b e r o f a s s u m p t i o n s b e c a u s e n e e d e d d a t a w a s n o t a v a i l a b l e t ot h e m . E v e n s o , s o m e f e a t u r e s o f t h e i r r e s u l t s w e r e c o n f i r m e db y s u b s e q u e n t i n v e s t i g a t i o n s . K e s t e r a n d P y t k o w i c z ( 6 7 ) a n dP y t k o w i c z a n d H a w l e y ( 6 8 ) u s e d p o t e n t i o m e t r i c m e t h o d s t o d e t e r m i n e t h e c o n c e n t r a t i o n s o f f r e e i o n s a n d o f i o n - p a i r s i n s e a w a t e ra n d w e r e a b l e t o a v o i d m o s t o f t h e a s s u m p t i o n s m a d e b y G a r r e l sa n d T h o m p s o n ( 6 6 ) .T h e r e s t i l l a r e s o m e c o n t r a d i c t i o n s i n t h e r e s u l t s o f d i f f e r e n t i n v e s t i g a t o r s r e g a r d i n g t h e i n t e r a c t i o n s a m o n g t h e m a j o r i o n so f s e a w a t e r . I n a d d i t i o n , f u r t h e r w o r k i s n e e d e d t o c h a r a c t e r i z ep o s s i b l e t r i p l e i o n s a n d t h e e f f e c t s o f t e m p e r a t u r e , s a l i n i t y , a n dp r e s s u r e u p o n i o n - p a i r i n g ( 6 8 ) .
A c t i v i t y C o e f f i c i e n t s
W e w i l l d w e l l a t s o m e l e n g t h u p o n t h i s t o p i c b e c a u s e m u c ho f t h e m a t e r i a l p r e s e n t e d h e r e h a s n o t b e e n p u b l i s h e d b e f o r e .A c t i v i t y c o e f f i c i e n t s a r e v a l u a b l e b e c a u s e t h e y p r o v i d e i n s i g h t si n t o s o l v e n t - i o n a n d i o n - i o n i n t e r a c t i o n s . A l s o , t h e y a r e u s e f u lf o r s t o i c h i o m e t r i c c o m p u t a t i o n s m a d e w h e n a p p a r e n t d i s s o c i a t i o nc o n s t a n t s a n d s t o i c h i o m e t r i c s o l u b i l i t y p r o d u c t s a r e n o t a v a i l a b l e .
O n e m a y u s e f r e e o r t o t a l m e a n a c t i v i t y c o e f f i c i e n t s a n df r e e o r t o t a l s i n g l e i o n a c t i v i t y c o e f f i c i e n t s , d e p e n d i n g u p o n t h ep r o b l e m u n d e r c o n s i d e r a t i o n . F r e e c o e f f i c i e n t s a r e t h o s e d e t e r m i n e d i n s o l u t i o n s w h i c h t h e r e a r e n o s p e c i f i c i o n i c i n t e r a c t i o n s . I n s e a w a t e r t h e y a r e c o n s t r u c t s w h i c h c o r r e s p o n d t o t h ef r e e i o n s i f t h e i o n - p a i r i n g m o d e l i s u s e d (6 8 ) o r t o l o n g - r a n g ei o n i c i n t e r a c t i o n s , o f t h e D e b y e - H u c k e l t y p e ( 6 9 ) , i f t h e s p e c i f i ci n t e r a c t i o n m o d e l o f B r ^ n s t e d ( 7 0 ) a n d G u g g e n h e i m (7 1 ) i s
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021/bk-1975-0018.c
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10 M A R I N E C H E M I S T R Y
T a b l e I I . F r e e A c t i v i t y C o e f f i c i e n t s o f P o t a s s i u m , S o d i u m ,C a l c i u m , M a g n e s i u m a n d C h l o r i d e V e r s u s t h e I o n i cS t r e n g t h a t 2 5 C , O b t a i n e d b y t h e M e a n - S a l t M e t h o d
I o n i c S t r e n g t h + + 2+ 2+( m o l a l ) K N a C a M g C l "0. 00 1. 000 1. 000 1. 000 1. 000 1. 0000. 05 0. 816 0. 826 0. 47 3 0. 486 0. 8160. 10 0. 769 0. 787 0. 392 0. 40 8 0 . 7 6 90. 15 0 . 7 3 9 0 .7 65 0. 351 0. 368 0 . 7 3 90. 20 0 . 7 1 8 0 . 7 5 0 0. 325 0. 343 0 . 7 1 80. 25 0 .701 0 . 7 3 9 0. 307 0. 32 6 0. 7010. 30 0. 687 0 . 7 3 2 0. 294 0. 313 0. 6870. 35 0. 676 0. 726 0. 284 0. 305 0. 6760. 40 0. 666 0. 72 1 0. 277 0. 298 0. 6660. 45 0. 657 0 . 7 1 8 0. 271 0. 293 0. 6570. 50 0. 650 0 . 7 1 6 0. 266 0. 290 0. 6500. 55 0. 643 0. 71 4 0. 263 0. 288 0. 6430. 60 0. 637 0. 712 0. 260 0. 286 0. 6370. 65 0. 631 0 .7 1 2 0. 258 0. 285 0. 6310. 70 0. 626 0 .711 0. 256 0. 285 0. 6260. 75 0. 622 0.7 11 0. 255 0. 286 0. 6220. 80 0. 618 0 .711 0. 254 0. 286 0. 6180. 85 0. 614 0 .711 0. 253 0. 288 0. 6140 . 9 0 0. 610 0 . 7 1 2 0. 253 0. 289 0. 6100 . 9 5 0. 607 0. 712 0. 253 0. 291 0. 6071. 00 0. 603 0 . 7 1 3 0. 253 0. 293 0. 603
m e t h o d s h o u l d n o t b e u s e d f o r a n i o n s u n l e s s t h e y d o n o t a s s o c i a t e w i t h p o t a s s i u m i o n s .M e a s u r e d m e a n a c t i v i t y c o e f f i c i e n t s r e f l e c t t w o t y p e s o fh y d r a t i o n e f f e c t s ; t h e d i r e c t e f f e c t o f i o n - s o l v e n t i n t e r a c t i o n su p o n c h e m i c a l p o t e n t i a l s a n d th e c h a n g e s i n c o n c e n t r a t i o n a n di o n i c s t r e n g t h d u e t o t h e r e m o v a l o f w a t e r o f h y d r a t i o n f r o m t h eb u l k s o l u t i o n . T h e f i r s t e f f e c t i s t a k e n i n t o a c c o u n t a u t o m a t i c a l l y i n t h e m e a n - s a l t m e t h o d a s t h e m e t h o d i s b a s e d u p o n m e a s u r e d m e a n c o e f f i c i e n t s . W e m a d e a c o r r e c t i o n f o r t h e s e c o n de f f e c t b y m e a n s o f t h e e q u a t i o n
I A = 1(1 + 0. 01 8h I A / n ) (5)
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1. P Y T K O W I C Z E T A L . C h e m i ca l E q u i l i b r i u m i n Seawater 11
a n d n i s 1 f o r 1 -1 s a l t s a n d 3 f o r 1 - 2 s a l t s . T h e e f f e c t o f t h ec h a n g e i n t h e i o n i c s t r e n g t h u p o n a c t i v i t y c o e f f i c i e n t s w a s f o u n dt o b e n e g l i g i b l e .
T h e d a t a i n T a b l e I I c a n b e u s e d f o r e s t u a r i n e a n d f o r p o r ew a t e r s a s f r e e a c t i v i t y c o e f f i c i e n t s a t a g i v e n i o n i c s t r e n g t h a r ei n s e n s i t i v e t o t h e c o m p o s i t i o n o f t h e s o l u t i o n ( 6 7 , 6 8 , 7 3 , 7 8 ) .F u r t h e r m o r e , w e c a l c u l a t e d f r o m t h e H a r n e d r u l e c o e f f i c i e n t so f R o b i n s o n a n d B o w e r ( 7 9 ) t h a t t h e m e a n a c t i v i t y c o e f f i c i e n t s o fN a C l a n d C a C l 2 , i n g o i n g f r o m a p u r e N a C l t o a p u r e C a C ^ s o l u t i o n a t 0 . 7 5 i o n i c s t r e n g t h , o n l y c h a n g e b y 1 . 8 a n d b y 0 . 1 %r e s p e c t i v e l y .
B a t e s e t a l . (7 4 ) u s e d a h y d r a t i o n e q u a t i o n t o e s t i m a t e t h ef r e e a c t i v i t y c o e f f i c i e n t s o f s i n g l e i o n s . T h e y a s s u m e dt h a t t h e D e b y e - H u c k e l e q u a t i o n c a n b e u s e d t o d e s c r i b e t h ee f f e c t s o f n o n - s p e c i f i c e l e c t r o s t a t i c i n t e r a c t i o n s f o r i o n i cs t r e n g t h s u p t o I = 6 a n d t h a t c h l o r i d e i o n s a r e n o t h y d r a t e d .O u r r e s u l t s , s h o w n i n T a b l e I I , a n d t h o s e o f B a t e s e t a l . ( 7 4 )d i f f e r b y a b o u t 3 % f o r p o t a s s i u m a n d s o d i u m a n d b y u p t o 1 6 %f o r c a l c i u m a n d m a g n e s i u m a t I = 1 . 0 . I t i s n o t p o s s i b l e t od e c i d e w h i c h s e t o f r e s u l t s i s m o r e a c c u r a t e b e c a u s e , a s w a sm e n t i o n e d e a r l i e r , t h e a c t i v i t y c o e f f i c i e n t s o f s i n g l e i o n s a r ec o n v e n t i o n a l .
M a r i n e c h e m i s t s o f t e n n e e d a c t i v i t y c o e f f i c i e n t s e x p r e s s e da s a f u n c t i o n o f t h e s a l i n i t y . T h e c o e f f i c i e n t s i n T a b l e I I w e r ee x p r e s s e d i n t e r m s o f t h e s a l i n i t y , a s i s s h o w n i n T a b l e I I I , b ym e a n s o f t h e i o n i c s t r e n g t h - s a l i n i t y r e l a t i o n s h i p o f L y m a n a n dF l e m i n g ( 8 0 ) . W e f o u n d t h a t t h e u s e o f t h e e f f e c t i v e i o n i cs t r e n g t h ( 7 3 ) i n s t e a d o f t h e c o n v e n t i o n a l o n e h a s a n e g l i g i b l ee f f e c t u p o n t h e a c t i v i t y c o e f f i c i e n t s .
T h e t o t a l a c t i v i t y c o e f f i c i e n t s o f t h e s i n g l e i o n s o b t a i n e d i nt h i s w o r k f o r K + , N a + , C a 2 + a n d M g 2 + , a n d s h o w n i n T a b l e I V ,w e r e c a l c u l a t e d f r o m t h e f r e e o n e s , E q u a t i o n 4 i n t h e f o r m* T = ^ F ^ M ^ ) , a n c * ^ e s p e c i a t i o n m o d e l o f P y t k o w i c z a n d H a w -l e y ( 6 8 ) . T h e c o e f f i c i e n t o f s u l f a t e w a s o b t a i n e d b y t h e m e t h o do f K e s t e r a n d P y t k o w i c z ( 6 7 ) w h i l e t h o s e o f b i c a r b o n a t e a n d c a r b o n a t e i o n s w e r e c a l c u l a t e d f r o m t h e r a t i o s o f t h e a p p a r e n t d i s s o c i a t i o n c o n s t a n t s o f c a r b o n i c a c i d t o t h e t h e r m o d y n a m i c o n e s ,t h e a c t i v i t y c o e f f i c i e n t o f c a r b o n i c a c i d , a n d t h e a c t i v i t y o fw a t e r i n s e a w a t e r . T h e t o t a l m e a n a c t i v i t y c o e f f i c i e n t s w e r et h e n c a l c u l a t e d f r o m t h o s e f o r t h e s i n g l e i o n s a n d a r e s h o w n i nT a b l e V . T h e r e s u l t s o f B e r n e r (81_) a n d o f v a n B r e e m e n ( 8 2 )w e r e e s t i m a t e d b y p r o c e d u r e s a k i n t o t h o s e o f G a r r e l s a n dT h o m p s o n ( 6 6 ) .
W h i t f i e l d ( 7 2 ) a s s u m e d t h a t n o n - s p e c i f i c i o n i c i n t e r a c t i o n s
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12 M A R I N E C H E M I ST R Y
T a b l e I I I . F r e e A c t i v i t y C o e f f i c i e n t s o f S i n g l e I o n s a t 25 CV e r s u s t h e S a l i n i t y
S a l i n i t y (%) K + N a * ^ 2+C a M g 2 + C l "25 0. 648 0. 71 5 0. 265 0. 289 0. 6482 6 0 . 6 4 6 0. 714 0. 264 0. 288 0. 6462 7 0. 643 0. 71 4 0 . 263 0. 288 0. 6432 8 0. 641 0. 713 0. 261 0. 287 0. 6412 9 0 . 6 3 7 0. 712 0. 260 0. 286 0. 6373 0 0. 635 0. 712 0. 259 0. 286 0. 63531 0. 633 0 . 7 1 2 0. 258 0. 285 0. 63332 0. 630 0 .711 0. 257 0. 285 0. 6303 3 0. 628 0 .711 0. 257 0. 285 0. 62834 0. 626 0 .711 0. 256 0. 285 0. 62635 0. 625 0 .711 0. 255 0. 285 0. 6253 6 0. 623 0 .711 0. 255 0. 285 0. 6233 7 0. 620 0 .711 0. 254 0. 286 0. 6203 8 0. 618 0 .711 0. 254 0. 286 0. 6183 9 0. 617 0. 711 0. 25 4 0. 287 0. 6174 0 0. 615 0. 711 0. 254 0. 287 0. 615
T a b l e I V. T o t a l A c t i v i t y C o e f f i c i e n t s o f S i n g l e I o n s a t a b o u t3 5%o S a l i n i t y a n d 25 C
R e f e r e n c e K + N a + ^ 2+C a M g C I *>.*-T h i s w o r k 0. 618 0. 6 9 5 0. 225 0. 254 0. 625 0. 084(8j_) 0. 624 0 .7 0 3 0. 237 0. 252 0. 630 0. 068(82) 0. 620 0. 6 9 5 0. 228 0. 25 4 0. 630 0. 090(72) 0. 617 0. 6 5 0 0. 203 0. 217 0. 686 0. 122(83) 0. 630 0. 6 8 0 0. 214 0. 23 4 0. 658 0. 108
H C G 3 ~ C 0 3 2 "
T h i s w o r k 0. 501 0 .0 3 0c a n b e d e s c r i b e d b y t h e m o d i f i e d D e b y e - H u c k e l e q u a t i o n w i t hB a = 1. H e d i d n o t i n t r o d u c e a h y d r a t i o n c o r r e c t i o n e v e n t h o u g hb o t h h y d r a t i o n e f f e c t s m e n t i o n e d e a r l i e r s h o u l d b e t a k e n i n t oc o n s i d e r a t i o n . T h e s p e c i f i c s h o r t r a n g e i n t e r a c t i o n s w e r ea c c o u n t e d f o r b y a d d i t i v e i n t e r a c t i o n t e r m s b e t w e e n c a t i o n s a n da n i o n s . T h e g o o d a g r e e m e n t b e t w e e n h i s c a l c u l a t e d m e a n c o e f -
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TableV.TotalMeanActviyCoecetsaaot3%Salniyand2C
Refernc
Thiswork
(8
(8
(7
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Sa KC1
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NaCl
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CaCl
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MgCl
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Na2S04
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CaS04
01
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01
KHCO3
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NaHC03
05
Ca(HC03)
03
Mg(HCOs)
04
K2C03
02
Na2C03
02
CaC03
00
00
(*
MgCQ3
00
06
06
06
06
06
06
06
06
06
06
06
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04
04
04
04
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04
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02
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14 M A R I N E C H E M I S T R Y
f i c i e n t s a n d e x p e r i m e n t a l d a t a i n d i c a t e s t h a t h y d r a t i o n e n t e r si n a d v e r t e n t l y i n t o t h e i n t e r a c t i o n t e r m s . L e y e n d e k k e r s ( 8 3 )i n c l u d e d i n t e r a c t i o n s b e t w e e n i o n s o f t h e s a m e c h a r g e t y p e s .
T h e t o t a l a c t i v i t y c o e f f i c i e n t s c a l c u l a t e d b y t h e v a r i o u sm e t h o d s a r e i n r o u g h a g r e e m e n t . A c o m p a r i s o n o f T a b l e s I Va n d V s h o w s t h a t t h e l o w v a l u e o f ( f i N a z S O ^ T o b t a i n e d i n t h i sw o r k r e l a t i v e t o t h a t o f W h i t f i e l d ( 7 2 ) i s p r i m a r i l y d u e t o t h ec o n t r i b u t i o n o f s u l f a t e i o n s . O u r v a l u e o f ( f s o ^ x w a s t a i n e dw i t h o u t r e s o r t t o t h e m e a n - s a l t m e t h o d a n d i s e s s e n t i a l l y b a s e du p o n p o t e n t i o m e t r i c m e a s u r e m e n t s . T h i s i n d i c a t e s a n i n c o m p a t i b i l i t y b e t w e e n t h e e x p e r i m e n t a l r e s u l t o f K e s t e r a n d P y t k o w i c z ( 6 7 ) o b t a i n e d w i t h g l a s s a n d i o n - e x c h a n g e e l e c t r o d e s a n dt h a t o f P l a t f o r d ( 8 7 ) w h i c h w a s m e a s u r e d w i t h a m a l g a m e l e c t r o d e s . R o b i n s o n a n d W o o d ( 8 4 ) c a l c u l a t e d t h e t o t a l m e a n a c t i v i t y c o e f f i c i e n t s b y a n e x t e n s i o n o f t h e m e t h o d o f F r i e d m a n ( 8 5 ) .
O t h e r E q u i l i b r i a
T h e e q u i l i b r i a i n v o l v i n g t h e c o m p l e x a t i o n o f t r a c e m e t a l sh a v e r e c e n t l y b e e n r e v i e w e d b y S t u m m (8 8 ) a n d a r e f u r t h e re x a m i n e d e l s e w h e r e i n t h i s v o l u m e . K e s t e r ( 8 9 ) p r e s e n t e d ar e v i e w o f g a s - s e a w a t e r i n t e r a c t i o n s . M a n y o t h e r a s p e c t s o fm a r i n e c h e m i s t r y a n d g e o c h e m i s t r y h a v e b e e n d e s c r i b e d i nH o m e ( 9 0 ) , R i l e y a n d C h e s t e r ( 6 J , B e r n e r ( 8 1 ) , G a r r e l s a n dM a c k e n z i e ( 9 1 ) , B r o e c k e r ( 9 2 ) , G o l d b e r g ( 9 3 ) , a n d P y t k o w i c z( 5 ) . W e w i l l , t h e r e f o r e , l i m i t t h i s w o r k t o t h e t o p i c s a l r e a d yd e s c r i b e d a n d t o a l o o k a t t h e e q u i l i b r i u m c h e m i s t r y o f e s t u a r i n ew a t e r s f o l l o w e d b y a b r i e f e x a m i n a t i o n o f t h e c o n t r o l o f t h eo c e a n i c c o m p o s i t i o n .
E q u i l i b r i u m i n E s t u a r i e sL i t t l e a p p e a r s t o h a v e b e e n d o n e c o n c e r n i n g e q u i l i b r i a i n
e s t u a r i e s . W e w i l l e x a m i n e , t h e r e f o r e , h o w o n e m a y a s c e r t a i nw h e t h e r e q u i l i b r i u m c o n s t a n t s m e a s u r e d i n s e a w a t e r c a n b ea p p l i e d t o e s t u a r i e s . T h i s w i l l b e i l l u s t r a t e d b y c o n s i d e r i n g t h ed i s s o c i a t i o n r e a c t i o n s o f c a r b o n i c a c i d .
T h e c o m p o s i t i o n o f r i v e r s d e p e n d s u p o n t h e g e o l o g i c a ln a t u r e o f t h e i r d r a i n a g e b a s i n s ( 9 1 ) . F o r i l l u s t r a t i v e p u r p o s e sw e w i l l , t h e r e f o r e , d i s c u s s t h e e f f e c t s o f m i x i n g s e a w a t e r w i t ha h y p o t h e t i c a l r i v e r o f a w o r l d - a v e r a g e c o m p o s i t i o n w h i c h i ss h o w n i n T a b l e V I . T h e r e l a t i v e c o m p o s i t i o n o f r i v e r w a t e rd i f f e r s f r o m t h a t o f s e a w a t e r a n d t h e i r m i x i n g y i e l d s i n p r i n c i p l ee s t u a r i n e w a t e r s i n w h i c h t h e p r o p o r t i o n s o f t h e m a j o r i o n s
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1. P Y T K O W I C Z E T A L . C h e m i c a l E q u i l i b r iu m in Seawater 15
T a b l e VI . C o n c e n t r a t i o n P a r a m e t e r s f o r M i x t u r e s o f R i v e rW a t e r a n d S e a w a t e r . T h e C o n c e n t r a t i o n s a r e E x p r e s s e d
i n M o l a l i t y x 1 0 3 . i s t h e T o t a l I o n i c S t r e n g t h .
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2 8 . 68 2 2 . 80 1 7 . 01 1 1 . 30 5. 671 . 1166H C Q 3 - 2. 122 1. 88 3 1. 646 1 .414 1. 184 . 9 5 7 5
. 7 0 7 8 . 5626 .4196 . 2785 . 1393 . 002074
d i f f e r f r o m t h o s e i n t h e o c e a n s . T h u s , e s t u a r i n e w a t e r s c e a s et o b e i o n i c m e d i a o f c o n s t a n t c o m p o s i t i o n , t h e s i m p l i f y i n g f e a t u r e w h i c h r e n d e r s a p p a r e n t c o n s t a n t s u s e f u l . F o r t u n a t e l y ,h o w e v e r , r i v e r w a t e r i s s o d i l u t e t h a t e s t u a r i n e w a t e r s t e n d t or e t a i n t h e m a j o r i o n p r o p o r t i o n s o f s e a w a t e r d o w n t o f a i r l y l o wc h l o r i n i t i e s .
T h e e x t e n t o f m i x i n g i n a n e s t u a r y d e p e n d s u p o n a l a r g en u m b e r o f f a c t o r s s u c h a s t h e s e a s o n a l l y v a r i a b l e r i v e r f l o w ,t h e t i d a l c y c l e , t h e w i n d s t a t e , t h e t o p o g r a p h y , a n d t h e r e l a t i v et e m p e r a t u r e s o f t h e r i v e r w a t e r a n d th e s e a w a t e r . O n e m u s ta l s o c o n s i d e r i n a c t u a l e s t u a r i e s t h e i n f l o w o f g r o u n d a n d m e l tw a t e r s . T h e c o n v e n t i o n a l s a l i n i t y d e p e n d s u p o n t h e r e l a t i v ec o m p o s i t i o n o f s e a w a t e r a n d , t h e r e f o r e , t h e c h l o r i n i t y a n d t h et o t a l s a l t c o n t e n t a r e b e t t e r c o m p o s i t i o n a l v a r i a b l e s t h a n t h es a l i n i t y t o a s c e r t a i n t h e e x t e n t o f m i x i n g a t a n y g i v e n l o c a t i o n .
I n T a b l e VII w e p r e s e n t t h e r a t i o s o f t h e c o n c e n t r a t i o n s o ft h e m a j o r i o n s i n s e a w a t e r a n d i n e s t u a r i n e w a t e r a t t h e s a m ec h l o r i n i t i e s . I t c a n b e s e e n t h a t t h e c o n c e n t r a t i o n s r e m a i ns i m i l a r i n t h e t w o m e d i a d o w n t o l o w v a l u e s o f t h e c h l o r i n i t y .N e x t , l e t u s c o n s i d e r b y h o w m u c h e q u i l i b r i u m c o n s t a n t sd e t e r m i n e d i n s e a w a t e r m a y d i f f e r f r o m t h o s e i n e s t u a r i n ew a t e r s a t t h e s a m e c h l o r i n i t i e s . T h e e x a m p l e w i l l b e h y p o t h e t i c a l b e c a u s e w e a r e c o n s i d e r i n g a w o r l d - a v e r a g e r i v e r a n d
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16 M A R I N E C H E M I S T R Y
80 60 40 20
1 .0000 . 9 9 9 9 . 9 9 9 7 . 9 9 9 3.998 1 . 9 9 6 4 . 9 9 1 9 . 9 7 8 6. 9 9 9 3 . 9 7 8 1 . 9958 . 9889. 9 9 0 9 . 9 7 4 2 . 9 4 7 8 . 8721
. 9 9 9 0 . 9 9 7 5 . 9 9 4 3 . 9 8 5 2 999 . 9 9 8 2 . 996 1 . 98 97
T a b l e V I I . R a t i o s o f C o n c e n t r a t i o n s a n d o f t h e I o n i c S t r e n g t h i nS e a w a t e r t o T h o s e i n t h e E s t u a r i n e W a t e r a t t h e
S a m e C h l o r i n i t y% SW 100
N a + 1. 00K + 1.00M g + 2 1.00C a + 2 1. 00C l " 1. 00S O / 2 1 .004I T L O Ob e c a u s e a p p a r e n t d i s s o c i a t i o n c o n s t a n t s h a v e n o t y e t b e e nd e t e r m i n e d a t t h e l o w c h l o r i n i t i e s w h i c h m a y b e f o u n d n e a r t h eh e a d s o f e s t u a r i e s .
A p p a r e n t d i s s o c i a t i o n c o n s t a n t s a r e r e l a t e d t o t h e c o r r e s p o n d i n g t h e r m o d y n a m i c c o n s t a n t s b y t o t a l a c t i v i t y c o e f f i c i e n t s .T h e s e c o e f f i c i e n t s i n t u r n a r e r e l a t e d t o t h e f r e e o n e s b y f*p =f F ( F ) / ( T ) w h e r e f p r e f l e c t s t h e i o n i c s t r e n g t h e f f e c t a n d ( F ) /( T )r e p r e s e n t s t h e i o n - p a i r e f f e c t .
T h e i o n i c s t r e n g t h e f f e c t c a n b e c a l c u l a t e d f r o m t h e d a t ai n T a b l e II a n d f r o m t h e f r e e a c t i v i t y c o e f f i c i e n t s o f b i c a r b o n a t ea n d c a r b o n a t e i o n s (94) . T h e e f f e c t o f i o n - p a i r i n g c a n be c a l c u l a t e d f r o m t h e e q u a t i o n s o f P y t k o w i c z a n d H a w l e y (68) w h i c hr e l a t e a p p a r e n t d i s s o c i a t i o n c o n s t a n t s t o s t o i c h i o m e t r i c a s s o c i a t i o n c o n s t a n t s a n d f r e e c a t i o n c o n c e n t r a t i o n s . F o r K \ , fo re x a m p l e , t h e e q u a t i o n s y i e l d
# c+( K 1>EW 1 + S K M H C O , ( M >F (EW)
= 2 _ ( 6 )( K ' l > S W 1 + S K M H C 0 3 ( M W )
w h e r e K i s t h e s t o i c h i o m e t r i c a s s o c i a t i o n c o n s t a n t , M r e p r e -s e n t s c a t i o n s , E W r e f e r s t o e s t u a r i n e w a t e r s a n d S W r e f e r s t os e a w a t e r . T h e r e s u l t s o f t h e c o m b i n e d e f f e c t s a r e s h o w n i nT a b l e V I I I .
T h e a s s o c i a t i o n c o n s t a n t s a n d th e f r e e i o n c o n c e n t r a t i o n s
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1. P Y T K O W I C Z E T A L . C h e m i c a l E q u i l ib r i u m in Seawater 17
T a b l e V I I L R a t i o s o f K ' j a n d K ^ , t h e A p p a r e n t D i s s o c i a t i o nC o n s t a n t s o f C a r b o n i c A c i d , i n S e a w a t e r t o T h o s e
i n E s t u a r i n e W a t e r s a t t h e S a m e C h l o r i n i t i e s
% S e a w a t e r ( K ^ ^ / ( K ^ ^ < K ' 2 > S W / ( KV E W1 0 0 1 .000 1 .000
8 0 0 .9994 0 .99816 0 0 . 9 9 8 6 0 . 9 9 4 34 0 0 . 9 9 7 7 0 . 9 8 7 72 0 0 . 9 9 5 3 0 . 9 6 7 01 0 0 . 9 9 1 4 0 . 9 2 9 0
a r e w e l l k n o w n o n l y a t 19%o c h l o r i n i t y . S t i l l , o n e m a y e s t i m a t et h e m a x i m u m a n d t h e m i n i m u m e f f e c t s o f c o m p o s i t i o n a l d i f f e r e n c e s u p o n t h e a p p a r e n t d i s s o c i a t i o n c o n s t a n t s b y u s i n g v a l u e s o f
i n E q u a t i o n 6 a t 19%o c h l o r i n i t y a n d a t i n f i n i t e d i l u t i o n r e s p e c t i v e l y . T h e a s s o c i a t i o n c o n s t a n t s a t i n f i n i t e d i l u t i o n a r e c o n s i d e r a b l y l a r g e r t h a n t h o s e a t 19%o a n d e n h a n c e t h e e f f e c t o f c o m p o s i t i o n a l v a r i a t i o n s . O n l y t h e m a x i m u m e f f e c t s a r e s h o w n i nT a b l e V I I L
I t c a n b e s e e n f r o m t h e r e s u l t s i n T a b l e VIII t h a t K ^ a n d K ^d e t e r m i n e d f o r o c e a n i c w a t e r s c a n b e u s e d i n e s t u a r i e s s u p p l i e db y a h y p o t h e t i c a l w o r l d - a v e r a g e r i v e r d o w n t o e s t u a r i n e w a t e r sw h i c h c o n t a i n o n l y 2 0 % s e a w a t e r . T h i s c a n b e d o n e w i t h a ne r r o r o f l e s s t h a n 4%, w h i c h i s w i t h i n t h e l i m i t s o f u n c e r t a i n t yo f m e a s u r e d a p p a r e n t c o n s t a n t s (20) .
C o n t r o l o f t h e O c e a n i c C o m p o s i t i o n
A n u n d e r s t a n d i n g o f t h e c o n t r o l m e c h a n i s m s f o r t h e c h e m i c a l c o m p o s i t i o n o f t h e o c e a n s i s i m p o r t a n t b e c a u s e i t h e l p s u su n d e r s t a n d t h e g e o c h e m i c a l h i s t o r y o f t h e o c e a n s a n d t h e i m p a c to f p e r t u r b a t i o n s u p o n t h e c h e m i c a l n a t u r e o f s e a w a t e r . T h i ss u b j e c t w a s e x a m i n e d c r i t i c a l l y b y P y t k o w i c z (5J a n d w i l l o n l y b em e n t i o n e d b r i e f l y h e r e .
T h e c o n t r o l o f t h e c o m p o s i t i o n o f s e a w a t e r c a n b e a p p r o a c h e df r o m t w o p o i n t s o f v i e w ; t h a t o f v a r i a t i o n s i n t i m e a n d s p a c ew i t h i n t h e o c e a n s a n d th e b r o a d g e o c h e m i c a l v i e w i n w h i c h t h eo c e a n s a r e b u t on e o f s e v e r a l l i n k e d r e s e r v o i r s . T h e f i r s ta p p r o a c h c o n s i s t s b a s i c a l l y i n d e t e r m i n i n g t h e p a r a m e t e r s f o ra n d s o l v i n g t h e e q u a t i o n
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d N ^ d A . o NT T = ) ^
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1. P Y T K O W I C Z E T A L . C h e m i c a l E q u i l i b r i u m i n Seawater 19
A a n d B a r e t h e c o n t e n t s o f a g i v e n c o n s t i t u e n t i n t h e w e a t h e r i n ga n d i n t h e o c e a n i c r e s e r v o i r s , B e i s t h e v a l u e o f B a t e q u i l i b r i u m , a n d k ^ B a n d k e r e p r e s e n t t h e r a t e c o n s t a n t s f o r t h e r i v e ra n d t h e e x c h a n g e f l u x e s . I t c a n b e s e e n f r o m E q u a t i o n 8 t h a te q u i l i b r i u m i n p o r e w a t e r s w o u l d l e a d t o a n e v e n t u a l s t e a d y s t a t eB i n t h e o c e a n s d i f f e r e n t f r o m t h e e q u i l i b r i u m v a l u e B e u n l e s st h e r i v e r i n p u t w a s m u c h s m a l l e r t h a n t h e f l u x i n t o t h e s e d i m e n t s . I t c a n a l s o b e s e e n t h a t t h e t e r m B e w o u l d b e a b s e n t i ft h e p o r e w a t e r s w e r e n o t a t e q u i l i b r i u m w i t h t h e s e d i m e n t s . T h u se q u a t i o n s g o v e r n i n g t h e r e m o v a l o f p o l l u t a n t s c o u l d b e q u i t ed i f f e r e n t i n t h e p r e s e n c e o r i n t h e a b s e n c e o f e q u i l i b r i a .
I t i s i m p o r t a n t f o r t h e m o d e l l i n g o f f l u x e s i n t h e p r e s e n c e o fm a n - m a d e p e r t u r b a t i o n s t o d e t e r m i n e a n d u s e a c t u a l r a t e l a w sf o r t h e t r a n s f e r o f c h e m i c a l s b e t w e e n n a t u r a l r e s e r v o i r s . A s a ne x a m p l e , D o n a g h a y , S m a l l a n d P y t k o w i c z ( u n p u b l i s h e d r e s u l t s )m a d e p r e l i m i n a r y l a b o r a t o r y s t u d i e s o f t h e t r a n s f e r o f i n c r e a s i n g a m o u n t s o f c a r b o n d i o x i d e i n s e a w a t e r t o m a r i n e p h y t o p l a n k -t o n . T h i s i s a v i t a l t o p i c b e c a u s e t h e o c e a n i c b i o t a c a n t a k e u p ac o n s i d e r a b l e f r a c t i o n o f t h e c a r b o n d i o x i d e r e l e a s e d t o t h ea t m o s p h e r e a n d t h e o c e a n s b y t h e c o m b u s t i o n o f f o s s i l f u e l s a n d ,t h u s , a t t e n u a t e t h e g r e e n h o u s e e f f e c t .
T h e e x p e r i m e n t s w e r e p e r f o r m e d i n c h e m o s t a t s , w i t h a nI s o c h r y s i s g a l b a n a c u l t u r e , w h i l e b u b b l i n g a i r c o n t a i n i n g v a r i o u sa m o u n t s o f c a r b o n d i o x i d e t h r o u g h t h e s y s t e m . T h e b i o m a s sw e n t f r o m 7 m g / 1 f o r a s e a w a t e r w i t h a n o r m a l c a r b o n d i o x i d ec o n t e n t t o 1 6 m g / 1 a t f i v e t i m e s n o r m a l t o 1 3 m g / 1 a t t e n t i m e s
n o r m a l c a r b o n d i o x i d e . T h u s , a t e n f o l d i n c r e a s e i n c a r b o n d i o x i d e c a n d o u b l e t h e b i o m a s s . T h e d e c r e a s e f r o m 1 6 t o 1 3 m g / 1m a y p e r h a p s r e f l e c t t h e e f f e c t o f t h e d e c r e a s i n g p H u p o n b i o l o g i c a l a c t i v i t y , a h y p o t h e s i s t h a t i s u n d e r s t u d y . B y g e n e r a l i z i n gt h e e q u a t i o n s a n d t h e e x t r a p o l a t i o n s o f P y t k o w i c z ( 9 6 ) t o i n c l u d et h e m a r i n e p h y t o p l a n k t o n , o n e f i n d s t h a t t h e a t m o s p h e r i c c a r b o nd i o x i d e m a y i n c r e a s e i n a c e n t u r y b y a f a c t o r o f t e n i n s t e a d o ff o u r t e e n , t h e v a l u e o b t a i n e d i n t h e a b s e n c e o f t h e m a r i n e b i o t a .O f c o u r s e , t h i s i s o n l y a p r e l i m i n a r y r e s u l t s i n c e a s i n g l e p h y t o p l a n k t o n s p e c i e s w a s u s e d A l s o n u t r i e n t l i m i t a t i o n , t h e l a n d b i o t a ,a n d b i o t i c a d a p t a t i o n w e r e n o t c o n s i d e r e d , a n d t h e p r e d i c t i o n o ft h e f u t u r e c o n s u m p t i o n o f f o s s i l f u e l s ( 9 6 ) w a s p e s s i m i s t i c . I ti l l u s t r a t e s , h o w e v e r , t h e i m p o r t a n c e o f d e t e r m i n i n g r a t e l a w sf o r t h e c h e m i c a l f l u x e s i n n a t u r e .A c k n o w l e d g e m e n t
T h i s w o r k w a s s u p p o r t e d b y t h e O c e a n o g r a p h y S e c t i o n o f t h e
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N a t i o n a l S c i e n c e F o u n d a t i o n t h r o u g h G r a n t D E S T 2 -0 1 63 1 a n d b yt h e O f f i c e o f N a v a l R e s e a r c h C o n t r a c t N 0 0 0 1 4 - 6 7 - A - 0 3 6 9 - 0 0 0 7u n d e r N R 0 8 3 - 1 0 2 .
AbstractConcurrent chemical, biological and geologicalprocesses,
in addition to the presence of the gravitational potential and oftemperature andpressure gradients must be taken into consideration in the study of chemical equilibria in the oceans. A simplifying feature occurs because the approximate constant ratios ofthe concentrations of the major ions mean that seawater is anionic medium of constant relative composition. Estuarine watersdiffer from normal seawater because of time and spacial variations in composition due to the input of river water. The equilibrium chemistry of estuarine waters has not been studiedtoany significant extent but it will be shown that equilibrium data
for open ocean waters are often applicable to estuaries.Literature Cited1. Pytkowicz, R. M., Kester, D. R., "Oceanogr. Mar. Biol.
A n n . Rev., "H. Barnes, ed., Vol. 9, pp. 11-60, Allenand Unwin, London, 1971.2. Culkin, F., "Chemical Oceanography," J. P. Riley and G.Skirrow, eds., Vol. 1, pp. 121-161, Academic, NewYork, 1965.3. Barth, T. F. W . , "Theoretical Petrology," Wiley, New York,1952.4. Goldberg, E. D., "Chemical Oceanography," J. P. Riley andG . Skirrow, eds., Vol. 1, pp. 163-196, Academic, NewYork, 1965.5. Pytkowicz, R. M., Earth Sci. Rev., Vol. 11, p. 1, 1975.6. Riley, J. P., Chester, R., "Introduction to Marine Chemistry," Academic, New York, 1971.7. Sillen, L. G., "Oceanography," M. Sears, ed., Am. Assoc.A d v . Sci., Washington, D. C., 1961.
8. Pytkowicz, R. M., "The Changing Chemistry of the Oceans,"D. Dyrssen and D. Jagner, eds., pp. 147 -152, Almqvistand Wiksell, Stockholm, 1972.9. Pytkowicz, R. M., Schweizer. Zeitsch. Hydrol. (1973) 35, 8.10. Broecker, W . S., Quatern. Res. (1971) 1, 188.11. Siever, R., Earth Planet. Sci. Letters (1968) 5, 106.
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12. Pytkowicz, R. M., Duedall, I. W . , Connors, D. N., Science(1966) 152, 640.13. Buch, K., Harvey, H . W . , Wattenberg, H., Gripenberg,S., Rapp. Cons. Int. Explor. Mer (1932) 79, 1.14. Pytkowicz, R. M., Ingle, S. E., Mehrbach, C. , Limnol.Oceanogr. (1974) 19, 665.15. Hansson, I., Deep-Sea Res. (1973) 20, 46.16. Hansson, I., Deep-Sea Res. (1973) 20, 479.17. Culberson, C., Pytkowicz, R. M., Hawley, J. E., J. Mar.Res. (1970) 28, 15.18. Buch, K., Acta Acad. Aeboensis Mat. Phys. (1938) 11, 1.19. Lyman, J., Ph. D. Dissertation, University of California,Los Angeles, 1956.20. Mehrbach, C., Culberson, C. H., Hawley, J. E., Pytkowicz, R. M., Limnol. (1973) 18, 897.21. Disteche, A., Disteche, S., J. Electrochem. Soc. (1967)114, 330.22. Culberson, C., Kester, D.R., Pytkowicz, R. M., Science(1967) 157, 59.23. Culberson, C., Pytkowicz, R. M., Limnol. Oceanogr.(1968) 13, 403.
24. Park, P. K., Limnol. Oceanogr. (1969) 14, 179.25. Dyrssen, D., Sillen, L. G., Tellus (1967) 19, 113.26. Manheim, F., Stockholm Contrib. Geol. (1961) 8, 27.27. Grasshoff, K., Bull. Cons. Int. Explor. Mer (1964) 123, 1.28. Kester, D. R., Pytkowicz, R. M., Limnol. Oceanogr.(1967) 12, 246.29. Goldhaber, M . B., Ph.D. Dissertation, University of California, Los Angeles, 1974.30. Culberson, C. H., Pytkowicz, R. M., Mar. Chem. (1973)1, 309.31. Bates, R. G., Macaskill, J. B., "Analytical Methods ofOceanography, " R. F. Gould, ed., American ChemicalSociety, Washington, D. C., in press.32. Wattenberg, H., Wiss. Ergebn. Dt. Atlant. Exped. 'Meteor' (1933) 8, 1.33. Mclntire, W. G., Bull. Res. Bd. Canada No. 200,Ottawa, 1965.34. Ingle, S. E., Culberson, C. H., Hawley, J. E., Pytkowicz,R. M., Mar. Chem. (1973) 1, 295.35. Pytkowicz, R. M., Connors, D.N. , Science (1964) 144, 840.36. Pytkowicz, R. M., Limnol. Oceanogr. (1965) 10, 220.37. Pytkowicz, R. M., Disteche, A., Disteche, S., EarthPlanet. Sci. (1967) 2, 430.
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39. Hawley, J. E., Pytkowicz, R.M . , Geochim. Cosmochim.Acta (1969) 33, 1557.40. Berner, R. A. , Geochim. Cosmochim. Acta (1965) 29, 947.41. Millero, F. J., Berner, R. A. , Geochim. Cosmochim.Acta (1972) 36, 92.42. Duedall, I. W ., Geochim. Cosmochim. Acta (1972) 36, 729.43. Pytkowicz, R.M . , J. Geol. (1965) 73, 196.44. Chave, K. E., Suess, E., Limnol. Oceanogr. (1970) 15,633.45. Pytkowicz, R.M . , Am. J. Sci. (1973) 273, 515.46. Berner, R. A. , Geochim. Cosmochim. Acta, in press.47. Weyl, P. K., Stud. Trop. Oceanogr. Miami(1967) 5, 178.48. North, N. A . , Geochim. Cosmochim. Acta (1974) 38, 1075.49. Kitano, Y.,Bull. Chem. Soc. Japan (1962) 35, 1973.50. Kitano, Y., Kanamori, N., Tokuyama, A., Am. Zool.(1969) 9, 681.51. Bischoff, J. L., Fyfe, W. S., Am. J. Sci. (1968) 266, 65.52. Peterson, M. N. A . , Von Der Borch, C. C., Bien, G. S.,Am . J. Sci. (1966) 264, 257.53. Clayton, R.M . , Jones, B. F., Berner, R. A. , Geochim.Cosmochim. Acta (1968) 32, 415.54. Chave, K. E., Deffeyes, K.S., Weyl, P.K., Garrels, R.M . , Thompson, M. E., Science (1962) 137, 33.55. Edmond, J. M . , Deep-Sea Res. (1974) 21, 455.56. Pytkowicz, R.M . , Geochim. Cosmochim. Acta (1970) 34,836.57. Berger, W. H. , Mar. Geol. (1970) 8, 111.
58. Heath, G. R., Culberson, C. H. , Geol. Soc. Amer. Bull.(1970)81, 3157.59. Morse, J. W ., Berner, R. A. , Am. J. Sci. (1972) 272,840.60. Pytkowicz, R.M . , Geochim. Cosmochim. Acta (1967) 31,63.61. Roberson, C. E., M.S. Thesis, University ofCalifornia,San Diego, 1965.62. Krauskopf, K. B., Geochim. Cosmochim. Acta (1956) 10,1.63. Jones, M. M . , Pytkowicz, R.M . , Bull. Soc. RoyaleSci.Liege (1973) 42, 125.64. Krauskopf, K.B., Geochim. Cosmochim. Acta (1956) 9, 1.65. Siever, R., Woodford, N., Geochim. Cosmochim. Acta(1973) 37, 1851.
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