Equilibrium and Kinetic Problems in Mixed Electrolyte Solutions - ACS

33 Equilibrium and Kinetic Problems in Mixed Electrolyte Solutions

Downloaded by INDIANA UNIV BLOOMINGTON on May 29, 2014 | http://pubs.acs.org Publication Date: October 29, 1980 | doi: 10.1021/bk-1980-0133.ch033

RICARDO M . PYTKOWICZ and M . R. COLE Oregon State University, Corvallis, OR 97331

Mixed aqueous electrolyte solutions such as body fluids, rivers, lakes, oceans and, at times, laboratory and industrial fluids present important problems which are not found in single electrolyte solutions. New perceptions and results are being obtained in complex media and some examples will be covered in this paper. The behavior of carbonates will be used to illustrate hetero geneous processes, with emphasis upon the formation of inorganic surface coatings and solid solutions. This is a vital topic in the study of solid-solution interactions since it is coatings rather than bulk phases which are sensed by liquid solutions. Homogeneous reactions will be studied in terms of the competition of coulombic ion pairs with true complexes for anions. An extended form of the phase rule will be used. Phase Rule The phase rule is often used in the form f = c - p + 2 to ascertain the number of degrees of freedom of a system even when the concentration units in the aqueous phase are molal im) or molar. This is not correct because the phase rule is derived in terms of mole fractions (X). Thus, an additional quantity, the total number of moles, is required to convert X into m. This is illustrated by equations below which we shall find useful later on. For t h e s y s t e m CO2-H2O w i t h two p h a s e s , v a p o r and aqueous s o l u t i o n , i f we assume f o r s i m p l i c i t y t h a t pr^O and t h e a c t i v i t y c o e f f i c i e n t s f o r a l l t h e components a r e known, t h e e q u a t i o n s a r e

Ρ = pC0 + ξ ρ .

(1)

2

[C0 ] = k 2

K

h

I =

P

C0

(2)

2

rH C0 ]/[C0 ][H 0] 2

3

2

2

0-8412-0569-8/80/47-133-643$05.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

(3)

644

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

^'

= a [HC0 -]/[H C0 ]

(4)

K '

= a [C0

(5)

H

2

H

K ' +

TC0

3

_

]

3

2

2

2

(6)

2

= [HC0 "]+ 2 [ C 0

+ [H 0] Downloaded by INDIANA UNIV BLOOMINGTON on May 29, 2014 | http://pubs.acs.org Publication Date: October 29, 1980 | doi: 10.1021/bk-1980-0133.ch033

3

']/[HC0

2

+

+ TH 0 = [C0 ]

2

3

2

• [Η ][0Η"]/ΓΗ 0]

w

[H ]

3

3

"] +

2

[OH"]

(7)

+ [H C0 ] + LHC0 "] + 2

+ [H ] +

3

+

3

(8)

[OH"]

T h u s , t h e r e are e i g h t e q u a t i o n s i n n i n e unknowns. The phase r u l e t e l l s us t h a t f = 2 - 2 + 2 = 2 s o t h a t , i f Ρ and Τ a r e f i x e d t h e n t h e s y s t e m i s a t e q u i l i b r i u m and i s s p e c i f i e d . T h i s i s t r u e i n t e r m s o f mole f r a c t i o n s i n s o l u t i o n b u t , f o r m o l a l i t i e s , f = f + 1 = 3 and c = f 2. The t e r m c i s the number o f c o m p o s i t i o n a l v a r i a b l e ? w h i c h must be s p e c i f i e d . Its v a l u e i s 3 - 2 = 1 i n a c c o r d w i t h t h e a n a l y s i s o f t h e above s y s t e m o f e q u a t i o n s , t h a t i s , i n a c c o r d w i t h a system o f e i g h t e q u a t i o n s i n n i n e unknowns. In t h e a b s e n c e o f a v a p o r p h a s e , f = 3 and f = 4 with c = 2. m m m

Solid-Solution

Interactions

A t t h i s p o i n t I s h a l l f o c u s upon t h e e f f e c t o f t h e f o r m a t i o n o f Ca Mg-|. C03 s o l u t i o n s , e i t h e r i n b u l k phases o r i n s u r f a c e c o a t i n g s , upon t h e k i n e t i c and t h e e q u i l i b r i u m b e h a v i o r of carbonates. My t h o u g h t s have r e s u l t e d i n p a r t from t h e e x t e n s i v e l i t e r a t u r e i n t h i s f i e l d , w i t h s p e c i a l r e f e r e n c e to the p a p e r s by Plummer and M a c k e n z i e (1_) and by W o l l a s t and R e i n h a r d Derie (2). C o n s i d e r an aqueous s o l u t i o n c o n t a i n i n g Ca , Mg and CI i o n s t o w h i c h enough Na2CÛ3 i s added t o i n d u c e s u p e r s a t u r a t i o n o f CaC0 . I t has been w e l l e s t a b l i s h e d t h a t , f o r ( M g ) / ( C a ) < 4 , m a g n e s i a n c a l c i t e s o f f o r m u l a CaxMg-j_ C03 p r e c i p i t a t e w h i l e f o r r a t i o s above f o u r a r a g o n i t e s e t t l e s down (3_, £ ) · S e a w a t e r f a l l s i n the l a t t e r c a t e g o r y . The r e a s o n f o r t h e a r a g o n i t e p r e c i p i t a t i o n i s n o t i t s i n t r i n sic stability. The s o l u b i l i t i e s o f c a l c i u m c a r b o n a t e s i n c r e a s e f r o m p u r e c a l c i t e t o m a g n e s i a n c a l c i t e s c o n t a i n i n g up t o a b o u t 10 m o l e p e r c e n t MgC03, t o a r a g o n i t e , and t h e n on t o h i g h m a g n e s i a n calcites. T h u s , a r a g o n i t e i s l e s s s t a b l e than low-magnesian c a l c i t e s [5). I s u s p e c t t h a t a r a g o n i t e comes down b e c a u s e , a t h i g h v a l u e s o f [ M g ] , t h e c a l c i t e n u c l e i a r e q u i t e s o l u b l e due t o t h e i r h i g h magnesium c o n t e n t s and t h e f o r m a t i o n o f c r i t i c a l n u c l e i i s i m p r o b a b l e . T h i s type o f r a t e c o n t r o l o f the polymorph formed i s one a s p e c t o f t y p i c a l s o l i d - m i x e d e l e c t r o l y t e s o l u t i o n systems. L e t us f o c u s upon t h e l o w [Mg ] / [ C a ] c a s e as i t y i e l d s x

x

s

o

l

l

d

2 +

2 +

3

2 +

x

2 +

2

2 +



33.

PYTKOWICZ A N D COLE

645

Mixed Electrolyte Solutions

i n t e r e s t i n g s o l i d s and i s r e l e v a n t t o many f r e s h w a t e r s y s t e m s . A s t e a d y s t a t e i s e v e n t u a l l y r e a c h e d when a s o l i d i s e x p o s e d t o a s o l u t i o n and t h i s s t a t e may be t h e r e s u l t o f r a t e f a c t o r s o r o f thermodynamic o n e s . We s h a l l s e e t h e t h e r m o d y n a m i c c a s e w h i c h o c c u r s i s n o t t h e c o n v e n t i o n a l one a l o n e . 2+ I t i s known t h a t c a l c i t e s formed i n t h e p r e s e n c e o f Mg ions t u r n o u t t o be m a g n e s i a n c a l c i t e s w i t h 0.70 < χ < 1 (1_, 6). The c a l c i t e s may be b u l k p r e c i p i t a t e s a s , f o r e x a m p l e , i n m a r i n e cements o r , i n t h e c a s e o f seeded r u n s , may form c o a t i n g s o f a d i f f e r e n t c o m p o s i t i o n from t h a t o f t h e b u l k p h a s e . Under s p e c i a l c i r c u m s t a n c e s d o l o m i t e may r e s u l t ( 6 ) . D i f f e r e n t r a t e s o f p r e c i p i t a t i o n c a n c a u s e d i f f e r e n t amounts of Mg t o be i n c o r p o r a t e d i n t o t h e s o l i d . One may e x p e c t t h a t a h i g h r a t e , a c h i e v e d by a l a r g e r i n i t i a l a d d i t i o n o f ^ C O s , s h o u l d c a u s e a l a r g e r u p t a k e o f MgC03 and an i n c r e a s e i n t h e solubility of calcite. T h i s w o u l d o c c u r due t o c o l l i s i o n s o f Mg w i t h t h e g r o w i n g c a l c i t e c r y s t a l s w i t h o u t a s much o f a c h a n c e f o r e q u i l i b r a t i o n as i n slower r u n s . T h i s i s i n d e e d shown t o be t h e c a s e i n T a b l e I i n w h i c h t h e r u n s were seeded w i t h c a l c i t e so t h a t we a r e o b s e r v i n g t h e e f f e c t o f c o a t i n g s a n d t o w h i c h d i f f e r e n t amounts o f Na£C0 were a d d e d . The p r i n c i p l e i s t h e same f o r b u l k p h a s e s formed i n unseeded r u n s , n a m e l y , t h a t m e t a s t a b l e s o l i d s c a n be f o r m e d and may p e r s i s t f o r l o n g t i m e s . The p a r t i c u l a r importance o f s u r f a c e c o a t i n g s i s t h a t t h e y , r a t h e r than t h e i n t e r n a l b u l k p h a s e s , g o v e r n t h e i n t e r a c t i o n s w i t h aqueous solutions. The i n c r e a s e i n t h e f i n a l pH r e s u l t s f r o m an enhanced s o l u b i l i t y o f t h e magnesium c a l c i t e s a s t h e pH i n c r e a s e s w i t h a 2 h i g h e r [CO3 -] o f t h e magnesium c a l c i t e s . The i n c r e a s e s o l u b i l i t y r e s u l t s from a h i g h e r magnesium c o n t e n t . 2 +

2 +

3

K^

C a )

= [Ca

K'(M9) = [ M g X

CaC0

3

+

K

2 +

2 +

][C0

][C0

MgC0

3

=

3

2

3

2

"]

(9)

-]

(10)

1

where t h e K values p e r t a i n t o the presence o f a s o l i d s o l u t i o n . These a r e t h r e e e q u a t i o n s i n f o u r unknowns so t h a t t h e r e i s an a d d i t i o n a l degree o f c o m p o s i t i o n a l freedom. I n t e r m s o f t h e phase r u l e t h e s y s t e m w i t h t h e components C a ^ - M g ^ - C O ^ - r ^ O and w i t h s p

(Ca2+) (molal) 0.01 0.01 0.01

Table I Seeded r u n s a t s e v e r a l i n i t i a l s u p e r s a t u r a t i o n s C a l c i t e added (Mg' ) Na C0 (g/kq-SW) (molal) (m moles/kg-SW) O.ul 0.§2 1.1 0.01 2.3 0.82 3.5 0.01 U.82 +

2

3

a

d

d

e

d

pH

f

7779 7.83 7.90


THERMODYNAMICS

646

OF

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

one s o l i d , one l i q u i d , and one v a p o r phase has f = 3 , f = 4 , and c« = 2 . T h i s a g r e e s w i t h what e q u a t i o n s (1) t h r o u g h (11) t e l l u s . The v a r i a b l e s t o be f i x e d may b e , f o r e x a m p l e , and χ = XçaC0 T h i s t e l l s us t h a t , f o r e a c h s o l i d c o m p o s i t i o n , t h e r e i s o n l y one e q u i l i b r i u m aqueous s o l u t i o n o f a g i v e n c o m p o s i t i o n y = [Ca ]/{[Ca ] + [Mg ]}. T h i s i s shown i n F i g . 1 by X Y and f2 f2« i is i n i t i a l s u p e r s a t u r a t e d s o l u t i o n w h i l e X ^ and X f 2 a r e t h e aqueous s o l u t i o n s i n e q u i l i b r i u m w i t h t h e s o l i d s Y f | and Y f 2 - We s h a l l see n e x t why t h e i n i t i a l aqueous c o m p o s i t i o n Χ · i s shown t o y i e l d two ( a c t u a l l y many) e q u i l i b r i u m s y s t e m s . C o n v e n t i o n a l t h e r m o d y n a m i c s shows t h a t f o r each X - t h e r e i s one and o n l y one b u t does n o t t e l l us a n y t h i n g a b o u t t h e r e l a t i o n s h i p between i n i t i a l s o l i d s and aqueous s o l u t i o n s and t h e f i n a l e q u i l i b r i u m s y s t e m . T h i s i s where t h e a p p r o a c h o f W o l l a s t and R e i n h a r d - D e r i e (2j), upon w h i c h I have e l a b o r a t e d somewhat, comes i n . These a u t h o r s (2) p r e s e n t e d t h e i r argument f o r d i s s o l u t i o n . In t h e c a s e o f p r e c i p i t a t i o n , w h i c h I t r e a t , i t s t a r t s w i t h m

3

2 +

x

2 +

Y

2 +

x

t

h

f l

f l

e

η


fl

D. = Ρ + D

(12)

where ϋ · i s t h e amount o f i n i t i a l s o l u t e s and Ρ and D a r e t h e amounts o f t h e p r e c i p i t a t e and o f D«j l a t e r o n . The r a t i o s o l i d / s o l u t i o n i m p l i e s the s o l i d s u r f a c e / t o t a l s o l u t e s r a t i o . Let χ be t h e mole f r a c t i o n o f C a C 0 i n t h e s o l i d and y be m / ( m + m g). Then, f o r calcium Ί

3

C a

C a

M

y D 1

1

= xP + yD

Through the m a n i p u l a t i o n o f Eqns. y D.

(12)

D. - D

(13) and (13)

one a r r i v e s

at

T h i s i s t h e c o n d i t i o n f o r c o n s e r v a t i o n o f mass shown i n F i g . 2 . Note t h a t 1 s e t χ = X w h i l e W o l l a s t and R e i n h a r d - D e r i e u s e t h e symbol χ = X . The e q u i l i b r i u m c o n d i t i o n i s o b t a i n e d i n a . s t r a i g h t f o r w a r d manner f r o m t h e r a t i o o f * n ' = Y+CaC03 s p / caC03 CaCy3 * s i m i l a r e x p r e s s i o n f o r K^tjg). T h i s f i g u r e shows t h a t t h e e q u i l i b r i u m v a l u e s x-f, y f depend upon t h e s o l i d / w a t e r r a t i o . T h e r e i s no thermodynamic i n c o n s i s t e n c y i n t h i s b e c a u s e , i n terms o f F i g . 1 a l l t h a t F i g . 2 i m p l i e s i s t h a t Χ · f o r two s o l i d / w a t e r r a t i o s w i l l y i e l d two v a l u e s o f X^, e a c h w i t h i t s t h e r m o d y n a m i c a l l y c o r r e s p o n d i n g Y f ( s e e F i g u r e C a

M g

K

x

x

a

n

d

0T

a

K

a

η

T h u s , l a r g e r s o l i d / w a t e r r a t i o s s u c h as a r e e n c o u n t e r e d i n p o r e w a t e r s o f s e d i m e n t s l e a d t o s m a l l e r MgC0 c o n t e n t s i n t h e e q u i l i b r i u m 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 i n e i t h e r c a s e t h e mag nesium c o n t e n t o f t h e s o l i d i n c r e a s e s . W o l l a s t and R e i n h a r d - D e r i e p r e s e n t e d data t o s u p p o r t the t h e o r y from the s t a n d p o i n t o f d i s s o l u t i o n and some o f o u r r e s u l t s f o r t h e p r e c i p i t a t i o n c a s e 3



PYTKOWICZ AND COLE

Figure 1.

647


Triangular solid solution-aqueous solution equilibria

Increasing water/ solid ratio

l-x Figure 2. Equilibrium Curve A and conservation of mass Curve B. The equilibrium point D corresponds to a very large solid/water ratio and the reverse is true for E.

American Chemical Society Library 1155 16th St. N. W. In Thermodynamics of Aqueous Systems with Industrial Washington, D. C.Applications; 20036 Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

648

APPLICATIONS

a r e shown i n T a b l e I I . A k i n e t i c c o n t r o l would l e a d t o a f a s t e r p r e c i p i t a t i o n a n d , c o n s e q u e n t l y , t o a h i g h e r MgC0 c o n t e n t and s o l u b i l i t y f o r a l a r g e r a d d i t i o n o f c a l c i t e as more s u r f a c e f o r n u c l e a t i o n would be a v a i l a b l e . 3

Table II The e q u i l i b r i u m pH i n t h e m u l t i s t a t e e q u i l i b r i u m as a f u n c t i o n o f t h e s o l i d / w a t e r r a t i o ( C o l e and P y t k o w i c z , i n p r e p a r a t i o n ) f o r a r t i f i c i a l seawaters w i t h m o d i f i e d (Mg ). The l a s t two columns f o r c a l c i t e r e f e r t o successive additions of s o l i d . (Ca* ) l M g ^ ) N a C 0 x added C a l c i t e added S t e a d y C a l c i t e Steady ( m o l a l ) ( m o l a l ) ( m o l / k g SW) (g/kgSW) S t a t e pH added s t a t e pH 0.01 0.01 3.27 0.62 0.62 7.88 0.01 0.01 1.61 0.20 7.95 0.20 7.89 0.01 0.01 1.31 0.07 8.01 0.07 8.01


2 +

+

+

2

We o b s e r v e t h e o p p o s i t e t r e n d , e x p e c t e d f r o m t h e m u l t i p h a s e h y p o t h e s i s as a h i g h e r s o l i d / s o l u t i o n r a t i o l e a d s t o a s m a l l e r mole f r a c t i o n o f MgCOq a n d , c o n s e q u e n t l y , t o a l o w e r s o l u b i l i t y (and pH) o f t h e s o l u t i o n . In t h e f i r s t r u n t h e h i g h N a C 0 3 added i s o f f s e t by t n e l a r g e amount o f c a l c i t e a d d e d . In t h e d i s s o l u t i o n p r o c e s s t h e magnesium c o n t e n t o f t h e s o l i d d e c r e a s e s and does so t o a g r e a t e r e x t e n t f o r s m a l l e r s o l i d / s o l u t i o n r a t i o s . For f a b l e m t h e s o l u b i l i t y p r o d u c t s o f CaC03 and M g C 0 were p l a c e d i n t h e form , 2

3

2

X

K

sp

ι

λ was c a l c u l a t e d f o r known v a l u e s o f γ and K i n s e a w a t e r and from assumed v a l u e s o f X . Then y ^ w a s ~ c a l c u l a t e d from t h e e q u i l i b r i u m e q u a t i o n and compared t o y * = 0 . 0 1 / ( 0 . 0 1 + 0 . 0 5 ) = 0 . 1 6 7 f o r seawater. I t c a n be seen t h a t t n e most s t a b l e c a l c i t e i n s e a w a t e r must c o n t a i n r o u g h l y l e s s t h a n one mole p e r c e n t MgC03« The t i m e b e h a v i o r s f o r t h e v a r i o u s t y p e s o f p r o c e s s e s a r e shown i n F i g u r e 3 . The t h r e e u p p e r c u r v e s c o r r e s p o n d t o a k i n e t i c c o n t r o l w h i l e t h e t h r e e l o w e r ones r e s u l t from thermodynamic c o n trol. I t s h o u l d be n o t e d t h a t a t i n t e r m e d i a t e r a t e s o f p r e c i p i t a t i o n t h e two t y p e s o f mechanisms may a c t a t t h e same t i m e i n t e r m s o f t h e d i f f e r e n c e between t h e i o n p r o d u c t and Κ ' . The i m p o r t a n t c o n c l u s i o n i s t h a t c o m p l e x c o n t r o l l i n g p r o c e s s e s c a n o c c u r i n s o l u b i l i t y phenomena i n m i x e d e l e c t r o l y t e solutions. T h i s i s e s p e c i a l l y t r u e o f s u r f a c e c o a t i n g s formed k i n e t i c a l l y o r by m u l t i s t a t e t h e r m o d y n a m i c s and w h i c h p r e v e n t t h e aqueous s o l u t i o n f r o m i n t e r a c t i o n w i t h i n t e r n a l b u l k p h a s e s . One s h o u l d remember o f c o u r s e t h a t , when t h e d e g r e e o f s u p e r s a t u r a t i o n i s l a r g e enough f o r b u l k p r e c i p i t a t i o n t o o c c u r , t h e k i n e t i c and m u l t i p h a s e thermodynamic p r o c e s s e s s t u d i e d above w i l l a p p l y t o the a c t u a l bulk phases. +

S £ )



33.

PYTKOWICZ AND COLE


649

Figure 3. Controls of precipitation (idealized curves) A, B, C result from the addition of different amounts of Na CO, . At D and Ε Ig of calcite was added per kg of seawater for Curve DEF, at D 2g were added for curve DF, and 3g for DG. 2

{


THERMODYNAMICS OF

650

AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

Table III C a l c i t e mole f r a c t i o n X , s o l i d s t a t e a c t i v i t y c o e f f i c i e n t s λ , and Y p , t h e s o l u t e m o l e f r a c t i o n s of calcium at e q u i l i b r i u m i n seawater. X

A


0.99 0.98 0.97 0.88

CaC0

A

3

MgC0

3

166 83.0 55.3 13.8

1 .13 1.14 1.15 1.27

0.174 0.178 0.179 0.218

Ion P a i r - C o m p l e x C o m p e t i t i o n The c o n c e p t s o f i o n i c m e d i a , f r e e and 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 , p r o p e r t i e s o f e q u i l i b r i u m c o n s t a n t s , and e f f e c t i v e i o n i c s t r e n g t h t o be u s e d h e r e were examined i n an e a r l i e r p a p e r i n t h i s volume. T h i s s e c t i o n i s based upon t h e p a p e r s o f J o h n s o n and P y t k o w i c z {]) and o f S i p o s et_ a l _ . ( 8 ) . The c o n c e p t s used a r e t h e f o r m a t i o n o f c o u l o m b i c i o n - p a i r s between t h e m a j o r i o n s o f s e a w a t e r ( N a C i o , N a H C 0 ° , N a C 0 " , N a S O ^ , and s i m i l a r p a i r s f o r C a and M g ) and t h e f o r m a t i o n o f t r u e c o m p l e x e s s u c h as P b C l , P b C l ° , C d C l , P b O H , PbC0 , e t c . The c o e x i s t e n c e o f t h e s e two t y p e s o f e n t i t i e s i m p l i e s c o m p e t i t i o n , e . g . , f o r C T i o n s , one has NaClo and P b C l , and y i e l d s t r a c e m e t a l s p e c i a t i o n q u i t e d i f f e r e n t from those o b t a i n e d i n the absence o f i o n p a i r s . In T a b l e IV a r e shown t h e f r a c t i o n s o f t h e m a j o r i o n s w h i c h a r e f r e e and i o n paired. 3

2 +

3

2 +

2

+

+

+

3

+

Table

Na K+ Mg Ca2+ etc. +

2 +

IV

% Free

M-Cl

M-SO4

84.0 78.5 50.9 45.8

T2T2 17.2 39.1 43.8

3.8 4.3 9.7 10.0

a =

YT(T)

100% change i n C 0 (ïC0 )T 3

= (YC0 )F/n

3

+

sp" K* = K * ( t ) K

=

K

K

F

3

M-C0

3

0.0 0.0 0.0 0.1

Y (F) F

NaC0

sp/(YCa)T ( ) ( Y C a

0.0 0.0 0.2 0.3

-»• 1% change i n

2 _

3

-

M-HC0

Y C 0 3

(18

)

(d")p

and

2

(M

2 +

)

F

(Cl')p

where ( c j i n d i c a t e s t h e c o r r e c t e d v a l u e s . T h i s was done a t t h e e f f e c t i v e i o n i c s t r e n g t h o f t h e s e a w a t e r o f i n t e r e s t w h i c h was roughly 0.7. U n c o r r e c t e d and c o r r e c t e d r e s u l t s f o r t h e t r a c e m e t a l s p e c i a t i o n o f l e a d a r e p r e s e n t e d i n T a b l e V . I t c a n be seen t h a t t h e c o m p e t i t i o n between t r u e c o m p l e x e s and c o u l o m b i c i o n - p a i r s m o d i f i e s c o n s i d e r a b l y the s p e c i a t i o n o f l e a d . The f r a c t i o n s do n o t add up t o 100% b e c a u s e s p e c i e s s u c h a s P b C l ° , P b c l " , e t c . , were n o t e n t e r e d i n t o t h e t a b l e . A g l o s s a r y o f s y m b o l s c a n be f o u n d i n T a b l e V I . 2

3

Table V Lead s p e c i a t i o n i n s e a w a t e r c o r r e c t e d a n d uncorrected f o r C I " i o n - p a i r s . Corrected Uncorrected [Pb2+] 0.57% 1.94% 1.57% [HbCl*] 4.48% [PbOH ] 35.89% 61.55% [PbC0 °] ϋ2.53% 44.33% +

3


THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

652

T a b l e VI Symbols. number o f components amount o f s o l u t e d u r i n g t h e c o u r s e o f an e x p e r i m e n t amount o f i n i t i a l s o l u t e s number o f d e g r e e s o f f r e e d o m 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 o f CaC03

c D D-j f sp K

K^Mg) m [Na ]p [Na ]j Ρ +


+

ρ pC0 pH Τ X χ y f

2

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 o f MgCU3 molality free ion concentration of Na total concentration of Na amount o f s o l i d d u r i n g t h e c o u r s e o f an e x p e r i m e n t ; a l s o the pressure number o f p h a s e s p a r t i a l pressure o f C0 f i n a l pH temperature mole f r a c t i o n m o l e f r a c t i o n o f component s u c h a s CaCU3 i n t h e s o l i d s o l u t e m o l e f r a c t i o n o f t h e e l e m e n t i n t h e aqueous solution mean m o l a l a c t i v i t y c o e f f i c i e n t +

+

2

Literature Cited

1. Plummer, N.L.; Mackenzie, F.T., Am. J. Sci., 274, 61-83, 1974. 2. Wollast, R.; Reinhard-Derie, D., "The Fate of Fossil Fuel CO in the Ocean", Ν. Andersen and A. Malahoff, eds., pp. 479493, Plenum, New York, 1977. 3. Kitano, Y.; Hood, U.W., J. Oceanogr. Soc. Japan, 18, 141-145, 1962. 4. Möl1er, P.; Rajagopalan, G., Z. Phys. Chem., Neve Holge, 94, 297-314, 1975. 5. Chave, K.E.; Deffeyes, K.S.; Weyl, P.K.; Garrels, R.M.; Thompson, M.E., Science, 137, 33-34, 1962. 6. Berner, R.A., "Principles of Chemical Sedimentology", Mc-Graw Hill, New Jersey, 1971. 7. Johnson, K.; Pytkowicz, R.M., Am. J. Sci., 278, 1428-1447, 1978. 8. Sipos, L.; Raspos, B.; Nurnberg, H:W.; Pytkowicz, R.M., Mar. Chem., In press.

2

RECEIVED

February 14, 1980.


Equilibrium and Kinetic Problems in Mixed Electrolyte Solutions - ACS

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