Chemical Modeling of Aqueous Systems II - American Chemical Society

Chapter 31

Revised Chemical Equilibrium Data for Major Water—Mineral Reactions and Their Limitations 1

2

3

Darrell Kirk Nordstrom , L. Niel Plummer , Donald Langmuir , Eurybiades Busenberg , Howard M . May , Blair F. Jones , and David L. Parkhurst 2

4

2

4

Downloaded by UNIV OF MICHIGAN ANN ARBOR on March 11, 2013 | http://pubs.acs.org Publication Date: December 7, 1990 | doi: 10.1021/bk-1990-0416.ch031

1

U.S. Geological Survey, Water Resources Division, 345 Middlefield Road, Mail Stop 420, Menlo Park, CA 94025 U.S. Geological Survey, 432 National Center, Reston, VA 22092 Department of Chemistry and Geochemistry, Colorado School of Mines, Golden, CO 80401 U.S. Geological Survey, Denver Federal Center, Mail Stop 418, Lakewood, CO 80225 2

3

4

A revised, updated summary of equilibrium constants and reaction enthalpies for aqueous ion association reactions and mineral solubilities has been compiled from the literature for common equilibria occurring in natural waters at 0-100°C and 1 bar pressure. The species have been limited to those containing the elements Na, K, Li, Ca, Mg, Ba, Sr, Ra, Fe(II/III), Al, Μn(II, III, IV), Si, C, C l , S(VI) and F. The necessary criteria for obtaining reliable and consistent thermodynamic data for water chemistry modeling is outlined and limitations on the application of equilibrium computations is described. An important limitation is that minerals that do not show reversible solubility behavior should not be assumed to attain chemical equilibrium in natural aquatic systems. C h e m i c a l m o d e l i n g r e s u l t s f o r aqueous systems i s dependent on t h e primary thermodynamic and k i n e t i c data needed t o p e r f o r m t h e calculations. F o r aqueous e q u i l i b r i u m c o m p u t a t i o n s , a l a r g e number of thermodynamic properties of solute-solute, solute-gas and s o l u t e - s o l i d reactions are a v a i l a b l e f o r a p p l i c a t i o n t o natural waters and o t h e r aqueous s y s t e m s . U n f o r t u n a t e l y , an i n t e r n a l l y consistent thermodynamic data base that i s accurate for a l l m o d e l i n g o b j e c t i v e s , has n o t been a c h i e v e d . Nor i s i t l i k e l y t o be a c h i e v e d i n the near f u t u r e . The b e s t t h a t c a n be hoped f o r i s a t o l e r a b l e l e v e l o f i n c o n s i s t e n c y , w i t h c o n t i n u i n g p r o g r e s s toward t h e U t o p i a n g o a l t h r o u g h n a t i o n a l and i n t e r n a t i o n a l c o n s e n s u s . An e s s e n t i a l a t t r i b u t e o f a c c u r a t e thermodynamic d a t a i s i t s i n t e r n a l c o n s i s t e n c y (see next s e c t i o n ) . Another c h a r a c t e r i s t i c o f such d a t a i s t h a t i t has been r e p r o d u c e d by d i f f e r e n t i n v e s t i g a t o r s using different t e c h n i q u e s and/or methods o f e v a l u a t i o n . The tremendous need f o r such evaluations has been stressed by Stockmayer (1) , and L i d e (2) , because t h e use o f e r r o n e o u s numerical values can have severe consequences for a highly technological society. Aqueous c h e m i c a l models, f o r example, a r e f i n d i n g i n c r e a s e d use by water q u a l i t y s p e c i a l i s t s , geochemists, hydrologists and engineers as an important tool f o r the i n t e r p r e t a t i o n o f n a t u r a l water c h e m i s t r y . R e s e a r c h i n v e s t i g a t o r s w i t h i n t h e Water R e s o u r c e s D i v i s i o n o f t h e U.S. G e o l o g i c a l S u r v e y have d e v e l o p e d a s e r i e s o f computer

0097-6156/90/0416-0398$06.00/0 © 1990 American Chemical Society

In Chemical Modeling of Aqueous Systems II; Melchior, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.


31. NORDSTROM ET AL.

Data for Major Water-Mineral Reactions

399

programs t h a t c a n p e r f o r m v a r i o u s t y p e s o f e q u i l i b r i u m c o m p u t a t i o n s f o r chemical r e a c t i o n s i n n a t u r a l waters. Over f i f t e e n y e a r s ago the o r i g i n a l programs WATCHEM ( 3 ) , WATEQ (4), and SOLMNEQ (5) were introduced t o p e r f o r m s p e c i a t i o n c a l c u l a t i o n s f o r s e l e c t e d major components i n n a t u r a l w a t e r s . S i n c e t h e n , a s e r i e s o f U.S.G.S. r e p o r t s have p r o v i d e d m o d i f i c a t i o n s o f t h e o r i g i n a l WATEQ program (6 - 13) . The o r i g i n a l thermodynamic d a t a b a s e f o r t h e WATEQ s e r i e s was p u b l i s h e d i n t h e f i r s t p a p e r (4j as a t a b l e o f e q u i l i b r i u m c o n s t a n t s and e n t h a l p i e s of reaction. Later reports revised or added selected values t o t h e database but d i d not reproduce u n a d j u s t e d numbers. C o n s e q u e n t l y , no s i n g l e document c o n t a i n s a l l values o f t h i s e x t e n s i v e l y r e v i s e d database. One o b j e c t i v e f o r this paper i s to provide such documentation, f o r both major constituents (Ca, Mg, Na, K, H C 0 , C 0 , C l , S 0 , F, S i (OH) , H and OH) and s e l e c t e d minor and t r a c e e l e m e n t s (Ba, S r , Ra, L i , A l , Fe(II), Fe(III) and Mn) . F u r t h e r r e v i s i o n s are being planned t o i n c l u d e more t r a c e e l e m e n t s . The e x p e r i e n c e g a i n e d from numerous a p p l i c a t i o n s o f t h e WATEQ s e r i e s o f programs has a f f e c t e d e a r l i e r d e c i s i o n s r e g a r d i n g which components and r e a c t i o n s s h o u l d be i n t h e program and how t h e r e a c t i o n s s h o u l d be p o r t r a y e d . Furthermore, p r o g r e s s i n thermodynamic d a t a e v a l u a t i o n , and i n u n d e r s t a n d i n g t h e behavior of mineral d i s s o l u t i o n / p r e c i p i t a t i o n reactions and o f redox s p e c i e s , has a f f e c t e d n o t o n l y t h e v a l u e s i n t h e d a t a b a s e b u t a l s o how t h e y a r e used. The main o b j e c t i v e s o f t h i s p a p e r a r e : (1) t o document t h e r e v i s e d e q u i l i b r i u m c o n s t a n t s and t h e i r t e m p e r a t u r e dependencies found most reliable f o r applications to natural w a t e r s ; (2) t o e x p l a i n why some m i n e r a l r e a c t i o n s a r e b e s t l e f t o u t o f r o u t i n e a p p l i c a t i o n s o f c h e m i c a l m o d e l i n g ; (3) t o e x p l a i n some of t h e d i f f i c u l t i e s inherent i n the i n t e r p r e t a t i o n of aquatic geochemical processes; and (4) t o describe examples of the d i f f i c u l t y of achieving thermodynamic c o n s i s t e n c y i n equilibrium d a t a (e.g., c a l o r i m e t r i c v s . s o l u b i l i t y d a t a ) . 3

3

4

4

REQUIREMENTS FOR THERMODYNAMIC CONSISTENCY Thermodynamic consistency c r i t e r i a a r e met (JL4) :

is

achieved

when

the

following

The fundamental thermodynamic relationships and their consequences a r e obeyed. This criterion permits the comparison o f c a l o r i m e t r i c and s o l u b i l i t y d a t a . Common s c a l e s a r e u s e d f o r t e m p e r a t u r e , and t h e fundamental p h y s i c a l c o n s t a n t s . Conflicts resolved.

and

inconsistencies

among

energy,

measurements

•

An a p p r o p r i a t e m a t h e m a t i c a l model i s chosen t e m p e r a t u r e and p r e s s u r e dependent d a t a .

•

An a p p r o p r i a t e aqueous aqueous s o l u t i o n d a t a .

chemical

model

are

t o f i t a l l the

i s chosen

An a p p r o p r i a t e c h o i c e o f s t a n d a r d s t a t e s to a l l s i m i l a r substances.

a t o m i c mass

to f i t a l l

i s made and a p p l i e d

Numerous d i s c r e p a n c i e s c a n be f o u n d i n t h e l i t e r a t u r e when comparing measurements o f t h e same s y s t e m r e p o r t e d by d i f f e r e n t i n v e s t i g a t o r s o r when comparing s o l u b i l i t y d a t a w i t h c a l o r i m e t r i c , electrochemical o r vapor pressure data, etc. There i s no universally-acccepted aqueous chemical model. There i s no u n i v e r s a l l y - a c c e p t e d model f o r t e m p e r a t u r e o r p r e s s u r e dependence o f thermodynamic f u n c t i o n s . O f t e n t h e o n l y a v a i l a b l e measurement



400

CHEMICAL MODELING OF AQUEOUS SYSTEMS II

o f some p r o p e r t y does not a d e q u a t e l y c h a r a c t e r i z e t h e s o l i d o r t h e aqueous phase. I n c o n s i s t e n c i e s a r e common among aqueous c h e m i c a l models and they can be very difficult to resolve. One inconsistency is that non-ideality can be interpreted using d i f f e r e n t e l e c t r o l y t e t h e o r i e s such as the i o n - a s s o c i a t i o n t h e o r y (15), t h e s p e c i f i c - i o n i n t e r a c t i o n t h e o r y (16^, 17) , o r t h e i o n hydration theory (_18) . Further i n c o n s i s t e n c y can arise from n e g l e c t i n g t o f i t s i m u l t a n e o u s l y a l l t y p e s o f s o l u t i o n d a t a (heat measurements, v a p o r p r e s s u r e measurements, d e n s i t y measurements, electrochemical measurements, freezing and boiling point measurements) w i t h a s i n g l e , r e l i a b l e model u t i l i z i n g the best a v a i l a b l e data f o r t h e d e n s i t y and d i e l e c t r i c constant of the solvent. An e x c e l l e n t example o f a comprehensive approach t o r e s o l v i n g such i n c o n s i s t e n c i e s i s g i v e n i n papers by Ananthaswamy and A t k i n s o n (19, 20) , i n t h e i r e v a l u a t i o n o f t h e p r o p e r t i e s o f aqueous c a l c i u m c h l o r i d e . S i m i l a r e v a l u a t i o n s need t o be done f o r other solutes relevant to n a t u r a l water chemistry and then c o r r e l a t e d where common i o n s o c c u r . E v a l u a t e d aqueous s o l u t e d a t a must a l s o be f i t t e d t o g e t h e r w i t h s o l u b i l i t y and s o l i d phase d a t a i n a thermodynamic network (21, 2 2 ) . In f a c t , t h i s i s t h e approach u s e d by t h e Committee on Data f o r S c i e n c e and T e c h n o l o g y (CODATA) . After this e v a l u a t i o n has been done, t h e e n t i r e thermodynamic network must be r e f i t t e d i f a new v a l u e o f an* i m p o r t a n t p r o p e r t y i s reported. As a r e s u l t p r o g r e s s i s slow and o n l y a t o l e r a b l e l e v e l o f i n c o n s i s t e n c y can be hoped f o r . F o r t u n a t e l y , many e q u i l i b r i u m c o n s t a n t s r e p o r t e d f o r t h e same r e a c t i o n can be i n good agreement i n s p i t e of these i n c o n s i s t e n c i e s . A l l of these i n c o n s i s t e n c i e s need not be totally r e s o l v e d f o r the o b j e c t i v e s of chemical m o d e l i n g , a l t h o u g h no one has r e a l l y d e f i n e d how w e l l thermodynamic p r o p e r t i e s must be known. The i o n - p a i r d a t a p r e s e n t e d i n t h i s p a p e r i s r e s t r i c t e d t o t h e i o n - a s s o c i a t i o n model which i s l i m i t e d t o an upper c o n c e n t r a t i o n o f about 1 m o l a l because i t uses a modified, extended Debye-Hiickel expression for the activity c o e f f i c i e n t s (_4) . The advantage o f t h i s approach i s t h a t much more d a t a a r e a v a i l a b l e f o r use i n multicomponent, m u l t i p h a s e systems o f i n t e r e s t t o geochemists and t h e p r e c i s i o n o f t h e d a t a i s o f t e n b e t t e r f o r low i o n i c s t r e n g t h s o l u t i o n s — the m a j o r i t y of n a t u r a l waters. THE

USE

OF

FREE ENERGIES VS

EQUILIBRIUM CONSTANTS

The thermodynamic d a t a b a s e f o r an aqueous c h e m i c a l model i s g e n e r a l l y p r e s e n t e d as a t a b u l a t i o n o f f r e e e n e r g i e s o r e q u i l i b r i u m constants. The use o f f r e e e n e r g i e s b o t h f o r t h e database and t o calculate equilibrium constants has been avoided as much as p o s s i b l e i n t h e p r e s e n t c o m p i l a t i o n because such an a p p r o a c h can i n t r o d u c e much l a r g e r e r r o r s t h a n t h e use o f e q u i l i b r i u m c o n s t a n t s . As examples, f r e e e n e r g y - b a s e d s o l u b i l i t y product constants, f o r t h e common m i n e r a l s q u a r t z , c a l c i t e and gypsum, w i l l be compared t o v a l u e s f o r t h e same c o n s t a n t s based on h i g h l y r e l i a b l e s o l u b i l i t y data. F r e e energy d a t a f o r t h e s e m i n e r a l s and t h e i r a s s o c i a t e d s o l u t e s i n the d i s s o l u t i o n r e a c t i o n s : Si0

+ 2H 0 = Si(OH) °

2

CaC0

2

3

= Ca

4

2 +

+ C0 ~

CaS0 -2H 0 = C a 4

2

2

3

2+

2

+ S 0 " + 2H 0 4

2

a r e shown i n T a b l e 1, o b t a i n e d from s i x i m p o r t a n t sources: The N a t i o n a l Bureau o f S t a n d a r d s (NBS, 23); t h r e e U.S. Geological Survey (USGS) s o u r c e s i n which t h e d a t a on q u a r t z a r e from t h e r e c e n t e v a l u a t i o n by Hemingway (24), t h e d a t a on c a l c i t e a r e from R o b i n s o n e t a l . (25) and t h e r e m a i n i n g USGS d a t a a r e from Robie e t


31.

NORDSTROM ET AL.

Table

1.

401


Gibbs f r e e e n e r g i e s o f f o r m a t i o n from t h e e l e m e n t s f o r species i n the d i s s o l u t i o n s of quartz, c a l c i t e and gypsum, and d e r i v e d s o l u b i l i t y p r o d u c t constants at

298.15 Κ Species

G °(kJ/mol) f

CODATA Quartz Calcite Gypsum Si( OH)


+

-1129..074 -1797, .359

4 ( a q l

-552. -527, -744. -237.

H

2°(l) logK logK logK

s p

s p

s p

Quartz Calcite Gypsum

.803 .898 .002 .141

- 8 . .47 - 4 . .60

USGS

NBS

-856. 64 - 1 1 2 8 . 79 - 1 7 9 7 . 28 -1316. 6 - 5 5 3 . ,58 -527. 81 -744. 53 -237. ,129 - 2 . ,51 - 8 . ,30 - 4 . ,36

- 8 5 6 . 2 188 - 1 1 3 0 . 610 - 1 7 9 7 . 197 -1308. 0 - 5 5 3 . 54 - 5 2 7 . 90 -744. 630 - 2 3 7 . 141 - 3 . 95 - 8 . 61 - 4 . 34

al. (26) ; and two CODATA Recommended Key V a l u e s s o u r c e s i n which t h e d a t a on c a l c i t e and gypsum a r e from G a r v i n e t a l . (2_7) and t h e r e m a i n i n g CODATA v a l u e s a r e from Cox e t a l . (2j8) . Comparison o f t h e NBS and t h e USGS l o g Ksp v a l u e s shows t h a t q u a r t z s o l u b i l i t y i s d i s c r e p a n t by more t h a n an o r d e r o f magnitude. The g e n e r a l l y a c c e p t e d s o l u b i l i t y a t 2 98.15 Κ i s about 6 mg/L, e q u i v a l e n t t o l o g Ksp = - 3 . 9 8 (29), i f we make t h e s a f e a s s u m p t i o n s that no activity coefficient corrections a r e needed and that m o l a r i t y equals m o l a l i t y . A l t h o u g h s e v e r a l p e r c e n t e r r o r may be a t t a c h e d t o t h i s s o l u b i l i t y v a l u e , i t cannot p o s s i b l y be as h i g h as t h e NBS d a t a i m p l i e s . The main s o u r c e o f e r r o r i s t h e f r e e energy value for s i l i c i c acid. The v a l u e , d i s c u s s e d i n Hemingway (30) , must be c o n s i d e r e d the more r e l i a b l e b e c a u s e t h e r e s u l t i n g l o g Κ i s c l o s e r t o t h e measured v a l u e . C a l c i t e s o l u b i l i t y p r o d u c t c o n s t a n t s range o v e r 0.3 log units. The major t a b u l a t e d d i f f e r e n c e s a r e i n t h e f r e e e n e r g i e s o f c a l c i t e and of the calcium ion. The most reliable measurement and e v a l u a t i o n o f c a l c i t e s o l u b i l i t y i s t h a t o f Plummer and Busenberg (31). They found l o g Ksp = - 8 . 4 8 ( + 0.02) a t 2 9 8 . 1 5 Κ which a g r e e s e x c e l l e n t l y w i t h t h e CODATA v a l u e o f - 8 . 4 7 . The main s o u r c e o f e r r o r can be t r a c e d t o a 2 kJ/mol d i f f e r e n c e between t h e CODATA and USGS v a l u e s f o r the e n t h a l p y of formation of c a l c i t e from the elements. The r e c e n t CODATA r e v i s i o n s o f t h e c a l c i u m i o n and calcite values take into account many different properties i n c l u d i n g t h e Plummer and Busenberg s o l u b i l i t y v a l u e (31). Hence, t h e y a r e t h e most r e l i a b l e v a l u e s f o r t h i s system. The gypsum s o l u b i l i t y p r o d u c t constant, l o g Ksp = -4.58(+ 0. 015), i s known w i t h h i g h p r e c i s i o n and a c c u r a c y a t 2 9 8 . 1 5 Κ due t o t h e c a r e f u l measurements o f L i l l e y and B r i g g s (32,), as w e l l as good agreement w i t h many o t h e r measurements ( c f . 33) . The CODATA f r e e e n e r g i e s a r e t h e o n l y ones c o m p a t i b l e with the solubility determinations since they were based on several high-quality s o l u b i l i t y experiments and on c a l o r i m e t r i c d a t a . The USGS f r e e e n e r g i e s a r e b a s e d on NBS d a t a t h a t p r e - d a t e s t h e Wagman e t a l . (23) and CODATA r e v i s i o n s . The main p o i n t o f t h e s e examples i s t h a t t h e most reliable thermodynamic p r o p e r t y i s t h e one o b t a i n e d by t h e most d i r e c t p a t h , 1. e. t h e one c l o s e s t t o t h e a c t u a l measurement. Free energies of individual phases or species are always d e r i v e d v a l u e s , never d i r e c t l y measured ones. Only c e r t a i n p r o p e r t i e s , such as heat capacities, heat contents, e n t r o p i e s and volumes are directly measured f o r a s i n g l e s p e c i e s o r phase. Free energy measurements are measurements of processes and reactions. Reported free e n e r g i e s o f i n d i v i d u a l s p e c i e s a r e n e a r l y always d e r i v e d from f r e e



402


e n e r g y measurements o f p r o c e s s e s such a s an EMF measurement o r a s o l u b i l i t y measurement. Reversing the calculation to obtain a solubility product constant from free energies can i n t r o d u c e additional errors. Hence, t h e b e s t d a t a f o r use i n chemical m o d e l i n g w i l l be t h o s e v a l u e s b a s e d on r e a c t i o n e q u i l i b r i a and n o t t h o s e b a s e d on f r e e e n e r g i e s o f i n d i v i d u a l r e a c t a n t s and p r o d u c t s . When i n d i v i d u a l free energies have t o be u s e d ( i . e . when no r e a c t i o n e q u i l i b r i a d a t a e x i s t ) t h e n i t becomes v e r y i m p o r t a n t t o t i e t h e v a l u e s t o r e a c t i o n e q u i l i b r i a t h a t a r e w e l l - e s t a b l i s h e d , as Cox e t a l . (20) have done. T h i s i s n o t t o s a y t h a t e r r o r s and inconsistencies don't appear when i n t e r p r e t i n g solubility data, e s p e c i a l l y r e d u c i n g d a t a from h i g h i o n i c c o n c e n t r a t i o n s , b u t j u s t that t h e more d i r e c t t h e measurement, t h e more r e l i a b l e the thermodynamic p r o p e r t i e s a r e l i k e l y t o be. DEBYE-HUCKEL SOLVENT PARAMETERS The c a l c u l a t i o n o f a c t i v i t y c o e f f i c i e n t s f o r aqueous s p e c i e s r e q u i r e s Debye-Huckel t h e o r y t o r e p r e s e n t l o n g - r a n g e electrostatic i n t e r a c t i o n s among i o n s . These i n t e r a c t i o n s a r e a f u n c t i o n o f t h e d e n s i t y , p, t h e d i e l e c t r i c c o n s t a n t , £, and t h e t e m p e r a t u r e o f t h e solvent. A l l o t h e r p a r a m e t e r s a r e e i t h e r fundamental p h y s i c a l constants o r e m p i r i c a l f i t t i n g parameters. F o r example, t h e DebyeH u c k e l s o l v e n t p a r a m e t e r s , A and B, appear i n t h e e x t e n d e d DebyeHuckel e q u a t i o n ( 1 4 ) . A and Β a r e b o t h a f u n c t i o n o f t h e ρ and ε o f water. New d a t a and r e c e n t e v a l u a t i o n s f o r water and r e v i s i o n s i n the fundamental p h y s i c a l c o n s t a n t s p o s t d a t e t h e o r i g i n a l values u s e d i n t h e WATEQ program. G i l d s e t h e t a l . (_34) have e v a l u a t e d t h e d e n s i t y o f water, from b o t h t h e i r measurements (5-80"C) and t h o s e o f o t h e r s , t o an a c c u r a c y o f 3 ppm. The f u n c t i o n t h a t g i v e s t h e best f i t i s : 2

p = 1 - (t - 3.9863) (t + 288.9414) + 0.011445e 508929.2(t + 68.12963)

m3A

where t i s i n d e g r e e s C e l s i u s . Uncertainties i n this function, over t h e range 0-100*C, a r e overshadowed by u n c e r t a i n t i e s i n t h e value of ε. There have been f o u r r e c e n t e v a l u a t i o n s o f t h e d i e l e c t r i c c o n s t a n t f o r water. The e a r l i e s t i s t h a t o f H e l g e s o n and Kirkham (35) , who f i t a s i n g l e e q u a t i o n t o measurements f o r t h e p r e s s u r e and t e m p e r a t u r e ranges o f 1 - 5 0 0 0 b a r s and 0 - 6 0 0 ' C . B r a d l e y and P i t z e r (3_6) d e v e l o p e d an e q u a t i o n f o r t h e d i e l e c t r i c c o n s t a n t up t o 350 *C and 5 0 0 b a r s . The most comprehensive e v a l u a t i o n appears t o be t h a t o f Uematsu and F r a n c k (37^) , i n which e r r o r s were w e i g h t e d a c c o r d i n g t o t e m p e r a t u r e range f o r t h e t o t a l range o f 0 - 3 5 0 * C and up t o 5 k b a r . F i n a l l y , Khodakovsky and D o r o f e y e v a (38) e v a l u a t e d the dielectric constant from 0 - 3 0 0 *C and up to 5 kbar. Ananthaswamy and A t k i n s o n ( 1 ^ ) p o i n t o u t t h a t t h e B r a d l e y and P i t z e r (3J5) e q u a t i o n a g r e e s e x c e l l e n t l y w i t h t h e IUPAC recommended values (39) , i t does n o t depend on t h e d e n s i t y o r s a t u r a t i o n p r e s s u r e o f water as do o t h e r e q u a t i o n s , and seems a r e a s o n a b l e compromise compared t o o t h e r v a l u e s . On t h e o t h e r hand, comparing results from t h e f o u r p r o c e d u r e s over t h e range o f 0-100'C, d e v i a t i o n s a r e n o t g r e a t e r than 0 . 1 % . A l l o f t h e s e e q u a t i o n s a r e quite lengthy because o f t h e l a r g e range o f t e m p e r a t u r e and p r e s s u r e t o which t h e y have been f i t t e d . The t e m p e r a t u r e range i s l i m i t e d t o 0 - 1 0 0 " C i n t h i s p a p e r and we have chosen t h e Uematsu and F r a n c k (37^) e q u a t i o n , m o d i f i e d as f o l l o w s :

ε = 2727.586 + 0.6224107T - 466.9151 In Τ - 52000.87/Γ This

fits

to within 0.01 units of the empirical d i e l e c t r i c


constant

31.

NORDSTROM ET AL.

Data for Major Water—Mineral Reactions e

(about 0.013%) up t o 1 0 0 C and of o t h e r p u b l i s h e d e v a l u a t i o n s .

agrees

q u i t e w e l l with

the

403

results


REVISED EQUILIBRIUM DATA The thermodynamic d a t a c i t e d i n T a b l e 2 (at t h e end o f t h i s d i s c u s s i o n ) a r e r e s t r i c t e d t o 0-100'C and 1 b a r (100 kPa) p r e s s u r e , standard state conditions for solids and infinite dilution reference state f o r aqueous s p e c i e s . The m i n e r a l and aqueous s p e c i e s have been l i m i t e d t o t h o s e a p p l i c a b l e t o n a t u r a l waters t h a t c o n t a i n t h e f o l l o w i n g e l e m e n t s : Na, K, L i , Ca, Mg, Ba, Sr, Ra, Fe, A l , Mn, S i , C, C l , S and F. Only s u l f a t e i s c o n s i d e r e d f o r s u l f u r s p e c i e s , but b o t h F e ( I I ) and F e ( I I I ) s p e c i e s are t a b u l a t e d . No s o l i d s o l u t i o n models a r e c o n s i d e r e d . A range o f s o l u b i l i t y p r o d u c t c o n s t a n t s i s g i v e n f o r m i n e r a l s whose s o l u b i l i t i e s depend s i g n i f i c a n t l y on t h e "degree o f c r y s t a l l i n i t y , i.e. particle size effects, o r d e r - d i s o r d e r phenomena and d e f e c t s t r u c t u r e s . These minerals are dolomite, siderite, rhodocrosite, gibbsite, f e r r i h y d r i t e / g o e t h i t e and q u a r t z / c h a l c e d o n y . [ I t now appears t h a t the r e p o r t e d range of solubilities f o r quartz and chalcedony ( m i c r o c r y s t a l l i n e quartz) r e f l e c t s c r y s t a l o r d e r i n g and particle s i z e e f f e c t s f o r the same b a s i c s t r u c t u r e (S.R. G i s l a s o n and R.O. F o u r n i e r , p e r s . comm.)]. Kaolinite, s e p i o l i t e and k e r o l i t e are a l s o e x p e c t e d t o be a f f e c t e d by t h e degree o f c r y s t a l l i n i t y , but inadequate data e x i s t to describe these e f f e c t s at t h i s time. E n t h a l p i e s o f r e a c t i o n a r e g i v e n i n k c a l / m o l because t h e programs were o r i g i n a l l y s e t up w i t h t h e s e u n i t s . E q u i l i b r i u m constants are g e n e r a l l y g i v e n t o one more f i g u r e t h a n i s s i g n i f i c a n t f o r p u r p o s e s of a v o i d i n g r o u n d - o f f e r r o r s . In t h e p a s t , s p e c i a t i o n computations a p p l i e d t o water a n a l y s e s o f t e n i n c l u d e d i o n a c t i v i t y product (IAP) v a l u e s and s a t u r a t i o n indices for minerals that have never displayed reversible s o l u b i l i t y behavior e i t h e r i n l a b o r a t o r y s t u d i e s or i n n a t u r a l waters. Some o f t h e s e m i n e r a l s a r e u n s t a b l e a t 298 Κ and 1 b a r , others dissolve incongruently, and still others are not t h e r m o d y n a m i c a l l y i d e n t i f i a b l e phases i n t h e t r a d i t i o n a l phase r u l e sense. I f r e v e r s i b i l i t y has n e v e r been shown and t h e r e i s good r e a s o n t o b e l i e v e t h a t t h e y do not a t t a i n e q u i l i b r i u m s o l u b i l i t y , t h e y s h o u l d be d e l e t e d from e q u i l i b r i u m - b a s e d m o d e l i n g computations and from t h e i n t e r p r e t a t i o n o f low-temperature e q u i l i b r i u m m i n e r a l assemblages (41) . F o r example, m i n e r a l groups such as s m e c t i t e s , illites and micas have never been shown to control water c o m p o s i t i o n as r e f l e c t e d by a c o n s t a n t IAP f o r a known c o m p o s i t i o n of that mineral in an a q u i f e r where water composition has significantly varied. Such d e m o n s t r a t i o n s , however, are p l e n t i f u l for minerals such as gypsum and calcite. Consequently, the f o l l o w i n g m i n e r a l s o r m i n e r a l groups a r e b e i n g d e l e t e d from t h e present compilation: smectites, illites, chlorites, micas, f e l d s p a r s , amphiboles, p y r o x e n e s and p y r o p h y l l i t e . Talc also i s deleted because i t i s only known t o form i n b r i n e s at low t e m p e r a t u r e s and such h i g h i o n i c s t r e n g t h s o l u t i o n s are o u t s i d e o f t h e range o f a p p l i c a b i l i t y o f t h e c h o s e n c h e m i c a l model. It i s i m p o r t a n t t o remember t h a t a l t h o u g h n a t u r a l water systems may not achieve equilibrium s a t u r a t i o n with respect to this list of s i l i c a t e s , t h e s e m i n e r a l s may s t i l l a f f e c t the o v e r a l l water-rock mass b a l a n c e r e l a t i o n s h i p a l o n g a f l o w p a t h , as might be d e s c r i b e d by t h e models d e v e l o p e d by G a r r e l s and Mackenzie (_42) and P a r k h u r s t et a l . (43) . Important c h e m i c a l components can always be added o r removed from a water body w i t h o u t a c h i e v i n g r e v e r s i b l e s o l u b i l i t y control. This p a r t i a l equilibrium condition exists when the chemical potentials of some components in a system reach e q u i l i b r i u m w h i l e o t h e r s do not (e.g. c a l c i t e and b a r i t e may reach e q u i l i b r i u m s o l u b i l i t y but c o - e x i s t i n g b i o t i t e o r p l a g i o c l a s e may never reach t h i s s t a t e ) . The advantages o f b o t h approaches s h o u l d 1 1


404


Table 2. Summary of Revised Thermodynamic Data. I. Fluoride and Chloride Species

0

Reaction

ΔΗ, (kcal/mol)

+

3.18

+

4.55

H + F = HF° H + 2F = HF 2

+

....

2+


Na + F = NaF°

log Κ

3.18 3.76

Ref.

Reaction

ΔΗ ° (kcal/mol)

(a)

Al* + F = A1F

2+

Al* + 2F = A1F

(2)

log Κ

Ref.

1.06

7.0

(54)

1.98

12.7

(54)

16.8

(54)

γ

+

2

-0.24

(4£)

Al* + 3F = A1F °

2.16

4.12

0.94

(50)

Al* + 4F = A1F"

2.20

19.4

(54)

2+

3.2

1.82

(b)

Al* + 5F = A1F '

2

1.84

20.6

(54)

2+

....

0.84

(23)

Al* + 6F = A1F*

-1.67

20.6

(54)

...

1.0

(c)

2.7

6.2

(50)

30.18

(55)

Ca + F = CaF Mg + F = MgF Mn + F = MnF 2+

Fe + F = FeF Fe* + F = FeF

2+

Fe* + 2F = FeF

+ 2

Fe* + 3F = FeF ° 3

2+

Mn + CI" = MnCl

+

2+

Mn + 2Cr = MnCl ° 2

2+

Mn + 3C1" = MnCl ' 3

Mineral

4.8

10.8

(50)

5.4

14.0

(50)

3

4

5

-16.26

+

Si(OH) + 4H + 6F 4

2

= SiF ' + 4H 0 6

2+

2

+

....

0.14

(d)

2+

5.6

1.48

(52)

Fe + CI" = FeCl

....

0.61

(23)

Fe* + CI' = FeCl

....

0.25

(23)

Fe* + 2Cr = FeCl *

....

2.13

(52)

....

-0.31

(23)

Fe* + 3Cr = FeCl °

....

1.13

(56)

2

3

Reaction

ΔΗ ° Γ

log Κ

Ref.

(kcal/mol) Cryolite

NajAlFe = 3Na + Al* + 6F +

9.09

-33.84

(e)

Fluorite

CaF = Ca

+ 2F

4.69

-10.6

(f)

2

2+

Redox Potentials

0

ΔΗ, (kcal/mol)

2+

Fe = Fe* + e

9.68

2+

Mn = Mn* + e"

25.8

Reaction +

H + F = HF° 2+

CaF = Ca + 2F

log Κ

Ref.

-0.770

-13.02

(g)

-1.51

-25.51

00

Analytical Expressions for Temperature Dependence

Ref.

legits = -2.033 + 0.012645T + 429.01/T

(a)

log^FUjORrre

2

E° (volts)

=

6 6

'

3 4 8

42

" 98.2/T - 25.271 log Τ

(f)

References for fluoride and chloride species 0

a.) log Κ, Δ Η , and temperature dependence from Naumov et al. (47) in agreement with the critical evaluations by Bond and Hefter (48) and Garvin et al. (27); b.) log Κ from Sillen and Martell (5D, Δ Η , from Smith and Martell (52); c.) estimated from a measurement of 0.83 at I = 1 M and the tendency for divalentfluoridesto have log Κ » 1 (53); d.) based on Davison (108) which agrees well with Turner et al. (109): e.) log Κ from Roberson and Hem (57) and ΔΗ, from (58) for cryolite and from (28) for ions; f.) based on reference (50) but forced to go through logK = -10.6 at 298.15 Κ to be in agreement with the solubility data of Macaskill and Bates (59) and Brown and Roberson (60); g.) E° and log Κ from Whittemore and Langmuir (61), Δ Η , from V. Parker, personal communication; h.) based on (23) in agreement with Bard et al. (62). 0

0

0

Continued on next page


31.

NORDSTROM ET AL.


405

Table 2. Summary of Revised Thermodynamic Data. Π. Oxide and Hydroxide Species Reaction

0

Δ^ log Κ (kcal/mol) +

H 0 = H + OH" +

0

Li + H 0 = LiOH + H

+

2

+

0

Na + H 0 = NaOH + H

+

2

+

K + H 0 = KOH° + H

10.4

-2.19

(65)

0.0

-13.64 (65) Fe* + 2H 0 == Fe(OHV + 2H 17.1

-5.67

(c)

0.0

-14.18 (65) Fe* + 3H 0 == Fe(OH) ° + 3H 24.8

-12.56 (c)

+

2


+

Mg + H 0 = MgOH + H

+

(54)

-13.47 (65) Al* + 2H 0 == AKOHV + 2H 26.90 +

-10.1

(54)

-13.49 (66) Al* + 3H 0 == Al(OH) ° + 3H 39.89

+

-16.9

(54)

(65) Al* + 4H 0 == Al(OH) " + 4H 42.30

-22.7

(54)

2+

+

+

+

2

Fe + H 0 = FeOH + H

+ 4H 14.3 +

2

Ra + H 0 = RaOH + H

2

+

13.2

2

2+

-5.00

5+

4

2

+

+

(65)

11.49

3

-13.29 (65) Al* + H 0 = A10H + H

2

2+

-6.3

2

2

+

Ba + H 0 = BaOH + H 2+

(65)

+

2Fe* + 2H 0 = Fe^OH), * + 2H 13.5

-11.44 (65) 3Fe* + 4H 0 = Fe (OH)

2

2+

(c)

-2.95

4

4

-12.78 (b)

2

+

-21.6

+

+

2

+

2

Sr * + H 0 = SrOH + H

3

-14.46 (65) Fe* + 4H 0 == Fe(OH)" + 4H 31.9

Ca + H 0 = CaOH + H 2+

+

2

+

+

2

2

2

+

2

2+

0

Fe* + H 0 = FeOH * + H

13.362 -14.000 (a)

2

log Κ Ref ΔΗ, (kcal/mol)

Ref. Reaction

+

Mn + H 0 = MnOH + H

+

+

-9.5

2

4

-10.59 (65)

14.4

2

3

Reaction

Portlandite

CatOH), + 2H = : Ca + 2H 0

Ref.

-31.0

22.8

(65)

-27.1

16.84

(65)

-65.11

41.38

(d)

-100.64

61.03

(d)

-—

25.34

(23)

....

15.2

(65)

-22.8

8.11

(62) (e)

ΔΗ, (kcal/mol) +

2+

2

Brucite

log Κ

0

Mineral

+

2+

Mg(OH) + 2H = Mg + 2H 0 2

2

Pyrolusite

Mn0 + 4H + 2e" = ]Mn + 2H 0

Hausmanite

Mn 0 + 8H + 2e" = 3Mn +4H 0

Manganite

MnOOH + 3H + e~ == Mn + 2H 0

Pyrochroite

Mn(OH) + 2H = Mn + 2H 0

Gibbsite (crystalline)

Al(OH) + 3H = Al*+ 3H 0

Gibbsite(microcrystalline)

Al(OH) + 3H = Al*+ 3H 0

(-24.5)

9.35

Al(OH) (amorphous)

Al(OH) + 3H = Al*+ 3H 0

+

(-26.5)

10.8

(f)

Goethite

FeOOH + 3H =: Fe*+ 2H 0

-1.0

(22)

Ferrihydrite(amorphous to microcrystalline)

Fe(OH) + 3H = Fe*+ 3H 0

+

2+

2

2

2+

+

3

3

4

+

2+

2

+

2+

2

2

+

3

2

+

3

3

2

3

2

+

2

+

3

Reaction

2

— —

3.0 to 5.0

(g)

Analytical Expressions for Temperature Dependence +

H 0 = H + OH

logK = -283.9710 + 13323.00/T - 0.05069842T + 102.24447 log Τ -1119669/Γ

2

w

2

Al* + H 0 = AlOH * + H

+

(54)

\o$

(54)

+

\og$ = 226.374 - 18247.8/T - 73.597 log Τ

2

Al* + 3H 0 = Al(OH) ° + 3H 3

+

2

4

(a)

+

2

Al* + 4H 0 = Al(OH) " + 4H

2

logiq = -38.253 - 656.27/Γ + 14.327 log Τ

Al* + 2H 0 = AKOHV + 2H 2

Ref.

= 88.500 - 9391.6/Γ - 27.121 log Τ

2

(54)

3

1ο β = 51.578 - 11168.9/T - 14.865 log Τ δ

(54)

4

References for oxide and hydroxide species a.) refitted from Olafsson and Olafsson (63), in good agreement with Marshall and Franck (64); b.) CODATA compatible (27), in good agreement with (65); c.) log Κ from (65) except logp is corrected to I = 0 from Rester et al. (67) and enthalpies are estimatedfromfreeenergies of reaction and entropies estimated from a correlation plot; d.) Robie and Hemingway (68) using ion valuesfrom(23); e.) Hem and Roberson (70) for log Κ and enthalpy estimated by assuming that it changes by the same amount as the free energy; f. ) Feitknecht and Schindler (71) for log Κ and enthalpy derived as above and considered highly uncertain; g. ) data based on the range of reported valuesfrom(72), Schwertmann and Taylor (73) and Norvell and Lindsay (74). _ . , 3



406

CHEMICAL MODELING OF AQUEOUS SYSTEMS II Table 2. Summary of Revised Thermodynamic Data. ΠΙ. Carbonate Species ΔΗ,

Reaction

log Κ Ref.

0

ΔΗ,

Reaction

CO (g) = C0 (aq) z

0.982 (77)

...

1.95 (78)

Na + H C 0 = NaHCO,

...

2.0

2.177

HCO3- = H + C 0

3.561

+

2

3

2

+

Ca

2+

2 3

+ HCO3- = CaHCCV

2+

Mg


5.56

+ co = CaCO Mg* > + co = MgCO Si»* + co = SrC0 ° Ba + co = BaCO Mn > + co = MnCO Fe + co = FeCO Na + co - = NaC0 "

-4.776

2

C0 (aq) + H 0 = H + H C 0 '

3

Sr * + HC0 - = SrHC0 2

3

2+

Ba

3

+ HC0 - = BaHC0

+

3

+ HC0 " = M n H C 0

2+

3

3

+

Fe + HC0 - = FeHC0 * 2+

3

3

Mineral

3

2

0

3

3

-10.329(31)

3

1.106 (31)

0.79

2+

Ca

-6.352 (31)

2

3

0

3

2H

3

2+

3

0

2

3

0

2

3

2 3

+

0

3

3

1.18 (76)

2

2

2+

1.07 (75)

6.05

+

3

Mn

-1.468 (31)

2.69

+ HC0 " = MgHCO/

0

log Κ Ref.

(kcal/mol)

(kcal/mol)

3

+

(72)

Ra

+ co - = 2 3

RaCO

ΔΗ,

Reaction

3.224 (31)

2.713

2.98

(80)

5.22

2.81

(76)

3.55

2.71

(77)

...

4.90

(81)

...

4.38

(53)

8.91

1.27

(82)

-0.25

(15)

2.5

(66)

...

3

2+

3.545

1.07

0 3

log Κ

0

Ref.

(kcal/mol) Calcite

CaC0 = Ca

2+

Aragonite

CaC0 = Ca

2+

Dolomite(Ordered)

CaMgtCO,), = Ca

Dolomite(Disordered)

CaMg(C0 )2 = Ca

Strontianite

SrC0 = Sr* + C 0 '

Siderite(crystalline)

FeC0 = Fe

2+

2+

3

2

-2.297

-8.480

(31)

2

-2.589

-8.336

(31)

+ C0 " 3

3

+ C0 " 3

2

+ Mg + 2C0 -

2+

2+

3

2

+ Mg + 2C0 "

2+

2+

3

3

3

3

S iderite(precipitated)

FeC0 = Fe

Witherite

B a C 0 = Ba

Rhodocrosite(crystalline) Rhodocrosite(synthetic)

3

+ C0

-2.48

2 3 2

+ C0 -

...

2

+ C0 " 3

M n C 0 == Mn

2+

+ C0 "

M n C 0 == Mn

2+

+ C0 -

3

2

3

3

2

3

-17.09

(a)

-16.54

(b) (76)

-9.271

3

2+

3

Reaction

-11.09 -0.40

2

3

-9.436

-10.89

(c)

-10.45

(d) (77)

-8.562

0.703 -1.43 ...

-11.13

(e)

-10.39

(e)


Ref. 2

CO (g) = C0 (aq)

logK = 108.3865 + 0.01985076T - 6919.53^ - 40.45154 log Τ + 669365/T

CO (aq) + H 0 = H + HC0

logKj = -356.3094 - 0.06091964T + 21834.37/T + 126.8339 log Τ - 1684915/T

z

2

z

(31)

H

2

2

(31)

+

3

+

2

2

HC0 " = H + C0 " logK = -107.8871 - 0.03252849T + 5151.79/T + 38.92561 log Τ - 563713.9/T 3

Ca

2+

3

2

+ HC0 " = CaHC0 3

Mg

2+

3

3

Ba

2+

Ca

2+

+

+ HC0 " = BaHC0

Mg

2

+ CO, " = CaCO

+ C0 " = MgCO 3

2

2

3

+ C0

2

0 3

= BaCO

3

CaCO, = Ca

2+

CaC0 = Ca

2+

0 3

+ CQ

0

0

3

M g C O 3

logK

SrC03

logK

BiC03

(77)

= -3.0938 + 0.013669T = -1228.732 - 0.299444T + 35512.75/Γ + 485.818 log Τ

0

logK

(76)

+

(31)

= 0.9910 + 0.O0667T

(80)

° = -1.019 + 0.012826T

(76)

° = 0.113 + 0.O08721T

(77) (31) (31)

logK

(76)

2

2+

B t H C 0 3

(75)

= -3.248 + 0.014867T

l o g l C ^ c ^ ^ = -171.9773 - 0.077993T + 2903.293/T + 71.595 log Τ

3

3

logK

(31)

2

+ C0 '

SrC0 = Sr * + CO, ' BaC0 = Ba

+ & Η 0 Ο 3

= -59.215 + 2537.455/T + 20.92298 log Τ

l o g l C ^ ^ = -171.9065 - 0.077993T + 2839.319/Γ + 71.595 log Τ

+ C0 ' 3

2

+ 3

+ M g H C 0 3

(31)

2

3

3

logK

logKc^

3

2

Sr * + C0 " = SrCO 2+

0

+ 3

^Κ

3

3

2+

l o g l C ^ ^ = 1209.120 + 0.31294T - 34765.05yT - 478.782 log Τ

3

+ HC0 * = MgHC0

Si* + HC0 - = SrHC0

Ba

+

2 3

S T R O N T I A N r r E

= 155.0305 - 7239.594/T - 56.58638 log Τ

l o g l C ^ ^ ^ = 607.642 + 0.121098T - 20011.25/T - 236.4948 log Τ

(77)



31.

NORDSTROM ET AL.


407

Table 2. Summary of Revised Thermodynamic Data. IV. Silicate Species ΔΗ, (kcal/mol)

Reaction

0

Si(OH) ° = SiO(OH) - + H 4

+

2

+

Si(OH) ° = Si0 (OH) ' + 2H 2

Mineral

Ref.

-9.83

(87)

6.12

3

4

log κ

17.6

2

-23.0

(88)

ΔΗ,

Reaction

0

log Κ

Ref.


(kcal/mol) Kaolinite

-35.3

+

Al Si 0 (OH) + 6H = 2A1* + 2Si(OH) ° + H 0 2

Chrysotile

2

5

4

4

+

2

2+

Mg Si 0 (OH) + 6H = 3Mg + 2Si(OH) ° + H 0 3

2

5

4

4

2

7.435

(a)

-46.8

32.20

(b)

-10.7

15.76

(c)

25.79

(20)

Sepiolite

Mg Si 0 (OH)-3H 0 + 4H + 0.5 H 0 = 2Mg + 3Si(OH) °

Kerolite

Mg Si O (OH) -H O + 6H + 3H 0 = 3Mg + 4Si(OH) °

-

Quartz

Si0 + 2H 0 = Si(OH) °

5.99

-3.98

(22)

Chalcedony

Si0 + 2H 0 = Si(OH) °

4.72

-3.55

(22)

Amorphous Silica SiQ + 2H 0 = Si(OH) °

3.34

-2.71

(22)

+

2

3

75

2+

2

2

+

3

4

10

2

2

Si(OH) ° = SiO(OH) - + H

+

3

4

4

4

2

Reaction

4

2

2

2

2+

2

2

2

4

4


Ref.

logiq = -302.3724 - 0.050698T + 15669.69/T + 108.18466 log Τ - 1119669/Γ

(87)

1ο β = -294.0184 - 0.072650T + 11204.49/T + 108.18466 log Τ - 1119669/T

(88)

logKcHRYSOT^ = 13.248 + 10217.1/T - 6.1894 log Τ

(b)

(22)

2

2

+

Si(OH) ° = Si0 (OH) " + 2H 4

2

2

δ

2

2

+

Mg Si 0 (OH) + 6H = 3Mg + 2Si(OH) ° + H 0 3

2

$

4

2+

4

2

Si0 + 2H O = Si(OH) °

logKQ

Si0 + 2H 0 = Si(OH) °

logKcHALCEDo^ = -0.09 - 1032/Γ

(22)

Si0 + 2H 0 = Si(OH) °

logK^oRpHo^

(22)

2

2

2

z

4

2

2

4

4

U A R T C

= 0.41 - 1309/T

S I L I C A

= -0.26 - 731/Γ

References for silicate species a.) (41) for log K, (26) for enthalpy; b.) log K, obtainedfrom(89) data after conversion using our equation and least squares fitting, is consistent with (26) data; c.) log Κfrom(20); ΔΗ, obtainedfrom273373 Κ fit of (2Q) data. 0

References for carbonate species a.) (26). using ion valuesfrom(23): b.) from Helgeson et al. (83) using ion values of (23): c.) log Κ of Smith (84) recalculated using the present aqueous model at 303 K, adjusted to 298 Κ using ΔΗ, calculated using ion valuesfrom(23) and Robie et al. (85) for solid; d.) Singer and Stumm (86) recalculated to be consistent with the present aqueous model; e.) log ΚfromGarrels et al. (82) and Δ ϊ ^ from (23) and Robie et al. (85) for the solid. 0

0



408


Table 2. Summary of Revised Thermodynamic Data. V. Sulfate Species Δ Η ,

Reaction

1 ogK

0

Ref.

+

2

H + SO, " = HS0 -

1.988

....

0.64

Na + S0 " = NaSO/

1.12

0.70

κ + so - = K S O -

2.25

0.85

1.65

2.30

2

Li +S0 ' = LiS0 " 4

4

+

2

4

+

2

4


4

2+

2

Ca + S0 - = CaSO 4

2+

Mg + S0 2

0

4

2

= MgSO

4

0

4

2

Sr * + S0 " = SrS0 ° 4

2+

4

2

Ba + S0 " = BaSO 4

2+

0

4

2

Ra + S0 " = RaSO 4

0

4

Mineral

Ref.

3.37

2.25

(22)

3.23

2.25

(c)

...

1.08

(102)

3.91

4.04

(c)

4.60

5.38

(c)

...

2.48

(102)

2.15

3.02

(54)

2.84

4.92

(54)

...

0.46

(104)

0

(kcal/mol)

3.85

4

+

log Κ

ΔΗ,

Reaction

(kcal/mol) 0

(21)

Mn + S0 " = MnSO

(52)

= FeSO Fe + S0 " =

(a)

Fe + HS0 " = FeHS0

(b)

= FeS0 Fe* + S0 " =

(26)

Fe* + 2S0 " = Fe(S0 )

2+

2

4

4

2+

0

2

4

4

+

2+

4

4

4

+

2

4

2

4

4 2

4.55

2.37

(22)

Fe* + HS0 - = FeHS0

2.08

2.29

(28)

Al* + S0 " := A1S0

...

2.7

(52)

Al* + 2S0 " = A1(S0 ) -

1.3

2.75

(66)

Al* + HS0 - = A1HS0

4

2

2+ 4

+

4

4

2

4

4 2

4

2+ 4

ΔΗ,

Reaction

log Κ

Ref.

-0.109

-4.58

(d)

-1.71

-4.36

(d)

-1.037

-6.63

(106)

6.35

-9.97

(d)

9.40

-10.26

(66)

0

(kcal/mol) Gypsum

2+

2

CaS0 -2H 0 = Ca + S0 " + 2H 0 4

2

4

Anhydrite

CaS0 = Ca + S0 "

Celestite

SrS0 = Sr * + S0 "

2+

2

2

4

4

2

2

4

4

Β ante

BaS0 = Ba + S0 "

Radium sulfate

RaS0 = Ra + S0 "

2+

2

4

4

2+

2

4

4

Melanterite

FeS0 -7H 0 = Fe + S0 " + 7H 0

Alunite

KA1 (S0 ) (0H) + 6H = K + 3A1* + 2S0 ' + 6H 0

2+

4

2

4

4 2

2

H + S0 " = HS0 " 4

4

2

2

4

2+

2

2

CaS0 = Ca + S0 " 4

2

SrSQ = Sr * + S0 ' 4

4

2

-50.25

-2.209

(107)

-1.4

(e)


Ref.

logK = -56.889 + 0.006473T + 2307.9/T + 19.8858 log Τ

(21)

logKoypsuM 1ο

4

2

2

2

2+

CaS0 -2H 0 = Ca + S0 ' + 2H 0 4

+

6

Reaction +

2

+

3

4.91

2

4

= 68.2401 - 3221.51/T - 25.0627 log Τ

8 ΑΝΗΥΙ»ΠΈ = !97.52 - 8669.8/T - 69.835 log Τ κ

(d) (d)

logKcELEsrrrE = -14805.9622 - 2.4660924T + 756968.533/Γ - 40553604/T + 5436.3588 log Τ

(106)

logK

(d)

2

2+

2

BaS0 = Ba + S0 ' 4

4

2+

2

RaS0 = Ra + S0 ' 4

2

FeS0 -7H 0 = Fe + S0 " + 7H 0 4

2

= 136.035 - 7680.41/T - 48.595 log Τ

logK^so, = 137.98 - 8346.87/T - 48.595 log Τ

4

2+

BARITB

4

2

logKj^gLAj^pEjyyg

= 1.447 - 0.004153T - 214949/1*

(66) (107)

References for sulfate species a.) log Κ from Rhiealetto and Davies (22), Δ Η , from Austin and Mair (23); b.) log ΚfromTruesdell and Hostetler (24), Δ Η , ° from Siebert and Christ (25) refitting of (24); c.) log Κ values are in good agreement between (52), (25) and Stipp (103): enthalpies are derivedfromthe Fuoss fitting method of Siebert and Christ (25) except for the iron(m) sulfate ion triplet which assumes a value equivalent to that for the aluminum sulfate ion triplet; d.) Langmuir and Melchior (33), where the gypsum data is refitted from Blount and Dickson (105) and is in excellent agreement with the highly precise data of Lilley and Briggs (32) at 298 K; e.) log ΚfromAdams and Rawajfih (100) and Δ Η , calculatedfromenthalpies of formation found in Kelley et al. (101) and Robie et al. (26). 0

0





409

be c l e a r — one i s needed t o d e t e r m i n e t h e t e n d e n c y f o r mineral s o l u b i l i t y c o n s t r a i n t s on water c o m p o s i t i o n and t h e o t h e r i s needed t o d e s c r i b e mass t r a n s f e r s o u r c e s and s i n k s i n a g e o c h e m i c a l l y r e a c t i n g flow system (44). It may a l s o be argued t h a t the s i m u l a t i o n of water-rock interactions should allow for solubility equilibria involving f e l d s p a r s , micas, e t c . F o r such s t u d i e s t h e c h o i c e o f s o l u b l i t y p r o d u c t c o n s t a n t s and f r e e e n e r g i e s must and s h o u l d be made by t h e investigators. We cannot p r o p o s e such v a l u e s here when an enormous range o f v a l u e s and p r o p e r t i e s ( s o l i d - s o l u t i o n s , interlayering, d e f e c t s , s u r f a c e a r e a s , e t c . ) i s known t o e x i s t f o r t h e s e m i n e r a l s and r e v e r s i b l e s o l u b i l i t y b e h a v i o r has n o t been d e m o n s t r a t e d . A b r i e f summary o f t h e s t a t u s o f t h e thermodynamic p r o p e r t i e s for water-mineral r e a c t i o n s u s i n g t h e i o n - a s s o c i a t i o n t h e o r y and r e v i s e d data i s : 1.

These computations a r e r e l i a b l e f o r t h e range O-100'C and up t o 1 m o l a l i o n i c s t r e n g t h f o r major u n i v a l e n t and d i v a l e n t i o n s , a l i m i t e d s e t o f minor and t r a c e elements, and i r o n and manganese redox s p e c i e s .

2.

M a j o r c a r b o n a t e m i n e r a l s o l u b i l i t i e s and t h e i r a s s o c i a t e d i o n p a i r s a r e r e l i a b l e except f o r d o l o m i t e , s i d e r i t e and r h o d o c r o s i t e , f o r which ranges o f Ksp v a l u e s a r e e s t i m a t e d .

3.

Oxide and h y d r o x i d e s o l u b i l i t i e s a r e g e n e r a l l y r e l i a b l e f o r c a l c i u m , magnesium, aluminum and i r o n , b u t t h e Ksp v a l u e s can range over s e v e r a l o r d e r s o f magnitude d e p e n d i n g on degree o f c r y s t a l l i n i t y , e s p e c i a l l y p a r t i c l e s i z e a f f e c t s . There are continuing controversies regarding the a c t u a l r e a c t i v e phases b e i n g measured i n s o l u b i l i t y s t u d i e s , and f u r t h e r r e f i n e m e n t s have been p r o p o s e d (^5), ^ 6 ) .

4.

Quartz, kaolinite, chrysotile, sepiolite and kerolite s o l u b i l i t i e s a r e r e l i a b l e f o r estimates i n chemical modeling a t low t e m p e r a t u r e s . Ksp v a l u e s f o r t h e s e m i n e r a l s a r e a l s o strongly i n f l u e n c e d b y degree of crystallinity. Other s i l i c a t e m i n e r a l s o l u b i l i t i e s a r e e i t h e r u n r e l i a b l e , o r do not describe the behavior o f these minerals i n natural waters.

5.

Common s u l f a t e m i n e r a l s o l u b i l i t i e s and t h e i r a s s o c i a t e d i o n p a i r s a r e r e l i a b l e w i t h i n o t h e r r e s t r i c t i o n s o f t h e model.

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