Chemical Modeling in Aqueous Systems - ACS Publications

36

WATEQ2—A and

Computerized Chemical

M a j o r E l e m e n t Speciation a n d

of N a t u r a l

Model

Mineral

for

Trace

Equilibria

Waters

JAMES W. BALL and EVERETT A. JENNE

Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: March 19, 1979 | doi: 10.1021/bk-1979-0093.ch036

U.S. Geological Survey, Water Resources Division, Menlo Park, CA 94025 DARRELL KIRK NORDSTROM Department of Environmental Sciences, University of Virginia, Charlottesville, VA 22903 The p r o t e c t i o n of ecosystems, upon which our h e a l t h and l i v e s depend ( 1 ) , r e q u i r e s that we understand n a t u r a l processes and develop the c a p a b i l i t y to p r e d i c t the e f f e c t of changes, such as the a d d i t i o n of p o l l u t a n t s , on these ecosystems. The p r e d i c t i o n of trace-element behavior i n ecosystems r e q u i r e s a multicomponent model by which one can: 1) c a l c u l a t e aqueous s p e c i a t i o n of the t r a c e elements among both n a t u r a l organic and i n o r g a n i c l i g a n d s ; 2) evaluate s o l u b i l i t y hypotheses: 3) account f o r s o r p t i o n d e s o r p t i o n processes; and 4) i n c o r p o r a t e chemical k i n e t i c s . This paper documents a chemical model that p a r t i a l l y accomplishes the f i r s t two of these four g o a l s . The present model has evolved from WATEQ, the e a r l i e r water-mineral e q u i l i b r i a model w r i t t e n i n P l / 1 by T r u e s d e l l and Jones (2, 3), and from WATEQF, the F o r t r a n v e r s i o n of Plummer et a l . ( 4 ) . These models, i n t u r n , drew on the preceding model of Barnes and C l a r k e ( 5 ) . The r e l a t e d PL/1 model, SOLMNEQ (6) , drew on the models of Barnes and C l a r k e (5) and a p r e p u b l i c a t i o n v e r s i o n of T r u e s d e l l and Jones (2) as w e l l as the thermodynamic data treatment of Helgeson (7) and Helgeson et_ a l . ( & ) . The WATEQ program contains an extensive thermodynamic data base which was c a r e f u l l y s e l e c t e d f o r use w i t h low-temperature n a t u r a l waters (9, 2 ) . A c t i v i t y c o e f f i c i e n t s f o r the major ions are c a l c u l a t e d from a computer f i t of an extended Debye-Huckel equation c o n t a i n i n g two a d j u s t a b l e parameters (2, 3_) . These a c t i v i t y c o e f f i c i e n t s are considered more r e l i a b l e than the standard Debye-Huckel equation or the Davies equation f o r 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 (up to 1-3 m o l a l ) . The method of c a l c u l a t i o n i n WATEQ i s b a c k - s u b s t i t u t i o n f o r the c a t i o n s and successive approximation f o r the anions w i t h convergence on mass balance f o r anions. WATEQF changed to the more r a p i d backs u b s t i t u t i o n method f o r anion mass balance convergence. I n a d d i t i o n , manganese s p e c i a t i o n i s included i n WATEQF, and an o p t i o n f o r c a l c u l a t i n g a c t i v i t y c o e f f i c i e n t s by e i t h e r the Debye-Huckel or the Davies equation i s provided. WATEQ2 r e t a i n s most of these f e a t u r e s , and a d d i t i o n a l m o d i f i c a t i o n s are explained below.

0-8412-0479-9/79/47-093-815$05.25/0 This chapter not subject to U.S. copyright Published 1979 American Chemical Society Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


816

CHEMICAL

MODELING IN AQUEOUS

SYSTEMS

We have added ten a d d i t i o n a l elements (Ag, As, Cd, Cs, Cu, Mn, N i , Pb, Rb, and Zn), complexes of Br and I , s e v e r a l metastable s o l i d s , some s p a r i n g l y s o l u b l e s a l t s , and s e v e r a l i o n p a i r s of major c o n s t i t u e n t s t o the model. Other changes i n c l u d e r e o r g a n i z a t i o n of the computer code i n t o a s e r i e s o f e x t e r n a l sub r o u t i n e s and changing the mode of convergence t o decrease the number o f i t e r a t i o n s r e q u i r e d . Because of the i n t e r a c t i v e nature o f aqueous s o l u t e s p e c i a t i o n c a l c u l a t i o n s , i t would be d e s i r a b l e t o enter a t once i n t o the chemical model the r e a c t i o n s and thermodynamic data f o r a l l elements whose i n c l u s i o n might a f f e c t the computed a c t i v i t y o r e q u i l i b r i u m s o l u b i l i t y o f other s o l u t e s p e c i e s . However, our experience i s that the g r e a t e s t r e l i a b i l i t y i s obtained by adding only the data f o r one element, or f o r one l i g a n d group, a t a time; then t e s t data s e t s and r e a l world water sample analyses are r u n before making f u r t h e r a d d i t i o n s t o or changes i n the model. Various a s s o c i a t e s , whom we have f r e q u e n t l y c a l l e d on f o r s p e c i a l i z e d knowledge and i n f o r m a t i o n , have m a t e r i a l l y a s s i s t e d i n t h i s modeling e f f o r t . C o l l a b o r a t i v e s t u d i e s have o f t e n pro vided the impetus t o add some s p e c i f i c element, l i g a n d group, o r group of s o l i d phases t o the model. Apparent oversaturâtion w i t h one or more s o l i d phases o f an element has o f t e n prompted us t o seek out and add data f o r a d d i t i o n a l s o l u t e complexes o r more s o l u b l e s o l i d phases. The p a r t i t i o n i n g of an unexpectedly l a r g e p o r t i o n of an element i n t o a p a r t i c u l a r complex has l e d us to make an expanded c o m p i l a t i o n f o r the complex or t o c o n s u l t w i t h colleagues t o a s s i s t i n s e l e c t i n g best v a l u e s . Colleague c r i t i c i s m s ( c o n s t r u c t i v e and k i n d f o r the most p a r t ) of s t u d i e s i n press and i n p r e p a r a t i o n have prompted us to make s p e c i f i c t e s t s and proceed immediately w i t h some change o r a d d i t i o n , which would otherwise have awaited a "more opportune time." L. N. Plummer provided frequent c o n s u l t a t i o n and s u p p l i e d a p r e p u b l i c a t i o n copy of the r e a c t i o n s and a s s o c i a t e d thermodynamic data f o r the man ganese s e c t i o n of the WATEQF chemical model ( 4 ) . B. F. Jones and A. H. T r u e s d e l l have a l s o been p a r t i c u l a r l y h e l p f u l on many occasions. I n our e f f o r t t o c o l l e c t the appropriate data and develop the r e q u i s i t e understanding of geochemical processes, we have developed some adjunct computer programs. These i n c l u d e AACALC (Atomic Absorption and emission spectrometry CALCulation), EQLIST ( E Q u i l i b r i u m computation L I S T i n g ) , and EQPRPLOT ( E Q u i l i b r i u m computation P R i n t i n g and PLOTing). AACALC (FORTRAN) reduces atomic a b s o r p t i o n o r emission spectrometry data t o c o n c e n t r a t i o n s , EQLIST (PL/1) c o n s t r u c t s t a b l e s from the WATEQ2 (input) card f i l e , and EQPRPLOT (FORTRAN) c o n s t r u c t s r a t i o and s c a t t e r p l o t s o f d i s s o l v e d c o n s t i t u e n t s , a c t i v i t y products (AP), o r a c t i v i t y product to s o l u b i l i t y product r a t i o s (AP/K) v i a computer t e r m i n a l p r i n t e r or tape-driven p l o t t e r .

Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

BALL

36.

817

Computerized Chemical Model

ET AL.

A d d i t i o n s and M o d i f i c a t i o n s to the Model


The thermochemical r e a c t i o n values vary according to the way the r e a c t i o n i s w r i t t e n . Therefore, a l l r e a c t i o n s i n the present model which have been added o r r e v i s e d , together w i t h the s e l e c t e d thermochemical v a l u e s , and o p e r a t i o n a l i n f o r m a t i o n t o f a c i l i t a t e input and output of the data, are a v a i l a b l e i n an adjunct r e p o r t (10). Elements. Rather l a r g e sets of s o l u t e complexes and m i n e r a l phases have been added f o r Ag, As, Cd, Cu, Mn, N i , Pb, and Zn. A d d i t i o n a l l y , Cs and Rb have been added t o the model. The merit of i n c l u d i n g Cs and Rb i n the model, i n s p i t e o f the near absence of s o l u t e complexes o r pure s o l i d s , i s that i n the f u t u r e the a c t i v i t i e s of the uncomplexed a l k a l i metal ions can be used t o compute t h e i r probable s u b s t i t u t i o n i n t o c e r t a i n s i l i c a t e minerals and to examine ion-exchange processes. Alkali metals complex w i t h 0H~, CI , and NO3 only a t such high i o n i c strengths that the b a s i c assumptions of a multicomponent i o n a s s o c i a t i o n model are no longer v a l i d . I n a d d i t i o n , thermodynamic data f o r these complexes are h i g h l y u n c e r t a i n . For these reasons, such complexes have been dropped from the model. S i m i l a r l y , there are data o n a l k a l i metal compounds such as Rb2S which might have been i n c l u d e d . However, the pure a l k a l i metal s u l f i d e s a r e known t o be h i g h l y unstable and/or deliquescent (11) and a r e r a r e l y found as m i n e r a l s . Therefore, they have not been i n c l u d e d i n the model. The manganese s e c t i o n s of WATEQF (4) were h e a v i l y u t i l i z e d i n preparing a s i m i l a r s e c t i o n f o r WATEQ2 (10). The s o l u t e por t i o n was u t i l i z e d i n i t s e n t i r e t y , b u t the MnOH"" and Mn(0H) a s s o c i a t i o n r e a c t i o n s were expressed i n terms o f H2O and H*" i n s t e a d o f OH , and the HMn0 complex, a d u p l i c a t i o n o f the Mn(0H)3 complex, was excluded. The f o l l o w i n g subset of the m i n e r a l species was s e l e c t e d : p y r o l u s i t e , b i r n e s s i t e , n s u t i t e , b i x b y i t e , hausmannite, p y r o c h r o i t e , manganite, r h o d o c h r o s i t e , M n C l 2 ' 4 H 2 0 , MnS(green), MnSO^, M n ( S O ) , Μ η ( Ρ 0 ) and MnHP0 . The f o l l o w i n g subset was excluded: MnO, M n ( 0 H ) , M n C l , MnCl2-H 0, Μη01 ·2Η 0, M n 2 S i 0 i and M n S i 0 . To the s e l e c t e d set were added s i x minerals f o r which thermochemical data are unknown, i n order t o o b t a i n l o g AP values of the i n d i v i d u a l minerals f o r d i f f e r e n t waters. The s i x minerals are^_ cryp£omelane (Ko^Mnf^gMn^ O^y), h o l l a n d i t e 1

3

2

2

i+

3

3

4

3

+

2

2

2

2

3

(Bao,78

F e

§.57

M n

6.59

M n

^ ° 1 6 ) > psilomelane

(Ba [ C a * 1 gK 1 ^ ί η Ί Α η ^ 0 2

0

4

2

7 8

0

0 #0

ι6

· 2. 5H 0) , t o d o r o k i t e 2

( 0 . 3 9 3 g 0 . 4 7 3 ? t l 3t+Mn^ 0 ·2Η 0) , l i t h i o p h o r i t e ( L i 2 A l M n i M n ^ 0 5 - 1 4 H O ) , and r a n c i e i t e (Ca^ Mn^ Μηίί 0 -3H 0). Ca

M

Mn

+

12

2

+

8

+

3

2

h

56

9

2

Aqueous Complexes. A l l s o l u t e r e a c t i o n s are w r i t t e n as a s s o c i a t i o n (formation) r e a c t i o n s whereas the s o l i d r e a c t i o n s a r e w r i t t e n as d i s s o c i a t i o n ( d i s s o l u t i o n ) r e a c t i o n s . For mass



818

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS

b a l a n c i n g purposes, a l l s o l u t e r e a c t i o n s are w r i t t e n i n terms of the f r e e form of the parent s p e c i e s , so t h a t a l l constants are f o r o v e r a l l r a t h e r than stepwise r e a c t i o n s , P o l y s u l f i d e s and S u l f i d e . The p o l y s u l f i d e complexes of Ag and Cu have been added to the model i n an attempt to reduce the apparent o v e r s a t u r a t i o n w i t h Ag2S(s) c a l c u l a t e d f o r San Fran c i s c o Bay waters (12). C a l c u l a t i o n of the a c t i v i t y of p o l y s u l f i d e ions r e q u i r e s the assumptions: 1) the q u a n t i t y of Sg ( f r e e _ s u l f u r ) i s not a l i m i t a t i o n on i t s r e a c t i o n w i t h b i s u l f i d e (HS ) to form p o l y s u l f i d e s ; and 2) p o l y s u l f i d e s are i n e q u i l i b r i u m w i t h bisulfide. I n a d d i t i o n to the s u l f i d e complexes of the added t r a c e elements, the Fe(HS)2 and Fe(HS)3 complexes (13) have been i n cluded to i n c r e a s e the r i g o r of the s u l f i d e s p e c i a t i o n . The s u l f i d e r e a c t i o n s have been r e w r i t t e n i n terms of HS r a t h e r than S s i n c e HS i s the dominant s u l f i d e i o n i n most waters. S u l f a t e . V a r i o u s p u b l i s h e d v a l u e s f o r the a s s o c i a t i o n constants and a s s o c i a t i o n e n t h a l p i e s of metal s u l f a t e i o n p a i r s and t r i p l e t s (14, 15, 16, 17) show good agreement _(± 10%) except f o r NaSOi4. Log Κ v a l u e s f o r the formation of NaSOi4 range from the 0.226 v a l u e of Lafon and T r u e s d e l l (18) to the 1.17 v a l u e of Pytkowicz and Rester (19), as c i t e d by F i s h e r (20). I f the one low v a l u e of Lafon and T r u e s d e l l (18) and the h i g h values of F i s h e r and Fox (21) and F i s h e r (20) are dropped, the remaining four v a l u e s average 0.70 + 0.05 (22, 23, 24, 25) which i s i d e n t i c a l to the v a l u e s e l e c t e d by Smith and M a r t e l l (26), who may have used the same e v a l u a t i o n technique. G. M. Lafon (Johns Hopkins U., personal communication, 1978) has suggested t h a t the low v a l u e should be discounted and t h a t the formation of a sodium s u l f a t e i o n t r i p l e t i s u n l i k e l y . Most of the other a s s o c i a t i o n constants were obtained from R. M. S i e b e r t and C. L. C h r i s t ( C o n t i n e n t a l O i l Co., U. S. Geol. Survey, p e r s o n a l communication, 1976) a f t e r comparing t h e i r values w i t h those reported i n the l i t e r a t u r e . Enthalpy v a l u e s were a l s o s e l e c t e d from the p r e l i m i n a r y data of R. M. S i e b e r t and C. L. C h r i s t which had been evaluated by the Fuoss equation (27). C a r e f u l checking w i t h published l i t e r a t u r e values showed no s e r i o u s d i s c r e p a n c i e s and i t was f e l t that u s i n g data from one source would help m a i n t a i n i n t e r n a l c o n s i s t e n c y . The i o n t r i p l e t Fe(S0i )2 was one e x c e p t i o n . The l o g Κ f o r t h i s com p l e x i s the average of the r e s u l t s of I z a t t et a l . (25) and Mattoo (28) which d i f f e r by l e s s than 1%. The enthalpy of a s s o c i a t i o n has not been p u b l i s h e d but i t has been estimated by assuming t h a t the d i f f e r e n c e between i t and FeS0"t i s equal to the d i f f e r e n c e between Α 1 ( 8 0 ) and A1S04. Although the r e l i a b i l i t y of t h i s e s t i m a t i o n cannot e a s i l y be determined, i t c e r t a i n l y i s b e t t e r than assuming ΔΗ = 0. F l u o r i d e . For e q u i l i b r i u m c a l c u l a t i o n s i n a c i d s o l u t i o n s , s t a b i l i t y constants are needed f o r HF0 H F 2 , and ( H F ) s p e c i e s . These species become important when the pH drops below 4.5 and f l u o r i d e c o n c e n t r a t i o n r i s e s above 5 χ 10 M. S e v e r a l 2

+

4

2

2

-4



BALL ET AL.

36.

819

measurements have been made on the d i s s o c i a t i o n of HF° a t 298.15°K and the agreement i s e x c e l l e n t (29-37). The weighted mean value of l o g Κ = 3.169±0.010 (1σ, unweighted) given i n B a l l e t a l . (10) was c a l c u l a t e d from these i n v e s t i g a t i o n s a f t e r dropping the high value of P a t e l e t a l . (34) and the low value of V a s i l e v and K o z l o v s k i i (37) which i s necessary i n order to m a i n t a i n con s i s t e n c y w i t h the k i n e t i c data of Kresge and Chiang (_38, 39) . For the r e a c t i o n : T


HF°

+

F~

t

HF~

CI)

the s t a b i l i t y constant has a l a r g e r u n c e r t a i n t y owing t o the competing HF° a s s o c i a t i o n e q u i l i b r i u m . Reported l o g Κ values range from 0.49 t o 0.70 (29, 30, 32, 33, 35, 36) and the weighted mean value i s 0.58 ± 0.05. Aqueous HF dimers have been shown t o e x i s t by Warren (35) who measured a l o g Κ of 0.43 ± 0.05 f o r the r e a c t i o n : 2HF°

t

(HF)°.

(2)

Enthalpy values f o r the c a l c u l a t i o n o f temperature dependence are not a v a i l a b l e f o r r e a c t i o n 2. The l o g Κ f o r the d i s s o c i a t i o n of HF° and f o r r e a c t i o n 1 have been measured between 0 and 100°C by Broene and DeVries (29), E l l i s (30) and Hamer and Wu (33). V a s i l ' e v and K o z l o v s k i i (37) have a l s o obtained enthalpy data f o r these r e a c t i o n s by c a l o r i m e t r i c t i t r a t i o n . The average ΔΗ = -3.46 ±0.75 k c a l m o l " f o r HF° d i s s o c i a t i o n and ΔΗ = 1.09 ± 0.30 k c a l mol f o r r e a c t i o n 1. S i l i c a t e m i n e r a l s are more s o l u b l e i n n a t u r a l waters having high f l u o r i d e c o n c e n t r a t i o n s and low pH values than i n other waters. High c o n c e n t r a t i o n s of d i s s o l v e d s i l i c a may be maintained by the formation of h e x a f l u o r o s i l i c i c a c i d : 1

1

0

+

S i (OH). + 6F" + 4 H ? S i F ^ " 4 6

+ 4H 0. 2

(3)

o

The e q u i l i b r i u m constant f o r t h i s r e a c t i o n has been measured a t 25°C by Roberson and Barnes (40) and the enthalpy i s estimated from the data of Wagman et_ a l . (41). Reaction 3 i s important i n many a p p l i c a t i o n s : a) chemical processes i n v o l v i n g v o l c a n i c gases and condensates (40), b) chemical r e a c t i o n s i n a c i d , h a l o g e n - r i c h hot s p r i n g s (42, 43), c) waters r e c e i v i n g e f f l u e n t from phosphate processing p l a n t s (44), d) f l u o r i d a t i o n of water s u p p l i e s (45), e) a n a l y t i c a l chemistry, such as i n the d e t e r m i n a t i o n of e i t h e r f l u o r i d e or d i s s o l v e d s i l i c a (46) and f ) the formation and hydrothermal a l t e r a t i o n of ore d e p o s i t s (47., ^8» 49). The l o g Κ and ΔΗ f o r the formation of the aqueous_complexes CaF , F e F , FeF^, F e F , B F ( 0 H ) , B F ( 0 H ) and BF (OH) have been evaluated by Nordstrom and Jenne (50) and are i n good agree ment w i t h those s e l e c t e d by Smith and M a r t e l l (26) who used a d i f f e r e n t e v a l u a t i o n procedure. This a d d i t i o n to WATEQ2 +

2 +

3

3

2

2

3



820

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS

makes a f a i r l y complete inventory of aqueous f l u o r i d e complexes. N e u t r a l and Polymeric Aluminum and I r o n . The a s s o c i a t i o n constants and e n t h a l p i e s of aluminum and i r o n hydrox ides have been evaluated by comparing the c r i t i c a l l y s e l e c t e d data of Baes and Mesmer (51) w i t h that of R. M. S i e b e r t and C. L. C h r i s t (personal communication, 1976). D i f f e r e n c e s between the two data s e t s are n e g l i g i b l e and the f i n a l s e l e c t i o n was from Baes and Mesmer (51) because data on more complexes are found there. Important new species added to tljie model are the polynuclear complexes Fe2(0H)2 and Fe3(0H)5+4 . Some controversy has a r i s e n over the e x i s t e n c e of Fe(0H)3 and A1(0H)3. Baes and Mesmer (51) have i n d i c a t e d that although the formation constant of A1(0H)§ i s o n l y known from one measurement (52) and has a l a r g e u n c e r t a i n t y , i t i s r e a l , with a log Κ -15.0 f o r the r e a c t i o n

Al

3 +

+ 3H 0

+

A1(0H)

2

+ 3H .

(4)

Baes and Mesmer (51) a l s o suggest that the l o g Κ f o r Fe

3 +

+ 3H 0

Fe(0H)

2

+ 3H

+

(5)

i s l e s s than -12 and t h i s agrees w i t h the g e n e r a l l y accepted value of -13.6 (53). Recently, Byrne (54) and Kester et a l . (55) have presented evidence f o r the e x i s t e n c e of Fe(0H) and r e confirmed the v a l u e of the l o g K. We have t h e r e f o r e included both n e u t r a l species i n the model. Others. E q u i l i b r i u m a s s o c i a t i o n constants c a l c u l a t e d from f r e e energy data (41) f o r two aqueous a r s e n i c f l u o r i d e s p e c i e s , As0 F and HAs0 F , were so h i g h that the two species accounted f o r v i r t u a l l y a l l the A s i n s e v e r a l water samples, p r a c t i c a l l y i r r e s p e c t i v e of the f l u o r i d e c o n c e n t r a t i o n . The E c a l c u l a t e d from the a c t i v i t i e s of A s and As5+ under these c o n d i t i o n s was near -4 v o l t s , i . e . w e l l below that at which water decomposes (0 to -0.83 v o l t s from pH 0 to 14). From the o r i g i n a l data of Dutt and Gupta (56) the l o g Κ = 2.832 f o r 2

3

3

5 +

H

3 +

H As0 3

+ F" = HAs0 F" + H 0 3

(6)

2

and l o g Κ = -3.037 f o r 2

H3AsO4 + F" = A s 0 F " + H

+

+ H20 .

(7)

Thus, there appears to have been a computational e r r o r i n con v e r t i n g the s t a b i l i t y data of Dutt and Gupta (56) to standard f r e e energies of formation. E q u i l i b r i u m l o g K£ values c a l c u l a t e d from f r e e energy data (41) f o r two lead hydroxychlorides (PbOHCl, Pb2(0H) Cl) d i d not agree w i t h those of the o r i g i n a l authors (57). However, r e v i s e d AG data (10) from NBS (B. R. S t a p l e s , N a t ' l Bur. Stand., personal 3



36.

BALL

ET AL.


821

communication, 1978) agree very w e l l w i t h the o r i g i n a l data. Organic Ligands. The model has been expanded to permit s e n s i t i v i t y analyses of n a t u r a l l y o c c u r r i n g organic l i g a n d s . These composite l i g a n d groups are r e f e r r e d to as f u l v a t e and humate. The model d e f a u l t s to molecular weights of 650 and 2000, r e s p e c t i v e l y , f o r these two l i g a n d groups. Reported molecular weights f o r these substances vary w i d e l y (S. A. Jacobs and E. A. Jenne, unpub. data, 1978). Therefore, i f a c o n c e n t r a t i o n f o r e i t h e r substance i s used as input data, without an accompanying a n a l y t i c a l l y determined molecular weight, a warning message i s p r i n t e d , and a l l p e r t i n e n t output data a r e f l a g g e d . Reported e q u i l i b r i u m constants f o r these m e t a l - l i g a n d complexes a l s o vary widely and should t h e r e f o r e be user s u p p l i e d . I n the absence of s u p p l i e d v a l u e s , the model d e f a u l t s t o data from Smith and M a r t e l l (26) f o r o x a l i c a c i d (10). S o l i d Phases. S u l f a t e s . S o l u b i l i t y product constants and f r e e energies of formation f o r the j a r o s i t e m i n e r a l group ( j a r o s i t e , n a t r o j a r o s i t e , and hydronium j a r o s i t e or c a r p h o s i d e r i t e , as the hydrogen form i s termed i n the o l d e r l i t e r a t u r e ) have been compiled by Nordstrom (58). Considerable d i s c r e p a n c i e s occur between d i f f e r e n t i n v e s t i g a t i o n s because the s o l u t i o n e q u i l i b r i a are very complicated: s e v e r a l strong complexes are formed and attempts a r e seldom made to account f o r the e f f e c t of hydroxide and s u l f a t e complexation of the c a t i o n s i n v o l v e d on apparent s o l u b i l i t y . There i s a l s o a l a c k of consistency between values f o r the j a r o s i t e s o l u b i l i t y product constant, p a r t l y because d i f f e r e n t complexes were used. Of the four i n v e s t i g a t i o n s made on j a r o s i t e , Browne r e s u l t s (59, 60) must be discounted because of very l a r g e u n c e r t a i n t i e s i n the r e s u l t s . A mean value of -98.80 + 1.1 f o r the log K has been s e l e c t e d f o r WATEQ2 from the works of Zotov e t a l . (61), Vlek et a l . (62) and Kashkai et a l . (63). I f the d i s s o l u t i o n r e a c t i o n i s w r i t t e n as: s p

6H

+

+

+ KFe (S0 ) ( 0 H ) (s) t K + 3 F e 3

2

3 +

+ 2S0^" + 6^0

(8)

then the l o g Κ i s -14.8 + 1 . 1 . The l o g Κ f o r n a t r o j a r o s i t e , w r i t t e n i n the same manner as r e a c t i o n 8, i s -11.2 + 1 . 0 from the work of G. C l i f t o n ( C o n t i n e n t a l M a t e r i a l Co., personal communication, 1977) and agrees w i t h the value obtained by Kashkai et a l . (63). Only one l o g Κ value i s a v a i l a b l e f o r hydronium j a r o s i t e (63) . The ΔΗ f o r the r e a c t i o n 8 has been estimated to be -31.28 k c a l m o l " by u t i l i z i n g the data of Zotov e t a l . (61) f o r the entropy of j a r o s i t e , the p r e v i o u s l y c i t e d i n v e s t i g a t i o n s f o r the mean AG° value and Wagman e t / a l ^ (41, 64) f o r the e n t h a l pies of the i o n s . The enthalpy f o r n a t r o j a r o s i t e d i s s o l u t i o n i s d e r i v e d from the entropy and f r e e energy values given by G. C l i f t o n (personal communication, 1977) and f o r hydronium j a r o s i t e a l i n e a r c o r r e l a t i o n between f r e e energies and e n t h a l p i e s was assumed f o r the j a r o s i t e group s i n c e no data a r e a v a i l a b l e . 1


822

CHEMICAL

MODELING IN AQUEOUS

SYSTEMS

We have observed m e l a n t e r i t e , FeSOi4· 7H 0 , to be one of the common s u l f a t e m i n e r a l s produced by the o x i d a t i o n of p y r i t e during weathering. U n f o r t u n a t e l y , i t s s o l u b i l i t y and r e l a t e d thermo dynamic p r o p e r t i e s are not w e l l e s t a b l i s h e d . The l o g Κ f o r m e l a n t e r i t e d i s s o l u t i o n has been d e r i v e d from the f r e e energies of formation of the c o n s t i t u e n t species and the g r e a t e s t source of u n c e r t a i n t y l i e s w i t h the AGf f o r F e . We p r e f e r the v a l u e of -21.8 ± 0.5 (65) which r e s u l t s i n a l o g Κ of -2,47. The enthalpv of d i s s o l u t i o n i s 2.86 k c a l m o l - based on ∆Ηf = -22.1 k c a l mol f o r Fe2+ from Larson and Hepler (65). The l o g Κ and ΔΗ values i n B a l l et a l . (10) f o r the d i s s o l u t i o n of epsomite have been obtained from the f r e e energy and enthalpy data given i n Wagman e t a l . (41) and Parker e t a l . (66). For the l o g Κ and ∆Η o f potassium alum s o l u b i l i t y , values were obtained from the f r e e energies and e n t h a l p i e s of Wagman et a l . (41) and K e l l y e t a l . (67). F l u o r i t e . The s o l u b i l i t y and r e l a t e d thermodynamic p r o p e r t i e s of f l u o r i t e have had l a r g e u n c e r t a i n t i e s , i . e . 2 to 3 orders of magnitude. Nordstrom and Jenne (50) u t i l i z e d s i m u l taneous m u l t i p l e r e g r e s s i o n a n a l y s i s (68) t o evaluate these thermochemical data. The r e v i s e d l o g Κ (10) agrees q u i t e w e l l w i t h the upper l i m i t of f l u o r i t e i o n a c t i v i t y product c a l c u l a t i o n s of many geothermal waters i n the western United S t a t e s . Although a t o t a l u n c e r t a i n t y of ± 0.5 was assigned t o the l o g Κ (to i n clude a n a l y t i c a l and computational e r r o r s ) , more recent i n v e s t i g a t i o n s i n d i c a t e that the l o g Κ f a l l s between -10.5 and -11.0 (69, 70, 71) so that the u n c e r t a i n t y i n the l o g Κ a t 298.15K i s ±0.25. At t h i s l e v e l of d e v i a t i o n the a n a l y t i c a l and computational u n c e r t a i n t i e s inherent i n the c a l c u l a t i o n s of the i o n a c t i v i t y product are l i k e l y to be g r e a t e r than those i n the thermodynamic properties. Other a l k a l i n e e a r t h f l u o r i d e s ( B a F , S r F ) have been added to the model. However, they are l e s s l i k e l y than t h e i r r e s p e c t i v e s u l f a t e s or carbonates t o be s o l u b i l i t y l i m i t i n g phases. Others. Thermochemical data f o r the f e r r o u s c h l o r i t e , g r e e n a l i t e ( F e S i 0 ( 0 H ) ) , and p h l o g o p i t e ( K M g l S i s O i 10(0H) ) d i s s o l u t i o n were taken from Plummer ejt a l . (4) who used the f r e e energy v a l u e s of Eugster and Chow (72) f o r g r e e n a l i t e and B i r d and Anderson (73) f o r p h l o g o p i t e . S o l u b i l i t y c a l c u l a t i o n s were added f o r two allophanes, f o r which the e q u i l i b r i u m constants and formulae are a f u n c t i o n of pH. Paces (74) found c o l d ground waters c o l l e c t e d from s p r i n g s i n g r a n i t i c rocks of the Bohemian M a s s i f of Czechoslovakia t o be supersaturated w i t h respect t o k a o l i n i t e w h i l e being unsaturated w i t h respect to amorphous s i l i c a . He i n t e r p r e t e d t h i s as an i n d i c a t i o n that a metastable a l u m i n o s i l i c a t e more s o l u b l e than k a o l i n i t e was c o n t r o l l i n g the c o n c e n t r a t i o n s of alumina and s i l i c a i n these waters. This a l u m i n o s i l i c a t e was f u r t h e r hypothe s i z e d to be of v a r i e d chemical composition, c o n t r o l l e d by the mole 2

2


1

2

3

2

5

2

4


2

36.

BALL


ET AL.

823

f r a c t i o n of s i l i c a and d i s s o l v e d by the r e a c t i o n : [Al(OH) ] 3

( 1 x )


(l-x)Al

3 +

[ S i 0 ] ( s ) + 3(l-x)H 2

+

x

+ xH SiO

+ (3-5x)H 0 .

4

(9)

2

In equation 9, x i s the mole f r a c t i o n of s i l i c a and i s equal t o 1.24 - 0.135pH. This expression d e s c r i b e s the l i n e a r v a r i a t i o n between pure amorphous hydrous alumina and s i l i c a as a f u n c t i o n of pH (75). The e q u i l i b r i u m constant f o r t h i s substance was c a l c u l a t e d by combining two endmember constants from the l i t e r a ture and i n c o r p o r a t i n g the pH-dependence equation i n t o the r e s u l t i n g e x p r e s s i o n , y i e l d i n g an expression f o r the e q u i l i b r i u m s o l u b i l i t y (75) of: l o g Κ = -5.7 + 1.68pH.

(10)

Under f i e l d c o n d i t i o n s the s o l u b i l i t y of t h i s m a t e r i a l should be lower due to the l a r g e d i f f e r e n c e i n the speed of c r y s t a l l i z a t i o n of amorphous alumina versus amorphous s i l i c a . In f a c t , a b e s t f i t l i n e to f i e l d samples from the S i e r r a Nevada i s described by the equation (75): log Κ = -5.4 + 1.52pH.

(11)

Copper f e r r i t e s have been i n c l u d e d i n the model, but have as yet not been found to be e q u i l i b r i u m c o n t r o l s on copper or i r o n s o l u b i l i t y . The c a l c u l a t e d a c t i v i t y products f o r the two m i n e r a l s , cuprous f e r r i t e and c u p r i c f e r r i t e , are c h a r a c t e r i s t i c a l l y s e v e r a l orders of magnitude oversaturated when compared to t h e i r respec t i v e e q u i l i b r i u m constants i n a wide v a r i e t y of surface waters. Ponnamperuma et_ a l . (76) d e s c r i b e a f e r r o s o f e r r i c hydroxide (Fe3(0H)s), o f f e r i n g evidence that most i r o n ( I I ) i n reduced s o i l s other than a c i d s u l f a t e s o i l s i s present i n t h i s form. Using a l o g Κ of 17.56 from Ponnamperuma et a l . (76) f o r the reaction: 2Fe(0H)(s) + F e J

2 +

+ 20H

_

Fe(0H)(s) J o

(12)

and l o g Κ values f o r the i o n i z a t i o n of water and f e r r i c hydroxide d i s s o l u t i o n , we c a l c u l a t e a l o g Κ of 20.222 f o r the r e a c t i o n : F e ( 0 H ) ( s ) + 8H J o

+

2Fe

3 +

+ Fe

2 +

+ 8H0 . Ζ

(13)

Biedermann and Chow (77) d e s c r i b e a f e r r i c h y d r o x y - c h l o r i d e ( F e ( O H ) 2 . 7 C l 0 3 ) which has been seen to p r e c i p i t a t e from sea water, having a log Κ of 3.04 + 0.05 (51) f o r the r e a c t i o n : Fe(0H)

2

7

C 1 ( s ) + 2.7H 3

+

Fe

3 +

+ 2.7H0 +

0.3Cl-.


(14)

824

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS

Chien and Black (78) c a l c u l a t e a l o g Κ of -114.4 f o r the fluorocarbonato a p a t i t e r e a c t i o n : C a

9.5Na 3 Mg i e

6

e l

+ l t

(C0 ) 3

l e 2

+

0.36Na + 0.144Mg

F

2 f l

2+

, (PO )i 8

l t

+ e 8

( s ) t 9.5Ca

2+

+

+ 1.2C0 + 2.48F~ + 4.8P0L*~ . 3

(15)

These r e a c t i o n s have been added to the model. Morey e_t a l . (79) have c a l c u l a t e d an e q u i l i b r i u m constant f o r amorphic s i l i c a which best f i t s t h e i r f i e l d data. The l o g Κ f o r t h i s r e a c t i o n of -2.71 has a l s o been added. Redox Couples. The model c a l c u l a t e s the redox p o t e n t i a l of the couples: H 0 / 0 , H 0 / 0 , F e / F e , N0 /N0 , S "/S0C , and A s / A s , given the r e q u i s i t e c o n c e n t r a t i o n s of the couple mem bers. D i s s o l v e d oxygen i s a l l that i s r e q u i r e d f o r c a l c u l a t i o n of both the H 0 / 0 and H 0 / 0 couples. The H 0 / 0 couple i s k i n e t i c a l l y i n h i b i t e d and i s g r o s s l y out of e q u i l i b r i u m except at elevated temperatures (80). Therefore, the o p t i o n of u s i n g pE from d i s s o l v e d oxygen f o r redox s p e c i a t i o n has been dropped from the model. Recent s t u d i e s (81) show that when the f o l l o w i n g three c o n d i t i o n s are f u l f i l l e d , the platinum e l e c t r o d e provides a r e l i a b l e and accurate estimate of the f e r r o u s - f e r r i c redox p o t e n t i a l , Fe /Fe ' drainage waters. The c o n d i t i o n s are: 1) l a r g e volumes of water must f l o w past the e l e c t r o d e s during emf measurement; 2) water samples must be p r o p e r l y f i l t e r e d (30%; 4) r e v i s e d anion mass balance c a l c u l a t i o n , a l l o w i n g f o r f a s t e r 2

+

2


BALL


36.


ET AL.

827

convergence; and 5) improved set of headings used i n the p r i n t e d r e s u l t s of the s o l u t e modeling c a l c u l a t i o n s . S p e c i f i c conductance c a l c u l a t e d from input major c o n s t i t u e n t data using the method of Laxen (83) has been added t o the model as a check on a n a l y t i c a l input data. D i f f e r i n g input and c a l c u l a t e d s p e c i f i c conductances i n d i c a t e that one or more e r r o r s may e x i s t i n the a n a l y t i c a l input data. A mass balance s e c t i o n f o r the hydrogen s u l f i d e species was added t o the anion mass balance c a l c u l a t i o n s when we observed that strong HS complexing of some t r a c e metals sometimes rendered c a t i o n mass balance convergence i m p o s s i b l e . A c t i v i t y c o e f f i c i e n t s were o r i g i n a l l y c a l c u l a t e d using the extended Debye-Huckel equation and whenever a new complex was added t o the program i t was necessary to estimate the a parameter. This problem was overcome by s u b s t i t u t i n g the more general Davies equation which has adequate r e l i a b i l i t y a t low i o n i c strengths and i s u s u a l l y more accurate a t high i o n i c strengths (84). Since a c i d mine waters can have i o n i c strengths approaching that of sea water, i t i s d e s i r a b l e to use a theory f o r a c t i v i t y c o e f f i c i e n t s that can reach somewhat above 0.1 m o l a l , the u s u a l upper l i m i t f o r extended Debye-Hiickel c a l c u l a t i o n s . The Davies equation i s considered s a t i s f a c t o r y to 0.5 m o l a l . The extended Debye-Huckel equation w i t h f i t parameters (2, 3) has been r e t a i n e d f o r the major i o n s , Ca, Mg, Na, K, CI and SO^, and the Debye-Huckel equation i s used t o c a l c u l a t e the p o l y s u l f i d e a c t i v i t y c o e f f i c i e n t s , f o r which a parameters have been estimated by Cloke (85). There are i n c o n s i s t e n c i e s i n the model f o r the c a l c u l a t i o n of a c t i v i t y products f o r the " c l a y s . " ^Exchangeable c a t i o n s are disregarded f o r the low exchange c a p a c i t y k a o l i n i t e , h a l l o y s i t e , c h l o r i t e , and moderate c a p a c i t y i l l i t e . For c e r t a i n expansible l a y e r s i l i c a t e s and two z e o l i t e s , the l o g i o a c t i v i t y of s e l e c t e d c a t i o n s i s added i n t o the sum of the a c t i v i t y products. The m i n e r a l phases treated i n t h i s manner, and the s o l u t e c a t i o n s considered as exchangeable c a t i o n s , are b e i d e l l i t e ([A ] i + A + + A +), c l i n o p t i l o l i t e and mordenite (A + + A +), B e l l e Fourche m o n t m o r i l l o n i t e and Aberdeen m o n t m o r i l l o n i t e (A + + A + + A +). Note that the square root of the d i v a l e n t c a t i o n i s used i n the sum i n keeping w i t h the p r a c t i c e i n the i o n exchange l i t e r a t u r e (86) . R e v i s i o n of the c a l c u l a t i o n of exchangeable c a t i o n c o n t r i b u t i o n to the a c t i v i t y product has been delayed pending the p e r t i n e n t reviews of K i t t r i c k (87), as w e l l as that of Bassett elt a l . (88) presented a t t h i s symposium. o f

t

n

e

2 +

M g

H

Na

Na

K

Na

K

K

M o d i f i c a t i o n s i n the Code The PL/1 language computer code has been e x t e n s i v e l y a l t e r e d i n the process of b u i l d i n g i t i n t o WATEQ2; i n f a c t , minor a l t e r a t i o n s are f a r too numerous to mention here. Several e r r o r s i n the o r i g i n a l code were c o r r e c t e d and some major changes, noted below, were made to improve program execution and ease of use



828

CHEMICAL

MODELING IN AQUEOUS

SYSTEMS

and to broaden i t s u s e f u l n e s s . The i n p u t and output aspects of program o p e r a t i o n are g i v e n , along w i t h the thermodynamic data base, i n a supplementary r e p o r t (10). Arrays which must be increased i n s i z e when species a r e added are now a u t o m a t i c a l l y a d j u s t a b l e i n dimension merely by supplying a p p r o p r i a t e input data. The r e s u l t s of s o l u t e and m i n e r a l c a l c u l a t i o n s w i l l not appear i f the a c t i v i t y o r a c t i v i t y product, r e s p e c t i v e l y , has not been c a l c u l a t e d . This e l i m i n a t e s extraneous non-information and shortens the l i s t i n g c o n s i d e r a b l y , an advantage e s p e c i a l l y when a simple l a b o r a t o r y s o l u t i o n i s considered and/or a low-speed remote computer t e r m i n a l i s utilized. Some data are entered i n t o the model as " c a r r i e d - o n l y " data, p r i m a r i l y f o r p l o t t i n g u s i n g a subsequent computer program. How ever, as the model evolves, some of these c a r r i e d - o n l y data be come input to the model i t s e l f o r t o adjunct c a l c u l a t i o n s . S p e c i f i c conductance, which was i n i t i a l l y c a r r i e d - o n l y data, i s now compared t o a computed " s p e c i f i c conductance" as a q u a l i t y o f - a n a l y s i s screening technique. The l i s t i n g o f the r e s u l t s of the m i n e r a l e q u i l i b r i u m c a l c u l a t i o n s has been d r a s t i c a l l y a l t e r e d , w i t h the d e l e t i o n of AG , AG per e q u i v a l e n t c a t i o n , and a l l v a l u e s i n base 10 form. Information now p r i n t e d f o r each species f o r which an a c t i v i t y product i s c a l c u l a t e d i n c l u d e s l o g AP/K, SIGMA ( A n a l y t i c a l ) , SIGMA (Thermodynamic), l o g A P / K ^ n , and l o g ΑΡ/Κ^χ. As discussed p r e v i o u s l y , SIGMA(A) i s the propagated standard d e v i a t i o n i n the a n a l y t i c a l values and SIGMA(T) i s the standard d e v i a t i o n i n the thermodynamic data. The l o g i o K i and logioKmax values have been changed from + 5% of the l o g i o K v a l u e (2) t o e x p e r i m e n t a l l y determined v a l u e s which may represent a l e s s s o l u b l e or more s o l u b l e form o f the s o l i d phase than that s e l e c t e d as the "best" v a l u e . WATEQ2 c o n s i s t s of a main program and 12 subroutines and i s patterned s i m i l a r l y to WATEQF ( 4 ) . WATEQ2 (the main program) uses input data to set the bounds of a l l major a r r a y s and c a l l s most of the other procedures. INTABLE reads the thermodynamic data base and p r i n t s the thermodynamic data and other p e r t i n e n t i n f o r m a t i o n , such as a n a l y t i c a l expressions f o r e f f e c t of tempera ture on s e l e c t e d e q u i l i b r i u m constants. PREP reads the a n a l y t i c a l data, converts concentrations t o the r e q u i r e d u n i t s , c a l c u l a t e s temperature-dependent c o e f f i c i e n t s f o r the Debye-Huckel equation, and t e s t s f o r charge balance of the input data. SET i n i t i a l i z e s values of i n d i v i d u a l species f o r the i t e r a t i v e mass action-mass balance c a l c u l a t i o n s , and c a l c u l a t e s the e q u i l i b r i u m constants as a f u n c t i o n of the input temperature. MAJ_EL c a l c u l a t e s the a c t i v i t y c o e f f i c i e n t s and, on the f i r s t i t e r a t i o n o n l y , does a p a r t i a l s p e c i a t i o n of the major anions, and performs mass a c t i o n mass balance c a l c u l a t i o n s on L i , Cs, Rb, Ba, Sr and the major c a t i o n s . TR_EL performs these c a l c u l a t i o n s on the minor c a t i o n s , Mn, Cu, Zn, Cd, Pb, N i , Ag, and As. SUMS performs the anion mass r

r

m

n


36.

BALL

ET

AL.


829

action-mass balance c a l c u l a t i o n s , and t e s t s the r e s u l t s _ a g a i n s t input c o n c e n t r a t i o n values f o r the anions C03~, S0^~, F , P0$ , CI and S , and p r i n t s the r e s u l t s of each set of i t e r a t i v e c a l c u l a t i o n s . MAJ_EL, TR_EL and SUMS are executed r e p e t i t i v e l y u n t i l mass balance to w i t h i n 0.1% of the input c o n c e n t r a t i o n s i s achieved f o r the s i x anions, or u n t i l 40 i t e r a t i o n s have elapsed. I f convergence i s not reached i n 40 i t e r a t i o n s , a warning message i s p r i n t e d and execution continues j u s t as through convergence had been reached. SOLUTES performs computations not r e l a t e d to the mass balance c a l c u l a t i o n s , such as E , s p e c i f i c conductance, pC^and pCH^ c a l c u l a t i o n s , p r i n t s out a l l the s o l u t e d a t a , and performs necessary l o g a r i t h m conversions f o r use i n subsequent c a l c u l a t i o n s . RATIO c a l c u l a t e s and p r i n t s mole r a t i o s c a l c u l a t e d from a n a l y t i c a l m o l a l i t y and l o g a c t i v i t y r a t i o s . APCALC c a l c u l a t e s thermodynamic a c t i v i t y products f o r the v a r i o u s m i n e r a l species considered by WATEQ2. OUTPNCH generates a card deck of a subset of the c a l c u l a t e d a c t i v i t i e s , a c t i v i t y products and i n put c o n c e n t r a t i o n s f o r subsequent use w i t h p l o t t i n g programs. ERRCALC, d i s c u s s e d p r e v i o u s l y , uses i n p u t a n a l y t i c a l standard d e v i a t i o n s to c a l c u l a t e the propagated standard d e v i a t i o n i n the log of the a c t i v i t y products f o r a subset of m i n e r a l s considered. PHASES p r i n t s the r e s u l t s of the a c t i v i t y product and e r r o r c a l c u l a t i o n s , and computes and p r i n t s the s a t u r a t i o n s t a t e of each m i n e r a l w i t h respect to a thermodynamic e q u i l i b r i u m constant f o r each r e a c t i o n considered. 2


H

Acknowledgements We are pleased to acknowledge the e f f o r t s of L. N. Plummer and R. W. P o t t e r I I , both of the U. S. G e o l o g i c a l Survey, f o r t h e i r c a r e f u l reviews of t h i s manuscript; to Β. F. Jones, U. S. G e o l o g i c a l Survey, f o r many h e l p f u l d i s c u s s i o n s ; and to J . M. Burchard, whose help i n many aspects of t h i s work i s e s p e c i a l l y appreciated. Abstract The computerized aqueous chemical model of Truesdell and Jones (2, 3), WATEQ, has been greatly revised and expanded to include consideration of ion association and solubility equilibria for several trace metals, Ag, As, Cd, Cu, Mn, Ni, Pb and Zn, solubility equilibria for various metastable and(or) sparingly soluble equilibrium solids, calculation of propagated standard deviation, calculation of redox potential from various couples, polysulfides, and a mass balance section for sulfide solutes. Revisions include expansion and revision of the redox, sulfate, iron, boron, and fluoride solute sections, changes in the possible operations with Fe (II, III, and II + III), and updating the model's thermodynamic data base using c r i t i c a l l y evaluated values (81, 50, 58) and new compilations (51, 26; R. M. Siebert and


830

CHEMICAL

MODELING IN AQUEOUS

SYSTEMS

C. L. Christ, unpublished data 1976). Mechanical revisions include numerous operational improvements i n the computer code. Literature Cited 1. 2.


3.

4.

5.

6.

7.

8.

9. 10.

11. 12.

13.

Odum, E. P. The emergence of ecology as a new integrative discipline: Science 195, 1289-1293 (1977). Truesdell, A. H., and Jones, B. F. WATEQ, a computer program for calculating chemical equilibria of natural waters: NTTS-PB2-20464, 77 p. (1973). Truesdell, A. H., and Jones, B. F. WATEQ, a computer program for calculating chemical equilibria of natural waters: U. S. Geol. Survey J. Res. 2(2) 233-274 (1974). Plummer, L. Ν., Jones, B. F., and Truesdell, A. H. WATEQF A Fortran IV version of WATEQ, a computer program for calcu lating chemical equilibrium of natural waters: U. S. Geol. Survey Water-Resour. Invest. 76-13, 61 p. (1976). Barnes, Ivan and Clarke, F. E. Chemical properties of ground water and their corrosion and encrustation effect on wells. U. S. Geol. Survey Prof. Paper 498-D, 58 p. (1969). Kharaka, Υ. Κ., and Barnes, Ivan. SOLMNEQ: Solution -mineral equilibrium computations: U. S. Geol. Survey Water Res. 73-002, 88 p. (NTIS PB-215 899) (1973). Helgeson, H. C. Thermodynamics of hydrothermal systems at elevated temperatures and pressures. Amer. J. S c i . 267, 729-804 (1969). Helgeson, H. C., Brown, Τ. Η., Nigrini, Α., and Jones, T. A. Calculation of mass transfer i n geochemical processes i n volving aqueous solutions. Geochem. Cosmochem. Acta, 34, p. 569-592 (1970). Nathenson, M., "Thermodynamic calculations," NTIS Tech. Report PB214372, 29 p. (1973), B a l l , J. W., Jenne, Ε. Α., and Nordstrom, D. K. Additional and revised thermochemical data and computer code for WATEQ2-A computerized chemical model for trace and major element speciation and mineral equilibria of natural waters. U. S. Geol. Survey Water Res. Invest. 78-116 (in press). Weast, R. C., ed., "CRC Handbook of Chemistry and Physics" Chemical Rubber Co., Cleveland, Ohio, 51st Ed. 1970-1971. Jenne, Ε. Α., Girvin, D. C., B a l l , J. W., and Burchard, J. M. Inorganic speciation of silver i n natural waters - fresh to marine, Chapter 4, p. 41-61, i n Klein, D. Α., ed., "Environ mental Impacts of Nucleating Agents Used i n Weather Modifi cation Programs," 256 p. Dowder, Hutchinson and Ross, Stroudsberg, Pa. 1978. Naumov, G. B., Ryzhenko, Β. N. and Khodakovsky, I. L. "Hand book of Thermodynamic Data," 328 p. U. S. Geol. Survey WRD-74-001, NTIS PB 226 722/AS. 1974.


36.

14.

15.

16.

17.


18.

19.

BALL


ET AL.

Sillen, L. G., and Martell, A. E. Stability constants of metal ion complexes: Chem. Soc. Spec. Publ. No. 17, London, 754 p. (1964). S i l l e n , L. G., and Martell, A. E. Stability constants of metal ion complexes. Suppl. No. 1: Chem. Soc. Spec. Publ. No. 25. 865 p. (1971). Yatsimirskii, Κ. B. and Vasil'ev, V. P. "Instability Con stants of Complex Compounds." 218 p. (Tr. from Russ., D. A. Paterson), Pergamon Press, New York, 1960. Ashcroft, S. J., and Mortimer, C. T. "The Thermochemistry of Transition Metal Complexes." 478 p., Academic Press, New York, 1970. Lafon, G. M., and Truesdell, A. H. Temperature dependence of sodium sulfate complexing i n aqueous solutions, [abst.] Amer. Geophys. Union Trans. 52, p. 362 (1971). Pytkovicz, R. M. and Kester, D. R. Harned's rule behavior of NaCl-Na SO solutions explained by an ion association model. Amer. J . S c i . 267, 217-229 (1969). Fisher, F. H. Dissociation of Na SO from ultrasonic -absorption reduction i nMgSO -NaClsolution. J . Sol. Chem. 4, 237-240 (1975). Fisher, F. H. and Fox, A. P. NaSO 4 ion pairs i n aqueous solutions at pressures up to 2000 atm. J . Sol. Chem. 4, 225-236 (1975). Righellato, E. C., and Davies, C. W. The extent of dis sociation of salts in water. Part I I . Uni-bivalent salts. Trans. Faraday Soc. 26, 592-600 (1930). Jenkins, I. L., and Monk, C. B. The conductances of sodium, potassium and lanthanum sulfates at 25°C. J. Amer. Chem. Soc. 72, 2695-2698 (1950). Austin, J . Μ., and Mair, A. D. Standard enthalpy of for mation of complex sulfate ions i n water. I. HSO , LiSO , NaSO- . J. Phys. Chem. 66, 519-521 (1962). Izatt, R. M., Eatough, D., Christensen, J . J . and Bartholomew, C. H. Calorimetrically determined Log Κ, ΔΗ°, and ΔS° values for the interaction of sulfate ion with several biand tervalent metal ions. J . Chem. Soc. A, 47-53 (1969). Smith, R. Μ., and Martell, A. E. " C r i t i c a l Stability Constants. V. 4. Inorganic Complexes." 257 p., Plenum Press, New York, 1976. Bockeris, J .O'M.,and Reddy, Α. Κ. N. "Modern Electro chemistry," 1432 p., Plenum Press, New York, 1970. Mattoo, Β. N. Stability of metal complexes i n solution. III. Ion association i n f e r r i c sulfate and nitrate solutions at low Fe III concentrations. Z. Phys. Chem. [Frankfurt] 19, 156-167 (1959). Broene, Η. Η., and DeVries, T. The thermodynamics of aqueous hydrofluoric acid solution. J. Amer. Chem. Soc. 69, 1644-1646 (1947). 2

20.

831

4

2

4

4

21.

22.

23.

24.

-

4

4

25.

26.

27. 28.

29.


4

832 30. 31.

32.

33.


34.

35.

CHEMICAL

MODELING IN AQUEOUS

E l l i s , A. J. The effect of temperature on the ionization of hydrofluoric acid. J . Chem. Soc., 4300-4304 (1963). Vanderborgh, Ν. E. Evaluation of the lanthanum fluoride membrane electrode response i n acidic solutions. Talanta 15, 1009-1013 (1968). Baumann, E. W. Determination of s t a b i l i t y constant of hydrogen and aluminum fluorides with a fluoride-selective electrode. J. Inorg. Nucl. Chem. 31, 3155-3162 (1969). Hamer, W. J., and Wu, Y.-C. The activity coefficients of hydrofluoric acid i n water from 0 to 35°C. J . Res. Nat'l. Bur. Stand 74A, 761-768 (1970). Patel, P. R., Moreno, E. C., and Patel, J . M. Ionization of hydrofluoric acid at 25°C. J . Res. Nat'l. Bur. Stand 75A, 205-211 (1971). Warren, L. S. The measurement of pH i n acid fluoride acid solutions and evidence for the existence of (HF) . Anal. Chim. Acta 53, 199-202 (1971). Kresge, A. J., and Chiang, Y. Solvent isotope effects on the ionization of hydrofluoric acid. J. Phys. Chem. 77, 822-825 (1973). Vasil'ev, V. P., and Kozlovskii, Ε. V. Thermochemistry of acid-base reactions i n aqueous hydrofluoric acid solutions. Russ. J. Inorg. Chem. 18, 1544-1546 (1973). Kresge, A. J., and Chiang, Y. Acid catalysis i n hydrofluoric acid buffers. J. Amer. Chem. Soc. 90, 5309-5310. (1968). Kresge, A. J., and Chiang, Y. Vinyl ether hydrolysis. V. Catalysis i n dilute hydrofluoric acid solution. J. Amer. Chem. Soc. 94, 2814-2817 (1972). Roberson, C. E., and Barnes, R. B. Stability of fluoride complex with s i l i c a and i t s distribution in natural water systems. Chem. Geol. 21, 239-256 (1978). Wagman, D. D., Evans, W. Η., Parker, V. B., Halow, I., Bailey, S. Μ., and Schumm, R. H. Selected values of chemical thermodynamic properties. Table for the f i r s t thirty-four elements i n the standard order of arrangement. Nat'l Bur. Stand. Tech. Note 270-3, 264 p. (1968). E l l i s , A. J. Chemical processes i n hydrothermal systems-a review, p. 1-26, in Ingerson, E., ed., "Proceedings of Symposium on Hydrogeochemistry," v. 1, Clarke, Washington, D. C. 1973. Ozawa, T., Kamada, M., Yoshida, Μ., and Sanemasa, I. Gene sis of acid hot spring, p. 105-121, i n Ingerson, E., ed., "Proceedings of Symposium on Hydrogeochemistry," v. 1, Clarke, Washington, D. C. 1973. Martin, D. F. and Taft, W. H. Occurrence and implication of sedimentary fluorite i n Tampa Bay, F l a . , p. 202-210, i n Gibb, T. R. P., ed., "Analytical Methods i n Oceanography." Amer. Chem. Soc. Mono. Ser. 147. 1975. 2

36.

37.

38. 39.

40.

41.

42.

43.

44.

SYSTEMS


36.

BALL


ET AL.


45.

833

Crosby, Ν. T. Equilibria of fluorosilicate solution with special emphasis to the fluoridation of public water supplies. J. Appl. Chem. 19, 100-102 (1969). 46. Shapiro, L. Spectrophotometric determination of s i l i c a at high concentrations using fluoride as a depolymerizer. U. S. Geol. Survey J. Res. 2, 357-360 (1974). 47. Lovering, T. S., and Shepard, A. O. Hydrothermal alteration zones caused by halogen acid solutions, East Tintic District, Utah. Amer. J. Sci 258-A, 215-229 (1960). 48. Cadek, J . , and Malkovsky, M. Transport of fluorine i n natural waters and precipitation of fluorite at low tempera tures. Acta Univ. Carolinae Geol. 4, 251-270 (1966). 49. Shawe, D. R., ed. Geology and resources of fluorine i n the United States. U. S. Geol. Survey Prof. Paper 933, 99 p. (1976). 50. Nordstrom, D. Κ., and Jenne, E. A. Fluorite solubility equilibria i n selected geothermal waters. Geochim. Cosmochim. Acta 41, 175-188 (1977). 51. Baes, C. F. J r . , and Mesmer, R. E. "The Hydrolysis of Cations," 458 p. John Wiley and Sons, New York, 1976. 52. Nazarenko, V. Α., and Nevskaya, Ε. M. Chemistry of the reactions between the ions of multivalent elements and organic reagents. XVII. Interaction of aluminum and gallium ions with methylthymol blue. J . Anal Chim. USSR 24(6), 670-673 (1969). 53. Langmuir, D. The Gibbs free energies of substances i n the system Fe-O -H O-CO at 25°C. U. S. Geol. Survey Prof. Paper 650-B, B180-B184 (1969). 54. Byrne, R. H. J r . "Iron speciation and solubility i n seawater," Ph. D. Thesis, Univ. Rhode Island, Kingston, R.I., 1974. 55. Kester, D. R., Byrne, R. H. J r . , and Liang, Y.-J. Redox reactions and solution complexes of iron i n marine systems, p. 56-79, i n Church, Τ. Μ., ed., "Marine Chemistry i n the Coastal Environment," Amer. Chem. Soc. Symp. Ser. 18, 1975. 56. Dutt, Ν. K. and Gupta, A. Fluorarsenates and their analogues with sulphates. Part III. Stability of fluorarsenate ion and i t s comparison with fluorphosphate ion. J . Indian Chem. Soc. 38, 249-252 (1961). 57. Deschamps, Pierre, and Charreton, Barthe. Determination of the solubility products of the hydroxide and basic chlorides of lead. Acad. Sci. Comptes Rendus 232, 162-163 (1951). 58. Nordstrom, D. K. "Hydrogeochemical and microbiological factors affecting the heavy metal chemistry of an acid mine drainage systems." Ph. D. Thesis, Stanford University, 1977. 59. Brown, J. B. A chemical study of some synthetic potassium -hydronium jarosites. Amer. Mineralog. 10, 696-703 (1970). 60. Brown, J. B. Jarosite-goethite s t a b i l i t i e s at 25°C, 1 atm. Mineral. Deposita 6, 245-252 (1971). 2

2

2


834 61.

CHEMICAL

MODELING IN AQUEOUS

SYSTEMS

Zotov, Α. V., Mironova, G. D., Rusinov, V. L. Determination of the Gibbs free energy ∆G° of jarosite synthesized from a natural solution. Geokhimiya, 739-745 (1973). Vlek, P. L. G., Blom, Th. J . M., Beek, J . , and Lindsay, W. L. Determination of the solubility product of various iron hydroxides and jarosite by the chelation method. Soil S c i . Soc. Amer. Proc. 38, 429-432 (1974). Kashkai, C., Borovskaya, Y. B., and Babozade, M. A. ΔG° determination of synthetic jarosite and i t s sulfate analogues. Geokhimya 5, 778-784 (1975). Wagman, D. D., Evans, W. H., Parker, V. B., Halow, I, Bailey, S. Μ., and Schumm, R. H. Selected values of chemical thermo dynamic properties. Tables for elements 35 through 53 i n the standard order of arrangement. Nat'l Bur. Stand. Tech. Note 270-4, 141 p. (1969). Larson, J. W., and Hepler, L. G. Calorimetric measurements on metal sulfates and their hydrates: electrode potentials and thermodynamic data for aqueous ions of transition elements, p. 195-201, i n "Analytical Calorimetry," Plenum Press, New York, 1968. Parker, V. B., Wagman, D. D., and Evans, W. H. Selected values of chemical thermodynamic properties. Tables for the alkaline earth elements (Elements 92 through 97 i n the standard order of arrangement): Nat'l Bur. Stand. Tech. Note 270-6, 106 p. (1971). Kelly, K. K., Shomate, C. H., Young, F. E., Naylor, B. S., Salo, Α. Ε., and Huffman, Ε. Η. Thermodynamic properties of ammonium and potassium alums and related substances with special reference to extraction of alumina from clay and alunite. U. S. Bur. Mines Tech. Paper 688. 104 p. (1946). Haas, J. L. J r . , and Fisher, J . R. Simultaneous evaluation and correlation of thermodynamic data. Amer. J. S c i . 276, 525-545 (1976). Stearns, R. I., and Brandt, A. F. Solubility product v a r i a b i l i t y at constant temperature and pressure. J. Phys. Chem. 80, 1060-1063 (1976). Macaskill, J . B., and Bates, R. G. Solubility product con stant of calcium fluoride. J. Phys. Chem. 81, 496-498 (1977). Brown, D. W., and Roberson, C. E. Solubility of natural f l u o r i t e at 25°C. U. S. Geol. Survey J. Res. 5, 509-517 (1977). Eugster, H. P., and Chou, I.-M. The depositional environments of precambrian banded iron-formations. Econ. Geol. 68, 1144-1168 (1973). Bird, G. W., and Anderson, G. M. The free energy of formation of magnesium cordierite and phlogopite. Amer. J. S c i . 273, 84-91 (1973). Paces, Tomas. Active mineral surfaces: origin and possible effects on trace elements i n natural water systems, p. 361368, in Hemphill, D. D., ed., "Trace Substances i n Environ ments Health-VI: Univ. Missouri, Columbia." 1973. f,298

62.

63.


64.

65.

66.

67.

68.

69.

70. 71. 72.

73.

74.

f,298


36.

BALL ET AL.


835

75.

Paces, Tomas. Steady-state kinetics and equilibrium between ground water and granitic rock: Geochim. Cosmochim. Acta 37, 2641-2663 (1973). 76. Ponnamperuma, F. Ν., Tianco, Ε. M., and Loy, Teresita. Redox equilibria i n flooded s o i l s : I. The iron hydroxide system. Soil Sci. 103, 374-382 (1967). 77. Beidermann, G., and Chow, J . T. Studies on the hydrolysis of metal ions. Part 57. The hydrolysis of iron(III) ion and the solubility product of Fe(OH) Cl0.30in 0.5 M (Na )Cl medium. Acta Chem. Scand. 20, 1376-1388 (1966). 78. Chien, S. H., and Black, C. A. Free energy of formation of carbonate apatites i n some phosphate rocks. Soil Sci. Soc. Amer. J . 40, 234-239 (1976). 79. Morey, G. W., Fournier, R. O., and Rowe, J . J . Solubility of amorphous SiO at 25°C. J. Geophys. Res. 69, 1995-2002 (1964). 80. Sato, Motoaki. Oxidation of sulfide ore bodes, l. Geochemical environments i n terms of Eh and pH. Econ. Geol. 55, 928-961 (1960). 81. Nordstrom, D. Κ., Jenne, Ε. Α., and B a l l , J. W. Redox equili bria of iron in acid mine waters, i n Jenne, Ε. Α.,ed.,"Chem i c a l Modeling in Aqueous Systems. Speciation, Sorption, Solu b i l i t y , and Kinetics," Amer. Chem. Soc., (this volume). 82. Bevington, P. R. "Data Reduction and Error Analysis for the Physical Sciences," 336 p., McGraw-Hill Book Co., New York, 1969. 83. Laxen, D. P. H. A specific conductance method for quality control i n waters. Water Res. 11, 91-94 (1977). 84. Butler, J . N. "Ionic Equilibrium, A Mathematic Approach," 547 p., Addison-Wesley, New York, 1964. 85. Cloke, P. L. The geologic role of polysulfides - Part I I . The solubility of acanthite and covelite i n sodium poly sulfide solutions. Geochim. Cosmochim. Acta 27, 1299-1319 (1963). 86. Helffrich, Friederich, "Ion Exchange." 624 p., McGraw-Hill, New York, 1962. 87. K i t t r i c k , J. A. Ion exchange and mineral s t a b i l i t y : Are the reactions linked or separate? i n Jenne, Ε. Α., ed., "Chemical Modeling i n Aqueous Systems, Speciation, Sorption, Solubility, and Kinetics," Amer. Chem. Soc., (this volume). 88. Bassett, R. L., Kharaka, Υ. Κ., and Langmuir, D. C r i t i c a l review of the equilibrium constants for clay minerals, i n Jenne, Ε. Α., ed., "Chemical Modeling i n Aqueous Systems, Speciation, Sorption, Solubility, and Kinetics," Amer. Chem. Soc., (this volume). +

-


2.70

2

Disclaimer: The reviews expressed and/ or the products mentioned in this article repre sent the opinions of the author(s) only and do not necessarily represent the opinions of the U.S. Geological Survey. RECEIVED November 16, 1978.


Chemical Modeling in Aqueous Systems - ACS Publications

Recommend Documents