WATEQ2âA Computerized Chemical Model for Trace and Major

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.

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ET

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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


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C. L. Christ, unpublished data 1976).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


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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.


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