17 Estimated Free Energies of Formation, Water Solubilities, and Stability Fields for Schuetteite ( H g O S O ) and 3
Corderoite ( H g S C l ) at 298 3
2
2
4
Κ
GEORGE A. PARKS and DARRELL KIRK NORDSTROM Downloaded by UNIV OF PITTSBURGH on April 11, 2017 | http://pubs.acs.org Publication Date: March 19, 1979 | doi: 10.1021/bk-1979-0093.ch017
2
1
Department of Applied Earth Sciences, Stanford University, Stanford, CA 94305 Mercury forms many double s a l t s of which a few occur natu r a l l y ; these i n c l u d e e g l e s t o n i t e , Hg40Cl and t e r l i n g u a i t e , H g 0 C l ( 1 ) , s c h u e t t e i t e , Hg 02S04(_2), and c o r d e r o i t e , Hg3S2Cl2 O). S o l u b i l i t y and thermodynamic data u s e f u l i n a s s e s s i n g the impor tance of these compounds i n c o n t r o l l i n g the mercury content of n a t u r a l waters are l a c k i n g . Only an enthalpy of formation f o r s c h u e t t e i t e i s r e p o r t e d . We have estimated the standard f r e e energies of formation of s c h u e t t e i t e and c o r d e r o i t e by f i r s t e s t i mating t h e i r absolute e n t r o p i e s and the m i s s i n g enthalpy of form a t i o n of c o r d e r o i t e . Independent estimates were d e r i v e d from s o l u b i l i t y data f o r s c h u e t t e i t e and from vapor-phase s y n t h e s i s data f o r c o r d e r o i t e . The two s e t s of estimates are compared and the r e s u l t s were used to determine the s t a b i l i t i e s of these miner a l s r e l a t i v e to the more common mercury m i n e r a l s . The s t a b i l i t y f i e l d diagrams and s o l u b i l i t i e s are used to comment b r i e f l y on c o n d i t i o n s r e q u i r e d f o r f i e l d occurrence. 2
2
3
E s t i m a t i o n of E n t r o p i e s The Debye theory of the heat c a p a c i t i e s of s o l i d elements y i e l d s an expression f o r t h e i r e n t r o p i e s , S = 3R(£nT - K
2
+ Κ )
(4)
(1)
i n which Κχ i s a u n i v e r s a l constant. K i s a constant f o r each element and i s determined by the i n t e r a t o m i c f o r c e constant and atomic mass. Equation 1 assumes that the heat c a p a c i t y and en tropy are dominated by v i b r a t i o n a l c o n t r i b u t i o n s . E l e c t r o n i c , d i s o r d e r , r o t a t i o n a l , s t r u c t u r a l , and mixing c o n t r i b u t i o n s are small f c r most monatomic s o l i d s , and are neglected. P o s t u l a t e s by Latimer (5) and Kopp (see P i t z e r and Brewer (4)) make i t pos s i b l e to p r e d i c t e n t r o p i e s of polyatomic s o l i d s or compounds. Latimer assumed that the c o n t r i b u t i o n of i n t e r a t o m i c f o r c e 2
1
Current address: Department of Environmental Sciences, University of Virginia, Char lottesville, VA 22903. 0-8412-0479-9/79/47-093-339$05.00/0 © 1979 American Chemical Society Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.
340
CHEMICAL MODELING IN AQUEOUS SYSTEMS
constants to entropy was s m a l l , and p o s t u l a t e d that the entropy of each element i n a s o l i d compound could be approximately accounted f o r by i t s mass alone, F
S = R£nM + S ο
(2)
where SQ has the same v a l u e f o r a l l elements. Kopp proposed that the heat c a p a c i t y of a s o l i d compound could be approximated by the s t o i c h i o m e t r i c sum of the heat c a p a c i t i e s of i t s c o n s t i t u ent elements. On the b a s i s of Kopp s p o s t u l a t e d a d d i t i v i t y of heat c a p a c i t i e s , Latimer suggested t h a t the entropy of a s o l i d compound, M-jA-j , c o u l d be approximated by the s t o i c h i o m e t r i c sum of the c o n t r i b u t i o n s of i t s c o n s t i t u e n t elements,
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1
s
vr a = iS™M + J SA · (3) M. A. ι J Latimer used Equation 2 to o b t a i n entropy c o n t r i b u t i o n s f o r c a t ions and Equation 3, together w i t h experimental e n t r o p i e s of compounds and the c a t i o n c o n t r i b u t i o n s , to estimate a n i o n i c con t r i b u t i o n s . Naumov, Ryzhenko and Khodakovsky (6) extended L a t i mer's t a b l e s of c o n s t i t u e n t c o n t r i b u t i o n s . For e s t i m a t i n g the entropy of a p a r t i c u l a r compound w i t h Equation 3, D r o z i n (7) used a n i o n i c c o n t r i b u t i o n s d e r i v e d from compounds of metals i n the same p e r i o d i c subgroup r a t h e r than o v e r a l l averages as Latimer (5) had used. Equations 2 and 3 can be combined to express the entropy of one compound i n terms of another, thus A
S
M.A. 1
S
J
f
+
- N.A. ι 3
( \ 7/
R
£η
W/
,
(4)
N
P i t z e r and Brewer (4) suggest t h i s approach f o r e s t i m a t i o n i f Nj_Aj i s s i m i l a r , i n terms of s t r u c t u r e and p r o p e r t i e s , to M^Aj . This approach should minimize e r r o r a r i s i n g i n n e g l e c t of nonmass-related entropy c o n t r i b u t i o n s . I f the heat c a p a c i t i e s and e n t r o p i e s of s o l i d s are simply the weighted sums of those of t h e i r elemental c o n s t i t u e n t s , then the entropy change should be zero f o r symmetrical r e a c t i o n s such as, 2HgX + P b 0 S 0 2
2
4
= 2PbX + Hg 0S0 2
2
(5)
4
i n which the number of molecules produced i s the same as the num ber consumed and the number of atoms i n each product molecule i s the same as the number i n a corresponding r e a c t a n t molecule (7)· X i s a monovalent anion i n Equation 5. Using t h i s p r i n c i p l e , the entropy of Hg^SO^ i s given by S
Hg 0S0 2
= 4
S
Pb 0S0 2
4
"
2 S
PbX
+ 2
2 S
HgX
( 6 ) 2
Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.
17.
PARKS AND NORDSTROM
Schuetteite
and
Corderoite
341
and can be estimated i f the other entropies are known. This meth od should y i e l d r e s u l t s s i m i l a r to those obtained w i t h Equation 4 but could introduce greater e r r o r s i n c e c l o s e s i m i l a r i t y i n s t r u c ture and p r o p e r t i e s among four compounds of two d i f f e r e n t types i s u n l i k e l y . For t h i s reason Drozin (7) suggests u s i n g compounds of metals i n the same p e r i o d i c subgroup i n comparisons u t i l i z i n g Equation 6.
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Tests of E s t i m a t i o n Methods Equation 3. We estimated the e r r o r to be expected i n the use of Equation 3 by comparing e m p i r i c a l e n t r o p i e s w i t h those c a l c u l a t e d u s i n g c o n t r i b u t i o n s t a b u l a t e d by Latimer (5) without m o d i f i c a t i o n . The e m p i r i c a l data were taken from Hepler and Olofsson ( 8 ) , Robie, Hemingway and F i s h e r (9) and the N a t i o n a l Bureau of Stan dards T e c h n i c a l Note 270 s e r i e s (11). Data f o r mercury are l i s t e d i n Table I . E m p i r i c a l and c a l c u l a t e d e n t r o p i e s are compared
Table I . Thermodynamic P r o p e r t i e s of Mercury M i n e r a l s and Compounds a t 298.15K, I n c l u d i n g Estimates.
s°, 1
JK m o l
1
+ 76.02
Hg(£)
ΔΗ°,
AG°,
kJ mol ^
kJ mol
0.0
0.0
- 36.23
+170.16
+164.703
montroydite Hg0(c,red,orth. ,) + 70.29 calomel
2+
Hg (aq)
- 90.83
- 58.555
Hg Cl (c)
+191.42
-265.579
-210.773
HgCl (c)
+146.0
-225.9
-180.3
cinnabar
HgS(c,red)
+ 82.4
- 54.0
- 46.4
corderoite
Hg S Cl (c)
[301±17]
2
2
2
3
2
2
[(
