Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Anodic oxidation of cuprous sulphide in aqueous solutions Fraser, Michael J. 1965

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1965_A7 F7.pdf [ 5.87MB ]
Metadata
JSON: 1.0104854.json
JSON-LD: 1.0104854+ld.json
RDF/XML (Pretty): 1.0104854.xml
RDF/JSON: 1.0104854+rdf.json
Turtle: 1.0104854+rdf-turtle.txt
N-Triples: 1.0104854+rdf-ntriples.txt
Original Record: 1.0104854 +original-record.json
Full Text
1.0104854.txt
Citation
1.0104854.ris

Full Text

ANODIC OXIDATION OF CUPROUS,SULPHIDE IN AQUEOUS SOLUTIONS by MICHAEL J . FRASER A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n t h e Department o f METALLURGY We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d Members o f t h e D e p a r t m e n t o f M e t a l l u r g y THE UNIVERSITY OF BRITISH COLUMBIA September 19 65 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study* I f u r t h e r agree that per m i s s i o n f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t , c o p y i n g or p u b l i  c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission*. Department of M e t a l l u r g y The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8. Canada Date August 26, 1965 ABSTRACT The o x i d a t i o n o f a r t i f i c i a l c u p r o u s s u l p h i d e e l e c t r o d e s (Cu/S r a t i o = 1.93) was s t u d i e d i n a c i d i f i e d c o p p e r s u l p h a t e s o l u t i o n s i n t h e t e m p e r a t u r e r a n g e 20 t o 35° C. R e s t p o t e n t i a l measurements gave V° = 0.490' v o l t s f o r t h e e l e c t r o d e o r h a l f c e l l p o t e n t i a l . T h i s i s w i t h i n t h e l i m i t s o f a c c u r a c y o f V° f o r : C u 2 S — C u S + C u + + + 2e V° = 0.535 + 0.13 v o l t s The d i s c r e p a n c y was t h o u g h t t o be r e l a t e d t o t h e l a r g e Cu d e f i c i e n i n t h e s u l p h i d e . I n s o l u t i o n s w i t h pH>4, t h e r e s t p o t e n t i a l measurements were c o n s i s t e n t w i t h t h e f o l l o w i n g r e a c t i o n : C u 2 S + 2H 20 — C u S + C u ( O H ) 2 + 2 H + + 2e P o l a r i z a t i o n measurements a t low o v e r p o t e n t i a l gave v a l u e s f o r t h e f o l l o w i n g k i n e t i c p a r a m e t e r s : (3> , t h e symmetry f a c t o r = 1/2 /\ , t h e number o f e l e c t r o n s i n v o l v e d i n e a c h a c t o f t h e r a t e d e t e r m i n i n g s t e p = 2 i , t h e exchange c u r r e n t ^ 2 x 1 0 - ^ A/cm 2 o AH Q*, t h e s t a n d a r d h e a t o f a c t i v a t i o n = 26.5 k c a l / m o l e CuS was t e n t a t i v e l y i d e n t i f i e d as one o f t h e r e a c t i o n p r o d u c t s . A r e a c t i o n mechanism was d i s c u s s e d . i i i . ACKNOWLEDGEMENT I w i s h t o th a n k M r s . A. M. A r m s t r o n g f o r h e r a s s i s t a n c e and c o n s t r u c t i v e c r i t i c i s m d u r i n g t h e work p e r i o d and t h e t h e s i s p r e p a r a t i o n . A p o r t i o n o f t h e e x p e r i m e n t a l work and t h e f i n a l p r e p a r a t i o n o f t h e t h e s i s were done i n t h e R e s e a r c h and Development D e p a r t m e n t o f The S t e e l Company o f Canada, L i m i t e d , H a m i l t o n . I w i s h t o t h a n k t h e f o l l o w i n g p e r s o n s f o r t h e i r c o n s i d e r a b l e a s s i s t a n c e : J . C. McKay, Dr. W. G. H i n e s , M r s . J . Cooke, C. E. O h e n n e s i a n , M i s s P. A. K r i t e r and Mrs. M. L e e d a l e . i v . TABLE OF CONTENTS Page INTRODUCTION 1 P h y s i c a l P r o p e r t i e s o f C u p r o u s S u l p h i d e 2 The C o p p e r S u l p h u r B i n a r y S y s t e m 2 The S t r u c t u r e o f t h e C o p p e r S u l p h i d e s 5 C o n d u c t i v i t y o f C u 2 S 6 The E f f e c t o f S e m i c o n d u c t i v i t y o f S u l p h i d e s on t h e i r E l e c t r o c h e m i c a l B e h a v i o u r 9 Thermodynamics o f O x i d a t i o n o f CU2S 10 C h e m i c a l O x i d a t i o n o f C u p r o u s S u l p h i d e 13 E l e c t r o c h e m i c a l O x i d a t i o n o f C u p r o u s S u l p h i d e 14 G e n e r a l D i s c u s s i o n o f E l e c t r o d e K i n e t i c s 17 O b j e c t and Scope o f P r e s e n t Work 21 APPARATUS AND EXPERIMENTAL PROCEDURES 22 The E l e c t r o l y t i c C e l l . 22 M e a s u r i n g C i r c u i t . 22 Anodes 25 O t h e r E l e c t r o d e s 2 7 S o l u t i o n s 2 7 R e s t P o t e n t i a l Measurements. 2 8 P o l a r i z a t i o n Measurements 2 8 RESULTS AND DISCUSSION 30 A n a l y s i s o f C u 2 S 30 R e s t P o t e n t i a l Mesurements 30 P r e l i m i n a r y P o l a r i z a t i o n T e s t s 37 K i n e t i q P a r a m e t e r s i n Low O v e r p o t e n t i a l R e g i o n . . . . . 40 R e a c t i o n P r o d u c t s 4 7 E f f e c t o f T e m p e r a t u r e on t h e P o l a r i z a t i o n C u r v e s . . . 48 C a l c u l a t i o n of, AH Q* 48 The R e a c t i o n Mechanism 51 CONCLUSIONS . 5 3 RECOMMENDATIONS FOR FUTURE INVESTIGATIONS 55 REFERENCES., 56 APPENDIX A. A n o d i c O x i d a t i o n o f T i n S u l p h i d e . . . , 59 APPENDIX B. S i g n C o n v e n t i o n f o r E l e c t r o c h e m i c a l Measurements 64 APPENDIX C. C o m p i l a t i o n o f Thermodynamic D a t a 67 T a b l e o f C o n t e n t s C o n t i n u e d Page APPENDIX D. APPENDIX E, APPENDIX F. APPENDIX G. APPENDIX H. E l e c t r o d e P o t e n t i a l s o f Some M e t a l S u l p h i d e s P o t e n t i a l s a t t h e E l e c t r o d e - S o l u t i o n I n t e r f a c e D e r i v a t i o n o f K i n e t i c R e l a t i o n s h i p s f o r A c t i v a t i o n - C o n t r o l l e d E l e c t r o d e R e a c t i o n s C a l c u l a t i o n o f A c t i v i t y C o e f f i c i e n t s i n C u S 0 4 - H 2 S 0 4 S o l u t i o n s X - r a y Powder P a t t e r n s 72 75 80 88 98 v i . L I S T OF TABLES Page TABLE I . C o p p e r S u l p h i d e C r y s t a l S t r u c t u r e s 5 TABLE I I . C o n d u c t i v i t y o f C u 2 S . 7 TABLE I I I . E l e c t r o n i c C o n d u c t i v i t y o f Cu S a t 400° C 7 TABLE IV. R e s t P o t e n t i a l s f o r C u 2 S and CuS E l e c t r o d e s a t 25° C 14 TABLE V. V a l u e s o f t h e Exchange C u r r e n t f o r V a r i o u s E l e c t r o c h e m i c a l R e a c t i o n s 19 TABLE V I . The P o t e n t i a l o f t h e S a t u r a t e d C a l o m e l E l e c t r o d e 2 7 TABLE V I I . E l e c t r o d e P o t e n t i a l o f C u p r o u s S u l p h i d e Anode, w i t h and w i t h o u t S i l v e r F o i l C o n t a c t 31 TABLE V I I I . E l e c t r o d e P o t e n t i a l V° i n CuSO a t 25° C ?rx§ 4 32 TABLE IX. Y + + i n CuSO -MgSO.-IUSO. S o l u t i o n s C u o f C o n s t a n t I o n i c S t r e n g t h a t 25° C 32 TABLE X. V ° C u s i n C u S 0 4 - M g S 0 4 - H 2 S 0 4 S o l u t i o n s x o f C o n s t a n t I o n i c S t r e n g t h a t 25° C 33 TABLE X I . R e s t P o t e n t i a l Measurements i n C u S 0 4 ~ H 2 S 0 4 - N a H S 0 4 S o l u t i o n s a t 25° C 34 TABLE X I I . i , X * a n d ^ f o r t h e C u p r o u s S u l p h i d e Anode 4 4 TABLE X I I I . C o r r e c t e d V a l u e s o f i Q and d t O / d l o g i A . . . . 47 TABLE XIV. C a l c u l a t i o n o f l o g ( J Q / T ) 50 TABLE A - I . R e s t P o t e n t i a l s f o r T i n S u l p h i d e E l e c t r o d e a t 25° C i n S n c l 2 S o l u t i o n 60 TABLE C - I . Thermodynamic D a t a a t 29 8° K 69 TABLE C - I I . C a l c u l a t e d H a l f C e l l P o t e n t i a l s 70 TABLE D-I. E l e c t r o d e P o t e n t i a l s f o r S e v e r a l S u l p h i d e s . . . 72 v i i . L i s t o f T a b l e s C o n t i n u e d Page TABLE D - I I . TABLE G-I. TABLE G - I I . TABLE G - I I I . T e n t a t i v e E l e c t r o c h e m i c a l S e r i e s f o r Some M e t a l S u l p h i d e s D e t e r m i n a t i o n o f G, y and N f r o m D a t a o f H o l l a n d and Bonner C o m p u t a t i o n o f # C u S 0 • Mean I o n i c A c t i v i t y C o e f f i c i e n t o f CuSO^ i n some CuSO^-R^SO^ S o l u t i o n s 74 93 94 95 v i i i . L I S T OF FIGURES Page F i g u r e 1. C o p p e r - S u l p h u r B i n a r y D i a g r a m 3 F i g u r e 2. C ^ S - C u S P o r t i o n o f t h e C o p p e r S u l p h u r B i n a r y D i a g r a m 4 F i g u r e 3. P o t e n t i a l / p H D i a g r a m f o r t h e S y s t e m Cu-S-H 20 11 F i g u r e 4. P o t e n t i a l / p H D i a g r a m f o r t h e System C U - S - H 2 O , o m i t t i n g O x i d a t i o n R e a c t i o n s w i t h M e t a l l i c C o p p e r 12 F i g u r e 5. C e l l f o r P o t e n t i a l Measurements w i t h C o p p e r S u l p h i d e E l e c t r o d e s 2 3 F i g u r e 6. C i r c u i t f o r P o t e n t i a l and C u r r e n t M e a s u r e  ments w i t h C o p p e r S u l p h i d e E l e c t r o d e s . . . 24 F i g u r e 7. Mounted C o p p e r S u l p h i d e E l e c t r o d e 26 F i g u r e 8. P o t e n t i a l o f t h e C u x S E l e c t r o d e as a F u n c t i o n o f pH 36 F i g u r e 9. T y p i c a l P o l a r i z a t i o n C u r v e f o r C u p r o u s S u l p h i d e Anode a t 25° C 38 F i g u r e 10. C u p r o u s S u l p h i d e Anode S u r f a c e b e f o r e and A f t e r P o l a r i z a t i o n 39 F i g u r e 11. Decay o f A n o d i c O v e r p o t e n t i a l w i t h Time.... 41 F i g u r e 12. T y p i c a l C u r v e s : E f f e c t o f T e m p e r a t u r e on t h e P o l a r i z a t i o n o f t h e C u p r o u s S u l p h i d e Anode o 42 F i g u r e 13. E f f e c t o f T e m p e r a t u r e on t h e P o l a r i z a t i o n o f C u p r o u s S u l p h i d e a t Low O v e r - p o t e n t i a l s 43 F i g u r e 14. F i t o f R e c a l c u l a t e d L i n e t o E x p e r i m e n t a l D a t a 45 F i g u r e 15. A n o d i c and C a t h o d i c P o l a r i z a t i o n C u r v e s f o r t h e C u p r o u s S u l p h i d e E l e c t r o d e a t Low O v e r p o t e n t i a l s .. 46 ix. L i s t o f F i g u r e s C o n t i n u e d . . . Page F i g u r e 16. P l o t o f l o g J Q / T v r s 1/T. . . . 49 F i g u r e A l . A n o d i c P o l a r i z a t i o n C u r v e f o r T i n S u l p h i d e E l e c t r o d e 62 F i g u r e F l . R e a c t i o n P a t h and Energy. B a r r i e r s f o r a S e r i e s o f C o n s e c u t i v e R e a c t i o n s 81 F i g u r e F2. R e a c t i o n P a t h and E n e r g y B a r r i e r s when P o t e n t i a l A <£) A p p l i e d . . . . . . . . . 82 F i g u r e G l . P l o t o f G v e r s u s N f r o m D a t a o f T a b l e G I . . . 96 F i g u r e G2. Mean A c t i v i t y C o e f f i c i e n t as a F u n c t i o n o f I o n i c S t r e n g t h f o r CuSO^ i n H^SO^ S o l u t i o n s a t 25° C... 97 F i g u r e HI. X - r a y Powder P i c t u r e s f o r C ^ S , CuS and t h e R e a c t i o n P r o d u c t 9 9 INTRODUCTION The o x i d a t i o n o f s u l p h i d e m i n e r a l s t o r e c o v e r m e t a l s i s a c c o m p l i s h e d on a c o m m e r c i a l s c a l e by b o t h p y r o m e t a l l u r g i c a l and h y d r o m e t a l l u r g i c a l methods, examples o f w h i c h a r e s u s p e n s i o n r o a s t i n g , p r e s s u r e l e a c h i n g and a n o d i c o x i d a t i o n . S i n c e 1954, t h e I n t e r n a t i o n a l N i c k e l Company o f Canada, L i m i t e d , has p r o d u c e d n i c k e l by a p r o c e s s i n w h i c h c a s t n i c k e l s u l p h i d e anodes a r e o x i d i z e d i n e l e c t r o l y t i c c e l l s . 1 ' 2 ' 3 The s u c c e s s o f t h i s p r o c e s s i n d i c a t e d t h a t a t t e m p t s s h o u l d be made t o a p p l y s i m i l a r t e c h n i q u e s t o o t h e r s u l p h i d e m i n e r a l s , so a p r e l i m i n a r y s t u d y o f t h e a n o d i c o x i d a t i o n o f c u p r o u s s u l p h i d e and t i n s u l p h i d e was u n d e r t a k e n . The m a j o r p o r t i o n o f t h e s t u d y was d e v o t e d t o c u p r o u s s u l p h i d e and i s r e p o r t e d i n t h i s t h e s i s . A summary o f t h e work c a r r i e d o u t w i t h t i n s u l p h i d e i s r e p o r t e d i n A p p e n d i x A. C u p r o u s s u l p h i d e i s a compound s e m i c o n d u c t o r . The e l e c t r o c h e m i c a l b e h a v i o u r o f e l e m e n t a l s e m i c o n d u c t o r e l e c t r o d e s ( e . g . Ge) d i f f e r s f r o m t h a t o f m e t a l l i c e l e c t r o d e s b e c a u s e o f d i f f e r e n c e s i n c o n d u c t i v i t y and c o n d u c t i o n mechanisms, and b e c a u s e o f t h e p r e s e n c e o f a s p a c e c h a r g e l a y e r i n t h e s o l i d a t t h e s o l i d - e l e c t r o l y t e interface„ T h e s e same e f f e c t s p r o b a b l y o c c u r w i t h compound s e m i c o n d u c t o r e l e c t r o d e s , b u t t h e b a c k g r o u n d t h e o r y i s n o t w e l l - d e v e l o p e d and e x p e r i m e n t a l d a t a a r e v i r t u a l l y n o n - e x i s t a n t . The f o l l o w i n g s e c t i o n s r e v i e w b o t h t h e p r e s e n t knowledge o f t h e d e f e c t s t r u c t u r e s and c o n d u c t i o n mechanisms i n t h e Cu-S s y s t e m , and some thermodynamic and k i n e t i c a s p e c t s o f t h e o x i d a t i o n o f c u p r o u s s u l p h i d e . P h y s i c a l P r o p e r t i e s o f C u p r o u s S u l p h i d e - 2 - The C o p p e r S u l p h u r B i n a r y System The s t a n d a r d c o p p e r - s u l p h u r b i n a r y s y s t e m 4 4 i s shown i n F i g u r e 1. A more d e t a i l e d d r a w i n g o f t h e CU2S-CUS p o r t i o n o f t h e b i n a r y , b a s e d on d a t a f r o m Hansen 1* 1* , R u h l and S a u r 4 2 , Wagner 9, and B u e r g e r 5 7 , i s shown i n F i g u r e 2. T h e s e f i g u r e s r e v e a l t h e t h r e e c o p p e r - s u l p h u r compounds w h i c h have been i d e n t i f i e d : c h a l - c o c a t e o r c u p r o u s s u l p h i d e ( a p p r o x i m a t e l y C u 2 S w i t h two a l l o t r o p i c f o rms - <x. and p. ) ; d i g e n i t e ( a p p r o x i m a t e l y CucjS 5) ; and c o v e l l i t e o r c u p r i c s u l p h i d e ( a p p r o x i m a t e l y C u S ) . The p h a s e a r e a s i n F i g u r e 2 a r e a p p r o x i m a t e o n l y , b e c a u s e l i m i t e d d a t a a r e a v a i l a b l e on t h i s p o r t i o n o f t h e b i n a r y . The oc - P> t r a n s f o r m a t i o n i n C u 2 S a t 105°C i s w e l l e s t a b l i s h e d , and t h e p o i n t A on t h e (2> Cu 2S-Cu9S 5 b o u n d a r y a t 400°C was d e t e r m i n e d d u r i n g e l e c t r o c h e m i c a l s t u d i e s by Wagner and Wagner 9. The e x i s t e n c e o f d i g e n i t e has been amply c o n f i r m e d 4 4 , b u t t h e n a t u r e o f t h e r e a c t i o n o r t r a n s f o r m a t i o n o c c u r r i n g a t 78°C i s i n d o u b t ; t h e change i s shown as t h e d e c o m p o s i t i o n o f d i g e n i t e t o f o r m a m i x t u r e o f c h a l c c c i t e and c o v e l l i t e , b u t i t may w e l l be a t r a n s f o r m a t i o n t o an a l l o t r o p i c f o r m . The l a r g e m i s c i b i l i t y gap and t h e l i m i t e d s o l i d s o l u b i l i t y o f s u l p h u r i n c o p p e r (0.0005 w e i g h t % a t 6 0 0 ° C 4 4 ) a r e n o t u n u s u a l f e a t u r e s o f s u l p h u r - m e t a l b i n a r y s y s t e m s * . * B i n a r i e s o f S w i t h A l , Sb, C r , Cu, I n , Mn, Pd, Ag, T l and Sn have . l a r g e i m m i s c i b i l i t y g a p s ; t h o s e w i t h B i , Co, F e , N i , Se, Te and V do n o t . The s o l i d s o l u b i l i t y o f s u l p h u r i s e x t e n s i v e i n Se (5-6 w e i g h t %) and Te (2-4 w e i g h t % ) , b u t v e r y l i m i t e d i n a l l o t h e r s . - 3 - W e i g h t P e r c e n t S u l p h u r 10 20 30 1 / / / 1- 1 . \ \ \ \ 1 1 1200 " / Two M e l t s 2.9% 1105° 32.9% \ 1129° • 1083° N / 1000 V - .1,5% 1067° \ 800 _ U o u 5 600 U OJ CU 400 200 - 10 20 30 40 A t o m i c P e r c e n t S u l p h u r 50 F i g u r e 1. C o p p e r - S u l p h u r B i n a r y D i a g r a m •i ( A f t e r Hansen' 1 ,f) - 4 - 2.0 Cu/S A t o m i c R a t i o 1.9 .1.8 500 400 300 u o M -P a> 200 En A O / \ 100 6 c u 9 s / } \ ( / ^Cu2S+Gu'9'S!5 1.7 1.0 ) \ . CK,CU 2S G u 9 S 5 C u 9 S 5 + C u S Cu 2S+CuS 33 34 35 36 37 A t o m i c P e r c e n t S u l p h u r 50 F i g u r e 2. Cu 2S-CuS P o r t i o n o f t h e C o p p e r S u l p h u r B i n a r y D i a g r a m - 5 - The S t r u c t u r e o f t h e C o p p e r S u l p h i d e s The c r y s t a l s t r u c t u r e s o f t h e t h r e e c o p p e r s u l p h i d e s a r e summarized i n T a b l e I , as r e c o r d e d by H a n s e n 4 4 . TABLE I C o p p e r S u l p h i d e C r y s t a l S t r u c t u r e s C h a l c o c i t e »o c2> D i g e n i t e C o v e l l i t e A p p r o x i m a t e c o m p o s i t i o n C u 2 S C u 2 S C u 9 s 5 CuS C l a s s o r t h o r h o m b i c h e x a g o n a l f . c . c . h e x a g o n a l L a t t i c e P a r a m e t e r s b A c c / a 11.90 27.28 13.41 3.89 5.575 6.68 1.717 3.75 16.2 4.32 Atoms p e r u n i t c e l l 6 12 F o r m u l a w e i g h t s p e r u n i t c e l l 96 C u p r o u s s u l p h i d e c r y s t a l s c o n s i s t e s s e n t i a l l y o f ' r r o n o v a l e n t c o p p e r i o n s and d i v a l e n t s u l p h u r i o n s . A c c o r d i n g t o ,,x-ray s t u d i e s by R a h l f s 5 8 , t h e c o p p e r i o n s a r e d i s t r i b u t e d v i r t u a l l y a t random among a l a r g e number o f n e a r l y e q u i v a l e n t l a t t i c e s i t e s , w i t h t h e d e g r e e o f randomness i n c r e a s i n g w i t h t e m p e r a t u r e . The s u l p h u r i o n s a p p e a r t o be q u i t e h i g h l y o r d e r e d i n t h e l a t t i c e 5 8 ' 5 9 . D i f f u s i o n s t u d i e s * i n d i c a t e t h a t t h e . c o p p e r i o n s a r e q u i t e m o b i l e , w h i l e i n c o n t r a s t , t h e s u l p h u r i o n s a r e v i r t u a l l y i m m o b i l e . I n t h e c a s e o f c u p r o u s s u l p h i d e d e f i c i e n t i n c o p p e r (which a p p e a r s t o be t h e n o r m a l s i t u a t i o n 9 ) , t h e c h a r g e b a l a n c e * see r e f e r e n c e 9, p.1603 i s m a i n t a i n e d by t h e d e v e l o p m e n t o f e x c e s s e l e c t r o n s and e l e c t r o n h o l e s . The s e v e r a l s p e c i e s w h i c h e x i s t i n t h e c u p r o u s s u l p h i d e a r e : C u + : m o n o v a l e n t c o p p e r i o n i n a more o r l e s s - random d i s t r i b u t i o n . S~ d i v a l e n t s u l p h u r i o n , i n more o r l e s s r e g u l a r , l a t t i c e p o s i t i o n s . C u 4 ® : e l e c t r o n h o l e - a c u p r o u s i o n w h i c h has g i v e n up one e l e c t r o n i . e . a c u p r i c i o n . 9 : e x c e s s e l e c t r o n - an u n a t t a c h e d e l e c t r o n . P o w a r e n n y c h 5 9 r e v i e w e d v a r i o u s c r y s t a l l o g i a p h i c s t u d i e s o f t h e c o p p e r s u l p h i d e s , and s t a t e d t h a t t h e c o r r e c t f o r m u l a e o f t h e v a r i o u s compounds a r e as f o l l o w s : c h a l c o c i t e Cu 2 s d i g e n i t e Cu^gCu S 5 c o v e l l i t e * C u + 2 C u + ® S 3 . C o n d u c t i v i t y o f C ^ S H i r a h a r a 6 2 ' 6 3 m e a s u r e d t h e i o n i c and e l e c t r o n i c c o n d u c t i v i t y o f C ^ S a t v a r i o u s t e m p e r a t u r e s , and h i s r e s u l t s a r e summarized i n T a b l e I I . T h i s f o r m u l a f o r c o v e l l i t e r e q u i r e s t h e p r e s e n c e o f a s e c o n d s u l p h u r s p e c i e s S~ 2 t o m a i n t a i n c h a r g e n e u t r a l i t y , v i z : ( 2 C u + ) ( C u + ® ) ( S = ) ( S = 2 ) - 7 - TABLE I I C o n d u c t i v i t y o f C u 2 S T e m p e r a t u r e I o n i c C o n d u c t i v i t y E l e c t r o n i c C o n d u c t i v i t y °C o hm - 1 c m - 1 o h m - 1 c m - 1 2 5 ^ 0 55 100 ^ 0 62 150 0.0031 10 200 0.0144 13.1 300 0.089 14.6 400 0.20 15.7 I t i s c o n c l u d e d t h a t i o n i c c o n d u c t i v i t y i s o f l i t t l e s i g n i f i c a n c e b elow 150°C. Wagner and Wagner 9 s t u d i e d c u p r o u s s u l p h i d e i n a s o l i d s t a t e c e l l Cu CuBr C u x S g r a p h i t e (1) and f o u n d t h a t t h e s t o i c h i o m e t r y o f t h e s u l p h i d e s t r o n g l y i n  f l u e n c e d t h e c o n d u c t i v i t y . Some o f t h e i r r e s u l t s a t 400°C a r e summarized i n T a b l e I I I . TABLE I I I E l e c t r o n i c C o n d u c t i v i t y o f C u x S a t 400°C Cu/S R a t i o C e l l P o t e n t i a l E l e c t r o n i c C o n d u c t i v i t y V o hm - 1 cm" 1.9996 0 0.3 1.9992 0.05 0.5 1.9975 0.10 6 1.9935 0.15 70 1.98 0.20 170 - 8 - T h e i r e x p e r i m e n t s a l s o showed a s t r o n g d e pendence between t h e Cu/S r a t i o and t h e c e l l p o t e n t i a l , and t h e f o l l o w i n g i s a s i m p l i f i c a t i o n o f t h e i r i n t e r p r e t a t i o n . F o r C u 2 QQQS, X 9 ° and ( x C u + ® ) ° a r e t h e c o n c e n t r a t i o n s o f e x c e s s e l e c t r o n s and c u p r i c i o n s ; Wagner and Wagner c a l c u l a t e d x 9° = ( x . C u + ® ) ° < 3.5 x 1 0 - V p e r u n i t S (2) I f Cu i s removed f r o m t h e C u x S by t h e f o l l o w i n g r e a c t i o n s : C u + C u x S *~ C u + C u B r <3> e C u x S ^ Q g r a p h i t e (4) and t h e c h a r g e n e u t r a l i t y i n t h e C u v S i s m a i n t a i n e d by t h e f o l l o w i n g r e a c t i o n : c u + c u x s - ^ c u + ® C U x S + e C U x S , (5) t h e n t h e n e t r e a c t i o n i s 2 C u + C u x S - * - C u + ® C U x S + C u + C u B r + G g r a p h i t e (6) Thu s , as t h e Cu/S r a t i o i n C u x S d r o p s , t h e r e i s a n e t i n c r e a s e i n t h e c o n c e n t r a t i o n o f e l e c t r o n h o l e s and no n e t i n c r e a s e i n t h e c o n c e n t r a t i o n o f e x c e s s e l e c t r o n s i n C u x S . As t h e l a t t e r v a l u e i s s m a l l t o s t a r t w i t h , t h e r e s u l t i s a c o r r e s p o n d i n g d e c r e a s e i n t h e number o f m u t u a l l y a n n i h i l a t o r y c o l l i s i o n s between e x c e s s e l e c t r o n s and c u p r i c i o n s , v i z : C u + e + 0 P- Cu+ (7) so t h e m o b i l i t y o f C u + ® i n c r a a s e s as w e l l as t h e c o n c e n t r a t i o n . The c o n d u c t i v i t y i s a f u n c t i o n o f b o t h t h e m o b i l i t y and c o n c e n - t r a t i o n , so t h e c o n d u c t i v i t y o f Cu , and i n t u r n t h e c e l l p o t e n t i a l , i n c r e a s e a s t h e Cu/S r a t i o d r o p s . The i n f l u e n c e o f s t o i c h i o m e t r y on c e l l p o t e n t i a l s w o u l d p r o b a b l y be s i m i l a r when a l i q u i d e l e c t r o l y t e r e p l a c e s t h e s o l i d s t a t e CuBr e l e c t r o l y t e . No r e f e r e n c e t o t h i s s i t u a t i o n c o u l d be f o u n d . •The E f f e c t o f S e m i c o n d u c t i v i t y o f S u l p h i d e s on t h e i r E l e c t r o c h e m i c a l B e h a v i o u r  S e m i c o n d u c t o r s i n g e n e r a l and compound s e m i c o n d u c t o r s i n p a r t i c u l a r d i f f e r f r o m m e t a l s w i t h r e s p e c t t o t h e i r p o t e n t i a l s and p o t e n t i a l d i s t r i b u t i o n s i n two i m p o r t a n t ways: (a) The e l e c t r o c h e m i c a l p o t e n t i a l o f e l e c t r o n s i n a compound s e m i c o n d u c t o r c a n be v a r i e d o v e r a w ide r a n g e by t h e a d d i t i o n o f s u i t a b l e i m p u r i t i e s * and, as p r e v i o u s l y n o t e d , by c h a n g e s i n t h e s t o i c h i o m e t r i c r a t i o . F o r example: a t 400°C, t h e e l e c t r o c h e m i c a l p o t e n t i a l o f Cu i n c u p r o u s s u l p h i d e c h a n g e s by a b o u t 125 m i l l i v o l t s when t h e Cu/S r a t i o c h a n g e s f r o m 2 t o 1.996 9 and a t room t e m p e r a t u r e , t h e e l e c t r o c h e m i c a l p o t e n t i a l o f t h e e l e c t r o n s i n Ge c h a n g e s by a b o u t 60 m i l l i v o l t s w i t h t h e a d d i t i o n o f 3 x 1 0 1 4 a t o m s / c c o f A s . (b) The d i e l e c t r i c c o n s t a n t o f most s e m i c o n d u c t o r s i s i n t h e r a n g e o f 10-20, w h i l e t h a t o f t h e m e t a l s a p p r o a c h e s z e r o by d e f i n i t i o n . T h i s f a c t o r , c o u p l e d w i t h t h e l o w e r f r e e c a r r i e r d e n s i t y i . e . l o w e r c o n d u c t i o n e l e c t r o n c o n c e n t r a t i o n , e n a b l e s s e m i c o n d u c t o r s t o s u p p o r t e x t e n s i v e s p a c e c h a r g e s . When a m e t a l f o r m s t h e two p l a t e s o f a c o n d e n s e r , t h e p o t e n t i a l I s u n i f o r m t h r o u g h o u t t h e b u l k o f e a c h p l a t e up t o a p o s i t i o n v e r y n e a r t h e s u r f a c e , so t h e p o t e n t i a l d i f f e r e n c e . between t h e two p l a t e s i s e s s e n t i a l l y t h e same as t h a t between t h e s u r f a c e s o f t h e two p l a t e s . However, when a s e m i c o n d u c t o r i s made one p l a t e o f t h e c o n d e n s e r , a s u b s t a n t i a l p o r t i o n o f t h e * Examples o f s u i t a b l e i m p u r i t i e s : c a t i o n s o f d i f f e r e n t v a l e n c e t o n o r m a l c a t i o n s , e . g . L i + and A l + + + i n NiO; and a n i o n s o f d i f f e r e n t v a l e n c e t o n o r m a l a n i o n s , e . g . C l " i n 0 = l a t t i c e . - 10 - p o t e n t i a l d i f f e r e n c e may o c c u r w i t h i n t h e s e m i c o n d u c t o r b e c a u s e t h e s p a c e c h a r g e has e s t a b l i s h e d a n o n - u n i f o r m p o t e n t i a l d i s  t r i b u t i o n i n t h e s e m i c o n d u c t o r . The i n t e r n a l s p a c e c h a r g e i s e q u a l b u t o p p o s i t e i n s i g n t o t h e s u r f a c e s p a c e c h a r g e . The s i t u a t i o n a t t h e s e m i c o n d u c t o r - e l e c t r o l y t e i n t e r  f a c e i s g e n e r a l l y t h e same as t h a t a t a m e t a l - e l e c t r o l y t e i n t e r f a c e , w i t h t h e e x c e p t i o n o f t h e added i n f l u e n c e o f t h e s p a c e c h a r g e . U s u a l l y , t h e s p a c e c h a r g e i s o n l y o f s i g n i f i c a n c e i n c a s e s when t h e s u r f a c e o f t h e e l e c t r o d e has been p r e f e r e n t i a l l y c o n c e n t r a t e d w i t h d o n o r o r a c c e p t o r a t o m s 1 5 . The s p a c e c h a r g e l a y e r has a t h i c k n e s s o f 100-10,000 A i n most s e m i c o n d u c t o r s . The H e l m h o l t z d o u b l e l a y e r ( t h e r e g i o n between t h e e l e c t r o d e and t h e p l a n e o f o c l o s e s t a p p r o a c h o f i o n s i n t h e e l e c t r o l y t e ) i s a b o u t 3 A. Thermodynamics o f O x i d a t i o n o f CU2S The u s e o f p o t e n t i a l / p H d i a g r a m s t o sho\-/ t h e r e g i o n s o f thermodynamic s t a b i l i t y o f v a r i o u s s p e c i e s i n aqueous s o l u t i o n s has been w e l l d e v e l o p e d , p a r t i c u l a r l y , by P o u r b a i x and h i s s c h o o l 2 7 ' ^ 3 . D i a g r a m s have been c o n s t r u c t e d f o r a l l . t h e m e t a l - w a t e r s y s t e m s , and f o r a number o f t h r e e - c o m p o n e n t s y s t e m s . H o r v a t h and Novak 1* 8 p u b l i s h e d a d i a g r a m f o r t h e c o p p e r - s u l p h u r - w a t e r s y s t e m ( F i g u r e 3) w h i c h i s u s e f u l i n t h e s t u d y o f t h e e f f e c t o f S on t h e c o r r o s i o n o f Cu. They have s i m p l i f i e d t h e s y s t e m by i g n o r i n g a l l m e t a s t a b l e s u l p h u r - w a t e r f o r m s , a s i m p l i f i c a t i o n w h i c h a p p e a r s n e c e s s a r y a f t e r e x a m i n i n g t h e c o m p l e x i t y o f t h e s u l p h u r - w a t e r b i n a r i e s c o n s t r u c t e d by V a l e n s i 2 8 . - 11 -- 12 - K to •P rH o > rci •H -P c 1) 4-> O 0< 0.8 0.6 _ 0.4 0.2 -0.2 -0.4 J L F i g u r e 4. o N \ J L 8 10 pH 12 14 P o t e n t i a l / p H D i a g r a m f o r t h e S y s t e m C u - S - ^ O , O m i t t i n g O - x i d a t i o n R e a c t i o n s w i t h M e t a l l i c Cu. A l l s p e c i e s a t ' U n i t A c t i v i t y . - 13 - A somewhat d i f f e r e n t d i a g r a m has b e en c o n s t r u c t e d ( F i g u r e 4) s t a r t i n g w i t h C u 2 S r a t h e r t h a n Cu m e t a l . No s u l p h u r f o rms o t h e r t h a n S a r e shown on t h e d i a g r a m , e v e n t h o u g h S 0 4 ~ i s t h e r m o d y n a m i c a l l y s t a b l e (see T a b l e C - I I , r e a c t i o n s 6 and 1 2 ) . The SOq~ r e g i o n s have been o m i t t e d b e c a u s e t h e r e a c t i o n S + 4H 20 S 0 4 = + 8 H + + 6e~ (8) i s e x t r e m e l y s l o w , and t h u s p r o b a b l y u n i m p o r t a n t i n t h e e l e c t r o  c h e m i c a l o x i d a t i o n o f C u 2 S . C h e m i c a l O x i d a t i o n o f C u p r o u s S u l p h i d e W a r r e n 4 9 s t u d i e d t h e a c i d p r e s s u r e l e a c h i n g o f t h r e e c o p p e r m i n e r a l s - c h a l c o p y r i t e , c h a l c o c i t e and c o v e l l i t e - u n d e r t h e f o l l o w i n g c o n d i t i o n s : t e m p e r a t u r e : 100-200°C p r e s s u r e : 10-350 p s i a c i d i t y : 20-50 g p l H 2 S 0 4 P o 2 : 10-80 p s i . He c o n c l u d e d t h a t a t w o - s t a g e mechanism was o p e r a t i n g i n t h e o x i d a t i o n o f c u p r o u s s u l p h i d e , i m p l y i n g t h a t t h e r e a c t i o n s were: C u 2 S + 1/2 0 2 + 2F. +—6- C u + + + CuS + H 20 ..... (9) CuS + 1/2 0 2 + 2 H + — C u + + + S + H 20 (10) On t h e b a s i s o f r e a c t i o n r a t e measurements, he c a l c u l a t e d t h e a c t i v a t i o n e n e r g i e s o f t h e r a t e - c o n t r o l l i n g s t e p s o f t h e two r e a c t i o n s t o be 6.6 and 1 . 8 : k c a l / m o l e , r e s p e c t i v e l y . S u l l i v a n 5 0 s t u d i e d t h e o x i d a t i o n o f c h a l c o c i t e by f e r r i c s u l p h a t e i n n e u t r a l and a c i d s o l u t i o n s a t t e m p e r a t u r e s up t o 50°C. He n o t e d t h a t l i t t l e o r no e l e m e n t a l s u l p h u r was f o u n d i n t h e r e a c t i o n p r o d u c t s u n t i l a p p r o x i m a t e l y o n e - h a l f o f t h e c o p p e r i n t h e c u p r o u s s u l p h i d e had gone i n t o s o l u t i o n . He c o n c l u d t h a t t h e r e a c t i o n p r o c e e d e d i n two s t e p s : C u 2 S + F e 2 ( S 0 4 ) 3 — ^ C u S 0 4 + 2 F e S 0 4 + CuS ( f a s t ) . (11). CuS + F e 2 ( S 0 4 ) 3 — * C u S 0 4 + S + 2 F e S 0 4 (slow) (12) E l e c t r o c h e m i c a l O x i d a t i o n o f C u p r o u s S u l p h i d e Noddack and W r a b e t z 1 1 ' 1 2 and S a t o 4 5 ' 4 7 s t u d i e d t h e b e h a v i o u r o f s e v e r a l s u l p h i d e e l e c t r o d e s , i n c l u d i n g c u p r o u s and c u p r i c s u l p h i d e , as p a r t o f g e o l o g i c a l i n v e s t i g a t i o n s o f s u l p h i d e o r e b o d i e s * . They n o t e d t h a t t h e r e s t p o t e n t i a l s ( i . e . open c i r c u i t p o t e n t i a l ) o f t h e C u 2 S and CuS e l e c t r o d e s were i n d e p e n d e n t o f pH and ( S 0 4 = ) i n a c i d s o l u t i o n , b u t were d e p e n d e n t on ( C u + + ) . S a t o c o n c l u d e d t h a t t h e p o t e n t i a l - d e t e r m i n i n g r e a c t i o n s were f o r t h e C u 2 S and CuS e l e c t r o d e s r e s p e c t i v e l y : C u 2 S — t - C u S + C u + + + 2e~ (13) CuS — ^ C u + + + S + 2e~ (14) E x p e r i m e n t a l v a l u e s a r e compared i n T a b l e IV w i t h t h o s e c a l c u  l a t e d f r o m f r e e e n e r g y d a t a . TABLE IV R e s t P o t e n t i a l s f o r C u 2 S and CuS E l e c t r o d e s a t 25°C E l e c t r o d e P o t e n t i a l , V (NHS) E l e c t r o d e Noddack and S a t o 4 7 W r a b e t z 1 1 ' 1 2 C a l c u l a t e d C u 2 S 0.504 0.47** 0.535 (+0.13) CuS 0.567 0.58** 0.588 (+0.13) * T h e i r r e s u l t s a r e summarized and d i s c u s s e d b r i e f l y i n A p p e n d i x D ** Noddack and Wrabetz p e r f o r m e d t h e i r e x p e r i m e n t s a t t e m p e r a t u r e s o t h e r t h a n 25°C, and u s u a l l y a t 1 8 ° C . The d i f f e r e n c e between - 15 - In b a s i c s o l u t i o n s , the p o t e n t i a l was a f u n c t i o n o f pll, presumably because of the h y d r o l y s i s of Cu , v i z : C u + + + 2H 20 ^ Cu (Oil) 2 + 2H + (15) The r e s u l t i n g o v e r a l l r e a c t i o n s are, f o r the Cu 2S and CuS e l e c t r o d e s r e s p e c t i v e l y : Cu 2S + 2II 20-*~CuS + Cu(OH) 2 + 2H 4 + 2e~ .....(16) V = 0.802 - 0.0591 pH CuS + 2 H 2 0 C u ( O H ) 2 + S° + 2H + + 2 e - (17) V = 0.862 - 0.0591 pH. Sato suggested t h a t the p o t e n t i a l - d e t e r m i n i n g r e a c t i o n f o r the Cu 2S e l e c t r o d e may i n v o l v e d i g e n l t e : 5Cu 2S — - C u + + + C u 9 S 5 + 2e" (a) C u g S 5 5CuS + 4 C u + + + 8e~ (b) (18) CuS C u + + + S + 2e~ (c) Ke p o s t u l a t e d t h a t the 0.031 V d i f f e r e n c e between h i s experimental value and the c a l c u l a t e d value of the e l e c t r o d e p o t e n t i a l (Table IV) might be due to r e a c t i o n s (18 a) or (18 b) being p o t e n t i a l - d e t e r m i n i n g . However, the accuracy of the thermodynamic data from which the e l e c t r o d e p o t e n t i a l s were c a l c u l a t e d i s such t h a t a d i f f e r e n c e o f 0.031 V i s hot unreasonable (see Tables IV and C - I I ) . Furthermore, s t o i c h i o m e t r i c d e v i a t i o n s have a s i g n i f i c a n t e f f e c t on the e l e c t r o d e p o t e n t i a l ; Sato d i d not r e p o r t the a n a l y s i s of h i s e l e c t r o d e , but i t may have had a l a r g e Cu d e f i c i e n c y which c o u l d have a l t e r e d the e l e c t r o d e p o t e n t i a l . No (cont'd from p.14) V ° , the e l e c t r o d e p o t e n t i a l , c a l c u l a t e d at 18 and 25°C would o n l y be about 0.005 V f o r most e l e c t r o d e s 6 0 , so no c o r r e c t i o n has been made. - 16 - t h e r modynamic d a t a a r e a v a i l a b l e f o r d i g e n i t e . I t w o u l d a p p e a r , t h e n , t h a t d i r e c t o b s e r v a t i o n o f t h e r e a c t i o n p r o d u c t s i s n e c e s s a r y t o r e s o l v e t h e n a t u r e o f t h e p o t e n t i a l - d e t e r m i n i n g r e a c t i o n u n e q u i v o c a l l y . D u r i n g t h e i r s t u d y o f t h e o x i d a t i o n o f n i c k e l . s u l p h i d e e l e c t r o d e s , R e n z o n i e t a l ' 1 b r i e f l y e xamined t h e o x i d a t i o n "of c u p r o u s s u l p h i d e , and s u g g e s t e d t h a t t h e mechanism i n v o l v e d t h e f o l l o w i n g s t e p s : C u 2 S —*» C u + + CuS + e~ . . . . . . ( a ) . . : C u + —*- C u + + + e" V , . . . . . ( b ) (19) CuS C u + + + S + 2e . . . . . ( c ) However., no r e s t p o t e n t i a l measurements were r e p o r t e d . T h e i r i d e n t i f i c a t i o n o f CuS as an i n t e r m e d i a t e r e a c t i o n p r o d u c t a p p e a r s p l a u s i b l e , b u t no s u p p o r t i s g i v e n f o r t h e i r s e l e c t i o n o f C u + as t h e i n i t i a l aqueous i o n . The f i n a l r e a c t i o n p r o d u c t s were s t a t e d t o be C u + + and S. A y l e n 6 1 d e t e r m i n e d t h e r e s t p o t e n t i a l o f a C u 2 S e l e c t r o d e t o be 0.477 V i n a c i d c o p p e r s u l p h a t e s o l u t i o n a t 25°C. When t h e y o x i d i z e d t h e n i c k e l s u l p h i d e and c o p p e r s u l p h i d e a n o d e s , R e n z o n i e t a l 1 n o t e d t h a t t h e n i c k e l " a n d c o p p e r d i s s o l v e d i n t h e e l e c t r o l y t e s o l u t i o n l e a v i n g an e s s e n t i a l l y i n t a c t s t r u c t u r e o f s u l p h u r , an o b s e r v a t i o n w h i c h i s c o n s i s t e n t w i t h t h e s u l p h i d e s t r u c t u r e d e s c r i b e d e a r l i e r ( i . e . s t a b l e s u l p h u r l a t t i c e , m o b i l e Cu a t o m s ) . In t h e c o m m e r c i a l n i c k e l s u l p h i d e p r o c e s s , t h e anodes a r e p l a c e d i n p o r o u s bags d u r i n g - 17 - e l e c t r o l y s i s t o p r e v e n t t h e c o n t a m i n a t i o n o f t h e e l e c t r o l y t e w i t h s u l p h u r . A number o f m e t a l s , p a r t i c u l a r l y s e l e n i u m , r e m a i n w i t h t h e s u l p h u r s l u d g e and a r e r e c o v e r e d i n a s u b s e q u e n t p r o c e s s . G e n e r a l D i s c u s s i o n o f E l e c t r o d e K i n e t i c s The r a t e s o f e l e c t r o d e r e a c t i o n s c a n most c o n v e n i e n t l y be f o l l o w e d by m e a s u r i n g t h e c u r r e n t d e n s i t y as a f u n c t i o n o f t h e e l e c t r o d e p o t e n t i a l . The r e s u l t i n g r e l a t i o n s h i p , when p l o t t e d , i s c a l l e d a p o l a r i z a t i o n c u r v e . I f i t i s p o s s i b l e t o m i n i m i z e e x t r a n e o u s d i f f u s i o n and ohmic e f f e c t s (see A p p e n d i x D ) , t h e n t h e p o l a r i z a t i o n c u r v e s c a n be a n a l y s e d t o a i d i n d e t e r m i n i n g t h e e l e c t r o d e r e a c t i o n mechanism. I n A p p e n d i x E, a d e r i v a t i o n o f s e v e r a l i m p o r t a n t p o l a r i z a t i o n r e l a t i o n s h i p s i s p r e s e n t e d . Two o f t h e s e a r e s t a t e d b e l o w : f o r an a c t i v a t i o n - c o n t r o l l e d r e a c t i o n , when 2.303 RT ( i . e . u o > ~ 20 mV) t h e n t h e n where GO > l n . i j = I n i Q + (1- ft) A"> uo RT f o r an a c t i v a t i o n - c o n t r o l l e d r e a c t i o n , when < 2.30 3 RT ( i . e . LO < ^ 20 mV) RT OO <~*~3 = O v e r p o t e n t i a l i& = Net a n o d i c c u r r e n t d e n s i t y i g = E x c h a n g e c u r r e n t ' (20) . . .. (21) - 18 - = A c t i v a t i o n b a r r i e r symmetry f a c t o r = S t o i c h i o m e t r i c f a c t o r = F a r a d a y c o n s t a n t R = Gas c o n s t a n t T = A b s o l u t e t e m p e r a t u r e In t h e r e s t s t a t e , a p o t e n t i a l i s d e v e l o p e d a t t h e e l e c t r o d e - s o l u t i o n i n t e r f a c e w h i c h i s c o n s i s t e n t w i t h t h e c h e m i s t r y o f t h e two p h a s e s , s o l i d and s o l u t i o n . A l t h o u g h t h e r e i s a l m o s t c e r t a i n l y a f l o w o f e l e c t r i c a l c h a r g e s i n b o t h d i r e c t i o n s a c r o s s t h e a n o d e - s o l u t i o n i n t e r f a c e i n t h e r e s t s t a t e , t h e r e i s no n e t f l o w i n one o r o t h e r d i r e c t i o n ; i . e . t h e c u r r e n t i s t h e same i n b o t h d i r e c t i o n s , t h u s m a i n t a i n i n g t h e e l e c t r i c a l n e u t r a l i t y o f t h e s y s t e m . The c u r r e n t d e n s i t y i n b o t h d i r e c t i o n s a c r o s s t h e s o l u t i o n - s o l i d i n t e r f a c e i n t h e r e s t s t a t e i s c a l l e d t h e exchange c u r r e n t * . T a b l e V l i s t s v a l u e s o f t h e exchange c u r r e n t f o r v a r i o u s e l e c t r o  c h e m i c a l r e a c t i o n ; t h e d a t a f o r a n o d i c d i s s o l u t i o n o f m e t a l s o r compounds a r e v e r y meagre. A s i m p l e d e s c r i p t i o n o f t h e e x c h a n g e c u r r e n t i s t h a t i t i s a measure o f t h e r e l a t i v e a b i l i t y o f t h e e l e c t r o d e t o t a k e p a r t i n t h e p a r t i c u l a r e l e c t r o d e r e a c t i o n . F o r t h e c a s e o f h y d r o g e n e v o l u t i o n on m e t a l c a t h o d e s , B o c k r i s 1 4 has p o i n t e d o u t t h a t t h e r e i s a s t r o n g r e l a t i o n s h i p between LQ, t h e i s a measure o f t h e e a s e w i t h w h i c h e l e c t r o n s l e a v e t h e m e t a l ; e xchange c u r r e n t , t h e t h e r m i o n i c work * F o r h e t e r o g e n e o u s r e a c t i o n s , t h e c u r r e n t w i l l be e q u i v a l e n t t o an a p p a r e n t c u r r e n t d e n s i t y . - 19 - TABLE V Values o f the Exchange C u r r e n t f o r Vari o u s E l e c t r o c h e m i c a l Reactions S i t u a t i o n Exchange Current A/cm 2 a t 25°C Reference Metal D i s s o l u t i o n : C u / C u + + i n 1 M CuS0 4* F e / F e + + i n 1 M FeS0 4 Metal D e p o s i t i o n : Cu on Cu from 1 M CuS0 4* Fe on Fe from 1 M FeS0 4 Hydrogen E v o l u t i o n : on Au i n 1.0 N Hcl Cd i n 1.0 N Hcl Hg i n 0.1 N Hcl Pb i n 0.1 N H c l Pt i n 1.0 N H c l Oxygen E v o l u t i o n : on Pt i n 0.1 N H 2S0 4 F e + + - F e + + + redox system i n sulphate s o l u t i o n on Type 304 4.5 x 10~ 8 S t a i n l e s s S t e e l 1 - 2 x 10" 3 (0H~) dependent 2 x 10~ 5 10" 8 10" 5 - 10~ 6 i o - 7 5 x 1 0 " 1 3 2 x 1 0 " 1 3 10" 3 2 x I O " 1 0 32 33 14 14 14 14 14 14 14 14 21 * These r e s u l t s are anomalous; the i g va l u e s should be the same f o r the same c o n c e n t r a t i o n o f C u + + , a l l o t h e r f a c t o r s being e q u a l . The symmetry f a c t o r , , i n d i c a t e s the p o r t i o n o f the o v e r p o t e n t i a l which i s a c t u a l l y o p e r a t i n g between the i n i t i a l p o i n t o f the r e a c t i o n and the peak of the energy b a r r i e r e x i s t i n g between the i n i t i a l and f i n a l s t a t e . T h i s i s the important r e g i o n along the r e a c t i o n path, f o r once a r e a c t i n g s p e c i e s passes over the peak of the energy b a r r i e r , i t r e q u i r e s no f u r t h e r d r i v i n g f o r c e to reach the f i n a l s t a t e . Although i t i s convenient t o t h i n k o f the energy b a r r i e r as having a p h y s i c a l shape, t h i s i s not necessary f o r a formal development of the r a t e e x p r e s s i o n s ; - 20 - t h e t e r m (3> c a n be c o n s i d e r e d t o be o n l y a m a t h e m a t i c a l c o n  v e n i e n c e , a number between 0 and 1. Q u i t e o f t e n , |3> has t h e v a l u e o f 1/2 and i n t h e s e c a s e s , t h e e n e r g y b a r r i e r , r e g a r d l e s s o f t h e i n t e r p r e t a t i o n o f i t s p h y s i c a l s h a p e , i s t r u l y s y m m e t r i c a l . The s t o i c h i o m e t r i c f a c t o r A. i s a two-component f a c t o r : A = n/>) (22) where n i s t h e number o f e l e c t r o n s i n v o l v e d i n t h e o v e r a l l e l e c t r o d e p r o c e s s , and ^ i s t h e number o f t i m e s t h e r a t e d e t e r m i n i n g s t e p o c c u r s w h i l e t h e o v e r a l l r e a c t i o n o c c u r s o n c e . Then A i s t h e number o f e l e c t r o n s i n v o l v e d i n one a c t o f t h e r a t e d e t e r m i n i n g s t e p . I f r e a s o n a b l e d a t a a r e a v a i l a b l e and c a n be t r e a t e d by t h e m a t h e m a t i c a l methods d e s c r i b e d a bove, some i n f o r  m a t i o n on t h e n a t u r e o f t h e e l e c t r o c h e m i c a l r e a c t i o n s s h o u l d be r e v e a l e d upon d e t e r m i n a t i o n o f t h e p a r a m e t e r s A , n, p> and ^ . Such d a t a can be u s e d f u r t h e r i n some c a s e s t o g i v e t h e h e a t o f a c t i v a t i o n . H u r l e n 3 h > 3 5 d e v e l o p e d a f o r m u l a f o r d e t e r m i n i n g t h e s t a n d a r d h e a t o f a c t i v a t i o n , AH Q*, f o r r e a c t i o n s where (2> = 0 . 5 , v i z : AH * = 2.303 R d l o g ( J n / T ) + 1 AH D (23) d (1/T) 2~5 where AH Q* = S t a n d a r d h e a t o f a c t i v a t i o n R = Gas c o n s t a n t J Q = S t a n d a r d exchange c u r r e n t d e n s i t y (see-Appendix.;F) T = A b s o l u t e t e m p e r a t u r e AH,-. = S t a n d a r d h e a t o f r e a c t i o n O b j e c t and Scope o f P r e s e n t Work C u p r o u s s u l p h i d e e l e c t r o d e s were p r e p a r e d and b o t h r e s t p o t e n t i a l and p o l a r i z a t i o n measurements were, o b t a i n e d i n v a r i o u s s o l u t i o n s o - The r e s t p o t e n t i a l measurements have been a n a l y s e d t o p r o v i d e a v a l u e f o r t h e e l e c t r o d e p o t e n t i a l V° f o r c u p r o u s s u l p h i d e , and t h e d i s c r e p a n c i e s between t h i s v a l u e , t h a t c a l c u l a t e d f r o m f r e e e n e r g y d a t a , and t h a t d e t e r m i n e d by S a t o have been d i s c u s s e d . M ost o f t h e p o l a r i z a t i o n measurements were made a t low v a l u e s o f t h e o v e r p o t e n t i a l between 2.0 and 35°C as t h i s r e g i o n p r o v i d e d t h e o n l y r e p r o d u c i b l e r e s u l t s . C e r t a i n k i n e t i c p a r a m e t e r s were c a l c u l a t e d . The r e s u l t s a r e r e v i e w e d i n t e r m s o f p o s s i b l e r e a c t i o n mechanisms, and t h e a d d i t i o n a l d a t a r e q u i r e d t o d i f f e r e n t i a t e between t h e s e v e r a l p o s s i b i l i t i e s a r e d i s c u s s e d . - 22 - APPARATUS AND EXPERIMENTAL PROCEDURES The E l e c t r o l y t i c C e l l The e l e c t r o l y t i c c e l l u s e d i n t h i s work ( F i g u r e 5) c o n s i s t e d o f a 4 - l i t e r p y r e x b e a k e r w i t h a c l o s e f i t t i n g l i d and c o n t a i n e d t h r e e e l e c t r o d e s - anode, c a t h o d e , and r e f e r e n c e -, a g l a s s s t i r r i n g r o d d r i v e n by a v a r i a b l e s p e e d m o t o r , a gas i n l e t and a t h e r m o m e t e r ( r a n g e : -1 t o + 101°C i n d i v i s i o n s o f 0 . 1 ° C ) . The c e l l was p l a c e d i n a 20 l i t e r w a t e r b a t h h e a t e d by an e l e c t r i c c o i l and c o o l e d when n e c e s s a r y by e i t h e r t a p w a t e r i n a c o p p e r c o i l o r i c e c u b e s . The t e m p e r a t u r e was c o n t r o l l e d w i t h i n + 0 . 1 ° C by a P h i l a d e l p h i a M i c r o s e t C o n t r o l l e r i n s e r i e s w i t h a M e r c - t o - M e r c r e l a y s w i t c h . A n i t r o g e n a t m o s p h e r e was u s u a l l y m a i n t a i n e d i n t h e c e l l t o m i n i m i z e o x i d a t i o n by C o m m e r c i a l g r a d e N 2 was p u r i f i e d by p a s s a g e t h r o u g h a chromous s u l p h a t e s o l u t i o n . M e a s u r i n g C i r c u i t A s i m p l e p o t e n t i a l - and c u r r e n t - m e a s u r i n g c i r c u i t ( F i g u r e 6) was u s e d . P o t e n t i a l s were i m p r e s s e d a c r o s s t h e anode and c a t h o d e u s i n g t h r e e 2V l e a d - a c i d b a t t e r i e s i n s e r i e s and a s l i d e w i r e r h e o s t a t as a p o t e n t i a l d i v i d e r . The p o t e n t i a l s between t h e v a r i o u s e l e c t r o d e s were measured by a Pye p o t e n t i o m e t e r and an a u x i l i a r y m i r r o r g a l v a n o m e t e r . The p o t e n t i o m e t e r had t h r e e r a n g e s - 0-0.01799 V, 0-0.1799 V and 0-1.799 V. C u r r e n t s up t o one mA were measured w i t h an RCA u l t r a - s e n s i t i v e DC micro-ammeter ( f u l l - s c a l e movement = 0.5 V ) ; a f t e r c a l i b r a t i o n w i t h t h e p o t e n t i o m e t e r , t h e - 2 3 - c o v e r ' s t a n d a r d c a l o m e l e l e c t r o d e mounted CU2S L u g g i n c a p i l l a r y t h e r m o m e t e r p l a t i n u m c a t h o d e g l a s s gas p o r t g l a s s s t i r r i n g r o d 4 l i t e r b e a k e r F i g u r e 5. C e l l f o r P o t e n t i a l Measurement s ,.-- 24 - p p o t e n t i o m e t e r Rs s a f e t y r e s i s t a n c e G g a l v o n o m e t e r SCE r e f e r e n c e e l e c t r o d e Am = ammeter C c a t h o d e B power s u p p l y A anode R r h e o s t a t M, N = s w i t c h e s F i g u r e 6. C i r c u i t f o r P o t e n t i a l and C u r r e n t Measurements a c c u r a c y o f t h e u n i t was a b o u t +2% o f t h e f u l l - s c a l e r e a d i n g . C u r r e n t s above one mA were measured w i t h a H e a t h k i t M u l t i m e t e r w i t h an a c c u r a c y o f a b o u t +2% o f t h e f u l l - s c a l e r e a d i n g (most measurements were t a k e n on t h e 150 mA r a n g e , so t h e a c c u r a c y i n t h i s c a s e was a b o u t +3 mA). Anodes The c u p r o u s s u l p h i d e anodes were p r e p a r e d by d i r e c t c o m b i n a t i o n o f c o p p e r and s u l p h u r i n a c l a y c r u c i b l e a t 4 0 0°C. The r e s u l t i n g s u l p h i d e was p l a c e d i n a g r a p h i t e c r u c i b l e , m e l t e d i n a g a s - f i r e d f u r n a c e a t a b o u t 1130°C and c a s t i n t o 1/2" x 3/8" x 2" p i e c e s . A f t e r s o l i d i f y i n g , t h e s u l p h i d e was h e l d a t a b o u t 100°C f o r one h o u r t o p r e v e n t c r a c k i n g due t o r a p i d c o o l i n g t h r o u g h c r y s t a l l o g r a p h i c t r a n s f o r m a t i o n t e m p e r a t u r e s . The m a t e r i a l was a n a l y s e d t o d e t e r m i n e t h e s t o i c h i o m e t r y . A p i e c e o f s i l v e r f o i l was c u t t o f i t one s i d e o f t h e c a s t s u l p h i d e and a l e n g t h o f c o p p e r w i r e was s o l d e r e d t o t h e s i l v e r . The s i l v e r f o i l was p r e s s e d f i r m l y a g a i n s t t h e s u l p h i d e s u r f a c e and t h e c o m b i n a t i o n was mounted i n M o l d p a c * so t h a t o n l y one s u r f a c e o f t h e s u l p h i d e r e m a i n e d e x p o s e d . T h i s s u r f a c e was p o l i s h e d by s t a n d a r d m e t a l l o g r a p h i c t e c h n i q u e s ( F i g u r e 7) and t h e n p l a c e d i m m e d i a t e l y i n t h e e l e c t r o l y t i c c e l l . * "Moldpac" i s a r e p a i r a c r y l i c ( m a n u f a c t u r e r : M o t l o i d Company, C h i c a g o , 111.) w h i c h i s v i r t u a l l y i n s o l u b l e i n a c i d s o l u t i o n s . - 26 - F i g u r e 7. Mounted C o p p e r S u l p h i d e E l e c t r o d e O t h e r E l e c t r o d e s The c a t h o d e o f t h e w o r k i n g c e l l was e i t h e r a s t a n d a r d a n a l y t i c a l p l a t i n u m g a u z e e l e c t r o d e o r a p l a t e o f c o p p e r . The r e f e r e n c e e l e c t r o d e was a Beckman s t a n d a r d s a t u r a t e d c a l o m e l e l e c t r o d e mounted i n a L u g g i n c a p i l l a r y t u b e . The c o n s t r u c t i o n o f t h e l a t t e r was b a s e d on t h e d e s i g n p r o p o s e d by P i o n t e l l i 2 3 , a d e s i g n w h i c h a l l o w s t h e r e f e r e n c e e l e c t r o d e t o be i n c o n t a c t w i t h t h e s o l u t i o n i m m e d i a t e l y a d j a c e n t t o t h e anode (see F i g u r e 5 ) . The p o t e n t i a l s e x e r t e d by t h e r e f e r e n c e e l e c t r o d e a t s e v e r a l t e m p e r a t u r e s a r e shown i n T a b l e V I , as c a l c u l a t e d f r o m t h e f o l l o w i n g h a l f - c e l l r e l a t i o n s h i p 1 7 : Hg, H g 2 c l 2 ( S ) , s a t u r a t e d K c l S =-0.2415 + 0.00076 ( 1 - 2 5 ) (24) TABLE V I The P o t e n t i a l o f t h e S a t u r a t e d C a l o m e l E l e c t r o d e T e m p e r a t u r e , °C O x i d a t i o n P o t e n t i a l e , v o l t s (NHS) E l e c t r o d e P o t e n t i a l V, v o l t s (NHS) 20 -0.2453 0.24 53 25 -0.2415 0.2415 30 -0.2377 0.2377 35 -0.2339 0.2339 S o l u t i o n s S t o c k s o l u t i o n s o f C u S 0 4 , H 2 S 0 4 , MgS0 4, NaHS0 4 and H c l 0 4 were p r e p a r e d f r o m e i t h e r r e a g e n t g r a d e c h e m i c a l s o r known s t a n d a r d s , a n a l y s e d , and d i l u t e d w i t h d i s t i l l e d w a t e r t o p r o v i d e e x p e r i m e n t a l - 28' - s o l u t i o n s o f t h e r e q u i r e d c o n c e n t r a t i o n . The f o l l o w i n g a n a l y t i c a l t e c h n i q u e s were u s e d : f o r C u + + , e l e c t r o l y t i c r e c o v e r y o f Cu; f o r H +, p o t e n t i o m e t r i c t i t r a t i o n w i t h b o r i c a c i d ; and f o r S, t h e E s c h k a p r o c e d u r e 6 4 . R e s t P o t e n t i a l Measurements The t e s t s o l u t i o n was p r e p a r e d and a l l o w e d t o come t o the. d e s i r e d t e m p e r a t u r e u n d e r s t i r r e d c o n d i t i o n s . N i t r o g e n was p a s s e d t h r o u g h i t f o r s e v e r a l h o u r s b e f o r e t h e e l e c t r o d e was i n s e r t e d . A f t e r b e i n g p o l i s h e d and c l e a n e d w i t h e t h a n o l , t h e e l e c t r o d e was i n s e r t e d and t h e L u g g i n c a p i l l a r y a d j u s t e d t o be i n i m m e d i a t e c o n t a c t w i t h t h e e l e c t r o d e s u r f a c e . P o t e n t i a l measurements were made i n t e r m i t t e n t l y o v e r a p e r i o d o f h o u r s . I n t h e e a r l y t e s t s , p o t e n t i a l s were measured f o r a p e r i o d o f 40-50 h o u r s , b u t as t h e r e a d i n g s were v e r y c o n  s i s t e n t , l a t e r measurements were t e r m i n a t e d a f t e r a p e r i o d o f 10-20 h o u r s . The e l e c t r o d e s were c o n n e c t e d t o t h e m e a s u r i n g p o t e n t i o m e t e r o n l y a t t h e t i m e o f measurement t o m i n i m i z e t h e o p p o r t u n i t y f o r s t r a y c u r r e n t s f r o m v a r i o u s s o u r c e s t o a c t on t h e e l e c t r o d e . P o l a r i z a t i o n Measurements The e l e c t r o d e and s o l u t i o n were p r e p a r e d as b e f o r e . The a p p l i e d p o t e n t i a l was v a r i e d i n c r e m e n t a l l y by u s e o f t h e s l i d e w i r e r h e o s t a t , and t h e e l e c t r o d e p o t e n t i a l and c e l l c u r r e n t were - 29 - m e a s u r e d . W i t h o v e r p o t e n t i a l s o f up t o 50-100 mV, t h e r e a d i n g s were v e r y s t a b l e ; a t h i g h e r o v e r p o t e n t i a l s c o n s i d e r a b l e v a r i a t i o n was n o t e d . A t low o v e r p o t e n t i a l s , a t i m e o f a b o u t 1 m i n u t e was a l l o w e d a t e a c h p o t e n t i a l ' s e t t i n g t o d e t e r m i n e i f t h e r e was any n o t i c e a b l e f l u c t u a t i o n . I f no f l u c t u a t i o n was n o t e d , t h e p o t e n t i a l was t h e n i n c r e a s e d ; i f a f l u c t u a t i o n was n o t e d , i t was f o l l o w e d f o r s e v e r a l m i n u t e s o r u n t i l a s t e a d y c o n d i t i o n was a t t a i n e d . A t t h e c o n c l u s i o n o f some o f t h e p o l a r i z a t i o n r u n s , t h e s u r f a c e o f t h e e l e c t r o d e was o b s e r v e d u n d e r t h e m i c r o s c o p e , and a p o r t i o n o f t h e c o r r o d e d e l e c t r o d e was a n a l y s e d c h e m i c a l l y and s t u d i e d by x - r a y methods. - 30 - RESULTS AND DISCUSSION A n a l y s i s o f C u 2 S C h e m i c a l a n a l y s i s o f t h e c u p r o u s s u l p h i d e gave t h e f o l l o w i n g r e s u l t s : Cu = 78.5 +0.2 wgt. % S = 2 0 . 5 + 0 . 4 wgt. % A t o m i c r a t i o , Cu/S = 1 . 9 3 T h i s a n a l y s i s i n d i c a t e s t h a t t h e e l e c t r o d e i s c u p r o u s s u l p h i d e w i t h a l a r g e c o p p e r d e f i c i e n c y . The Cu/S r a t i o o f 1.93 p l a c e s t h e m a t e r i a l i n e i t h e r t h e (2>Cu 2S + d i g e n i t e r e g i o n o r t h e Q c C u 2 S + CuS r e g i o n o f t h e Cu-S s y s t e m ( F i g u r e 2 ) , d e p e n d i n g on t h e t e m p e r a t u r e . An x - r a y powder p a t t e r n was o b t a i n e d and i t s a n a l y s i s ( A p p e n d i x II) s u g g e s t s t h a t t h e e l e c t r o d e i s c h a l c o c i t e . R e s t P o t e n t i a l M easurements R e s t p o t e n t i a l measurements were made w i t h s e v e r a l e l e c t r o d e s . I t was p r e v i o u s l y n o t e d t h a t s i l v e r f o i l had been u s e d a t t h e e l e c t r o d e - c o n n e c t i n g w i r e j u n c t i o n i n o r d e r t o m i n i m i z e t h e c o n t a c t p o t e n t i a l , b u t when r e s t p o t e n t i a l measurements were made w i t h two e l e c t r o d e s , one w i t h t h e s i l v e r f o i l and one w i t h o u t , l i t t l e v a r i a t i o n was o b s e r v e d (see T a b l e V I I ) . The n i t r o g e n was n e c e s s a r y i n t h e e l e c t r o l y t i c c e l l i n o r d e r t o o b t a i n c o n s i s t e n t r e s u l t s . F o r example, when N 2 was t u r n e d o f f o v e r n i g h t i n one r e s t p o t e n t i a l measurement, t h e p o t e n t i a l r o s e f r o m a b o u t 0.2 t o a b o u t 0.4 V. When n i t r o g e n was u s e d , t h e p o t e n t i a l r e m a i n e d c o n s t a n t f o r l o n g p e r i o d s (up t o 50 h o u r s ) . - 31 - TABLE V I I E l e c t r o d e P o t e n t i a l o f C u p r o u s S u l p h i d e A n o d e s , W i t h and W i t h o u t S i l v e r F o i l C o n t a c t E l e c t r o d e P o t e n t i a l S o l u t i o n s * w . r . t . R e f e r e n c e E l e c t r o d e , V W i t h s i l v e r f o i l W i t h o u t s i l v e r f o i l 0. 01 M C u S 0 4 -0.171 -0.172 0. 1 M C u S 0 4 -0.195 -0.194 0. 77 M C u S 0 4 -0.215 -0.215 0. 77 M C u S 0 4 -0.211 -0.211 0. 5 M N a 2 S 0 4 * S o l u t i o n A n a l y s i s a p p r o x i m a t e o n l y . R e s t p o t e n t i a l s were measured i n C u S 0 4 a t s e v e r a l l e v e l s o f c o n c e n t r a t i o n . U s i n g t h e a c t i v i t y c o e f f i c i e n t s m e a s u r e d by R o b i n s o n and J o n e s 1 6 , v a l u e s o f t h e e l e c t r o d e p o t e n t i a l , V ° C U x g , have been c a l c u l a t e d ( T a b l e V I I I ) u s i n g t h e r e l a t i o n s h i p S c e l l = V S > C < E > - V C u x S = V S . C . E . - ( V ° C u x S + RT I n a C u++) .....(25) n ^ where c e ] _ ] _ i s t h e m e a s u r e d p o t e n t i a l and n i s assumed t o e q u a l 2. The c a l c u l a t i o n s g i v e V ° C U x g = 0.490 +0.002 V a t 25°C. Measurements made i n C u S 0 4 - M g S 0 4 - H 2 S 0 4 s o l u t i o n s o f c o n s t a n t i o n i c s t r e n g t h have been i n t e r p r e t e d i n two ways: (a) U s i n g . V ° c s = 0.490 V, v a l u e s ' o f u C u + + were c a l c u l a t e d ( T a b l e I X ) . T h e s e v a l u e s r a n g e d f r o m 0.077 t o 0.104. (b) U s i n g (5 Q u++ = 0.1 (see A p p e n d i x G) and a s s u m i n g Q C u + + r e m a i n s c o n s t a n t i n s o l u t i o n s o f c o n s t a n t i o n i c s t r e n g t h , d e s p i t e c h a n g e s i n m o l a r i t y , v a l u e s o f V ° r c were c a l c u l a t e d - 32 - (Table X ) . These values ranged from 0.487 to 0.491 V. TABLE V I I I E l e c t r o d e P o t e n t i a l V 0 - ' i n CuSO,, at 25°C U Ux >3 h Run No. 6-cell/ V M C u++ mCu++* (Ref. 16) RT l o g a C u++ n? V V ° C u x S / SM 1 -0.205 0.559 0.562 0.058 -0.0439 0.490 SM 2 -0.213 1.665 1.923 0.0345 -0.0348 0.489 SM 3 -0.2015 0.273 0.274 0.087 -0.0479 0.492 SM4 -0.197 0.158 0.159 0.118 •0.0510 0.489 * moles/1000 gm water TABLE IX ft c u + + i n CuS04-MgS04-H 2S04 S o l u t i o n s o f Constant I o n i c Strenght a t 25°C Run £ c e i i , C o n c e n t r a t i o n * , M RT l o g ap u++ ac u++ ] $ c u + +  No. V CuSO 4 MqSOa H?SOd V x 1 0 5 SF 1 -0.186 0. 100 0 0.100 -0.0625 768 0.077 SF 2 -0.1585 0. 010 0.090 0.100 -0.0900 90.1 0.090 SF 3 -0.130 0. 001 0.099 0.100 -0.1185 9.76 0.098 SF 4 -0.1103 0. 0002 0.0999 0.100 -0.1382 2.09 0.104 * m o l a r i t y ^ m o l a l i t y at these c o n c e n t r a t i o n s . Some support f o r the l a t t e r assumption i s giv e n by Lewis and R a n d a l l 1 8 ' 4 0 , who s t a t e t h a t f o r a s i n g l e e l e c t r o l y t e i n s o l u t i o n , the f o l l o w i n g r e l a t i o n s h i p holds f o r d i l u t e s o l u t i o n s i . e . g e n e r a l l y under 0.01 M - 33 - l o g ft Z + Z_ JX°'5 ......(26) where Z + and Z_ a r e t h e e l e c t r o n i c c h a r g e s o f t h e p o s i t i v e and n e g a t i v e i o n s and A i s a c o n s t a n t f o r a p a r t i c u l a r s o l v e n t a t a p a r t i c u l a r t e m p e r a t u r e . Then i f j < \ r e m a i n s c o n s t a n t and Z + and Z_ r e m a i n c o n s t a n t , $ s h o u l d r e m a i n c o n s t a n t . The u n i f o r m i t y o f t h e v a l u e s o f V ° C U x S c a l c u l a t e d by t h i s method s u g g e s t s t h a t t h e v a l u e s °f ^ Pn + + o b t a i n e d f r o m e l e c t r o m o t i v e f o r c e measurements by t h e method o f A r g e r s i n g e r 2 5 ( A p p e n d i x G) have some v a l i d i t y . However more e x t e n s i v e t e s t work t h a n was u n d e r t a k e n h e r e w o u l d be r e q u i r e d t o c o n f i r m t h i s p o i n t . TABLE X V ° c u x S i n CuS04-MgS04-H 2S04 S o l u t i o n s o f C o n s t a n t I o n i c S t r e n g t h a t 25°C Run <S cell» C o n c e n t r a t i o n s , M a c u + + RT l o g a p n++ V ° c U x s r  No. V C u S 0 4 MqSC-4 HoS04 ( S rN++ = 0.1) n?- V V SF I -0.186 0.100 0 0.100 0.01 -0.0591 ~ 0.487 SF 2 -0.1585 0.010 0.090 0.100 0.001 -0.0886 0.489 SF 3 -0.130 0.001 0.099 0.100 0.0001 -0.1182-. 0.490 SF 4 -0.1103 0.0002 0.0999 0.100 0.00002 -0.1398 0.491 The c e l l p o t e n t i a l was measured i n CuSC^-^SC^-NaHSC^ s o l u t i o n s o f c o n s t a n t C u + + c o n c e n t r a t i o n and v a r y i n g H2SO4 c o n c e n  t r a t i o n . The NaHSO"4' was added i n an a t t e m p t t o m a i n t a i n t h e i o n i c s t r e n g t h a t a c o n s t a n t v a l u e . The i o n i c s t r e n g t h p r o b a b l y d i d n o t r e m a i n c o n s t a n t , however, b e c a u s e o f f u r t h e r d i s s o c i a t i o n o f HSO4""*. V a l u e s o f i o n i c s t r e n g t h a r e c a l c u l a t e d i n T a b l e X I * F o r H S 0 4 ~ ^ H + + 304 = , K d i s . = 1*26 x 1 0 ~ 2 , a c c o r d i n g t o L a t i m e r 1 9 . TABLE XI R e s t P o t e n t i a l Measurements i n CuS0. 4-H2S0 4-NaHS0 4 S o l u t i o n s a t 25°C C o n c e n t r a t i o n a t I o n i c pH C e l l M o l a r i t y E q u i l i b r i u m S t r e n g t h (measured) P o t e n t i a l , C u S 0 4 H 2 S 0 4 NaHS0 4 s o 4 - HS0 4~ H+ A V SF 1 0.100 0.100 - 0.045 0.155 0.045 0. 390 - -0.186 SF 5 0.100 0.050 0.050 0.072 0.128 0.022 0- 444 1.45 -0.185 SF 6 0.100 0.010 0.090 0.102 0.098 0.012 0. 504 1.5 -0.184 SF 8 0.100 0.001 0.099 0.109 0.101 0.010 0. 523 1.75 -0.184 A C a l c u l a t e d from e q u i l i b r i u m c o n c e n t r a t i o n s . 35 - a s s u m i n g e q u i l i b r i u m d i s s o c i a t i o n ' o f 1 HSO4"" . B e c a u s e o f t h e a p p a r e n t • • v a r i a t i o n o f t h e i o n i c , s t r e n g t h , t h e same v a l u e o f 0 cu++ c a n n o t be u s e d i n a l l c a s e s , so no a t t e m p t has been made t o c a l c u l a t e v a l u e s o f V ° C u ^ s . The c o n s t a n c y o f t h e measured c e l l p o t e n t i a l i n d i c a t e s t h a t t h e r e i s l i t t l e o r no v a r i a t i o n w i t h pH, a t l e a s t i n t h e r a n g e pH=l-2. A few r e s t p o t e n t i a l s were m e a s u r e d i n b u f f e r e d s o l u t i o n s a t h i g h e r pH, u s i n g t h e M c l l v a i n e ' s s t a n d a r d b u f f e r s o l u t i o n s 2 1 * . up t o pH = 8 and a 0.1 m o l a r s odium b i c a r b o n a t e - s o d i u m c a r b o n a t e b u f f e r a t pH = 10.5. They a r e shown i n F i g u r e 8 and compared w i t h s i m i l a r r e s u l t s o b t a i n e d by S a t o 1 * 7 . The agreement, i s r e a s o n  a b l e w i t h t h e c a l c u l a t e d l i n e f o r t h e r e a c t i o n : C u 2 S + 2II 20-»-CuS + C u ( O H ) 2 + 2 H + + 2e~ (27) In summary, t h e r e s t p o t e n t i a l measurements a p p e a r t o be c o n s i s t e n t w i t h t h e f o l l o w i n g p o t e n t i a l d e t e r m i n i n g r e a c t i o n s : a t pH < 4 , C u 2 S — C u S + C u + + + 2e~ .(28) a t pH > 4 C u 2 S + 2H 20 — * - CuS + C u ( O H ) 2 +. 2H+""+ 2e" .....(29) The e x p e r i m e n t a l l y d e t e r m i n e d v a l u e o f V ° C u 2 g i s 0.490 V, w h i c h c a n be compared w i t h t h e c a l c u l a t e d v a l u e o f 0.535 V. The d i s c r e p a n c y i s a c t u a l l y w i t h i n t h e p o s s i b l e e r r o r o f +0.13 V f o r t h e c a l c u l a t e d v a l u e , b u t i t may a l s o be a f u n c t i o n o f t h e q u i t e l a r g e Cu d e f i c i e n c y i n t h e e x p e r i m e n t a l e l e c t r o d e . - 37 - Preliminary P o l a r i z a t i o n Tests The general shape of the anodic p o l a r i z a t i o n curves i s shown i n Figure 9. There are three regions of note: 1. The region up to to = 5 0 mV. In t h i s region, the current density was very stable at a p a r t i c u l a r s e t t i n g over periods of up to 10 hours. The points were also quite reproducible from test to t e s t . Microscopic examination of the anode surface a f t e r 10 hours at to =25 mV showed l i t t l e or no p r e f e r e n t i a l grain boundary attack. When the current flow was stopped, the over- potential returned to approximately zero within a few seconds. 2. The region where 50 < <~o <. 200 mV. In t h i s region, the p o l a r i z a t i o n curves became less reproducible and there was considerable f l u c t u a t i o n with time of both the anode pote n t i a l and the current density for a given c e l l p o t e n t i a l . Microscopic examination of the anode surface a f t e r 60 hours at an overvoltage of approximately 150 mV showed considerable grain boundary attack (see Figure 10). When the current flow was stopped i n t h i s range, the overpotential returned to approximately zero within a minute. The fluctuations i n t h i s region are probably the r e s u l t of rapid changes i n the e f f e c t i v e surface area of the anode due to prefer e n t i a l reaction at the grain boundaries. 3. The region beyond 0 0 = 200 mV. The behaviour i n th i s region was very e r r a t i c . The overpotential fluctuated over a range of about 50 mV even though the apparent current density was increasing. Microscopic examination of the anode a f t e r about 5 hours at an overpotential of about 250 mV showed more severe grain boundary attack than at lower overpotentials. The open c i r c u i t decay of the overpotential took a considerable^length of - 38 - Run SH9 C u S 0 4 , 0.01 M H 2 S 0 4 , 0.01 M L o g A n o d i c C u r r e n t D e n s i t y , mA/cm 2 F i g u r e 9. T y p i c a l P o l a r i z a t i o n C u r v e f o r C u p r o u s S u l p h i d e Anode a t . 25° C - 39 - F i g u r e 10. C u p r o u s S u l p h i d e Anode S u r f a c e (a) b e f o r e and (b) a f t e r P o l a r i z a t i o n a t L&J = 0.15 v o l t s f o r 60 h o u r s i n 0.01 M C u S 0 4 , 0.1 M H „ S O . a t 25-30° C Z 4 - 40 - time and an example i s i l l u s t r a t e d i n F i g u r e 11, Such behaviour would be c o n s i s t e n t with the e x i s t e n c e o f a d i f f i c u l t l y s o l u b l e f i l m on the anode s u r f a c e , but the r e was no v i s i b l e i n d i c a t i o n of such a f i l m i n these runs. S t e r n 2 0 ' 2 1 has shown t h a t the d i f f e r e n c e i n the slope of the p o l a r i z a t i o n l i n e i n r e g i o n s 1 and 2 i s not n e c e s s a r i l y the r e s u l t o f the presence o f a second e l e c t r o d e r e a c t i o n , but i n t h i s case, r e g i o n 2 might w e l l be a t r a n s i t i o n r e g i o n between two e l e c t r o d e r e a c t i o n s i . e . Cu 2S — s * - CuS + C u + + + 2e~ ..,..(30) CuS —*- C u + + + S + 2e o . . . . (31) The e l e c t r o d e p o t e n t i a l s o f the two r e a c t i o n s are q u i t e s i m i l a r (0.535 and 0.588 V r e s p e c t i v e l y ) . I t i s p o s s i b l e t h a t one r e a c t i o n i s o c c u r r i n g on the g r a i n s u r f a c e s while the other i s o c c u r r i n g a t the g r a i n boundaries. K i n e t i c Parameters i n Low O v e r p o t e n t i a l Region The r e g i o n up t o CO = 0.05 V was s t u d i e d f u r t h e r to pr o v i d e data to t e s t the k i n e t i c r e l a t i o n s h i p s o u t l i n e d i n the I n t r o d u c t i o n . T y p i c a l p o l a r i z a t i o n curves o b t a i n e d i n 0.1 M H2SO4 - 0.1 M CUSO4 s o l u t i o n s are p l o t t e d i n F i g u r e s 12 and 13 (sem i l o g a r i t h m i c and a r i t h m e t i c p l o t s r e s p e c t i v e l y ) . Values o f LQ (the exchange c u r r e n t ) , /V (the s t o i c h i o m e t r i c f a c t o r ) and (2> (the symmetry f a c t o r ) have been c a l c u l a t e d from the sl o p e s of these l i n e s and are t a b u l a t e d i n Table X I I . The s t r a i g h t p o r t i o n s o f the l o g a r i t h m i c p l o t s are q u i t e s h o r t , so c o n s i d e r a b l e i n a c c u r a c y i s probably i n t r o d u c e d to values o f d C O / d l o g i A , and then t o i Q , X and p > . In f a c t , - 41 - 0.20 w -P H O > f0 -H -P C OJ •P o > o u O 0.15 0.10 0.05 -0^*— a t t = 0 Run PE6 C u S 0 4 , 0.2 M H 2 S 0 4 , 0.4 M 35° C 1 1 i i 1 -1 0 1 2 3 Lo g Time, m i n u t e s F i g u r e 11. Decay o f A n o d i c O v e r p o t e n t i a l w i t h Time - 42 - -2.0 -1.0 L o g A n o d i c C u r r e n t D e n s i t y , ma/cm 2 F i g u r e 12. Example C u r v e s : E f f e c t o f T e m p e r a t u r e on t h e P o l a r i z a t i o n o f C u 9 S Anode - 43 - CO •P o > (0 •H •P c cu -p o Qu U CU > O CJ -H o 0.025 ~ 0.020 0.015 - 0.010 - 0.005 | Runs LV 2, 3, 4, 5, 8, 9, 10, 11. CuS0 4, 0.1 M H 2 S 0 4 , 0.1 M J 0.01 0.02 0.03 A n o d i c C u r r e n t D e n s i t y , itiA/cm 2 0.04 F i g u r e 13. E f f e c t o f T e m p e r a t u r e on P o l a r i z a t i o n o f CU2S Anode a t Low O v e r p o t e n t i a l s ( E x p e r i m e n t a l p o i n t s o m i t t e d w i t h one e x c e p t i o n tb'; s i m p l i f y p l o t . ) - 4 4 - TABLE XII i Q , A and ( b for the Cuprous Sulphide Anode Run No. Temperature • c V/A/cm2 da/d log i A V i 0 x II) 5 S/cm2 X e> LV 3 2 0 1 3 6 0 . 0 0 . 0 5 8 8 0 . 9 5 1 . 9 6 0 . 5 LV 2 2 5 6 4 2 o 5 0 . 0 5 9 1 1 . 9 5 2 . 0 5 0 . 5 1 LV 1 0 2 5 6 6 2 . 5 0 . 0 6 1 6 2 . 1 4 1 . 8 1 0 . 4 7 LV 1 1 2 5 6 7 7 . 5 0 . 0 6 2 3 2 . 1 6 1 . 7 6 0 . 4 6 LV 9 2 5 6 4 0 . 0 0 . 0 6 1 2 2 . 1 2 1 . 8 9 0 . 4 9 LV 4 3 0 5 9 7 * 5 0 . 0 6 6 8 2 . 6 2 1 . 6 7 0 . 4 5 LV 5 3 5 2 6 2 . 5 0 . 0 6 4 7 4 . 9 5 2 . 0 4 0 . 5 4 LV 8 3 5 3 0 5 . 0 0 . 0 6 4 5 5 . 3 1 . 6 4 0 . 4 2 S t e r n 2 0 ' 2 1 states that the straight l i n e portion should extend over several logarithmic units to provide parameters of good accuracy. Both A and (3 generally have values involving integers ( e . g . A = 1 , 2 , 3 ; p> = 1 / 4 , 1 / 3 , 1 / 2 ) and the values from Table XII are close to A = 2 and = 1 / 2 , so these values w i l l be used i n the following c a l c u l a t i o n s . I t was stated e a r l i e r that OJ = RT i A This can be rewritten: = RT 1 o o o o . ( 3 2 ) dco d i A o o o o o ( 3 3 ) G J - 7 I Q A Values of dco were quite precise (Figure 1 3 ) so using A = 2, d l A corrected values of 1Q were calculated (Table X I I I ) . Further, using the corrected values of i 0 , and A = 2 and (3 = 1 / 2 , corrected values of doyd log i A were calculated (Table XIII) which f i t the experi mental points quite well (Figure 1 4 ) . - 45 - co -P o > m -H +J C d) -P O Ou u cu > o o •H T3 O 0.06 0.05 0.04 0.03 0.02 0.01 U b LV 3 C u S 0 4 , 0.1 M H 2 S 0 4 , 0.1 M O -2.0 -1.0 L o g A n o d i c C u r r e n t D e n s i t y , mA/cm 2 F i g u r e 14. F i t o f R e c a l c u l a t e d L i n e t o E x p e r i m e n t a l D a t a - 46 - to •P • H O > +J c cu -p o Cu u CD > o •0.015 0.010 0.005 •0.005 -0*010 -0.015 Runs SH4 and SH2 C u S 0 4 , 0.01 M H 2 S 0 4 , 0.01 M 0c2 X F i g u r e 15, 0.1 0 0.1 0.2 C u r r e n t D e n s i t y , mA/cm 2 A n o d i c and C a t h o d i c P o l a r i z a t i o n C u r v e s f o r t h e C u 2 S E l e c t r o d e a t Low O v e r p o t e n t i a l s - 47 - Examples of the anodic and c a t h o d i c p o l a r i z a t i o n curves f o r the cuprous s u l p h i d e e l e c t r o d e (Figure 15) show l i t t l e or no d i s c o n t i n u i t y . T h i s l a c k o f d i s c o n t i n u i t y a t and near to = 0 has been i n t e r p r e t e d by St e r n and G e a r y 2 0 to i n d i c a t e t h a t o n l y one o x i d a t i o n - r e d u c t i o n r e a c t i o n system i s o p e r a t i n g a t the e l e c t r o d e . TABLE XIII C o r r e c t e d Values o f i g and da/d l o g i A Run Temperature i g x 10 5 duyd l o g I A No. °C A/cm 2 V LV 3 20 0.93 0.0582 LV 2 25 2.00 0.0591 LV 10 25 1.94 0.0591 LV 11 25 1.90 0.0591 LV 9 25 2.01 0.0591 LV 4 30 2.19 0.0601 LV 5 35 5.06 0.0611 LV 8 35 4.35 0.0611 Reac t i o n Products A cuprous s u l p h i d e anode was o x i d i z e d i n a .0.1 N p e r c h l o r i c a c i d s o l u t i o n a t about 30°C wi t h a c u r r e n t flow o f about t e n mA/cm2 and CU = 0.2 V. A f t e r 18 days, the anode was s e v e r e l y c orroded. The remaining m a t e r i a l was washed thoroughly i n carbon b i s u l p h i d e to remove any f r e e sulphur and the r e s i d u e was washed i n a l c o h o l and d r i e d under vacuum» The r e s i d u e was analysed f o r Cu and S, w i t h the f o l l o w i n g r e s u l t s : Cu = 6-3.9 wgt. % S = 35o2 wgt. % Cu/S atomic r a t i o = 0=916 - 48 - The r e s i d u e i s t h e r e f o r e probably CuSo An x-ray powder p i c t u r e was taken o f a p o r t i o n o f the r e s i d u e , and the r e s u l t i n g p a t t e r n i s very s i m i l a r to one obt a i n e d from c h e m i c a l l y pure CuS (Appendix H). The e l e c t r o l y t e was analysed a t the completion o f the t e s t f o r d i s s o l v e d compounds of S (valence s t a t e s lower than +6); there was no i n d i c a t i o n o f the presence o f S. No attempt was made to analyse f o r f r e e sulphur i n the c o r r o s i o n residue„ E f f e c t o f Temperature on P o l a r i z a t i o n Curves The r e a c t i o n r a t e i n c r e a s e s w i t h temperature i n the range 20°C to^35°C (Figure 13)„ Although the range o f temperatures s t u d i e d was q u i t e s m a l l , a s i m i l a r r e l a t i o n s h i p probably e x i s t s over a much wider range. C a l c u l a t i o n o f AH 0* A value o f S = 1/2 has been accepted a f t e r a n a l y s i s o f the p o l a r i z a t i o n d a t a . With t h i s c o n d i t i o n ^ a value o f AH Q*, the heat of a c t i v a t i o n , can be c a l c u l a t e d by t h e method o f Hurlen 3** (Appendix F ) . The main r e l a t i o n s h i p i s r e s t a t e d below: AH 0* = 2.303 R d l o g f J p / T ) + l AH ..(34) d (1/T) 20 Values o f l o g ( J Q / T ) were c a l c u l a t e d (Table XIV) and p l o t t e d a g a i n s t the r e c i p r o c a l temperature (Figure 16), and the best f i t l i n e gave -2,303 R d l o g (J n / T ) = 14.9 kcal/mole .....(35) d ( 1 / T f £ In a d d i t i o n t o £> = 1/2, K (the t r a n s m i s s i o n c o e f f i c i e n t ) and 0 (the frequency f a c t o r ) should be the same f o r both the forward and r e v e r s e r e a c t i o n a c r o s s the a c t i v a t i o n b a r r i e r . I t i s g e n e r a l l y assumed t h a t these c o n d i t i o n s h o l d t r u e . - 49 - -6.6 'r ' ""3 ,~3 3. 4 1/T X 1 0 3 F i g u r e 16. P l o t o f l o g ( J Q / T ) v r s ( 1 / T ) : D e t e r m i n a t i o n o f AH Q* f o r t h e C u p r o u s S u l p h i d e E l e c t r o d e 50 - TABLE XIV C a l c u l a t i o n o f l o g ( J Q / T ) Run No. if) x 10 5 Jo x 10 5 Temperature °K 1/T x 10 3 J 0 x 10 ? T log J n/T LV 3 0.93 9.3 293 3.411 3.17 -6.498 LV 2 2.00 20.0 298 3.354 6.71 -6.174 LV 10 1.94 19.4 298 3.354 6.51 -6.187 LV 11 1.90 19.0 298 3.354 6.37 -6.196 LV 9 2.01 20.1 298 3.354 6.74 -6.172 LV 4 2.19 21.9 303 3.299 7.22 -6.141 LV 5 5.06 50.6 308 3.245 16.4 -5.785 LV 8 4.35 43.5 308 3.245 14.11 -5.850 If the o v e r a l l reaction i s Cu 2S CuS + C u + + + 2e~, .....(36) then when the value of AH0 for t h i s reaction (23.3 kcal/mole) i s placed i n equation ( 3 5 ) , a value of 26.5 kcal/mole i s obtained for AHQ*. T h i s v a l u e can be compared w i t h 15.2 k c a l / m o l e d e t e r m i n e d by H u r l e n f o r t h e C u / C u + + a q e l e c t r o d e . AH 0* i s a mean v a l u e between t h e v a l u e s o f AH Q* ( c a t h o d i c ) and AH 0* ( a n o d i c ) , t h e s e l a t t e r v a l u e s b e i n g r e l a t i v e t o t h e h y d r o g e n s c a l e . The a c c u r a c y o f t h e v a l u e o f AH Q* c a l c u l a t e d h e r e i n i s a bout + 7 k c a l / m o l e . B e c a u s e o f t h i s i n a c c u r a c y and t h e d i f f i c u l t y o f r e l a t i n g t h e h y d r o g e n s c a l e v a l u e s and a b s o l u t e s c a l e v a l u e s , no f u r t h e r i n t e r p r e t a t i o n o f t h i s i n f o r m a t i o n has b een a t t e m p t e d . - 51 - The R e a c t i o n Mechanism The e x p e r i m e n t a l r e s u l t s a r e c o n s i s t e n t w i t h t h e f o l l o w i n g low o v e r p o t e n t i a l a n o d i c o x i d a t i o n r e a c t i o n f o r c u p r o u s s u l p h i d e : C u 2 S — » . CuS + C u + + + 2e (37) The e v i d e n c e o f CuS as a r e a c t i o n p r o d u c t a p p e a r s t o be r e a s o n a b l e , b u t i t was n o t d e m o n s t r a t e d t h a t f r e e s u l p h u r was a b s e n t as a r e a c t i o n p r o d u c t . T h e r e f o r e , i t i s p o s s i b l e t h a t a s e c o n d r e a c t i o n was a l s o o c c u r r i n g , v i z : CuS — C u + + + S + 2e (38) The p r e v i o u s l y d i s c u s s e d work o f W a r r e n 4 9 , S u l l i v a n 5 0 and S a t o 4 7 w o u l d i n d i c a t e t h a t t h e two r e a c t i o n s s h o u l d o c c u r d u r i n g the. c o m p l e t e o x i d a t i o n o f C u 2 S , b u t w h e t h e r t h e y were o c c u r r i n g s i m u l t a n e o u s l y o r c o n s e c u t i v e l y i n t h e p r e s e n t c a s e i s n o t known. The o b s e r v a t i o n o f s e v e r e g r a i n b o u n d a r y c o r r o s i o n a t o v e r p o t e n t i a l s above a b o u t 50 mV w o u l d be c o n s i s t e n t w i t h t h e d e v e l o p m e n t o f a s u r f a c e f i l m o f p o o r l y c o n d u c t i n g , n o n - p o r o u s CuS on t h e g r a i n s u r f a c e s , b u t s u c h f i l m s were n o t o b s e r v e d . I f t h e low o v e r p o t e n t i a l p o l a r i z a t i o n r e a c t i o n i n v o l v e d o n l y ( 3 7 ) , t h e n t h e c a l c u l a t e d k i n e t i c p a r a m e t e r s a r e c o n s i s t e n t w i t h t h e f o l l o w i n g r e a c t i o n s t e p s : 2 C u + P l l E — f 2 C u + ® ,, G + 2e~ . .... (a) u u x b c u x b (39) Cu C l j s •» Cu aq ... . . (b) x I n t h i s c a s e , two c o p p e r i o n s i n t h e s o l i d a r e i n v o l v e d when one c o p p e r i o n i s t r a n s f e r r e d i n t o t h e s o l u t i o n . P o s s i b l e r a t e c o n t r o l l i n g s t e p s a r e : (a) t h e c r e a t i o n o f a c u p r i c i o n ( i . e . e l e c t r o n h o l e ) i n t h e s o l i d b y t h e r e m o v a l o f an e l e c t r o n : C u \ s - c o % + v •(40a) - 52 - (b) the removal of an e l e c t r o n through the e x t e r n a l c i r c u i t : e Cu xS (i n e x t e r n a l c i r c u i t ) (40b) (c) t r a n s f e r o f e l e c t r o n between two s i t e s i n the s o l i d : 0 Cu S x S i t e 1  + Cu Cu xS Cu n Cu xS S i t e 2 S i t e 2 (40c) (d) d i s s o l u t i o n o f c u p r i c i o n : Cu +© Cu xS C u + + a q (40d) Reactions (40a) and (40c) are probably q u i t e r a p i d because of the f a i r l y l a r g e e l e c t r o n i c c o n d u c t i v i t y i n Cu 2S (see Table I I ) . A d d i t i o n a l e x p e r i m e n t a l work would b e ^ r e q u i r e d t o d i f f e r e n t i a t e between steps (40b) and (4'0d) . The s i m p l e s t method would be to determine the i n f l u e n c e , i f any, o f (Cu + +aq) on the r e a c t i o n r a t e Although the value of A H q * i s of q u e s t i o n a b l e accuracy, i t i s i n the range u s u a l l y found f o r a c t i v a t i o n - c o n t r o l l e d e l e c t r o  chemical r e a c t i o n s . A much l a r g e r value (say? SO kcal/mole) would be expected i f the r a t e was c o n t r o l l e d by mass t r a n s f e r through a f i l m , u nless o f course the f i l m i s very porous. CONCLUSIONS Rest p o t e n t i a l measurements on an a r t i f i c i a l cuprous s u l p h i d e e l e c t r o d e i n a c i d i f i e d copper sulphate s o l u t i o n gave V° = 0.490 v o l t s f o r the e l e c t r o d e p o t e n t i a l . In s o l u t i o n s o f pH<4, the r e l a t i o n s h i p between the e l e c t r o d e p o t e n t i a l and ( C u + + ) was c o n s i s t e n t w i t h the Nernst equation. For the r e a c t i o n : Cu 2S —»•* CuS + C u + + + 2e", the c a l c u l a t e d h a l f c e l l p o t e n t i a l V° i s 0.5 35 + 0.13 v o l t s . Although the experimental value o f 0.490 v o l t s i s w i t h i n the l i m i t s o f accuracy o f the c a l c u l a t e d v a l u e , the experimental e l e c t r o d e s had a l a r g e Cu d e f i c i e n c y which may account f o r a t l e a s t a p o r t i o n o f the d i s c r e p a n c y . In s o l u t i o n s o f pH>4, the r e s t p o t e n t i a l measurements were c o n s i s t e n t with the f o l l o w i n g e l e c t r o d e r e a c t i o n : Cu 'S-. -f 2H 20 —>- CuS + Cu(0H) 2 + 2H + +• 2e~ P o l a r i z a t i o n measurements a t low o v e r p o t e n t i a l gave values f o r the f o l l o w i n g k i n e t i c parameters: (9> , the symmetry f o r f a c t o r = 1/2 /\, the number o f e l e c t r o n s i n v o l v e d i n each a c t of the r a t e determining step = 2 i Q , the exchange c u r r e n t ^ 2 x 10~^ A/cm 2 AH Q*, the standard heat o f a c t i v a t i o n = 26.5 kcal/mole CuS was t e n t a t i v e l y i d e n t i f i e d as a r e a c t i o n product, but the presence or absence o f S was not determined. T h e r e f o r e , i t i s not known to what ext e n t the r e a c t i o n : CuS »* C u + + + S + 2e" took p a r t i n the o v e r a l l o x i d a t i o n . The apparent absence of a s u r f a c e f i l m and the value o f A H Q * i n d i c a t e t h a t the anodic o x i d a t i o n r e a c t i o n i s a c t i v a t i o n c o n t r o l l e d , r a t h e r than bulk mass t r a n s f e r c o n t r o l l e d , at l e a s t at low values o f the o v e r p o t e n t i a l . - 55 - RECOMMENDATIONS FOR FUTURE INVESTIGATIONS 1. The e f f e c t o f ( C u + + ) on the r e a c t i o n r a t e should be determined to c l a r i f y the r e a c t i o n mechanism. 2. A s e r i e s o f Cu xS e l e c t r o d e s should be prepared with d i f f e r e n t Cu/S r a t i o s i n order t o assess the i n f l u e n c e o f s t o i c h i o m e t r y on the e l e c t r o d e p o t e n t i a l . S o l i d - s t a t e e l e c t r o l y t i c c e l l s 7 " 1 0 c o u l d be used to prepare the e l e c t r o d e s . S i n g l e c r y s t a l s u r  faces would probably be d e s i r a b l e . 3. I n v e s t i g a t i o n s at h i g h e r o v e r p o t e n t i a l s would be o f c o n s i d e r a b l e i n t e r e s t , but a more s o p h i s t i c a t e d measuring c i r c u i t should be used. : For example, p o l a r i z a t i o n techniques wherein a square wave a l t e r n a t i n g c u r r e n t i s used can pr o v i d e i n f o r m a t i o n on the nature o f p a s s i v a t i n g f i l m s . 4. P o l a r i z a t i o n s t u d i e s should be extended to hi g h e r temperatures and t o i n c l u d e more c o r r o s i v e s o l u t i o n s . -56 - REFERENCES 1. L. S. R e n z o n i , R. C. M c Q u i r e and M. V. B a r k e r , AIME p r e p r i n t , New Y o r k , (1958). 2. L. S. R e n z o n i , R. C. M c Q u i r e and M. V. B a r k e r , J . M e t a l s , 10, 414 (1958). 3. K. S p r o u l e , G. A. H a r c o u r t and L. So R e n z o n i , i b i d . , 12, 214 ( 1 9 6 0 K 4. T. S. L i c h t and A. J . d e B e t h u n e , J . Chem. E d . , 3_4 , 433 (1957) 5. J . S. A n d e r s o n and M. C. M o r t o n , P r o c . R o y a l S o c , A,184, 83 (1945). 6. W. C. D u n l a p , "An I n t r o d u c t i o n t o S e m i c o n d u c t o r s , " J o h n W i l e y and Sons, New-York 1957. 7. C. Wagner, J . Chem. P h y s . , 21, 1819 (1953). 8. J . B r u c e Wagner and C. Wagner, i b i d . , 26, 1597 ( 1 9 5 7 ) . 9. J . B r u c e Wagner and C. Wagner, i b i d . , 26, 1602 ( 1 9 5 7 ) . 10. H. K o b a y a s h i and C. Wagner, i b i d . , 26, 1609 (1957). 11. W. Noddack and K. E. W r a b e t z , Z. E l e k t r o c h e m . , 59, 96 (1955). 12. K. E. W r a b e t z , i b i d . , 60, 722 ( 1 9 5 6 ) . 13. G. Kortum and J . O'M. B o c k r i s , " T e x t b o o k o f E l e c t r o c h e m i s t r y , E l s e v i e r , Amsterdam 1951. 14. J . O'M. B o c k r i s , "Modern A s p e c t s o f E l e c t r o c h e m i s t r y , " ( e d i t o r : J . O'M. B o c k r i s ) , B u t t e r w o r t h S c i e n t i f i c P u b l i c a t i o n s , L ondon, volume 1 ( 1 9 5 4 ) , c h . 4. 15. Mino G r e e n , i b i d . , volume 2 (1959) c h . 5. 16. R. A. R o b i n s o n and R. S. J o n e s , J . Am. Chem. S o c , 58_, 959 (1936). 17. S. G l a s s t o n e , " E l e m e n t s o f P h y s i c a l C h e m i s t r y , " D. Van N o s t r a n d Co. I n c . , New Y o r k 1952. 18. G. N. L e w i s and M e r l e R a n d a l l , "Thermodynamics," 2nd e d . ( e d i t e d by: P i t z e r and B r e w e r ) , McGraw H i l l , New York 1961. 19. W. L a t i m e r , "The O x i d a t i o n S t a t e s o f t h e E l e m e n t s and T h e i r P o t e n t i a l i n Aqueous S o l u t i o n , " 2nd e d . , P r e n t i c e H a l l , I n c . , E n g l e w o o d C l i f f s , N . J . 1952. - 57 - 20. M. S t e r n and A. L. G e a r y , J . E l e c t r o c h e m . S o c . , 104, 56 (1957). 21. M . S t e r n , i b i d . , 104, 559 (1957). 22. M . S t e r n , i b i d . , 10_4, 645 (19 5 7 ) . 23. R. P i o n t e l l i , G. B i a n c h i , U. B e r t o c c i , C. G u e r c i and B. R i v o l t a , Z. E l e k t r o c h e m . , 5JB, 54 (19 5 4 ) . 24. Handbook o f C h e m i s t r y and P h y s i c s , 35 e d . , 1953-1954. 25. W. J . A r g e r s i n g e r , J . P h y s . Chem., 58, 792 (19 5 4 ) . 26. V. F. H o l l a n d and O. D. Bo n n e r , J . Am. Chem. S o c , 77, 5833 (19 5 5 ) . 27. M. P o u r b a i x , "Thermodynamics o f D i l u t e Aqueous S o l u t i o n s , " A r n o l d , London 1949. 28. G. V a l e n s i , C I T C E , Compt. Rend. R e u n i o n , 51 (19 5 0 ) . 29. R. P a r s o n s , s e e r e f e r e n c e 14, c h . 3. 30. B u t l e r , " E l e c t r o c a p i l l a r i t y , " Methuen, London 1940. 31. D. D. E l e y and M. G. E v a n s , T r a n s . F a r a d a y S o c , 34, 109 3 (193 8 ) . 32. T. H u r l e n , A c t a Chem. S c a n . , 15_, 630 (19 6 1 ) . 33. T. H u r l e n , i b i d . , 14, 1533 ( 1 9 6 0 ) . 34. T. H u r l e n , i b i d . , 14, 1564 ( 1 9 6 0 ) . 35. T. H u r l e n , i b i d . , 15, 621 (1961). 36. F. D. R o s s i n i , " S e l e c t e d V a l u e s o f C h e m i c a l Thermodynamic V a l u e s , U.S. Government P r i n t i n g O f f i c e , W a s h i n g t o n 1952. 37. J . H a l p e r n , u n p u b l i s h e d m a n u s c r i p t . 38. A. J . d e B e t h u n e , J . E l e c t r o c h e m . S o c , 102, 288C (1 9 5 5 ) . 39. T. H u r l e n , A c t a Chem. S c a n . , 15, 630 ( 1 9 6 1 ) . 40. G. N. L e w i s and M e r l e R a n d a l l , J . Am. Chem. S o c , 43, 1112 (192 1 ) . 41. L. Young, " A n o d i c O x i d e F i l m s , " A c a d e m i c P r e s s , New Y o r k 1961. 42. W. R u h l and E . S a u r , B e r . Ober. Ges. N a t u r u n d H e i l k u n d e , 26-29, 35 (1954-1958). 43. M. P o u r b a i x and G. G o v a e r t s , " F i r s t I n t e r n a t i o n a l C o n g r e s s on M e t a l l i c . C o r r o s i o n , " 1961, B u t t e r w o r t h , London 1962. 44. M. Hansen, " C o n s t i t u t i o n o f B i n a r y A l l o y s , " McGraw H i l l , New Y o r k 195 8. 45. R. Schuhmann and 0. W. M o l e s , J . M e t a l s , 3_, 235 (19 5 1 ) . 46. M. S a t o , E c o n . G e o l . , 5_5, 928 (19 6 0 ) . 47. M. S a t o , i b i d . , 55, 1202 (19 6 0 ) . 48. J , H o r v a t h and M. Novak, C o r . S c o . , £ , 1 5 9 (1964). 49. I . H. Warren, Aus. J . App. S c i . , 9_, 36 (1958). 50. J . D. S u l l i v a n , USBM T e c h . p a p e r 473 (1930). 51. . J . F. E l l i o t t and M. G l e i s e r , " T h e r m o c h e m i s t r y f o r S t e e l - m a k i n g , " A d d i s o n - W e s l e y , R e a d i n g 1960. 52. T. R o s e n q v i s t , J . I r o n S t e e l I n s t . , 176, 37 (19 5 4 ) . 53. B. E. Conway, " E l e c t r o c h e m i c a l D a t a , " E l s e v i e r , London 1952. 54. F. F e n w i c k , J . Am. Chem. S o c , 4_8, 860 (1926). 55. H. B r i t t o n , J . Chem. S o c , 127, 2110 (1925). 56. G. J . J a n z and D. J . G. I v e s , " R e f e r e n c e E l e c t r o d e s , " A c a d e m i c P r e s s 1961. 57. N. W. B u e r g e r , E c o n . G e o l . , 3_6,- 19 (1941). 58. P. R a h l f s , Z. p h y s i k . Chem., B31, 184 (1936). 59. A. S. Powarennych, G e o l o g i e , 4_, 377 (19 6 3 ) . 60. A. J . d e B e t h u n e , T. S. L i c h t and N. Swendeman, J . E l e c t r o c h e m . Soc. , 106, 616 (1959).. 61. P. E. J . A y l e n , R e s e a r c h R e p o r t , U n i v e r s i t y o f B r i t i s h C o l u m b i a , A p r i l 1959. 62. E. H i r a h a r a , J . P h y s . S o c. J a p a n , 6_, 422 (1951). 63. E. H i r a h a r a , i b i d . , 6_, 428 (1951). 64. N. W. L o r d and D. J . Demarest, " M e t a l l u r g i c a l A n a l y s i s , " McGraw H i l l , New Y o r k 192 4. APPENDIX A A n o d i c O x i d a t i o n o f T i n S u l p h i d e C o n s i d e r a b l e t i m e was e x pended i n i t i a l l y on a s t u d y o f e l e c t r o c h e m i c a l o x i d a t i o n i n t h e Sn-S s y s t e m . A l t h o u g h t h i s work" was: t e r m i n a t e d b e c a u s e o f t h e l a c k o f r e p r o d u c i b i l i t y o f t h e e x p e r i m e n t a l d a t a , t h e r e s u l t s and p r o b l e m s e n c o u n t e r e d a r e summarized h e r e f o r c o n s i d e r a t i o n i n f u t u r e work. P r e p a r a t i o n o f T i n S u l p h i d e S t a n n o u s s u l p h i d e was p r e p a r e d by c a r e f u l l y m i x i n g s t o i c h i o m e t r i c amounts o f m o l t e n Sn and S i n an e v a c u a t e d V y c o r t u b e . A f t e r m i x i n g a p p e a r e d t o be c o m p l e t e , t h e SnS was p l a c e d i n a m u f f l e f u r n a c e and h e l d a t 900°C t o e n c o u r a g e h o m o g e n e i t y . By s l o w c o o l i n g o f t h e f u r n a c e t h r o u g h t h e m e l t i n g t e m p e r a t u r e o f SnS ( a p p r o x i m a t e l y 8 8 0 ° C ) , i t was e x p e c t e d t h a t t h e m a t e r i a l w o u l d s o l i d i f y as e i t h e r a s i n g l e c r y s t a l o r a s e r i e s o f l a r g e c r y s t a l s . However, i t u s u a l l y s o l i d i f i e d as a s m a l l d ense p o r t i o n t o p p e d by a v e r y p o r o u s network o f d e n d r i t e s . One o f t h e b e t t e r p i e c e s was a n a l y s e d and mounted i n a manner s i m i l a r t o t h a t u s e d w i t h t h e CU2S. The m a t e r i a l a n a l y s e d (one a n a l y s i s ) a b o u t 67% rSn ( a n a l y t i c a l method: i o d i n e t i t r a t i o n ) compared t o 78.8% Sn f o r s t o i c h i o m e t r i c SnS and 6 5% i n s t o i c h i o m e t r i c SnS2. The Sn d e f i c i e n c y i s s u r p r i s i n g ; t h e t i n s u l p h i d e c o u l d w e l l be a m i x t u r e o f SnS, SnS2 and Sn, b u t t h e a n a l y s i s o f a r e a s o n a b l y l a r g e p i e c e o f m a t e r i a l s h o u l d r e f l e c t t h e o r i g i n a l s t o i c h i o m e t r y . The r e s u l t , o f c o u r s e , i s s u s p e c t as o n l y one a n a l y s i s was p e r f o r m e d . The e x a c t c o m p o s i t i o n o f t h e t i n s u l p h i d e i s t h u s unknown. - 60 - P o t e n t i a l Measurements Some r e s t p o t e n t i a l measurements i n Sncl2 s o l u t i o n s are summarized i n Table A - I . TABLE A-I Rest P o t e n t i a l s f o r T i n Sulphide E l e c t r o d e a t 25°C i n Sncl2 S o l u t i o n S n + + ' Anode P o t e n t i a l Run H+ pH w.r.t. Calomel Number M M V SE 1 0.091 0.568 0.35 -0.074 2 0.084 0.592 0.38 -0.079 3 0.082 0.597 - -0.114 5 0.074 0.575 0.55 -0.072 6 0.072 0.578 0.31 -0.066 7 0.0374 0.25 0.25 -0.072 8 0.0201 0.157 0.3 -0.074 9 0.00358 0.0815 0.61 -0.082 The average value i s about -0.08 v o l t s . Using the r e l a t i o n s h i p e c e l l = VS.C.E. - V A N O D E then V anode 0.2415 - (-0.08) « 0.32 V where V A N O D E = V ° A N O D E + RT In [ OX.j. nf [RED.] S e v e r a l e l e c t r o d e r e a c t i o n s should be considered: SnS SnS' Sn ++ S n + + + S + 2e~ Sn + 2S + 4e~ Sn + < + + 2e- V° = 0.253 V V° = 0.418 V V° = 0.150 V The a c t i v i t y o f S n + + i s probably i n the range 0.01-0.1 i n the t e s t s o l u t i o n s , so the measured anode p o t e n t i a l corresponds t o va l u e s o f - 61 - v°anode i n t n e range 0.35-0=38 V. The l a c k of agreement between the measured value and the t h e o r e t i c a l values suggests t h a t e i t h e r some oth e r r e a c t i o n or a mixture of two or more of the above r e a c t i o n s was determining the e l e c t r o d e p o t e n t i a l . P o l a r i z a t i o n Curves Nineteen p r e l i m i n a r y k i n e t i c runs were made, and the f o l l o w i n g g e n e r a l o b s e r v a t i o n s recorded: •1. The p o l a r i z a t i o n curves were not unusual, as can be seen i n the example i n F i g u r e A - l . The s t r a i g h t l i n e p o r t i o n (semi-log p l o t ) was f a i r l y uniform over about two l o g a r i t h m i c c y c l e s , but t h e r e was no measure of r e p r o d u c i b i l i t y from one run to the next. 2. The method of anode s u r f a c e p r e p a r a t i o n had an important e f f e c t on the p o l a r i z a t i o n curves. For example, a higher o v e r p o t e n t i a l was necessary to achieve a c e r t a i n c u r r e n t flow when the anode was cleaned with toluene than when f r e s h l y p o l i s h e d or etched s l i g h t l y with a c i d . 3. A f t e r a number o f days u s i n g the same s o l u t i o n , & g e l a t i n o u s p r e c i p i t a t e was observed a t the bottom of the e l e c t r o l y t i c c e l l . T h i s m a t e r i a l was not analysed, but was l i k e l y a h y d r o l y s i s product. For example S n + k h y d r o l y s e s very r e a d i l y as Sn(OH) 4. The pH should exceed 1.9 before the h y d r o l y s i s o f S n + 2 becomes d o m i n a n t 5 5 . No f u r t h e r comment can be made without the a n a l y s i s o f the m a t e r i a l . - 62 - 0.12 •H -P <U -P O S-l > o u •H t i O C <; o . i o w 0.08 o > 0.06 0. 02 0.04 h 0.001 0.01 0.1 1.0 C u r r e n t D e n s i t y , / ^ A / c m 2 F i g u r e A l . A n o d i c P o l a r i z a t i o n C u r v e f o r T i n S u l p h i d e E l e c t r o d e - 63 — 4. R e p r o d u c i b l e r e s u l t s were u n o b t a i n a b l e w i t h t h i s p a r t i c u l a r t i n s u l p h i d e e l e c t r o d e . On t h e b a s i s o f t h e s e o b s e r v a t i o n s and because o f t h e g r e a t d i f f i c u l t y e x p e r i e n c e d i n t h e attempt t o produce a s a t i s  f a c t o r y e l e c t r o d e , t h e work w i t h t i n s u l p h i d e was t e r m i n a t e d . - 64 - APPENDIX B S i g n C o n v e n t i o n f o r E l e c t r o c h e m i c a l Measurements An a r e a o f c o n s i d e r a b l e c o n f u s i o n i n e l e c t r o c h e m i c a l s t u d i e s c e n t r e s a r o u n d t h e s i g n o f e l e c t r o d e p o t e n t i a l s and v o l t a g e s i n e l e c t r o c h e m i c a l c e l l s . The c o n v e n t i o n u s e d i n t h i s work i s p a t t e r n e d a f t e r t h a t p r o p o s e d by d e B e t h u n e 4 and i s c o n s i s t e n t w i t h t h e IUPAC - S t o c k h o l m c o n v e n t i o n 5 5 . The e s s e n t i a l f e a t u r e i s t h a t e a c h h a l f c e l l i n an e l e c t r o c h e m i c a l c e l l i s a s s i g n e d an e l e c t r o d e p o t e n t i a l w h i c h i s i n d e p e n d e n t o f t h e d i r e c t i o n i n w h i c h t h e h a l f c e l l i s w r i t t e n . To s t a r t , t h e t e r m s "anode" and " c a t h o d e " a r e d e f i n e d . An anode i s an e l e c t r o d e where o x i d a t i o n i s o c c u r r i n g o r i s assumed t o o c c u r by t h e c h e m i c a l r e a c t i o n w r i t t e n t o d e s c r i b e t h a t e l e c t r o d e , and a c a t h o d e i s an e l e c t r o d e where r e d u c t i o n o c c u r s o r i s assumed t o o c c u r , i r r e s p e c t i v e o f w h e t h e r t h e r e a c t i o n i s s p o n t a n e o u s o r i s f o r c e d by an e x t e r n a l emf. Then f o r o x i d a t i o n a t an anode, A F e = + n"fV e and f o r r e d u c t i o n a t a c a t h o d e , A F 0 = - n?V c > where V e i s t h e e l e c t r o d e p o t e n t i a l a s s o c i a t e d w i t h a p a r t i c u l a r e l e c t r o d e r e a c t i o n , r e g a r d l e s s o f w h e t h e r o x i d a t i o n o r r e d u c t i o n i s o c c u r r i n g a t a p a r t i c u l a r moment. F o r example, i f t h e o x i d a t i o n o f c o p p e r i n a c u p r i c s o l u t i o n i s c o n s i d e r e d : C u — ^ C u + + + 2e~ .'.I AF° = ( A F ° f ( C u + + ) > 2A . F - f t e - , ) - : - ( A F ° f ( C u ) ) : - 65 - = (15.5 + 0) - (0) = 15.5 k c a l . / m o l e AF° = + n?V° V° = + AF_ = 15.5 = 0.337 V n ? 2 (23.06) C o n v e r s e l y , i f t h e r e d u c t i o n o f c u p r i c i o n a t a c o p p e r c a t h o d e i s c o n s i d e r e d : C u + + + 2e~ — * - Cu AF° - A F ° f ( C u ) - ( A F ° f ( C u + + ) + 2A P f f f ( e - ) > = 0 - (15.5 + 0) = 15.5 k c a l . / m o l e AF° =-n'?V0 V = - AF°_ = ~ (-15.5) „= 0.337 V n ^ 2 (23.06) Thus an unambiguous p o t e n t i a l * c a n be a s s i g n e d t o e a c h e l e c t r o d e r e a c t i o n , c o m p l e t e l y i n d e p e n d e n t o f t h e assumed d i r e c t i o n o f t h e e l e c t r o d e r e a c t i o n . To i l l u s t r a t e t h e use o f t h e e l e c t r o d e p o t e n t i a l i n t h e thermodynamic t r e a t m e n t o f wh o l e c e l l s , c o n s i d e r t h e i r o n - c o p p e r r e a c t i o n i n a c i d s o l u t i o n (i„e. t h e c e m e n t a t i o n r e a c t i o n i n c o p p e r r e f i n i n g ) . F i r s t c o n s i d e r t h e o v e r a l l r e a c t i o n : Fe + C u + + -z=* F e + + + Cu ( R e a c t i o n 0) A F 0 = A F 0 ° + RT I n aFe++ ^Cu++ A F 0 = - n ? £ , 0 and A F 0 ° = -n ? £ 0 ° * The e l e c t r o d e p o t e n t i a l s V ° a r e n u m e r i c a l l y e q u a l b u t o p p o s i t e i n s i g n t o t h e o x i d a t i o n p o t e n t i a l s t a b u l a t e d by L a t i m e r ^ 9 . - 66 - Then £ Q = £ 0 ° - RT I n a F ( ?++ a C u + + Now c o n s i d e r t h e h a l f c e l l s : F e — » . F e + + + 2e V F ° = 0.440 V ( R e a c t i o n F) A F F = A F F ° + RT I n a F e + + A F F = + n ? V F and A F F ° = + n ^ v y Cu —P- C u + + + 2e~ V r ° = 0.337 V ( R e a c t i o n C) AF~ = A F C ° + RT I n a C u + + AF c = + n ? V c and A F C ° =. ;n'?V I B u t A F Q = A F F - AFQ A F p ° + RT I n a F e + + n " ? ( V F 0 - V c ° ) + RT I n aw.c++ (AF C ° + RT I n a C u++) a C u + + B u t T hen A F Q = £ 0 = ° 0 - n ? £ , -0 ( V c ° - V p ° ) - RT I n a F e + + n ^ a C u + + V C ° ~ v F ° I n t h e p r e s e n t c a s e , t h e c e l l c a n be r e p r e s e n t e d i n t h e f o l l o w i n g way: F e , Fe ++ C u + + , Cu Then e ° = V c ° - V F ° = V ° ( r i g h t s i d e ) - V ° ( l e f t s i d e ) V c ° = 0 . 3 3 7 V, and V F ° = -0.440 V E,° = 0.337 -(-0.44 0) = 0.777 V AF° = - n T- £ ° AF° = - 2 ( 2 3 . 0 6 ) ( 0 . 7 7 7 ) = 35.8 k c a l / m o l e T h i s i s e q u a l t o t h e v a l u e , b o t h n u m e r i c a l l y and i n s i g n , c a l  c u l a t e d , f r o m t h e l i s t e d f r e e e n e r g i e s . T h e r e f o r e , i t i s c o n  c l u d e d t h a t t h e s i g n c o n v e n t i o n u s e d h e r e f o r t h e h a l f c e l l p o t e n t i a l s i s c o n s i s t e n t w i t h s t a n d a r d t h ermodynamic c o n v e n t i o n s , Now Then Now so ' - 67 - APPENDIX C C o m p i l a t i o n o f A p p r o p r i a t e Thermodynamic D a t a The thermodynamic d a t a f o r t h e v a r i o u s c h e m i c a l s p e c i e s o f i n t e r e s t i n t h i s s t u d y a r e compilfed i n T a b l e C-I„ I n most c a s e s , t h e y have been t a k e n f r o m s t a n d a r d s o u r c e s - E l l i o t t and G l e i s e r 5 1 , R o s s i n i 3 6 and L a t i m e r 1 9 . The m a j o r e x c e p t i o n i s t h e f r e e e n e r g y o f t h e c u p r o u s i o n . I t was. c a l c u l a t e d as shown below. A c c o r d i n g t o F e n w i c k 5 4 , Keq = 1 x 1 0 6 +10% a t 25°C f o r t h e r e a c t i o n 2 C u + •===* C u + + + Cu Then AF° = -RT I n Keq = -8.18 +0.8 k c a l / m o l e R o s s i n i 3 6 a s s i g n s A F ^ 0 f o r C u + + e q u a l t o 15.5. k c a l , L a t i m e r 1 9 a s s i g n s 15.53 k c a l and L e w i s and R a n d a l l 1 8 a s s i g n 15.91 k c a l . The c h o s e n v a l u e was 15.5 + 0 , 5 ' k c a L Then A F f ° f o r C u + = 1/2 [ ( A F f 0 ) C u + + + ( A F f ° ) C u - A F ° J = 1 1 . 8 4 +0.65 k c a l / m o l e By u s i n g t h e r e l a t i o n s h i p AH° = AF° + T A S ° , a v a l u e of. 17.3 k c a l / m o l e was c a l c u l a t e d f o r AH^° f o r C u + . S i m i l a r l y , % S° f o r C u ( O H ) 2 = 16.1 e.u. S° f o r C u 2 S 0 4 = 41.3 e.u. The most r e c e n t v a l u e s f o r t h e f r e e e n e r g y and h e a t o f f o r m a t i o n o f s u l p h i d e s were g i v e n by E l l i o t t and G l e i s e r 5 1 u s i n g S 2 ( g a s ) as t h e s t a n d a r d s t a t e . T h e s e have been c o n v e r t e d f o r t h i s - 68 - work u s i n g S ( r h o m b o h e d r a l ) as t h e s t a n d a r d s t a t e . The p o s s i b l e e r r o r s o r s t a n d a r d d e v i a t i o n s were c a l  c u l a t e d i n t h e f o l l o w i n g manner. Assume t h e r e l a t i o n s h i p i s A + B = C Take l o g a r i t h m s : I n (A+B) = I n C D i f f e r e n t i a t e : d I n (A+B) = d I n C U s i n g t h e i d e n t i t y dx = d I n x x c o n v e r t t o d (A+B) = dC (A+B) C dA + dB •. dC A + B C R e p l a c e d i f f e r e n t i a l w i t h e x a c t i n c r e m e n t A: AA + AB = AC A + B C AA, AB and AC a r e t h e s t a n d a r d d e v i a t i o n s f o r A, B and C. I f two o f t h e v a l u e s a r e known, t h e t h i r d c a n be c a l c u l a t e d . U s i n g t h e d a t a o f T a b l e C - I , t h e h a l f c e l l p o t e n t i a l s o f a number o f e l e c t r o d e r e a c t i o n s o f i n t e r e s t i n t h i s work have been c a l c u l a t e d , and a r e p r e s e n t e d i n T a b l e C - I I . -69 - TABLE C - l : Thermodynamic D a t a a t 29 8° K S p e c i e s H+ H 2 (g) e" o 2 ( g ) OH - (aq) H 20 Cu C u + ( a q ) A F ° f k c a l / m o l e 0 (36) 0 (36) 0 (36) 0 (36) -37.6 (36) •56.69±0.02 (51) 0 (51) 1 1 . 8 4 i 0 . 6 5 ( c a l c ) C u + + ( a q ) 15 .5±0.5 (36) C u 2 0 -36 .4±1.5 (51) CuO -31 . 7 i 2 . 0 (51) CuS -11 .63±5.5 (51) CU2S -20 .84±1.5 (51) Cu(OH) 2 -85.3 (36) C u S 0 4 -158.2 (19) s 2 (g) 19 .13±1.0 (51) S (rh) 0 (19) S= (aq) 22.1 (19) H 2S -7. 9 1 ± 0 . 7 (51) H 2 S ( a q ) -6.54 (19) HS"(aq) 3.01 (19) H S 0 4 " -179.9 (19) H 2 S 0 4 -177.3 (19) s o 4 = -177.3 (19) A g 2 S -9. 44±1«0 (51) ZnS (sph) -47.4 (19) FeS ( p y r r ) -23 ,08±1.0 (51) N i 3 S 2 -47 .97±5.0 (51) N i S -21 .14±2.5 (51) PbS -22 .34±1.5 (51) SnS -17 .94*1,5 (51) S n S 2 -38 .07*5.0 (51) A g + ( a q ) 18.43 (19) Z n + + ( a q ) -35.18 (19) F e + + -20.30 (19) Ni++ -11.53 (19) P b + + -5.81 (19) S n 4 + ( a q ) -6.275 (19) S n + 4 ( a q ) 0.650 (19) A H°f k c a l / m o l e 0 (36) 0 (36) Q (36) 0 (36) -55.0 (36) - 6 8 . 3 1 7 ± 0 . 0 1 (51) 0 (51) 17.3 ( c a l c ) 15.4 (36) -41.8*1.5 (51) - 3 8 , 3 ± 2 . 0 (51) -11.61*1.5 (51) -19.48*1.0 (51) -106.1 (36) -184.0 (19) 30.84±1.0 (51) 0 (19) 8.56 (19) -4.82±0.6 (51) -9.4 (19) -4.22 (19) -211.7 (19) -216.9 (19) -216.9 (19) -7 . 5 5 ± 1 . 0 (51) -48.5 (19) -2 2 . 4 ± 1 . 0 (51) -47.66*4.0 (51) -21.68*2.5 (51) -22.28+1,0 (51) - 1 8 . 4 ± 1 . 5 (51) - 3 9 . 9 6 ± 5 . 0 (51) 25.31 (19) -36.43 (19) -21.0 (19) -15.3 (19) 0.39 (19) -2.39 (19) e. u. 0 (36) 31.2 (36) 15.6 (36) 49,0 (36) -2.52 (36) 16.7 (36) 97 (51) 4 (37) 7 9 -26.3 24.1 10 .4 15.9 28.9 16.1 27.1 (53) (36) (36) (19) (19) ( c a l c ) (19) 7.62 (19) -6. 4 (19) 49. 15 (19) 29 . 2 (19) 14. 6 (19) 30. 3 (19) 4. 1 (19) 4. 1 (19) 34. 8 (19) 13. 8 (19) 16. 1 (19) 21. 8 (19) 23. 6 (19) 17.67 (19) -25.45 (19) -27.1 (19) 5.1 (19) -5.9 (19) ( R e f e r e n c e s i n b r a c k e t s ) TABLE C - I I C a l c u l a t e d H a l f C e l l P o t e n t i a l s E l e c t r o d e R e a c t i o n P o t e n t i a l , V V° D e v i a t i o n , , + 1 C u 2 S 2 C u + + -s- S + 4 e _ 0.563 + 0.0295 l o g a c u + + 0. 563 0. 027 2 C u 2 S 2 C u + + S + 2e~ 0.965 + 0.0591 l o g a C u + 0. 965 0. 061 3 C u 2 S -*> CuS + C u + + + 2 e _ 0.535 0.0295 l o g a C u + + 0. 535 0. 130 4 Cu 2S-*- CuS + C u + + e~ 0.913 + 0.0591 l o g a C u + 0. 913 0. 267 5 C u 2 S + 4H 20 -s» 2 C u + + + HS0 4~ + 7 H + + 10e~ 0.428 + 0.0118 l o g a C u + + -0. 0414 pH 6 C u 2 S + 4 H 2 0 - * - 2 C u + + + S 0 4 ~ + 8 H + + 10e~ 0.440 + 0.0118 l o g a C u + + -0. 0472 pH 7 2 C u 2 S + H 2 0 - ^ C u 2 0 + 2CuS +2H + + 2e~ 0.840 - 0.0591 pH 8 C u 2 S + 2H 20 -*-Cu(OK) 2 + CuS + 2 H + + 2e~ 0.807 - 0.0591 pH 9 CuS C u + + + S + 2e~ 0.588 + 0.0295 l o g a C u + + 0. 588 0. 130 10 CuS ~ i * C u + + S + e - 1.018 + 0.0591 l o g a C u + 1. 018 0. 267 11 CuS + 4H 20 - » - C u + + + H S 0 4 " + 7 H + + 8e~ 0.401 + 0.0074 l o g a C u + + -0. 0517 pH 12 CuS + 4H 20 C u + + + S 0 4 = + 8 H + + 8e~ 0.415 + 0.0074 l o g a C u + + -0. 0591 pH 13 CuS + 2H 20 -*-Cu(OH) 2 + S + 2H + + 2e" 0.860 -- 0.0591 pH 14 2CuS + H 20 -*CuO + C u + + + 2S + 2 H + + 4e" 0.690 - 0.0295 pH 15 C u + + + 2H 20^5r C u ( O H ) 2 + 2 H + l o g a C u + + + 2pH = 9 .2 16 2 C u + ^ C u + + + Cu Keq. = = 1 x 1 0 6 TABLE C - I I (cont'd) E l e c t r o d e Reaction P o t e n t i a l , V V° D e v i a t i o n , + 17 Cu -~ C u + + + 2 e - 0.336 + 0.0296 l o g a C u + + 0. 336 18 Cu_«-Cu + + e - 0.513 + 0.0591 l o g a C u + 0. 513 19 S 0 4 = + H + =:-- H S 0 4 - pH = 1 9 f aHS04 - = a S 0 4 = ) 20 H 2S (aq) ^ H S " + H + pH = 7 ( aH 2S = aHS" ) 21 S + 4H20-*> IS0 4~ + 7H + + 6e~ 0.339 - 0.069 pH 22 Ag 2 L . -+~ A g + + S + 2e 1.002 + 0.0591 l o g a A g + 1. 002 23 Ag 2S -^AgS + A g + + e 24 AgS -*-Ag + + S + E 25 N i 3 S 2 ~ * ~ 3 N i + + + 2S + 6e~ 0.0962 - 0.0295 i l o g a N i++ 0. 0962 26 N i 3 S 2 - ^ 2 N i S + N i + + + 2e~ -0.126 +0.0295 l o g a N i + + -0. 126 27 NiS - * ~ N i + + + S + 2e~ 0.209 + 0.0295 l o g a N i + + 0. 209 28 PbS -*~Pb + + + S + 2e~ 0.358 + 0.0295 l o g a p b++ 0. 358 29 ZnS ( s p h a l e r i t e ) Z n + + + S + 2e~ 0.265 + 0.0295 l o g a Z n + + 0. 265 30 F e S 2 — * - F e + + + 2S + 2e~ 0.060 + 0.0295 log a F e + + 0. 060 31 SnS 2-*-Sn + +"+ 2S + 2e~ 0.688 + 0.0295 l o g a S n + + 0. 688 32 SnS ~*-Sn + + + S + 2e 0.253 + 0.0295 log a S n + + 0. 253 33 S n++_^ S n+4 + 2 e - 0.150 + 0.0295 l o g a S n+4 a S n + + 0. 150 72 - -APPENDIX D E l e c t r o d e . P o t e n t i a l s o f M e t a l S u l p h i d e s Noddack and W r a b e t z 1 1 ' 1 2 and S a t o 4 7 m e a s u r e d t h e p o t e n t i a l o f A g 2 S , C u 2 S , CuS, PbS, F e S , F e S 2 and ZnS e l e c t r o d e s i n a c i d and b a s i c s o l u t i o n s . T h e i r r e s u l t s a r e summarized i n T a b l e D-I and d i s c u s s e d b r i e f l y . TABLE D-I E l e c t r o d e P o t e n t i a l s f o r S e v e r a l S u l p h i d e s . M e a s u r e d P o t e n t i a l , V C a l c u l a t e d E l e c t r o d e E x p e c t e d R e a c t i o n Noddack & Wrabetz S a t o P o t e n t i a l , V C u 2 S C u 2 S — * C u S + C u + + + 2e~ 0.474 0. 504 0.535 CuS C u S - — C u + + + S + 2e 0.58 0. 567 0.588 PbS PbS — * - P b + + + S + 2e 0. 367 0. 370 0.354 A g 2 S A g 2 S 2Ag ++ S + 2e •0.812 0. 82 1.002 ZnS Z n S ( s p h a l e r i t e j Z h + + + S + 2e 0.5 0.26 F e S 2 F e S 2 — V F e + + + S 2 + 2e 0*5 0. 7 0.757 S a t o e x p l a i n e d t h e d i s c r e p a n c y between t h e measured.and. c a l c u l a t e d v a l u e s f o r t h e p o t e n t i a l o f t h e A g 2 S e l e c t r o d e by a s s u m i n g t h a t a t w o - s t a g e r e a c t i o n was t a k i n g p l a c e , v i z : A g 2 S —*>- AgS + A g + + e Ag.S — A g + + e~ No v a l u e o f t h e f r e e e n e r g y o f AgS i s a v a i l a b l e , so t h i s mechanism c a n n o t be s u b s t a n t i a t e d . However, i f t h e m^#iS^fea-i v a l u e o f 0.82 V i s assumed t o be t h e e l e c t r o d e p o t e n t i a l f o r t h e r e a c t i o n Ag 2S — A g S + A g + + e~, then the f r e e energy o f formation o f AgS can be c a l c u l a t e d t o be - 8,890 cal/mole. The measurements o f Noddack and Wrabetz demonstrated the i n f l u e n c e o f the Ag/S r a t i o on the e l e c t r o d e p o t e n t i a l . For example, f o r an e l e c t r o d e with Ag/S = 1.99, V° = 0.812 V; and f o r an e l e c t r o d e w i t h Ag/S = 1.84, V° = 0.853 V. Sato does not r e v e a l the s t o i c h i o m e t r y o f h i s e l e c t r o d e , but i t l i k e l y had Ag/S = 2, approx i m a t e l y . Although n i c k e l s u l p h i d e i s o x i d i z e d e l e c t r o c h e m i c a l l y on a commercial s c a l e , no e l e c t r o d e p o t e n t i a l s were noted i n the l i t e r a t u r e . Renzoni e t a l 1 c h a r a c t e r i z e the n i c k e l s u l p h i d e o x i d a t i o n by the f o l l o w i n g o v e r a l l r e a c t i o n : Ni 3S 2—>"3 N i + + + 25° + 6e V° = 0.417 V Sev e r a l o t h e r n i c k e l s u l p h i d e s are known to e x i s t 5 2 , so i t i s l i k e l y , i n view o f the o x i d a t i o n mechanism suggested f o r o t h e r p o l y v a l e n t s u l p h i d e s (e.g. copper s u l p h i d e ) , t h a t s e v e r a l s t e p  wise processes are i n v o l v e d i n the o x i d a t i o n o f N i 3 S 2 . One p o s s i b l e mechanism i s : N i 3 S 2 — ^ N i + + + 2 NiS + 2e V° = -0.126 V NiS —»- N i + + + S° + 2e~ V° = 0.209 V An e l e c t r o c h e m i c a l s e r i e s f o r the s u l p h i d e s has been e s t a b l i s h e d based on the above i n f o r m a t i o n , and i s shown i n Table D - I I . - 74 - TABLE D - I I T e n t a t i v e E l e c t r o c h e m i c a l S e r i e s f o r Some M e t a l S u l p h i d e s E l e c t r o d e E l e c t r o d e P o t e n t i a l , V° A g 2 S 0.82 F e S 2 0.7 CuS 0.59 C u 2 S 0.53 PbS 0.35 ZnS 0.26 N i S 0.21 N i 3 S 2 -0.13 - 75 - APPENDIX E P o t e n t i a l s a t the E l e c t r o d e - S o l u t i o n I n t e r f a c e E l e c t r o d e P o t e n t i a l Metal s u l p h i d e e l e c t r o d e s g e n e r a l l y f o l l o w the Nernst r e l a t i o n s h i p i n a c i d s o l u t i o n . When N e r n s t i a n behaviour i s fo l l o w e d by an e l e c t r o d e , a d e f i n i t e p o t e n t i a l i s e s t a b l i s h e d between the e l e c t r o d e and s o l u t i o n , f u l l y p r e d i c t a b l e from a knowledge of the a c t i v i t i e s and f r e e e n e r g i e s o f the e l e c t r o d e and s o l u t i o n c o n s t i t u e n t s . Quite o f t e n t h i s p o t e n t i a l i s c a l l e d the r e v e r s i b l e p o t e n t i a l , but t h i s term should o n l y be used when the e l e c t r o d e r e a c t i o n i n q u e s t i o n i s t r u l y r e v e r s i b l e , i . e . when a small change i n p o t e n t i a l from one s i d e o f the r e v e r s i b l e p o t e n t i a l to the ot h e r w i l l r e v e r s e the d i r e c t i o n o f the e l e c t r o d e r e a c t i o n . A more ge n e r a l and u n i v e r s a l l y a p p l i c a b l e term f o r the p o t e n t i a l e s t a b l i s h e d between an e l e c t r o d e and a s o l u t i o n i s the r e s t p o t e n t i a l ; t h i s term appears most a p p r o p r i a t e when c o n s i d e r i n g compound e l e c t r o d e s such as the s u l p h i d e s because a t r u l y r e v e r s i b l e r e a c t i o n i n v o l v i n g the compound and i t s components i s h i g h l y improbable i n a c i d s o l u t i o n s because o f the s t a b i l i t y o f the sulphur atoms or molecules. I t presupposes o n l y t h a t the s e v e r a l r e a c t i o n s o c c u r r i n g spontaneously a t the e l e c t r o d e s u r f a c e are i n e l e c t r i c a l balance. E l e c t r o d e - S o l u t i o n I n t e r f a c e A d e t a i l e d and s o p h i s t i c a t e d d i s c u s s i o n o f the e l e c t r o d e - s o l u t i o n i n t e r f a c e has been presented by P a r s o n s 2 9 . When an e l e c t r o d e i s p l a c e d i n an aqueous s o l u t i o n , there i s a r e d i s t r i b u t i o n of the e l e c t r i c a l charge a s s o c i a t e d with the p a r t i c l e s which come from the bulk of the two phases ( e l e c t r o d e and s o l u t i o n ) to form the i n t e r f a c e o r i n t e r f a c i a l l a y e r . T h i s r e d i s t r i b u t i o n of charge forms a r e g i o n which i s c a l l e d the double l a y e r . The- s p e c i e s which are i n v o l v e d i n the e l e c t r o c h e m i c a l r e a c t i o n a c r o s s the double l a y e r e x i s t i n energy w e l l s : i n the e l e c t r o d e , the w e l l i s produced by the i n f l u e n c e of the o t h e r atoms and i o n s i n the metal (or s u l  phide, or oxide) l a t t i c e ; i n the s o l u t i o n , the w e l l i s produced by the i n f l u e n c e o f water molecules (hydrated s p e c i e s ) o r o f o t h e r ions (complexed s p e c i e s ) . I t i s u s e f u l to p i c t u r e an energy w e l l i n the e l e c t r o d e moving c l o s e enough t o an energy w e l l i n the s o l u t i o n so t h a t the energy b a r r i e r between the two w e l l s i s s m a l l enough t h a t a t r a n s f e r o f s p e c i e s between the two w e l l s can be e f f e c t e d . Depending on the r e l a t i v e depth o f the two energy w e l l s , the t r a n s f e r can be e i t h e r anodic o r c a t h o d i c , but t h e r e i s a tendency f o r the two t r a n s f e r s to move towards a balanced s t a t e where the anodic and c a t h o d i c processes are v i r t u a l l y balanced. The p o t e n t i a l and the c u r r e n t flow a c r o s s the energy b a r r i e r are c a l l e d the r e s t p o t e n t i a l and the exchange c u r r e n t r e s p e c t i v e l y . B u t l e r 3 0 c a l c u l a t e d t h a t s e v e r a l e l e c t r o n v o l t s are r e q u i r e d to l i f t bare u n s o l v a t e d c a t i o n s from t h e i r energy w e l l s i n the metal l a t t i c e , and e n e r g i e s o f the same or d e r of magnitude would l i k e l y be necessary to remove a bare unsolvated c a t i o n from a s u l p h i d e l a t t i c e . A l s o , B u t l e r 3 0 and E l e y and E v a n s 3 1 c a l c u l a t e d t h a t s e v e r a l e l e c t r o n v o l t s are r e q u i r e d to l i f t a bare c a t i o n out of i t s h y d r a t i o n sheath. However, the t r a n s f e r o f a c a t i o n from a metal (or metal compound) l a t t i c e t o the s o l u t i o n r e q u i r e s o n l y about 5 mV p o t e n t i a l . Thus the energy w e l l s i n the two phases must be very c l o s e t o g e t h e r . The water molecules are touching the e l e c t r o d e and may be even bonded to i t by a d s o r p t i o n bonds even st r o n g e r than t h e i r own i n t e r m o l e c u l a r b o n d s 2 9 . ' O v e r p o t e n t i a l When an a d d i t i o n a l e l e c t r o d e i s added to the s o l u t i o n to complete the g a l v a n i c c e l l , and an e x t e r n a l p o t e n t i a l i s a p p l i e d , the r e s t c o n d i t i o n i s a l t e r e d to a net c a t h o d i c o r anodic c o n d i t i o n depending on the d i r e c t i o n o f the a p p l i e d p o t e n t i a l . The a d d i  t i o n a l p o t e n t i a l a c r o s s the double l a y e r c o n s t i t u t e s a d r i v i n g f o r c e f o r e l e c t r o c h e m i c a l r e a c t i o n s a t the e l e c t r o d e , and tends to i n c r e a s e the c u r r e n t flow through the c e l l . A new term, the over- p o t e n t i a l , i s d e f i n e d . The o v e r p o t e n t i a l a t a c e r t a i n c u r r e n t d e n s i t y i s the d i f f e r e n c e between the measured p o t e n t i a l and the p r e v i o u s l y e s t a b l i s h e d r e s t p o t e n t i a l ; i f the o v e r p o t e n t i a l i s r e p r e s e n t e d by OJ, then C O -<p0 where <f>i and <t>0 are the h a l f - c e l l p o t e n t i a l s at net c u r r e n t d e n s i t i e s i and zero r e s p e c t i v e l y . V a r i o u s types o f o v e r p o t e n t i a l have been d i s t i n g u i s h e d (see, f o r example, r e f e r e n c e 13, pp 395-398), but the t h r e e important types are ohmic, c o n c e n t r a t i o n , and a c t i v a t i o n o v e r p o t e n t i a l . An ohmic o v e r p o t e n t i a l i s developed when a f i l m i s formed on the e l e c t r o d e and s e t s up a r e s i s t a n c e to the passage of c u r r e n t across-'"it-; the f i l m can be an oxide or s u l p h i d e , sulphur o r some other substance. I f the c u r r e n t s t r e n g t h i s i and the f i l m r e s i s t a n c e R, then the ohmic o v e r p o t e n t i a l w i l l be i R. Values o f s e v e r a l hundred v o l t s are p o s s i b l e f o r the ohmic o v e r p o t e n t i a l 1 * 1 . A c o n c e n t r a t i o n o v e r p o t e n t i a l i s caused by the e x i s t e n c e o f a d i f f e r e n c e i n c o n c e n t r a t i o n o f ions between the e l e c t r o d e - s o l u t i o n i n t e r f a c e or double l a y e r and the bulk o f the s o l u t i o n . As the p o t e n t i a l o f the e l e c t r o d e i s r e l a t e d to the i o n i c concen t r a t i o n i n the double l a y e r , and the p o t e n t i a l measured by a r e f e r e n c e e l e c t r o d e i s r e l a t e d to the bulk i o n i c c o n c e n t r a t i o n , s e r i o u s e r r o r s would be i n t r o d u c e d i n p o t e n t i a l measurement i f the c o n c e n t r a t i o n o v e r p o t e n t i a l was not r e c o g n i z e d and e i t h e r allowed f o r o r removed. The phenomenon o f c o n c e n t r a t i o n o v e r p o t e n t i a l forms the* b a s i s o f polorography and p o l a r o g r a p h i c a n a l y s i s . The t h i r d t y p e , a c t i v a t i o n o v e r p o t e n t i a l , i s developed when a r e a c t i n g s p e c i e s encounters a b a r r i e r which i t must climb b efore i t can proceed along the r e a c t i o n path; thus the a c t i v a t i o n o v e r p o t e n t i a l i s r e l a t e d to the energy o f a c t i v a t i o n ( i . e . the energy "height" o f the b a r r i e r ) and, i f c a r e f u l l y determined, can p r o v i d e both the i d e n t i f i c a t i o n of the r a t e - d e t e r m i n i n g step and the r a t e o f r e a c t i o n i n a c t i v a t i o n - c o n t r o l l e d e l e c t r o c h e m i c a l r e a c t i o n s . For the s i m p l e s t case, the a c t i v a t i o n b a r r i e r e x i s t s between two adjacent energy w e l l s , one i n the e l e c t r o d e and the other i n the s o l u t i o n . I f a p h y s i c a l d e s c r i p t i o n i s to be a t t a c h e d to the a c t i v a t i o n b a r r i e r i n t h i s case, i t i s easy to p i c t u r e the b a r r i e r being e s t a b l i s h e d by the r e d i s t r i b u t i o n of the e l e c t r i c a l - 79 - charges of the v a r i o u s bulk phase s p e c i e s when the two phases are brought i n c o n t a c t with one another. The success o f experiments to determine the a c t i v a t i o n o v e r p o t e n t i a l depends on the m i n i m i z a t i o n of ohmic and c o n c e n t r a t i o n o v e r p o t e n t i a l s . The procedures necessary to minimize the unwanted o v e r p o t e n t i a l s are d e s c r i b e d i n the s e c t i o n on Experimental Procedure. - 80 - APPENDIX F K i n e t i c R e l a t i o n s h i p s f o r A c t i v a t i o n C o n t r o l l e d E l e c t r o d e Reactions A g e n e r a l i z e d c a t h o d i c r e a c t i o n has been chosen to i l l u s t r a t e the development o f e l e c t r o d e k i n e t i c r e l a t i o n s h i p s . The d i s c u s s i o n i s e s s e n t i a l l y a s i m p l i f i c a t i o n o f t h a t presented by B o c k r i s 1 The o v e r a l l r e a c t i o n i s r e p r e s e n t e d by equation (Fl) : Reactants + ne~ Products (Fl) L i k e l y s e v e r a l steps are i n v o l v e d i n t r a n s f e r r i n g the r e a c t i n g s p e c i e s a c r o s s the s o l u t i o n - e l e c t r o d e i n t e r f a c e and p l a c i n g them on the cathode, but normally one of these steps w i l l have a l a r g e r f r e e energy b a r r i e r than the o t h e r s and thus w i l l c o n t r o l the r e a c t i o n r a t e . F i g u r e F l i l l u s t r a t e s a h y p o t h e t i c a l energy p r o f i l e along a r e a c t i o n c o - o r d i n a t e . The h i g h e s t peak r e p r e s e n t s the r a t e - c o n t r o l l i n g b a r r i e r , and unle s s the r e a c t i n g s p e c i e s a t t a i n t h i s f r e e energy l e v e l , they cannot pass on to become products. When a r e p r e s e n t a t i v e p o i n t o f a r e a c t i o n e x i s t s a t t h i s peak ( a l b e i t f o r an ex c e e d i n g l y s h o r t t i m e ) , i t i s c a l l e d the a c t i v a t e d complex o f the r e a c t i n g s p e c i e s . The a c t i v i t i e s o f the r e a c t i n g s p e c i e s a t p o i n t x ( j u s t before the h i g h e s t b a r r i e r ) are r e l a t e d t o the a c t i v i t i e s o f the spe c i e s i n the i n i t i a l s t a t e at p o i n t 1, and i f the two stattfB are cons i d e r e d t o be i n e q u i l i b r i u m , the r e l a t i o n s h i p can be d e s c r i b e d thus: ( T T a r ) x = ( I T a , . ) ! exp /-AF°l^-x ) (F2) I RT / where (1lar)^ and ( l l a r ) x are the products o f the a c t i v i t i e s o f the - 81 - tn U CD W CD CD U Pn t f CD a cd -P CO 7T\ / F o r w a r d / AF x-*-x+l AF° R e v e r s e / / I n i t i a l S t a t e (I) x+1 F i n a l S t a t e ( I I ) D i s t a n c e A l o n g R e a c t i o n C o - o r d i n a t e F i g u r e F l . R e a c t i o n P a t h and E n e r g y B a r r i e r s f o r a S e r i e s o f C o n s e c u t i v e R e a c t i o n s - 82 - u C W <D n T S c m +J CO A c t i v a t i o n E n e r g y R e q u i r e d When A ( j > c A p p l i e d 1 - f i A p p l y A < £ > ( - H D i s t a n c e A l o n g R e a c t i o n C o - o r d i n a t e F i g u r e F2. R e a c t i o n P a t h and E n e r g y B a r r i e r s when P o t e n t i a l A ( b c A p p l i e d - 83 - r e a c t a n t s i n the i n i t i a l and x t h s t a t e s r e s p e c t i v e l y , (each a c t i v i t y being r a i s e d to the power e q u i v a l e n t t o the number o f moles i n  v o l v e d i n the r e a c t i o n ) and A F ° 1 —> x i s the f r e e energy change du r i n g t r a n s i t i o n from 1 to x. The forward v e l o c i t y o f the r e a c t i o n a c r o s s the r a t e - c o n t r o l l i n g b a r r i e r can be expressed c o n v e n i e n t l y as \T = ( T T a r ) x l T (F3) where k, the s p e c i f i c r a t e c o n s t a n t , i s g i v e n by: k = K K T exp -AF°x — > X+l ..... (F4) ~E RT In equation ( F 4 ) , K i s the t r a n s m i s s i o n c o e f f i c i e n t ( i . e . the f r a c t i o n o f the s p e c i e s r e a c h i n g the a c t i v a t e d complex s t a t e which proceeds t o products) , and 1s. , T, h and R have t h e i r u s u a l p h y s i c a l s i g n i f i c a n c e . The c u r r e n t d e n s i t y i s a convenient measure of the v e l o c i t y o f e l e c t r o d e r e a c t i o n s and i s r e l a t e d t o the v e l o c i t y by " i * = V** X T (F5) where A i s the number o f e l e c t r o n s necessary so t h a t one a c t of the r a t e - d e t e r m i n i n g step can occur and i s the Faraday constant. Furthermore, i f the r a t e determining step occurs 0 times when the o v e r a l l r e a c t i o n (Fl) occurs once, then: A. = n (F6) I f a p o s i t i v e p o t e n t i a l d i f f e r e n c e A4>c i s a p p l i e d between the f i n a l and i n i t i a l s t a t e o f the r e a c t i o n (Figure F - 2 ) , the flow of r e a c t a n t s over the r a t e - d e t e r m i n i n g b a r r i e r i s r e t a r d e d . The a p p l i e d p o t e n t i a l d i f f e r e n c e A(f> c i n c r e a s e s AF°* _^ + j _ by an amount - 84 - P> A,'T 2-A(f) c, where p>A(J}c i s the p o r t i o n of the a p p l i e d p o t e n t i a l which r e t a r d e d the passage o f s p e c i e s t o the a c t i v a t e d complex s t a t e ; i t i s not necessary to account f o r the p o t e n t i a l d i f f e r e n c e beyond the a c t i v a t e d s t a t e because work done on the system a f t e r i t has passed the a c t i v a t e d s t a t e does not a l t e r the r e a c t i o n v e l o c i t y . The term d e s c r i b e s the symmetry o f the energy b a r r i e r i n r e l a t i o n to the o v e r a l l r e a c t i o n d i s t a n c e s . By combining (F2), (F3), (F4) and (F5), the f o l l o w i n g r e l a t i o n s h i p f o r the forward c u r r e n t d e n s i t y i s o b t a i n e d : ^ + ^ A A C ] ) c 3 !*= K A ^ - £ T (l\ar)1 exp h AF°i _ » y + AF< RT .....(F7) o r , on s i m p l i f i c a t i o n : i = B c ( T T a r)-L exp _ AF°p + A A < t > r ^ - RT (F8) By a s i m i l a r argument, the r e l a t i o n s h i p f o r the r e v e r s e r e a c t i o n , i . e . anodic d i s s o l u t i o n , i s o b t a i n e d : _„4 i = B A ( T T a r>2 exp -(1-p) A ACfr r~? RT (F9) As a b a s i s f o r d e v e l o p i n g p o t e n t i a l - c u r r e n t d e n s i t y r e l a t i o n s h i p s , the e q u i l i b r i u m o r r e s t s i t u a t i o n ( i . e . no itet c u r r e n t flow) i s f i r s t c o n s i d e r e d : i - i = 0 1 = 1 = 1, (F10) where XQ i s the exchange c u r r e n t . The o v e r p o t e n t i a l o O can be d e f i n e d as: ^ = Ac|> c - i ( j ) 0 ..... ( F l l ) where ^4*0 ^ s t * i e P o t e n t i a l w h e n i = XQ. When equation (F8) , (F9), (F10) and ( F l l ) are combined, the f o l l o w i n g are o b t a i n e d : 85 - l = i n exp 1 = 1Q exp (1-p) A U J RT x c = i Q exp and s i m i l a r l y , i A = i Q exp - (b X t o 1~ RT - exp X i o > RT (1-p) X c o > RT - exp ft X L P > RT (F12) (F13) (F14) (F15) where i c and i A are the r e s u l t a n t c u r r e n t d e n s i t i e s f o r c a t h o d i c p r e c i p i t a t i o n and anodic d i s s o l u t i o n r e s p e c t i v e l y under an a p p l i e d p o t e n t i a l S e v e r a l s i m p l i f i c a t i o n s o f equation (F15) are important. I f c o i s q u i t e l a r g e ( i . e . i f o o > 2.303 RT^* then 7v> i - i Q exp (1-P) (F16) RT Th i s can be r e w r i t t e n as CO = - RT In i n + RT In i , (F17) T T - p T x ^ ° TT^^fxT" A or = A + B In i a (F18) Equation (F18) i s the most common r e l a t i o n s h i p i n e l e c t r o d e k i n e t i c s , the s o - c a l l e d " T a f e l " l i n e . Now i f i s s m a l l ( i . e . i f (jj) s 2.303 RT) , then equation (F15) , on expansion of the e x p o n e n t i a l s , becomes iA " 10 ^ OO . .... (F19) RT or CO = RT i a (F20) * 2.303 RT ^ 20-30 mV i f A = 2 a t 25°C. - 86 - H u r l e n 3 " * ' 3 5 has developed a method f o r determining the standard heat o f a c t i v a t i o n of c e r t a i n e l e c t r o d e r e a c t i o n s . The standard heat of a c t i v a t i o n ( A H Q * ) f o r any r e a c t i o n i s d e f i n e d as the change i n standard heat content (on the hydrogen s c a l e ) o f , t h e r e a c t i o n system when going from i t s i n i t i a l to i t s a c t i v a t e d s t a t e : A H 0 * « H Q * - H 0 ( i ) (F21) In order to d e f i n e the standard heat content o f the a c t i v a t e d s t a t e i n terms c o n s i s t e n t with those u s u a l l y used f o r the r e a c t a n t , the frequency f a c t o r 0 must be i n t r o d u c e d : A H 0 * = H Q * - 1 H Q ( i ) (F22) 0 F u r t h e r , i f i t i s assumed the same frequency f a c t o r a p p l i e d to both the forward and r e v e r s e r e a c t i o n a c r o s s the a c t i v a t i o n b a r r i e r , then A H Q * - " A H Q * = 1 A H ^ (F23) At t h i s p o i n t the standard exchange c u r r e n t , J Q , i s d e f i n e d : J 0 - i 0 |j TTar) ( H a p ) P J (F24) U t i l i z i n g t h i s d e f i n i t i o n of J Q , the r e x a t i o n s h i p s expressed i n equations (F7), (F8), (F9), (F14) and (F15) can be d e s c r i b e d by an A r r h e n i u s equation of the f o l l o w i n g type: l o g J Q = C - ftn^-Afo - A H N * (F25) T 2.303 0 RT 2.303 RT The term n r e p r e s e n t s the number of e l e c t r o n s consumed d u r i n g one a c t of the o v e r a l l r e a c t i o n ( p o s i t i v e f o r c a t h o d i c and n e g a t i v e f o r anodic r e a c t i o n s ) . Constant C c o n s i s t s mainly of temperature independent c o n s t a n t s and i n c l u d e s the standard entropy o f a c t i  v a t i o n and the a c t i v i t y c o e f f i c i e n t of the a c t i v a t e d complex; both of which are here c o n s i d e r e d temperature independent. The G a l v a n i p o t e n t i a l A (j) cannot be determined e x p e r i m e n t a l l y , but i f the - 87 - r e a c t i o n i s symmetrical, i . e . the forward and r e v e r s e r e a c t i o n a c r o s s the a c t i v a t i o n b a r r i e r are the same, then the term i n equation (F25) c o n t a i n i n g A c|) w i l l be equal i n magnitude but o p p o s i t e i n s i g n f o r the forward and r e v e r s e r e a c t i o n . Then 2 l o g (J 0 / T ) = "cT + IT" - A~H^* + A H p * ...... (P26) 2.303 RT I f equation (F26) i s d i f f e r e n t i a t e d with r e s p e c t t o 1/T and -combined wi t h eguation (F23), then A H * = -2.303 R d l o g ( J n / T ) + 1 A H Q . . . . . (F27) d (1/T) 27 Thus i f the a c t i v a t i o n b a r r i e r i s symmetrical, i . e . i f fb = 1/2, and i f the assumptions i n h e r e n t i n the above d e r i v a t i o n are a c c e p t a b l e , i t i s then p o s s i b l e to determine the standard heat o f a c t i v a t i o n of t h a t e l e c t r o d e r e a c t i o n * . * I t i s t a c i t l y assumed t h a t the t r a n s m i s s i o n c o e f f i c i e n t K i s the same f o r both forward and r e v e r s e t r a n s f e r a c r o s s the a c t i v a t i o n b a r r i e r . - 88 - APPENDIX G A c t i v i t y C o e f f i c i e n t s i n CUSO4-H2SO4 S o l u t i o n s One of the d i f f i c u l t i e s i n determining e l e c t r o d e p o t e n t i a l s i n mixed s o l u t i o n s i s the l a c k o f good val u e s f o r the a c t i v i t y c o e f f i c i e n t s o f the v a r i o u s i o n i c s p e c i e s . A r g e r s i n g e r 2 5 d e r i v e d r e l a t i o n s h i p s f o r d e t e r m i n i n g the a c t i v i t y c o e f f i c i e n t s o f e l e c t r o l y t e s i n mixed aqueous s o l u t i o n from e l e c t r o m o t i v e f o r c e d a t a . H o l l a n d and B o n n e r 2 6 i n v e s t i g a t e d CUSO4-H2SO4 mixed aqueous s o l u t i o n s and o b t a i n e d a s e r i e s o f e l e c t r o m o t i v e f o r c e measurements; however, they d i d not extend t h e i r work to i n c l u d e an a p p l i c a t i o n of A r g e r s i n g e r ' s procedure to determine mean a c t i v i t y c o e f f i c i e n t s f o r the i n d i v i d u a l e l e c t r o l y t e s . Such an e x t e n s i o n i s attempted here. C o n s i d e r the g a l v a n i c c e l l 0 + A 0 - ( m l ) Q 6 + A e - (m2) Q where A ^ - and Q £ + A & _ are the two e l e c t r o l y t e s i n aqueous s o l u t i o n . The c e l l p o t e n t i a l £ i s d e f i n e d by £ = £ ° + R T l n a, * / K l (Gl) where a-^  = a c t i v i t y o f P ^ A ^  _ a 2 = a c t i v i t y o f Q g | A ^ . K l - < 0 + ) (Z p) - ( 0") (Z A) K 2 = ( 6 + ) (Z Q) = C B " ) (Z A) ZQ, Zp, Z A = charges on ions Then, u s i n g the procedure o f A r g e r s i n g e r 2 5 , the f o l l o w i n g r e l a t i o n s h i p s can be d e r i v e d : l r $ = Z P Z A P 1 jU-y? 9 G + N 5 G -1_ z p + z A J y L 3y 3H. V - 89 - dy . ....(G2) In h_ JLSj^_ . l 2 ° z Q + z A ^ o |_ <5y J N . + Z A ^ O y 9G - N <3G dy . (G3) where &^  = mean a c t i v i t y c o e f f i c i e n t o f component 1. = a c t i v i t y c o e f f i c i e n t o f component 1 i n i t s pure s o l u t i o n i n the s o l v e n t ( i . e . water) a t the same value o f N as i n the mixed s o l u t i o n . N = 1000 M s o l v e n t g-lJSl + N2JS2-~| _ nsolvent J m^  + m2 K 2 for water, where m^  and m2 are molalities. JElJSl. m^ K-^  + m 2 K 2 X, (1 + 1 ) Q l (gp 2 X ) G = - In y ( i _ + l _ ) 0 2 ( Z Q Z A ) The data o f Holland and B o n n e r 2 6 , d e r i v e d from e l e c t r o m o t i v e f o r c e measurements, are i n the form o f value s o f (5^  H 2SO^ f o r v a r i o u s ft2 CuS0 4 v a l u e s o f mH+ and Jj^ , the t o t a l i o n i c s t r e n g t h . I t i s necessary m C U + + to r e l a t e these measurements to the terms of equations (2) and (3) I f H2SC>4 and CuS0 4 are s o l u t i o n s 1 and 2 r e s p e c t i v e l y , then Z P = 1 , Z A = 2 and ZQ = 2. Now G = - In *1 ^ + 1 / 2 = - 1/2 i n V X 2 1/2 + 1/2 T22 - 1/2 In ft 3 H O S O J (G4) I 2 CuS0 4 - 90 - A l s o , or y = ElJSl + m 2 K 2 y = 2m-\ = m-|  2m^ + 2m2 ni^ + ni2 m_ H2S0 4. m H 2 S 0 4 + m C u S 0 4 But mH+ = 2mH 2S0 4 and mSO| = 1 / 2 m H + + m C u + + T h e r e f o r e y = 1/2 mH+ - ran* 1/2 mH+ + n» C u++ mH+ + 2)*^++ I f mjjjh = R (G5) "Cu ++ then y = R + 2 A l s o The t o t a l i o n i c s t r e n g t h , )X , i s d e f i n e d as \,i ii i 2 l = 1/2 4- C ± Z± (G6) N = + Tf\2 K 2 = 2 (m^ + m2) = 2 * mH 2S0 4 + m C u S 0 4 ) N = m„+ + 2nu ++ (G7) H Cu For t h i s s o l u t i o n - 91 - JJ^ = 2 m H + + 4 m C u + + ..... (G8) 2 By combining equations (G5), (G7) and (G8), the f o l l o w i n g i s o b t a i n e d : N = 2 U R + 2 ..... (G9) 3R + 8 Thus equations (G4), (G6) and (G9) p r o v i d e the r e l a t i o n s h i p s necessary to use the data of H o l l a n d and B o n n e r 2 6 i n equations (G2) and (G3). The v a l u e s o f G, y and N are compiled i n Ta b l e G-I. The important r e l a t i o n s needed f o r equations (G2) and (G3) are /c)G ] l ^ N i y and p G \ . F i g u r e G - l i s a p l o t of G vs N a t constant y, and i s c h a r a c t e r i z e d by c o n s i d e r a b l e i r r e g u l a r i t y . In f a c t (^G/ON) v i s f i r s t a l a r g e p o s i t i v e v a l u e , then zero, then a l a r g e n e g a t i v e v a l u e , then zero, and f i n a l l y above N = 0.5, a p o s i t i v e v alue a g a i n . These data should be analysed by the Gibbs-Duhem i n t e g r a t i o n technique to g i v e a reasonable p r e c i s i o n over the wide range o f N. For the r e g i o n above N = 0.5 however, the slope (<^G/ON)V i s reasonably uniform, so as an approximation, the average value of these s l o p e s has been used. I t i s r e a l i z e d t h a t c o n s i d e r a b l e e r r o r i s probably i n t r o d u c e d by t h i s approximation, but t h e r e i s a p o s s i b i l i t y t h a t the r e g i o n s of l a r g e p o s i t i v e and n e g a t i v e s l o p e w i l l i n e f f e c t l a r g e l y c a n c e l each o t h e r i n a Gibbs-Duhem i n t e  g r a t i o n . From the approximation, the f o l l o w i n g v a l u e i s o b t a i n e d . p G \ = -0.040 f o r N >0.5 ,....(G10) Fu r t h e r treatment of the data g i v e s : c)_G\ = 0.282 f o r N y 0.5 . . . . . ( G i l ) d y J N - 92 - Equation (G3) i s i n t e g r a t e d : In 5 2 = 1/2 y 2 - N3G y (G12) C a l c u l a t e d v a l u e s of u CUSO4 3 n u i n ^ e r °^ CUSO4-H2SO4 s o l u t i o n s are shown i n Table G-II. These val u e s are compared i n Table G-III w i t h those determined by H u r l e n 3 9 from e l e c t r o d e p o t e n t i a l measurements. The v a l u e s o f ^cuS0 4 a r e P l ° t t e d a g a i n s t J\ , the i o n i c s t r e n g t h , i n F i g u r e G-2. The d i f f e r e n c e between the values of Hurlen and those c a l c u l a t e d h e r e i n i s e q u i v a l e n t to a d i f f e r e n c e i n the e l e c t r o d e p o t e n t i a l of about 0.005 V ( f o r n = 2). Hurlen's v a l u e s depend on some assumed valu e s of l i q u i d j u n c t i o n p o t e n t i a l s , so they probably have a l i m i t e d accuracy. The present values are probably even l e s s dependable because of the approximation used i n t h e i r c a l c u l a t i o n , but they should be a p p l i c a b l e f o r v a l u e s of N g r e a t e r than 0.5 and f o r v a l u e s of y g r e a t e r than 0.7. F o r N = 0.5 and y = 0.7, the c o n c e n t r a t i o n s a r e : C u + + , 0.075 M, and H +, 0.35 M. Thus, the c a l c u l a t e d a c t i v i t y c o e f f i c i e n t s are probably most a p p l i c a b l e to s o l u t i o n s of r e l a t i v e l y high c o n c e n t r a  t i o n (say C u + + >0.01 M, H + >0.1 M) . The use o f the c a l c u l a t e d v a l u e s of ^cuS04 ^ a v e a s a t i s f a c t o r y r e s o l u t i o n of the e l e c t r o d e p o t e n t i a l measurements i n 0.1 M CuSO^ - 0.1 M H2SO4 s o l u t i o n s o b t a i n e d i n t h i s work. The c a l c u l a t e d v a l u e s o f $cuS04 are probably not a b s o l u t e l y c o r r e c t , but the use of the approximate c a l c u l a t i o n r a t h e r than a proper i n t e g r a t i o n probably develops a constant e r r o r . TABLE G-I 9 3 Determination of G, y and N from Data of Holland and Bonner 2 E H ± _ mcu++ 'X:JH2S04 ft 2CuS04 G y A R 3R + 2 + 8 N 7.178 1.795 -0.293 0.783 1*319 0 .311 0.820 1.726 -0.273 0.897 0.558 1.698 -0.265 0.509 0.316 1.686 -0.262 0.2522: 0.157 1*547 -0.218 •V- 0«,l2fo« 0,0797 1.535 -0.218 0.0638 0.397 1.304 -0.133 0.0307 0.0191 0.932 +0.035 0.0154 0.00959 5,435 1»712 -0.269 0.732 1.359 0 .306 0.832 1.672 -0.257 0.926 0.567 1,634 -0.246 0.522 0.319 1.596 -0.234 0.2637 0.161 1.647 -0.250 0.13L4 0.0805 1.610 -0.238 0.0634 0.0388 1.442 -0.183 0.0312 0.0191 1.009 - 0.0159 0.00974 3.294 1.634 -0.24 5 0.623 1.309 0 .297 0.777 1.572 -0.226 0.878 0.521 1.596 -0.2 34 0.500 0.297 1.633 -0.246 0.319 0.189 • 1.523 -0.211 0.1409 0.0836 1.670 -0.257 0.0634 0.0376 1.476 -0.195 0.0312 0.0185 1.168 -0.0778 0.0159 0.00945 1.660 1.466 -0.192 0.454 1.334 0 .282 0.752 1.442 -0.183 0.878 0.495 1.488 -0.189 0.520 0.293 1.547 -0.218 0.2353 0.133 1.634 -0.246 0.1303 0.0735 1.692 -0.263 0.0652 0.0368 1.547 -0.218 0.0317 0.0179 ' • 1.254 -0.113 0.0159 0.00898 1.026 1.376 -0.160 0. 339 1.477 0 .273 0.806 1.355 -0.152 0.010 0.552 1.420 -0.175 0.576 0.315 1.523 -0.210 0.2874 0.157 1.672 -0.258 0.1441 0.0788 1.698 -0.265 0.0717 0.0392 1.622 -0.242 0.0351 0.0192 1.314 -0.137 0.0139 0.0076 0.361 1.313 -0.136 0.265 1.401 - 0 .260 0.730 1.295 -0.129 0.950 0.494 1.356 -0.152 0.689 0.358 1.477 -0.195 0.344 0.179 1.600 -0.254 0.1374 0.0715 1.713 -0.270 0.0693 0.0360 1.573 -0.227 0.0275 0.0143 1.400 -0.168 0.0160 0.00835 TABLE G-II Computation of fl'cuSC^ E q u i v a l e n t S o l u t i o n M CuS0 4, M H 2 S 0 4 M = = nt2 = mi i o n i c s t r e n g t h R N i r C u S 0 4 S C u S 0 4 1 = 5 2 ° 62° - b CuSO 4 0.01 0.05 0.19 10 0.12 0.03 0.05 0.27 3.33 0.16 0.10 0.05 0.55 1.0 0.3 0.30 0.05 1.35 0.33 0.7 0.10 0.10 0.7 2.0 0.4 0.06 0.210 0.833 -0.09384 0.191 0.08 0.175 0.625 -0.05108 0.166 0.15 0.121 0.333 -0.01167 0.120 0.35 0.076 0.143 +0.00111 0.077 0.2 0.104 0.50 -0.02725 0.099 * v a l u e s from r e f e r e n c e 16 - 95 - TABLE G-III Mean I o n i c A c t i v i t y C o e f f i c i e n t of CuS0 4 i n some CuS0 4-H 2S0 4 S o l u t i o n s Molarity" 1" CuSO-4 H2SC>4 I o n i c Strength = M. ^CuS0 4 a t 25°C CUSO4 a f t e r a t 20°C H u r l e n 3 9 25°C* 0.01 0.05 0.19 0.191 0.280 0.286 0.03 0.05 0.27 0.166 0.224 0 . 2 3 0 0.10 0.05 0.55 0.120 0.161 0 . 1 6 6 0.30 0.05 1.35 0.077 0.129 0 . 1 3 3 0.10 0.10 0.7 0.099 (0.150) K + M o l a r i t y <= * l o g T 2 5 = i> M o l a l i t y l o g V 20 at the c o n c e n t r a t i o n s (293/298) H Estimated from F i g u r e G-2 - 96 - -0.28 •0.24 -0.20 -0.16 A 0 / >N 1 E? / \ i I 1 1 / ' 1 I / \ A y = 0.783 • Y = 0.732 O Y = 0. 339 II / il / TI / ij / fT, i i o \ -0.12 r o . i 0.3 0.5 0.7 _ J J 0.9 N F i g u r e G l . P l o t o f G v r s . N f r o m D a t a o f T a b l e G-I - 97 - 0. 35 0.05 !• j L - t — I i i I _ J L _ l 0 0.4 0.8 1.2 I o n i c S t r e n g t h , yU x F i g u r e G2. Mean A c t i v i t y C o e f f i c i e n t as a F u n c t i o n o f I o n i c S t r e n g t h f o r C u S 0 4 i n H 2 S 0 4 S o l u t i o n s a t 25° C - 98 - APPENDIX H X - r a y Powder P a t t e r n s D e b y e - S c h i r r e r p h o t o g r a p h s were o b t a i n e d f o r t h e c u p r o u s s u l p h i d e e l e c t r o d e , a n a l y t i c a l g r a d e CuS, and an a n o d i c o x i d a t i o n r e a c t i o n p r o d u c t ( F i g u r e HI) . The t h r e e p r i n c i p a l l i n e s on t h e c u p r o u s s u l p h i d e p i c t u r e o ( F i g u r e H l - a ) a r e e q u i v a l e n t t o d s p a c i n g s o f 2.28, 1.88 and 1.79 A; • - - n O t h e a c c e p t e d v a l u e s ( x - r a y d a t a c a r d 12-227) a r e 2.40, 1.97 and 1.88 A. The agreement i s n o t u n r e a s o n a b l e , e s p e c i a l l y w i t h t h e s m a l l camera. I t i s c o n c l u d e d t h a t t h e e l e c t r o d e i s c u p r o u s s u l p h i d e , p r o b a b l y t h e r h o m b o h e d r a l - c h a l c o c i t e . The p h o t o g r a p h s f o r t h e a n a l y t i c a l g r a d e CuS and t h e r e a c t i o n p r o d u c t ( F i g u r e s H l - b and H l - c ) a r e v e r y s i m i l a r , so i t i s c o n c l u d e d t h a t t h e r e a c t i o n p r o d u c t i s p r o b a b l y CuS. - 99 - F i g u r e H i . X - r a y Powder P i c t u r e s : (a) C u 2 S , (b) CuS and (c) R e a c t i o n P r o d u c t 

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 5 0
China 2 8
City Views Downloads
Ashburn 4 0
Shenzhen 2 8
Redmond 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0104854/manifest

Comment

Related Items