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Kinetics of the Cu(II) catalysed reduction of Dichrmoate by hydrogen in aqueous solutions Hahn, Edmund Alexander 1960

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KINETICS OF THE Cu^11^ CATALYSED REDUCTION OF DICHROMATE BY HYDROGEN IN AQUEOUS SOLUTIONS by EDMUND ALEXANDER.HAHN A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE-REQUIREMENTS FOR THE DEGREE OF :' MASTER OF APPLIED SCIENCE; i n the Department of MINING AND METALLURGY We accept" t h i s ' t hesis as conforming to the standard-required' from-candidates f o r the Degree of Master of Applied Science THE UNIVERSITY OF BRITISH COLUMBIA March, i960 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 . a n advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t 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 r e f e r e n c e and study.- I f u r t h e r agree t h a t permission f o r e x t e n s i v e 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 copying 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 g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of Mining and Metallurgy The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada, Date A p r i l 11. i960.  «. i _ ABSTRACT The k i n e t i c s of the C u + + catalysed reduction of dichromate by hydrogen i n aqueous perchlorate solutions were investigated between 160° and 200°C„ A s i g n i f i c a n t dependence of rates on Cr (VI) was observedo The mechanism proposed to account f o r the k i n e t i c s gave r i s e to a rate law of the form dt r- !—i 1 . r - . . - i T : r - / T , T M + + j 3 _ [ C r ( V l O where the rate constant f o r the hydrogen a c t i v a t i o n step, k^, i s given by -2^ ,900 -12a ^  k i = i L - e RT x Cl R h The rate constant r a t i o s k_^/k 2 and k = i / k 3 are beli e v e d t o be temperature independent i n the temperature range under consideration, and have approximate values of 0.38 and 0o02 respect!vely. As a consequence of these studies a s i m i l a r mechanism was proposed f o r the C u + + catalysed hydrogen-oxygen recombination r e a c t i o n investigated by McDuffie and co-workers. According t o t h i s mechanism an apparent discrep-ancy between the observations of Halpern et a l and those of the former workers can be explained. - i i -ACKNOWLEDGEMENT The author wishes to express h i s gratitude f o r the advice and encouragement given by the members of the Department of Mining and Metallurgy. In p a r t i c u l a r he wishes t o thank Dr. E. Peters f o r his stimula-t i n g d i r e c t i o n of t h i s i n v e s t i g a t i o n and f o r the constructive c r i t i c i s m given during the preparation of the manuscript. The author i s g r a t e f u l to the Canadian National Research Council f o r f i n a n c i a l assistance and to the Consolidated Mining and Smelting Company of Canada Limited f o r the Cominco Fellowship held i n 1959-60. SUMMARY OF STAFF COMMENTS ON THESIS EXAMINATION OF E.A. HAHN This was regarded as a good t h e s i s . The work involved an extensive amount of time preparing the reaction v e s s e l so that i t would y i e l d good experiments. The experiments were performed with exc e l l e n t p r e c i s i o n and the re s u l t s were good enough to be inter p r e t e d q u a n t i t a t i v e l y i n sp i t e of the complex nature of the system. No major c r i t i c i s m was made. The complex p l o t s on pages 27, 28 and 29 were questioned because there appear t o be d e f i n i t e trends among the i n d i v i d u a l experiments p l o t t e d , and that these trends represented s u b s t a n t i a l departures from the s t r a i g h t l i n e s that were drawn. The reasons f o r t h i s l ay i n the type of measurements and the form of the f u n c t i o n used i n the p l o t , which res u l t e d i n a much poorer q u a l i t y of experimental point near the ends of the l i n e s , e s p e c i a l l y the high end, than i n the middle. This type of p l o t could not have been made at a l l except with the most excellent of rate measurements„ The candidate was asked a number of questions r e l a t e d to the content of t h e ' t h e s i S j , but not d i r e c t l y relevant t o Its discussion or conclusions. Among* these was a question of whether there would be any hope of observing the CuH + complex, one on whether any other mechanisms could be postulated to account f o r the observed k i n e t i c s , and one on the s i g n i f i c a n c e of the a c t i v i t y of C u + + and Ag + i n terms of e l e c t r o n i c s t r u c t u r e . The candidate's o r a l presentation was acceptable and he was able to answer the more relevant questions that were dire c t e d to him from the s t a f f . His t o t a l performance was very good and the th e s i s was accepted without reser v a t i o n . TABLE OF CONTENTS Page I N T R O D U C T I O N o o o o o o o o o o o o o o o o o o o o o o o o o o o o 1 A c t i v a t i o n of Hydrogen by Metal Ions i n Aqueous Solution „ . <, 1 E f f e c t s of Complexing . O . . . . . . . . . . . . . . . . o o 5 E f f e c t s of Solvent . . . . . . . . . . . . . . . . . . . . . . 6 Purpose and Scope of the Present Investigation „ „ » . o . . « 8 E X P E R I M E N T A L o O O O O O O O O O O O O O O O O O O O O O O O O O p O 9 McL"ti ©l"*13,lS O O O O O d O O O O O O O O O O O O O O O O O O O O O 9 A p p 3.1* c i t MS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o o o o o o o o o o o 9 Experimental Procedure 0 . . . . . . . » . . . . . . . . . . <, 11 RESULTS AND DISCUSSION „ . , „ „ . . „ . . . . . . . . . . . . . o . 11 Ef f e c t o f A c i d i t y on Rates „ „ . . . . . . . . . . . . . » <> . 16 E f f e c t of Chromium VI Ion Concentration on Rates . . . . . . . 26 Ef f e c t of C u + + Ion Concentration on Rates . . . . . . . . . . . 33 E f f e c t of Hydrogen Pressure, S t i r r i n g V e l o c i t y and Titanium Surface Area on Rates . . . . . . . . . . . . . . . . . o 39 Proposed Mechanism f o r the C u + + Catalysed Hydrogen-Oxygen Recombination Reaction . . . . . . . . . . . . . . . o o • ' 4 0 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 R E F E R E N C E S o o o o o o o o o o o o o o o o o o o o o o o o o o o o hU-APPENDIX A . . . . . . . . . . . . . . . . . . . . . . . . . . . o 4-6 APPENDIX B . . . . . . . . . . . . . . . . . . . . . . . . . o . . 47 APPENDIX C . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 APPENDIX D . . . . . . . . . . . . . . . . . . . . . . . . o o 9. 50 APPENDIX E 0 . 0 0 0 0 0 0 . . 0 0 . o o . o . o . o o o o c o o o 57 APPENDIX F . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 APPENDIX G . 61 - i v -LIST OF FIGURES Page 1 0 Dependence of Rates on H + Concentration; 160°C . . . . 0 13 2 0 Dependence of Rates on H + Concentration; 3<. Dependence of Rates on H + Concentration; 4. Dependence of Rate" 1 on H + Concentration; 160°C . . . . . . . . . . 17 5. Dependence of Rate""'- on H + Concentration; ISO C o o o o o o o o o o -LS 60 Dependence of.Rate" 1 on H + Concentration; 200°C . . . . . . . . . . 19 7. Plots of Slopes" 1, S, of the Curves i n Figures 4, 5 and 6 Versus C r ^ 1 ) Concentration . . . . . . . . . . . . . . . . . . . . 21 80 Plot of log | i Versus T" 1 f o r the C u + + Catalysed Hydrogen Reduction o f C r ( V I ) . . . . . . . . . . . . . . 25 9. Plot of Rate Function, R, Versus C r ( V I ) Concentration; 160°C . . . 27 10. Plot of Rate Function, R, Versus C r ( V I ) Concentration; 180°C . . . 28 11. Plot of Rate Function, R, Versus C r ^ V I ^ Concentration; 200°C . . . 29 12. Schematic P o t e n t i a l Energy Diagram f o r the A c t i v a t i o n of H 2 by C u + + 32 13. Dependence of Rates on C u + + Concentration; 160°C; 0.1M.H+ 34 14. Dependence of Rates on C u + + Concentration; 200°C; C.1M H + 35 15. Dependence of Rates on C u + + Concentration; 200°C; 0.5M H + . . . . . . 36 16. E f f e c t of C u + + Concentration on Rates at Several Temperatures, Acid Concentrations and Cr (VI) 17. Consumption of H1" Ions Due to Reduction of C r ^ 1 ^ . . . . . . . . . 48 18. Comparison of C r ^ V 1 ^ Reduction Curves Showing Negligible S t i r r i n g V e l o c i t y E f f e c t on Rates „ 59 19. Comparison of Cr (VI) Reduction Curves Showing Ne g l i g i b l e Titanium Surface Area E f f e c t on Rett QQ o o o o o a p o e o o a o o o o 60 - V LIST OF TABLES Page 1. Values of k-[_ Calculated from Mean Intercepts of Figures L, 5 and 6 and Other Pertinent Data „ . 24 2. (a) Values of and from Intercepts and Slopes of Plots i n Figures 9j 10 and 11 30 (b) Values of ^ ~1 and k"l from Intercepts and Slopes of Plots i n ~"^ 2 ^ 3 3. E f f e c t of Hydrogen P a r t i a l Pressure on Rates . . . . . 39 4. (a) E f f e c t of Pe r c h l o r i c Acid Concentration on the Rate of the C u + + Catalysed Hydrogen Reduction of C r ( V I ) 50 (b) E f f e c t of Dissolved Cupric Perchlorate on the Rate of C r ( V I ) Reduction by Hydrogen . . . . . . . . . . . 52 (c) Rate Measurements and Rate Function, R, at Various C r ^ 1 ) XJ€ V 6 lS o o o o e o o o o e o o o e o p o o o v o v o o 33 5. Slope Measurements of R a t e - 1 vs H + Plots of Figures k, 5 and 6, and Values of S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 57 60 (a) Order of C u + + Dependence of Rates, Related to Percent Change of K + K' Qr*] + K + K' W i t h C h a n S i n g K (i-'e' ) at 200°C . . 61 (b) Order of C r ^ 1 ) Dependence of Rates, Related to Percent Change of with Changing K' ( i . e . fcr^^ ) \¥lf\+ K + K» at 200^ 0 62 KINETICS OF THE C u ( I T ) CATALYSED REDUCTION OF DICHROMATE BY HYDROGEN IN AQUEOUS SOLUTIOIS INTRODUCTION The growing i n t e r e s t i n the a p p l i c a t i o n of hydrogen as a reducing 1 agent f o r the p r e c i p i t a t i o n of metals e„g„ Ni, Co"") or low valence metal oxides 2,3 (e.g. V 2 0 3 , U0 2 ) from hydrometallurgical leach solutions has given r i s e to extended studies of the k i n e t i c s and mechanisms of some of the reactions involved. These studies resulted i n the accumulation of a body of evidence showing that hydrogen, which at ordinary temperatures i s quite i n e r t , w i l l be activated i n both aqueous and non-aqueous solutions by c e r t a i n metal ions and some of t h e i r complexes. For example, C u + + , Hg + +, H g 2 + + , Ag + anr* some of t h e i r complexes were found to a c t i v a t e hydrogen homogeneously,'*' e i t h e r i n t h e i r reduction to the m e t a l l i c state (e.g. Hg°, Ag°) or i n the reduction of substrates to a lower valence (e.g. 0Tz07= to C r ^ 1 1 ^ ) . Of s p e c i a l i n t e r e s t i n t h i s respect i s the C u + + catalysed recombination r e a c t i o n of hydrogen and oxygen i n aqueous solutions at temperatures between 200° and 300°C.^ This r e a c t i o n may a t t a i n i n d u s t r i a l importance due to i t s possible a p p l i c a t i o n i n the recombination of r a d i o l y t i c decomposition products of water i n homogeneous aqueous nuclear r e a c t o r s . A c t i v a t i o n of Hydrogen by Metal Iohs i n Aqueous Solutio n. As e a r l y as 1909,Ipa.tieff and Werschowski^ found that cupric acetate i n aqueous so l u t i o n s could be reduced by hydrogen to m e t a l l i c copper at high temperatures and pressures. However, at that time the k i n e t i c s were not studied i n d e t a i l and thus the, c a t a l y t i c a c t i v i t y of dissolved Cu^-^) was not recognized as such. 7 Halpern and Dakers have shown re c e n t l y that cupric acetate could ac t i v a t e hydrogen homogeneously i n aqueous sol u t i o n s , the r e s u l t being the reduction of Cu^"^ to cuprous oxide with the f o l l o w i n g proposed mechanism: CuAc 2 + H 2 —• CuAc 2„H 2 (slow) (a) 1 CuAc 2„H 2 + CuAc 2 + H 20 — Cu 20 + 4 HAc ( f a s t ) (b) g Subsequently Peters and Halpern found t h a t hydrogen reduced dichro-mate i n aqueous solutions of cupric acetate, the reaction being; C r 2 0 7 = + 3 H 2 + 8 H + — 2 C r + + + + 7 H 2Q. 2 Since t h i s r e a c t i o n would proceed only i n the presence of di s s o l v e d cupric acetate, i t was i n f e r r e d that the l a t t e r was a c t i n g as a true homogeneous catalyst„ Later i t was shown that dissolved cupric perchlorate also catalysed Q the hydrogen reduction of dichromate 0 In t h i s medium, complexing of Cu +t by ClO^ - i s believed to be n e g l i g i b l e and the k i n e t i c s were observed to be consistent with a mechanism i n v o l v i n g the f o l l o w i n g sequence of steps: k-1 C u + + + H 2 .Z^ GuH+ + H + (a) CuH + + C u + + — - 2 Cu + + H + (b) 3 f a s t 6 Cu++ C r 2 0 7 " + 14 H + —> 6 C u + + + 2 C r + + + + 7 H 20 (c) Equation 3(a) represents a pre-equilibrium process i n v o l v i n g the h e t e r o l y t i c s p l i t t i n g o f a hydrogen molecule. Since one product i s a hydrogen ion, the r e a c t i o n rate depends i n v e r s e l y on the hydrogen ion concentration i n s o l u t i o n , and the rate of reduction of dichromate expressed i n terms of the stoichiometric hydrogen consumption i s given by the expression 2 -d[y - m[cu++r[X| which was derived by a steady state approximation of CuH +. According to t h i s equation reaction rates may appear to be e i t h e r f i r s t or second order i n C u + + depending on the r e l a t i v e magnitudes of the two terms i n the denominator. For example, i f k_±/kzTw] ^[pu+tl then the rate expression w i l l reduce to the form -- d j H ^ = k3_[Cu + 3[H 2] 0 5 dt Peters and Halpern 1^ showed t h a t at 0.1M Cu(C104) 2 and a HCIO4. concentration range varying from 0.004M to 0.10M the rate law given by Equation 5 described the k i n e t i c s between 80° and 140°C. 5 McDuffie and h i s co-workers found the same rate law to hold i n t h e i r studies on the cupric perchlorate catalysed hydrogen-oxygen recombination at 250°C. This k i n e t i c behaviour i s a c t u a l l y unexpected i n terms of the above mechanism since i n t h e i r work £H h[]^ >[Cu +f] , and i f the value of k_]/k 2 i s not 9 too d i f f e r e n t from that found by Halpern and co-workers 7 at 110°C, a second order r e a c t i o n i n C u + + would have been expected. A number of other metal ions besides C u + + have been found to a c t i v a t e hydrogen homogeneously i n aqueous s o l u t i o n s . Of p a r t i c u l a r i n t e r e s t are hydrogen reactions catalysed by Ag +, H g + + and H g 2 + + , and the oxyanion MnOi,.-. 11,12 Thus Webster and Halpern showed that s i l v e r perchlorate w i l l catalyse the hydrogen reduction of dichromate or other s u i t a b l e substrates i n aqueous solutions by two possible r e a c t i o n paths. The f i r s t or low temperature ( 5 0 ° to 90 CC) path involves predominantly a termolecular rate determining step where hydrogen i s s p l i t h omolytically, e.g., k 2 Ag + •+ H 2 2 AgH + (slow) (a) 6 AgH + + substrate -*• Ag + + products (fast) (b) The second path which predominates at temperatures of 100° to 120°C i s bimole-cu l a r and-involves h e t e r o l y t i c s p l i t t i n g of hydrogen, e.g., k l Ag + + H 2 ^ z t AgH + H + (slow) (a) k - l 7 k 2 f a s t AgH + Ag + +' substrate —»• intermediate products, (b) The combined k i n e t i c s f o r both paths are represented by " l M - k [ H j [Ag3 2 + k n [Agg [ H j . 8 dt k_i[Hf[ + [Ag+] k 2 I t should be noted that the second term i n t h i s r a t e expression i s i d e n t i c a l to the ra t e law proposed f o r the C u + + catalysed hydrogen reduction of dichro-mate (Equation k). The second path was also postulated as the rate determining step i n studies on the rates of a c t i v a t i o n of hydrogen by s i l v e r s a l t s i n pyridine 13 solut ions, Another reaction i n which AgH + has been postulated as an intermediate i s the hydrogen reduction of MnCV" to Mn02 i n acid s o l u t i o n (Webster and H a l p e r n 1 4 ) . The k i n e t i c s are o f the form - D ^ = K M |MWVD L V ] 9 and the rate determining step i s beli e v e d to be -- 5 -Ag + + MnO^-(or AgMnO^) + H 2 -* AgH + + MnO^ + H + ID followed by f a s t reactions of AgH + and MnO^ which y i e l d Mn02 and regenerate Ag +, The r o l e of MnCV i n reac t i o n 10 may be regarded as that of replacing one of the Ag + ions i n reaction 6; i t s effectiveness i n doing so i s connected with i t s high one-electron a f f i n i t y . Permanganate w i l l also react homogeneous-l y with hydrogen"^ whereby i t i s reduced to Mn02 i n acid solutions and t o MnO^ i n basic s o l u t i o n s . Also of i n t e r e s t i s the H g + + and H g 2 + + catalysed a c t i v a t i o n of hydrogen. Thus, i n perchlorate s o l u t i o n s of these ions, where both H g + + and H g 2 + + activate hydrogen simultaneously, two mechanisms have been p o s t u l a t e d , 1 ^ I Hg + +(aq) + H 2 - Hg° + 2 H +(aq) (slow) (a) Hg c + H g + + - H g 2 + + (fast) (b) 11 II H g 2 + +(aq) + H 2 — 2 Hg° + 2 H +(aq) (slow) (c) Equation 11 suggests that the rate determining steps involve i n each case a two-electron reduction o f the metal i o n with release of two protons to the k solvent. Although the Hg° intermediate seems favoured on energetic grounds there i s s t i l l some uncertainty about the mechanism of a c t i v a t i o n . E f f e c t s of Complexing The above disc u s s i o n has been concerned only with homogeneous c a t a l y s i s of hydrogen by metal ions that are believed to be e s s e n t i a l l y uncomplexed. Experimental evidence 1^*17*18 s n o w s that complexing of the metal ions discussed above has a profound influence on the rate of hydrogen a c t i v a -t i o n by these ions. The rates are a f f e c t e d p a r t i c u l a r l y by metal-ligand bond strength and by the degree of b a s i c i t y of the anionic s p e c i e s . 4 In general, rates w i l l be slowed down by complexing agents e x h i b i t i n g high metal-ligand bond strength, e s p e c i a l l y with reactions i n v o l v i n g h e t e r o l y t i c s p l i t t i n g of the hydrogen molecule i(e.g. a c t i v a t i o n steps i n Equations 3 and 7), and w i l l be enhanced with increased b a s i c i t y of the anion because of proton s t a b i l i z a t i o n . There are also some metal ions whose a c t i v i t y has been observed only 19 20 i n the form of complexes. These are palladium and rhodium chloro-complexes ' which have been found to catalyse the reduction of f e r r i c c h l o r i d e . They are second order, being f i r s t order i n H 2 and f i r s t order i n PdCl^"-or RhClg*. The a c t i v i t y of these complexes i s believed to be evidence f o r the possible a c t i v i t y of uncomplexed P d + + and R h + + + , These a c t i v i t i e s , however, could not be measured d i r e c t l y due to interference of heterogeneous reactions r e s u l t i n g from m e t a l l i c Pd or Rh that are p r e f e r e n t i a l l y p r e c i p i t a t e d when the ions are uncomplexed. E f f e c t s of Solvent Certain metal s a l t s d i s s o l v e d i n non-aqueous solvents have also been shown t o a c t i v a t e hydrogen homogeneously. For example, C a l v i n 1 ^ found cuprous acetate to be c a t a l y t i c a l l y a c t i v e i n quinoline solutions i n reactions i n v o l v -ing the reduction of quinone to hydroquinone and Cu^"^ to C u ^ . C u ^ 1 ) 17 i t s e l f was found to be i n a c t i v e i n t h i s s o l u t i o n . Weller and M i l l s , who studied the k i n e t i c s of t h i s system i n d e t a i l , postulated that the rate deter-mining step involved the complex formation between a Cu^) dimer and H 2 because of the second order r a t e dependence on cuprous acetate. The e f f e c t -iveness of the dimer as a homogeneous ca t a l y s t was thought t o l i e i n the f a c t that due to i t s e l e c t r o n i c structure i t possessed two s i t e s capable of accommodating two hydrogen atoms simultaneously permitting e l e c t r o n t r a n s f e r from the H atom to the dimer i n the a c t i v a t i o n step. 18 Recently Chalk and Halpern reported the homogeneous a c t i v a t i o n of hydrogen by both cuprous and cupric heptanoates i n heptanoic a c i d and other non-polar media such as diphenyl and octadecane. Two d i s t i n c t a c t i v a t i o n paths were proposed both of which show h e t e r o l y t i c s p l i t t i n g of the hydrogen molecule, e.g., . CuHp 2 + H 2 — (CuH)Hp + HHp (a) 12 CuHp + H 2 — CuH + HHp (b) The a c t i v i t y of CuHp2 i n these solutions i s much lower than that of cupric carboxylate s a l t s fe.g. acetate, propionate, butyrate) i n aqueous s o l u t i o n . It 21 i s suggested that *'. t h i s behaviour i s probably re l a t e d to the requirement f o r s t r e t c h i n g of the metal ligand bond i n the t r a n s i t i o n s t a t e ; i n view of the charge separation involved t h i s would require more energy i n a non-polar medium. Furthermore, the magnitude of t h i s medium e f f e c t should depend i n v e r s e l y on the charge of the metal ion: i n l i n e with t h i s i t i s found that the r a t i o of the r e a c t i v i t i e s of cuprous s a l t s to those of the correspond-ing cupric s a l t s increases markedly i n going from aqueous solutions to non-polar media. 1• S i l v e r s a l t s have also been found to activa t e hydrogen i n non-aqueous 22 . s o l u t i o n s . Thus Wilmarth and Kapanan observed that s i l v e r acetate w i l l a c t i v a t e hydrogen i n pyridine by h e t e r o l y t i c s p l i t t i n g of H 2 and formation of AgH. The a c t i v a t i o n energy i n t h i s solvent i s much smaller (^14 kcal) than that of the corresponding r e a c t i o n i n v o l v i n g Ag + i n aqueous s o l u t i o n (23 kcal ) f This d i f f e r e n c e . i s p r i n c i p a l l y ascribed t o the higher b a s i c i t y of the solvent r e s u l t i n g i n greater s t a b i l i z a t i o n of the proton released during h e t e r o l y t i c s p l i t t i n g of H 2. • This means that complexing of Ag + ions w i l l r e s u l t i n h e t e r o l y t i c s p l i t t i n g becoming more favourable than homolytic s p l i t t i n g . 4 Hp = heptanoate; HHp = heptanoic a c i d . - 8 -Purpose and Scope of the Present Investigation, The mechanism and rate law (Equations 3 and 4> pages 2 and 3) depict-i n g the k i n e t i c s of the C u + + catalysed hydrogen reduction of dic h r o m a t e 9 * 2 3 have also been found t o apply to the p r e c i p i t a t i o n of copper from aqueous perchlorate ZL 25 solutions as shown by MacGregor and MacGregor and Halpern. In t h i s case, the t h i r d reaction step (Equation 3(c)) i s replaced by the disproportionation reaction of Cu +, i . e . , 2 Cu" ^  Cu° + C u + + 13 which also i s believed t o be f a s t . In these studies values of k i and k-1 were calculated by means of k 2 Equation 4 from rate measurements obtained from the i n i t i a l portion of the copper reduction curves. I t was observed that k i f o r 160°C^ was consistent 9 thermodynamically with the value obtained by Halpern et a l at 110°C. The r a t i o lr ZL -1 was found to be between 0.97 and 1.7 at 160°C as compared to 0.26 at 110°C.7 The apparent increase of t h i s r a t i o with temperature suggests that the back reaction i n the a c t i v a t i o n step, i . e . , k - l * CuH + H + ^ Z t C u + + + H 2 3-(a) k l becomes favoured, i n other words, the a c i d e f f e c t i s enhanced by r i s i n g tempera-t u r e . McDuffie e t a l ^ , however, working at 250°C, f a i l e d t o f i n d an a c i d e f f e c t on the rates of the C u + + catalysed hydrogen-oxygen recombination r e a c t i o n f o r s o l u t i o n s that-were 0.001 M i n C u + + and from 0.005M to 0.050M i n HCIO^. Assuming that a ten percent decrease i n rate was observable due to the t e n f o l d increase i n a c i d i t y and that the oxygen reduction occurred by a mechanism t -(a) denotes the back rea c t i o n of Equation 3(a). - 9 -analogous to Equation 3, then the value of j-1 must be less than 0,002 i n t h e i r case. This shows an apparent decrease of k - l with r i s i n g temperature and k 2 i s i n consistent with the e a r l i e r postulated temperature dependence of the r a t i o . In view "of t h i s apparent discrepancy i t was decided to extend the studies of the Cu++ catalysed hydrogen reduction of dichromate to 200°C i n order to determine i f , p o s sibly, a change of mechanism taking place at the higher temperatures might account f o r t h i s anomaly,, EXPERIMENTAL Mat e r i a l s . ' A l l materials used were of Baker and Adamson reagent grade q u a l i t y . Stock s o l u t i o n s of cup r i c perchlorate and sodium dichromate were made up and used f o r preparing the experimental s o l u t i o n s , the cupric perchlorate s o l u t i o n being prepared from cupric oxide and d i l u t e d HCIO^, D i s t i l l e d water was used throughout. Hydrogen and nitrogen gases were supplied by Canadian Liquid A i r Company i n 2000 p s i g c y l i n d e r s . Apparatus. The experimental apparatus comprised a 1 gal l o n , 1200 ps i g s t a i n -l e s s s t e e l autoclave manufactured by Autoclave Engineers Inc. Thermowell, sampling system and gas i n l e t and o u t l e t connections were made through the autoclave cover. The s t i r r e r was driven by a 3/4 H.P. e l e c t r i c motor v i a a s t i r r e r shaft f i t t e d through a pressure gland i n the center of the autoclave cover. A l l parts i n contact with the so l u t i o n , e.g., s t i r r e r , thermowell, and sampling system, were made of titanium, The s o l u t i o n s were contained i n a titanium l i n e r f i t t e d into the autoclave v e s s e l , The l i n e r was provided with b a f f l e s made of titanium sheet i n order to ensure s u f f i c i e n t g a s - l i q u i d - 10 -i n t e r f a c e during s t i r r i n g thus preventing hydrogenation rates from becoming d i f f u s i o n c o n t r o l l e d . The use of titanium was e s s e n t i a l since i t was found that at the temperatures and p e r c h l o r i c a c i d concentrations used i n the experiments s t a i n -l e s s s t e e l would be attacked and cause rapid reduction of dichromate by i r o n ft i n the absence of hydrogen. Moreover, a t e f l o n s h i e l d was placed on top of the titanium l i n e r to prevent splashing of the solutions against the s t a i n l e s s s t e e l autoclave cover and thereby cause reduction of dichromate. The s o l u t i o n s were heated e x t e r n a l l y by a set of two ring-type gas burners of which one served as a p i l o t burner and the other as a booster. Gas flow to the burners was regulated by means of a Brooksmite twin flowmeter. Temperature c o n t r o l was maintained with a Leeds and Northrup Micromax C o n t r o l l e r -Recorder, which c o n t r o l l e d gas flow to the booster burner by means of an auto-matic valve. In order t o provide s u f f i c i e n t heat condu c t i v i t y f o r good tempera-ture c o n t r o l between the autoclave v e s s e l and the s o l u t i o n , the space between the titanium l i n e r and the v e s s e l (approximately 1/16") was f i l l e d with 240 ftft mesh s i l i c o n - c a r b i d e powder. The powder was then covered with glass wool t o prevent i t from s p i l l i n g into the s o l u t i o n . In t h i s way a temperature c o n t r o l of ±0.3°C at 200°C was obtained. Hydrogen gas pressure was maintained and regulated with a standard type gas b o t t l e pressure regulator and measured with a Bourdon°type gauge to an accuracy of * Jja. ft Two grams of S t a i n l e s s s t e e l : f i l i n g s i n a 2.5 x 1 0 ~ % Cr 20 7= ; s o l u t i o n of pH » 0 caused complete reduction of the dichromate i n approximately 50 minutes at 200°C. ftft SiC has. good thermal conductivity and excellent chemical s t a b i l i t y at high temperatures (J.W. Mellors A Comprehensive T r e a t i s e on Inorganic and T h e o r e t i c a l Chemistry, V o l . V, p. 883) thus making i t unreactive with respect to the experimental s o l u t i o n s used. I t also does not seem to have any measurable e f f e c t on r a t e s . - 11 -j Experimental Procedure, The experimental procedure comprised the following steps; ( l ) f l u s h i n g three times of the autoclave with nitrogen to remove a l l r e s i d u a l a i r from the space above the s o l u t i o n so that the atmosphere at temperature and before hydrogen a d d i t i o n would consist of steam and a l i t t l e r esidual'nitrogen, (2) heating to the desired temperature,, (3) sampling of s o l u t i o n at temperature (two t o three times) before hydrogen add i t i o n to t e s t the s t a b i l i t y of dichro-mate, (4) addition of hydrogen to the desi r e d pressure,, (5) p e r i o d i c sampling of the s o l u t i o n to follow the course of the disappearance of dichromate. The sample solutions were passed through a cooling c o i l of tit a n i u m tubing immersed i n a beaker of col d tap water before they entered the sampling b o t t l e s i n order to prevent t h e i r f l a s h i n g and consequent loss of steam. Analyses were made as follows? the samples were d i l u t e d v o l u m e t r i c a l l y and the a c i d i t y adjusted. Then the dichromate content, of each sample was deter-mined with a Beckman Model D,U, spectrophotometer at a wavelength of 350 m/^  the absorption peak f o r dichromate, C r + + + or C u + + did not give a r e s i d u a l reading a t the a c i d i t y chosen f o r making the spectrophotometric determination. A c i d i t i e s of the undiluted sample solutions were measured by potentiometric ± t i t r a t i o n with a 0.1N sodium tetraborate solution.. The cupric ion concentra-t i o n was determined g r a v i m e t r i c a l l y by de p o s i t i o n of copper on platinum electrodes„ RESULTS AND DISCUSSION E a r l y i n t h i s i n v e s t i g a t i o n i t was observed that the plots depicting the reduction of Cr 207~ by hydrogen in the presence of C u + + ions were not ± Ac Vogels Textbook of Inorganic Quantitative Chemical Analysis, 2nd Ed„,p„231 9 s t r a i g h t l i n e s , as found previously by Peters J and Halpern et a l , but showed a d e f i n i t e dependence of rates on dichromate concentration,, These observations apply to the range of 160° to 200°C f o r solutions containing about 0„02 M C u + + and an i n i t i a l concentration of 3 x lCT-% CrgO?" whereas the e a r l i e r measurements were made at 110°C with s o l u t i o n s 0„1M i n C u + + and an i n i t i a l concentration of about 5 x 1CT4M C r 2 0 7 . The reduction plots depicted In Figures 1, 2, and 3 f o r 160°, 180°, and 200°C r e s p e c t i v e l y show that, with increasing a c i d i t y , the rates tend to s h i f t from zero- toward f i r s t - o r d e r with respect to C r ^ " ^ 0 ^ Due to t h i s development, the e a r l i e r method of measuring rates by simply determining the slopes of the l i n e a r reduction p l o t s could not be applied i n the present case; rather, i t was necessary to obtain rate measure-ments from the slopes of tangents to the reduction curves. In order to minimize errors i n these rate measurements, the best smooth curve was drawn through the experimental points of a run with a f l e x i b l e r u l e r , a f t e r which tangents were pl o t t e d to t h i s curve at s e v e r a l C r ^ ^ l e v e l s by the mirror image method. The best accuracy of slope measurements was obtained at intermediate l e v e l s (i„e„, 1,6 x 10" 3 to 4,0 x 1 0 " % C r ( V I ) ) although t h i s u s u a l l y was the region of j greatest curvature of the reduction p l o t s . At high C r ^ 1 ^ concentrations ( i , e , , 5,2 x 10"3 to 6,0 x 10~^M) toward the s t a r t of reduction the accuracy i n rate measurements f e l l o f f , which may be due to such transient phenomena as the time lag involved i n the saturation of s o l u t i o n with hydrogen. At C r ^ 1 ^ l e v e l s below 1,6 x 10"measurements again became l e s s accurate because of the d i f f i c u l t y i n obtaining s u f f i c i e n t experimental points near the end of a run. This was p a r t i c u l a r l y so i n f a s t reduction experiments. In general, ± The term, G r ( v l ) , rather than C r 2 0 7 ~ , w i l l be used from here on because the exact nature of t h i s species i s not known at the temperatures at which the present experiments were conducted. For example, Tong and King^" have shown that at room temperature the predominant C r ( ^ - 0 species i n a c i d i c aqueous solutions of unit i o n i c strength i s HCrOv"", Time - Minutes Fi£ o__l 0 Dependence of Rates on H + Concentration! 160°C 0 10 atm„ H 2; 0.02M Cu(C10 4) 2 1 Time - Minutes Dependence of Rates on H + Concentration; 200°C 10 atm. H 2; 0„02M Cu(C104)2"> - 16 -about L to 10 rate measurements, each associated with a given C r ^ 1 ^ l e v e l (not n e c e s s a r i l y an experimental point;, were taken f o r a single experiment. E f f e c t of A c i d i t y on Rates A s e r i e s of experiments, i n which the a c i d i t y of the solutions was var i e d , was conducted at each temperature ( i . e . 160°, 180° and. 200°C) and the r e s u l t i n g reduction plots depicted i n Figures 1, 2 and 3* show, not only that rate 3decrease, but also that the C r ^ 1 ) dependence of rates s h i f t s i n c r e a s i n g l y toward f i r s t order with higher a c i d i t y . According to the mechanism and rate law proposed by Halpern and co-workers 7 (see Equations 3 and 4, pages 2 and 3) a plot of r a t e ~ x vs H + should y i e l d a s t r a i g h t l i n e of slope k.! x 1 k 2 k l [ C u + - ] 2 [ H 2 ] and inte r c e p t ki[?u++]Ef Figures 4, 5, and 6 show plot s of t h i s kind f o r the three experi-mental temperatures r e s p e c t i v e l y . Rates measured at four d i f f e r e n t C r ^ 1 ) l e v e l s of each reduction curve y i e l d four s t r a i g h t l i n e s on t h i s plot with a common inter c e p t at = 0, but with slopes that decrease-with increasing * A f t e r completion of the 1.5M HCIO^, reduction experiment (see F i g . 3) a white p r e c i p i t a t e was found to adhere t o a l l titanium parts i n contact with the s o l u t i o n . This powder may have been some form of hydrated titanium oxide formed by the oxidation of the metal by p e r c h l o r i c aci d although no conclusive analysis jould be made on i t . ** R a t e " 1 = I- d[H 2]^ dt - 17 -b U^l Cv?—: 073 074" 075" HCIO^  - Mole - Liter" X Fig. 4. Dependence of Rate - 1 on H + Concentration at Several Cr( V I) Levels; 160°C. 0.02M Cu(C104)2; 10 atm. H2. - 18 r F i g . 5. Dependence of Rate on H + Concentration at Several Cr(VI) Levels; 180°C. 0.02M C u ( C 1 0 j 2 ; 10 atm. H 2. - 19 -HC1C> Mole-Lite r - l F i g . 6. Dependence of Rate" 1 on H + Concentration at Several Cr(VI) Levels ; 200°C. 0.02M Cu(C10 4) 2; 10 atm. H 2. - 20 -concentration.* This v a r i a t i o n of slope with C r ^ 1 ) concentration together with the greater-than-zero dependence of rates on C r ^ 1 ) suggest that the e a r l i e r mechanism cannot be invoked f o r the present case, although i t may-apply at [H"f] = 0, because the common intercept indicates that the Cr (VI) dependence disappears at that point. In view of the inverse r e l a t i o n s h i p between C r ^ 1 ) concentration and the slopes of Figures 4, 5 and 6, the r e c i p r o c a l s , S, of the l a t t e r were pl o t t e d against C r ^ 1 ) , and, as shown i n F i g . 7, three l i n e a r p l o t s , one f o r each temperature, were obtained. Each of these p l o t s may be represented by an Equation o f the form S = S l o p e " 1 = C + C» [ c r ^ ^ 14 C and C» are, r e s p e c t i v e l y , the temperature dependent intercept and slope of any one of the three p l o t s . From Equation 14 i t i s evident that the r e c i p r o c a l s , S, of the slopes of the r a t e - 1 vs H + plots i n Figures 4, 5, and 6 consist of a Cr (VI) independent term C and a Cr (VI) dependent term C'[cr(VI)]. This suggests that the reduct-ion of C r ^ 1 ) by hydrogen takes place v i a two d i s t i n c t paths, namely, a C r ^ 1 ^ independent one, and a C r ( V I ) dependent one. Assuming the Cr (VI) independent reduction path i s according t o the mechanism of Halpern and co-workers'7" (Equation 3* page 2), i t can be shown that the term C i s equal to 2 ^2 x ^[cu"1"^ \j}z} a n c * 14 may be re-written as follows: k_x S-/«2 U l l C u H JHol + C « | C r ^ v ± J L 15 !^Jkl|Cu+f| [HJ + C'[cr(VlJ 4 S l i g h t adjustments of a c i d i t y were made f o r each Cr (VI) l e v e l at which rates were measured to account f o r H + i o n d e p l e t i o n owing t o reduction of C r ( V l ) . HCIO4 concentrations were estimated f o r each l e v e l from i n i t i a l acid measure-ments by use of F i g . 17, Appendix B. P-* 7» Plots of S l o p e s " 1 , 3, of the Curves i n Figures 4, 5 and 6 Versus C r ( V I ) Concentration f o r 160°, 180° and 200°C. - 22 -The second Cr (VI) dependent path could involve e i t h e r d i r e c t a c t i v a -t i o n of hydrogen by C r ^ 1 ^ by e i t h e r h e t e r o l y t i c or homolytic s p l i t t i n g of the molecule, or d i r e c t r e a c t i o n of Cr(VI) with the CuH + intermediate, taking place simultaneously with the reduction of Cr^^"^ by Cu + (see Equation 3(c), page 2), The f i r s t of these,two p o s s i b i l i t i e s , analogous to that observed f o r MnO*,- by 14 •& Webster and Halpern, seems u n l i k e l y . The second,more probable,one would involve the reaction / T T - p \ k f a s t CjAViJ + C u H + _> intermediates -+ C u + + + Products . ,16 By combining Equation 16 with the C r ^ 1 ) -independent mechanism of Halpern et a l 9 (Equation 3) the f o l l o w i n g sequence i s obtained: k l C u + + + H 2 ^ Z ± CuH + + H + (a) k-1 k 2 CuH + + C u + + — 2 Cu + + H + (b) k 3 f a s t 1 7 CuH + + C r ^ V I ^ — Intermediates — C u + + + Products (c) f a s t Cu + + C r ( V I ) — C u + + + Products (d) & Direct a c t i v a t i o n of hydrogen by C r ^ 1 ) i s u n l i k e l y i n the l i g h t of the s i g n i f i c a n c e of the plots i n Figures 4* 5, and 6. These p l o t s show that the s e n s i t i v i t y o f rates to Cr(VI) concentration r i s e s with i n c r e a s i n g a c i d i t y . I f a c t i v a t i o n of H 2 by Cr(^I) would take place by h e t e r o l y t i c s p l i t t i n g of the molecule according to Cr< V I) + H 2 ^ ! C r ^ H " + H+ ^ P r o d u c t s then p l o t s of r a t e " 1 vs H + (Figs. 4, 5 and 6) should show an e f f e c t of that i s decreasing, rather than increasing, with i n c r e a s i n g a c i d i t y . Also i f a c t i v a t i o n by C r t v l ) should involve homolytic s p l i t t i n g of H 2 a f t e r 2 C r ( V I ) + H 2 2 C r ( V I ) H f-^ S tProducts then changes i n a c i d i t y would not be expected t o a f f e c t the C r ^ 1 ) depend-ence of the rates at a l l which, too, i s contrary to experimental observa-t i o n s . - 23 -which leads t o a rate expression of the form " d [ H 2 ] - k i T c u ^ f r a ] jia [Cu++] + ±1 [ c r ^ l 18 dt derived by a steady state approximation of the CuH + intermediate. On i n v e r t i n g and rearranging, Equation 18 i s changed to -<- d j d l " 1 - M * 1 19 which i s the equation of a s t r a i g h t l i n e whose dependent and independent v a r i a b l e s are r a t e - 1 and H + r e s p e c t i v e l y , and whose slope and intercept are re s p e c t i v e l y , , kl[Cu++] M (I* + [cr™]! 19(a) v —1 ~1 J and kl[cu+3 [}Q 19(b) I t i s now apparent t h a t each of the f a m i l i e s of s t r a i g h t - l i n e plots i n F i g s . L} 5 and 6 are represented by Equation 19 and t h e i r Cr(^-) dependent slopes given by 19(a). On i n v e r t i n g expression (19a) Equation 20, which i s equivalent to 15, i s obtained, i . e . , > . 20 Thus, i t may be seen t h a t the constant C (which represents slopes i n F i g . 7) i n Equation 15 i s C = kifCu+g [H 2] 2i_ . 20(a) k - l "-1 k n Values of the r a t i o s —^- and _ji± f o r the three experimental temperatures which * - l k-— and 2=. <2 ^ 3 can be calculated by Equation 20 from inte r c e p t s and slopes i n F i g . 7, are shown i n Table 2(b), - 24 -It i s now also apparent that the expression 19(b) f o r the common intercepts of the plot s i n Figures 4, 5 and 6 i s i d e n t i c a l to that derived from the e a r l i e r mechanism (see expression of i n t e r c e p t , page 16). With t h i s expression, values of k]_ at 160°, 180° and 200°C weie ca l c u l a t e d from the mean intercepts i n the above Figures and are shown i n Table 1. TABLE 1 Values o f k]_, Calculated from Mean Intercepts of Figures 4. 5 and 6, and Other Pert^nerr' Data. Temp. °C Inter- cept., ^-min-mol - 1 Intercept -1-kiDu+liXl mol-Z~~JrS-min~ 1 [ C u - J . mol - ^ T 1 - ^ 1 m o l - ^ " 1 k l JL-mol-^-sec"! 110° - I x l O " 1 - 9.5 xlO-5 ( b ) 160° (I3.1±1.0)xl0 3 (7.6.':i0.58)xl0-5 2 x l 0 - 2 1.18x10-2 (5.40±0.73)xlO"3 18©° (3.32±0 . 2)xl0 3 (3.01±0.18)xlO~/' 2 x l 0 " 2 1.35xl0"2 (l.83 ±0.22)xl0-2 200° (0.92±0,05)xl03 (1.09 ±0.06)xl0-3 2 x l 0 - 2 1.58x10-2 (5.74 ±0.67)xlO- 2 (a) .See Reference 27 (b) Obtained from Reference 9. A good Arrhenius p l o t of log ' ^ 1 vs 1 depicted i n F i g . 8, i s obtained T T from these values of k-j_. The a c t i v a t i o n enthalpy estimated from the slope of t h i s p l o t i s A H * = 24.9*1.7 kcal/mol. which i s i n good agreement with t h a t given by Peters23 who obtained A H * = 24.6 kcal/mol. The corresponding entropy of a c t i v a t i o n , A S f = 12.1*4.5 c a l - "K"1 - mol" 1, which also agrees .well with Peters' value, i . e . , A S * = -13.1 e.u., i s considered normal f o r a bimolecular r e a c t i o n . Hence, k i may be represented by R 21 2 ' 1 2 ' 2 2.3 2.4 2.5 2.6 2.7 1 x IO3 T k l 1 P l o t of l o g - y - Ve-Rus T f o r the C u + + Catalyzed Hydrogen Reduction of C r ™ . 0.02M Cu(ClCV) 2; ±0 atm. H 2; - 26 -where k and h are Boltzman's and Planck's constants r e s p e c t i v e l y . The f a i r l y large errors, both i n & H* and A S * are ascribed to the uncertainty i n estimating k]_, f o r which a t o t a l error of ±13$ i s assumed (see Appendix C f o r e r r o r estimations). E f f e c t of Chromium VI Ion Concentration on Rates. The dependence of reduction rates on concentration i n s o l u t i o n i s seen i n Figures 9, 10, and 11 i n the form of plots of the rate f u n c t i o n , R, vs j C r ( V I ) ] f o r 160", 180° and 200°C r e s p e c t i v e l y . This rate function, which was derived from the ra t e expression, Equation 18, i s r e l a t e d to C r ^ 1 ) "iy the l i n e a r equation R = (Rate) x M « k, fcu+jl + k^ [cr(VI)] . 22 (Ro - Rate) k _ i k_]_ where Rate = -dJHgj/dt and Ro = ki[Cu +^] Qi^] . Values of R were calculated from rate measurements of at l e a s t three experiments,each of d i f f e r e n t a c i d i t y , at each of the three temperatures, with Ro being the r e c i p r o c a l of the respective intercepts i n Figures L, 5, and 6. The p l o t s i n Figures 9, 10, and 11 show reasonably good l i n e a r i t y i n the region of (0.4 to 4.0) x 10"3M C r ( v l ) , with the points of the i n d i v i d u a l runs coinciding quite w e l l i n that region. The l a r g e r deviations from l i n e a r -i t y and the spreading of points at higher Cr(Vl) l e v e l s r e f l e c t the f a c t that rate measurements become inaccurate i n that r e g i o n . From intercepts and slopes of Figures 9, 10, and 11, the rate constant r a t i o s ^-J, and k - l may be c a l c u l a -k 2 k 3 ted f o r each of the experimental temperatures, since from Equation 22, Intercept = kg_ [Cu +"^ 22(a) and Slope = k_3 . 22(b) k - l - 27 -2 4 6 C r ( V I ) x 103 M o l e - L i t e r - x F i g . 9. Plot of Rate Function,R,Versus Cr(VI) Concentration; 0.02M CuCClO^^j 10 atm. H 2; l60 eC - 20 -o 2 n : 6 C R ( V I ) X I Q 3 M o l e - L i t e r " ! F i g . 10 Plot of Rate Function, R, Versus C r ^ V I ^ Concentration; 0.02M Cu(C10 i f) 2; 10 atm. H 2; 180°C. - 29 -o.5r 0.4 H 1 U I Q> H » o . i O A • O H C l O ^ ( i n i t l a l ) Cu(C10 4) 2 0.20 M 0.35 0.50 0.50 0.02 M 0.02 • 0.02 0.01 2 4 C r ( V I ) x 10 3 M o l e - L i t e r " 1 F i g . 11. Plot of Rate F u n c t i o n ^ V e r s u s C r ( V I ) Concentrat 10 atm. H 2; 200°C„ ion; - 30 -Values of these r a t i o s should agree with those obtained i n a s i m i l a r fashion from the intercepts and slopes i n F i g . 7 and the corresponding intercept and slope expressions i n Equation 20. Table 2, which l i s t s k - l and ^-1, obtained by both methods, shows that the agreement i s q u i t e good indeed, despite the f a c t that the u n c e r t a i n t i e s i n measurements are quite high f o r both r a t i o s , i . e . , *19$ f o r ^1 and ±8% f o r ^ 1 . k 2 k 3 Within l i m i t s of e r r o r , both k - l arrf ^-1 appear to be independent of k 2 k 3 temperature between 160° and 200°C. The value of 0.26 f o r k - l at 110°C suggests that t h i s r a t i o i s constant i n the range of 110° to 200°C. These r e s u l t s i n d i c a t e that the r e a c t i o n steps - ( a ) * , (b) and (c) of Equation 17. TABLE 2 (a) Values of k - l and k ~ l from Intercepts and Slopes • k 2 k 3 of Plots i n Figures 9, 10, and 11, Temperature °C Intercept = k 2 /k_ l L Vf] m o l - l " 1 Slope " k3/k_i k_i/k2 110° . — . 0.26^* 160° 0.054*0.01 44*6*4,0 0.'37*0.07 (2.24*0.20) x 10* -2 180° 0.053*0.01 51.0±4.0 0.38±0„08 (1.96*0.18) x 10" -2 200° 0.051*0.01 49.6*4.0 0.39*0.08 (2.02*0.16) x 10" -2 4 Reaction step -(a) denotes the back reaction of (a) i n Equation 17. ±k See Reference 9 . - 31 -TABLE 2 (cont'd.) (b) Values of k-1 a n d k - l from Intercepts and Slopes k 2 k 3 of Plots i n F i g . 7. Temp, Intercept <-l mo l 2 - J e - 2 m i n - 1 Slope k _ i mol-jET^min**1 k - l / k 2 k.]/k 3 160° 180° 200° 4.10xl0~6 1.36x10-5 5.60x10"5 3.25x10-3 1.6lxl0- 2 0.53X10"1 0.37 0.44 0.39 ,-2 2.36x10' 1.86xl0~2 2.04xl0"2 a l l have approximately the same a c t i v a t i o n energy, which i s evident from the follow i n g . Consider the equations -and log k-1 = l o g A _ - L 2 - ( E - i - E a) (a) k2 '• ' 2.3 RT iog k _ i = log A_lf3 - (E_ ! - E 3) (b) k 3 2.3 RT 23 where A_]_^2 and A _ - j _ ^  are r a t i o s of the frequency f a c t o r s f o r the reactions .(see Equation 17) i n v o l v i n g rate constants k _ i , k 2 and k 3, and E_]_, E 2 and E 3 are t h e corresponding a c t i v a t i o n energies. Since k _ i and k-1 are nearly tempera-k7" k l ~ ture independent, a p l o t o f t h e i r logarithms against T ~ l should r e s u l t i n a st r a i g h t l i n e of approximately zero slope, wherefrom i t follows that — 3 _ 1 + E. ~ 0 • (a) and -3_1 + E 3 ~ 0 (b) 2 4 hence E _ x =* E 2 ^ E 3 (c). - 32 -The simplest conclusion to be drawn from t h i s r e s u l t i s that E_;j_, E 2 and E 3 are p o s s i b l y a l l zero, i . e . , reactions (a), (b) and (c) of Equation 17 have no a c t i v a t i o n energies, and k_]_, k 2 and k 3 are temperature dependent only with respect to t h e i r entropies of a c t i v a t i o n . A p o t e n t i a l energy diagram f o r the proposed a c t i v a t i o n mechanism may a conceivably be represented as shown i n F i g . 129 where E-j_ i s the a c t i v a t i o n CuH++ H + Products Reaction Coordinate F i g . 12 Schematic P o t e n t i a l Energy Diagram f o r the A c t i v a t i o n of H 2 by C u + + energy of reaction (a) Equation 17. This scheme implies that CuH + i s the activated complex and that the r e a c t i o n of t h i s complex with each of the species H +, C u + + or Cr(Vl) involves only a d i r e c t decrease i n energy. The differences i n the magnitudes of the rate constant? k_-^ , K 2 and k 3, therefore, would be o n l a consequence of the differences in the bucropy changes r e s u l t i n g from the r e a c t i o n of these species with CuH +. ft These conditions do not r e j e c t the p o s s i b i l i t y that CuH + i s i n f a c t more stable than the a c t i v a t e d complex i t s e l f . However, i n such a case the p o t e n t i a l energy curve would be approximately symmetrical about the (CuH + + H +) configura-t i o n to account f o r approximately equal a c t i v a t i o n energies i n a l l d i r e c t i o n s . - 33 -E f f e c t of C u + + Ion Concentration on Rates Figures 13, 14 and 15 i l l u s t r a t e the dependence of rates on C u + + ion concentration i n s o l u t i o n at 160° and 200°C. Of the three series of experiments shown, two were c a r r i e d out at 200°C, one at 0.1M HC10 4, the other at 0.5M HCIO4. The 160 CC se r i e s was 0.1M i n HCIO^. I t i s evident that (1) reduction rates increase, and (2) the dependence of rates on Cr (VI) decreases from apparent f i r s t order toward zero order, with i n c r e a s i n g C u + + ion concentration. Compari-son of Figures 1 4 and 15 indicates a l s o that, although the C r ( ^ l ) e f f e c t i s enhanced considerably with the higher a c i d i t y (Fig.15), i t becomes nevertheless suppressed by i n c r e a s e d - C u + + ion concentration. In F i g . 16, rates measured at the 4x10"3 Cr^^"^ l e v e l are shown plo t t e d against C u + + f o r each of the three s e r i e s . An apparent f i r s t order dependence of r a t e s on C u + + i s evident. In a d d i t i o n to these three p l o t s i s one f o r which rates had been measured at the 1.6xlO _ 3M C r ^ V I ^ l e v e l f o r the 0.5M HCIO^ s e r i e s . It i s seen that a s h i f t of rate dependence from apparent f i r s t - toward second-order i n C u + + occurs when rate measurements are made at the lower Cr(Vl) l e v e l . This s h i f t together w i t h the decreasing dependence of rates on C r ^ 1 ) with increasing C u + + ion concentration w i l l now be explained i n terms of the rate expression Equation 18 which reads -fk 2 k 3 \ - d j H j - ki[Cu+tl [ H 3 1 * - I [CU + +> k_i§r(vl)jf . 18 dt (H+n +iS2_ICu+t] + k 3 _ [ C r T O ] k - l k - l In Equation 18 consider the expression k 2 |cu+3 + k 3 [crO/I)) 18(a) * C l - ^ 1 H + k a Qu+''ll + k 3 rCr(VPl k - l k - l which re-written f o r s i m p l i c i t y , becomes K + K' 18(b) + K + K» Time - Minutes F i g . 13o Dependence of Rates on Cu++ Concentration; 160°C. 10 atm.H2; . O.IM HClOi, ( i n i t i a l ) . 1 1 1 r Time - Minutes F i g . 14. Dependence of Rates on C u + + Concentration; 200°C 10 atm. H 2; 0.1M HC10 4 ( i n i t i a l ) - 37 -F i g . 16. E f f e c t of C u + + Concentration on Rates at Seyeral Temperatures, Acid Concentrations and CrA^ 1' Levels; 10 atm. H 2. - 38 -where K = k 2 \cu ++\ and K* = k 3 lcr( V I)l k - l k - l I t i s found that the order of the dependence of rates on C u + + i s a function of the magnitude of the change i n the numerical value of expression 18(b) as K ( i . e . , [Cu"1"^) i s va r i e d , while [~H+] and K» are kept constant. S i m i l a r l y , the order of the dependence of rates on C r ^ " ^ i s a function of the magnitude of the change i n the numerical value of 18(b) as K' ( i . e . , [ C r ^ ^ ) i s varied, while [k+]] and K are kept constant. The magnitude of the change i n the numerical value of 18(b) depends i n both cases on the r e l a t i v e magnitudes of (1) the sum of the two terms that are held constant ( i . e . , [j""^ + K' or 0"^ ] + K), and (•£) the term that i s v a r i e d ( i . e . , K or K*)» I t i s shown i n Appendix G, Table 6(a) that i f the change i n - K + K* i s small as K ( i . e . , |Cu+'H ) i s varied, then rates appear to be fH +J+ K + K» f i r s t order i n [Cu+"*[] (see F i g . 16, curves A and B). However, when-this change i s large, the r a t e s w i l l s h i f t toward apparent second order i n [Cu+f] (see F i g . 16, curve C). S i m i l a r l y , i t i s shown i n Apoendix G , Table 6(b), that the dependence of rates on appears t o be zero order (see F i g . 15, curve A and F i g . 3, curve A) i f the change i n K + K' i s small as K' ( i . e . , r t S\ CH +J + K + K« [Cr(VI)J ) i s v a r i e d , and th a t i t s h i f t s toward apparent f i r s t order i f t h i s change i s large (see F i g . 15, curve E and F i ^ . 3, curve F ) . Consequently i t i s noted that the r a t e equation 18 may vary from f i r s t - to second-order i n (Cu + +]]and from zero- to f i r s t - o r d e r i n [cr(VD], or a combination of these p o s s i b i l i t i e s , depending on the s e n s i t i v i t y of the expression M Jj to changes i n ei t h e r K or K», [ H + > K + K» 6 These observations explain the f a c t that Peters and Halpern 1^ observed no CrOHO .effect, no acid e f f e c t and just a f i r s t order C u + + e f f e c t on 9 ( \ rates,and that Halpern et a l also observed no C r ^ 1 ) e f f e c t although they d i d - 39 -f i n d an acid e f f e c t and a pseudo second order e f f e c t of C u + + . This may e a s i l y be v e r i f i e d by applying the present rate law (Equation 18) to the preceding authors* data and c a l c u l a t i n g changes i n K + K* as shown i n Appendix G. £H+] + K + K» E f f e c t of Hydrogen Pressure. S t i r r i n g V e l o c i t y and Titanium Surface Area  on Rates. The data f o r rate measurements at 5 and 10 atm. hydrogen p a r t i a l pressure at each experimental temperature, exhibited i n Table 3* indicate that rates are f i r s t order i n PH2« This not only i s i n agreement with the e a r l i e r r e s u l t s of Peters and Halpern, 1^ but also adds support to the proposed . mechanism (Equation 17). ; TABLE 3 E f f e c t of Hydrogen P a r t i a l Pressure on-Rates. C r(VI) l e v e l » 4X10_3MV Temp. °C P H 2 atm. mol-Jr1 m o l - J - 1 Rate = -dM/dt mol- mn" 1 160° 160° 180° 180° 200° 200° 5 10 5 10 5 10 0.02 0.1 .2.66x10-5 5.82x10-5 l . l O x l O " 4 2 . 3 4 x l 0 - 4 3.86xlO" 4 7.50xlO - 4 Two experiments, performed to study the e f f e c t s of s t i r r i n g v e l o c i t y , and of surface area of t i t a n i u m i n contact with the s o l u t i o n gave the following r e s u l t s at 200°C. Reduction of the s t i r r i n g v e l o c i t y from the usual 620 rpm to i+10 rpm had no e f f e c t on the reduction rates except t o increase the time required f o r saturation of the s o l u t i o n with H 2 as shown i n F i g . 18, Appendix F. This indicates that the s t i r r i n g v e l o c i t y was s u f f i c i e n t l y high to eliminate any p o s s i b i l i t y of rates being d i f f u s i o n c o n t r o l l e d . Doubling the surface area of titanium i n contact with the solution by addition of s u f f i c i e n t " f i n e - 40 -titanium turnings alao had no e f f e c t on the rate, which confirms the assumption that surface e f f e c t s on reduction rates are n e g l i g i b l e (see F i g . 19, Appendix F). Proposed Mechanism f o r the Qii++ Catalysed Hydrogen-Oxygen Recombination Reaction. In t h e i r k i n e t i c studies on the C u + + catalysed hydrogen-oxygen recombination, McDuffie and co-workers^ had found - as discussed i n the Intro-duction - that rates were seemingly f i r s t order i n C u + + and that a c i d i t y changes were without e f f e c t on r a t e s , which i s i n apparent disagreement with the obser-9 vations of Halpern et a l . Hence, t h e i r observations seemed t o indicate that the r a t i o k_]/k 2 (see Equation 4) became n e g l i g i b l y small at 250°C. In other words, the back reaction-(a) (see Equation 3) became unimportant. This i s i n contrast to the findings o f MacGregor and Halpern 2^ who noted an increase i n k _ i / k 2 from 0.25 (at 110°C) to 1.3 ( f o r 160°C), suggesting that the back re a c t i o n becomes i n c r e a s i n g l y important as the temperature i s r a i s e d . Assuming that the temperature independence of k_j/kz, as found i n the present i n v e s t i g a t i o n , (see Table 2) also applies at 250°C, i t i s suggested that the r e s u l t s of McDuffie et a l can be reconciled with those of Halpern et a l by proposing f o r the reduction of 0 2, an analogous mechanism, to that f o r the reduction of C r ^ ^ ^ s e e Equation 1?). This mechanism can be w r i t t e n as follows * k l C u + + + H 2 ^ = ± CuH + + H + (a) k-1 CuH + + C u + + i2 2 Cu + + H + ( b) 24 CuH+ + 1/2 0 2 + H + ^ C u + + + H20 (c) f a s t 2 Cu + + 1/2 0 2 + 2 H + — 2 C u + + + H 20 (d) The corresponding rate law being — - 41 -- US = k l ]Cu+tl M 1^1 fax+*\* ^ 1 [0J dt CH+]+ fei-+t]+ fe M Equation 25 contains the expression fe |u+g + fe[o2i 5^ H+l + [^cV+I + hJ[o 25(a) which may be written as K + K«» [H +] + K + K» 25(b) where K i s again [Cu+3 and K»» = [jb ~J McDuffie et a l worked with s o l u t i o n s that were 0.00IM i n C u + + and i n i t i a l l y 4 about 0,076M i n 0 2 . ( i n i t i a l oxygen p a r t i a l pressure: 400 psig) with the a c i d i t y ranging from 0,005 to 0.05M i n HC10/,.. Knowing k _ i / k 2 and assuming k_]_/k^. to be approximately the same as k_^/k 3, i t can be shown that the change i n the expression K + K'' i s only about 1 percent as a r e s u l t [JH+1. + K + K " of the t e n f o l d increase i n a c i d i t y , f r o m which i t i s c l e a r that no a c i d e f f e c t on rates can p o s s i b l y be detected. Moreover, the numerical value of K + K , f i s so close to u n i t y (0.99) under the given conditions that Dr*"l + K + K»» the rate law must read - dJHjj = ^ [Cu+3 [HjJ 5 dt as i n f a c t observed by McDuffie .et a l . No explanation can be given f o r the increase of k_;j/k 2 with 4 S o l u b i l i t y of 0 2 was estimated from data of Pray, Schweichert and Minnich temperature as observed by MacGregor and Halpern. Their value i s admittedly of low p r e c i s i o n because of the method used f o r measuring r a t e s , which was the estimation of i n i t i a l slopes on r a t e curves that were not mathematically analysed along t h e i r e n t i r e length. I f the high value i s i n f a c t v a l i d , the explanation must l i e i n a yet unexplained d e v i a t i o n i n the mechanism when copper i t s e l f i s being reduced. CONCLUSIONS The k i n e t i c s of the homogeneous a c t i v a t i o n of hydrogen by C u + + i n aqueous s o l u t i o n were investigated i n the temperature range of 160° to 200°C. A s i g n i f i c a n t dependence of rates on concentration was observed and a mechanism, s i m i l a r to that developed e a r l i e r by Halpern and 9 co-workers, was proposed to account f o r t h i s observation. The r a t e constant k-|_ f o r the hydrogen a c t i v a t i o n step and the r a t i o s of rate constants of subsequent steps,' k_^/k 2 and k_]_/k 3, were determined f o r 160°, 180° and 200°C by means of the rate expression derived from the above mechanism. The enthalpy of a c t i v a t i o n calculated from the slope of a l o g ^1 T vs i p l o t was the same w i t h i n l i m i t s of err o r as that found by P e t e r s 2 ^ i n a T "v s i m i l a r study. The r a t i o s k _ i / k 2 and k_]_/k3 were found to be temperature independ-ent within l i m i t s of e r r o r suggesting that the a c t i v a t i o n energies f o r the reactions with rate constants k.^, k 2 and k 3 are equal and p o s s i b l y n e g l i g i -b l y small, which implies that CuH + may be the ac t i v a t e d complex. - L3 -It was shown that a mechanism s i m i l a r to that found i n t h i s i n v e s t i -gation may explain s a t i s f a c t o r i l y the apparent discrepancy between the k i n e t i c s of the C u + + catalysed hydrogen reduction of C r ^ 1 ^ and the hydrogen-oxygen recombination r e a c t i o n . On the basis of the observations i n t h i s i n v e s t i g a t i o n and the conclusions derived thereof a general mechanism f o r the a c t i v a t i o n of H 2 by C u + + and the oxidation of the intermediate CuH + may be written as follows? k I C u + + + H P CuH + + H + (a) 26 Zkji f a s t CuH + + ZOx —• Intermediates -»• Products (b) where S ) x i s the sum of a l l oxidants capable of o x i d i z i n g CuH + and J JCTJ the sum of the corresponding r a t e constants. - 44 -REFERENCES 1. F.A. Forward, Can. Inst. Min. and Met. B u l l . , ^6: 677 (1953). 2. R.N. O'Brien, F.A. Forward and J . Halpern, Trans. C.I.M.M., £6:369 (1953). 3. I.H. Warren, to be published. 4. J . Halpern, Advances i n C a t a l y s i s , 11:301 (1959). 5. H.F. .McDuffie and Co-workers, J . Phys. Chem. 26:1030 (1958). 6. V.N. I p a t i e f f and W. Werschowski, Ber. ^2:2078 (1909). 7. J . Halpern and R.G. Dakers, J . Chem. Phys. 22:1272 (1954). '8. E. Peters and J . Halpern, Can. J . Chem. 3_3j356 (1955). 9. J . Halpern, E.R.-MacGregor and E. Peters, J . Phys. Chem. 60:1455 (1956). 10. E. Peters and J . Halpern, J . Phys. Chem. J59/-793 (1955). 11. A.H. Webster and J . Halpern, J . Phys. Chem. 60:280 (1956). 12. A.H. Webster and J . Halpern, J.. Phys. Chem. 61:1239 (1957) 13. L. Wright, S. Weller and G.A. M i l l s , J . Phys. Chem. j£:1060 (1955) 14. A.H. Webster and J . Halpern, Trans. Farad. S o c , 53_:51 (1957). 15. G.J. Korinek and J . Halpern, J . Phys. Chem. 60:285 (1956) 16. M. Cal v i n , J . Am. Chem. Soc. 61:2230 (1939) 17. S. Weller and G.A. M i l l s , J . Am. Chem. Soc. 25_;769 (1953) 18. A . J . Chalk and J . Halpern, J . Am. Chem. Soc. 81:5846, 5852 (1959 19. H. Halpern, J . F . Harrod and P.E. Potter, Can. J . Chem. 3.7.1446 (1959). 20. J . F . Harrod and J . Halpern, Can. J . Chem. 3_7_:1933 (1959). 21. J . Halpern, J . Phys. Chem. 63j398 (1959). 22. W.K. Wilmarth and A.F. Kapanan, J . Am. Chem. Soc. 7Jhl308 (1956) 23. E. Peters, Ph.D. Thesis, The Univ e r s i t y of B r i t i s h Columbia, 1956 24. E.R. MacGregor, Master's Thesis, The U n i v e r s i t y of B r i t i s h Columbia, 1956. 25. E.R. MacGregor and J . Halpern, Trans. A.I.M.E. 212:244 (1958). 26. J.Y-P. Tong and E.L. King, J . Am. Chem. Soc. 7£:6l80 (1953) - 45 -REFERENCES (cont'd.) 27. R.T. McAndrew, private communication. 28. H.A. Pray, C.E. Schweichert and B.H. Minnich, Ind. Eng. Chem. L±tllk6 (1952) - U6 -APPENDIX A Compounds Tried f o r Possible Use as Substrates Several compounds besides N a 2 C r 2 0 7 were t r i e d to determine i f any might serve as sui t a b l e substrates f o r observing the rate of a c t i v a t i o n of hydrogen by C u + + ions. The f o l l o w i n g r e s u l t s were obtained: Compound N a 2 C r 2 0 7 NaV(OH)^ NalO, NaCIO, NaBrO. Re suit was found t o be stable i n s o l u t i o n and r e a d i l y reducible by hydrogen. On heating V(0H ) 4 ~ decomposed with the formation of a reddish brown p r e c i p i t a t e , presumably V 2 0 5 . Reduction of I 0 3 ~ to both I" and I 2 took place causing loss of I 2 by evaporation. C10 3~ decomposed on heating to C l ~ and probably C10 2 (solution turned yellowish green). Br0 3~ decomposed to B r 2 and Br~ upon heating of s o l u t i o n . (VI) - 47 -APPENDIX B Consumption of H + Ions Due to Reduction of C r ^ V I ^ H + ions w i l l be consumed upon hydrogen reduction of Cr (VT) 26 Assuming f o r convenience that CrK J i s mostly HCrCV, t h i s reduction w i l l take place according to the equation; HCrOiT + 3/2 H 2 + 4 H + — C r + + + . + 4 H 20 (27) T h e o r e t i c a l consumption curves and experimental points obtained, by potentiometric t i t r a t i o n w i t h 0.1 N borax s o l u t i o n , from runs at 160°, 180° and 200°C at several i n i t i a l a c i d l e v e l s , are depicted i n F i g . 17. I t appears that i n most cases the acid consumption i s les s than t h e o r e t i c a l which i s probably a r e s u l t of p a r t i a l regeneration of H + ions by hydr o l y s i s of C r + + + . 6 i u © I .a Q o o 2 -o A P 0.05 0.1 F i g - 17. 0.2 0.3 Mole-Liter -1 0.35 0.4 Consumption of H + Ions Due to Reduction of Cr (VI) — Theoretical Curves; O • A Points Obtained from Various Experiments at 160°, 180° and 200°C. 0.5 i i - 49 -APPENDIX C Estimation o f Errors Occurring i n the Evaluation of k i Based on the maximum deviations of the intercepts i n Figures 4, 5 and 6 and on errors i n hydrogen s o l u b i l i t y and hydrogen p a r t i a l pressure-measurements, the average e r r o r i n was estimated to be il3%o In the calcu-l a t i o n of these values i t was assumed that the s o l u b i l i t y of hydrogen (which was measured f o r d i s t i l l e d water) was e s s e n t i a l l y unaffected by 3 x 10"% -3 Na 2Cr 20 7, 2 x 10 1 Cu(C10 i f) 2 and 0.05 to 0.5M HCIO4 i n s o l u t i o n . It was fu r t h e r assumed that Henry's Law was obeyed i n the region of pressures used, i . e . , 5 to 10 atm, H 2 gas. The f o l l o w i n g errors were taken into account: 1) Er r o r s i n the concentration of H 2 dissolved i n s o l u t i o n due to the l i m i t of accuracy of pressure gauge readings *3$. 27 2) Errors i n H 2 s o l u b i l i t y measurements ±3%. 3) Er r o r s i n cupric perchlorate concentration were les s than 0.5$ and were not considered. 4) Errors due to inaccuracy i n drawing of the reduction curves and i n [Jr^^J analysis were estimated t o be of the order of wit h i n the region of greatest curvature of the reduction p l o t s . These errors were greater at both ends of the reduction p l o t s (Figures 1, 2 and 3) p a r t i c u l a r l y at the s t a r t of reduction. Hence, rate measurements f o r determination of k]^ were confined t o the region of highest curvature o f the reduction p l o t s . 5) Errors i n rate measurements by the mirror-image method *3%. 6) Errors i n intercept measurements (Figures 4, 5 and 6) *6$. Since errors 4) and 5) are inherent i n 6), an average er r o r of (6% + 3% + 5%)* 2 =r7% was assumed. APPENDIX D - 50 -Summary of Rate Measurements TABLE 4 (a) Effect of Perchloric Acid Concentration on the Rate o f the Cu + + Catalyzed Hydrogen Reduction of Cr( V I ) . Cu(C10^)2 " 0.02M, P H = 10 atm. Expt. Q-cioJJ (CrCVlOlevel .d[Hj/dt** (-d[H3 / d t j - 1 No. mol-JT 1 mol-X" 1 mol-_£-Ji-niirr-L j^-min-mol"-1-(i) 160°C (Fis. U) • ~> 0.009 1.6x10-3 6.95x10-5 1.44x10^ '• • 1 t 2.4 »» 7.43 " 1.34 " t l 3.2 •' 7.65 " 1.31 " 0.01 4.0 » t 8.06 1.24 " A c 1 ^ 0.039 1.6 t t 5.23 " 1.91 " 0.042 2.4 " 5.47 " 1.83 " 0.045 3.2 " 5.73 " 1.74 " 0.047 4.0 " 5.92 •• 1.69 " A c 1 ^ 0.087 1.6 t » 4.63 " 2.16 tt 0.090 2.4 " 5.02 " 1.99 " 0.092 3.2 " 5.35 " 1.87 ' t 0.094 4.0 " 5.82 " 1.72 tt A 1 6 0-,-, Ac —11 0.1B9 1.6 »» 3.12 t t 3.20 tt 0.191 2.4 " 3.49 " 2.86 tt 0.193 3.2 " 3.82 t t 2.62 tt 0.195 4.0 " 4.32 " 2.31 " Ac 1! 0^ 0.345 1.6 " 1.92 " 5.22 t t 0.346 2.4 »» 2.34 " 4.28 tt 0.348 3.2 t . 2.72 tt 3.67 " 0.350 .4.0 «« 3.07 " 3.26 t, Ac 1! 0^ 0.484 1.6 " 1.50 " 6.66 " 0.487 2.4 " 1.77 t t 5.63 " 0.490 3.2 " 2.06 tt 4.85 »• 0.493 4.0 »» 2.31 " 4.18 t, 4 Slight adjustments of acidity which were made for each Cr (VI) level at which rates were measured were estimated from Fig. 17 5 Appendix B, and i n i t i a l acidities. dpj/dt - 3/2 x ^ d & r O ^ (Table 4 continued - 51 -APPENDIX D - Table 4 (cont'd.) Expt. D i C l O j (Gr(VI)J l e v e l - d f H j / d t No. mol-/-1 mol-2.-1 mo 1-2-1 -min-1 - d ^ / d t - 1 X-min-mol-I . • r. . ( i i ) 180°C ( F i g . 5) 130 Ac - 2 0.035 0.038 0.041 0.045 1.6x10-3 2.4 " 3.2 " 4.0 " 2.21x10-4 2.29 " 2.43 " 2.50 " 4,52x103 4.36 " 4.12 " 4.00 " 180 Ac - 1 0.087 0.090 0.092 0.094 1.6 " 2.4 " 3.2 " 4.0 '' 1.80 " 2,02 " 2.18 " 2.34 " . 5.50 " 4.95 " 4.58 «• 4.27 " 180 Ac - 5 0.189 0.191 0.193 0.195 1.6 " 2.4 " 3.2 " 4.0 " 1.26 " 1.45 1.60 " 1.75 " 7.97 " 6.90 " 6,23 " 5,70 " 180 Ac - 4 0.341 0.343 0.345 0.346 1.6 " 2.4 '* 3.2 " 4.0 " 0.826 '' 1.01 •» 1.20 »• 1.32 »* 12,1 " 9.90 " 8.34 " 7.58 " 180 Ac - 3 0.484 0.487 0.490 0.493 1.6 " 2.4 " 3.2 " 4.0 f t 0,606 " 0.793 " 0.886 »' 1,00 «« 16.5 " 12.6 " 11,3 '' 10.0 '' ( i i i ) 200°C (F i g , 6) Ac2Q0 2 200 Ac - 7 200 Ac - 6 Ac 2°°3 200 Ac - 4 0.045 1,6x10-3 9,0x10 T4- 1.11x103 » ' '• : 2.4 " 0 9 N.B, used average •i r • »t » » 3.2 " 9 9 rate and a c i d - » » » » 4.0 " » 9 i t y values. 0.088 1.6 " 6.66x10"4 1.50xl03 0.090 2.4 ; " 7.08 « » 1.41 » » 0,092 3.2 " 7.29 ? ? 1.37 0.095 4.0 " 7.50 1 1 1.33 t ? 0.189 1.6 " 4.18 »t 2.39 «t 0.191 2.4 " 4.74 »t 2.11 1 1 0.193 3.2 «» 5.66 »t 1.77 » t 0.195 4.0 " 6.13 » » 1.63 »t 0,340 1.6 " 3.06 3.26 » ? 0,343 2.4 " 3.69 » » 2,71 ? i 0,345 3.2 " 4.16 »t 2.40 » ? 0.346 4.0 " 4.47 i» 2.24 » « 0.484 1.6 " 2.27 » ? 4.40 » 9 0.488 2.4' " 2.79 « ? 3.58 9 9 0.490 3.2 " 3,24 » ? 3.08 t t 0.493 4,0 " 3,65 t« 2,74 9 9 - 52 -APPENDIX D - Table 4 (cont'd.) (b) E f f e c t of Dissolved Cupric Perchlorate on the Rate of Cr(Vl) Reduction by' Hydrogen. PH 2 = 10 atm. (Fig. 16). a 9 Expt. I n i t i a l ' [Hcial [0u++ ] [ C r ™ ] l e v e l -d[H 2]/dt No. mol-/ ~ L mol-X~^" m o l - X " 1 mol--min"1 ( i ) 160°C 160 Ac - 5 Cu' - 2 0.1 » t »t 11 11 0.02 0.04 0.06 ,0.08 0.10 4.0xlO"3 i t » i 1 1 i » .0 .582x10""-* 1.12 " 1.53 " 2.02 »» 2.54 ( i i ) 200°C r 200-Cu - 2 Ac 2 0. 0? Cu2°°I Cu 2 0°5 0.1 » t t ! t t « » 0.0074 0.01 0.02 0.03 0.04 4.0xl0- 3 i » 1 1 « i • i 2.84x10"^ 4.11 " 7.50 " 10.9 " 15.7 " G4> Ac - L Cu 2 2°8 Cu 2 ° °9 0.5 » 1 » t J 1 » t 0.01 0.02 0.04 0.06 0.08 » i 11 ? t 11 «» 1.84 '* 3.65 , " 6.98 " 9.75 " 14.8 t i u 2°°8 C u 2 2 ° 9 1 « t t t t t t t t 0.01 0.02 0.04 0.06 0.08 1.6x10-3 1 1 1 1 • t 11 1.01 t i 2.27 " 5.06 t i 8.13 " 11.4 " Continued,...... - 53 -APPENDIX D - Table 4 (cont'd.) (c) Rate Measurements and Rate Function R* at Various C r ^ 1 ^ Levels. ( i ) 160°C, [Cu + +J =.0.02 mol, P H = 10 atm (F i g . 9) k x [Cu + +]] JH2] = 1.27x10-6 m o l - i - 1 -sec-1 Expt. [ H C l O j [ c r ( V I l e v e l IdQjJ/dt M R N o ' m o l - / " 1 m o l - X " 1 m o l - ^ " 1 -sec-1 m o l - i " 1 AO 1- 6 0!! 0.186 0.4x10-3 0.436x10-6 0,098 0.187 0.8. " 0.460 " 0.106 0.188 1.2 " 0.488 »» 0,118 0.189 1.6 »» 0.519 " 0,131 0.190 2.0 " 0.550 •» 0.145 0.191 2.4 »' 0.583 0.162 0.192 2.8 ' • 0.621 " 0.184 0.193 3.2 " 0.637 0.194 0.194 3.6 " 0.678 " 0.222 0.195 4.0 " 0.723 " 0.258 0.196 4.4 " 0,742 •» 0.275 0.198 4.8 " 0.781 »• 0.316 0.199 5.2 0,789 " 0.326 0.338 0.4 *' 0,236 " 0.077 0,339 0.8 »» 0,243 " 0.082 0.340 1.2 »• 0,299 " 0.105 0.341 1.6 " 0,320 ' • 0.115 0.342 2.0 '' 0,364 " 0.137 0.343 2.4 " 0.389 " 0.151 0.344 2.8 «• 0,421 " 0.171 0.345 3,2 " 0.468 »» 0.201 0.345 3.6 " • 0,490 " 0.217 0.346 4.0 " 0.512 0.234 0.347 4.4 " 0,555 " 0,269 0.348 4.8 " 0.575 " 0,288 0,349 5.2 •» 0.610 »* 0,323 160 Ac - 13 0,480 0,4 " 0,172 " 0.075 0,481 0.8 0,190 " 0.085 0,483 1.2 «« 0,214 " 0,098 0.484 1.6 " 0.250 »' 0,118 0,486 2.0 '» 0,276 " 0.135 0.487 2,4 " 0,296 " 0,148 0,489 2,8 »' 0,324 " 0,167 0.490 3.2 «» 0.343 " 0.181 0.492 3.6 '« 0.361 " 0.196 0.493 4.0 •' 0.386 »» 0,215 0,495 4.4 " 0,407 " 0,234 0.496 4.8 " 0,427 " 0.251 0,498 5.2 " 0.456 0,279 £ R « (Rate) xCH +H w h R a t e = _ dr H-J a n d R o = kxfcu+firH (Ro - Rate) -4=^ 1. - " - i - - " -ft* -d[H 2]/dt = 3/2. x l/60(-d[Cr(VI ) J/dt) APPENDIX D- - Table 4 (cont'd.) (c) cont'd. ( i i ) 180°C, [ C u + + J = 0.02 mol,PH = 10 atm (Fig.10) k] [Cu +- ;J[K 2] = 5.02x10-6 m o l - i - l - s e c " 1 Expt. No. R m o l - i " 1 m o l - / " I mol-X"-'— s e c " 1 mol-^" 1 0.186 0.4x10-3 1.53x10=6 0,082 0.187 0.8 J » 1.73 » « 0.098 C188 1.2 V 8 1.91 8 0 0.116 0.1«V 1.6 t t 2.09 9 9 0.135 0.190 2.0 t J 2.27 t 8 0.157 0.191 2.4 . 8 « 2.42 9 9 0.178 0.192 2.8 t 8 2.56 » 8 0.200 0.193 3.2 t ! 2.68 t ? 0.221 0.194 3.6 8 ! 2.82 J ? 0.248 0.195 4 . 0 « 8 2.92 9 9 0.271 0.196 4 . 4 8 » 3.09 9 t 0.314 0.198 4.8 t 8 3.17 9 9 0,342 0.199 5.2 8 8 3.28 » 9 . 0,376 0.338 0.4 8 8 0.997 9 8 0,084 0.339 0.8 8 8 1.12 9 9 0.097 0.340 1.2 ? » 1.22 9 9 0,109 0.341 1.6 « J 1.38 9 9 0.128 0.342 2.0 t 8 1.54 9 9 0,151 0.343 2.4 8 ? 1.68 9 9 0.173 0.344 2.8 t t 1.85 9 9 0.201 0.345 3.2 8 8 2.00 8 8 0.230 0.346 3 .6 f 8 2.08 S 8 0,244 0.346 4.0 9 t 2.20 9 8 0,270 0.347 4.4 9 » 2 .34 T 8 0,302 0.348 4.8 t 1 2.51 9 8 0,348 0.349 5.2 ? 9 2.62 1 f 0,381 0.480 0.4 9 ? 0,620 1 8 0,068 0.481 0.8 9 » 0,813 8 8 0.094 0.483 1.2 ! 9 b0.932 8 8 0.110 0.484 1.6 8 ! 1.07 9 9 0,131 0.486 2.0 8 9 1.20 9 8 0.154 0.487 2 o 4 8 9 1.32 9 9 0.174 0.489 2.8 8 5 1.39 8 9 0.189 0.490 3.2 8 8 1.48 8 8 0.204 0.492 3 .6 8 8 1.57 8 8 0,224 0.493 4 . 0 t 8 1.67 0 8 0,246 0.495 4o4 8 J 1.71 8 9 0,255 0.496 4.8 8 8 1.75 8 8 0,266 0.498 5.2 8 J i 1.83 8 8 0,287 A c 1 8 ^ 180 Ac - 4 A c 1 8 ° 3 Continued...... APPENDIX D - Table 4 (cont'd.) (c) cont'd, ( i i i ) 200°C, £Cu+fj 0,02 mol, P H 2 = 10 atm (Fig, 11) = l & L x H T 6 m o l - / " 1 - s e c " 1 Expt, No. [HCIO^D mol-£~l Dr(vD: mol-^ J l e v e l -d[H 2]/dt molrA - s e c - 1 R mol-/-1 0,186 0,4x10-3 .4.87x10-6 0.067 0.187 0.8 8 0 5.72 8 8 0,086 0.188 1,2 8 5 7.00 8 8 0,118 0.189 1.6 8 5 7.66 9 8 0.139 0.190 2.0 J 8 8,31 0 9 0,161 0.191 2.4 8 8 8.73 9 9 0.178 0.192 2.8 9 9 9.02 8 9 0,191 0.193 3.2 9 8 9.53 8 8 0 . 2 1 4 0.194 3.6 9 9 9 .89 9 9 0,233 0.195 4.0 8 9 10.3 9 3 0,257 0,196 4.4 0 9 11,0 9 8 0,302 0.198 4.8 8 8 11.3 9 8 0.3*29 0.199 5.2 8 8 11,3 8 8 0 . 3 3 0 0.336 0,4 8 8 3 . 4 4 8 9 0,079 0,338 0.8 8 8 4.06 9 9 0,101 0.339 1.2 1 t 4.60 1 8 0,116 0 . 340 1,6 9 8 5.11 8 8 0,134 0.342 2.0 9 8 5 . 6 4 8 8 0.155 0.343 2.4 9 9 6.15 8 9 0,176 0.344 2.8 8 8 6 .60 8 8 0,197 0.345 3.2 8 8 6,93 9 9 0 , 2 1 4 0 . 3 4 6 3.6 8 8 7 . 29 9 9 0,233 0 . 346 4.0 8 9 7.45 8 9 0,242 0.347 4.4 8 8 7.73 t ! 0.258 0,348 4.8 1 9 7.86 9 » 0.268 0.349 5.2 T 9 • 7.90 »"» 0,270 0,480 0.4 9 9 2,69 8 9 0.084 0.481 0,8 8 9 2.97 9 8 0.096 0,483 1.2 9 8 3.36 8 9 0,110 0.484 1.6 8 9 3.78 8 9 0,128 0,486 2.0 8 8 4.18 8 8 0,150 0.487 2,4 8 9 4.68 8 8 0-„ 168 0.489 2.8 8 8 5.10 8 8 0,192 0.490 3.2 8 8 5 .40 9 0 0,208 0,492 3.6 0 8 5.78 9 8 0,231 0.493 4.0 9 8 6,08 9 9 0,250 0.495 4.4 9 8 6,43 8 8 0,273 0,496 4.8 9 8 6,93 8 8 0,308 0.498 5.2 9 8 7.43 3 8 0.347 200, Ac - 6 200 Ac - 3 . 200. Ac - 4 Continued ....... APPENDIX D - Table L (cont'd.) (c) ( i i i ) cont'd. 200°C, [ C u + + ] = 0.02 mol, P H = 10 atm (Fig.11) k l C3u+"-l L~HJ = 1 8 i x 1 0 " 6 m o l - i ' 1 -sec-1 Expt. £HC10j | c r(VI)] l e v e l - d f r t j / d t R N o - mo 1-^-1 mol-/-l mo>/-l -sec"! m o l - i ' l 0.480 0.4x10-3 0.91xlO"6 0.054 0.481 0.8 " 1.21 " 0.074 0.483 1.2 " 1.46 " . 0.093 0.484 1.6 " 1.68 " 0.110 0.486 2.0 ' » 1.91 " 0.130 0.487 2.4 " 2.13 " 0.150 0.489 2.8 t . 2.43 " 0.178 0.490 3.2 " 2.72 " 0.211 0.492 3.6 " 2.83 " 0.224 0.493 4.0 " 3.06 " 0.252 0.495 4.4 " 3.16 " 0.266 0.496 4.8 " 3.26 " 0.279 0.498 5.2 " 3.31 " 0.288 * [Cu + +] = 0.01 M - 57 APPENDIX E TABLE 5 Slope Measurements of Rate~l vs [H"1] Plots of Figures 4* 5 and 6 , and Values of S*„ [ p r l V i j J l e v e l Slope ' S mol-£-l ^ 2 „min-mol*" 2 m o l 2 - X ° 2 -min*"! ( 1 ) 160° C 1.6xl0 =3™~*™~" 10o8 x l O ^ 0,927x10=> 2„4 0 9 8,54 0 8 1.17 5 0 3o2 8 8 7.12 " 1.40 8 8 4.0 8 8 5.62 1 8 ** ( i i ) 180 °C 1.6x10=3 2,64x104 3,79x10-5 2,4 0 8 1 088 " 5,32 8 8 3»2 8» 1,55 " 6,46 8 5 4.0 8 8 1,28 5 5 7.84 8 8 ( i i i ) 200 oC 1.6x10-3 2,4 8 8 3,2 5 5 4.0" 8 8 0 , 7 1 4 x l 0 4 0 , 5 4 6 8 8 0 , 4 3 6 8 8 0 , 3 7 4 8 8 14,0x10 18,3 8 8 22.9 8 8 26,7 8 8 -5 4 S = S l o p e " 1 - ^ [ C u ^ ] ^ ] j k 2 / k = 1 [ c u + ^ + k 3 / k = 1 (Equation - 58 -APPENDIX F E f f e c t of S t i r r i n g V e l o c i t y and Surface Area on Rates. Two experiments were performed to t e s t whether at 200°C rates are c o n t r o l l e d by d i f f u s i o n of hydrogen from the gas-to the liquid-phase, and whether the titanium surface i n contact with the s o l u t i o n had any c a t a l y t i c e f f e c t on r a t e s . In the f i r s t case, the s t i r r i n g v e l o c i t y was reduced from the normal 620 rpm to 410 rpm, and the r e s u l t i n g reduction curve was compared with one obtained under i d e n t i c a l conditions but at the usual s t i r r i n g r a t e . It i s evident, as seen i n F i g . 18, that the reduction rates are unaffected by lowering of the s t i r r i n g v e l o c i t y except i n i t i a l l y where the time required f o r d i s s o l u t i o n of H 2 i s greater f o r the 410 rpm run. Hence, i t may be assumed that reduction rates are not d i f f u s i o n c o ntrolled under the experi-mental conditions used. In the second case, approximately f i v e grams of f i n e titanium turnings, whose surface area was estimated to be equal to that of a l l titanium parts i n contact with the s o l u t i o n , were added. The r e s u l t i n g reduction curve, shown i n F i g . 19, and compared with one r e f e r r i n g to the normal titanium surface area, indicates that the c a t a l y t i c a c t i v i t y of titanium i s n e g l i g i b l e . In order to t e s t also the s t a b i l i t y of C r ^ V I ^ the s o l u t i o n was held f o r 5 hours at 200°C p r i o r to hydrogen addition. As shown In F i g . 19, a s l i g h t decomposition of C r ^ 1 ^ , which soon l e v e l l e d o f f d i d take place i n i t i a l l y . " This decomposition probably resulted from the oxidation of the surface of the titanium turnings by C r ^ V I ^ although they had been bo i l e d f o r 10 minutes i n 50% HN03 p r i o r to the experiment. Its eventual stopping may be due to the p a s s i v a t i o n of titanium by formation of a coherent oxide f i l m . F i g . 18. Comparison of Cr ^  ' Reduction Curves Showing Negligible S t i r r i n g V e l o c i t y E f f e c t on Rates. For Both Experiments: i 200°C; 0.02M Cu(C10 4) 2| 0.35M HC10 4 ( i n i t i a l ) ; 10 atm.H2. 1 -1 Pre-reduction plot showing some disappear-ance of Cr'*I); apparen-cy owing to reduction by f r e s h titanium turnings. Note l e v e l -l i n g of curve. -Time required to heat solution from room temperature to 200°C. introduced Note 1 2 2 Hours 1 — r Q C r ^ l ) reduction with twice the usual titanium surface area i n contact with the s o l u t i o n . • C r ^ " ^ reduction with the usual titanium surface area i n contact with the s o l u t i o n . change of time scale 10 Time Minutes F i g . 19. Comparison of Cr Reduction Curves Showing'Negligible Titanium Surface Area Effect'on Rates. For Both. Experiments: 200 6C; 0.02M C u ( C 1 0 j 2 ; 0.35M H C 1 0 4 ( i n i t i a l ) ; 10 atm. H 2. APPENDIX G The order of dependence of rates on G u + + or Cr (VI) i s a function of the magnitude of the change i n the numerical value of the expression K + K' * 9 (Equation 18(b)', 5with a change i n e i t h e r K or K° respective-'[H+3 + K + K° l y s while the other terms of the expression are held constant. The subsequent table shows "that dependence of rates on e i t h e r C u + + or C r ^ - ^ i s s h i f t e d toward higher order whenever the magnitude of the above change, expressed i n percent, i s large, TABLE 6 (a) Order of C u + + Dependence of Rates Related to K + K" Percent Change of J*H+] + K + K° With Changing K (i„e, , E 3 u + 41) a t 200°C, &*] |Gr(VI)j Ratios K + K fH+1+ K + K' Percent Increase i n Ratio 0,0075 0,04 0,1 0,1 4x10-3 4x10-3 0,69 0.75 Observations Rates approximately f i r s t order i n C u + , Curve A, F i g . ,16 0.01 0,08 0.5-0,5 4x10-3 xlO-3 0,31 0.44 L2% Observations Rates approximately f i r s t order i n Cu +' + s Curve B, F i g , 16, 0,01 0,08 0.5 0,5 1.6x10-3 1,6x10-3 0.16 | 0.36 1 125% Observations Rates s h i f t toward second order i n C u + + , Curve C 9 ,Fig„ 16, ± K = k 2/k_ 1|Ju + t l K« = k a / k . i l g r C ^ ' J . For s i m p l i c i t y k^/kg = 0,40 and k = i / k 3 = 0.02 (compare with Table 2) - 62 -APPENDIX G - Table 6 (cont'd.) (b) Order of Cr( V I) Dependence of Rates Related to Percent Change of fcH4^ + K + K* With Changing K« (i.e.,[Cr(V I)J) at 200°C. [Cu++1 JJH+j Qcr(VI)] Ratio: K + K' Percent Increase m-^-I m-Jt1 m-l'1 1^2 + K + K' in Ratio 0.08 0.5 1.6x10-3 0.36 I . 0.08 0.5 4.0x10-3 0.44 f Observation: Rates approximately'zero order in C r ^ ^ Curve A, Fig. 15. 0.01 0.5 1.6x10-3 0.16 I ' 0.01 0.5 4.0x10-3 0.31 * V V Observation: Rates approaching f i r s t order i n C r ^ 1 ^ Curve E, Fig. 15. 0.02 0.05 1.6x10-3 0.72 I -.c^ 0.02 0.05 4,0x10-3 0.83 \ Observation: ' Rates approximately zero order i n C r ^ 1 ) Curve A, Fig,-3 0.02 1.50 1.6x10-3 0.08 I 0.14 J 7 5 / 3 .(VI) 0.02 1.50 4.0x10-3 Observation: Rates approaching f i r s t order in CrKyxj Curve F, Fig, 3. 

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