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Kinetics of copper reduction by hydrogen from aquaeous solutions. Hahn, Edmund Alexander Joachim 1963

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KINETICS OF COPPER REDUCTION BY HYDROGEN FROM AQUEOUS SOLUTIONS by EDMUND ALEXANDER JOACHIM HAHN A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of .METALLURGY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1963 In presenting t h i s thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of British"Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study.. I further agree that permission for extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Metallurgy  The University of B r i t i s h Columbia, Vancouver 8, Canada. Date May 3, 1963 ABSTRACT The k i n e t i c s of the hydrogen reduction of aqueous cupric perchlorate and sulphate solutions were studied at l60°C and 5 to 10 atm hydrogen pressure. In sulphate solutions the observed rates were consistent with a rate law, derived from previously proposed mechanisms, that has the form -d [He] = k J C u 1 1 ] 2 ^ ] + k 3 [ C u I I ] 2 [ C u I ] [ H 2 ]  dt ^ [ H + M c u 1 1 ] !=*• [ H + M C u ^ i y ^ z a [H +] + [Cu i j-]^ The rate constants of the hydrogen a c t i v a t i o n steps of the reaction are II represented by k i and k 3 which r e f l e c t the a c t i v a t i o n rates by Cu and Cu 1 r e s p e c t i v e l y and have the values 3.2 X 10" 3M" 1sec" 1 and 6.h X 10~ 2M - 1sec~ at 160°C. The r a t i o s of the back- to net forward-reaction rate constants are k-j f o r the C u ^ a c t i v a t i o n step and k- 3 for the Cu"'" a c t i v a t i o n step. These k 2 k 4 have values of approximately 0.13 and 0 A 5 r e s p e c t i v e l y at l60°C. In perchlorate solutions the rates were a l s o consistent with the rate law applying to sulphate solutions i f a necessary c o r r e c t i o n due to perchlorate decomposition was taken i n t o account. In t h i s system the second term of t h i s rate law was found to be much smaller and more d i f f i c u l t to resolve. For the f i r s t term the value of k i was found to be 6.7 X 1 0 - 3M _ 1sec at 160°C and the value of k-^ was 0.51. k 2 Exchange experiments with deuterium i n place of hydrogen were also done. These gave rates consistent with previously proposed mechanisms, but i n perchlorate solutions much higher exchange rates were observed than i n sulphate solutions. The indi c a t e d value of k 3 i s approximately the same i n perchlorate as i n sulphate solutions and the indic a t e d value of k- 3 i s much k 4 greater i n perchlorate solutions. ACKNOWLEDGEMENTS i i i o The author wishes to express his gratitude to Dr. E. Peters for his inspiring direction of this study and the advice, help, and encouragement given throughout. He wishes to thank the members of the faculty and staff of the Department of Metallurgy for their continued support and interest in this work. The cooperation of Dr. J. A.Stone of Atomic Energy of Canada Limited in performing the mass spectrometric analyses is gratefully acknow-ledged. The author wishes to thank the National Research Council for the award of two studentships (I96O-62) and for financial aid through the N.R.C. Grant No. A-1^63. The award of a Fellowship (1959-60) by the Consolidated Mining and Smelting Company Limited is gratefully acknowledged. TABLE OF CONTENTS Page INTRODUCTION 1 Hydrogen Reduction Reactions i n Sol u t i o n 1 Mechanism of Copper Catalyzed Hydrogen Reduction Reactions i n Aqueous Solutions h Purpose and Scope of the Present Investigation 9 EXPERIMENTAL 10 Materials 10 Apparatus 10 Experimental Procedure and Analyses 11 RESULTS AND DISCUSSION 15 Reduction of Cupric Perchlorate 15 The E f f e c t of A c i d i t y on Rates . . 17 The E f f e c t of Cuprous Ions on Rates 2k The E f f e c t of Cupric Ions on Rates 27 Disproportionation E q u i l i b r i a and K i n e t i c s JO The Integrated • Rate Law . . jh-Reduction of Cupric Sulphate kl i The E f f e c t of A c i d i t y on Rates 1+2 The E f f e c t of Cupric Sulphate on Rates 50 The E f f e c t of Free Sulphate on Rates 55 Summary of Rate Constants 62 The Integrated Rate Curve 65 The E f f e c t of Temperature car Rates . . . .| 65 The Deuterium .Exchange Experiments 70 •The A c t i v a t i o n of Hydrogen by Cuprous Ions 8 l CONCLUSION ' . 85 REFERENCES 87 APPENDIX A - Report on Research Work f o r the Period of May 1st to'September 1st , i960 " 91 APPENDIX B - Rate Measurements f o r Experiments i n Perchlorate System 9k APPENDIX C - Determination of the Perchlorate Reduction Rate Constant k ^ 97 APPENDIX C - Thermodynamic Data f o r C a l c u l a t i n g A F T f o r the Disproportionation Reaction 100 V . Table of Contents Continued Page APPENDIX E - Integrated. Eate Curves f o r the Perchlorate System . 101 APPENDIX F - Estimation of Hydrogen Ion Concentration i n Sulphate System at l60°C 10k APPENDIX G - Rate Measurements f o r Experiments i n Sulphate System 105 APPENDIX H - The Integrated Rate Curve f o r the Sulphate System . 107 APPENDIX I - Rate Curves and Rates of Exchange•Experiments . . . 108 v i . LIST OF FIGURES Page Figure 1. Schematic Diagram of Experimental Apparatus with Pressure Sampling System . . . 13 Figure 2. T y p i c a l Rate Plots, of [Cu +] vs Time Before and A f t e r D i s -proportionation 16 Figure 3• Rate Curves as a Function of I n i t i a l P e r c h l o r i c Acid Concentration . . . . . 18 Figure k. Plots of | ^ d ^ u + ^ 1 vs' [H +] at D i f f e r e n t [Cu +] Levels 19 Figure 5. Plots of (Rate F u n c t i o n ) " 1 vs [H +] at D i f f e r e n t [Cu +] Levels 23 Figure 6. Rate Curves f o r Determination of Cuprous A c t i v i t y . . . . 25 Figure "J. Dependence of Rate on Cuprous Concentration 26 Figure 8. Rate Curves as a Function of I n i t i a l Cupric Perchlorate Concentration . . . " 28 Figure 9. Plots of [Cu + +]/(Rate Function) vs [ C u + + ] _ 1 at D i f f e r e n t [Cu +] Levels 29 Figure 10. Rate Plots of [Cu +], [ C u + + ] and Amount of [Cu + + ] Depleted; Together with a Calculated Curve as a Function of [ C u + + ] and K = 26 M"1 33 Figure 11. Comparison of Experimental and Calculated Rate Curves . . 37 Figure 12. Comparison of Experimental and Calculated [ C u + + ] Rate Curves f o r Reduction in"the Presence of M e t a l l i c Copper 39 Figure 13. Rate Curves as a Function of I n i t i a l Sulphuric A c i d Concentration U3 Figure 1 .^ Plots of Rate vs.CCu"1"] as a Function of A c i d i t y kk Figure 15. Plots of I 1 vs [H +] f o r Acid Series of Experiments . . . k6 L i s t of Figures Continued Page Figure 16. Plot of I vs [H +]' f o r Acid Series of Experiments . . . . 47 S Figure 17. Plots of S" 1 vs [H +] and [H ] 2 f o r A c i d Series of Experiments 49 Figure 18. Rate Curves as a-Function of I n i t i a l Cupric Sulphate Concentration 51 Figure 19. Plots of Rate vs [Cu^] as a Function of I n i t i a l Cupric Concentration 53 Figure 20. Plots of S vs [ C u 1 1 ] and. [ C u 1 1 ] 2 f o r Cupric Series of Experiments 5^ Figure 21. Plot of [ C u ^ ] vs 1 f o r Cupric Series of Experiments 56 ~ i [ c u ^ T Figure 22. Rate Curves as a Function of Free Sulphate Ion Concent-r a t i o n 58 Figure 23. Plots of Rate vs [Cu"1"] as a Function of Free Sulphate Concentration 59 Figure 24. Plot of I vs Free [ 8 O 4 ] f o r Sulphate Series of Experiments 60 Figure 25. Plot of S vs [ S O 4 ] f o r Sulphate Series of Experiments . . 61 Figure 26. Comparison of Experimental and Calculated Rate Curves . . 64 Figure 27. Rate Curves as a Function of Temperature 66 Figure 28. Plots of Rate vs [Cu^] as a Function of Temperature . . . 67 Figure 29. Plots of log kj, and log k 3 vs T - i 68 Figure 30. Rate Curves of T o t a l Cu 1, HD, H 2 and (HD + 4H2) Experiment D2-A 72 Figure 31. Rate Curves of T o t a l Cu 1, HD, H 2 and (HD + 4H2) Experiment D2-B 73 Figure 32. Rate Curves of T o t a l Cu +, HD, H 2 and (HD + 4H2) Experiment D2-C 74 v i i i . L i s t of Figures Continued Page Figure 33. Rate Curves of T o t a l Cu 1, HD, D 2 and (RD + k~D2) Experiment H2-D 75 Figure 34. Plots of Net Forward Rate and Exchange Rate vs Cu 1 for, Each Exchange Experiment 77 Figure 35- Plots of Exchange Rate over Net Forward Rate vs Cu* f o r Each Exchange Experiment 80 ix„ LIST OF TABLES Page Table I. Values of k i and Obtained from Figure 5 and • E a r l i e r S t u d i e i .; 22 Table I I . Summary of Values of k x and Obtained i n the Perchlorate System . . . 2 30 Table I I I . Values of the Equ i l i b r i u m Constant K f o r the Cu +-Cu + +-Cu° Eq u i l i b r i u m at 160°C and Varying [H +] . 31 Table IV. Experimental Conditions f o r Sulphate Series and • Estimated Free Sulphate,•Bisulphate and Hydrogen Ion Concentrations 57 Table V. Summary of Rate Constants f o r Sulphate Solutions at 160°C 62 Table VI. Values of k i , k 3 and Dissolved H 2 at D i f f e r e n t Temperatures 65 Table VII. Summary of A c t i v a t i o n Energies and Entropies 69 Table VIII. Experimental Conditions f o r Exchange Experiments . . . 71 Table IX. Values of and from'Exchange Experiments . 78 k 2 k4 J KINETICS OF COPPER REDUCTION BY HYDROGEN FROM AQUEOUS. SOLUTIONS INTRODUCTION Hydrogen Reduction Reactions i n Solutions The p r e c i p i t a t i o n of copper p o w d e r ^ f r o m aqueous solutions of cupric s a l t s by the a c t i o n of hydrogen occurs r e a d i l y at elevated temperatures and pressures, and since the discovery of t h i s r e a c t i o n considerable work has been done to e s t a b l i s h i t s mechanism. . I t was shown from the beginning of t h i s work that the p r e c i p i t a t i o n of copper was e a s i l y distinguishable from that of n i c k e l and cobalt ' , which required seeding with nucleating powder to obtain reduction, while such seeding was unnecessary f o r copper. The n i c k e l and cobalt reduction mechanisms were therefore heterogeneous i n nature and based on the c a t a l y t i c properties of the surfaces of these metals toward hydrogen, while the copper reduction mechanism could be described as homogeneous as no metal surfaces were needed f o r the reaction to proceed,-nor d i d they s i g n i f i c a n t l y a f f e c t the re a c t i o n rates. These reactions are c a r r i e d out i n high pressure reactors at temperatures between 150 and 250°C and hydrogen p a r t i a l pressures up to 400 p s i g . The metals are obtained i n powder form and are at l e a s t as pure as e l e c t r o l y t i c a l l y r e f i n e d products of commerce. In the case of copper a process^ has been developed whereby the cupric species i n ammonium sulphate leach solutions i s reduced with hydrogen to me t a l l i c powder with a demonstrated p u r i t y of 99«51$> and.closely c o n t r o l l e d screen size - 2 -k down to -320 mesh. A modification of t h i s process i s employed at present f o r the recovery of copper powder mostly from scrap brass, at a rate of about 20,000 l b per day. Interest i n the homogeneous reduction of cupric solutions has centered l a r g e l y around k i n e t i c studies of t h i s and r e l a t e d reactions, p a r t i c u l a r l y those where C u + + catalyzes the hydrogen reduction of oxidants such as dichromate"'"^' 12 and molecular oxygen . The chief reason f o r i n t e r e s t i n these reactions has been to elucidate q u a n t i t a t i v e l y the mechanism of a c t i v a t i o n of hydrogen by k i n e t i c experiments i n a homogeneous system, a task that has been found to be experimentally much simpler than one of obtaining u s e f u l measurements i n such heterogeneous systems as n i c k e l and. cobalt where metal surfaces serve as c a t a l y s t s . Interest i n the k i n e t i c s of the copper catalyzed hydrogenation of oxygen or i g i n a t e d from the possible a p p l i c a t i o n of t h i s r e a c t i o n f o r the r e -combination of the r a d i o l y t i c decomposition products of water i n aqueous homo-12 geneous nuclear reactors . The e a r l i e s t recorded work on the hydrogen reduction of cupric s a l t s 15 i n aqueous s o l u t i o n to the .metallic state i s that of I p a t i e f f and.Werschowski , although they probably d i d not r e a l i z e then the homogeneous nature of t h i s reaction. Ik 15 This was probably suspected f i r s t by Halpern and Dakers ' y who studied the homogeneous p r e c i p i t a t i o n of Cu 2 0 from cupric acetate solutions which took place according to the o v e r a l l reaction 2 CuAc 2 + H 2 + H 2 0 —»» Cu 2 0 + k HAc (1) The k i n e t i c s of t h i s reaction, between 80 to l40°C and buffered between pH 3 "to 5 could, adequately be expressed by a second order rate law of the form - d[CuAc 2] = k[CuAc 2][H 2] . . . . . ( 2 ) dt where Ac = acetate and [H 2] = molarity of d i s s o l v e d hydrogen. - 3 -Subsequently Peters and Halpern"^ showed that substrates such as dichromate or iodate were reduced with hydrogen i n the presence of cupric acetate, and thus established the homogeneous c a t a l y t i c property of cupric ions i n the 16 hydrogen reduction of aqueous so l u t i o n s . These workers also studied the e f f e c t on dichromate reduction rates of complexing C u + + with various ligands. By choosing as a standard the perchlorate system, i n which C u + + i s believed to be complexed only as the aquo ion, they established that CI", S0 4 and carboxylate ions such as acetate, propionate and butyrate enhanced the rates. This enhancement of the cupric a c t i v i t y by anions was ascribed to t h e i r a b i l i t y to act as proton acceptors i n the hydrogen a c t i v a t i o n reaction and thereby to lower the a c t i v a t i o n energy. On 'the other hand, a lowering of the cupric a c t i v i t y by such ligands as ethylenediamine and glycine was a t t r i b u t e d to strong metal-ligand bonding. It i s noteworthy that several other metal ions besides cupric can a c t i v a t e hydrogen and e i t h e r become reduced d i r e c t l y or a l t e r n a t e l y act as homogeneous c a t a l y s t s f o r the reduction of substrates i n aqueous so l u t i o n s . Among these are A g + ^ > ^ } Ag+ amine complexes"1"^,' H g + + 20,21^ g g 2 + + 2 1 a n c \ =22 - 2 3 c e r t a i n complexes of the platinum group metals such as P d C l 4 , RhCl 6 I I I 2h 25 26 and chloride complexes of Ru ' . Moreover, i t was reported recently that Cu"'' i n sulphate solutions catalyzed the hydrogen reduction of Cu"'"*, with Cu"' j]U -j i- | | j being more act i v e than the l a t t e r . Ni , Fe" , Co and Cr , on the other hand, were found t o be i n a c t i v e up to 260°C (Appendix A). Related to these are s i m i l a r reactions i n non-aqueous solvents. For example, cuprous acetate d i s s o l v e d i n quinoline was found to'catalyze the 27 hydrogenation of quinone to hydroquinone or the^retacttiwam of cupric acetate, Pfi which i t s e l f i s i n a c t i v e i n t h i s solvent . Also, cuprous and s i l v e r acetate 29 have been found to e x h i b i t c a t a l y t i c a c t i v i t y i n pyridine and dodecylamine - k -i n the reduction of s i l v e r and cupric acetate, cupric acetate again being i n a c t i v e . On the other hand, both cupric and cuprous heptanoates were observed to a c t i v a t e hydrogen i n such organic media as diphenyl, octa-decane and heptanoic a c i d i n the reduction of cupric ions, with cuprous being the more active of the two30. I t i s noteworthy that only few metal ions possess the a b i l i t y to acti v a t e hydrogen,-whose inertness has been ascribed to i t s high d i s s o c i a t i o n energy (ca^ 10J kcal),and the closed s h e l l e l e c t r o n i c configuration of the molecule. This property has been r e l a t e d to the r e l a t i v e e l e c t r o n a f f i n i t i e s of the corresponding (gaseous) ions which show that the ions that a c t i v a t e hydrogen homogeneously have higher e l e c t r o n a f f i n i t i e s and therefore lower l y i n g vacant o r b i t a l s than ions not possessing t h i s pr©perty31>32. i t was further suggested that the optimum e l e c t r o n i c configuration f o r c a t a l y t i c a c t i v i t y e x i s t s when the d - s h e l l i s f i l l e d or nearly f i l l e d but when the ion has or can make a v a i l a b l e by electron promotion empty d - o r b i t a l s . This explains for example the a c t i v i t y of C u + ( 3 d 1 0 ),and Ag + ( 4 d 1 0 ) . The lack of c a t a l y t i c a c t i v i t y of the. isoelectronic, Z n + + and T l + + + ( 3 d . 1 0 ) and.Cd + + ( 4 d 1 0 ) has been ascribed to t h e i r i n a b i l i t y to promote electrons due to a l a r g e r separation of the d- and s - l e v e l s r e s u l t i n g from a higher nuclear charge. Mechanism of Copper Catalyzed Hydrogen Reduction Reactions i n Aqueous Solutions The mechanism by which cupric ions a c t i v a t e hydrogen i n reactions involving the reduction of copper or other o x i d i z i n g substrates i n aqueous solutions i s given by the following equations: - 5 -C u + + + H 2 CuH^' + H + or *2 k _ i CuH + + C u + + k s 2Cu + + H + . . . . . ( 4 ) + f a s t „ , . 2Cu Cu° + C u + + . . . . . ( 5 ) K Cu + + Ox , f a s t C u + + + Products . . . . . ( 6 ) where Ox = oxidant. This mechanism was established by Halpern and coworkers^ i n perchlorate solutions where C u + + i s believed not to be complexed except as the aquo ion. It proceeds by the 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 n the a c t i v a t i o n step r e s u l t i n g i n the formation of a cupric hydride intermediate and a hydrogen ion, followed by reaction of the intermediate with another cupric ion and the production of two cuprous ions and a proton. The cuprous ions w i l l e i t h e r disproportionate when an equilibrium l e v e l has been reached ++ or be oxidized to Cu i n the presence of oxidants, e.g., dichromate. The rate law derived from t h i s mechanism by a steady state approximation i n CuH + i s given by - d[R a] = k x [ C u + + ] 2 [ H 2 ] .....(7) dt' , k ^ i [ H+] + [ C u++] k 2 - 5 - l - l k-i with k x having a value of 9-5 x 10" M sec and Y^T & value of 33 0.26 at 110°C from dichromate reduction rate measurements. The a c t i v a t i o n energy f o r the hydrogen a c t i v a t i o n step (equation 3) was found to be about 26 k c a l / m o l e 1 1 . According to equation 7 r e a c t i o n rates may appear to be e i t h e r f i r s t or second order i n [Cu + +] depending on the r e l a t i v e magnitudes of the two terms i n the denominator. For example i f [H +] <^ [ C u + + ] , the rate expression k 2 w i l l reduce to -d[H 2j = k ! [ C u + + ] [ H 2 ] . . . . . ( 8 ) dt - 6 -A rate law of t h i s form was i n fa c t observed by Peters and Halpern^ 1 between 80 and l40°C.at 0.1 M> [Cu(C104) 2 ] and 0.004 to 0.1 M [ H C 1 0 4 ] . I t i s the same as that obtained by Halpern and Dakers f o r cupric acetate s o l u t i o n at pH 3 t o 5 , as shown above. Macgregor and' Halpern subsequently studied the copper p r e c i p i t a t i o n i t s e l f at temperatures between 150 and 175°C. i n both perchlorate and sulphate solutions. Although they d i d not analyse the complete rate curves they'were able t o check out the above mechanism (equations 3* ^> and 5) i n the per-chlorate system from i n i t i a l rate measurements, and obtained the following constants f o r the rate law (equation 7) at l 6 0°C: k x = 7 .5 X l O ^ M ^ s e c - 1 , k-jL = 1.3. This value of k i i s consistent with k x = 4 . 5 X 10" 3M" 1sec - 1, , k 2 11 obtained by extrapolation of the Arrhenius p l o t i n the dichromate work . I t was therefore apparent that i n i t i a l copper reduction rates and the homogene-ously catalyzed reduction of dichromate y i e l d e d the same values under the same conditions and thus the same mechanism appeared applicable to both systems. The l a r g e r value of k-^ (1 . 5 ) at 160°C than that at 110°C ( 0 . 2 6 ) 5 5 suggested k 2 that t h i s r a t i o might be increasing with temperature. However, McDuffie and coworkers-1-^ were not able to f i n d any acid •dependence at 250°C i n t h e i r k i n e t i c studies of the C u + h - c a t a l y z e d hydrogen-oxygen recombination re a c t i o n although t h i s would be expected i f the above mechanism were extrapolated t o that temperature with oxygen replacing dichromate as the oxidant. Their solutions were 0.001 M i n [ C u + + ] and from 0 .005 to 0 .050 M i n [ H C I O 4 ] . Under these conditions an a c i d dependence should have been observable^ unless k - i was much smaller at 250°C than the 0 .26 value at k 2 110°C. Hence these r e s u l t s suggested a decrease i n k_ x with increasing temp-k 2 erature which was not consistent with the observations, of the copper reduction react • 34 ion^ , & An a c i d e f f e c t i s observable when k - i [H +] i s of the order of [ C u + + ] or greater. k 2 To resolve t h i s anomaly Hahn arid Peters35 studied the dichromate reaction again, t h i s time i n the 160 and 200°C range. Because of the strong temperature e f f e c t , which doubled the re a c t i o n rates, f o r every 10°C increase i n temperature the cupric perchlorate concentration was lowered from 0.10 M (used e a r l i e r i n the range of 80 to l 4 0 ° C t o 0.02 M and the i n i t i a l d i -chromate concentration r a i s e d s u b s t a n t i a l l y i n order to obtain re a c t i o n times long enough f o r good rate measurements. The r e s u l t s of t h i s study showed that a dichromate dependence appeared under these conditions that indicated a d i r e c t attack by the oxidant on CuH +, the re a c t i v e intermediate. The former mechanism (equations 3, 4, 6) s t i l l applied but with the add i t i o n of a supplementary reaction to account f o r the dichromate dependence, i . e . , CuH + + C r V I ^ C u + + + Products .....(4a) The rate law resulting by i n c l u s i o n of equation 4a i n t o the mechanism i s r + + i r Ikg_ [ C u ++] + ka_ [ C r V I ] \ dt ,[H+J + k 2 [ C u ^ J + k 3 [CrVlJ The values obtained at l60°C f o r k x, g2-j- and were 5.4 X 10" 3M- 1sec- 1 > i k o k-a 2.7 and 42 r e s p e c t i v e l y . I t was found also that both g ^ — and ^sa^- were quite i n s e n s i t i v e to temperature, being 2.6 and 49 r e s p e c t i v e l y at 200°C. I t i s apparent from equation 9 that the a c i d dependence would f a l l o f f i f [Cr ] y [H +], and by trancellati on the rate law would take the form k_! of equation 8. I f oxygen reacts with CuH + d i r e c t l y , l i k e Cr^-, the anomaly i n the rate law observed by McDuffie et a l . " ^ could be explained by replacing ^£L_ [ C r ^ ] with j ^ 4 - - [ 0 2 ] ^ i n equation 9, assuming that the rate constant r a t i o s are temperature i n s e n s i t i v e up to 250°C. & More than one species of Cr • i s present i n s o l u t i o n at these temperatures and a c i d i t i e s (see reference 36). - 8 The inverse of i s 0.37 at l60°C which i s comparable to the value of = 0.26 at 110°C^^. However, the value of 1.3 from the copper k 2 p r e c i p i t a t i o n work i s considerably higher and represents >;an a d d i t i o n a l anomaly. The r e s u l t s of the dichromate work now appear to contain conclusive evidence f o r the v a l i d i t y of the mechanism i n c l u d i n g equation ha. and of the rate law given i n expression 9 f Q r & H copper catalyzed reactions i n which an oxidant e x i s t s that i s capable of preventing the appearance of the cuprous state. In the p r e c i p i t a t i o n of m e t a l l i c copper, however, considerable amounts of cuprous ions make t h e i r appearance at l e a s t t r a n s i e n t l y and a knowledge of t h e i r r o l e i n the k i n e t i c s i s e s s e n t i a l for the complete understanding of the reaction mechanism. In t h i s regard i t i s of i n t e r e s t that Dunning and Potter reported a c a t a l y t i c a c t i v i t y of cuprous i n the hydrogen reduction of cupric sulphate solutions which accounted f o r a considerable portion of the observed rates. In perchlorate and sulphate solutions no cuprous a c t i v i t y was reported by Macgregor and Halpern-^ . Their copper reduction curves were analyzed by measuring i n i t i a l rates only, and under these conditions C u + l e v e l s never became s i g n i f i c a n t . Another point that needed explanation was the marked slowing down of the reduction rates observed by Macgregor and Halpern, which was much greater than predicted by the rate law (equation 7)- Although the rate slows down as a-result of decreasing [ C u + + ] and increasing [H +] i t should not decrease to nearly zero a f t e r only about 60$ of a l l C u + + has been reduced (see f o r example Figure 11)j p a r t i c u l a r l y since thermodynamic estimates by Macgregor^T in d i c a t e d that the reaction-at t h i s point was f a r from equilibrium. Hence, f o r the complete understanding of t h i s system, p a r t i c u l a r l y the r o l e of C u + i n the k i n e t i c s , further work appeared necessary. - 9 -Purpose and Scope of the Present Investigation In view of the foregoing discussion i t i s evident that several points s t i l l remained to he c l a r i f i e d f o r a complete understanding of the mechanism and rate law of the hydrogen reduction of cupric ions i n aqueous solutions. Accordingly the present i n v e s t i g a t i o n was undertaken with the following objectives. 1. To explain the large value of obtained by Macgregor and Halpern, i n the copper reduction work. 2. To investigate the cuprous e f f e c t i n both perchlorate and sulphate solutions. 3. To explain the marked slowing down of rates i n the l a t e r stages of copper reduction from perchlorate solutions as observed by Macgregor and Halpern. k. To e s t a b l i s h whether m e t a l l i c copper appearing a f t e r the disproportion-a t i o n of C u + had any e f f e c t on the reaction k i n e t i c s . The copper reduction mechanism predicts that part of the hydrogen consumed w i l l be regenerated from aqueous protons i n the back reaction, equation 3-In order to v e r i f y t h i s p r e d i c t i o n a number of isotope exchange experiments were performed by r e p l a c i n g hydrogen with deuterium i n e i t h e r the gas or aqueous phase and measuring the rate of appearance of HD i n each case. Since cuprous ions disproportionate r a p i d l y on cooling t h i s reaction - ^4 was u t i l i z e d by Macgregor and Halpern-^ to measure rates of copper reduction. In the present work, however, i t was decided to determine the [Cu +] l e v e l s at experimental temperatures i n order to obtain rate curves that would show the e f f e c t of cuprous on the reduction rates. Hence, part of the experimental problem i n t h i s study was to develop a method of determining high temperature'cuprous concentrations. - 10 -EXPERIMENTAL Materials A l l materials used were of Baker and Adamson Reagent Grade q u a l i t y . Stock solutions of 2 M cupric perchlorate and about 1.3 M.cupric sulphate were prepared by d i s s o l v i n g excess cupric oxide powder i n a hot aqueous so l u t i o n of the appropriate a c i d , f i l t e r i n g a f t e r d i s s o l u t i o n was complete and d i l u t i n g s u f f i c i e n t l y to prevent c r y s t a l l i z a t i o n of the copper s a l t s at room temperature D i s t i l l e d water was used throughout. Hydrogen, Nitrogen and'Helium of commercial grade were supplied by Canadian L i q u i d A i r Company i n cylinders and used without further p u r i f i c a t i o n . For the exchange experiments 100 l i t e r s (NTP) of D 2 was obtained at 500 p s i g i n a 2.8 l i t e r c y l i n d e r and a l s o 1200 grams of D 2 0 i n 100 gram ampoules. Both were supplied by the Liquid'Carbonics D i v i s i o n of the General Dynamics Corporation. Both had a p u r i t y of bet t e r than 99*5 mole the chief impurity i n D 2 being approximately 0.3^ mole % HD. Apparatus A l l experiments were performed i n e i t h e r one of two autoclaves capable of working pressures up to 1000 p s i g at 300°C. One of these, of one-gallo n capacity, was manufactured by Autoclave Engineers Inc., the other a 2 - l i t e r v e s s e l , by the Parr Instrument Company. Both were of s t a i n l e s s s t e e l , , but, because of the corrosive solutions used i n t h i s work, they were l i n e d with titanium. These l i n e r s were f i t t e d c l o s e l y into the v e s s e l ^ and provided,with A S h r i n k f i t t e d i n t o the Parr v e s s e l . - 11 -a welded flange at the top which served as the gasket seat. In t h i s way possible entrance of the experimental solutions or steam,into the annular space between the l i n e r and v e s s e l was prevented. A l l other parts i n contact with the s o l u t i o n , such as sampling-tube and -valve, s t i r r e r , and thermowell were a l s o of titanium. The lower end of the sampling tube was provided with a f r i t t e d glass f i l t e r which was attached with a t e f l o n adapter, i n order to prevent m e t a l l i c copper p a r t i c l e s from entering the sampling system. The s t a i n l e s s s t e e l autoclave covers were protected from the splashing so l u t i o n with t e f l o n s h i e l d s . The s t i r r e r shafts were b e l t driven at speeds between 700 and 1000 rpm. The solutions were heated with external r i n g type gas burners and,the gas flow accurately c o n t r o l l e d with a Brooksmite twin flow gas meter. Temperature con t r o l was maintained to within * 0.3°C with e i t h e r a Leeds and Northrup Micromax.controller-recorder or a Thermistemp temperature c o n t r o l l e r made by the Yellowsprings Instrument Company. Pressure was regulated with standard high pressure regulators and measured with a Bourdon type pressure gauge to within * 3 p s i g . The gauge c a l i b r a t i o n was checked p e r i o d i c a l l y against steam pressure at various temperatures. Experimental Procedure and Analyses The experimental procedure comprised the following steps: 1. f l u s h i n g of the gas space above the s o l u t i o n to purge the r e s i d u a l a i r with nitrogen or helium, 2. heating of the s o l u t i o n to the desired temperature under the i n e r t atmosphere at a pressure close to the t o t a l hydrogen and steam pressure during reduction, - 12 -3- f l u s h i n g of the i n e r t gas at temperature, k. a d d i t i o n of hydrogen and, 5. p e r i o d i c sampling of the s o l u t i o n to follow the rate of appearance of cuprous ions. The C u + concentration was determined by o x i d i z i n g the sample solu t i o n with a measured volume of dichromate s o l u t i o n . The excess dichromate was analyzed with a Beckman Model DU spectrophotometer at 350 m u using s i l i c a c e l l s , and the amount of C u + c a l c u l a t e d by d i f f e r e n c e . No interference from absorption by both C u + + or C r + + + took place at t h i s wavelength. Sampling posed a s p e c i a l problem i n t h i s study because cuprous ions disproportionate r a p i d l y on cooling and thus cause low r e s u l t s i n the dichromate method of a n a l y s i s . Hence a method was devised f o r removing s o l u t i o n samples from the autoclave and o x i d i z i n g them with dichromate before disproportionation from, cooling could occur. This sampling arrangement i s shown schematically i n Figure 1. The sample s o l u t i o n flows v i a 0.062" O.D. X 0.052" I.D. titanium tubing i n t o a 100 ml volumetric f l a s k located i n a v e s s e l which i s pressurized s u f f i c i e n t l y to prevent f l a s h i n g of the s o l u t i o n . A measured volume of d i -chromate s o l u t i o n i s introduced from a pressure "burette" v i a a titanium "Tee" and reacts with the sample s o l u t i o n on i t s way to the f l a s k . The pressure i n the "burette" i s adjusted i n i t i a l l y to that i n the autoclave and during sampling i t drops to that i n the sampling v e s s e l . Sampling time was 7 to 15 seconds depending on the autoclave pressure, and the r e s u l t i n g sample volumes 55 to 50 ml. These volumes were determined by difference a f t e r cooling the s o l u t i o n to room temperature and f i l l i n g the f l a s k with d i s t i l l e d water from a burette. As a further precaution the sampling valve body, the "Tee" and the interconnecting titanium tube were wrapped with an Electrothermal heating tape g a s - > T inlet ^ I stirrer d o Experimental -Autoclave gas inlet f r i t t e d 'gas f i l t e r V - h Pressure "Burette" ,062" O.D. X .032" I.D. tubing Sampling Vessel gas r i n l e t 100 ml sampling flask Figure 1. Schematic Diagram of Experimental Apparatus with Pressure Sampling ..System - Ik -and heated to a temperature close to the experimental. I t was a l s o found necessary to prepare the dichromate solutions with oxygen free water and keep them under a nitrogen atmosphere at a l l times, because small amounts of dissolved oxygen reacted with C u + and lowered the dichromate consumption. Nitrogen was a l s o used i n the pressure sampling v e s s e l . The dichromate method, of analysis was checked by p r e c i p i t a t i n g C u + with NH4CNS,'NaBr and KI or by l e t t i n g C u + disproportionate i n the sample f l a s k on cooling to room temperature. Analyses were then made by d i s s o l u t i o n with n i t r i c a c i d and e l e c t r o l y s i s . The r e s u l t s agreed.well with those obtained by the dichromate method, except i n the disproportionation procedure which - -y i e l d e d generally lower C u + values. This may have been due to incomplete d i s p r o p o r t i o n a t i o n or to a c c i d e n t a l oxygen contamination. T o t a l cupric ( i . e . cupric and oxidized.cuprous) was determined e i t h e r ^8 e l e c t r o l y t i c a l l y or by t i t r a t i o n with EDTA s o l u t i o n ^ using Murexide as i n d i c a t o r . [H +] was determined by t i t r a t i o n with sodium tetraborate-^, [S0 4] as barium sulphate, and [CI ] appearing i n perchlorate solutions, by the Volhardt method-59. In the exchange experiments gas samples were taken, at the same time as l i q u i d samples, i n t o evacuated sample b o t t l e s of about 1.5 ml capacity. The gas mixtures were analyzed with a mass spectrometer for D 2, HD and H 2 content by the Research Chemistry Branch, • Chemistry and'Metallurgy D i v i s i o n , Atomic Energy of Canada Limited, Chalk River, Ontario. RESULTS AND DISCUSSION Reduction of Cupric Perchlorate The k i n e t i c experiments were conducted under various i n i t i a l conditions ranging from 0.01 to 0.10 M-[Cu(C10 4) 2] and 0.01 to 0.10 M [HC10 4] with a hydrogen p a r t i a l pressure of 10 atm. Reduction rates were measured at s t i r r i n g speeds varying between 'JOO and 1000 rpm. No differences were observed at these extremes, from which i t was concluded that the rates were not c o n t r o l l e d by a mass transport mechanism. Moreover i t was found that no reduction took place i n the absence of hydrogen. The experimental temperatures ranged from 160 to 220°C$ however most experiments were performed.at l60°C. T y p i c a l rate curves are shown i n Figure 2 as plot s of [Cu +] vs time. I t i s evident that the i n i t i a l rates and the maximum [Cu +] l e v e l s .are a function of the s t a r t i n g C u + + concentrations. The maxima of the upper two curves occur at the onset of C u + disproportionation which takes place according to the following stoichiometry K 4—4-2 C u + - — C u ° + Cu . . . . . ( 5 ) r where the disproportionation constant i s given by K = [Cu + + ] . (10) T C u ^ F A f t e r the s t a r t of disproportionation the [Cu +] l e v e l s t a r t s to f a l l since i t remains i n equilibrium with the d e c l i n i n g C u + + content of the sol u t i o n . I t i s also evident i n Figure 2. that below an i n i t i a l [Cu + +] of 0.03 M no disproportionation occurs at the experimental temperature. This may r e s u l t from the rate becoming s u f f i c i e n t l y slow so that [Cu +] cannot b u i l d up to the disproportionation l e v e l within the duration of the experiment. - 17 -A n a l y t i c a l r e s u l t s on samples a f t e r a s i g n i f i c a n t amount of reaction had. taken place revealed a copper to a c i d stoichiometry consistent with the o v e r a l l equations H 2 + 2 C u + + 2 C u + + 2 H + .....(11) and H 2 + C u + + e» Cu° + 2 H + .....(12) Equation 11 only applies to conditions before disproportionation at the experimental temperature, while both equations apply to conditions a f t e r disproportionation has begun. Under the former conditions the reaction rate - d[H 2] i s simply equal to + 1 d[Cu +] while a f t e r disproportionation dt 2 dt A begins the hydrogen consumption rate i s - d[Cu ] - 1 d[Cu ] . Some dt 2 dt + ++ experiments were performed with Cu i n i t i a l l y e q u i l i b r a t e d with Cu and met a l l i c copper to study the reduction k i n e t i c s under conditions at which the disproportionation reaction occured from the s t a r t of a run. The E f f e c t of A c i d i t y on Rates A number of experiments were performed to investigate the e f f e c t of a c i d i t y on the copper reduction rates, with i n i t i a l [HC104] varying between 0.015 a n ( i 0.1 M and [ C u + + ] o being 0.03 M. The rate curves of t h i s series are shown i n Figure 3 . Rates were measured along these curves at f i v e d i f f e r e n t [Cu +] l e v e l s and are shown p l o t t e d i n Figure k as inverse rate, i . e . , 1 d[Cu +] I , against [ H + ] . These plo t s are non-linear e s p e c i a l l y for the x2 dt , higher [Cu ] l e v e l s and• suggest a square dependence of r a t e " 1 on [H +]. A rearrangement of equation 7 requires that such a p l o t of inverse rate vs [H +] should be l i n e a r with an intercept given by ft Rate measurements f o r each experiment are l i s t e d i n Appendix B. ftft The intercepts of the curves i n Figure k were ca l c u l a t e d t h e o r e t i c a l l y with equation 13 using kj. = 5.4 X lO^M'-'-sec"1 55 because they were d i f f i c u l t to estimate as a r e s u l t of the n o n - l i n e a r i t y of the p l o t s . 120 2*»0 360 480 600 Time mirutes Fig-gre 5 • Rate Curves as a Function of I n i t i a l P e r c h l o r i c A c i d Concentration; 0.03 M[Cu(C10 4 )]°, 10 atm H 2, l60°C „ - 19 -o CQ I CO I o X! 12 10 6 U 4 L 2 L 20 Figure k. ho 60 [HC10 4] ,M X 103 Plots of 1 d [ C u + ] \2 dt Di f f e r e n t [Cu +] Levels; 0.03 M[Cu"'"r]0, 10.atm H 2 , 160°C vs.-[H +] at 120 - 2 0 -and a slope corresponding to s = k P kTrcu^FTlsT ( i 4 ) This r e l a t i o n s h i p assumes that there are no i n t e r f e r i n g side reactions that consume hydrogen by the copper a c t i v a t i o n route but do not reduce e i t h e r cupric or cuprous s t o i c h i o m e t r i c a l l y . During the experiments, however, chloride ions made t h e i r appearance due to decomposition of perchlorate. Since the stoichiometry of t h i s r e a c t i o n i s probably 8 Cu + + 8 H + + C 1 0 4 - P - 8 C u + + + C l " + 4 H 2 0 . . . . . ( 1 5 ) the appearance of chloride ions corresponds to a d d i t i o n a l hydrogen consumption and becomes a serious i n t e r f e r i n g side reaction An experiment performed under the usual conditions but without cupric perchlorate added to the s o l u t i o n f a i l e d to produce measurable amounts of C l i n d i c a t i n g that the presence of C u + i s probably responsible f o r perchlorate decomposition. Thus, i t became necessary t o take i n t o account the rate of perchlorate reduction i n order to obtain a meaningful k i n e t i c a nalysis of the experimental r e s u l t s . This was achieved by assuming a simple rate expression f o r the appearance of C l " of the form d[Cl"] = k [ C u + ] [ H + ] [ C 1 0 4 ~ ] ( 1 6 ) Perchlorate decomposition was found to be more serious at 1 8 0 to 2 2 0°C. - 21 -and incorporating i t i n the rate equation f o r the reduction of copper,i.e., 1 a f c u + J = k 1 [ C u + + ] 2 [ H 2 ] - - kA v [ C u + ] [ H + ] [ C 1 0 4 - ] . . . . . ( 1 7 ) 2 cit *__i.[H +MCu + +3 k 2 The value of k ^ was estimated by a graphical i n t e g r a t i o n of equation 16 to the time at which [Cl ] was measured, and c a l c u l a t e d with the following expression [ c i " ] + . *C1 ~ [CIO*-] f S r ^ + ia _ r ^ + T r t r + i ^ . . . . . ( 1 8 ) J ( [ C u + ] 2 + [ C u ] [ H + ] 0 ) dt where [Cu ] was measured d i r e c t l y from the rate curves. The d e t a i l s of the i n t e g r a t i o n are shown i n Appendix C. The value of k determined from eight d i f f e r e n t experiments was found to be k ^ = 2.07 X 10~ 4± 7$ M ~ 2 s e c _ 1 . Although no attempt was made to e s t a b l i s h i f the rate law for C l ~ appearance was r i g o r o u s l y correct as given by equation 16, i t appeared to be adequate f o r explaining the deviations from l i n e a r i t y of the plots i n Figure h. The corrected rate law, equation 17, can be rearranged to the form 1 - = £=1 [H +] 1 (19) l i l S p + l H ^ [Cu+][H +][C10 4-] jg [ C u + + ] 2 [ H 2 ] k l t C u + + ] [ H 2 ] Since 1 d[Cu +] + k k c l [ C u + ] [ H + ] [ C 1 0 4 _ ] = - d[H 2] the function 2 dt dt 1 . c a n ^e p l o t t e d against [H +] and should y i e l d 1 d[Cu +] + k k [ c y][lT][C104"] 2 dt L 1 a s t r a i g h t l i n e with intercept and slope of the same form as given by equations ± The f a c t o r k r e s u l t s from the stoichiometry of the re a c t i o n - 1 d[Cu +] - d[H 2] k d[Cl~] 2 dt ^ dt = = = = dt - 22 -13 and Ik, i . e . 1, and hiL x 1 • 'Plots of t h i s form k J c u + ' - H H a ] k 2 k 7 [ c V n l i T i 2 T are shown i n Figure 5. Intercepts and slopes were determined f o r each p l o t from k i -. - i J . the best s t r a i g h t l i n e drawn through the points and values of k x and ——^-calculated . k 2 They are l i s t e d i n Table I together with the values of the e a r l i e r dichromate^ 54 and copper^ reduction studies. TABLE I. Values of kn and k 2 Obtained from Figure 5 and E a r l i e r Studies Curve No. k i M _ 1 s e c - 1 k 2 Ref. 1 2 3 k 5 20.4 X 1 0 - 3 19.3 X 1 0 - 3 9.6 X 1 0 - 3 6.4 X 10" 3 4.0 X 10" 3 (5.4 * 15^)X 1 0 - 3 7.5 x 10- 3 3-0 2.3 O.85 0.54 0.28 0.37 * I 1.3 500 35 34 Average values of k j . and ^r^- were calculated from the values of curves 3> 4 and 5 only, and are k x = 6.7 X 10- 3M~ 1sec~ 1 and = O.56. The values obtained k 2 from curves 1 and 2 are inconsistent with the other values shown i n t h i s table. The discrepancy i n k x (hence £=A- ) i s probably due to the small values of k 2 the intercepts f o r these two curves i n Figure 5. Also the magnitudes of these intercepts are very s e n s i t i v e to the choice of the best st r a i g h t l i n e . Larger intercepts and smaller slopes g i v i n g more consistent values of these constants would be obtained i f the i n i t i a l rates of the low a c i d experiments were slower. They may be too f a s t due to a con t r i b u t i o n from a hydrolyzed cupric species of higher a c t i v i t y such as Cu(OH) . This would give r i s e to a c t i v a t i o n of hydrogen A Assuming the hydrogen s o l u b i l i t y to be equal to that of pure water, i . e . = 11.8 X 1 0 - 4 M atm" 1 at l60°C. See reference 40. Figure 5. Plots of (Rate F u n c t i o n ) - 1 vs. [H +] at D i f f e r e n t [Cu +] Levels; 0.03 M [Cu + +]°, 10 atm H 2, l60°C. - 2k -according to Cu(OH) + + H 2 k + ^ . CuH + + H 2 0 1 (20) k _ This explanation i s supported by the observation (seepage 38) that for low a c i d experiments the experimental rate curves exhibited considerably f a s t e r i n i t i a l ' r a t e s than those obtained from c a l c u l a t e d rate curves. As C u + + i s reduced and [H +] increases t h i s e f f e c t w i l l disappear as evidenced by the lower values of k x and fe.-i. obtained from curves 3 , k and 5. k 2 The E f f e c t of Cuprous Ions on Rates Several experiments were performed to determine i f the s u b s t a n t i a l amounts of C u + produced during reduction had any e f f e c t on the rates i n the of. perchlorate system,, since Dunning and Potter had observed a strong c a t a l y t i c a c t i v i t y of cuprous ions i n sulphate solutions. The i n i t i a l C u + + and H + con-centrations were so chosen that i n a series of three experiments the [ C u + + ] and [H +] l e v e l s would remain constant across the series although the [Cu +] concentrations d i f f e r e d from one experiment to the next. The rate curves of t h i s series are shown i n Figure 6 and p l o t s of rate*' vs [Cu +] f o r three l e v e l s of [ C u + + ] and [H +] are depicted i n Figure 7- T n e intercepts of these curves at zero [Cu +] were ca l c u l a t e d with equation 7 using k x and ~X from the dichromate work^. k 2 I t i s evident that the rates increase measurably with [Cu ] (20 to 30$ at the highest cuprous values). This contribution to the rates by cuprous ions probably e xplains the somewhat la r g e r values of k x obtained by Macgregor and Halpern and i n the present work as compared to the value from the dichromate work (see Table I . ) . A Corrected f o r the perchlorate decomposition e f f e c t . CO o Figure 7. Dependence of Rate on Cuprous Concentration; 10 atm H 2, 160°C. ro - 27 -Although the curves i n Figure 7 were drawn l i n e a r , the exact nature of the cuprous e f f e c t i s d i f f i c u l t t o assess, f i r s t l y because i t i s r e l a t i v e l y small and secondly because of the uncertainty introduced by the perchlorate reduction e f f e c t . Moreover, the cuprous e f f e c t i s hardly noticeable i f the correction f o r perchlorate reduction i s disregarded i n the rate measurements. The E f f e c t of Cupric Ions on Rates The inverted form of the rate law, equation 19, which contains a perchlorate decomposition correction but neglects contributions to the rate by Cu + may be rearranged to the form k - i rw +l [ C u + + ] = ET + 1 . . . . . ( 2 1 ) 1 d[Cu +] + k k [Cu +][H +][C10 4-] k l [ C u + + ] [ H 2 ] k x [H 2] 2 dt C 1 and l i n e a r p l o t s of the l e f t hand side of t h i s equation against Y*g u^ + ] yield-k-i [11+] intercepts of 1 and slopes of k 2 . ki[H 2J k l [Hg] A s e r i e s of experiments of varying i n i t i a l cupric concentration was made to check out t h i s equation. The rate curves of t h i s series are depicted i n Figure 8, and i n Figure 9 a number of l i n e a r p l o t s of the l e f t hand side of equation 21 against 1 are shown. The average value of k x obtained from Tcu^T the intercepts i s 6.7 X 10 - 3M" 1sec 1 and — i - estimated from the slopes i s 0.51. k 2 These values are i n good agreement with those obtained i n the a c i d s e r i e s ; k x again i s somewhat l a r g e r than that from the dichromate work which may be due to neglecting the C u + e f f e c t on rates i n t h i s case. The values of k x and fe-j, obtained i n both the a c i d and copper series k 2 of the present work are compared i n Table II with those of the e a r l i e r studies. 35 Those obtained from the dichromate work^-^ are t o be considered the most r e l i a b l e because of the absence of i n t e r f e r i n g side reactions, i . e . , the perchlorate decomposition and the cuprous e f f e c t s , encountered i n the copper reduction work. - 28 -0 120 240 360 ,480 600 'Time minutes Figure 8 . Rate Curves as a Function of I n i t i a l Cupric Perchlorate Concentration; 0.10 M[HC104]o; 10 atm, H_, l60°C. 0" 10 20 30 ' ko 50 60 - [ C u t + ] - 1 M " 1 Figure 9. Plots of [Cu + +]/(Rate Function) vs [ C u ^ ] " 1 at ^ D i f f e r e n t [Cu +] Levels. 0.10 M_HC104]O , 10 atm >^ H 2, 160°C. ' - 30 -TABLE I I . k Summary of Values of k x and — O b t a i n e d i n the Perchlorate System k 2 Temperature k i k - i Ref. °C . M~ 1sec" 1 __~ - or Figure 160 4.8 X 1 0 _ 3 , f t - 4 l 160 7.5 X 10" 3 1.3 34 160 5.4 x 10-3* 15$ o.37± 30/0 35 160 6.7 X 10" 3 ± 45/0 O.56* 5O/0 Figure 5 160 6.7 X 1 0 _ 3 ± 20$ O .5I* 20$ Figure 9 ft By extrapolation from Arrhenius Plot According to equation 21 the p l o t s made from rate measurements at d i f f e r e n t [Cu +] l e v e l s should a l l have a common intercept, instead of the spread shown i n Figure 9- This observed spread i s a t t r i b u t a b l e to neglecting the C u + e f f e c t on rates. I f contributions to the rate due to cuprous are deducted from the rate measurements these curves would be s h i f t e d upward and the l a r g e s t correction would apply to those curves having the highest C u + l e v e l s , i . e . , the bottom curves. Thus they would be brought together as required by equation 21. Corrected curves of t h i s kind are not presented because the form of the cuprous dependent con t r i b u t i o n has not been resolved i n perchlorate solutions. Also according to equation 21 the slopes of the plots i n Figure 9 should s h i f t s l i g h t l y upward as the a c i d i t y increases during the course of a run. However, t h i s s h i f t i s hardly observable f i r s t l y because the i n i t i a l a c i d i t y i s high (0.1 M) and does not increase s i g n i f i c a n t l y i n the region where rate measurements were taken, and secondly because of the unc e r t a i n t i e s introduced by both the perchlorate and cuprous e f f e c t s . Disproportionation E q u i l i b r i a and K i n e t i c s I t i s evident from equation 5 that the disproportionation reaction i s responsible f o r the appearance of m e t a l l i c copper. This emphasizes the need f o r determining the extent to which the disproportionation reaction -affects the copper reduction k i n e t i c s . Separate experiments were therefore conducted - 51 -at l60°C to determine the disproportionation constant under equilibrium conditions. A cupric perchlorate s o l u t i o n was e q u i l i b r a t e d with about 2100 cm2 of copper f o i l cut i n t o small squares. An i n e r t atmosphere of helium was used over the solutions. Samples were withdrawn i n the usual way and several additions of p e r c h l o r i c a c i d were made during the experiment. The disproportion-ation equation,i.e., K 2 Cu -=r-*~ C u ° + C u + + (5) indicates that the reaction i s pH independent but i f a s i g n i f i c a n t amount of cupric i s hydrolyzed to Cu(0H) + an apparent pH dependence of the r e s u l t i n g constant due to the associated equilibrium 2 C u + + H 2 0 >- Cu(0H) + + Cu° + H + (22) w i l l appear. The r e s u l t s of t h i s experiment are given i n Table III and indicate that above 0.03 M [H +] l e s s than 15$ of the cupric i s hydrolyzed. TABLE I I I . Values of the E q u i l i b r i u m Constant K f o r the Cu +-Cu + +-Cu° Equ i l i b r i u m at l60°C and Varying [H + ] HCIO4 M [ C u + ] 2 0.007 kk.j ± 5.1 0.035 26.1 ± 2.0 O.O83 25.5 * 2.0 The r e s u l t i n g disproportionation constants at l60°C. f o r equation 5 i s [ C u + + ] K [Cu ] ^ = 2 6 * 2 M "1 k2 i f the a c t i v i t y c o e f f i c i e n t r a t i o i s assumed t o be unity. Heinerth found t h i s to be a v a l i d assumption between 20 and 60°C f o r copper sulphate solutions of varying i o n i c strength. In a d d i t i o n complexing of C u + with small amounts of C l ~ - 32 -ions, appearing from decomposition of perchlorate, was ignored as i t s e f f e c t was found to be within the given l i m i t s of accuracy of K, even, i f i t was assumed that a l l C l " was,complexed a s C u C l . When K i s used to c a l c u l a t e the equilibrium [Cu +] l e v e l s corresponding to the determined [ C u + + ] l e v e l s i n a k i n e t i c experiment, good agreement with the measured cuprous l e v e l s i s obtained as shown i n Figure 10. There appears a small amount of supersaturation at the maximum i n the experimental curve, i n d i c a t i n g that nucleation of m e t a l l i c copper may be somewhat slow,in t h i s region. However, the amount of supersaturation shown could also be within experimental l i m i t s of p r e c i s i o n , since very small n u c l e i of m e t a l l i c copper could pass through the sample f i l t e r and be determined as cuprous through oxidation by dichromate. Rates of nucleation f o r the disproportionation reaction have been k 3 measured by Courtney at room temperature. The method used involved the observation of the time of appearance of a Tyndall e f f e c t i n a so l u t i o n of cuprous ammonium sulphate that was r a p i d l y a c i d i f i e d to destroy the stable cuprous ammine complex ions. A tenth power dependence on cuprous concentration f or the r e c i p r o c a l of t h i s time was interpreted as evidence that the c r i t i c a l nucleus contained 5 copper atoms., The same nucleation mechanism probably applies i n the case of hydrogen reduction, but does not become rate determining, except perhaps t r a n s i e n t l y at the onset of copper p r e c i p i t a t i o n . The value of K = 26 M - 1 at l60°C for the disproportionation reaction i s s i g n i f i c a n t l y lower than that c a l c u l a t e d for t h i s reaction (equation 5) with the r e l a t i o n A F ° = A F i 9 8 ° K - A S ! 9 8 o K (T - 298) (23) by extrapolation of room temperature thermodynamic data (Appendix D) to l60°C. This extrapolation i s based on the approximation that __.Hrp- ___.H2g8 = T(ASrp- A S 2 9 8 ) . Time minutes , Figure 10. Rate Plots of [Cu +], [Cu + +] and Amount of [ C u + + ] Depleted; 1^ Together with a Calculated -[Cu +] Curve as a Function of , [Cu + +] and K = 26 IVT1; 0.01 M[HC10 4]o, 10 atm H 2, l60°C. - 34 -The value of the equ i l i b r i u m constant K i s 89 M - 1 when cal c u l a t e d with equation 23. This l a r g e r than experimental value i s a t t r i b u t a b l e to the foregoing approximation which, however, does not appear to be e n t i r e l y v a l i d . Very l i t t l e has been done e i t h e r experimentally or t h e o r e t i c a l l y to show accurately the v a r i a t i o n of thermodynamic properties from room temperature to high temperature (above, 100°C .) i n i o n i c aqueous solutions. In t h i s regard the method of C r i s s ^ o f f e r s some promise f o r c a l c u l a t i n g the high temperature values of the entropies of ions with the a i d of empirical equations. From these the correct values of the diff e r e n c e between A H T - A H 2 g 8 and T( A S T- A ^298) c a n t h e o r e t i c a l l y be deter-mined. The Integrated Rate Law Confirmation of the p r a c t i c a l v a l i d i t y of a proposed rate law can be obtained by i n t e g r a t i n g the rate equation, using the derived constants to calculate a t h e o r e t i c a l rate curve, and comparing i t with one obtained experimentally under the same conditions. The rate law given i n equation 7 can be integrated mathematically both before and a f t e r disproportionation of cuprous ions. To perform t h i s i n t e g r a t i o n the d i f f e r e n t i a l form, i . e . , - d[Hg] = k 1 [ C u + + ] 2 [ H P ] (7) dt k ^ [ H+] + [ C u+ +] k 2 must be defined i n terms of a single dependent v a r i a b l e which may be e i t h e r [Cu +] or [Cu + +] depending on the experimental rate curve with which the t h e o r e t i c a l curve i s to be compared. Thus f or [Cu +] as the dependent v a r i a b l e the r e l a t i o n s h i p before disproportionation i s - d[H 2] = • 1 d[Cu +] (24) dt 2 dt which represents the stoichiometry of equation 11.. - 35 -Also before disproportionation the following r e l a t i o n s apply: [ C u + + ] = [ C u + ; f ] o - [ C u + ] and [H +] = [H +] 0+ [Cu +], the subscript r e f e r r i n g to i n i t i a l concentrations. The rate law rewritten with [Cu +] as the dependent v a r i a b l e i s then i d[Cu +] = 2 k! ( [ C u + + ] o - [ C u + ] ) 2 [H g] (25) ^ k ^ i ( [ H + ] o + [Cu +]) + [ C u + + ] o - [ C u + ] k 2 Integration of equation 25 y i e l d s an expression f o r t as a function of [Cu +] as follows t = k-! ( [H +]c + [ C U + + ] Q - [H +]c - 1 2 k 1k 2[H 2] V L C u T T J o + [ C u T [ C u i + ] o + / ^ ~ 1 | x 2.3 l o g ([Cu + +]°-[Cu +] ) (26) 1 2k\£H 2] j I . [Cu + + ] o / For the case a f t e r disproportionation i t i s convenient to use [Cu**] as the dependent v a r i a b l e . Thenone writes - d[H 2] = - d [ C u + + ] - 1 d[Cu +] (27) dt dt 2 dt and since [Cu+] = (SSf^j 2 (28) equation 27 can be written d[H 2] _ + , i I r ++-, - d t " " " I 4KV2 [ C U + + ] V 2 J * *[Cu ] (2 9 ) dt At the same time [H+] = [H +]. + 2(Cu + +]. - 2[Cu + +) -By s u b s t i t u t i n g equations 29 and 30 i n t o equation 1 the rate law v a l i d a f t e r disproportionation i s obtained, e.g.^ 36 -d[Cu +-M dt k 1 [ C u + + ] 2 [ H 2 ] k - i f - [H + ]o+ 2 [ C u + t ] 0 - 2 [ C u " J - /.Cu". k 2 &1 + [ C u + + ] 1 1 + 4 K y 2 [cu + + ]y 2 (31) The integrated form associated with equation 31 i s 1 t = - - 1 x x Q J k i k 2 [H 2 J Q - 4K ) + (1 -kg-) 2.3 l o g f x j \2 k 2 / k i K W l H s I +/1 - 1 where x = [ C u + + ] x n = [ C u + + ] 0 k - i Q 6k 1 k 2 K J /2LH 2 J x -Q = [ H + ] 0 + 2 [ C u + + ] 0 [32) Equations 26 and 32 may then he used to calculate t h e o r e t i c a l rate curves f o r given experimental conditions both i n the absence and presence of met a l l i c copper, and these curves can be compared with those obtained experimentally under the same conditions. A comparison of t h i s kind i s depicted i n Figure 11 where curve A was cal c u l a t e d with equation 26 (Appendix E ) . I t i s seen that the agreement i s quite good i n i t i a l l y except f o r a s l i g h t l a g i n the experimental curve at the s t a r t of the run due to undetermined transient e f f e c t s ; however, i n the l a t e r stages of the run the experimental rates decrease much f a s t e r than 0 those predicted t h e o r e t i c a l l y . This discrepancy between experimental and theo-r e t i c a l rates undoubtedly r e s u l t s from the perchlorate decomposition e f f e c t which was not included i n the integrated rate law. 0 120 240 360 480 600 Time minutes Figure 11. Comparison of - Experimental and Calcu l a t e d Rate i Curves; 0.03 M[Cu ( C 1 0 4 ) 2 ] ° , 0 .0? M[HC10 4 ]o , 10 atm H 2, 160°C. - 38 -To check the v a l i d i t y of the p e r c h l o r a t e e f f e c t as given by equation 16 the c o r r e c t e d r a t e law (equation 17) was a l s o i n t e g r a t e d . The r e s u l t i n g curve B shown i n Figure 11 i s i n good agreement w i t h the experimental r a t e curve and i l l u s t r a t e s the magnitude of the p e r c h l o r a t e decomposition e f f e c t . Rate curves were a l s o c a l c u l a t e d f o r low a c i d experiments (0.01 M [ H C 1 0 4 ] o ) . I t was found t h a t the i n i t i a l r a t e s of the experimental curves were f a s t e r than c a l c u l a t e d . This discrepancy probably r e s u l t s from p a r t i a l h y d r o l y s i s of c u p r i c ions t o Cu(0H) + which would give r i s e t o a c t i v a t i o n of hydrogen t h a t i s f a s t e r than t h a t by C u + + . One r e d u c t i o n experiment was performed w i t h m e t a l l i c copper ( f o i l cut i n s m a ll pieces) present a t the beginning of the run t o determine whether the rate law a p p l y i n g before d i s p r o p o r t i o n a t i o n continues t o be v a l i d when copper begins t o p r e c i p i t a t e . The experimental s o l u t i o n , which was 0.137 M i n [Cu(C10 4) 2] and 0.103 M i n [HC10 4] i n i t i a l l y , was heated under an atmosphere of helium and held - a t l60°C f o r 70 minutes t o a l l o w f u l l e q u i l i b r a t i o n between C u + + , C u + and m e t a l l i c copper before adding hydrogen. The experimental rate curves f o r - [ C u + + ] , [Cu +] and [C u + + ] + [ C u + ] are depic t e d i n Figure 12, w i t h the values of [ C u + + ] obtained by d i f f e r e n c e from the measured [Cu +] and [Cu + +]+[Cu +] l e v e l s . The rate curve f o r [ C u + + ] i s compared w i t h curve A, c a l c u l a t e d by g r a p h i c a l i n t e g r a t i o n of a r a t e law t h a t i n c l u d e s equation 31 and the p e r c h l o r a t e decomposition c o r r e c t i o n . This c o r r e c t i o n i s s i g n i f i c a n t f o r t h i s experiment because of the l a r g e amounts of C u + present i n i t i a l l y . The r a t e law has the form it Equation 17 was i n t e g r a t e d g r a p h i c a l l y (Appendix E ) . 200 Time minutes Figure 12. Comparison of Experimental and Calculated [Cu ] Rate Curves for Reduction i n the Presence of M e t a l l i c Copper; O.137 M [Cu(C10 4) 2]o, 0.103 M[HC104jo, 10 atm Ez, l60°C. - ho -d [ C u + + ] = J k J C u + + ] 2 [ H g j dt 1 k~[ [ H + M C u + + J k 2 h k C l ^ + + ] j ^ [ H + ] [ C 1 0 4 - ] 1 + 4 K y 2 LCU + + JV 2 where [H +] i s given by equation 30. (33) The experimental curve i s steeper, at l e a s t • i n i t i a l l y , than. the, , ,, calculated curve A. This i s not too s u r p r i s i n g i n view of the fac t that the c a t a l y t i c e f f e c t of cuprous ions was not taken i n t o account when c a l c u l a t i n g curve A. Both curves show that the rate of copper reduction eventually decreases to zero. -This decrease, as evident from equation 33 > r e s u l t s from the perchlorate decomposition e f f e c t which increases markedly with the buildup of the hydrogen ion concentration. When t h i s e f f e c t becomes equal to the forward rate, no net reduction of copper w i l l occur u n t i l the perchlorate concentration i s depleted s u f f i c i e n t l y to slow down i t s rate of decomposition. These observations also explain the r e s u l t s of Macgregor and Halpern3\ Their copper reduction rates i n the perchlorate system slowed to v i r t u a l l y zero at considerably higher [ C u + + ] l e v e l s than expected from thermodynamic estimates'^ that indicated the reduction reaction at these l e v e l s was f a r from equilibrium. kl I Reduction of Cupric Sulphate Reduction experiments with cupric sulphate revealed a' considerable increase i n rates with r i s i n g Cu"'" concentration despite decreasing [ C u ^ ] (Figure 13) which i s evidence that a reaction mechanism involving the cuprous species i s involved. The k i n e t i c s of cupric sulphate reduction had been studied e a r l i e r by Dunning and P o t t e r ^ who had al s o observed t h i s e f f e c t and had proposed the following mechanism f o r t h i s reaction, k x C u 1 1 + H 2 _ *~ -CuH+ + H + (34) k_ l CuH + + C u 1 1 k 2 b 2CuZ + H + (35) I ' K 3 + Cu + H 2 CuH + H (56) k-•3 CuH + C u 1 1 k * CuH + + Cu 1 (57) T f a s t I I 2 Cu 1 » Cu° + Cu (5) K A two term rate law derived from t h i s mechanism by a steady state approximation i n CuH + and CuH has the form - a [ H 2 ] = k 1 [ C u I I ] 2 [ H 2 j + k 3 [ C u I I ] 2 [ C u I ] [ H g ] = R p I I + R T -~d£~ k ^ [H +] + [ C u ^ J / k ^ [H +] + [ C u l l J \ l^s [H +] + [ C u ^ J \ C u C u i k 2 (^k2 M k 4 ) (38) where R ^ JJ. and R Q I a r e r e s p e c t i v e l y the rate of d i r e c t reduction of cupric and the cuprous dependent part of the t o t a l r a t e. - k2 -•Several s e r i e s of experiments performed i n the present study, revealed that the above mechanism and rate law appear to describe adequately the hydrogen reduction k i n e t i c s of the aqueous copper sulphate system. Dunning and Potter v e r i f i e d the f i r s t term of t h i s rate law, however, t h e i r cuprous dependent term was l i n e a r i n both [Cu 1^ and [H +] i n the denominator. The experimental series i n t h i s work included studies of the ef f e c t s on rate of a c i d i t y , i n i t i a l cupric concentration, free sulphate concentration and temperature. Throughout these series the t o t a l sulphate concentration was kept constant at 1 M by addi t i o n of a s u f f i c i e n t amount of a "n e u t r a l " ^ s a l t such as MgS04, to keep the i n i t i a l formal i o n i c strength r e l a t i v e l y constant f o r a l l s e r i e s . The E f f e c t of A c i d i t y on Rates A ser i e s of experiments to investigate the a c i d i t y on rates, was performed under the following i n i t i a l conditions: [CuS0 4] o 0.15 M, [ H 2 S 0 4 ] o O.5 to O.85 M, s u f f i c i e n t MgS04 to make the so l u t i o n 1 M i n t o t a l sulphate, hydrogen p a r t i a l pressure 5 atm and temperature l60°C. Rate curves f o r t h i s s e r i e s are shown i n Figure 13. Rates were measured along these curves at several [Cu^] l e v e l s and p l o t t e d against [Cu^] as seen i n Figure Ik. The l i n e a r i t y of these p l o t s indicates that the cupric reduction rate i s f i r s t order i n [Cu 1]. The interc e p t s , I, of these curves obtained by extrapolating to zero cuprous correspond to rates independent of [Cu 1], i . e . , the d i r e c t a c t i v a t i o n of hydrogen by cupric according to equation 3k. -These rates should follow the f i r s t term of the rate equation 38 and as i n the perchlorate case one ± C a t a l y t i c a l l y i n a c t i v e toward hydrogen, ftft Appendix G. - kk -- ^ -may write 1 = 1 = k 2 [H +] + , 1 , (39) K C U H I k i [ C u i - L > [ H 2 ] k x t C u ^ J l H g J which i s a l i n e a r equation of I - 1 i n [H + ] . A plo t of t h i s form i s depicted i n k-n Figure 15, and average values of k x and ^ i calculated from the expressions f o r intercept and slope i n equation 39 are r e s p e c t i v e l y k x = 3-2 X 1 0 - 3 M - 1 s e c _ 1 k and —=i = 0.13. The spread shown i n Figure 15 f o r the values of the hydrogen k 2 ion concentration r e s u l t s from the assumption that K^, the bisulphate d i s s o c i a t i o n constant, which i s not known at l60°C, has a value between 10 - 3 and 10 _ 2M, and that complexing of S0 4 by cupric ions can be neglected (Appendix F). The cuprous dependent part of the rate, R Q I,can be evaluated from the i n i t i a l slopes of the rate vs [Cu Z ] plot s i n Figure 13. According to the expression f o r R Q U I i n equation 38 these slopes are given by S = ^ Cu1- = k 3 [ C u i : E ] 2 [ H g ] , (kO) TC^I / k - , [ H + ] + [ C u S i J l /k-3 [ H + M C u 1 1 ^ (I 2 / \ k4 I I ns I f the expression f o r R Q u i n equation 38 i s divided by S one obtai ^CuE£= I = £1 .( ^ . [ H + M C u 1 1 ] , ( k v S S , k 3 I k 4 J l 4 X ' which i s a l i n e a r expression of I in" [H +] with an intercept I = ki_ [Cu +] and a S k3 slope S = k x.k_ 3 . The p l o t of I vs [H +] i s depicted i n Figure 16. Using k 3 k 4 S the average value of k x (3-2 X 1 0 - 3 M - 1 s e c _ 1 ) , obtained from Figure 15, the following average values of k 3 and k-3 were c a l c u l a t e d from the intercept and k 4 slope i n Figure 16: k 3 = 6.4 X 1 0 - 2 M - 1 s e c _ 1 and k_ 3 = O.45. k 3 i s therefore k 4 II considerably l a r g e r than k x. This accounts f o r the fact that the Cu reduction rates are enhanced markedly with increasing Cu-'- concentration. - 48 -This i s of i n t e r e s t i n view of t h e , r e l a t i v e l y low cuprous a c t i v i t y i n perchlorate solutions and suggests that complexing with sulphate (or p o s s i b l y bisulphate) i s responsible f o r the considerable enhancement of c a t a l y t i c a c t i v i t y of cuprous ions. Because of the f a i r l y large un c e r t a i n t i e s i n the J_ values shown i n S Figure 16. the second term i n equation 38, i . e . , R Q U I > was compared with that of a simpler mechanism f o r the cuprous catalyzed reduction path. This mechanism simply omits the back reaction igiven i n equation 36, i n other words, k- 3 i s assumed to be n e g l i g i b l y small. The corresponding complete rate law also obtained by the steady state approximation i n CuH + and CuH i s - d[Hg] = k 1 [ C u I I ] 2 [ H 2 ] + k a [ C u I I ] [ C u I . [ H a _ (42) "dt k ^ [H+J + [CuIIJ k ^ [H +] + [Cu l l ] k 2 k 2 A comparison of equations 38 and 42 shows that the f i r s t terms of these rate laws are i d e n t i c a l , and the second part i n equation 42 i s obtained by cancellation, because k_ 3 [H +] i s absent i n the denominator of equation 38. k 4 Taking the cuprous dependent term i n equation 42 separately, one obtains by i n v e r t i n g and'multiplying both sides with [Cu^-] [Cu 1] = 1 = k.^ [H +] _1 R c u l " S ' k ? + k 3 [ H 2 ] (43) ]^[Cu i- L][H_] which in d i c a t e s that a p l o t of 1 vs. [H +] should be l i n e a r . A ,plot was made with S : the previously obtained values of S f o r the a c i d series and i s depicted i n Figure 17. I t i s reasonably l i n e a r i n i t i a l l y but curves upward at higher [H +] values suggesting a greater than f i r s t power dependence of 1 on [ H + ] . -The value of k 3 S estimated from the intercept of the l i n e a r approximation at low [H +] i s 6.2 X 1 0 - 2 M~ 1sec" 1 which agrees w e l l with that obtained from the intercept i n Figure 16. [H +] 2M 2 0 0 .1 0.2 0..3 O.k 0^5 CU5 0/7 0.8 o o.i 0.2 0.3 o.k 0 .5 o.6 0 .7 0 . 8 [H ] M Figure 17. Plots of S - 1 vs [H +] and [ H + ] 2 f o r A c i d Series of Experiments; 0.15 M[CuS04]o, 5 atm E2, l 6 0°C. 1 - 50 -Thus the s i m p l i f i e d rate law (equation 42) may be considered a good approximation at low [H +], However the deviation from l i n e a r i t y with increasing a c i d i t y of the p l o t i n Figure 17 i s greater than expected from probable errors i n the measurements and suggests that t h i s rate law i s i n e r r o r . Therefore a p l o t of 1 vs [ H + ] 2 was a l s o made as shown i n Figure 17. This pl o t appears to be l i n e a r S and supports the v a l i d i t y of the second term of the rate law as given i n equation 38 since i t contains a term i n [ H + ] 2 i n the denominator. The [ H + ] 2 dependence of 1 i s demonstrated in' equation 44,e.g. , which i s derived from the second term i n equation 38. As expected the intercept of the 1 vs [ H + ] 2 p l o t at [H +] = 0 i s close S to that of the 1 vs [H ] p l o t and w i l l therefore y i e l d the same value of k 3. S + Although equation 44 contains both a l i n e a r and square term i n [H ] i t can be seen from the l.vs [ H + ] 2 p l o t that the l a t t e r term i s s u f f i c i e n t l y important S i n t h i s equation to permit the p l o t to appear l i n e a r i n confirmation of t n e rate law given by equation 38. The E f f e c t of Cupric Sulphate on Rates A series of rate curves i l l u s t r a t i n g the e f f e c t on rates of varying the i n i t i a l CuS0 4 concentration i s shown i n Figure 18. The experimental conditions were as follows: 0.05 to 0.25 M [CuS0 4]°, 0.7 M [ H 2 S 0 4 ] o , s u f f i c i e n t [MgS04] to make the s o l u t i o n 1 M i n t o t a l sulphate, H 2 p a r t i a l pressure 5 a"tm and l60°C.. The a c i d i t y was kept as high as p r a c t i c a l so that free sulphate i n s o l u t i o n f or complexing of cupric and cuprous ions was minimized. 60 1 2 0 ! 8 0 -2l+0 300 .360 420 Time mirutes -Figure 18. Rate Curves as a-Function of I n i t i a l Cupric Sulphate. Concentration; 0.70 M[H 2 S0 4 ]o, 5 atm H 2, l60°C. , VJl H - 52 -Rates were measured, as i n the a c i d s e r i e s , at several [Cu*3 l e v e l s along the reduction curves and are depicted i n Figure 19 as p l o t s of rate vs. [Cu*]. These p l o t s are l i n e a r i n i t i a l l y hut tend to decrease i n slope at the higher [Cu*] l e v e l s p a r t i c u l a r l y f o r the experiments with high i n i t i a l [CUSO4]. The slopes decrease because the reaction i s also • [Cu**] dependent and the cupric l e v e l s are d e c l i n i n g i n that region. For a n a l y s i s of the p l o t s i n Figure 19, the [Cu* ] dependent part of the rate, i.e.., the slopes S w i l l be considered f i r s t . I t i s evident that i n the i n i t i a l portions of these curves the slopes increase from a low value f o r the experiment with low i n i t i a l cupric sulphate (O.O5 M) to an approximately constant value f o r the runs with high i n i t i a l [CuS0 4] (0.20 to 0.25 M). The s i g n i f i c a n c e of t h i s observation i s i l l u s t r a t e d i n Figure 20 where the i n i t i a l slopes of R I Figure 19, i . e . , S = C U T , have been p l o t t e d against both [Cu* 1] and [Cu**] 2. LCu-1 J The S vs. [Cu ] curve indicates that at low i n i t i a l cupric concentrations the dependence of S i s second order i n [Cu**]; as [Cu**] i s increased t h i s dependence s h i f t s to f i r s t and f i n a l l y to nearly zero order at the highest i n i t i a l cupric sulphate l e v e l s . The shape of t h i s curve i s consistent with the .expression! f o r the slope, S, (equation 40) which may be explained as follows. At low i n i t i a l [Cu* 1] both k-x [H+] and k- 3 [H +] w i l l be the dominant terms i n the k 2 k 4 denominator of 40 and t h i s equation w i l l approach the form , I I l 2 ( S = k 3[Cu l x] g[Hp] (4 5) k ^ k j . [H F k 2 k 4 r e s u l t i n g i n a second order dependence of S on [Cu**]. As the i n i t i a l [ C u ^ ] i s increased the dependence of S on [Cu**],will s h i f t to f i r s t and f i n a l l y to zero order at the highest [Cu** ] l e v e l s . In t h i s l i m i t i n g case when [Cu** ] >^ k-3 [H+] and ^ k- x [H+] equation 40 w i l l reduce to ^4 k 2 S = k 3 [ H 2 ] (46) - 53 -'I O <L> CQ <°0 H X 14 -12 L_ 10 8 L 6 U 4 L 20 30 [Cu 1] X 103 M Figure 19. Plots of Rate vs. [Cu 1] as a'Function of I n i t i a l Cupric Concentration;-O .7O M H 2, 160°C. [H 2 S 0 4 ] ° , 5 atm. [ C u 1 1 ] 2 M 2 0 0.01 0.02 0 03 0 04 0 05 0 .06 0.07 0.08 o.oo 0.05 o . i o 0.15 0 .20 -0 .25 ° - 3 ° °-55 [Cu 1 1] M Figure 2 0 . . Plots of S vs [ C u 1 1 ] and [ C u 1 1 ] 2 f o r Cupric Series of Experiments; 0.70 .M [ H 2 S 0 4 ]O, 5 atm H 2, l 6 0°C. - 55 -and further increases i n the i n i t i a l cupric sulphate concentration should have no e f f e c t on S as seen i n Figure 19. The arguments are supported by the shape of the second, curve i n Figure 20, i.e., the S vs [ C u 1 1 ] 2 plot ;which, as would be predicted, i s l i n e a r i n i t i a l l y and curves toward zero slope at high [Cu-'-1]2 values. k 3 can be estimated with equation 46 from the asymptote that the p l o t s i n Figure 20 approach at high' [ C u 1 1 ] l e v e l s and has a value of approximately 3.5 X 1 0" 2M - 1sec - 1. .The value obtained from the e a r l i e r a c i d series i s 6.4 X 10~2 M~ 1sec~ 1. The inte r c e p t s , <I, of the rate vs [Cu 1] pl o t s i n Figure 19 were used to determine values of k i and k_! f o r R Q U I I , the f i r s t term i n the r a t e aquation 38. k 2 Inverting the expression for R Q U I I and mult i p l y i n g both sides with [ C u 1 1 ] y i e l d s [ C u 1 1 ] _ [ C u 1 1 ] _ [ H ] + 1 (47) Bcu.II I k i [ C u 1 1 ] [ H 2 J k_.[H_] and from a l i n e a r p l o t of [Cu^ --'-] vs. 1 values of k i and may be ~ ~ i — _ T C ^ T T J k 2 extimated from the slope and i n t e r c e p t ' r e s p e c t i v e l y . This p l o t i s shown i n Figure 21. The large un c e r t a i n t i e s i n the [Cu 1 1 3 values make i t d i f f i c u l t ; to I draw a s a t i s f a c t o r y s t r a i g h t l i n e . Values of k i and k - i obtained from the k 2 intercept and slope of the best s t r a i g h t l i n e that can be drawn are r e s p e c t i v e l y . 2.6 X lO^M-^-sec" 1 and O.O5. The E f f e c t of Free Sulphate on Rates A number of experiments were performed to investigate the e f f e c t of free sulphate ions on the rates of copper reduction. . A l l experiments were c a r r i e d out at l60°C and a hydrogen p a r t i a l pressure of 5 atm. Further experimental d e t a i l s are l i s t e d i n Table IV together with the estimated free sulphate, bisulphate and hydrogen ion concentrations. - 57 TABLE IV. Experimental Conditions f o r Sulphate Series and Estimated Free Sulphate, Bisulphate and Hydrogen Ion Concentrations Experiment [CuS0 4] [H 2S0 4 ] 0 [MgS04; 1 [so 4 A ]free [HS0 4]* [ H + ] * H 2S0 4 - 2 0.15M 0.50M 0.55M 0.05 - 0.1 O.97 - 0.9 0. .05 - 0.1 •so4~ - 1 0.15 0.40 0.45 0.2 - 0.25 0 .8 - O.77 0. .004 - 0.05 S 0 4 _ - 2 0.15 0.50 O.55 0.4 - 0.42 0.6 - 0.58 0. .002 - 0.02 so 4 " - 3 0.15 0.20 O.65 0 .6 - 0.61 0.4 - O.59 0. .0007 - 0.01 so 4 " - 4 0.15 0.10 0.75 0 .8 0.2 0.005 A Free sulphate, bisulphate and hydrogen ion concentration estimated by neglecting complexing with Cu** and assuming the bisulphate d i s s o c i a t i o n constant K b ^ 10" 3 - 1 0 - 2 M - 1 (Appendix F) . The experimental rate curves-*- obtained i n t h i s series are depicted i n Figure 22 and the p l o t s of rate vs. [Cu*] are shown i n Figure 23. These figures show that the rates increase i n i t i a l l y with increasing free sulphate concentration but then l e v e l o f f . This i s a l s o i l l u s t r a t e d i n Figures 24 and 25, where the values of the i n t e r c e p t s , I, and slopes, S, of Figure 25 are p l o t t e d against [ S 0 4 _ and i t i s apparent that the l e v e l l i n g o f f occurs -at about 0.4 M free sulphate concentration. This enhancing e f f e c t i s r e l a t i v e l y small and quite p o s s i b l y within the l i m i t s of an e f f e c t that can be explained i n terms of hydrogen ion concentration changes within the s e r i e s . I t has therefore not been possible to determine the complexing e f f e c t of sulphate on the rate constants kj. and k 3 respresenting the hydrogen a c t i v a t i o n steps. Peters and Halpern*6j who studied the e f f e c t of complexing on dichromate reduction rates were able to show an enhancing e f f e c t on k x of about a factor of 1 i n a s e r i e s of measurements of increasing sulphate concentration. A The break i n the rate curve of experiment S0 4 - 4 may be a t t r i b u t e d to hydrolysis of cuprous ions due to the low a c i d i t y i n that run. - 59 i o CD CQ H X! .Figure 2k. Plot of I vs. Free [S0 4 ] f o r Sulphate Series of ' Experiments; 0.15 M[CuS0 4 ]o , 5 atm Ez, l60°C. CA O - 62 -At high sulphate concentrations and low a c i d i t i e s the rate equation 58 reduces to - d[Hg] = k x t C u 1 1 ] [H 2 ] + k 3 [Cu 1 ] [H 2 ] ..!..(4'8) dt and the values f o r k x and ka obtained from the l i m i t i n g (high '[S04 =]) asymptotes of the curves i n Figures 24 and 25 are k x = 4.5 X 10 _ 3M~ 1sec- 1 and k 3 = 9.6 X I O - 2 M - 1 s e c - 1 . Summary of Rate Constants The values of the rate constants obtained i n the aci d , copper and sulphate ser i e s of experiments have been summarized f o r comparison i n Table V. TABLE V. -Summary of Rate Constants f o r Sulphate Solutions at l60°C. k k 1 M " 1 s e c - 1 k 3M" 1sec" 1 k-3 k 4 Series Estimated from Figure 3.2Xio _ 3*io$ 0.13*30^ - Acid 15 6.4X10-2*25$ 0.45*40$ Acid 16 6.2X10"2 - A c i d 17 5-5X10 - 2 - Cupric 20 2.6X10" 3±10$ 0.05*30$ - Cupric 21 4.5X10- 3 -- Sulphate 24 9 . 6 X 1 0 " 2 - Sulphate 25 The magnitudes of these constants are of the same order f o r a l l three s e r i e s . V ariations i n t h e i r values can be a t t r i b u t e d to the errors inherent i n the method of analysis of the sulphate system.These errors are a l l subjective - 63 -except those of [Cu 1] determination. They r e s u l t from the following: 1. f i t t i n g of rate curves to the experimental points, 2. estimation of slopes along the non-linear rate curves, 3. estimation of intercepts and slopes from the rate vs [Cu 1 ] p l o t s , and 4. f i t t i n g of curves to p l o t s derived from the l a t t e r measurements. The values of k x obtained here are somewhat low compared to that from the dichromate reduction work35 i n perchlorate solutions ( k i = ^.k X 10" 3M _ 1sec" 1), and t h i s i s probably only due to the use of hydrogen s o l u b i l i t i e s i n water i n the c a l c u l a t i o n s . Sulphate solutions are known to have lower hydrogen s o l u b i l i t i e s at room temperature^^ which probably a l s o applies at elevated temperatures. For example, an observed 30$ decrease i n the dichromate reduction rate at 100°C. by a d d i t i o n of 0 .75 M [MgS04] or [Na 2S04] to cupric acetate solutions has been a t t r i b u t e d to the lowering of H 2 s o l u b i l i t y due to these s a l t s ^ 1 . Also, recent 46 measurements have shown that the s o l u b i l i t y of CO i n aqueous solutions decreases markedly with increasing ammonium sulphate concentration (40$ i n 1 M [(NH 4) 2S© 4 i ] at 160°C). The Integrated Rate Curve The v a l i d i t y of the rate law f o r copper reduction i n the sulphate system, as given i n equation 38, i . e . , - d[H 2] _ k J C u 1 1 ] 2 ^ ] + k 3 [ C u I ] [ ] 2 [ C u l 3 [ H 2 ] = p T I R z ~ d t k ^ [H +] + [ C u ^ ] fk-j_ [H + ] + [CU1MY/__3_ [ H + ] + . C U T T ] \ C U + C U k 2 l,k 2 J(^k 4 j (38) was checked by numerical i n t e g r a t i o n of t h i s expression for the experimental conditions of one run. One experiment from the a c i d series was chosen f o r t h i s comparison and the constants (Table Vi) obtained from t h i s s e r i e s were used i n the c a l c u l a t i o n s (Appendix H). Figure 26 depicts the r e s u l t i n g integrated rate curve together with that obtained experimentally. I - 65 -The E f f e c t of Temperature on Rates The e f f e c t of temperature on the copper reduction rates was -studied to obtain an estimate f o r the a c t i v a t i o n energies f o r both the [Cu**] and [Cu*] reaction paths. -Rate curves f o r t h i s series are depicted i n Figure 27. They were obtained under the following experimental conditions: 0.15 M i n i t i a l [CuS0 4], 0.70 M i n i t i a l [ H 2S0 4], 0.15 M;[MgS0 4], 5 atm hydrogen p a r t i a l pressure and 120, 140, 160 and l80°C temperature. The rate vs [Cu 1] p l o t s of t h i s series are shown i n Figure 28. As only one experiment was made at each of the four temperatures, except at l60°C, i t was not possible to measure kx a n d k 3 d i r e c t l y , but they could be estimated,from measured intercepts, - I, and i n i t i a l slopes,-S, i n Figure 28 through t h e i r r e l a t i o n s h i p s as defined by equation 58. The assumption was, made that both of the rate constant r a t i o s k m l and k_ 3 do not change k g k 4 with temperature . The values chosen f o r these two r a t i o s were k-j = 0.15 k 2 and k-3 = O.45 (Table V). The values of k x and k 3 calculated f o r each k 4 temperature are l i s t e d i n Table VI. TABLE VI. Values of k1} k 3. and Dissolved H 2 at D i f f e r e n t Temperatures Temperature k i M - 1 s e c -1 ksM'-'-sec"1 [H 2] M 120 °C 140 160 180 1.9 X 10 1.1 X 1 0 - 3 5.2 X I O - 3 7.8 X I O - 3 1.5 X 10 " 2 2.4 X 1 0 - 2 6.4 X i o ~ 2 16.2'X 1 0 - 2 4.50 X 1 0 - 3 5.15 X I O - 3 5.90 X I O - 3 6.80 X10-3 M Estimated range f o r k x * 10$, f o r k3 * 25$ f o r each temperature as i n Table V f o r 160°C. H 2 s o l u b i l i t y at 5 atm H 2 pressure f o r pure water' 40 These rate constants are shown p l o t t e d i n Figure 29 as l o g k i and k 3 r e s p e c t i v e l y ± l£=X was i n f a c t observed to be nearly constant with temperature i n k 2 e a r l i e r work i n the perchlorate system35. Figure 27. Rate Curves as a Function of Temperature; 0.15 M[CuS0 4]o, 0.70 M[H 2S0 4]°, 0.15 M [MgS0 4], 5 atm H 2. - 67 -- 6 9 ' -vs T ~ 1 O K _ 1 . From the slopes of these Arrhenius plots the following experimental activation energies were obtained: Ei = 22.4 ± 2.2 kcal/mole E 3 = 15.3 * 1.4 kcal/mole Values of __\ S* for each rate constant were also calculated with the above figures of E and the relation k_^ = ekT / e x P lexp -E Y A S * (reference 47^ (49) and are A S i = - 21 * 5 eu A s | = - 31 ± 3 eu These data are summarized for comparison in Table VII together with those of other workers. TABLE VII. Summary of Activation Energies and Entropies . , 1£ at System E i kcal/mole A Si eu E 3 kcal/mole &S 3 eu Source Sulphate 22. .4 * 2. .2 - 21 * 5 15.3 * 1.4 - 31 * 3 This work Sulphate 24 - 9-3 - ref. 26 Sulphate 23. .5 - 10.4 15.9 - 34.5 ref. 48 Perchlorate 25. ,•8 * 1. • 7 - 12.1 * 4.5 - - ref. 35 Although possible variations in ^—_ with temperature were not taken into account in the estimation of errors in k x the values of E x and sf_ are in reasonable agreement with the other data. A similar good agreement is apparent for E 3 and A S 3 where the same approximations as shown above were used in calculating ?6 4ft k 3. The low value of 9-3 kcal for E 3 is from published work relating to a thesis - 70 -and could be an er r o r i n i n t e r p r e t a t i o n by the authors since the same experimental work i s described i n both references. The Deuterium 'Exchange Experiments The re a c t i o n steps f o r a c t i v a t i o n of molecular hydrogen shown i n the mechanisms of copper reduction (equations 34 and 36) indicate that both the reactive intermediates CuH + and CuH should react with hydrogen ions i n s o l u t i o n to regenerate molecular hydrogen. Hence, i f deuterium i s substituted f o r hydrogen i n a copper reduction experiment i t should be possible to determine the rate of the back reaction by measuring the appearance of HD i n the gas phase. This r e a c t i o n takes place according to ' k C u 1 1 + D 2 — C u D + + D + (34) CuD + + H + k - 1 C u 1 1 + HD (-34f f o r the cupric a c t i v a t i o n path. For the cuprous catalyzed r e a c t i o n path i t i s C u 1 + D 2 J ^ * . CuD + D + (36) CuD + H + k " 3 C u 1 + HD (-36) Experiments i n v o l v i n g the use of D 2 0 enriched ordinary water instead of s u b s t i t u t i n g D 2 f o r H 2 had been suggested e a r l i e r by Macgregor^''' f o r the copper 4Q reduction work. .Webster ' had observed the appearance of HD i n exchange experiments -L. i n v o l v i n g the Ag catalyzed hydrogen reduction of dichromate, by using water with a 20 mol$ D 2 0 content. The rate of appearance of HD was found to increase with a c i d i t y , and i n the absence of A g + no exchange took place. Q u a l i t a t i v e experiments 48 by Potter using copper sulphate solutions and a mixture of H 2 and D 2 showed an enrichment of the gas i n HD content which was interpreted as being due to c a t a l y s i s by copper ions i n s o l u t i o n . ft The - -sign designates the back reaction of equation 3^. - 71 -Evidence f o r copper catalyzed deuterium exchange i n non-aqueous solvents has been reported i n the l i t e r a t u r e ^ * 50. A small number of exchange experiments were a l s o done i n the present work. These included,using both copper sulphate and perchlorate solutions and deuterium was introduced from e i t h e r the gas phase as D 2 or the solvent as D 2 0 . Five exchange experiments were performed i n a l l and the experimental conditions are shown i n Table VIII. The rate of exchange was measured by. taking gas samples p e r i o d i c a l l y and analyzing them mass spectrometrically f o r D 2, HD and H 2. TABLE VIII. Experimental Conditions f o r Exchange Experiments Experiment ~ " " Sol vent ™ ^ Temperature r +. Number [ C u " ] * [ H 2 S 0 4 ] o [ H C 1 0 4 , ] o S ° 1 V e n t P D 2 P H 2 V [H 3° D 2 -A*^  0 . 1 5 M 0 . 5 0 M H 2 0 5 atm. 1 6 0 r - O . j ^ M D2-B 0 . 1 5 O . 8 5 H 2 0 5 1 6 0 0 . 7 2 D2-C 0 . 0 7 - 0 . 1 0 M H 2 0 15 1 6 0 0 . 1 0 H2-D 0 . 1 5 O . 8 5 D 2 0 5 a ^ m 1 6 0 0 . 7 2 D 2 - E T 0 . 0 0 0 . 5 0 H 2 0 5 1 6 0 ^ 0 . 1 A C u S 0 4 except f o r experiment D2-C i n which C u ( C 1 0 4 ) 2 was used. M S o l u t i o n O . 3 5 M i n [ M g S 0 4 ] Assuming the bisulphate d i s s o c i a t i o n constant i s 1 0 _ 2 M _ 1 at l 6 0 ° C . * Solution 0 . 5 0 M i n [ M g S 0 4 3 In a d d i t i o n several l i q u i d samples were taken, usually d i r e c t l y a f t e r a gas sample, to measure the rate of appearance of cuprous ions. The normalized r e s u l t s (Appendix I) f o r these experiments are shown i n Figures. 3 0 to 3 3 • - 72 -Figure 3 0 . Rate Curves of T o t a l C u , HD, H 2 and (HD + hE2) Experiment D2-A) 0.15 M [ C u S 0 4 ] ° , O.5O M [ H 2 S 0 4 ] o , O .35 'M [MgS0 4 ] , I n i t i a l D 2 5: atm, l 6 0°C. - 73 -0 60 120 180 240 Time minutes Figure 31. Rate Curves of T o t a l Cu 1, HD, H 2 and (HD + 4H 2), Experiment D2-B; 0.15 M [CuS0 4]°, O.85 M[H 2S0 4] o, I n i t i a l D 2 5 atm, l60°C. - 74 -0 60 120 180 240 300 360 Time .minutes Figure 32• Rate Curves of To t a l Cu , HD, H 2 and (HD + 4H 2), Experiment D 2-CJ 0.07 M[Cu(C10 4 ) 2 L, 0.10 M[HC10 4]°, I n i t i a l D 2 15 atm, 160°C. - 75 -H •Time minutes Figure 55. Rate Curves of T o t a l Cu HLV D 2 and (HD + k D 2),• Experiment H2-D; 0.15 M •[CuS0 4]o, O.85 M[H 2S0 4]o, I n i t i a l H 2 5 atm, 160°C. - 76 The appearance of H 2 in the gas phase results from exchange following the reaction of H D with copper ions and back reaction with H + to form hydrogen. The plot of ( H D ; + 4H 2) is the rate curve for the total exchange taking place during the experiment assuming that the only reactionswhereby exchange occurs are those given by equations -34 and -36. No exchange was observed in the experiment D 2 - E without copper in solution, indicating that the presence of either cupric or cuprous is required to support the exchange reaction. It is known that deuterium exchange may also be catalyzed by hydroxyl ions-^ but the exchange rate due to this i s too small to be observable in the present acid solutions. .Rate measurements were made at several Cu* levels of both the net forward rate 1 dCu • and the exchange rate d ( H D + 4H 2 ) and are shown plotted 2 dt dt in moles/sec against Cu* in Figure 34. Kinetically the exchange rates can be related to the net forward rates by the following equation a(HP = R e x c h = k ^ [ £ ] 1 dCu£ + K - 3 [H +] R g j / k - x [H dt k 2 [Cu 1 1 ] 2 dt k l [Cu±J-J I k s [c : + ] , + ^ (50) where R Q ^ I is the cuprous catalyzed portion of the net forward rate. i\ The factor 4 before H 2 results from the exchange following the reaction of HD with CuH (or Cu 1) which f i r s t of a l l gives rise to a factor of 2. An additional factor of 2 must be used because this exchange can take place by two equally probable paths i f isotope effects are neglected, i.e., , Cu** + HD \ CuD* + H + CuH + D + and k CuD+' + H + ^ ' Cu** + HD CuH+ H 2 kk Rate measurements are l i s t e d in Appendix I. Figure $k. Plots of Net Forward Rate and Exchange Rate vs. Cu 1 f o r Each Exchange Experiment - 78 -Equation 50 was derived from the copper reduction mechanism (equations 34 "to 37) by using the steady state approximation i n CuH + and CuH together with the expression f o r the net forward rate (equation 38). At Cu 1 = 0, R Q U 1 1 s a l s o z e r ° and equation 50 reduces to Rexch = __=_ [ H + J , • 1 ( 5i)) k 2 [Cu-1-1] 2 dt Equation 51 maybe used to estimate k - i from the exchange and net forward rates k 2 and zero cuprous, i . e . , the intercepts of the plot s i n Figure 3 k provided isotope e f f e c t s are disregarded. .Values of t h i s r a t i o are l i s t e d i n Table IX. for each experiment together with figures f o r k-3 estimated with equation 50 from the rates measured at Cu 1 = 0.01 k 4 moles (Figure 34) and the previously obtained values of k-j.. k 2 TABLE IX. Values of k - i and k-3 from Exchange Experiments k 2 k 4 Experiment k 2 k 4 at Cu-1 = 0.01 moles D2-A 1.15 0.33 D2-B 0 . 4 l O.kl D2-C 2.24 H2-D 0.15 0.03 Although these values e x h i b i t some v a r i a t i o n those obtained f o r the high a c i d experiment (,D2-B) are of the same order of magnitude as the r a t i o s obtained previously i n the a c i d series (Table V ) . This can be considered as evidence that the exchange reac t i o n takes place, at l e a s t i n part, according to the mechanism of reduction of cupric sulphate given i n equations 34 to 37• - 79 -The ratios of exchange rate to net forward rate were determined for each experiment and are shown plotted in Figure 35 • , In sulphate solutions these ratios are greater for the high acid (D 2-B) than for the low acid (D2-A) experiment, and this i s as expected from the copper reduction mechanism. The exchange rates of the low acid experiment are slightly higher than those of the high acid run (Figure J>k) although the opposite should be tru according to equations -3k and -36. A possible explanation for this discrepancy' might be that additional deuterium exchange occurs by other unobserved reactions, e.g., Cu(OH)+ + D2 Cu(OD)+ + HD .....(52) The exchange rates measured in the cupric perchlorate experiment, D2-C are much greater than those of the sulphate runs (Figure 3 k)• Also the ratios of exchange to net forward rate (Figure 35) a r e considerably greater and increase markedly with cuprous. The strong effect of the cuprous ion on the exchange rate suggests that this species catalyzes the exchange between D 2 and H+. This is of interest in view of the earlier reported low catalytic activity of cuprous in the reduction of cupric perchlorate (Figure 71) • If in perchlorate solutions a similar mechanism applies for hydrogen activation by cuprous as in the sulphate system the above results would suggest a much greater ratio of k-3 in the perchlorate system. k 4 The exchange rates measured in experiment H2-D, where D20 was the solvent, are considerably lower than those of D2-B although the acidity and i n i t i a l cupric concentrations were the same in both. This difference in rates might be a solvent effect and l i k e l y due to a lower thermodynamic activity of ± The net forward rates were corrected for the perchlorate decomposition effect. - 80 -- Figure 35. Plots of Exchange Rate over Net Forward Rate vs Cu 1 f o r Each Exchange Experiment. - 81 -D + i n D 20 r e l a t i v e to that of H + i n H 20, r e s u l t i n g from the a b i l i t y of D 20 to 51 hydrate ions more strongly than H 2 C r . The net forward.rates were also measured i n terms of moles/liter/sec, i i . e . , 1 d[Cu* ] , and compared with those obtained from experiments i n which 2 dt H 2 was used (Appendix.I). -They were about 20 to 50$ slower than the l a t t e r , and t h i s may be a t t r i b u t e d to the isotope e f f e c t . This e f f e c t i s s i m i l a r i n magnitude to that observed i n the reduction of cupric acetate i n quinoline 52 s o l u t i o n s ^ , The net forward rates i n experiment H2-D, using D 20 and H 2 were however, v i r t u a l l y the same as those of the corresponding experiment with ordinary water and H 2, i n d i c a t i n g that i n sulphate s o l u t i o n D 20 as solvent has no e f f e c t on the a c t i v i t y of Cu** and Cu"'" toward hydrogen. This observation i s i n l i n e with that of Harrod and Halpern^^ w n o found that the r a t i o of rate constants kH 20 was close to unity (0.93) f ° r hydrogenation reactions i f KD 20 cupric ions were complexed with acetate. For cupric aquo complexes t h i s r a t i o was found to be la r g e r (1.20) and the differe n c e was ascribed to the a b i l i t y of D 2 0 to hydrate metal ions more strongly^* than H 20 (hence k^ Q k H 2 o ) ' Therefore, one explanation f o r the zero solvent e f f e c t i n the present experiment II I i s that both Cu and Cu may be complexed with sulphate rather than with D 2 0 . The A c t i v a t i o n of Hydrogen by Cuprous Ions The experimental evidence of t h i s study indicates that i n aqueous sulphate solutions both cupric and cuprous ions activ a t e hydrogen. This probably takes place by h e t e r o l y t i c s p l i t t i n g of the H 2 molecule r e s u l t i n g i n the formation of a copper hydride (CuH + or CuH) and the simultaneous release of a proton i n the a c t i v a t i o n step. Atlhough the nature of these hydrides i n aqueous s o l u t i o n has not been determined by d i r e c t observation, t h e i r existence appears f a i r l y + conclusive on k i n e t i c evidence. CuH appears to have been observed spectro-- 82 -s c o p i c a l l y 5 ^ and i t s formation i n the a c t i v a t i o n of hydrogen by aqueous hi cupric ions was shown to be probable on energetic grounds . CuH has been 5 5 prepared i n the s o l i d s t a t e ^ and thermochemical data of the gaseous species have been-published 5^' I t i s analogous to AgH which has been proposed to account i n part f o r the k i n e t i c s of hydrogen a c t i v a t i o n by aqueous Ag + 1^. Using published thermochemical^data the endothermicity of the a c t i v a t i o n reaction can be represented as follows, • Cu 1 + H 2 p. CuH + H +; A H = 53 k c a l + A H S C u R (530 where AHSQ UJJ i s the solva t i o n energy of gaseous CuH. With AH^ = 14.5 k c a l t h i s requires that /\Hg^^j i s - 38.5 kcal/mole i f CuH i s e f f e c t i v e l y the a c t i v a t e d complex and more negative than t h i s i f CuH i s s i g n i f i c a n t l y more stable than the activa t e d complex. T T T The mechanism f o r hydrogen a c t i v a t i o n by Cu and-Cu (equations 3 k 30 to 37) i s s i m i l a r to that given by Chalk and Halpern f o r the a c t i v a t i o n of H 2 by cupric and cuprous heptanoates i n organic solvents such as diphenyl octadecane and heptanoic a c i d above 120°C. This mechanism a l s o involves hetero-l y t i c s p l i t t i n g of the hydrogen molecule by both copper species. C a l v i n and 28 Wilmarth , on the other hand•observed a homolytic a c t i v a t i o n of hydrogen by cuprous ions i n quinoline solutions at 100°C. according to 2 Cu 1 + H 2 • 2Cu IH (5k) but t h i s was not found i n the heptanoate and aqueous sulphate systems. ft The following standard enthalpies of formation were used: _Cu | a q j 17.1 k c a l 5 8 ; H 2 ( a q j 0.9 k c a l (calculated f o r 25°C from Figure 1, reference 59); CuH^g^ 71 k c a l 5 7 ; H + ^ a q ) °-- 83 -l 8 The cuprous mechanism may be compared with that of s i l v e r ions i n aqueous perchlorate solutions where a c t i v a t i o n of hydrogen by both homolytic and h e t e r o l y t i c s p l i t t i n g takes place. The l a t t e r path predominates at higher temperatures (100 to 120°C) and d i l u t e s i l v e r solutions (<-v»0.01M) whereas the former i s prevalent i n the range of 30 to 50°C.at higher con-centrations of A g + 0.10 M). In view of t h i s i t i s p l a u s i b l e that cuprous i ions a l s o a c t i v a t e H 2 by homolytic s p l i t t i n g i n aqueous systems but t h i s r eaction never becomes important because at high temperatures i t i s masked by the h e t e r o l y t i c path and at low temperatures the cuprous ions disproportion-ate to such an extent i n a c i d solutions that concentrations high enough to permit observation of any a c t i v i t y cannot be obtained. An important observation from the present study i s the considerable a c t i v i t y of cuprous ions i n both sulphate and perchlorate solutions toward deuterium exchange. However i n the reduction of cupric ions the enhancing e f f e c t of Cu* i s s i g n i f i c a n t only i n sulphate solutions, and appears r e l a t i v e l y small i n the perchlorate system. I f i t i s assumed that the mechanism of hydrogen a c t i v a t i o n by cuprous ions i s the same i n both systems t h i s would mean that the r a t i o k-3 must be considerably l a r g e r i n perchlorate solutions than k 4 the value of O.45 obtained i n the sulphate system. From the reactions associated with these rate constants, i . e . , CuH + H + k"s Cu 1 + H 2 (-36) CuH + C u 1 1 CuH + + Cu 1 (37) i t appears l i k e l y that the change i n k-3 i s due p r i m a r i l y to a change i n k 4. k 4 Reaction 37 i s an electron t r a n s f e r process which would proceed more r a p i d l y 60 6 l i f a bridging l i g a n d such as sulphate were present to f a c i l i t a t e the t r a n s f e r ' - 8k -Thus k 4 would be expected to be l a r g e r i n sulphate than i n perchlorate solutions where Cu** i s complexed as the aquo ion only. Provided that k_ 3 i s not much d i f f e r e n t i n both systems, t h i s w i l l explain why Cu* makes a very small c o n t r i b u t i o n to copper reduction but a s u r p r i s i n g l y large contribution to deuterium exchange i n perchlorate solutions r e l a t i v e to sulphate solutions. Thus i t seems that t h i s a nalysis has permitted an e f f e c t to be observed that involves a very*fast reaction, namely the electron t r a n s f e r process of equation 37, because i t competes with another s i m i l a r l y f a s t reaction which i s the back r e a c t i o n , equation -36. This argument can a l s o be applied to the Cu** ac t i v a t e d reduction path where k-x i s about 0.13 i n sulphate solutions and O.k to 0.5 i n perchlorate solutions. Thus, the complexing of Cu i n the sulphate system would enhance the value of k 2 over that i n the perchlorate system i n much the same way as for k 4. - 85 -CONCLUSION The present work describes an i n v e s t i g a t i o n of the reduction of cupric ions by molecular hydrogen i n aqueous perchlorate and sulphate solutions. The objective was to resolve the k i n e t i c s of t h i s reaction and p a r t i c u l a r l y to e s t a b l i s h the r o l e of cuprous ions i n the reduction mechanism. In the sulphate system considerable c a t a l y t i c a c t i v i t y of cuprous ions was found and the mechanism describing the reduction k i n e t i c s has been postulated to be v IT k-v + + C u x + H 2 > CuH + H k - i CuH + + C u 1 1 2CU1 + H + T k 3 Cu 1 + H 2 *> CuH + H k-3 CuH + C u 1 1 k ^ CuH + + Cu 1 This mechanism gives r i s e to a two term rate law of which one depends on cupric only and the other exhibits a f i r s t order dependence on cuprous concentration. This rate law has the form -d[H 2] = k ^ C u 1 1 , 2 , ^ ] + k 3 [ C u I I ] g [ C u I ] [ H P ]  dt £z__[H +]+[Cu i : C] f k - l [H +] + [ C u n ] V - ^ L [H +] + [CuII] k 2 \k 2 / \ k * The studies i n perchlorate solutions showed that the k i n e t i c s are adequately described by the f i r s t two reactions i n the above mechanism represented by the f i r s t term of the rate law and that the enhancing e f f e c t of C u + on rates was only s l i g h t . A correction of rate measurements due to perchlorate decomposition had to be taken i n t o account i n order that a meaningful- analysis of the data could be obtained and only then was the small C u + e f f e c t observable. - 86 -Exchange experiments with deuterium i n place of hydrogen gave rates consistent with the proposed .mechanism although i n perchlorate solutions much higher exchange rates were observed than i n sulphate solutions. This indicated that k- 3 i s much greater i n perchlorate than i n sulphate solutions. k 4 REFERENCES - 8 7 -1. F. A.• Schaufelberger and T. K. Roy, Trans. Inst. Min. and Met. 64, 375 (1955). 2. F. A. Schaufelberger, Trans. A.I.M.E., 206, 695 (1956); J . Metals 8 , 695 (1956). 3. D. J . I. Evans, S..Romanchuk and V. N. Mackiw, C.I.M.M. B u l l , 5_4, 530, (1961). 4. V. H. Ryan and H. J . Tschirner,.Proc. Metal Powder Assoc. 1, 2 5 (1957). 5 . F. A. Forward, Trans. C.I.MM., 5_6, 3 6 3 (1956). 6. F. A. Forward, B u l l . Inst. Metals, 2, 1 1 3 (1954). 7 . V. N. Mackiw, W. C. Lin, and W.-Kunda,,Trans. A.I.M.E.,• 209, 786 (1957). 8 . R. F. Pearce, J . P. Warner and V. N Mackiw, J . Metals, 12, 2 8 ( i 9 6 0 ) . 9 . J . Halpern, Trans. A.I.M.E., 209, 280 (1957); J . Metals, %, 280 (1957). 10. E. Peters and J . Halpern, Can. J . Chem, 35, 5 5 6 (1955). 11. E. Peters and.J. Halpern, J . Phys. Chem, 5_£, 795 (I955). 12. H. F. McDuffie, E. L. Compere, H. H. Stone,,L. F. Woo a n d C . H . 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Inc., .Englewood C l i f f s , , N J . (1952), p. 184. 57. F..D. Rossini,.D. D. Wagman,.W. H. Evans,-S.-Levine, and I. J a f f e , "Selected Values of Chemical Thermodynamic Properties", National Bureau of Standards C i r c u l a r ^>0Q, U- S. Government P r i n t i n g O f f i c e , Washington D.C., (1952), p. 208. 58. D. D. Wagman, J . Am. Chem.-Soc 7_3, .5^63 (1951). 59. D. M. Himmelblau, J . Chem. and-Eng. Data, 5_, 11 (i960). 60. D. R. Stranks i n J . Lewis and R. G. Wilkins, "Modern Coordination Chemistry", <Interscience'Publishers,•Inc., New York (i960), p. 78. 61. J . Halpern, Quarterly Reviews, 15_, 207 (1961). - 9 0 -APPENDICES APPENDIX A Report on Research Work f o r the Period.of May 1st to September 1st, i960  Introduction: The purpose of t h i s i n v e s t i g a t i o n was to determine whether N i 1 1 , Fe , Co and Cr i n aqueous solutions were active as c a t a l y s t s i n the hydrogen reduction of dichromate. These ions had been studied p r e v i o u s l y 1 f o r t h e i r c a t a l y t i c a c t i v i t y i n the hydrogen reduction of oxygen between 200 and 300°C, and a pressure drop method was used f o r following the rates. Although no a c t i v i t y had been observed i n that work i t was decided to reinvestigate these ions by measuring the rate of disappearance of dichromate, since t h i s method i s more s e n s i t i v e f o r observing rates than that of determining pressure drops. Most experiments were performed at 258°C using both sulphate and perchlorate s o l u t i o n s . Experimental: The experiments were carried-out i n a one-gallon high pressure p 1 autoclave described e a r l i e r . The s i l i c o n - c a r b i d e powder packing i n the annular space between the titanium l i n e r and the autoclave v e s s e l was removed since corrosion attack on the titanium l i n e r and the vessel was observed at 258°C. Although the l i n e r was placed loosely, i n t o the v e s s e l with only a steam-gas mixture i n the annular space, good temp-erature c o n t r o l (* 0.5°C).was obtained up .to 258°C. The s t i r r e r shaft s t u f f i n g box was f i t t e d with John Crane Chemlon (molded t e f l o n ) V-rings which provided .an excellent pressure s e a l . However r a p i d wear of the rings at the extreme conditions of 258°C and 800 p s i g required addition of an extra V-ring a f t e r each run. A l l chemicals were of reagent grade q u a l i t y manufactured by Baker and Adamson Company Limited. Hydrogen and nitrogen were supplied by Canadian - 92 -L i q u i d A i r Company and used without further p u r i f i c a t i o n . The experimental procedure comprised heating of the s o l u t i o n to temperature under a nitrogen atmosphere, sampling once- or twice within one hour to check i f reduction of dichromate took place i n the absence of hydrogen, flu s h i n g nitrogen, adding hydrogen, and pe r i o d i c sampling to follow the •course of dichromate reduction. Analyses of dichromate were made e i t h e r spectrophotometrically or b y ' t i t r a t i n g with ferrous ammonium sulphate s o l u t i o n . Results and Discussion: Most experiments were made at 258°C and 10 atm hydrogen p a r t i a l pressure with an i n i t i a l dichromate concentration of 0.005 M, and the experimental r e s u l t s for. each ion investigated are summarized below. - N i 1 1 - A number of• experiments with 0.1 to 0.2 M[NiS0 4] and 0.2 to O.72 r - l II M L H 2 S O 4 J solutions showed that Ni i s not active as a ca t a l y s t f o r hydrogenation of dichromate. C o + + - No reduction of dichromate was observed during 160 minutes f o r solutions O.O75 "t° °.l M i n Co(C10 4) 2 and 0.1 M i n HC10 4. F e + + + - No reduction of•dichromate took place during 100 to 170 minutes i n s o l u t i o n s - o f 0.004 M[Fe(C10 4) 3](prepared from 99-9$ pure i r o n t e s t wire) and-0.1 to 0 .5 M[HC10 4]. Dichromate reduction d i d take place when reagent grade FeCl3 was used, but t h i s was probably due to small amounts of active impurities present i n the s a l t (e.g. 0.005$ C u + + ) . In a l l experiments p a r t i a l hydrolysis of F e + + + occurred and i t s extent depended on the a c i d i t y of the sol u t i o n . - 93 -Cr - No reduction of dichromate occurred using 0 .01 M C r C l 3 , 0 .1 M H C 1 0 4 , 10 atm.-H2 and 258, 220, and 210°C. The solutions were heated under 10 atm. H 2 to prevent oxidation of C r + + + by CIO4 to dichromate. C r + + + hydrolyzed slowly i n each experiment at temperature. The r e s u l t s of t h i s i n v e s t i g a t i o n have shown co n c l u s i v e l y that sulphate or perchlorate s a l t s of N i 1 1 , ' F e + + + v C o + + and C r + + + possess no c a t a l y t i c a c t i v i t y toward hydrogen i n aqueous so l u t i o n s . 1. 2. H..F. McDuffie et a l . , J . Phys. Chem. 62, 10J0 (I958). E. A. Hahn, Master's Thesis, The U n i v e r s i t y of B r i t i s h Columbia, i 9 6 0 . - 9k -APPENDIX B. • A V W V Rate Measurements f o r Experiments i n Perchlorate System TABLE B - l Aci d S e r i e s : 0 . 0 3 0 M [ C u ( C 1 0 4 , 2 ] o , 1 0 atmH 2, l 6 0°C, Experiment ' H + -5, 0 . 0 1 5 M [ H C 1 0 4 ] o [Cu +]M i d[Cu +] Msec"1 " ^ l 2 - Msec"1 [H+]M ^ dT dt i n-3 k X i o - 3 1 . 9 3 x 1 0 - 6 1 . 9 3 X 1 0 " 6 1 9 8 1 . 6 0 1 . 6 1 2 3 1 2 1 . 0 0 1 . 0 2 2 7 1 6 0 . 4 4 5 0.48 3 1 1 8 0 . 2 7 3 0 . 3 1 3 3 Experiment H + - 1 0 , 0 . 0 3 0 M . H C 1 0 4 ] ° k X 1 0 - 3 1 . 3 8 X 1 0 " 6 1 . 3 9 X I O - 6 3 4 8 1 . 0 2 1.04 , 3 8 1 2 0 . 7 1 3 0 . 7 5 42 1 6 0 . 3 3 0 O . 3 8 46 1 8 0 . 1 9 5 9 . 2 6 48 Experiment H + - 8 , 0 . 0 5 0 .M [ H C 1 0 4 ] o k X 1 0 - 3 0 . 8 0 0 X 1 0 " 6 0 . 8 2 X 1 0 " 6 5 4 8 0 . 6 6 2 0 . 7 0 5 8 1 2 O.39O 0 . 4 6 - 6 2 1 6 0 . 1 9 0 0 . 2 9 6 6 1 8 0 . 1 1 2 0 . 2 2 6 8 ,-3 Experiment H + - 11, 0-070 M[HC10 4] o 4 X 10- 3 0.647 X 10-6 0 . 6 8 X 10" 6 7 4 X IO" 3 8 0.546 0 . 6 0 7 8 12 0.282 O . 3 7 8 2 1 6 0 . 1 1 7 0 . 2 6 8 6 Experiment H + - 9, 0.100 M[HC10 4] o 4 X IO" 3 0 . 4 1 6 X 10" 6 0.47 X IO" 6 104 X 10" 3 8 0 . 2 8 5 0.40 108 12 O.I57 0.34 112 A Rate measurements were made with the mirror image,,method at several [Cu-+] l e v e l s along the rate carves of each experiment. M In the perchlorate system, measured rates were corrected f o r the perchlorate decomposition e f f e c t i . e . , -d [H 2 ] = 1 d[Cu +] + k^, dt 2 dt [Cu +][H +][C10 4] , k d = 2.07 X 10- 4M" 2sec-i (Appendix C). - 95 -TABLE B-2. Cuprous S e r i e s : 10 atm H 2, l60°C. Experiment C u + - 20, >0.060<M[Cu(C10 4) 2]O, 0.070 M[HC10 4] C [Cu +] M | i l g i H Msec-i " ilSai M s e c - i [H +] M [ C U + + ] M 20 x 1 0 - 3 1.50 x i o - 6 1.78 X 10-6 90 X i o - 3 ho x 10- 3 25 1.10 i.hi 95 55 50 0.66 1.15 100 30 Experiment C u + --21, O.O5O M[Cu(C10 4 2 ] O , 0.080'M[HC104]o 10 x i o - 3 1.29 X I O - 6 1.45 X I O " 6 90 X I O - 3 1+0 X I O " 3 15 1.05 1.26 95 35 20 O.76 1.06 100 30 .Experiment C u + --22, 0.040 M[Cu(C10 4 ) 2 ] o , O.O9O M[HC104]o 10 X I O - 3 0.68 X I O " 6 ,.0.82 X I O - 6 100 X I O - 3 30 X I O - 3 TABLE B-5. Cupric S e r i e s : 0.100 M_HC10 4]O ; 10 atm E2, l60°C. Experiment H + - 9, 0 .030M[Cu (C10 4 ) 2 ]° [Cu +] M i % i M s e c - i -5_|alMsec-i [ C u + + ] M 4 X 10' -3 X 0.416 X 10" 6 0.47 X I O - 6 26 X 10" -3 8 O.285 0.40 22 12 O.I57 0.34 18 14 0.082 0.30 16 Experiment [Cu + +] - 1, o.o4o M [ C U ( C I O 4 ; ) 2 ] ° 4 X 10' -3 0.794 X I O " 6 0.86 X I O " 6 36 X 10" -3 8 0.678 0.81 32 12 0.554 0.75 28 14 0.430 0.67 26 16 0.290 0.57 24 18 0.185 0.50 22 Experiment [ C u + + ] - 2, 0,050 M [ C U ( C I O 4 ; )2]o 4 x 10" -3 1.173 X I O " 6 ' 1.24 X I O " 6 46 X 10" -3 8 1.058 1.20 42 12 0.981 1.20 38 14 0.880 1.14 36 16 0.777 1.08 34 18 O.607 0.97 32 Experiment [Cu + +] - 3 , 0.060 M [ C U ( C I O 4 ; ) 2]o 4 X 10' .3 1.68 x 10- 6 1.76 x 10- 6 56 X 10" -3 8 1.68 1.84 52 12 1.49 1.73 48 14 1.38 1.67 46 16 1.27 1.61 44 18 1.12 1.51 42 r ++1 Experiment LCu J - 0.070 M [ C U ( C I O 4 ; ) 2 ] ° 4 x 10' -3 1.98 X I O " 6 2.06 X 10" 6 66 X 10--3 8 2.10 2.27 62 12 2.04 2.31 58 14 1.94 2.26 56 16 1.83 2.20 54 18 I . 7 8 2.20 52 k c i = — . - • •• - ^ (c"3) APPENDIX C. Determination of the Perchlorate Reduction Rate Constant kg-. Chloride- ions r e s u l t i n g from attack of CIO4 by Cu w i l l appear ++ during the hydrogen reduction of Cu according to the stoichiometry 8Cu+ + 8H+ + CIO4" • 8Cu + + + C l " + 4H 20 (C-l) The rate of t h i s r e a c t i o n i s assumed to be -represented, by d[Cl"] = kpT [Cu +][H +][C10;] .....(c-2) dt Solving f o r kg-]_, t h i s equation i n the integrated form becomes [Cl~] t [CIO4] P ( [ c u + f + [H + J o[Cu +]) dt since [H +] i s [H +] 0+[Cu +]. [C10 4] i s assumed to remain constant during the course of an experiment because the amount reduced i s small. The subscript t i s the time at which [Cl~] i s measured, u s u a l l y at the end of a run, and to which the in t e g r a t i o n i s performed. The i n t e g r a l i n equation C-3 i s evaluated g r a p h i c a l l y by estimating [Cu +] values from the rate curve of a C u + + reduction experiment (e.g. Figure ft C-1) f o r a number of equal time i n t e r v a l s up to time t . The value of the i n t e g r a l thus obtained from the rate curve i n Figure C - l i s 0.65^ M 2 min at t = 600 min, and with [ C I O 4 ] = 0.13 M ,and [ C l " ] t = O.99 X 1 0 - 3 M k ^ i s cal c u l a t e d to be I .93 X 1 0 - 4 M~zsec~x. Values of k ^ were' c a l c u l a t e d f o r eight experiments and are l i s t e d i n Table C - l together with the i n i t i a l experimental conditions f o r each run. Experiment H -11; see Table C - l f o r experimental conditions. 20 . 99 -The average value obtained f o r t h i s constant i s 2.07 X 1 0 - 4 * 7$ M _ 2 s e c _ 1 . TABLE C - l . Values of kg-^ from Eight'Experiments and Data* of I n i t i a l • Experimental Conditions Experiment Number k c i M ^ s e c - 1 [ C u + + J 0 M [H +]o M [CIO;] M '[Cl" " ] M Time min C u + + - 1 2.1k X 1 0 " 4 0.04 0.10 0.18 1.01 X 10-3 330 C u + + - 2 2.27 0.05 0.10 0.20 1.46 300 Cu + + - 3 1.94 0.06 0.10 0,22 1.90 300 C u + + - 4 1.94 0.07 0.10 0.24 2.65 300 H + - 8 2.15 O.OJ 0.05 0.11 O.56 480 .H +- 9 I . 8 5 0.03 0.10 0.16 1.18 600 H+-10 2.27 0.03 0.03 0.09 0.43 480 H + - l l 1.9k 0.03 0.07 0.13 O.99 600 Average 2.07 x i o " 4 * 7$ M ^ s e c - 1 ft 10 atm H 2 and l60°C f o r a l l experiments. Using t h i s value and the equation [ C u + ] o x i d i z e d = 8 [ C 1 _ ] = 8 k c i [ e i ° 4 ] / ( [ C u + ] 2 + [ H + ] 0 [ C u + ] ) dt .....(C-4) ^o a t h e o r e t i c a l curve for the oxidation of cuprous ions was c a l c u l a t e d f o r experiment + H -11 and i s shown i n Figure C - l . As expected, the rate of cuprous oxidation at f i r s t increases with r i s i n g [Cu +] but then becomes constant as the [Cu +] rate curve l e v e l s o f f . APPENDIX D. - TABLE D - l . Thermodynamic Data* f o r C a l c u l a t i n g A F ° T f o r the Disproportionation Reaction A F ° s° kcal/mole t eu Cu + +(aq) 15.5 -23.6 Cu +(aq) 12.0 Cu°(s)• 0.0 8.0 ft A l l data are from W. M. Latimer, "Oxidation P o t e n t i a l s " 2nd ed. Prentice H a l l , Inc.,. Englewood C l i f f s N.J., (1952), except those f o r Cu+(aq.) which are taken from'D. D..Wagman, J. Am. Chem. S o c , JJ5, 5463 (1951). - 101 -APPENDIX E Integrated Rate Curves f o r the Perchlorate System (a) Before disproportionation of Cu +. The rate curve was cal c u l a t e d i ) , w i t h equation 26 and i i ) by graphical i n t e g r a t i o n of equation 17 that includes the perchlorate decomposition c o r r e c t i o n . The i n i t i a l experimental conditions were: 0.03 M[Cu (C10 4 ) 2 ] , 0.07 M[HC104j, 10 atm. H 2, l60°C. i ) Values of t as a function of [Cu +] obtained with equation 26 are l i s t e d i n Table-E-l and were obtained by using k x = 6.0 X 1 0" 3M~ 1sec - 1, k - i = 0 A 5 , ' [H 2] = 11.8 X 10" 3 M. k 2 TABLE E - l . t as a Function of [Cu +] Calculated with Equation 26 [Cu +] M t min k X 10" 3 36 8 85 12 151 16 252 20 425 2k 809 i i ) Equation 17 was rearranged to the form t = f [f(e + x) + (b - x)] dx  j a(b - x ) 2 - gx (e + x ) [ f ( e + x) + (b - x)] —0 and t ca l c u l a t e d as a function of x by graphical i n t e g r a t i o n j the symbols being: x = [Cu +] M A x = 2 X IO" 3 M - 102 -a = 2 k 1 [ H 2 ] = 2 X 6.6 X 10" 3 X 11 .8 X 10" 3 s e c " i b = [Cu + +]° = 30 X 10" 3 M e = [H +]° = 70 X IO" 3 M f = k - i = 0.49 * k 2 g = 8 k c l[C104J = 8 X 2 .07 X 10" 4 X 0.13 M ^ s e c " 1 TABLE E-2. t as a Function of [Cu +] from Graphical Integration of Equation 17. [Cu +] ,M t min 2 X 1 0 " 3 16 4 36 6 58 8 85 10 119 12 162 14 225 16 321 18 562 (b) A f t e r disproportionation of Cu"1". The i n i t i a l experimental conditions were 0.137 M[Cu ( C 1 0 4 ) 2 ] , 0.103 M[HC10 4 ] , 10 atm H 2, l 6 0°C. The rate curve was c a l c u l a t e d by graphical i n t e g r a t i o n of an expression that included the rate law a f t e r disproportionation, equation 3 1 , -and the perchlorate decomposition c o r r e c t i o n , i . e . , 4 kQj_[Cu +] [H +] [C10 4 ], This expression has the form t = - f (l + 1 + 4K1/g xY2 j dx / / a xs - c xx/2 LH1 J \ ^x D \b[ir] + x K^2 J in D i f f e r e n t values of k x a n d - w e r e used here than i n i ) to check i f these s l i g h t changes had any e f f e c t on the shape of the rate curves. The e f f e c t was however, found to be small. where x = [Cu ] M Ax = 5 X I O - 3 M a = k i [ H 2 ] = 6.0 X IO" 3 X 11.8 X IO" 3 s e c " 1 b = k_!_ = 0.50 k 2 c = 4k [CIO4] = 4 X 2.07 X IO" 4 X O.356 M"1 s e c " 1 K = 2 6 U XM-i [H +] = ([H +]o + 2 x Q - 2x - ( J)7 2 j M Values of t as a function of [Cu ] are l i s t e d i n Table E - 5 . t as a Function of [Cu ] A f t e r Disproportionation TABLE E - 5 . of Cuprous Ions [ C u + + ] M t min 105 X 10-3 17 46 96 162 270 495 100 95 90 85 80 Average value of [CIO4] over course of e n t i r e run- taking i n t account los s due to decomposition to C l " . - 104 -APPENDIX F. Estimation of Hydrogen'Ion Concentration i n Sulphate System at l60°C. No information was available f o r the bisulphate dissociation constant, Kt>,.at l60°C. Hence, f o r determining hydrogen ion concentrations i n the sulphate system-K-b was estimated to be within the range of I O - 3 to I O - 2 M at that temp-erature . This estimate i s based i n part on the published change i n K^ i n the range of 5 to 55°C where i t i s found to decrease from 1 .8 X I O - 2 M at 5°C to 4.1 X I O - 3 M at 55°C. 1 Extrapolation of a l i n e a r log K^ vs temperature p l o t of the published data gave a value of 2.2 X 10"4.M at l60°C. However, t h i s decrease i s o f f s e t to some extent by the high i o n i c strengths i n the experimental s o l u t i o n s . For example, the average values of K^ i n the range of 20 to 50°Cwas shown ' to increase from 2.5 X I O - 2 M at 0.1 M H 2S0 4 to 1.0 X 1 0 - 1 M at about 1.4 M H 2S0 4 . This increase w i l l be enhanced i f H 2S0 4 i s replaced i n part by CuS0 4 and MgS04, and, assuming the i o n i c strength e f f e c t to be s i m i l a r at 160°C, t h i s i s l i k e l y to b r i n g the value of K^ int o the range of 10~ 3 to 1 0 - 2 M at that temperature. In c a l c u l a t i n g the hydrogen ion concentrations at l60°C the e f f e c t of complexing of sulphate by cupric ions was neglected. Although some inform--ation e x i s t s on the association constant f o r the reaction ++ - K a Cu + S0 4 » CuS0 4 3 i 4 at room temperature ( K a = 4.5 M" ) and at 110°C (K a = 6.1 M"1) no data are ava i l a b l e f o r l60°C. 1. R. W. Gurney, "Ionic Processes i n Solution", Dover Publications Inc., New York, 1962, p. 121. 2. M. E..Wadsworth and D. .R. .Wadja, J . Metals J_, 755 (1955). 5. R. Na.sa.nen and B. K l a i l e , . Suomen Kh e m i s t i l e h t i , B 27, 50 (1954). 4. E. Peters and J . Halpern, .Can. J . Chem., 3J+, 554, (1956). - 105 -APPENDIX G. ft Rate Measurenents f o r i Experiments i n Sulphate System TABLE G-l. Acid Series: 0.15 M[CuS0 4]o, 5 atm H 2 , l60°C. Experiment: H 2 S 0 4 - 2 H 2 S 0 4 - 1 C u 1 1 - 1 H 2 S 0 4 - 3 [H 2S0 4 ] o M: O.5O 0.60 0.70 O.85 [MgS04] M: O.35 0.25 0.15 0.00 [Cu T ] M dt Msec- 1 5 X IO" 3 4.32 X 10-6 3.66 X 10" 6 - 2.04 X I O - 6 6 - 2.98 X IO" 6 10 5.9O 4.65 3.48 2.51 20 9.01 6.68 4.90 3.01 30 12.2 ' 8.66 6.10 3.59 40 14.8 10.7 7.15 3.98 TABLE G-2. Cupric Series: O.7O M[H 2 S0 4 ]° , 5 atm H 2, l60°C. Experiment: Cuxl- 5 Cu x - 2 Cu x - 1 C u 1 1 - 3 C u 1 1 - 4 [ C u S 0 4]o M: 0.05 0.10 0.15 0 .20 0.25 [MgS0 4 ] M: O.25 0.20 • O.I5 0.10 O.O5 [Cu 1] M - d[H 2] _! ~WT~ M s e c 2 X IO" 3 O.58 X IO" 6 1.46 X 10-6 _ 4 - - - 2.92 X 10-6 5 0.66 I . 7 0 - - 4.44 x lO" 6 . 6 - 1 - 2.98 X IO" 6 -10 0.71 1.99 3.48 4.09 5.38 20 0.71 2.58 4.90 5.88 7-37 30 - 2.94 6.10 7.67 9.35 40 - - 7-15 9-36 10.9 50 - - - 10.6 11.8 60 - - 11.3 13.1 ft By mirror image method. ftft -d[H 2] = 1 d l C u 1 ] dt 2 dt Experiment [MgS04] M [H 2S0 4]° M TABLE G-3. Sulphate S e r i e s : .0.15 M[CuS0 4] o,, 5 atm H 2, l60°C. 1 SCU - 2 H 2S0 4 - 2 0.35 O.5O S0 4" 0.45 0.40 Oi O.55 .0.30 so* - 3 0.65 0.20 - 106 S0 4" - 4 0.75 0.10 [Cu 1] M a[H 2] M M s e c 5 x 10- 3 4.32 x i o - 6 5.04 10 5.90 7.32 20 9.01 11.3 30 12.2 15.2 40 14 .8 18.7 X 10-6 6.46 X I O - 6 8.66 14.1 20.2 24.5 6.46 X 10" 9-99 14.8 21.1 24.2 5.95 X I O - 6 8.5O 15.1 TABLE G-4. Temperature S e r i e s : 0.15 M[CuS0 4]°, O.7O M[H 2S0 4]o 0.15 M[MgS04], 5 atm H 2 Experiment: T - 5 T - 1 C u 1 1 - 1 T - 2 Temperature °C: 120 140 160 180 [Cu 1] M -d[Hg] M s e c - ! 2 X IO" 3 0.148 X 10-6 - _ 6.60 X 10"' 5 0.175 0.825 x IO" 6 - 7.55 6 - - 2.98 x 10-6 _ 8 O.251 - -10 - 1.06 5.48 9.76 12 0.336 - - -20 - 1.46 4.90 13.2 50 - 1.81 6.10 15.6 40 7.15, APPENDIX H. The Integrated Rate Curve for the Sulphate System - 107 -The i n t e g r a t i o n was performed g r a p h i c a l l y f o r one experiment-using an expression obtained by rearranging the rate law, equation 38, e.g., where x = [Cu ] A x = 0.01 MtCu 1] a = [ C u n ] o = 0.15 M b = 2k 1[H 2] = 2 X 3.2 X IO" 3 x 5.9 X 10-3 s e c " 1 c = k-^ [ H + ] M = 0.13 X 0.7 M k 2 e = k_3_ [H+] = 0.44 X 0.7 M k 4 f = 2k 3[H 2] = 2 X 6.2 X IO" 2 X 5.9 X IO" 3 s e c " 1 The values of t obtained as a function of [Cu ] are shown i n Table H-l. o TABLE H-l. t as a Function of [Cu ] [Cu 1] M t min 5 X 10 -3 22 kl 73 100 127 152 10 20 30 40 50 Experimental conditions: 0.15 M[CuS0 4]°, O.85 M[H2S04]<=, 5 atm H; 160°C. The increase i n [H ] due to [Cu ] reduction was disregarded as a f i r s t approximation. - 108 -APPENDIX J . Rate Curves and Rates of Exchange Experiments (a) Data f o r Rate Curves TABLE I - l Experiment D2-A: 0.15 M[CuS0 4]°, O.5O M[H 2S0 4]o, O.55 M[MgS04], 5 atm D 2, 160°C, solvent H 20. Time min. HD * H 2 $ V gas at 160°C ml p M atm HD* moles X 10* 3 moles X 1 0 t 3 [ C t t I ] M X 10+3 V s o l u t i o n * at 25°C. .Cu1 moles X '10 * 3 2 0.59 915 5-1 0.77 950 20 2.44 0.05 956 4.9 5.10 0.07 - 950 --21 - - 995 - - - 7.45 912 7.08 36 - - 995 - - - 15.2 876 14.15 40 6.11 0.25 995 ^•5 7.60 0.52 - 876 -50 8.93 0.48 995 ^•5 11.14 0.61 - 876 -51 - - 1040 - - - 25.2 851 22.91 65 15.75 1.17 104 0 5-2 18.49 1.66 - 851 -66 - - 1090 - - - 39-4 789 34.71 80 18.70 2.66 1090 4.7 25.62 5.81 - 789 -81 - - 1157 - - 53-6 746 49.41 95 19.95 3.68 1157 4.1 27.22 6.45 - 746 -A A f t e r sampling of s o l u t i o n ikk Excluding steam pressure +. Moles present i n gas phase; amount dissolved i n s o l u t i o n and amounts removed with gas and l i q u i d samples were disregarded. - 109 -TABLE 1-2. Experiment D2-B: 0.15 M[CuS0 4 ] o , O.85 M[H 2 S0 4]o, 5 atm D 2 > l60°C solvent H 2 0 . Time HD H 2 V gas P HD H 2 [Cu-E] V so l u t i o n C u 1 min. 1o at 160°C atm moles moles M at 25°C. moles ml .X 1 0 + 3 X 10+3 X 1 0 t 3 X 10* 3 3 0.6 915 5.0 O.78 -950 ko 3-99 0.08 915 4.80 4.96 - 0.10 - 950 -80 9-63 0.45 915 4.67 11.73 O.54 - 950 -81 - - 954 - - - 10.3 915 9.78 120 16.03 1.23 954 4.27 19.05 1.42 - 915 -125 - - 996 - - - 15.5 877 14 .5 160 22.6 2-55 996 4.00 •26.21 2.90 - 877 -163 - - 1040 - - - 20.2 837 18.7 200 30.0 5.04 1040 4.67 36.33 6.30 - 837 -202 _ _ 1082 - - - 29.2 799 26.0 240 36.0 9.18 1082 4.67 44.84 12.18 - - -243 - - 1135 - - - 36.0 751 31.3 - 110 -TABLE 1-3. Experiment D2-C: 0.07 M [ C u ( C 1 0 4 ) 2 ] O , 0.10 M[HC10 4 ]o, 15 atm D2, 160°C, solvent H 20 Time HD H 2 V gas P H D [Cu 1 j V so l u t i o n C u 1 min. $ $ at l60°C atm. moles moles M at 25°C moles X 1 0 + 3 X 10+3 X 10+3 X 10* 3 2 0.53 - 915 14 .8 2.02 - - 950 -60 10.4 O.54 915 15.2 40 .6 2.07 -, 8 A 950 -62 - - 880 - - - 880 15.0 80 - - 85I - - - 19. ,1 851 17.8 120 26.7 3.50 85I 14 .1 107 14 .1 - 851 -122 - - 813 - - - 27. .0 813 24 .6 180 38.9 10.4 813 14.3 159 43.6 - 813 -182 - - 769 - - - 33. .8 769 30.2 240 42 .9 19.4 769 13-7 176 82.2 - 769 -300 44 .2 29.4 769 13.5 182 125 - 769 -302 - - 730 - - - 39. .0 730 34.2 360 40 .5 36.3 730 12.5 166 153 - 730 -362 - - 691 - - - 39. .8 691 34.7 A Estimated by i n t e r p o l a t i o n from [Cu +] vs time pl o t - I l l -TABLE 1-4. Experiment H2-D: 0.15 M[CuS0 4] o, O.85 M[H 2S0 4] o, 5 atm H 2, l60°C, solvent D 20. Time • HD D 2 V gas P HD D 2 [Cul] V s o l u t i o n Cu 1 min. * * at 160°C atm moles moles M at 25°C moles ml X 10 +3 X 10+3 X 1 0 + 3 X 1 0 + 3 3 0.2 18.55* 860 5-0 0.24 1000 33 2.17 14.25 860 5.0 2.52 - - 1000 -60 5.04 14.73 860 k.l 5.78 0.55 - 1000 -63 - - 902 - - - 15.6 962 15.6 92 9.1 14.86 902 4.1 10.0 0.68 - 962 -95 - - 933 - - - 26.8 934 24 .6 120 13.3 15.60 933 3-8 14.2 1.42 - 934 -122 - - 957 - - - 34.6 912 33-7 152 18.23 1 6 A 0 957 3-5 18.8 2.17 - 912 -154 - - 989 - - - 40 .7 883 39-2 181 2k. 8^ 17.85 989 3-7 25.6 3.66 - 883 -183 - - 1024 - - - 44.5 851 42.6 ft Helium used f o r f l u s h i n g autoclave was measured as D 2 j therefore assumed zero $ D 2 up to 33 min. TABLE I - 5 . Experiment D 2-E: 0.00 M[CuS04]-, 0.5 M[H 2S0 4] 0.5 M[MgS04], 5 atm D 2, l60°C solvent H 20 Time $ HD 4 min O.58 45 O.55 80 O.57 120 0.51 Cylinder Sample O.59 - 112 -(b) 'Rate Measurements f o r Exchange Experiments TABLE 1-6. Experiment D2-A .Cu1 moles Time min. 1 2 dCux A dt ( H D + 4H 2 ) moles d(HD + 4 H 2 ) M ,dt , 7 2 X, I O - 3 2.82 X IO' 6 2.4-X IO" 3 2.42 X I O - 6 28 10 4.07 4.8 4.18 4 7 20 4.95 12.0 1 8.62 61 30 6.76 21.8 14.05 72 40 7.64 32.0 ,18.00 Experiment -D2-B 22 2 X I O - 3 0.83 X I O - 6 2.6 X I O - 3 2.10 X I O - 6 93 10 •1.08 16.0 4.20 130 15 - •27.5 6.00 165 20 1.23 42 .0 7.67 197 25 - 60.0 10.50 ,228 30 1.43 82.0 15.60 Experiment D2-C C u T 1 dCu"*" MA moles 2 dt moles/sec 19 5 X I O - 3 .2.11 X I O - 6 10 X IO" 3 11.1 x 10" 6 40 10 2.10 27 16.9 90 20 1.90 97 50.8 133 26 1.61 200 44.8 180 30 1.53 350 56.5 Cu 1 moles Experiment H2-D 1 dCu 1 2 dt moles/sec (HD + 4 D2; moles d(HD + 4 D 2' — — moles/sec 10 45 76 94 ,2 X 10 " 3 10 20 26 1.67 X I O - 6 .2.56 • 2.74 2.88 0.6 x 10-4.0 9.0 12.8 1.29 x 10 •2.16 •3.36 3.78 -6 A Wet forward rate Ak Exchange rate - The rate of oxidation of HD and H 2 by Cu was not added t o the rate measurements as i t only came to 5 to 6$ at the highest HD+4H2 l e v e l s toward the end of the experiments. AAA Corrected for,perchlorate decomposition e f f e c t (Appendix C). (c) Isotope E f f e c t s on Net Forward Rates at l 6 0°C. TABLE I - 7 . i ) Experimental conditions: 0 .15 M[CuS04]o, 0 .5 M[H 2S0 4]°, O .35 M [ M g S 0 4 s o l v e n t H 2 0 , 5 atm D 2 or H 2 \ Experiment: D2-A H2S04-2 i [Cu 1] M 1 d[CuI] ft -d[H 2] B^T 2 dt dt R M s e c - 1 M s e c - 1 " H 2 10- x 10-3 4.4 X I O - 6 2 0 6 . 7 8 3 0 9 - 7 7 ko . 1 1 . 6 0 5 . 9 X IO" 6 9 . 0 1 2 . 2 ,14.8 O .69 O .76 0 . 8 0 O .78 i i ) Experimental conditions: : 0 . 1 5 M [ C u S 0 4 ] ° , solvent H 2 0 , 5 0 . 8 5 M[H 2 S0 4 atm D 2 or H 2 Experiment: D2-B H 2 S 0 4 - 3 10 X IO" 3 1 . 2 0 X IO" 6 2 0 I . 5 7 3 0 2 . 0 3 2 . 5 1 X 1 0 " 6 3 . 0 1 3 - 5 9 0 . 4 8 O .52 0 . 5 7 .ii).Experimental conditions; : 0 . 0 7 M[Cu(C10 4 ) solvent H 2 0 , 1C 2]o,- 0 . 1 0 M [ H C 1 0 4 ) atm D 2 or H 2 Experiment: D2-C Cu + +-4 r c u + l M 1 dLCu TJ H 2 dt M s e c - 1 10 x 1 0 " 3 1 . 6 7 X 10"6 * 2 0 1 . 7 2 2 . 2 6 X 1 0 " 6 2 . 1 6 * 0 . 7 4 0 . 8 0 iv) Experimental conditions: : 0 . 1 5 M[CuS0 4]o, solvent D 2 0 or-0 . 8 5 M[H 2 S0 4 H 2 0 , 5 atm H 2 Experiment: H2-D H 2 S 0 4 - 3 LCu-LJ M 1 dLCu-LJ 2 dt M s e c - 1 i n D 2 0 -d[H 2J dt M s e c - 1 i n H 2 0 « D S 0 R H 2 0 10 X 10-3 2 A 7 X IO" 6 •20 3 . 1 2 2 . 5 1 X IO" 6 3 . 0 1 O .99 1 . 0 3 A Net forward rate using D 2. Rate measurements corrected to 5 ( 1 0 f ° r experiment D2-C) atm D 2 pressure. $ Corrected f o r perchlorate decomposition e f f e c t (Appendix 

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