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Reduction of aqueous cupric sulfate by hydrogen, carbon monoxide, and their mixtures Stenhouse, Joanne Helen 1982

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REDUCTION OF AQUEOUS CUPRIC SULFATE BY HYDROGEN, CARBON MONOXIDE, AND THEIR MIXTURES B.Sc, The University of B r i t i s h Columbia, 1976 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Metallurgical Engineering) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA by JOANNE HELEN STENHOUSE A p r i l 1982 Joanne Helen Stenhouse, 1982 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Hr*J-/z//urj J C / L I ^ ^ y / z j j The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date A p r i l IF , J?r^: DE-6 (3/81) ABSTRACT Investigations into the reduction of high concentration aqueous copper sulfate solutions with hydrogen, carbon monoxide and mixtures of these gases were conducted. The effect of increasing the copper sulfate concentration was to enhance the rate of reduction in both the hydrogen and carbon monoxide systems. The rate of reduction was increased by increasing pressure, temperature, and the concentration of ammonium sulfate buffer. Under mixtures of hydrogen and carbon monoxide the rate of reduction was intermediate between the rate under pure hydrogen and pure carbon monoxide. Based on the reaction mechanisms and rate equations developed by previous investigators a mathematical model of the reduction processes under hydrogen and carbon monoxide was developed. By f i t t i n g the model to the experimental results, rate constants for the high concentration reduction were determined. The use of carbon monoxide, with or without hydrogen, was found to reduce or minimize the plastering problem associated with the hydrogen reduction of copper. i i i TABLE OF CONTENTS Page CHAPTER 1 INTRODUCTION 1 Thermodynamics of Hydrogen and Carbon Monoxide Reduction 2 Kinetics of Copper Reduction by Hydrogen . . . . 6 Kinetics of Copper Reduction by Carbon Monoxide . 11 Investigations into Gas Mixtures 13 Purpose and Scope of the Present Investigation . 14 CHAPTER 2 EXPERIMENTAL 15 Reagents 15 Apparatus 15 Experimental Procedure 16 Analysis 18 Reagents 18 Instrumentation 19 Ana l y t i c a l Method , 20 Sample Calculation 22 CHAPTER 3 RESULTS AND DISCUSSION 2 5 Mathematical Model of the Reduction Process . . . 25 Hydrogen Model 25 Carbon Monoxide Model 31 V e r i f i c a t i o n of the Models 34 Hydrogen Reduction Experimental Results 40 Effect of Pressure 44 Determination of Rate Constants 47 Effect of Temperature 61 Formation of H+ Ion 61 Effect of (NH a) 2SO u Salt 64 Carbon Monoxide Reduction Experimental Results . 64 Determination of Rate Constants 67 Effect of Temperature 75 Formation of H + Ion/Effect of (NH„) 2SO a Salt 76 Gas Analysis of CO Reduction 79 Summation and Comparison of Independant Hydrogen or Carbon Monoxide Reduction Results 81 iv Reduction Using Mixtures of Hydrogen and Carbon Monoxide 82 Variable Carbon Monoxide/Hydrogen Ratio Experiments 82 Fixed Carbon Monoxide/Hydrogen Ratio Experiments 89 Effect of ( N H 4 ) 2 S O , Salt 94 Summation of Results of Mixed Gas Experiments . . 94 Attempt to Model the Mixed Gas Process 97 Nature of Metal Product Formed 97 CHAPTER 4 CONCLUSIONS 102 CHAPTER 5 SUGGESTIONS FOR FUTURE RESEARCH . . 105 REFERENCES 106 APPENDIX A - Estimation of Thermodynamic Parameters at High Temperature 108 APPENDIX B - Program to Model Hydrogen Reduction . . 115 APPENDIX C - Program to Model Carbon Monoxide Reduction 119 APPENDIX D - Program to Model Mixed Gas Reduction . . 123 APPENDIX E - Error Analysis 128 V LIST OF FIGURES Page Figure 1.1 Eh - pH Diagram For Hydrogen Reduction 4 Figure 1.2 Eh - pH Diagram For Carbon Monoxide Reduction ' 5 Figure 3.1 Comparison of H 2 Model to Experimental Results 35 Figure 3.2 Comparison of H 2 Model to Experimental Results . . . . . 38 Figure 3.3 Comparison of CO Model to Experimental Results 39 Figure 3.4 Comparison of H 2 Rates at High and Low C u S O i , Concentrations 42 Figure 3.5 Effect of H 2 Pressure on Reduction Reaction 45 Figure 3.6 I n i t i a l Rate vs H 2 Pressure . 46 Figure 3.7 Comparison of H 2 Model to Experimental 1 Results 48 Figure 3.8 F i t of H 2 Model to Experimental Results 140°C 49 Figure 3.9 Effect of Changing Equilibrium Constants on Cu + Curve 51 Figure 3.10 F i t of H 2 Model to Experimental Results 140°C 55 Figure 3.11 F i t of H 2 Model to Experimental Results 120°C 58 Figure 3.12 F i t of H 2 Model to Experimental Results 160°C 59 Figure 3.13 Arrhenius Plot: H 2 Reduction 62 Figure 3.14 H + Production During H 2 Reduction . . . 63 Figure 3.15. Effect of (NH„) 2SO a on H 2 Reduction . . 65 v i Figure 3.16 Comparison of CO Model to Experimental Results 67 Figure 3.17 F i t of CO Model to Experimental Results 140°C 69 Figure 3.18 F i t of CO Model to Experimental Results 120°C 72 Figure 3.19 F i t of CO Model to Experimental Results 160°C 73 Figure 3.20 Arrhenius Plot: CO Reduction 77 Figure 3.21 H + Production During CO Reduction . . . 78 Figure 3.22 Effect of (NH q) 2SO q on CO Reduction . . 80 Figure 3.23 Effect of H 2 Pressure on Cu 2 + Curve in Presence of CO 84 Figure 3.24 Effect of H 2 Pressure on Cu + Curve in Presence of CO 85 Figure 3.25 Eff e c t of CO Pressure on Cu + Curve in Presence of H 2 86 Figure 3.26 Comparison of Pure H 2 Reduction Rates with Rates Under Mixed Gas 88 Figure 3.27 Gas Analysis of Mixed Gas Reduction Process 90 Figure 3.28 Copper Concentration as a Function of. Time Under Mixed Gas 140°C 92 Figure 3.29 Copper Concentration as a Function of Time Under Mixed Gas 160°C 93 Figure 3.30 Effect of (NH„) 2S0 1 ) on Mixed Gas Reduction Rates 95 Figure 3.31 Comparison of H 2, CO and Mixed Gas Reduction Rates 96 Figure 3.32 Comparison of Mixed Gas Model to Experimental Results 98 Figure 3.33 Metal Produced by H 2 Reduction 99 Figure 3.34 Metal Produced Under Influence of CO . . 101 v i i LIST OF TABLES Page Table I - Rate Constants for Reduction by H 2 . . . 10 Table II - Relationships for Calculating Equilibrium Concentrations : H 2 Model . . 28 Table III - Relationships for Calculating Equilibrium Concentrations : CO Model . . 32 Table IV - Rate Constants Used to F i t Hahn's Experimental Results 35 Table V - Relative A c t i v i t i e s of Copper Complexes and pKa' s of Ligands 43 Table VI - Comparison of Rate Constants at Low and High [CuSO„] T=140°C 56 Table VII - Rate Constant from F i t t i n g of H 2 Model 60 Table VIII - Comparison of Rate Constants to F i t CO Reduction at 140°C 70 Table IX - Rate Constants from F i t t i n g CO Model . . 74 v i i i ACKNOWLEDGEMENTS I w o u l d l i k e t o e x t e n d my s i n c e r e a p p r e c i a t i o n t o D r . E. P e t e r s f o r h i s g u i d a n c e and s u p p o r t t h r o u g h o u t t h e c o u r s e of t h i s s t u d y . I would a l s o l i k e t o thank o t h e r members o f t h e Dep t . o f M e t a l l u r g i c a l E n g i n e e r i n g f o r t h e i r a s s i s t a n c e d u r i n g t h i s t i m e . A s p e c i a l acknowledgement must be e x t e n d e d t o Mr. G r e g R i c h a r d s f o r h i s i n v a l u a b l e a s s i s t a n c e w i t h t h e computer p r o g r a m i n g and h i s encouragement w i t h t h i s p r o j e c t . The f i n a n c i a l s u p p o r t of NSERC i s g r a t e f u l l y a c k n o w l e d g e d . 1 CHAPTER 1 INTRODUCTION Gaseous reduction of metal ions using hydrogen or carbon monoxide has been extensively investigated in the past. Hydrogen has been shown to be an e f f e c t i v e reductant for a variety of metal ions most notably copper, s i l v e r , nickel and cobalt (1-6). I n d u s t r i a l l y , hydrogen i s used to produce nickel and cobalt from aqueous solutions (3). Although the reducing power of carbon monoxide has also been demonstrated for such ions as copper, s i l v e r (7-8), and nickel (9), i t has not been used in i n d u s t r i a l practice primarily due to the apparent slower rate of the reduction reaction. However some of these e a r l i e r results appear to be somewhat misleading as this study w i l l show. As a re s u l t , hydrogen was considered to be the most promising gaseous reductant. However, though th i s method of reduction works well for certain metals such as nickel and cobalt, for the production of copper- p a r t i c u l a r l y from low pH sulfate solutions- i t suffers from the rather serious problem of plastering and agglomeration (3). Plastering, which is the adherence of the reduced metal to the sides, impellors and sparging l i n e s in the reactor, and agglomeration can be only p a r t i a l l y controlled by the addition of organic surface active reagents such as ammonium polyacrylate and l i g n i n derivatives (3). Therefore, although hydrogen has been used in the past to produce copper at S h e r r i t t Gordon and other places, the 2 processes have been severely hampered by this plastering problem, and currently i t is not produced by this method. A potential solution to the problem l i e s in the use of carbon monoxide in copper production, either independantly or in combination with hydrogen. It has long been known that solutions of cupric ions s l u r r i e d with metallic copper powder w i l l absorb CO, producing the cuprous carbonyl. Under an atmosphere containing a s i g n i f i c a n t pressure of CO, t h i s species i s stable and does not readily disproportionate. Thus, based on previous investigations, a possible process for producing copper would be to use mixtures of hydrogen and carbon monoxide gas, where the hydrogen would act as the primary reductant and the CO as an agent to complex the cuprous species. The solution saturated with cuprous carbonyl could then be transferred to another vessel, the CO flashed o f f , and the Cu + allowed to disproportionate. In the absence of H 2 gas, the Cu + ion w i l l disproportionate without plastering. In order to appreciate more f u l l y the potential of t h i s proposal,it i s useful to consider the present understanding of CO and H 2 as separate reductants. Thermodynamics Of Hydrogen And Carbon Monoxide Reduction Hydrogen The thermodynamics of hydrogen reduction i s best considered as an electrochemical redox reaction where the hydrogen atom loses an electron which is picked up by the metal ion. We can, 3 therefore, describe the driving force of the reaction as an electrochemical potential (EMF). This i s most e a s i l y i l l u s t r a t e d by a modified Eh-pH diagram (10). Figure 1.1 shows the hydrogen oxidation l i n e (commonly referred to as the 'a' line) of an Eh-pH diagram at 25 °C and at 1 atms H 2. At potentials below this l i n e the hydrogen is in i t s reduced form, and above the li n e i t i s the oxidize ion. Also shown are the metal ion boundaries for copper, n i c k e l , cobalt and zinc. The pH ranges where the metallic form l i e s above the hydrogen l i n e are regions where the ions may be reduced by H 2 to the metal. One can determine the EMF of any of these reactions at a given pH by the difference between the metal ion boundary and the H 2 l i n e . The driving force for the reaction i s influenced by the hydrogen pressure. Increased pressure s h i f t s the H 2 l i n e down,- thereby increasing the d r i v i n g force of the reaction. Higher temperatures w i l l also influence these boundaries. Appendix A gives the d e t a i l s of the thermodynamics of hydrogen reduction of copper at higher temperatures. The pH at which the reduction reaction i s c a r r i e d out w i l l also have considerable influence. For example, one can s e l e c t i v e l y reduce nickel from a solution containing both cobalt and nickel by maintaining the pH just below the point where cobalt w i l l begin to p r e c i p i t a t e . This method i s used by S h e r r i t t Gordon (3) to separate the nickel from the cobalt in the leach solution. 6 Carbon Monoxide Unlike hydrogen oxidation which i s an electron loss, carbon monoxide oxidation i s a change in the formal oxidation state of carbon from C(II) to C(IV) due to the addition of an oxygen atom. Thus, i t i s not quite as convenient to view the reaction as a redox reaction, but for the sake of comparison, th i s w i l l be done. F i g . 1.2 is similar to F i g . 1.1 except that the bondaries of CO(g) to C0 2(g) oxidation at 1 atmosphere have been included. We can see then that the oxidation potential for CO to C0 2 l i e s below the hydrogen oxidation l i n e , thus the EMF for reduction using CO for the ions shown i s greater. This situation also implies that carbon monoxide in the presence of water should combine to produce hydrogen and carbon dioxide. That i s , the s h i f t reaction should take place. However, the kinetics of th i s reaction at low temperatures i s i n s i g n i f i c a n t except in the presence of a catalyst (12). It should be noted that pressure, temperature and pH exert the same influence as in hydrogen reduction. Appendix A contains high temperature thermodynamic data for CO reduction. Kinetics Of Copper Reduction By Hydrogen Ip a t i e f f and Werchowsky (12) f i r s t observed that under a hydrogen atmosphere, cupric acetate was reduced to cuprous oxide. Dakers and Halpern (13) later showed that t h i s reaction proceeded homogeneously and developed a mechanism and rate •equation to describe the reaction. Peters -and Halpern then 7 demonstrated that hydrogen activated by cupric ions would reduce dichromate according to the overall reaction: C r 2 0 7 2 - + 3H2 + 8H+ = 2Cr 3 + + 7H20 (1.1) Also, the mechanism of c a t a l y s i s developed postulated that a metastable hydride species was formed as the reaction intermediate. Thus, the mechanism proposed for the catalysed reduction of dichromate ions was: Cu 2 ++H 2 = CuH++H+ (1.2) k. , CuH ++Cu 2 t -> 2Cu++H+ (1.3) fast 2Cu ++Substrate -> Products + Cu 2 + (1.4) ( C r 2 0 7 2 - ) ( C r 3 + ) Using steady state treatment of the intermediate CuH+ leads to the rate equation: -dH2 = k,[Cu 2+] 2[H 2] (1.5) dt {[Cu 2 + ]+k_. ,[H +]} These studies also demonstrated that the type of copper complex influenced the rate of the reaction. The f i r s t studies of copper metal production by hydrogen were done in perchl'orate • and sulfate solutions (15). These 8 studies showed that the rate of reduction was not influenced by the addition of powdered copper metal (or any other powder) to the reaction, and was therefore, t r u l y homogeneous. Also noted was the fact that the reaction rate was faster in the sulfate solution than in the perchlorate system, due primarily to the sulfate ions a b i l i t y to act as a buffer. This observation concurred with the inverse hydrogen ion dependence that had been established. F i n a l l y , although the thermodynamics indicate that the reaction should go to completion, i t stopped at a kinetic end point. However, th i s study did not reveal the influence that the cuprous ion had on the reaction. The cuprous ion ef f e c t was observed by Dunning and Potter (16). They showed that the Cu + species enhanced the rate of the reaction and they proposed a mechanism where Cu + activated hydrogen and was the c o n t r o l l i n g factor in the reduction react ion. k, Cu 2 + + H 2 = CuH+ + H + (1.6) k- i k 2 CuH+ + Cu 2 + -> 2Cu+ + H+ (1.7) " . k 3 Cu + + H 2 = CuH + H + (1.8) k-3 CuH + Cu 2 + -> Cu + + CuH+ (1.9) Using steady state treatment of CuH+ amd CuH, the rate equation for this mechanism i s : R= 0.315 [ H , ] [ C u 2 4 ] 2 + 7l[H 7][Cu 2+ ] 2[Cu*] (1.10) { [ C U 2 +]+0.105[H +]} {[Cu 2 +]+0.9[H +] } 9 Thus the cuprous dependant term has a much higher rate constant than the cupric term. No d e t a i l s were given as to how the rate constants were derived. The most complete study of hydrogen reduction of aqueous cupric ion (in sulfate and perchlorate solutions) was made by Hahn (4). He v e r i f i e d the cuprous activation of hydrogen, and derived rate constants for the reaction at 120, 140, and 160°C. The mechanisms for the reaction i s the same as that proposed by Dunning and Potter, but the rate equation was modified to: - d i b = > i t C u 2 * ] ' [ H 2 ] +. k , [ C u 2 + ] 2 [ Cu +] [H ?] {k_.1[H+] + [Cu 2 +]}{k_. 3 [H + ] +[Cu 2 +]} k~2 k 2 k n (1.11) The rate constant for the sulfate system at the three temperatures are shown in Table I. As can be seen, k 3 i s much larger than k, at a l l temperatures. Thus, Cu + plays a very s i g n i f i c a n t role in the reduction k i n e t i c s . To confirm the results of the reduction reaction analysis, isotope exchange experiments were also done (4). The results of these experiments demonstrated two other s i g n i f i c a n t features. In the perchlorate system, where the cupric ion is e s s e n t i a l l y uncomplexed (aquo-co-ordinated), the rate of the forward and back reactions at step 3 in the reaction sequence are very high: Cu++H2 = CuH + H+ (1.12) k.3 Thus in the next step, reduction of Cu 2 + by CuH must be much slower than the H + back reaction. In the sulfate system, th i s i s 10 not true. Secondly in the sulfate system, the extent of the exchange reaction did not increase with increasing a c i d i t y . In fact, the extent of exchange in the low s u l f u r i c acid experiment was greater than that in the high s u l f u r i c acid experiment. Since base catalysed exchange had been ruled out, another plausible explanation was necessary. Table I Rate Constants for Reduction by H 2 Constants (Units) 1 20°C 140°C 1 60°C 180°C k, (sec" 1M" 1) 1 . 9E-4 1 . 1E-3 3.2E-3 7.8E-3 k 3 (sec- 1M" 1) 1.3E-2 2.4E-2 6.4E-2 16.2E-2 k. , k 2 1.3E-1 1.3E-1 1.3E-1 1.3E-1 k-3 k. 4.5E-1 4.5E-1 4.5E-1 4.5E-1 [H 2] (M) 4.5E-3 5.13E-3 5.90E-3 6.80E-3 Hahn suggested that the sulfate complexes of both Cu + and Cu 2 + are more reactive toward hydrogen than.are undissociated s a l t s . At low H + concentrations most of the copper species would exist as sulfate complexes and the H+ as HSO<,-. As the concentration of H+ increased, the sulfate is t i e d up as 11 b i s u l f a t e , thus the copper ions are present as free or aquo-co-ordinated ions. Since the rate of exchange reaction dropped off as the copper sulfate complexes were dissociated, i t appears that the ion pair i s more hydrogen a c t i v a t i n g . The most recent study of hydrogen reduction of copper from aqueous soltuion was directed toward developing a continuous reduction process (17). The reaction did not go to thermodynamic equilibrium, as in a l l other studies. At temperatures above-140°C, residence times longer than 10 minutes did not enhance the extraction. The plastering phenomena was s t i l l present, but the authors suggested that the problem could be overcome by modifying reactor design. Kinetics Of Copper Reduction By Carbon Monoxide The kinetics of the reduction of aqueous Cu 2 + by CO have been previously investigated (19) in acetate, perchlorate, and sulfate systems. The experiments were conducted between 100 and 123 °C and a CO pressure between 6.0 and 80.0 MPa. The result of thi s study gave a three term rate law of the form: -dCu 2 + = k ' ' dt Cu 2* 3[Cu*] + k V[Cu 2*] 2PCO + k 3'[Cu 2*] 2PCO H*] [H*] (1.13) The mechanism which best f i t s t h i s equation i s : 12 Path A Ka Cu2++CO+H20 = (Cu-C-(OH) 2) 2 + ka (Cu-C-(OH) 2) 2 + +Cu2 + -->C02 + 2Cu + + 2H + Kb 0 Cu2++CO+H20 = (Cu-C-OH)++H+ 0 kb (Cu-C-OH)++Cu2 +-->C02 + 2Cu + +H +Path B fast Cu + +CO—> Cu(CO) + Kc Q Cu(CO)*+H20 = (Cu-fc-OH)+H+ 0 kc (Cu-C-OH)+Cu2 + -->C02+CuH + +Cu + CuH + +Cu2 +—>2Cu + +H +Where Kckc=k,' Kbkb=k2' Kaka=k3' Path A is the i n i t i a l reduction of Cu 2 + by CO and consists of an acid dependant and acid independant term. Path B i s the Cu + catalysed reduction of Cu 2 + and accounts for about 90% of the observed reaction at moderate pressures ( 1 - 5 MPa). The cuprous species exists almost e n t i r e l y as the carbonyl Cu(CO) +. The p o s s i b i l i t y of using CO to refine copper has been suggested by Peters et a l ( 1 8 ) . Using th i s technique, copper metal i s dissolved by a cupric sulfate solution under CO pressure. The product is cuprous carbonyl: Cu 2 ++Cu°+2CO = 2Cu(CO)+ (1.22) 13 The cuprous carbonyl saturated solution can then be transferred to another vessel, depressurized and the CO steam stripped from the cuprous ion and recovered. The Cu + in solution w i l l disproportionate producing Cu 2 + and copper powder. The properties of the copper powder produced can be controlled by the stripping conditions. Carbon monoxide, therefore appears to possess properties which would be useful in a copper producing system. Investigations Into Gas Mixtures There i s only one reference in the l i t e r a t u r e to using mixtures of hydrogen and carbon monoxide (19). The study was concerned with producing copper and s i l v e r metal from sulfate solutions. For both systems under the condition of the study (90 min, P=6 MPa, T=90°C Ag, T=160°C Cu) the presence of CO in the gases reduced the amount of metal produced, copper being much more affected than s i l v e r . However, no attempt was made to look at the cuprous species or the rate of reduction of cupric to cuprous. The authors concluded that hydrogen was the superior reductant. 14 Purpose and Scope of the Present Investigation Considering the l i m i t a t i o n s shown by either hydrogen or carbon monoxide as reducing agents for copper, i t was decided that a further study into a combination of the two gases would be useful. This thesis, therefore presents preliminary investigations into using these mixed gases as a reductant for aqueous cupric sul f a t e . The study w i l l attempt to determine whether or not the copper reduction reaction using mixed gases is affected by interactions between hydrogen and carbon monoxide or i s a simple sum of the separate reactions. Since previous investigations into independant use of either CO or H 2 have been done in d i l u t e copper solution, these experiments w i l l be repeated at higher concentration over a temperature range of 120 to 160 °C. The rate constants for these conditions w i l l be determined by the use of computer models of the reactions. 15 CHAPTER 2 EXPERIMENTAL Reagents Reagent grade copper sulfate and ammonium sulfate were used throughout the experiments. Su l f u r i c and n i t r i c acids were supplied by Anachemia. Standard grade hydrogen and nitrogen gas was supplied by Linde. Carbon monoxide was supplied by Matheson and a c e r t i f i e d mixture of 33.8% H 2, balance CO was supplied by Canada Liquid A i r . Gas chromatography of the hydrogen and carbon monoxide showed no contamination of these gases. Apparatus A l l experiments were performed in a Parr 2 1 titanium autoclave equipped with a temperature well, s t i r r i n g shaft and sampling tube. The end of the sampling tube was f i t t e d with a medium porosity sintered glass f r i t , held in place by a titanium nut. This e f f e c t i v e l y blocked passage of a l l p a r t i c l e s > 15 *i into the sampling tube. The s t i r r i n g shaft was equipped with two titanium impellors, situated at 14 and 23 cms from the autoclave head. Since, for a l l runs the volume of solution was 1 1, these positions ensured that both impellors were below the, l e v e l of the l i q u i d . The autoclave was set into an insulated, e l e c t r i c a l l y 16 heated a i r cooled jacket. To maintain solution temperature the autoclave was alternately heated and cooled. The temperature was regulated by a thermister probe inserted into the temperature well. The temperature was measured using a single junction chromel-alumel thermocouple (with the reference junction at 0°C) connected to a Sargeant-Welch s t r i p chart recorder or a Pye potentiometer. The thermocouple was calibrated against b o i l i n g water and the freezing point of t i n , 231.9°C. The stainless steel sampling valve was s p e c i a l l y designed to reduce problems of clogging. The teflon disc and stai n l e s s steel plate were f l e x i b l e enough to allow the solution to pass in and out of the valve under the pressure of the autoclave. The gas pressure was measured using a 0-6.50 MPa (0-1000 PSI) gauge at the autoclave head and/or 0-6.5 MPa (0-1000 PSI) Honeywell pressure transducer and a Sargeant-Welch s t r i p chart recorder. The transducer was c a l i b r a t e d against steam pressure in the autoclave. Experimental Procedure For a l l experiments, 1 1 of a copper sulfate solution was used. Since i t has been shown that both H 2 and CO reduction produce H + and that both reactions are inhibited by a b u i l d up of H + in solutions, a l l runs were buffered by ammonium sul f a t e . A small amount of s u l f u r i c acid was added i n i t i a l l y to prevent copper hydroxide formation. T y p i c a l l y the solution composition 17 was: 0.70 M Cu 2 + as CuSO„.5H 20 0.60 M (NH 4) 2SO« 0.10 M H2SOfl Variation in this s t a r t i n g solution was plus or minus 5%. An attempt was made to use higher copper concentrations (80 gpl C u 2 + ) ; however, this created considerable problems in sampling due to p r e c i p i t a t i o n of the Cu(NH q) 2(SO„) 2 double s a l t . For experiments using pure hydrogen, pure carbon monoxide or c e r t i f i e d mixtures of CO and H 2, the procedure was as follows: i) The autoclave was charged with 1 1 of solution, sealed and placed into the heating jacket. i i ) The solution was heated, with s t i r r i n g , to a minimum of 100°C (max 105°C) and maintained at that temperature for 15 mins. During th i s period, the gas bleed valves were opened and a i r flushed from the autoclave with steam. After 15 minutes the bleed valves were closed. i i i ) The solution was heated to the desired temperature and allowed to s t a b i l i z e . The gas was admitted and the timer started. Samples were extracted at 10 or 15 minute intervals for the f i r s t half hour, every 30 minutes up to two hours, and every hour to the end of the run. For mixed gas runs, gas samples were taken at the appropriate intervals during the run. 18 Sampling i) Liquids The sampling tube and valve were flushed with minimum of 20 mis of solution. Then, about 10 mis l i q u i d sample was discharged into an N 2 flushed 25 ml erlemeyer flask. i i ) Gas Gas samples were taken into a 50 ml p l a s t i c syringe f i t t e d with a 22 gauge needle. Two sampling devices were used, a rubber hose f i t t e d to the bleed l i n e and clamped or a s t a i n l e s s steel tube with a s i l i c o n rubber diaphragm attached to an HIP f i t t i n g on the bleed l i n e . The bleed l i n e , syringe and sampling device were flushed at least twice before the sample was taken. Maximum storage time for any gas sample was 6 hours. For experiments involving mixtures of CO and H 2, the procedure was sim i l a r . Analysis Reagents Approximately 0.2 M EDTA solutions were prepared from "Baker Analyzed" EDTA. The EDTA was not dried before weighing. The resultant solution was standardized against standard Cu 2 + solution prepared from 99.99% copper shot dissolved in 20% (v/v) HN03. Acetate buffer solution (pH=5.5) was prepared from reagent 19 grade sodium acetate and "Anachemia" g l a c i a l acetic acid. Sodium hydroxide solutions were prepared from "Anachemia Acculute" NaOH concentrates. Instrumentation A l l t i t r a t i o n s were performed using the Radiometer automatic titrimeter at 25°C. For the copper ion t i t r a t i o n s , a copper ion sensitive electrode was used. Free acid was determined using a Corning glass electrode having an internal Ag/AgCl reference electrode. The end points of the t i t r a t i o n s were automatically determined using the derivative mode of the microprocessor on the t i t r i m e t e r . This feature allows one to record the derivative of. the t i t r a t i o n curve, the end point being the point of i n f l e c t i o n of the t i t r a t i o n curve. Gas analyses for CO and H 2 was done on a Perkin Elmer gas chromatograph equipped with a hot wire detector and a molecular sieve column using an argon c a r r i e r gas. A variety of column temperatures were used, but most sati s f a c t o r y results were obtained with a stable column temperature of 80°C. The injector and detector temperatures were, t y p i c a l l y , 25°C higher than the oven temperature. Integration of the peak retention time measurements was done by the microprocessor with which the gas chromatograph was equipped. S t r i p chart recordings of the peaks were also made. The standard curve was generated by using the c e r t i f i e d CO/H2 gas mixture plus mixtures generated using glass reservoirs. The quantity of CO and H 2 gas admitted to the 20 r e s e r v o i r was determined by H 2 0 displacement. Samples were then taken from these r e s e r v o i r s and run through the gas chromatograph to c r e a t e the standard curve. A n a l y t i c a l Method There were two important c o n s i d e r a t i o n s i n doing the analyses of the r e d u c t i o n run. F i r s t , H 2 0 was l o s t from the sample due to f l a s h i n g so that the c o n c e n t r a t i o n s of the species i n the sample d i d not represent the c o n c e n t r a t i o n s of the s p e c i e s i n the bulk s o l u t i o n . Secondly, some method for determining the Cu + c o n c e n t r a t i o n needed to be developed. Cu + as a f r e e ion i s not s t a b l e . I t r e a d i l y d i s p r o p o r t i o n a t e s to Cu° and C u 2 + v i a : 2Cu + — > C u 2 + + Cu° (2.1) Free Cu + i s a l s o s u s c e p t i b l e to a i r o x i d a t i o n . Complexed with CO to form the cuprous c a r b o n y l i t i s somewhat more s t a b l e , p a r t i c u l a r l y i n an atmosphere with a s i g n i f i c a n t CO p a r t i a l p r e s s u r e . However, i t i s not s u f f i c i e n t l y s t a b l e as to allow EDTA t i t r a t i o n of C u 2 + or NaOH t i t r a t i o n of H + without i t s i n t e r f e r e n c e . In order to overcome the f i r s t of these problems, i t was decided that the s u l f a t e i o n , S O „ 2 " , should be used as an i n t e r n a l standard, s i n c e i t s q u a n t i t y i s not changed dur i n g the course of the r e a c t i o n . T h e r e f o r e , i n a l l samples, the amount of SO, 2" present was determined by p r e c i p i t a t i o n with B a C l 2 to form 21 BaSO„ and gravimetrical analysis. The f i r s t sample discharged at temperature from the autoclave (no gas added) into a septum sealed v i a l was used as the standard (assume no flashing while sampling). A l l other samples were compared to this and their volumes calculated. (See sample c a l c u l a t i o n ) . The Cu + in the sample was determined by forcing the Cu + to disproportionate. The l i q u i d sample taken from the autoclave was placed in a hot water bath (approximately 80°C) and N 2 bubbled through the solution for a minimum of 15 min. This had the eff e c t of breaking down the cuprous carbonyl ( i f present) and allowing the Gu+ to disproportionate. The aqueous solution was then f i l t e r e d through a fine porosity Gooch crucible and transferred to a 100 ml volumetric flask (Soln A). The metal retained by the Gooch was dissolved in hot 20% (v/v) HN03 and transferred to a second 100 ml volumetric (Soln B). From solution A, 25 mis was taken for SO„ 2~, 10 mis for H +, and 10 mis for Cu 2 + determinations. From solution B, 10 ml was taken for Cu 2 + determination. The t o t a l Cu 2 + in solution B represents 1/2 Cu + o r i g i n a l l y present, ( i e . t o t a l Cu + = 2 x Cu 2 + solution B) The Cu 2 + o r i g i n a l l y present can be calculated by the difference of Cu 2 + in solution A and t o t a l Cu 2 + in solution B. Total H+ and SO,2" present were calculated from d i l u t i o n factors. The same procedure was used for H 2 reduction for consistancy. 22 Sample Calculation (H 2 Reduction 30/9/81) Part I Sample Volume Calculation of the Original Sample Volume The undiluted sample taken at time zero is used as the • standard. Using this solution, the concentration of SO, 2 - per m i l l i l i t r e of autoclave solution was determined. The subsequent samples were diluted to 100 mis, thoroughly mixed and 25 mis taken for SO,,2" determination. Column 3 contains the weight of BaS04 formed by the 25 mis taken from each sample. The volume of each solution sample equals four times the weight of BaS04 formed by the 25 mis divided by the weight of BaSOft determined from the standard. These volumes are contained in column 5. Sample No. Volume Prec ip. Weight BaSO„ Standard BaSO, Sample Volume mis. gms. gms./ml mis. Standard 2.0 0.6750 0.3375 1A 25.0 0.7264 8.61 2A 25.0 0.7006 8.33 23 Part II NaOH T i t r a t i o n s Free Acid Determination The concentration of H+ was determined by t i t r a t i o n with 1 M NaOH. The fraction of o r i g i n a l sample t i t r a t e d for a l l samples except the standard equals (0.10 x sample volume) (Column 3). From the volume of 1 M NaOH required to t i t r a t e t h i s f r a c t i o n , the [H +] i s calculated (Columns 3 and 4). ([NaOH] = 1.0 M.) Sample No. Volume Tit r a t e d Volume Original Sample Volume NaOH [H +] Autoclave mis. mis. mis. M. Standard 2.0 2.0 0.41 0.21 1A 10.0 0.861 0.31 0.36 2A 10.0 0.833 0.69 0.83 24 Part III EDTA T i t r a t i o n s C u 2 +; Cu + Determination The concentrations of Cu 2 + and Cu + were determined by EDTA t i t r a t i o n . Once the Cu + had been disproportionated and the metal dissolved, 10 mis of solutions A and B were t i t r a t e d . The volumes of o r i g i n a l samples and volumes of EDTA required to t i t r a t e the copper contained in these volumes are given in columns 2 and 3. Columns 4 and 5 hold the f i n a l C u 2 + and Cu + concentrations in the autoclave solution. ( [EDTA] = 0.175 M.) Sample No. Volume Origin a l Sample Volume EDTA [Cu +] [Cu 2 +] mis. mis. M. M. Stand. 2.0 7.88 0.0 0.69 1A 0.861 3.10 0.13 0.56 2A 0.833 1 .93 0.17 0.32 1B 0.861 0.33 2B 0.833 0.41 25 CHAPTER 3 RESULTS AND DISCUSSION Mathematical Model of the Reduction Process The previous investigations into hydrogen or carbon monoxide reduction of aqueous cupric s a l t s have provided both reaction mechanisms and rate equations for the reduction reactions. Based on these rate equations, a mathematical model for each of the reduction processes has been developed. The hydrogen reduction model was developed f i r s t and w i l l be discussed in d e t a i l in the following section. A later section w i l l deal with the CO model, which has the same format as the hydrogen model. These mathematical models can be compared with the results of experiments and used to predict the effect that changing certain parameters (eg. concentrations, equilibrium constants, pressure) would have on the reduction process. Hydrogen Model The basis of the hydrogen reduction model i s the rate equation, which i s used to calculate the change in the Cu 2 + and H+ ion concentrations over an increment of time. Accompanying the rate equation i s a double precision routine used to calculate the equilibrium concentrations of a l l the solution species at the zero time and after each reduction increment. The .basic algorithm of the program is to f i r s t calculate the 26 concentrations of a l l species in solution at time zero with the equilibrium routine. Once the i n i t i a l concentrations have been established, the incremental changes in the copper species and H + ion are calculated. The changes in these species are then adjusted to bring the system back to equilibrium, using the equilibrium routine. These two steps are repeated over the length of time specified for the reduction run. To calculate the incremental changes in Cu 2 +, Cu +, Cu° and H + equation 3.1 is used: ACu 2 + = 2.0k,[Cu 2*] 2PH ?At + 2.0k 3[Cu 2+j 2[ Cu+]PH2At {k_- i l H + ] + [Cu 2 + ]} {k_- 3 [ H + ] + [ Cu 2 + ]}{k_. 3 [ H + ] + [Cu 2 + ]} k 2 k 2 k i, (3.1) This equation i s based on the rate equation developed by Hahn (4) describing the rate of H 2 gas consumption. Two important changes have been made in the equation. F i r s t , the H 2 concentration has been replaced by a pressure term, PH 2, rather than H 2 concentration in solution, introducing the assumption that H 2 s o l u b i l i t y obeys Henry's law. The second change in the rate equation i s of greater s i g n i f i c a n c e . The equation i s written to describe the rate of Cu 2 + reduction, as a function of the rate of H 2 consumption. To write an equation describing the true rate of C u 2 + consumption would require incorporating the disproportionation process into the rate equation to account for the Cu 2 + produced by that reaction. Writing an equation to simultaneously account for the disproportionation and reduction reactions is not straight forward, and no s a t i s f a c t o r y equation has been determined. Consequently, the best way to describe the 27 Cu 2 + - time behavior i s by r e l a t i n g i t to the H 2 consumption which i s governed only by the concentration of the various species in solution. The concentrations of a l l species can then be corrected to equilibrium, p a r t i c u l a r l y disproportionation equilibrium, after each reduction step via the equilibrium rout ine. As can be seen in the reaction mechanism described in equations 1.6 to 1.9, the stoichiometry of H 2 consumption r e l a t i v e to Cu 2 + disappearance is given by: 2Cu 2 + + H 2 --> 2Cu+ + 2H+ (3.2) For every H 2 consumed, two Cu 2 + are reduced, thus introducing a factor of two into the AH2 form of the reduction equation. By multiplying the resultant equation by a selected time i n t e r v a l , At, the change in Cu 2 + concentration over that i n t e r v a l can be determined (equation 3.1). Once th i s change has been calculated, i t can be related to the concentration of the other species in solution, and the f i n a l equilibrium concentrations calculated. The ca l c u l a t i o n of the concentrations of various solution species i s r e l a t i v e l y complex. Since CuSO« and HS04~ are not completely dissociated, i t i s not possible to describe the solution adequately by using only mass balances. Consequently, the routine i s based upon the mass balance and equilibrium relationships described in Table II below. MS04 represents a non-reactive s a l t added as a buffer. M may be NH 4 +, Na +, K+, or Mg 2 + depending on the solution. 28 Table II Relationships for Calculating Equilibrium Concentrations. H 2 Model A) Mass Balances 2Cu+ = Cu 2 + + Cu° X= [Cu + ] Di sproportionat ing Cu 2 + + SO,2" = CuSO, Y= [Cu 2 + ] Forming CuSO, HSO," = H++SO, 2 Z = [HSO,"] Dissociating MSO, = M + SO, _ Q= [MSC >J Dissociating Spec ies I n i t i a l Amounts moles Fi n a l amount moles Cu + [Cu + 3*v [Cu++ACu-X]*V Cu 2 + [Cu 2 f ]*v [Cu2+-ACu-Y+X/2]*V Cu° Cu° Cu°+[X/2]*V CuSO, [CuSO,]*V [CuSO,+Y]*V H + [H +]*V [H++Z+ACu]*V HSO, " [HSO, - ]*v [HSO,--Z]*V M [M]*V [M+Q]*V MSO, [MSO,]*V [MSO,-Q]*V 29 Table II (continued) B) Equilibrium Relationships EQ1 = •  [H +][SO a 2" [HSO«] ] B i s u l f a t e Equilibrium EQ2 = = [Cu 2 +][SO, 2 - ] Copper Sulfate Equilibrium [CuSO„ ] EQ4 = = [M][SO u 2"] Metal Sulfate Equilibrium [MSO«] Kd = [ C u + ] 2 [Cu 2 +] Cuprous Disproportionation As can be seen from Table II, there is a maximum of four interdependant equilibrium relationships which govern the concentrations of various solution species. These are; the b i s u l f a t e equilibrium which controls the level of free H+ ion; the CuSO„ and the MSO, relationships which aff e c t the free S0 f l 2" concentration, and the Cu + disproportionation process which influences the Cu 2 + and Cu + concentrations. Each reduction increment w i l l reduce the concentration of C u 2 + species in solution and produce H + ion, and these changes in concentration must be adjusted according to the four relationships described above. The general approach used was to e s t a b l i s h variables which described the s h i f t in the equilibrium reactions created by the reduction process. An estimate of the value of one variable was then made, and the dependant values of the other three changes calculated. The i n i t i a l estimate and the calculated values were then checked against a mass balance expression, and the estimate adjusted u n t i l the values were 30 w i t h i n the t o l e r a n c e f o r the mass balance. A more d e t a i l e d d e s c r i p t i o n of the method used i n the c a l c u l a t i o n i s d e s c r i b e d below: i ) The value of Z, the change i n HSO„- c o n c e n t r a t i o n i s estimated based on the c u r r e n t l e v e l s of H + ion and the ACu c a l c u l a t e d . i i ) Using the estimated Z, the changes i n sulphate c o n c e n t r a t i o n due to MSO„ ( n o n - r e a c t i v e b u f f e r s a l t ) and CuSO„ d i s s o c i a t i o n are c a l c u l a t e d as Q and Y r e s p e c t i v e l y . If MSO„ i s present, Y i s a f u n c t i o n of Q and Z. I f t h i s b u f f e r s a l t i s not present, Y i s c a l c u l a t e d as a f u n c t i o n of Z o n l y . i i i ) I f the c o n c e n t r a t i o n of Cu* i s gr e a t e r than (Kd*[Cu 2 + ] ) 0 , 5 , the c o n c e n t r a t i o n of Cu + which d i s p r o p o r t i o n a t e s , X, i s c a l c u l a t e d as a f u n c t i o n of Y. iv) The estimated Z, and dependant Q, Y, and X values c a l c u l a t e d are checked a g a i n s t the o v e r a l l CuSOtt e q u i l i b r i u m [CuSO,]=[Cu 2+][SO, 2-] EQ2 which, with s u b s t i t u t i o n s rearranges t o : S=[Cu 2 ++X/2-Y-ACu]*[SO«+Z-Y+Q]/EQ2-CuSO«-Y When t h i s d i f f e r e n c e , S, f a l l s w i t h i n the s p e c i f i e d t o l e r a n c e , the f i n a l c o n c e n t r a t i o n s of a l l sp e c i e s i n s o l u t i o n are c a l c u l a t e d u s i n g the r e l a t i o n s h i p s given i n Table I I . In order to improve the accuracy of these c a l c u l a t i o n s the e q u i l i b r i u m constants have been a d j u s t e d t o values more c o r r e c t fo r higher temperatures. Appendix A g i v e s the d e t a i l s of these 31 adjustments for the HSO,- ion, the CuSO„ and MSO, s a l t s , as well as the disproportionation constant Kd. No attempt has been made to correct the calculations for a c t i v i t y c o - e f f i c i e n t s , due to lack .of information for concentrated solutions at high temperatures. Carbon Monoxide Model The model for CO reduction is based on the rate equation 1.13. ACu 2 + ={k,'[Cu 2* [Cu*] + k, '[Cu 2*] 2PCO + k 3'[Cu 2*] 2PCO}At TH*~1 (3.3) [H* As in the hydrogen reduction equation, the disproportionation of Cu* has not been included in the rate expression, and must be accounted for in the routine c a l c u l a t i n g the equilibrium concentrations. The equilibrium routine in the CO reduction model is similar to the routine in the hydrogen model. However, the introduction of the cuprous carbonyl ion, Cu(CO)*, and the equilibrium relationship which governs i t s formation renders the cal c u l a t i o n of the variables more complex. This i s p a r t i c u l a r l y true for the X variable which must now account for Cu(CO)* di sproport ionat ion. 32 Table III Relationships for Calculating Equilibrium Concentrations, CO Model A) Mass Balances 2Cu+ = Cu 2 + + Cu° Cu 2 + + SO a 2- = CuSO„ HSO„- = H ++SO„ 2-MSO, = M + S0„ 2-Cu + + CO = Cu(CO) + X=[Cu +] Di sproport ionat ing Y=[Cu 2 +] Forming CuSO„ Z=[HSOtt-] Di ssoc iat ing Q=[MSOj Dissociating T=[Cu +] Forming Carbonyl Spec ies I n i t i a l Amounts Fi n a l amount moles moles Cu + [Cu +]*V [Cu++ACu-X-T]*V Cu(CO) + [Cu(CO) +]*V [Cu(CO) ++T]*V Cu 2 + [Cu 2 +]*V [Cu2+-ACu-Y+X/2]*V Cu° Cu° Cu°+[X/2]*V C U S O 4 [CuSO a]*V [CuSO(,+Y]*V H + [H +]*V [H++Z+ACu]*V HSOft [HSO„]*V [HSOu-Z]*V M [M]*V [M+Q]*V MSO„ [MSO„]*V [MSO«-Q]*V 33 Table III (continued) B) Equilibrium Relationships EQ1 = EQ2 -EQ3 = EQ4 = Kd = [H*3 [ so f l 2 - ] [HSO„-] [Cu 2+][SO u 2'] [CuSO«] Cu(CO)*] Cu+]*PCO [M][SO e 2-] [MSOft ] Cu + ] Cu 2 + ] Bisulfate Equilibrium Copper Sulfate Equilibrium Cuprous Carbonyl Equilibrium Metal Sulfate Equilibrium Cuprous Disproportionation The rela t i o n s h i p between Cu(CO) +, Cu + and Cu° can be described two ways, as shown below: Cu(CO) + = Cu* + CO 2Cu+ = C u 2 + + Cu° (3.4) (3.5) and: 2Cu(C0) + = Cu 2 + + Cu° + 2CO (3.6) Obviously, 3.6 i s the sum of twice 3.4 and 3.5. The equilibrium between Cu(CO) + and metal should then be able to be expressed as a single equilibrium. However, since the s t a b i l i t y of the Cu(CO') + species is high, i t i s better to express the disproportionation process as reactions 3.4 and 3.5. The exact value of the equilibrium constant for equation 3.4 (EQ3) i s unknown, but i t i s estimated to be large due to the s t a b i l i t y of the carbonyl species. 34 Because of the increased complexity of the Q, Y, and X terms, the f i n a l CuSO, balance has d i f f i c u l t y in approaching zero. The function now appears to cross zero at two points which l i e within the range of the Z estimates. Consequently, the values of Z chosen may force the S value away from zero. In order to overcome the problem, the variables SST and SSM were introduced, which allowed the Z value to be adjusted to bring S to zero. A l i s t i n g of the H 2 and CO reduction models is given in Appendices B and C respectively. V e r i f i c a t i o n of the Models In order to check the v a l i d i t y of the models, both were compared to experimental results obtained by previous investigators. The a b i l i t y of the model to match the experimental results i s reasonably good as can be seen in the following figures. A comparison of the results of Hahn's unbuffered (no MgS04 s a l t added) experimental results (4) with the predictions of the model for the same i n i t i a l conditions is shown in Figure 3.1. The f i t of the curve 1 to the experimental data i s quite good. The rate constants used to obtain the curve are the values determined by Hahn for a sulfate solution at 160°C, corrected for expressing the H 2 factor as pressure rather than concentration. This adjustment was made using the H 2 s o l u b i l i t y ro O O 7 0 | _ I i i I I ^ A - ^ A . O Experimental O Model, H S 0 4 EQ2= 4 .96E-4 A ' A Model, H S 0 4 EQ2= 5 . 0 E - 5 / QCD"] 5 0 H / O O , . 30 A Ai 4$ 0 60 120 180 Time (min) Figure 3.1 Comparison of Model to Experimental Results. Conditions: [CuSO.] = 0.15 M. ; [H_S0.] = 0.85 M. ; [MgSO. ] = 0.0 M. ; u. T = 160°C.; P„ =0.5 MPa. H 2 36 data quoted in Table VI in Hahn's thesis (4). A further s l i g h t adjustment was made to the constants, but the f i n a l values l i e within the tolerance estimated by Hahn for the rate constants. The f i n a l value of these rate constants i s given in column 1 Table IV. Table IV Rate Constants Used to F i t Hahn's Experimental Results At 160°C and 0.5 MPa. Constants Unbuf fered System Buffered System Units k, 4.0E-5 5.0E-5 MPa"1 sec - 1 k 3 9.4E-4 1.50E-3 MPa'1 sec" 1 L- i k 2 V.3E-1 9.0E-1 k.a k« 4.5E-1 2.7E-1 Some discrepancy exists between the predicted maximum of Cu + species in li n e 1 and the experimental r e s u l t s . The difference i s probably due to errors in estimating the bi s u l f a t e and copper sulfate equilibrium constants. The values chosen for these constants can have considerable influence on the behavior predicted for the Cu + species. For example, l i n e 2, which was calculated using the same rate constants as l i n e 1 but with a dif f e r e n t HSOa~ equilibrium constant, does not match the experimental curve. The HSOa" constant used in generating l i n e 2 37 was corrected for the effect of temperature only, and not for ionic strength influences, which increases the value of the constant by about a factor of ten. The constant used in c a l c u l a t i n g the Cu + values in l i n e 1 was corrected for both factors. Apparently, correct S0„ 2' equilibrium constants are essential for accurate prediction of the Cu + curve, and in a l l subsequent model calculations, the HSO," constant w i l l be corrected for both ionic strength and temperature e f f e c t s . As a further check of the H 2 model, the predicted Cu + curve was compared to the experimental results from solutions containing MgSO„ s a l t . Figure 3.2 shows two model generated curves along with the experimental curve. Line 2 " was generated using the same rate constants as used to obtain the f i t of the unbuffered curve. These rate constants do not appear to apply to th i s system. Further adjustment of the rate constants was necessary to obtain a f i t of the model to the experimental curve, most notably, a decrease in the k. 1/k 2 and k. 3/k„ r a t i o s . The values of and k 3 were also increased s l i g h t l y . Column 3 in Table IV l i s t s the rate constants used to f i t the model to the buffered system. The CO model was checked in a similar manner against the results of Byerley's sulfate experiment (7). The rate constants used to obtain curve 2 in Figure 3.3 are those determined by Byerley for an acetate system, where the experiments were conducted at higher pressure and lower i n i t i a l C u 2 + concentration than was the sulfate experiment. Nonetheless, the 20 30 4 0 50 60 Time (min.) 70 80 90 100 110 F i g u r e 3.2 Comparison of Model to Experimental R e s u l t s C o n d i t i o n s : T = 160°C.; P [CuSO^] = 0.15 M, [H oS0.] = 0.40 M.; [MgSO.] = 0.45 M. ; H. = C.5 MPa LO OO iao F i g u r e 3.3 O Experimental A Model 120 3 0 0 360 180 240 Time (min) C o m p a r i s o n o f CO Model to E x p e r i m e n t a l R e s u l t s . C o n d i t i o n s : [ C u S O j = 0.0187 M.; [ H 2 S 0 ^  ] = 0.01 M.; [ N a ^ O j = 0.091 M.; Co vO T = 120°C CO = 6.8 MPa. 40 curve predicted by the model follows the experimental results reasonably well. The rate constants from the acetate system appear to be too large. Byerley had calculated a k, for the sulfate system which was larger than the constants used to generate th i s curve. Obviously, that value would not be correct. Also, the equilibrium constants can be expected to influence the f i t of the predicted curve, although no attempt was made in t h i s instance to adjust them. It should be noted that the Cu + term in the rate equation has been expressed as Cu(CO) + in t h i s and a l l subsequent model predictions. This is reasonable since the proposed reaction mechanism indicates that the Cu(CO) + i s the active Cu + species. Hydrogen Reduction Experimental Results The f i r s t objective of t h i s work was to determine the effects of increasing the concentration of the cupric salts on the rate of reduction by hydrogen. E a r l i e r studies, in d i l u t e solution, supplied information which had limited a p p l i c a b i l i t y to i n d u s t r i a l situations, where solutions having higher copper concentrations would be used. It was expected that increasing the CuSOu concentration in solution would result in a s i g n i f i c a n t increase in the rate of reduction. This expectation was based on the results obtained by Peters and Halpern (6) who demonstrated that solutions with a high concentration of the CuS04 ion pair exhibited greater H 2 activating capacity than did solutions of free (aquo-co-ordinated) C u 2 +. By increasing the i n i t i a l concentration of CuS04 in solution, p a r t i c u l a r l y in the 41 presence of a S 0 a 2 _ buffering s a l t , the concentration of the ion pair in solution would increase and presumably result in a higher rate of reduction. Figure 3.4 shows the Cu 2 + versus time (min) curve obtained at 140°C experiment using an i n i t i a l solution composition of; 0.71 M CuSO„; 0.60 M (NH 4) 2S0 4, and 0.10 M H 2SO« under a H 2 pressure of 0.68 MPa ( l i n e 1). Also shown are Cu 2 + curves generated from the results of Hahn's experiments at 160°C using solutions with i n i t i a l concentrations of 0.15 M CuSOa, 0.65 M MgSO„ and 0.20 M H 2SO„ (line 2 ). Apparently the i n i t i a l slope of l i n e 1 i s much greater than the i n i t i a l slope of 2 despite a decrease in temperature of 20°C. By f i t t i n g the computer model to the experimental curve an estimate of the rate constants for the reduction reaction can be obtained. Using these rate constants and the concentrations calculated by the model for the species of the rate equation, the i n i t i a l rate of Cu 2 + reduction can be determined. The same, procedure can be carried out for curve 2, using the rate constants from Table IV, column 2. The results of these calculations are given below. The increase in i n i t a l rates i s obviously much greater than the factor of fiv e increase in concentration. I n i t i a l rate l i n e 1. = 1.66E-4 moles/sec I n i t i a l rate li n e 2 = 7.16E-6 moles/sec 4> F i g u r e 3.4 C o m p a r i s o n o f H R a t e s a t H i g h and Low CuSO. C o n c e n t r a t i o n s . M 43 As expected, the increase in the ion pair concentration enhances the rate of reduction in excess of the effect expected from the increased concentration. One reason for this increased a c t i v i t y i s that the presence of the associated sulfate acts as a base to t i e up the H+ ion produced by the reduction reaction. If t h i s i s a v a l i d hypothesis, i t should be possible to see a c o r r e l a t i o n between the r e l a t i v e a c t i v i t i e s of various copper complexes, as reported by Peters and Halpern (6) and the low temperature pKa's of the ligand species. (pKa = -log Ka; association constant H + + A - = HA). This data i s c o l l e c t e d in Table V. Table V Relative A c t i v i t i e s of Copper Complexes and pKa's of Ligands Complex Rate Relative to Cu 2 + pKa CuBu2 1 50 -4.81 CuPr 2 1 50 -4.87 CuAc 2 120 -4.75 CuSOft 6.5 -1.92 CuCl 2 2.5 Cu 2 + 1 .0 It would appear then, that the b a s i c i t y of the associating ligand has a s i g n i f i c a n t e f f e c t on the a c t i v i t y of the 44 associated species. Peters and Halpern also observed that chelating compounds such as glycine or EDA did not s i g n i f i c a n t l y enhance the rate at low pH. This is reasonable since at low pH, the amine group w i l l be completely protonated and unable to act as a buffer. Effect of Pressure An experimental series was conducted to determine the eff e c t of increasing hydrogen pressure on the rate of the reaction. E a r l i e r work (Peters and Halpern (20)) has demonstrated a linear dependance of the rate of H 2 activation on pressure when observing dichromate disappearance (perchlorate and acetate systems). Figure 3.5 shows the results of the most recent study. Conditions for the experiments were as follows: 0.70 M [CuSO,], 0.1 M [H 2SO„], 0.65 M [(NH„) 2 S O a], T=140°C, P=0.68 or 1.33 or 2.00 or 2.72 MPa. In order to better assess the effect of pressure on the rate, the i n i t i a l slope of each of the lines in Figure 3.5 was plotted against pressure. The apparent linear dependance is shown in Figure 3.6. The scatter of the points about the l i n e i s most probably due to errors in i n i t i a l slope estimates and s l i g h t fluctuations in i n i t i a l CuSOi, concentrations. If one assumes that the s o l u b i l i t y of H 2 obeys Henry's law, then the rate i s proportional to the pressure of H 2. Since the rate expression i s written in terms of PH2, the rate constants therefore contain the Henry's law constant for H 2 s o l u b i l i t y . 0.70 0.50 + CM Z3 o 0.30 0.1 oh-90 120 Time (min) 150 180 F i g u r e 3.5 E f f e c t of P r e s s u r e on R e d u c t i o n R e a c t i o n Cond i t i o n s T = 1 4 0 ° C . [CuSO^ ] 0.70 M, [ H 2 S 0 J 0.10 M, [ ( N H 4 ) 2 S 0 J = 0.60 M, o O X o • CM 3 o PH 2 (MPa) F i g u r e 3 . 6 I n i t i a l R a t e v s . I I 2 P r e s s u r e . 47 Determination of Rate Constants By f i t t i n g the curve predicted by the model to the experimental re s u l t s , i t i s possible to obtain values of the rate constants forthe rate equations. The f i t i s most e a s i l y obtained by matching the experimental cupric curve. F i t t i n g the cuprous curve is more d i f f i c u l t since the l e v e l of cuprous in solution i s dependant on the free Cu 2 + concentration which i s governed by the CuSO„, HSOft" and MSO„ equilibrium constants. Thus, in order to f i t the cuprous curve, correct values for the equilibrium constants must be a v a i l a b l e . The results of the reduction experiment conducted at 140°C are shown in Figure 3.7 (Line 1). Also plotted are the predictions of the model using the rate constants derived by Hahn for his low concentration low pressure experiments at 140°C. The large difference between the predicted and observed rate again i l l u s t r a t e s the rate enhancement due to the increased concentration of the CuSOu ion pai r . Measurements of the i n i t i a l slopes suggest a rate increase of about 13 times. Figure 3.8 i l l u s t r a t e s the f i t obtained by adjusting the rate constants used in the rate equation. The values of the equilibrium constants used here are those calculated by the high temperature estimation methods described in Appendix A. The di s s o c i a t i o n constant for (NH^)2SO« was assumed to be the same as that estimated for K 2SO a. As can be seen, i t i s possible to obtain a good f i t of the Cu 2 + curve using these equilibrium 0 60 120 180 240 Time (min) F i g u r e 3.7 C o m p a r i s o n o f Model to E x p e r i m e n t a l R e s u l t s a t 1 A 0 ° C . Model P r e d i c t i o n Based on R a t e C o n s t a n t s D e t e r m i n e d by Hahn f o r 1 A 0 ° C . 0 60 120 180 240 Time (min) g u r e 3.8 F i t of \\^  M o d e l to E x p e r i m e n t a l R e s u l t s 1 4 0 ° C . C o n d i t i o n s : [ C u S O j = 0.73 M. ; [ l^SO^] = 0.11 M. ; [ ( N H ^ S O ^ ] = 0. T = 1 4 0 ° C ; P u = 2.7 MPa. 50 constants. However, the f i t of the predicted Cu + curve to the experimental curve i s poor. As in the f i t s of the Cu + curves discussed above, th i s s i t u a t i o n can be improved by adjusting the equilibrium constants. If i t i s assumed that the b i s u l f a t e d i s s o c i a t i o n constant is correct, having accounted for both temperature and ionic strength e f f e c t s , then the error in the equilibrium constant must l i e in the estimate of the CuSO„ and MSOa d i s s o c i a t i o n constants. To assess the effect that changes in these constants would have on the Cu + curve generated, they were each altered and the results compared to the experimental curve. The results of these changes are shown in Figure 3.9. Line 2 corresponds to the generated Cu + curve shown in Figure. 3.8. Line 3 i s the curve generated when the CuSO,, constant is increased by a factor of 10. The rationale for t h i s increase i s that the CuSO„ ion pair may be susceptible to ionic strength effects in the same way as the HSO«" and experience a similar increase in i t s tendency to dissociate. This increase in the constant brings the predicted Cu + closer to the experimental curve. The net effect of increasing the CuSO,, constant is to increase the l e v e l of free Cu 2 + in solution. A similar increase in Cu 2 + can be obtained by decreasing the (NH 4) 2SO f l d i s s o c i a t i o n constant. Curve 4 and 5 are created when t h i s constant i s decreased to 0.07 M and 0.01 M respectively. The d i s s o c i a t i o n constant for (NH„)SO,,- was assumed to be 0.07 | > . . i C u S 0 4 (NH 4 ) SO4 Equilibrium Equilibrium constant ,M constant ,M O Experimental 0.05[— A Q £ \ V Model 2 8.9 X I O 4 3.42 .' ^ A n> Model 3 9.0 V I 0" 3 3 4 ? / O odel  .  X I _3 3.4 2 \ X A • Model 4 9 . 0 X 1 0 ^ 0.07 a, A Model 5 9.0 X 1 0 0.01 " 0 - . . A - A - o I I I I I . I L 6 0 120 180 2 4 0 Time (min) F i g u r e 3.9 E f f e c t o f C h a n g i n g E q u i l i b r i u m P r e d i c t e d by H 2 M o d e l . C o n d i t i o n s : [CuSO^] = 0.73 M.; T = 1 4 0 ° C . ; P = 2 . 7 MPa. C o n s t a n t s on C u p r o u s C u r v e [ H 2 S 0 4 ] = 0.10 M.; [ N ( N H 4 ) 2 S 0 4 ] 52 t h e same as K S O „ - , s i n c e i n t h e a v a i l a b l e thermodynamic d a t a , K + was t h e l a r g e s t i o n and more c l o s e l y a p p r o a c h t h e N H a + i o n s i z e . However, t h e r e i s c o n s i d e r a b l e d i f f e r e n c e between t h e c o n s t a n t s o f t h e two s a l t s a t room t e m p e r a t u r e . [K + ] [SOu 2 -3 = 0 . 9 5 (32) (3.7) [ K S O „ : ] [NHa + HSOg 2-] = 0.07 (34) (3.8) [ ( N H 4 J S O 4 - ] C l e a r l y t h e n , t h i s a s s u m p t i o n i s n o t good. However, i n as much as b o t h t h e NaSO^" and t h e KSO f t" c o n s t a n t s i n c r e a s e w i t h t e m p e r a t u r e , one would e x p e c t s i m i l a r b e h a v i o u r from t h e ( N H „ ) S 0 4 - s p e c i e s . The r e s u l t s f o r t h i s f i t t i n g e x p e r i m e n t s u g g e s t t h a t t h i s i s n o t t h e c a s e , and t h a t t h e d i s s o c i a t i o n o f t h e (N^JSO,,- s p e c i e s may d e c r e a s e w i t h t e m p e r a t u r e , a l t h o u g h t h i s s u g g e s t i o n i s b a s e d on t h e a s s u m p t i o n t h a t t h e i n c r e a s e i n t h e CuSO a d i s s o c i a t i o n c o n s t a n t i s l i m i t e d t o a f a c t o r o f 10. F u r t h e r work would be r e q u i r e d t o d e t e r m i n e t h e e x a c t b e h a v i o u r of t h e s e s p e c i e s i n s o l u t i o n s o f h i g h i o n i c s t r e n g t h and a t e l e v a t e d t e m p e r a t u r e s . However, s i n c e t h e b e h a v i o r of t h e C u + i o n i s d e p e n d a n t on t h e f r e e C u 2 + i o n , by v i r t u e o f t h e i r r e l a t i o n s h i p t h r o u g h t h e d i s p r o p o r t i o n a t i o n c o n s t a n t , i t i s p o s s i b l e t o p r o p o s e some e x p l a n a t i o n f o r t h e b e h a v i o r seen i n F i g u r e 3.9. By i n c r e a s i n g t h e CuSO„ e q u i l i b r i u m c o n s t a n t , t h e C u 2 + c o n c e n t r a t i o n i s b e i n g i n c r e a s e d . D e c r e a s i n g t h e (NH„)SOi," d i s s o c i a t i o n has t h e same a p p a r e n t e f f e c t on t h e C u 2 + , s i n c e t h e r e i s a r e s u l t a n t i n c r e a s e i n t h e C u + c o n c e n t r a t i o n . 53 Actually, decreasing this constant reduces the concentration of free S 0 a 2 _ , which would tend to promote the d i s s o c i a t i o n of Cu 2 + from CuS0 4. It i s known that other ammonium sulfate sa l t s exist in solution, p a r t i c u l a r l y (NH4)HSOft and the double salt Cu(NH f t) 2(S0„) 2. The l a t t e r s a l t has been shown to precipitate from more concentrated CuSO«-(NH 4) 2S0 4 solutions (35). If these s a l t s exist as associated species in solution, the effect of their presence would be to dramatically reduce the l e v e l of free sulfate in solution. The free Cu 2 + concentration would then be determined by the r e l a t i v e amounts of the CuSOu , Cu(NH 4) 2(S0 4) 2 and C u 2 +. It seems l i k e l y that accounting for these e q u i l i b r i a would provide a better description of the solution. However, there i s l i t t l e thermodynamic data available on these aqueous species. It i s also apparent that.the model does not reduce the Cu + concentration from the maximum as quickly as occurs in the real system. This may be due to either errors in the disproportionation constant, though no attempt has been made to adjust t h i s constant to obtain a better f i t , or to the weaknesses in the treatment of other equilibrium relationships. In t h i s discussion of the e f f e c t s of changing the model parameters to f i t experimental re s u l t s , i t must be rembered that errors do exist in the experimental r e s u l t s . This is p a r t i c u l a r l y true in the Cu + determination, where the formation of Cu° might contribute a s i g n i f i c a n t uncertainty. If atomic sized p a r t i c l e s of Cu° formed in the autoclave, they would not 54 be screened out by the f i l t e r on the sampling tube. Because of the method of analysis the concentration of copper in the form of these p a r t i c l e s would be interpreted as twice as much Cu +, and contribute to an unreasonably high report of Cu +. E a r l i e r work (4) was also plagued by th i s problem. Therefore, although a reasonable explanation can be offered for changing the equilibrium constants of the model to obtain a f i t of the Cu + curve, the v a l i d i t y of the experimental results must also be considered. The a l t e r a t i o n of the equilibrium constants has l i t t l e or no effect on the Cu 2 + curve. Figure 3.10 compares the experimental curve of Figure 3.8 with the Cu 2 + curve generated by the model using the increased CuSO,, equilibrium constant and the reduced (NHtt)SO„" constant. The rate constants are the same as those used to generate the plot in Figure 3.8. It seems reasonable to suggest that the rate constants determined by this method are correct and that the prediction of the cuprous curve is a function of the equilibrium constants, not the rate constants. Table VI compares the rate constants for the high concentration solution with those developed by Hahn (corrected to MPa"1 sec" 1) at 140°C. 0.70 0.50 + CVJ O 0.30 O Experimental A Model 0.10 120 Time (min) 180 2 4 0 F i g u r e 3.10 F i t o f H M o d e l to E x p e r i m e n t a l R e s u l t s 1 4 0 ° C . C o n d i t i o n s : T = 14 0 ° C . ; P [CuSO . ] 0.73 M.; [H SO^] = 0.10 M, [ ( N H 4 ) 2 S 0 / ( ] = 0.60 M, H, 2.7 MPa. 56 Table VI Comparison of Rate Constants at Low and High [CuSO„] T=140°C. Constants (Units) Hahn's value Value From F i t Relative Increase (MPa'1 sec" 1) 1.1E-5 2.2E-4 20.0 k 3 (MPa-1 sec" 1) 2.4E-4 2.2E-4 0.9 k. i k 2 1.3E-1 8.0E-1 6.1 k.3 4.5E-1 8.5E-1 1 .9 The largest increase in the rate constants is in the k, value. This suggests that the i n i t i a l a c t ivation of the H 2 by the Cu 2 + is the most enhanced by the presence of the ion pair. The second term of the rate equation, containing the Cu + term appears to be unaffected by the ion pair. It also implies that i f a CuSO„- complex forms, i t does not influence the rate of reaction. The a c t i v i t y of the H+ ion seems to be enhanced in this more concentrated solution, as seen in the increase in the k_i/k2 and k. 3/k u r a t i o s , i . e . the r e l a t i v e rates of the reverse reaction increase. This situation is somewhat surprising in that the bisulphate dissociation constant i s known to increase in these solutions of high ionic strength (25) which would indicate a reduction in H' ion a c t i v i t y . However, i f we consider the 57 e a r l i e r discussion on the fate of the SO,,2- ion in these solutions, t h i s apparent increase in H+ ion a c t i v i t y seems reasonable and would tend to support the hypothesis of reduced SO,,2- ion a c t i v i t y in solution. It i s possible that (NH„)SO„- or other mono-valent cationic sulfate s a l t s do not have the buffering capacity anticipated. The rate constants derived by the f i t t i n g technique do not take into account the difference in the rate of H 2 activation that may occur between the free Cu 2 + ion and the CuSO, associated complex. Based on the e a r l i e r results as compared to the results of this study, one would expect such a difference. Using the adjusted equilibrium constants for CuSOa and (NH„)SO a-diss o c i a t i o n (0.009 and 0.01 respectively at 140°C; Figure 3.10), the r a t i o of free Cu 2 +/CuSO u in a 0.70M t o t a l copper solution i s about 0.14. This r a t i o increases as the reaction proceeds, and consequently so does the contribution of the Cu 2 + species to the t o t a l rate. However, no attempt has been made to determine the Cu 2 + rate contribution and the rate constants obtained by f i t t i n g the model are a combination of the rate of reduction of the free ion and the CuSO« ion pair . Figures 3.11 and 3.12 show experimental results at 120 and 160°C respectively along with f i t t e d curves obtained from the model. Table VII reports the values of the rate constants obtained for 120, 140, and 160°C. Comparing these constants with those in Table I, we see that at a l l three temperatures, the largest increase has been in the k, constant.. Also, the 3 0.1 0 I 2 0 ° C O Experimental A Model j ^ / A A A ft ip- ft 6 0 120 Time (min) 180 F i g u r e 3.11 A . 4* 2 4 0 F i t o f ^2 M o d e l to E x p e r i m e n t a l R e s u l t s 120°C. C o n d i t i o n s : [ C u S O j = 0.71 M.; [ I ^ S O J = 0.10 M.; [ ( N H ^ S O ^ = 0.60 M.; T = 120°C.; P II, 2.7 MP a OO 0.70 0.50 3 o 0.30 I 6 0 ° C O Experimental A Model 0.10 _ 4x A -Cu+ -A-0 20 40 Time (min) 60 F i g u r e 3.12 F i t o f H 2 M o d e l to E x p e r i m e n t a l R e s u l t s 1 6 0 ° C . C o n d i t i o n s : [CuSO ] = 0.74 M.; [11 SO ] = 0.12 M. ; [ ( N H ^ S O J 0.74 M T = 16 0 ° C . ; P H , 2.7 MP a U i VO 60 temperature independence of the rate constant r a t i o has been preserved. Table VII Rate Constant from F i t t i n g of H 2 Model Constants (Units) 1 20°C 1 40°C 1 60°C k, (MPa - 1 sec" 1) 4.0E-5 2.2E-4 1.2E-3 k 3 (MPa"'sec"1) 8.0E-5 2.2E-4 5.8E-4 k. , k 2 8.0E-1 8.0E-1 8.0E-1 k.3 k« 8.5E-1 8.5E-1 8.5E-1 In concluding t h i s section, i t appears that the rate constants obtained by f i t t i n g the model to the experimental results are v a l i d . It must be remembered though, that owing to the lack of information on the exact nature of the behavior of the species in solution, these constants are in a sense empirical and must contain allowances for the errors in describing the solutions and for the assumption that the H 2 s o l u b i l i t y obeys Henry's law. 61 Eff e c t Of Temperature Using the rate constants determined by the f i t t i n g of the model curve at 120, 140 and 160°C, i t i s possible to determine the effect of increasing temperature on the rate of reaction. Figure 3.13 shows the plot of log k, versus 1000/T°K and log k 3 versus 1000/T°K. From the slope of the l i n e , i t i s found that the activation energy for the reactions i s : E, = 123 kJ/mole E 3 = 71.1 kJ/mole These values are s l i g h t l y greater than those determined by Hahn for his low concentration experiments (E,=93.7 kJ/mole; E3=64.0 kJ/mole), as would be expected from the increase in reaction rate observed at the higher concentrations. Formation of H + Ion From the stoichiometry of the reduction reaction, i t can be seen that for every Cu 2 + reduced to Cu +, one H+ ion i s produced. By monitoring the production of H+ ion during the course of the reduction run, the analysis of the Cu 2 + ion can be checked. Figure 3.14 shows the H + production and the C u 2 + reduction curves for 120, 140 and 160°C. Also shown are the H + curves predicted by the model. The 160°C experimental curve shows H+ ion in excess of that expected from the Cu 2 t reduction, but this i s l i k e l y due to experimental error. 230 2.40 250 2.60 1000/T K g u r e 3.13 A r r h e n i u s P l o t : H 2 R e d u c t i o n . Log k as a F u n c t i o n of 1000/T°K, .5 0 1.00 0.50 0' 20°C 140 °C _ 0 Or— A A O Experimental A Moae! T T 60 °C ^ o - O -P A A o 120 240 60 80 20 60 Time (min) F i g u r e 3.14 H P r o d u c t i o n D u r i n g H 0 R e d u c t i o n . 64 Effect of (NH«) 2SO u Salt The e a r l i e r discussion has suggested that the a b i l i t y of the (NH(|)2SO<t s a l t to act as a buffer in the high concentration CuSO„ solution is somewhat limited. Nevertheless, the addition of the s a l t to the solution promotes the reduction reaction, p a r t i c u l a r l y in the l a t t e r stages of the process (Figure 3.15). This is reasonable since during this period the concentration of the H+ ion w i l l be great enough that i t w i l l have considerable ef f e c t on the rate. Also, the l e v e l of t o t a l Cu 2 + w i l l now be reduced , thus the tendency to form the ammonium copper sulfate double s a l t w i l l be lower and the SO, 2 - ion w i l l be free to form the HSO„- ion. Carbon Monoxide Reduction Experimental Results Owing to the technique used in previous kinetic investigations of Cu 2 + reduction by CO, the results are severely limited in t h e i r a p p l i c a b i l i t y to i n d u s t r i a l systems. The use of the high pressure spectrophotometric c e l l enabled Byerley (7) to determine the rate equation and the reduction mechanism for the reaction. However, the c e l l limited the volume of solution used in the reaction. Furthermore, the concentrations used were very low to ensure that deviations of the spectrophotometric properties of the solution from Beer's law were minimized. Byerley had observed, that under pressures up to 40 MPa (400 atm) , the Cu 2 + time curve .assumed ,.a sigmoidal shape, 0.70 0.50 O 0.30 O Unbuffered [ ( N H 4 ) 2 S0 4 ] =0 .0M • Buffered [ ( N H 4 ) 2 S0 4 ] =0.60M •o-L Q . 120 Time (min) 240 F i g u r e 3.15 E f f e c t o f (Nil, ) SO, on H-. 4 4 C o n d i t i o n s : 140°C 1) [CuSO ] 2) [ C u S O ^ l R e d u c t i o n . 7 MP a . P = 2 H "2 0.73 M. 0.61 M. [HSO ] [H^soj] 0.10 M, 0.10 M, O N U l [(NH ) SO ] i < N H 4 > 2 S ° 4 ] = 0.60 M. ; = 0.0 M. 66 indicating that an autocatalytic process was occuring. Comparing Byerley's results at 120°C, 6.8 MPa (68 Atm.) and 0.0187 M Cu 2 + with results using 2.7 MPa (27 Atm) and 0.70 M Cu 2 + at the same temperature shows that the rate of reaction is much slower, probably due to the lower pressure (Figure 3.16). Most experiments in the previous study were performed at pressures greater than 6.0 MPa (60 atm) since the experimental technique introduced large uncertainties at low pressures due to CO depletion in the solution. The problem of CO depletion did not occur in the present investigation because of larger solution volumes and better mixing techniques. As a consequence of these differences in experimental approach, i t i s d i f f i c u l t to make meaningful comparisons between the present study and Byerley's work. Determination of Rate Constants As in the H 2 reduction experiment, i t i s possible to determine rate constants for the reduction reaction by f i t t i n g the calculated values of the CO model to the experimental curve. However, the f i t t i n g of the CO model has greater d i f f i c u l t i e s associated with i t . Consider the Cu(CO) + species, which i s formed during the reaction as a stable complex and which could reach concentrations approximating the i n i t i a l Cu 2 + l e v e l s . Since t h i s complex contributes to one term of the rate law, i t is quite important that i t s behavior be predicted accurately in order to obtain meaningful rate constants. E a r l i e r discussion of 0 120 240 T i m e (m in ) F i g u r e 3.16 C o m p a r i s o n o f CO M o d e l to E x p e r i m e n t a l R e s u l t s . C o m p a r i s o n of Low [CuSO.] S o l u t i o n a t P „ n = 6.8 MPa. w i t h o> 4 C U -j H i g h [CuSO^] S o l u t i o n a t P c 0 = 2.7 MPa, T = 1 2 0 ° C . 68 the H 2 model demonstrated the s e n s i t i v i t y of the free Cu + species to the equilibrium constants selected for the S 0 „ 2 _ species in solution. These constants w i l l influence the Cu(CO) + formation through the Cu + species. There i s also the problem associated with determining the value of the Cu(CO) +/Cu + equilibrium r a t i o . Because of these uncertainties in the workings of the CO model, i t i s useful to examine what effect changing these parameters w i l l have on the predicted curve. The experimental results at 140°C experiment are shown in Figure 3.17, along with curves predicted by the model. The model was f i r s t f i t t e d to the experimental Cu 2 + curve using the adjusted equilibrium constants determined for 140°C in f i t t i n g the H 2 model (HSO„- EQ1=0.0013 M; CuSO„ EQ2=0.009; MSO, EQ4=0.01 M). The corresponding f i t of the Cu* curve i s quite good. The value of the Cu(CO) +/Cu + constant used to obtain this f i t was 5.0, and was determined by attempting to match the apparent decrease in the Cu + curve at t=240 min. Obviously further small corrections would improve the f i t at that time. The rate constants derived from t h i s f i t are given as Line 1 in Table VI11. 0 6 0 1 2 0 1 8 0 2 4 0 T ime (min) F i g u r e 3.17 C o m p a r i s o n o f CO Model to E x p e r i m e n t a l R e s u l t s 14 0 ° C . C o n d i t i o n s : [CuSO, ] = 0.72 M. ; [H-SO.] = 0.12 M. ; [ ( N H . ) „ S 0 , ] = 0.65 M. ; S T = 1 4 0 ° C . ; P_ n = 2.7 MPa. 70 Table VIII Comparison of Rate Constants to F i t CO Reduction at 140°C Constants (Units) Figure Line 3.17 1 Figure Line 3.17 2 (sec " 1 ) 1 . 5E-5 5.8E- 6 (MPa-1 sec" 1) 1 . 4E-8 1 . 4E-8 (MPa"1M-1 sec" 1) 1 .8E-5 2.8E- •5 Carbonyl Equilibrium 5.0 20.0 Using these same rate constants, a second set of curves was generated by decreasing the CuSO,, constant to 0.00089 (the high temperature value calculated in appendix A) and increasing the NH„SO„- constant to 0.07. This results in a dramatic change in the behavior of both the Cu 2 + and Cu* curve. Using this CuSO,, equilibrium constant requires that the rate constant, k,', be increased to obtain a f i t of the curves and that the Cu(CO) + constant be increased to 5 times the value obtained in the f i r s t f i t . The rate constants used to make thi s l i n e match the experimental results are given as Line 2 in Table VIII. It i s apparent that the rate constants determined by this method for CO reduction are contingent upon the equilibrium constants used in the model, unlike the H 2 model where the Cu 2 + curve could be f i t t e d independant of the equilibrium constants selected. Consequently, the rate constants determined by thi s 71 method for CO reduction must specify the equilibrium constants upon which they depend. Since the results of the H 2 f i t t i n g suggest that the lowered MS04 constant and higher CuSOa create a better model of the Cu + curve, these values w i l l be used throughout the f i t t i n g of the CO model to the experimental r e s u l t s . Figures 3.18 and 3.19 show the experimental curves at 120 and 160°C respectively, along with the f i t t e d curves generated by the model. The rate constants and the Cu(CO) + equilibrium constants used in the ca l c u l a t i o n of the curves at three temperatures are given in Table IX. It i s interesting that k 2', t n e a c i d dependant-pressure dependant term of the rate equation is unaltered, and is in fact the same value as reported by Byerley for his acetate system. One possible explanation for this feature i s that the pressures at which these experiments were conducted were too low to influence t h i s term as the temperature increased. The second term describes the activation of CO by the Cu 2 + ion. The value of the rate constant reported by Byerley for t h i s term i s considerably lower than the value returned for the pressure dependant-acid independant constant of the t h i r d term. The situation would suggest that the second term i s only important at high pressure. 120 240 360 T i m e ( m i n ) F i g u r e 3.18 F i t o f CO Model to E x p e r i m e n t a l R e s u l t s 1 2 0 ° C . C o n d i t i o n s : [CuSO ] = 0.70 M. ; [ H „ S 0 . ] = 0.10 M. ; [ ( N H ( ) n S 0 j = 0.70 M. : T = 1 2 0 ° C . ; P „ n = 2.7 MPa. 0 60 120 Time (min) F i g u r e 3.19 F i t o f CO Model to E x p e r i m e n t a l R e s u l t s 1 6 0 ° C . C o n d i t i o n s : [CuSO^] = 0.70 M.; [HjSO ] = 0.11 M. ; [ (N11 A) 2 S 0 A ] = 0.66 M . ; • ->J T = 1 6 0 ° C . ; P C Q = 2 . 7 MPa. 74 Table IX Rate Constants from F i t t i n g CO Model Constants (Units) 1 20°C 140°C 1 60°C (sec" 1) 2.2E-6 1.5E-5 1 .5E-5 k 2' (MPa"1 sec" 1) 1.4E-8 1.4E-8 1.4E-8 (MPa" 'M-1 s e c 1) 6.5E-6 1.8E-5 5.0E-4 Carbonyl Equilibrium 5.0 5.0 1 .0 Experiments were conducted to attempt to determine the Cu(CO) +/Cu +PCO equilibrium constant at the experimental temperatures. The procedure involved using a buffered CuSO, solution containing an i n i t i a l concentration of 0.30 M Cu 2 +, 0.60 M (NH<,)2SO«,r and 1.0 M H 2SO«. To the autoclave, charged with t h i s solution, was added 0.60 moles copper powder at 200 mesh. The mixture was s t i r r e d under approximately 2.7 MPa CO for twenty-four hours at each of the temperatures of inte r e s t . The solution was analysed for Cu + and Cu 2 + at the end of each twenty-four hour period and the equilibrium constant calculated as below: 75 i) Assume free [Cu +] = (Kd[Cu 2 + ]) °-5 i i ) [Cu(CO) +] = to t a l [ C u + ] - free[Cu +] i i i ) EQ3 = [Cu(CO)*] MPa'1 [Cu+]PCO 120°C 140°C 160°C •2.98 3.59 1 .82 Comparison of these figures with the results in Table VIII indicate that the experimentally determined constants would not work in the model. However, the above EQ3 cal c u l a t i o n i s based on the analysed Cu 2 + having an a c t i v i t y c o - e f f i c i e n t of one. If the Cu 2 + was ti e d up as a Cu(NH f l) 2(S0 f t) 2 double s a l t then the Cu 2 + a c t i v i t y would be reduced and the analysed Cu 2 + would not represent the free Cu 2 + in equilibrium with Cu +. Obviously, a better understanding of the solution behavior is necessary before such calculations can be made. Eff e c t of Temperature One of the most s i g n i f i c a n t results of the CO reduction experiments was the demonstration of the marked temperature dependance of the CO reduction process. Based on previous observations at 120°C i t was not thought that the rate of reduction under CO would approach that under H 2, except at very high presssure. However, at 140°C and 160°C, the rate of CO reduction approaches that of H 2 reduction, when both systems are run at the same pressure (2.7 MPa). 76 An attempt was made to generate an Arrhenius plot based on the k,' and k 3' values reported in Table IX. The results shown as l i n e s 1 and 2 respectively in Figure 3.20 indicate a non-linear temperature dependance. But, since these rate constants are dependant on the selected equilibrium constants, they cannot simply represent the acti v a t i o n energy (Ea), and i t i s doubtful that the non-linear responce has any significance other than to indicate these are not true rate constants for the reaction. Line 3, which i s a plot of log of the i n i t i a l slope of the experimental curves vs 1000/T °K" 1 i s linear and an estimate of Ea i s made from this l i n e . Ea = 149 kJ/mole Formation of H + Ion/ Effect of (NH a) 2SO u Salt As in H 2 reduction, the CO reduction process produces H+ ion as a product, and i t s production can be monitored as a check on the Cu analysis. Figure 3.21 contains the H + production curves for a l l three temperatures, and the results of the analysis concur with the Cu a n a l y t i c a l r e s u l t s . The model predictions of H+ concentrations over the reduction reaction have also been included. By removing the H + ion from solution with a buffer the I.30i 1.00 + x 0.50 0 I 4 0 ° C — o -A Model O O Experimental A ' -A A - I 2 0 ° C O' / ^ A I 6 0 ° C • Q A — A A Model D Experimental 120 2 4 0 360 6 0 120 Time (min) F i g u r e 3.21 H P r o d u c t i o n d u r i n g CO R e d u c t i o n . C O 79 tendency of the reduction' reaction to go to completion is increased. Also the rate equation for CO reduction has an inverse H + ion dependence in the f i r s t term (assuming the second term i s inoperative at these pressures).. Since this term, being Cu(CO) + dependant, accounts for the greatest rate of reduction, a s i g n i f i c a n t increase in rate could be expected i f the H + ion concentration was reduced. This i s , in fact, the ef f e c t of the (NH4)2SO(, buffer on the reduction reaction, as can be seen in Figure 3.22, which shows Cu 2 + curves produced by both buffered and unbuffered runs. Gas Analysis of Carbon Monoxide Reduction It has been observed that certain aqueous species w i l l catalyse the s h i f t reaction by oxidizing CO to C0 2 with water and producing H 2 ( 1 1 ) . Normally, the kinetics of this process render the reaction i n s i g n i f i c a n t at temperatures lower than 400°C. In as much as the f i n a l part of this study i s concerned with the reducing a b i l i t y , of combinations of CO and H 2 gas, i t was important to determine whether or not C u 2 + would catalyse the oxidation of CO and thereby produce H 2. Gas analysis of the f i n a l gas mixture of a 160°C CO reduction reaction showed no H 2 gas was present. The absence of H 2 at th i s temperature indicates the s h i f t reaction does not occur measurably over the temperature range considered in these experiments. 0 60 120 Time (min) F i g u r e 3.22 E f f e c t of (NH ) SO * on CO R e d u c t i o n . C o n d i t i o n s : T = 1 4 0 ° C ; P = 2.7 MP a 1) [CuSO ] = 0.72 M. ; [II SO 2) [CuSO, ] = 0.72 M. ; [ICSO h 2. _ L _ 180 L_ 240 0.12 M. ; [ (Nil ) SO ] = 0.0 M. ; 0.12 M. ; [ (NH,)^SO, ] = 0.65 M. 4 2 4 co o 81 Summation and Comparison of Independant Hydrogen or Carbon Monoxide Reduction Results Since the next section deals with the reduction process under mixtures of CO and H 2 gases, i t i s useful to b r i e f l y consider the results of the preceding sections, and to assess the s i m i l a r i t i e s and differences between the two processes. That the increase in i n i t i a l CuSO„ concentration enhances the rate of Cu 2 + reduction under H 2 has been demonstrated. This rate enhancement appears to be primarily due to the increased a b i l i t y of the Cu z + species to activate H 2. The autocatalytic nature of H 2 reduction dependant on the Cu + concentration does not appear to be enhanced, and evidence of a sigmoidal curve i s reduced. Under CO, the higher i n i t i a l concentration of CuSO„ appears to have l i t t l e effect on the a b i l i t y of Cu 2 + species to activate CO, and the reduction reaction i s an autocatalytic process at these concentrations. The temperature dependance of the two processes has been shown, with the most s i g n i f i c a n t results a r i s i n g from the CO temperature series, where the magnitude of the effect was unanticipated. At 160° C, the rates of CO and H 2 reduction can be considered the same. A comparison of the rate constants in Tables VII and IX confirms this observation, since the important rate constants are approximately the same order of magnitude at 160°C. 82 The effect of adding a S 0 „ 2 - s a l t as a buffer i s more pronounced for the CO reduction since in that system the buffer enhances the rate of reduction quite s i g n i f i c a n t l y as well as moving the reaction closer to completion. With th i s increased understanding of the independant gas systems, we can now consider the e f f e c t of mixtures of the two gases. Reduction Using Mixtures of Hydrogen and Carbon Monoxide Gases In order to assess the e f f e c t s the mixing the reducing gases, two series of experiments were done. The f i r s t series was conducted using changing ratios of gases over the course of the reduction run. This was accomplished by admitting a specified pressure of one gas (A) and maintaining the pressure at a constant value of 2.7 MPa (27 atm) with the second gas (B). The experiments were performed using both H 2 or CO as gas (A), and the results w i l l be reported below. The second series of mixed gas experiments were conducted using an input gas of a fixed CO/H2 r a t i o (66.2%CO/33.8%H2). These results w i l l be reported in a later section. Variable Carbon Monoxide/Hydrogen Ratio Experiments By maintaining the t o t a l pressure of the system with one p a r t i c u l a r gas (B), the effect is to add (A) to a gas (B) run. The results are most e a s i l y interpreted by comparison to a pure 83 (B) run. A l l experiments were conducted at •140°C, and the gases were not admitted u n t i l the system was up to temperature. Consider f i r s t H 2 as gas (A) and CO as gas (B). By comparing the C u 2 + curves in Figures 3.8 and 3.17, i t is apparent that the rate of Cu 2 + reduction is greater under H 2 than under CO. Thus, we would expect that the addition of H 2 to a CO run should enhance the i n i t i a l rate of Cu 2 + reduction. The series of curves in figure 3.23 which show the effect of adding 0.68, 1.36 and 2.04 MPa H 2 (6.8, 13.6, 20.4 atm) at time zero, and maintaining the pressure with CO. As the H 2 fraction increases, the sigmoidal shape of the reduction curves i s reduced. Since the i n i t i a l slow stage of the CO reduction curve is due to the slower Cu 2 + reduction to Cu* we can conclude that the addition of H 2 enhances th i s process. A corresponding effect i s seen in the Cu + curves (Figure 3.24) where the addition of increasing pressures of^H 2 gas enhances the rate of Cu + formation. Also evident from these curves is that the presence of H 2 gas, p a r t i c u l a r l y at a higher p a r t i a l pressure, may promote the reduction of Cu(CO) + to a limited extent. This may be due to the low CO gas pressure. Under greater pressures of H 2 more reduction may occur. Figure 3.25 shows the Cu + curves resulting from experiments where H 2 gas was in excess (Gas A = CO; Gas B = H 2). The reduction of the Cu(CO) + species i s again limited, even under the predominantly H 2 atmosphere present at the end of the runs. 0.70 0.50 + C M 3 Init ial P H 2 o 0.0 M P a O 0.68 M P a — • 1.30 M P a V 2.00 M P a 20 T i m e (min) 180 O F i g u r e 3.23 2 + C u r v e i n P r e s e n c e o f CO. T o t a l P r e s s u r e s M a i n t a i n e d a t 2.7 MPa. by CO,' T = 1 4 0 ° C ; E f f e c t o f II^ P r e s s u r e on Cu [ C u S 0 4 ] * 0.72 M. ; [ ( N H 4 ) 2 S 0 4 1 ^ 0.60 M. ; [ H ^ S O J ^ 0.10 M. 0 60 120 180 240 T i m e (min) i F i g u r e 3.24 E f f e c t o f P r e s s u r e on C u + C u r v e i n P r e s e n c e o f CO. T o t a l M a i n t a i n e d a t 2.7 MPa. by CO, T = 1 4 0 ° C ; °° [CuSO^] ^ 0.72 M. ; [(NH^) S 0^ ] ~ 0.60 M. ; [H SO^] * 0.10 M. 0.60 0.40 + o 0.2 0 r -T i m e ( m i n ) F i g u r e 3.25 E f f e c t on CO P r e s s u r e on Cu C u r v e i n P r e s e n c e o f H„. T o t a l P r e s s u r e M a i n t a i n e d a t 2.7 MPa. by 11^, T = 140°C. ON [CuSO,] ^ 0.70 M. ; [ ( N H ^ S O J * 0.60 M. ; [ ^ S O ^ ] ^ 0.10 M. 87 Gas analysis at this point indicates CO present at a low fra c t i o n in the 2.04 MPa i n i t i a l CO experiment. Thus i t seems that Cu(CO) + exhibits considerable s t a b i l i t y under a H 2 atmosphere. If the results of H 2 pressure series are compared to the mixed H 2 - CO experiments (Gas A = H 2; Gas B = CO) i t i s possible to begin to assess the r e l a t i v e effect of these gases on the reduction rate. Figure 3.26 compares the rate of pure H 2 reductions at 0.68 and 2.04 MPa with the corresponding H 2 - CO mixed gas experiments. At 0.68 MPa H 2, the i n i t i a l slopes of the mixed gas run is comparable to the pure H 2 run. (H 2 i n i t i a l slope = 0.000083; Mix i n i t i a l slope = 0.000115 M s e c " 1 ) . At la t e r stages, the rate of the mixed gas reduction becomes much greater than the pure H 2, presumably under the ef f e c t s of CO reduction at close to 2.7 MPa CO. The comparison of the 2.04 MPa pure H 2 reduction with i t s corresponding H 2 - CO mixture suggests a more interesting r e s u l t . Results discussed previously show that the rate of reduction under pure H 2 exceeds that under CO, thus i t would be expected that in a mixed gas system H 2 would be the dominant reductant. However, comparison of the 2.04 MPa pure H 2 curve with the mixed gas at comparable H 2 pressures shows that the i n i t i a l rate under the mixture is slower than that under the pure gas indicating that the H 2 reduction i s hindered by CO. This situation could be explained i f i t was assumed that the Cu(CO) + species does not pa r t i c i p a t e in the H 2 reduction mechanism. The H 2 reduction process would involve mainly the Cu 2 + -activation and not the autocatalytic .process 0 30 60 90 0 30 60 90 Time (min) F i g u r e 3.26 C o m p a r i s o n o f P u r e R e d u c t i o n R a t e s w i t h R a t e s u n d e r M i x e d Gas T o t a l P r e s s u r e M a i n t a i n e d a t 2.7 MPa. by CO i n M i x e d Gas; T = 1 4 0 ° C ; co CO [CuSO,] ^ 0.71 M.; [ N ( N H . ) „ S O . ] ^ 0.60 M.; [H SO.] * 0.10 M. 4 4 2 4 I 4 89 requiring Cu +. The net effect would be to cut the H 2 reduction rate in half, and thereby make i t slower than the CO process. This is p a r t i c u l a r l y true at 140°C where k, = k 3 for H 2 reduction. Consequently under gas mixtures we would see i n i t i a l reduction"of the Cu 2 + species by H 2, and during the l a t t e r stages of the reaction, the CO would act as the primary reducing agent. Fixed Carbon Monoxide/Hydrogen Ratio Experiments The experiments conducted using the prepared gas mixture attempted to ascertain the extent to which CO acted as a reductant in the mixed gas system. The ratio of the gases was selected on the assumption that the H 2 would act as the primary reductant and that the CO would act as a co-ordinating agent. A r a t i o of 33% H 2 to 66% CO would remain constant over the course of the reduction run i f the above assumptions were true. The consumption of one H 2 would y i e l d two Cu +, which would in turn co-ordinate two CO. If the CO reacted as a reducing agent, then the r a t i o of gases would be shifted over the course of the experiment. The composition of the gases over the solution was monitored by gas chromatography, and Figure 3.27 shows the gas analysis of a reduction run at 140°C. The decrease in the CO percentage and the. accompanying C0 2 increase demonstrates the a c t i v i t y of CO gas as a reductant. The increase in the H 2 curve during the CO decrease is most l i k e l y due to the fact that H 2 does not act as F i g u r e 3.27 Gas A n a l y s i s of M i x e d Gas R e d u c t i o n P r o c e s s 91 a co-ordinating agent as does the CO. The solution analysis of the 140°C run i s shown in Figure 3.28. The C u 2 + - time curve shows the sigmoidal shape, indicative of the CO influence on the reduction run. The Cu* curve is similar to that seen in the e a r l i e r mixed gas experiments, showing the same decrease from a peak value to the concentration plateau. The behavior of the copper species at 160°C resembles that at 140°C (Figure 3.29). The Cu + species again shows a tendency to undergo i n i t i a l rapid'reduction from a maximum concentration to a plateau l e v e l . Such behavior of the cuprous species appears to be c h a r a c t e r i s t i c of the mixed gas runs at higher temperature. (At 120°C the reaction rate is considerably slower and does not exhibit this behavior.) The shape of the curve suggests that the Cu + species is coming to equilibrium with the Cu 2 + species. During the i n i t i a l stages of reduction there is a rapid increase in the Cu(CO) + species and some increase in the free Cu + as determined by the Cu(CO) +/Cu + equilibrium relationship. There i s a corresponding decrease in the Cu 2 + l e v e l . At some point the free Cu + w i l l reach a concentration greater than ([Cu 2 + ]*Kd) 0 - 5 and w i l l begin to disproportionate. The decrease in Cu* due to metal formation w i l l s h i f t the Cu(CO) + to Cu +. This process w i l l continue u n t i l the Cu +, Cu(CO) +, Cu 2 + and CO are in equilibrium. There are two determining factors contributing to this 0 60 120 180 240 Time (min) F i g u r e 3.28 Copper C o n c e n t r a t i o n as a F u n c t i o n o f Time u n d e r M i x e d Gas 1 4 0 ° C . C o n d i t i o n s : [ C u S O j = 0.71 M.; t ^ S O ^ = 0.11 M. ; [ ( N H ^ S Q ^ ] = 0.60 M. ; T = 1 4 0 ° C ; P T = 2.7 MPa., 33% H 2/66% CO. 0 6 0 1 2 0 1 8 0 2 4 0 Time (min) F i g u r e 3.29 C o p p e r C o n c e n t r a t i o n as a F u n c t i o n o f T i m e , M i x e d Gas 160°C. C o n d i t i o n s : [CuSO ] = 0.69 M.; [ R ^ S O J = 0.10 M.; [ ( N H ^ S O ^ ] = 0.60 M.; T = 1 6 0 ° C ; P T = 2.7 MPa., 3 3 % H 2 / 6 6 % CO. 94 equilibrium s i t u a t i o n . F i r s t , the disproportionation reaction can only occur i f the Cu 2* concentration i s s u f f i c i e n t l y low, since the concentration of the free Cu + at any time under a CO atmosphere i s very low. Under mixed gas, the l e v e l of Cu 2 + i s reduced to low levels much faster than under pure CO at 140°C because of the added reducing a b i l i t y of H 2 . The second factor i s the CO pressure, which when reduced, as in the mixed gas sit u a t i o n , w i l l tend to push the Cu(CO) + toward the free Cu + contributing further to the disproportionation process. The f i n a l Cu +, Cu(CO) +, Cu 2 +, Cu° levels w i l l s h i f t as the CO pressure changes during the l a t t e r stages of the run. Effec t of'(NH,) 2SO, Salt Figure 3.30 shows the results of a mixed gas reduction experiments at 140°C with and without ( N H u) 2SO« added. As expected, the addition of (NHi,)2SO(, to the solution has an effe c t comparable to that observed in the CO and H 2 reductions. Summation of Results of Mixed Gas Experiments As a result of the experiments using mixed gases, two important features regarding the reaction mechanism have been determined. F i r s t , despite a s i g n i f i c a n t l y greater H 2 rate than CO rate when used independantly, the H 2 reduction process does not appear to dominate the mixed gas reaction except perhaps at 160°C (Figure 3.31). This observation has led to the hypothesis that the Cu(CO) + species is not active in the H 2 reduction 0.800 0.60 O Buffered • Unbuffered 0.4 0 i — i + CM 0.2 0 0 0 F i g u r e 3.30 6 0 E f f e c t of (NH.).SO. hi h C o n d i t i o n s : •o •o 120 180 Time (min) on Mixed Gas Reduction Rates. T = 140°C. ; P_ 2 4 0 2. 7 MPa. , 33% II / 6 6 % CO; 1) [CuSO . ] 4 2) [CuSO. ] . 4 0.76 M. ; [HSO ]. = 0.10 M. 0.71 M.; [ H 2 S 0 4 ] = 0.11 M. [N(NH 4) 2S0 / (] 0 . 0 M [ (NII 4) 2S0 43 - 0. 60 M. VO 0 60 0 60 0 60 120 Time (min) F i g u r e 3.31 C o m p a r i s o n of H , CO, and M i x e d Gas R e d u c t i o n R a t e s . ^ L O N C u p r i c C o n c e n t r a t i o n as a F u n c t i o n o f Time. 97 mechanism. Because of the very low Cu + concentration the rate of the autocatalytic portion of the H 2 mechanism approaches zero and the t o t a l H 2 reduction rate i s about h a l f . The second important feature.which has become apparent i s that Cu(CO) + i s stable under H 2 pressure in the presence of CO, and although some disproportionation reaction occurs, i t only proceeds to a limited extent, or very slowly. Attempt to Model the Mixed Gas Process By adding the H 2 rate equation to the CO model, the rate of reduction in a system where both reaction mechanisms are operative can be determined. A l i s t i n g - of t h i s program is contained in Appendix D. Figure 3.32 compares the calculated results to the mixed gas experiment r e s u l t s . The curves generated by t h i s model indicate a somewhat greater rate than observed experimentally. Nature of Metal Product Formed One of the objectives of this study was to determine i f the plastering problem, which plagued the attempts to use H 2 as a reductant,- could be overcome by the use of CO. "Figure 3.33 demonstrates the extent to which plastering and agglomeration can occur during a H 2 reduction run. The results of the CO -and mixed gas experiments showed that 0 120 2 4 0 6 0 180 0 6 0 Time (min) F i g u r e 3.32 C o m p a r i s o n o f M i x e d Gas C u p r i c C o n c e n t r a t i o n as M o d e l t o E x p e r i m e n t a l R e s u l t s , a F u n c t i o n o f T i m e . Co 99 100 the adherence of the metal to the reactor could be reduced or eliminated by the presence of CO. Under pure CO at- 140°C, where Cu 2 + reduction to Cu* was v i r t u a l l y complete, no metal was produced, thus no problems with plastering could occur. At 160°C where metal was produced the product did not adhere t i g h t l y to the reactor and a granular material was produced. A similar result was obtained under gas mixtures i f they were allowed to go to the point of metal production. If the reaction i s depressurized before metal i s produced, and the CO stripped from the Cu(CO) + by b o i l i n g the solution, the quality of the metal product produced i s improved. As can be seen from Figure 3.34, the coarse powder produced by this method exhibits regular facets. The size of these p a r t i c l e s i s about 10 microns although some larger agglomerations occur. There was no attempt made to investigate the e f f e c t s of s t i r r i n g rate or depressurization rate, and both these factors would l i k e l y contribute to product formation properties. 101 Figure 3.34 Metal Produced Under I n f l u e n c e of CO (a) x 100 (b) x 1000 102 CHAPTER 4 CONCLUSIONS Mathematical models describing the H 2 and CO reduction processes have been developed. Increasing the i n i t i a l concentration of CuSO,, dramatically increases the rate of reduction by H 2. The eff e c t of the increased concentration is to enhance the rate of reduction due to H 2 activation by the Cu 2 + species. Rate constants developed by f i t t i n g the mathematical model to the experimental curve show an increase in the k, constant. Reduction reactions under CO at high Cu 2 + concentrations, moderate pressures and temperatures up to 160°C were studied. The results indicate that at higher temperatures the rate of reduction by CO approaches the rate of reduction by H 2. The mechanism proposed by Byerley does not completely apply at these pressures and the second term of the rate equation does not influence the reduction rate. An attempt was made to determine the k,' and k 3' rate constants by f i t t i n g the mathematical model to the experimental results, but the results are inconclusive. Preliminary investigations of effects of gas mixtures on the reduction reaction indicate that this process appears to be a summation of the H 2 and CO mechanisms. The autocatalytic nature of the H 2 reduction reaction is reduced or eliminated 103 because of the formation of the Cu(CO) + species which does not appear to activate H 2. The reaction mechanism responsible for the most s i g n i f i c a n t reduction rate under the mixed gases is as follows: Path A Cu 2 + + H 2 = CuH+ + H + CuH+ + Gu 2 + = 2Cu+ + H + Path B Cu 2 + + CO + H 20 = (Cu-C-(OH) 2) 2 + (Cu-C-(OH) 2) 2 + + Cu 2 t = 2Cu+ + 2H+ + C0 2 Path C Cu* + CO = Cu(CO) + 0 Cu(CO) + + H 20 = Cu-C-OH + H + 9 Cu-C-OH + Cu 2* = C0 2 + CuH+ + Cu + CuH+ + Cu 2 + = 2Cu + . + H + 104 The addition of (NH a) 2SO„ to reactions under H 2, CO and mixtures of H2-CO enhanced the rate of reduction and promoted the tendency of the reaction to go to completion. Formation of the metal product was improved by the presence of CO which either prevented or limited the tendency of the copper to agglomerate or plaster. 105 CHAPTER 5 SUGGESTIONS FOR FUTURE RESEARCH The results of this study have shown that the gas mixtures of CO and H 2 show considerable promise as reductants for aqueous copper sulfate solutions. However, several factors need to be investigated further in order to completely understand t h i s system: i) Although a reaction mechanism has been suggested, further experimental investigation would be necessary to confirm or modify i t i i ) The exact nature of the solution species and their interaction could be further defined. Thermodynamic information related to these species would be invaluable i i i ) If CO is to be used in gas mixtures for producing copper metal, then considerable potential exists for co n t r o l l i n g the nature of the product produced. A further study could be conducted into factors which influence the nature of the product (e.g. S t i r r i n g rates, effect of steam str ipping). 106 REFERENCES T. A. R. Burkin and F. D. Richardson, Powder Met., j_0 33 (1967) 2. B. Meddings and V. N. MacKiw, in "Unit Processes in Hydrometallurgy", Met. Soc. Con., Vol. 24, 345, M. E. Wadsworth, F. T. Davis (eds.) Gordon and Breach, New York (1964) 3. D. J. I. Evans, "Adv. in Extr. Met.", I.M.M. Symposia, (1967) 4. E. Hahn, Doctoral Dissertation, University of B r i t i s h Columbia (1963) 5. J . Halpern, J. Phys. Chem., 63, 398 (1959) 6. J. Halpern and E. Peters, J. Chem. Phys., 23, 605 (1955) 7. J. J. Byerley, Doctoral Dissertation, University of B r i t i s h Columbia (1963) 8. R. T. McAndrew and E. Peters, Can. Met. Quart., 3, 153 (1964) 9. E. Hirsch and E. Peters, Can. Met. Quart., 3_, 137 (1964) 10. M. Pourbaix, "Atlas of Electrochemical E q u i l i b r i a in Aqueous Solution", Pergamon, Brussels (1966) 11. R. D. MacDonald, Masters Thesis, University of B r i t i s h Columbia (1963) 12. V. N. Ipa t i e f f and W. Werchowski, Chem. Ber., 42, 2078 (1909) 13. R. G. Dakers and J . Halpern, Can. J . Chem., 32, 969 (1954) 14. E. Peters and J. Halpern, Can. J . Chem., 3_4, 554, (1956) 15. J. Halpern, E. R. MacGregor, and E. Peters, J. Phys. Chem., 60, 1455 (1956) 16. W. J. Dunning and P. E. Potter, Proc. Chem. S o c , 244 (1960) 17. K. M. Sista and C. M. Sliepcevich, Met. Trans. B, 12B, 565 (1981 ) 18. E. Peters et a l . , "A Carbonyl - Hydrometallurgy Method for Refining Copper", Joint -Meeting MMIJ - AI-ME, Tokyo (1972) 1 07 19. G. Bauch, F. Pawlek and K. P l i e t h , Z. Erzbergbau Metallhuttenw, JJ_, 1 (1958) 20. E. Peters and J. Halpern, Can. J . Chem., 33, 356 (1955) 21. C. M. Criss and W. J . Cobble, J . A. C. S., 86, 5385 ( 1 9 6 4 ) ; 86, 5390 (1964) 22. H. E. Barner and R. V. Schuerman, "Handbook of Thermochemical Data for Compounds and Aqueous Solutions", John Wiley, New York, 1978 23. D. D. Wagman et a l . , N. B. S. Technical Note 270-4 (1969) 24. King et a l . , N. B. S. Technical Note 270-3 (1969) 25. C. F. Baes, J. A. C. S., 79, 5611 (1957) 26. D. W. Taylor, J. Electrochem. S o c , 808 (1978) 27. "Handbook of Chemistry and Physics", C. R. C. (1980) 28. P. Duby, "The Thermodynamic Properties of Aqueous Copper Systems", INCRA Series on the Metallurgy of Copper (IV) (1974) 29. L. M. Gedansky et a l . , J. of Chemical Thermodynamics, 2, 561 (1970) 30. H. C. Helgeson, J . of Phys. Chem., 7J_, 3121 (1967) 31. R. M. Izatt et a l . , J. Chem. Soc. A, 45 ( 1 9 6 9 ) ; 47 (1969) 32. J . Bjerrum et a l . , " S t a b i l i t y Constants: Part II, Inorganic Ligands", The Chemical S o c , 1958 33. W. L. Marshall, J. Phys. Chem. , 7J_, 3584 (1967) 34. C. W. Davies, "Ion Association", Butterworths (1962) 35. A. S e i d e l l , " S o l u b i l i t i e s of Inorganic and Metal Organic Compounds", Vol I and II, American Chemical S o c , Washington (1958) 108 APPENDIX A Equilibrium Constants at High Temperature 1) Bisulfate Dissociation HSO„- = H + + SO« 2" EQ1 = [H+][SO,2'] [HSO,-] Using the method of Criss and Cobble (21) the values of th i s constant at 120, 140 and 160°C were determined for solutions of high and low ionic strength. In doing the calculations for the high ionic strength solutions the A G ° 2 9 8 was corrected but i t was assumed that the entropies of the ions remained unchanged at higher concentrations. The pertinent equations used are l i s t e d below. It should be noted that the values of a and fi at the temperatures were calculated from plots of a vs T and b vs T. Equat ions 1) Calculation of c and £ a = a  ln(T/298) 0 = (b - 1) ln(T/298) 109 2) Average Heat Capacity for Ions Between 298°C and T T C p | 2 9 8 = a + . pS° 2 9 8 3) Change in Average Heat Capacity T ' T T A C p | 2 9 8 = E C p | 2 9 8 " ECp| 2 9 8 products reactants 4) Change in Entropy at 298°K AS ° 2 9 8 = ^ - S ° 2 9 8 _ ^ S 2 9 8 prod. react. 5) Free Energy Change and Equilibrium Constant at Temperature T AG = A G ° 2 9 8 - AS° 2 9 8AT+ACp| 2 9 8(AT - T ln( T/298)) T EQ1=exp(-AG/(RT)) Bisulfate Equilibrium Constant A) A G ° 2 9 8 For High Ionic Strength Solutions T AG0 EQ! References °C kJ/mole M 1 20 18.9 0.00306 22,23, 1 40 22.8 0.00131 24,25 160 27.4 0.00085 31 110 B) A G ° 2 9 8 For Low Ionic Strength Solutions T AG° EQ1 References °C kJ/mole M 1 20 25.9 0.00036 22,23, 1 40 29.8 0.00017 24,27 1 60 34.4 0.00007 2) Calculation of Disproportionation Constant and Free Energy Changes for Reduction Reaction Cu 2 + + Cu° = 2Cu+ Cu 2 + + H 2 = Cu° + 2H+ Cu 2 + + CO + H 20 = Cu° + C0 2 + 2H+ Using the Taylor modifications of the Criss and Cobble method (26), the disproportionation constant was determined at the temperatures of inte r e s t . This technique was also used to calculate the free energy change of the H 2 and CO reduction reactions at the higher temperatures. The Taylor modification uses temperature independant constants a and b to determine the c o - e f f i c i e n t s necessary to calculate the heat capacity of ionic species. This technique then allows thermodynamic analysis of systems containing both ionic and non-ionic species. 111 In c a l c u l a t i n g the disproportionation constant at higher temperature i t was found that considerable discrepancy existed in the l i t e r a t u r e over the entropy assigned to the Cu + species. The value selected below appears to be most reasonable since i t is comparable to the value assigned to other univalent cations. Equations 1) Calculation of Heat Capacity c o - e f f i c i e n t s for Ions B = a + b S ° 2 9 8 2) Change in Enthapy and Entropy over T-298 AH = AA(AT) + AB_(T2-298 2 ) - AC ( 1/T-1/298) 2.0 2.0 AS = AAln(T/298) + AB(AT) - AC(1/T 2-1/298 2) 2.0 where AA, AB and AC are the-changes in the heat capacity co- e f f i c i e n t s over the reaction. 3) Change in Free Energy and Equilibrium Constant at T AG = A G ° 2 9 8 + AH - TAS - A S ° 2 9 8 A T Kd=exp(-AG/RT) 1 12 A) Disproportionation Constant T AG° Kd=[Cu +] 2 References °C kJ/mole [Cu 2*] M 1 20 17.6 0.00482 28,22, 1 40 13.4 0.0196 23,24, 1 60 9.6 0.0720 29 B) Reduction by H 2 T AG° References °C kJ/mole 120 -7 .86E+6 27,22 1 40 -8.49E+6 1 60 -9.29E+6 C) Reduction by CO T AG° References °C kJ/mole 1 20 -3.74E+7 27 ,22 1 40 -3.63E+7 1 60 -3.56E+7 3) Dissociation Constants for Neutral Ion Pairs Since the Cri*ss and Cobble and Taylor methods are intended 113 for ionized aqueous species, they are not suitable for unionized neutral s a l t s . In order to estimate temperature effects on the dis s o c i a t i o n of these s a l t s , the method proposed by Helgeson (30) was used. The expression used for these calculations i s given below. It should be noted that the enthalpies and entropies of dissocia t i o n at room temperature are required and for some s a l t s , this information i s unavailable. For. example, (NH a)SO a _ was assumed to behave as KSO„ -, since neither AH nor AS data was available for t h i s s a l t . Equat ion Calculation of log K at temperature logK = A S ° 2 9 a [Tr-6{1-exp[exp(b+aT)-C + (T-Tr)] }] 2.303RT[ W{ 0 }] where: R= 8.311 J/mole°K Tr= 298°K a= 0.01875 C= exp(b+Tr) b= -12.741 W= 1+aCG 0= 219.0 E q u i l i b r i a Calculated a) CuSOfl = Cu 2 + + SO,2" b) MgSO„ = Mg 2 + + SO a 2 -c) Na-SO," = Na + •+ SO a 2" d) KSOu- = K+ + SO„ 2-AH 2 9 8 2.303RT Calculated Values Species T log K References °C CuSO„ 120 -2.900 22,23, 1 40 -3.051 24,27, 1 60 -3.217 28,30 MgSO, 1 20 -3.915 32,33, 1 40 -4.225 34 1 60 -4.521 NaSO„- 1 20 0.029 1 40 0.059 160 0.073 KSO„" 120 0.562 1 40 0.534 1 60 0.509 APPENDIX B Program to Model Reduction of Cupric Ion from Aqueous Sulfate Solutions by Hydrogen. REAL N0ME,MS04T REAL*8 XT,YT,ZT,Bl,D1,E1,S,ZMAX,ZMIN,X,Y,Z,CU1,CU2, 1HPLUS,S04,DELCU,KD,EQ1,EQ2,K1,K3,KR1,KR2,CUS04,CUACT, 1 METAL,ATEM1,ATEM2,DELT,CUO,EQ4,QT,M,MS04,Q DATA X/0.0/,S/0.0/ C C C C C C INPUT DATA C READ (8,18)K1 READ (8,18)KR1 READ (8,18)K3 READ (8,18)KR2 READ (7,20) KD READ (7,25) EQ1,EQ2,EQ4 READ (7,30) CUST,ACIDT,MS04T READ (7,35) DELT,PH2,V,T 18 FORMAT (F2 4.22) 20 FORMAT (F8.6) 2 5 FORMAT (F9.7,F9.7,F10.8) 30 FORMAT (F6 . 3,F5.3,F6.3) 35 FORMAT (F6.2,F5.1,F5.2,F5.1) C C ECHO INPUT C 46 WRITE (6,45) 45 FORMAT ('1','REDUCTION BY H2',//,'INPUT DATA *,//) WRITE (6,50) K1,K3,KR1,KR2 WRITE (6,52) KD,EQ1,EQ2,EQ4 WRITE (6,54) CUST,ACIDT,MS04T WRITE (6,56) DELT,PH2,V,T 50 FORMAT ("RATE CONSTANTS',//,'K1=',F8.6,3X,'K3=',F8.6,3X, 1'KR1=',F4.2,3X,'KR2=',F4.2,//) 52 FORMAT ('COPPER DISPRO. KD=',F6.4,3X,*BISULPHATE EQ1=',F9 1,3X,'CUS04 EQ2=',F8.6,//,'MS04 EQ4=',F10.8,//) 54 FORMAT ('CUST=',F5.3,' M/L',3X,'ACIDT=',F4.2,' M/L',3X, 1'MS04T=',F5.3,' M/L',//) 56 FORMAT ('TIME INTERVAL=',F5.2,' SEC',3X,'PH2=',F5.1,' ATM 13X,'VOL=' ,F5.2, ' L' ,3X,'TEMP. = ' ,F 5.1,' K.',//) C C SET INITIAL CONDITIONS C DELCU=0.0 S04=DSQRT(EQ4*MS04T) IF (MS04T .EQ. 0.0) S04=DSQRT(EQ2*CUST) 1 16 HPLUS=EQ1*2.0*ACIDT/(SO4+EQ1) HS04=2.0*ACIDT-HPLUS CU2=EQ2*CUST/(S04+EQ2) CUS04=CUST-CU2 M=EQ4*MS04T/(EQ4+S04) MS04=MS04T-M S04=MS04T+CUST+ACIDT-MS04-HS04-CUS04 CU1=0.0 CUO=0.0 TITRE=0.0 TYME=0.0 TIME=0.0 R=0.0 P=0.0 IFLAG=0 C c c c C SET PAGE SPACING AND HEADINGS C C 85 IF (TYME .LT. 1800.0) P=P+15.0 IF (TYME .GE. 1800.0) P=P+90.0 WRITE (6,90) WRITE (6,91) 90 FORMATC1',' TIME ',4X,' HPLUS ',3X,' HS04 ',4X,' S04 ',1X, 1CUS04 ',3X,' CU2 ',5X,' CU1 ',5X,' CU0',6X,' X ',7X, 1' MS04 ',3X,1 M ',//) 91 FORMAT(1X,' MIN ',5X,' M/L ',5X,' M/L ',5X,' M/L ',6X, 1'M/L',5X,' M/L ',5X,' M/L ',5X,' MOLES ',3X,' M/L ',5X, 2' M/L ',5X,' M/L ',//) C C C CALCULATE INTIAL EQUILIBRIUM CONDITIONS C c GOTO 200 C C CALCULATION OF REDUCTION STEP C C C 100 CUACT=CUS04+CU2 IF (TYME .GT. 14400.0 .OR. CUS04 .LT. 0.000055) GOTO 400 IF (CU1 .GT. DSQRT(CU2*KD) .OR. CU0 .GT. 0.0) IFLAG=1 C C C C C EMON1=2.0*K1*CUACT**2*PH2/(KR1*HPLUS+CUACT) EMON2=2.0*K3*CUACT**2*CU1*PH2/((KR1*HPLUS+CUACT)* 1(KR2*HPLUS+CUACT)) NOME=EMON1+EMON2 1 17 DELCU=NOME*DELT C C C C DOUBLE PRECISION ROUTINE TO CALCULATE EQUILIBRIUM C CONCENTRATIONS OF SOLUTION SPECIES. C C 200 ZMAX=HS04 ZMIN=-1.0*(HPLUS+DELCU) C B1=-1.0*(2.0*CU1+2.0*DELCU+KD/2.0) D1=(CU1**2+DELCU**2+2,0*CU1*DELCU-KD*CU2+KD*DELCU) 210 ZT=(ZMAX+ZMIN)/2.0 QT=((HPLUS+ZT+DELCU)*EQ4*MS04-EQ1*M*(HS04-ZT))/ 1(EQ1*(HS04-ZT)+EQ4*(HPLUS+ZT+DELCU)) IF (M .EQ. 0.0) YT=-1.0*(HS04-ZT)*EQ1/(HPLUS+ZT+DELCU) 1+S04+ZT IF (M .EQ. 0.0) GOTO 205 YT=(S04+ZT+QT)-(MS04-QT)*EQ4/(M+QT) 205 E1=B1**2-4.0*D1-4.0*KD*YT IF (E1 .LT. 0.0) GOTO 212 XT=(-1.0*B1-DSQRT(B1**2-4.0*D1-4.0*KD*YT))/2.0 IF (IFLAG .NE. 1) XT=0.0 C S=(CU2-DELCU+XT/2.0~YT)*(S04+ZT-YT+QT)/EQ2-YT-CUS04 211 F0RMAT(4X,E16.9,3(4X,E12.5)) C IF (DABS(S) .LE. 0.000001)GOTO 220 IF (S .GT. 0.0) GOTO 215 212 ZMAX=ZT GOTO 210 215 ZMIN=ZT GOTO 210 C C C C 220 Z=ZT X=XT Y=YT Q=QT C CU1=CU1+DELCU-X CU2=CU2-DELCU+X/2.0~Y CU0=CU0+X*V/2.0 HPLUS=HPLUS+DELCU+Z C CUS04=CUS04+Y S04=S04+Z-Y+Q . HS04=HS04-Z MS04=MS04-Q M=EQ4*MS04/S04 ,S = S+X C c 1 18 300 IF(TYME .LT. R) GOTO 350 TIME=TYME/60.0 C C CONTROL OF PRINT OUT OF RESULTS C IF (TYME .LT. 1800.0) R=R+60.0 IF (TYME .GE. 1800.0) R=R+300.0 WRITE(6,3 4 5)TIME,HPLUS,HS04,S04,CUS04,CU2,CU1,CU0,S,MS04,M 345 FORMAT(F7.2,4X,F7.5,3X,F7.5,3X,F7.5,3X,F7.5,3X,F7.5,3X,F7.5 1,6X,F7.5,3X,F7.5,3X,F7.5,3X,F7.5,//) S = 0.0 C C INCREMENT OF TYME CONTROL C C 350 TYME=TYME+10.0 IF(TIME .EQ. P) GOTO 85 GOTO 100 400 STOP END 1 19 APPENDIX C Program to Model Reduction of Cupric Ion from Aqueous Sulfate Solutions by Carbon Monoxide REAL MSO4T,NOME REAL*8 XT,YT,ZT,X,Y,Z,B1,A1,C1,C2,C11,S,ZMAX,ZMIN,CU1,CU2, 1 HPLUS,S04,DELCU,KD,EQ1 ,EQ2,K1 ,K2,K3,CUS04,CUACT,METAL,ATEM1 1 ATEM2,DELT,CUO,CARB,EQ3,EQ4,PCO,U,SST,SSMIN,QT,M,MS04,Q DATA S/0.1E+10/ C c c c c INPUT DATA READ READ READ READ READ READ READ FORMAT FORMAT FORMAT FORMAT FORMAT (8 (8 (8 (7 (7 (7 (7 18) K1 18) K2 18) K3 20) KD 25) EQ1,EQ2,EQ3,EQ4 30) CUST,ACIDT,MS04T 35) DELT,PCO,V,T F14.12) F8'.6) F9.7,F9.7,F7.4,F10.8) F6.3,F5.3,F6.3) F6.2,F5.1,F5.2,F5.1) C ECHO INPUT C 46 WRITE (6,45) 45 FORMAT ('1','INPUT DATA',//) WRITE (6,50) K1,K2,K3 WRITE (6,52) KD,EQ1,EQ2,EQ3,EQ4 WRITE (6,54) CUST,ACIDT,MS04T WRITE (6,56) DELT,PCO,V,T 50 FORMAT ('RATE CONSTANTS',3X,'K1=',E12.5,3X,'K2=',E12.5,3X, 1'K3=',E12.5,//) 52 FORMAT ('COPPER DISPRO. KD=',F6.4,3X,'BISULPHATE EQ1=',F9.7 1,3X,'CUS04 EQ2=',F8.6,//,'CARBONYL FORM. EQ3=',F5.2,3X, 1'MS04 EQ4=',F8.6,//) 54 FORMAT ('CUST=',F5.3,' M/L',3X,'ACIDT=',F4.2,' M/L',3X, 1'MS04T=',F5.3,' M/L*,//) 56 FORMAT ('TIME INTERVAL=',F5.2,' SEC',3X,'PCO=',F5.1,' ATM', 13X,'VOL=' ,F5.2,' L' ,3X,'TEMP. = ' ,F5 . 1,' K.',//) C C SET INI IAL CONDITIONS C DELCU=0.0 S04=DSQRT (EQ4'*MS04T) IF(MS04T .EQ.0.0) S04=DSQRT(E.Q2*CUST) HPLUS=EQ1*2.0*ACIDT/(SO4+EQ1) 120 HS04=2.0*ACIDT-HPLUS CU2=EQ2*CUST/(S04+EQ2) CUS04=CUST-CU2 M=EQ4*MS04T/(EQ4+S04) MS04=MS04T-M S04=MS04T+ACIDT+CUST-MSO4-HS04-CUS04 CU1=0.0 CU0=0.0 CARB=0.0 X=0.0 SST=0.0 TYME=0.0 TIME=0.0 R=0.0 P=0.0 C C C C C SET PAGE SPACING AND HEADINGS C C 85 IF (TYME .LT. 1800.0) P=P+15.0 IF (TYME .GE. 1800.0) P=P+90.0 WRITE (6,90) WRITE (6,91) 90 FORMATC1',' TIME ',4X,' HPLUS ',3X,' HS04 ',4X,' S04 ', 11X,'CUS04',3X,' CU2 ',5X,' CU1 ',5X,' CARB ',2X,' CUO ', 15X,' MS04 ',4X,' M ',//) 91 FORMAT(1X,' MIN ',5X,' M/L ',5X,' M/L ',5X,' M/L ',5X, 1*M/L',5X,' M/L ',5X,' M/L ',5X,' M/L ',5X,' MOLES ',4X, 1' M/L ',5X,' M/L ',//) C c C CALCULATE INTIAL EQUILIBRIUM CONDITIONS C GOTO 200 C C C CALCULATION OF REDUCTION STEP C C C C 100 CUACT=CU2+CUS04 IF (TYME .GT. 21600.0 .OR. CUS04 .LT. 0.000055) GOTO 400 IF (CU1 .GT. DSQRT(CU2*KD) .OR. CUO .GT. 0.0) IFLAG=1 C C C C NOME=(K1*CUACT*CARB/HPLUS) + (K2*CUACT** 2*PCO/HPLUS) + (K3* 1CUACT**2*PCO) DELCU=NOME*DELT C C 121 C C DOUBLE PRECISION ROUTINE TO CALCULATE EQUILIBRIUM C CONCENTRATIONS OF SOLUTION SPECIES C c c c c 2 00 ZMAX=HS04 ZMIN=-1.0*(HPLUS+DELCU) SSMIN=ZMIN C U=1.0/(1.0+EQ3*PCO) A1 = 1.0+(U*EQ3*PCO)**2-2.0*U*EQ3*PCO B1=-1.0*(2.0*CU1+2.0*DELCU+KD/2.0+2.0*(U*EQ3*PCO)**2*(CU1+ 1DELCU) +U*EQ3*PCO* (-2 . 0*U*CARB-4 . 0*CU1 ~4 . 0*DEL'CU) +2 . 0*U*CARB C1=CU1**2+DELCU**2+2*CU1*DELCU-KD*CU2+DELCU*KD+(U*EQ3*PCO) 1**2*(CU1**2+DELCU**2+2.0*CU1*DELCU) C2=U**2*EQ3*PCO*(-2.0*CU1*CARB-2.0*DELCU*CARB)+U*EQ3*PCO* 1(-2.0*CU1**2-4.0*CU1*DELCU-2.0*DELCU**2)+U**2*CARB**2+2.0*U 1*CU1*CARB+2.0*U*DELCU*CARB C C 205 ZT=(ZMAX+ZMIN)/2.0 C QT=(MS04*EQ4*(HPLUS+ZT+DELCU)-EQ1*M*(HS04-ZT))/(EQ1*(HS04 1-ZT)+EQ4*(HPLUS+ZT+DELCU)) C IF (M .EQ. 0.0) YT=(S04+ZT)-EQ1*(HS04-ZT)/(HPLUS+ZT+DELCU) IF (M .EQ. 0.0) GOTO 208 C YT=(S04+ZT+QT)-EQ4*(MS04-QT)/(M+QT) C 208 CI1=C1+C2+YT*KD C E1=B1**2-4.0*A1*C11 IF (E1 .LT. 0.0) GOTO 212 C XT=(-1.0*B1-DSQRT(B1**2-4.0*A1*C11))/(2.0*A1) IF (IFLAG .NE. 1) XT=0.0 C C SST=S S=(CU2-DELCU+XT/2.0-YT)*(S04+ZT-YT+QT)/EQ2-CUS04-YT C c c IF(DABS(S) .LE. 0.00001)GOTO 220 IF (S .GT. 0.0 .AND. SST .GT. 0.0 .AND. S .GT. SST) GOTO 21 IF(S .GT. 0.0) GOTO 215 212 ZMAX=ZT GOTO 205 215 SSMIN=ZMIN ,ZMIN=ZT GOTO 205 1 22 216 ZMAX=ZMIN ZMIN=SSMIN S=0.1E+10 GOTO 205 C C C 220 Y=YT X=XT Z = ZT Q=QT C S = 0.1OE+10 CU2=CU2-DELCU+X/2.0~Y IF (IFLAG .EQ. 1) GOTO 225 DCARB=(EQ3*PCO*(CU1+DELCU)-CARB)/(1.0+EQ3*PCO) CARB=DCARB+CARB CU1=CU1+DELCU-DCARB GOTO 230 225 CU1=DSQRT(CU2*KD) CARB=EQ3*PCO*CU1 230 CU0=CU0+V*X/2.0 HPLUS=HPLUS+DELCU+Z C CUS04=CUS04+Y S04=S04+Z-Y+Q HS04=HS04-Z MS04=MS04-Q M=EQ4*MS04/S04 C c c c IF(TYME .LT. R) GOTO 3 50 TIME=TYME/60.0 C C CONTROL OF PRINT OUT OF RESULTS C IF (TYME .LT. 1800.0) R=R+60.0 IF (TYME .GE. 1800.0) R=R+300.0 WRITE(6,345)TIME,HPLUS,HS04,S04,CUS04,CU2,CU1,CARB,CU0, 1MS04,M 345 FORMAT(F7.2,4X,F7.4,3X,F7.4,3X,F7.4,3X,F7.4,3X,F7.4,3X,F7.4 13X,F7.4,3X,F7.4,3X,F7.4,3X,F7.4,//) C C INCREMENT TIME INTERVAL 'DELT' C 350 TYME=TYME+10.0 IF(TIME .EQ. P) GOTO 85 GOTO 100 C 400 STOP END 123 APPENDIX D A Program to Model the Reduction of Cupric Ion by Mixtures of Hydrogen and Carbon Monoxide REAL MS04T,NOME REAL*8 XT,YT,ZT,X,Y,Z,B1,A1,C1,C2,C11,S,ZMAX,ZMIN,CU1,CU2, 1 HPLUS,S04,DELCU,KD,EQ1 ,EQ2,K1 ,R2,K3,CUS04,CUACT,METAL, 1 ATEM1 ,ATEM2,DELT,CUO,CARB,EQ3,EQ4,PCO,U,SST,SSMIN,QT,M, 1MS04,Q,KH1 ,KH2,KRH1 ,KRH2 . DATA S/0.1E+10/ C A PROGRAM MODELLING CUPRIC REDUCTION FROM AQUEOUS SULFATE C SOLUTION BY MIXTURES OF H2 AND CO . C c C INPUT DATA C READ (8,18) K1,K2,K3 READ (8,18) KH1,KH2,KRH1,KRH2 READ (7,20) KD READ (7,25) EQ1,EQ2,EQ3,EQ4 READ (7,30) CUST,ACIDT,MS04T READ (7,35) DELT,PCO,PH2,V,T 18 FORMAT (F14.12) 20 FORMAT (F8.6) 25 FORMAT (F9.7,F9.7,F7.4,F7.5) 30 FORMAT (F6.3,F5.3,F6.3) 35 FORMAT (F6.2,F5.1,F5.1 ,F5 . 2,F5.1) C ECHO INPUT C 46 WRITE (6,45) 45 FORMAT ('1',*INPUT DATA',//) WRITE (6,50) K1,K2,K3 WRITE (6,51)KH1,KRH1,KH2,KRH2 WRITE (6,52) KD,EQ1,EQ2,EQ3,EQ4 WRITE (6,54) CUST,ACIDT,MS04T WRITE (6,56) DELT,PCO,PH2,V,T 50 FORMAT ('RATE CONSTANTS',3X,'K1=',E12.5,3X,'K2=',E12.5,3X, 1'K3=',E12.5,//) 51 FORMAT (17X,'KH1=',F10.8,3X,'KH2=',F10.8,3X,'KRH1=',F4.2,3X 1'KRH2=',F4.2,//) 52 FORMAT ('COPPER DISPRO. KD=',F6.4,3X,'BISULPHATE EQ1=',F9.7 1,3X,'CUS04 EQ2=',F8.6,//,'CARBONYL FORM. EQ3=',F5.2,3X, 1'MS04 EQ4=',F8.6,y/) 54 FORMAT ('CUST=' ,F5.3,' M/L ' ,3X,'ACIDT=' ,F4.2,' M/L',3X, 1'MS04T=',F5.3,' M/L',//) 56 FORMAT ('TIME INTERVAL=',F5.2,' SEC',3X,'PCO=',F5.1,' ATM', 1'PH2=',F5.1,* ATM' ,3X,'VOL=' ,F5.2,' L' ,3X,'TEMP. = ' ,F5.1,' K 1//) C C SET INITIAL CONDITIONS 124 DELCU=0.0 S04=DSQRT(EQ4*MS04T) IF(MS04T .EQ.O.O) S04=DSQRT(EQ2*CUST) HPLUS=EQ1*2.0*ACIDT/(SO4+EQ1) HS04=2.0*ACIDT-HPLUS CU2=EQ2*CUST/(S04+EQ2) CUS04=CUST-CU2 M=EQ4*MS04T/(EQ4+S04) MS04=MS04T-M S04=MS04T+ACIDT+CUST-MS04-HS04-CUSG4 CU1=0.0 CUO=0.0 CARB=0.0 X=0.0 SST=0.0 TYME=0.0 TIME=0.0 R=0.0 P=0.0 C C C C C SET PAGE SPACING AND HEADINGS C C 85 IF (TYME .LT. 1800.0) P=P+15.0 IF (TYME .GE. 1800.0) P=P+90.0 WRITE (6,90) WRITE (6,91) 90 FORMAT('1',' TIME ',4X,' HPLUS ',3X,' HS04 ',4X,' S04 ',1X, 1CUS04',3X,' CU2 ',5X,' CU1 ',5X,' CARB ',2X,' CUO ',5X, 1' MS04 ',4X,' M ',//) 91 FORMAT(1X,' MIN ',5X,' M/L ',5X,* M/L ',5X,' M/L ',5X,' M/ 15X,' M/L ',5X,' M/L ',5X,' M/L ',5X,' MOLES ',4X, 1' M/L ',5X,' M/L ',//) C C C CALCULATE INTIAL EQUILIBRIUM CONDITIONS C GOTO 200 C C C CALCULATION OF REDUCTION STEP C C C C 100 CUACT=CU2+CUS04 IF (TYME .GT. 21600.0 .OR. CUS04 .LT. 0.000055) GOTO 400 IF (CU'1 .GT. DSQRT(CU2*KD) .OR. CUO .GT. 0.0) IFLAG= 1 C C C 125 C C C CU1S=CU1+CARB NOME=(K1*CUACT*CARB/HPLUS)+(K2*CUACT**2*PCO/HPLUS)+ 1(K3*CUACT**2*PCO) NOME2=2.0*KH1*CUACT**2*PH2/(KRH1*HPLUS+CUACT) NOME3 = 2 .0*KH2*CU2**2*CU1S*.PH2/( (KRH 1 *HPLUS+CUACT) * 1(KRH2*HPLUS+CUACT)) DELCU=(NOME+NOME2+NOME3)*DELT C C C C C C ROUTINE FOR CALCULATING EQUILIBRIUM CONCENTRATIONS OF C SOLUTION SPECIES C c c 200 ZMAX=HS04 ZMIN=-1.0*(HPLUS+DELCU) SSMIN=ZMIN C U=1.0/(1.0+EQ3*PCO) A1 = 1.0+(U*EQ3*PCO)**2-2.0*U*EQ3*PCO B1=-1.0*(2.0*CU1+2.0*DELCU+KD/2.0+2.0*(U*EQ3*PCO)**2* 1(CU1+DELCU)+U*EQ3*PCO*("2.0*U*CARB~4.0*CU1-4.0*DELCU)+ 12.0*U*CARB) C1=CU1**2+DELCU**2+2*CU1*DELCU~KD*CU2+DELCU*KD+ 1(U*EQ3*PCO)**2*(CU1**2+DELCU**2+2.0*CU1*DELCU) C2=U**2*EQ3*PCO*(-2.0*CU1*CARB-2.0*DELCU*CARB)+U*EQ3*PCO* 1(-2.0*CU1**2-4.0*CU1*DELCU-2.0*DELCU**2)+U**2*CARB**2+2.0*U 1CU1*CARB+2.0*U*DELCU*CARB C c 205 ZT=(ZMAX+ZMIN)/2.0 C QT=(MS04*EQ4*(HPLUS+ZT+DELCU)-EQ1*M*(HS04-ZT))/ 1(EQ1*(HS04-ZT)+EQ4*(HPLUS+ZT+DELCU)) C IF (M .EQ. 0.0) YT=(S04+ZT)-EQ1*(HS04-ZT)/(HPLUS+ZT+DELCU) IF (M .EQ. 0.0) GOTO 208 C YT=(S04+ZT+QT)-EQ4*(MS04-QT)/(M+QT) C 208 C11=C1+C2+YT*KD C E1=B1**2-4.0*A1*C11 IF (E1 .LT. 0.0) GOTO 212 C XT=(-1.0*B1-DSQRT(B1**2-4.0*A1*C11))/(2.0*A1) IF (IFLAG .NE. 1) XT=0.0 C C 1 26 SST=S S= (CU2-DELCU+XT/2 . O-YT) * (S0.4 + ZT-YT+QT) /EQ2-CUS04-YT C IF(DABS(S) .LE. 0.00001)GOTO 220 IF(S .GT. 0.0 .AND. SST .GT. 0.0 .AND. S .GT. SST) GOTO 216 IF(S .GT. 0.0) GOTO 215 212 ZMAX=ZT GOTO 205 215 SSMIN=ZMIN ZMIN=ZT GOTO 205 216 ZMAX=ZMIN ZMIN=SSMIN S=0.1E+10 GOTO 205 C C C 220 Y=YT X=XT Z = ZT Q=QT C S=0.10E+10 CU2=CU2-DELCU+X/2.0-Y IF (IFLAG .EQ. 1) GOTO 225 DCARB=(EQ3*PCO*(CU1+DELCU)-CARB)/(1.0+EQ3*PCO) CARB=DCARB+CARB CU1=CU1+DELCU-DCARB GOTO 230 225 CU1=DSQRT(CU2*KD) CARB=EQ3*PCO*CU1 230 CU0=CU0+V*X/2.0 HPLUS=HPLUS+DELCU+Z C CUS04=CUS04+Y S04=S04+Z-Y+Q HS04=HS04-Z MS04=MS04-Q M=EQ4*MS04/S04 C c c c IF(TYME .LT. R) GOTO 350 TIME=TYME/60.0 C C CONTROL OF PRINT OUT OF RESULTS C IF' (TYME .LT. 1800.0) R=R+60.0 IF (TYME .GE. 1800.0) R=R+300.0 WRITE(6,345)TIME,HPLUS,HS04,S04,CUS04,CU2,CU1,CARB,CUO, 1MS04,M 345 FORMAT(F7.2,4X,F7.4,3X,F7.4,3X,F7.4,3X,F7.4,3X,F7.4,3X,F7.4 1 27 1,F7.4,3X,F7.4,3X,F7.4,3X,F7.4,//) C C INCREMENT TIME INTERVAL 'DELT' C 350 TYME=TYME+10.0 IF(TIME .EQ. P) GOTO 85 GOTO 100 C 400 STOP END 1 28 APPENDIX E Error Analysis The following sources of error have been i d e n t i f i e d and the maxium tolerance on the experimental results estimated: I) Volume of Sample: i) Volumetrics; ± 0.2% i i ) Weights; ± 0.0002 gms. Maximum error on volume determination; ± 0.3% II) Copper determination: i)EDTA concentration; ± 2.0% ii)Volumetrics; ± 0.2% iii)EDTA volume; ± 0.02 mis. Maximum error on Cu 2 + or Cu + concentration; ± 8.0% III) H + determination: i)NaOH concentration; ± 0.5% i i ) Volumetrics ± 0.2% i i i ) NaOH volume; ± 0.02 mis. Maximum error on H+ concentration; ± 6.0% 

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