T 1397
KINETICS OF COPPER CEMENTATION
ON IRON FROM COPPER SULFATE SOLUTIONS
by
N* A. Sareyed-Dim ProQuest Number: 10781739
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A thesis submitted to the Faculty and the Board of
Trustees of the Colorado School of Mines in partial ful fillment of the requirements for the degree of Master of
Science.
Signed: JWfiHl
Golden, Colorado Pate;«\nu»iL- 2. , 1971 „
Approved Dr^T T. Balberyszski Thesis Advisor
P. G. Herold Head, Department of Metallurgical Engineering
Golden, Colorado Date: ~3 . 1971
ii T 1397
Cb / ' % v % , % > XXX ^rv ^ > ABSTRACT ^ Oobo/ X % / °X -
The kinetics of cementation of copper on iron, from sulfate solutions has been studied using a rotating disc geometry.
The influence of initial copper ion concentration in solution, rotational speed of the disc, temperature and atmosphere, on the kinetics of the cementation process was determined.
At low initial Cu++ concentration in solution the pro cess was found to be diffusion-controlled with an activa tion energy of 3.4 ± 0.2 kcal/mole and, initially, the kinetics followed the expected behavior for diffusion to a rotating disc as determined by the Levich theory^1^.
However, following the initial period there was a signifi cant enhancement in the reaction rate and deviation from the theoretical values. The process, however, remained diffusion-controlled with an activation energy of 3.05 ±
0.2 kcal/mole. A further indication of a diffusion-control mechanism was that the specific rate constants for low
Cu++ initial concentrations varied linearly with the square root of the rotation speed.
At high Cu++ initial concentrations, the kinetics of the reaction did not follow the Levich analysis and after a period of time there appears to occur a change in the controlling
iii T 1397
mechanism from diffusion of Cu++ through the boundary layer to diffusion of Fe++ through the deposited copper film.
It was observed that as the oxygen potential in the system increases, the rate of reaction decreases, and the iron consumption increases.
iv T 1397
TABLE OF CONTENTS
Page
ABSTRACT ...... iii
INTRODUCTION ...... 1
Statement of the Problem...... 1
Scope of the Study...... 3
REVIEW OF THE LITERATURE...... 7
MATHEMATICAL ANALYSIS OF MASS TRANSFER TO A ROTATING DISC SURFACE...... 15
EXPERIMENTAL APPARATUS AND PROCEDURE ...... 20
Experimental Apparatus...... 20
Experimental Procedure...... 22
Disc Preparation ...... 22
Solution Preparation ...... 27
Atmosphere Control ...... 27
Speed Control...... 30
Sampling and Analytical Procedure...... 30
pH Measurements...... 30
EXPERIMENTAL RESULTS ...... 31
The Effect of Temperature ...... 31
The Effect of Rotation Speed of the Disc.... 32
The Effect of Initial Copper Ion Concentration in Solution ...... 33
The Effect of the Atmosphere in the System. . . . 33
General Method for the Calculation of the Specific Reaction Rate Constant ...... 3^
v T 1397
Page
DISCUSSION...... 48
Effect of Temperature...... 51-
Effect of Speed of Rotation ...... 53
Effect of the Initial Cu++ Concentration in S o l u t i o n ...... 55
Effect of the Atmosphere in the System...... 57
Experimental Error Considerations .••••... 59
CONCLUSIONS...... 68
SUGGESTIONS FOR FUTURE WORK...... 70
APPENDIX I - Calculations of the equilibrium constants for the reaction: Cu++ + Fe * Fe++ + Cu...... • • • ...... 71
APPENDIX II - Summary of published information on cementation kinetics...... 73
APPENDIX III - Activation energy fbr cementation . . . 7^
APPENDIX IV - Least-square computer program for fitting an expression of the type: log(C/C0) ® - k t ...... 75
APPENDIX V - Least-square computer program for fitting an expression of the type: log (C/CQ) = -kt + b ...... 7b
APPENDIX VI - Computer program for the calculation of the hydrodynamic and diffusion boundary layer thicknesses...... 77
APPENDIX VII - Full experimental data for the tests where the temperature was varied. Initial Cu++ concentration: 50 ppm...... 79
APPENDIX VIII - Full experimental data for the tests where the temperature was varied. Initial Cu++ concentration: 500 p p m ...... 83
APPENDIX IX - Full experimental data for the tests where the rotational speed was varied. Initial Cu++ concentration: 50 p p m ...... 87 vi T 1397
Page
APPENDIX X - Pull experimental data for the tests where the rotational speed was varied. Initial Cu++ concentration: 500 ppm...... 91
APPENDIX XI - Full experimental data for the tests where the initial Cu++ concentration in solu tion was v a r i e d ...... 93
APPENDIX XII - Pull experimental data for the tests where the atmosphere in the reactor was varied. . 100
APPENDIX XIII - Calculation of solution potentials . . 103
BIBLIOGRAPHY ...... 106
vii T 1397
LIST OP FIGURES /
Figure Page
1. Diagram of the experimental apparatus...... 21
2. Experimental apparatus...... 23
3. Experimental apparatus ...... 23
4. Aluminum mounting j i g ...... 25
5. Aluminum casting mold. .••••••.••••• 26
6. Precipitant disc ...... 28
7. Two views of finished discs...... 29
8. Graph of dimensionless concentration versus time for the temperatures 25, 30, 35, and 40°C. Initial du++ concentration in solution: 50 p p m ...... 35
9. Graph of dimensionless concentration versus time for the temperatures 25, 30, 35, and 40°C. Initial Cu++ concentration in solu tion: 500 p p m ...... 36
10. Arrhenius plot. Initial Cu++ concentration: 50 p p m ...... 39
11. Graph of dimensionless concentration versus time for the rotational speeds of 300, 450, 600, and 750 rpm. Initial Cu++ concentration: 50 ppm 40
12. Graph of dimensionless concentration versus time for the rotational speeds of 600 and 750 rpm. Initial Cu++ concentration: 500 ppm. . 41
13. Graph of the square root of the rotational speed versus specific rate constant. Initial Cu++ concentration: 50 ppm...... 43
viii T 1397
Figure Page
14. Graph of dimensionless concentration versus time for initial Cu++ concentrations of 25, 50, 100, 200, 500, 800, and 1000 pp m ...... 45
15. Graph of dimensionless concentration versus time for the argon, air, and oxygen atmosphere experiments. Initial Cu++ concentration: 50 p p m ...... 47
16. Copper deposit on the iron disc obtained with 500 ppm initial Cu++ concentration, temperature 25°C, 600 rpm rotational speed ...... 60
17. Copper deposit on the iron disc obtained with 50 ppm initial Cu++ concentration, temperature 25°C, 600 rpm rotational speed ...... 60
18. Side view of the copper deposit showing the deposit thickness. Deposit obt.ained with 50 ppm initial Cu++ concentration, temperature 25°C, 750 rpm rotational s p e e d ...... 6l
19. Copper deposit on the iron disc obtained with 800 ppm initial Cu++ concentration, 25°C temperature, 600 rpm rotational speed...... 6l
20. Copper deposit on the iron disc obtained with 500 ppm initial Cu++ concentration, 25°C temperature, 750 rpm rotational speed. . . . * . 62
21. Plot of the overall specific reaction rate versus initial Cu++ concentration...... 63
22. Copper deposit on the iron disc obtained with 200 ppm initial Cu++ concentration, 25°C temperature, 600 rpm rotational speed . . . 64
23. Potential-pH diagram for the Cu-0 system .... 65
24. Copper and iron concentrations in solution as a function of time with an oxygen atmosphere. 66
25. Copper and iron concentrations in solution as a function of time with an air atmosphere . . 67
ix T 1397
LIST OP TABLES
Table Page
1. Equilibrium constants for the basic cemen tation reaction: Fe + Cu++ = Fe++ + Cu. . . . . 4
2. Industrial copper recovery by cementation. . . . 5
3. Impurities conterr in Ferrovac E iron. • • • • . 24
4. Temperature effecc- on the specific rate constants. Initial Cu++ concentration: 50 ppm . 37
5. Temperature effect on the specific rate constants. Initial Cu++ concentration: 500 ppm. 38
6 . Rotational speed effect on the specific rate constants. Initial Cu++ concentration: 50 ppm . 42
7. Rotational speed effect on the specific rate constants. Initial Cu++ concentration: 500 ppm. 44
8. Initial Cu++ concentration effect on the specific rate constants...... 46
x T 1397
LIST OP APPENDICES
Appendix
I. Calculations of the equilibrium constants for the reaction: Cu++ + Fe = Fe++ + Cu . . .
II. Summary of published information on cementation kinetics ......
III. Activation energy for cementation......
IV. Least-square computer program for fitting an expression of the type: log(C/CQ ) « -kt . .
V. Least-square computer program for fitting an expression of the type: log(C/C0 ) - -kt + b. .
VI. Computer program for the calculation of the hydrodynamic and diffusion boundary layer thicknesses......
VII. Full experimental data for1 the tests where the temperature was varied. Initial Cu++ concentration: 50 ppm ......
VIII. Full experimental data for the tests where the temperature was varied. Initial Cu++ concentration: 500 ppm.
IX. Full experimental data for the tests where the rotational speed was varied. Initial Cu++ concentration: 50 ppm ......
X. Full experimental data for the tests where the rotational speed was varied. Initial Cu++ concentration: 500 ppm ......
XI. Full experimental data for the tests where the initial Cu++ concentration in solution was varied......
XII. Full experimental data for the tests where the atmosphere in the reactor was varied . . .
XIII. Calculation of solution potentials ...... T 1397
ACKNOWLEDGMENTS
The author wishes to extend his appreciation to:
Dr, T. Balberyszski for his guidance and advice through out the course of this investigation.
Dr, P. G. Herold and Dr. W. R. Bull, for acting as thesis committee members.
Dr. F. Lawson, for his many helpful discussions.
Mr. J. Kintner, for preparing the specimens used in this study.
Mr. G. V. G. Rao, for the design of the equipment used in this research.
Lastly, but by no means least,, the author wishes to thank his wife, Toia, without whose continued encouragement and understanding the work described in this thesis could not have been undertaken.
The author dedicates this thesis to his mother and brother.
xii T 1397
INTRODUCTION /
This work reports an investigation that was undertaken to study the kinetics of copper cementation with iron, in dilute sulfate solutions*
Although the process of cementation has been of indus
trial importance for many y e a r s $ very little work has been done on the subject until recent years.
The main industrial applications of cementation of copper with iron ares
a. The recovery of copper from effluent mine waters.
b. The recovery of copper from copper-bearing solu tions resulting from the leaching of low-grade mineral bodies and tailing dumps by natural mine waters or by enriched lixiviants.
c. The recovery of copper from pregnant solutions obtained by acid leaching of oxidized copper ores.
d. The removal of trace amounts of copper from elec trolyte streams, as a purification step, prior to elec trolysis; as, for example, the purification of tin elec- trolytes^^.
Statement of the Problem
The process whereby a metal is precipitated, usually from a solution of its salts, by a more electropositive T 1397 2
metal is called ”cementation•w
Cementation reactions are regarded as electron-transfer redox reactions involving the simultaneous reduction of the more noble species (M),
M1®* + me’ + M (1) and oxidation of the less noble precipitant species (N),
N Nn+ + ne" (2)
Partial reactions (1) and (2) can be combined giving:
nMm+ + mN nM + mNn+ (3)
In the cementation of copper with iron, the main reac tion that takes place is;
Cu++ + Fe t Fe++ + Cu (4)
However, the following side reactions may occur:
2Fe++ + h02 + 2H+ + 2Fe+++ + HgO (5)
2Fe+++ + Fe X 3Fe++ (6)
2H+ + Fe $ Fe++ + H2 (7)
From equation (4) it is seen that one mole of iron is required to precipitate one mole of copper. This cor responds to a theoretical iron to copper ratio of 0.88.
However, if dissolved oxygen is present in solution, reac tions (5) and (6) take place, thus resulting in a higher
iron consumption. At very low pH values equation (7) may
contribute significantly to the iron consumption. T 1397 3
(7 ) It has also been suggested^1' that copper may react
directly with ferric ion, according to:
Cu + 2Fe+++ t Cu++ + 2Fe++ (8)
Thus, the resulting cupric ion would consume additional
iron by the normal cementation reaction (1).
In the absence of dissolved oxygen, however, the only reaction which occurs to an appreciable extent is reaction
(1 ):
Cu++ + Pe Z Fe++ + Cu
for which the equilibrium constants at various tem peratures are given in Table 1 (for calculations refer to
Appendix I).
From this, table it is clear that, thermodynamically, all copper should be precipitated; that is the reaction is
strongly shifted to the right. But in industry this is not always the case, as can be seen from Table 2 ^ ^ . The average recovery is about 90%, although recoveries as high as 97% are not uncommon. This is an indication that cemen tation is a kinetic problem, and thus this study was carried out,
Scope of the Study
This work was undertaken in order to gain a deeper knowledge of the rate of precipitation of copper by iron in dilute sulfate solutions, and some of the factors that T 1397
Table 1 Equilibrium constants for the basic cementation reaction: •f Fe + Cu++ = Fe++ + Cu
Temperature Equilibrium (°K) Constant
293 2.403 x 1026
298 8.418 x 1025
303 3.053 x 1025
308 1.144 x 1025
313 4.427 x 1021*
318 1.764 x 10211
323 7.235 x 1023 T 1397 5
Table 2. Industrial copper recovery by cementation^^.
Copper Content Copper Launder in head Waters Recovered Name of the Plant System (g/&) (%)
Inspiration Copper Zig zag 0.85 97.4 (Miami, Arizona)
Kennecott Copper Corp. Straight 2.04 97.3 (Bingham Canyon, Utah) line
Anaconda Straight 0.31 95.0 (Butte, Montana) line
Andes Copper Zig zag 2.41 97*2 (Chile)
Cananea Zig zag 3*30 89.1 (Mexico) T 1397 6
influence it.
In order to make this investigation meaningful, and the results reproducible, it was necessary to satisfy the follow ing conditions:
- provide a uniformly accessible surface area.
- provide a hydrodynamically defined flow pattern.
One of the few geometries that satisfies both of the above conditions and is yet simple enough to be handled in the laboratory is the rotating disc system^*9,10,11,12)^
For this reason a rotating disc geometry was chosen for this investigation.
Using the rotating disc, the following factors were studied: ++ - effect of the initial Cu concentration in solution.
- the nature of the copper deposit.
- effect of the rotational speed of the disc.
- effect of temperature
- effect of the atmosphere in the system. 7 T 1397
REVIEW OF THE LITERATURE
Cementation reactions have been known for many years.
There are references to cementation of copper with iron dating from the year 1500^^). jn the "Book Concerning the
Tincture of Philosophers," Paracelsus cites the use of iron to prepare Venus (copper) by the "rustics of Hungary" .
Agricola^1^ , in his "De Re Metallica" (1546), reports about a strange water which is drawn from a shaft near
Schmolnitz in Hungary, that erodes iron and turns it into copper. The cementation reactions have been used widely from the middle ages and are still used.
Different industrial equipment designs have been employed to cement copper. Among these the zig-zag launder equipment and the straight line launder arrangement are (14) described by Jacobi' . Both of these arrangements are currently used industrially. The former has the advantage of being more compact and somewhat cheaper to operate. On the other hand, the latter is more flexible when the volume of the material to be treated is not constant.
Another type of industrial equipment used to pre cipitate copper from copper-bearing solutions is the drum precipitator. It has been found to be less satisfactory (IS) than the launder' because of added labor requirements
for charging and discharging operations, and higher T 1397 8
maintenance costs. Furthermore, the tumbling action often breaks the copper precipitates into fine particles, thus presenting additional operating problems.
A relatively recent development is the Kennecott Copper
Corporations (15) cone precipitator. It is a con tinuously operated unit; it does not require cleaning opera tions and can handle large volumes of solutions. It is CIS) claimed'- that the introduction of the cone will enable
Kennecott to increase the production of copper from waste dump leaching to about 25# of that company’s total produc tion in the United States.
In spite of the wide use of the cementation process, process design is generally based on empirical data and previous experience. It is only in recent years that the importance of research to obtain fundamental data regarding the process became apparent to the metallurgical industry.
Since then, a great number of papers have been pub- (i fi) lished on the subject. Centnerszwer and Heller^ studied the displacement of copper by metallic zinc, using zinc strips attached to the stirring propeller blades. They con cluded that at low stirring speeds the rate was governed by diffusion, and at high stirring speeds the chemical reactions at the surface become the controlling factor, when the rate becomes constant. They reported the reaction to be of first order. Their work was later criticized by King (17) and Burgerv who investigated the rate of displacement T 1397 9
of copper from its sulfate solutions by cadmium and zinc.
These authors used a rotating cylinder geometry for their experiments. They report the reactions to be of first order and that, contrary to what was found by Centnerszwer and
Heller, the rate was controlled by diffusion and electrolytic transport of the Cu ions to the surface of the more active metal, up to peripheral speeds of the metal surface of at least 44,000 cm/min; and that there was no indication that the chemical reaction rate was slow enough to be a con trolling factor at any stirring speed studied. In order to maintain a clean surface for deposition the surface was scraped frequently, and baffle plates were fitted to the reaction vessel walls to encourage turbulence.
The results obtained by these authors can only be analyzed semi-quantitatively because of the lack of a definite flow pattern and uniformly accessible surface.
They are only valid for the particular geometry used, and for the specific apparatus. In both studies the rate con stant was calculated by:
k = 2^3V £o tP s c where V = volume of solution in cc, F = the exposed metal o surface in cm , t - time m minutes, CQ = the concentration of the solution at start, and C « the concentration at time t minutes. /tON Rickard^ reports that the cementation of copper with T 1397 10
iron can be described as a galvanic corrosion cell; that the process is controlled by diffusion of the reactants to the cathode surface, and thus it is a first order process. He reports further that increased agitation will increase the rate of the reaction, but that there is a limit after which additional agitation will not produce an increased reaction rate; this occurred at linear surface velocities of 2700 cm/ min. Rotating cylinders vie re used in this study.
Alkatsev^1^ studied the cementation of copper with iron by using a vibrating iron plate. The rates obtained were close to the theoretical. He used vibration to remove the deposit, thus maintaining a clean surface continuously exposed. He reports that the mass transfer coefficient during cementation, for the Cu-Fe system, depends on the amplitude and frequency of vibration of the plate. The same technique was employed by Kvyatovskii et. a l . ^ ° \ on the Cu-Zn system.
A kinetic study of copper precipitation on iron from (21 22) sulfate solutions vias reported by Nadkarni et. al. *
Rectangular iron sheets were used as the precipitating sur face. A stirrer was introduced in the center of the reac tion vessel to provide the desired agitation. The rates obtained were reported to be of first order, proportional to the surface area of the iron, and to increase with speed of stirring until a maximum rate was observed (at about
36OO rpm). An activation energy of 5.06 ± 0.71 kcal/mole T 1397
was determined, suggesting diffusional control through a boundary film. A fine copper film coated the iron plate at
very high speeds, and the rate became independent of speed.
The authors explain this phenomenon by suggesting that
solution diffusion through a limiting boundary film is rate- controlling in this region.
In 19^2, a new experimental method was proposed by
L e v i c h ^ ^ . This author showed that for laminar diffusion to a plane rotating disc in an infinite aqueous medium the mass flux is given by:
3 = 0.62 D2/3 v ~ 1 / 6 j = mass flux of diffusing species to the surface (ML-2 T-1) D = diffusion coefficient (L^ T ) O —1 v = kinematic viscosity of solution (L T ) —1 a) * angular velocity of disc (T ) Cg = concentration of diffusing species in the bulk of the solution (ML“^), and the effective diffusion layer thickness, 6, is defined by: The rotating disc geometry proposed by Levich provides an evenly-accessible surface, and its hydrodynamics can be T 1397 12 analyzed mathematically. This method makes it possible not only to obtain reproducible results and preserve the pre determined hydrodynamic mixing conditions, but also to compare the experimental and theoretical reaction rates and to compare the absolute values of the reaction rate con stants. After the publication of the Levich analysis a con siderable amount of work has been published using the rotating disc geometry. Episkoposyan and Kakovskii studied the kinetics of copper and silver cementation with metallic iron from chloride solutions^**) and from sulfate solutions^-^, using the rotating disc technique. In both studies it was observed that the copper cementation with iron followed a first order kinetics, and an activation energy of 3 kcal/ mole was determined. Furthermore, it was reported that the specific reaction rates were proportional to the number of disc revolutions to the 0.5 power. These results are in accordance with the Levich theory for diffusion-controlled processes. Mackinnon and Ingraham^ ' found for the cementation of copper on aluminum, in acidic sulfate solutions, that there are two rate-controlling processes: ionic diffusion control at temperatures above 40°C, and surface reaction control at temperatures below 40°C. The authors also T 1397 report that at high initial copper ion concentrations (5 x 10~3 M) and high temperatures (75°C)> the rate which was initially constant increases with increasing deposi tion. An activation of about 10 kcal/mole was determined, thus supporting the hypothesis of mixed control. A similar / p 7 28} effect was reported by Strickland and Lawson^ . These authors studied a number of cementation reactions, namely: Cu-Zn, Cu-Fe, Ag-Zn, Ag-Cd, Ag-Cu, Pb-Zn and Cd-Zn, using a rotating disc geometry. All the reactions studied showed an enhancement in the rate after a certain amount of the precipitated metal was deposited on the disc surface. The reactions studied were found to be of first order. The rate in the first region (that is, before any substantial amount of the precipitating species was deposited), was found to vary linearly with the square root of the rota tional speed, and the activation energies determined were around 3 kcal/mole. This indicates a very close agreement with the Levich^1^ theory for laminar diffusion to a clean plate. Strickland and Lawson also report that the enhanced rates increased with increasing initial copper ion concen trations in solution (for the Cu-Zn system), in the range of concentrations studied, that is from 5*0 to 100 ppm. Another type of geometry often used is the rotating (29) cylinder. This geometry was used by Ingraham and Kerbyv on the cementation of cadmium on zinc in buffered solutions. T 1397 14 Here again the enhancement effect of the deposit was observed, and an activation energy of 4.0 kcal/mole was determined. Similar studies are reported by von Hahn and Ingraham, on the systems Pd-Cu^0^ and Ag-Zn^*^. A mixed control was found for the Pd-Cu system, with an activation energy value of about 9*5 kcal/mole, and diffusion control for the Ag-Zn system, with activation energy of 5 to 6 kcal/mole. It is worth noting that on the Ag-Zn system, in per chloric acid solutions, the rate constant, which was initially constant, increased with increased deposition. Appendices 2 and 3 present a summary of some of the cemen tation works referred to above. From the foregoing review, it, is apparent that except for a few cementation reactions such as the cemen- (32) tation of copper on nickel' , where an activation energy of 25.4 kcal/mole was reported, and some mixed control reactions mentioned earlier^*^6, 30), cementation reactions appear to be first order reactions, controlled by diffu sion processes. A strong confirmation of mass-transfer control is shown in the works where a rotating disc geometry has been used (Appendices 2 and 3). T 1397 15 MATHEMATICAL ANALYSIS OF MASS TRANSFER TO A ROTATING DISC SURFACE It was shown by Levich^^ that, for laminar diffusion, of a species to a plane rotating disc surface, in an infinite aqueous medium, the mass flux is given by: j = 0.62 D2/3 v " 1 / 6 (ML"2T_1) D = diffusion coefficient (L2T ) 2 —1 v = kinematic viscosity of solution (L T ) to » angular velocity of disc (T-1) CB =* concentration of diffusing species in the bulk of the solution (ML"*^) and the effective diffusion layer thickness, 6 (mass trans fer boundary layer), is defined by: 6 = (10> It is assumed that the variations in diffusivity and viscosity of the solution during an experimental run are small enough to be neglected. Thus, if diffusion is the rate determining process, first order kinetic behavior should be expected for the cementation system. T 1397 16 In order to allow for deviations from ideal behavior, especially in the presence of a deposit, the heterogeneous first order equation may be expressed by: - kT CB (11) where j* =» apparent mass flux based on the initial exposed precipitant area (ML~2T~1) krp = apparent mass transfer coefficient or specific rate constant (LT **•). A material balance on the batch system.yields: J* = fr (12) where m = mass of deposit at time t per unit initial pre- —2 cipitant area (ML ) and dm = _ 1 f d(YCB> _ c df) (13) dt XVTVE------B dt J U3; p where A » initial exposed precipitant area of disc (L ) V ® volume of solution at time t (L^) Cn * bulk concentration of reactant ion (Cu++) at 'B time t (ML~^). Thus, dCR V dtT = "AkTCB Rearranging and integrating for the case of constant apparent mass transfer coefficient: T 1397 17 C-O t Jf l n p = -kTA / (15) °Bo o v where CBq is the value of the concentration of Cu++ in the bulk at time t - 0. Equation (15) is a general equation and gives a direct evaluation of the specific rate constant kT> allowing for the change in total volume with the removal of samples for analysis at irregular intervals of time. Since the total volume withdrawn for analysis during each experimental run (130 ml) was less than ten percent of the total volume of solution used (1500 ml), an average value of 1493 nil can be used for V, and expression (15) is reduced to: C-Q kmA log (-—) = - 2 303v--- t (16) cBo ave o where Vaye - average solution volume (I< ) 53 1493 ml P 2 A » initial area (L ) - 5.06 cm . Equation (16) is represented by a straight line on a semi-logarithmic plot. It was also shown by Levich^^ that the thickness of the hydrodynamic boundary layer (<$0)* is given by: SQ = 2 . 8 ^ (17) and that the thickness of the mass transfer boundary layer (6) can be expressed as follows: n 1/3 , 6 = 0.5 (~) 60 (IB) 18 T 1397 For dilute copper sulfate solutions, v = 0.008937 cm2/sec^3^ and the diffusivity of Cu++ ions, D = 0.0000073 em2/sec(28) From equations (17) and (18) 6 = 1.4 v1/6 10-1/2 D1/3 (19) For first order reaction kinetics: § - - k C = - § 7 t (20) Rearranging and integrating (20): m ( — ) = - § f t (21) Therefore, kT = | (22) Expression (22) provides a means of calculating the theoretical values of the specific rate constant kT as a function of 6, and of comparing the theoretical values of krp with those obtained experimentally. From equations (19) and (21): „/C%n n2/3D Aw A 1/2 +. ln(^-) ---- y T T { 3) O 1.4 V V Equation (23) can be used to calculate the change in the dimensionless concentration (C/C0) with time for various 19 T 1397 speeds of rotation, u>. The computer program designed for this purpose is shown in Appendix XI. The variation of the specific rate constant with tem perature can be expressed by: -E/RT kT * kQe (24) where kQ = frequency factor (cm sec”'*') E * energy of activation (cal/mole) T « absolute temperature (°K) R - gas constant (cal/(mole)(°K)) Taking the natural logarithm of both sides of expres sion (24): In kip = In kQ - (25) Therefore, a plot of 1/T versus In' kT should yield a straight line of slope -E/R. This allows the calculation of E, the activation energy for the process. From equation (23), it is seen that if diffusion is the only controlling mechanism, and v and D are constants, the specific rate constant (k^) is directly proportional to the square root of the rotational speed (oj). Therefore, a plot Of ^0) versus kT should yield a straight line passing through the origin. T 1397 20 EXPERIMENTAL APPARATUS AND PROCEDURE Experimental Apparatus A sketch of the experimental apparatus used is shown in Figure 1. The reaction vessel used consisted of a S-34530 2 liters capacity resin reaction kettle covered by a lid with four ground taper joints. The center joint was used to introduce the shaft-disc holder assembly, and two of the remaining three joints were used for atmosphere control and solution sampling. The fourth joint was s \led off. The reaction vessel was placed in a constant tempera ture bath, the temperature of which was controlled to ±0.1°C by a 2149 Cole-Parmer electronic control relay connected to a heater unit. Agitation in the bath was obtained by means of a 4170 T American Instrument stirring pump. The top of the thermostatic bath was covered with a layer of insulat ing isopor to reduce heat transfer and evaporation. A CUA7515A3, 115 V AC/DC Carter variable speed motor, fitted to a holder which allowed vertical movement, was used to rotate the disc; the disc was mounted on a 1/4 inch diam eter 316/SS shaft. The motor speed was controlled by a UC1M Superior Electric Co. Voltbox, which was connected to a D34239 Sola constant voltage transformer. The latter was connected to the power supply. T 1397 21 10 11 16 12 (1 ) power supply (10) sampling opening (2) temperature relay ,(11) gas inlet (3) variable speed motor (12) mirror (4) varivolt (13) reaction vessel (5) constant voltage transformer (14) disc assembly (6) stirring pump (15) constant temperature bath (7) heater (16) insulating isopor layer (8) temperature sensor (9) thermometer Figure 1. Diagram of the experimental apparatus. T 1397 22 The rotational speed was measured by means of a Strobotac stroboscope. Figures 2 and 3 show the experi mental setup. The metal ion analyses were performed using a Techtron AA4 atomic absorption spectrophotometer. The pH measurements were made with a Beckman Zeromatic II pH meter. Experimental Procedure Disc Preparation; One-inch diameter iron discs, punched from a 1/8 inch thick sheet of Ferrovac E iron, were used in all experiments. The analysis for Ferrovac E iron is shown in Table 3. The disc assembly was made in the following way: a. A 1/2 inch diameter by 1 inch height plexiglas cylinder was drilled to take the 1/4 inch diameter 316 SS shaft, and the shaft was mounted into the cylinder. The plexiglas cylinder was designed for the purpose of attach ing the disc to the shaft. b. The Ferrovac E iron disc was glued to the plexiglas cylinder shaft assembly using Locktite glue. To ensure perfect concentricity, an aluminum mounting jig was used. The mounting jig is shown in Figure 4. c. A 20-8124 AB Buehler castoglass tapered mounting was centrally cast around the disc shaft system by means of an aluminum mold, shown in Figure 5. After the plastic was T 1397 23 Figure 2 . Experimental apparatus* Figure 3* Experimental apparatus. T 1397 Table 3. Impurities content in Ferrovac E iron. Impurity Percent by Weight Carbon 0.007 Phosphorus 0.002 Silicon 0.01 Chromium 0.01 Manganese 0.001 Sulfur 0.006 Nickel 0.05 Vanadium 0.004 Nitrogen 0.0027 Tin 0.005 Cobalt 0.005 Oxygen 0.023 Aluminum 0.003 Copper 0.01 25 T 1397 I -4vf j*— T 1" » i * 1/8i 1 2 »t Figure 4, Aluminum mounting Jig T 1397 Figure 5. Aluminum easting mold T 1397 27 hardened it was machined to give the final disc holder shape as shown in Figure 6 . This shape was chosen in order to reduce edge effects and undesirable convection currents. d. After machining, the disc was spun to check for eccentricity. e. The disc surface was then polished with emery paper in the following order: no. 2, no. 1, no. 0, no. 2/0. The surface was then washed with distilled water and dried with acetone. This surface preparation was carried out immediately before each test. Two views of a finished disc are shown in Figure 7. Solution Preparation:' The copper sulfate solutions were prepared with reagent grade CuSOj^S^O (Mallinckrodt Chemical Works) and distilled water. After being homo genized, 1500 ml of the solution were carefully measured and placed in a stoppered flask inside the thermostatic bath to attain the required temperature. After 24 hours in the bath, the solution was introduced into the reaction vessel, the lid of the vessel was sealed with silicone grease, and the disc lowered through the center joint. Atmosphere Control: The atmosphere in the reaction vessel was controlled in order to prevent any side reactions from occurring (see equations 5, 6, and 7) Since the main possible side reactions involve oxygen, most studies were conducted under an inert argon atmosphere. Before an T 1397 13 in — in.l«— -J s (•— 1 in.— 1.24 in. (1) Shaft (2) Plexiglas cylinder (3) Ferrovac E disc Figure 6. Precipitant disc. T 1397 29 Figure 7. Two views of a finished disc. T 1397 experiment was begun the reactor was flushed with argon for one hour. This flushing period was considered to be sufficient to reduce the oxygen concentration in the solu tion to a level sufficiently low to be neglected. Through out the test a positive argon pressure was maintained above the solution to prevent oxygen from diffusing in. Speed Control: The approximate voltage required to give the desired disc rotation speed was determined before the disc was placed in the solution. During the experi ments, readings of the rotation speed were taken every 10 minutes by means of a Strobotac stroboscope, and the volt age was adjusted when necessary. The rotation speed was maintained within ±2# of the desired value. Sampling and Analytical Procedure: 10 ml samples of the solution were taken at 10 minute intervals for the first hour. Thereafter, a 10 ml sample was taken after each hour, for the duration of the test. The samples were diluted with distilled water to a concentration suitable for analysis, and were analyzed for copper and iron with a Techtron AAH atomic absorption spectrophotometer. Cali bration standards were prepared diluting standard 1000 ppm Volucon Cu and Fe solutions. pH Measurements: All experiments were done at natural pH. The pH of the solutions were measured before and after each test using a Beckman Zeromatic II pH meter. T 1397 31 EXPERIMENTAL RESULTS The effect of the following four variables on the rate of cementation of copper with iron, in dilute sulfate solu tions, was investigated: 1. Temperature 2. Rotation speed of the disc 3. Initial copper ion concentration in solution A. Atmosphere in the reactor The results obtained in the experimental work are given below. Unless otherwise indicated, the standard reaction con ditions were: a. Rotation speed - 600 rpm b. Atmosphere in the reactor - Argon c. Temperature - 25°C d. pH-natural pH (obtained by dissolving CuSOjj-S^O in distilled water) e. Initial iron ion concentration in solution, The Effect of Temperature For this study two different initial copper ion concen trations were used: 50 ppm and 500 ppm. T 1397 32 The temperatures at which the tests were carried out were: 25, 30, 35, and 40°C. All experimental data are given in Appendices VII and VIII. Semi-logarithmic plots of the dimensionless concentra tions, C/CQ , against time are given in Figures 8 and 9* The specific rate constants calculated from the experi mental data are shown in Tables 4 and 5* ■I* ■f The Arrhenius plot for the 50 ppm initial Cu concen tration is presented in Fig. 10. No similar Arrhenius plot was made for the 500 ppm ini tial Cu++ concentration, because the Cu++ concentration variation in the early stages of the experiments could not be determined accurately. The Effect of the Rotation Speed of the Disc Two different initial Cu++ concentrations were used in this study: 50 ppm and 500 ppm. The rotation speeds of the disc used were 300, 450, 600, and 750 rpm. All experimental data are given in Appendices IX and X, and the results are shown graphically in Figures 11 and 12. For the experiments conducted with an initial copper ion concentration of 50 ppm, the specific rate constants calculated for the two rate periods, together with the T 1397 rotation speeds of the disc, and the square root of the disc rotation speeds used are given in Table 6 . A plot of the square root of the disc rotation speed against the specific rate constants is shown in Figure 13. The specific rate constant data for the experiments conducted with initial copper ion concentration of 500 ppm are shown in Table 7* The Effect of Initial Copper Icr. Concentration in Solution Tests were run at seven di erent initial copper ion concentrations. These initial concentrations were: 25, 50, 100, 200, 500, 800, and 1000 ppm. All experimental data are given in Appendix XI. The results are shown graphically in Figure 14. No significant variation from the expected initial rate, as calculated from the Levich equation (16), could be detected. The specific rate constants for the enhanced rate stage of each test are given in Table 8 . The Effect of the Atmosphere in the System Tests were conducted under 3 different atmospheres, i.e., three different oxygen potentials. These were: argon air, and oxygen. The experimental data are given in Appendix XII, and the results are shown graphically in Figure 15. T 1397 34 General Method for the Calculation of the Specific Reaction Rate Constant In most of the experiments, two rates of reaction were observed: an initial rate corresponding to laminar dif fusion to a clean disc, and an enhanced rate observed after a certain reaction time, when deposits were present on the disc surface. The experimental dimensionless concentrations (C/CQ ) were determined for all experimental data and, for each experiment, these ratios were plotted on a semi-logarithmic scale. The curves obtained were computer-fitted to equa tion (16) by a least square program shown in Appendix IV. The same procedure was adopted to fit the second part of the curves corresponding to the enhanced rate period, and the corresponding computer-fitting program is shown in Appendix V. These programs were designed to determine the slopes of the curves obtained which are equal to: (26) where k - reaction rate constant (T""1). The specific reaction rate constant krp can be calculated from the slopes obtained by means of the corresponding expression: v - -k*V»2.303 T ” A (27) T 1397 35 VOo o oo co 0 u 3 45 cd u 0 s o 0 o -p £ oo P. 0 Pi jG -pO LP G o G 0 O o a -H ^3* •H -P CM ■P 05 U 0 4* 3 G 0 0 G o 0 G > O G o G o'i o+ oo ^ *rH+ rH 4> G 0 o5 O £ U •H 4> EH G cd 0 •H o 45 G •H o G o o CM 0 i—I 0 • 0 O 0 HO u G o 0 o -=r JG •H P. 0 TJ 0 G G 0 cd 8 £ -P •H ^ £ cd o T5 in o o o o P. VO oo o o o o fn G in o in o O o * CM oo oo •=r O hO o O U G OO VO a P. o < o □ cd *» ip O CM L_U i—I CO o I o CO VO CM O 0 rH i—I fn 3 I O hO O lo •H o o|o 10 10“^ iue , rp fdmnines ocnrto vru time versus concentration dimensionless of Graph 9, Figure T 1397 T 10 -1 0 argon atmosphere argon 0 rpm 600 60 nta u* ocnrto i slto: 0 ppm. 500 solution: in concentration Cu+* Initial for the temperatures of 25, 30, 35, and 40°C. and 35, 30, 25, of temperatures the for ie (min•) Time 120 180 eih ie o 60 rpn 600 for line Levich 240 300 360 T 1397 Table 4. Temperature effect on the specific rate constant Initial Cu++ concentration in solution: 50 ppm Rotational Speed: 600 rpm Atmosphere: Argon Temperature First Period Enhanced Period (°C) (cm sec-1) (cm sec-1) 25 4.77336 x 10-3 2 .363X6 x 10-2 30 5.13992 x 10~3 2.81392 x 10“2 35 8.3735 x 10-3 3.11661 x 10-2 40 7.14593 x 10“3 3.38159 x 10“2 T 1397 Table 5* Temperature effect on the specific rate constants. Initial Cu++ concentration in solution: 500 ppm Rotational Speed: 600 rpm Atmosphere: Argon First Enhanced Second Enhanced Temperature Period Period (°C) (cm sec"^-) (cm sec~^*) 25 1.31114 x 10-2 2.95459 x 10“2 30 1.66651 x 10-2 4.50823 x 10“2 35 3.40281 x 10“2 6.21773 x 10“2 40 3.50310 x 10“2 7.26395 x 10-2 Specific Hate Constant (cm sec 10 -3 iue 0 Areis lt Iiil u+ concentration: Cu++ Initial plot. Arrhenius 10. Figure T 1397 T 3 . 3.5 3.1 0 ppm.50 3.2 1000/T 3.3 Argon atmosphere Argon 0 rpm 600 is Period First Period ^ Enhanced 39 40 T 1397 o VO on o o on ■H i—I •H O CM O C O o CMc—I -P o O o o o in o LTV o on ■=r VO 50 50 ppm. speeds speeds of 300, 450, 600, and 750 rpm. Initial Cu++ concentration: o i—i °o co vo -=r 1. o cm ‘ o rH O O rH Figure Figure 11. Graph of dimensionless concentration versus time for the rotational T 1397 41 O VO CO o o CO o ^r CM £ £ O v-' CO rH Q) £ Eh o CM H o o O o o VO o in in VO C*— C\J speeds speeds of 600 and 750 rpm. Initial Cu++ concentration: ppm. 500 I—I o 1 o CO VO CM o I—I rH o Ilo ° Figure Figure 12. of dimensionless Graph- concentration versus time for the rotational T 1397 Table 6. Rotational speed effect on the specific rate constants. Initial Cu concentration in solution: 50 ppm Temperature: 2 5°C Atmosphere: argon Rotational Theoretical Speed (Levich(D) First Period Enhanced Period (rpm) (cm sec~^) (cm sec“"^-) (cm sec^) 300 3.30722 x 10~3 3.06695 x 10-3 1.70294 x 10~2 450 4.05050 x 10-3 4.37734 x 10~3 2.07342 x 10“2 600 4.67712 x 10“3 4.77336 x 10“3 2.36316 x 10-2 750 5.22918 x 10"3 6.67650 x 10"3 2.94071 x 10“2 Specific Rate Constant (cm sec 0.000 0.012 0.004 0.008 0.020 0.016 0.028 0.024 iue 3 Gaho h sur ro o h rttoa speed rotational the of root square the of Graph 13. Figure 1397 T Argon atmosphere Argon 5 5 C 25 ess pcfc ae osat Iiil Cu++ Initial constant. rate specific versus ocnrto: 0 ppm. 50 concentration: 10 15 20 25 30 Enhanced Region Levich Region Levich 43 T 1397 Table 7. Rotational speed effect on the specific rate constants. Initial Cu++ concentration in solution: 500 ppm Temperature: 25°C Atmosphere: Argon Rotational Speed First Enhanced Period Second Enhanced Period (rpm) (cm sec"1) (cm sec"*1) 600 1.3111*1 x 10-2 2.95*159 x 10-2 750 5.13355 x 10-3 1.90228 x 10-3* *reaction practically stops after 240 minutes. T 1397 O 25 ppm O 50 ppm □ 100 ppm A 200 ppm A 500 ppm ©800 ppm B 1000 ppm 25°C Argon atmosphere 0 60 120 180 240 300 360 Time (min .) Figure 14. Graph of dimensionless concentrations versus time for the tests in which initial Cu++ concentrations were varied. T 1397 Table 8. Initial Cu++ concentration effect on the specific rate constants. Temperature: 25°C Rotational Speed: 600 rpm Atmosphere: Argon Initial Cu*"1' Concentration First Enhanced Second Enhanced in Solution Period Period (ppm) (cm sec"-*-) (cm sec"1) -2 25 2.17674 x 10 -2 50 2.36316 x 10 —2 100 4.41319 x 10 200 2.32910 x 10-2 6.64566 x 10-2 500 1.31114 x 10-2 2.95459 x 10“2 800 0.83067 x 10”2 0.08311 x 10-2 1000 ■''0.467712 x 10-2 reaction stops Note: In all cases, the reactions follow the ideal behavior (Levich eqn.^1^) at the very beginning, and then deviate from it. The rate of reaction correspond ing to ideal behavior is: 4.47712 x 10“ ^ cm"1 sec. T 1397 47 B o O* VO ** a CO E l •H O Gj LT\ e: e: o o o bQ *H o U -P vo 05 cd E i o © 43 o 43 El CO 0 O E i e : O o o 0 + B + •H 3 •H 43 O o 0 rH CM E* cd 0 *h El 43 0 *H > E! M eO: •H «H • 43 0 O'-' 05 43 oo u a I—1 0 43 0 d £ •H 0 *H O E« e : 0 o. a o X 0 0 0 0 O 0 El CM rH 0 e: 43 o a 0 ES B 0 43 B 05 -H •o e; 0 in rH O 0 u o E5 o CO VO CM o rH bO I— I •H OIO T 1397 48 DISCUSSION As can be seen from Figures 8, 9, 11, 12, 14, and 15, two rate regions can be defined for the cementation reaction under all experimental conditions. An initial period which at low initial concentrations of copper and at 25°C, cor responds to a rate calculated from the Levich^^ equation, and a secondary period during which the rate deviates con siderably from the Levich equations^"^ . Before discussing the effect of individual parameters on the kinetics of the cementation reaction, it is important, therefore, to clarify this particular aspect of the rate curves. Two phenomena need clarification. Firstly, the devia tion of the rate from the Levich equation and, secondly, the enhancement of the rate with time. The first can be seen best from Figure 9 and Figure 14 where the rate curves are plotted for high initial concen trations of copper. At these initial concentrations the surface of the disc is covered almost instantaneously with a coarse deposit, and the Levich analysis, which assumes a laminar boundary layer at a uniformly accessible surface, can be applied over an experimentally undetectable period of time only. As can be seen from Figure 9 (for 25°C), the deviation from the Levich equation (Eqn. 16) is very marked even in the initial period. This rate is further T 1397 49 enhanced with time. Although Figure 9 shows two straight lines as being-indicative of the two rate periods, a con tinuous curve can be fitted to the experimental data, as indicated by the dotted line. The straight lines are used to calculate the initial and final reaction rate constants but they do not provide an adequate explanation for rate enhancement. On the other hand, a continuous curve indi cates that for a first order heterogeneous reaction, for which k, the reaction rate constant, is independent of con centration, the available surface area is a function of time. This is readily apparent from the earlier analysis of first order reaction kinetics. From equation 14, the change in concentration with time for a heterogeneous reaction, is given by: - § = k £ c (28) which upon integration for constant ~ results in m —• = - k | t (29) However, if A = f(t), the above integration is no longer possible unless we know the function relating the available surface area to time. Assuming that such a function can be expressed by a polynomial: A = a + bt + ct2 + ... (30) upon integration, equation (29) will yield: T 1397 50 In = | (at + ^ + ...) (31) Q Prom equation (31) we can see that a plot of In tt- v s . t °o will result in a continuous curve, as approximated by the dotted lines in Figure 9. Since the cementation reaction is an electrochemical ++ reaction involving cathodic reduction of Cu ions and ++ anodic oxidation of Fe to Fe , its rate is directly pro portional to the total number of tl" 3 cathodic sites avail able (or to the total cathodic surface area). This, in turn, depends on the morphology of the deposit. As the deposits become coarser with increasing concentration, the total surface area of deposited copper decreases, decreasing the total cathodic area available. This results in a reduced rate, as observed in Figure 14. At very low initial concen trations of copper (below approximately 100 ppm), and pro vided .the initial surface area is sufficiently large, the thickness of the deposited copper layer may be considerably smaller than the thickness of the theoretical hydrodynamic boundary layer. Under such conditions it is likely that a enhancement in the theoretically predicted rate will result due to the introduction of microturbulence within / O 7 Q Q \ the diffusion boundary layer! '* }. However, as soon as the thickness of the protruding deposit has exceeded the thickness of the hydrodynamic boundary layer, v/hich at T 1397 51 concentrations above 100 ppm occurs very rapidly, laminar conditions assumed by the Levich analysis no longer exist; full turbulence is developed and the rate then becomes a function of the morphology of the deposit and of the time- dependence of the cathodic areas available. Thus, the deviation of the experimental rates from the theoretical rates calculated from the Levich equation (Eqn. 16) is accounted for by the absence of the two conditions which are essential to a proper application of the Levich analysis: a uniformly accessible surface and a laminar flow in the boundary layer at the surface of the disc. The enhancement in the rate with time is due to the time-dependence of the available cathodic sites. Effect of Temperature From the Arrhenius plot for the 50 ppm initial Cu concentration data (Fig. 10) the rate equations for the initial and enhanced periods are given by kin = 1 *5 exp((-1710 ± 100)/T) and ken = 4.1ilexp((-1525 ± 100)/T) respectively. The corresponding activation energies determined from the above equations are ± 0.2 kcal/mole for the initial period, and 3*05 ± 0.2 kcal/mole for the enhanced period. The values of these activation energies indicate that in both T 1397 52 the initial and enhanced rate regions the rate-controlling step is the diffusion of Cu++ ions to the iron disc surface, since from theoretical considerations one would expect an activation energy of about 3 kcal/mole for a diffusion con- ( Q Q oh) trol process, in the rotating disc geometry^J . Figure 8 shows another interesting feature. After an initial enhanced period at higher temperatures, 35° and 40°C, the rate commences to slow down. This phenomenon could be due to the formation of a low porosity copper layer which "blinds" the anodic sites on the iron disc. A similar behavior was noticed at 25°C with initial copper ion con centrations of 800 ppm and above. A microscopic examination of the deposits obtained from the higher temperature runs, for 50 ppm initial Cu4 -+ concentration, showed completely different morphological properties compared to those obtained at lower temperatures. The former appeared as a fine-grained yellowish coating, whereas the latter exhibited coarse and dark brown, grains. At higher concentrations (above 100 ppm), a large por tion of the deposited copper did not adhere to the disc surface, which was covered in a very irregular fashion as can be seen from Figures 16 and 22. The difference in deposit appearance can be seen by comparing Figure 16 with Figure 17,which was obtained for 50 ppm initial Cu con centration, at 25°C. T 1397 53 Effect of the Speed of Rotation From the evidence of the Arrhenius plot presented as Figure 10, the rate-controlling step is expected to be diffusion of the copper ions across the mass transfer boundary layer, at least for the 50 ppm initial Cu con centration. If this is true, the plot of the specific rate constants as a function of the square root of the rotation speeds ought to be linearand pass through the origin. Figure 13 shows the plot of the specific rate constants, ++ for an initial Cu concentration of 50 ppm, against the square root of the rotational speed. Since at an initial ++ Cu concentration of 50 ppm the assumptions of the Levich analysis are reasonably satisfied, the theoretical behavior can be expected. This is indicated by the two straight lines (Figure 13) passing through the origin, which repre sent the initial and final specific reaction rate constants. This behavior differs somewhat from that found by Strickland (2.7) and Lawsonv ‘ who report that,for the cementation of copper with zinc in dilute aqueous sulfate solutions, the two lines intersect at a rotation speed of about 100 rpm. It should be noted that the value of the specific rate constant at 750 rpm, in both sections of Figure 13, lies slightly above the respective lines. This can be due to experimental scatter but, more likely, it is a consequence of the onset of boundary layer turbulence near the edges of the disc (see Fig. 18). If a turbulent condition prevails T 1397 at the edges of the disc, the thickness of the diffusion boundary layer will be significantly reduced at the edges, thus giving an average boundary layer thickness which is smaller than the expected boundary layer thickness for diffusion through a laminar boundary layer only. The enhancement in the specific reaction rate has been attributed to the onset of microturbulences in an essen tially laminar boundary layer^2^. Such a situation would lead to a mass transfer coefficient which is larger than one obtained for diffusion to a clean surface. The assump tion is that the cathodic surface area remains essentially constant and that the thickness of the deposit is consider ably smaller than the theoretical boundary layer. When a large quantity of material has been deposited on the disc surface, the onset of turbulence becomes the most important factor. Figure 19 shows the deposit O i I , obtained at 600 rpm, 25 C, and 800 ppm initial Cu concen tration. It cari be seen that a well defined, thick, den dritic deposit is formed around the edges of the disc, in contrast to a finer and smoother deposit in the center. The coarseness of the deposit is a clear indication that laminar flow conditions were not maintained. A series of experiments were conducted using an ++ initial Cu concentration of 500 ppm, and the results have been shown in Figure 12. At 600 rpm, a two region rate is evidenced, whereas at 750 rpm the reaction rate dropped to T 1397 55 almost zero after approximately 240 minutes. Examining the deposit obtained at 750 rpm under a microscope, it could be seen that it was a fine-grained, dense film with some dendritic growths. This is shown in Figure 20. As was mentioned earlier, the decrease in rate is attributed to the decrease in the anodic areas on the iron disc. This would suggest also a change in the diffusion mechanism from diffusion of Cu++ ions to the surface of the disc to diffusion of Fe++ ions through the fine adherent copper film. A similar behavior was observed at high initial Cu++ concentrations, namely 800 and 1000 ppm, as shown in Figure 14. This effect was also apparent at the 50 ppm initial Cu concentrations at high temperatures (Fig. 8). ++ The Effect of the Initial Cu Concentration in Solution The results obtained for the experiments conducted with a variation in initial concentration have been shown in Figure 14. The most important feature of these results is the fact that the overall reaction rate increases to a maximum and then decreases when the initial copper ion concentration in solution is greater than about 100 ppm. This is shown in Figure 21. Three distinct regions can be observed here: T 1397 5 6 ++ a. Initial Cu concentration ranging from 25 tc 100 ppm. ++ As the initial Cu concentration in solution increases, the coarseness of the Cu deposit on the disc increases. This increase in the coarseness of the deposit leads to an increase in flow perturbations near the depositing iron surface, thus resulting in an increased diffusivity of the copper ions and in an enhancement of the cementation rate. b. Initial Cu concentration ranging from 100 to 500 ppm. The rate of reaction in this region decreases as the ++ initial Cu concentration in solution increases. The reason for this behavior has been explained in the first part of this discussion. ++ c. Initial Cu concentration ranging from 500 to 1000 ppm. ++ At high initial Cu concentrations in solution, the form of the copper deposits obtained on the iron disc sur face changes significantly, becoming finer and more coherent as shown in Figures 19 and 20. This type of deposit appears to form a very fine and impervious film that covers the surface of the disc. This would lead to a "blinding” of the ++ anodic sites for Fe counter diffusion, and under these conditions, this diffusion might become the rate controlling step in the cementation process. From Figure 14 it can be seen that for high initial ++ Cu concentrations in solution the reaction practically T 1397 stops after a certain period of time. The Sffect of the Atmosphere in the System The results of the tests carried out to determine the effect of different oxygen potentials on the rate of cemen tation have been shown in Figure 15. As can be seen from the above figure, the rate of the cementation process decreases as the oxygen potential increases. This fact can be explained by the formation of a protective cuprous oxide coating on the surface of the deposited copper at high oxygen potentials and high pH values. This can be seen from the potential-pH diagram for the Cu-0 systeirr , shown in Figure 23. In this diagram the equilibrium posi tions, at the experimental pH conditions of 4.5, for the oxygen potentials of 1 and 0.21 atmospheres, are shown as points A and B, respectively (calculations of theseequilib rium positions are given in Appendix XIII). As is apparent from Figure 23, in order to go from the metallic copper (deposited on the disc) to the equilibrium position ++ of Cu one has to cross the stability region of cuprous oxide. Therefore, CU2O is expected to form at the surface of the deposit for both the air and oxygen experiments. This will create a protective layer of C ^ O over the deposit surface and thus result in a decreased reaction rate. T 1397 58 At Pq ^ « 1 atm there is a larger driving force than at Po2 ~ 0.21, and hence, a thicker protective Cu20 layer will be formed. This will result in a slower reaction rate, as indicated by the experimental results. The samples taken during this series of experiments were analyzed for iron as well as for copper. These data are shown in Figures 24 and 25, which are drawn in such a way that if there is a stoichiometric replacement of copper by iron the copper and iron concentration points should coincide. As can be seen from these figures, the iron consumption in the presence of air and oxygen is much higher than the theoretical mass ratio of 0.88 expected from equation (4). When an air atmosphere was used, the quantity of "excess" iron used was much greater than that observed in the case of oxygen atmosphere. This fact may be explained by an enhanced formation of a cuprous oxide layer at a higher oxygen poten tial which, whilst not preventing the reaction from taking place, will significantly reduce the rate. With air, i.e., Pq 2 = 0.21 atm, a much thinner oxide layer is formed and some redissolution of copper by the ferric ions may be ( 7) occurringv1J according to equation (8). This is indicated ++ by the fact that Cu concentration appears to level off at about 17 ppm (Figure 25). The same effect is observed in Figure 15 where in the presence of air, there is a sub stantial decrease in the rate of copper cementation. T 1397 Experimental Error Considerations The main sources of error in the data presented in this work are: a. Analytical error: an accuracy of 1% transmission, in middle scale conditions, can be obtained in the atomic absorption spectrophotometer. This corresponds to an error of 1.32# in absorption and consequently in the concentra tion readings. b. Variations in rotation speed: due to voltage oscillations, the speed readings are estimated to involve an error not larger than 2%, However, since the mass flux is a function of the square root of the rotation speed, the error produced in the reaction rate will be about 1 c. Variations in the solutio'n volume: due to the withdrawing of samples the error introduced is estimated to be k% maximum. d. Pipeting and dilution errors: these are regarded as negligible. e. Temperature control: the temperature was con trolled to ±0.1°C and, therefore, the error is negligible. T 1397 60 Figure 16, Copper deposit on the iron disc obtained with 500 ppm initial Cu++ concentration, temperature 25°C, 600 rpm rotational speed. Figure 17, Copper deposit on the iron disc obtained with 50 ppm initial Cu++ concentration, temperature 25°C, 600 rpm rotational speed. T 1397 61 Figure'18. Side view of the copper deposit showing the deposit thickness. Deposit obtained with 50 ppm initial Cu++ concentration, temperature 25°C, 750 rpm rotational speed. Figure 19. Copper deposit on the iron disc obtained with 800 ppm initial Cu++ concentration, 25°C temperature, 600 rpm rotational speed. T 1397 Figure 20. Copper deposit on the iron disc obtained with 500 ppm initial Cu++ concentration, 25°C temperature, 750 rpm rotational speed. T 1397 o o o -p o o o o in o ft vo CM o ft CO co rl o C o o VO *H -P -P O O in o oO o P ^r o o CM O o tration in solution. OC 1— I o on CM oin 01 x (.^oas-uio) aq.T2y uoxq.o^aH oxjToads Figure 21. Plot of the overall specific reaction rate concep versus initial Cuz1* T 1397 Figure 22. Copper deposit on the iron disc obtained with 200 ppm initial Cu++ concentration, 25°C temperature, 600 rpm rotational speed. T 1397 65 1.6 1.4 CuO 1.2 1.0 0.8 ++ Eh (v) °-6 Cu 0.4 0.2 0.0 - 0.2 Cu -0.4 - 0.6 - 0.8 - 1.0 - 1.2 -2 -1 0 12345 6789 10 pH Figure 23* Potential-pH diagram for the Cu-0 system. Iron Concentration (ppm) 15 10 20 iue 4 Cpe n io cnetain i slto a a as solution in concentrations iron and Copper 24. Figure 0 T 1397 T 25°C 0 rpm 600 60 ucin ftm iha oye atmosphere. oxygen an with time of function 120 ie (rain.) Time 180 240 Iron Copper 300 360 66 20 10 Copper Concentration (ppm) Iron Concentration (ppm) 20 10 15 iue 5 Cpe n io cnetain i slto a a as solution in concentrations iron and Copper 25. Figure 0 T 1397 T 25°C 0 rpm 600 function of time with an air atmosphere. air an with time of function 120 . ie (min.) Time 180 Iron 24.060 O O Iron □ Copper Copper 300 360 67 10 20 Copper Concentration (ppm) T 1397 CONCLUSIONS The following conclusions can be reached from the experimental data observed in this investigation. 1. Cementation of copper with iron is a diffusion- controlled process with an activation energy of approxi mately 3.4 kcal/mole. The rate-controlling step is the ++ diffusion of Cu ions to the cathodic reaction sites through a surface boundary layer. 2. Under certain conditions, a change in the reaction mechanism occurs and the rate-controlling step becomes the diffusion of Fe ++ ions away from the anodic sites through a solid layer of deposited copper. 3. The possible non-linear behavior of the plot C In against time is probably due to the non-linear increase or decrease in the available cathodic surface areas with time. This conclusion is tentative and yet to be verified. 4. The dependence of the specific reaction rate con stant on the speed of rotation of the disc is given by: k = A(RPM)0*5 5. The morphology of the copper deposit is a function ++ of the initial concentration of Cu ions. At low concen trations, a fine-grained, smooth deposit is obtained. As the concentration increases, the grain size increases and T 1397 69 the deposit becomes irregular and coarse. 6. At initial concentrations of Cu ions below approximately 100 ppm, the initial rate of the cementation reaction follows reasonably well the Levich analysis. This indicates that, at low concentrations and with a sufficiently large area of deposition, a uniformly accessible surface and laminar flow in the boundary layer are maintained. 7. An increase in the oxygen potential of the system results in a decrease in the rate of the reaction and in an increase in the iron consumption. T 1397 70 SUGGESTIONS FOR FUTURE WORK This investigation has pointed out a number of problems which require further research before a comprehensive kinetic model of the cementation process can be established, 1. Effect of surface roughness on mass-transfer to the surface of a rotating disc and a re-examination of the applicability of the Levich analysis to cementation systems, 4.4. 2. Effect of the initial Cu ion concentration on the morphology of the deposited copper. 3. The change in the available cathodic and anodic areas as a function of process variables. 4. Further investigation of ‘t-he suggested change in ++ the rate-controlling step from diffusion of Cu ions through a boundary layer to the porous diffusion of Fe++ ions through a layer of deposited copper, at high initial concentrations of Cu ions. 5. Effect of the purity of iron on the rate of the cementation process. 6. Kinetics of the three side reactions expressed by equations (5), (6), (7), and (8). T 1397 71 APPENDIX I - Calculations for the equilibrium constant’s for the reaction: Cu++ + Fe = Fe++ + Cu (4) The equilibrium constant is related to the standard free energy change by: a-cFe^ ++ • a- Cu AG° = -RT In (32) Cu Fe where AG° = free energy change for the reaction R = gas constant T « absolute temperature ape+.{. - activity of ferrous ion in solution aCu++ = activity of cupric ion in solution aFe = activity of metallic iron aCu ~ activity of metallic copper In the assumption that iron and copper are in their standard states (pure solids), equation (32) can be written as: AG? = -RT In A (33) However, AG° = AH° - TAS° (34) where, AH^ = standard enthalpy change for the reaction AS^ = standard entropy change for the reaction and over a narrow temperature range AH^ and AS° can be taken T 1397 72 as constants. Prom Latimer(37) these data are given as: AH° AS° Metal (cal/mole) (cal/mole/deg.) Fe++, . -21,000 -27.1 (aq) Cu++(aq) 15,390 -23.6 For reaction (32) then, AG° = -36,390 + 3.5 T (34) and at?~++Fe+ ,18,314 . K = ----- = exp (— if2 1.761) (35) aCu++ The equilibrium constants for reaction (4) over the temperature range of 293 to 323°K are given in Table 1. T 1397 APPENDIX II - Summary of published Information on cementation kinetics. i Approx. r- < Ceometry System j initial Solution type Controlled Influence o f deposit I References concn atmosphere I (p.p.m .) j Hatch reactors Kith separate ctjitutor Sample a: bottom of ve»j;I C u-Zn 103 Technical ZnSO * H ; (ftcm high Not c.insiJetrd. Author's J Iltin(l95S) acid) results indicate enhance ment Separate suspended plates Cu-Fe I0 3 S O *2 - , pH s. 2.5 N 3 ( + others) Stripped otYby opciation Nadkarnt and Wadswoitlt under extreme agitation (I9i»7) conditions ! 1 I *C u -N i 1 103 SO*2 - . pH % 1-2 Attached—effect not 1 MilUr and Wadsworth i j discussed j ( IVr-sj Plates mounted concentric Cu-Zn 10* S O *2 - , acid None Attached—analyses at end van Stra-.en and Khret (1939) x\ith stirrer j of experiment only : Hatch reactors irisk precipitant attached to stirrer Snips an propeller blades Cu-Zn ! 103 SO*2 “ .acid None Fell off. effect not con Ceiitncrsrwer and Heller ( — others.) (■) others) sidered ( t ‘».‘ 2> Rotating cylinJcr :Cu-Zn 103 SO 2 - None Scraped off King and liltrgcr (I'-t j» 103 s o * 2 - Scraped otr King and lfuiger tlvJ4> 1 Cu-Cd j As-Zn 1-10 n o 3- None Rate apparently enhanced Ciluksn:.in.’Mounuin, and Ag-Cu !—10 None Rate apparently enhanced King il-»53) Cu-Fe j n o 3 - N 2 ( -i- others) Rate appjieiv.ly enhanced Kickard and Pucrstcnau s o * 2 - I l ’JuS) ! *Pd-Cu H C !0 3, various N, Rate retarded son Hahn and Ingraham 10 1 pH (.1966) Ag-Cu h c i o 3 N a Rate enhanced von Hahn and lnginham (1907) Ag-Cu C M ", alkaline N y Rate retarded i son Hahn and Ingraham j (1967) Ag-Zn 5 H C IO s Rate enhanced | von Hahn and Ingraham Nj 1 (t9«S> Ag-Zn 5 C N ~. alkaline N y Rale retarded | von f l.ihn and Ingraham (196S) Cd-Zn buffered S O *2 - . N 2 Rate enhanced p H > 6-4 Ingraham and Kerby (I9 o 9 ) 5 pH 3-9 bulTered S O *1 - . Rota tins disc Cd-Zn 5 p H 3-9 n 2 Not studied (pH < 6-4) Ingraham and Kerby (I960) Cu-Fe JO3 C l- , acid None N o t Studied Fpixkcpsyan (1964): Ag-Fe 103 C l- , add None N o t studied Fpkkepsyan and Kakovskii (1965) Cu-Fe 103 S O *2 - , acid None N ot studied Fpixkcpsyan and Kukoxshii (1966) Ag-Fe 103 SO*2 -, acid None N o t studied ilpisfcepsyan and Kakovskii (I960) Ag-Zn ic -io o C N - , alkaline None N o t studied, disc replaced Knkcs:kii and Shcherbakov regularly (196*) Au-Zn 10-1CO C N - , alkaline None N ot studied, disc teplaccd Kakovskii and Shcherbakov regularly (1907) Cu-Zn 5-100 S O *2 - , Rate enhanced Strickland and Lawson natural pH (19701 Cu-Fe 10 S O *2 - , I * 1 Rate enhanced Strickland and Lawson natural pH (1970) Ag-Zn 3-200 SO*2 -, natural N 2 | Rate enhanced Strickland and Lawson (tL-s ! »H , work) Ag-Cd 10 ! SO* “ .natural [ Rate enhanced St< lckland and l.awson (this PH work) Ag-Cu 10-50 1 SO* , natural Rate enhanced Strickland and Lawson (this 1 pH „ j* work) Pb-Zn 24 i SO*2 -,natural ! n 2 I Rate enhanced Strickland and Lawson (this ; pH wot!:) Cd-Zn 5-100 SO*2 -, natural ! N'a ! Rate enhanced Sttirkland and l.awson(this | pH work) Continuous reactors Fixed bed o f precipitant jM ’b-Fc NaCI ! None Present, but effects not Hanulorf (1961) A ,- le 10*,0i and CaCK brines N r ic considered llan-.dort (1461) Ag-Fb 10J | None H.in-.dotf (1961) R o u tin e disc 1 Cu-Zn , SO .2 - , natural n 2 Steady state enhancement Strickland and Lawson (197lt) i I* ; f h * Activation centra! siiitiifiant. After Strickland and L a w s o n ^ 8 ) T 1397 APPENDIX III - Activation Energy of Cementation. Activation Geometry Energy Reference System______*____ (kcal/g mole) ______ Cu with Fe, (SO4 ) Disc 3.15 Episkoposyan and Kakovskii (1966) Ag with Fe , (SOif) Disc 3.02 ibid Cu with Fe, (Cl") Disc 3.08 ibid (1965) Ag with Fe, ( c m Disc 2.99 ibid Cu with Fe, (ci-) Disc 3.02 Episkoposyan (1964) Ag with Zn, (CN-) Disc 3.05 Kakovskii and Shcherbakov (1967) Au with Zn, (CN") Disc 3.05 ibid Ag with Cu, (eiof) Cylinder 5.0±0.5 von Hahn and Ingraham (1967) Ag with Cu ( c m Cylinder 5 .0±0.5 ibid Pd with Cu, (CLO if ) Cylinder 7.4(pH = 3) ibid (1966) 9•5(pH » 1) Cd with Zn, (SOjf) Cylinder 4.7 Ingraham and }±0.8 Kerby (1969) Disc 4.0 Cu with Fe, ( S O f ) Suspended 5 .0±0 .71 Nadkarni and plates Wadsworth (1967) *Except for the suspended plates of Nadkarni and Wadsworth with which a separate agitator was used, the geometry refers to the shape of the exposed precipitant rotated in the solution under study. After Strickland and Lav/son (27>28). T 1397 75 APPENDIX IV - Least-square computer program for fitting an expression of the type: log (C/C0 ) = - kt. 18 DIM X C108) i Y ( l 00 > 20 READ N* A* V 38 LET SI= S2=0 48 FOR 1=1 TO N 58 READ C 68 LET Y=L06CC> 78 NEXT I 88 FOR 1=1 TO N 90 READ T 100 LET XCI> = -T 110 LET S1=S1+ READY T 1397 APPENDIX V - Least-square computer program for fitting an expression of the type: log(C/C0 ) =» -kt+b. 10 DIM XC100)*YC100>*F<100> 23 READ SI * V*N 30 LET A-0 43 FOR M=1 TO N 59 READ 60 LET A=A+XCM> 70 NEXT M 80 LET B=0 90 FOR M = 1 TO N 130 READ F( M) 110 LET Y( M) =LOGC F< M )) 120 LET S=B+Y(M> 130 NEXT M 140 LET C=0 150 FOR M=1 TO N 160 LET C=C+X READY T 1397 APPENDIX VI - Computer program for the calculation of the hydrodynamic and diffusion boundary layer thicknesses LIST DISC 15:.59 24-MAR- ,71 10 READ V,D 20 PRINT "CALCULATION OF THE THICKNESS OF THE HYDRODYNAMIC' 30 PRINT "AND MASS TRANSFER BOUNDARY LAYERS AS FUNCTIONS 40 PRINT "OF THE ROTATIONAL SPEED" 50 PRINT ****«■#•• 60 PRINT 70' PRINT 80 PRINT NOMENCLATURE: 90 PRINT 100 PRINT " , " ROTATIONAL SPEED (RAD./SEC) 110 PRINT ","N=ROTATIONAL SPEED CR.P.M.)”p. 120 PRINT ","D1=HYDR0DYNAMIC BOUNDARY LAYER THICKNESS CCM)" 130 PRINT ","D2=MASS TRANSFER BOUNDARY LAYER THICKNESS (CM) 140 PRINT ","D=DIFFUSIVITY= 0*0000073 CM2/SEC" 150 PRINT ”,"V=KINEMATIC VISCOSITY* 0.008937 CM2/SEC" 160 PRINT 170 PRINT 180 PRINT 190 PRINT "ROTATIONAL","HYDRODYMAMIC","MASS TRANSFER" 200 PRINT "SPEED ” BOUNDARY. ","BOUNDARY 210 PRINT "CR.P.M.) " ", "LAYER CCM>_ "LAYER CCM) 220 PRINT 230 LET M=0 240 LET N=N+50 250 LET vv«N*3. 14159/30 260 LET Dl'=2.8*SQRCV/W> 270 LET D2=0.5*C CD/V)~< 1/3>)*D1 280 PRINT N,D1,D2 2901F N > 1000 THEN 999 300 GO TO 240 310 DATA 0*008937,0.0000073 999 END READY 78 T 1397 APPENDIX VI - (Continued) CALCULATION OF THE THICKNESS OF THE HYDRODYNAMIC ’\':D MASS TRANSFER BOUNDARY LAYERS AS FUNCTIONS OF THE ROTATIONAL SPEED v- x- •:> -x- -x- *> *> -x- * -x- -x- * -x- -x- *» -x- -x- -x- -x- -x- -x- -X- -x- -x- x- x- -s * -x- -x- -s -x- x- Iv= ROTATIONAL SPEED CRAD./SEC) N=ROTATIONAL SPEED CR*P*M.) 9 D1=* HYDRODYMAMIC•BOUNDARY LAYER THICKNESS (CM> D2=MASS TRANSFER BOUNDARY LAYER THICKNESS CCM) D=DIFFUSIVITY= 0*00000 73 CM2/SEC V=KINEMATIC VISCOSITY= 0*008937 CM2/SEC HO TATIOM.AL HYDRODYMAMIC MASS TRANSFER SPEED BOUNDARY BOUNDARY CR -'2 • ) LAYER CCM) LAYER CCM) Jc nV C *115679 5*40674 E-3 100 8 *17975 E- 2 3*82314 E-3 1 50 6 * 67873 E-2 0*00312158. 200 5*78395 E-2 2*70337 E-3 2 30 5*17333 E-2 2*41797 E-3 2 0 0 A*.722 58 E-2 0*00220729 350 4*37226 E-2 2*04355 E-3 400 4*08987 E-2 1*91157 E-3 A 50 3*85597 E-2 1*30225 E-3 500 3*65809 E-2 1*709 76 E-3 550 3*437.86 E-2 1*63019 E-3 '00 3*33937 E-2 0*00156079 C 50 3*20836 E-2 1*49956 E-3 700 0*0309165 1*44501 E-3 750 2*98682 E-2 1*39601 E-3 f- r* f ? 2*89198 E-2 1*35168 E-3 >50 2*80563 E-2 1*31133 E-3 9 p 9 2* 72658 E-2 1*27438 E-3 9 5 0 2*65386 E-2 1*24039 E-3 • 0 0 0 2*58666 E-2 1*20898 -E-3 ' 0 50 2* 52432 E-2 1*17985 E-3 THE*C* 6 8 SECS* T 1397 APPENDIX VII - Full experimental data for the tests where the temperature was varied. Initial Cu++ concentration in solution: 50 ppm. Initial Cu++ Concentration: 50 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min.) Concentration c/c0 0 49.96 1 2 49.96 1 10 49.41 0.989 20 49.01 0.981 30 48.26 0.966 40 45.96 0.920 50 42.66 0.854 60 41.02 0.821 120 28.88 0.578 180 20.68 0.414 240 16.44 0.329 300 12.49 0.250 360 9.74 0.195 fitted line equations: first period: ln(C/CQ ) = -0.970657 x 10-^ t enhanced period: ln(C/CQ) = 5.36927 x 10“2 -4.80546 x 10~3 t T 1397 80 Initial Cu++ Concentration: 50 ppm Temperature: 30°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min.) Concentration C/C0 0 49.59 1 5 49.39 0.996 10 49.09 0.989 20 47.48 0.957 30 45.96 0.927 40 41.63 0.839 50 40.12 0.809 60 37.80 0.762 120 29.33 0.591 180 27.62 0.557 240 14.51 0.293 300 9.47 0.191 360 7.06 0.142 fitted line equations: first period: ln(C/CQ) = -1.0452 x 10“ ^ t enhanced period: ln(C/CQ) = 0.152388 - 5.72208 x 10"^ t T 1397 Initial Cu++ Concentration: 50 ppm Temperature: 35°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min.) Concentration c/c0 0 50.82 1 5 50.67 0.997 10 50.21 0.988 20 48.94 0.963 30 45.23 0.890 40 42.69 0.840 50 38.62 0.760 60 37.61 0.740 120 32.83 0.646 180 25.66 0.505 240 24.44 0.481 300 21.55 0.424 line equations first period: ln(C/CQ) = -1.70274 x 10“3 t enhanced period: ln(C/CQ ) =» 6.69141 x 10~2 - 6.33759 x 10“ ^ T 1397 82 Initial Cu++ Concentration: 50 ppm Temperature: 40°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ \ O O (min.) Concentration O 0 50.22 1 5 50.22 1 10 49.32 0.982 20 44.95 0.895 30 41.43 0.825 40 37.76 0.752 50 34.90 0.695 62 34.10 0.679 120 25.01 0.498 180 21.54 0.429 242 16.72 0.333 301 12.86 0.256 fitted line equations: first period: ln(C/C0) » -1.45312 x 10“3 t enhanced period: ln(C/CQ) = 1.00866 x 1Q~^ - 6.87643 x 10*“3 t T 1397 83 APPENDIX VIII - Full Experimental Data for the Tests Where the Temperature was Varied. Initial Cu++ Concentration in Solution: 500 ppm. Initial Cu++ Concentration: 500. ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Argon n ++ Time Cu (min.) Concentration C/CQ 0 499*68 1 1 499.68 1 10 487.19 0.975 20 471.19 0.943 30 460.21 0.921 40 435.72 0.872 50 419.73 0.840 60 410.24 0.821 120 347.78 0.696 180 300.81 0.602 240 307.80 0.516 300 206.38 0.413 360 143.9 0.288 fitted line equations first enhanced period: ln(C/C0 ) = 2.85629 x 10~2 - 2.66619 X- 10~3 t second enhanced period: ln(C/CQ) * 0.918127 - 6.00812 x 10“3 t T 1397 Initial Cu++ Concentration: 500 ppm Temperature: 30°C Rotation Speed: 600 rpm At mo s phe re: Argon Time Cu++ (min.) Concentration c/cQ 0 50.0 1 5 48.0 0.97 10 48.0 0.96 20 47.0 0.94 30 45.0 0.90 40 43.O 0.86 50 41.0 0.82 60 39.5 0.79 120 33.0 0.66 180 28.5 0.57 240 21.0 0.42 300 13.0 0.26 360 7.5 0.15 fitted line equations first enhanced period: ln(C/CQ ) - 1.4337*1 x 10“2 - 3.38212 x 10-3 t second enhanced period: ln(C/CQ) = 1.40316 - 9.16744 x 10“3 t T 1397 85 Initial Cu++ Concentration: 500 rpm Temperature: 35°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min.) Concentration C/CQ 0 50 1 10 48 0.96 20 45 0.90 30 42 0.84 40 41 0.82 52 40 0.80 60 39 0.78 120 26 0.52 180 17 0.34 240 9.7 0.194 300 4.3 0.086 361 2.1 0.042 fitted line equations: first enhanced period: ln(C/C0) = 0.169949 - 6.91957 x 10"3 t second enhanced period: ln(C/CQ) = 1.37619 - 12.6437 x 10"3 t T 1397 Initial Cu++ Concentration: 500 ppm Temperature: 4Q°C Rotation Speed: 600 rpm Atmosphere: Argon ++ Time Cu (min.) Concentration c/c0 0 50.0 1 5 48.0 0.96 10 47.0 0.94 20 45.4 0.91 30 43.0 0.86 40 39.0 0.78 50 36.0 0.72 60 33.5 0.67 xt O O 120 20.0 • 180 8.9 0.178 240 3.3 0.066 300 1.4 0.028 360 0.6 0.0120 fitted line equations first enhanced period: ln(C/C0) = 3.521)76 x 10~2 - 7.12351 x 10-3 t second enhanced period: ln(C/C0) = 0.873326 - 14.7712 x 10-3 t T 1397 87 APPENDIX IX - Pull Experimental Data for the Tests Where the Rotational Speed was Varied. Initial Cu++ Concentration in Solution: 50 ppm. Initial Cu++ Concentration: 50 ppm Temperature: 25°C Rotation Speed: 300 rpm Atmosphere: Argon ++ Time Cu (min.) Concentration 0/CQ 0 50.12 1 10 49.87 0.995 20 49.47 0.987 31 47.76 0.953 41 46.51 0.928 50 44.41 0.886 60 43.60 0.870 120 35.63 0.711 180 24.96 0.498 240 23.05 0.460 300 18.59 0.371 360 15.29 0.305 fitted line equations first period: ln(C/0o) = - 6.23661 x 10-1) t enhanced period: ln(C/C„) = 3.83026 x 10“2 - 3.46252 x 10“3 t T 1397 Initial Cu++ Concentration: 50 ppm Temperat ure: 2 5°C Rotation Speed: 450 rpm Atmosphere: Argon Time Cu++ (min*) Concentration C/C0 0 50.17 1 5 49.92 0.995 10 49.51 0.987 20 49.50 0.986 31 48.80 0.973 40 48.50 0.966 50 47.92 0.955 60 41.89 0.835 120 33.01 0.658 180 24.98 0.498 240 20.12 0.401 300 14.40 0.287 360 12.29 0.245 fitted line equations first period: ln(C/CQ) = -8.90128 x 10-4 enhanced period: In(C/C0) = 7.29019 x 10“2 - 4.20794 x 10-3 T 1397 89 ++ Initial Cu Concentration: 50 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min.) Concentration C/C0 0 49.96 1 2 49.96 1 10 49.41 0.989 20 49.01 0.981 30 48.26 0.966 40 45.96 0.920 50 42.66 0.854 60 41.02 0.821 120 28.88 0.578 180 20.68 0.414 240 16.44 0.329 300 12.49 0.250 360 9.74 0.195 fitted line equations: first period: ln(C/C0) = -9.70657 x 10-1* t enhanced period: ln(C/C0) = 5.36927 x 10"2 - 4.80546 : io~3 t T 1397 90 Initial Cu++ Concentration: 50 Temperature: 25°C Rotation Speed: 750 rpm Atmosphere: Argon Time Cu++ (min*) Concentr; C/CQ 0 50.66 1 5 50.49 0.996 10 50.05 0.988 21 49.17 0.971 31 46.29 0.914 40 44.71 0.882 50 41.47 0.819 60 39.72 0.784 120 26.77 0.528 180 18.55 0.366 240 13.56 0.268 300 8.84 0.175 360 6.65 0.132 fitted line equations first period: In(C/C0) = -1.35766 x 10" enhanced period: ln(C/CQ) = 9.45992 x 10~2 - 5.97991 x 10"3 t T 1397 91 APPENDIX X - Pull Experimental Data for the Tests Where the Rotational Speed was Varied. Initial Cu++ Concentration in Solution: 500 ppm. Initial Cu++ Concentration: 500 ppm Tempe rat ure: 2 5°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min.) Concentration c/c0 0 499.68 1 1 499.68 1 10 487.19 0.975 20 471.19 0.943 30 .460.21 0.921 40 435.72 0.872 50 419.73 0.840 60 410.24 0.821 120 347.78 0.696 180 300.81 0.602 240 307.80 0.516 300 206.38 0.413 360 143.90 0.288 line equations first enhanced iod: ln(C/CQ) » 2.85c25 x 10-2 - 2. 66615 x 10~3 second enhanced period: m ( c / c 0 ) » 0.918127 - 6.00812 x 10“ 3 t T 1397 92 Initial Cu++ Concentration: 500 ppm Temperature: 25°C Rotation Speed: 750 rpm Atmosphere: Argon -t.4> Time Cu (min.) Concentration c/c0 0 498.33 1 5 498.33 1 10 493-73 0.991 20 489.13 0.981 30 479.93 0.963 41 475.33 0.954 50 472.27 0.948 60 461.53 0.926 120 432.40 0.867 180 415.54 0.834 240 400.20 0.802 300 387.53 0.778 360 381.80 0.766 fitted line equations first enhanced period: ln(C/CD) = 4.36875 x 10"3 - 1.04390 x 10-3 t slow down period: ln(C/C0) = -0.129612 - 3.86828 x 10 t T 1397 93 APPENDIX XI - Full Experimental Data for the Tests Where the Initial Cu++ Concentration in Solution was Varied, Initial Cu++ Concentration: 25 ppm Temperature: 25°C Rotation Speed: 600 rpra Atmosphere: Argon Time Cu++ (min.) Concentration C/CQ 1 25.10 1 16 24.67 0.983 30 24.40 0.972 40* 24.04 0.958 50 23.10 0.920 60 22.51 0.897 120 17.81 0.710 180 12.88 0.513 240 10.32 0.411 300 7.91 0.315 360 6.02 0.240 fitted line equation enhanced period: m(c/c0) = 0.165932 - 4.42638 x io“3 t T 1397 94 Initial Cu++ Concentration: 50 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu (min) Concentration C/Cq 0 49.96 1 2 49.96 1 10 49.41 0.989 20 49.01 0.981 30 48.26 0.966 40 45.96 0.920 50 42.66 0.854 60 41.02 0.821 120 28.88 0.578 180 20.68 0.414 240 16.44 0.329 300 12.49 0.250 360 9.74 0.195 fitted line equation enhanced period: In (C/C0) = 5.36927 x 10“2 - .80546 x 10-3 t T 1397 95 Initial Cu++ Concentration: 100 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ min.) Concentration c/cQ 0 202.10 1 1 197.72 0.978 14 196.62 0.973 22 191.14 0.946 30 186.02 0.920 40 183.47 0.908 50 183.47 0.908 60 173.59 0.859 120 112.19 0.555 180 66.15 0.327 240 36.18 0.179 360 13.16 0.065 fitted line equation: enhanced period: In (C/C0 ) = 0.1(79111 - 8.971(18 x 10-3 t T 1397 96 Initial Cu++ Concentration: 200 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmo sphe re: Argon ++ Time Cu (min.) Concentration c/c0 0 207.29 1 1 207.29 1 10 200.96 0.969 20 199.24 0.961 30 181.41 0.875 40 174.22 0.840 50 168.18 0.811 60 162.44 0.783 120 120.75 0.582 180 90.56 0.437 240 59.80 0.288 300 28.75 0.139 360 11.79 0.057 fitted line equations first enhanced period: In (C/C0) = 2.67433 x 1CT2 - 4.73619 x 10" 3 t second enhanced period: In (C/C0) « 2.02598 - 1.35139 x 10-2 t T 1397 97 Initial Cu++ Concentration: 500 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min.) Concentration c/c0 0 499.68 1 1 499.68 1 10 487.19 0.975 20 471.19 0.943 30 460.21 0.921 40 435.72 0.872 50 419.73 0.840 60 410.24 0.821 120 347.78 0.696 180 300.81 0.602 240 307.80 0.516 300 206.38 0.413 360 143.9 0.288 fitted line equations first enhanced period: In (C/CQ) = 2.85625 x 10-2 - 2.66619 x 10“3 t second enhanced period: In (C/C0 ) = 0.918127 - 6.00812 x 10-3 t T 1397 98 Initial Cu++ Concentration: 800 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min.) Concentration C/C o 0 807.917 1 2 806.46 0.998 10 802.08 0.993 20 784.59 0.971 30 775.83 0.960 40 762.71 0.944 50 749.58 0.928 60 733.54 0.908 120 675.21 0.836 180 672.29 0.832 240 663.54 0.821 300 654.79 0.810 360 650.42 0.805 line equations enhanced period: In (C/C0) = 7.74061 x 10-3 - 1.68916 x 10-3 slow down period In (C/C0) = -0.156995 - 1.69008 x 10"■4 t T 1397 Initial Cu++ Concentration: 1000 ppm Temp e rat ure: 2 5 °C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min.) Concentration C/C0 0 1035.14 1 0.16 1035.14 1 10 1016.98 0.982 20 977.35 0.944 30 965-79 0.933 40 960.85 0.928 50 952.59 0.920 60 944.33 0.912 120 899.76 0.869 180 — — 240 888.20 0.858 300 888.20 0.858 360 888.20 0.858 Note: almost all points fell on the theoretical Levich line before blinding occurred. See Figure 14. T 1397 100 APPENDIX XII - Pull Experimental Data for the Tests Where the Atmosphere in the Reactor was Varied, ,4 Initial Cu++ Concentration: 50 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Argon Time Cu++ (min,) Concentration c/c0 0 49.96 1 2 49.96 1 10 49.41 0.989 20 49.01 0.981 30 48.26 0.966 40 45.96 0.920 50 42.66 0.854 60 41.02 0.821 120 28.88 0.578 180 20.68 0.414 240 16.44 0.329 300 12.49 0.250 360 9.74 0.195 T 1397 101 Initial Cu++ Concentration: 50 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Air Time Cu++ Iron (min •) Concentration C/C0 Concentration 0 49.917 1 5 48.751 0.976 10 48.50 0.971 0.73 2.0 47.67 0.955 1.70 30 46.33 0.928 2.93 40 44.08 0.883 7.32 50 42.17 0.844 8.54 60 41.25 0.826 10.73 120 31.42 0.625 19.99 180 25.08 0.502 27.80 240 21.50 0.431 31.95 300 19.25 0.385 37.07 360 18.50 0.371 38.04 T 1397 102 Initial Cu++ Concentration: 50 ppm Temperature: 25°C Rotation Speed: 600 rpm Atmosphere: Oxygen Time Cu++ Iron (min.) Concentration c/c0 Concentration 0 51.33 1 5 51.08 0.995 10 51.08 0.995 0.25 20 50.75 0.988 0.25 30 50.33 0.980 0.50 40 50.17 0.977 0.75 50 50.00 0.974 0.75 60 50.17 •0.977 1.0 120 43.67 0.8506 7.25 180 34.58 0.674 16.5 240 25.58 0.576 20.5 300 26.08 0.508 24.25 360 21.75 0.424 28.75 T 1397 103 APPENDIX XIII - Calculation of Solution Potentials, In the electrolysis of water the following reactions take place: cathode reaction: H2 I- 2H+ + 2e“ (36) for which the potential is given by^®). E = 0.0 - 0.0591 PH - 0.0295 log p h 2 (37) anode reaction: 2H20 02 + 4H+ + lie" (38) for which the potential is expressed b y ^ : E = 1.228 - 0.0591 pH + 0.0147 log Pq 2 (39) At the pH of the experiments (pH 4.5)> equation (39) gives: for pn = 1 atm -*• E = O.962 v 2 for Pq 2 * 0.21 atm + E a 0.952 v The Eh-pH diagram for the Cu-0 system (Fig. 23) shows the stability regions for Cu, Cu++, Cu20, and CuO0 whiwhich are determined by the following stability boundaries (36). 1. Cu++ + H20 = CuO + 2H+ (40) log Cu++ - 7.89 - 2 pH (41) T 1397 104 2. Cu = Cu++ + 2e~ (42) E2 = 0.337 + 0.0295 log Cu++ (43) 3. Cu20 + H20 = 2CuO + 2H+ + 2e~ (44) E 3 = 0.669 - 0.0591 pH (45) 4. 2Cu + H20 = Cu20 + 2H+ + 2e~ (46) Ej, = 0.471 - 0.0591 pH (47) 5. Cu20 + 2H+ = 2Cu++ + H20 + 2e“ (48) E 5 = 0.203 + 0.0591 pH + 0.0591 log Cu++ (49) Figure 23 has been drawn using these equations for a copper concentration of 50 ppm. A' reduction in the copper concentration shifts the positions of the lines down and to the right. T 1397 105 APPENDIX XIII - (Continued) 10 READ C*P5*P 6 20 LET C l=C /C 1 0 0 0 *6 3 .54> 30 LET L l= C L O G (C l))/2 .3 0 3 43 LET P l= C L l-7 .8 9 > /< -2 > 50 PRINT **PH FOR 1 IS".?" "5P1 60 PRINT 70 LET E2=3.337+0.0295*L1 80 PRINT "E2 IS”;” E2 90 PRINT 100 LET E3=0* 6 6 9 -0 .8591*P 5 110 LET E = 0.6 9 9 -0 .0591*P6 126 PRINT ” E3*S "PH" 130 PRINT E3* P5 140 PRINT E*P6 150 PRINT 160 LET E 4=0.4 7 1 -0 .0591*P5 170 LET E = 0 .4 7 1 -0 .659 I*P 6 180 PRINT "E4"*"PH" 190 PRINT E4*P5 200 PRINT E*P 6 210 PRINT 220 LET E5=0.203+C0.3591*P5)+(0.0591*Ll) 230 LET E=E5 + 0 .0 5 9 1 *(P6-P5> 240 PRINT "E5"*"PH" 250 PRINT E5..P5 260 PRINT E* P 6 270 DATA 50*2*6 280 END READY RUN POR 10: 32 2 5 - MAY** 71 PH FOR 1 IS 5.49676 E2 IS 0.245446 E3 PH 0.5508 2 0. 3444 6 E4 PH 0.3528 2 0 .1 1 6 4 6 E5 PH 0.137782 2 0.374182 6 TIME: 0.20 SECS READY T 1397 106 BIBLIOGRAPHY 1. Levich, V. G., Physicochemical Hydrodynamics: Prentice Hall, Inc., N.J. (1962). 2. Grenwood, C. C., Underground leaching at Cananea: Eng. Min. Jour., v. 121, p. 518-21 (1926). 3. Jacobi, J. S., The recovery of copper from dilute process streams: Conf. Met. Soc. AIME, v. 24, p. 617-644 (1963). 4. Wartman, P. 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