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Effect of strain on corrosion rates of copper in sulfuric acid solutions Johnston, Hugh Alex 1955

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EFFECT OF STRAIN ON CORROSION RATES OF COPPER IN SULFURIC ACID SOLUTIONS by HUGH ALEX JOHNSTON A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE IN CHEMICAL ENGINEERING in the Department of CHEMICAL ENGINEERING We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE Members of the Department of Chemical Engineering THE UNIVERSITY OF BRITISH COLUMBIA September 1955 i i ABSTRACT The corrosion rate of copper i n deaerated aqueous, sulfurie-.acid solutions, with regard to the e f f e c t of s t r a i n , temperature and e l e c t r o l y t e concentration was studied.' Copper i n the form of wire was subjected t o applied stresses of 172S, $640, and 17,230 pounds per square inch. Five temperatures i n the range 15°C to 75°C. were investigated f o r e l e c t r o l y t e concentrations of 0.1, 0.5 and 1.0 molar s u l f u r i c a c i d . The rate of corrosion was followed by noting the rate of copper uptake by the solution through a polarographic analysis run p e r i o d i c a l l y f o r up to 30 hours. Reproducible r e s u l t s were obtained, i t was found that: 1. The rate of reaction f o r the d i s s o l u t i o n of copper i n s u l f u r i c acid was f i r s t order with respect to cupric ion concentration. 2. E x p e r i m e n t a l l y , the reaction rate was pseudo-first order with respect to hydrogen ion a c t i v i t y . 3. Stress, i n general, increased the reaction rate s l i g h t l y , the e f f e c t becoming less at higher temperatures. 4. The a c t i v a t i o n energy f o r unstressed corrosion was 10.6 Kcal. f o r the temperature range 1 5 - 7 5 degrees. 5. For 1.0M and 0.5M acid solutions, stress decreased the a c t i v a t i o n energy and hence increased the reaction rate. 6. • The average increase i n reaction rate f o r 10 degree changes i n temperature between 15 and 75 degrees was about 1.5. 7. A d i f f u s i o n controlled mechanism could be proposed f o r the d i s s o l u t i o n of copper i n s u l f u r i c acid solutions. ACKNOWLEDGMENT The author i s s i n c e r e l y indebted to Dr. L. W. Shemilt and othe r members of the Dep-artment o f Chemical E n g i n e e r i n g f o r t h e i r h e l p -f u l guidance and encouragement, to the N a t i o n a l Research C o u n c i l f o r t h e i r f i n a n c i a l a s s i s t a n c e , and to Standard O i l of C a l i f o r n i a L i m i t e d f o r the f e l l o w s h i p h e l d d u r i n g the yea r 195>l|-55* i v TABLE OF CONTENTS Page Acknowledgement i Abstract i i Table of Contents iv List of Illustrations v i List of Tables . v i i i I INTRODUCTION 1 II PREVIOUS INVESTIGATIONS k III THEORETICAL DISCUSSION . . . 10 A. ELECTROCHEMICAL CORROSION 10 B. EFFECT OF STRESS 13 IV APPARATUS AND MATERIALS 16 A. APPARATUS 1 6 1. Polarograph 16 2 . Constant Temperature Bath 16 3 . Test Cells 17 B. MATERIALS l Q 1. Purification of Mercury 18 2 . Nitrogen Purification 1,9 3 . Preparation of Solutions 2'0 (a) Sulfuric Acid Solution 20 (b) Solutions for calibra-tion Curves 20 (c) Agar-Agar Solutions 2j-h. Copper Wire 2 1 . TABLE OF CONTENTS (Continued) Page V EXPERIMENTAL PROCEDURE 22 A. TREATMENT OF WIRE. 22 B. POSITIONING OF WIRE 22 C. EXPERIMENTAL 22 D. VARIABLES 2I4. 1. Temperature 21). 2. Oxygen C o n c e n t r a t i o n i n C e l l 2l|_ 3. S t r e s s 25 k.. A g i t a t i o n 26 5>. S o l u t i o n C o n c e n t r a t i o n s 26 VI EXPERIMENTAL RESULTS 27 A. EFFECT OF TEMPERATURE 28 B. EFFECT OF CONCENTRATION 30 C. EFFECT OF STRESS 30 VII DISCUSSION OF RESULTS 31 A. RATE DEPENDENCE 31 B. POSITIVE INTERCEPT 33 C. EFFECT OF STRESS 3^ D. EFFECT OF TEMPERATURE ~ ACTIVATION ENERGY 35 V I I I SUMMARY 38 IX BIBLIOGRAPHY 39 X APPENDIX I EXPERIMENTAL DATA k-3 XI APPENDIX I I POLAROGRAPHY 1 0 9 v i LIST OF ILLUSTRATIONS Figure Page 1. Constant Temperature Bath . l 6 a 2. Test Ce l l 17 a 3 . Photographs of Experiment Arrangement . . . 18a k. Nitrogen Purification 20a 5 . Effect of Temperature 28a 6. Effect of Temperature on Reaction Rates for 1.0M Sulfuric Acid 29a 7 . Effect of Temperature on Reaction Rates for 0.5M Sulfuric Acid 29b 8 . Effect of Temperature on Reaction Rates for 0.1M Sulfuric Acid 29c 9. Effect of Concentration . . 30a 10. Effect of Hydrogen Ion Activity on Reaction Rates for 10 Kgm Stress 30b 11. Effect of Hydrogen Ion Activity on Reaction Rates for 5 Kgm Stress 30c 12. Effect of Hydrogen Ion Activity on Reaction Rates for 1 Kgm Stress 30d 1 3 . Effect of Stress for 1.0M Sulfuric Acid . . 30e l*f. Effect of Stress for 0.5M Sulfuric Acid . . 3 0 f 15. Effect of Stress for 0.1M Sulfuric Acid . . 30g 16. Effect of Stress on Reaction Rates for 1.0M Sulfuric Acid . . 30h 17. Effect of Stress on Reaction Rates for 0.5M Sulfuric Acid 3 0 i 18. Effect of Stress on Reaction Rates for 0.1M' Sulfuric Acid 3 0j 19-27. Experimental Data for 15 degrees Centigrade 63-71 v i i LIST OF ILLUSTRATIONS (Continued) Figure Page 28 - 36 Experimental Data for 25 degrees Centigrade 72-80 37 - !+5 Experimental Data for 35 degrees Centigrade . 81 -89 k6 - $h Experimental Data for 55 degrees Centigrade 9 0 - 9 8 55 - 63 Experimental Data for 75 degrees Centigrade 99-107 6*4- Experimental Data for 50 hours . . . . 108 65 Experimental Polarogram of the Reduction of Copper in Sulfuric Acid Showing Method of Calculation 113 66 Calibration Curves for Polarographic Readings versus Copper Concentration • 117 67 Effect of Temperature on Calibration Curve - Capillary A 118 68 Effect of Temperature on Calibration Curve - Capillary B 119 v i i i LIST OF TABLES Page 1. Influence of Acid Concentration on Corrosion of Copper in Unaerated Sulfuric Acid Sol-utions 5 2. Reaction Rate -K Versus Temperature for Various Stresses and Sulfuric Acid Concentrations . . . 28 3. Values of the Constants i n the Equation -K E 29 k » Ae T ; K = R: k. Average Increase in Reaction Rate for 10 Degree Rise in Temperature 29 5. Effect of Temperature on Activity Coefficients for Sulfuric Acid 30 6. List of Experimental Runs . . . . kh 7. Time of Immersion Versus Cupric Ion Concentra-tion for #18 B&S Soft Copper Wire at 1?± 0„2°C . kl 8. Time of Immersion Versus Cupric Ion Concentra-tion for #18 B<SS Soft Copper wire at 25 t 0.2°C . k9 9. Time of Immersion Versus Cupric Ion Concentra-tion for #18 B&S Soft Copper Wire at 35 1 0.2°C . 52 10. Time of Immersion Versus Cupric Ion Concentra-tion for #18 BcSS Soft Copper Wire at 55 -0.2°C . 5o 11. Time of Immersion Versus Cupric Ion Concentra- , tion for #18 B &S Scft Copper Wire at 75 ±0.2°C . oO 12. Time of Immersion Versus Cupric Ion Concentra-tion for #18 B<&3 Soft Copper Wire at 15 i G.2°C for 50 Hours . 62 13. Data for Polarographic Calibration Curves . . . 115 1 IHTRCDTJCTIGN The engineering need for information of the relative durability of metallic materials has led to widespread use of corrosion tests. These vary widely in character from exposure for prolonged periods to the actual environments in which the metals are to be used to laboratory tests of great variety. Such tests, while of considerable assistance in the selection of suitable materials for given purposes, have not generally furnished sufficient Information as to the processes of corrosion to permit prediction as to what will happen under slightly different conditions. The relatively long period of time required to obtain measure-able results under natural conditions led to the development of accelerated corrosion tests in which the reaction rates are accelerated by modifying the natural environment. However the results of these tests are sometimes difficult to correlate to natural conditions, and usually the mechanism of the corrosion process is uninterpretable. One of the more recent trends in corrosion investigation has been the study of corrosion processes with experimental techniques of sufficient sensitivity to measure the actual reaction rates occurring in natural en-vironments. In this way significant information can be obtained in a reasonable time without the danger of distortion introduced by accelerating the corrosion process. Burns (A) in 1931 was the first to point oat the possibility of using the polarograph to follow corrosion rates. Later van Rysselberghe (A3) successfully designed apparatus capable of following the corrosion rate by measuring the consumption of oxygen as the reaction proceeded. No published papers have used the polarograph to directly follow the increase in metal ion concentration with time, although considerable 2 unpublished work has been conducted at this university. This investigation used the polarograph to follow directly the corrosion of copper i n sulfuric acid solutions* A c e l l was designed (Fig«2) so that polarograms could be taken during the course of the corrosion pro-cess* An extensive search of the literature concerning the corrosion of copper i n sulfuric acid solutions has shown only sparse data that are directs l y interpretable i n terms of mechanism* The majority of the data available for the corrosion rates of copper i n sulfuric acid solutions are based on metal weight loss divided by the time of the corrosion run (8,42,3)* Often no attempts are made to deter-mine the effect of time as a variable, hence the rate constants so determined may be time independent* Such rate constants are very d i f f i c u l t to apply and the prediction of copper corrosion rates i n sulfuric acid solutions are there-fore uncertain* More recent investigators (33, 25, 22, 26, 30, 18) have included time as a variable and thus performed a kinetic study of the corrosion process. The above investigators a l l dealt with one or a l l of the following variablessj* time, temperature, acid concentration, agitation, and oxygen concentration. To study the effect of agitation both Lu and Graydon (33) and Glauner (18) used rotating metal specimens* Their results agree to the extent that agita-tion has l i t t l e or no effect on the corrosion rate* However, there seems to be no such agreement i n the published data concerning the exact effect of the other variables. Another variable often encountered i n corrosion processes i s that of applied stress* Until recently the relationship between corrosion and the variables of external and internal stress and resultant strain has been largely neglected* Early investigators of stress corrosion have found seemingly different and conflicting results ( l l ) . An excellent discussion concerning the effects of stress on the internal structure and energy characteristics of metals with relationship to t h e i r influence on corrosion reactions has been presented by Harwood (2l)» The object of this investigation was to study the effect of strain on the corrosion rates of copper wires i n stagnant deaerated sulfuric acid solutions* A recording polarograph was used to follow the change of copper concentration with time. Other variables studied were temperature and sulfuric acid concentration (hydrogen ion a c t i v i t y ) , i n an endeavor to understand the mechanism and kinetics of the dissolution of copper i n sulfuric acid. 4 PREVIOUS INVESTIGATIONS In the past few years there has been a number of investigations into the corrosion of copper by sulfuric acid. However, u n t i l quite recently no one has covered the mechanism and kinetics of this reaction. No reference has been found concerning the effect of stress as a variable. However, the general effect of stress has been discussed quite thoroughly by U.R. Evans ( l l ) , Uhlig (56), Harwood (21), Speller (49) and referred to frequently i n the literature. Examination of stress corrosion data gives a confused picture] some authors have found sta t i c stress to increase corrosion, others have found no effect, and s t i l l a few others report a decrease i n corrosion. The effect i n a l l cases seems to be specific both for the metal and for the environment. Usually what* ever effects static stress may have are relatively small (21). It has frequently been stated ( l l ) that the energy stored i n dis-torted metals makes such metals anodic to stress free material, and that as a result galvanic effects may cause rapid corrosion of the distorted metals. Numerous attempts have been made to arrive at this potential difference. Re-sults vary, but i n general indicate that the difference i n potential i s only a few m i l l i v o l t s . This difference i n potential i s too small to have much effect on corrosion and could easily be upset by other factors. The effect of oxygen concentration on the corrosion of copper i n 1.2 normal sulfuric acid solutions was studied by Russell and White (42). The concentration of dissolved oxygen was varied by saturating the acid solutions with atmospheres of differing oxygen content. The acid was saturated with these atmospheres for one hour and then the test piece submerged for from 2 hours to 2 weeks. In a l l cases the corrosion rates were determined from the loss i n weight. From their results the following conclusions were reached:-5 1. The oorrosion of copper i n dilute sulfuric acid i s dependent on the presence of dissolved oxygen or some other oxydizlng agent. 2. The corrosion rates of copper i n dilute sulfuric acid i s d i r e c t l y proportional to the concentration of dissolved oxygen* 3. Oxide-free copper i s not corroded by dilute oxygen-free solutions of t h i s acid. This test method i s useful i n predicting long term corrosion effects. However, i t does not give any indication as to what effect time has on the corrosion process. Because of this the data are of no use i n the prediction of a mechanism or a study of the kinetics involved. The investigation by Damon and Cross (8) was also a weight loss deter-mination after a period of time type of experiment. They were primarily interest-ed i n determining the effect acid concentration had on the corrosion rates of copper. Their results are shown below i n Table 1. TABLE I INFLUENCE OF ACID CONCENTRATION ON CORROSION OF COPPER IN UNAERATED SULFURIC ACID SOLUTIONS H2 S 04 NORMALITY AVERAGE CORROSION RATE Mg/sq.dm / day RjSOfc NORMALITY AVERAGE CORROSION RATE Mg/sq.dm. /day 0.01 26.4 10 9.4 0.1 29.7 12 7.9 0.2 35.4 15 5.5 0.5 33.2 17 4.2 0.7 31.4 20 2.3 1.0 30*5 22 2.1 2.0 25.4 24 2.1 3.5 19.7 26 1.9 5.0 16.6 28 1.7 7.0 12.8 30 2.6 35 5.0 Test runs lasted anywhere from 3 to 7 days. As can be seen the data shows that the wia-H mim corrosion rates come i n solutions at or near 0.2N, This invest!', gation also suffers from the fact that time i s excluded as a variable and hence 6 no insight into the mechanism or kinetics of the process can be obtained* The i n i t i a l corrosion rate of copper i n sulfuric acid solutions were investigated by Brown (3) by following the decrease i n oxygen concentration during the course of the reaction. Their data indicates a fast i n i t i a l period lasting for perhaps 5 minutes followed by a linear region for about the next hour. Since they were ma,inly interested i n studying the differences i n i n i t i a l rates for a large number of metals, their data for copper i n sulfuric acid are limited to one condition. Katz (26) has conducted numerous tests on copper i n very dilute de-aerated aqueous solutions. In his work he followed the change i n copper con-centration with time by withdrawing small samples and analyzing for copper. He arrived at the conclusion that the dissolution of copper i n acid salt solu-tions containing sulfate ion i s a f i r s t order reaction provided oxygen i s absent. The presence of oxygen retards this reaction. He postulates that cupric ions • are depolarized at the cathode and reduced to cuprous ions and the corrosion i s then believed to be cathodically controlled. The work of Hasse (22) was conducted i n dilute unaerated aqueous acid solutions. The results show that the corrosion of copper i s a cathodically controlled process and that this affords an explanation for the increase i n rate of attack with time or copper content of the solution. He postulates that as the copper content of the solution increases, the surface films of oxygen decrease i n thickness by amounts which vary with the nature of the solution. This decrease i s an indication of release from the normal oxygen depolarization process, resulting from an increase i n the rate of discharge of cupric ions to cuprous ions at the cathode. This reaction predominates when high rates of corrosion occur. Glauner (18) used a rotating copper specimen i n his work on copper i n sulfuric acid and found l i t t l e variation i n corrosion rate between 150-350 R.P.M. 7 H i l l (25) has done an extensive study of the corrosion of copper i n aqueous solutions. The data obtained are interpretated i n terms of rate laws during the i n i t i a l (5-60 s e c ) , intermediate (2-10 min.) and long term (10-A0 min.) cor-rosion periods, A mechanism i s proposed to account for the i n i t i a l phase of the corrosion process. The following reaction sequence i s suggested. 2Cu • 0 2 + H* Kj y 2Cu+ + HOjj (l) 2Cu+ • HO2 • 2Cu * 2 > 2Gu20 + H* (2) In reaction ( l ) , the slow step, an oxygen molecule occupies a si t e consisting of a pair of copper atoms, removes two electrons from them, and becomes a per-oxide ion. A proton associates with the peroxide ion at the same time, forming a bi-peroxide ion, H0~. In step 2, a rapid reaction, a pair of electrons from an adjacent pair of copper atoms breaks the oxygen-oxygen bond i n the b i -perioxide ion, allowing each O 3 to associate with a pair of the cuprous ions and releasing the proton to a water molecule i n the solution. They also showed f i r s t order dependence on oxygen for the slow reaction i n the i n i t i a l corrosion process. The rate constant for a period less than 60 seconds was 1.9 x 102 l i t e r mol.'l sec,"^" In the concentration range studied s l i g h t l y lower than f i r s t order dependence on hydrogen ion concentration was observed. For the corrosion interval from 2-10 minutes, the reaction followed the parabolic rate law, the slow step being diffusion of copper ions through the film of corrosion products just formed. For the corrosion interval 10-40 minutes, the reaction rate i s dependent on the logarithm of the corrosion time, suggesting that the slow step i n the reaction i s a function of a process or surface, the nature of which i s i t s e l f changing with time. Lu and Graydon (33) also conducted tests on copper i n aerated sulfuric acid. A l l data were obtained under conditions where the hydrogen ion and Or concentrations were i n great excess. The copper flux was of the order of 5 x 10~5 8 moles per li t e r per hour. The oxygen concentration in the bulk of the solutions was of the order of 2 x 10**^  moles per li t e r and i t was continuously replenished by bubbling. The hydrogen ion concentration in the bulk of the solution was at least 10**3 mole per li t e r and remained constant throughout the corrosion process. From their results the following conclusions were reached: 1. The reaction rate in a l l cases was proportional to the square root of the cupric ion concentration. 2. Variations in R.P.M. over the range 25O-4800 changed the reaction rate less than B percent. 3. The reaction rate in a l l cases was proportional to the square root of the oxygen concentration. 4. Activation energies obtained from a plot of logarithm of reaction rate versus reciprocal of the absolute temperature were about 14 Kcal. They summarized their conclusions In the form of the following equation. -d/Cu/ = K e = ^ T : (Cu* )£ ( K L ) * (3) d + Where lent B copper concentration t = time K - rate constant R z gas constant T s absolute temperature P02 « oxygen pressure in atmosphere in contact with solution. To arrive at equation (3) In and Graydon (33) assumed the following: 1. The cupric ion concentration in the bulk of the solution was assumed to be essentially the same as the cupric ion concentration at the copper solution interface. 2. The cuprous ion, cupric ion equilibrium was assumed to be estab-lished at the interface. 3. The rate of dissolution of copper was assumed to be controlled by the removal of cuprous ions from the interface by a reaction which was f i r s t order with respect to cuprous ion. -d(Cu/) • K (Cui+) (4) dt where the subscript i refers to the copper solution interface, or d(Cu») - K 1(Cb 1 +) (5) dt by assumption (2) d(Cu*) a KnK1 (Cu+)£ (6) dt 1 where Kl n (Cu*l (7) (Culrjs and by assumption (1) dCCu*) • K ( C u ( 8 ) dt To the above equation they add the observed rate dependence on oxygen pressure and calculated value of the activation energy to arrive at equation (3)< Examination of the literature shows there is no agreement as to the mechanism for the dissolution of copper in sulfuric acid. However, Katz (26) and Basse (22) agree that the reaction is cathodically controlled. The order of the reaction is also undecided. Lu and Graydon (33) in aerated solutions show less than first order dependence, Hasse (22) for similar conditions shows greater than first order dependence, and Katz (26) in deaerated solutions, shows first order dependence. Because of these discrepanoses it was decided to study the dissolution of copper in sulfuric acid in an attempt to substantiate the work of the above authors. Due to polarographic limitations the work was conducted in stagnant deaerated solutions. Another important factor studied was the effect of applied stress* 10 THEORETICAL DISCUSSION A, TCTrF.nronCHEMICAL CORROSION The chemical reactions which occur i n the corrosion of metals are often complex and varied. They depend upon the composition, physical state and surface condition of the metallic material, as well as upon the chemical components of the environment, - their phases and concentrations. These reactions are affected by temperature and temperature fluctuations, by the movement or circulation of the electrolyte, by the nature and the s o l u b i l i t y of the corrosion products and particularly by the position i n which solid corrosion products are precipitated with reference to the surface of the corroding metal. Moreover, changes i n con-centration within the electrolyte may occur during the corrosion process. In recent years considerable progress has been made i n the elucidation of corrosion reactions. It has been well established, for example, that corrosion i n the presence of moisture i s an electrolytic process i n which the metal dissolves at certain areas or points, - the anodes of small corrosion cells the cathodes of which are the adjacent areas on the metal surface at which hydro-gen i s deposited. The driving force of these cells arises either from some chemical or physical inhoraogeneity of the metal or environment. Their electro-l y t i c operation i s influenced by the composition, size and distribution of the anodic and cathodic areas, by the character of the corrosion products and by the chemical nature and the conductance of the surrounding environment. The essential step i s that metal ions replace hydrogen ions i n the electrolytic en-vironment. A second step of equal importance i n the process l i e s i n what happens to the electr©deposited hydrogen since the continuation of the attack depends upon i t s disposal. It may be evolved as molecular hydrogen by metallic cathodes of low overvoltage, or i t may be removed by combination with oxygen or other oxidants. In either case, when the corrosion rate depends upon the rate of 11 hydrogen disposal, the process is said to be anodically controlled. In other words, the progress of corrosion may be controlled by the extent of polari-zation at either cathode or anode or at both. Anodic processes i n oorrosion cells consist i n either the dissolution of metal ions or the precipitation of anions at the metal surface. Anodic polar* ization i s most readily observed i n solutions containing strong oxidants or anions which form relatively insoluble salts with the metal. The process of anodic polarization of a metallic surface is a progressive action proceeding from the more anodic to the less anodic region until;the; surface becomes substan» t i a l l y f i l m coated or passivated. By following the change i n electrode potential with time i t i s possible to determine which process controls. If the observed electrode potential becomes more electronegative with time, i t i s indicative of increased cathodic polarization, and the process i s probably cathodically con-> tr o l l e d . If, however, the observed electrode potential becomes more electro-positive or more noble with time, anodic polarization and anodic control of the process i s apparent. (4)» The dissolution of a metal i n a solution containing an oxidant has been found to be usually the result of three consecutive reactions (44) • These are the transport of oxidant to the surface, chemical reaction at the surface and removal of the reaction products from the surface. The slowest of these processes i n general w i l l determine the rate. When the transport of material i s the rate determining step, the process i s termed "diffusion" controlled (44)• Theoretical treatments have been proposed to account for corrosion under con-ditions such that diffusion of electrons, ions or atoms through the surface films i s the rate determining step (59» 36, 12, 38, 9)« The generally accepted c r i t e r i a for diffusion control areas follow (44)• 1, Different solids dissolve at nearly the same rate i n the same reagent under the same conditions, 2, The speed of sti r r i n g has a large effect, the exact nature of which 12 depends on the type of st i r r i n g used, 3. The dissolution fates with a series of reagents are proportional to a fractional power of the diffusion coefficient (about 0,75)• 4* The dissolution rate i s inversly proportional to the viscosity, other factors remaining constant, 5. The temperature coefficients are lower than for homogeneous re-actions, usually between 1,1 and 1.5 per 10 degree rise i n temperature, 6. The dissolution rate increases with increasing concentration of reagent, the curve being linear, 7. The previous treatment of the surface has only a very minor effect i f any. 8. Diffusion controlled rates are generally higher than nondiffusion controlled rates. Non-diffusion controlled reactions have previously been referred to as "chemically" controlled. S t r i c t l y speaking, however, this should refer only to those^cases i n which the rate determining step i s the actual chemical reaction (electron transfer). There has been as yet no clear cut case of true chemical control ( 4 4 ) . Cases where the slowest or rate determining step i s the removal of material from physical contact with the surface should be considered to be under desorption control ( 2 9 ) . The c r i t e r i a for desorption control as l i s t e d by Salzberg (44) are:** 1. Different solids dissolve at different rates i n the same solution under the same conditions. 2. The speed of s t i r r i n g has a slight effect, but not as pro» nounced as i n diffusion control. 3. The dissolution rates should not be dependent on the diffusion coefficients of the reagents. 13 4* The dissolution rate i s independent of viscosity, u n t i l the solution becomes so viscous that the rate of transport i s slower than the rate of desorption. 5. The temperature coefficients are much higher than i n diffusion control being anywhere from 2-4 per 10 degree rise i n temperature* 6. The dissolution rate increases with reagent concentration i n a non-linear fashion, slowly and reaching a maximum, 7. Surface conditions are important, a polished surface giving a higher rate than an unpolished one, 8. Different crystals dissolve at different rates, (20) 9. Desorption controlled rates should i n general be slower than diffusion controlled rates, B. EFFECT OF STRESS In considering the influence of stress upon the corrosion of metals, i t i s desirable to begin with a brief discussion of stress and a description of the effects of stress upon the internal and external structure of the metal* Stress may be defined as the intensity of force reactions that are set up within a body on application of external loads, or by non-uniform dilation of the body. Strain is the change in dimension that accompanies the development of stresses; either elastic or plastic, the lat t e r s t i l l existing after the stress has been relieved, leaving permanent deformation. The deformation or flow behavior when a metal i s externally loaded can be shown on a stress-strain diagram (21), The linear portion of the curve represents elastic deformation, where strain i s proportional to stress. However, above the elastic limit, this proportionality no longer exists, and plastic deformation occurs. The elastic limit, f o r very ductile metals, i s not clearly defined, McKeown and Hudson (34) have measured the stress-strain characteristics of copper, silver and gold and found that copper has no clearly defined elastic 14 limit i n the f u l l y annealed condition. Their results show for copper that stress and strain are not completely proportional i n the elastic region of the curve. When a metal i s deformed internal changes occur i n the metal. It i s obvious that work i s being done on the metal system, much of which i s dissipated in the form of heat. However, a significant fraction of this work (14)» ranging from 5 to 15 percent i s stored up by the metal as latent energy, thus increasing the energy level of the system. It i s this increase i n internal energy, re-sulting from the strain hardening operation that causes changes i n the physical and chemical behavior of the metal as compared to unstressed metal. The area under the stress-strain curve represents the t o t a l amount of energy introduced into the metal during deformation and has been shown to be as large as 15 calories per gram (21). Plastic deformation is generally accompanied by an increase i n strength and a decrease i n d u c t i l i t y . In addition, atomic, crystallographic and micro-structural changes may occur, as a result of deformation. The process of plastic deformation involves such disturbances as s l i p , twinning, warping of crystal planes, rotation and elongation of grains, orientation effects, and a general breakdown of the crystal structure into highly disorganized states. The extent i s dependent upon the magiitude of strain, the strain rate, grain orientation and the temperature at which deformation occurs (2). As a consequence, plastic de-formation i s essentially a non-homogeneous operation, not only from a microscopic point of view, but on a macroscopic scale as well. As indicated earlier, plastic deformation of metals tends to increase their internal energy, and this increase should be manifest i n a greater free energy change. From the following relation proposed by Gibbs (2) -A F • -nfE (9) 15 where A F - the change in the free energy of the system f a Faraday constant n a number of electrons involved E s Electrode potential this should result in a change in the reducible electrode potential. Calculations have shown that within the elastic limit, the effect of stress on the free energy change is very small and would therefore not have much influence upon the cor-rosion reaction. The above equation cannot be used in the plastic region because the process is not reversible, therefore no simple thermodynamic relation can predict the effect of strain in this region. So far we have considered stress and corrosion separately, now let us consider what happens when a metal (copper) is immersed in an electrolytic solution (sulfuric acid) and stress is applied. Bengough and May (l ) , Evans (11,13), Basse (23), and Thomas (5) have shown that cuprous oxide film was, in general, formed in aqueous solutions, and that i f this film is stable, i t ex-hibits inhibitive properties, and retards the rate of metal dissolution. It then follows that at the moment of immersion of a copper specimen in an aqueous solution, the surface i s covered with a film of cuprous oxide and i s divided into anodes (at film discontinuities) and into cathodes at the continuous oxide film. When the metal is immersed in a solution and stress is applied the in-ternal energy of the metal increases and the relatively brittle cuprous oxide film is damaged. If the stress is sufficient the film will be ruptured or at least the pore size of the oxide will be increased. The rupture of the film will increase the anodic areas, due to the presence of copper metal, with a resultant increase in corrosion rate. If oxygen is present in the solution the ruptured film w i l l tend to repair itself by forming new oxide layers. As this oxide film grows, provided that diffusion through this oxide layer i s the controlling step, the reaction rate should slow down. 16 APPARATUS AND MATERIALS A. APPARATUS 1. POLAROGRAPH A Sargent Model XXI Visible Recording Polarograph was used through out this investigation. The polarograph had been previously calibrated by Cordingley (7) using a Rubicon type B potentiometer, a voltage divider, a standard c e l l and a portable G.E, Galvanometer, 2. CONSTANT TEMPERATURE WATER BATH The container was a square glass vessel of about 0,4 cubic feet capacity, A 250 watt knife heater supplied the necessary heat to the water. The bath was also equipped with a copper tube c o i l connected to a cold water supply for use at temperatures below room temperature. A variable speed st i r r e r was used to agitate the water. The s t i r r e r was mounted so that vibra-tions, which would influence the drop-time of the dropping mercury electrode, were eliminated. The temperature was controlled with a cenco mercury thermostat con-nected to a Nurnberg two tube relay. Such a thermostat consists of a large mercury reservoir connected to a fine capillary. As the mercury expands up the capillary i t makes contact with a kneedle contact thus closing the c i r c u i t . This type of thermostatic control was found to be effective i n maintaining a constant temperature to within 0^.1° C. A long thermometer graduated from 0 - 200° C i n divisions of 0,2° C and standardized against a platinum resistance thermometer with a Bureau of Standards Certificate was used for temperature measurements. In a l l cases the thermostat was set so that the desired temperature was maintained i n the test c e l l and not i n the constant temperature bath. In this way any cooling or heating effects accompanying the transport of water to the test c e l l were eliminated. a v O r-J W A T E R F R O M T E S T C E L L ' H U M I D I F I E D P U R E N I T R O G E N p T O T E S T C E L L ••fl C O O L I N G C O I L S ' I N S U L A T I O N 2-i (fl ~) % P U R E D R Y " N I T R O G E N \ C'O HUMIDIFIER \ C O L E A D S T O N U R N B E R G R E L A Y 1 HEATER THERMOSTAT V c otto \ T H E R M O M E T E R y 'Or' WATER TO T E S T C E L L P U M P FIG.I C O N S T A N T T E M P E R A T U R E W A T E R B A T H 17 A centrifugal pump was used to move the water from the water bath to the test c e l l . The pump was rubber mounted and Srmly fastened to eliminate any vibrations. A diagramatic presentation of the constant temperature bath i s shown on Fig (1). 3. TEST CELL Fig (2) shows a scale drawing of the test c e l l s used for the corrosion runs. The interior c e l l was of constant cross-section to avoid any errors in« troduced i n f i l l i n g the c e l l s . In this way an approximately constant volume of solution to volume of wire ratio was maintained. The capillary sleeve through which the wire passed was of sli g h t l y larger diameter than the #18 wire used. Because of the small clearance l e f t when the wire was i n position, no solution entered this portion of the c e l l . With the dropping mercury electrode i n position 15 ml. of solution f i l l e d the c e l l to about the exit of the water jacket. Nitrogen could be passed into the c e l l i n two ways. To scrub out oxygen and agitate the solution nitrogen was passed into the sidearm and through the sintered glass bubbler. The small bubbles of nitrogen formed on the bottom of the bubbler and were thrust downward. This promotes more efficient scubbing and agitation of the solution i n the c e l l . When nitrogen was not being passed into the solution by means of the bubbler i t was passed over the surface of the solution i n the c e l l . This was accomplished by means of an oval shaped rubber stopper i n which three holes had been placed. One hole permitted the entrance of nitrogen; the second hole was to accomodate the dropping mercury capillary and the third hole was for the test wire. The hole for the wire was lined with a glass sleeve so that the wire did not come i n contact with the rubber stopper. In most cases, except when occasional nitrogen fluctuations caused severe agitation, the solution never came i n contact with the rubber stopper. 17a WATER JACKET C API LLARY SLEEVE FOR COPPER WIRE N I T R O G E N I N L E T S I N T E R E D G L A S S B U B B L E R ^•MERCURY RESERVOIR - PLATINUM CONTACT MERCURY CONTACT ARM FOR POLAROGRAPH LEAD SCALE- FULL SIZE FIG.2 T E S T CELL IS The dropping mercury capillary was positioned about £ of an inch above the sintered glass bubbler and slightly to one side of i t , so that the drops could form correctly and f a l l between the wall of the vessel and the bubbler to the cathode pool below. A platinum wire connected the cathode pool to the mercury f i l l e d sidearm containing the polarographic lead. The capacity of the cathode reservoir was about 1.5 cubic centimeters which permitted about 15-20 polarograms to be taken before the pool was f i l l e d . The capillary was 8 cm. i n length of type S-29351 (48) connected to an 8 num. glass tube. A sidearm just above the capillary was connected to an adjustable mercury reservoir by neoprene tubing to supply mercury to the glass tube. The height of mercury above the capillary and hence the drop time could be adjusted by raising or lowering the reservoir. The second polarographic lead was placed i n the mercury reservoir. Fig (3) shows a photograph of the experimental arrangement. B. MATERIALS 1. PURIFICATION OF MERCURY A commercially pure form of mercury was further purified by a number of standard procedures (45). F i r s t l y dry, clean f i l t e r e d a i r was bubbled through the mercury covered by a dilute solution of approximately 1% n i t r i c acid. This procedure oxidized any of the base metals such as copper, zinc and lead that may have been present. The oxidized metals appeared as a scum on the surface of the aqueous solution and was later removed by "pinhoJing" through a fi n e l y drawn capillary. This oxidation procedure was carried on for a period of about three days with frequent changes i n the n i t r i c acid solution. The mercury was then passed through a "scrubber" which consisted of a column some 150 cm. long term-inating i n a bent capillary i n the form of a trap at the bottom. This scrubber was f i l l e d with a 5% n i t r i c acid solution. The mercury f a l l s through the solution in the form of a fine spray which was effected by passing the mercury through a 2 .Overall Apparatus. FIG.i? PHOTOGRAPHS OF EXPERIMENTAL ARRANGEMENTS 19 funnel drawn to a fine j e t . Thus any remaining a l k a l i metals are oxidized. Next the mercury was sprayed through a scrubber containing 5% sodium hydroxide solution and f i n a l l y sprayed twice through a scrubber containing d i s t i l l e d water and collected i n a well cleaned and dried container. After removing any visible traces of water with f i l t e r paper, the mercury was transferred to a dis-t i l l a t i o n apparatus. Here i t was t r i p l e d i s t i l l e d under vacuum to remove any traces of the noble metals such as gold, silver or t i n . 2. NITROGEN PURIFICATION The nitrogen used was premium grade tank nitrogen containing 99.85$ nitrogen. The remaining 0.15$ was mostly oxygen and the rare gases. Of these, oxygen was the only harmful ingredient. The most popular agents f o r removing oxygen from tank nitrogen are hot finely divided copper, such as copper carbonate precipitated onto Kieselguhr or trains of chromous sulfate solutions. Although either absorb oxygen sub-stantially completely, both have disadvantages that render their use inconvenient. Not only i s a copper heater somewhat tedious to construct and place i n operation, but much time i s required to attain operating temperatures. Chrom-ous sulfate solutions, generally prepared by the reaction of metallic zinc and acidified chromic sulfate, must be allowed to stand for many hours before they are ready for use. Also, because the hydrous chromic oxide formed on aging i s dissolved and reduced only slowly on addition of acid, the regeneration of these solutions i s slow. Another sometimes useful means of oxygen removal is by use of Fieser's solution (15), however, for this work i t had two disadvantages. F i r s t l y , i t cannot be regenerated; and secondly, and most important i t was found to evolve hydrogen sulfide after i t started to degenerate. It was f i n a l l y decided to use vanadous sulfate solutions to remove the oxygen (35). A solution i n i t i a l l y 0.1M i n vanadyl sulfate and containing some free sulfuric acid i s ready for use 20 within a few minutes after amalgamated zinc i s added, and regeneration by addition of sulfuric acid proceeds almost instantly. Unlike alkaline suspensions of hydrous chromic oxide, alkaline sus-pensions of hydrous vahadic oxide are highly effective i n oxygen removal, being oxidized to vanadite, which i t s e l f strongly absorbs oxygen and i s con» verted to vanodate. Meites and Meites (35) have shown that vanadous sulfate solutions w i l l remove oxygen from tank nitrogen sufficiently for use i n polaro-graphic work. Fig (4) shows the schematic arrangement of equipment for the p u r i f i -cation of tank nitrogen. From the tank the nitrogen passes through two bubblers i n series containing a solution of 0.1M vanadyl sulfate i n contact with amal-gamated zinc and glass raschig rings. The zinc plus the raschig rings assure intimate contact of the solution with the nitrogen. From the vanadyl sulfate solution the nitrogen stream passed through another scrubber containing dis-t i l l e d water to remove any entrained vanadyl sulfate. Next i t passed through two drying tubes containing activated alumina to assure that the nitrogen was perfectly dry. 3. PREPARATION OF SOLUTIONS (a) . SULFURIC ACID SOLUTIONS Approximate 1.0, 0.5 and 0.1 molar solutions were made up from C.P. concentrated sulfuric acid and d i s t i l l e d water. A l l glassware used was care-f u l l y cleaned and dried to avoid any contamination of solutions. The approximate solutions were then titrated against standard sodium hydroxide to determine the exact concentrations. These exact concentrations were 1.040, 0.502 and 0.104 molar. The solutions were stored i n large glass stoppered flasks, the tops of which were again covered by an upturned beaker. (b) SOLUTIONS FOR CALIBRATION CURVES Finely ground, dry, A.R. copper sulfate was used to prepare the standard SCRUBBERS TUBES I 1 MANOMETER FIG .4 N I T R O G E N P U R I F I C A T I O N S T R E A M 21 solutions for construction of the calibration curve of microamps versus cupric ion concentration (Fig 6 6 ) . Small volumetric flasks containing accurately weighed quantities of copper sulfate were used for each data point (58). Utmost care was .again observed to assure against contamination, (c) AGAR-AGAR SOLUTIONS A 0.05$ solution was prepared from finely ground, A.R., agar-agar in distilled water to be used as a maxima suppressor (50). 4. COPPER WIRE For a l l work done #18 A.W.G. solid drawn copper wire was used. The following manufacturing procedure was used as supplied by Canada Wire and Cable Company limited:-"0.064 inch copper wire cold drawn on our machine #104 ® 490 feet per minute using new diamond dies; the wire was softened by annealing at 1050° F in a B & P Furnace for 90 minutes. 22 EXPERIMENTAL PROCEDURE In essence an experimental run consisted of immersing a copper wire (#18 B f S) i n an aqueous solution of sulfuric acid and following the change in copper concentration by means of polarographic analysis. A. TREATMENT OF WIRE The wire was coiled on a 5 inch wooden spool and kept i n the same room as the test runs were being performed. No effort was made to keep the spool i n an isolated atmosphere. Twenty hours prior to the wire being used a suitable length (about 24 inches) was removed from the spool and suspended i n air with a weight of 70 grams attached to i t . A weight of 70 grams produced l i t t l e or no strain on the copper wire but did help to straighten the wire. Immediately prior to a test run the wire was cleaned of any grease or other organic materials by drawing the wire 10 times through a kleenex soaked i n CP. carbon tetrachloride and 10 times through a kleenex soaked i n CP. acetone. B. POSITIONING WIRE After cleaning, the wire was immediately placed i n position i n the test c e l l . This was accomplished by passing the wire up through the capillary sleeve at the bottom of the c e l l and then through the glass sleeve of the rubber l i n i n g . The wire was connected at one end to a cross-beam by means of a screw clamp about 12 inches above the top of the c e l l . At the lower end of the wire, about 3 inches below the bottom of the c e l l a weighed scale pan was attached. The point where the wire passed through the c e l l (capillary sleeve) was sealed by wrapping the wire and glass with rubber tape. This tape allowed the wire to elongate freely as the weight was added to the weight pan. C EXPERIMENTAL Prior to any immediate treatment of the wire the test c e l l was placed in position and clamped firmly. The external water jacket was connected to the 2 3 constant temperature bath and brought up to the desired temperature. The nitrogen stream from the purification unit was passed through an o r i f i c e where the flow rate was indicated on a calibrated manometer. The nitrogen flow rate was maintained constant f o r a l l runs at 0 . 0 0 5 cubic feet per minute. From the o r i f i c e the nitrogen passed through a humidifier situated within the constant temperature bath. The humidifier contained the same solu-tion that was to be used i n the ensuing run, thus insuring that the nitrogen was completely saturated at the temperature of the run. By this means changes i n concentration due to evaporation could be minimized. From the humidifier the nitrogen passed directly to the test c e l l . One line was connected to the sint-ered glass bubbler and the other line to the rubber stopper where i t was passed over the surface of the solution. Five drops of t r i p l e d i s t i l l e d mercury were now placed i n the c e l l to act as the cathode. Sulfuric acid, contained i n the large glass stoppered vessels was transferred to a smaller glass stoppered vessel of about 3 0 ml. capacity. This smaller flask was immersed for a short time i n a water bath maintained at approximately the same temperature as the ensuing run. Fifteen ml. of t h i s solution was now transferred by means of a pipette to the test vessel and the time recorded as the beginning of the test run. Five drops of 0 . 0 5 $ agar-agar solu-tion was added to act as a maxima suppressor. The dropping mercury electrode was lowered into the test c e l l and a weight was placed carefully on the pan sus-pended from the wire. Once the copper wire was i n place and the sulfuric acid and weight had been added nitrogen was bubbled through the solution f o r exactly five minutes, the time being indicated by a stop-watch. After five minutes bubbling a polar-ogram was taken to obtain the copper concentration i n the c e l l . During the course of the test run polarograms were taken at intervals, i n a l l cases nitrogen c 24 was admitted to the c e l l for exactly f i v e minutes prior to the polarogram being taken. At no other time during the course of the run, except before a polaro-gram, was nitrogen passed into the solution, however, at a l l times a nitrogen atmosphere was maintained over the surface of the solution. The time recorded for the polarograms was taken as the time at which the curve of the polarogram passed through the half wave potential* The time recorded was accurate to about 1 minute which i n a 12 hour run was an insig-nificant error. The duration of runs was generally 8 to 15 hours, although some were continued to 50 hours. At the end of a run the test c e l l was stripped and the solution and copper wire removed. The c e l l was then rinsed with tap water for about 20 minutes, followed with rinsings with d i s t i l l e d water and dried with acetone. The dropping mercury electrode was rinsed with d i s t i l l e d water and dried with a kleenex. The rubber stopper was also rinsed with tap water and d i s t i l l e d water and dried with acetone. D. VARIABLES 1 . TEMPERATURE A l l temperature measurements were constant w i t h i n i 0.2°C. Five temp-eratures were studied:- 15, 25, 35 , 55 and 75° C. No effort was made to go below 1 5 ° C because i t would have involved radical changes i n the apparatus and furthermore, the corrosion rate at 1 5 ° C was very low. Similarly, no effort was made to go beyond 75° C because again i t would have involved changing the appar-atus to avoid evaporation effects. At 75° 0 the effect of evaporation becomes noticeable even with the humidifier, for after 12 hours about 3 ml. of solution had evaporated. The exact amount of evaporation at the end of a test run was noted and recorded i n a l l cases. 2 . OXYGEN CONCENTRATION IN CELL The rate and length of time that nitrogen was bubbled through the solu-25 tion pretty well determined the amount ofoxygen in the solution. Initially the cell was. bubbled for five minutes at a nitrogen flow rate of 0.005 cubic feet per minute. With this procedure the oxygen concentration was reduced to a point so that i t did not interfere with the copper polarograms. Since at a l l times after scrubbing with nitrogen, a nitrogen atmosphere was maintained over the solur» tion, i t is thought that the test cell remained at a constant oxygen concentration during the run. It may be thought that 5 minutes bubbling does not reduce the oxygen concentration to a minimum which is indeed true, however, to reduce the oxygen concentration to a minimum might require a whole day of steady bubbling. The fact that 5 minutes bubbling reduces the oxygen concentration so that i t does not interfere with copper polarograms indicates that the oxygen concentration was quite low. Standard procedures were used to determine the amount of dissolved oxygen (47, 41, 54, 55, 57, 53)» In deaerated 1,0M sulfuric acid at room temper--5 ature the amount of oxygen was found to be about 6 x 10 molar. Tests have also shown that to reduce this concentration further requires a prolonged period bubbling. A short period of bubbling reduces the oxygen content from about 3 x 10-4 to 6 x 10^ 5 molar. It can be seen therefore although the oxygen content in the cell was not a minimum, that additional bubbling before each polarogram does not appreciably alter the oxygen concentration in the c e l l , 3. STRESS Three different wei^its were used to apply tension to the copper wirej 1, 5 and 10 Kgm. These weights result in stresses of 2040, 9060 and 18000 p.s.i. (pan weights being included in the calculated stress.) The yield stress of copper wire is about 35000 p.s.i. Weights of 1 and 5 Kgm. produced no visible elongation of the wire, however, with 10 Kgm there was a slight but noticeable elongation of the wire. The diameter of the copper wire has been measured before 26 and after application of weights and shows no change being constant at 0.04 inches. 4. AGITATION The control of agitation was the same as that for oxygen concentration in the c e l l i . e . agitated for 5 minutes prior to polarogram being taken, and l e f t stagnant u n t i l 5 minutes prior to another polarogram being taken.- Two runs have been done at 15° C using continuous agitation by bubbling, except during record-ing of polarograms. Results showed that corrosion rate was only slightly i n -creased over similar runs done under stagnant conditions. 5. SOLUTION CONCENTRATION Three concentrations of sulfuric acid were studied; 0.1, 0.5 and 1.0 molar. Readings of pH were attempted before and after a test run to determine whether there had been any change i n concentrations, however, due to the very low values of pH and the short length of time the solution was exposed to the copper wire i t was impossible to detect any difference in i n i t i a l and f i n a l concentra-tions. 27 EXPERIMENTAL RESULTS The results of over one hundred test runs, lasting anywhere from 6 to 50 hours, for #18 B&S soft copper wire i n sulfuric acid at varying temperature, stress and molarity are shown graphically on Figs (19)to (63) of Appendix I. The experimental data i s tabulated i n Tables (7) to (12) of Appendix I. Table (6) of Appendix I gives a compilation of the conditions undef which each run was per-formed; i.e. run number, temperature, stress, sulfuric acid concentration, table number and figure number. This table serves as a means of locating the experi-mental data presented i n tabular form from the same experimental data presented i n graphical form. Every test run was performed following the procedure previously des-cribed and the copper concentrations at specific times recorded as a polarogram by means of a Model XXI Sargent Polarograph. The method, of calculating the copper concentration from the polarograms obtained i s described i n Appendix I I . In a l l cases the data shown i n Figs. (19) to (63) could be best repre-sented by straight lines, the slopes of these straight lines being calculated by the method of least squares (48). The s t a t i s t i c a l confidence limits: ef the straight lines obtained were tested by a method outlined by Wilks (60) and i n every case the confidence limits • were very high. In other words the chance that the data would f i t some other kind of curve oyer the range studied i s very remote. Table (2) below shows the values of the slopes obtained from Figs. (19) to (63), the slope K being the specific reaction rate,,. 28 TABLE 2 REACTION RATE K VERSUS TEMPERATURE FOR VARIOUS STRESSES AND SULFURIC ACID CONCENTRATIONS SULFURIC ACID CONCENTRATION TEMPERATURE °c STRESS KGM K x 10> MLLIMOLES/LITER MINUTE . K x 1CP MILLIMOLES/LITER MINUTE K x 10? MILLIMOLES/LITER MINUTE 75 10 5 1 353 293 354 316 315 315 286 232 194 55 10 5 1 145.6 109.0 122.0 113.5 97.6 96.2 89.3 82.0 78.2 35 10 5 1 65.1 37.5 40.2 57.4 45.4 46.1 33.8 28.9 26.3 25 10 5 1 ;36;7 20.8 26.6 32.1 19.7 19.8 17.7 15.4 13.4 15 10 5 1 22.6 13.6 13.3 21.3 17.6 12.2 10.8 8.9 8.3 ' A. EFFECT OF TEMPERATURE Fig (5) shews the typical effect for this data of temperature on cor-rosion rate. This graph was prepared by laying off the line for 75 degrees as i t actually was, i.e . with same slope and intercept from Fig (63). For the other four temperature lines only the calculated slope was used, the intercept being taken as that for 75 degrees. Although this method of presentation does not show the actual experimentally determined lines, i t does show more clearly the changes produced due to temperature. To f i t an equation to the relationship between reaction rate and temper-ature, the logarithm of the reaction rate was plotted against the reciprocal of 0 ! 2 , 3 4 ' 5 6 7 8 9 10 II .12 TIMF MR 29 the absolute temperature Fig.(6,7, 8) K K - A e ^ ( 1 0) For the majority of cases straight lines were obtained and by the method of least squares, the values of the constants, A and K, i n the above equation were calculated (Table 3). The activation energy E for the corrosion of copper i n sulfuric acid was calculated from the slope K, E s 2.303EK (11) R being the gas constant TABLE 3 VALUES OF THE CONSTANTS IN THE EQUATION K • Ae T , K B E R H2S0, CONCENTRATION STRESS KGM A M.M.(105)/L/MIN K (SLOPE) E = 2.303(1.987)K K-CAL/GM-MOLE 1.0 1.0 1.0 10 5 1 8233 8953 9254 -1.983 -2.265 -2.343 9.1 10.4 10.7 0.5 0.5 0.5 10 5 1 7992 8590 9135 -1.926 -2.143 -2 322 8.8 9.8 10.6 0.1 0.1 0.1 10 5 1 9199 9U2 8971 -2.361 -2.365 -2.326 10.8 10.8 10.6 Using the values of the reaction rate at given temperatures from Table (2), the average values of the increase i n reaction rate for a ten degree rise i n temperature were calculated (Table 4). TABLE 4 AVERAGE INCREASE IN REACTION RATE FOR TEN DEGREE RISE IN TEMPERATURE. SULFURIC ACID CONCENTRATION STRESS KGM l.OM 0.5M 0.1M 10 1.43 1.42 1.61 5 1.53 1.53 1.61 l 1.62 1.65 1.58 FIG. 6 E F F E C T OF T E M P E R A T U R E ON R E A C T I O N R A T E S F O R 1.0 M. S U L F U R I C ACID 1 _ L _ 3.0 O I KGM. X 5 KGM. A|0 KGM. 30 B.- EFFECT- -OF CONCENTRATION - - • -Fig« ( 9 ) shows the typical effect for this data of temperature on cor-rosion rate. This graph was prepared i n the same way as Fig (5) . In an attempt to find a relationship between reaction rate and sulfuric acid concentration, the values of the reaction rate were plotted against the a c t i v i t y of the hydrogen ion (Fig 10, 11, 12) The values of the hydrogen ion ac t i v i t y at various temperatures were obtained from the data i n Conway (6) using the expression: a - f c (12) where a s a c t i v i t y f » ac t i v i t y coefficient c » concentration i n moles per l i t e r . Table (5) below gives the values obtained by interpolation. TABLE 5 EFFECT OF TEMPERATURE ON ACTIVITY COEFFICIENTS FOR SULFURIC ACID TEMPERATURE C = O.IO4M c » 0.502M C = 1.040M o c f a « f c f a = f c f a = f c 15 0.292 0.030 0.173 0.087 0.146 0.152 25 0.265 0.02s 0.154 0.077 0.130 0.135 35 0.243 0.025 0.140 0.070 0.117 0.122 55 0.203 0.021 0.113 0.057 0.096 0.100 75 0.176 0,018 0.094 0.047 0.079 0.082 C. EFFECT OF STRESS Fig. (13, 14, 15) i l l u s t r a t e the effect of stress on corrosion rate for the three concentrations studied. As can be seen stress has a different effect for each concentration. In an attempt to find a relationship between reaction rate and stress Fig (16, 17, 18) were plotted. or UJ 12 Ul UJ _J 1.0 o _J 2 0 8 o < or o o o 0 6 UJ O 04 02 0 F1G.9 EFFECT OF CONCENTRATION i M H 0 S0 4 TEMP 75° C STRESS 10 KGM 30b 30 c 30d T I M E H R . o 0 I 2 3 4 5 6 7 8 9 10 II 12 T I M E HR. 3 0 h 30i 4 5 6 STRESS KGM. 31 DISCUSSION OF RESULTS  A. RATE DEPENDENCE Inspection of Figs. (19) to (63) will show that in a l l cases a linear relationship was obtained when time of immersion was plotted against copper con-centration for the dissolution of copper in sulfuric acid. This indicates that the reaction rate is f i r s t order with respect to cupric ion concentration, the slope of this line being the specific rate constant. Thus for the conditions used in this work we may write -dtCu* ) = K(Cu+* ) (13) dt Katz (26) and Szabo (51) have both shown similar first order dependence. The observed independence of the rate of stirring (33) (IS) indicates that the rate of dissolution is not controlled by diffusion to and from the metal surface. These facts can be accounted for by the following three step mechanism proposed by Szabo (5l) Cu + |02 + 2H* a Cu* Ar H20 (14) Cu44 -I- Cu = 2Cu+ (15) 2Cu+ + 2H + + £0 2 m 2Cu*+ H20 (16) The above equations and the rate dependence can be proposed on the basis of the following considerations. 1. The cupric ion concentration in the bulk of ike solution is assumed to be the same as the cupric ion concentration at the copper solution interface (33). This assumption was reached due to the fact that the rate of stirring has l i t t l e or no effect on the reaction rate, therefore diffusion to and from the metal sur-face is not the limiting step. 2. The cuprous ion, cupric ion equilibrium Cu + Cu4* a 2Cu+ 32 is assumed to be established at the interface, (33)« 3. The rate of dissolution of copper is assumed to be controlled by equation (16), the slow and limiting reaction. This conclusion was reached be-cause reaction (15) is in equilibrium, and because the oxidation potential Cu /Cu is very much higher than Gu/Cu*, Therefore reaction (14) proceeds rapidly from left to right (51). From reaction (16), -d(Ou+) = K 1(Cu +) 2(©)(H+) 2 (17) With the equilibrium constant (Cu+)V(Cu ) «* Kx (7) and letting = K we get that -d(eu+) - K(Cu*)(H+)2(0) (18) dt or since -d(Cu+) - d(Cu H) (19) dt dt then d(Cu H) z K(Cu-H)(H+)2(0) (20) dt The f i r s t order dependence on oxygen concentration as given by equation (20) is confirmed by thework of Russell and White (42) and H i l l (25). In the work reported here, however, the oxygen concentration in the bulk of solution was held fairly constant. The oxygen concentration in this work was reduced to 6 x 10-5 molar by periodic nitrogen bubbling. It could be expected to increase slightly through diffusion from the air through the liquid between bubblings in spite of the nitrogen atmosphere. If corrosion reactions such as (14), (15) and (16) were occuring, i t would depend on a continuing supply of oxygen. It i s believed that the actual concentration of oxygen remained at approximately 6 x 10"5 molar as determined analytically. This s t i l l provided a continuous source of oxygen but at a low concentration level. 33 Equation (20) also confirms the f i r s t order dependence on cupric ion concentration observed i n this work. The work of Katz (26) i n deaerated solu-tions also confirms this f i r s t order dependence on cupric ion concentration. There is a sharp disagreement between t h i s work and that of Hasse (22) and Lu and Graydon (33). Basse (22) i n unaerated solutions obtained a second order dependence on cupric ion concentration. Lu and Graydon (33) for rotating copper specimens in aerated solution obtained a one-half order dependence on cupric ion concentration. Equation (16) as written indicates that the reaction rate is second order with respect to hydrogen ion activity. Referring to Figs. (10, 11 and 12), the results for the concentration range studied (0.1M to 1.0M) seem to indicate that the reaction rate i s f i r s t order with respect to hydrogen ion concentration. How-ever, the straight lines obtained are the results of only three experimental points and could quite possibly show second order dependence. Further investi-gation of acid concentration as a variable would decide this definitely. If the data indicate apparent f i r s t order dependence then another reaction involving hydrogen i s occurring simultaneously. A reaction that might occur is the following. Cu20 +• 2H + = Cu *+ Cu + H20 (21) Although equations (16) and (2l) both show second order dependence on hydrogen ion concentration i t is possible that a combination of these or other reactions might result i n the observed f i r s t order dependence. B. POSITIVE INTERCEPT Referring again to Figs. (1°) to (63) i t can be seen that a l l the data show a positive intercept at zero time, the value of this intercept tending to increase with temperature. Lu and Graydon (33) suggest that this value results partly due to a soluble copper salt on the metal surface which goes into soluw tion immediately after contact with sulfuric acid. From the data of Miley and 34 Evans (37), they have estimated that this might possibly account for an intercept corresponding to about 2 x 10~^ moles per l i t e r of cupric ion at 25 degrees. The intercept from our data at 25 degrees corresponds to about 2 x 10'"-' moles per l i t e r of cupric ion. This value i s identical to that reported by Lu and Graydon (33). They consider the positive intercept at zero time to result from the ad-sorption of copper ions on the dissolution vessel. In our work we tested this theory by performing runs on previously unused vessels and the. results were the same as those obtained with previously used vessels washed as described under pro-cedure. It would appear that neither solubility nor adsorption w i l l explain the positive intercept at zero time. The positive intercept i s therefore due to an i n i t i a l very fast reaction. The work of Brown (3) who found a very fast i n i t i a l reaction lasting for perhaps 5 minutes, followed by a linear region substantiates t h i s . H i l l (25) also has shown that i n the period 2-10 minutes, the reaction follows the parabolic rate law, the slow step being diffusion of copper ions through the f i l m of corrosion products just formed. C. EFFECT OF STRESS For the data obtained using 0.1M sulfuric acid a l l the rate constants (Table 2) follow the same pattern&r each temperature, i . e . the greater the stress the greater the reaction rate. At this concentration there exists a linear re-lationship between stress and reaction rate for a l l temperatures investigated. (Fig. 16), the slope of these lines increasing with temperature. The fact that the slopes increase with temperature suggests a relationship between stress or l. the effect produced by stress and temperature. Figs. 13, 14 and 15 i l l u s t r a t e the effect of stress at the three con-centrations studied. For every temperature studied the trends illustrated were as follows:-35 1. For 1.0M sulfuric acid the reaction rate for 10 kgm. stress was greater than the reaction rate for 1 kgm. stress, which i n turn had a reaction rate greater than that for 5 kgm. stress, 2. For 0.5M sulfuric acid the reaction rate for 10 kgm. stress was greater than the reaction rate for 5 kgm. stress, while the l a t t e r had a reaction rate almost the same as that for 1 kgm. stress. 3. For'#0.1M sulfuric acid the reaction rate for 10 kgm. stress was greater than the reaction rate for 5 kgm. stress which in turn had a reaction rate greater than that for 1 kgm. stress. The only conclusions to be reached from the foregoing observations are that the reaction rate for a metal stressed to the plastic region, (10 kgm.) i s greater than the reaction rate for a metal stressed i n the elastic region ( l and 5 kgm.) and that as the temperature is increased the difference i n these reaction rates becomes less. D. EFFECT OF TEMPERATURE — ACTIVATION ENERGY Increase in the temperature almost invariably increases the rate of a chemical reaction to a marked extent; for a chemical reaction the specific rate i s usually increased by a factor of about two or three for every 10 degree r i s e in temperature, whereas for a heterogeneous diffusion controlled process this factor may be only 1.1 to 1.5 (17). From this work the average increase i n re-action rate for a ten degree r i s e in temperature was about 1.5 (Table 4). This indicates that the dissolution of copper i n sulfuric acid solutions i s diffusion controlled. It has already been stated that diffusion through the bulk of the solution i s not the controlling step because st i r r i n g has been shown to have l i t t l e effect. This indicates that the limiting step must be diffusion through the corrosion products on the metal surface. Equation (16) which i s assumed to be rate controlling i s this type of diffusion controlled reaction* 36 The most satisfactory method of expressing the influence of temperature on the reaction velocity constant can be derived by plotting the logarithm of the specific rate |log K) against the reciprocal of the absolute temperature. Figs. 6, 7 and 8 show that a straight l ine i s obtained. The variation of the rate con-stant of a reaction with temperature can thus be expressed by means of an equation of the following form. log k * A - K (21) T where A and K are constants of the given reaction. By writing equation (21) i n the exponential form involving the Boltzmann factor e~^®~, where R i s the gas constant; K * A e - E / R T (10) Equation (10) i s one form of the Arrhenius equation, where A i s called the fre-quency factor and E, the energy of activation. This shows that as the activation energy increases the specific rate constant decreases. From the values of E i n Table 3, i t may be noted that for l.OM and 0.5M sulfuric acid solutions the a c t i -vation energy E decreases with increasing stress, or that by increasing stress the specific reaction rate i s increased. For 0.1M sulfuric acid the activation energy is constant over the stress range covered. Also, over the concentration range covered the activation energy i s constant for the unstressed ( l kgm.) metal at 10o6 K-cal . A low energy of activation indicates that the reaction i s probably diffusion controlled (17). Salzberg (44) has stated that two other c r i t e r i a for diffusion control are l ) temperature coefficient about 1,5 and 2) dissolution rate increasing with concentration of reagent, the curve being l inear . In th i s work the temperature coefficient was about 1.5 and the curve for reaction rate versus sulfuric acid concentration (hydrogen ion act iv i ty) was l inear . These facts along with the low activation energy show that the rate controlling reaction 37 i s diffusion controlled. Since diffusion through the bulk of the solution i s not controlling, the controlling step must be diffusion of oxygen through the layer of corrosion products on the surface of the metal. This further substan-tiates the selection of equation ( 1 6 ) as the rate controlling step. If this i s the controlling step the reaction rate should slow down after a length of time because the thickness of the corrosion products increases and hence the diffusion path increases. To test this a run (Fig. 6 5 ) was performed for a longer time than normal. The results of this run show that the reaction rate does decrease. However, up to 1 2 hours the curve i s linear. The results of this investigation, which are s t a t i s t i c a l l y significant and reproducible, help elucidate the mechanism and kinetics f o r the dissolution of copper i n stagnant deaerated sulfuric acid solutions and show the effects of the variables:- applied stress, temperature and corrodent concentration. 38 SUMMARY 1. The rate of the reaction for the dissolution Of copper in sulfuric acid was found to be f i r s t order with respect to cupric ion concentration for the conditions studied. 2. Experimentally i t was found that the reaction rate was pseudo first order with respect to hydrogen ion activity. 3. Stress, in general, increases the reaction rate slightly, the effect be-coming less at higher temperatures. 4. The activation energy for unstressed corrosion was 10.6 K-cal for temper-atures range 15~75°C 5. For 1.0M and 0.5M solutions, stress decreased the activation energy and thus increased the reaction rate for corrosion of the metal. 6. The average increase in reaction rate for 10 degree changes in temperature between 15 and 75 degrees was about 1.5. 7. A mechanism was derived for the dissolution of copper in which i t is pro-posed that the rate of dissolution of copper i s controlled by diffusion of oxygen through corrosion products on the metal surface. 3 9 BIBLIOGRAPHY (1) Bengough, G. D., and May, R., J, Inst. Metals, 12> 1 0 8 (192*0 (2) Bohnenblush, H. P., and Dewey. P., Trans. Am. Soc. Mech. Eng., 22» 222 ( 1 9 W (3) Brow, R. H., and Roetheli, B. E., Ind. Eng. Chem., £i, 350(1931) (tO Burns, R. M., J . App. Phys., 8 , 398 (1937) (5) Campbell, W. E., and Thomas, U. B., Nature, 253 (1938) (6) Conway, B. 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H., "The Corrosion Handbook", John Wiley and Sons, New York, (1953) (57) Ulmer, R. C , Reynar, J. M., and Decker, J . M., Proc. Am. Soc. Testing Mat., !^t» ll» (1931*) (58) Vogel, A. I., "Quantitative Inorganic Analysis" 2nd ed*, Longmans, Green and Co., New York, (195D (59) Wagner, C , Z. Physik Chem., 21B. 25, (1933); 32B, kk7, (1936); kOB, kk5, (193$) (60) Wilks, S. S., "Elementary S t a t i s t i c a l Analysis" p.195-276, Princeton University Press, Prince-ton, New Jersey, (195k) APPENDIX I EXPERIMENTAL DATA 1. TABULATED 2. GRAPHICAL O Data c o n s i s t a n t 0 Data i n c o n s i s t a n t kk TABLET 6 LIST OF EXPERIMENTAL RUNS Temperature °C Figure Number Table Number Concentration R^O^ Strei KGM 19 7 l.OM 10 19 7 l.OM 10 20 7 l.OM 5 20 7 l.OM 5 21 7 l.OM 1 22 7 0.5M 10 22 7 0.5M 10 23 7 0.5M 5 2k 2k 7 0.5M l 7 0.5M l 25 7 0.1M 10 26 7 0.1M 5 26 7 0.1M 5 27 7 0.1M l 1 § 15 15 15 15 15 15 15 15 15 15 15 15 15 lk$ ik? Ik6 152 lh8 Ikl lfo ikk lk9 139 IkO 25 159 25 163 25 160 25 16* 25 158 25 166 25 157 25 167 25 156 25 161 25 155 25 162 25 169 25 153 25 165 25 99 25 15* 25 170 25 100 25 168 28 8 l . O M 10 28 8 l . O M 10 29 8 l . O M 5 29 8 l . O M 5 30 8 l . O M 1 30 8 l . O M 1 31 8 0.5M 10 31 8 0.5M 10 32 8 0.5M 5 32 8 O . 5 M 5 33 8 O . 5 M l 33 8 O . 5 M l 33 8 O . 5 M l 8 0.1M 10 3 * 8 0.1M 10 35 8 0.1M 5 35 8 0.1M 5 35 8 0.1M 5 36 8 0.1M l 36 8 0.1M l k$ TABLE 6 (cont'd) 35 83 35 89 35 35 85 35 132 35 138 35 171 35 87 35 13^ 35 172 35 * 88 35 92 35 96 35 35 35 90 35 86 35 9k 35 93 35 97 35 131 35 91 35 101 35 130 35 133 35 136 35 95 35 102 35 129 37 9 l . O M 1 0 37 9 l . O M 1 0 37 9 l . O M 1 0 38 9 l . O M 5 38 9 l . O M 5 38 9 l . O M 5 38 9 l . O M 5 39 9 l . O M 1 39 9 l . O M 1 39 9 l . O M 1 ko 9 0.5M 1 0 ko 9 0.5M 1 0 ko 9 O . 5 M 1 0 ko 9 0.5M 1 0 kl 9 O . 5 M 5 kl 9 O . 5 M 5 kz 9 O . 5 M l k2 9 O . 5 M l ft 9 0 . 1 M 1 0 ft 9 0 . 1 M 1 0 ft 9 0 . 1 M 1 0 kk 9 0 . 1 M 5 kk 9 0 . 1 M 5 kk 9 0 . 1 M 5 kk 9 0 . 1 M 5 kk 9 0 . 1 M 5 9 0 . 1 M l 9 0 . 1 M 1 k$ 9 0 . 1 M 1 5 5 5 5 5 5 5 5 ii 5 5 5 5 5 5 5 5 119 »*6 10 l.OM 10 121 , k6 10 l.OM 10 120 k7 10 l.OM 5 12k k? 10 l.OM 5 122 k8 10 l.OM 1 123 k8 10 l.OM 1 126 k8 10 l.OM 1 111 k9 10 0.5M 10 113 k9 10 0.5M 10 117 k9 10 0.5M 10 TABLE 6 (cont'd) 55 112 50 10 0.5M 5 55 116 50 10 O.5M 5 55 11* 51 10 O.5M 1 55 115 51 10 O.5M 1 55 1 1 8 51 10 O.5M 1 55 125 51 10 O.5M 1 55 103 52 10 O . I M 10 55 105 52 10 0 . 1 M 1 0 55 1 2 7 52 1 0 O . IM 1 0 a 173 52 1 0 O . I M 10 55v 10* 53 10 O . I M 5 S3 107 53 10 O . I M 5 55 110 53 10 O . I M 5 55 17* 53 10 O . I M 5 55 106 10 O . I M l 55 108 10 O . I M l 55 109 10 O . I M l 55 128 5* 10 O . I M 1 75 181 55 11 l . O M 1 0 75 183 55 11 l . O M 10 75 18* 56 11 l . O M 5 75 182 56 11 l . O M 5 75 185 57 11 l . O M l 75 186 57 11 l . O M l ?S 187 58 11 O.5M 10 75 189 58 11 O.5M 10 75 188 59 11 O.5M 5 75 190 ?9 11 O.5M 5 7 § 191 6 0 11 O.5M l 75 192 60 11 O.5M l 75 175 61 11 O . I M 10 75 177 61 11 O . I M 10 75 176 62 11 O . I M 5 75 178 62 11 O . I M 5 75 179 63 11 O . I M l 75 180 63 11 O . I M i 15 193 6* 12 0.5M 10 k7 TABLE 7 TIME OF IMMERSION VERSUS CUPRIC ION CONCENTRATION FOR #18 B S SOFT COPPER WIRE AT 15* 0.2°C Run Time Cu# Concentra- Run Time Cu# Concentra-Number Hr-Min. tion Number Hr-MIn. tion Millimoles/LIter Millimoles/Liter Ik? 15 .025 152  25 50 .038 1-50 .051 2-55 .071 **-i5 .086 5-**5 .108 6-50 .117 7-50 .130 10-35 .171 12-30 .195 15 .017 **5 .025 lJ+5 .03*+ 2-35 .039 ^-35 .053 5-35 .063 6-55 .070 7-55 .086 10-30 .102 11-35 .11*+ i**5 15 .028 Ik8 15 .025 1-0 .037 k$ .029 2-15 .o$k l-if5 k-k$ .oak 2-50 6- M-5 .112 *t-io .05if 7- 50 .128 5-^5 .068 »o .072 6- 5( 7- k[ 5 .085 IO-30 .108 Ik6 15 .025 12-30 .121 1- 15 .028 2- 15 .033 . k-kj .055 ~ 6- 55 .078 Ikk 10 .026 7- 55 .085 1-0 . 0 3 ^ 2-k$ .oko 5-W5 .060 7-0 .078 800 .087 10-0 .102 lkl 15 .033 1-0 .037 . ( £ 7 2-10 3-10 .061 5-35 .077 5-30 .092 7-50 .122 TABLE 7 (Cont'd) 151 15 50 1- 50 2- *0 *-*0 5- 50 6- 55 7- 55 10- 30 11- 35 .021 .032 .0*6 .057 .081 .098 .108 .125 .155 .173 1*9 20 50 1- 55 2- 55 *-55 5- 50 6- 50 7- 50 i o - * o 13-0 .028 .03* .039 .0*6 .058 .066 .07* .08* .101 .118 1*3 10 .030 139 10 .027 1- 0 .0*2 50 .032 2- *5 .056 1-50 .038 5-*5 .089 2-50 .0*? 7- 0 .103 *-20 .05* 8- 0 .11* 5-55 .065 10-0 .135 8-0 .078 1*0 10 .029 150 15 .02* *5 .031 *5 .028 1- *5 .038 i - * 5 .03* 2- 55 .0*1 2-50 .038 * - l 5 .0*6 *-50 .050 5-50 .050 5-*5 .056 7-15 .060 7-*5 .070 13-*0 .097 10-*o .083 13-55 .100 , 13-0 *095 1*2 15 .036 1- 0 .038 2- 5 . 0 * * -5 .050 -30 .056 5-30 .062 7-*5 .072 1+9 TABLE 8 TIME OF IMMERSION VERSUS CUPRIC ION CONCENTRATION  FOR #18 B S SOFT COPPER WIRE AT 2 5 * 0.2 QC Run Time Cu# Concentra- Bun Time Cu# COneentra-Number Hr.-Min. tion Number Hr-Mln. tion Millimoles/Liter Millimoles/Liter 159 15 .032 16k 15 .030 55 *0k7 50 .Ok2 1- 55 .063 2-25 .062 2- 55 .081+ 3-10 .070 1+-5 .106 5-10 . 0 9 0 5-5 .131 6-5 .106 5-50 .153 7-5 .118 8-0 .20$ 9-0 .1^ 7 11-0 .273 12-30 .30t 163 15 .01+3 55 .053 2- 30 .073 3 - 15 .087 5- 10 .137 6- 10 .15*+ 7- 10 .182 9-0 .218 158 15 k$ .039 .058 1-1+0 .060 2-kO .071 k-kO .098 5-55 .118 7-0 .H+2 7-50 .156 11-25 .216 12-30 .239 160 15 .027 166 15 .029 55 .03»+ *+0 .031+ 1- 50 .052 2-5 .ofo 2- 50 .067 2-5© .057 h-0 .078 5-20 .091+ 5-o .090 5-1+0 .101 5-^5 .103 6-50 .117 8-5 .133 7-^0 .136 11- 10 .159 8-J+5 .15^ 12- 30 .183 10-0 .177 50 TABLE 8 (Cont'd) 157 167 156 155 15 Hp 2-*5 *-*5 6- 0 7- 0 7-55 11- 30 12- 30 15 1- 0 2- 0 3 - 15 5- 0 6- 0 8-5 15 * 0 1- *5 2- *5 * - 2 0 7-30 15 *5 1- *5 2- *5 * - 3 0 7-30 .Oi+6 .055 .069 .086 .132 .153 .172 .186 .258 .278 161 :8? .060 .089 .12* .1*0 .169 .038 . 0 * 7 .059 .076 .090 .12* .050 .072 .092 .121 .16* .233 162 169 15* 153 15 .035 . 0 * 1 i - * 5 .050 2-*5 .059 * - * 0 .078 5-*5 .090 6-*5 .099 7-35 .110 15 \% 7- 5 8 - 0 12-0 12-30 15 i - * 5 3 - 0 5- 0 6- 0 7- *5 10- 15 11- 25 15 *o 1- 50 2- *0 *-35 5- *5 6- *5 7- 35 .0*1 . 0 * 8 .062 .069 .091 .112 .132 .195 .203 10 .029 50 .036 i - * 5 . 0 5 * 3 - 0 .059 5-15 7-0 .086 .115 8 - 0 .127 12-0 .165 12-30 .171 .030 .0** .055 .072 .092 .109 . 13* .168 .186 .027 .032 .0*5 .055 .072 . 0 8 2 .095 .102 51 TABL 8 (Cont'd) 165 15 . 0 3 7 50 . 0 * 3 i - 5 o . 0 * 7 fc*o .057 .069 5-55 .081 7-*5 .110 8-30 .117 10-55 .1*0 12-30 .158 99 15 l - * 5 £? 7- 15 8 - 10 10-25 n - 5 0 13-20 .059 .075 .106 .151 .15* .161 .182 'Ul 1316 170 *5 1-50 3 - 0 5- 0 6 - 0 7- *5 10- 10 11- 25 .025 10^8 .061 .067 .081 .098 .111 100 15 * 0 1-35 2r25 til 5 - 5 5 U 10-15 n-*o 13-10 .029 .035 . 0 * 1 .0*6 .051 .062 .068 .079 .089 .132 .135 .1*2 52 TABLE 9 TIME OF IMMERSION VERSUS CUPRIC ION CONCENTRATION  FOR #18 B S SOFT COPPER WIRE AT 35 ± 0.2°C Run Time Cu# Concentra- Run Number Hr - Min. tion Number Millimole/Liter Time Cu# Concentra-Hr - Min. tion Millimole/Liter 83 89 138 10 .065 30 .075 1-0 .100 1-50 .135 2-50 .175 *-35 .2*5 5-*o .29** 6-50 .331 7-55 .37,6 10-15 , * 6 * n - * o .516 13-0 .598 10 1- ^ 5 2- 50 * - i o 5- *o 6- * 0 7- 10 8- 10 . 0 * * .085 . . 1 0 0 .120 .205 .2*5 .280 .306 .386 .0*3 .052 .070 .095 .120 .150 .190 .208 .292 135 85 132 15 . 0 * 3 ?° . 0 5 * i - * 5 .076 2-*0 .098 * - 0 .120 5-15 .152 6-30 .176 7-30 . 2 0 0 87 15 .070 .095 i - * 5 .125 2-*5 .155 *-*o .232 5-30 .271 7-20 .369 7-50 .389 11-55 .550 13-0 .570 15 . 0 * 3 * 0 .0*6 1-35 .059 2-30 .078 3-5 .083 * -25 .116 6-0 .1*2 7-20 .178 8 - 0 .188 9-55 .235 l l - * 5 .269 13-0 .295 10 . 0 2 * *0 . 0 3 * l - * 5 .053 2-55 .072 * - 2 0 .111 5-35 .138 6-25 .160 7-10 .180 8 - 0 .202 12-50 .318 TABLE 9 (Cont«d) 171 20 k$ 1- 50 2- 15 3 - 20 *-35 5-50 7-55 12-30 .052 .058 .083 .093 .102 .132 .156 .191 .31^ 13W 15 1- 1+0 2- *+0 3 - 1+0 5- 0 6- 10 7.35 10-5 .039 .057 .lOW .181 .271 .386 :S8 .921 88 96 15 ft 2-50 If-20 5- 30 6- 30 7- 5 8 - 0 12-50 15 »+5 1- ^5 2- t+5 5-0 9-55 .0^ +6 .059 .088 .160 .216 .256 .283 .325 .350 .525 172 92 20 .0i+3 ^5 .055 ?° i - * 5 .058 .O67 2-55 .130 ^-15 .178 5-20 .221 6-30 .256 7-*5 .310 10-25 .395 13-15 .520 .0»+8 .057 :IU .155 .177 .225 .292 .358 137 98 15 1- S+O 2- 50 1+-25 5-*+o 7-50 12-30 15 JS tt 5-20 7- 10 8 - 0 12-5 20 1+0 1- 30 2- 55 3 - 55 5- 0 6- 15 7- 5 8 - 10 10- 10 11- 50 13-0 .03 2 .Ok7 .057 .076 .120 • 11+6 .190 .3^0 .057 .085 .116 .152 .190 .2^+0 .302 .OL5 .053 .070 :2S .l>+9 .190 .212 .236 .283 .3^ 0 .399 TABLE 9 (Cont'd) 90 20 .037 93 25 .070 »*5 .053 1-20 .075 1-55 .077 2-1+0 .097 2-55 .101* 3-50 .11^ . 1+-20 .172 5-5 .1^3 hP 6-kQ .207 7-5 .182 .239 9-55 .230 .2*+0 8-10 .285 10-30 86 15 .01+1 97 15 .051 35 .d+8 1+0 .062 1- 35 2- hO .072 1-35 .083 .10*+ 2-50 .092 3-55 .138 1+-0 .111+ 5-0 .175 5-0 .11+1+ 5-35 .196 6-20 .172 6-50 .230 7-5 .185 7-35 .2*+7 8-10 .209 9-&+0 .309 10-10 .21+9 11-15 .360 11-50 .281+ 13-0 .393 li+-0 .323 101 15 1- i+o 2- 55 1+-10 5- 25 6- 1+5 8-5 10-15 10-50 20 ft 1- ^5 2- 50 1+-0 5- i o 6- 1+0 8-0 .01+5 .050 .069 .096 .121+ .15W .190 .23*+ .287 .31^ .068 .078 .115 .169 .193 .21*+ .288 .308 131 15 50 1- 55 2- 50 **-5 5- 20 6- 1+0 8-5 .067 .072 .080 .098 .112 .11+3 .170 .197 102 20 .050 ft .051+ 1-1+0 .075 2-1+5 .089 3-55 .118 5-15 .138 6-35 .160 800 .182 5 5 TABLE 9 (Cont'd) 91 15 .052 136 *5 . c m i - * 5 .056 -30 .086 -50 .112 5- 50 , i j 3 6- 55 .160 8-10 .193 10-30 .2** 12-5 .275 15 .0*0 .0*9 i - * 5 .066 2-*5 .078 *-*0 .098 5-30 .115 7-20 .13* 7-50 n -55 .186 12-25 .193 15 .058 55 .066 2-0 .081 3-0 .096 * - l 5 .112 5-15 .130 6-*5 .158 8-0 .178 10-0 .200 130 15 .0*6 95 *0 .067 1- *5 .068 2- 50 .089 *-25 .17? 5-*5 .23* 7-0 .298 7-55 .3*1 9-*5 .*26 12-0 .533 133 15 .0*6 .053 .067 2-50 .087 3-50 .099 5-10 .130 6-20 .159 7-*0 .181 10-10 .231 11-30 .259 1*-10 .319 129 15 .050 *0 .068 l - * 0 .083 3-0 *-30 .100 .127 5-50 .150 7-0 .176 8-0 .18? 9-*5 .22* l l - * 5 .271 56 TABLE 10 TIME OF IMMERSION VERSUS CUPRIC ION CONCENTRATION  FOR #18 B S SOFT COPPER WIRE AT 5 5 * 0.2°C Run Time Cu# Concentra- Run Time Cu# Concentra-Number Hr - Min. tion Number Hr- Min. tion Millimoles/Liter MUlimole suiter 119 120 10 .076 * 0 .122 i - * 5 . 18* 2-50 .280 * - 5 .369 5-15 . * 7 0 6 - * 0 .628 7-*5 .738 10-10 .990 12-10 1.160 15 .079 1+0 .101 1-50 .161 2-55 .216 *-10 .301 H i .391 6-*5 .506 7-*5 .571 10-10 .727 12-10 .887 12* 121 10 .075 * 0 .135 l - * 0 .190 2-30 .296 * -5 . * 0 2 5-20 .*6* 6-50 .592 7-*5 .688 10-30 .935 123 15 *o l - * 0 1-0 h-0 5- 20 6- 50 8-10 10-10 n - i 5 13-0 15 i-*+5 5- 30 6- 55 8-15 10-20 .055 .11? .15* .221 .291 .553 . 7 3 * .780 .850 122 15 . 1 0 * *0 .1*9 l - * 0 .220 2-*0 .303 * - 5 . * 0 3 5-25 .505 6-55 .635 7-50 .716 10-30 .8*5 .121 .200 .309 .*23 .532 .633 .718 .782 .926 57 TABLE 10 (Cont'd) 126 15 .061* 112 20 .08? 1*5 .152   50 .098 1-50 .173 2-50 ,2h0 * - 5 .322 5-io .M-25 7-15 .5^5 8-10 .628 111 15 .10»+ 1*0 .11*1 1-50 .201* 1+-10 .2»+6 .318 5-^5 .t+oo 6-50 A 9 7 8-0 .596 12-1*0 .960 117 15 .119 ft .180 1-^5 .261 .327 S-35 MQ 5-50 .553 6-55 .650 8 - 0 .685 12-20 .960 125 15 .073 .123 .177 2-1+5 .251 1+-0 .307 5-10 .368 7-15 .1+85 8-10 .570 1-1+5 .203 - 0 .262 -15 .3*5 5- 15 .£09 6- 1+5 A 8 2 8-0 .610 12-1+0 .856 116 15 .088 1+0 .130 1-1+5 .190 3-5 .25*+ H-20 .307 5-20 .367 7-35 .583 10-25 .675 11-25 .795 12-30 .905 lli+ 15 .083 1+0 .105 1-1+5 .205 2-35 .259 *-35 . f t 3 5-25 M ? 7-20 .1+88 10-1+0 .685 12-30 .790 115 15 .115 1+0 .125 i-!+5 .209 3-5 .280 5-25 .373 5-25 .H63 7-35 .515 10-30 .538 U-25 .Z1*© 12-30 ,890 5 8 TABLE 10 (Cont'd) 118 15 .087 103 1*5 .120 l-*+0 .237 5 - 5 0 A 7 3 5- 55 .762 6 - 55 .895 8-0 .970 12-30 1.390 105 15 .071* 35 .086 1-30 .li+O 3-0 .220 *-35 .300 6- $0 .S+28 7- **5 MO 12-10 .710 12- 25 .710 13- 25 .727 2»+-0 .905 2»+-25 .850 26-1*0 1.068 107 , 1 5 .073 1*0 .092 1-35 •13> 2-**5 .183 3-35 .210 5 - f t .305 7-0 .362 8-1*5 .1+51* 110 15 .078 ^5 .101* 1-50 .160 2-55 .220 W° .308 5-l*o .368 8-5 10 .076 1*0 .126 1-5 . i i * 5 1-55 .183 2-50 .228 3-50 .280 5-0 .332 6-1*0 . * * l i * 7-50 .1*86 11-55 .715 13-25 .725 127 10 .096 h5 .121* 1-^5 .166 2-50 .218 3-55 .256 5-io .312 7-20 .^32 8-5 .1*68 12-20 .735 173 15 .086 50 .107 1-50 .155 2-30 .187 3-10 .259 tf-55 .350 5-30 .J+80 10-25 .620 101* 10 .062 35 .081* 1-30 .136 2-25 .192 3-^5 .261 8-10 .505 9-1*0 .586 59 TABLE 10 (Cont 'd) 17* 15 .057 108 15 .069 *5 .077 55 .100 1- *5 .138 l - * 0 .106 2 - 25 .182 3-5 .190 3 - 5 . 2 0 * * - i o .2*0 *-5o .291 5-25 . * i * 5-25 .322 7-20 ,*39 • 5*' 7-35 .*29 10-25 . 7 LO-30 .5*2 10-*5 .560 10-3  12-0 .562 106 15 .055 35 . .070 1-30 .121 3 - 0 .206 * - 3 0 .289 6-35 . * 2 0 7-*5 . *70 12-20 .650 109 15 .098 *5 .125 1-50 .173 ?-? .220 * - 5 0 5 -*o .332 . * 0 2 8-5 .553 128 10 .059 35 1-30 .183 2-35 .218 3-*5 .263 5-5 . 3 3 * 7-5 .*1* 7-50 .*79 12-10 .659 6 0 TABLE 11 TIME OF IMMERSION VERSUS CUPRIC ION CONCENTRATION  FOR #18 B S SOFT COPPER WIRE AT 75- 0.2°C Run Time Cu# Concentra- Run Number Hr.- Min. tion Number MinimaLes/Liter Time Cu# Concentra-Hr.-MIn. tion Millimoles/Liter 181 10 .105 182 10 .118 .202 ^5 .182 1-1*0 .1*21 1-1*0 .360 2-20 ..632 2-^ 20 .1*90 l:°o .808 t°o .631 1.010 .791 5-20 1.287 5-20 I.O69 6-0 1.1*00 6-0 1.152 183 15 **5 1- 30 2- 25 -5 -15 5- 0 6- 10 .122 .311* .536 .672 .912 1.075 1.280 185 10 ft 1- 1*5 2- 20 - 0 -5 5- 0 6- 0 .132 .292 A52 .673 .700 .971 1.251 1.398 181* 15 .11*1 •215 1-30 .361 2-25 .*+96 3-5^ .615 .819 5-0 .9*+0 6-0 1.115 10 .136 **5 .300 1-55 .517 2-30 .610 3-10 .736 I+-20 .886 5-20 1.132 6-0 1.190 186 15 ft 1- 1*5 2- 20 -15 5- 0 6- 0 .128 .263 .1*86 .631* .761 1.020 1.200 1.350 187 190 10 1*0 1-30 15 - 0 i+-i*5 6^0 .125 .258 .1*22 .702 .897 l.Ott) 1.21*0 61 TABLE 11 (Cont'd) 189 .227 .335 191 15 .160 *5 55 .302 1-35 • 532 l - * 0 . * 0 0 & .781 2-30 .552 .965 3-10 .602 *-*5 1.1*0 J+-50 1.010 1.265 5-25 1.152 6-35 1.510 6-10 6-50 1.280 l . * 3 0 188 10 .120 192 15 .225 50 .225 i - * o . .382 1-55 . * 5 0 .515 2-50 .600 2-30 .660 * - o .875 3-10 .810 6 - 0 1.200 175 10 .17* 178 10 .105 *5 .2*8 *5 .179 1- 30 .329 1-30 .262 2- 15 .501 2-15 .396 3 - 25 .670 3-15 .*85 * - l 5 .902 * - 0 .650 5- 15 1 .02* 5-0 .782 6 - 0 1 .06* 6-0 .961 179 10 .105 *5 .176 1- *o .312 2- 15 .390 3 - 0 .*79 * - l 0 .609 5- 0 .732 6- 35 .795 177 10 .121 *5 .197 1-30 .388 2-15 . * 6 2 3-15 .680 * - l 5 . 8 * 2 5-20 .981 6-0 1.150 10 .110 *5 .180 1-30 .280 2-15 .366 3-25 .551 * - l 5 .655 5-15 .802 6 - 0 .851 176 180 10 . 085 *5 . 1*0 1- * 0 .201 2- 15 -10 .516 5- 0 . 6 * 2 6 - 35 .8*6 62 TABLE 12 TIME OF IMMERSION VERSUS CUPRIC IOH CONCENTRATION  FOR #18 B S SOFT COPPER WIRE AT 15 - 0.2°C Run Tim© Cu# Concentration Number Hr -Min. Millimoles/Liter 193 20 . 0 * 9 1- 20 .057 2- 20 .065 3 - 55 .08* 5-10 . 0 9 * 7-25 .117 10-0 .1*2 12-20 .168 2*-0 .2*3 26- 25 .261 27- 50 .268 31-25 . 3 1 * 37-35 .3*7 * 8 - 0 . * 2 0 5 0 . 0 , * 5 * 55-0 . * 9 0 6 7 T I M E HR. Cu* 4 C O N C E N T R A T I O N M I L L I M O L E S per L I T E R b b o b - *- -ro O) 03 o ro * cn 19 .1 6 _I CD CL .1.2 _ J _ J 2.0 8 < 0 6 o r r-z UJ u.o.4 o o 5.0.2 | 1—: r 1 i > • I i i t i ! ; i ; i ' I 1 • 1 i i • 1 — • j : ^ •.. . . i ... .. . . . • ; . i ' •• ! •i • i • i . . i • ^ • : i ' i i .! j . ; i i • ! • i i • L l r L _ __]_' , i i i i i I - • I j' ]' t •i |.0 M- H 2 S 0 4 ; j TEMP. I5°C ' | i ; STRESS I KGM. , 1 ! • : i ' i ! ro o 6 7 TIME HR. 8 10 12 C u n C O N C E N T R A T I O N M I L L I M O L E S per L I T E R 9 9 CD 6 7 TIME HR. 0 I 2 - 3 4 5 6 7 8 9 10 II 12 T I M E HR. C u 4 * C O N C E N T R A T I O N M I L L I M O L E S per L I T E R ol - 0 M T I M E HR. 0 I 2 . 3 4 5 6 7 8 9 10 I I 12 T I M E H R . 33 o ro CP T I M E H R . 5.0.2 0 0.5 M. H 2 S 0 4 TEMP. 2 5 ° C STRESS 5 KGM. 0 6 7 T I M E HR. 8 10 T I M E HR. .L' I 4 L i * CO UJ _J o . 1 0 _J .0 8 O < 0 6 or -z. UJ O.0 .4 o CJ t O.0.2 . 0.1 M.; H 2 S 0 4 TEMP. 25°C STRESS 10 KGM. 3 p 4^  0 -0 OO 0 7 T I M E HR. 12 C O o TIME HR. 2} o Co T I M F HR 0 i 2 3 4 5 6 7 8 * 9 10 II 12 T I M E H R . 0 I 2 3 , 4 5 6 7 8 9,-. 10 II 12 T I M E H R . T I M E H R . cc L U r -.25 Q. C O L U .20 _J -J .15 < .10 CC LU O z o o o 05 0 • i I | i I I 1 I ! i 1 '! i ; ;! ' 1 t. i i . i . ' .1 ! i •.' t ' : : j i i ! \ i i : . o . ! i i ; i ' \ ' 1 ' : i • ~"~o"~-: ' j . • ; o o • o j - i i i i • f - " i 1 ) ! t i : i ; 1 Or i . •' ' i 0.1 M. H2 SO 4 ' TEMP. 35 °C i " i STRESS 1 KGM. • ; 1 ; 1 i . ! 1 a 0 5 0 6 7 T I M E H R . 8 10 0.8 0 I 2 3 4 5 6 7 8 9 10 II 12 T I M E H R . 0.8 0 I 2 3 4 5 6 7 8 9 10 II 12 T I M E H R . 0.8 or LU r - 0 . 7 0 1 . 2 3 4 5 6 7 8 9 10 II 12 T I M E H R . TIME HR. 001 o H 0 1 2 3 4 5 6 7 8 TIME HR. TIME HR. TIME HR. Cu*CONCENTRATION MILLIMOLES pei L I T E R O O O o - - — TIME HR. TIME HR. 108 APPENDIX II 1. P0LAR0GRAPHY 2. CALCULATIONS 109 POLAR OGRAPHY INTRODUCTION The polarographic method of chemical analysis, invented by Jaroslav Heyrovsky at the Charles University i n Prague about 1920 (2k), i s based on the unique char-acteristics of the current-voltage curves(polarogram)ob-tained when solutions are electrolyzed i n a c e l l i n which one electrode consists of mercury f a l l i n g dropwise from a fine bore capillary glass tube. From such polarograms i t i s possible not only to identify but also to determine the concentrations of several or a l l of the reducible or oxi-dizable substances present. In some cases as many as five or six substances, present in concentrations ^.aQgfejg'ied from 10"^ to 0 .01 M, can be identified from a single polarogram. Its use for very small concentrations plus the fact that the volume of solution required for analysis can be a fraction of a millimeter, places polarography among the most sensitive analytical techniques. POLAROGRAPHY OF COPPER Half wave potentials and values of ld/CM 2/3 tn./6 for cupric copper In a number of common supporting electro-lytes have been l i s t e d by Lingane ( 3 1 ) . 110 From the following standard potentials of the couples involving simple cupric ion, simple cuprous ion and metallic copper i t follows that reduction of simple cupric ion to the metal requires less enerb^y than i t s reduction to simple cuprous ions , -Cu+ + e = Cu; E° = 0 . 2 8 0 vs . S.C.E. ( 1 8 ) Cu* +2e = Cu; E° = 0 . 1 0 3 vs . S.C.E. ( 1 9 ) Cu* * e = Cu +; E° = 0,07k vs. S.C.E. ( 2 0 ) In other words, simple cuprous Ion i s Incapable of existing in any appreciable concentration and disproportion-ates into cupric ion and metallic coppers 2Cu + = Cu +• Cu*; K = 1 x 1 0 6 ( 2 1 ) Consequently i n the absence of complexing agents, e.g., i n nitrate, perchlorate or sulfate supporting electro-lytes, the polarogram of cupric ion comprises only a single wave corresponding to direct reduction to the metal. ( 2 8 ) Fig. ( 6 5 ) shows a typical polarogram obtained from a test run for copper in sulfuric acid. In a l l cases only a single wave was obtained Indicating the absence of complexing agents, which supports the work of Lingane ( 3 1 ) . Lingane ( 3 1 ) , has shown for copper in O.fJ.M.H.^O^ at 25 degrees that the half wave potential as referred to the saturated calomel elec-trode i s 0.00 volts or -0 . 2 * 2 volts as referred to the hydrogen electrode. In a l l cases in our work the half wave potential was calculated as a check and the value averaged out to be I l l - 0 . 3 2 5 volts. The standard reduction potential of Cu* + 2e • Cu (19) as referred to the hydrogen electrode Is - 0 . 3 * 0 volts (17). MEASUREMENT OF THE DIFFUSION CURRENT AND HALF WAVE POTENTIAL To quantitatively and gualitatively intrepret the polarogram, the diffusion current and half wave potential of the step must be measured. Many methods for making these measurements have appeared in the literature (28)(52) ( 3 9 ) , and, i n particular, the determination of the diffusion cur-rent has been subject to considerable discussion. Fig. (65) shows the construction used throughout this work for evalu-ation of the diffusion current and half wave potential. To make these measurements proceeds as follows: 1. Draw mid-line AA' and BB1 dividing i n half the residual and diffusion current plateaus respectively. 2. Draw mid-line CC1 dividing the sharply rising portion of the step in half. 3 . Draw lines FF' and GG1 through points 0 and N and parallel to the vertical axis of the polarogram. *• Draw lines DD1 and EE 1 through points 0 and N and parallel to the horizontal axis of the polarogram. 5 . Draw line HH' through points M and P. 6 . Draw line JJ' through point of intersection L and parallel to the vertical axis of the polarogram. FIG. 65 EXPERIMENTAL PO LAP. 0 GRAM FOR THE REDUCTION OF GO 'PES IN SULFURIC ACID SHOTNIHG THE METHOD OF CALCULATION * Ilk The diffusion current, i n microamps, may then be calculated by multiplying the step-height JJ», expressed i n millimeters, by the setting on the sensitivity control. The observed half wave potential Is taken as the potential at point L. The value of the diffusion current Is proportional to the concentration of the ion reduced at that particular value of the half wave potential. To obtain the concentra-tion a calibration curve has to be prepared. According to the original Ilkovic equation the diffusion current constant is defined as: z 9 . l d , { 2 2 ) CM2/3tl/6 For a particular capillary of constant mercury head M and t are constant for a given temperature and solution therefore i d = KC ; K = lM2/3tl/6 (23) If now polarograms are taken on solutions of known copper concentration and the diffusion current calculated as des-cribed a calibration curve can be drawn (Fig.6 6 ) . As can be seen this calibration curve refers to one capillary at one temperature. To extend this curve to another capillary, values of M and t were calculated. From the values of M and t and the slope of the straight line (Fig. 66) a vaule for I was calculated. From this value of I calibration curves were obtained for another capillary at various temperatures by evalutation of M and t under the different conditions. Fig. (67) and Fig. (68) show the cali -bration curves and table (13) gives the calculated values. 115 TABLE (13) I = 2 .976 = K M 2 / 3 t l / 6 CAPILIARY A  Temperature °C M mg/sec. t Sec. M 2 / 3 t l / 6 K (Slope) 15 1.598 *.138 1.7*2 5.185 25 1.6*5 *.017 1.7*7 5.200 35 1.681 3.887 1.773 5.277 55 1.766 3.698 1.829 5.*** 75 1.832 3.518 1.859 5 .532 CAPILLARY E Temperature M mg/sec. t sec. M 2 / 3 t l / 6 K (Slope) 15 2.585 3 .077 2.272 6 .763 25 2.679 2.937 2.309 6.873 35 2.727 2.857 2.325 6.920 55 2.880 2 .662 2.395 7.129 75 3.010 2.*91 2.**7 7 .282 POLAROGRAPHY NOMENCLATURE id » average current in microamperes during the l i f e of the drop "diffusion current". © = concentration in millimoles per l i t e r of the oxidizable or reducible substance. 116 :M - rate of flow of mercury from the dropping electrode capillary, (mg per sec.) t - mercury drop time (sec.) E° = standard electrode potential. I = diffusion current constant, n = number of farodays of e l e c t r i c i t y required per mole of the electrode reaction. D - diffusion coefficient of the reducible or oxidizable substance (cm^ per s e c ) . CONCENTRATION 

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