An Investigation of the System Cr(III)/Cr(II) by Digital Polarography, at Different Cr(III) Concentrations, at Varying pH, and in Different Supporting Electrolytes Citation Rathjen, Nancy Katherine (1969) An Investigation of the System Cr(III)/Cr(II) by Digital Polarography, at Different Cr(III) Concentrations, at Varying pH, and in Different Supporting Electrolytes. Master's thesis, California Institute of Technology. doi:10.7907/N5V3-H153. https://resolver.caltech.edu/CaltechTHESIS:05042010-123622070 Abstract One of the implications of Marcus theory of electron transfer is that d, the electrochemical transfer coefficient, would not be constant, but would be a function of potential. Recent work has tended to confirm this implication. To examine this possible potential-dependence d, the system Cr(III)/Cr(II) was investigated by digital polarography, at different Cr(III) concentrations, at varying pH, and in different supporting electrolytes. Most of the resulting rate data do suggest a potential-dependence of d. Apparent heats of activation were obtained for three of the supporting electrolytes investigated, and from these a calculation was made of the magnitude of the potential-dependence predicted by Marcus theory. There was little correlation between the magnitude of the potential-dependence predicted by Marcus theory, and that actually found. Item Type: Thesis (Master's thesis) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Anson, Fred C. Thesis Committee: Unknown, Unknown Defense Date: 27 December 1968 Additional Information: Typographical error in title on title page: An Investigation of the System Cr(III)/Cr(II) by Digital Polarography, at Dirrerent (sic) Cr(III) Concentrations, at Varying pH, and in Different Supporting Electrolytes Record Number: CaltechTHESIS:05042010-123622070 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:05042010-123622070 DOI: 10.7907/N5V3-H153 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 5770 Collection: CaltechTHESIS Deposited By: Tony Diaz Deposited On: 09 Aug 2010 22:41 Last Modified: 06 May 2024 19:26 Thesis Files Preview PDF - Final Version See Usage Policy. 1MB Repository Staff Only: item control page

An Investigation of the System Cr(III)/Cr(I1L) by Digital Polarography, at Dirrerent Cr(III) Concentrations, at Varying pH, and in Different Supporting Electrolytes. Thesis by Nancy Rathjen In Partial Fulfillment of the Requirements For the Degree of Master of Science California Institute of Technology Pasadena, California 1969 (Submitted December 27, 1968) Acknowledgements Abstract .... Introduction . Experimental Preparation Preparation Preparation Preparation pH Study of Heat of Act Results Discussion . Summary . References TABLE OF CONTENTS Cr(III) Solution . oO ry of Nac1lO), Solution . of KI Solution... . of A1(C10,)3 Solution . Cr(III) in 0.5 F NaC1o, . ivation Studies. . Oo OO OO WO’ A ii iii . il ll 12 - 35 45 . AT LIST OF TABLES AND FIGURES TABLES Table I. Comparison of rate data obtained in NaclOy from two sets of values for J, the outer Helmholtz poten- tial 2... 1 ew we ew ee we ww we CY Table II. Comparison of corrected and uncor- rected rate data for the potassium halides . . . 6 6 «© «© © © © © «© © 2 22 Table III. Potential-dependent and votential- independent slopes for the potassium halides... .. 6. ee ee ee ee 24 Table IV. Corrected and uncorrected rate data for A1(C10,)4 and NaClO, ..... . 28 Table V. Potential-dependent and potential- independent slopes for aluminum and sodium perchlorate .... +... +. 3O Table VI. Heat of activation data for KI, NaCl0, and A1(C10,)3 . oe ee ew we ew BE FIGURES Figure 1. “Schematic of cell design ...... 7 Figure 2. Effect of variation of pH on the polarographic behavior of Cr(III) . 14 Figure 3. Calculation of @, potentials versus potential for Al C10); rs Figure 4, Rate data at various temperatures for KI, NaCl0, and A1(C10y )3 - 2 es 32 ACKNOWLEDGEMENTS I wish to thank my research advisor, Dr. Fred Anson, for his patient and helpful advice on this work. I am also indebted to New York State, the John Stauffer Chemical Company, and American Cyanamide for financial support during the course of this research. My heartfelt thanks are also extended to Mrs. Roberta June Riese, whose typing of this manuscript was only one of her many generous encouragements. ii ABSTRACT One of the implications of Marcus theory of electron transfer is that A, the electrochemical transfer coefficient, would not be constant, but would be a function of potential. Recent work has tended to confirm this implication. To examine this possible potential-dependence of A, the system Cr(III)/Cr(II) was investigated by digital polarography, at different Cr(III) con- centrations, at varying pH, and in different sup- porting electrolytes. Most of the resulting rate data do suggest a potential-dependence of a, Apparent heats of activation were obtained for three of the supporting electrolytes investigated, and from these a calculation was made of the magni- tude of the potential-dependence predicted by Marcus theory. There was little correlation between the magnitude of the potential-dependence predicted by Marcus theory, and that actually found, iii INTRODUCTION For an electrochemical redox reaction, one may distinguish five states for a soluble oxidized species O and reduced species R. I. O in bulk of solution outside diffuse double layer and n electrons e in the electrode. It. O in outer plane of closest approach and n electrons e in electrode. f= Transition state. III. R in outer plane of closest approach. IV. R in bulk of solution outside diffuse double layer. Delahay, ! following Parson's formulation, defines _the electrochemical transfer coefficient x in terms of the potential-dependent part of the standard free energy difference F?ry-F?y. In this way, the cal- culation of FG » needed for the rate constant, can be formulated without a detailed model of the trans- ition state, by assuming the potential-dependent part of the free energy difference between states f~ and II may be expressed as a constant fraction Aof the potential-dependent part of the free energy difference between states II and III. Thus, (PY). -(FEp). = * [te -(Fine | where the subscript e denotes the potential depen-~ dent part. Van Rysselberghe, * however, considers A must be defined in terms of FO,, -F?z and not in terms of the potential-dependent part of this differ- ence. These formulations lead to the prediction, in absence of double-layer effects, that & would be independent of potential. That is, . _ ie] fo) if AF*= FQ -F ke ko. exp (rental f,n~ “pyn °*P \ RTS Ink = 242 a yin 1° , RT fyh dink Pyh iw _ ant a: RT Here the subscripts f,h indicate the forward (f) rate -constant of a heterogeneous (h) reaction. R, T, and Ff nave their usual significance. However, Marcus>~8 has. formulated a theory of electron transfer which attempts to construct exactly what is avoided in the above, i.e., a detailed model of the transition state. This model assumes only a weak electronic interaction between, in the electro- chemical case, the electrode and reactant. Marcus also considers that an electron transfer reaction may proceed by way of intermediate states whose elec- trical polarization is not in equilibrium with the field arising from the charges present. This model may be considered to be an application of the Frank- Condon principle. His final equations are thus de- rived for non-equilibrium conditions: AF¥ = w+ mY m= -(3+ nfy + w? ow) - "ey AF* r Y 4 n$n + weaw? (nF yn + wow")? ) SS wr ( rr rs eT) ry2 ¥ ng wP 4 wr (nFq + wP-w hoe" 2 w Uy 1 = overvoltage = E-E’, where Bg is the standard potential. (Note this is different from the electrochemical overvoltage, V= E-Eney where Eney isthe equilibrium potential. ) wi = work needed to bring reactant and electrode together. wP = comparable quantity for products. re i energy required to reorganize the coordination shell during activation = Y,o4+ Yo: See Ref- erence 9. These equations may be applied for a "“nonadiabatic reaction", i.e., a reaction where the probability of passage along the potential energy surface character- istic of reactants to the potential energy surface characteristic of the products is small. -One may assume wP — O =w", if double-layer effects are neglected (or if the data have been pre- viously corrected for double-layer effects); then. mn 2° uy fe) ~ AF* Then Kp y= Kp 7° exp (=42 ) — -AF* in Ken RT + ¢ -jink RT 1 = set (g)= (3+ 8) Thus Marcus theory would predict a potential depven- dence of &. This particular set of equations applies to a heterogeneous reaction of the type Marcus clas- sifies as Class 111,19 i.e., redox reactions in which the coordination shell of the oxidized form has quite different interatomic distances compared to the re- duced form. One example of this type of reaction is the one studied in this research, Cr(H,0),7* + ne“—» Cr(H,0)¢°*. This is presumed to be an outer-sphere reaction, tt and so fulfills Marcus! condition of weak interaction between the reactant and electrode. Also, the rela- tively low rate constantl? (1.0 x 107? em/sec at 20°C in 1M KCl) fulfills the condition of non-adia- baticity. Koutecky'si3,14 analysis of irreversible elec- trode processes of the type O+ ne~= R relates the ratio i/ig to \, where i— current ig = diffusion current \ = (22/7)" Kp yt Do role Do = diffusion constant of oxidized species QO. t = drop time in sec. The relation between /\ and i/ig has been tab- ulated, and reproduced by Delahay.15 Thus, it is obvious that if i/ig is known, \ may be found, and because in i\ = 1n Kp nt C the slope of a plot of In/\ versus potential should » yield &, for an irreversible process. 16 Parsons and Passeron published some data for the Cr*3/cr** reaction, indicating that a potential dependence was observed for the transfer coefficient. This work is a continuation of their investigation.. To clearly establish the potential-dependence of of would be evidence favoring the Marcus theory of elec- “tron transfer, and evidence against the older for- mulation typified by Parson's presentation. EXPERIMENTAL Normal procedure was to obtain a current-voltage curve using D.C. digital polarography. Philbrick P65 and P6SAU amplifiers were used as a current measurer and follower, respectively. All data were corrected for background current by graphical sub- traction, and the i/ig ratios were corrected for mass transfer using Koutecky's analysis.t? Points. on the polarograms were usually recorded at 10 mV. intervals. Drop times were kept approximately constant, and were obtained from chart speed and peak spacing. If the variation was greater than £ 0.03 sec., the values were corrected to 4.15 sec. Uniess otherwise noted, the temperature was 25.09 4 0.2°. The cell design is shown in Figure l. A gas train was constructed using chromous and vanadous traps; high purity (Matheson, silver tank) nitrogen was used for deaeration. Nitrogen was also passed over the surface of the solution during a run. Exceot where otherwise specified, all runs were made at pH of 2.040.1. Cell compartment inlets Lor DME. and fitted glass No. disperser refere nee € lec trode Com partm ent a a ry a = -——— to Constant bempecatuce bath Le _ [ ls to , AWK eatin temperature \- \ ey K Ken. recess bor = “4 pool duxilavy electrode fitted glass dase Pt wit Figure 1. Schematic 9f cell design. A commercial electrode (Sargent SCE) was used as the cell reference electrode, with NaCl crystals and solution rather than KCl. A modified saturated calomel electrode was used, with NaCl rather than KCl, to avoid precipitation at the liquid-electrode junction of KC10,, in the perchlorate solutions. This cell reference electrode was checked against a massive SCH electrode, construct- ed according to the method described in Ivest8, Over a@ period of a few months, the potential of the cell reference electrode was found to be constant tot 1 mV. Purified charcoal was prepared by leaching act- ivated charcoal (Matheson, Coleman and Bell, CX 655) with concentrated HCl under an Ny atmosphere in a Soxhlet extractor until the extract was clear, then extracting with water until the extract was the sane. pH as the distillate. The purified charcoal was kept in the extractor under No until ready for use. Some solutions were treated with this purified charcoal, but no systematic variations were observed in the polarographic behavior of the treated solutions com- pared to the untreated solutions. | Preparation of Cr(III) Solution: A solution of 0.1 F Cr(H,0)2 was prepared by reduction of Cr0z (Baker and Adamson, reagent grade) with a 10% solution of H50,. solution was boiled to remove traces of H The resulting dark blue 2%: and made 1 F in HC10,. All solutions were made with triply-distilled water. A u.v.-visible spectra was taken. According to the criterion established by Altman and King, 19 the size and appearance of the peak at 230 m« indicated a very small degree of | polymerization. The ratio of absorbance at 230 mx and 260 mu was: A530 _ Preparation of NaCl0, : NaCl10, was prepared by combining approximately equimolar concentrations of NaOH and HC10). The pH was then adjusted to 2.0. Preparation of KI Solutions: The KCl and KBr solutions were made directly from the salts (Matheson, reagent grade) and were adjusted to pH of 2.0 before a run. This procedure was not suitable for the KI solutions, because of air oxidation of the acidic solution. Therefore, the KI solutions were acidified after deaeration, and the uncertainty of the pH in these solutions was®0.2 pH units. Preparation of A1(C10y )z Solutions: A mother solution of A1(C10, ); was prepared by attack at room-temperature .(to avoid reduction of C10,” to C17) of 54 g. of Al in one liter of 3M HC10),. Attack was initiated by a globule of mercury. Ina few hours, most of the Al had dissolved, with some remaining to prevent mercury attack. An attempt was made to determine Al gravimetrically as the oxide, and gave unsatisfactory results. <A determination was then done by precipitating the Al with 8-hydroxy- quinoline, and yielded satisfactory precision. However, it was noticed that the pH, initially ad-. justed to 2.0 before a run, increased during the course of the run, and would stabilize after a period of a few hours to 3.4, Consultation with the liter- ature@9,21 indicated that a slow equilibrium was involved in the hydrolysis of A1(C10, )5 solutions, with the hydrolyzed species uncertain, but believed > to ve [A1,(0H)3}"* ana (A1,3(0H)551 7°. The aata gathered with this solution were also obviously | spurious; the currents would change with time, and more dilute concentrations of the electrolyte gave Slower rates, before double-layer corrections, than more concentrated ones, for the same Cr(III) concen- trations at the same potentials. An attempt was made to salvage this solution by titrating with HC10, to a pH of 2.0, and adding 10 titrant as the pH changed, until a pH of 2.0 was maintained for 16 hours. However, satisfactory results were still not obtained, so this solution was discarded, and a new one prepared.: The second Al solution was prepared in the same manner as the first, except that 54 g. of Al were used in one liter of solution 6 M in HC10,. The Al was again analyzed as the oxine. The solution prepared in this manner maintained a constant pH, and gave reasonable results. pH Study of Cr(III) in 0.5 F NaCl0): A series of solutions was prepared, with the pH ranging from 2.0 to 4.0. Care was taken to avoid “exposing the Cr(III) solution to a pH greater than 4.0, to avoid problems with polymerization, etc. A Leeds & Northrup oH meter was used to determine the pH, with a modified saturated calomel electrode (NaCl instead of KCl). | Heat of Activation Studies: A constant temperature bath, equipped with stirrer and heater, was used to control the bath temperature to + 0.05°. A centrifugal pump circu- lated the bath water through the water jacket of the cell. The temperature variation-within the cell il itself did not exceed £ 0.3° for a given run, in ‘those cases where heat losses were greatest. RESULTS The first variable studied in the Cr(III) system was the Cr(III) concentration, at constant electro- lyte strength (0.5 F NaC10)). There, of course, should be no effect on the rate constant for varia- tions in the chromium concentration. Over a range of dilute Cr( TIT) concentrations, (0.3 mM - 1.0 mM), this proved to be the case. For concentrations great- er than 1 mM (2 mM, 3 mM, 3.5 mM, 4.0 mM) the data were increasingly erratic. At 2 mM concentrations there occasionally would be polarograms demonstrating maxima behavior; less frequently, there would be distortion of the peak shape. For concentrations of 3.0 mM and greater, the maxima behavior would be more frequent and more pronounced. Even those polar- ograms at 2 mM Cr(III), which did not appear obvious- ly to demonstrate maxima behavior, gave results some- what different than the more dilute Cr(III) concen- trations. The scatter in the results grew larger as the’ Cr(III) concentration was increased over 2 mM, Hence, it was concluded that all data taken at con-- 12 centrations greater than about 1 mM were question- able, and may be demonstrating incipient or overt maxima. The very dilute Cr( IIT) concentrations were also not very reliable, because the magnitude of the corrected current was not much greater than the magnitude of the background current. To optimize these two conditions, i.e., freedom from maxima and smallest errors in background current corrections, “a Cr(III) concentration of 0.5 mM was chosen. All future work was done with this concentration of Cr(IIT). Previous work by Parsons and Passeron!® had been done on a Cr(III)/Cr(II) system, in NaC1l0y medium, at a pH of 3.4. Calculation indicated that at this pH, with a Cr(IIZ) concentration of 5 mM, about half of the reactive species would be in hy- drolyzed form. (This is using a hydrolysis constant of log K= -hO1.) This would suggest that the pH in the area of the electrode was essentially unde- fined, and rendered their rate data suspect. To confirm this suspicion, a series of polarograms was taken in 0.5 F NaCl0,, with a Cr(III) concentration of 0.5 mM, with the pH varying from 2.0 to 4.0. The 13 ° Ps 2.o + 2.5 ° = 3.0 x: 3,57 °o - / * 4.0 low N OSco~ a é abee log x ok | 0.400 ~ % 2 *% a: a ee + O.1l@ — xn 6 + r-) > 5 x Pan ¢ ° 0.° J 0.00 7 “yy % 6 * . : 0 “deo 7 % e .S % Sad = foo" x % Q co) x 6 , + O a ° ° “690 * x ee H : Y a — foo 7 an — 20a ~.3215 —$50 _ i ' U T 7 > v 1 7 T = - 0 — Bee =350 ~ Fao ~ 9s E vs. SCE Figure 2. Effect of pH on the polarographic behavior of Cr(III). Data is for 0.5mM Cr(IIT) in 0.5 F NaClOy, at varying pH. 14 results are shown in Figure 2. Here it is seen that ‘ata pH of 4.0, the results are divergent from those at more acidic solutions. Also, by a pH of 3.4, thé peak heights were becoming irregular and non-repro- Gucible for a given potential. By a pH of 4.0, this was true to such an extent that some amount of arbi- trariness was introduced in measuring the polarograms. The more concentrated the Cr(III) solution, the great- er the uncertainty in the pH that would be introduced in the electrode area. Parsons and Passeronl© did: not publish the Cr(III) concentration at which they collected their data, but private communication with Passeron indicated this concentration was avproxi- mately 5 mM. At a Cr(III) concentration of 5 mM, | in a solution of oH 3.4, there. are more hydroxyl ions in the hydrolyzed chromium species than there are hydronium ions in solution. The data shown in Figure 2 was taken at a chromium concentration an order of magnitude less than the Parsons and Passeron data. This is perhaps why the data at a pH of 3.4 . appears consistent with more acidic pH's, for this low Cr(III) concentration. To confirm that hydrolysis was substantial for a Cr(III) solution at a pH of 3.4, a pH titration was done, using standard perchloric acid, and a 15 0.100 F Cr(III) solution, prepared from the mother Cr(III) solution. A blank was run, titrating from a pH of 3.4 to 2.0. The titration was monitored by a Leeds and Northrup pH meter. The response, of course, became relatively insensitive at a pH of 2.0, but within this accuracy the titration of the Cr(III) solution consumed 70% more titrant than the blank, and this excess corresponded roughly to the difference of the hydrolyzed amounts of Cr( IIT) at a pH of 3.4 and 2.0, respectively (which is near- ly equal to the hydrolyzed concentration at a pH of 3.4, because the amount of hydrolyzed Cr(III) at a pH of 2.0 is very small). All future work was therefore done at a pH of 2.0. All the data up to this point had been corrected for mass-transfer, but not for double-layer effects. Double-layer theory@* develops the following equation: 1. 4a ig ef tn-#)F 82 [p> antag ~e(1-+ nk a] Where a= transfer coefficient f£ = F/at Bo = potential at the outer Helmholtz plane q = overvoltage One implication of this equation is that a plot of 16 log \ (or log k) against potential would not be linear, but would have a potential-dependent slope. By applying an appropriate correction (for the case of the irreversible reaction Cr(III)/Cr(II)) log Ay = log -(%-3)6,F/RT one would then expect (if double-layer theory applies) to get a linear plot for log k vs. potential (or overvoltage), only after appropriate double-layer corrections had been made. However, the Marcus effect would also predict @ potential-dependent slope of log k versus over- voltage. Therefore, before an attempt could be made to demonstrate with some confidence whether or not a Marcus effect was operative in this system, reason- able double-layer corrections would have to be made. Correction for double-layer effects, taking into account any specific adsorption, should give a rate constant that would be independent of the concentra- tion or nature of the supporting electrolyte. To determine if this was indeed the case, a series of polarograms was run using different con- centrations of NaClO),. The effect of double-layer corrections would be largest at the more dilute con- centrations of supporting electrolyte; hence, it 17 would be desirable to obtain data at low electrolyte concentration. However, a practical minumum was imposed on how dilute a supporting electrolyte con- centration could be used, by the appearance of max- ima behavior at low electrolyte concentrations. It was found that concentrations more dilute than 0.5 F NaC1l0y could not be used for this reason. The concentrations that were used were: 0.3 F, 0.5 F, 0.7 F, 1.0 F. Two sets of values for Bo in perchlorate media were found in the literature: one given by Bockris and coworkers*? for NaC10), and one by Parsons and Payne, 24 for HC10,. The slope, 69,/dE, was, not very different in the two sets of values, but the absolute values for Bo at a given potential, for a given per- chlorate concentration, differed substantially in the two cases. Both sets of f, data were tried. The results for the corrected rate constant function, log , ‘are shown in Table I, for representative potentials. Because of some ambiguities in the data-gathering process as reported by Bockris et. al., and also because of the agreement between the Payne data and similar data gathered by other workers in this 1abd- 18 au/a °g(¢-%) - YVSot 6T°T- ty’ t- TS°Tt- O° T- ¢h°t- 2Q°T- L6°T- Gl°e- Ce°e- CE °S- 4Oo°T a’O 4S°O oq FU 29 2(L/2T) T T T qt LG° Qh't- TS'T>ghtt- — S6TT- Tote 6T*e- ¢6°T- LU er TE’e- tite Te" ce" - €l'- cc" gS°S- ty e- te — ELYS- TQS 68° ~ LL°- 19° ~ og EO - gO°T 4L°O &S"O ae"O | SUOTABIZUSOUOH 24 BtIOTYOUEg gOenTeA Jo sgasg zeuked » SuOoscTeg cg le "48 *sTauyoog Tetquezog z4Touwitey aweqno eu, ‘¢g aog omy, Worsy TOTOeN UE peuTesaQ BIeq eteYyY Jo uOoSsTueduiOg I aidva = V Sot 7 Bot V SOT ‘A 0G6°- Ay Bot N BOT "A 0O6'- *y BOT Ne SOT "A OGG’ Hy Bot NM SOT “A OOg8’> Hos "SA Tetquezog 19 oratory, it was felt the Payne data was more reliable, and this data was used in the double-layer correction of the perchlorate data. The value of the transfer coefficient, &, changes from the uncorrected log k © vs. potential plots to the corrected plots. There- fore, equation 1 was used to evaluate the "true" value of &, by equating the slope oink. -anf + (an-Z)$ JH 0 or (cathodic range). By determining d 25/3 (linear over small potential ranges) one could then get a "true" value for a. | It can be seen that the corrected rate constant is not constant for a given potential, for different electrolyte concentrations, as it should be accord- ing to double-layer theory. Therefore, it was decided to collect data in a series of monovalent electrolytes which demonstrat- ed varying amounts of specific adsorption. The series KCl, KBr and KI was chosen. At the potentials used, KCl demonstrates essentially no specific adsorption, and therefore J. data for NaReo (a monovalent, non- svecifically adsorbed electrolyte) was used. The concentrations used were 0.2 F, 0.5 F and 0.8 F KCl. 20 The $5 data for KBr was taken from Parsons, Lawrence 26 and Payne. This data was available only for 1.0 F and 0.1 F KBr. However, 0.2 F, 0.5 F and 0.8-F KBr were also studied for comparison with the other halides. The $> data for KI was taken from Breiter et. a1l.?? The concentrations of KI were 0.3 F, 0.5 F and 0.8 F. The results are summarized in Table IT. Here it is seen that. the double-layer correction for KI applies quite well, in giving internally consistent rate constants for different concentrations of KI, . at a given potential. The corrections also apply — fairly well in the case of KCl. The corrected data for KBr is somewhat more sketchy, and interpretation is difficult. Agreement between the magnitude of the rate constants for KCl and KI is also fairly good. Because this data seems to give reasonable double- layer corrections (especially in the case of KI), an analysis of the plots of log k vs. potential was done for this data. Two curves were fit to each data set, using the least-squares criterion of goodness of fit: one was linear (i.e., constant, potential-independent slope) and, the second was a second-order expression’ 21 afd ¢(<- %) 2a ou, z4 2(L/et) - AU BOT SOPTTeH wuMTssejog aug dog eyeq oyey peqyooducoug » peqooddog jo uosTueduiog II didve €Q°t- TS*T- glL°Tt- Tg*t- og’t- L9°~ 61° €e° Ot" 66° 10° gc" 00°T Gy'o~ et’ 2" 6°27 76° I~ €L°e- yl'e- Te'e- 99°- OL'- Q9L°- WW" co’ L0°- = &t" Qt’ - Ze°r Tt’ Q6"2- 26°2- G6 *e- ge*e- 69 °e- EG°e- O9t2- 69°- = €ht- = 6L°- OL°- 99°- = gG°-) =6TT*- St” LL’- Otto Qy°e- Oe Ot en gt’ 60°€- cL°- =o OL = SQ ThL’- =e" 06°- ‘Feo aS°O ac'’o ao°t ag’o dS°O ad2e’o datT’o ag’oO aS°O de’o IM Igy TOM = ty BOL = N BOT Hy B0T JV dot "A 006°0- ~AY Bol )W BOT "A 0S8°0* 4U Got N SOT “A O08"O- 1, Sot ‘NW SOT "A OGL°O- | qOS “SA [eTque4og 22 ZL of the type: Ink = ajtaygt a, (potential- dependent slope). The second order coefficient, Bo, then gave the magnitude of the potential-depend- ence of the curve. The results are summarized in / o? follow- Table IIT, It should be noted that = E-& ing the notation of Marcus theory. A value of -0.641 v. vs. SCE was used for Bo.28 Thus it is seen that for two monovalent electro- lytes, KCl and KI, it is possible to obtain reason- able double-layer corrections (KBr is doubtful); while for another monovalent electrolyte, Nacl0,, the double-layer theory does not seem to yield sat- isfactory results. Asada, Delahay and Sundaram? suggest that the failure of the double-layer theory is to be expected for mixtures of electrolytes with different ionic valences because of local variations of potential in the plane of closest approach. This effect they call the local field effect, and arises because the Poisson equation is solved for only one dimension, and hence does not take into account variations of potential in planes parallel to the electrode. They publish data for the discharge of Gat? on mercury in perchlorate media; the double-layer corrections 23 Ley + ly=F xx CY =P x LG*- = Ot" cS* O°T Th’- =LE° — Qt” 8°0 Hee: 6S° TS* 80 3° 61," 9c" 8°O “JakelL Tl'- 3 €t° tt" G°0O GG° L9° S° GO qT°T 99° 09° G°o -aTqnop 10g QT°- = tt" Ot’ €°O 6c° T° g9° zZ*O GT°Tt 26° ol," c°O 39 payoautoo -un ge'- 9° Ld. T°O Bye O9T°T- gE" €9* O°T Ly'- 4St T9° 8°0 Tt’ 4G" Cay" 8°0 rasel ~aTqnop 00°O 860g" 09° S*O ch 9S° Tt’ GO IOs peyoaudo5 Go*- =gsc’ T9* e°O ZO"*e- =e" 99° T’O 09° 65° Ltr’ ran) e7eq (teoutT) UOT} Edy (aBeouTT) uotyes4 (aeauTT) (AV TTe 2 -us0U0y Zz” O “~UZ0U0g O ~ULIOF ) vty Oy | Vv xe°V oxxly x°V | uoTzea4 -~Us0U0N IM Jy TOM SOpTTeY umtssejog doj sedotg qyuepuedaepul-Tetqjuezog pus yuepusedeg-Tetque4og IIT WTdvb a fail for the univalent and divalent salts (Na? and Mgtt) put hold for the trivalent sait (Alt), Fur- thermore, the Met salt double-layer correction is better than the Na? salt double-layer correction. It was therefore decided to collect data for the Cr(III)/Cr(II) system, using a trivalent elec- trolyte. A1(C10y)3 was chosen, to permit comparison with NaclO, , where the double-layer correction failed. Some difficulty was experienced in solution preparation, because of the slow hydrolysis of alumi- num in perchlorate medium (See Experimental, Dp. 6). To facilitate comparison with the sodium perchlorate data, the same ionic strengths were used for the aluminum salt as had been used for the sodium salt: 0.0500 F (“w=0.3), 0.0833 F (4= 0.5), 0.1167 F (= 0.7) and 0.1667 F (“=1.0). To get $, data for A1(C10y)5, the Joshi-Parsons equation:°9 rule ™ = A ¢ Be \ gts te 2(kTe /87)2 \En, (a5 1)| where q™. charge on electrode € = dielectric constant n;= concentration of ions of species in the bulk of the solution Ug= exp (-e,8,/kT) €g= charge on electron 2) was used. The indicated numerical integration was ‘performed in a Citran program to generate a series of values of q™ vs. 5 for the desired A1(C10,)3 concentrations. The assumption was then made that there was no perchlorate adsorption at the potentials of interest (-0.800 v. to -1.050 v. vs. SCE). Data for q™ vs. Bo was then available from Russell for a monovalent electrolyte?! (NaF). Then, the aluminum data was compared to Russell's tables for a given ionic strength; for a given charge on the electrode, aN Sor bo A1 (C104) - B5 NaF could be found. It was assumed that this difference in AS, could be equated to the difference AE for the two electro- lytes. This then gave a series of values of Bo vs. E for A1(C10,),. This calculation is summarized in Figure 3. The resulting data analysis for A1(C10,), is Ziven in Table IV. The NaClo) data is also present- ed for comparison, It can be seen that the rate constants at a given potential are reasonably constant for different aluminum concentrations. However, these corrected constants for aluminum differ substantially from those of NaClO,; it can also be seen that the rate 26 Al (Coy), for lonic Strength Me Natio for fone Strength AL AE = Og, Figure 3. Calculation of 5 potentials vs. potential for A1(C10,)5. 27 6U'T- 19° qi’ T- = TSG°T- OL T- QL T- QT’ Ge’ Ee" 9l.° el Tt- cg°t- 16° T- 6T°e- TE°- co*- €T’- Zc" Gl'e- = €e*e- EE S- QGP 69°- LL° 7 19° > Og *- O°T L°O ze) €°O TotoeNn w/a “6(<-)- Bot = Fy Botex 20q W'SxH 29 e(L/2T) = V B0tx {7 t Glt- ty? wh'- 6 L,°- YU Bot Qc" 6t" 09° 9th’ V Sot OS6°- LU‘t- gt't- z22°t- oz't- VY Sot Ot’- 00°0O 10° Ge’ Vv Sot "A 006'- lLott- 49°t- = TAT zt t- Hy Sot GQ°- G*- Bt ee N SOT , "A 0Gg°- LO*2~ +y Bot q* NV SOT "A 009'- O°T L4°O G*O c°O YAsusdyS OTUOT L99t° LOTT’ ¢€€g0° 0090" (A9 TF Teuios) UOT4BAIAZUBOUND © Noto) tv Notoen pue £("oto)tv aos eava AT Wlavib a4ey peqoouuoougQ pues pe yoodtog 28 constants in aluminum are considerably larger than ‘those in the halides, by .5 to .8 log units. Curve-fitting analysis was also done on the A1(C10y)5 and NaCl0, data. The same procedure was followed as for the halide series, and the results are presented in Table V. These results indicate that the curvature of the In k vs. potential plots increase with increasing concentration. It is pos- sible, through Marcus theory, to obtain an estimate of the magnitude of the second-order coefficient. The equation Are. Wt wy n Fn rn (nFn + we-w 2 h 2° "hy ry? was presented in the Introduction. If one corrects for double-layer effects, w? and w™ will be zero. One then obtains (with n = 1) Y ,F (Fy ye AP¥=2 2424 in 2° + re If the potential is at the equilibrium potential, the overvoltage is zero; if internal contributions to the entropy of the system during reaction are neglected, one can equate the A FS, = ir (at 1= ) to the experimental heat of activation, Ao pp = : The transfer coefficient then becomes -~ AF 1 1 \ a= POY = 5 + at 5 lara )"t 29 bey + ly = YO #* oO Vr yvx oL°T 16° 0S° THT 96° 83° O°t 66°T 66° GG° go*Tt 6g" T9° L°O TI£VT -eTqnop Tg" ¢..° 95° GT° 09° c9° G°O AOg pez cooutdooun HO°T 178° €9* 71° 65° 9S°* €°O eq eq ge°Tt 19° cc° . 62°T 29° EG* O°T 9c’? 88° 6¢° gO°T Tg" GG" 2.°O afk@T, ~aTqnop 60°T 6S° Ge" LE*- Ot" 9G° S’°O “dog pegoeddoo- Gt" 65° 6i7" TO*- 617" 617" ane) 27 eq ( teauTT ) (agsuTtT) (uy susays ¢ yy! oFuer xe V xx V * V xx CV xx ly eV uot ety ~UBdUND TOLOBN €( toto) tw -Oe4BtoTYoieg umtpog pue umuypumTy doj sedots Zuspusdepult-Tet4uezog pue JUuepusedseq-Tet4uUse4og A ata vb 20 Evaluation of AH* would then allow one. to cal- culate the second-order coefficient, (a) . 8( AH*) If one obtains rate data at different temperatures, the slope d ink may be used for calculation of the dt yi apparent heat of activation, Aapp- The apparent heat of activation is obtained because double-layer corrections are not available for the desired NaC10, -or A1(C10, )5 concentrations at different temperatures. Also, there seems to be a dearth of reliable data on the. temperature coefficient of the standard poten- tial of this couple. It appears from previous cal- culations? that the true heat of activation is high- er than the apparent value. Rate data was obtained at different temperatures (25°, 35°, 45°) for NaC10),, KI and A1(C10,)3. A heat of activation was found for Naclo); even though the double-layer corrections failed, for comparison with Parsons and Passeron's data. KI and A1(C10,) were chosen because the double-layer corrections appeared to apply for these two electrolytes. The graphs of log N vs. (1/T) for these three electrolytes are shown in Figure 4. The apparent heats of activation, and predicted second-order coefficients, are shown 21 1 0.0833 F A\(C1Oq)s ~. bed =, Foo | { 0. 226 x io” ‘ 3 ~ . log A S ope = = book ° ~, B60 & i i 1 i L . yr x 10> 3,lb6 3.190 Bee 31480 3. Jeo 3.490 , 660. e 0,509 Fict oo . ‘ Lo4 \ 3 Doe . Sloge = -0.259 x10 6.00 F _ : t i 1 t i rl \ Kx/o sho 4.1 bo 350 3.200 325d 3.3¢0 3.360 3400 YT 0.500 F Nalid, dco]. ° log \ 4% TLee|~ : . y © Slope = — 0.357 x/0 = Yel - =.bov] + k dy 1 i 1 3 N x10 3.100 $.150 3.200 3-286 . 3.Bcn . J3sv B.q ow YT Figure 4, Rate constants at various temper- atures for 0.0833 F Al(C10,),, 0.5 F KI, and 0.5 F NacioO. Slopes are used to calculate A¥Zpp- 32 in Table VI. Two notations are used, A Happ» and A app: A Happ = Apparent heat of activation at the standard potential. NA Happ = Apparent heat of activation at a given potential. It is desirable to use A Happ; however, A Hany is the quantity directly obtained from the Figure 4. The two are related as follows: ‘ In k Atgpp= -R (2 Xs) (1/T)/. Where kg = k° exp(-anF&/a7) € 5 = standard potential referred to SCE _ re) an FE> Ink, = in kg - an Fee) ; In kg = In ke - (an Fe ) where kg is the rate constant at potential €. ~ -anF c_ ylan ky) _ alin x) -(anF) 3(1/T) 9 (1/T) R This implies a (€ 3o (1 \ (26-€) o7 ©) _ - 0, for a range of 20°. /T) Then \'= (=*) t? Ke Do in (v= Ink, + In Te to Do =2 din &~ dln ke 3 (1/7) ~ OWT Jin ks\ _ p (do(inn) _ (dnF) (e’_¢ A ¥app= “aay )* * Pata x (Ee a) OI 23 92°0 00°T Teoy tt Teoy °° TL Tsoy% TT TBoy cg*c TeVoy Co°t puoulesseg » SUOSTeg 9 ToOTOeN £( toto) ty 6L°0 Teoy S* tT Teoy zg°e (°4 0GL°-) Teoy 6t°T Ix TA dievad Ag = cy 91°O cy ‘quotdt55005 Japsto~puoovas Tey el acy Visa . dde,, Teoy T°gt xh (HOS SA A 00g’-) (quapusedep -[T8tquejz0d) Teoy €°OT ddeny TOLOBN 3u DISCUSSION To determine clearly whether Marcus theory is correct in predicting a potential-dependence of M, it is necessary to have a well-behaved system where the double-layer theory appears to yield satisfactory results. Otherwise, it would be impossible to deter- mine whether any curvature in a log k vs." plot was due to failure of the double-layer correction, sone -idiosyncrasy of that particular system, or indeed to the type of effect Marcus theory would predict. Because of the previous work done by Parsons 16 and Passeron, data were first obtained in NaC10y, media. However, the double-layer corrections failed in this case. Nevertheless, the data were analyzed for second-order potential-dependence, to permit comparison with the results of Parsons and Passeron. The magnitude of second-order coefficient, Ay, changed with NaCl0, concentration. The result for 0.5 F NaC10, (the concentration used by Parsons and Passeron) was Aj5= 1.09, compared to a value of 0.26 obtained by Parsons and Passeron. There are several reasons why the data obtained by Parsons and Passeron may differ from the results of the work. First, they used a pH of 3.4. As the 35 pH study on Cr(III) indicated, the Cr(III) system is relatively sensitive to pH, and at a pH of 3.4 sufficient hydrolysis may take place to render the pH in the vicinity of the electrode indeterminate. secondly, Marcus theory defines the overvoltage as V= E-ES, where EY is the standard potential refer- red to some convenient reference potential (usually the potential of the SCE). However, in their work Parsons and Passeron apparently used the convention-~ al overvol tage, | = EAE » where Enev is the equi- librium potential for a given concentration of oxi- dized and reduced species. The overvoltage as used in Marcus theory would then correspond to the over- ‘voltage used by Parsons and Passeron only in that case where the concentrations of oxidized and reduced species were equal, i.e., where EG = ney This work used the Marcus theory overvoltage, 1.e€., Q=5 HES. Because Parsons and Passeron did not publish the concentrations of Cr(III) and Cr(IT) with which they were working, it is therefore not possible to convert their data to a form which would be strictly comparable to the data obtained in this work. One of the impressive correlations obtained by 36 Parsons and Passeron was the agreement between the experimental second-order coefficient, A, and an estimate of that coefficient predicted by Marcus theory, by equating the apvarent heat of activation to A Fog: No such correlation was obtained in this work, The coefficient predicted from Marcus theory * Bop was 0.16; the experimental second-order and AH coefficients were all considerably larger. than this, ranging from 0.49 for 0.3 F NaC10), to 1.38 for 1.0 F NaClO). However, even if agreement had been obtained, little faith could be placed in it, because the double- layer corrections failed. A skeptic might then claim that any curvature resulted from this failure, and that agreement with predictions of Marcus theory was simply fortuitous, There is no way to decide if double-layer cor- rections did apply for the data of Parsons and Passeron, because this data was collected for only one NaClOy concentration, Also, the high pH used in their work, and the use of an inanpropriate definition of over- voltage, makes it difficult to assess the signifi- cance of their agreement between As from curve anal- ysis and Ay predicted by Marcus theory. In an attemot to find.a system where reasonable 2T double-layer corrections could be made, a series of potassium halides was run: KI, KBr, KCl. For KI, the double-layer corrections held strikingly well; for KCl, the corrections were also good. Double- layer data could only be found for 0.1 and 1.0F KBr. There was little overlap between the data at these two concentrations, so it is difficult to de- termine the extent to which the double-layer correc- tions applied. The rate constant obtained in KCl differed by no more than 0.4 log units, at a given potential, from that obtained for KI. Neglecting KBr for the moment, here are then two electrolytes in which one would look for the presence or absence of potential-depvendence of c& with some confidence in its significance. The KCl data do seem to demonstrate curvature, implying a “ potential-dependence of oO. Furthermore, using a weighted error function as a measure of goodness of fit, the second-order curves fit the data better than linear ones, Again, however, the magnitude of the second- order coefficient seems to vary with concentration of electrolyte. In the case of KCl, I do not believe this variation is significant. These data were anal- 38 yzed for several different sets of points; includ- ing or excluding a few points at each end of the curve resulted in a variation of the second-order coefficient, for a given concentration, of about the order observed for the variation of Ay among aifferent KCl concentrations, Each electrolyte concentration covered a slightly different number of points; because of the shift of the half-wave potential with electrolyte concentration, different ranges were covered before reaching the hydrogen wave. Essentially, what one does by fitting a sec- ond-order equation to these points is to fit a sec- tion of a parabola; and it is obvious that the co- -efficients involved will be a fairly sensitive func- tion of which section is chosen, Thus, the fact that the KCl data do appear to demonstrate second-order potential-dependence seems clear, although no great confidence should be placed in the quantitative values for this dependence. The KI data are somewhat more ambiguous. First, the sign of the second-order potential-dependence is different than for either KCl or Nac10,- Also, the potential-dependence is not as large as that for KCL. The largest potential-dependence is shown by 39 0.8 F KI; however, this is the one data set for which the weighted error function indicates a better fit with a linear curve than with a second-order curve. The 0.5 F KI data shows no curvature, and the curvature of the 0.3 F KI data is small. Further- more, the magnitude of the linear constant (i.e., potential-independent ot) is indeed constant for all three concentrations. There thus seems to be little justification for invoking any Marcus effect with this data; it fits very well into the assumption that cl is potential-independent. Because the KI data also demonstrates the best double-layer corrections, one might be tempted to relate apparent second-order potential-dependence with failure of double-layer theory rather than any Marcus effect. However, it should be pointed out that the rate constants, uncorrected for double- layer, of the different KI concentrations differ very little. Also, oe for KI is very small. Thus, one would expect the absolute error in double-layer corrections to be small, because the data is already so Similar for different KI concentrations. The corrected KI data may look good not because double-- LO layer theory held so well here, but because there was not much test of double-layer.theory. Any cor- relation based on the KI data between the applica- bility of double-layer theory, and apparent second- order potential-dependence, would therefore be some- what tenuous. The experimental heat of activation data, ac- cording to approximations made from Marcus theory, - would predict a large second-order coefficient for ‘KI (0.79). This is rather remarkable, in view of our earlier conclusion that the KI data does not justify a potential-dependent O. The plot used to evaluate A Happ was based on only three points, and the deviation of these points from the best line was appreciable. This data is therefore not complete- ly reliable. Even so, the experimental error is not great enough to explain a difference of this magnitude between predicted and experimental results. One explanation is that the assumptions involved are faulty (e.g., that the entropy term can be neg- lected, and AFo, = Alapp). Also, this could be interpreted as evidence against the validity of Marcus theory. The A1(C10y )z study was undertaken to test the 41 significance of the local field effects cited by Delahay et. al.°9 Certainly, the NaC10, double- layer corrections did fail; and if they failed be- cause of local field effects, Al (C10, )5 should give satisfactory double-layer corrections. The double- layer corrections did hold for A1(C10,),. However, there are some disturbing elements in these data. First, the rate constants, after double-layer cor- rection, are significantly higher in A1 (C10, )5 than in the other electrolytes, for a given potential. It was mentioned earlier that the slow hydrolysis of aluminum in perchlorate media was a problem; al- though precautions were taken to overcome this prob- lem, it may be that this slow equilibrium was still in some way affecting the data. It has been shown that the polarographic behavior of Cr(III) is affect- ed by pH, in certain ranges; and it may be that in A1(C10y)3 the Cr(III) data is in some way anomalous. However, even if this is not the case, local field effects seem inadequate to explain why the double-layer corrections apparently failed for Nacl0,, and apparently held for A1(C10,)5. For two monovalent electrolytes, KCl and KI, the double-layer corrections applied reasonably well; the local field He effects which were present in NaC10, should also be present in these electrolytes. It perhaps might have been interesting to try a divalent electrolyte. If one could duplicate Delahay's result, i.e.; if the double-layer correc- tion was intermediate for the case of a divalent electrolyte, for the Cr(III) system, this would tend to confirm the importance of local field effects, in spite of the halide data. _ Because the double-layer correction did seem to apply for A1(C10y ) 3; an analysis of possible po- tential-dependence of @& was also done here. Once again, the second-order coefficient appeared to be dependent on the concentration of A1(C10) ), this time in a monatonic fashion. The sign change at 0.0833 F A1(C10,)5 is interesting, but may not be significant, for the reasons given in connection with the KCl and KI data. The apparent heat of activation was low, 2.82 keal; this, when used with Marcus theory, led to a prediction of 1.00 for a second-order coefficient. The heat of activation studies were done on 0.0833 F A1(C10) ) 33 comparison with the experimental second- order coefficient at this concentration of A1(C10,), (-0.37) shows little correlation. Again, this would 43 seem to imply that either the assumptions about neg- lecting the entropy term are false, or else that this is evidence against the Marcus theory. Another possibility is that the data itself cannot be simply interpreted because of the hydrolysis problem. The standard rate constant, available from the apparent heat of activation for A1(C10y)s, would appear to be anomalously low. However, double-layer corrections would have the effect of increasing the rate data, by a factor of about 2 logjg units; it is likely that the true heat of activation would be higher than that of the apparent value. This would help explain the abnormally low standard rate constant that would be calculated from the given apparent heat of activation for A1(C10y )3. However, the standard rate constant for Nacl0y and A1(C10y)5 would still not be. in agreement, by a factor of about 1.5 10810 units, even after double layer corrections, This may indicate that the A1(C10,)z heat of activation data is suspect, possibly for reasons already mentioned in connection with the A1(C10y4)s data. ‘It should perhavs be pointed out here that determin- ing a potential-depvendence of eo has considerable importance, apart from any implications about Marcus Ab theory. It may also be that, if & is potential-dependent, the relationship may not be the simple A= ajt ao one predicted by Marcus theory. A more complex relation could perhaps account for the seemingly regular variation of the potential-dependent coefficient with concentration of electrolyte. SUMMARY The NaclO, data was shown to disagree with previous data for NaCl0, published by Parsons and Passeronl®, A variety of reasons for this discrepancy was suggested. Because the double-layer corrections failed for Nacl0,, no significant conclusions could be dravm from this ‘work about the validity of Marcus theory predictions. Three electrolytes were investigated for which double-layer corrections did apply fairly well: KCl, KI and A1(C10,) The KI data seemed to fit the 3 assumption of a potential-independent oc. The KCl and A1(C10L)5 data both seemed to imply a potential-dependence of o . However, no quantitative agreement was found between Marcus theory prédictions and the magnitude of the potential-dependent coefficient. The local field effect, suggested by Delahay et. a1.©9 for the failure of double-layer corrections in the case 45 of mixed electrolytes, does not seem adequate to explain the failure of double-layer corrections for Naclo). 46 REFERENCES Delahay, P., "Double Layer and Electrode Kinetics," New York: Interscience Publishers, 1965, pp. 155-177. Van Rysselberghe, Electrochim. Acta, 8 (1963). 583, 709. Marcus, , J. Chem. Phys., 43 (1965) 679. R. A. Marcus, R. A., J. Chem. Phys., 24 (1956) 966. Marcus, R. A., Can. J. Chem., 37 (1959) 155. Marcus, R. A., Trans. Symp. Electrode Processes, Phila., Pa., 1959, 239-245 (I961). 7. Marcus, R. A., J. Phys. Chem., 67 (1963) 853. 10. ll. 12. 13. 14. 15. 16. Marcus, R. A., Ann. Rev. Phys. Chem., 15 (1964) 155. Y appears as A.in Marcus' papers. This change of notation has been made to avoid confusion with /\ introduced by the Koutecky analysis. Marcus, R. A., ov. cit., Can. J. Chem., p. 156. Hunt, J. P. and H. Taube, J. Chem. Phys., 19 (1951) 602; ibid., 18 (1950) 757. Randles, J, FE. B. and K. W. Somerton, Trans. Faraday Soc., 48 (1952) 937. " Delanay, P., "New Instrumental Methods in Elec- trochemistry," New York: Interscience Publish- ers, 1954, especially Chapter 4. Vetter, K. J., "Electrochemical Kinetics," New York: Academic Press, 1967. Delahay, op. cit., "New Methods...", p. 79. Parsons, R. and H. Passeron, J. Electroanal. Chem., 12 (1966) 524. AT 17. 18, 19. 20, al. 22. 23, 24, 25. 26. 27. 28, 29. 30. Ji. 32. Delahay, op. cit., “New Methods. . .," Dp. 79. Ives, D. J. G. and G. J. Janz, "Reference Electrodes: Theory and Practice," New York: Academic Press, 1961. : Altman, C. and E. L. King, JACS, 83 (1961). 2825. Aveston, J., J. Chem. Soc. (London), (1965) 4438. a Sillen, L. G., Quart. Rev., 13 (1959) 146. Delahay, op. cit., "Double Layer. . .", pp. 199-201. Wroblowa, Kovac and Bockris, Trans. Faraday Soc., 61, (1965) 1523. Parsons, R. and R. Payne, mentioned in Reference 16 as unpublished data. Russell, J. Electroanal. Chem., 6 (1963) 486. Lawrence, Parsons and Payne, J. Electroanal. Chem., 16 (1968) 193. Breiter, M., M. Kleinerman and P. Delanay, JACS, 80 (1958) 5115. _ Charlot, M., "Selected Constants: Oxidation- Reduction Potentials," New York: Pergamon: Press, 1954. Asada, K., P. Delahay and A. K. Sundaram, JACS, 83 (1961) 3398. a Joshi, kK. M. and R. Parsons, Electrochim. Acta, 4 (1961) 129. See Reference 25. Joshi, K. M., W. Mehl and R. Parsons, Transactions of the Symposium on Electrode Processes, Phila- delphie, 1959, edited by E. Yeager, New York: Wiley, 1961. 48