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Catalytic Polarographic Current of a Metal Complex.1 IV.
Effect of the
Electrode Double Layer on the Ni( II)-o-Phenylenediamine Prewave2 by Lowell R. McCoy, Harry B. Mark, Jr., Department of Chemistry, University of Michigan, Ann Arbor, Michigan. 48104
and Lucien Gierst Department of Chemistry, Free University of Brussels, Brussels, Belgium
(Received July 8, 1068)
A study of the Ni(I1)-o-phenylenediamine prewave has shown that a pronounced double-layer effect is observed when measurements are made of polarographs obtained with various types and concentrations of supporting electrolytes. The effect on the prewave is qualitatively consistent with theoretical predictions when the concentration of the electrolyte is not SO high as to invalidate the assumptions employed in the theoretical treatment. The results of this investigation support the existence of a surface-controlled chemical reaction involving an adsorbed ligand and the nickel ion diffusingto the electrode. The conclusion by Tur’yan and Malyavinskaya that the chemical rate-limiting reaction involves the formation of an electroactive Ni(I1)o-phenylenediamine complex in the bulk of the solution well beyond the influence of the electrode double layer is therefore incorrect. A quantitative analysis of the relationship between the height of the prewave and the potential of the outer Helmholtz plane indicates that the charge on the electroactive species in the ratedetermining step is +1 rather than +2 as expected from the charge of the hexaaquonickel ion. The reason for this disagreement may lie in the adsorption behavior of the ligand.
A number of investigator^^^^-^ have reported the appearance of prewaves during the polarographic reduction of Ni(I1) in the presence of complexing agents such as pyridine, o-phenylenediamine, ethylenediamine, triethylenetetramine, chloride ion, etc. These prewaves can arise several hundred millivolts positive to the main reduction wave of Ni(H20)62+. The height of the prewave varies directly with the concentrations of ligand and nickel ion. Shifts of the entire Ni(I1) wave to more positive potentials in the presence of certain anions of the supporting electrolytes such as chloride and thiocyanate and large excesses of pyridinium salts have been recognized for some time and have been used as an analytical method of separating the nickel wave from that of other metal ions having similar half-wave potentials, i.e., cobalt.* I n these cases the complexing agent is present in great excess with respect to the nickel ion concentration, and no separate prewave can be distinguished. From a study of the prewave obtained with Ni(I1) and phenylenedi diamine,^^^^^^^ it was concluded that the mechanism involved a rate-limiting chemical reaction between the hexaaquonickel ion and the adsorbed ligand in the sequence shown in eq 1 and 2. The adsorbed ligand is cyclically regenerated by the electrochemical reduction of the adsorbed complex. This view has been disputed by Tur’yan and Malyavins k a ~ awho , ~ stipulated that the electroactive complex is formed in the bulk of the solution in a rate-limiting homogeneous reaction between the hexaaquonickel ion and the regenerated ligand diffusing outward from the electrode surface. These writers supported their con-
clusion by a calculation of a reaction layer thickness based on an estimated equilibrium constant for the Ni(I1)-ligand complex. Gierst’O has shown that the observed rate of an electrode process will be affected by the state of the electrode double layer where the reaction layer thickness for a rate-limiting chemical reaction is small relative to the thickness of the diffuse layer. A surfwe reaction involving an adsorbed ligand must fulfil this condition. Conversely, Tur’yan and Malyavinskayag state that their calculated reaction layer thickness (3 X cm) precludes any double-layer effect. As the structure of the electrode double layer can be varied at (1) This research was supported in part by grants from the National Science Foundation, Grants No. GP-4620 and GP-6425, and the U. S. Army Office of Research, Durham, N . C., No. DA-31-124ARO-D-284. (2). For other papers of this series see: (a) H. B. Mark, Jr. and C. N. Reilley, J. Electroanal. Chem., 4, 189 (1962); (b) H. B. Mark, Jr., ibid., 7, 276 (1964); (e) H. B. Mark, Jr., L. R. McCoy, E. Kirows Eisner, and H.C. MacDcnald, Jr., J . Phys. Chem., 7 2 , 1083 (1968). (3) H. B. Mark, Jr.‘and C. N. Reilley, Anal. Chem., 35, 195 (1963). (4) H. B. Mark, Jr., ibid., 36, 940 (1964); J. Electroanal. Chem., 8 , 263 (1964). (5) Ya I. Tur’yan and G. G . Serova, Zh. Fiz. Khim., 31, 1976 (1957); Ya. I. Tur’yan, Dokl. Akad. Nauk SSSR, 148, 848 (1962); Zh. F i g . Khim., 39, 257 (1965). (6) I. V. Nelson and R. T. Iwamoto, J . Electroanal. Chem., 6, 234 (1963). (7) D. C. Olson, Anal. Chem., 39, 1786 (1967). (8) I. M. Kolthoff and J. J. Lingane, “Polarography,” 2nd ed, Vol. 11, Interscience Publishers, New York, N. Y., 1962, p 486. (9) Ys, I. Tur’yan and 0. N. Malyavinskaya, Electrokhimiyu, 2, 1186 (1966); Sov. Electrochem., 2, 1082 (1966). (10) L. Gierst, Trans. Symp. Electrode Processes, 109 (1969).
Volume 7.8,Number 19 December 1068
4638
will by changing the nature and/or concentration of the supporting electrolyte, a study of the effects of these variables on the observed height of the prewave thus offers an experimental method of resolving this question. This paper will present the detailed results of such a study of the Ni(I1)-o-phenylenediamine (OPDA) system." The prewaves produced by this combination arise at potentials well separated from the main hexaaquonickel wave, permitting calculations to be made with minimum interference or overlap from the main hexaaquo wave. Also the pK,, of this ligand12(pKa, = 4.5) permits measurements to be made in a reasonably broad pH range (6.5-7.5) where little of the Ni(I1) is present as the hydroxyl complex, and yet the ligand exists almost wholly in its nonprotonated form in this range. a , 4
Experimental Methods The methods and procedures employed in making the polarograms were generally the same as those reported p r e v i ~ u s l y with ~ ~ ~a~few * exceptions. The drop time of the dropping mercury electrode (dme) was controlled mechanically a t 4.0 f 0.05 sec.13 No maximum suppressors such as the Ca2+ion, used in the previous investigation^,^^^^^ were used here as they would complicate the double-layer studies. A threeelectrode polarograph with a scan rate of 100 mV/min was emp10yed.l~ The supporting electrolytes and ligand solutions were prepared from triple-distilled water and analytical reagents. The latter were further purified where necessary by standard practices.13 As the ligand (ophenylenediamine) solutions are unstable in the presence of air, these were prepared using aliquots of deaerated electrolyte solution. Storage of the ligand solutions for prolonged periods was found to be feasible if these were frozen immediately after preparation and thawed just prior to use. The pH of the polarographic solutions were adjusted to 7.0 f 0.5 where necessary by the addition of an acid or base corresponding to the cation or anion of the specific supporting electrolyte. The pH was monitored continuously during the course of the polarographic measurements, as some drifting was evident in dilute solutions of unbuffered reagents. The temperature of the solution in the polarographic cell was maintained at 25 f 0.1". The Journal of Physical Chemistry
L. R. McCoy, H. B. MARK,JR.,AND L. GIERST
Qualitative Effect of the Type and Concentration of the Supporting Electrolyte Where an electrochemical reaction is preceded by a surface rate-limiting chemical reaction involving an uncharged ligand, Gierst'O has shown that the following expression describes the relationship between the "apparent" and "true" velocities of the reaction
v*
=
vo exp
(-E+o) ZF
(3)
I n eq 3, v* is the apparent velocity of the reaction calculated from the wave height where the surface concentration of a charged reactant is subject to perturbation by the electrode double layer; vo is the true velocity that would be obtained in the absence of any effect from the double layer; Z is the charge of the reactant; and +O is the potential of the outer Helmholtz plane.'O The symbols, F, R, and T have their usual electrochemical significance. For a preelectron-transfer association reaction taking place in the bulk of the solution, vo is given by vo = [L]XdDOKlcr
(4) where [L] is the ligand concentration, D is the diffusion coefficient for the hexaaquonickel ion, X is the stoichiometric coefficient of the ligand, K is the formation equilibrium constant for the Ni(I1)-ligand complex, and kr is the forward reaction rate constant. As this relationship has been derived for the case of a homogeneous equilibrium reaction of the type described by Tur'yan it is not directly applicable to the and Malyavin~kaya,~ proposed surface-reaction r n e ~ h a n i s m . ~ JThe * ~ quantity d D X f may be calculated from the ratio of the observed prewave height to the diff usion-limiting height, using a relationship derived by K ~ u t e c k y . ' ~ Where a double-layer effect exists, however, v* rather than vo will be obtained by this process. The calculated value of v* will then vary with +O in the manner shown in eq 3. The quantity, 2, is expected to be +2 for the hexaaquonickel ion, and will be negative over the electrode potential range of the prewave. Under otherwise identical conditions, v* and therefore the prewave height will decrease as becomes less nega-
+"
(11) See ref 2c for a preliminary communication of part of the results of this study. (12) R. T. Morrison and R. N. Boyd, "Organic Chemistry," Allyn and Bacon, Inc., Boston, 1959,p 544. (13) L. R. McCoy, Ph.D. Thesis, University of Michigan, Ann Arbor, Mich., 1967; L. R. McCoy, H. B. Mark, Jr., and L. Gierst, unpublished results, 1967. (14) J. Koutecky, Coll. Czech. Chem. Commun., 18, 597 (1953).
CATALYTIC POLAROGRAPHIC CURRENT OF
A
METALCOMPLEX
4639
tive. At t,hese electrode potentials, the Gouy-Chapman relationship shows that $O will decrease as the concentration of the supporting electrolyte is in2,o creased.16 Also for a given supporting electrolyte concentration, the choice of an electrolyte whose ions are specifically adsorbed will result in a more (anion adsorption) or less (cation adsorption) negative value of $O than would be obtained for an electrolyte whose ions are not adsorbed. Thus measurement of polarograms obtained with various types and concentrations 0. of electrolytes and with invariant reactant concentra/ tions affords a ready means of observing the effect, if -0.6 - 0.8 - 1.0 1.2 -I4 any, of the electrode double layer on the prewave. POTENTIAL, VOLTS, S.C.E. I n the study of the effect of variation of the concentration of the supporting electrolyte, lithium salts were Figure 2. The effect of varying concentrations of lithium used. The Li+ ion is the least specifically adsorbed nitrate upon the prewave height (high-concentration range, 5 x 10-4 M Ni*+, 1.6 x 10-4 M OPDA): , 1.0 M cation available and its effects on #o as a function of LiNOa; , 3.0 M LiNOs; ,5.0 M LiNOa. concentration are known.’O Lithium perchlorate and lithium nitrate were the preferred electrolytes in these investigations, as neither anion is specifically adsorbed to a significant degree at electrode potentials of concern to the prewave region a t moderate c o n c e n t r a t i ~ n s ~ ~ ~ ~ ~ 2D and neither forms stable complexes and/or ion pairs with the Ni(1I) cation.1ai16 Prewaves obtained using a series of concentrations of lithium perchlorate are shown in Figure 1. Within the concentration range shown here, attenuation of both the prewave and the main hexaaquonickel wave with increasing electrolyte concentration is evident. The same results were obtained where lithium nitrate or lithium acetate were employed as the supporting electrolytes. When the concentration of these electrolytes POTENTIAL , VOLTS, S.C.E. exceeded 0.5 MI however, the opposite effect was produced, and the prewave either became static or began Figure 3. The effectof varying concentrations of lithium to rise in height with an increasing concentration of rtcetate upon the prewave height (high-concentration range, 5 X 10-4 M Nit+, 1.6 X 10-4 M OPDA): , 1.0 M electrolyte. Prewaves obtained with the more conLiCzHaOz; , 2.0 M LiCzHa02; , 4.0 M LiC2H3Oz. centrated solutions are shown in Figures 2 and 3.
‘t
y-y:::;:~ ,
b
,
-
---
- --
-
‘F
-
/
-0.6
- 0.8
I
-1.0 POTENTIAL, VOLTS, S.C.E.
- 1.2
Figure 1. The effect of varying concentrations of lithium perchlorate upon the prewave height (low-concentration range, 5 X 10-4 M NiZ+, 1.6 X 10-4 M OPDA): -, 0.05 M LiClO4; - -, 0.1 M LiClO4; - -, 0.2 M LiClO,; - - - -, 0.5 M LiC104.
-
-
-1.4
--
Coincident with the reversal of the trend of wave height with electrolyte concentration, a rather pronounced shift of both the prewave and main wave toward more positive potentials was observed in both lithium perchlorate and lithium nitrate. Dandoy and Gierst” have noted this effect in the case of the hexaaquonickel wave alone, attributing the phenomenon to changing activity of the reactant ion in these very concentrated solutions. I n the concentrations 50.5 M , the observed changes in prewave height are therefore in accordance with the anticipated double-layer effect upon a surface reaction. At higher concentrations, the reverse is true. Interpretation of the results obtained in the latter case is (16) P. Delahay, “Double Layer and Electrode Kinetics,” Interscience Publishers, New York, N. Y.,1966,p 42. (16) L. Gierst, private communication, 1966. (17) J. Dandoy and L. Gierst, J . Electroanal. Chem., 2 , 116 (1961). Volume 78, Number IS December 1968
L. R. McCoy, H. B. MARK,JR., AND L. GIERST
4640
$!
4 I
I
LiC104,Molar
I
I
t
Conc.
It-
t I-
-0.G
- 0.8
- 1.0
-1.2
POTENTIAL ,VOLTS , S L . E .
Figure 4. The dependence of the rate parameter, X, and the mean ionic activity coefficient upon the concentration of lithium perchlorate.
subject to a number of uncertainties. These include pronounced activity changes for both reactants, an increase in specific adsorption of the electrolyte anion, salting out effects on the ligand,I6 a possible increase in the equilibrium concentration of less highly aquated nickel ions (regarded by Dandoy and Gierst” as the electroactive species in the absence of the ligand), and, perhaps, an increasingly dubious applicability of classical double-layer theory. That activity effects may play a major role in the more concentrated electrolyte is indicated by Figure 4,where the change in the observed rate, v* (shown here as A, defined below), and the mean ion activity coefficient, yi, appear as functions of the concentration of this electrolyte. The concentration at which the prewave height reverses its trend is roughly coincident with an accelerating rise in y* with concentration. The static behavior of the prewave in higher concentrations of lithium acetate may be attributed to the fact that the acetate ion forms a moderately stable (pKBt= 1.0) complex with the nickel ~ation.’~~’O The experiments described above were performed with electrolytes whose anions are subject only to limited degrees of specific adsorption.‘0*lB The effect of changes in the electrode double layer on the prewave characteristics may also be studied by employing electrolytes whose anions are subject, to different degrees of specific adsorption. The halogen salts offer a convenient group of electrolytes for this purpose. Values of $0, obtained by Grahame and Soderberg20 in 0.1M solutions of KI, KBr, KCl, and NaF, are shown in Figure 5.21 The disparity in the values of $O at electrode potentials from -0.6 to -0.9 V arises from the fact that the specific adsorption of these anions is different and decreases in the order I >> Br > C1> F. At an electrode potential of -0.9 V, desorption of the anions is nearly complete, and the values of $0 are the same for all of these salts. In view of the earlier discussion, a greater prewave height should result from more negative values of $0. The polarographic results obtained with The Journal of Physical Chemistry
Figure 5. Variation of the outer Helmholtz potential, pol with the electrode potential in 0.1 N solutions of potassium halides: -, KF; - - - -, KC1; ---, KBr; --- , KI.
0.1 M solutions of the lithium halides are shown in Figure 6, where it may be seen that the prewave heights are in the order predicted by the #O values for these salts. The same order is retained also in 1.0 M solutions.’* The prewave obtained with lithium iodide is particularly interesting, as desorption of the anion a t more negative electrode potentials results in the appearance of a pronounced “hump” in the prewave. The effect of changes in the electrode double layer on the prewave was also investigated by varying the cation of the supporting electrolyte. Although Ca2+ is not specifically adsorbed, values of $O for a 1:2 electrolyte will be significantly lower than those pertaining to a 1 : 1 electrolyte at the same Concentration. Values of $0 for the former type have been calculated by Grahame.22 The result of substituting calcium nitrate for lithium nitrate as the supporting electrolyte on the prewave height is shown in Figure 7. The decrease in prewave height is consistent with a decrease in $0. Tetraalkylammonium ions are specifically adsorbed and thus also decrease values of $0.23,24 A comparison (18) L. G. S i l l h and A. E. Martell, “Stability Constants of MetalIon Complexes,” The Chemical Society, Burlington House, London, 1964,p 366. (19) The polarographic study of Ni(I1) and Ni(I1)-complex systems of this type shows numerous anomalous characteristics which cannot be explained in terms of the W effect treatment given in this paper. Part of these anomalies appear to result from the formation of Ni(I1)-acetate complexes in the bulk of the solution. Also, it appears from doublelayer capacitance studies that the acetate ion, although not specifically adsorbed to an appreciable extent, 16 effects the surface excess of the adsorbed ligand (H. B. Mark, Jr., H. C. MacDonald, Jr., and E. Kirowa-Eisner, unpublished results, 1968). (20) D. C. Grahame and B. A. Soderberg, Technical Report No. 14 to the Office of Naval Research, Amherst College, Amherst, Mass., Feb (1954). (21) The electrode potential scale used here has been changed to sce rather than the nhe scale used by Grahame. (22) D. C. Grahame, J . Chem. Phys., 21, 1054 (1953). (23) J. Koryta, Electrochim. Acta, 6 , 67 (1962). (24) A. N. Frumkin, Aduan. Electrochem. Electrochem. Eng., 1, 96 (1961).
4641
CATALYTIC POLAROGRAPHIC CURRENT OF A METALCOMPLEX
’I-
t
zm5
sot-
7
20
-
/
-
0.6
- 0.8
-1.0 POTENTIAL ,VOLTS, S.C.E.
POTENTIAL, VOL1S.S.C.E.
Figure 6. The effect of anion adsorption upon the shape and amplitude of the prewave (0.1 N solutions of lithium halides, 5 X 10-4 M NPf, 1.6 X 10-4 M OPDA): , LiCl; -.-- , LiBr; , LiI.
-
---
-1.2
Figure 8. The effect of cation adsorption upon prewave height: , 0.1 N lithium acetate; -- -, 0.1 N tetramethylammonium acetate; , without OPDA.
-
---
1.0
-0.6
POTENTIAL ,VOLTS, S.C.E.
Figure 7. Comparison of prewaves obtained in 0.1 N solutions of lithium and calcium nitrate (5 X 10-4 M Nia+, , LiNOa; --- , Ca(N0s)i. 1.6 x 10-4 M OPDA):
-
of the prewaves obtained in 0.1 M solutions of lithium acetate and tetramethylammonium acetate appears in Figure 8. Interpretation of this result requires some caution, however, as adsorption of this cation may also decrease the reaction rate by a reduction in the effective electrode area. If adsorption of the ligand does occur, the cation competes for electrode surface area and may reduce the surface concentration of the reacting species. Studies of the effect of the alkali metal cations on the rates of other electrode reactions have shown that these produce an effect akin to that of cation adsorption, increasing in the order Li, Na, K, and Cs.” Figure 9 shows the polarograms obtained with lithium, potassium, and cesium nitrate supporting electrolytes. The results are again consistent with a double-layer effect on a surface-rate-limiting reaction. Qualitatively, the results obtained in these investigations with a wide variety of concentrations and types of electrolytes are consistent with a pronounced doublelayer effect on the prewave and clearly invalidate the
-0.8
-1.0’ POTENTIAL, VOLTS , S.C.E.
-1.2
Figure 9. The effect of the alkali metal cations upon the height of the prewave (0.1N nitrate solutions): , LiNOa; KNOa; --- CSNOa.
-
---
concept of a rate-limiting “bulk” chemical reaction as proposed by Tur’yan and Malyavinskaya.9 Quantitative Analysis of the Prewave
It should be possible to verify quantitatively the mechanism described in reactions 1 and 2 using eq 3 and 4. Some modification of eq 4 will be required first, however, if the reaction does involve an adsorbed ligand. The ligand concentration, [L], in eq 4 is defined in terms of a volume concentration. This difficulty can be avoided if the assumption is made that near-equilibrium coverage of the adsorbed ligand is attained quickly within the life of the drop. The surface concentration of the adsorbed species can then be effectively regarded as a time-invariant quantity. While this is ordinarily a dangerous assumption in view of the known slow attainment of equilibrium coverage by many adsorbed organic molecules, sufficient evidence was a t hand to permit such an assumption as a reasonable first-order approximation a t the concentration of OPDA used in the polarographic r n e a s u r e m e n t ~ . ~I~ ~ f , ~Koutecky’s Volume 71, Number 13 December 1968
L. R. McCoy, H. B. MARK,JR.,AND L. GIERST
4642
relationship^'^ for a heterogeneous electrochemical reaction are written in somewhat modified formz6
i - = F(X) id
(5)
The quantity in brackets in eq 6 represents the surface concentration of the reactant species at time t. In the context of reaction 2, it 'may be equated with the surface concentration of the hexaaquonickel ion at the electrode surface. With the assumption that [L]sds is virtually a constant over the life of the drop, k f h , the normal heterogeneous rate constant, can then be replaced by kf[L],dSX,where kr is the forward chemical reaction rate constant for reaction 1. The quantity X in eq 5 is then defined as
(7) The quantity X calculated from the height of the prewave, is, however, clearly subject to the effect of the electrode double layer as shown in the previous section. The reaction velocity, vo, in eq 3 is now defined for a surface reaction as 210
= kf[L]adsX
(8)
where [L]O is the bulk ligand concentration and Kh is the Henry's law constant. The stoichiometric coefficient, X , may then be evaluated through a series of measurements of the prewave height as a function of the ligand concentration in the same supporting electrolyte. If X is calculated at the same electrode potential in each case and if the adsorbed ligand surface concentration is not so large as to cause $o to differ significantly from that of the electrolyte itself, the exponential term becomes a constant. At a constant time of current measurement, eq 11 then becomes simply log X = constant
+ X log [L]O
(12) The results obtained in such an experiment are shown in Figure 10. The slope of the curves at lower ligand concentrations clearly indicates a 1:1 combining ratio for the ligand and the hexaaquonickel ion. The result is evidently not critically dependent on the choice of electrode potential. The deviation from linearity suggests that either a deviation from Henry's law occurs or adsorption of the ligand is great enough to cause a significant change in $0 as the concentration increases. It should be noted also that eq 12 would apply equally well to a bulk chemical reaction having a reaction layer thickness well within the diffuse zone of the double layer. In this instance, the Henry's law approximation would not be involved, and greater rigor would be expected from the relationship. In a nega-
The apparent velocity, v*, then becomes (9)
These equations may then be combined in the form of eq 3 to give
The above relationships have been derived on the basis that the rate of the electrode process is controlled wholly by the forward rate of the chemical reaction. They may be strictly applied therefore only to data taken at electrode potentials that are sufficiently negative to the rising portion of the prewave to ensure that the rate of the charge-transfer reaction exceeds the chemical rate. Inspection of Figures 1, 3, and 6-9 suggests that the applicable electrode potential ranges from about -0.8 to -0.9 V sce. At electrode potentials more negative than -0.9 V, serious interference from the main hexaaquonickel wave is encountered. If a Henry's law relationship is assumed to exist between the surface concentration of the ligand and its bulk concentration (at low ligand concentrations), eq 10 may be written as
I
-4.5
I
-4.0
I -3.5
I
-3.0
L O G CONC. O P D A , M.
Figure 10. The dependence of the rate parameter, A, upon the bulk concentration of OPDA (0.1 N lithium perchlorate solutions, 5 X 10-4 M Ni*+): -0.85 V sce; -A-, -0.75 V sce.
+,
(26) The original relationship derived by K o u t e y l d was written in terms of the symbol x ; X used here equals 4 7 / t q . The Journal of Physical Chemistry
CATALYTIC POL.AROGRAPH~C CURRENT OF
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METALCOMPLEX
4643
41
- 0.2 -
-
-0.4-
-0.6
-
-
A
::-0.8-
J i:
0.2
I
P
0.4
A-06
-
CD
s
-I
-“I-
-0.8-
-1.0
-1.2
-0.04
-0.06
-0.08
-IoZ
t
-0.06
$:
-0.08
VOLTS
Figure 12. The dependence of the rate parameter, A, upon $0 in 0.1 N lithium nitrate solutions (5 x 10-4 M OPDA): -A-, M Ni2+, 1.6 X -0.75 V; +, -0.80 V.
tive sense, the observed deviation from linearity argues against this possibility. Unfortunately, changes in Jp by adsorbed ligand, even if this species did not participate in the electrochemical reaction, could also produce the curvature noted in Figure 10. If the experimental conditions involve changing $0 through the use of a range of concentrations of supporting electrolyte at constant reactant concentrations, eq 10 may be employed t o determine the dependence of X on this variable. If [L]& is reasonably insensitive to a range of electrolyte concentrations, it may be regarded as substantially constant under these conditions, and eq 10 is reduced to ZF
I
-0.04
Figure 11. Dependence of the rate parameter, X, upon $0 in 0.1 N lithium perchlorate solutions (5 X 10-4 M Ni2+, 1.6 x M OPDA): +, -0.70 V; -A-, -0.75 V; -X-, -0.85 V.
- 2.3RT -----go
-
/ ,‘2= +I
/
f,VCLTS
logX = constant
/
/
(13)
The results of such experiments using lithium perchlorate and lithium nitrate are shown in Figures 11 and 12. I n both instances, the values of $0 were taken from Russell’sz6 tables after correction of the electrode potentials shown there to sce. It has therefore been assumed that anion adsorption is negligible in both instances. While this assumption is untenable at higher concentrations of these electrolytes, the data of PayneZ7 and Wroblowa, et a1.,28offer assurance that errors from this source are minor in the potential region of the prewave and a t the electrolyte concentrations (50.5 M ) employed here. Figures 11 and 12 include only the data calculated at this lower concentration range of supporting electrolyte, where the predictions of the double-layer theory were found to be qualitatively obeyed in the previous section. While a
linear relationship between log X and log $0 is observed in these cases, the slopes of the lines do not conform to a reaction involving an uncharged ligand and the hexaaquonickel with a charge 2 = + 2 . Dotted lines have been included on these figures with slopes equal to ZF/2.3RT, where 2 equals +1 and +2. To the extent that Z must be an integer, the experimental results agree more closely with a reactant charge of + l . The results obtained by Dandoy and Gierst” in experiments involving the hexaaquonickel ion alone have shown that the electroactive species has a +2 charge as expected. The cause of this difference could lie either in the behavior of the ligand or in the assumptions employed in the development of the relationship presented above. Of the latter, the treatment of [Llads as a constant with respect to both time and electrolyte concentration is certainly suspect. On the other hand, experimental evidence obtained from differential capacitance measurements indicates that the errors introduced by these assumptions are not great enough to account for this charge v a l ~ e .This ~ ~capacitance ~ ~ ~ evidence does suggest, however, that adsorption of o-phenylenediamine may involve the coadsorption of the electrolyte anion. This aspect of this problem will be discussed in a subsequent paper. (26) C. D.Rusaell, J. Elecboanal. Chem., 6,486 (1963). (27) R. Payne, private communication of unpublished results to L. R. McCoy, 1966. (28) H. Wroblowa, Z. Kovac, and J. O’M. Bockris, Trans. Faraday floc., 61, 1623 (1965).
Volume 78, Number 18 Decembsr 1068
