Oct. 5, 195s
STRUCTURE OF DOUBLE LAYERAND ELECTRODE PROCESSES [CONTRIBUTION F R O M THE COATES CHEMICAL
LABORATORY, LOUISIANA STATE
5111
UNIVERSITY]
Structure of the Double Layer and Electrode Processes1 BY MANFRED RREITER, 2a MARCOS KLEINERMA AND N ~P~A U L
DE1,AHAY
RECEIVED APRIL 28. 1958 The influence of the double layer structure 011 the kinetics of electrode processes is discussed for simple processes without and with specific adsorption of electrolyte and for processes with coupled chemical reaction. Interpretation of processes without chemical reaction rests on two fundamental ideas advanced by Frumkin and studied in detail by him and his school; (a) the double layer structure influences the effective difference of potential which favors the forward electrochemical reaction and hinders the backward reaction; (b) the effective concentrations of reactants, particularly for ions, are different from the bulk concentrations because of the double layer structure. Frumkin’s quantitative treatment for processes without adsorption is discussed and additional equations are given in Appendix for fast processes. Application is made to reduction of iodate ion on mercury in alkaline solution. The analysis of processes with specific adsorption of electrolyte is based on Ershler’s model of the double layer and on Grahame’s treatment for the differences of potentials between inner and outer Helmholtz planes and solution. I t is shown that interpretation of the salt effect based upon the shift of the point of zero charge is open to question. Application is made to the reduction of nitromethane on mercury in acidic iodide medium. The effect of iodide on current-potential characteristics is essentially accounted for by variation of the difference of potential between the inner Helmholtz plane and solution. The salt effect for processes with a coupled chemical reaction is explained by variation of the concentrations of reactants in the reaction layer. Approximete correction is possible when the thickness of the reaction layer is small in comparison with that of the double layer. Results are given for the current-step method and are applied to the discharge of Cd(CN)d-- on mercury. Implications are discussed: shift of half-wave potentials for irreversible polarographic waves, distortion of log i 8s. E diagrams in kinetics and correction of transfer coefficients and exchange currents, inadvisability of control of ionic strength for z-e’ electrolytes; effect of foreign electrolytes 011 the discharge of certain complex ions. A4detailed bibliography is given.
The structure of the double layer is of importance in electrochemical kinetics for a t least two reasons. (a) It influences the effective difference of potentials which favors and hinders the electrochemical reaction. (b) The effective concentrations of reacting species, particularly in the case of ions, are different from the “bulk” concentrations because of the double layer structure; and the rate of the electrode reaction is affected accordingly. The study of these two effects was progressively developed by Frumkin and his school mostly for the reduction of hydrogen ions,3-10 the electrolytic oxidation of hydrogen, l 1 the reduction of anions12-17 and the reduction of o ~ y g e n . l ~ - ~ ~ A few other authors applied these ideas. Bock(1) Paper presented a t the National Meeting of t h e Electrochemical Society, S e n York, K. Y., April, 1958; see booklet of extended abstracts. ( 2 ) (a) Research associate, 1957-1958; on leave from t h e Technical University, Munich; (b) Predoctoral fellow, 1957-1 958. (3) A. N. Frumkin, Z . 9 h y s i k . C h e m . , 8 1 6 4 , 121 (1933); Acta Pizysicochim. U.R.S.S., 6 , 502 (1937); 7, 475 (1937). ( 4 ) S. Levina and V. Zarinskii, ibid., 6, 491 (1937); 7 , 485 (1937); Z h u r . Fia. Khim.,10, 586 (1937). (5) A. N. Frumkin, Disc. Faraday Soc., 1, 57 (1947). (6) P . D. Lukovtsev, Z h u r . Fiz. K h i m . , 21, 589 (1947). (7) P. Lukovtsev and S. Levina, ibid., 21, ,599 (1947). (8) N . XIeiman, ibid., 2 2 , 1454 (1948). (9) V. S. Bagotskii. ibid., 22, 1466 (1948). (10) A. PIT. Frumkin, ibid., 24, 244 (1950); see detailed bibliography. (11) A. N. Frumkin and E . A. Aikazyan, Doklady A k a d . N a u k , S.S.S.R., 100, 315 (1955). (12) A. N. Frumkin, “Couche doiible, Electrocapillarit6, Surtension,” Actualitks scientifiques e t industrielles, KO. 373, Herman e t Cie, Paris, 1936. (13) M. A. Vorsina a n d A . N. Frumkin, Z h u r . F i z . K h i m . , 17, 295 (1943). (14) A. N. Frumkin and G. M. Florianovich. Doklndy A k n d . N o u k , S.3.S.R , 80, 907 (1951). (15) T. V. Kalisb and A. N. Frumkin, Z h u r . F i r . K h i m . , 28, 473 (1954). (18) G. M.Florianovich and A. N. Frumkin, i b i d . . 29, 1827 (1955), see this paper in particular for most complete treatment. (17) A S . Frumkin, Z. Elektrochem., 69, 807 (1955); see detailed bibliography in this review. (18) V . S. Bagotskii and I. E. Yablokova, Zhur. Fie. Khim., 26, 1663 (1953). (19) For a general review see A. N. Frumkin, V. S. Bagotskii, 2. A. Iofa and B. N. Kabanov, “Kinetics of Electrode Processes,‘’ Moscow, University Press, Moscow, 1952.
risZ0and de B6thune2l used them in investigations of hydrogen overvoltage. Lothe and Rogersz2correlated the shifts of the point of zero charge and the half-wave potential for irreversible processes upon addition of a specifically adsorbed electrolyte. GerischeP pointed out the necessity of correction for the double layer structure in a.c. electrolysis. Bigwood and GierstZ4took into account double layer effects in a detailed polarographic study of the reduction of chromate ion. In a very recent thesis, which was received after completion of this work, Gierst2j investigated the influence of the double layer structure on several polarographic and related processes. Electrostatic influences in electrochemical kinetics were invoked by several investigators : Heyrovsky,z6Krjukova, z7 Randles,2(i Laitinen and OnstottZ9(see also related papers”-;j2). Two cases can be distinguished in double layer effects according to whether or not there is specific adsorption. Furthermore, the electrochemical reaction can be preceded or followed by chemical reactions. Only simple electrode processes without (20) (a) J. O’hI. Bockris, C h . V I 1 in “Electrical Phenomena a t Interfaces,” J . A. V. Butler, Editor, hlethuen and Co , London, 1951, p. 183 (b) see review in J. O’M. Bockris, Ch. IT in “Modern Aspects of Electrochemistry,” J. O’M. Bockris, Editor, Butt erworths Scientific Publications, London, 19.54, pp. 208-208. (21) A. J. de Bethune, THISJOVRNAI. 71, 1556 (1949). ( 2 2 ) J. J. Lothe and I,. B. Rogers J . E k d w c k e m Soc., 101, 258 (1954). (23) H. Gerischer, Z . ph?srh. Ckem , 202, 293. 302 (1953). (24) A . Bigwood and L. Crierst, article in “Contributi Teorici e Sperimentali di Polxrografia,” Vol. 111, Suppl. A, Ricerca Sci.. 1957, p p 62-78. ( 2 5 ) L. Gierst, “Cinktique d’approche et rkactions d’dectrodes irrkversibles,” these d’agrkgation, University of Brussels. 1958. ( 2 6 ) J. Heyrovsky, Disc. Faraday Soc., 1, 212 (1947) (27) T. A. Krjukova, Doklady A k a d . N a u k , S.S.S.R.,66, 517 (1949). (28) J. E . Randles and K. U‘. Sommerton, T r a n s . Farnday Soc , 48, 957 (1952) (29) H. A. Laitinen and E. I. Onstolt, THIS J O U R N A L , 72, 4565 (1950). (30) P. Kivalo and H. A. Laitinen, i b i d . , 7 7 , 5205 (l955), and references therein t o other investigators. (31) P. Kivalo, J . Phys. Ckem., 61, 1126 (1957). (32) A. N. Frumkin and P;. V. Nikolajera, J . Chrm. Ph3>5.,2 6 , 1.552 11957).
MANFRED RREITER. 3fARCOS
5112
I(LE1NERMAN
kinetic complications in the absence of specific adsorption were considered in detail by previous investigators except for GierstZ5who also studied processes with coupled chemical reactions. Dif ferent possible processes will be discussed. Simple Electrode Processes without Specific Adsorption Fundamentals. Current-Potential Characteristics.-The following treatment, which is not our original contribution, is given because a simple and general discussion is not readily available. The model of Fig. 1.4 for the double layer is satisfactory
Vol. 80
AND P A U L D E L A H A Y
eq. 1 is not applicable, and an interpretation based on the shift of the point of zero charge with electrolyte concentration may be open to question as LT ill be pointed out below. For an ion of valence G, the concentration C* o f reactants in the Helrnholtj. plane is
where z is taken with its sign and CS is the concentration outside the double layer (more rigorously in the region of solution where variations of concentration due to the double layer structure become negligible). If the reactant is a neutral species which is not adsorbed one has approximately C* Cs. Variations of the concentration of a neutral substance resulting from the electrical field in the double layer could be treated, in principle, on a thermodynamic basis,34 the electrical field strength being calculated from double layer theory. This effect will not be considered here. It follows from eq. 1 and 2 that, a t constant current density, the shift AE in electrode potential corresponding to a change A ( ~ H- 4s) is
-
I I
I I
i
o
B
A
Fig. 1.-Models for the double layer a t a metal-electrolyte interface: A, without specific adsorption; B, with specific adsorption.
in the absence of specific adsorption. The double layer is composed to two parts: the diffuse double layer and the Helmholtz double layer between the metal and the plane of closest approach. The structure of the double layer has an influence 011 the current-potential characteristic for an electrode process involving a single rate-determining step for two reasons: (a) the effective cgncentrations of reacting species niust be taken in the plane of closest approach, and (b) the differences of potent i a l ~ +H ,~~ r$s, must be subtracted from the electrode potential. Cathodic reactions involving a rate-determining step with n a electrons will be considered because fundamental results can be expressed with a minimum of algebra. The more complicated case of fast reactions is treated in the Appendix. Thus, one has for the cathodic current density (a similar equation can be written for the backward reaction)
where k is a proportionality constant, C* is the concentsation of reactant in the Helmholtz plane, LY the transfer coefficient, E the usual electrode potential (European convention) and R, T and F have their usual significance. Xote that the potential E is not referred to the point of zero charge E , in eq. 1. In the absence of specific adsorption E , is independent of the electrolyte concentration and the introduction of E , offers no particular advantage. In the case of specific adsorption, the current still varies exponentiallv with potential as a first approximation but
-
+
(33) T h e difference 48 is noted a s in t h e Russian literature, and t h e electrode potential or the difference between t h e electrode potential and t h e potential a t the point of zero charge are designated by m. l‘hese notations are not used here because + and 4 (not q ) generally designate outer and inner potentials, respectively.
(3)
if CY is constant. If z = 0, AE = A(+H - +s), and the change of potential is entirely caused by variation of the difference of potentials across the diffuse double layer. Equation 3 holds regardless of the cause of the change in +H - 4s. For instance, +H - 4s can be changed by addition of a foreign electrolyte which is not reduced or oxidized in the range of potentials being considered. If CY varies, one has a t constant current density (oE - a’E’)n, = (on, - z)(+pn
-
+S)E
-
(a’%,- z)(+n
- +s)E’
(4)
and the shift of potential readily is obtained Equations 3 and 4 also give the shift of half-wave potential for irreversible polarographic waves provided that the diffusion current does not vary appreciably (constant current density a t E,,) upon variation of the electrolyte concentration. Calculation of (&I - &).-The difference (+H - 4s) is such that the sum of the charges on the tnetal and in the diffuse double layer is equal to zero (see Frumkin) .lo Thus K , [ ( E- E,) - (6H
- 4S)I
=
where K i is the integral capacity of the Helmholtz double layer, E , the electrode potential a t the point of zero charge, E the dielectric constant35(assumed to be constant in the double layer), and Ci the bulk concentration of ion i of valence z i (with its sign) in moles cm.-3, The right-hand member in eq. 3 is taken from the classical Gouy-Chapman theory. 36 (34) E. A. Guggenheim, “Thermodynamics,” 8rd Ed.,InteTsciencc Publishers, Inc., New I’ork. N. I’ , 1995, pp. 410-416, (35) Szturation cf the dielectric ran be neglected as a first approximation. (313) (a) For a review see, for instance, D. C. Grahame, Chcm. Revs., 41, 441 (1947); (b) also, R . Parsons, Chap. 3 in ref. 21, pp. 144-148.
Oct. 5, 1958
51 13
STRUCTURE OF DOUBLE LAYERAND ELECTRODE PROCESSES
If only z-z electrolytes are present, eq. 5 reduces to KiliE
- E,)
- ( 6~
&)I
=
where ] z / is now taken in absolute value, and Ct is the sum of the electrolyte concentrations. Variations of +H - 6s with E - E, are shown in Fig. 2 for different molar concentrations of a 1-1 electrolyte and for the constant value, Ki = 20 microfarads. cm. -z. ( K i actually varies somewhat with E in the range considered.) A similar diagram is given by Frumkin, et al.37
-0.2 I -
>:
I
d I
d
I
-0.i
2
1.5 LOG
i
(
i
I N IO-~A.CM:').
Fig. 3.--E v w m s log i plot for the reduction of 5 X M KIO, in 2 X lo-* 144 KOH with varying molar conceiltrations of KC1 a t 30'. 0
0
-2
-I
E-E, Fig. 2.--Variations of d~ - 6 8 with E molar concentration of a 1-1 electrolyte.
(v.).
- E.
for different See data in text.
It is seen from Fig. 2 that one can easily change - 4s) by 0.1 volt by variation of the electrolyte concentration, and consequently the change AE of eq. 3 can be quite pronounced. 0.05 volt, eq. 6 yields approximately for a given E (+H
-&
RT
= f -In Ct
+ constant
(7) Izl F where the constant can be written in an explicit form from eq. 6, and the positive and negative signs hold, respectively, for the cathodic and anodic ranges of potential as referred to the point of zero charge. Equation 7 is useful because it readily gives the dependence of +H - +s on Ct, but the more rigorous eq. 6 (or eq. 5 for 2-2' electrolytes) must generally be applied. +H
Experimental Study for the Reduction of Iodate Ion.Iodate ion is reduced in alkaline solution (PH > 12) on mercury a t potentials (for a given current density) which are independent of p H . At lO-5-lO-' amp. cm.-2 potentials are in therange -1.0 to -1.2 volts (us. S.C.E.), %.e.,outside the range of specific adsorption of the anions I-, IOa-, OH-. The effect of electrolytes on the reduction of iodate was previously studied in this Laboratory under polarographic conditions by application of the treatment of irreversible waves.% Results were explained on the assumption that cations reduce the electrostatic repulsion of iodate ions by the electrode. (37) Ref. 19,p. 17. (38) P. Delahay and C. C. Mattax, THIS JOURNAL, 76, 5314 (1964). See ref. thereiu for the polarography of iodate.
Linear plots of E u e m u log i (i, instantaneous current at the end of drop life) were obtained (Fig. 3) with a dropping mercury electrode in the absence of practically any concentration polarization (i < 0.0lid). Plots of log i 11s. E were shifted toward less negative potentials upon the addition of potassium chloride. The product, ans = 0.81, was independent of electrolyte concentration and in good agreement with the value, ana = 0.77 =k 0.02, previously obtained by polarography. Similar results were obtained with lithium chloride and potassium sulfate. Experimental and calculated shifts are compared in Table I. The agreement is good for potassium and lithium chloride but not entirely satisfactory for potassium sulfate. Anyhow, it is concluded that changes in the double layer structure upon the addition of electrolyte essentially account for the salt effect in the reduction of iodate on mercury in alkaline media. Approximate values of the shift AE calculated from eq. 7 are also listed in Table I to indicate the approximation achieved by this equation, especially for large changes in electrolyte concentration. I t was assumed in this calculation that the constant of eq. 7 is independent of potential over the interval AE . Data used in these computations and not previously quoted were as follows: T = 303.1; B = 79. The integral capacity Ki hardly varied between -1.0 and -1.2 volts (vs. S.C.E.), and consequently the K,'s a t -1.1 volts (us. S.C.E.) were used. The following values in units, microfarads. were determined and additional ones were interoolatcd. For KCl series: 16.4 (no KCl added). 16.7 (0.02'M KCI), 19.6 (0.5 Af KCl). For LiCl: 1S:O (no LiCl added), 16.6 (0.02 M), 20.4 (0.5 AI). For KpSOa: 16.5 (no KpSO4 added), 17 10.02 M ) , 18.8 (0.5 M). The point of zero charge in the absence of specific adsorption, E, = -0.45 volt zwsus S.C.E., was used in all calculations. The shift AEosicd.varies only by a few millivolts even when E2 is changed by as much as 0.05 volt. Liquid junction potentials were quite negligible. For KCl series: -2.5 mv. without addition of KC1; -1.1 mv. for the 0.5 M KCl solution. For the K2SOt series: $3.9 mv. for the 0.5 M solution. KO evaluation was made for LiCl. The minus sign indicates that the liquid junction potential was positive from the reference electrode to the dropping mercury electrode.
Simple Electrode Process with Specific Adsorption Fundamentals.-The following discussion is based on a model of the double layer (Fig. 1B) with
5114
MANFRED
BREITER,LIARCOS
KLEINERRIAN AND P A U L
DEL.III.\T
VOI. 80
inner and outer Helmholtz planes (for review see Nitromethane was selected for tiir following reasons: (a) polarography has been studied44; (b) it is reduced in ref. 36). The inner plane is the locus of adsorbed its acid solution a t potentials for which values of +i - $B and ions. The outer plane corresponds to the closest 40 - 45 are given by Grahame; (c) nitromethane does not approach to the electrode outside the range of ad- affect, within experimental error, the electrocapillary curve sorption forces. As in the case of no specific ad- of iodide and consequently it is not strongly adsorbed on mercury; (d) the solubility of nitromethane in water is sorption, corrections in the rate equation should be sufficiently high. made for the concentration of the reducible (or Irreversible waves for nitromethane were analyzed by oxidizable) species and for the effective difference the Koutecky Results were expressed in terms of potentials. However, two difficulties arise : of a global rate constant k' defined by i = k'Cs, CS being concentration of nitromethane outside the double layer (a) The plane for which the difference of inner po- the with eqs. 1 and 2 ) . tentials, - +s, is needed must be properly se- (compare Values of K' ~ : / z / D ' / z(T dron time, D diffusion coefficient lected; (b) the corresponding difference of poten- of nitromethane) were directly deduced from the ratio ilid tials cannot be calculated directly by the Gouy-- of the instantaneous current a t the end of drop life to the instantaneous diffusion current, and the corresponding Chapman theory. ( k ' ) ' s were then calculated ( T = 4.2 sec., within 5YGalong If the substance being reduced or oxidized is an the wave; D = 1.66 X cm.-*sec.-l, practically indeanion, which is adsorbed much in the same way as pendent of the iodide concentration). The rather linear the anion of the foreign electrolyte, interpretation plots of log k' us. E which were obtained (Fig. 5) were toward more cathodic potentials upon the addition may quite safely rest on the difference +i - +s. shifted of iodide. This shift is in the opposite direction of the one In other cases an a priori choice of + - +s is not observed for the reduction of iodate upon the addition of possible. The magnitude of the effect of a foreign electrolIzte (Fig. 3). The slope of the lines in Fig. 5 varied electrolyte on kinetic parameters, however, may somewhat with the iodide concentration, and consequently the experimental shift AE,,, between the 0.1 -11 line and give an indication of the difference - +S which any other one depends on the value of k'. Comparison for must be considered. k' = 10-2.8cm.sec.-l, ; . e . , in the middle of the range in Variations of - +s upoii addition of electrolyte Fig. 5 , was made between 4E,,, and A(& - +s), A ( q i cannot be simply equated to the shift of the point &), and the shift A E z of the point of zero charge. T'alues of - &I, A ( 4 i - +B) and 4Ee,, are hardly different from of zero charge. It is possible that in some cases A(+o those in Fig. 6 if the extreme values of k' in Fig. 5 are used. the shift of the line E tis. log i for the reduction or The liquid junction potential was evaluated a t 2.2 mv. for oxidation of an uncharged particle is approximately 0.1 lf K I and 0.7 niv. for 1 -If K I , the significance nf aign equal to the shift of the point of zero charge, but being the same as for the case of iodate. I t is seen from Fig. 6 that AE,,, is not very different from this conclusion cannot be drawn a priori. I n this A(+i - 4s) and that AE,,,, is in complete disagreement with respect, i t should be noted that the relation, A(+(, - 4s) (even the wrong sign) and A&. Thus, the correction of the electrode potential for 4(4i - &) es 4(+i - 4s) = A&> does not hold, E , being the point of zero charge. This equality which was thought accounts for the effect of the double layer in this p case. An interpretation based on the shift of the point of valid, leads to an incorrect dependence of the point zero charge woulrl lead to values of AE,,, which are much ton ~~~~~ of zero charge 011 the activity of e l e c t r ~ l y t e . large. This is the reason why the point of zero charge is A word of caution is in order it1 the interpretation of the above results. Firstly, values of 4(4i - 4s) and A(#o - 4s) not introduced in eq. I. by Grahame4?cannot be verified directly by exA method for the evaluation of +i - +S and 4 0 calculated periment (although conclusions derived from these calcula- +S was reported recently by Grahame4"by ex- tions are verified experinlentally). Secondly, the kinetics tension of ideas first developed by Esin and Shikov40 of the nitromethane reduction were interpreted in a formal and improved by Ershler. 41 The analysis takes manner on the assumption that the reduction rate is proportional to the nitromethane concentration. This relainto account the discreteness of adsorbed ions ar- tion leads to a linear plot of log k' as. E (Fig. 5 ) which is ranged in a hexagonal array. Grahame applied essentially obcyxl experimentally b u t , ncrerthrless, there the treatment to potassium iodide at concentra- may be kinetic coinplications. tions between 0.025 and 1 X (see Fig. 4 for some of his results). B y the use of such data it is pos- Electrode Processes with Coupled Chemical Reaction sible to interpret, to a certain extent, the effect of electrolytes on the kinetics of electrode reactions We consider processes in which the electroas will now be shown. chemical reaction is preceded or followed by a The following interpretation is not complicated chemical reaction.46 The double layer structure by variation of the electrode coverage for the ad- has not been considered in previous analysis of sorbed anion because, as pointed out by E r ~ h l e r , ~such ~ processes, and particles have been treated as this coverage is relatively small (< 0.2) even for points. Thus, it has generally been assumed that high electrolyte concentrations. Hence, the con- concentrations are independent of the distance centration C* in eq. 1 for n neu.tral species is essen- from the electrode before electrolysis. Modificatially independent of the coT-erage for the spe- tions of existing theories would be very involved if cifically adsorbed anion. the double layer structure were rigorously taken Experimental Study for the Reduction of Nitromethane .into account. However, a simple interpretation The effect of iodide ion on the kinetics of the reduction of which accounts for experimental data obtained SO nitromethane was studied under pnlarographic conditions. far can be developed on the assumption that the (39) 0. A. Esin and R . F. Markov, Artu Pkysicochinr. I . R .q .S , 10, double layer thickness is either small or large in
+
+
+
236 (1943). (40) 0 . A . Esin and V. 31,Shikov, 2 h u v -62. K i i i w . , 17, 2:iG i l D 1 X ) . i l l ) II T. F:r+hler, i h i d . . 20, A79 ( 1 q I G ) . (42) Revien- of R. Parsons. rei. 2 1 , pp. 159-1131. (43; D. C. (:rahame, Technical Regorti t o the Ofice o i Savi11 Research, Nos. 1 and -5 (second series!, Contract S-onr-2309 (11, 19.57; Z Elekfvorhem., 62, 264 (1958).
(44) F. PPtrii, Coilerlion Czechoslo~~nkC h e m Coni?vrtns., 12, 620 (191171. (45) J. Iioutecky, z b i t ! , 18, 597 (195:i). (46) For a review i e e for instance P. Delahry. "h'e\% I n s t r u m e ~ i t n l Methods in Electrochemistry," Interscience Publishers. i i e n . y r i r k , N. \-., 1 D i - l .
STRUCTURE OF DOUBLE LAYER AND ELECTRODE PROCESSES
Oct. 5, 1958 1
-0.221 I
5113
I
I
-> -
0.02
0
Y 8 8
a
-0.051
I
-0.061 1 -0.70
I
1
- 0.80
-0.75
E
(
~
VS. N.C.E.
V.
-0.10
I
I
-0.80 POTENTIAL (V. VS N C E
).
Fig. 5.--Analysis of nitromethane polarographic waves obtained a t 25'. Solution composition: 1.2 X lop3 M nitromethane, 2.1 X M HI, and varying amounts of KI t o make up the total molar iodide concentration indicated in each line.
comparison with the reaction layer thickness. I n the first case the double layer structure is quite unimportant; in the second case there is a definite effect of the double layer. A similar approach was developed independently by Gierst. 25 The simple approach v-ill be discussed for the particular process Z $ 0 n, e = R in which Z is not reduced or oxidized, but the analysis can be transposed to other types of re- e = 2K k'r exp actions. Only resultsfor the current-stepmethod willbe discussed because of their direct verification from existing data. Extension to the potential-step method and to polarography is immediate. The transition time T k for the process z 0 n, e = R under the usual conditions of the current-step method is such that 47
+
3
+
I 1
I
).
Fig. 4.-Differences of potentials in t h e double layer in the case of specific adsorption. D a t a for 25" and for mercury and potassium iodide at different molar concentrations according t o G ~ - a h a m e . ~ ~
-0.75
\
-I
-0.5
0 LOG
C.
Fig. 6.-Effects of iodide on the kinetics of the nitromethane reduction and certain properties of the double layer. See d a t a and notations in text.
constant for this reaction; and T d the transition time that would be measured if Z were reduced directly, all other conditions being the same. The product i T d l / ' is independent of current density. It follows from eq. 8 that a plot of i n 1 / 1 against 1 is linear. The formal rate constants kr and kb can be deduced from this plot provided that K is known. The reaction layer thickness for the above process is p = D ' l a / k b 1 I 2 ,D being the common value of the diffusion coefficients for 2 and 0 (assumed to be equal). For example, 1.1 0 2 X lo-' cm. for D = 5 X l o w 6cm.2 set.-' and kb = l o 5 set.-'. The thickness of the diffuse double layer is somewhat larger than this value of p, a t least for fairly dilute electrolytes. I n the absence of specific adsorption, one can then assume, as a first approximation, that the reaction Z e 0 occurs mostly in a layer in which concentrations of ions can be corrected on the basis of eq. 2 . The salt effect on the kinetics of the reaction proper (variation of activities) is neglected in such a correction. I n the case of specific adsorption, correction is more delicate because of the difficulty in the selection of the proper value of 4 - 4s (see above j . By noting that the formal k ' s in eq. S are the products of rate constants k' by the exponential factor in eq. 2 , one obtains for the slope of the ir'/a versus i line
[-
*
where kf and kb are the formal rate constants for 2 e 0; i is the current density; K the equilibrium (47) P. Delahay a n d T. Berzins, THISJOURNAL, 76, 2486 (1953).
where zz and zo are the valences of ions Z and 0 with their sign, respectively. When K
