Chronopotentio metry with Current ReversaI of the Hg/Hg2+’ System at the Hanging Mercury Drop Deviations from Semi-infinite Linear Diffusion Control STEIN DERON’ and
H. A.
LAITINEN
Noyer Chemical laboratory, University of Illinois, Urbana, 111.
b The principle of the additivity of small perturbations of semi-infinite linear diff usion-controlled chronopotentiometry with current reversal is developed and illustrated by an investigation of the oxidation of a hanging mercury drop electrode in a perchloric acid solution under a constant anodic current and the subsequent constant current reduction of the mercurous ions formed. As the forward electrolysis time is varied between a fraction of a millisecond and several seconds, the influence of spherical diffusion and distortion of the chronopotentiogram by double layer charging is considered. Three models are presented for the determination of the change in the electrode charge during the forward electrolysis. The determination of the amount of an absorbed species or insoluble film formed on the surface of the electrode is discussed. The present approach gives a basis for obtaining very accurate chronopotentiometric data.
C
with current reversal is a convenient tool for the investigation of processes following an electrochemical reaction ( 1 , S , 16,16, 16, 66, 67). To use this method for studying processes following the electrochemical oxidation of mercury, it became necessary to exmine the factors that cause deviations from the ideal case of semi-infinite linear diffusion at the hanging mercury drop electrode (H.M.D.E.) : the sphericity of the electrode, the incompleteness of the electrolysis, and the charging and discharging of the electrical double layer. Although the experimental results pertain specifically to the mercury(1)-mercury system, the approach is a general one and the consequences are of general signiicance. Consider first a planar electrode and suppose that a chemical species A , which exists on the surface of the electrode or HRONOPOTENTIOMETRY
‘Present addreas, Service d’halyse et de C h m e Appli u b , Section de ContrBle des Ma%naux%ucl6aires, Centre d’Etudes Nuclhires de Grenoble, Grenoble, France. 1290
0
ANALYTICAL CHEMISTRY
in solution, is electrolyzed for a timet, at a constant current density, I,, into a soluble species B according to Reaction 1.
aA -+ bB
+ ne
(1) If the process is strictly governed by the semi-infinite linear diffusion of species B and if on reversal of the current to a density Z, at time t f the reverse reaction proceeds, the reverse electrolysis time, 7, = 7,*, required for the surface concentration of species B to return to the initial value zero, is related (61) to the forward electrolysis time, t/ = t,*, by Relation 2.
+ 77*)1/* = (I, + Z,)7,*1/2
Z,(t,*
(2)
Thus, in this ideal csse the ratio 7,*/ depends solely upon the ratio of the current densities ZI/ZI, while in general the actual ratio of the electrolysis times, 7,/tj, is also a function of several other variables. We limit the discussion to the three factors mentioned above. If the influence of these factors is measured, respectively, by variables u1, UZ, and 211, then tj*
7,/tf
= j(Zr/Z,, u1,m,
(3)
For simplicity of the discussion the reversible electrochemical Reaction 1 is assumed to be fast enough so that the
Nernst equation applies even when current flows. Let us now define variables UI, UZ,and ua. Theory and experience (9) of chronopotentiometry lead to the 2 choice of the expression u1 = 0 ~ 1 1 tll/*/r as the first variable which measures the magnitude of the “diffusion layer” with respect to the radius, t , of the electrode at the time of current reversal. The other two factors to be discussed arise from the distortion of the potential-time curves, from which the electrolysistimes are determined, by the electrical double layer charging and discharging. Because of this distortion the experimental reverse transition time, 7,, represents the time required for the surface concentration of species B to return from the value C, at the time of current reversal to a value C., small but still different from zero. Thus the incompleteness of the reverse electrolysis can be expressed by the ratio CJC, = m. Finally, if Qo is the change in the electrical charge of the electrode per unit area during the forward electrolysis, the ratio of Qe to the quantity of electricity passed during the forward electrolysis is taken as the third variable: ua = Qc/Zft,. when electrolysis times t, and 7, are measured as shown on Figure 1, variab1.e~Z,/Zf, ul, u*,and ua completely describe the process, as then both the surface concentration of B and the
Figure 1. Meawrement of the electrolysis times from the potential-time curve
c=0 t=O
TIME
are certainly continuous functions, it is legitimate to write: jut‘( Ir/I/, 0, 0, 0) = lim
y/, ut-0
W O , 0)
x
- f(Zr/Z/,
1
0, 0,O)
u1
Figure 2.
Block diagram of the controlled current electrolysis circuit
charge of the electrode are the same at points F and R. Now, two cases should be considered. When each of variables u1, %, and us is small, a first-order Taylor series of Itelation 3 constitutes a valid approximation: Tr/t/
=
.f(z*/zf,0, 0, 0) + 3 Cfu;’ U V / I / , 0, 070) %-1
(4)
is the derivative of function j with respect to variable u;. I n that case 7,/tj is a linear function of variables ut, u2, and us. When these variables are no longer small, the first-order approximation is insufficient. Yet often only one variable becomes important. Then, instead of using higher order approximations, it may be more useful to design a reasonable model taking this factor into account and to consider the other two variables as small perturbations of this model. For example, if a satisfactory functionf (Z,/Zf, 0, 0, QJZfi,) can be found to describe the influence of double layer charging when variables ut and % are negligible, then, as long as ut and u2remain small,
fui’
order of 0.03 sq. cm. The solutions were deoxygenated by bubbling purified nitrogen (7) through the cell, and were initially free of mercurous ions. The electrolysis times were determined as shown on Figure 1from the potentialtune curves, which were displayed on screen of a 53552 Tektronix oscilloscope and recorded by photographing the screen with a G 1 2 Polaroid camera. The controlled current source is described in Figures 2 and 3. It was designed as a plug-in unit to a Heath E m - 1 9 A operational amplifier module, combined with the 53592 Tektronix oscilloscope, which provided the controlling square pulses. Maximum current outputs of 20 ma. were obtained. The rise time of the pulses was 10 psec. CASE 1.
SMALL DEVIATIONS FROM SEMIINflNlTE LINEAR DIFFUSION
In the case of small deviations from a process governed strictly by semi-infinite linear diffusion, Relation 4 pertains. Because the derivatives of function j
(6) and similarly for the other derivatives. In other words, it is not necessary to know the general expression for the function f(Z,/Z/, ut, %, ua); the knowledge of the influence of each deviation factor when the others are negligible is sufficient to compute the simultaneous contribution of all the perturbing factors when this restriction no longer holds provided that the deviations remain small. Influence of Sphericity of Electrode. The solution of chronopotentiometry with current reversal with spherical diffusion (21) is represented by the following equation:
As here r,/t/ = j(Z,/Zf, ul, 0, 0 ) , the derivative fui‘ is obtained by developing
both members of Equation 7 int0.a firstorder MacLaurin’s expansion. This leads to Equation 8, 7 d t / = r,*/t,* *1/2(I/
x
+ Z,)2
where t,* and r,* obey Equation 2. When ua = C./C, is kept constant and by using AE = 90 mv. equal to
25 K
IO K
om HMDE 1
The two cases will be examined successively and illustrated with experimental data obtained with the Hg/ Hgs+* system in perchloric acid solutions. EXPERIMENTAL
The 2M HClOI supporting electr+ lyte was prepared by diluting double vacuumdistilled 70% perchloric acid (G. F. Smith Chemical Co.) with d i s tilled water. The H.M.D.E. was identical to the one described by Chambers (7). Ita area was calculated from ita meahred weight, sseuming it waa exactly qherical. The area was of the
DB”2t/’/2
fo
COUNTER ELECTRODE IK
SOALH
+
Figure 3.
R1,R~.RpWESTERN ELECTRIC 275 B RELAYS
Controlled current source VOL 38, NO. 10, SEPTEMBER 1966
0
1291
I
1
I
I
-
where C A is the initial concentration of species A , DA and DB are the diffusion coefficients of species A and B, and LUC‘is defined by Figure 1. But as long
0.34
as C,/CA is small compared to -b DB“’ a DA‘/~ the relation simplifies to
c0/cr= exp (- nFAE E)
I
1
0
I
0.5
1.0
Figure 4.
Variation of
(Figure l), and when = Qo/ZJtl is made smaller than 2 X 10-3, so that it can be neglected, the Hg/Hg2+2system satisfactorily follows Equation 8 (Figure 4 ) . Indeed the experimental slope of -0.024 f 0.005 sec.-1/2 compares favorably with the theoretical slope of -0.026 sec.-1/2 calculated from Equation 8 and a value of 0.9 X 10-6 sq. cm. per second for the diffusion coefficient of mercurous ion in a perchloric acid solution (24). Influence of Incompleteness of Electrolysis. Following the same procedure, the influence of the variable u2 = C,/C, is first determined when 0, it is the only deviation factor. f(z?/zJJ ~20 , ) is directly obtained from the time dependence of the surface concentration of species B in the case of linear diffusion control (6, 1 9 ) :
CdC, = (1 -
$)
7+J*
20
as a function of tJ1”
0.851
I
I
1
I
OD2 Figure 5.
(9)
A first-order approximation of Equations 9 and 10 yields t f = tl* and
In the case of the chronopotentiometry of mercury, n = 2, b = 1, and the activity of A = H,’ remains constant, so that Equation 13 always holds. I n fact, for a given chronopotentiogram a linear relationship is observed between T , / t J and exp (-2FAEIRT) (Figure 5). However, the experimental slope (Table I) appears to be consistently only half of the theoretical slope expected from
1
I
1.5
1/2
CdC, =
Tr/tl
I
sEc’/r
I
1
a08
404 Q06 EXP (-nFAE/RT)
Plot of
T./T,*
(13)
I
1
aio
vs. exp (-nFAE/RT) 1
b
I
I
-
0.40
= (ri*/tl*)
035AE:60 MV
Experimentally the variable u2 = C./C, can be determined from the Nernst equation. For the general electrochemical Reaction 1, when both species A and B are diffusing
CdC, =
I
I
1
0
I
2&tp,IdCMZ/C
Figure 6.
1292
ANALYTICAL CHEMISTRY
I
Plot of 7,/tl as a function of (lltl)-l
I 4
J
5
-- -
EXPERIMENTAL
CALCULATED FROM EQ I?
I
50 Figure 7.
+
Tr)1/2
- 2(Z, + I,)T,1/2 =
If the integral is small, a satisfactory approximation is obtained by setting t, = t/* and expanding T , into a firstorder Taylor series with respect to the integral, which is taken as the perturbing variable: =
Tr/t,
(1
(~r*/t/*)
-
X
+
I , I, I,1/2(2Z, Z r ) 1 / 2
+
100
Slope of 7,/f, vs. (/,f,)-l
Equation 13. This can be explained only by a consistent 10-mv. instrumental error on the measured value of AE due possibly to an inaccurate correction of I R drop through a consistent error in the estimation of u (Figure 1). Influence of Double Layer Charging. Because of double layer charging the total current applied to the cell is the sum of the electrolysis current proper and the charging current, I,. When this is the only deviation factor,
2Z,(t,
AE,MV
.-
as a function of A€
Then Equation 15 becomes =
TJt,
(Tl*/t,*)
Actually with the Hg/Hgz+* system for a given value of Z,/Z,, t,, and AE-i.e., ut and uz constant-ratio r./t, increases linearly with the reciprocal of I,t, (Figure 6). If the model were exact and if the double layer capacity were independent of potential, the slope would be proportional to AE. In this region of potential concerned this is far from the case and the slope increases rapidly with AE (Figure 7). Nevertheless for AE less than 60 mv. the experimental results compare well with the predicted behavior for an electrode with a 70 pf. per sq. cm. double layer capacitance. Equations 15 and 18 consider only the contribution of variable us, while on Figure 6, if u1 is indeed negligible, u2
1
The integral can be determined experimentally, for example, from the potential-time curve and the ditrerential double layer capacity as a function of potential, but unfortunately the analytical solution is not known. Nevertheless, even when the double layer capacitance is not known, a roughly approximated model can help to estimate the influence of the double layer charging. For example, it can be assumed that :
and when
n
tortions from double layer charging rapidly become the most important factor of deviation. Rather than using arbitrarily smaller and smaller values for AE in an attempt to correct for this distortion, it is more significant to determine experimentally the quantity of electricity involved in the double layer charging and to account for the other deviations by a relation of the type of Equation 5.
Z,t,'/* Table 1.
when
x
is not, although it remains constant along each line. Thus, according to Equation 4, the intercepts of these lines depend only on uz and actually they decrease with increasing values of u2. Discussion. It is clear t h a t u2 and u1 are both functions of AE and therefore are not entirely independent variables; however, it was practical to consider them as such because their effects are opposite and the validity of this approach is supported by the agreement between the experimental data and Equation 4. Figure 6 illustrates the additivity of the u2 and ua contributions, while Table I gives an example of the addition of the u1 and uz contributions. I n summary, spherical diffusion and the incompleteness of the reverse electrolysis decrease the ratio ~ , / t , of the electrolysis times, while double layer charging increases it. It is usually possible by the choice of proper experimental conditions to make the influence of the first two factors negligible or to correct accurately for them. For a partial correction of the deviations due to double layer charging, a practical procedure is to use a small value of AE in measuring the electrolysis times. Figure 8 and Table I1 show how much more effective it is to use AE = 60 mv. compared to AE = 120 mv. However, if the quantity of electricity, Z,t,, is de100 creased below - pc. per sq. cm., dis-
Slopes and Intercepts for Plots of rr/7,* vs. exp (-nFAE/RT)
Slopes msec. I,, ma./sq. cm. Zr/Z, Ideal Expt. Intercepts 5.70 423 1.00 2.31 1.15 1.01 58.8 72.3 2.16 2.10 1.03 0.93" 58.8 72.3 0.46 2.70 1.28 0.94" Values low because of appreciable influence of sphericity of electrode. According to Equation 8, correction is +0.04. tl,
0
Table 11.
Variations of
Tr/f,
with
ti, w e e .
Zit,, pc./sq. cm.
10.63 10.20 11.63 11.63 11.60
59.0 56.7 428 428 427
T,*/f/*
Parameters for Equation 7,/t, =
a 1.13 1.01 1.05 1.03 1.02
b 0.058 0.035 0.017 0.015 0.013
Ah',mv.
VOL 30, NO. 10, SEPTEMBER 1966
120 60 120 90 60
1293
c - AE
120MV 60MV -IDEAL LINE
0
-A€
X
I -----'DIFFUSION
CONTROLLED PROCESS --.-GENERATION OFAN INSaLUBLE SPECIES
t
*
1
I
1
a
CASE II. DETERMINATION OF SURFACE ELECTRICAL CHARGE IN CHRONOPOTENTIOMETRY WITH CURRENT REVERSAL
Clessical chronopotentiometry (8,N) has been used to measure the quantity of an electroactive species adsorbed on the electrode by determining the limit of the quantity of electricity, I T ,when the current, I , is increased to infinity. Similarly in chronopotentiometry with current reversal the quantity of electricity accumulated on the surface of the electrode by double layer charging or
Table 111.
I,, ma./sq. em.
0
generation of an insoluble species during a given forward electrolysis can in principle be determined by measuring the limit of the quantity of electricity, I l ~ r , recovered during the reverse electrolysis when I , is increased to infinity in order to eliminate the contribution of diffusing reactant B during the reverse electrolysis. The extrapolated values of Q0 should be independent of
Slopes and Intercepts of Plots of t,,
mec.
1.87 8.94 11.6 8.97 9.00
25.9 13.5 36.8 13.5 13.5
Figure 9.
corrected
h, vs. 1, 1,t,
21,
slopem
Intercept
0.88 0.96 0.97 0.96 0.96
0.14 0.062
+ 1,
IS, mv. 60 60
0.022
60
0.078
90
0.085 120 Corrected for contributions of factors ILL and w according to Equation 5.
Table IV.
Slopes and Intercepts of Plots of
I,, ma./aq. om.
t,, mec.
corrected slope
Intercept
IS, mv.
25.9 13.5 36.8 13.5 13.5
1.87 8.94 11.6 8.97 9.00
0.93 1.00 1.00 1.01 1.01
0.095 0.036 0.015 0.015 0.053
60 60 60
a
Corrected for contributions of factors u1 and ut.
1294 0
A N u r n u l L CHEMS ITRY
90 120
I
Plot of
/,Tr//,f,
vs.
1, ~
21,
+ 1,
the extrapolation procedure. Thus if only the magnitude of Qcis wanted, the model used to describe the physical process may not need to be accurate. But the cruder the model the higher Z, must be made before extrapolation to to a reliable value of Qc is attempted. It is difiicult to decide a priori how much I , should be increased. Thus when the accurate model is not known or when it is difficult to handle, as in the case of simultaneous electrolysis and double layer charging, it is important to compare very different models. Three different extrapolation procedures are discussed now. Direct Comparison with Ideal Diffusion-Controlled Process. According to Equation 2, in the diffusioncontrolled case,
On the contrary, if the forward electrolysis generates a totally insoluble species, ratio Z,r,/Z,t! is constant and equal to 1. In the csse of interest, when double layer charging interferes with simple diffusion the ratio of t L quantities of electricity takes an intermediate value I , ) (Figure 9). between 1 and Z,/(2Z, In fact, when the ratio of current densities, Z,/Z,, is varied between 0.2 and 17 straight plots of Z,T~/Z,~, 88. Z,T,*/Z~,* are obtained. Indeed, although the model has little bearing on reality, if it is assumed that the diffusion-controlled
+
electrolysis and the double layer charging are completely independent, so that the quantities of electricity involved by each process are simply additive, Equation 20 is derived, when uI and u2 are negligible:
According to Equation 20, the sum of the slope and intercept should be equal to unity. Thus experimental data appear to follow this model best for small values of AE (Table 111). Capacitative Current Constant during Forward or Reverse Electrolysis. This model is defined by Conditions 16 and 17. I t s solution is obtained simply by replacing in Equation 2 the forward current density, I,, by Z ,
- Q. t/
and the reverse current density, I,, by
I,
- Q>.
Thus we have:
TI
ZITI - = (1 z/t/
-&) x 1
Experimentally Z,I,/Z,~/
is a linear
function of the expression (1
+ );
112
7,
- t/
(,)l'*
IV). The model fits best experiment for small values of AE, as then the variac tions with time of the electrode potential are minimum and consequently the assumption of the constancy of the
0.4
Figure 1 1 .
x
(Figure 10 and Table
I
I
0.2
I
0.6
z
G(z, m ) as a function of
capacitive current during a half cycle is better followed. Electrical Double Layer Charges First and Discharges Last. The solution of this model has been given (16) when the forward and the reverse current densities are equal. Equation
I
22 is valid for all values of the ratio of current densities, I J Z ! : Qc
= (I/
+ Z T ) T ~2 arc COS(T,*/I,)~/*n.
(22)
The computer program designed by Bard and coworkers (16, 86) may be adapted for computing Q. according to Equation 22. When a computer is not readily available, the following simple graphical method can be used. Consider the two functions, G,(z) and H,(z) , of variable z defined below :
(23) where
H,(z) =
1 . m(m+ 2)
Figure 10.
Plot of IrT,/lltl
vs.
If parameter m is chosen equal to the ratio of the current densities, VOL 38, NO. 10, SEPTEMBER,1966
1295
coordinates z i and G, of the intersection of curve G,,(z) with the corresponding straight line, H,,(z), are simply related to the solution of Equation 22: = mo(mo
Qc
I,+
=
+ 2)GiI/7,
(27) (28)
ZiTl
Numerical tables for the construction of a set of G curves (Figure 11) have been computed and are available (10). For a given forward electrolysis and AE = 60 mv. the values of Q. calculated by this method increase strongly with the ratio Z,/Z, (Table V), so that clearly the model here is a fairly crude approximation of the charging and discharging of the double layer. However, when A E = 120 mv. is used, the results depend much less on the current density ratio. Indeed for large values of AE a greater fraction of Qo results from the change in the surface charge during the initial period of the forward electrolysis and the final stage of the reverse electrolysis, and therefore the model is then a better approximation of the physical process. Nevertheless only the extrapolation of the values calculated according to Equation 27, when ratio I , / I f tends toward infinity, is meaningful. A practical procedure for such an extrapolation is to plot the result of Equation 27 against the corresponding value of zi and extrapolate to zero (Figure 12). Discussion. Models 2 and 3 are based on conflicting assumptions, although model 2, when AE is small, and
Table V.
Variations of Q, = m, X
I, I/
(m, +2)Gi/g, with the Ratio m, =-
I, = 13.5ma./sq. cm. t f = 9 msec.
Qe, MC./
A E s m,
0.828 1.66 4.15 8.28 16.6
Table VI.
60mv. 1.28 1.67 1.75 2.66 3.02
sq. cm.,
a = a=
90mv. 120mv. 2.78 2.82 4.15 3.06 4.26 3.90 5.00 3.93 5.10
0
eq. om.
25.9 13.5 36.8 13.5 13.5
12%
I
I
I
I
I
1
t
0.2
0.3
0.4
0.5
0.6
0.7
0.0
Figure 12.
sec.l/* 1.12 1.28 3.90 1.28 1.29
+
Qo,rc./sq. cm.
AE,my. 60 60 60 90 120
ANALYTICAL CHEMISTRY
1.0
Plot of "Q," vs. zi
model 3, when AE is large, give a reasonable picture of the electrolysis of mercury in perchloric acid solutions. Yet the values of Qo extrapolated according to these two models differ by less than 1 pc. per sq. cm. and they agree with the ones that can be computed from the a.c. impedance measurements of double layer capacity reported by Rehbach-Sluyters and Sluyters (24) (Table VI). It is probable then that these results are accurate within 1 pc, per sq. cm. Thus contrary to implications in the literature (2, 2.3, the extrapolated chronopotentiometric measurements of changes Qc in surface charge should be independent of the model, even imperfect, used to described the physical process, provided that the extrapolation is conducted to sufficiently high electrolysis current densities. The restriction is illustrated by the cruder model 1, which in the present case gives higher results for QLthan the other two models. If the above statements are correct, measurements at still greater ratios of reverse to forward electrolysis currents will produce a curvature on plots of Zv7,/Z,t/ us. Z//(2Z/ I,) and undoubtedly the discrepancy would be removed between the values of Qc obtained through model 1 and the other procedures. The present discussion applies also when surface charge changes because of film formation or adsorption. But, if for the electrolysis of mercury in HClO, solutions models 2 and 3 are preferred because a reliable extrapolated value of Qc is obtained even when the current
Comparison of the Q, Values Calculated According to Various Models
ma. em.-*
0.9
Zi
Zftf"',
If,ma./
\
I
0.1
Model 1 7.0 7.5 9.5 9.5 10.5
Model 2 4.5 4.4 6.4 5.5 6.5
Model 3 5 3.6 4.5 5.5
According to (84)
4.7 5.6 6.6
ratio IJZ, is not made larger than 16, adsorption or film formation may be better described by other models. Yet models 2 and 3 can still be used if Z, is made sufficiently large. However, because there is no simple way to describe the ever-present contribution, Q d l , of double layer charging alone, only extrapolation to an infinite reverse current density can here too yield a meaningful result for Qe = Q d l Q., even if the contribution of other surface effects, Q,, alone can be expressed accurately. For example, the value adopted by Bard and coworkers (16) for a monolayer of adsorbed leucoriboflavin is questionable because their chronopotentiometric measurements were conducted only with equal forward and reverse electrolysis currents. The estimation of Biegler and Laitinen ( b ) , as measured by differential double layer capacity, is lower by a factor of 2. This emphasizes that the value of QE is to be considered exact only if all extrapolation procedures yield the same value. Of course, when discussing reaction mechanisms only the model which agrees with the experimental data over the widest range of current densities and still yields a correct extrapolated value of Q,, should be retained. Like potential step techniques, chronopotentiometry cannot differentiate between smultaneous surface effects. But the use of a small value of AE is a simple and advantageous way to minimize the contribution of double layer charging. For example, with AE = 60 mv. and a double layer capacity of 25 pf. per sq. cm., the contribution of double layer charging is only 1.5 pc, per sq. cm., and yet the reverse electrolysis of a rapid electrochemical system with n = 2 is 99% complete. On the other hand, phenomena like film formation may be essentially determined by the electrode potential (13) and are therefore more conveniently studied by controlled potential techniques. However, in the case of fast processes large uncompensated and
+
time-dependent I R drop interferes with the potential control. On the contrary, with a constant current the I R drop is constant and the electrode potential is known within that constant. CONCLUSION
The very general principle according to which small perturbations are additive can be applied to chronopotentiometry with current reversal. Indeed, investigators have described, sometimes only qualitatively, the effects of one or two perturbing factors in classical chronopotentiometry as well as other techniques: Spherical diffusion and migration ( g ) , electrical migration (ZO), double layer charging ( 4 ) , electrode geometry, and edge eflects (14, 18, 16) have been considered. Because chronopotentiometric measurements with proper experimental techniques can probably reach a relative precision of 0.2’%, it is believed that the correction of all small perturbations along the line developed here gives a basis for obtaining an excellent accuracy. Such corrections are necessary for a sensitive and accurate diagnosis of secondary reactions accompanying the electrochemical step. Thus Evans (11) and Lingane (17’) successfully corrected chronopotentiometric data for double layer charging using a very simple model. Investigation of the charging of the
electrical double layer during electrolysis of mercury in HClO, solutions, as an example of such a secondary reaction, indicates that the technique may be used advantage to measure the charge of the electrode at potentials where extensive electrolysis takes place. Changes in surface charge can be determined through simple extrapolation procedures, which do not necessarily reflect accurately the actual process mechanism. ACKNOWLEDGMENT
The contribution of J. A. Plambeck, who wrote the 7094 IBM computer program for the calculation of G,(z), is gratefully acknowledged.
(10) Deron, S., Ph.D. thesis, University of Illinois, 1964. (11) Evans, D. H., Lingane, J. J., ANAL. CHEM.36,2027 (1964). (12) Feldberg, S. W., Auerbach, C., Zbid., 36, 505 (1964). (13) Fleischman, M., Think, H. R., Advan. Electrochem. Electrochem. Eng. 3,123-210 (1963). (14) Hashino, T., Nishi, T., Electrochim. Acta 20, 67 (1965). (15) Hermann, H. B., Bard, A. J., ANAL. . CHEM.3 6 , 5 i o (196‘4). . (16) Hermann, H. B., Tatwawadi, S. V., Bard, A. J., Zbid., 35, 2210 (1963). (17) Linaane, J. J., J. Electrounal. Chem. 1; 379-(1960). . (18) Lingane, P. J., ANAL. CHEM. 36, 1723 (i964). (19) Mattax, C. C., Delahay, P., J . Am. Chem. SOC.76, 874 (1954). (20) Morris, M. D., Lingane, J. J., J. Electrounal. Chem. 6, 300 (1963). (21) Murrav. R. W.. Reillev. C. N.. -~~~~ Zbid., 3 , i 8 2 (1962).‘ (22) Osteryoung, R. A., Anson, F. C., ANAL.CHEM.36, 975 (1964). (23) Osteryoung, R. A,, Lauer, G., Anson, F. C., Zbid., 34, 1833 (1962). (24) Rehbach-Sluyters, M., Sluyters, J. H.. Rec. Trau. Chim. 83, 217, 967, 983 (1964). (25) Soos, 2. G., Ling:me, P. J., J . Phys. Chem. 68, 38121 (1965). (26) Tatwawsdi, S. V., Bard, A. J., (1964). .nmuth, W. H., Zbid., \--I
LITERATURE CITED
( 1 ) Anderson, L. B., Macero, D. J., ANAL.CHEM.37, 322 (1964); J. Electroanal. Chem. 6 , 221 (1963). (2) Anson, F. C., ANAL. CHEM.36, 932 (1964); 35, 1979 (1963). (3) Ashley, J. W., Reilley, C. N., J. Electround. Chem. 7 , 253 (1964). (4) Bard, A. J., ANAL. CHEM.35, 340 (1963). (5) Biegler, T., Laitinen, H. A., J. Phys. Chem. 68, 2374 (1964). (6) Bersins, T., Delahay, P., J . Am. Chem. SOC.75, 4205 (1953). (7) Chambers, L. M., thesis, University of Illinois, 1963. (8) Chambers, L. M., Laitinen, H. A,, ANAL.CHEM.36, 5 (1964). (9) Delahay, P., Mattax, C. C., Berzins, T., J. Am. Chem. SOC.76, 5319 (1954).
I .
RECEIVED for review January 17, 1966. Accepted June 2, 1966. Taken in part from the Ph.D. thesis of Stein Deron, 1964. Research supported by the Nstional Science Foundation under Grant N SF-G2 1049.
Polarographic Kinetically Controlled Currents in Systems Containing Persulfate, Copper(II), and an Agent Which Reacts with Sulfate Free Radical R. WOODS and I.
M. KOLTHOFF
School of Chemistry, University of Minnesofa, Minneapolis, Minn.
b A minimum on the persulfate current potential curve occurs in the presence of both copper(l1) and arsenic(lll), but does not occur in the presence of either constituent alone. The decrease in current is interpreted in terms of a chain reaction involving sulfate free radical and arsenic(lV) as intermediates. The chain is initiated by the reaction of persulfate with copper(1) at the electrode surface. The mechanism accounts for the variation of the decrease with copper(ll), arsenic(lll), and persulfate concentrations and with potential, and for the independence of the decrease of the presence of oxygen. The mechanism is substantiated by the similar effects of alcohols to arsenic(ll1).
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(If) the polarography of mixtures of copper(I1) and persulfate in the presence of chloride was presented and discussed. The current at potentials corresponding to the first copper wave was interpreted as the sum of the copper(I1) to copper (I) current and a kinetic current arising from reaction of copper(1) with persulfate. At these potentials, reduction of persulfate at the dropping mercury electrode (D.M.E.) was postulated to be completely suppressed by adsorption of copper(1) chloride complex at the electrode interphase. Minima on persulfate current-voltage curves have received extensive investigation (6). The copper(I1)-catalyzed oxidation of arsenic(II1) by persulfate in perchlorate N A PREVIOUS PAPER
medium was studied by determining polarographically (16) the persulfate concentration during the reaction. A minimum different from the above type of minimum on the persulfate polarographic wave was observed in the presence of both copper(I1) and arsenic (111) which does not occur with either constituent alone. However, this decrease does not affect the polarographic determination of persulfate because its diffusion current can be measured at potentials more positive than that at which the current starts to decrease. The characteristics of the minimum on 1 Present address, Chemistry De artment, Univenit $arkville N. 2, vic., IuYusotalPbourne~
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