268
HENRYA. CATHERINO
The Electrochemical Oxidation of Arsenic(II1). A Consecutive Electron-Transfer Reaction
by Henry A. Catherino Department of Chemistry, University of Michigan, A n n Arbor, Michigan
(Received M a y $3,1966)
Analysis of log i vs. E curves for the electrochemical oxidation of arsenic(II1) in 1.0 M perchloric acid shows two well-defined linear sections in the potential region where concentration polarization effects are negligible. This observation is inconsistent with mechanisms involving a single transition state. The experimental results show excellent agreement with the theoretical predictions based on a mechanism involving two consecutive one-electron-transfer steps. The simplest mechanism assignable to the reaction is As(II1) ++ As(1V) A As(V). These findings provide evidence in support of the existence of the intermediate As(1V) which has been postulated from kinetic effects observed in homogeneous solution studies.
Introduction The principles developed in the study of electrochemical kinetics have provided a powerful tool for elucidating the mechanisms of electrode reactions.’ Essentially, each fundamental step can be considered as involving an activation energy barrier. The chargetransfer step, however, is characterized by the unique quality of having a potential-dependent activation energy barrier. Consequently, via the application of varying applied potentials, the electrochemical effects caused by changes in the rate-determining step can be studied. Two distinct methods2of approaching the problem of consecutive electron-transfer processes can be identified: (a) the steady-state method and (b) the quasiequilibrium method. The former method equates the rates of each of the conceivable steps through a steadystate approximation. The solution of these equations is tedious and, as a result, little has been done in applying this method. The latter approach assumes that a single rate-determining step exists. The rate constants of the preceding and subsequent steps are assumed to be large and can be thought of as being at equilibrium. This approach is readily amenable to mathematical formulation. I n the discussion which follows, the steady-state method is applied with the modification that all chemical steps are taken to The Journal of Physical Chemistry
be at equilibrium as in the quasi-equilibrium method. The approach has as its purpose the formulation of a mathematical expression which takes into account a possible change in the rate-determining step attributable solely to a sequence of consecutive charge-transfer steps. Expressions have been derived describing the possible current-voltage curves obtainable at microindicator electrodes for the three simplest mechanistic sequences of an over-all electrode reaction written as3 A+2e=B
(1)
The intermediate, if any, is taken to be of short chemical half-life and of low concentration so as not to be isolable by ordinary chemical means. These mechanisms are (I) a two-electron-transfer step via a single activated complex, (11) two consecutive one-electron-transfer steps, and (111) two discrete one-electron-transfer steps wherein the intermediate disproportionates rapidly. It is assumed in these mechanisms that all other steps preceding and subsequent to the electron-transfer re(1) P. Delahay, “Double Layer and Electrode Kinetics,” Interscience Publishers, Inc., New York, N. Y., 1965. (2) B. E. Conway, “Electrode Processes,” Ronald Press Co., New York, N. Y., 1965,p 109. (3) J. Jordan and H. Catherino, J. Phys. Chem., 67, 2241 (1963).
269
ELECTROCHEMICAL OXIDATION OF ARSENIC(III).
action are fast. Unfortunately, mechanism I has a current-voltage (CV) curve identical with special cases of mechanisms I1 and I11 and therefore cannot be unambiguously determined by voltammetric methods. An example of mechanism I11 is the thallic-thallous electrode reaction in perchloric acid on a clean platinum e l e c t r ~ d e . ~The ? ~ discussion which follows will be limit,ed to an electrode reaction involving mechanism 11. Originally, Vettel.5 derived an expression for the current-voltage curve peculiar to an electrode reaction proceeding via two consecutive one-electron-transfer steps in terms of apparent exchange currents. Later, a similar expression was derived in a paper by Catherino and Jordan4in terms of specific rate constants. Vetter's derivation is, no doubt, simpler to use in an operational sense. The other derivation, however, makes clear certain fundamental chemical principles that are implied in Vetter's equation. Below is the essence of this derivation together with its conclusions.
Theoretical Section An expression for the voltammetric wave resulting from mechanism I1 S3 e = Sz (2)
+ S2 + e = SI
(3)
can simply be derived by noting that the cathodic and anodic current contributions are given by io =
+ FAkz,laoz
FAks,2a03
-FAkl,2aoi - FAkz,3a0z (5) where F is the faraday, A is the electrode area, k is the electrochemical rate constant whose subscript indicates the reaction to which it refers, and a is the activity of the electroactive species where the subscript indicates the electroactive species to which it refers and the superscript zero refers to the location at the electrode surface. The activity of the intermediate S2 is eliminated by applying the steady-state requirement, rate of form& tion of Sz = rate of decomposition of S2
+
ka,za03 ki,zaoi = kz,3a0z kz,1a02 (6) The potential dependencies of these heterogeneous rate constants are F k3,2 = k03,2 exp(-m,~)(E - E " a . 2 ) ~ (7) kz,3
= k03,2 exp(1
k2.1
= kOz.1
-
F
- E03,2)-RT
ff3,2)(E
exp(-az,1)(E
F
- E02,1)--RT
ko2,1 exp(1
- cuz,l)(E - E"2,l)-RT 1'
(10)
where ko is the specific rate constant defined when E = E", a is the transfer coefficient having a value 0 < CY < 1, R is the gas constant, and T is the absolute temperature. These expressionswere used so as to define each of the electron-transfer steps in terms of a specific rate constant and an applicable standard potential. Although these standard potentials are unknown, they must be related by the restriction imposed by the law of conservation of energy
In order to take into account the effect of concentration polarization, the mass transport restrictions are given as
i
=
i n F A m ( a - uo)
(12)
where i is used depending on the cathodic or anodic direction of the current, n is the number of faradays involved per mole, and m is the mass transport coefficient. A limiting current is defined when aobecomes negligible compared to a
*nFAma (13) Combining these relationships and eliminating the activity terms, the following expression is obtained
il
=
+ ki--&h,a + + ma + kiml h,Zh,l
(4)
ia
+
a
kl,z =
2 =
m3
,zkz ,3 ,
Z1,a
il,,
k3
2kz 1
2kz
3
(14)
k2,i
where the potential dependence of the rate constants is given by eq 7-10. il,,is the cathodic limiting current and il,, is the anodic limiting current. The preceedng equation describes all of the possible CV curves for a reaction involving two consecutive one-electron-transfer steps where the intermediate is of very small concentration in order that 6 will hold. An important observation is made when a qualitative assignment of standard potentials is attempted. Themodynamically, it is clear that E03,2 cannot be greater than or equal to EOZ,las this would require that the intermediate have a large equilibrium concentration. This is inconsistent with the requirement that SZ be an intermediate of low concentration. Therefore
(8)
E"8,z < E"2.1
(9)
(4) H. Catherino and J. Jordan, Talanta, 11, 159 (1964). (5) K.J. Vetter, 2. Naturforsch., Ai', 328 (1952); A8, 823 (1953).
(15)
Volume 71, Number P January 1967
HENRYA. CATHERINO
270
from the reverse reactions, the following Tafel equations are obtained applicable to totally irreversible waves : cathodic In io =
In 2 F A d 3 + In
k3,2k2,1
k2,1
+
(16)
k2,a
anodic In (-ia) = In 2FAuOl
+ In
ki , 2 k 2 , 3 k2,i
Figure 1. Relative magnitudes of the electrochemical rate constants for each of the steps of a consecutive electron-transfer sequence. The potential of the origin is the standard potential of the over-all reaction, Eoa,l. The y axis represents the magnitude of the electrochemical rate constant. This value is always positive. The magnitudes above and below the x axis refer to increasing k for the cathodic and anodic electrode processes.
and consequently, it follows that the intermediate is unstable with respect to disproportionation. This argument was made by Heyrovsky in attempting to interpret oscillographic data obtained from multiple electron-transfer reductions.6 Two reasons based on kinetic considerations can be given to explain the nonoccurence of the disproportionation reaction: (a) the steady-state concentration of the intermediate is very small so as to favor the first-order electrode reaction rather than the second-order disproportionation and (b) the activation energy of the disproportionation is large. The current-voltage curve equation describes the possible forms of the CV curves consistent, with this mechanism. In this connection, Riddiford has pointed out that often various mechanisms can yield identical CV curves thus making such comparisons meaningless.' It is important then to pick out only those cases where a unique effect results and this can best be done by looking at an irreversible CV curve in the region where concentration polarization is negligible. By solving eq 4-43 to eliminate uo2and the contribution The Journal of Physkal Chemistry
+
h,3
(17)
where the potential dependence of k is given by eq 7-10. Of interest are the limiting cases wherein k2,1 >> k2,3 and kz,l k3,z so that S3 -t S2 is the rate-determining step at negative (reducing) potentials. Since k2,1 >> k 2 , 3 at these potentials
then the applicable equation describing the foot of the curve occurs in the usual Tafel form
F In i, = In 2FAU03k03,2 - L Y ~ , ~ (E03,2)E
RT
(19)
I n case I1 (k'3.2 >> k O 2 ~ )where k3,2 becomes substantially large, k2,l and k2,3 reverse their relative magnitudes so that two separate and distinct situations can exist: (a) at larger reducing potentials, k 2 , 3 < k2,1so that
in which case the curve is given in the usual Tafel form given in eq 19, and (b) at smaller reducing potentials, k2 ,S > k2 ,I k3,2k2,1
k2,1
+
k2,3
-
k3,2k2 .I
(21)
k2,3
and consequently, an unusual Tafel-like equation results In i,
=
In 2FAu03
+ In kz k3.2k2,l ,3
J. Heyrovsky, Discussions Faraday Soc., 1, 220 (1947). (7) A. C. Riddiford, J. Chem. Soc., 1175 (1960). (6)
(22)
ELECTROCHEMICAL OXIDATION OF ARsENIc(III)
271
or, by substituting and rearranging In i,
=
+
In 2FAa03k02,1
F (E"s.2 - a2,1E02,1)RT
F
- (1 + CYZ,I)ERT
(23)
Evidently, a plot of In i us. E under the conditions present in case I1 should yield two linear portions having the slopes - (1 a2,t) (FIRT) at smaller reducing potentials and - a3,Z (FIRT) at larger reducing potentials. These conclusions are basically identical with those of Vetterns However, the physical interpretation of this inflection is evident from Figure 1. That is, at less reducing potentials, the step
+
+e
Sa
is at equilibrium and
SZ
+e
SZ
+
-
SI
is rate determining with the requirement that Sz is of small concentration and at steady state. At more reducing potentials S3 e +SZ
+
is rate determining, whereas
Sz
+e
+SI
is fast.* It is apparent from Figure 1 that cases I and I1 are actually identical when rotated 180" around an axis perpendicular to the origin. Consequently, the same arguments can be given for the anodic Tafel region occuring at positive (oxidizing) potentials. I n case I at lower oxidizing potentials In (-is)
=
In 2FAa01k03,z- (1
F - a3,Z)Eo3,ZRT
and at higher oxidizing potentials as well as always in case I1
+
In (-is) = In 2FAaOlkOz,1
F RT
(1 - a2,1)(E - E"z,I)-
YDltS
Figure 2. A current-voltage curve calculated on the basis of an assumed mechanism having two consecutive electron-transfer steps.
Computer solutions for the shape of the currentvoltage curve were obtained for various values of the kinetic parameters a, kO, and E". A curve illustrating the effect characteristic of two consecutive one-electron-transfer steps is seen in Figure 2. The curve shown is totally irreversible allowing measurements on the foot of the waves to be converted directly to a Tafel plot. The anodic and cathodic Tafel plots are shown in Figures 3 and 4. The two linear portions on the cathodic Tafel plot are solely characteristic of mechanism 11. This effect, as mentioned earlier, is obtained whenever (a) the composite wave is irreversible and (b) the specific rate constant for one electrontransfer step is sufficiently different from the other. Generally, the inflected Tafel slope is seen when the specific rate constants vary by at least two orders of magnitude. When the specific rate constants are of the same size, the current-voltage curve is consistent with the three mechanisms given earlier.
(25)
Some important observations are that (1) if the inflected Tafel slope occurs on one wave, it will not occur on the other and (2) the inflection will occur on the wave whose first electron-transfer step has the largest specific rate constant.
(8) Should k%,2 >> k%,, so that kz,~wiIl be Iess than ka,z at all reducing potentials, no inflection in the Tafel curve will be observed. If this is the case, the concentration of the intermediate will continually increase a t reducing potentials until (a) a substantial concentration gradient will exist between the electrode and the bulk of the solution causing a loss of the intermediate by mass transport away from the electrode and (b) the steady-state assumption will not be applicable. Such a situation violates the original model and so is not applicable in this analysis.
Volume 71, Number I January 1967
HENRYA. CATHERINO
272
I
-0.1
I
I
-0.2
4 3
Volts
Figure 3. A Tafel plot of the foot of the cathodic portion of the calculated current-voltage curve shown in Figure 2 where y = current//limitingcurrent/.
The conclusions of this analysis are in complete agreement with the criteria given by H ~ r d whose ,~ study was based on Vetter's equation for consecutive single-electron-transfer steps. These criteria are (a) two well-defined linear logarithmic portions of the Tafel curve must be obtained, (b) agreement between the reIative sizes of the exchange currents, and (c) agreement between the transfer coefficients. I n terms of specific rate constmts, essentially identical statements could be made. In the application of these criteria it is important to consider the possible effects caused by abrupt changes in the electric field of the double layer.' It was assumed in the derivation that the influence of the double-layer field was either negligible or constant over the range of potentials wherein the measurements are made. This assumption is reasonable when the supporting electrolyte concentration is 0.1 M or greater and the potential region studied does not include the potential of zero charge. Should these conditions be absent, the doublelayer field will undergo a considerable change causing substantial variations in the electrochemical rate constants, inconsistent with eq 7-10. Under these conditions, conclusions based on the above-mentioned criteria must be reviewed with caution.
Experimental Section 0.
-1.
--
.2.
m
8
-3.1
4.c I
I
:0.B
I
I
0.4
I
I
I
0.Z
TO161
Figure 4. A Tafel plot of the foot of the anodic portion of the calculated currentcvoltage curve shown in Figure 2 where y = current/llimiting current/.
1 0.0
The experimental technique employed was hydrodynamic voltammetry. The details of this technique were described earlier.lO Since the studies were performed on the foot of the wave where concentration polarization is negligible, strict control of the solution flow was not necessary. A platinum microindicator electrode was used. It was pretreated by ignition to red heat and, after cooling, was used to scan the range of potentials 0.5-1.4 v until reproducible curves were obtained, Two preliminary scans were needed. A saturated silver-silver chloride electrode with a barrier sleeve compartment was used as a reference electrode. The added compartment served to eliminate possible contamination caused by diffusion to and from the reference electrode. The current-voltage curves were recorded with the ORNL controlled-potential voltammeter, Model 19888 (Indiana Instruments, Inc.), in conjunction with a Photovolt recorder, Model 43. The scan rate used was 100 mv/min toward positive potentials. The experiments were carried out at 25.0'. Reagent grade chemicals and conductivity water were used. Theoretical current-voltage curves, based on the ex(9) R. M. Hurd, J . Ebctrochem. SOC.,109, 327 (1962). (10) J. Jordan, Anal. Chem., 27, 1708 (1955).
ELECTROCHEMICAL OXIDATIONOF ARSENIC(111)
273
pression for the consecutive oneelectron-transfer step mechanism described earlier, were computed by the IBM 7090 computer on the campus of the University of Michigan.
would be prima facie evidence for a process involving consecutive electron-transfer steps.13 A direct identification of the mechanism is made by comparing the arsenic oxidation wave with the unique
Discussion of Results Figure 5 shows the anodic wave resdting from the oxidation of arsenic(II1) at a platinum microelectrode in 1.0 M perchloric acid. The appearance of the minimum in the region corresponding to the plateau of the wave is caused by the passivating influence of the formation of platinum oxide.’l I n the following discussion, only the foot of this wave will be considered where concentration polarization is negligible and the electron-transfer reaction is rate determining. It is important to note that arsenic(V) is not reducible anywhere in the range of potentials accessible for study at the platinum electrode. Furthermore, As(V) is not reduced on a mercury cathode whose range of accessible potentials exceeds that of platinum toward reducing potential.12 Evidently, if a measurement of the specific rate constant were made assuming a singlestep mechanism from the anodic and cathodic reactions at the standard potential of the arsenic-arsenious couple, +0.56 v us. nhe (+0.36 v us. ssce), the measurement from the hypothetical reduction reaction would be very large as compared to that determined from the anodic wave. For a single-stage two-electron transfer to occur, it is mandatory that the specific rate constant calculated from the anodic and cathodic waves be identical. Therefore, from an inspection of the data, the observed discrepancy in the relative overpotentials of the anodic and cathodic processes, when compared with reference to the standard potential,
-5.1
-
-5.3
-
-5.7
-
I
0.75
0.70
0.05
0.83
P o t c n t h l of Indicator Electrode (YOlta) V I . 5 . t w a t e d Silver-Silver Chloride Reference Electrode
Figure 6. A Tafel plot of the foot of the arsenic oxidation wave showing two discrete linear portions. Correction was made for the residual current.
effects Predicted by the kinetic equation for the following aSsUmed m ~ h a n i s m As(II1)
+As(1V)
As(1V) - + A s p )
+e +e
step 1
(26)
step 2
(27)
with the over-all reaction As(II1)
As(V)
+ 2e
The most prominent characteristic of this mechanism is that the wave having the smaller overpotential should have an inflected Tafel slope (vide supra). The Tafel curve for the oxidation of arsenic(II1) is shown in Figure 6. It has been shown earlier that the slope of the curve at smaller currents should be
I
1.4
I 1.2
I
1 0.8
1.0 Volts
YS.
I
0.6
SSCE
Figure 5. An experimental current-voltage curve of millimolar arsenic(II1) in 1.0 M perchloric acid under a forced convective mass transport. The direction of scan was toward positive potentials.
I
0.4
(11) V. A. Zakharov and 0. A. Songina, Zh. Fis. Khim.,38, 767 (1964). (12) L. Meites, “Polarographic Techniques,” Interscience Publishers, Inc., New York, N. Y., 1965, p 656. (13) K. J. Vetter, “Transactions of the Symposium on Electrode Processes,” E. Yeager, Ed., John Wiley and Sons, Inc., New York, N. Y., 1961,p 65.
Volume 71, Number 8 January 1067
274
HENRYA. CATHERINO
and at higher currents (29) where the subscripts refer to the energy barrier of a particular electron-transfer step. Since a can only have a value between 1 and 0, the quantity (2 - w , 4 ) must have a numerical value between 1 and 2 and (1 a4,%j. must have a numerical value between 0 and 1. If these slopes are analyzed as having the empirical form (1 - P)nF = slope 2.34T the experimental data yield at lower currents (1 - P)n = 1.3 0.1
+
and at higher currents (1 - P)n = 0.6 f 0.1 on the basis of a sample of ten determinations. These values were found to be unaffected in the concentration to 1.0 X M As(II1) and in the range 5.0 X flow-velocity range 5-100 cm/sec. It therefore follows that the specific rate constant for step 1 is very much larger than that for step 2, i e . , k 0 4 , a >> ko5,4. I n addition, the appropriate standard potentials are related as E05,4
