Determination of E,"-EP for Overlapping Waves in Stationary Electrode Polarography R. Lee Myers and Irving S h a h Chemistry Department, University of Wisconsin, Madison, Wis. 53706
A NUMBER of organic materials are known to undergo a reversible two-electron reduction ( I ) . In a few cases, these reactions have been shown to be two one-electron charge transfers, sometimes with an interposed reversible protonation reaction. For example, in studying the reduction of methylene blue (2), two one-electron waves are observed in nonaqueous solvent, and on addition of acid, the second wave moves anodically until, when an excess of proton donor is present, the two-electron wave is obtained. In the methylene blue case, the two-electron reduction apparently is reversible by most of the criteria of stationary electrode polarography. That is, the current function i,/d< (where i, is the peak current and v is the rate of voltage scan) is independent of the rate of voltage scan over a wide range, and the ratio of the cathodic to anodic peak currents is unity over the same range. However, a careful analysis of the shape of the wave indicates that it is slightly broader than expected for a simple two-electron reversible charge transfer: the difference between the peak potential, Ep, and the half-peak potential, E,/p, was about 34 mV, rather than 28.25 mV as expected. This was attributed to a small difference between the E" values for the two individual oneelectron transfers. A theory derived earlier in this laboratory (3) was used to calculate AE", and the value obtained was +51 mV, with the second charge transfer taking place at more anodic potentials than the first charge transfer. Since this mechanism may be fairly common as new systems are investigated, it appeared useful to extend the previous work, so that values of AE" could be more conveniently evaluated from experimental values of E, - Ep/2. Calculations were carried out using the numerical method and programs described by Polcyn (3, 4). For the reactions (1) D. J. Pietrzyk, ANAL.CHEM., 40, 194 R (1968). (2) R. H. Wopschall and I. Shain. ibid., 39, 1527 (1967). (3) D. S.Polcyn and I. Shain, ibid.,38, 370 (1966). (4) D. S. Polcyn, Ph.D. Thesis, University of Wisconsin, Madison, Wis., 1965.
Table I. Peak Width (E, - b , ~and ~ )Location of Peak Potential (E, - Elo)as a Function of f i 0 - Elo Ezo- Elo, mV E, - Elo, mV Ep - Ep/2,mV 179.8 89.9 77.1 64.3 41.1 30.8 20.6 10.3 0.0
-10.3 -20.6 -30.8 -41.1 -51.4
29 31 32 33 34 35 37 39 41.5 44 48 54 61 69
74.5 28.8 22.1 15.4 3.6 -2.6 -8.7 -14.7 -21.1 -27.2 -34.4 -42.6 -51.9 -62.2
-ii h
W I
a
W
E:-Ef
Figure 1. Peak width (E, - E,jZ) as a function of Ez" - Elo for overlapping multistep waves in stationary electrode polarography e
ANALYTICAL CHEMISTRY
e
A$B$C
or
* B * B' * C E
A
kl
k- 1
e
(2)
involving two one-electron steps, and where kl and k-l are very large, the results are shown in Figure 1. When is very anodic of El", the value of E, - Ep12approaches 28.25 mV, and the wave appears as a concerted two-electron reaction. As EZ" shifts toward less anodic values, the wave broadens. Calculations were not carried out for cases in which EZ" is cathodic of Elo by more than about 60 mV, because the wave becomes distinctly misshapen and the two one-electron waves begin to separate (5). For accurate work, a large scale plot similar to Figure 1 would be required. Data for construction of such a plot are listed in Table I. The location of the peak with respect to Elo can also be determined from the data in Table I. When E z O is so anodic of Elothat a normal two-electron wave is obtained, the peak appears at a potential centered between Elo and as discussed previously (3). As Ez" is shifted to less anodic potentials, the entire wave moves toward Elo; and when Ez"is cathodic of El", the peak shifts to potentials cathodic of It must be emphasized that these results cannot be used to calculate AEo or to locate El" unless all other criteria, over a wide range of scan rates, indicate that the reaction is reversible and not complicated by chemical reaction.
a"
a",
a".
RECEIVED for review February 6, 1969. Accepted March 20, 1969. Work supported in part by the U. S . Atomic Energy Commission under Contract No. AT(l1-1)-1083. Other support received from the National Science Foundation under Grant No. GP-3907. (5) See Figure 2 in Ref. 3.
980
(mv)
