Mixed Potentials Experimental Illustrations of an Important Concept in Practical Electrochemistry G. P. Power and I. M. Rltchle' Department of Physical and Inorganic Chemistry, University of Western Australia, Nedlands, W.A. 6009. Australia If a typical chemistry graduate were shown a copper wire immersed in a solution of comer sulfate and invited to talk about the factors controlling t i e potential of that wire relative to the potential of some reference electrode dipped into the same solution, it is likely that the answer would be reasonably comolete. However. if the same graduate were asked the same quedtion concerning a copper wire dipped into a solution of ferric sulfate, it is vrohahle that the response would be far less satisfactory. The problem, as we see it, isnot so much that chemists are confused about the potentials of reacting systems, sometimes called mixed potentials for reasons that will emerge later, but that they know almost nothing whatsoever about the topic. Two factors have contributed to this state of ipnorance. The first is that most university courses givea thorough grounding in electrochemical thermodynamics, but electrode kinetics, which are essential to an understanding of mixed potentials, are treated in a much more cursory fashion. The shadow of Bockris's Nernstian hiatus (11 still lies heavilv" unon . the chemistry curriculum. The second factor is the mathematical emphasis given to electrode kinetics, so often starting with the derivation of the Butler-Volmer equation from absolute rate theory, rather than the experimentally observed currentpotential curves (2). In addition, the importance of mixed potentials in a wide variety of practical fields, especially corrosion and hydrometallurgical processing, is often omitted from textbooks of electrochemistrv (2.31, and virtuallv never mentioned in standard texts on chemistry. In this paner, we present a largelv experimental approach to the cohcept of mixed potentials, pointing out thk close narallel that exists between equilibrium potentials and mixed potentials. We then discuss anumber of important examples of mixed potentials.
cations in the form of unwanted potential drops due to a high solution resistance are minimized. The addition of an inert electrolyte to the solution containing the redox couple under investigation has a second advantage, namely that, by suppressing the electric field in the solution, it reduces the ion mieration. Three electrodes are needed for the measurement of a polarization curve: the workinr electrode. which in our case is a rotating-disk electrode; the counter or auxiliary electrode which carries the current flowing through the working electrode; and the reference electrode against which the potential of the working electrode is measured. It is commun practice these days to make potentiostatic measurements, a potentiostat being a device for fixing the potential of the working electrode a t some preselected value (5).The current flowing through the electrode is then a unique function of electrode potential. Alternatively, the measurements may be made galvanostatically (i.e., at some chosen current). However, in this case, the potential is not always a unique function of current. The conventions adopted concerning the sign of potentials and currents are those recommended by IUPAC (6):(11 The ootentials auoted are reduction notentials on the standard kydrogen &ale. (2) The anodic (oxidation) currents are considered oositiveand the cathodic (reduction) currents nerative. All current-voltage curves are then displayed on Cartesian coordinates I t ihould bt, noted th,~tsome d ~ s c ~ l c = i o n ~ o i ~ n ~ x e d at. p ~ l v n t i a assume l~ a11 curwllts are pmiti\.e 17,. l(w.vt~$cr, I~clivw.and will show l~rlow.th;~tt hvrr we tw~.itiw teachin?: advantages in adhering to the IUPAC convention. Using a potentiostat, the potential-current curve l ( a ) given in Figure 1 was obtained for the oxidation of a 0.002 mol dm-:' solution of hexacyanoferrate(I1).
The Equilibrium Potential of a Redox Couple
We w ~ ltake, l as our example of the redox couple, the hexacyanoferrate(1l)-hexacyanoferrate(II1)system on an inert gold electrode. It is convenient to measure the rate of an electrochemical reaction in terms of the current flowing through the electrode. This varies with the electrode potential; a plot of current against electrode potential is known as a oolarization curve. Since the shane of the oolarization curve generally depends, a t least in part, on diffusion of reactants to, or products from, the electrode surface, the design of the electrode and the way the solution is stirred must be such that convection is a reproducihle process. This result is most satisfactorily achieved by constructing the electrode in the form of a disk which can he rotated about its axis under conditions of laminar flow ( 4 ) . Accordingly, we will suppose that the oolarization curves for the hexacvanoferrate svstem and all k h e r systems considered in thisbaper are measured at rotating-disk electrodes. W; will also suppose that the polarization measurements are made in the presence of a large excess of inert electrolyte; sodium hydroxide is a convenient choice for the hexacyanoferrate redox couple. By carrying out the meaurements in the presence of a large excess of indifferent electrolyte compli-
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Author to whom correspondence whould be sent.
1022
Journal of Chemical Education
I Figure 1. Current-voltage curves for the hexacyanoferrate system in t mol d m 3 KOH, at a rotating platinum disk electrode. Rotation speed 900 RPM. electrode area 6.00 X 70.' m2. (a)Polarization curve for the oxidation of 2 X tou3 mol d m P hexacyanoferrate(l1).(b) Polarization curve for the reduction of 3X mol dm-3 hexacyanoferrate(ll1).(c) Polarization curve for a mixture of 2 X mot am-3 hexacyanofenate(1lland 3 X mol dm-3 hexacyanoferrate(llll.The points marked X were calculated by adding (a)and (b).
T h e curve l ( a ) may be considered to consist of two regions. In the first of these, the current is a sigmoidal function of potential. However, a t sufficiently high potentials, we come to the second region in which the current becomes essentially constant. and indeoendent of potential. This constant current is determined by ihe speed i t which the oxidizable species, Fe(CN)64-, can move through the solution to the electrode surface and is called the limiting current. This current depends on the convection conditions near the electrode surface, which are fixed by the disk rotation speed (4). The curve l ( a ) is also a function of concentration. and the limiting current is linearly dependent on this quantity. Curve l ( b ) is the corresponding reduction curve for a 0.003 mol dm-" solution of hexacyanoferrate(II1) ~
~
Fe(CN)s:'-
+ e-
-
F4CN1e4-
I t too shows a potential-dependent portion, and a potentialindeoendent, convection-limited portion. Curve l(c) is the experimentally obtained current-voltage curve for a solution containine 0.002 mol dm-:' of hexacvanoferrate(I1) and 0.003 mol dm-:iof hexacyanoferrate(111): Superimposed on curve l(c) are a number of points calculated by algebraically summing curves l ( a ) and l(b). The coincidence between the measured curve and the calculated points is consistent with the hypc,thesis that the anudicand 'athodic halfrt!actiuns in the wlutiun wnta~ninrhot11hexacyanut'errate sprcies proceed
in the absence of appreciable amounts of copper(1) in solution .. i. shown in curve 21al (Fig. 21. 'l'hi; curve i* a n a l o g ~ tocurve ~s 11alexcept that nu limitntiun to t he current is d ~ i e r v r duntil very high current densities are reached, a behavior which is typical of metal dissolution reactions since the supply of reactant, copper metal, is virtually unlimited. On the other hand, the curve corresponding to curve l(h) for the reduction of copper(1) ~
Cut
~~~
~
.~.
~~
Cu
to the metal in the absence of the metal is clearly not directly accessible. Attempts to measure it only give the combined curve, 2(c), for the reduction of copper to the metal in the presence of the metal. It is, however, convenient to imagine a polarization plot for the discharge of copper(1) which can be calculated as the difference between curves 2(c) and 2(a). The computed curve is shown dashed as 2(h). As with the hexacyanoferrate system, the potential at which curve 2(c) cuts the potential axis (zero current) is the reversible potential. The Mlxed Potential of Two Different Redox Couples We will now turn our attention to systems in which the two half reactions come from different redox couples. One example of this is the dissolution of copper by iron(lI1) in strong chloride solutions. T h e anodic reaction Cu - C u t
...-.r.-
In terms of our discussion of mixed potentials, the most important feature of Figure 1is that the equilibrium potential fur the system containing both the oxidized and reduced forms in annr&iahle amounts is the notential a t which there is no net currrnt 110uingthrough the electrde: the anodic currrnt from the oxidation of hexacv;~noferr~le(II~ is exactly balanwd by the cathodic current from the reduction of hexacyanoferrateiIII). It is not always possible to obtain experimentally the individual anodic. cathodic. and combined polarization curves. Difficulties arise when we move from a sistem with an inert electrode to one with an active electrode. Consider, for examplr, the c o p p t w l ~coppt,rlt)l couple in a s t n v chloride solution. 'The anwlic r u r w for the d ~ s s d u t ~ odn8 opper
-
+ e-
~
+ e-
is the same as that of our previous example, and so the current-voltage curve, Xa), (Fig. 3). is the same as curve 2(a). A polarization curve for the cathodic reaction Fel+ + eFe?t
-
copper over
