An Effective Approach to Teaching Electrochemistry Viola I. Birss and D. Rodney TNaX The University of Calgary, Calgary, AB. Canada T2N IN4 Students who learn electrochemistry from most high school and first-year university textbooks ( I ) are likely to experience some confusion and unexpected difficulty with more advanced topics on this subject. Typically, much of the freshman material will have to be unlearned and replaced by a broader and more complete picture. This can be a frustrating experience for students and instructors alike and consequently, students, who initially find electrochemistry a fascinating topic, tend to become disenchanted by the apparent lack of consistency and logic in its presentation. We believe that this experience is unnecessary and avoidable. By interweaving concepts from thermodynamics and chemical kinetics with those of electrochemical measurement. we can orovide our students not onlv with an enriched unde;standin(: of electrochemistry hut &o with a deeper aooreciation of the utility of ideas from kinetics and thermodGamics. We hope t h a t t h e approach that we have adopted will stimulate teachers to rethink how they teach electrochemistry and motivate authors of f r e s h m i texts to incorporate our approach to electrochemistry in their future works. Potentlal Problems Below, we mention the most important problems that students are likely to encounter. (a) Most texts ( 1 ) do not describe clearly the instrumental requirements for the measurement of the potential between two electrodes. Neith~rdo they deacrihe the changes in circuitry required for current to pass through an electrochemical cell. (b) A syntactical difficulty Linked with point (a) relates to the concept of equilibrium potentials. Indeed, what does the term "equilibrium" refer to in electrochemicalprocesses? (c) Although reversing the sign of the potential of electrode reactions that are written as oxidation reactions is normal oractice. it does create unnecessary conceptual problems for students when they subsequently learn about polamgraphy, voltammetry, corm
-.....,-
(d) \Vhy do operating galvanic cells have lower voltages than r half-cell by thr Nernst those computed from the potentials f ~ , each equation? This imporcant ubrervation ir rarely dracussed in freahman texts, and thkrefore students miss an important connection between the real world and our conceptualization of it. (e) .~. In contrast to ealvanic cells. electrolvtic cells reauire lareer voltages than those computed on the basis of the Nernsr equation. In freshman term, the term overpotential ar ovemoltage is seldom mentioned, let alone explained adequately.Thia notion ra central to understanding why one electrode is preferred over another in electrolytic cells.
Often, there are pedagogical reasons to use simple approaches to electrochemistry in freshman courses. Nevertheless. i t is essential for students a t some time in their undergraduate career to be exposed to more realistic models. In the followine section. we show how these tooics can be included in theTreshmk curriculum relatively Asily. Current Solutions
Figure 1. Experimental setup for measurlngthe potential of an electrochemical cell.
Figure 1,we illustrate such a measurement for a cell combining copper and silver electrodes. The left-hand compartment (half-cell) consists of a copper electrode immersed in a co~oer(I1) . . nitrate solution. The rieht-hand comoartment has a silver electrode immersed in a silver nitrate solution. A seoarator orevents the metal ions in the two solutions from mixing hut permits anion transport between the two comoartments? When each electrode is first immersed, the met& electrode and the ions in the solution come to equilibrium. In so doing, either a very small amount of metal will dissolve or traces of the metal ion in solution will be reduced. The extent of these processes is small and normally occurs in less than a microsecond. Accordinelv. a small transfer of charee will occur a t each metal/solu& interface during the oroach to eouilibrium. A ootential difference will d e v e l o ~at kach~metaliso~ution interface that opposes further charge transfer. These orocesses are the oriein of all electrode DOtentials (2).2F O ~ O U I particular example, the pertinent halfcell reactions, or half reactions for short, are given in Figure
-
&.
6-
1. -.
Once eauilibrium between each electrode and the corresponding metal ions in solution has been established, each electrode is attached to one of the inputs of a high input resistance voltmeter. The difference between the udlages a1 the two metallsolution interfacesis then meawred.The use of a high input resistance voltmeter ensures that the cell
'
In many texts (l),a salt bridge Is used In place of the separator shown in Fiaure 1. It is noioosslble to- measure the aatentlal difference ~. s t a sinale electrodelso!ution interface as the solution side of the interfa& cannot be prooed without introducing a second, unknown. interfacial potential. This is why reference electrodes. composed of unchanging interfacial potentials, are required in order to develop a scale of electrode potentials. 7~~~
Equilibrium Considerations and Standard Reduction Potentials In relation to problem (a) above, we outline the experimental conditions (2,3) for the measurement of cell voltages when no current is permitted to flow through the system. In
~~~~
~
~
7
-
~
~
-
~
Volume 67 Number 5 May 1990
403
potential is measured under the conditions of no current flow,3 and therefore no net electrochemical reactions can occur. All voltmeters have two inputs to measure the difference in potentials of two electrodes in a cell. One input is red (+) and one is hlack (-). The meter is constructed to indicate the sign and magnitude of the potential of the electrode connected to the red (+) input relative to that a t the hlack (-) input. If the potential of the electrode attached to the red (+) input ismore positive than that attachedto the black (-) electrode, then the meter needle will move in a positive direction, usually to the right, or a sign appears before a digital voltage reading.4 In this situation, the electrode attached to the red (+) input can he thought of as an electron sink relative to the electrodeat the hlack (-) input, which we can view as an electron source. Alternatively, the latter electrode can be described as having a higher electron pressure. This implies that when a low impedance pathway is prouided, electrons would flow from the more negatiue to the more positiue electrode. Next, we address issue (h) above by making a distinction hetween two usages of the term "equilibrium" in electrochemistry. The first type of equilibrium refers to the situation in which no current flows a t either a single half cell or a pair of half cells. Figure 1shows an example of this type of equilibrium for a pair of half cells connected by a high input resistance voltmeter. Since no current is permitted to flow, no electrochemical reactions can occur. Used in this sense, the term equilibrium may heunfamiliar tomany readersand so we distinguish i t with the name electrochemical equilibrium. The term "equilibrium" has also been used to refer to the state of the system after two half cells, such as those shown in Figure 1, have been allowed to react with each other, i.e., current has been allowed to pass through the cell, until the cell voltage as read on the voltmeter is zero. At this point, activities of all species in the cell (concentrations of ions and partial pressures of gases) have reached their "equilibrium values." We call this state chemical equilibrium. This is the equilibrium concept normally encountered in freshman texts (I). Since no current flows a t zero cell potential, chemical equilibrium is a special instance of electrochemical eouilihrium. In both cases, the Nernst equation, to be discussed later, applies. Returning to point (a), the mode by which a galvanic cell achieves chemical equilibrium is shown in Figure 2. Now, a low resistance pathway must he provided so that the two half can react. half-cell reactions will occur in their cells ..-. ~ Both ~ ~ ~ spontaneous directions with the oxidation reaction occurring (1-8) a t the more negative electrode (anode) and the
+
~
Figure 2. Experimental setup for measuring cell potential and cunent flowing through a discharging electrochemical cell.
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Journal of Chemical Education
Selected Standard Reduction Potenllals
+
Fdg) 2e- * 2FCldg)+ 2e- +XI-(aq) O,(g) + 4Ht(aq)+ 4eC + 2H*0(1) Ag+(aq)+ e +Ag(s) Cuqaq) Ze- +Cu(r) 2Ht(aq) + Ze- +H&) (SHE) ZnZt(aq) + 28- + Zn(s) Lli(aq) + e- + Li(s)
+
+2.866 +1.358 +1.229
+0.800 +0.342 0.000 -0.762 -3.040
reduction reaction at the more positive electrode (cathode). As current passes through the cell, net electrochemical reactions occur-at each electrode, the concentrations of the ions in each compartment change, and the cell voltage will decrease with time. Strictlv soeakina, the Nernst equation the cell ianot a t cannot be used5 during ihi~-~eriod-since electrochemical eouilibrium (2-8). When the cell reaches chemical equilibrium, current no longer flows (1, 3, 7) and ECEI, = 0 V. The period of uninterrupted current flow, when net electrochemical reactions occur in the cell, is the domain of chemical kinetics. With these comments in mind, we reconsider the table of standard reduction potentials. In the table, we provide a selection of electrochemical equilibria and their values (9) for reference throughout this paper. EachEo value given in these tables refers t o an elecirochemical equilibri"m in which all reactants and products are in their standard states, i.e.. unit activities. Although the reactions are written bv convention in the direction Gf reduction, i t should he emphasized that these reactions are equilibria and that the measured Eo values do not change simply because we write the equilibria in the reverse direction. I t is important to recall that all EDvalues are measured with respect to the standard hydrogen electrode2,VSHE). For such a measurement, the SHE is attached to the black (-) input of the voltmeter and the second half is attached to the red (+). The Eo for the SHE (1-10) is assigned2 the value of 0.000V. This universal reference reaction has been chosen in order to be consistent with the definition of the free energy of formation of all elements and protons as equal to zero joules/mole. By convention (1-9). the eouilibrium with the most oositive Eo value is placed a t thetop of the table while the equilibrium with the most neeative Envalue is put a t the bottom. Manv freshman texts do not show these reactions as equilibria but as net reactions, another source of confusion for students. Let us assume for the moment that we have a cell configuration such as that shown in Figure 1, in which the half cell attached to the hlack (-)input is replaced by the SHE and a Ag+(l M)/Ag half cell is connected to the red (+) input. This is an ideal situation. The typical resistance of the hlgh quality voltmeter, required for this measurement, is -loi2 to $2. and therefore very small currents of lo-" to 10W2 A do flow. These currents are considered to be tcu small to perturb significantly the eouilibrium in each half cell. If the elenrode ahachments to me meter are reversed, a voltage of opposite sign w II be tndicated. Under certain circumstances encountered in polarography (8). for example, when the soiut on concentrations of the species mvolved in the reaction are relatively low and the electron transfer process is relatively fast, electrochemical equilibrium can still be maintained even though current is flowing1In this case, a local electrochemical eauilibrium oertains at the electrodelsolutioninterfaceand the Nernst ed-ation can st l be app ied. However, the concentrations of the spec es used in the Nernst equation are not oulk soi.tion concentrations, butratner the concentrations in a rh n, unstlrred layer ol solution at the electrode surface. A standard hydrogen electrode is a Pt electrode in a 1 M Hf solution and with 1 atrn H2 gas passing continuously over it.
Then the cell voltage7 displayed would be E o = 0.800 V. This implies that, if a low resistance pathway were provided, electrons would flow from the more negative SHE (anode) to the more positive Ag+(l M)lAg half cell (cathode), which would act as an electron sink. The electrochemical reactions that would then occur a t each electrode would be,
equation for the half cell, and 9 is the Faraday constant (19). The reaction quotient, Q, is,
for the sample half-reaction, uU+uV+ne-+wW+yY
Under these circumstances, single arrows must he used to indicate that each half cell is no longer a t equilibrium and that net reactions would occur. What happens when Eo < 0 V, as, for example, it is when a Zn electrode immersed in a Zn2' ion solution, which is hypo1 M ineinc ion. isattached to the red (+) input and theticallv .--the SHE^^ the black (-j in a setup similar to that shown in Fieure I ? Now. the voltaee7 would read -0.762 V indicating t h l tendency for electro& to be transferred out of the Z; electrode toward the SHE. If current were allowed to pass through the cell, the Zn half-cell reaction would tend to proceed spontaneously as an oxidation reaction, Zn Zn2++ 2e(3) ~~~~~
-
and the Zn electrode would act as the anode. Then the SHE half cell would be the cathode with H+ ions spontaneously undergoing reduction,
For both reactants and products, the activities of pure substances are u n i -t ~. while . the activities of eases are normally approximated by their partial pressures a i d solutes in solition bv their concentrations. Note that when all species are a t unit activity, Q = 1, and consequently, E, = E'. Predicting Galvanlc Cell Voltages and Reaction Directions When neither half cell is the SHE, how can one predict the direction of electron flow when the cell is allowed to discharge, as in Figure 2? T o answer this question, we follow the same reasoning used in the previous section but now refer to the Cu/Ag cells shown in Figures 1 and 2. In practice, by connecting the Agf (1 M)/Ag electrode to the red (+) input and the Cu2+(lM)/Cu electrode to the black (-1 input of a voltmeter (Fig. I), the meter would indicate that the Agf(l. M)/Ag electrode is 0.458 V more positive than the Cu2+(1 M)lCu electrode. This implies that the Cu2+(lM)/Cu electrode is the electron source. Connecting these electrodes as in Figure 2, the following reaction will occur,
+
2Ag+(aq) Cu(s) The concept of spontaneity is familiar to us from thermodynamics. When the change in Gibb's free energy, AG, for a reaction is negative, then the reaction will proceed spontaneously in the direction written. Therefore, all half-cell reactions with positive E D values will tend to proceed in the reduction direction when combined with the SHE, as in Figure 2. When all half-cell equilibria are written in the reduction direction, then the following equation links thermodynamics and electrochemistry (1-8,101,
(8)
-
2Agfs) + Cu2+(aq)
(9)
(5)
Because the Eo for the Agf (1 M)/Ag electrode is more positive than that of the Cu2+(1M)/Cu electrode, the AgYl M)/ Ag electrode will be the cathode and the Cu2+(1M)/Cu the anode. Note that a unidirectional arrow is used in eq 9 to indicate that the reaction is proceeding in the direction written in a cell configured as shown in Figure 2. The use of equilibrium arrows in a reaction such as eq 9 is reserved for cells at electrochemical equilibrium (Fig. 1). Now, to relate this to thermodynamics, for standard or nonstandard states,
In the case of the Agf(1 M)/Ag and SHE cell, the reduction of Ag' a t the Ag electrode will be spontaneous since Eo = 0.800 V. In contrast, for the Zn2+(1M)/Zn half cell, E o = -0.762 V, indicating the electron richness of this electrode relative to the SHE. Using eq 5, a positive AGO is obtained, indicative of the nonspontaneity of the Zn2+(1M)/Zn reaction as a reduction proreas. If substances in nonstandard states are present, the new potentials. E,, for these equilibria, written as reductions, are determined from the Nernat equation,^
where AEr is the difference of the two half-cell E, values, obtained from eq 6. For the discharge of the cell to occur in a spontaneous manner, AG,,n must be negative, and therefore, AE, must he positive. This can only be the case if one subtracts a less positive E, from a more positive E,. Furthermore, we know that the half cell with the more positive E, must be the cathode and that with the less positive E,, the anode. These ideas lead to the following simple expressiong for cell voltage (10):
AGO = -n3E0
AG,], = -n9AE.
(10)
AE, = E,(cathode) - E,(anode) where R is the universal gas constant, T the Kelvin temperature. n the number of electrons in the balanced chemical
T h e measured cell voltage would also include the liquid junction potentials at the solutionlseparator interfaces as well as a metaimetal contact in the voltmeter (2,4, 8). In practice, one tries to minimize these contributions, and we have chosen to neglect them here. "r" refers to the fact that E. Is measured at electrosubscrlat The ~. .---chemical equilibrium, i.a., E, is a reversibleeleclrode polenl~al.If a cell is charging or discharging at an mfinitesimaily small current, the Nernst equation still applies. The only cnange in cell potentials s due to the infinitesimal changes in concentrations of species in solution. Other symbols such as E, (3and &, (3) are also used. This definition is analogous to the convention used in many texts in which the anode is placed on the left and the cathode on the right in cell notation (1-3). Then AE, = E,(right)- E,(left). ~
7~
~~~
~
~
(11)
Note that this approach isdifferent from that employed in many first-year texts (I), where students are taught to reverse the sign of the electrode reaction that will occur a t the anode and then add Edcathode) and EJanode) to obtain AE,. This procedure leads to the conceptual confusion, mentioned in ~ r o h l e m(c) above. that the relative oxidizinnl reducing capability of any el'ectrodelsolution combination chanees simolv . -bv- writing the esuilibrium in the reverse diredion (e.g., from +0.342 V, f i r Cu2+ 2,- e Cu, to -0.342 V for C u e Cu2+ 2e-). The use of expression 11has several advantages. First, we retain the sense of "potential difference" between two half cells, a notion that is lost when signs are reversed and two potentials are added. In this sense, if we think of an electrode as exerting an electron pressure, then AE, is the difference between the electron pressures of the twoelectrodes in thecell. Second, if we think of the standard reduction potentials as points on a line, such as the E axis of Figure 3, then AE, is simply the distance
+
+
Volume 67 Number 5 May 1990
405
Flgure 4. A schematic plot of current versus potential when current Is allowed to flow. Astheanodic current. + I , , flows, the potential at theenode becomes more poslive than the equilibrium potential of the Cu electrode. As the cathodicwnent. -1'. f l o w the potentialst the cathode is more negativethan the equilibrium potential of the Ag electrode,
Figure 3. A plot of current versus potential w l h no current flow. The E, and P values cited are equlllbrlum values.
between the two reduction potentials for the half reactions participating in the cell. Therefore, AE? has a geometric interpretation that we conveniently exploit in the next section. In addition, the positive sign of the silver cathode and the negative sign of the copper anode make sense in the light of their relative positions on the Laxis in Figure 3. Finally, when a cell has reached chemical equilibrium, = AE?= 0 V, and so, using the Nernst equation for each half cell, we get AEo = Eo(cathode) - ED(anode)= (RTInS) In K,p. where Keq is the equilibrium constant for the cell reactlon (1). We remark that this method of evaluating equilibrium constants applies to all redox processes whether or not they are part of an electrochemical cell as constructed in Figures 1or 2. Current/Potential Plots
In the first part of this section, we emphasized that eouicalculated from the bilk solution concenlibrium trations bv the Nernst eauation can onlv have relevances when no current passes through the electr~delsolutiouinterface or cell. T o examine the situation when current is allowed to pass through the cell, we propose that potentials (in V relative to the SHE) be plotted on the x axis and that current be plotted on the y axis. Such a graph is called a currentlpotential or IIE plot and is routinely used in more advanced presentations of electrochemistry (2-8, 11). In Figure 3, we show an IIE plot when no current is flowing (I= 0 A). When all electrode reactions are a t electrochemical equilibrium, points are confined to the potential axis. Also in Figure 3, we have shown the positions for the standard copper and silver half cells as well as for the SHE. As concentrations and pressures deviate from standard values, the potentials, E,, slide along the E axis in a manner determined by the Nernst equation (eq 6). The value of E, = 0.257 V for a Cu electrode in a [Cu2+]= 2.0 X M solution is shown for demonstration purposes. Similarly, the potentialfor the hydrogen electrode will shift negatively as the pH of the solution increases.1° The potential, AEr, for the copoer-silver cell of F i m e 1 under standard conditions is , that the Cu electrode in the ihown in Figure 3. A G ~notice C U ~solution + with the lower concentration is more stronalv . this demonstra'tk reducing than Cu in 1M C U ~ +Clearly, the fact that a concentration cell is a source of voltage. (i) Galuanic cells. In the galvanic cell in Figure 2, the resistance in the external circuit is now finite and current is allowed to flow spontaneously. As discussed previously, the natural tendency for this cell is for the following net reactions to occur, 406
Journal of Chemical Education
Flgwe 5. An electrolytic cell in which the external power source is driving a CulAg cell In the nonrpomaneousdlrectian.
Note that reaction 12 is occurring in the oxidation direction: Cu metal is the anode. The silve; electrode acts as the cath: ode. Since electrons are passing from the copper anode to the silver cathode at all times during cell discharge, the rate of electron flow at the anode must be equal in magnitude to the rate of electron flow into the cathode. Bv convention (4-8. l l ) , anodic current is defined to be posikve (electron flow out of the anode) and cathodic current is taken to be negative (electron flow into the electrode). On the current axis, anodic current is plotted upward and cathodic current downward, as sho& in ~ i g u r 4. e As current passes through the cell of Figure 2 during its discharge, Cu2+(aq) ions are being created a t the anode and silver ions are being removed from solution a t the cathode. Such a discharging cell is capahle of doing electrical work. If thcrcll discharges at infinitesimally low rates,suchas when the resistance in the external circuit i s very large, the cell discharges reversibly and the cell voltage7 is essentially eoual to AE, a t all times. AE, decreases with time as the sdlution con~entrationschange infinitesimally slowly. The Nernst equation applies and we remain on the voltaee axis in Figure 3 at all times. Under reversible conditions, &e maxi~~~
~
~
l o When theactivity of H+ Ion Is not equal to 1, theterm SHEcan no longer be used.
mum potential and hence the maximum work is available, -W,., = -AG, = nfFAEr. Cells with small resistances in their external circuits operate irreversibly. A typical I I E plot for each of these two electrodes operating irreversibly is shown schematically in Figure 4. An important point to stress here (2-8,lI) is that when current flows, theNernst equation no longer applies and the potential a t each electrode must change, since the electrode is no longer a t electrochemical equilibrium. In fact, an anodic (positive) current causes a positive shift away from the equilibrium potential, E,, of the Cu electrode. In contrast, cathodic (negative) current produces a negative shift from E, of the Ag electrode. This shift away from E, at each electrode can be referred to as an overpotential or overvoltage, usually denoted (2-8.11) by n. The meater the cell discharge rate o r current, the great& is q. 1fwe assume that the cell in Figure 2 is discharging a t a current, It,then the voltage of the anode and the cathode are shifted away from their original equilibrium values, by q, and q,, respectively." As a consequence, the voltage available from a discharging cell, E,,n, will always be less than AEr, as measured in Fieure 1and shown in Fieure 3. This means that E,I~ .".. = A E , v, - q, and the work a&lable from the cell is less than - W.... . When the rell is fullv disrharaed.. E,,II --..= 0 V: the cell current is zero, and the two half celis are now a t chemical equilibrium. The description we have just given for a galvanic cell has addressed the problem we mentioned in problem (d) above. (ii) Electrolytic cells. T o tackle the difficulties raised in problem (e), we can use IIEplots to demonstrate clearly why electrolytic cells require a voltage greater than AEr. In such cells. both half-cell reactions are forced to ~ r m e e din their n ~ n ~ ~ o n t a n edirections. ous In Figure 5, an example of an electrolytic cell is shown. Here, the cathode (negative electrode) is the Cu2+/Cu half cell and the anode (positive electrode) is the Ag+/Ag half cell. The overall cell reaction, which must now be written in the nonspontaneous direction,
=
must he driven by an external power source. As current flows through the cell, the concentration of Cu2+ a t the cathode decreases, while the concentration of Agf a t the anode increases. In Figure 6, we have drawn schematically the IIE curves for thecellshown in Figures. At rheannde, anodic (~ositive) or oxidation current flows, and as before, &idationcurrents cause a positive shift, q., of the potential a t that electrode from its equilibrium value. At the cathode, the cathodic (neeative) or reduction current will cause a negative shift of theklectrode potential, q,, from its equilibrium value. Since the magnitude of the current a t each electrode must be identical, and if the cell current is I", then Figure 6 tells us 7, q, > AE,. The work that necessarily, E,a = AE, reauired to drive the electrolvtic cell is ereater than -W,.". (iii) Ouerpotentials and f~ drops. ?he exact origineGf ovemotentials are numerous. The over~otentialreferred to in fdotnote 11,and depicted scbemati&lly in Figures 4 and 6, applies to relatively simple electrode processes such as metal dissolution and deposition reactions (Figs. 2 and 5) and gas evolution reactions, as for example in eq 4. In these
cases, the reactants are generally plentiful, and therefore the electron transfer process itself is likelv to be the slow sten in the reaction when current flows. under these conditions;the predicted exponential dependence of current on q is generally observed and the shift of E (by q) away from E, is termed (2-8). 11) the "activation overpotential". Another type of overpotential arises when reactants are present a t low concentration^,^ as for example, in the trace balysis of Zn2+ ions by their reduction at a mercury electrode (polarography). At low cathodic currents, as Zn2+ ions are reduced a t the electrode surface, the surface concentration of Zn2+, [Zn2+],,will diminish, due to its low concentration in the bulk solution and the onset of diffusionprocesses. When the electron transfer process is comparatively fast, the Nernst equation can continue to apply, but onlywithrespect t o [Zn2+],,rather than the hulk Zn2+concentration. Inspection of eq 6 shows that the potential will shift negatively as [Zn2+],decreases. This shift of potential is due to (2-8, 11) "concentration overpotential" and leads to a similar IIE relationship as shown in Figure 6 at low currents. Finally, overpotentials related to resistive factors also ~ l a an v i m ~ o r t a n role. t Whenever current flows throueh a Leu, such as that shown in Figures 2 or 5, the solution acts as a resistor (2-4. 6-8. 11)with resistance determined hv its conductivity and the distance between the two electrides. Consequentlv, as current passes throueh the solution, a voltage drop (E IR) occursHcross the solution. The impact of the presence of an IR drop is that, in galvanic cells, some of the cell voltage is dissipated across the solution and therefore, theavailable voltage iseven less than shown in Figure 4. For this reason, battery manufacturers make every effort to maintain very high solution conductivities and minimize the size of the ean between the electrodes. therebv maximizine available celivoltage during cell discharge, &rticularly 2 hieh currents when the IR droo is laree. For electrolvtic cells. not only must a voltage greater t6an AEr be applied td achieve a net reaction at each electrode (Fig. 6), hut additional voltage must be applied to overcome the solution IR d r o ~Thus, . secondarv batteries should be constructed so as to minimize the soluiion IR drop so that less energy is expended for battery recharge. We have chosen not to show IR drops in Figures 4 and 6. Another source of resistance in electrochemical cells can be due to films which form a t electrode surfaces. A classical example of this type of resistive overpotential is seen by the formationofa thin ~ l a t i n u moxide film at Pt electrodes 12.4. 7, 8, 10) during oiygen evolution from the electrolysis'of water,
=
~
~
~
2H,O
-
~
~
~
0,+ 4Ht+ 4eC
~~
~~
(15)
Although the EDfor this reaction is 1.229 V a t pH = 0,
+ +
" The IIErelationship at each electrode is frequently exponential. This occurs forfundamental reasons that are a direct conseauence of the exoonential relationshlo between the~rate feurrentl ~~ .aieiectrnn . ~ transferreaction and the height of the activation energy oarrier. A G . -
7
~
~
~~
~
for electron transfer, e . . rate = exp(-~313). When the potentiai :s shiftedaway from its equilibriumvalue,this lowers (or increases)A@ by an amount which is proportional to q. Inadvanced textbooks on this subject, these plots are often called llq plots when referring to a single electrode reaction (2-8. In.
Figwe 6. A schematic plot of current versus potentiai when current is allowed to flow. AS me anodic current. tP,flows. Me potential at the anode beromes more positive than me equilibrium potentiai of the Ag electrode. As the cathadic current. - r , flows,the potential atthe cathode is more negativethan me equilibrium potentiai of the Cu electrode. Volume 67
Number 5 May 1990
407
Figure 7.A schematic plot of current versus anodic ptentlal fw lk CI./CIand 0 2 / H t / H P half-celis.The I/Erelationshipfar platlnum oxide film fmb tion is not shown.
virtually no oxidation current is observed for this reaction until a t least a potential of 1.65 V. This is due to the formation of a thin electronically resistive platinum oxide film at the P t electrode surface. commencine a t a ootential of about 0.8 V versus the SHE: Not only is the-film a barrier to electron transfer, but the 0%evolution reaction is thought to involve the oxide surface, thus slowing the reaction down further. Once oxygen begins to form a t 1.65 V, the normal activation overpotential must also be applied, leading to a total overvoltage of 0.5 to 1.0 V. The effect of the platinum oxide film on the IIE plot for oxygen evolution is shown in Figure 7. It is of interest to note that chlorine evolution (from 1M chloride ion solution), having an EDvalue of 1.358 V, does not exhibit the additional overvoltage due to the presence of the platinum oxide film. This is thought to be related to the fact that chloride ions inhibit the formation of the platinum oxide film to some extent and to the relatively weak binding of chlorine atoms a t the platinum oxide surface (1.21, and therefore only the normal activation overpotentials are observed. This leads to the observation (Fig. 7) that chlorine can evolve more readily than oxygen a t ~t electrodes, even though the oxygen half-reaction has amore negative E o than the chlorine half-reaction. Recall that, the more negative the Eo, the greater the tendency for the reaction to occur in the oxidation direction, as this electrode serves as the electron source. We mention that onlv refs l a and l a discuss this interest-. ing observation in terms of the oveipotential for oxygen production at the platinum electrode. The other texts (Ib-fj merely mention that chlorine is produced a t the anode in the electrolysis of sodium chloride or hydrochloric acid solutions. Power Avallable The overall goal of this paper has been to challenge freshman chemistrv instructors and authors of introductorv chemistry texts to adopt a more progressive and contemporary mode of teaching electrochemistry. In order to achieve this, we have clarified a number of important aspects of introductory electrochemistry so as to avoid misconceptions that are inadvertently transmitted by current teaching practices to many students and to ease the introduction of more advanced el&trochemical ideas in subsequent courses. Now, we wish to summarize our main ideas. In the previous section, we explained the concept of electrochemical equilibrium and its relationship to chemical eauilihrium and the measurement of cell vol&ees. - . E.. or En. reiative to the SHE. In the course of this discussion, we emphasized the intimate relationship hetween thermodynamics and electrochemical equilibrium through the Nernst equation. The essential points are: (i) The equilihrium cell potential, AEr, can he measured 408
Journal of Chemical Education
only under conditions of no current flow, i.e., a t electrochemical eauilibrium. usine a hieh - inout . resistance voltmeter. (ii) '~hemical'equi~brium is a special case of electrochemical equilibrium for which AEr = 0 V. (iii) In principle, the Nernst equation has relevance for svstems a t electrochemical eauilibrium. - (iv) The measurement of cell potentials involves the attachment of one electrode to the red (+) input of a voltmeter and the other electrode to the black (-) input. If allowed to react, the electrode having the more positive potential acts as the electron sink (cathode), and that with the more negative potential acts as the electron source (anode), with electron flow from source to sink. We recommended the expression. AE, = EScathode) Edanodel. for the calculation of cell volta~es.as discussed in thd second part of the previous section. The use of this exoression is essential if we are to avoid leavina students wiihthe mistaken belief that the relativeoxidizin&educing caoabilitv of a half-cell changes simply by writing the equilibrium in reverse. In addition, it is central to our interpretation of IIE plots. The treatment of galvanic and electrolytic cells graphically shows the superiority of IIE plots, such as those in Figures 3.4.6. and 7. in the descrintion of orooerties of electrochemiklc e ~ sW; . highlight a number of important features: (i) On the potential axis, E, and E o values are all given versus the SHE. (ii) When current is zero. one readilv sees how E. changes with concentration by the Nernst equation. (iii) When current flows in the cell, E shifts away from E,, positively for oxidation and negatively for reduction. The currentipotential relationship reflects a number of factors, the activation energy for electron transfer (activation overpotential), the change in concentration of ions a t the electrodelsolution interface (concentration overpotential), and the formation of films on the electrode surface. All of these effects are normally referred to as overpotentials. (iv) Under the conditions of electrochemical equilibrium or reversible cell discharge, the cell yields the maximum = -AG, =,n3AEr. For a dischargwork obtainable: -W,., ing galvanic cell, E,,a = AEr - s, - q,, and the work available is less than n3AE, y E91i < AEr. To charge an electrolytic cell, E,II = AE, n, s, and the work required is greater than n3AEr as E,a> AEr. The authors have heard numerous accounts from students of the substantial benefits gained from exposure to IIE plots, especially in their ability to understand polaroeraohy or voltammetry experiments. Many students were in&dulous to observe that rhe potential at which Zn?- ions reduce at an He electrode is virtuallv the same as that at which ZniHe -reoxidizes. Students apparently find it easier to remember which s~eciesare more readilvreduced or oxidized when the potent& are placed in grapkcal form, as in Figures 3,4,6, and 7. For sDontaneous reactions. the soecies undereoine ., .. reduction has a more positive E, value. A I ~ O students , appreciate the eenseof"potentia1 difference"seen so clearlv in IIE plots. For instructors, it is not intended necessarily that all of this material he transmitted to students. Teachers may choose to go into as much depth as they wish concerning IIE plots, the remainder can be used as background information.
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Acknowledgment We gratefully acknowledge the helpful comments of A. S. Hinman, H. L. Yeager, and MichaelFarebrother in thepreparation of this manuscript. The authors also acknowledge the financial support of the Natural Sciences and Eugineering Research Council of Canada. Literature Cned 1. For example see la1 Broam.T. L.; LeMav, H. E. Chemistry: The Central Sciencs. 4th ed.; Prentiea-Hall: Englewood Cliffs, NJ, 1988. lh) Dickerson, R. E.; Gray, H.B.;
Dsrenahourg, M. Y.: Darensbourg, D. J. Chemical Plinciploa. 4th ed.; Benjamin1 Cummings: Menlo Park, CA, 1984. (c) Holtzclsw, H. F.: Robinson, W. R.; Neebrl 7th ed.; Heath: Lexington, MA, 1984. (d) Mshan, B. gall. W. H. C s n ~ r vChemistry, M.: Myccs, R. J. University Chamisfry, 4th ed.; BenjaminICumminga: Menlo Psrk. Freeman: CA, 1987. (e) MeQuarrie, D. A ; Rack, P. A. Ganrrai Chemistry, 2nd d.; New York, 1987. (0 Russell, J. B. General Chemistry; McGrau-Hill: New York, 1980. (g) Whitten, K. W.; Gailey. K. D.; Davis, R. E. Oenerol Chemistry, 3rd ed.: Saundera: New York, 1988. (h) Zumdahl. S. S.Chamisfry, 2nd ed.; Heath: Lerington. MA, 1986. 2. Bockris, J. O'M.;Reddy,A. K. N. ModarnEleclroehemiafry: Plenum: New Yorh, 1973: YO!. 2. 3. craw. D. R. Principle* and Applie.fiom of Eleclmch~miafry:Chapman and Hdl: New York, 1979.
4. Pietcher. D. Industrial El~clroch~misfry; Chapman and Hall: N w York. 1982.
Methods. i ~ ~ ~ ~ ~ n d ~ m ~ nand t o ~i pa p ~ i r o 7. B S T ~A. , J . : ' F ~ ~ I ~ &L.R. ~ ~ e e t r o ; h e m tiom; Wilcy: New York, 1980. New York. 1965. 8. Comuay,B. E. ThsoryondP~inciplesofElerfrodeProeolre~;Ronsid: 9. Handbook of Physics and Chemialry, 67th ed. CRC: Cleveland, OH, 1986-1987. 10. Bi1aa.V. I.:Truax,D. K.J. Chem.Educ.,suhmifted. 11. Vettes K. J.Eiacfmchamieo! Kinetics: T h r o r ~ t i r dand Exp~rimenta!Aspects; Academic: New York. 1967. 12. Conwsy,B.E.;Novsk.D.M. JElactroonal. Chem. 1979.99.133-168.
Volume 67
Number 5
May 1990
409
