Alleviating the Common Confusion Caused by Polarity in Electrochemistry Department of Materials Science and Engineering. G.W.C. Whiting School of Engineering, The Johns Hopkins University. Baltimore, MD 21218 E. Gileadi School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences. Tel-Aviv University, Ramat-Aviv, 69978, Israel This paper is directed to educators who teach electrochemistry and to students new to the field, who may he confused by issues of polarity. I t has been the common observation of the authors that the issue of polarity encountered in electrochemistrv and relevant to a varietv of electrochemical roncepts often confuses students and is an unnecessary deterrent to the studs of electrochemistr~.Part ofthe conf&on is due to misunderstandings of sign-conventions and part is due to simple, but very common, mathematical errors. In addition, there is some real difficulty in considering the sign of the terminals of a battery and how it is affected by the change in the direction of current flowing through it, i.e., when it is being charged and discharged. It is the intent of this paper to clarify these issues and provide assistance to educators in dealing with them in the classroom. Because of the unusual nature of this paper we find it expedient to present the paper as a series of issues, each with some confusion caused b; polarity, accompanied by our suggestionsor aids in dealing with it. It has been written in such a manner that those having a problem with a particular issue may proceed immediately to it without reading the entire paper. Emf Series
One of the first concepts encountered by students in electrochemistrvis the emf series. namelv. the series of standard reversible pbtentials. Two pr&lems concerning polarity are common, the first dealing with the sign of the potentials in
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the series and the second dealing with calculations of cell potentials from information in the series. The first is treated here, although it is merely a restatement of the convention (perhaps in a manner that lends more insight), and a suggestion is made for hypassing the second. The IUPAC Slgn Convention Concerning the sign associated with the potentials in the emf series, two simple concepts should be borne in mind: First it must be remembered that any half-cell potential listed in the tables of standard potentials is in fact the potential of a full cell, one half of which is the redox couple in question and the other half of which is the normal hydrogen electrode, NHE. (This stems from the very fundamental fact that it is impossible to measure the potential of a single half cell, which we need not discuss here.) The second is that the cell potential for the reaction, written in the direction in which it proceeds spontaneously, must always he positive. This stems from the thermodynamic relationship:
namely, from the fact that the electricalwork~erformedbva system under reversible conditions is equal & the decrease in free energy, and from the universally accepted convention that all spontaneous processes are associated witha decrease in free energy. Consider, as an example, the Cu2+/Cu half cell. Its stan-
dard potential is listed in the appropriate tables as Eo = 0.340 V vs. NHE. What is meant by this is that the cell shown below will have a standard potential of 0.340 V. Cu/Cu21IHt, H 2 P t and that the cell reaction
+
-
Cu2+ H2
+
CU 2Ht
(2)
proceeds spontaneously from left to right. We could have chosen a different convention, writing the above cell reaction in the opposite direction, namely The corresponding standard potential would have been Eo = -0.340 V vs. NHE. I t must be realized that there is nothing arbitrary about the sign of the potential, because the reaction as written cannot proceed spontaneously (copper does not dissolve in nonoxidizing acids), the corresponding change in free energy is positive and the standard potential must be negative. Why is it then that the potential of copper (and all other redox couples) was for many years listed as either positive and negative? Because in compiling a table of standard potentials one could always be referring to the reduction process (as shown in eq 2) or the oxidation process (as shown in eq 3). Both ways have been used in the past (one should perhaps feel fortunate that there were only two choices!), but in 1953the International Union of Pure and Applied Chemi s "t (IUPAC) ~. decided that all tables should be comdled with the sign of the potential corresponding to the reduction reaction. Havine made this choice, nothinr else is arbitrary. We know that copper does not dissolve ipontaneously in nonoxidizing acids, hence the reduction of cupric ions by molecular hydrogen (as shown in eq 2) is the spontaneous reaction and the standard potential (corresponding to the reduction process) must be assigned a positive value. For further illustration, it is well known (and can be demonstrated in the simplest high school laboratory) that iron dissolves in acid, namely, that the reaction
-
+
Fe + 2Hf Fez+ H2
(4)
proceeds spontaneously in the direction written above. It follows immediately that the reverse reaction, which represents reduction of ferrous ions by molecular hydrogen, is not spontaneous. Having agreed that all values of Eo listed in tables refer to the reduction reactions, we find Eo = -0.41 V vs. NHE for iron. The IUPAC convention of tabulating all EDvalues for the reduction reaction has been commonlv used in all books printed in the past two or three decades. If an older edition of some book is used, it is easy to check if this convention was followed, by noting that metals that dissolve in acid (like iron, zinc, magnesium, and aluminum) should have negative values of Eo while more noble metals like copper and silver must have postive values of En, according to the IUPAC convention.
simply the difference between their respective ED values. A few examples are given below: Ag-Cu Cu-Ni Cd-Mg
0.799 - 0.340 = 0.459 V 0.340 - (-0.230) = 0.570 V -0.403 - (-2.375) = 1.972 V
Although the above are simple arithmetic operations that can be mastered by high school students, when presented as a problem in a mathematics class, they seem to pose a problem in the framework of electrochemistry. I t has been the experience of the present authors over the past two decades of teaching electrochemistry, particularly as part of freshman chemistry courses, that students usually have difficulty in calculating cell potentials from listed Eo values. Similar difficulties are also encountered bv scientists and engineers who may have to use electrochemical data occasion&y and have not been trained in electrochemistrv DroDer. A simple change in the tabulation of I?'-vafues suggested below makes cell potentials easier to calculate, and may help electrochemistry as a whole appear less formidable to the outsider. To do this we first remember that the value of ED= 0.000 assigned to thenormal hydrogen electrode is arbitrary, and any other value could have been used instead. We propose here to use the value of E" = 3.000 V for the NHE instead of zero. (This value is chosen so that practically all E" values listed in tables will be positive.) This amounts to adding exactly 3.000 V to all Eovalues in existing tables. The resulting numhers are shown in Darentheses in the table and are appropriately referred toas ihe'.modified normal h y d w Zen . electrode" (MNHE) scale. If we repeat the calculation of the three cell potentials given above, employing the modified Eo values, we must, of course, arrive at the same results, as shown below (a nice way M demonstrate t o heginnerr in the field that the value assigned to the NHE is quite arbitrary). Ag-Cu Cu-Ni Cd-Mg
3.799 - 3.340 = 0.459 V 3.340 - 2.770 = 0.570 V 2.597 - 0.625 = 1.972V
This minor modification of the NHE scale leaves no room for confusion with resued to sim. as to which Eo has to be substracted from which, and why the result in sometimes the difference between the tabulated Eo values and sometimes the sum of their numerical values. The so-called oxidizing power or reducing power of different couples also becomes more clear using this modified scale of Eo. A higher value of Eo implies a greater tendency Abbreviated emf Serles on the Normal Hydrogen Scale (NHE) and
the ModHied Normal Hydrogen Scale (MNHE)
R e x Reaction
Standard PotentialdVolt WE) (MNHE)
Calculallon of Cell Potentials
The calculation of standard cell potentials from tables of Eo values should be an easy matter. For the purpose of demonstration we list in the table some of the more freauentlv used Eo values. which can be obtained from anv gandbook or textbook. ' The value for the H + B 7 redox c o u ~ l eis taken arbitrarilv as exactly zero, and the standard reversible potential of a ceil containingany twoof the redoxcouplesshown in the table is Volume 66
Number 11
November 1989
913
of the given couple to be reduced (i.e., to accept electrons) and hence stronger oxidizing power. This is correct, of course, regardless of the arbitrary value of Eo we use for the NHE, but with theusual scale the statement onemakes is "a higher positive or less negative value of En" or "a higher algebraic value of En", which are cumbersome to write and may cause confusion at times. For a cell consisting of, say, a Cu2+/Cuand a Zn2+/Znhalf cell, the spontaneous direction for the cell reaction is since Cu2+,having a higher Eo value, is a stronger oxidizing agent than Zn2+. Reference Electrodes Once the concept of electrochemical potential has been introduced (and the Nernst equation discussed), the subject of measuring potentials is generally encountered. Polarity can be confusing here in two ways. First, what is the proper polarity to be used in connecting a measuring device such as a voltmeter to a test electrode and a reference electrode in order to obtain the proper reading? Second, how does one convert from one reference electrode scale to another? The first question is easily addressed hy realizing that when one makes a reading with the aid of a reference electrode. one wishes to know the ~otentialof the test electrode relative to that of the reference electrode. If the potential of the test electrode is above. i.e.. more ~ositivethan. the reference electrode, one expects the measured to be positive. The opposite is true, of course, if the potential of ihe test electrode is below that of the reference electrode. It may seem ohvious that merely assuring that the reference electrode is connected to the negative terminal of the measuring device accomplishes this, but it evades many students, as well as technical personnel new to the subject. The appearance of a negative sign in the reading of a voltmeter sometimes confuses students. because thev assume (erroneously) that a voltage reading'should always be positive and suspect that they have connected the leads incorrectly. Problems of conversion from one reference electrode scale to another are nurelv arithmetical. but nevertheless auite common. The particular reference electrode chosen for a given study depends on the system investigated. Basically, the reference electrode must be stable and must not contaminate the solution being tested. Additional details conceming the selection of reference electrodes are beyond the scope of this paper. ~ h i i i;e is common to report electrochemicaldata relative to the normal hydrogen . . electrode (which is the manner used in a standard emf series), a different reference electrode (e.g., calomel) is used in most cases. In order to renort data relative to the NHE. but measured relative to some other reference, simple conversion is needed. Here main comolications associated with negative siens are often encounterkd. To clarify this simple poi;, it is ofien convenient to use the era~hicalaid shown in Fimre 1, in which the potentials of; f;?wof the common reference electrodes relative to NHE are shown. It is easy to see that, by marking the potential measured with respect to any reference on the potential scale in Figure 1, its value relative to the normal hydrogen electrode is readily obtained. The correct results can also be obtained by simply adding the value of the potential of the reference electrode, measured vs. the NHE, to the observed potential. To illustrate this point, assume that the three potentials El = 0.50;Ez = -0.10, and ES = -0.60 V were measured vs. a saturated calomel electrode. Since the potential of this electrode is -0.25 V vs. NHE, one has &
-
E, = 0.50 VSCE = 0.50 + 0.25 = 0.75V NHE E2= -0.10 V SCE = -0.10 + 0.25 = 0.15 V NHE 914
Journal of Chemical Education
POTENTIAL1 Volt
VS:
NZnE
NHE
SCE
MSE
0.645
0.403
1.408
SCE
0.242
0.000
1.005
-0.403
NHE
0.000
-0.242
0.763
-0.645
NZnE
-0.763
1.005
0.000
-1.408
MSE
0.000
Figure 1. Qaphic repeaentation for converting results of measuremenis taken against several reference electrcdes to U?eNHE scale.
E3= -0.60 V SCE = -0.60 + 0.25= -0.35 V NHE If the same three values of the potential would have been obtained with the use of a normal zinc electrode (NZnE) as the reference, which itself has a value of -0.76 V NHE, the conversion to the normal hydrogen scale would be done in exactly the same way, namely by adding -0.76 V to each of the measured potentials. This would yield values of E, = 0.50 V NZnE = 0.50 + (-0.76) = -0.26 V NHE E, = -0.10 V NZnE = -0.10 + (-0.76) = -0.86 V NHE E, = -0.60 V NZnE = -0.60 (-0.76) = -1.36 V NHE
+
At this point the reader should be able to appreciate the advantaee of the modified normal hvdroeen electrode scale (MNHES, in which the potential oi the-normal hydrogen electrode is taken to he 3.000 V rather than zero, by repeating the above conversions using this scale. The graphical aid assists in making conversions quickly and correctly and in the experience of the authors is more assuring to the student than the numerical calculation. Polarlty of the Electrodes in an Electrochemical Devlce Electrochemical devices are of basically two types: driving systems, which produce electrical energy from chemical energy, such as batteries, fuel cells, and spontaneous corrosion (although in the latter the energy produced cannot ordinarily be utilized), and driven systems, which produce chemicals from electrical energy, such as a battery on recharge, electroplating. electrowinnine. and electrooreanic svnthesis. The eonce$s of oxidation and reduction and of the anode and cathode are usually easily grasped by students. However, there is an unfortunate desire to identify the anode with the positive terminal and the cathode with the negative terminal. To understand fully why this is not the case, recall that oxidation is a loss of electrons and always occurs at the anode and reduction is a gain of electrons and always occurs at the cathode. If electrons are produced in the half-cell reaction, this is an anodic reaction and vice versa. Some examples are
Next, it is important to recall that current is by convention the flow of positive charge. But in a metallic conductor electrons carry the charge, and they are negatively charged. Therefore, the direction of the flow of current is opposite to the direction of flow of electrons. Now, envision a very simple electrical circuit shown in Figure 2. I t is a dc power supply and a resistor in series, serving as the load. The
I
RESISTIVE LOAD
P
BATTERY
I
+ POWER SUPPLY Figure 4. Banery swing as the load (driven mode), being charged by power SUPPlY. Figwe 2. Power supply wim resist= as Uw I d
RESlSTiVE
LOAD
13 + DRIVING BATTERY -
Figure 3. Battery w i n g as the power supply (driving mode), wim resismr as me load.
polarities and the direction of flow of current and electrons are properly indicated. If we replace the power supply by a battery we have the circuit shown in Figure 3, in which the b a t t e n is in the drivine mode. i.e.. it is the active element in the electrical circuit, Zetermhing the direction of flow of current and electrons. (the batten, is beine discharged in this case). It can be &ily determined whkh electrode is has current which in this case. The electrode marked flowing out of it and hence electrons flowing into it, and in the batterv there must be a reaction proceeding that consumes thene electrons. This is a cathodic reaction: Hence the positive electrode is the cathode fur a driving electrochemical device, i.e., a battery functioning as the power supply. The negative electrode is, of course, the anode this case. Now, consider a driven system, such as a battery being charged. To visualize this, one has to replace the resistor in Firmre 2 bv a batterv. Firmre 4 illuswates the resultine circ z t . ~ o t e i h ain t this case the battery serves as the lo;?d in the electrical circuit, and the direction of flow of current is determined by the power supply. Thus, the direction of flow of the current and of the electrons is maintained the same as in Figure 2. In this case, the current enters the electrode laheled in the batterv, and electrons exit this electrode. It becomes evident that there must be an anodic reaction takine place a t this electrode in solution. Thus, in a driven system the positive electrode is the anode, whereas in a driving system the positive electrode is the cathode. While the nolaritv of the two electrodes with resDect to each other is unchanged (as will be explained in more detail below) their role as the anode or the cathode in solution depends on whether the battery is being charged or discharged, i.e., whether it is ooerated in the driven or driving modes. The battery in our automobiles can serve to illustrite this point and a - label firmlv recorded on the further. It has a terminals. This might seem erroneous. 1s this marking correct when the hattery is being discharged, or when it is being charged? Referring back to Figures 3 and 4 it should be clear
+
that it is, in fact, correct for both cases. As we go from charge to discharge, the direction of flow of current in the battery chanzes. but the direction of flow of current throueh the circuyt i* unchanged, because it is always determinedky the Dower s u ~ ~ .. l(cf. .v . Fies. 3 and 4). Hence the ~olaritvof the two terminals is not c\anged. he role of thetwo el&trodes in solution does chanee. however. During discharge the positive electrode is the cithode and the negkive electrode is the anode, and the inverse is true during charging. If we start the car with the lights on, they will dim, showing that the battery is drained (it is in the driving mode) and its voltage has dropped, say, from 12-13 V on open circuit to 9-10 V. If, after starting, the engine is raced for a few seconds, the lights are very bright, showing that the voltage is back up to probably 13-14 V, while the battery is being charged. The polarity of the two terminals has not changed in the process. The case of the car batten, which evervbodv is familiar with, can be used to illustrateour point further. imagine that on a cold morning one is asked to help start a neighbor's car that has a "dead" battery. The two batteries are connected, with positive to positive and negative u) negative poles, as shown schematically in Figure 5. The two batteries are identical except fur the fact that one is fully charged while the other is iargely discharged. The charged battery has the higher voltage and will be in the driving mode (acting as the nower su~nlv). - . while the dischareed hatterv will be in the h e n mode. Electrons flow in t i e counterElockwise direction in Fieure 5. leavine the neeative terminal of the charged battery, &us making iithe an&, and entering the negative terminal of the discharged batterv, making it the cathode. The same kind of reversal of roles~ccursa t t h e two positive electrodes.
..
..
The Polarity of Overpotentlal When a current is flowing through a battery or through any other electrochemical system, the potential deviates to an extent that depends on from the reversible
+
'+I
+ DRWING BATTERY -
+
Figve 5. Two batleriss connected in parallel. Lower battery serves as me power supply (driving mode), and upper baltery serves as the load (driven mode).
Volume 66 Number 11 November 1969
915
POTENTIALIVOIt, NHE
(cathodic)
CURRENT (arbitrary scale)
(anodic)
Flgve 6. A C b Z n cell on discharge (drlvlng mode), showing me Earnodic Overpotential at me poshlve electrode and the anodic werpotential at the negative elWx&.
2.0
I II
ARBITRARY SCALE
Figus 7. A Cu-Zn w l l shoring ovemotentials boU~on charge and discharge. as a hlwtlon 01 Uw absolute value of the curent. Note that the plsrity ot W e electrodes d ~ e not s change wim the change in lhe dirmion of polarlzatlon.
the magnitude of the current and on the specific properties of the svstem. The difference between the ootential measured while a current is flowing and the reversible potential is called the overpotential, E(i) - E,e, The potential during current flow deviates from the reversible potential for a number of reasons that are physically unrelated. For the present discussion of polarity, we need not dwell on the origins of the resulting overpotential, and will consider this as an exoerimental uuantitv. Each half cell an oxidation has its own overpotential Hssociated i i t h it. reaction (i.e.. an anodic reaction) to occur at a finite rate. the potential'm&t be made more pdsitive (or more anodic) than the reversible potential for that half-cell reaction, and for a reduction reaction it must be made more negative (i.e., more cathodic). It follows that the anodic overpotential is always positive and the cathodic overpotential is always negative. It must be understood that when an electrochemical system is operated in either mode (driving or driven) one of the electrodes is the anode while the other is the cathode, since electrons that exit at one terminal must enter at the other. The sign of the overpotential in the battery as a whole is oositive when it is beine chareed (driven) and neeative when it is being discharged (irivini). The reason for the last statement can be readilv understood by analogy with thermodynamics. Consider agas being comoressed isothermallv. If the process is performed reversiblyiat a vanishingly low rate), the amo& of work needed to compress the gas will be equal to the amount of work performed by the gas upon expansion to the initial volume. If compression and expansion are conducted irreversibly, i.e., at a finite rate, more work will be needed in the former and less work will be gained in the latter. The difference is the extent of irreversibility of the process, namely, the penalty one has to pay for conducting the process at a finite rate. In electrochemistw the observed overootential is a measure of the degree of ir;eversibility. ~ u r i n gcharging (at a finite rate) the ~otentialmust be hieher than the reversible potential, since the irreversible woik is larger than the reversible work done on the system. Hence the total overpotential during charging is positive. For the same reason the overpotential during discharge must be negative. Consider, for example, a cell made of a Cu2+/Cu and a Znz+/Znhalf cell. We know already that the standard reversible cell potential will be 0.34 - (-0.76) = 1.10 V (3.34 - 2.24
or
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Journal of Chemical Education
= 1.10 V as calculated on the MNHE scale) and that the cell reaction will proceed spontaneously in the direction
+
Cu2+ Zn
-
Cu
+ Zn2+
(6)
We note that Cu is nositive with resoect to Zn. If we nlace a load resistor betweeithe two termin&, the situationkill be as shown in Fieure 6. The oositive comer electrode will act as a cathode, &d the negative zinc'electrode will be the anode. Since a finite current is allowed to oass. an overootential will develop at both electrodes. At the positive eiectrode a cathodic reaction is made to occur, and the potential will decrease, while at the negative electrode an anodic reaction is made to occur, and the potential will increase. The relationship between current i d potential is shown schematically in Figure 6. I t is more convenient to plot the currentlpotential relationship in the form shown in Figure 7, where the absolute value of the current. reeardless of sien. is shown. If we reverse the direkon of the & r e n t through the cell (forcine the reaction to occur in the direction oooosite to that which would occur spontaneously), the sit&tion will correspond to that shown in Figure 4. The copper electrode will still be the positive electrode, but, in this, driven, mode, it will be the anode, while the negative zinc electrode will be the cathode. This is shown in Figure 7. The important thing to note is that, while the overpotential developed at each electrode changes sign in going from the driven to the driving mode, the total overpotential may be a small fraction of the cell voltage, and the copper electrode remains positive with respect to the zinc electrode, regardless of the mode in which the cell operates. I t should perhaps be noted here that in electrochemical research the cell is, as a rule, in the driven mode, i.e., one applies a current &d measures the potential or viceversa. In this case the positive electrode serves as the anode, and the negative electrode is the cathode, as most electrochemists commonly perceive. It is only when the electrochemical cell functions& the source of to drive the current (as in batteries, in fuel cells, and in corrosion) that the role of the positive and negative terminals is reversed.
