Symposium on Use o f Theoretical Principles in Chemistry' A MODERN APPROACH TO THE TEACHING OF ELECTROCHEMISTRY
0
ARTHUR W. DAVIDSON University of Kansas, Lawrence, Kansas
INTHE FIELD of electrochemistry the choice of subject matter suitable t o the elementary course and of effective methods of presentation still constitute a problem for the teacher of general chemistry, despite several recent cont~ibutions~-~ which have been both interesting and valuable. Certain aspects of the problem, such, for example, as the once troublesome question of the sign of cell voltages and electrode potentials, have been so clearly and definitively dealt with3as to require little further discussion. The subject matter of the present paper is limited to four specific topics, each of them a source of perplexity t o many students, with respect t o which uniformity of practice among t,eachers and writers of textbooks has not yet been attained. Nost of. the ideas here presented have been expressed elsewhere, although not in any single article or textbook. The four topics referred to are:. (1) the difference between the free energy change in a reaction and the heat of reaction; (2) the mechanism of the chemical change that takes place in the operation of a volt,aic cell; (3) the application of the terms "cathode" and "anode" to the electrodes of both electrolytic and voltaic cells; (4) the still prevalent use of the term "depolnrizer" for the oxidizing agent in many common voltaic Cclls. In the first two cases, the difficulties are inherent in the nature of the phenomenon; in the last two, they rcsult mainly from the survival of early practices or conventions whose ol~solescencemight well be hastened. FREE ENERGY CHANGE IN
REACT'0NS
The student will usuallv " have lenrne(l earlv in his first chemistry course to regard the heat eiol;e;l in chemical reaction as a memure of the clifferencr in what might be designated as the levels of chemical enerxy of the reactants and the products, thus:
a
heat of ronction=chemical energy of reactants-ohcmicill enerev -" of ~ r o d t ~ a t , s ~
A~
~~~~~~~~
(The fact that the heat of reaction, as ordinarily measured and tabulated, is usually not ident>icalwith the change in internal energy may, at this be neg-
' Presented bcfore the Division of Chemical Eduration a t tho 113th meeting of the .4merican Chemical Soointp in Chicago, April 19-23, 1948. HALL,W. T.,. I CHEM. . EDUC.,21, 403-6 (l!Jl&i. LUDER,W.F.. A N I I A. .4. VERNON,ihid., 22, 63-7 (lY4.5). a TIMM.J. A,, ihid., 24, lfio-5 (3947).
lected.) It is only natural for the beginner to conclude that this quantity should provide a reliable memure of the tendency for the reaction to take place--of that criterion which, for want of a, better term, has been referred to by numerous authors as the "driving force" of the reaction. After all, the brilliant early workers in the field of thermochemistry, men like Thomsen and Berthelot, made the same error, and believed that they were establishing a sound basis for the prediction of chemical behavior. It should not be difficult to convince the student that this belief was illusory. It is only necessary to point out that there are even many endothermic changes which nevertheless proceed spontaneously; the melting of ice in marin water, the evaporation of water in dry air, and the dissolving of sodium chloride in water, serve as familiar physical examples, while a chemical instance is provided by the decomposition, a t ordinary temperatures, of dmmonium carhonate into ammonium'bicarbonate and ammonia. It-may t,hen be explained t,hat the true measure of the "driving force" of a chemical change is not the heat of reaction, but is rather to be found in the decrease of another quantity called free energy;. thus: "driving farce" of renction=free energ," of feactants-frco energy of products
A react,ion may he classed as R. spontaneous one when this "driving force" is positive; that is, when the reac; tion is accompanied by a decrease in free energy of the substances concerned. The concept of free energy, of course, cannot be rigorously defined in the elementary course from the thermodvnamic view~oint. It should not he too difficult,howtker, to present the idea t,hat the decrease in free energy in a reaction (often loosely called the free energy of the reaction) is measured not by the amount of heat evolved when the reaction takes place in a calorimeter, but rather by the maxinnml amount of actual-useful work, mechanical or electrical. t h a t can be obtained when the reaction takes place (at co,lstant pressure and under the most circumstances conceivable. This quantity is indeed oftenapproxilllate~ythe sallle as the heat of reaction-it would obviously be preposterously pedantic to add that, this is true when the elltropy &ange is small-hut is almost never identical with it. One may now proceed to the statement-which follows simply from t,he law of conservation of energy-
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that if the heat of reaction is greater than the free energy decrease, a certain amount of heat which cannot by any means be changed into work must always be given up to the surroundings in the course of the reaction. As an instance of this phenomenon, one might cite the freezing of very slightly supercooled water. There is no "driving force" to this reaction, despite the considerable quantity of heat evolved. I n the rare cases in which the free energy decrease is just equal t o the heat of reaction, there would he no thermal effect if the reaction could be made t o take place a t maximum efficiency. The oxidation of carbon to carbon dioxide a t room temperature, for example, evolves 94 kilocalories of heat per mole of carbon, and could, under the most favorable circumstanceswhich, incidentally, have never yet been experimentally attained-provide 94 kilocalo~iesof electrical work, in which case there would he no heat effect. The third possibility is a trifle more difficult to grasp although instances are sufficiently numerous. Before returning to a chemical illustration, it might he well to mention the case of an ideal gas, which on expansion is enabled to do mechanical work by virtue not of its decrease in energy but of its capacity for absorbing heat from its surroundings. Similarly, in all cases in which the free energy of a chemical reaction is greater than the heat of reaction (and these include, among others, all spontaneous reactions which are endothermic), the reacting system, when working at maximum efficiency, is able to absorb some heat from the surroundings and convert it into work. Such conversion might occur, for example, in a voltaic cell in which the reaction consisted in the displacement of mercury from calomel by silver. By means of such a presentation, the student may be brought into contact with the idea that chemical elements and compounds may serve not merely as containers or reservoirs of energy, hut also, in some cases at least, as machines through which energy from the surroundings may be converted into actual work. E
THE MECHANISM OF THE CELL REACTION
cussed. However, the last requirement, that of separation of the reactants, inevitably raises the question, "How can two substances possibly react spontaneously with one another if they are not in contact?" This question may best be dealt with through the consideration of a particular voltaic cell; and because of its familiarity and simplicity we may select for this purpose the copper-zinc displacement cell, in which the spontaneous reaction represented by the equation Zn + C u t + = Z n + + + C u
constitutes the source of energy. If the free energy of this reaction is to be obtained in the form of electricity, the two reactants, a rod of metallic zinc and a solution, say, of cupric sulfate, must be separated by some means, such as a porous partition. A conducting solution in contact with the zinc, and an electrode in the cupric sulfate solution, complete the cell. Since these latter portions of the cell do not participate in the reaction (as read from left to right) a wide choice of suhstances is available; however, in order that the number of elements involved may be kept at a minimum, we may choose to use a zinc sulfate solution as the electrolyte in contact with the zinc, and a copper rod as the inert electrode; we then have the particular combination of materials which constitutes the so-called Daniel1 cell. Presumably the student will have been told previously that neither of the changes known as oxidation and reduction can take place without the simultaneous occurrence of the other. Hence, he will not be surprised to learn that no change can occur in the cell ar, long as the electrodes remain unconnected. However, as soon as the zinc an3 copper are connected by a wire, it may be shown experimentally that zinc begins t o go into solution from the zinc electrode, copper is deposited from the solution on to the copper electrode, and a current (in the conventional sense) flows through the wire from the copper to the zinc. But the-question previously raised remains unanswered, although it may now be worded more specifically: "How can the zinc and the cupric ion react with each other when they are not in contact-when neither of them, so to speak, can possibly he aware of the presence of the other?" While no entirely satisfactory answer can be given to this question, the following explanation appears to the author t o be the best that is a t present available.=Let us suppose that whenever a metal rod is placed in water or in an aqueous solution, some of the metal atoms in the surface, because of their tendency t o lose electronsor, rather, because of the energy liberated when the cations combine with water--spontaneously pass into
Having at least approximately deiined the free energy decrease in a reaction, we may now proceed t o the discussion of the voltaic cell as a device in which the free energy decrease of a spontaneous reaction is changed into electrical work. Not every spontaneous reaction may be so utilized, however, for two other requirements, in addition to spontaneity, must be met. The total change must be separable into two partial react,ions (or half-reactions, as they are commonly called) in which, respectively, electrons are lost by one set of substances and gained by another, and these partial reactions must take place at two ditrerent points; that s T h e terms "electrolytic solution tension'' and "osmotic is, the substance that gives up electrons and the one pressure," carried over from the Nernst theory of the electrode that receives electrons must not be in direct physical process, which still appear occasionally in current textbooks, contact with one another. The concept of a partial seem to the author to be altogether inappropriate; first, because reaction which involves either the loss or gain of elec- they do not take into account the gain oi electrons which we nowknow to constitute a nepative electrical charge, and, secondly. trons, but not both, need not he regarded as a startling because the tendency of a cation to change to the corresponding innovation, for the occurrence of such changes a t the metal is not st all a n osmotic pressure, in the currently aerrpted electrodes in electrolysis will already have heen dis- sense of t h t~, ~ r m .
OCTOBER, 1948
solution as hydrated cations, according to the equation metal + water
=
hydrated cation
+ electron(8)
The electrons thus liberated remain behind in the metal, which thereby acquires a negative charge. The extent to which this change takes place depends upon the concentration of hydrated cation already present in solution in the vicinity of the electrode, decreasing with increasing concentration; but in any case it can occur to a very limited extent only, since the negative charge on the rod acts as a strong deterrent to the departure of any more cations; in other words, an equilibrium is soon reached between the metal and the solution. Since the tendency to form cations varies from one metallic element to another, we may further suppose that the reaction indicated by the above equation will proceed to a differentextent for each metal even when the cations are present at the same concentration; in general, the more active the metal, the greater will be the concentration of free electrons in the rod when equilibrium is attained. Thus, if each of two similar rods, one of zinc and the other of copper, is immersed in a solution containing the corresponding cation at the same concentration, a greater negative charge will be developed on the more active zinc than on the less active copper. These changes, it is true, are not susceptible to experimental verification. No increase in concentration of zinc ion or cupric ion in the solution can be discerned even by the most sensitive analytical methods. There is no perceptible decrease in the weight of either rod, nor can a charge be detected upon either electrode by means of any electrical instrument, however delicate. I t is for this reason that the entire explanation must be regarded as a hypothetical one only. Now the presence of excess electrons may be supposed to produce a sort of electron pressure within the metal. Since this electron pressure is greater in the zinc than in the copper, there is said to be a difference of po-. tential between the two electrodes, consists in.a tendency for electrons to pass from the zmc to the copper. Even though the two solutions may be in contact, this tendency must remain latent so long as the electrodes are not connected by a metallic conductor. As soon as such connection is made, however, the difference of potential manifests itself as an electromotive force which drives electrons through the wire from the zinc to the copper. (The student will have learned previously that the direction of the current, according to convention, is opposite to the direction of electron flow, so that current is conventionally said t o flow, under these conditions, from the copper to the zinc.) Because of this flow of electrons the two electrode reactions, represented by the simplified equations ~~
~
the wire into the copper and thence to the solution, where cupric ions pick them up and become atoms. Meanwhile, because of the continual arrival of electrons at the copper electrode, all of the positively charged ions in the solution, both Zn++ and Cu++, migrate toward this electrode. while the negatively charged sulfate ions migrate toward the zinc electrode, from which electrons are being dispatched into the wire. Thus, the electrical circuit is complete, and a continuous current passes through the wire and the cell. "ANODE" AND "CATHODE OF VOLTAIC AND ELECTROLYTIC CELLS
Although certain aspects of the problem of electrochemical nomenclature were competently discussed by Luder and V e r n ~ nthey , ~ did not consider the application of the terms "anode" and "cathode" t o the electrodes of electrochemical cells in general, nor the relation of these terms to the classical designation of electrodes as positive or negative. Some authors prefer to side-step this problem by taking the position that the words "anode" and "cathode" should never be used in connection with voltaic cells, since such use is certain to result in confusion. A few; in the attempt to attain a certain type of consistency, have unintentionally promoted such confusion by continuing t o define the anode as the electrode conventionally designated as "positive," and the cathode as that conventionally called "negative," even in the case of voltaic cells. Fortunately, however, our choice is not between these two alternatives, which seem to the writer to be almost equally undesirable. All ambiguity may be avoided by means of a preentation along the followinghes.
v0110ic Cell
L. Figuzo 1.
-C
-
Electrolytic Cell cConventionol current A-
J
k
a-
Nomenclature bf Electrochemical Cells
Let us first reemphasize the fact that the electrolytic and the voltaic cell may be regarded simply as the two general types of electrochemical cells, which have in common certain fundamental characteristics: each is a device for the interconversion of chemical energy and Zn = Zn++ + 26electrical energy, through the medium of an oxidationreduction reaction in which the oxidation and reduction and take place at two different points. The close relationCu++ + 2 e = Cu ship between these two types is, indeed, brought out in are enabled t o proceed freely and simultaneously, t,he Timm's paper,4 in which he shows how a voltaic cell electrons liberated by the zinc atoms flowing through may become an electrolytic cell merely as a result of a
536
slight shift of a movable contact along a slide-wire in the familiar potentiometric circuit. (The common storage battery, which during charge acts as an electrolytic cell and during discharge as a voltaic cell, may also be cited in this connection.) In the electrolytic cell, anonspontaneous reaction is caused to take place by the application of electrical energy from an external source; i. e., electrical energy is changed into chemical energy. In the voltaic cell, on the other hand, the free energy released in a spontaneous reaction is changed into electrical energy.6 In both types of cells, however, the electrode at which electrons leave the cell and enter the external circuit, and hence the one a t which oxidation takes placeand towardwhichthe anionsof the electrolyte migrate, is logically designated as the anode. The electrode a t which electrons leave the external circuit and enter the cell, and hence the one a t which reduction takes place and toward which the cations of the electrolyte migrate, is properly called the cathode. These designations are illustrated in Figure 1. Electricians, it is true, uniformly adhere to the practice of designating the terminals of a cell as "positive" and "negative"; and in an electrolytic cell, according to a firmly established convention, the anode is called the positive, the cathode the negative electrode. In a voltaic cell, however, the anode, as defined in the preceding paragraph, is called the negative, the cathode the positive electrode. Since it is this set of conventions which is the source of such confusion as still exists, and since the chemist, in any case, has nothing to gain from the designation of an electrode as positive or negative, it seems desirable that the use of this terminology be deaphasized as far as possible, and that preference always be given to the entirely logical and consistent designation as anode or cathode. Thus, for example, in the lead storage cell the lead dioxide plate (called by electricians the positive plate) is the cathode during discharge and the anode during charge; the xpongy lead plate called (negative by electrician$ is the anode during discharge and the cathode during charge. There is a further advantage t o be gained from the shift of emphasis away from the putative positive or negative character of electrodes. The complete eliminat,ion of such emphasis may be expected Permanently to dispose of the once vexatious practice of attempting to link the electrical "sign" of an electrode with the algebraic sign of the corresponding electrode there has been a long and potential. controversy over the question of whether, in a list of standard potentials, the sign of the potential of a metal-cation electrode such as Zn, Zn++ should be positive or negative.' 8 There is, it is true, one type of cell which does not appear to fall into either of these categories; namely, that in which a metal is merely transferred from one electrode to another, as in many varieties of electroplating. Although this process is, of course. commonly and correctly desipated as oleotrolysis, cells of this type might conveniently he regarded as lying on the border line between the two classes defined above. 'See reference 1, p. 405.
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The point a t issue simply disappears if no attempt is made to associate this sign with the charge on the electrode. Thus the way is cleared for the adoption of the much more satisfactory modern convention according to which, for purposes of compilation, each electrode is to be regarded as an anode, and the sign of the electrode potential is the same as that of the free energy decrease which accompanies the half-reaction of oxidation a t the electrode. Experimentally, the standard potential of the Zn, Zn++ electrode is identical with the voltage of the cell in which this electrode as anode is coupled with the standard hydrogen electrode as cathode, since the potential of the latter electrode is arbitrarily taken to be zero. Similarly, the free energy decrease for the hypothetical half-reaction is identical with that for the displacement reaction because the free energy of the hypothetical half-reaction , 2H+ (a = 1)
+ 2e-
=
H,
is arbitrarily taken to be zero. "DEPOLARIZER" OR OXIDIZING AGENT
Another unnecessary and confusing usage which has been carried over from the infancy of the voltaic cell is the application of the term "depolarizer" to the oxidizing agent which surrounds the "positive" terminal of cells of the zinc-carbon type,,inciuding the familiar dry cell. Curiottsly enough, the lead dioxide in the "positive" grid of a storage cell is never referred to as a "depolarizer." Yet the tradition persists that the fnnction of the manganese dioxide in a dry cell is to oxidize the free hydrogen which is liberated a t the cathode and would otherwise form an insulating or polarizing layer on the carbon. Actually, there is not a shred of evidence to indicate that hydrogen is fist liberated and then oxidized to water bv the mannanese d i ~ x i d e . ~ Such a stepwise change, inUfact,seems quite as improbable as the that, in the electrolysis of an sodium chloride solution, metallic sodium is liberated at the and then reacts nrith water with the formation of hvdroeen, " ~h~ halfWreactionat the cathode of a dry cell is probably somewhat complex; the main reduction product. however, appears to be manganic hydroxides (or hydrous rnanganic oxide). The cathode should therefore be regarded as a manganese dioxide-manganic hydroxide electrode. Free hydrogen does not enter into the picture at all, and the half-reaction may properly be represented by the equation MnOl + NHIt + 2Ha0+e- = Mn (OH), + NH,OH u
u
LATIMER, W. M., "The Oxidation States of the Elements, and Their Potentials in Aqueous Solution," Prentice-Hdl, Inr., New York, 1942, p. 224.
