provoccrtive opinion Electrochemical Cell Conventions in Allen C. West Lawrence University, P.O. Box 599, Appleton, WI 54912
We are studying electrochemical cells. Like all good lecturers, I use a demonstration: standard zinc-and-copper half-cells in beakers, connected hy a salt hridge and a digital voltmeter that displays the good news in bright red numerals: + 1.10 V. (If you use 1M sulfate solutions and a KzSOa agar hridge, that is what you really get!) "You see," I say, "that oxidation is occurring in the lefthand half-cell and reduction in the right, since the voltage is plus, so we can write according to the convention.. ." and I put on the blackhoard:
Eo for copper is +0.34 V
+ 1.10 V = +OX V - E;&, "And what is the E o of the zinc half-reaction? -0.76 V obviously. And since all E o values are reduction voltages, Eo = -0.76 V for the half-reaction. . .", and I put on the hlackboard: Zn2+(aq)+ 2e-
-, Zn(s)
"Are there any questions?" The class sits in silence. I am about to go on, half turning toward the hoard, when I see motion out of the corner of my eye, a timid hand going u p hack there in the anonymous middle. "Yes?" "But sir, zinc is on the right and copper is on the left. I don't understand." I am only momentarily nonplussed. "No problem. From where you're sitting zinc is on the rieht isn't it?" Mv laueh is iust a touch forced. "But rememher, 'left' and 'right' have nothing to do with the arrangement that's reallv there. Thev are iust shorthand conventions for 'the less" positive haif-cell'-and 'the more positive half-cell.' And if we use reduction voltages exclusively, the sign and rnagnirude of each half-cell voltage agree with elecrrustatic convention, which says that electrons (hnving negarive charge) now spontaneously from the less positive (more negsti\.e~electrode to the more positive (less negative)." "Yes. hot. . ."There isa moment of hesitation. I should be delighted with class response, but. . . "But, what?" "If oxidation is occurring a t the left, why isn't the voltage of that half-reaction for an oxidation? I mean,. whv . isn't El., .-." for oxidation?" I am ready for this one. "I see vour - orohlem. . .but.. remember, allEo's are reduction voltages so you can't use Eieli = E&- Ekftunless you use reduction voltages. Follow the conventions and you won't run into trouble. Don't worry about what's happening in the beakers." Another hand goes up. "What's the minus sign for?" Mercifully the hell rings. They are all either lost or bored or both.
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"That's part of the convention. Look i t u p in the book." "Look i t up in the hook.'' I have followed that advice for years, teaching general chemistry from a variety of textbooks. Many do not use these conventions, hut some do. (Analvtical chemistrv texts all do.) I have come t o believe ;hat ;hew conventi&s make electrochemistry harder for students to learn and much harder to remember. Why? Chemistry is a science of the physical world, of visible, taneihle. oonderahle materials. Difficult enough for stude&aGe;dy, it becomes more so when we discuss this world in terms of invisible, intangible, nonponderable entities, using symbols and equations. T o minimize confusion we must connect the microscopic and the macroscopic as closely as possible, which means (among other things) connecting what we write down on paper with what we observe in the laboratory and the environment. "Conventional" electrochemistry breaks this connection (as the italicized phrases in mv scenario emnhasize). increasine confusion. Two specific factors contribute to this confusion. First of all. the left-rieht convention sueeests that we alreadv know the cell, when, in f a d , we before we set what is must measure the direction of electron flow before we know. Secondly, the conventions are one more cluster of special information to he memorized, and since they do not connect directly either with the physical world of~electrochernical cells or with other patterns of handling chemical reactions, they are quickly forgotten. Therefore, they will not help most of our students in general chemistry, who are not going to be chemists at all, on those rare occasions when they need to use simple electrochemistry. That the conventions have the force of IUPAC writ surely need not bother us when working with beginning students. Mv thesis. then. is that we must connect our oresentation of 'cells more closely with the world of galvanic cells than "conventional" electrochemistry does. T o make this connection, we need only three items of information (assuming no significant flow of current): the two halanced half-reactions that describe the chemistry and the direction of electron flow in the external circuit. The latter is a key quantity. I t makes the chemistry vivid in a way that "plus" and "minus" or "cathode" and "anode" cannot. Texthook state direction of electron flow e x ~ l i c - nrohlems ~ ~ should ~ itly, in order to reinforce the connection between what is on paper and what happens in the lab. Furthermore, since we deduce relative electrostatic potentials from electron flow, not vice versa, congruence of electrostatic and thermodynamic potentials is unnecessary in practice. Now we can connect the half-reactions as they occur to the voltages of the half-cells, and the spontaneous redox reaction as it occurs to the voltage of the whole cell; that is, we can connect directly the chemistry and the electrochemistry.
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Volume 63 Number 7 July 1966
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This approach has another advantage: our students are used to working with quantities whose sign (andfor magnitude) depends on how the related chemical equation is written. AH, AG, AS, K: all of these must refer to a particular chemical equation written in a particular direction, but i t does not matter which way we write that equation. When we use Hess' Law we do not force our students t o write all the reactions in the exothermic direction. We do insist that enthalpy changes he connected to specific chemical equations. If we treat cell and electrode voltages in the same way, the dirertio,, of electnm tlow d e t e r m i k the spontunev~s direction of the redoa reaction (for which E is positireJ; m y lecture demonstration now goes like this: "We know," I say, "that electrons flow into the meter through the hlack wire. Since that wire is connected to the piece of zinc, we also know that the half-reactions occurring in the two balf-cells are. . ."and I write on the board: Zn(s) e Zn2'(aq) + 2e(midation) CuZt(aq)+ 2eC 9 Cu(s) (reduction) Cu"(aq) + Zn(s) * Zn2+(aq)+Cub)
EL = +O.% V E L = +0.34 V -Ed = +1.10 V
"This combination gives us a balanced redox reaction (no electrons created or destroyed) for which the meter reads +1.10 V. We know the voltage of the copper half-reaction. I t is En since [Cu2+]= 1M, and this gives +0.34 V from the table of standard voltages. So we can calculate the voltage of
610
Journal of Chemical Education
the zinc half-reaction, also a standard voltage since [Zn2+]= 1M. "It is easy to fit the standard zinc voltage into a table of standard reduction voltages, since, like other thermodynamic quantities you have studied, the sign of a voltage depends on which way we write the reaction: Zn(s) 9 Zn2+(aq)+ 2eC ZnZ+(aq)+ Ze-
F!
Zn(s)
E L = +0.76 V
EL = 0.76 V
"Tables of standard electrode voltaees are conventionallv given for half-reactions written as reductions, much the way tables of acid-base dissociation constants are conventionallv gi\,en for acid dissociation reactions, as K8'3. ".+r there any questions:'" T h r class sits in silence. 1 am about to go &half-turning toward the board, when I see motion out of the corner of my eye, a timid hand going up hack there in the anonymous middle. "Yes?" "Sir, what's a K.?" You cannot win, can you? My second demonstration seems to take much longer than the first. But of course that is no coincidence: conventions are shortcuts, but these in electrochemistry, like the concept of normalitv in solution stoichiometrv. break the connection between the physical world of chemistry and the written representation of that world, and, in doing so, agzravate &dents' difficulties. We ought not& do t h a t t o the; Come to think of it, we ought not to do that to them in analytical chemistry either.
