Pierre Van Ryrrelberghe
Stanford University Stanford, California
I
I
Sians C
of Tensions in Electrochemistry
Two international commissions, working jointly much of the time, have been trying since 1950' and 1953; respectively, to clarify the peculiarly confused domain of definitions of fundamental electrochemical concepts, electrochemical nomenclature, so-called "sign conventions," etc. These commissions took part in the discussions which led to the 1953 Stockholm "conventions concerning the sign of electromotive forces and electrode potentials." They gave their approval to the text which was published jointly by the chairmen of the Commission on Physico-Chemical Symbols and Terminology and of the Commission on Electrochemistry of the IUPAC (I) and republished several times since ($3, 5).3 This approval was meant essentially for the settlement, once and for all it was hoped, of the matter of the signs of electrode potentials (the standard electrode potential of the ZnlZn2+ electrode is -0.76 v, not 0.76 v). However, the two electrochemical groups have continued their efforts toward clarification and extensive reports on the whole subject have been published (4) and commented upon (7). The present author and his colleagues of the commissions have repeatedly noticed that in much of the current literature the Stockholm recommendations are sometimes not observed and often misunderstood or misquoted, and that the precise definitions which have been established over these many years are still insufficiently known. I n addition there have been occasional objections against the use in English of the various "tensions" (electrochemical, electric, chemical) which appear to be accepted in all other languages.
+
The present paper is an attempt by the chairman of these commissions (acting alone but with the support of his colleagues) to connect the present state of the commissions' work with current practice in textbooks and elsewhere. We shall take as point of departure the classical textbook formula AG = - z 5 E
(1)
connecting the so-called electromotive force E of a galvanic cell with the change in Cibbs energy (or free enthalpy) G corresponding to one occurrence of the cell reaction, z being the number of faradays 5 involved in the reaction. This fornlula is derived for reversibility and for given temperature and pressure. To see clearly what AC and E really are we take, for instance, the cell
consisting of the metal-solution electrode ZnlZn2+ and the solution-metal electrode Ag+ lAg and of the copper leads a and b. The double bar between phases 2 and 3 represents the liquid junction whose electric potential difference will be neglected or assumed corrected for. If a positive current I passes through the cell from left to right the following reaction takes place from left to right as written: Zn
+ 2 Agf + 2 e - ( b )
-
Znzf
+ 2 Ag + 2 e-(a)
At electrochemical equilibrium we have, in terms of the chemical potentials & and of the electric potentials q: PZ.+~PA.+-2Fq6=pZm,++2rr*.-2Fwn
'CITCE Commission an Electrochemical Nomenclature and Definitions. CITCE = Cornit6 International de Themodynltmique et de Cinbtique Electrochimiques" (International Committee of Electrochemical Thermodynamics and Kinetics), created in 1949, an affiliated commission of the IUPACa for many years. %IUPAC Subcommission on Electroehemied Symbols and Terminology of the Commission on Electrochemistry. IUPAC = International Union of Pure and Applied Chemistry. The recommendations referred to in the present paper are endorsed by the whole CITCE Committee, but, tas far as IUPAC is concerned, they are, for the time being, only those of the Commission on Electrochemistry, which hereby and through its published
in an explicit manner formulas of the type of our formulas (9) and (13) which we consider as cruoial to a direct and clear understanding of the subject. Such formulas easily settle the point raised by Anson ( 6 ) . As to the concept of "electron chemical potential" brought up by Ramsey ( 6 )it will be found treated in a straightforward manner in section 4.13 of the CITCE report (4)
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Journol of Chemical Education
(3)
(4)
since the chemical potential of the electron is the same in a and b and since the difference p2- p3is neglected or corrected for. Comparing (1) and (4) we find:
in which the subscript rar indicates reversihility. We thus see that the actual mieaning of (1) is that the condition of electrochemical equilibrium of the cell is: (q" - qh)lCU= AG/z 5 = - E
(7)
which shows that the reversible electric tension U,, = (qa - qP),_ is balanced by the chemical tension or electromotive force E: Um. E = 0 (9)
+
with E given by: E = -AG/z
3 = A/z 3
(10)
in which A is the chemical afinity of the cell reaction. If, keeping the diagram of the cell given in (2) but writing the reaction given in (3) in the opposite direction, the number of faradays carried from left to right in the cell during one occurrence of the reaction would now be -2. There would then be simultaneous changes of sign for AG and z or for A and z and it is thus seen that U,,, and E are invariant in magnitude and in sign with respect to this reversal in the writing of the cell reaction. Outside of equilibrium, i.e., with passage of current, U differs from U,,, on account of ohmic drops within the cell and of polarization a t the electrodes, while E remains constant, a t given temperature and pressure, as long as the composition of the phases is not altered. Let us now replace the right-hand electrode of cell (2) by the standard hydrogen electrode: CulZnlZn2+/lH+ (aa+ = l)IPt, & ( p a . = 1 atm)lCu a 1 2 3 4 b (11)
-
Reaction (4) is now replaced by: Zn
+ 2 H+ (an+
=
+
1 ) 2 e- ( b ) ZnP+ H2 ( p ~ =, 1 atm)
+
+ 2 e-(a)
(12)
The electric tension U,a,is now the electrode potential (m the Stockholm sense) of the Zn 1 Zn2+ electrode, while the chemical tension or emf E is now what has commonly been called the oxidation potential. A precise appellation for this qnantity is oxidatia affinity per coulomb. We have:
+
Urea EM*
=
0
(13)
If we place the standard hydrogen electrode on the left-hand side of the cell we have the following diagram: CulPt, HnlH+IlZn2+lZnlCu
(14)
with, in place of (13): in which the chemical tension or emf E,& is now what has commonly been called the reduction potential. A precise appellation for this quantity is reduction afjinity per coulomb. However, U',,, may not be called electrode potential, while the actual electrode potential U,e, of formula (13) is thus related to EOM and E,@as follows: For the standard ZnlZn2+ electrode we have U o , = - 0.76v, Eo,,,d = 0.76v, Eoled = - 0 . 7 6 ~ .
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The foregoing discussion shows that it is advisable t o give in textbooks the electromotive series with three columns of data corresponding to U9,,, Eod, and E0,&. This should clear up, among other matters, the old but persistent lore concerning so-called European and American signs or European and American conventions. E is not equal to Out of equilibrium the sum U zero any more. It is now equal to what may be called the electrochemical tension of the cell: E= U+EZO (17)
+
a quantity equal, in the case of a positive current passing from left to right inside the cell, to the sum of three positive terms: the ohmic drop in the cell, the anodic overtension a t the Zn/Zn2+electrode and the absolute value of the cathodic overtension a t the Ag+l Ag electrode in the case of cell (2). If the current from left to right is negative 8 is equal to the sum of three negative terms: minus the ohmic drop from right to left in the cell, the cathodic overtension a t the Zn 1Zn2+ electrode and minus the anodic overtension a t the Ag+lAg electrode. The product of E by the current is thus always positive and equal to the power of irreversibility of the cell, itself equal to the entropy production per unit time multiplied by the absolute temperature (8). It should be clear that the relative electric tension of an electrode (or its electrode potential, equal to the electric tension of cell (11) in the case of ZnI Zn2+)moves toward more positive (or less negative) values than the equilibrium one when the electrode functions anodically and toward less positive (or more negative) values when the electrode functions cathodically. Literature Cited
( 1 ) CHRISTIANSEN, J. A., AND POURBAIX, M., Pmc. XVIIth Cmfwmce IUPAC, Stockholm, 1953, Butterworths, London, pp. 82-5. ( 2 ) LICHT,T. S., AND DE B ~ T H U NA. E , J., J. CHEM.EDUC.,34. 433 (1957). J . A., J. Am. Chen. Sac., 82, 5517 (1960). ( 3 ) CARISTIANSEN, ( 4 ) VAN RYSSELBERGHE, P., Ekdrochim. Ada, 5, 28 (1961); 8 , 543 (1963); J . Electroanal. Chem., 2 , 265 (1961); 6 , 173 (1963). New complete report in English to appear to in Eled~oehim.Ada. Abbreviated re~ortin English . appear in J. EleUroanal. Chem. ( 5 ) ANSON,F.,J . CHEM.EDUC.,36, 394 (1959). J. B., J. Electroehem. Soc., 104, 255, 691 (1957); ( 6 ) RAMSEY, J. CHEM.EDUC.,38,353 (1961). P., J . Eleetroehem. ( 7 ) LANGE,E., AND VAN RYSSELBERQHE, Soc., 105, 420 (1958). LNGE, E., Electrochim. Acta, 8 , 657 (1963). P., "Ele~tro~hernical Affinity," Her( 8 ) VAN RYSSELBERGHE, rnann, Paris, 1955; "Thermodynamics of Irreversible Processes," Hermann, Paris, and Blaisdell, New York, 1963.
MACTLAC Fall Meeting
The Midwestern Association of Chemistry Teachers in Liberal Arts Colleges will hold its annual meeting at Lake Forest College, Lake Forest, Illinois, on October 23-24, 1964. Dr. John Coutts of Lake Forest College is the program chairman. Volume 41, Number 9, September 1964
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