0
RECENT DEVELOPMENTS CONCERNING THE SIGNS OF ELECTRODE POTENTIALS TRUMAN 5. LICHT a n d ANDRC 1. ~ ~ B E T H U N E Boston College, Chestnut Hill,Massachusetts
Tm
formulation of electrochemical definitions and sign conventions has received renewed attention in the period 1950-57. Mention should be made of committee reports issued by the International Union of Pure and Applied Chemistry (I.U.P.A.C.) meeting at Stockholm in 1953 (see J. A. Christiansen and M. Pourbaix (I)), by the Comitk International de Thermodynamique et Cinktique Electrochimiques (C.I.T.C.E.) (see P. Van Rysselberghe (2)), and of publications by E. Lange ( 5 ) , J. J. Lingane (4), A. J. deBkthune (5, 6), and J. B. Ramsey (7). I t is the purpose of this paper to review some of these recent developments, insofar as they pertain to the sign conventions governing what is commonly known as the "single electrode potential," the "halfreaction potential" or the "half-cell electromotive force." The allied problem of the s i p conventions governing the whole cell "potential" will be touched upon only in passing. A brief historical review may assist in understanding the background of these recent developments. HISTORICAL
The sign conventions governing electrode potentials have been a source of confusion ever since Walter Nernst (8) introduced his celebrated equation
in 1889. I n Nernst's picturesque but inaccurate language, E was described as the "potential difference m e t a l ~ e l e e t r ~ l ~ tP e ,as " the "solution pressure" of the metal, p as the "osmotic pressure" (by which Nernst meant the concentration) of the n-valent metallic ions in solution. R is the gas constant expressed by Nernst in volt-faradays (0.861 X v.-5/"K.-mole) and T is the absolute temperature. The sign of E was determined by the following criterion: when E is positive, i.e., in Nernst's own words (Qa), . . . when P > p, the solution becomes positively charged, the metal negatively charged, and E tends to produce in a closed circuit a, [positive] current which flows from metal to solution.
Since the measurement of E by means of a potentiometer requires a second electrode to complete the circuit, Nernst selected the Normal Hydrogen Electrode as a second or reference electrode to which the value zero was arbitrarily assigned. (The zero reference electrode was later redefined by G. N. Lewis (10a) as the Standard Hydrogen Electrode (SHE)). By applying his sign criterion, Nernst (Qb) then showed that VOLUME 34, NO. 9, SEPTEMBER, 1957
the potential E of an active metal such as Zn mas to be taken as +0.74 volts while that of a more noble metal such as Cu was -0.34 volts. These algebraic signs were preserved by G. N. Lewis and M. Randall (lob) in the tabulation of their "single electrode potentials" and by W. M. Latimer (11) in the tabulation of his "oxidation potentials." It should be pointed out that Nernst was not entirely self-consistent in the use of his E as a sign invariant quantity. His discussion of decomposition potentials (9bc) makes sense only when his E is interpreted as a sign bivariant quantity whose sign alters for different directions of the current flow. The E of an electrode was defined anew by Lewis and Randall (10c) in terms which make it a sign bivariant quantity. This is clear from the statement of their own sign convention (10d): . . . if we are considering the junction a t an electrode, we may represent this junction by the expression: electrode, electrolyte. We then say that the single p t e n t i a l measures the tendency for negative electricity to pass from right to left, that is from the electrolyte t o the electrode. On the other hand, we may express the junction as: electrolyte, electrode. Here again the potential measures the tendency of the negative current to pass from right to left. I t has the same magnitude as before, but the opposite sign.
The twofold sign of the E of Lewis and Randall has been illustrated by Latimer (11, 12) in the examples Zn, Znt+ Zn = Zn++ + 2e-,' E" = +0.76 volts (2) Zn++, Zu Zn++
+ 2e-
=
Zn E" = -0.76 volts
(3)
(These potential values must always be interpreted in conjunction with F t , HZ,H + Ha = 2Hf + 2e- E" = 0.0 volts). Latimer refers to (2) as the "relative oxidation potential" of Zn and to (3) as the "relative reduction potential" of Zn++. Of course, it is the "oxidation potential" (2) with the same sign as Nernst's original choice of sign, which has come to be popularly, albeit inaccurately, known as the "American sign convention (lla)." A completely independent criterion for the sign of electrode potentials had already been provided in the thermodynamic writings of J. Willard Gibbs (13). I n his monumental 'LEquilibriumof Heterogeneous Suhstances," written between 1875 and 1878, Gibbs dev e l o ~ sthe conce~tof the "electrical potential" of an The thermodynamic state of the electrons e- was not explicitly defined by Lewis and Randttll. This has recently been clarified by J. B. Ramsey (7). . See below.
electrode (ISa), which can be defined, in his language, as the measurable electrical potential difference between two "pieces of the same kind of metal connected with" the electrode in question and with the reference electrode, respectively. Since experiment shows that zinc is the negative terminal of the zinc-hydrogen cell, Gibbs' criterion leads to the conclusion that the electrode potential of zinc is negative. Ostwald (Id), using essentially the same criterion as Gibbs, prepared the first table of electrode potentials in 1887 (two years before Nernst's paper) with the dropping mercury electrode as a reference electrode. Ostwald remarked (144 : Zinc and cadmium were negative in all acids investigated, copper, antimony, hismuth, silver, and mercury were positive in all of them; tin, lead and iron show positive and negative values of 0.1 to 0.2 volt. On the average, the potentials are: zinc -0.7 V, cadmium -0.3, tin, iron and lead *0, copper +0.3 to +0.4, hismuth +0.4, antimony +0.3, silver +0.5 and mercury +0.8 volt. This is an expression of the 'potential series' of the metals in aqueous solutions, . . .
It is worth noting that the sign of the electrode potential deduced from the Gibbs-Ostwald criterion is not changed by a reversal of the direction of the half-cell reaction. The electrode potential based on Gibbs' and Ostwald's criterion of sign is a sign-invariant quantity. The Gibhs-Ostwald criterion leads to an opposite choice of sign for electrode potentials, from Nernst's criterion. This represents the genesis of a conflict that has continued to divide chemists, chemical engineers, teachers and students of chemistry up to the present time, especially in the United States (4-7, 15-30), Nernst's criterion was extensively adopted at first, except by Gibbs (21) who, in 1899, changed the sign of the Nernst equation (1) to conform to his own criterion of sign. The Gibhs-Ostwald criterion was revived by Abegg, Anerbach, and Luther ($2) in 1911, became generally adopted throughout Europe, and eventually found its way in the tables (hut not in the equations!) of later editions of Nernst's "Theoretical Chemistry" (23). The choice of the sign based on the Gibbs-Ostwald criterion has come to be known as the "European sign convention." I t is extensively used in America, also by practical electrochemists, engineers, metallurgists, physicists, analytical and biological chemists (16, 17). On the other hand, the signs deduced from Nernst's criterion have been preserved in the electrode potential tabulations given by Lewis and Randall (lob), by Latimer (11), and by a majority of American texts of physical chemistry (15). THE TEACHING PROBLEM
The divergence of meaning for the sign of the potential of a single electrode has presented a problem to teachers and students of chemistry. The need for defining a sign occurs in the first course of the chemistry curriculum when the electromotive series of the metals is introduced. American general chemistry texts are divided on this choice of sign (19, 20). Many of them present the active metals .above hydrogen with positive signs for the standard potentials ($0). This is the Nernst criterion which conforms with the tabulations of Lewis and Randall (lob) and of Latimer (11) and
with the practice of virtually all physical chemistry texts (16). Some general chemistry texts also discuss electrochemical cells or batteries, usually exemplified by the Daniell cell. The Daniell cell has an experimentally observed electromotive force of about 1.1 volts, with zinc the negative terminal and copper the positive terminal of the cell. Comparison with the electromotive series shows that the magnitude of the e.m.f. is numerically close to the difference of the standard potentials of zinc and copper. However, the observed polarities (Zn-, Cu+) do not agree with the signs of the standard potentials (Zn positive to Cu negative) tabulated in accordance with Nernst's criterion. The teaching problem introduced by the dual and divergent meanings of the signs recurs elsewhere, for example, in oxidation and reduction potentials, in electrodeposition and electroseparations, in electrochemical cells and batteries, in potentiometric titrations. For example, in the measurement of pH with the quinhydrone-calomel cell, a negative polarity for the qninhydrone electrode indicates an alkaline solution. The sign of the potential of the qninhydrone electrode (referred to calomel) must then he written a s positive or negative, according as Nernst's or Gibbs' criterion of sign is applied. RECENT DEVELOPMENTS
Several recent developments have contributed to the clarification of this problem. In 1953, Lingane (4) reiterated the sign invariance of the electrode potential when defined in a manner analngons to that already used by Gibbs (1Sa) in 1878. In the same year the International Union of Pure and Applied Chemistry (I.U.P.A.C.), meeting at Stockholm (I), distinguished between the sign bivariant E of Lewis and Randall and the sign invariant electrode potential and recommended a sign for the electrode potential which coincides with that already selected by Gibbs (13a, $1) and by Ostwald (14). In 1955, deBBthune (5) demonstrated that the I.U.P.A.C.'s "Stockholm" electrode potential coincides in practice with Gibbs' electrode potential (21) and proposed that the term Gibbs-Stockholm electrode potential and Gibbs' symbol V be applied to this quantity. He also showed by modern examples the thermodynamic information deducible from Gibbs' V. I n 1957, Ramsey (7) introduced the concept of the "electron chemical potential" E of an electrode-electrolyte system a t equilibrium, as a sign invariant quantity, measurable in volts, which represents an intensive thermodynamic property of the system, and whose numerical value has the same algebraic sign as that originally applied by Nernst to his electrode potential. Mention should also be made of Erich Lange's two masterful papers "Uber elektrochemische Grundhegriffe" (3), published in 1951 and 1952, and of the searching and exhaustive formulation of electrochemical concepts and definitions developed since 1950 by the ComitB International de Thermodynamique et CinBtique Electrochimiqnes (C.I.T.C.E.) (see P. Van Rysselberghe (2)). The discussion of these is largely beyond the scope of the present paper. However, it should be noted that the C.I.T.C.E.'s electrode potential while defined in language different from the I.U.P.A.C.'s JOURNAL OF CHEMICAL EDUCATION
is effectively identical ((Ba) with the quantity of the same name defined by the I.U.P.A.C.(i). THE SIGN INVARIANCE POTENTIAL
THE ELECTRODE
The sign invariance of the electrode potential when defined in the manner of Gibbs has been largely ignored, or even misunderstood, in many American texts. The sign bivariant E based on the thermodynamic system of Lewis and Randall (Joe), and of Latimer (is), has received much greater attention, instead. Lingane (4a) was the first American writer to point out, in 1953, that, although the sign of E depends on the direction in which the reaction is written, . . . the sign of the potential of the aclzral physical eleetmde a t which the half-reaction occurs with respect to the sign of the potential of the other electrode of the cell is, of course, fmed or invariant. For example, the zinc electrode in the . . . [zinchydrogen] cell is negative with respect to the hydrogen electrode regardless of the direction in which the schematic representation of the cell is written or the 'left-right' orientation of the actual cell on the laboratory bench. The potential of an actual eleeis distinct from the thermotrode (observed dynamio concept of the potential or e.m.f. of a half-reaction (defined quantity).
THE RECOMMENDATIONS OF THE I.U.P.A.C.
The Commission on Physicc+Chemical Symbols and Terminology and the Commission on Electrochemistry of the I.U.P.A.C. (1) meeting a t Stockholm in 1953, adopted certain "Conventions Concerning the Signs of
Electromotive Forces and Electrode Potentials." American members, or participants in the preliminary discussions, of the two commissions, included Roger G. Bates of the National Bureau of Standards, Frederick G. Iceyes of the Massachusetts Institute of Technology, Wendell M. Latimer of the University of California, Pierre Van Rysselberghe of the University of Oregon (now of Stanford University) and Thomas I?. Young of the University of Chicago. These conventions were put forward "to resolve the present serious conflict between two diametrically opposite but widely adopted practices in respect of electrode potentials (24)." The text of the I.U.P.A.C. conventions is included here, in extenso. The first part of the I.U.P.A.C. conventions deals with the e.m.f. of a cell: and ratifies the familiar whole-cell conventions of Lewis and Randall (Joe). The second part deals with the e.m.f. of a half-cell and with the so-called electrode potential. Inspection of the text of these conventions shows that the 1.U.P.A.C. uniquely defines the sign of the electrode potential while reaffirming the sign-hivariant electrode E of Lewis and Randall (10e) and of Latimer (12) already illustrated by equations (2) and (3). The I.U.P.A.C. denotes the latter quantity as the electrmnotiue force of a half-cell. I t stipulates that an E of the type of equation (3) with t,he electrons on the left may be called an electrode potential while an E of the type of equation (2) with the electrons on the right should NOT he called an electrode potential.
Convention Concerning the Signs of Electromotive Fomen and Electrode Potentials Adopted by the I.U.P.A.C. at StDekholm i n 1953 (1)
1.
The Eleetrorno!iae Force qfa Cell. The cell should he represented by a diagram, e.g., Zn
I
Znf+
I!
C u + + ( Cu we mean the electromotive forces of the cell^
The el~ctromotiveforce is e r p d in sign and magnitude to the elwtriral potentla1 of the metallic conducting lead an the right whcn that of the similar lead on the left is taken as zero, the r d l heing open. T h e n the ~eactionof the cell is written as l/Zn
+ l/.Cu++
-
+ '/Xu
L/zZn++
this implies a diagram so drawn that this reaction takes place when positive elert~irityflows through the cell from left to right. If this is the direction of the current when the cell is shorteircuited, as in the present example, the electromotive force will hc positive (nnless the ratio Cut+/Zn++ is extremely small). If, however, the reaction is written as
+
-
Pt, H2 I H L I Znt+
I
-- ++ +
Zn implying the reaction '/*Znt+ H+ '/Zn '/pH* P t , H1 IH'IICI- C b , P t . . . . . . . l/2H2 I/lC1? H + C1CI-+ Ag P t , H1 IHtllC1-AgCI, Ag.. . . .L/lH? AgCI-H+ Fe++ P t , H x H C J F e + +F, e + + + / P t ...l/zH1 F e t + + - H f
+
+ + +
+
where the electrode on the left is a standard hydrogen electrode. These electromotive forces may also be called relative elertrode potentials or, in brief, electrode potentials. When, on the other hand, we speak of the electromotive forces of the half-cells Zn lZn++ Pt. CI. ICI-
+
1 / 2 C ~ '/h++ I / p C ~ ~ + +' / Z n this implies the diagram Cu
we mean the electromotive forces of the cells
I Co++ 11 Zn++ I Zn
and the electromotive force of the cell so specified will he negative (unless the ratio C u + + / Z n f + is extremely small).
2. The Eleetmnotive F o m of a Half-Cell and the so-called Eketrode Potential. When we speak of the electromotive forces of the half-cells
VOLUME 34, NO. 9, SEPTEMBER, 1957
--
Zn Zn++llH+IH?, P t implying the reaction H+ l / ~ Z n + + 'I2H2 '/,Zn P t , Clr IC1-llHt IHz P t . . . . . . .C1H + '/lCln I/*H2 Ag, AgCl ICI-IIHf I H ~P ,t . . . . .Ag C1-+ H+-AgCl f lIpH2 '/sHs PtIFe++,Fef++llH+IH*,Pt. ..Fe,++ H + - F e t + +
+
+ ++
+
+
+
where the electrode on the right is a standard hydrogen elect~ude. These electromotive forces should NOT be called electrode patenti&.
Therefore, we may infer from the I.U.P.A.C. eonventions that the half-cell e.m,f. of the standard zinc electrode can have the two values +0.76 volts and -0.76 volts, depending on the orientation of the halfcell diagram and the associated direction of the electrode reaction, hut that only the value -0.76 volts may be referred to as the electrode potential of zinc. This essentially constitutes the "Stockholm" definition of the electrode potential. The Gibbs-Stockholm Electrode Potential. The 1.U.P.A.C. gave no symbol to its electrode potential and did not develop its relation t o thermodynamic properties. deB6thnne (6) showed that both can he done by starting from the beautifully elegant thermodynamic formulation of electrochemical cells developed by J. Willard Gibbs (IS), and proposed that the name Gibbs-Stockholm electrode potential and Gibhs' symbol V he assigned to this quantity. Consider the standard zinc-hydrogen cell Zn, Zn++l/H+, H*, Pt
(4)
where the double bar means that the liquid junction potential has been eliminated (10f, llb). Let the cell be connected to, and in balance with, a potentiometer (see figure). The observed potential difference (after recalculation back to the hypothetical standard state of the cell) is 0.76 volts with zinc connected to the neg-
ative terminal of the potentiometer. Therefore, one may represent the experimental facts by the equation Vo(Pt, H., H+) - Vo(Zn, Zn++) = +0.76 volts
V"(Pt, Hx,H')
=
0
I
-
+.76
V"(Zn, Zn++) = -0.76 volts
This quantity may be called the Cibbs-Stockholm electrode potential of the standard zinc electrode. The sign invariance of this quantity can readily he demonstrated as follows (6). Let the potentiometer be thrown out of balance by an infinitesimal amount. An infinitesimal current can be allowed to flow in the direction of reaction (2) or of reaction (3), without altering the electrical potential of the piece of metal connected with the zinc electrode by more than an infinitesimal amount from the value -0.76 volts, when the value 0 is assigned to the electrical potential of another piece of the same kind of metal connected with the hydrogen electrode. I n the limit of a reversible current flow in either direction, the potential is unaltered from the value -0.76 volts. Therefore, since V is sign invariant, one may write indifferently (8)
J. B. Ramsey (7) has introduced the concept of the electron chemical potential of an electrode. He showed that the difference of the electron chemical potentials of two different metals is a measurable quantity. I n contrast, the electrical potential difference between two points in dissimilar phases is not a measurable qnantity (3), and is even believed by E. A. Gnggenheim ( g 5 ) t o be devoid of physical significance (see, however, H. Strehlow (26)). Let the electron chemical potential, which may be ahbreviated to ECP, and denoted, following Ramsey, by the script capital 8, be defined by E C P = & = Fs-/5
.
Std. Zn Electrode
Std. HI Electrode
Sch-matic Diagram of Zinc-Hy&ogen Cell in its H y p o t h a t i d Standard Stet. Illuntrding the Various Con-t. Used to Repr-ont the Standszd Potential of a Zn. Zn + + Eleotrods
zn, Zn++. H + HXm e d l presumed to be in their standard states (actual or hypothetiaal) of unit activity. .O(Zn, Zn++) = 8 ( Z n + + . Zn) = fO.76 v. is the eleotron chemical DO-
tential (ECP) of the zinc phase of the standard Zn, Zn +*electrode when the second eleotrode of the cell is a SHE and the value 0 is assigned to the ECP 6 of the platinum phase of the SHE (Ramaey 1957). E0(Zn. Zn++) = 0.76 v. = -AFo/ZT, where A F " is the standard free 28- (in the SHE): energy change of the half.mIl reaction: Zn = Zn+* which is a shorthand notation for the whole-ceU reaation: Zn 2Ht(a = 1) = Zni+ Hl(o = 1) (Lewis and Rhoda11 1923). E0(zn++, zn) = -0.76~.= - A F 0 / 2 7 , where A F o is t h e standard free 28- (in the SHE) = Zn, energy ohange of the half-cellreaction: Zni* which is a shorthand nothtion for the lahole-ceu reaction: zn + + H,(s = 1) = Zn 2Hi(a = I)( Lewia and Randall 1923). Vo(Zn. Zn++) = VQ(Zn++,Zn) = -0.70 u. is the electrical ~ o t e o t i a of l a "pieoe of meter' connected with the standard Zn, Z n i + electrode when the second electrode of t h e cell is a SHE and the vslue 0 is asaigned to the eleotrioal potential of a second "pieoe of the ahme kind of metal" eonneoted with the SHE (Gibbs 1878, 1899; Ostwald 1887; Abegp. Auerbsoh and Luther 1911: Lingane 1953; IUPAC (Stockholm) 1953: CITCE 1955; deBBthune 1955).
+
+
+
+
+
(7)
The Electron Chemical Potential. I n a recent paper,
+
v
(6)
it follows that
V0(Zn, Zn++) = VQ(Zn++,Zn) = -0.76 volts
POTENTIOMETER
(51
where the V's denote, in the language of J. Willard Gibbs (1Sa) "the electrical potentials in pieces of the same kind of metal connected with the two electrodes," and the superscripto refers to the standard state (fog). Therefore, if one assigns
+
+
(9)
where Pa- is the partial molalfree energy (electrochemical potential) of the electrons in a given metallic phase and 5 is the faraday. The ECP & is therefore a potential, expressible in volts. When two metals, A and B, are brought in contact, they come to equilibrium. with respect to the exchange of electrons so that &(A) = &(B)
(10)
The zero state for the ECP & is selected as the ECP 8. of the platinum phase of the usual standard hydrogen electrode (SHE). Consider once again the hypothetical standard state zinc-hydrogen cell (4) in balance with a potentiometer (see figure). Let Cul and Cnz be the two copper leads. connecting the Zn and Pt, respectively, to the poten-. tiometer. Clearly ~ ( C n l ) = &(Zn) and &(Cud = &(Pt). The difference &(Cnl) - E(Cu2) is experi-. mentally determinable from the measurable electrica1. potential difference between Cul and Cu2. Since the. JOURNAL OF CHEMICAL EDUCATION;
electron chemical potential & increases as the electrical ~otentialbecomes more negative, we have &(Cu,) - &(Cul) = V(Cul)
- V(Cu,)
=
f0.76 volts (11)
Therefore
(a)] to occur, that is the greater the decrease in free energy ( -AF) accompanying this change [reaction (a)], the greater will be the value of F. in the metal electrode of that electrode system at equilibrium [reaction (b)]. In terms commonly used, it may be said that the greater the strength of the reduced state, as a reducing agent, the greater will be the value of Fa- in the electrode.
ILLUSTRATION OF THE SEVERAL CONCEPTS
In view of the selected zero state, and the fact that the cell is a standard state cell, this can be expressed as &'(Zn, Zn++) = +0.76 volts
(13)
The E, being a thermodynamic property of a system a t equilibrium, is a sign-invariant quantity. It is equal, both in magnitude and in sign, to Nernst's original "electrode potential" E [equation (I)]. However, it is fundamentally different in meaning from Nernst's E and also from Lewis and Randall's E. It is related to the GibbsStockholm electrode potential V by the general relation & =
-V
(2) The notation E(Zn, Zn++) refers to the electron chemical potential of the electrons in the zinc phase of a Zn, Zn++ electrode. The notation V(Zn, Zn++) does not denote the electrical potential of the zinc phase of a Zn, Zn++ electrode, but rather, as pointed out by Gihbs (lSa, $1) the electrical potential of the metallic conducting lead connecting the zinc electrode to the potentiometer, referred to the electrical potential of another conducting lead "of the same kind of metal" connecting the reference electrode to the potentiometer. Under isothermal conditions, the chemical nature of the metallic leads (usually copper) is immaterial. The popular colloquial phrase "the electrical potential of the zinc electrode" (e.g., Lingane, vide supra) usually means the same thing as V(Zn, Zn++), i.e., it does not mean what it literally says. The Themnodynamic State of the Electrons. Ramsey (7) has also clarified the thermodynamic state of the electrons which appear in all half-cell reactions as usually written, when he states The state of the electron substance is that of electrons in the electrode of the defined standard hydrogen electrode system at equilibrium.
He brings out a very interesting point by comparing the two half-cell reactions: '/1Zn = '/2Zn++ (b) '/.Zn = '/rZn++
+ e+ e-
Zn, Znt+ Cu, Cu'+
Zn = Znt+ Cu = Cufi
++ 2e2e-
E" +0.76 -0.34
V" -0.76 +0.34
6' +0.76 -0.34
(14)
Two words of caution are in order in applications of equation (14): (1) this equation is really a shorthand notation for the more complete equation & - s0(Pt, Hx, H + ) = Vo(Pt, H2, H+) - V (15)
(a)
The potentials of electrodes can be expressed in terms of the sign bivariant E of Lewis and Randall, or in terms of the sign invariant Gibbs-Stockholm electrode potential V, or of the sign invariant Ramsey electron chemical potential & (of opposite sign) as in the examples
(in the SHE) (in the Zn)
The free energy A F of reaction (b) is zero if the Zn, Zn++ electrode system is a t equilibrium. It can readily be proved that the partial molal free energy of the electrons in the Zn is then equal to the jree energy drop of reaction (a) where the electrons are in the SHE. In Ramsey's words, . . . the value of the partial molal free energy of the electrons,
iZ-,in the electrode of any electrode system at equilibrium is determined by the tendency of the substances constituting the reduced state to change to the substances, constituting the oxidized state, and to electrons in the atate in which they exist in the hydrogen electrode in the standard hydrogen electrode system a t eqoilibrium. The greater the tendency for this change [reaction
VOLUME 34, NO. 9, SEPTEMBER, 1951
The electrons e- are always understood to be in their standard state, i.e., that of electrons in the metallic phase of the standard hydrogen electrode (SHE). A half-cell reaction such as Zn = Zn++ 2e- is always understood to be a "shorthand" notation for the whole-cell reaction Zn 2H+ (a = 1) = ZnC+ Hz (a = 1). Calculations of interest include: the free energies of half-cell reactions, the electromotive forces of whole cells and the free energies of whole-cell reactions, the potentials of nonstandard state electrodes. The method of carrying out these calculations by use of E, V, and & will be illustrated below by examples. The Free Energies of Half-Cell Reactions. Consider a half-cell reaction written with the electrons on the right, i.e., an oxidation:
+
+
+
Zn = Zn++
+ 2e-
(16)
where the state of the electrons intended is that of electrons in the metallic phase of the SHE. The free energy change of this half-cell reaction can be computed through the thermodynamic relations, based on Gihbs' equation (699) (ISb), A F = -n5E = +n5V = -nSE (for oxidations)
(17)
For reaction (16), the standard free energy is (10h) AFO
=
-25(+0,76v.)
=
+25(-0.76v.) = -25(+0.76v.) = -1.52v.5 = -35.05 kcal.
(18)
Conversely, for a half-cell reaction written with the electrons on the left, i.e., a reduction: Zn++
+ 2e-
=
Zn
(19)
the free energy change can be computed through the relations AF = -n3E = -n5V = +nS& (for reductions)
(20)
For reaction (19), the standard free energy is AF" = -25(-0.76v.)
=
-25(-0.76v.) = +25(+0.76v.) = +1.52v.5 = f35.05 kcal. (21)
The Whole-Cell Electromotive Force. Consider the cell Zn, Zn++IlCu++, Cu
(22)
By the conventions of Lewis and Randall (10e) and of
the I.U.P.A.C. (I) the corresponding whole-cell reaction is
For example, for cell (22) and reaction (23), the standard frze energy is
+ (+0.34)lv.
AF" = -23(+1.10v.)
= -25[(+0.76) 25[(-0.76) - (+0.34)lv. 2%[(-0.:34) - (+0.76)lv. = -2.20 v.5 = -50.7 keal. = =
The standard vhole-cell e.m.f. Eo (cell) is given by the relationsZ Eo(cell) = ES(Zn, Zn++)
+ E"(Cut+, Cu)
=
(+0.76)
-
= VQrjlhr Voleit = (+0.34) - (-0.76) = &'lett Gopisat = (+0.76) - (-0.34) = +1.10 volts
+
(+0.34)
For cell (25) and reaction (26), the standard free energy is
+
= -2!3[(-0.34) 2%[(+034) - (-0.76)lv. = 2!3[+0.76) - (-0.34)lv. = +2.20v.S = +50.i kesl.
=
with the cell reaction
+ ne-
(31)
where the electrons e- are in their standard state (discussed above), the potentials can he expressed as follows: the Gibbs-Stockholm electrode potential V,
the standard whole-cell e.m.f. E o (cell) is given by the relations
-
(30)
The Potential of a Non-standard State Electrode. This, of coursc, is the quantity given by Xernst's celebrated equation (1). Rewritten in more modern form, and expressed in terms of the standard potential and the activities (log) or activity products (Ox) and (Red) of the oxidized and reduced forms of the electromotively active chemical substances appearing in the generalized electrode reaction Red = Ox
Eo(cell) = E0(Cu, Cu++)
+ (-0.7611~.
AFo = -25(-1.10v.)
(24)
The polarity of the cell can he conveniently determined from the V or the & values, as follows. The electrode having the larger (algebraic) value of V, in this instance Cn, is the terminal of the cell. The electrode having the larger (algebraic) value of the ECP &, in this instance Zn, is the -terminal of the cell, i.e., the source of electrons to the external circuit. For the cell written in the reverse direction
(29)
V
=
V"
+ (RTln.3) In (Ox)/(Red),
(32)
the Ramsey electron chemical potential &
+ ED(Zn++,Zn) = (-0.34) +
= VD,i.st VDl,rt = (-0.76) = (-0.34) = Eo~,rt = -1.10 volts
- (+0.34) - (+0.76)
(-0.76) (27)
Although the sign of the whole-cell e.m.f. is changed by a reversal of the whole-cell diagram and of the wholecell reaction, the polarity of the cell remains unchanged, i.e., Cu is still the terminal of the cell, as is clear from a comparison of the two Gibbs-Stockholm V values. The ECP values & of the two electrodes also remain unchanged. The Free Energy of a Whole-Cell Reaction. The free energy of a whole-cell reaction, such as (23) or (26) is conrenientlv calculated from the relations. based on Gibbs' eqnition (699) (ISb),
+
American chemists and engineers are in substantially complete agreement with the choice of sign of the whole-cel1e.m.f. embodied in equations (24) and (27), i.e., a positive E value corresponds to a spontaneous tendency for the flow of positive electricity through the cell from left to right. The I.U.P.A.C. st Stockholm has internationally ratified this ohoice of sign by defining E (cell) as VriZht - VL.T~ (1). European chemists appear to he divided on the choice of sign for the whole-cell "potential." Some European chemists prefer to take i t as Vl.rt - Vri.ht. The C.I.T.C.E. (reference (db)) has attempted t o unravel this conflict by introducing the alternative expnssions for a mhole-cell: eledrmotive f m e , elektrmotarische K m f t , fmee klectromtrice = Vright - Vllft
while Zellspannung, tension de cellule = V L *-~ V,iSbt
No use is made of C.I.T.C.E.'s Zellspannung in the present paper. P. Van Rysselberghe (67) has proposed the term electric tension of a cell as a translation of Zellspannung.
the Lewis and Randall E must be expressed in two ways: for reaction (31), it is while, for the opposite reaction Ox + nec = Red it is E
=
E'
- (RTInS) In (Red)/(Ox)
(35)
(36)
SUMMARY
The conflict regarding the signs of electrode potentials was originated by the adoption of two independent criteria for the selection of this sign: Nernst criterion (1889) which has evolved into the "American sign convention," and the Gihbs (1878-Ostwald (1887) criterion which has come to he known as the "European sign convention." These two criteria lead to opposite signs for the representation of identical observable laboratory information. The half-reaction potential E of Lewis and Randall and of Latimer is defined in such a way as to he capable of having either sign, de. pending on the postulated direction of the half-cell reaction. When this reaction is written as an oxidation, the corresponding "oxidation potential" E has the same sign as Nernst's original "electrode potential" E [equation (I)]. The I.U.P.A.C., meeting a t Stockholm in 1953, has recognized the sign-bivariant E of Lewis and Randall, and recommended further that the term electrode potential be applied only to the E whose sign is the same as the sign of the potential which can also be deduced from the Gibbs-Ostwald criterion. It seems appropriate therefore to refer to such a quantity as the JOURNAL OF CHEMICAL EDUCATION
Summary of T h e ~ m o d ~ n a mRelations ic for Reversible Electrodes e n d Cells Based o n t h e Lewis a n d Randall E. t h e Gibbs-Stockholm V, a n d t h e Ramsey 6. Reaction Oxidation : Red
-
-
or
Reduction: Ox n e
+
Red
-
Ox
[
+ nec
Ox
Red
+ nc-
-
-
Function in ezpresserl twms 1 of Standard state electrode Nanatmdard state electrode .Forms of the Nernst Equation
Electrode Electron Half-cell 8.m.f. potential chemical potential (Half-reaction. potenlid) & ( s i g n invariant) V (sign invariant) E (sign bivariant) -E" (oxidation) = V" = -6= E" (reduction) = V = -6 -E (oxidation) = E (reduction) k = V" (RT1n.J) E = 8' - IRT/nS) E (oxidation) = E" (oxidation) In (Ox)/fRedi In (Ox)/(Red) -(RT/nS) In (Ox)/(Red) E (reduction) = E' (reduction) -(RT/n%) In (Red)/(Ox)
+
0xidat.ioion free energy
= -n5E (oxidation) = +nRV = -nS& Reduction free energy 4F (reduction) = -nSE (reduction) = -n5V = +nJE 'e.m.f. of the whole cell: left electrode 1) right electrode E (cell) = E (oxidatian)~,n = Vri.ht - Vl.,t = E k r t - G.ert E (reduction),i.h. Redm = E (axidation)m Ox.i.ht = -E (oxidatian),i.ht Ox~.rt f Redpishi Whole cell reaction free energy 4F (cell) = -n5E (cell) = -nSE (cell) = -nSE (cell) = nS(Vl.r~ - V T i g d = nS(Eripht - E w J In all half-cell reactions, the electrons e- are in their standard state, i,e. that of the electrons in the metallic phase of the standard i, alway~understood to mean the whole-0-11-reaction: Red hydrogen electrode (SHE). A half-cell reaction such as: Red = Ox nHt(a = 1) = Ox (n/2)Hl(a = 1).
Ox
+ nec
4F (oxidation)
Red
+
+
+
+
L'Gibbs-Stockholm electrode potential" and to represent it by Gibbs' symbol V , as suggested by deBBthune in 1955. The sign invariance of this quantity was discussed by Lingane in 1953. Ramsey, in 1957, introduced the concept of electron chemical potential (ECP) 8 and showed i t to be an intensive thermodynamic property of an electrode, electrolyte system a t equilibrium. The ECP & is expressible in volts, is sign invariant, and is equal, in sign a.nd magnitude, to Nernst's original E [equation (I)], although fundamentally different in meaning. Ramsey's ECP E therefore provides a physically meaningful and illuminating description of the potentials tabulated in so many of our American texts with algebraic signs following the Nernst criterion. The Nernst criterion has been in continuous use for 68 years. Lewis and Latimer have successfully based their practical system of chemical thermodynamics on it, and it has become second nature to large numbers of American chemists. The Gibbs criterion, which is based on Gihbs' application of the first and second laws of thermodynamics to an electrochemical cell, is more convenient for laboratory work and for the handling of nonreversible electrodes and cells Its wide acceptance, under a variety of designations and symbols, by practical users of electrochemistry, attests to this, and bears witness to the practical side of Gibbs' theoretical genius. American students of chemistry and chemical engineering must, of necessity, become acquainted with the whole variety of meanings which the sign of an electrode potential can have. It is the hope of the authors that the present review mill have made a modest contribution to this goa,l. Far example Gibbs' equation (700), the last one in his Equilibrium of Heterogeneous Substances" (13b), contsins the genesis of the application of thermodynamics to irreversible electrochemical cells. This subject has rrwntly received considerable development at the hands of P. Van Rysselberghe (27).
VOLUME 34, NO. 9, SEPTEMBER, 1957
+
ACKNOWLEDGMENT
The authors wish to express their appreciation to Professor J. B. Ramsey for making his paper on the Electron Chemical Potential (7) available to them in advance of publication and for valued comments. They also wish to express their thanks to the International Nickel Comany for a Grant-in-Aid in partial support of this work. LITERATURE CITED
J. A., A N D M. POURBAIX, "Conventions Con(1) CHRISTIANSEN, cerning the Signs of Electromotive Forces and Electrode Potentials," Comples Rendus of the 17th Confwence of the Zntenatinal Union of Pure and Applied Chemist~y,held in Stockholm, 1953. Maison dc la Chimie, Paris, 1954, pp. 8284. P., "Electrochemicsl Nomenclature (2) VAN RYSSELBERGHE, and Definitions," Report of Commission 2, Proceedings of the fith Meetinn of the International Committee of Eledrochemical ~her&&namica and Kineties (c.I.T.c.E.) held in Poitiers, 1954, Butterwarths ScientXc Publications, London, 1955, pp. 20-49. (a) Definition 4.17; (b)definition4.10. (3) LANQE,E., Z. Elektmehem., 55, 76-92 (1951); 56, 94-106 (1952). (4) LINQANE, J. J., "Eleetroanalytical Chemistry," IntersciOD. 33.. 94.. 181-3: ence Publishers. New York. 1953.. .. (a),P. 33. (5) ~ ~ B ~ T H UA.N J., E , J. Eledroehem. Soc., 102, 288C-92C (19.55). \ --,-
(6) ~ ~ B ~ H u-4.NJ., E J. , Electmxhem. Soc., 101, 252C (1954). (7) RAMSEY, J. B., J. Electrochem. Soc., 104, 25560 (1957). (8) NERNST,W., (a) 2. physik. Chem., 4, 129-81 (1889); (b) "Theoretische Chemie," 2nd German edition, Enke, Stuttgart, 1898, pp. 66&8. (9) NERNST,W., Be?., 30, 1547-63 (1897); (a) p. 1548; ( b ) p. 1557; ( e ) p. 1550. "Thermodynamics and (10) LEWIS,G. N., AND M. RANDALL, the Free Energy of Chemical Substances," McGraw-Hill Book Co., Inc., New York, 1923, (a)pp. 404-5; (b) p. 433; (c) pp. 401-6; (d) p. 402; (e) Chaps. XXIX and XXX; (f) p 399; (g) Chap. XXII; (h) p. 434. (11) L A ~ M E R W., M., "Oxidation Potentials-The Oxidation States of the Elements and Their Potentials in Aqueous
Solutions," 2d ed., Prentice Hall, New York, 1952. (a) p. 3; (b) p. 7. (12) LATIMER, W. M., J. Am. Chem. Soe., 76, 1200 (1954). (13) GIBBS,J . WILLARD,"The Equilibrium of Heterogeneous Substances," Trans. Conn. Aead., 3, 108-248, 343-524 (1875-8), reprinted as pp. 55-349 in "The Collected Works of J. Willard Gihbs, Volume I, Thermodynamics,'' Longmans, Green & Co., Inc., New York, 1928. (a) Val. I, pp. 332-3; (b) equations (699) and (7W), Vol. I, p. 349. (14) OSTWALD, W., Z. physik. Chem., 1, 583-610 (1887). (a)
" r. and ""=. (15) The usage of the Nernst criterion of sign is exemplified by: (a) EWING,G. W., "Instrumentd Methods of Chemical
Analysis," MoGrrtw-Hill Book Co., New York, N. Y., 1954, p. 29; (b) MOORE,W. J., "Physica1 Chemistry," 2nd ed., Prentice-Hall, Inc., New York, 1955, Chap. 15; (c) PRUTPON,C. F., AND S. H. MARON,"Fundamental Principles of Physical Chemistry," Revised ed., The Macmillan Ca., New York, 1953, Chap. 17. (16) The usage of the GibheOstwald-Stockholm criterion of sign I. M., AND J. J. LINis exemplified by: (a) KOLTHOFF, GANE, " P o l ~ ~ o p p h y ,2nd " ed., Interscience Publishers, Inc., New York, 1952, Vol. I, p. 190; (b) PERRY,J. H., "Chemical Engineers' Handbook," 3rd ed., McGrawHill Book Co., Inc.. New York, 1950, pp. 1785-86; (c) WEST,E. S., AND W. R. TODD,"Textbook of Bioehemistry," The Macmillan Co., New York, 1952, Chap. XXII. (17) ~ ~ B ~ T H U A.NJ., E COTOSG~, , 9 , 3 3 6 4 4 (1953). (18) BANCROFT, W. D., T~ana.Eledrochem. Soc., 33, 79 (1918). (19) General chemistry texts based on the Gibhs-OntwaldStockholm criterion of sign include: (a) SNEED,M. C ,
J. L. MAYNARD, AND R. C. B ~ S T E D"Generd , College Chemistry," 2nd ed., D. Van Nostrand Co., Inc., New York, 1954, p. 296; (b) STEINER,L. E., AND J. A. CAMPBELQ "General Chemistry," The Macmillan Ca., New York, 195d, p. 431. (20) General Chemistry texts based on the Nernat criterion of JR., sign include: (a) HOPKINS,B. S., AND J. C. BAILAR, "General Chemistry far Colleges," 5th ed., D. C. Heath L., "General and Co., Boston, 1956, p. 89; (b) PAULING, Chemistry," 2nd ed., W. H. Freeman and Co., San Francisco, 1954, pp. 254-7. Letter to Professor Wilder D. Bancroft (21) G r ~ s sJ,. WILLARD, of Oornell University, May, 1899; reprinted in "The Collected Works of J. Willard Gihbs, Volume I, T h e c modynamics," Longmans, Green & Co , Inc., New York, 1928, p. 429. A N D R. LUTHER,"Messungen (22) ABEGG,R., F. AUERBACH, elektromotorischer Krafte galvenischer Ketten," Ahhandlungen der deutschen Bunsengesellschaft, No. 5, Halle (1911). (23) NERNST,W., "Theoretical Chemistry," translated from the 7th German Edition by H. T. Tizard, The Macmillan Co., Ltd., London, 1916, pp. 793-817. (24) Comptes Radus o j the 17th Conference o j the I.U.P.A.C., held in Stockholm, 1953, Maison de la Chimie, Paris, 1954.. D. 60. (25) GUGDENHEIM. E. A., J. Phy8. Chem., 33, 842 (1929) (26) STREALOW. . H... Z. Elektroehmn.. 56, 119-129 (1952). (27) VAN RYSSELBERGHE, P., "Electrochemical Affinity," Hermann et Comprtgnie, Paris, 1955. A. E., J. CREM.EDUC.,33, 564-74 (1956). (28) REMICK,
.
JOURNAL O F CHEMICAL EDUCATION
