T H E ELECTRODE, COKTACT, AND ELECTRO-KINETIC POTENTIALS OF GALVANIC CELLS BY JAROSLAV HEYROVSK+
The application of thermodynamics to the various mechanisms through which the electrode potentials may be supposed to arise lead to different formulae. All such expressions are of course correct when they have been obtained from a strictly reversible cyclic process and, moreover, must give coinciding results, independently of the assumed mechanism. Recently the author1 deduced a formula by assuming ionisation by collision as the origin of the charge at an electrode; in that way the basigenic property of the metal could have been included2. A still simpler formula for the electrode potential can be deduced in the following way. General Deduction of the Formula Imagine a monovalent metal, Me, dippingintoasolutionofitsions (Fig. 1 . A ) . Transfer one gram-atom of the metallic vapour from the metallic surface into an ionisation chamber, where the metallic atoms, the free metallic ions and electrons are all kept at a pressure p ; the work we A do in transferring is R T log ~ / P Mwhere ~, FIG.I PbIe denotes the metallic vapour tension. The Electrode, Contact, and ElectroNow ionise one gram-atom of the Kinetic Potentials vapour into ions and electrons, effecting this by collision with electrons moving between the electrodes of the chamber with an energy I.e, where I denotes the “ionisation potential” of the metallic vapour under the physical conditions of the chamber and e the charge of an electron. I n other words, the free energy of this process is for a gram-atom of the vapour - 1.F or we have to do work +I.F (when F denotes one faraday) to ionise the gram-atom. Next condense the electrons from this chamber back into the metallic electrode, transferring them first to the pressure P,, a t which they exist in the vapour phase close to the metallic surface and passing them across the metallic surface. The two work terms are x.RT log P,/p++F, the coefficient X ( = 0 . 0 4 1 7 ) has to be applied when treating the electrons as a gas3 (+ denotes the transition potential). ‘Proc. Roy. SOC., 102A, 628 (1923). This communication has been criticised by J. A. V. Butler, whose objections were shown to arise from an erroneous understanding of the transfer of metallic ions, where Mr. Butler confused concentration terms. (pee Chem. News 128; 294; 129, 329, (1924). 3 A . D. Fokker: Arch. n6erl. (3) 4, 394 (1918); A. H. Lorentz: “Bericht Solvay 1911;” Abh. Bunsen Ges. No. 7 p. 32 (1914). 2
POTENTIALS O F GALVANIC CELLS
343
The gaseous metallic ions have to be brought from the ionisation chamber into the electrode solution with a vapour pressure Psoland containing cations of the-metal in a concentration [Me’sol]. This transfer can proceed reversibly if the ions be brought from the pressure p , at which they existed in ionisation chamber to the very small pressure p’, a t which they are present unsolvated in the solution. This minute fraction of unsolvated bare ions must be in equilibrium with the solvated ions of the solution according to the action: Me’ + n solvent molecules-+Me’s,l,
with an equilibrium constant
Thus to bring the ions from the chamber into the solution requires work R T log p’/p, or substituting from the equilibrium constant, it becomes
[Me’’i1- RTlog
Ksol. P,,?. P The latter term expresses the free energy change when the gaseous ions get solvated and can be denoted as the “free energy of solvation,’’ HR4,.F, of ions entering a solution of the vapour tension Pso,. If no such solvating action existed, HM,.would be zero. R T log
When crossing the liquid-vapour interface, electric work might arise in overcoming a surface potential 7 , due to adsorption or to an orientation of solvent molecules. 4
Taking its sign as positive when the positive side of such a double-layer is closer to the surface, this work is -7.F.
To deposit the ions from the solution into the metal we have to bring them either directly from the unsolvated portion, or through this from the solvated one-across the interfacial double-layer potential, +, which exists a t the electrode equilibrium between the metallic and the solution phase. If the positive side of this double layer lies in the metal the work is
[email protected]. Summing up all the work terms of this cycle, we have o = R T log p/PA1e
+ I.F. + X. R T log P,/p + R T log [Me’,,ll - RT log K~,].
Pso,”+rl/
[email protected] P (1) The potentials +-q+@ are very closel? related to the electrcde potential of the metal in solution; this becomes evident if we imagine the following transfers in a cell consisting of two metals, Me and Me’, both in solutions of their ions: I. Transfer of one gram-ion of the metal Me into its surrounding solution /
[email protected]/; the transport of one-half gram cation from this solution into the other, and one-half gram anion in the reverse direction /(q-q’).F/ disregarding the diffusion potential between the two solutions; the deposition of one gram-ion of the second metal at the electrode Me‘ /@’.F/.
346
JAROSLAV HEYROVSKY
2. Transfer one F. of electrons from the first metal over the dry surface /-$.F/, condense it to the concentration of electrons existing above the second
dry metallic surface /x'RTlog.P'e/Pe/
and bring it into t,he second metal
/$'.F/. The result is that we have dissolved one gram-ion of the first metal and electrodeposited the equivalent of the second metal: thus the sum of the work terms in I . and 2 . must be equal to /n'- a/F, where T and d denote the real electrode potentials of the electrodes Me and Me', and T ' - T the E. M. F. of this galvanic cell. We have thus: T'
- T = - + + q -$
- ( -@'+q '
-#I)
+(x.RT/F) log Pk/Pe
from which RT a=#-q+++X.Tlog
P,+a constant.
Since we measure only differences of potentials, P will be characterised equally well without the constant, so that we can simplify equation (I) expressing :
Before verifying formula ( I ) by experimentally determinable constants, let us deduce similarly the potential of a metalloid electrode, (Fig. I . B). Evaporate from the metalloid electrode half a gram-molecule of the diatomic metalloid xz bringing it first to atmospheric pressure, dissociate it into atoms x and expand to a sniall pressure px, at which the metalloid atoms, their gaseous anions X' and the free electrons coexist in an equilibrium box; bring out of the electrode one faraday of electrons under the small pressure P,, a t which they exist above the electrode and place them in the same equilibrium box expanding to p,; let them unite to a gram-anion of X I , a t the pressure pxt in the equilibrium box and remove this gram-anion from the box. Now allow the anions to be solvated to the vapour pressure of the solution and concentrate them from pXt to the concentration [x',,~I of the solvated anions in the solution. Finally dip'them into the solution crossing the surface potential q and deposit them across the potent'ial @ a t the electrode completing thus the cycle. The sum of the free energy terms then is:
+
+
+
0=1/2 RTlog 1/Px2 D,,.F R T log PX/1- $.F. R T log p,/P,denotes the dissociation Hxl.F RT log ( X + ' ~ ~ J / ~q~. ~F-9.F. (Dx, energy).
+
+
Here again, as in the previous case, we can substitute for q--9-$-
RT log Pe=a, F
347
POTENTIALS OF GALVANIC CELLS
and for the logarithm of the constant of the equilibrium box, -RT log
p a PXl
the electron-affinity of the metalloid to the electron, +E. We obtain: 7~
=
RT - log g F
E - Dx,+ E + H,,
-
F ‘log [x’~,,~]
(3)
It will be observed, that the influence of the pressure, solvation and concentration upon the sign of the potential is reversed to that which was deduced for metallic electrodes. During these reversible processes, no attention was paid to the fact, that electrostatic attractions between the charged particles have to be overcome. However, these effects in the complete cycle almost cancel each other, so that their actual influence upon the potential must be small (hardly observable in concentration cells, if not compensated by the activity increase, which works in the opposite direction). The idea of introducing the photoelectric effect and ionization potentials into the theory of E. M. F. is due to I. Langmuir (Trans. Am. Electrochem. SOC.29,125 (1916)). In this work, however, the solution interfacial potential is disregarded. Fajans (1.c.) first used the thermodynamic cycle involving the “heat of hydration;” in this way he calculated the heat of hydration, from “absolute potentials” of potassium and hydrogen; this procedure was criticised by Haber (ibid. p. 750) owing to the disregard of the transition potentials from the metallic phase; however, as the difference of “absolute potentials” used by E’ajans happens to coincide with the difference of the electrode potentials, his result has to be regarded as correct.
Calculation of the Electrode Potentials If we could substitute in formulas ( 2 ) and (3) real values, we ought to obtain for different metals a series of potentials identical with the series of their “electrolytic potentials.” . When looking for available data, we find it possible to calculate the electrode potentials of lithium, sodium, potassium, rubidium, caesium (thallium, silver) hydrogen, iodine, bromine and chlorine in aqueous solutions of their ions. The following table gives the results as well as the values used in calculations :-
JAROSLAV HEYROVSKY
Energy of hydration of chlorides
R T log P M e XnF
H Cals, volts
volts
187.000 =8.13 180.000
=7.85 159.000 =6.91 I jo.000
=6.52 IjI.000
. 2 4 ( I - 0 . I 7) - - I .03 0 . 8 ; (1-0.29) = -0.60 0.62* 0.89 (1-0.29) = -0.63 0 . 8 0 (1-0.30) = -0.56 0 . 7 5 (1-0.30) - -0. j 2 I
=6.56 159.000 I . 71 ( I - 0 . 1 5 ) = -1.45 =6.91 =7.8; 2 . 7 6 ( I -0.14) 14.4 0 . 9 0 to 1 4 . 0 0 . 9
Energy of Ionization dissociation potential
E. P.
D volts
I volts
calculated
--
5.36
-1.74
j.11
-2.
4.32
-1.96
--
--
observed
I2
-1.81 --
3.87
-2.17
--
7.30
+I
--
7.41
+2.03) -0.6 +0.6
~ , ~ t1 3o. 5 1.2
,841
Electron affinity E -20.000
-0.108
0.637
2.57
4-0.96
-0.018
0.96
2.93
+I.
2.44
4.26
+I
= -0.87
- 9.000
56
= -0.39 0
* The pressure
0
.82
of sodium is t a k q from Miller: J. i2m. Chem. Soc. 45, 2323 (1923).
Notes to Table I For the energy of hydration Fajans’ values of the “heats of hydration” of chlorides were used (1.c.) which are the differences of heats of solution of the chlorides and their crystal-lattice energies. The value for silver is not directly obtainable, and was taken as identical with that of sodium because of the similarity of their ionic dimensions, upon which hydration depends. 1 The energy of hydration of hydrochloric acid was calculated from the energy necessary to ionise the gaseous molecule, I H c ~ , taking into account, that the tension of a 2 N aqueous solution of hydrochloric acid2is 0 . OOI I 7 mm Hg. Then
”CI
= IHCI
+ 2RT/F log o . ooI 7/760 =IHC1+0.9 volts. 2xzx22
I
Born: 1. c., Herzfeld; Jahrb. Rad. 19, 310 (1923). Gahl: Z.physik. Chem. 33, 178 (1900).
POTEXTIALS OF GALVANIC CELLS
349
The ionisation potential of hydrochloric acid was found by Foste and Mohlerl to be 14.0 volts, by Knipping2 1 4 . 4 ~ . Fajans finds the heats of hydration of bromides and iodides to be by 9.Cal and zo.Cal resp. lower than for chlorides; therefore for Brz and 1 2 the numbers have a minus sign. The vapour pressure terms of metals are taken from Haber’s communication3 and are corrected to 300’ abs. by using a Gruneisen’s approximation, that - R T log P R ~ ~ = D(IO-T/TB), where Do is the heat of sublimation a t absolute zero, TBthe absolute boiling point; the vapour pressures of iodine and bromine are 0 . 2 and 190 mm. Hg resp. (at room temperature). The energy of dissociation of hydrogen into atoms should be 2 . 0 volts, or 86,000 cal per gram. molecule are used; however, Horton and Davies4 find this energy as 1.2 volt. The energies of dissociation of halogens are those of Lewis and Randall6, that of chlorine is kaken as 2.44 volts (Knipping). The ionization potentials of the alkali metals and of thallium are taken from Franck’s report6, the value of silver is that calculated by Haber. The electron affinities of the halogen atoms were derived by Knipping. The numbers since calculated from the spectra, relate to total energies; however, a t ordinary temperatures differences between the total and free energies in such processes vanish. Although several data of the table are uncertain, e.g., the vapour pressures of metals, especially those of high melting points (Li, hg, Tl), yet the calculated values show distinctly the same series of potentials as observed and in some cases the agreement is close showing a constant difference ca % volt. A principal uncertainty, however, lies in the use of “heats of solution” instead of free energies. The Contact Potential The metallic surface potential is closely connected with the “contact potential,” x,which arises at the junction of two metals and becomes noticeable through the Peltier effect. In such a join of two metals we can imagine the electrons being carried out of one of the metals (work-+), brought over to the second metal (work T x.Rlog Pe’/Pe),put into its metallic phase (++’)and finally sent through F the contact potential t; inside of the metals; the sum will then be zero.
+
-
rc, + x. RT F
logPe’/Pe++1+(
J. Am. Chem. SOC.42, 1832 (1919) Z. Physik. 7, 328 (1921). Siteungsber. Akad. Berlin, 51, 506 (1919). Phil. Mag. (6) 46, 895 (1923). J. Am. Chem. SOC.36,2259 (1914);38,2348 (1916). BPhysik. Z. 22, 388 (1921).
3 50
JAROSLAV HEYROVSKY
.
RT F The partial pressure of electrons, P,, in the metallic vapour, PM,, can be Thus $ - $’
=
X . - log P,’/P,+[
calculated from the constant K
Pe0.04.P M e .
=
where
PbIe. denotes the
PM .-e _
partial pressure of metallic ions and the exponent 0.04 comes in as a necessary consequence of the corrected “electron-gas” treatment. Remembering that P, = PM,.,we obtain P, = ““VK. PM, The free energy of the ionisation process, Le., the affinity of the electron to the atom is experimentally determinable as the “ionisation potential” I; hence - RT _ log K = I . 0.04
Then I)-$’ = --
I .04
[
F
log P ’ M ~ / P R I~’~+-I
1+
[,
Xow the ionisation potentials of monovalent metals do not differ more than by about four volts and the logarithmic terms of metallic vapours by about one volt; the Peltier potentials amount only to millivolts. Therefore the potential difference $ - $’ cannot be greater than 0 . 2 volt, if the coefficient 0.04 can be relied upon. This shows that the electromotive forces due to the direct contact of metals and to the electron-transfer across the interface metal-vapour constitute only a small fraction of the total E.M.F. of galvanic cells, the largest part of their energy originating from the junction between the metallic conductor and the electrolyte, and being due to the solvation of metallic ions. The Electro-Kinetic Potential Consider now the interfacial potential 45. From the carrying out of the cycle it is evident that not the absolute value of 45, but 45-7 characterises the electrode potential (the small contact potential [ = X . RT - log P, being disregarded) ; then we have T = 45-7. F If @=o, the interfacial tension between the metal and the solution must be maximal, however 7 is far from being zero under such conditions, equalling - T , which denotes the solution surface potential. This potential might arise from the normal surface orientation of the solvent “di-pole” molecules if “surface-active” substances are absent.
++
Suppose now we change the potential @ by adding a “surface-active” substance, either containing ions, which are selectively adsorbed a t the surface (like iodides or sulphides) or consisting of non-electrolytes (amyl alcohol, caffein) which change the surface tension of the solution, affecting its orientated molecular surface layer. The change of the interfacial tension of the metal (e.g. mercury) then shows, that Qj has changed by a certain amount, to 45, but the electrode potential T of the metal remains unaffected, (Fig 2 . A).
r,
POTENTIALS OF GALVANIC CELLS
35‘
That such additions cannot change 7r becomes evident, if we remember that the new additional potential due to surface adsorption, (in other words Freundlich’s “electro-kinetic” potentiall) adds itself simultaneously also to the ordinary solvent surface potential 77. The a=@+{- (v+{) is unchanged; however the electrode potential 7r (denoted as “absolute zero”) a t which the new interfacial tension will be maximal (i.e. when @+ { = 0 ) equals - 7 - f being now quite different from the “absolute zero potential” noticed when adsorption is absent. Electro-capillary phenomena do not, therefore, inform us about T, but only about one of the constituents of the electrode potential, vie. @, which vanishes at the maximum of the interfacial tension; the so-called “absolute potentials” are not electrode potentials, since they include the “electrokinetic” potential, which does not appear in the E.M.F., and cancels in the circuit as we enter (with a charged particle) and leave the solution (e.g. between the bottom mercury layer potentials in Fig. 2 . A and B). Two sufficiently quickly-running Helmholtz-Paschen mercury dropping electrodes (Fig. z D and D’) will there- y’( fore attain equal potentials only when in either solution adsorption is absent; if an adsorption potential arises in one of ~7 the solutions, then in transferring the electric charge through such a cell from FIG.2 one mercury reservoir (D) to the other (D’) we would have to cross from one electrode over its zero interfacial potential (a”= 0 ) into the first solution, then over the adsorption potential [, (which occurs only in one of the solutions) into the other and thence into the second mercury reservoir, through a zero-potential again. The total potential encountered is {, although both mercury electrodes are kept uncharged by the vigorous dropping.
r,
The Mechanism of the “Zero Dropping Electrode”
It remains now to explain how dropping mercury can acquire the potential of the maximal interfacial tension. This electrode, consisting of a mercury jet splitting into numerous fine drops a t the surface of the solutjon, represents a continually enormously increasing interface. The increase of mercury drops we can imagine to occur in quick installments, each consisting in adding to the electrode-surface new uncharged mercury surrounded by a new unorientated and absolutely mixed up water layer. Consequently the electrode charge of the mercury will gradually disappear (just as according to the original Helmholtz’s explanation) and the adsorpFreundlich “Kapillarchemie,” 342
(1922.)
352
JAROSLAV HEYROVSKY
tion potential of the solution will be annihilated. In the limit, the electrode potential T ,of the dropping electrode will be such, that its interfacial component @ ” will totally vanish and consequently the value of 7r will be -7 in all surface inactive solutions, or -7-5 in the case of surface-active adsorptions (see Fig. 2 ) . I n these cases the dropping mercury has t o be regarded as entirely uncharged, whereas stationary mercury when at the maximum of its interfacial tension in solutions (the same electrode potential x ) is charged, having at the interface in reality two double-layer potentials (the ionic double layer and the surface potential), which cancel each other producing @= 0. The author’s warmest thanks are due to Professor F. G. Donnan for his encouragement and suggestive criticism.
Summary I. From a reversible process consisting of energy terms concerning the ionization of the electrode vapour, the solvation of ions, concentration change and transfer of electric charges over the electrode-interphases a simple thermodynamic formula is deduced for the electrode potential of metals and metalloids. 2 . This formula is verified from numerical data, all the terms being physically determinable. 3 . The contact E.M.F. of metals is shown to constitute only a small fraction of the total E.M.F. of galvanic cells, the largest part of their energy being due to the ionisation and subsequent solvation of the electrode ions. 4. The rBle of the “electro-kinetic” potential is discussed and its 1 elation to the so-called “absolute potentials” defined. Charles’ University, Prague.
