T H E ELECTRODE POTENTIALS AND T H E FREE ENERGY OF SOLVATION BY JAROSLAV H E Y R O V S K ~
In the previous communication1 the electrode potentials (T)of galvanic cells were deduced from physical constants, namely from the ionisation potential (I) of the electrode vapour (or, in the case of a metalloid its “electronaffinity”, E), the vapour tension (P) of the electrode, the free energy (H) of solvation of the electrode-ions and the concentration of solvated ions. Formulae RT RT T,,= - log P,, I - Hxre. log [ Me’sol] (2) F F and
+
+
~
( 3)
were obtained. The introduction of the term H is based upon the idea of Fajans2 of allowlng the ions first to be solvated before bringing them into solution. This can proceed reversibly, if we keep the ions in the vapour phase of the solvent, letting the vapour condense upon them until they become so far solvated that they acquire the vapour pressure of the electrode solution, during this operation the free energy of solvation, H , is gained. The di-pole nature of solvent molecules explains the free energy of this physical process.3 Although from this point of view the solvation process is regarded as a physical one, we may also, when following the modern tendency to explain chemical processes physically, look upon it chemically and apply to it-as it has been done in the previous communication-the law of mass action. The formulae ( 2 ) , (3) show us how the potential of an electrode depends upon the solvent since only the solvation term H changes in various solvents. Born4 has physically deduced this quantity H
[I(?:‘ =-
-$)I
,where r is
the ionic radius and n the valency showing how it should depend upon the dielectric constant. From his formula it appears that the difference of electrolytic potentials of one and the same metal in water and alcohol is only about a third of a volt. The Effect of Solvation For solutions in the same solvent H will depend upon their vapour-tenRT sions, i. e., on the total concentration of the solution, whereas - log c only
F
J. Phys. Chem. 29, 344 (1925). Ber. physik. Ges. 21, 249, 709 (1919). See Born: 2. Physik. 45 (1920); Hersfeld: Jahrb. Rad. Elektr. 19 (1923). 4 LOC.cit. p. 45.
ELECTRODE POTEXTIALS AND SOLVATION
40 7
changes with the partial concentration of the electrode ions, c; thus in concentration cells both the factors H and log c, determine the E. 34. F. In Nernst’s formula the solvation energy does not appear; however its importance becomes obvious from recent, measurements of cells with very concentrated solutions. From Formulae ( 2 ) and (3) we obtain, on subtracting, the E. M. F. of a cell consisting of a metallic electrode reversible in cations, Me’, and a metalloid electrode reversible in anions, X ’ l , as equal to
I n strongly concentrated solutions, where the vapour pressure of the solvent becomes considerably lowered and the amount of solvent molecules available for the solvation of ions is limited, the energies HMe.and H,’ decrease and consequently the observed E. M. F. is much smaller than that expected froiii the mere ionic concentration relationshipl. This is usually ascribed to the increase of ionic activities in most concentrated solutions. Using for the activity coefficient the symbol f , we can write the potential of a reversible electrode as: RT n=K log C. f .
+
and comparing this with formula
F
which can be written as H.F -RT RT n=K log e. a . e F n-e derive for the activity coefficient H.F -~ (2),
+
f=a. e
RT
where denotes the dissociation degree. To see to what ext,ent the energy of solvation varies with the vapour pressure of the solution let us return to the originally derived formula ( I ) (in the previous communication) writing
as free energy of ionic solvation. Here KSoldenotes the equilibrium constant of the process Me‘ +n solvent mol. +Me‘sO1 Then we obtain RT RT K =K - log c - - log KSOl. P:>,
+
F F Let us now substitute from the Raoult’s relation F - M -.-- C log,P p 1000
where p is the pressure of the pure solvent, p’ that of the solution, $1 the molecular weight of the solvent vapour, p the density and C the total concentration of particles per litre. Noyes and Mac Innes: J. Am. Chem. SOC.42, 239 (1920).
408
JAROSLAV
Substituting for
r=K’
Psol ( = p’)
+
HEYROVSKP
we obtain:
RT RT M C RT - [log Me‘sol]+ n . - - . - - log KS,,[. F F p 1000 F
Let us now calculate the effect due to the free energy change of ionic hydration when concentrating a normal aqueous solution of a binary electrolyte to a three times normal, assuming that Ksoi and n remain-within this concentration range-constant Then P = I , M
=
18,
RT - = 0 . 0 2 5 volt, F
Considering that there is hardly more room round an ion than for six water molecules (the eo-ordination number), we can take n = 6 and obtain then an activity increase of ca. I O millivolts corresponding to a 1.5 times larger ionic activity than that in the normal concentration. This order of the activity increase is indeed observable (e. g. in the work of Noyes and McInnes). We cannot, however, make precise calculations in this respect before the problem of mutual ionic attraction is solved. According to Debye‘ this attraction should become considerable in most concentrated solutions and would work in the opposite way, lowering the activities. For ethyl-alcoholic solutions, where M = 46 and p = 0.78 the “activity” effect, which is due to solvation, should be about three times larger; as a matter of fact, the great anomalous increase of activity of sodium ions in most! concentrated sodium ethoxide solutions, observed by M. Shikata2 is more than three times that observable in aqueous solutions. Moreover, in iso-amyl alcohol (M = 88) recent measurements on sodium and potassium alcoholates carried out by M. Shikata and 2 . Koutnikovh (hitherto unpublished) show again twice as large abnormal activity increases as in ethylalcohol of the same molarity. Thus the incomplete hydration makes the ions more easily to be deposited a t electrodes and this accounts for their increase in “activity”; the less completely solvated the ions are, the more numerous they appear to be when calculating their concentration from the simple Nernst formula. However, the electrolytic potential depends not only on the quantity of ions, but also on their quality, i. e., upon their degree of solvation. Electrochemically inactive electrolytes or non-electrolytes when present in large concentrations influence the electrode potentials, making them more positive,3 no doubt since the degree of solvation of the electrode-ions is reduced. The catalytic activity of ions must, of course, be parallel to their electrochemical activities, because a less firmly solvated ion is desolvated more easily, when entering the molecule, with which it makes an intermediate IPhysik. Z. 24, 191 (1923). Trans. Faraday SOC.“Electrode Reactions and Equilibria.’’ 19, p. 721 (1924). G. Scatchard: J. Am. Chem. SOC.45, 1716 (1923): W. A. Arkadjev: Z. pliysik. Chem. 104, 192 (1923); J. Irxeborowski: 107, 270 (1923); G. Poma: 107, 329 (1923).
ELECTRODE POTENTIALS AND SOLVATJON
409
compound. The well-known catalytic neutral salt action is thus easily interpreted, explaining the activity increase of the acid as due to the dehydrating influence of the neutral salts on the hydrions.’ In the same way the decrease in solubility of nonelectrolytes caused by salt additions can be understood, since the large desolvating power of the latter deprives the dissolved nonelectrolyte molecules of their hydrate-water necessary to keep them in solution. It might be pointed out, that the size of the solvated ion (which includes a large number of more or less firmly bound solvent molecules) has little to do with the energy of solvation, i. e., with the intensity with which especially the first layer of molecules sticks to the ion. The smallest of ions, the hydrion, which according to Fajans and Born should exhibit the greatest energy of solvation, might keep its little first shell of solvent molecules extremely firmly and yet be in size the smallest of all ions, with the greatest velocity of migration. Thus the transference phenomena influenced by the size of solvated ions cannot interfer with this idea of solvation energies.
Summary I t is shown, that the electrode potential depends not only on the number of ions in solution, but also on their degree of solvation and therefore on the vapour pressure of solution. This view allows to express the “activity coefficient” by means of the free energy of solvation and is shown to be in accordance with experimental facts. The Charles University, Prague IF. 0. Rice: J. Am. Chem. Soc. 45, 2808 (1923); N. Bjerrum: Z. physik. Chem. 108, 97 (1924).
