PETERA. ROCK
576
The Standard Oxidation Potential of the Ferrocyanide-Ferricyanide Electrode at 25" and the Entropy of Ferrocyanide Ion
by Peter A. Rock Department of Chemistry, university of California, Davis, Californth
(Received September 28, 1965)
The standard oxidation potential of the ferrocyanide-ferricyanide electrode has been redetermined in a cell free from salt bridges, in which the liquid junction potential has been minimized by an appropriate choice of reference electrode. The need for an extrapolation to infinite dilution has been avoided by treating the potassium ferrocyanideferricyanide solution as a mixed electrolyte system using the available activity coefficient data for the pure salts. The value obtained a t 25" is E" = -0.3704 i 0.0005 v. Using this potential and the available thermodynamic data, the standard partial molal entropy of aqueous ferrocyanide ion has been calculated as 3" = 22.8 cal/deg mole at 25". The entropy of ferrocyanide ion has in turn been combined with existing thermodynamic data to calculate So = 147.8 cal/deg mole for K4Fe(CN)6-3H2O(s)and So = 105 cal/deg mole for KhFe(CN),(s) both a t 25".
Introduction The study of electrochemical cells in which the electrode of interest involves soluble oxidized and reduced species yielding a mixed electrolyte system presents special problems in the interpretation of the cell data. It has not been possible to devise a cell involving such an electrode that is entirely free of liquid junctions. This fact of itself is not necessarily a serious problem, for, as Guggenheim has pointed out,l liquid junction potentials exist in every electrochemical cell. This problem can be overcome in many cases by the appropriate choice of reference electrode. I n the type of cell under discussion the liquid junction potential is predicted2 to approach zero as the electrolyte compositions of the two solutions forming the junction approach identity in the transport properties and ionic activities of their cations and anions. It is also to be noted that the use of salt bridges in such cells is to be avoided, first, because they are unnecessary and, second, because they can introduce significant uncertainties in the cell data.2 The problem of liquid junction potentials has been overcome in the present investigation by employing the Pb(Hg) (two-phase, 5 wt % Pb)lPbzFe(CK)6(~)/Fe(CN)~~-(aq) electrode as a reference in the determination of the Fe(CN)64(aq)-Fe (CN) P ( a q ) standard oxidation potential. The Journal of Physical Chemistry
The difficulties associated with the extrapolation to infinite dilution of the data for a cell involving a mixture of highly charged electrolytes in which ionic association effects are important has been circumvented by employing the available activity coefficient data for potassium ferrocyanide and potassium ferricyanide to treat the mixed electrolyte solution as a multicomponent system. The results obtained in this way are compared with the previously reported value for the ferrocyanide-ferricyanide oxidation potential. The standard potential obtained has been used in combination with existing data to calculate several thermodynamic properties of interest for ferrocyanides.
Experimental Section Reagents. J. T. Baker reagent grade K3Fe(CN)6 (assay: 99.9%) was used without further purification. J. T. Baker reagent grade K4Fe(CN)6.3H20 was recrystallized from a hot (55') aqueous solution under nitrogen, air dried, and stored over a saturated aqueous solution of NaBr.2H20 in the dark.3 Cell (1) E. A. Guggenheim, "Thermodynamics," North-Holland P u b lishing Co., Amsterdam, 1949,pp 342-347. (2) D. A. MacInnes, "The Principles of Electrochemistry," Dover Publications, Inc., New York, N. Y.,1939,Chapters 13, 14,and 16. (3) I. M.Kolthoff and W. J. Tomsicek, J . Phys. Chem., 39, 945 (1935).
OXIDATION POTENTIAL OF THE FERROCYANIDE-FERRICYANIDE ELECTRODE
577
Table I: Results of Measurements on the Cell Pb(2-phase Hg)~PbzFe(CN)a(s)~KSe(CN)~(mt)~K~Fe(CN)6(m~),K~Fe(CN)s(mJ)~Au ml ( Y L) a
0.1750(0.106) 0,1100(0.133) 0.0875(0.148) 0.1030(0.137) 0.1375 (0.118) a
mdr3"
(Lead negative) mdrda
O.lOOO(0.114) 0.0800(0.141) 0.0500(0.157) 0.1000(0.142) 0.1000(0.126)
0.1000(0.186) 0.0400(0.216) 0.0500(0.236) 0.00400(0.216) 0.0500 (0.199)
EQb
0.7803 0.7553 0.7703 0.6887 0,7575
Mean molal activity coefficients calculated as described under Activity Coefficients in this section.
- 0.3705 - 0.3709 - 0.3709 -0.3696 - 0.3695 Standard oxidation potential
of the ferrocyanide-ferricyanide electrode; see calculation of the standard oxidation potential.
solutions were prepared on a molal basis using nitrogensaturated distilled water. These solutions were stored in brown polyethylene bottles and always used on the same day as prepared. Electrical Cell Measurements. Voltages were measured with a Leeds and Northrup Type K-3 certified potentiometer and a Leeds and Northrup galvanometer. External guarding was employed in the galvanometer and working battery circuits. Electrode compartments were similar to those described by Hills and Ives, and the interiors of the electrode compartments were silicone ~ o a t e d . ~ The lead amalgam-lead ferrocyanide reference electrode was prepared as has been de~ c r i b e d . ~The liquid junction connector used was similar to that employed by Gordon and co-workers.6 I n the ferrocyanide-ferricyanide electrode a gold wire7 was brought in through a capillary to the base of the electrode compartment and wound in a coil of several turns. The end of the wire was then submerged in paraffin wax (used to seal the capillary opening) to avoid any sharp points that might give rise to spurious emf values. Air was excluded from both electrodes by a stream of purified nitrogen from a presaturator filled with electrode electrolyte solution. Light was excluded from the ferrocyanide-ferricyanide electrode3 by wrapping the electrode compartment in aluminum foil. The cell was maintained at 25.0 f 0.005" in a grounded water bath.
Results Cell Data. The cell employed was as follows: Pb(5 wt % in Hg) IPbzFe(CN)a(s) I&Fe(CN)dml) K4Fe(CN)~(m2) ,&Fe (CN)6(m3)1 Au, in which the two cell electrolytes were brought into contact in the liquid junction connector. Unfortunately, the cell electrolyte cannot be made uniform throughout the cell, even though lead ferricyanide is soluble, because the lead amalgam spontaneously reduces ferricyanide to ferrocyanide. The cells set up as indicated attained a steady voltage in less than 10 min, and, in three of
1
the five cells set up, the observed voltage was remarkably stable to within a few hundredths of a millivolt for several hours. Voltage fluctuations in all cells were within *O.l mv for a t least 3-5 hr, and three of the cells were stable for over 24 hr. I n all cases the observed cell voltages were insensitive to the renewal of the liquid junction. The results of experiments on this cell at various values of ml, m2,and m3are presented in Table I. Activity Coeficients. The mean molal activity coefficients of K4Fe(CN)6(aq) and KtFe(CN)e(aq) a t 25' have been reported.* These activity coefficients were determined isopiestically, and the data were not extrapolated to the conventional solute standard state [Le., a (of K4Fe(CN)6) = a K + 4 a F e ( C N ) 6 4 - and a (of K3Fe(CN)d) = a K ~ ~ a F e ( c N ) ~ a -but ], rather it was assumed for both salts that ~ ~ ( 0 . m, 0 50') = ~ ~ ( 0 . 0 5 m, 25'), where the value of ~ ~ ( 0 . m, 0 50 ') was obtained from the Landolt-Bornstein Tables. These T * values in turn were obtained from freezing point data by assuming the validity of the Debye-Huckel limiting law a t 0.001 m, and then yk values at higher concentrations were calculated from the freezing point data. Since there is no real assurance that the limiting law holds a t these concentrations for such highly charged electrolytes and the temperature variation of the y & values cannot be safely neglected, the T~ values reported for these saltss are, as the authors point out, based on an arbitrary standard state. It is desirable, therefore, to find a better method to establish the conventional solute standard state. Using the available (4) G. J. Hills and D. J. G. Ives, J . Chem. SOC.,311 (1951). (5) P. A. Rock and R. E. Powell, Inorg. Chem., 3, 1593 (1964). (6) W. J. Hornibrook, G. J. Janz, and A. R. Gordon, J . Am. Chem. SOC.,64, 513 (1942).
(7) G. N. Lewis and L. W. Sargent, ibid., 31, 355 (1909). (8) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, Butterworth and Co. Ltd, London, 1959. (9) Landolt-Bornstein Tabellen, 5th ed, 2nd supplementary volume, p 1121.
V o l u m e 70, Number 2 February 1966
578
freezing point datal0 and extrapolating to infinite dilution" yield B = 0.924 (0") for &Fe(CN)e(aq). A similar treatment of the freezing point data for K3Fe(CN)6 yields an extrapolation plot with considerable scatter, and a reliable B value cannot be obtained from the data. To correct yliLvalues at 0 to 25", the heat of dilution, and its temperature dependence are needed for both &Fe(CN)s(aq) and KJ?e(cN)~(aq). Although heat of dilution data are available,'* heat capacity data for these solutions are nonexistent. Since the ~ ( T-zTl) term cannot be safely neglected in correctng y*(Oo) to y*(25") and B is not known for K3Fe(CN)6(aq), an approximate procedure for the establishment of the conventional solute standard state has been employed. Brubaker and co-workers have reported the mean molal activity coefficients of K3C~(CN)613 and K ~ M O ( C N )obtained ~~ from isopiestic data which they successfully extrapolated to infinite dilution. It has been assumed that y+ for K3Fe(CN)6 is equal to yi of K3Co(CN)a at 0.1 m and from the value of yk for K&O(CN)~at 0.1 m and that reporteds for KaFe(CN)6 it was computed that by adding 0.0131 to the -1og y* values, the existing data could be converted to the conventional solute standard state; e.g., we compute at 0.20 m for K3Fe(CN)6 that yh = 0.206 whereas the reported value is y* = 0.210. Similarly, in treating the K4Fe(CN)6 data it was assumed that y* = 0.194 for this salt at 0.05 m (the value obtained for Kahlo(CN)s a t this concentration) and by subtracting 0.0113 from the -log y* values for &Fe(CN)6 the activity coefficients for this salt have been corrected to the conventional solute standard state; e.g., we compute for K4Fe(CN)6 at 0.1 m that y* = 0.143 whereas the reported value* isri = 0.139. The electrolyte solution in the ferrocyanide-ferricyanide electrode is a multicomponent system. From the Br#nsted-Guggenheim equation16 one obtains for K4Fe(CN)6 of molality mz in a sohtion containing K3Fe(CN)6of molality m3: log y* (mixture) - log yi (pure) = m3(4/5B3- 9/2~B~), wherein y* (mixture) refers to the mean molal activity coefficient of K4Fehaving the (CN)6 in the mixed same total ionic strength as that to which y* (pure) (the mean molal y I for KdFe(CNh(aq)) refers, and Bz and B3 refer to K4Fe(CN)6(aq) and KaFe(CN)6 (as), respectively. For K3Fe(CN)6 of molality m3 in a solution containing K4Fe(CNh Of molality m2 one obtains: log ya (mixture) - log yh (pure) = m2 (3/4Bz - 3/2Ba>Jwhere here again ~a (mixture) refers to the mean molal activity coefficient of K3Fe(CN)6in the mixed electrolyte solution having the same The Journal of Physical Chemistry
PETERA. ROCK
total ionic strength as that concentration to which y* (pure) refers. If we now assume that Harned's rulela applies to the mixture we obtain from the relationship 4/6B3 '/2& = 3/&2 - a/ZB3 = a,the result that B3 = 0.4826. Bz,which permits the calculation of B3 from Bz, and hence the estimation of CY. We compute a = 0.0241 (at 0"). If we now assume a(O0) = a(25"), an estimation of the contribution of the interaction terms am3 and amz to E" can be made. The magnitude of this contribution (see the following section) is 0.05916~~ (5m3 - 4m2)and the largest contribution that this term makes to any of the five cells (see Table I) is of the order of 0.0003 v. Since a is not accurately known and the experimental uncertainty in E" is *0.0005 v, this term has been neglected in the calculation of the standard potential. That is to say, for a solution containing K4Fe(CN)6 and K3Fe(CN)6 of molalities m2 and m3, respectively, having a total ionic strength of lorn2 6m3,the mean molal activity coefficients of the two salts are taken as the values of yi for the pure electrolytes at the same ionic strength as that of the mixture. In this way the y.. values for the mixed electrolyte solutions given in Table I (interpolated at intermediate concentrations from linear plots5 of log y* vs. log m) have been obtained. The standard oxidation potential of the lead amalgam-lead ferrocyanide electrode5 was calculated using the reportedsvalues of y* for &Fe(CN)6(aq) and therefore these values must be used for the pure K4Fe(CN)s(aq) (at molality ml, see cell diagram) solutions. Alternatively, of course, E" for this electrode could be recalculated with the new y* values; however, this is unnecessary for the present purposes. Calculation of the Standard Oxidation Potential. From the cell diagram one obtains the cell reaction
-
+
2Pb(Hg) (2-phase) 4- K4Fe(CN)~(rnd 44K+(4rnz f 3m3) 4K3Fe(CN)6(m3) S
+
PbzFe(CN)&) f 4K4Fe(CN)e(rnz) 4- 4K+(md and hence at 25' (10) For &Fe(CN)&q): A. A. Noyes and J. Johnston, J. Am. Chem. SOC.,31, 987 (1909). For KaFe(CN)n: "International Critical Tables," Vol. 4,p 260, and C. Robertson and V. K. La Mer, J. Phys. Chem., 35, 1953 (1931). (11) G. N. Lewis and M. Randall, "Thermodynamics," 2nd ed, revised by K. S, Pitaer and L. Brewer, McGraw-Hill Book Co., Inc., New Yo&, N, y . , 1961, 410. (12) E. Lange and W. Miederer, 2. Elelctrochem., 60,34 (1958). (13) R. A. Wynveen, J. L. Dye, and C. H. Brubaker, Jr., J. Am. Chem. Soc., 82, 4441 (1960). (14)c. H. Bmbaker, Jr,, ibid., 8,, 5762 (lgB5). (15) . I See ref ll.. _ 346, ecr 23-38, (16) See ref 11, p 568.
OXIDATION POTENTIAL OF THE FERROCYANIDE-FERRICYANIDE ELECTRODE
Since a K + = mKtYK+ and single-ion activity coefficients are not measurable properties of electrolytes, it is desirable, in order to bring about cancellation of the aK+terms in the numerator and denominator, that 4ml = 4m2 3m3 and that the ionic strengths of both solutions be a t least approximately equal, i.e., lOml = 10m2 6m3. These two requirements are not entirely compatible but are simultaneously satisfied, a t least approximately, when ml 'v m2 2 ma. The liquid junction in this cell is also negligible when ml 'v m2. I n choosing the cell concentrations the condition 4ml = 4m2 3m2was always satisfied, and in addition m3 5 m2 was maintained. The ultimate criterion for the validity of these assumptions was taken as the constancy of the calculated E" values. Applying the thermodynamic definition of activity and assuming U K + (at 4m1) = U K + (at 4m2 3m3) we have
+
+
+
+
Ea
+ 0.07395 log 256"'m1y&
-
E = Ea
+ 0.07395 log 256"'m1yk
-
E
=
[
0.05916 5 log yi(o)
- 4 log y*(i) log
+
m2(4m2m3+ 3ms)i
in which (0)and (i) refer to potassium ferrocyanide and ferricyanide, respectively. Inserting the data in Table I into this equation and taking the standard oxidation potential of the Pb(5 wt % in Hg, 2-phase)lPb2Fe(CN) B(s) Fe (CN)64-(aq) electrode6 as 0.3870 v, the values of the standard oxidation potential of the ferrocyanide-ferricyanide electrode given in Table I were computed. The average of these values is E" = -0.3704 1 0.0005 v at 25". The constancy of the calculated E" values lends support to the assumption that the liquid junction potential is negligible. As a further check on this point a saturated KCl salt solution was inserted in the second cell in Table I and had no effect (within 10.01 mv) on the observed cell voltage as would be expected if the liquid junction potential is indeed small.
I
+
Discussion The work of Lewis and Sargent? on the ferrocyanideferricyanide electrode was exploratory in nature and these workers did not obtain a standard potential.
579
Kolthoff and Tomsicek3 obtained E" = -0.356 v in their investigation of this electrode. We feel that the difference between the value of E" obtained in this study and that obtained by Kolthoff and Tomsicek is due to the difficulties in extrapolating their data to infinite dilution, especially since the limiting law was used in solutions of rather high ionic strength. The possible existence of nonnegligible junction potentials may also be a contributing factor to this difference since these workers employed a KC1 (saturated) in agar salt bridge in their cell. Lin and Breck" report E" = -0.3644 v for the standard oxidation potential. This value was obtained from the cell: Hg(l)/Hg2(21, (s)1 KCI (satd) 1 K4Fe (CN) 6,K3Fe(CY)6 1 Pt, for which cell data at equal molalities of K4Fe(CN)Band K3Fe(CN), were extrapolated to infinite dilution against ~ l / ~ / ( l p1I2), p = ionic strength. Although the agreement between the two potentials is good, the difference of 6.0 mv cannot be considered negligible. Since these workers did not attempt to assess the importance of the liquid junction potential in their cell and in particular did not vary the ferrocyanide to ferricyanide ratio at constant ionic strength to test experimentally their assumption of zero liquid junction potential, it remains a strong possibility that their E" has incorporated in it an nonegligible liquid junction potential. Lin and Breck also investigated the temperature dependence of the emf of their cell and obtained 49.0 cal/deg mole for the entropy difference between Fe(CN)s3-(aq) and Fe(CN)64-(aq), whereas the value obtained in this study (vide infra) is 40.6 cal/deg mole. From the enthalpies of formation of Fe(CN)64-(aq) and Fe(CN)63-(aq) from their respective ions'* and Latimer's values1g for the standard enthalpies of formation from the elements of CN-(aq), Fe3+(aq), and Fe2+(aq),we compute for Fe(CN)64-(aq), AHf" = 109.8 kea1 and for Fe(CN)63-(aq), AHf" = 135.1 kcal. From E" determined in this investigation we compute for Fe(CN)64-(aq) = Fe(cN)~~-(aq) e-, AGO = 8.54 kcal; combining this AGO with AH" = 25.3 kcal yields AS" = 56.2 cal/deg mole. Hepler and co-workers report20 so = 63.4 cal/deg mole for the standard partial molal entropy of Fe(CN)63-(aq). This yields 3" = 22.8 cal/deg mole a t 25" for Fe(CN)64-(aq) to be compared with 3" =
+
+
(17) J. Lin and W. G. Breck, Can. J. Chem., 43, 766 (1965). (18) G. D. Watt, J. J. Christensen, and R. M. Ieatt, Inorg. Chem., 4, 220 (1965). (19) W. M. L a t h e r , "Oxidation Potential," 2nd ed, Prentice-Hall, Ino., New York, N. Y., 1952. (20) L. G. Hepler, J. R. Sweet, and R. A. Jesser, J. Am. Chem. Soc., 82, 304 (1960).
Volume 70, Number 9 February 1966
NOTES
580
17 (*5-15) cal/deg mole, obtained by Hepler and coworkers,2ofrom their thermal data and Kolthoff and Tomsicek's standard oxidation potential. Since the values of -y* used in this study are probably uncertain to about *0.005, a recalculation of the entropy of ferricyanide ion is not warranted at this time. Hepler and co-workers used T * = 0.122 for a saturated solution of KsFe(CN)a,*whereas the value obtained by the approximate methods discussed in this investigation is T * = 0.118. This difference leads to a difference in AGO of solution for potassium ferricyanide of 0.06 kcal/mole and a difference of 0.2 in the entropy of ferricyanide ion. Accordingly, we take 3" = 22.8 f 0.3 cal/deg mole as the entropy of ferrocyanide ion. The entropy of ferrocyanide ion can be combined with the heat of solution20of K4Fe(CN)6*3HzO(s) and the free energy of solution of this salt (calculated using m (satd) = 0.8559,21T*(satd) = 0.0478 (based on the solute standard state established in this work), U ~ , O (satd soln) = 0.9623 (calculated from 9 = 0.498 given in ref 8) to yield AGoBoln = -RT In (4m)%. -yf6ua203 = 6.243 kcal) to give ASoaoln = 23.16 cal/ deg mole, from which we computelg So = 147.8 cal/deg mole for K4Fe(CN)6.3H20(s)at 25". of K4Fe(CN)6.3HzO(s) From the heats of and K4Fe(CN)6(s) and AH" at 25' for the process1g HzO(l) = H,O(g), we compute for the reaction: K4Fe(CN)6.3H20(s) = K4Fe(CN)&) 4- 3HzO(g), M" = 35.10 kcal. Schottkyz2 reports 7.35 mm at 20" for the dissociation pressure of the trihydrate. From the above AH" for the reaction we calculate 10.30 mm for the dissociation pressure at 25". From this dissociation pressure we compute A G O 2 9 8 = 7.65
kcal for the above reaction, and hence ASo = 92.08 cal/deg. This yields So = 105 cal/deg mole for the entropy of K4Fe(CN)6(s) at 25". Although this is not an unreasonable value for the entropy of this salt considering that Stephenson and Morrow report2a So = 100.4 cal/deg mole for K8Fe(CN)6(s)at 25", it may be too low a value since, if one considers that the average entropy per mole of hydrated water is 9.4 cal/deg mole,24the entropy of K4Fe(CN)&) may be estimated from the entropy of K4Fe(CN)6-3H20(s) as 119.6 cal/deg mole. The most likely source of error in the calculation of the entropy of KaFe(CN)e(s) is the dissociation pressure of K4Fe(CN)6*3Hz0, since the authorz2emphasized the difficulty in obtaining reliable dissociation pressures in his measurements. From the available thermal data1*and the entropies of the ion^,'^^^^ together with the entropy of ferrocyanide ion determined in this investigation, we compute the standard free energies of formation from the elements of ferrocyanide and ferricyanide ions at 25" as 167.1 and 175.6 kcal/mole, re~pectively.~~ (21) R. H. Vallance, J . Chem. Soc., 1328 (1927). (22) H. Schottky, 2. Physik. Chem., 64, 415 (1909). (23) C. C. Stephenson and J. C. Morrow, J. A m . Chem. SOC.,78, 275 (1956). (24) See ref 19, p 364. (25) NOTE ADDEDIN PROOF. R. H. Busey, J . Phys. Chem., 69, 3179 (1965), has recalculated the entropy of &Fe(CN)&) and obtained S o = 101.8 cal/deg mole at 25'. This entropy is 1.4 units larger than the previously reported value and leads t o an increase of 1.4 cal/deg mole in the entropies of Fe(CN)c'-(aq), K'Fe(CN)v 3HzO(s), and K'Fe(CN)+j(s) reported in this paper. The revised values for the entropies are 24.2, 149.2, and 106 cal/deg mole, respectively. AGt" and AH!' values reported here are unaffected by
this change.
NOTES Temperature Dependence of Absorption of Liquid Water in the Far-Ultraviolet Region
conflicting results have been Only a few data are available in these reports on the absorption a t other temperatures. For photochemical studies in dilute aqueous solutions in the far-ultraviolet region,'
by M. Hahnann and I. Platzner Isotope Department, The W e i m a n n Institute of Science, Rehouoth, Ierael (Received September 16, 1966)
For the absorption spectrum of liquid water in the 200- to 180-mp region at room temperature, several The Journal of Physical Chemistry
(1) J. Barrett and J. H. Baxendale, Trans. Faraday Soc., 56, 37 (1960). (2) J. Barrett and A. L. Mansell, Nature, 187, 138 (1960). (3) J. L. Weeks, G. M. A. C. Meaburn, and 8. Gordon, Radiation Res., 19, 559 (1963). (4) M. Halmann and I. Platsner, J . Chem. SOC.,1440 (1965).
