THE OXIDATION POTENTIAL O F THE SYSTEM POTASSIUM FERROCYANIDE-POTASSIUM FER~ICYANIDEAT VARIOUS IONIC S T R E N G T H S I. M. KOLTHOFF
AND
WILLIAM J. TOMSICEK
School of Chemistry, University of Minnesota, Minneapolis, Minnesota Received January 85, 1936
The oxidation potential of the ferrocyanide-ferricyanide system has been determined by a number of investigators (1, 3, 8, 9, 10, 11, 12, 13). After the introduction of the Debye-Huckel theory of strong electrolytes, this system becomes of special interest, since we are dealing here with highly unsymmetrical salts of high valence type. If potassium ferrocyanide and potassium ferricyanide behave like strong electrolytes, the oxidation potential should be greatly affected by a change of the ionic strength of the solution. In the first place, the purpose of this study was to determine the potential of the potassium ferrocyanide-potassium ferricyanide system a t varying ionic strengths and to extrapolate the value to an ionic strength of aero; in other words, to determine the normal potential of the system. In addition, the potential of a very dilute ferroferricyanide solution was determined in the presence of different neutral salts a t varying ionic strengths, in order to test the applicability of the Debye-Huckel equations. At extremely small ionic strengths, the relation between the activity coefficient of an ion and the ionic strength of the solution is given by the expression : . -log f = 0 . 5 ~di ~
(1) a t 25°C. in water, in which z is the valence of the ion, and 1.1 the ionic strength. The oxidation potential E of the system ferrocyanide-ferricyanide a t 25°C. then is given by:
=
€0
CFeT;fa + 0.0591 log *
CFeOC-
f 4
(2)
1 From the experimental part of a thesis submitted by William J. Tomsicek to the Graduate School of the University of Minnesota in partial fulfillment of the requirements for the degree of Doctor of Philosophy, 1934.
945
946
I. XI. KOLTHOFF AND WILLIAM J. TOMSICEK
The normal potential eo denotes the potential referred to the normal hydrogen electrode in a system in which the activity of the ferricyanide aF&;- is equal to that of ferrocyanide aFi;--. CF;;and CF~;;-represent the corresponding concentrations, whereas fs and f 4 represent the activity coefficients of the ferricyanide and the ferrocyanide ions. If the limiting Debye-Hudkel expression (equation 1) holds a t extremely small ionic strengths and the system contains equimolecular amounts of potassium ferricyanide and potassium ferrocyanide, it is found from equations 1 and 2 that: 54
Therefore if the limiting Debye-Huckel expression holds, the measured potential E should change by 0.2068 volt for one unit change in the square root of the ionic strength. The practical work in this study involves the use of a cell with liquid junction, the ferro-ferricyanide half-cell being measured against the quinhydrone electrode in a mixture containing 0.01 of an equivalent of hydrochloric acid and 0.09 of an equivalent of potassium chloride per liter, the saturated potassium chloride-agar salt bridge being used for making electrolytic contact between the two half-cells. No correction has been applied for the liquid junction potential, which is very small in dilute solutions containing potassium ferrocyanide and potassium ferricyanide, but may be greater in the presence of larger amounts of neutral salts. The introduction of the liquid junction potential, however, does not invalidate the conclusions arrived a t in this paper. EXPERIMENTAL PART
Materials used IGFe(CN)a.3Hz0. A C.P. product of potassium ferrocyanide was recrystallized twice from conductivity water and kept over deliquescent sodium bromide hydrate. An analysis of the salt showed that it had the theoretical composition. K3Fe(CN)s: A C.P. product of potassium ferricyanide was recrystallized twice from conductivity water and dried over anhydrous calcium chloride. The various salts used in this work had been analyzed by W. Bosch and had been used in a previous study (4). Conductivity water was used throughout this work.
.
Apparatus and method for the measurement of the potential The potential of the ferro-ferricyanide system was measured in a Pyrex cell as shown in figure 1, a piece of bright platinum gauze serving as elec-
OXIDATION POTENTIAL O F FERROCYANIDE-FERRICYANIDE
947
trode. One terminal of the potassium chloride-agar salt bridge was placed in the side well b, thus preventing diffusion of potassium chloride from the bridge into the main body of the solution. Nitrogen gas from a tank was introduced through e. Oxygen gas was removed from the nitrogen by passing the gas through electrically heated copper gauze a t 500°C. The solution in the standard reference half-cell (0.01 N hydrochloric acid, 0.09 N potassium chloride saturated with quinhydrone) was prepared fresh every day. The normal potential of the quinhydrone electrode is 0.6990 volt a t 25°C. Assuming that the paH of the acid mixture in the quin-
FIG.1
FIG.2 FIG. 1. THECELL FIG.2. Ratio of KsFe(CN)e to KIFe(CN)s:o, ratio 1 : l ; A, ratio 1O:l; 0 , ratio 1:lO. D. H., calculated from simple Debye-Huckel expression.
hydrone half-cell is equal t o 2.0755, we find that the potential of the latter against the normal hydrogen electrode is equal t o 0.5764 volt a t 25°C.2 All the measurements were made in a thermostat a t 25"C.f 0.05'. Various salt bridges were used, all yielding the same values. The measurements were made with a Leeds and Northrup student potentiometer. For the dilution experiments a stock solution containing 0.1 M potassium ferrocyanide and 0.1 M potassium ferricyanide was carefully prepared by weight from the pure salts. This stock solution was kept in the dark and a Recently Guggenheim and Schindler (J.Phys. Chem. 38,533 (1934)) gave evidence that the paH of the standard acid mixture used in the quinhydrone electrode is equal to 2.10.
948
I. M. KOLTHOFF AND WILLIAM J. TOMSICEK
prepared fresh each day. The solutions from 0.1 to 0.004 molar were found to give the same potential in air as in a nitrogen atmosphere. The potential of the 0.004 molar solution in air referred to the normal hydrogen electrode was 0.4009 volt after 5 minutes and 0.4011 volt after 60 minutes. The same solution in a nitrogen atmosphere gave readings of 0.4011 and 0.4012 volts after 5 and 60 minutes respectively. More dilute solutions gave higher readings in air than in nitrogen. The potential of the 0.0004 molar solution was measured a t least ten times during the course of the investigation. I n a nitrogen atmosphere, the values found after 5 minutes TABLE 1 Oxidation potential of equimolecular mixtures of potassium ferrocyanide and potassium ferricyanide E
M
P
0.1* 0.04 0.02 0.01 0.007 0.004 0.002 0.001 0.0008 0.0004 0.0002 0.0001 0.00008 0.00006 0.00004
1.6 0.64 0.32 0.16 0.112 0.064 0.032 0.016 0.0128 0.0064 0.0032 0.0016 0.00128 0.00096 0.00064
(AGAINST STANDARD QUINHYDRONE)
1.265 0.8 0.5657 0.4 0.334 0.253 0.173 0.1265 0.1131 0.08 0.0566 0.04 0.0358 0.031 0.0253
0.1178 0.1362 0.1490 0.1610 0.1670 0.1753 0.1856 0.1930 0.1950 0.2010 0.2O50 0.2100 0,2112 0.2122 0.2145
E (AGAINST NORMAL HYDROQEN ELECTRODI)
0.4586 0.4402 0.4276 0.4154 0.4094 0.4011 0.3908 0.3834 0.3814 0,3754 0,3714 0.3664 0.3652 0.3642 . 0.3619
* M = 0.1 designates that the concentrations of both potassium ferrocyanide and potassium ferricyanide are equal to 0.1 mole per liter. remained unchanged for periods of twelve hours and more. The various readings agreed within ~t0.0003 volt, the average being 0.3754 volt. The reproducibility of measurements with solutions from 0.0004 to 0.00006 molar was within 0.0005 volt. Each of the solutions was prepared fresh and measured a t least four times. Light was found to have a distinct effect on solutions whose concentrations were 0.0004 M or less, the E.M.F. tending to increase in light. All measurements were therefore made in a darkened room. Under these conditions, the potentials of even the most dilute mixtures remained constant for a t least one hour.
OXIDATION POTENTIAL OF FERROCYANIDE-FERRICYANIDE
949
Experimental results Table 1 gives the average of the results of measurements with equimolecular mixtures of potassium ferrocyanide and potassium ferricyanide, p representing the ionic strength. The value of E O was found by plotting the measured values of E against on large cross section paper and TABLE 2 Osidation potentials measured in a mixture containing K8Fe(CN)6and K,Fe(CN)s in the ratio 1O:i KaFe(CN)o
KdFe(CN)o
M
M
0.1 0.04 0.02 0.01 0.004 0.002 0.001 0.004
0.01 0.004 0.002 0.001 0.0004 0.0002 0.001 0.00004
TOTAL p
0.7 0.28 0.14 0.07 0.028 0.014 0.007 0.0028
0.8366 0.529 0.3742 0.2646 0.1673 0.1183 0.0837 0.0530
E
E
(AGAINST STANDARD QUINAYDRONE)
(AGAINST NORMAL HYDROGEN ELECTRODE)
0.0723 0.0898 0.1020 0.1130 0.1258 0.1337 0.1398 0.1462
0.5041 0.4866 0.4744 0,4634 0,4506 0.4427 0.4366 0.4302
CALCULATED
I
I
0.4450 0.4275 0.4153 0,4043 0.3915 0,3836 0.3775 0.3711
TABLE 3 Oxidation potentials measured in a mixture containing K3Fe(CN)8and KIFe(CN)8 in the ratio 1 : l O KaFe(CN)e
KpFe(CN)s
TOTAL
p
E
E
(AOAINST STANDARD QUINHY-
(AGAINST NORMAL HYDROQEN
DRONI)
M
M
0..01 0.004 0.002 0.001 0.0004 0.0002 0.0001 0.00004
0.1 0.04 0.02 0.01 0.004 0.002 0.001 0.0004
1.06 0.424 0.212 0.106 0.0424 0.0212 0,0106 0.00424
1.0295 0.6511 0.4604 0.3256 0.2083 0.1456 0.1029 0.0651
0.1895 0,2068 0.2188 0.2295 0.2420 0.2495 0.2555 0.2615
60 CALCULATED
ELECTRODE)
0.3869 0.3696 0,3576 0.3469 0.3344 0.3269 0.3209 0.3149
0.4460 0.4287 0,4167 0.4060 0'. 3935 0.3860 0.3800 0.3740
extrapolating to an ionic strength of zero. It was found to be equal to 0.3560 volt. The data are plotted in figure 2. The straight line represents the change of E , assuming that the limiting Debye-Huckel expression holds (equation 3). In addition, the @oxidation potentials were measured in mixtures containing ratios of potassium ferrocyanide and potassium ferricyanide of 10 :1 and 1 :10. The data are given in tables 2 and 3. They were recalcu-
950
I . M. KOLTHOFF AND WILLIAM J. TOMSICEK
0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
000000
000000 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
,
.
.
.
.
.
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
z
000000
951
OXIDATION POTENTIAL OF FERROCYANIDE-FERRICYANIDE
lated on the basis of a ratio of the concentrations of 1:1 and correspond to the e; values plotted in figure 2. These E: values are identical with the values of the potential E measured in the equimolecular mixtures of ferrocyanide and ferricyanide. The reproducibility of the measurements in the very dilute solutions containing unequal molecular ratios of ferrocyanide and ferricyanide i s not as good as of those reported in table 1; therefore, the extrapolated value of e: a t an ionic strength of zero is less reliable in the former cases.
T h e efect of neutral salts u p o n the potential In all of the following determinations a solution containing 0.0004 molar potassium ferrocyanide and 0.0004 molar potassium ferricyanide, freshly prepared by dilution of a 0.01 molar mixture, was used. Ten ml. of the TABLE 6 In hence of salts on the oxidation potential ~~
I TOTAL p
CONCENTRATION O F
NarPzOi
M
0.5064 0.2564 0.1064 0.0564 0.0314 0.0164
0.05 0.025 0.01 . 0.005 0.025 0.001
E
(AGAINST NORMAL HYDROGEN ELECTBODE)
CONCENTRATION OF Nan CITRATE
CONCENTRATION O F
0.4262 0.4154 0.4034 0.3953 0.3889 0.3826
0.125 0,0625 0.025 0.0125 0.00625 0.0025
0.0833 0.0416 0.0166 0.0083 0.00416 0.00166
(AGAINST NORMAL HYDROOEN ELECTRODE)
MgSOi
.ti
hi
0.4187 0.4097 0.3987 0.3918 0.3864 0.3809
E
(AGAINST NORMAL HYDROGEN ELECTRODE)
i
0.4584 0.4474 0.4344 0.4246 0.4152 0.4028
latter was diluted with conductivity water in a 2 5 0 4 . volumetric flask, a weighed amount of pure salt added, and the flask filled up to the mark. The results are given in tables 4, 5, and 6. “Total p” refers to the sum of the ionic strengths of the added salt and of the 0.0004 molar ferrocyanide-ferricyanide mixture ( p = 0.0064). From equation 3 it is found that 3 E - €0 log f=f4 0.0591
The values of log f3/f4 thus derived in various salt solutions are plotted in figure 3 against di. The straight line again gives the values calculated with the assumption that the ’limiting Debye and Huckel expression holds a t extreme dilutions. DISCUSSION OF RESULTS
1. The generally accepted value of the normal potential of the ferroferricyanide electrode of 0.44 volt is much too high. A t an ionic strength
952
I. M. KOLTHOFF AND WILLIAM J. TOMSICEK
of zero, a value of 0.356 volt was derived in this paper. From a practical viewpoint i t is of interest to mention that the oxidation potential increases very rapidly with the increasing ionic strength and that it even can exceed the value of 0.44 in equimolecular mixtures of ferricyanide and ferrocyanide. 2. Even a t infinite dilutions, the behavior of the system is not in harmony with the postulates of the simple Debye-Huckel expression. The slope of the curve giving the change of the oxidation potential or of log f3/f4 plotted against the square root of the ionic strength isgreater than
o
ai
FIG. 3 FIG.3. a, CsCl; b, RbCl; c, KCl and NHcC1; d, LiCl. D. H., calculated from simple Debye-Htickel expression.
FIG. 4. a, Mg(NOs)z; b, BaCl2; c, Ca(NOa)n; d, SrC12; e, NazSOa; f, Nas citrate; g, NarPzO,. D. H., calculated from simple Debye-Huckel expression.
that calculated on the basis of the Debye-Huckel limiting equation. It is impossible to account for this anomaly on the basis of ionic size, using the present form of the Debye-Huckd theory, for, as V. K. La Mer (6) states, “absurd negative values of ‘u’ would be demanded a t very high dilutions followed by positive values in more concentrated solutions.” Deviations of experimental data from the theoretically predicted curves have been described by various authors, a discussion of which is given in a paper by La Mer, Gronwall, and Greiff (7). Gronwall, La Mer, and Sandved (2) have shown that these discrepancies disappear if the influence of higher
OXIDATION POTENTIAL OF FERROCYANIDE-FERRICYANIDE
953
terms of the Debye-Huckel theory in the case of unsymmetrical valence type electrolytes is taken into account. On the basis of the extended Debye-Huckel equation, values are found which fit the experimental data without assuming ion association or incomplete dissociation of the strong electrolytes. Undoubtedly, in a quantitative interpretation of the data found in this study, the extended equation of Gronwall, La Mer, and Sandved should be applied, since we are dealing with highly unsymmetric valence type electrolytes. Still, we have evidence to believe that even the extended equation does not account quantitatively for the results obtained, and that potassium ferrocyanide has to be considered as an incompletely dissociated electrolyte. In a subsequent paper, it will be shown that the curve obtained in a study of the potential of the potassium molybdomolybdicyanide electrode, a system very similar to that of ferro-ferricyanide, does not intersect with the straight line calculated from the simple Debye-Huckel expression, but is found below this line even a t extreme dilutions. In addition it was found that the fourth dissociation of molybdocyanic acid HMo(CN)s---
+ H+
+ Mo(CN)s----
is complete whereas that of ferrocyanic acid HFe(CN)a---
H+ + Fe(CN)a----
is incomplete. This means that the proton combines with the ferrocyanide ion tof~rmHFe(CN)~---,anditis quite plausible that other cations behave similarly. In the study of the influence of salts upon the potential of a very dilute potassium ferrocyanide-potassium ferricyanide mixture described in this paper it was found that the effect is virtually independent of the type of the anions. Potassium bromide, chloride, and nitrate have an identical effect a t the same ionic strength; the same is true for sodium chloride, nitrate, and perchlorate on the one hand and sodium sulfate, oxalate, carbonate, and phosphate on the other. The type of cation, however, has a very pronounced effect. With the alkali cations it decreased in the order Cs, Rb, K = NH,, Na = Li, and we conclude that the degree of dissociation of the corresponding ferrocyanides decreased in the same order. The dissociation becomes more incomplete with the increasing valence of the cations, the effect of the various alkaline earths being of about the same order. This larger effect of the divalent ions is especially pronounced at the smaller ionic strengths. Since the concentration of the cation is of primary importance, it is easily understood why the oxidation potentials found in potassium ferrocyanide-potassium ferricyanide mixtures of various ratios and recalculated on the basis of a ratio of 1:1 are not the same a t the same ionic strength
954
I. M. KOLTHOFF AND WILLIAM J. TOMSICEK
(figure 2). The potentials found increase from the mixture with a ratio of 10 ferrocyanide to 1 ferricyanide to that with a ratio of 1 to 10. In the former, the potassium-ion concentration is much smaller than in the latter a t the same ionic strength. In a similar way, it is explained why the 1-2 valence types of electrolytes (sodium sulfate, carbonate, etc.) have a smaller effect than the 1-1 valence type of salts (sodium chloride, etc.). SUMMARY
1. The normal potential of the ferrocyanide-ferricyanide electrode is equal to 0.3560 volt a t 25°C. 2. The change of the potential of a very dilute ferrocyanide-ferricyanide solution with increasing ionic strength is greater than calculated on the basis of the simple Debye-Huckel expression. This is partly explained by incomplete dissociation of alkali and alkaline earth ferrocyanides. 3. For the same valence type of salts the anion effect upon the potential is the same for different anions a t the same ionic strength. A pronounced cation effect was observed, the effect decreasing in the order Cs, Rb, K = NHI, Na =‘Li for the alkali ions and being of about the same order for the alkaline earth ions. The latter, especially a t the smaller ionic strengths, have a much greater effect than the univalent cations. REFERENCES
FREDENHAGEN, C.: Z. anorg. allgem. Chem. 29, 396 (1902). T. H., LA MER,V. K., AND SANDVED, K.: Physik. Z. 29, 558 (1928). GRONWALL, KOLTHOFF,I. M.: Z. anorg. allgem. Chem. 110, 143 (1920). KOLTHOFF,I. M., AND BOSCH,W.: J. Phys. Chem. 36, 1685 (1932). KOLTHOFF, I. M. : The Determination of pH, Electrometric Titrations. John Wiley and Sons, New York (1931). (6) L A MER, V. K.: Trans. Am. Electrochem SOC.61, 543 (1927). (7) LA MER, V. K., GRONWALL, T. H., AND GREIFF,L. J.: J. Phys. Chem. 36, 2245 (1931). (8) LEWIS,G. N., AND SAROENT, L. W.: J. Am. Chem. SOC.31, 355 (1909). (9) LINHART,G. A,: J. Am. Chem. SOC.39, 615 (1917). (10) MULLER,E.: Z. physik. Chem. 88, 46 (1914). (11) SCHAUM, K., AND LINDE,R. v. D.: Z. Elektrochem. 9, 407 (1903). (12) SCHOCH, E. P.: J. Am. Chem. SOC.26, 1422 (1904). E. P., AND FELSING, W. A , : J. Am. Chem. SOC.38, 1928 (1916). (13) SCHOCH, (1) (2) (3) (4) (5)
