W. EATON, P. GEORGE, AND G. HANANIA
2016
Thermodynamic Aspects of the Potassium Hexacyanoferrate(II1)-(11) System. I. Ion Association1
by William A. EafOn,2 Philip George, and George I. H. Hanania Department of Chemistry and Graduate Group on Molecular Biology, University of Pennsylvania, Philadelphia, Pennsylvank 19104 (Received October 4, 1966)
A thermodynamic study has been made of the ion-association equilibria involving K + and the anions Fe(CN)s*- and Fe(CN)a3-. Conditions were determined under which a cationsensitive glass electrode could be used in this investigation. Using this electrode to measure K+ activity in aqueous solutions of K&‘e(CN)a and K,Fe(CN)e, the free-energy and enthalpy changes were obtained potentiometrically. The enthalpy changes were also determined in a precision solution calorimeter. The results show that ion binding is significant in both cases, and that the reactions are due to favorable entropy changes.
It has long been recognized that salts like the potassium hexacyanoferrates are incompletely ionized in aqueous solution. In fact, the classical work of Noyes and Johnston3 had shown that the “degree of ionization” as determined from conductivity measurements was different from that derived from colligative properties of the solutions. It was discrepancies of this type which led to the development of the concept of activities of ions. Nevertheless, in later work on electrolytic conductance, one interpretation of experimental conductances being less than those calculated by the Onsager-Fuoss limiting equation was to attribute this to incomplete dissociation of the salts, and on this basis to calculate ion-association constants for the chemical equilibria involved. Thus using conductivity data,4 Davies6calculated an association constant for the equilibrium K+
+ Fe(CN)a‘-
KFe(CN)s3-
(1)
and James and Monks using a similar method obtained an association constant for the corresponding equilibrium K+
+ Fe(CN)s3-
KFe(CN)sZ-
(2)
From changes in the ultraviolet absorption spectra of hexacyanoferrate(I1) salts with various cations, Cohen and Plane’ obtained values for the association constant of eq 1 and for analogous equilibria with Ba2+ and Mg2+. The Journal of Phyeiccc2 Chemistry
The recent introduction of reliable cation-sensitive glass electrodes has made possible the direct potentiometric determination of cation activity in salt solutions over a very wide range of conditions. Using this method, we have redetermined the ion-association constants and obtained thermodynamic parameters for the above equilibria. In part II,*we show that specific salt effects have a profound influence on the reduction potential of the hexacyanoferrate (111)-(11) couple. A preliminary account of this investigation has been presented elsewhere. Experimental Section Materials. K3Fe(CN)6,K4Fe(CN)6*3HzO,KCI, and Mg(N03)2-6Hz0were of AnalaR or Baker Analyzed (1) This work was supported by Grants AM-03187 and AM 04764 fromthe National Institutes of Health. (2) Scholar of the Pennsylvania Plan to Develop Scientists in Medical Research. (3) A. A. Noyes and J. Johnston, J . Am. Chem. Soc., 31,991 (1909). (4) G. Jones and F. C. Jelen, ibdd., 58, 2661 (1936). (6) C.W.Davies, ibdd., 59, 1760 (1937). (6) J. C. James and C. B. Monk, Trans. F a w h y SO&, 46, 1041 (1960). (7) 8. R. Cohen and R. A. Plane, J . Phys. C h . ,61, 1096 (1967). (8) G. I. H. Hanania, D. H. Irvine, W. A. Eaton, and P. George, aid.,71, 2022 (1967). (9) G. I. H. Hanania, W. A. Eaton, and P. George, Abstracts, 161st National Meeting of the American Chemical Society, Pittaburgh, Pa., March 1966, p 46N.
THERMODYNAMICS OF THE POTASSIUM HEXACYANOFERRATE(III)-(II) SYSTEM
grade, and were used from freshly opened bottles without further purification. Tetrapropylammonium bromide, PrdNBr, was purchased from Eastman Organic Chemicals and was used without further purification. Solutions were always made just before every measurement using distilled deionized water. Potentiometric Apparatus. The potentiometric cell employed consisted of a Beckman 39137 cation-sensitive glass electrode and a reference which was either a saturated calomel electrode with an agar-saturated KC1 bridge or an Ag, AgCl electrode. The cell was kept in a black-box Faraday cage and was thermostated by circulating water from a bath, temperature control being to zk0.05" or better. The emf measurements were made on a Radiometer PHM 4 meter to 0.1 mv. Behavior of Glass Electrode. The properties of cationsensitive glass electrodes have been extensively investigated (see, for instance, Eisenman'O). In the present work, we have found that the Beckman electrode is capable of precision to 0.1 mv, provided that the electrode is maintained free from thermal, mechanical, and electrical shocks, and is always kept in a solution of a potassium salt, in the dark. We have investigated the response of this electrode to potassium ion in a cell without liquid junction using Ag, AgCl as the reference electrode. Since the glass electrode has no standard potential, emf measurements on this type of cell can only yield ratios of mean molar ionic activity coefficients for KCl, YKCI. We have shown that in the ionic strength range 0.001 to 0.1 M , with or without added Mg(N03)z, neither electrode responding to magnesium or nitrate ions, the calculated Y K C ~ratios" are in excellent agreement with the published literature v a l u e ~ . ~ These ~ J ~ results show that the cell is thermodynamically reversible and hence that the cation-sensitive electrode responds to K + activity. Determination of I o n Association Constants. In order to determine the association constants for equilibria 1 and 2, it is necessary to measure the free (ie., unbound) K + activity, and hence the concentration, in a solution of known total salt concentration. For this purpose, we employed the cell
1
Hg, HgzCln(s) j salt / KC1 c1 glass satd KCl bridge j or K3Fe(CN)6 c2 / electrode i orK4Fe(CN)B c3 j In this cell, the glass electrode is immersed in 100 ml of a solution of KCI or KsFe(CN)a or K4Fe(CN)e; an
agar-saturated KC1 bridge makes connection with a saturated calomel electrode. It is readily shown that the concentration of free K + is given by
2017
Ys
log Yx
+ log [K+ls
(3)
where [K+]x is the molar concentration of free K + in the (unknown) hexacyanoferrate solutions, c2 or c3; [K+]s is the molar concentration of free K + in a (standard) KC1 solution, cl, assuming complete dissociation of the ions; and Ex and Es are the emf's for the unknown and standard solutions, respectively. Exj and Esj are the corresponding liquid junction potentials. yx and Z/S are the corresponding K + single molar ion activity coefficients obtained on the following two assumptions: (1) ys = YKCI, the mean molar ionic activity coefficient in the standard KC1 solution; and (2) yx = Y'KCI, the mean molar ionic activity coefficient at the calculated total molar ionic strength of the unknown hexacyanoferrate solution, taking ion association into account. Furthermore, the dilution of the solutions and the small temperature range employed about 25" were such that no practical distinction could be made between molal and molar activity coefficients. Values of the appropriate activity coefficients at the various temperatures were obtained from the data listed in ref 12 and 13. The difference in liquid junction potentials, Exj Esj, was evaluated for every pair of solutions used in the measurements employing the Henderson equation." In some cases, the value of this term was found to be zero and was never more than *0.1 mv; consequently, this term was neglected in the calculations. An attempt was made to use cells without liquid junction for the above measurements, the glass electrode being employed against Ag, AgCl as well as the recently introduced chloride-sensitive membrane electrode (National Instruments Labs, Inc.) as reference. In both cases, however, these electrodes were also sensitive to hexacyanoferrate ions and produced erratic results. The association (formation) constants, K,for equilibria 1 and 2 are defined in terms of the molar concentrations of all three species in each case. In dilute (10) G. Eisenman in Advan. And. Chem. Inatr., 4, 213 (1965). (11) W.A. Eaton, G. I. H. ISanania, P. George, and R. J. Witonsky, unpublished results. (12) W. M.Latimer, "Oxidation Potentials," 2nd ed, Prentice-Hall, Inc., New York, N. Y., 1952,p 355. (13) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed (revised), Butterworth and Co. (Publishers) Ltd., London, 1959,p481. (14) R. G. Bates, "Determination of pH," John Wiley and Sons, Inc., New York, N. Y., 1964,p 40.
Volume 71,Number 7 June 1967
W. EATON, P. GEORGE, AND G. HANANIA
2018
solutions, where a Debye-Huckel relation may be assumed, these association constants are related to the apparent thermodynamic association constants (MacInnes single-ion activity coefficient convention) , KO, by the equation log KO = log K
+ nI”’/(l + 1.511’*)
(4)
where at 25.0°, n = 4.08 for equilibrium 1 and 3.06 for equilibrium 2. The enthalpy changes for these equilibria are obtained from the temperature variation of the measured association constants at an ionic strength well within the region where the Debye-Huckel relation is obeyed. On this basis, using eq 4, the difference between the enthalpy changes at the low finite ionic strengths employed and the enthalpy changes at infinite dilution would only amount to about 0.1 kcal/mole, which is well within the limits of experimental uncertainty. We have therefore adopted the measured enthalpy change, A H , as a satisfactory approximation to the thermodynamic quantities, AH O . Calorimetric Measurements. An independent determination of the above enthalpy changes was made in a precision solution calorimeter. The apparatus and its calibration are described elsewhere. l5 A typical experiment consisted of the following: (a) 4.00 ml of a concentrated solution of K4Fe(CN)6was mixed with 950 ml of an appropriate KC1 solution at 25”, and the free K + concentration in the mixture was determined as described above; (b) 4.00 ml of the same K4Fe(CK)6 solution was mixed with 950 ml of water, and the free K + concentration was again determined. In both cases the heat evolved or absorbed was measured to the nearest 100 mcal. The difference between the observed heats of mixing, qa - qb, was found t o be slightly endothermic. This difference in the heats of mixing was attributed to the difference between the degree of ion association in the two mixtures. The number of moles of K + bound to Fe(CN)64- in the two cases, n8 and nb, respectively, can be calculated from the known composition of each mixture, the ionic strength, and the equilibrium constant. On this basis, the enthalpy change for the ion association equilibrium 1 is (5)
the corresponding case of equilibrium 2 being determined in an analogous manner. It is to be noted that this method neglects any difference between the heats of dilution of the potassium hexacyanoferrate salts into water and dilute KC1 solution which may arise from differences in ionic strength and ionic The Journal of Physical Chemistry
composition. In an attempt to preserve constant ionic strength in the final mixtures, two different types of calorimetric experiments were carried out. (1) A sample consisting of 4.000 g of KC1 was dissolved in 950 ml of 2.00 X M K3Fe(CN)6 and also in 950 ml of 1.00 X M KCI. Here the ionic strength is nearly the same in the two mixtures. The heats evolved were -224.8 f 0.4 and -224.4 f 0.4 cal, respectively, again indicating net endothermicity for the ion-binding reaction. Although this type of experiment has the advantage of constant ionic strength, the heat being determined comes out as the small difference between two large quantities and inevitably will carry a large uncertainty. (2) In this experiment, 4.00 ml of 0.475 M K3Fe(CN)6 was mixed with 950 ml of 0.0565 M KC1 and also with 950 ml of 0.0534 M Pr4NBr, the ionic strength being the same in the two mixtures assuming negligible binding of the tetrapropylammonium ion to Fe(CN)83-. The heats evolved were -1.94 f 0.10 and 1.44 f 0.13 cal, respectively. In this case, the strongly exothermic result is in sharp contrast with the above observations, and suggests that Pr4N+ ions exert strong specific salt effects on the solvent and/or solute ions. Quaternary ammonium salts were therefore not used for the adjustment of ionic strength in the present work. All calorimetric experiments referred to above were performed in triplicate. Spectrophotometric Studies. Another independent check on the effect of Pr4NBr on these solutions was made by examining the ultraviolet absorption spectra of hexacyanoferrate(I1) and (111) ions in the presence of excess Pr4NBr as well as KC1. The spectra quantitatively confirmed previous observations’ that K + has no perceptible effect on the Fe(CN),F spectrum but has an appreciable effect on the Fe(CN)c4- spectrum. Furthermore, Pr4NBr was found to have no appreciable effect on the absorption spectrum of either Fe(CN)63-or Fe(CN)e4-. All spectra were taken following the usual precautions, including careful blanking, using either a Cary 14 recording spectrophotometer or a Zeiss PMQ I1 spectrophotometer.
Results The potentiometric method described above has been applied in determining the ion-association constants for equilibria 1 and 2 over a range of ionic strength and temperature. The results are summarized in the following tables (where in all cases concentra(16) C. Wu! R. J. Witonsky, P. George, and R. J. Rutman, J . Am. Chem. SOC.,III press.
THERMODYNAMICS OF THE POTASSIUM HEXACYANOFERRATE(III)-(II) SYSTEM
tions are in moles per liter and the association constants in liters per mole). Tables I and I1 give the results at 25.0". Table I11 gives the values of the equilibrium constants at various temperatures between 9.9 and 45.0" at constant total salt concentration (the corresponding ionic strengths over this temperature range vary by about 1% or less). It is apparent from the data that the enthalpy change is small for both reactions and that there is some scatter in the isochore plots. Moreover, K values as determined in the present work have an average uncertainty of *5%. Only a mean AH value for the temperature range can therefore be obtained, and this comes out as 0.6 f 0.4 and 0.5 f 0.4 kcal/mole for ion association equilibria 1 and 2,values which we take as equal to the thermodynamic quantities, m" (see Experimental Section). The corresponding calorimetric data are given in Table IV. Here the AH values, as determined at 25", are 1.0 0.3 and 0.5 0.5 kcal/mole for equilibria 1 and 2, respectively, and as the measurements were made on dilute solutions,
*
*
Table I : Variation of Ion Association Constant K for Equilibrium 1 with Ionic Strength at 25.0'" [KtFe(CN)s] [Free K t ] x 10-8 x 10-8
0.350 0.400 0.500 0.700 0.800 1.00 2.00 3.00 4.00
1.35 1.53 1.91 2.65 3.01 3.73 7.28 10.6 14.2
Ionic strength
K
X 10-8
Log KO (eq 4)
126 136 132 108 104 101 77.2 83.8 59.6
3.30 3.72 4.62 6.38 7.24 8.92 17.1 24.4 32.7
2.32 2.36 2.34 2.32 2.33 2.34 2.33 2.44 2.35
-
Mean 2.35 It 0.02 a
See eq 4 and related text for definition of
K O .
Table 11: Variation of Ion Association Constant K for Equilibrium 2 with Ionic Strength at 25.0' '
x lo-'
K
Ionic strength X 10-8
2.95 3.67 5.84 7.27 14.3
19.4 17.6 14.6 14.3 10.8
5.84 7.27 11.5 14.3 28.0
[KaFe(CN)sl [Free K + ]
x
10-8
1.00 1.25 2.00
2.50 5.00
Log KO (eq 4)
1.50 1.48 1.45 1.46 1.44
Mean 1.46 f 0 . 0 2 a
See eq 4 and related text for definition of
KO.
2019
Table I n : Variation of Ion Association Constants K for Equilibria 1 and 2 with Temperature Temperature, "C Equilibrium 1
9 . 9 15.0 25.0 35.0
(1.00 x 10-*M
40.0
45.0
...
102
103
16.1 18.2 17.6 18.6
...
18.9
88.9 94.0 101
K 9 e ( C N 10 Equilibrium 2 (1.25 X lO-SM
KaFe(CN)d
these values are taken to be AH". The means b e tween the potentiometric and calorimetric values are therefore 0.8 f 0.4 and 0.5 f 0.5 kcal/mole, respectively. The corresponding thermodynamic entropy changes are obtained from the relation AS" = (AH"AG")/T yielding at 25.0": 13 f 2 eu and 8 2 eu for equilibria 1 and 2.
*
Table IV: Calorimetric Determination of AH at 25"
Equilibrium 1 Equilibrium 2
Qs,"
qb!
cal
cal
(na
- nb),
AX,
mmole
kcal/mole
-5.84 f 0.10 -5.15 f 0.10
0.65
1 . 0 f0 . 3
-1.94 f 0.10 -1.68 f 0.15
0.49
0.5 1 0 . 5
qa is the heat evolved when 4.00 ml of 0.727 M K I F ~ ( C Nor )~ 0.475 M KaFe(CN)s, is mixed with 950 ml of 0.0565 M KCl. q b is the heat evolved when 4.00 ml of the above solutions is mixed with 950 ml of water.
The above type of measurement was also extended to more concentrated solutions, about 0.01 M and above. The data indicate that a second K+ binds to the hexacyanoferrate(I1) ion. However, the uncertainties about assumptions concerning activity coefficients in these solutions preclude the calculation of reliable association constants.
Discussion In the present work, an attempt has been made to obtain reliable thermodynamic quantities for the ion association equilibria involving K + and the hexacyanoferrate anions. Previous workers have deduced the existence of these chemical equilibria from independent lines of evidence. From conductivity measurements, deviations from the limiting slopes predicted by Onsager's equation have been interpreted as due to the formation of ion pairs. Although this method has been successfully and extensively used in studying ion association equiVolume 71, Number 7 June 1967
W. EATON, P. GEORGE,AND G. HANANIA
2020
libria, l 6 , l 7 the reported thermodynamic constants for the hexacyanoferrate equilibria616 appear to carry a large uncertainty. The observed small changes in the ultraviolet absorption spectra resulting from the addition of KC1 to dilute K4Fe(CN)asolutions have been attributed to the existence of the chemical species KFe(CN)ea- and enabled the calculation7 of a more precise association constant. In this connection, we have observed that the addition of excess Pr4NBr to dilute K4Fe(CN)6 solutions has no perceptible effect on the absorption spectrum. The Pr4N+cation is known to have a small affinity for hexacyanoferrate anionP and is believed to have a large structure-promoting effect on the water solvent. l9 These considerations suggest that the spectral change with K + is not due to a medium effect but to the formation of an ion pair. However, this type of argument is not conclusive. In a study of the specific effects of cations on the rate of electron exchange between hexacyanoferrate(I1) and (111) ions,20 ion pairs were invoked as reaction intermediates in order to account for the observed kinetics. However, no quantitative conclusions were made regarding the extent of ion association. In our work, a different approach was employed. Using a cation-sensitive glass electrode, K + activity was measured, and consequently, association constants under a variety of conditions were determined. This method depends upon certain necessary assumptions concerning activity coefficients and liquid-junction potentials (see Experimental Section). The validity of these assumptions as well as the existence of ion pairs is borne out by the internal consistency of the results over the concentration range of our experiments (Tables I and 11). Furthermore, the enthalpy changes for the equilibria obtained calorimetrically a t 25" agree well with the mean enthalpy changes obtained from the temperature variation of the equilibrium constants (Table V). Perhaps the strongest evidence for the existence of ion association equilibria in hexacyanoferrate solutions is the agreement between thermodynamic constants determined by three independent methods: conductivity, spectrophotometry, and potentiometry (Table V). The present work confirms previous results which showed that ion association is appreciable in KaFe(CN)6 solutions and considerably more so in K4Fe(CN)s solutions. Thus in 5.00 X M KaFe(CN)o, 13% of the anions are complexed, and in 4.00 X M K4Fe(CN)s the extent of the association is 46%. In more concentrated solutions, the extent of binding will of course be greater, and at least in the case of Fe(CN)64-, the binding of a second K + also occurs. The Journal of Physical C h i s t r y
Table V : Summary of Thermodynamic Data at 25.0"
Log K O AHopot,kcal/mole" AHooal,kcal/moleb AS", eu Log K" (ref 5) Log K O (ref 6) Log KO (ref 7)
Equilibrium 1
Equilibrium 2
2.35 f 0.02 0 . 6 f0 . 4 1 . 0 i0 . 3 13 f 2
1.46 f 0.02 0 . 5 i0 . 4 0 . 5 =k 0 . 5 8 f 2
2.3
...
2.37
" AHopotfrom potentiometric measurements. calorimetric measurementa.
*.. 1.2
...
AHoosl from
Quantitative knowledge of these equilibria is important in determining the ionic composition, computing ionic strengths, and elucidating other specific salt effects in hexacyanoferrate solutions. An example is the role of ion association in interpreting oxidation-reduction potential data for the hexacyanoferrate(II1)-(11) couple. This aspect will be discussed in detail in part 11.8
The enthalpy changes for both ion association equilibria are slightly endothermic. Unless extensive desolvation is involved, this suggests that the chemical bonding is weak in both ion pairs. In fact, the reactions are driven entirely by the favorable entropy changes (Table V). Assuming the simple electrostatic picture of ion-pair formation to hold in these systems, one can calculate the distance of closest approach of the centers of the associating ions from the Bjerrum equation.21 Using our association constants, we have calculated 4.3 0.1 A for KFe(CN)sa- and 6.6 0.2 A for KFe(CN)P. Although this type of calculation can be criticized, the difference between the two cases nevertheless appears to be significant. On this basis, it may be concluded that the structures of the two ion pairs are significantly different. In this connection, it is interesting to note that although F ~ ( C N ) B forms ~two conjugate acids, HFe(CN)ea- and H ~ F ~ ( C N ) . Sacidimetric ~-, titration of
*
*
(16) G. H. Nancollas, Quart. Rev. (London), 14, No. 4, 402 (1960). (17) C. W. Davies, "Ion Association,'' Butterworth and Co. (Publishers) Ltd., London, 1962. (18) D.W. Larsen and A. C. Wahl, Inorg. Chem., 4, 1281 (1966). (19) H. S. Frank, J. Phys. Chem., 67, 1554 (1963). (20) R. J. Campion, Ph.D. dissertation, Washington University, St. Louis, Mo.,1963. (21) H.8.Harned and B. B. Owen, "Physical Chemistry of Electrolytic Solutions," 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1958, Chapter 5.
THERMODYNAMICS OF THE POTASSIUM HEXACYANOFERRATE(III)-(II) SYSTEM
F ~ ( C N ) B shows ~no evidence for the formation of conjugate acids above pH LZ2 Furthermore, whereas the ultraviolet absorption spectrum of F e ( C N ) P undergoes changes on the addition of various metal cations, no spectral changes are detected on the addition of various metal cations to Fe(CN)6*-, although ion association is known to occur. A possible explanation for the above observations is that there is a greater penetration of the hydration shell in the KFe(CN)&ion pair than in the K F e ( C N ) P ion pair. A similar conclusion has been reported in the case of the L a F e (CN)a ion pair.16*23
Achowledgment. We wish to thank Dr. R. J.
2021
Witonsky for much help and useful discussion of this work. (22) J. Jordan and G. I. Ewing, I w g . Chem., 1,587 (1962). (23) NOTEADDEDIN PROOF.Since submitting this paper, the work of R. W. Chlebek and M. W. Lister [Can. J . C h m . , 44, 437 (1966)l
has come t o our attention. In studying the kinetics of electron transthey found that the rate constante fer between KiFe(CN)o and KzSZO~ varied according to the Bransted equation, provided ion association by both reacting species was taken into account. They investigated the ion association equilibria using a cation-sensitive glass electrode with solutions containing the tetramethylammonium ion. The apparent disagreement between their thermodynamic data and those quoted above for solutions containing only the KCl cation may be due in part to their use of higher concentrations, and in part to the additional specSc salt effects which we have observed when tetraalkylammonium salts are employed (see Experimental Section and part IF).
Volume 71, Numbr 7 June 1967
