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2022
Thermodynamic Aspects of the Potassium Hexacyanoferrate(II1)-(11) System. 11. Reduction PotentiaF2
by George I. H. Hanania, Dennis H. Irvine, William A. E a t ~ nand , ~ Philip George Department of Chemistry and Graduate Group on Molecular Biology, University of Pennsylvania, Philadelphia, Pennsylvania 1Q l O 4 (Received October 9, 1068)
The reduction potential for the hexacyanoferrate(II1)-(11) couple has been measured potentiometrically over a range of temperature, pH, ionic strength, and in the presence of various 1:l salts. The following thermodynamic quantities were obtained at 25.0' and I = 0: E" = 0.355 f 0.001v, AH" = -26.7 i 0.3 kcal/mole, and AS" = -62.1 f 1.0 eu. The data on the variation of reduction potential with concentration are shown to be consistent with the assumption of cation binding to both oxidant and reductant anions (thermodynamic parameters for these ion association equilibria are presented in part I). The strong salting-out effect of tetraalkylammonium salts on the reduction potential suggests that these ions exert an additional specific salt effect. The data on the variation of reduction potential with pH in solutions of pH 6, where the measured reduction potential is independent of pH, and in sufficiently dilute solutions where multiple K + binding is negligible, eq 8 reduces to
KtFe(CN),P Following general practice, all acid-base equilibria are considered as dissociation, so that Kd = h X [Fe(cN))~~-]/[HFe(chT)s~-], etc., whereas the cationbinding equilibria are considered as association, viz. K1 = [KFe(CN)6a-]/[Fe(CN)64-] X k, etc. Furthermore, all equilibria are defined in terms of the molar concentration of K + and the activity of H+(using the symbols k and h, respectively), and of the molar concentrations of all other species. The effect of the above ionic equilibria on the measured reduction potential,
(3)
[reductant] =
Ei Fe(CN)P
2023
Ei=E--
RT 1 In F 1
+ kKr + kK1'
(9)
Experimental Section The two salts, K3Fe(CN)s and K4Fe(CN)6-3Hz0, were of AnalaR or Baker Analyzed grade and were (10) Delaware Valley Regional Meeting of the American Chemical Society, Philadelphia, Pa., Feb 1968,Abstract 14, p 71. (11) G. I. H. Hanania, W. A. Eaton, and P. George, Abstracts, 151st National Meeting of the American Chemical Society, Pittsburgh, Pa., March 1966,p 46N.
Volume 71, Number 7 June 1887
G. HANANIA, D. IRVINE, W. EATON, AND P. GEORGE
2024
used from freshly opened bottles without further purification. Tetraalkylammonium salts were purchased from Eastman Organic Chemicals and were not further purified. Tetrapropylammonium hexacyanoferrates were prepared on Dowex cation-exchange resin following conversion of the resin to the tetrapropylammonium form with subsequent washing to neutral pH. Solutions were freshly made for every set of measurements and were always kept in the dark. The most dilute solutions were deoxygenated with prepurified nitrogen. All solutions were prepared with deionized distilled water. No spurious effects were observed. Potentiometric measurements were carried out in a jacketed glass vessel using two or three bright platinum electrodes cleaned with boiling acetone and hot concentrated nitric acid. A preequilibrated saturated calomel electrode with an agar-saturated KC1 bridge was used as a reference electrode. The calomel electrodes employed were selected from a group of commercial calomel electrodes which agreed to within 0.0002 v at several temperatures. The fiber junction calomel electrodes from Beckman Instruments Co. (39970) were guaranteed to have a potential os. a standard hydrogen electrode of 0.2445 0.0005 v at 25” (including liquid-junction potential) and those from the Arthur H. Thomas Co. (4857-F10) were guaranteed to have a potential of 0.244 f 0.002 v at 25”. These values were confirmed by measurements against Ag, AgCl electrodes, prepared according to the method of Brown and MacInnes,12 in KC1 solutions of various concentrations. Taking 0.2224 v as the standard potential of the Ag, AgCl electrode at 25.0°13and using the activity coefficient data for KC1 from Latimer,14 the standard potential of the calomel electrodes (including liquid junction potential) was found to be 0.245 f 0.002 v over a 100-fold range of KC1 concentrations. Liquid junction potentials for the hexacyanoferrate solutions, as estimated from the Henderson equation, were found to vary between the narrow limits of 2 to 5 mv. It was therefore assumed that liquid junction makes a relatively constant or an insignificantly small contribution to the measured potentials in very dilute solutions, and no corrections to the emf data were applied. The uncertainty produced on this account in the derived thermodynamic quantities will be commented upon later in the Discussion. The apparatus was kept in a black-box Faraday cage, and the measurements were recorded only when the emf’s were constant with time and the pIatinum electrodes agreed to better than 0.0002 v. Temperature was controlled to within =t0.05” by circulating water from a thermostat. The emf was read to the nearest 0.0001 v on a Radiometer pHM4 meter. The mea-
*
Tho Journal
of Physical
Chemistry
sured reduction potential, E, refers to the emf against a standard hydrogen electrode, calculated from the data of BatesI6 on the saturated calomel electrode. The pH measurements were made with the same apparatus using glass and calomel electrodes, following the recommendations of Bates for standardization.l7 The heat of the reaction H + Fe(CN)64- HFe(CN)aS- was measured in a precision solution calorimeter using the following procedure: 4.00 ml of 0.727 M K4Fe(CN)a was mixed with 950 ml of approximately 0.006 M HClO4 and, as a control, 4.00 ml of 0.727 M K4Fe(CN)6 was mixed with 950 ml of H20. The pH of the final mixtures was measured and hence the enthalpy change for the above reaction could be calculated according to the method already described.‘ Appropriate corrections were applied to the observed heat to take into account contributions from the dissociation of KFe(CN)6a-, the formation of a small fraction of H2Fe(CN)62-,as well as the possible formation of HKFe(CN)e2- for which the heat of binding has been assumed equal to that for KFe(CN)63-. The value for H2Fe(CN)s2- was obtained from a similar experiment at a higher acidity.
+
Results E$ect of Ionic Strength and Ion Association; Determination of E O . The potential of equimolar mixtures of KaFe(CN)6and K4Fe(CN)6was measured over a wide range of concentrations. The results agreed to within 0.001 v with the data of Kolthoff and T o m s i ~ e k . ~ Figure 1 shows our data for the low ionic strength region at 25.0”. It can be seen that the measured reduction potential, E, deviates from the limiting theoretical Debye-Huckel slope even in the most dilute solutions, the apparent limiting slope being 0.260 v/M”’. On the other hand, taking ion association into account, the resulting Ei values fit the limiting theoretical Debye-Huckel slope of 0.209 VIM’’* up to an ionic strength of 0.003 M and show the expected type of deviation at the higher ionic strengths. Values of Ei were calculated from eq 9 by the following procedure: (1) for each mixture, the free K + concentration, k, was measured following the method already described;’ (2) for all these mixtures, (12) A. 8. Brown and D. A. hlacInnes, J . Am. Chem. Soe., 57, 1356 (1935). (13) D.J. G.Ives and G . J. Janz, “Reference Electrodes,” Academic Press Inc., New York, N. Y., 1961, p 189. (14) W. M.Latimer, “Oxidation Potentials,” 2nd ed, Prentice-Hall, Inc., New York, N . Y.,1962, p 355. (15) R. G. Bates, “Determination of pH,” John Wiley and Sons, Inc., New York, N. Y., 1984, p 40. (16) R. G.Bates, ref 15, p 278. (17) R. G . Bates, ref 15, Chapter 4.
THERMODYNAMICS OF THE POTASSIUM HEXACYANOFERRATE(III)-(II) SYSTEM
2025
I
I
0.2
Q9
I
I
08
08
24
Figure 1. Variation of reduction potential with ionic strength a t 25.0" for equimolar concentrations of KaFe(CN)s and KJ?e(CN)s: 0, measured reduction potential, E, the total molar ionic strength being computed on the basis of complete dissociation of both salts; 0 , Ei,the cation-independent reduction potential for equilibrium 1, calculated from eq 9. Ionic strength is computed taking ion-association equilibria into account. Linear extrapolation along theoretical Debye-Huckel slope of 0.209 v M-'" yields E o = 0.355 f 0.001 v.
pH >6 and consequently the terms h/K4 and h2/ K z a made no significant contribution to Ei; (3) in each case, the total molar ionic strength was calculated by successive approximations taking the presence of ion pairs into account; (4)the appropriate values of the cation association constants K1 and K1' at the ionic strengths of the mixtures were used;' (5) assuming Kz to be of the order of magnitude of KI', the term k2KlK2 was found to be insignificant except in the two most concentrated mixtures. The extrapolation of Ei to zero ionic strength gives the standard reduction potential at 25.0" for the couple in eq 1: Eo = 0.355 f 0.001 v. Other Salt Effects. The reduction potential was also measured in the presence of varying concentrations of added electrolytes. Figure 2 shows the effect of added 1 : 1 salts. The reduction potential rises progressively in all cases except where the added electrolyte is a tetraalkylammonium halide (R4NX). There is a gradation of salting-out effects with R4NX salts, reaching what appears to be a limit in the case of Pr4NBr and BQNBr. The same sharp salting-out effect is observed by varying the concentration of an equimolar mixture of tetrapropylammonium hexacyanoferrates. The extent of these specific salt effects can be seen for instance at 0.5 M added salt where the reduction potential measured in the presence of Pr4-
Figure 2. Variation of measured reduction potential, E, with the concentration of added 1:1 salts; 1.00 X 10-4 M each KJ?e(CN)e and &Fe(CN)s; T = 25.0'; (a) KBr (and similar salts'); (b) Me4NBr; (c) EkNBr; (d) n-Pr4NBr (A),and n-BudNBr (A).
NBr is about 0.15 v lower than it is in the presence of the "neutral salts" like KBr, NaCl, NHrC1, etc. Furthermore, when one of these salts is added to a hexacyanoferrate(II1)-(11) mixture containing excess R4NX, an immediate dramatic rise in the reduction potential is observed. Effect of Temperature. The reduction potential was measured at four temperatures between 15 and 30" at I = 0.064 M . At each temperature, Ei was calculated as described above. The mean value of v deg-l, which dEi/dT was -(2.69 f 0.04) X was taken as a first approximation to be thevalueof dE"/dT. Thus, for the parent cell reaction in eq 1 : AH" = -26.7 f 0.3 kcal/mole and AS" = -62.1 f 1.0eu. Effect of pH. The measured reduction potential is constant above pH 6 whereas in more acidic solutions its value increases progressively. From simultaneous measurements of E and pH in a solution containing equimolar concentrations of KaFe(CN)s and K4Fe(CN),, titrated with HC1O4, the ionization constants K4 and K3 were calculated from eq 8 in the following manner. At pH >6, the free K + concentration, k, is measured and the ionic strength is calculated.' Ei is then obtained from eq 9 using the appropriate ion association constants KI and K1'. In the more acidic solutions, the ionization constants Kq and Ka are calculated from eq 8 by successive approximations. In this calculation, the small changes in ionic strength and k are taken into account. The value of h, the activity Volume 71, Number 7 June 1967
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Table I: Variation of pK4 with Ionic Strength a t 25.0' Concn each, M
I, M PK4 pK2
2 . 5 0 X 10-3 0.036 3.76 4.28
1.OO X
0.015 3.92 4.28
a
5.00 X 0,0075 4.02 4.29
a pKp values were obtained from simultaneous measurements of E and pH in equimolar mixtures of K4Fe(CN)sand KsFe(CN)s titrated with HClOd. Calculation involves successive approximation using eq 8, as described in the text. pK2 = pK4 3.5611/'/ (1 1.51''2). Mean deviations are 3 ~ 0 . 0 2 .
+
+
I
I
2
3
I
I
4
5
I 6
PH
Figure 3. Variation of measured reduction potential, E, with pH a t 25.0 and a t I = 0.014-0.023 M . Curve a gives the theoretical variation in accordance with eq 8, while curve b gives the corresponding relation on the basis of only one conjugate acid for the hexacyanoferrate(I1) ion, ;.e., ignoring the term h*/KaK4 in eq 8.
of hydrogen ions, is obtained from the measured pH assuming that pH = -log h. The mean value of K4 is obtained from about 15 measurements in the range of pH 2.6 t,o 1.7. Figure 3 shows the variation of E with pH a t 25". Two theoretical curves have been drawn, one assuming the participation of only one conjugate acid of the hexacyanoferrate(I1) ion, and the other taking into account two overlapping ionizations. The experimental points are best fitted by the curve corresponding to two successive ionizations. It can also be seen that the limiting difference, E Ei, in neutral solution is 9.5 mv. This represents the effect of ion association in this experiment with 1.0 X M K4Fe(CN)6and 1.0 X M K3Fe(CN)6. The above method of calculation was also applied to the data at other ionic strengths. However, there is a limitation on the range of ionic strengths which can be covered in these measurements. For, at the extreme of dilute solutions, the ionic strength will vary appreciably as the pH is changed during an experiment, and a t the other extreme of I > 0.05 M , uncertainties about the various ionic equilibria which are involved preclude the precise determination of the parameters required in the calculations. We have therefore confined our measurements to the range shown in Table I. Here the results a t 25.0" are given together with the calculated thermodynamic ionization constant using the relation pK40 = pK4 3.5611/'/ (1 1.511"). Thus the mean value of pKdOis 4.28 f 0.02.
-
+
The Journal of Phyeical Chmietra,
+
The above treatment of the data also yielded a value for the third ionization constant: pK3 = 1.96 f 0.03 a t 25.0" and I = 0.020-0.025 M . Beyond this range, in either direction, uncertainties are involved which preclude any precise calculation. We have therefore taken the thermodynamic constant on the basis of the single determination, using the corresponding relation pK3O = pK3 2.5511'a/(1 1,511'2), and hence pK30 = 2.3 f 0.1 at 25.0", showing the maximum limits of uncertainty. Jordan and Ewing have determined K4 and K3 from acidimetric titrations of K4Fe(CN)~solutions. Their results are pK40 = 4.17 f 0.02 and pK3O = 2.25 f 0.15 at 25.0". When our pK4 data are treated taking no account of K f binding, the results become almost identical with those of Jordan and Ewing. Furthermore, when our data are analyzed as an acidimetric titration, again excluding K + binding, the results are also in accord. The apparent discrepancy in pK4' can thus be accounted for satisfactorily in terms of ion association. The calorimetric measurements yielded a value of AH4 = -0.5 f 0.5 kcal/mole for the ionization of HFe(CN)e3-. The limits of uncertainty in this value represent uncertainties due to the overlap of the two ionizations as well as uncertainties in the contribution to the observed heat from various ion association equilibria. Assuming AH4" = AH4, it follows that AS," = -21 f 2 eu. The enthalpy change for the ionization of one proton from HzFe(CN)62-was obtained calorimetrically using the same method as for AH4. In addition to uncertainties arising from heats of ion association, there are larger uncertainties due to the instability of the hexacyanoferrate(I1) ion in the more acidic solutions. AH3 was found to be approximately -1 kcal/mole. This yields an approximate value of A&" = - 14 eu. Jordan and Ewing report AH4 = AH3 = 0.0 from thermometric titrations of K4Fe(CN)6 with hydrochloric acid. However, the conditions of these experiments are not given in sufficient detail for comparison with our results.
+
+
THERMODYNAMICS OF THE POTASSIUM HEXACYANOFERRATE(III)-(II) SYSTEM
Discussion The standard reduction potential for the hexacyanoferrate(II1)-(11) couple (eq 1) as determined in the present study is E” = 0.355 i 0.001 v at 25.0’. This value is independent of both protonation and ionassociation equilibria. E” was obtained from the measured reduction potentials, corrected for ion association, and extrapolated to zero ionic strength from the region of extremely dilute solutions. I n this region, the data fit well the limiting Debye-Huckel function (see Figure 1). The same value is obtained using the extended Debye-Huckel function, I”’/(l BaI”*), the best fit being for a = 6 A. This agreement with Debye-Huckel behavior supports the assumption that any residual junction potential in the experimental cell, in the region of very low ionic strength, is either insignificantly small or is virtually constant but indeterminate. The above value is to be compared with the results of previous workers. Kolthoff and Tomsicek4 obtained 0.356 v by an empirical extrapolation from extensive measurements in extremely dilute solutions. Lin and BreckJ6whose measurements were made in somewhat more concentrated solutions, reported 0.3644 v. Two factors could account for this slightly higher value. In the first place, the slope of the plot of their data is considerably lower than the theoretical Debye-Huckel slope, as would be expected for the range of concentrations employed. Secondly, ion association is significant. Calculations using eq 9 show that the contribution from ion association varies from 0.006 to 0.020 v over the range of concentrations in their work. Using a cell without salt bridges in which the liquid junction potential was minimized by an appropriate choice of reference electrode, Rock6 arrived at a value of 0.3704 v for E”, based on measurements made on solutions of the order of 0.1 m. This author adopted a strong electrolyte standard state in order to take ionassociation effects into account. It may be that liquid-junction potentials account for part of the difference between Rock’s value and 0.355 v which was obtained in the present work by direct extrapolation of experimental data to infinite dilution. At any rate, the difference leads to an uncertainty in the entropy change associated with the cell reaction of about 1 eu; this is quite acceptable for the type of correlation between partial moIaI entropies of variously charged species which is presented in our discussion below. The present study shows that in the determination of the hexacyanoferrate(II1)-(11) reduction potential, three types of salt effects operate. (1) Ionic Equilibria, i.e., Binding of Cations, Protons, etc. It is the magnitudes and the difference
+
2027
in affinity of oxidant and reductant for the various ions which determine the magnitude of the effect of ion binding. For instance, in a 0.1 M mixture of potassium hexacyanoferrates the contribution is approximately 0.040 v. (2) Ionic Strength. After correcting for ion association, limiting Debye-Huckel behavior for highly charged ions can only be expected in extremely dilute solutions, e.g., in the present case a t I < 0.003 M. (3) Other Specific Salt Effects. Reference to Figure 2 shows that although the effect of various 1 : 1 salts on the reduction potential is similar in the limit of dilute solutions, there is very marked divergence at higher concentrations. In the case of NaCI, KBr, etc., and possibly MerNBr, the greater extent of binding of cation to reductant over that of oxidant accounts for the sharp rise in reduction potential with increasing concentration of added electrolyte. The larger tetraalkylammonium salts, however, cause a sharp reversal of the salt effect in an unusually low ionic strength region (I = 0.01 M). There is evidence that Pr4N+, and probably also BuIN+, have a weak affinity for hexacyanoferrate ions. ,18 Furthermore, estimates of the extent of binding a t concentrations above 0.1 M lead to the conclusion that ion association is quite insufficient to account for the rapid divergence of the curves for PrdNBr and KC1 in Figure 2, which reaches 0.15 v at I = 0.5 M. These observations indicate that the tetralkylammonium salts exert an additional specific salting-out effect of quite large magnitude. In recent years, effects of this kind have been well established for these salts and explanations are currently being sought in terms of the “structure promoting” influence of these organic cations on the solvent waterlg and in terms of nonideal configurational entropies of mixing due to the large size difference between these cations and the water molecule.*O The enthalpy change for the cell reaction in eq 1, as determined potentiometrically in this work, is -26.7 f 0.3 kcal/mole. The only other values reported in the literature are -27.6 obtained potentiometrically6 and -26.8 i 0.4 derived from the heat of oxidation of hexacyanoferrate(I1) by bromine.’ Since the standard reduction potential and enthalpy change seem to be well established, the uncertainty in the entropy change for this cell reaction cannot be more than 2 eu. Comparison of data for the hexacyanoferrate(II1)(11) oxidation-reduction couple with the corresponding (18) D.W.Larsen and A. C. Wahl, Inorg. Chem., 4, 1281 (1965). (19) H.S. Frank, J . Phys. Chem., 67, 1554 (1963). (20) R. E. Conway and R. E. Verrall, ibid., 70, 1473 (1966).
Volume 71, Number 7 June 1967
G. HANANIA, D. IRVINE, W. EATON, AND P. GEORGE
2028
Table II: Thermodynamic Data, a t 25" and I = 0, for Some Oxidation-Reduction Couples of Complex Ions in Aqueous Solution Charge, O/R
Feas Fe(CN)6 Fe (CN)4dipy Fe (dipyh Fe (dipy(CHI)z )a Fe(phen)a Ru(dipy )a Os (dipy )S Fe (pyridine-2aldoxime)s Fe (pyr-P,&dialdoxime)Z Fe (.P17-dihydroxyphen)a
3+/2+ 3-/41-/23+/2+ 3+/2+ 3+/2+ 3+/2+ 3+/2+ 0/11-/23-/4-
AH',
Eo,v
kcal/mole
0.771 0.355 0.542 1.120 0.941 1.141 1.374 0.878
-9.95 -26.7 -27.3 -32.7 -26.8 -32.5 -36.3 -24.7 -21.0 -24.7 -5
0.347 0.204 -0.20
AS', BU
26.4 -62.1 -49.5 -23.1 -17.1 -20.8 -15.4 -14.8 -43.6 -67.1 32
-
Reference
a, b This paper C
C
d C C
e
f f 9
D. H. Imine, J . Chem. Reference 23. * R. E. Connick and W. H. McVey, J . Am. Chem. Soc., 73,1798 (1951). Reference 9. Soc., 2977 (1959). G. T. Barnes, F. P. Dwyer, and E. C. Gyarfas, Trans. Faraday Soc., 48,269 (1952). G. I. H. Hanania, D.H. Imine, M. Michaelides, and F. Shurayh, Abstracts, 9t.h International Conference on Coordination Chemistry, St. Moritz, Switzerland, Sept 1966. G. I. H. Hanania, M. W. Makinen, P. George, and W. A. Eaton, unpublished results.
'
data for a number of other oxidation-reduction cell reactions allow certain generalizations to be made. The available thermodynamic data are summarized in Table 11. Thus, on comparing the dipyridyl complexes of iron, ruthenium and osmium, it is seen that the differences in their reduction potentials are reflected mainly in the enthalpy changes for their cell reactions. Presumably, for such a series of structurally similar low spin octahedral complexes of the same charge type, it is the bonding to the metal which is the major factor. One may also compare a series of nitrogen-coordinated octahedral iron complexes which differ principally in their net charge. The tris-o-phenanthroline and trisdipyridyliron(II1)-(11) couples have reduction potentials of about 1.1 v, whereas the analogous tris(4,7-dihydrc~xyorthophenanthroline)iron(III)-(II)couple has a reduction potential of about -0.1 v when all six hydroxyl groups are ionized. Thus the reduction potential decreases as the electrostatic charge in the neighborhood of the iron becomes more negative, spanning the exceptionally wide range of 1.34 v (Le., about 30 kcal/mole in free energy). The data show that this effect arises mainly from a decreased exothermicity of the cell reaction and to a lesser extent from the more unfavorable entropy change. Entropy effects may be compared in terms of the standard ionic entropies of the various species involved in the cell reaction where S'Rand S"0 represent the partial molal entropies of the reductant and oxidant species, respectively. The Journal of Physical Chemistry
Taking S " H=~ 31.2eu, a quantity 6s"can be evaluated, where 6s" =
SoR- Soo+ SOH+ = A#'
+ 15.6 eu
Lin and Breck5 concluded that the small negative values of SS",about -6 eu, in the case of some organic ligands such as dipyridyl, lend support to Gurney's "absolute" entropy scalez1 based on PH+ = -5.5 eu since it might be expected that with the charge buried in the center of the complex S O R and So0 would be almost i d e n t i ~ a l . ~ JHowever, ~ further data for this type of complex show rather greater variations, so although there may be some justification for this simple interpretat.ion it cannot be accepted as a general rule. Use of the absolute scale with So=+ = -5.5 eu makes s" for anions more positive and So for cations more negative by 5.5 eu per unit charge than values based on the practical scale where S O H + is arbitrarily put at zero. In comparing the magnitudes of ionic entropies, this has the important consequence that while the increments between the values for ions of the same charge remain unchanged, the increments between the values for ions of different charge are decreased by 5.5 eu per unit charge. However, in the comparisons made below, this latter consideration does not affect the conclusions, and since So=+is not yet known very precisely, all t,he So values have been calculated according to the practical scale. (21) R. W. Gurney, "Ionic Processes in Solution," McGraw-Hill Book Co., Inc., New York, N. Y.,1953. (22) P. George, G. I. H. Hanania, and D. H. Irvine, J. Chem. Phya., 22, 1616 (1954).
THERMODYNAMICS OF THE POTASSIUM HEXACYANOFERRATE(III)-(II) SYSTEM
2029
Another consideration in comparing the entropies for Table I11 : Partial Molal Entropies of Hexacyanoferrate Ions a series of structurally related compounds is the conat 25.0", Based on: Eo=+= 0, PK+ = 24.5 eulZ3and tribution from the symmetry number, u, which, by deS°Fe(CN)s8- = 64.8 eu.' AS" Values Obtained from creasing the rotational partition function, lowers the Oxidation-Reduction and Protonation Equilibria (This Work) and Ion-Association Equilibriab entropy by :in amount R In u. For pairs of compounds related by a chemical reaction, e.g., ionization Ion Oxidation state Bo,eu or complex formation, it is these symmetry numbers Fe (CN )e4 I1 18 f 1 that give rise to the more familiar "kinetic statistical Fe(CN)saI11 64.8 factors." For the ions under discussion, the maxiKFe(CN)5aI1 56 =k 3 HFe (CN)s3I1 39 f 3 mum symmetry numbers are 24 for Fe(CN)s4- and KFe ( CN)5e I11 97 =!z 2 Fe(CN)63-, 4 for HFe(CN)e3- and KFe(CN)ea-, 8 for HzFe (CN)s2I1 53 f.6 the trans configuration of H2Fe(CN)e2-, and 2 for the Reference 24. * Reference 1. cis configuration. Hence, if corrections for the maximum symmetry numbers were to be made so as to make the comparisons solely on the basis of the insome crucial difference in structure, charge distribution, trinsic contributions from each constituent structural solvent interaction, or some combination of these group, they would range from a maximum of 6.3 eu factors. In the case of the hexacyanoferrate system, to a minimum of 1.4 eu, and the maximum correction we proposed earlier that a H30+ion could be bonded to to the entropy change for any of the reactions would three cyanides at the corners of an octahedral face of be R In 6, Le., 3.6 eu. These corrections, like the use the complex.25 However, this structural feature alone of the absolute entropy scale, do not affect the following would not account for the observation that with the conclusions in any way, and so they have been left out tetracyanodipyridyl system the corresponding entropy of the calculations. The use of the unit mole fraction difference is significantly smaller. standard state to obtain Gurney's "unitary ionic enPresumably, in the conjugate acids the hydrogen is tropies"21 also does not affect the conclusions since covalently bonded, so in these complexes the ligands this would only shift the entropy scale by R In 55.5 eu are of two types, CN- and HNC. The ligand field without changing the differences between the ionic would thus have a lower symmetry. However, alentropies for any pair of ions. though an effect of this kind might be expected to Table I11 lists the entropies of the various hexacyanoferrate ions, taking S'K+ = 24.5 euZ3and S " F ~ ( C= N ) ~ have ~ - a marked influence in determining AH", it is difficult to envisage a mechanism by which it could 64.8 e u Z 4 In looking for correlations between 3" hold the 3"values at such low levels. and charge type, it is immediately apparent that while This peculiar property of the conjugate acids is not, the values for the potassium complexes are broadly however, restricted to the cyanoferrate complexes. in accord with expectation, those for the conjugate acid species are quite anomalous. With the former, 3' increases substantially in going from Fe(CN)e4to KFe(CN)63- to KFe(Cn')62-, i.e., 18, 56, and 97 eu, respectively. In addition, the value for K F e ( C N ) P is only 9 f 3 eu lower than that for Fe(CN)s3-, a relatively small difference which could be attributed to lack of complete charge cancellation within the complex. On the other hand, Sofor HFe(CN)e3- is much more negative, by 26 f 3 eu, than that of Fe(CN)2-, and the value for H2Fe(CN)62-is even more negative than POqthe values for the 3- species Fe(CN)2- and KFe(CN)e3- despite its more favorable charge. This same (a 1 (b) (C) feature appears, although to a lesser extent, in the case Figure 4. of the tetracyanodipyridyl complexes,9 where the value for HFe(CN)cdipy- is 20 eu more negative than that (23) W. M. Latimer, "Oxidation Potentials," 2nd ed, Prentice-Hall for Fe(CX)4dipy-. Inc., New York, N. Y., 1952. These very marked differences in 3" between the (24) R. H. Busey, J. Phys. Chem., 69, 3179 (1965). Fe(II1) complex and the conjugate acid species of the (25) P. George, G. I. H. Hanania, and D. H. Irvine, Rec. Tmv. Fe(I1) complex with the same charge suggest there is Chim., 7 5 , 759 (1956).
t""
t
Volume 71,Number 7 June 1967
2030
G. HANANIA, D. IRVINE, W. EATON, AND P. GEORGE
LatimeP pointed out some years ago that the entropies four ligands, respectively, are unknown. Nevertheless, of conjugate acid oxyanions are smaller than those for the discrepancy, amounting to about 26 eu, approxithe oxyanions having the same charge but with no mately twice that for the oxyanions, would be in keephydrogen. In Figure 4, typical data for oxyanions in ing with the whole HNC- group making a relatively small contribution to So, since HNC- has two struc(a) and (b) are compared to the present data for the hexacyanoferrates in (c). S'HCO~turally bonded atoms (in Cobble's2' sense) compared is about 12 eu to the one in HO-. In view of these similarities bemore negative than SO NO^-; ~ O H P O , * - is about 12 eu tween the two series of ionic species, we are inclined more negative than S08o4t-; while S'HF~(CN),~is to believe that the discrepancies originate in some about 26 eu more negative than S O F ~ ( C N ) ~ ~ - . In a common feature arising from the interaction between consideration of the magnitude of the discrepancy in the conjugate acid grouping and the solvent water the case of the oxyanions, Connick and Powell2Bshowed molecules, rather than in some special structural that the HO-group appears to make very little conproperty of the individual conjugate acids. tribution to s"; Le., to a first-approximation, species such as X02- and HY03-, or X0s2- and HY0d2-, etc. have the same So. This type of comparison cannot (26) R. E. Connick and R. E. Powell, J . Chem. Phys., 21, 2206 be made in the case of the cyanoferrates because spe(1953). cies of the t.ype Fe(CN)6a- or Fe(CN)42-with five and (27) J. W. Cobble, ibid., 21, 1451 (1953).
The Journal of P h y d Chsmistw
