Ion Pairing and the Reaction of Alkali Metal Ferrocyanides and Persulfates

Ion Pairing and the Reaction of Alkali Metal Ferrocyanides and Persulfates R. W. CHLEBEK AND M. W. LISTER Received April 29, 1971 Osmometric measurements have been made on the alkali metal persulfates, and these are interpreted in terms of formation of ion pairs, MSzOa-, by means of the method of Masterton and Berka (5). Equilibrium constants, and the derived thermodynamic quantities are deduced for the reactions M+ + Sz08'- MSz08-. These results are applied to the interpretation of the kinetics of the reactions With M = K+, Rb+, and Cs+, the reacting species are MFe(CN)63- + MSz08-, with very similar rate constants; with M = Li+, Na+ the species are MFe(CN)63- + SZOsZ-; and for lithium the reaction of Fe(CN)64- + SZOsZ- is also important. Rate constants and activation parameters are deduced. Les mesures osmomttriques ont Cte effectukes sur les persulfates d'un mctal alcalin; les resultats sont interprites en fonction de la formation d'une paire d'ions, MSZO8-, suivant la mcthode de Masterton et Berka (5). Les constantes d'iquilibre et les quantites thermodynamiques qui en dcrivent sont dkduites des reactions M+ + SZOsZ- + MSzOa-. Ces resultats sont utiliscs en vue de I'interpretation des cinitiques des reactions 2M4Fe(CN)6 + MzSzOa -> 2M3Fe(CN)6 + 2MzSO4 avec M = K+, Rb+ et Cs+, les espirces r6actionnelles sont MFe(CN)63- + MSZOa-, avec des constantes de vitesse tres semblables; avec M = Li+ et Na+ les espirces rcactionnelles sont MFe(CN)63- + SZOaZ-; pour le lithium la reaction Fe(CN)64- + S2082- est Cgalement importante. Les constantes de vitesse ainsi que les paramirtres d'activation sont deduits. Canadian Journal of Chemistry, 49, 2943 (1971) In two earlier papers (1, 2), we reported measurements on the rates of the reactions where M is an alkali metal. These were interpreted in terms of ion pairs, such as KFe(CN)63-, as the actual reacting species, and the criterion used was to discover which reaction path best followed the predictions of Bronsted's equation (3). This required a knowledge of the equilibrium constants of the reactions Values of these constants are available in the literature for ferrocyanides (4), and we had made measurements (1) with a glass electrode on KFe(CN)63- and KS208-, and also on the product ion pairs KFe(CN),'- and KS0,-. Values were not available for other persulfates, but since Masterton and Berka (5) had found fairly similar values for all alkali metal sulfates, it was assumed that the values of the equilibrium constants for all alkali metal persulfates were the same as the known value for KS208-. The present paper reports values for Masterton and Berka (5), who used osmometric measurements and these values are in turn used to interpret the kinetic data. Water was the solvent throughout. Experimental Alkali Metal Persulfates These were obtained by the methods already described (1, 2). Freshly prepared solutions were always used, and the concentrations were known, firstly from the weights of salt used, and secondly by titration. Two titrations were used: (i) excess ferrous ammonium sulfate solution was added and the excess was titrated with ceric ammonium sulfate, and (ii) potassium iodide was added and the resulting iodine was titrated with sodium thiosulfate. Osmometric Measurements These were done with a Mechrolab 301 A Vapor Pressure Osmometer. Potassium chloride solutions were used as the comparison solutions, and their osmotic coefficients were taken to be as given by Robinson and Stokes (6). The British Drug House AnalaR reagent grade of potassium chloride was used, the solution being made up by weight from the salt dried at 110 "C. Osmometric measurements were made at 25 and 37 "C. Results Table 1 gives the results of the osmometric measurements. The table gives the osmotic these constants obtained by the method of coefficient, I$,,, for various salt molalities rn.

2944 CANADIAN JOURNAL OF CHEMISTRY. VOL. 49, 1971 TABLE 1. Osmotic coefficients and equilibrium constants for ion pairing of alkali metal persulfates Run Salt T m 012 a Kc I KO From these are calculated the fractions of the ion pair dissociated, a, the ionic strength, I, and the equilibrium constant, defined as at the particular ionic strength. The calculations followed Masterton and Berka's method (5). It was assumed that their osmotic coefficients for completely dissociated electrolytes held at both 25 and 37 "C. Table 1 also gives values of the equilibrium constant extrapolated to zero ionic strength. This extrapolation was made by the usual equation for single ion activity coefficients, f, for an ion of charge z. Kielland found a value of a = 4 A for persulfate ions (7), and an average value of 0.25 was used for C, (8), so that the equation used was It may be noted that Masterton and Berka quote mean values of activity coefficients which approximately fit an equation and use of this would increase KO to about 8% above the values given in Table 1. In addition to the results given in Table 1, measurements were also made on lithium persulfate. The values of the osmotic coefficients were close to those given by Masterton and Berka for completely dissociated salts, so that we obtained no evidence of ion pairing in this case. As will be seen later, the kinetic measurements of lithium ferrocyanide and persulfate can be interpreted without invoking the participation of LiS,O,-. Measurements were also made on potassium persulfate which gave equilibrium constants somewhat higher (about 20%) than those obtained by use of a glass electrode (I). Attempts to obtain constants by use of a glass electrode for the other alkali metals were unsuccessful, as the glass electrode readings were not steady enough, and a small change in cell voltage can give a large change in equilibrium constant. Table 2 summarizes the results in the form of the average equilibrium constants, including those obtained earlier (1) for potassium per-' sulfate. The derived thermodynamic quantities, AGO, AH0, and AS0 are included. It may be

CHLEBEK AND LISTER: ON ION PAIRING TABLE 2. Values of thermodynamic functions for M+ + Sz08'- =S MSzO8 KO (M) AGO (25 "C) AH0 AS0 M+ 25 "C 37 "C (kcal/mol) (kcal/mol) (cal/deg mol) Na+ 3.8 5.0-0.79 4.3 17.0 K + 8.2 9.4-1.25 1.6 9.6 Rb+ 14.7 16.0-1.59 1.3 9.8 CS+ 26.0 24.4-1.93-1.0 1 2 noted that AGO changes much less than AH0, since AH0 and AS0 in effect oppose each other. Discussion The original object of this research was to investigate the effect of ion pairing on the reaction of persulfate and ferrocyanide ions. Kinetic measurements on this reaction have already been reported (1, 2). In the case of the lithium, sodium, rubidium, and cesium salts, the conclusions reached were tentative, because equilibrium constants for the formation of alkali metal - persulfate ion pairs were not known. It is now possible to make a more quantitative comparison of the reactions. The general method of treating the kinetic data, which appeared in Tables I to IV in ref. 2, was as follows. The concentrations of all the species present in a reacting mixture were calculated from the gross concentrations of the solutions, and from the equilibrium constants for ion pairing. These constants were those appropriate to the actual ionic strengths of the solutions, and were adjusted by means of activity coefficients calculated by eq. 2 above. Since the true ionic strength could only be found when the appropriate equilibrium constants were known, an iterative procedure was used, until the finally calculated ionic strength differed by less than 0.1% from that used in finding the equilibrium constants. Since the kinetic data were for 25 and 40 "C, the equilibrium constants for MS20,- formation (obtained at 25 and 37 "C) were extrapolated to 40 "C, with the usual assumption that log K was linear in T-'. A more serious assumption was necessitated by the fact that Shvedov and Nichugovskii's data on ferrocyanides (4) only applied to 25 "C, and data are not available for the other alkali metals. It was assumed that the temperature coefficients of all these equilibrium constants were the same as for the potassium ion pair, which was known from glass electrode measurements. As AH0 for formation of the ion pair KFe(CN)63- is only 3.86 kcal, and as fairly small values are also found for the other potassium ion pairs involved (I), it was felt that this assumption would not introduce much error. Small corrections were made for ion pairing of rubidium and cesium with chloride, from data of Davies (ref. 8, p, 169), and also for alkali metal ferricyanide ion pair formation. The only known appropriate equilibrium constant is that for KFe(CN),'-; this is close to one tenth of the value for KFe(CN),3-, and it was assumed that this value of one tenth held for other alkali metals. When all the concentrations were known, it was assumed that some particular pair of ions were the main reacting species, as follows: Reacting species Rate constant Path Values of k,, etc., were calculated, and it was then seen which rate constant most closely followed the Bronsted equation. This rate constant was then supposed to belong to the correct mechanism of the reaction. Some comments should be made on this procedure. Firstly, Bronsted's equation is log k = log k0 + 2Az,zbF(I) for reaction of ions of charge z, z,, and F(I) is the function of the ionic strength appearing in the extended Debye-Hiickel equation, [l] above. F(I) contains two constants Ba and C which vary somewhat from ion to ion, and it is not obvious which values should be used. Indeed, as we are dealing with various reacting species, and also a transition state species, it is not certain that the

CANADIAN JOURNAL OF CHEMISTRY. VOL. 49, 1971 TABLE 3. Values of d log kldf(1) obtained from various values of Ba and C; results for rubidium salts at 25 "C Ba C d log kl/df(i) d log k2/df(i) d log k,/df(i) - - - 1.0 0.2 12.0 8.25 2.67 1.0 0.25 12.8 8.75 2.83 1.0 0.3 13.6 9.35 3.02 0.9 0.3 12.8 8.8 2.84 0.93 0.3 13.0 8.95 2.89 1.3 0.3 16.3 11.2 3.62 Calculated value 8.14 6.11 3.05 TABLE 4. Best values of Ba and C from kinetic data M+ Path T("C) Ba C Slope 10gkO(M-'s-~ 1 same constants apply throughout. The values in eq. 2 were used in adjusting the equilibrium constants, and various combinations of Ba and C were investigated in obtaining a fit with Bronsted's equation. The range of Ba investigated was 1.0 to 1.65, and the range of C was 0.1 to 0.3, in accordance with the values found to fit observed activity coefficients. Except with lithium, it was found that these ranges never allowed any ambiguity about the mechanism; for lithium (as will be seen) it is probable that two paths are important. Table 3, which contains results for the rubidium salts, shows the extent of the variation. This table gives the slopes of plots of log k against F(I), which at 25 "C should have the value 1.018 z,z,. It can be seen that only k, gives agreement of observed and calculated slopes, which happens when Ba = 1.O, C = 0.3 approximately. Hence the reacting species are Rb~e(c~),,- and RbS,O,-. Similar calculations were made with Li', Na', and Cs'. Secondly, the equilibrium constants were taken to be those applying to the ionic strength at the start of the run. This ionic strength falls gradually, and calculations were made for the potassium salts at the mid point of the run, as well as at the beginning. The change in slope was always less than I%, so that calculations at the initial ionic strength were taken to be sufficient. Thirdly, with lithium a fit of the calculated and observed shapes was possible for both kt and k,. The method cannot distinguish between k, and k,, for both of which mechanisms the composition of the transition state species is MFe(CN),- S,0,5-, so that the k, path only was arbitrarily chosen. It was therefore assumed that for lithium, both the k, and k, paths simultaneously contributed to the rate, and values were thus i obtained for both constants. There was no evidence of this sort of behavior for sodium. Table 4 gives the results of these calculations. The reaction path is indicated by the charges on the reacting species; i.e. Fe(CN),4- + S2Oa2- is 412. The values of Ba and C are those that give observed slopes most closely fitting Bronsted's equation (within the ranges of Ba and C quoted above). k0 is the value of the rate constant extrapolated to zero ionic strength; k0 is in units of M-Is-'. The usual activation parameters, AH* and AS*, can be calculated from these results, and these are given in Table 5. Since the extrapolation to zero ionic strength follows slightly different equations for different M', Table 5 also contains values at I = 0.1. In the actual kinetic runs, the ionic strengths were varied from about 0.02 to 0.3 so I = 0.1 may be considered a typical value. Results reported earlier (I) on the 311 path for the potassium salts made AH* = 9.0 kcal/mol, and AS* =

CHLEBEK AND LISTER: ON ION PAIRING 2947 TABLE 5. Calculated values of AH* and AS** system, it would be the main route of the reaction, in spite of the lower concentrations of ion Z = O I = 0.1 pairs. The reason for this change of behavior, M+ path AH* AS* A * AS* which is evidently carried further in the lithium system, is not clear. AH* and AS* for all the Li + 412 15.1-27.5 16.5-15 reactions show some signs of a linear relation at 312 13.9-28.5 15.0-19 Na+ 312 13.7-25 14.6-18.5 = 0.1, but this is almost totally obscured at ~ b + 311 9.4-32 9.65-30 I = 0. It may be noted that AH* is on the CS+ 311 10.4-28.5 10.55-26.5 average larger for reactions of ions with larger *AH* in kcal/mol; AS* in cal/deg mol. charges, though only by a small amount, as is to be expected for aqueous solutions. -34.7 cal/deg mol at zero ionic strength; at Finally it may be noted that the 412 reaction I = 0.1, AH* = 9.5, and AS* = - 31. will presumably be occurring in all reaction A few ~ ~ be m made On ~ the quanti- ~ mixtures. ~ ~ However, s it can be calculated from the ties in Tables 4 and 5. It is found that the 311 rate constants and concentrations of various paths for cesium, rubidium, and potassium (for species, that in all the runs using an alkali metal which log k0 = at 25 OC, and - other than lithium, it contributes only a small at 40 OC) have fairly similar rate constants. Thus fraction to the total rate, and consequently went the ions do not seem to play a very specific role, undetected. and their behavior is perhaps merely a reflection of identical charge and not very different size 1. R. W. CHLEBEK and M. W. LISTER. Can. J. Chern. 44, (especially if hydrated). AH* rises slightly from 437 (1966). potassium to cesium, but this is offset by a rise 2. R. W. CHLEBEK and M. W. LISTER. Can. J. Chern. 453 in AS*. Possibly the somewhat smaller potas- 2411 3. N. J. BRONSTED. Z. Phys. Chern. Leipzig, 102, 169 sium ion permits a closer approach of the react- (1922); 115, 337 (1925). ing ions in the activated complex leading to a 4. V. P. SHVEDOV and G. F. NICHUGOVSKII. Radiosmaller AH* for electron transfer in the reaction, khirniya, 8, 63 (1966). and also to a somewhat more tightly bound 5. W. L. MASTERTON and L. H. BERKA. J. Phys. Chern. 70, 1924 (1966). with a negative AS*' Sodium 6. R. A. ROBINSON and R. H. STOKES. Electrolyte so1usalts behave differently, and this is just a lions. Butterworths Scientific Publications, London. reflection of a lower degree of ion pairing. In 1959. 2nd edition. fact if the 311 path for the sodium system had 7. J. KIELLAND. J. Am. Chern. Soc. 59, 1675 (1937). the same rate constant as for the potassium 8. C. W. DAVIES. Ion association. Butterworths, London. 1962. pp. 39,41.