ION PAIR EFFECTS IN THE REACTION BETWEEN POTASSIUM FERROCYANIDE AND POTASSIUM PERSULFATE

Transcription

1 ION PAIR EFFECTS IN THE REACTION BETWEEN POTASSIUM FERROCYANIDE AND POTASSIUM PERSULFATE R. W. CHLEBEK AND M. W. LISTER Department of Chemistry, University of Toronto, Toronto, Ontario Received August 3, 1965 ABSTRACT The rate of the reaction between potassium ferrocyanide and potassium persulfate has been measured over a range of conditions. The rate is dependent on the potassium ion concentration, and it is shown that this is explained if it is assumed that KFe(CN)03- and KS208- are the reacting species. The equilibrium constants governing the formation of these ion pairs were measured with a cation-sensitive glass electrode. Similar constants for the products KFe(CN6)" and KSO4-, and also for KNO3, were measured. From these equilibrium constants, the true rate constants of the reaction can be obtained, and it is shown that these vary with ionic strength in the manner predicted by Bronsted's equation. The reaction 2K4Fe(CN)s + ICzSzOs --t 2KaFe(CN)o + 2IC2SOa in aqueous solution was examined some time ago by Holluta and Herman (I). They found it to be a second-order reaction, but with rate constants that increased strikingly with the concentration of potassium ions. This might be attributed to an increase in ionic strength, and Bronsted's treatment (2) of the effect of ionic strength on reaction rate would, of course, predict such an increase, since the reacting ions are of the same sign. However, Holluta and Herman's results seem to correlate the rate constants with the potassium ion concentration rather than with the ionic strength; this is the sort of correlation that has been emphasized by Olson and Sinlonson (3) for other reactions. A possible explanation is that ion pairs such as KFe(CN) G3- are the real reacting species, and this sort of explanation has been suggested in other cases (4). The object of the present work was, firstly, to investigate the extent of ion pair formation for the reagents and products in this reaction. This was done by measurements with a cation-sensitive glass electrode. Secondly, this information was used to find the nature of the actual reacting species, and hence the true rate constants of the reaction. Finally, the dependence of these rate constants on ionic strength was examined and compared with the predictions of Bronsted's equation. EXPERIMENTAL Chemicals Potassiz~nz chloride.-mallinckrodt analytical reagent was dried at 110 OC and stock solutions were made up by weight. Tetramethylatnmonizint chloride.-the salt, stated to be more than 99y0 pure, supplied by Matheson, Coleman and Bell Co. was used. Stoclc solutions were standardized by silver nitrate titration. Tetramethylat~z?nonillln hydroxide.-the 10 yo solution supplied by Eastman Organic Chemicals was diluted and standardized with potassiunl hydrogen phthalate. Potassiritn nitrate.-the British Drug Houses AnalaR reagent was used after drying at 110 OC. Potassivm sulfate.-the Merck analytical reagent was used after grinding and drying at 110 OC. Potassiz~ttz perszilfate.-the Fisher certified reagent was used. After drying, the salt was analyzed by adding excess ferrous ammonium sulfate to a solution of the salt, and titrating the excess with ceric ammonium sulfate. The salt was 100yo pure within the error of the titration. Solutions were always used the same day that they were made up. Potassizinz ferricyanide.-the Baker and Adamson reagent salt was used. Solutions were made up by weight, and standardized with iodometric titration. Canadian Journal of Chemistry. Volume 44 (1966) 437

2 438 CASADlAN JOUKXAL OF CI-1EMlSTRY. VOL. 44, 1900 Polassiu?tz ferrocyat~ide.-the Fisher certified reagent was used. The purity was checked by titration with ceric aininoniu~l~ sulfate and found to be 100% within the experirnerltal error. Solutions were always used the same day that they were made up. RESULTS Eqzlilibrium Measurements The concentrations of potassiuill ions in various solutions were measured with a Beckinann cation electrode. A saturated caloinel electrode with a frit junction was used as a reference electrode, and the voltages were read on a Beclcrnann research PI-I meter. The voltages could be read to 0.05 mv. The apparatus \\-as first calibrated by solutions of potassium chloride, containing tetramethylami~~onium hydroxide and adjusted to a fixed ionic strength by tetran~ethylai~~il~onium chloride. The tetramethylammonium hydroxide was added to keep the hydrogen ion concentratioil low, since the glass electrode is sensitive to hydrogen ions. Calibrations were made at different temperatures, which were controlled to within A0.1 OC by a water thermostat. It was expected that the variation of the measured voltage lvith conce~ltration \vould follow the Nernst equation, in effect de/d log [K+] = ', where E is the voltage in rn\j and 1'is the absolute temperature. In fact, slightly different values for the slope of E against log [K+]\\-ere obtained, and instead of the follo\ving values were found. t ("C) kiean Slope These are for a range of [K+] from 0.1 to ,and are all at an ionic strength of 0.1. This deviation cannot be caused by formation of ion pairs of KCI, since this xvould have increased the slope; potassium chloride was chosen as the calibrating compound since earlier \vork (e.g. ref. 4, p. 169) had sho~vn that ion pair formation was very slight. Probably the electrode responds slightly to tetrainethylammonium ions. In practice, for the determination of equilibrium constants, the electrode was placed alternately in a calibrating solution of potassium chloride and in the salt solution whose equilibrium constant was being measured. Both solutions contained tetramethylaminonium hydroxide and tetramethylammonium chloride to bring them to the same ionic strength (usually 0.1). It was assumed that the experimental values for de/d log [K+] held for this comparison. Results for the various compounds investigated are given in Table I. The constants so obtained can be claimed to be only moderately accurate, as an error of 0.1 mv in 6E (the difference between the voltage observed with the salt solution and with the calibrating solution) would cause a considerable change in K. For instance, for the second solution of potassium nitrate, a change of 0.1 mv in 6E would increase K from to Table I1 summarizes the thermodynamic data calculated from the data in Table I, The equilibrium constants were measured at an ionic strength of 0.1. These can be converted to zero ionic strength, if single ion activity coefficients are assumed to be of the usual form, log f = Az (1 +Zdi - cp).

3 CHLEBEK AND LISTER: ION PAIR EFFECTS 430 Kielland (5) has found that values of a = 4 a for the SzOs2- ion and a = 5 A for the Fe(CN)64- ion fit the activity coefficient data for salts of these ions. For potassium ions a = 3 A is a commonly used value. The results in Table I1 were calculated using these values, 3.5 a for sulfate and nitrate ions, and values for the ion pairs equal to that for the anion they contain. The values for KO in Table I1 may be compared with results in the literature obtained by other methods of measurement, mostly by conductivity. These are: KNOB, 0.72 to 0.78 at 18 "C (6, 7) and 0.55 (7) to 0.63 at 25 "C (8); KzS04, 6.6 at 18 "C and9.1 at 25 "C (9); K3Fe(CN)6, 20 at 18 "C and 25 at 25 "C (10,ll); 1<4Fe(CN)6, 200 at 25 "C (12, 13). Considering the different methods of measurement, and the adjustment to zero ionic strength, these values are in reasonable agreement with the present ones. Two other comments may be made on Table 11. Firstly, AH0 plotted against ASo gives an approximately straight line with slope about 220 OK. Secondly, A9 becomes larger as the charge on the ion increases. This would be expected if it arises from polarization of the 'I'XBLE I Equilibrium measurements 'rota1 salt Calibrating 6E Calcd. Equilibrium Salt t ("C) concn. (M) [I<CI] (mv) [I<+] Constarit (M-I)

4 440 CANADIAN JOURNAL OF CHEMISTRY. VOL. 44, 1966 TABLE I1 Thermodynamic data calculated from the data in Table I (AFO and AHo are in kcal/g mole, AS0 in cal/deg g mole, K and KO in g mole/l) Salt t ('C) K (p = 0.1) KO AFO AHo AS0 ICNO, s ICZSO~ KzSzOa I<aFe(CN) K4Fe(CN) solvent (the "Born charging effect") which has been applied by Laidler in treating the entropy of hydrated monatomic ions (14). His equation for these ions was (SO in cal/deg mole) where M is the atomic weight, z the charge, and r the radius of the ion. The last term is the one arising from polarization and, though many other effects must be involved in determining the entropy of these ions, it is worth noting that qualitatively the order for ASO is that predicted from considerations of polarization. Kinetic Measurements The reaction between potassium ferrocyanide and potassium persulfate was followed by taking samples from the reacting mixture and measuring the optical absorbance at 420 mp with a Beckmailn DU spectrophotometer. At this wavelength, the extinction coefficient is 1025 cm-i (g mole/l)-i for potassium ferricyanide, for potassium ferrocyanide, and negligibly small for all other substances present. Previous work (15) on the spontaneous decomposition of potassium persulfate showed that, under the conditions used, less than 1% of its total disappearance was due to spontaneous decomposition. This observation was confirmed in the present work by iodometric titration of the reaction mixtures at the beginning and end of a run. The titre, which measures both ferricyanide and persulfate, did not decrease detectably during the reaction. The reaction is first order in both reagents. Rate constants, calculated on this assumption, did not drift during the runs, which were frequently continued until the reaction was 8OY0 complete. Table I11 gives such constants defined by No assumption is made at present about whether free ions or ioil pairs are the actual reacting species; hence these are apparent rate constants (indicated by k,,, throughout). Table I11 gives the initial reagent concentrations and also the concentration of potassium nitrate, which was added to control the ionic strength. In addition, all reaction mixtures were M in potassium hydroxide to prevent formation of hydrolyzed species, particularly HFe(CN) 63-.

5 CHLEBEK AND LISTER: ION PAIR EFFECTS Apparent rate constant, k,,,,, TABLE 111 (g rnole/l)-i rnin-i (all mixtures contained M ICOH) Run t Initial Initial No. ("C) [K4Fe(CN)6] [KzSzOsl [ICNO3] ~,PP DISCUSSION The results in Table I11 show the dependence on potassium ion concentration previously noted by Holluta and I-Ierman (I). This is not simply a matter of ionic strength. For instance, runs 1, 3, and 4 all have an apparent ionic strength of almost exactly 0.10; but in run 4 k,,, is 0.56 with total [Kt] = 0.043, in run 1 k,,, is 0.88 with total [I<+] = 0.058, and in run 3 k,,, is 1.48 with total [K+] = M. Runs 33, 34, and 35 form a similar series. The most plausible theory of this behavior is to suppose that one or both of the reacting species are ion pairs. The various possible combinations were examined, and the choice made on the basis of whether (i) the rate constants fell on a snlooth curve when plotted against ionic strength, and (ii) whether the effect of ionic strength followed the predictions of Bronsted's theory. The details of these calculations were as folloxvs. Calculation of Ionic Strength This was calculated for each run, with allowance for the effect of ion pairing. As it inevitably changes a little during each run, the calculation was made for a time halfway through each run. The procedure consisted of first calculating the ionic strength as if no ion pairing has occurred. Activity coefficients for this ionic strength were then calculated for all the species present, using the extended Debye-I-Iiickel equation (i.e. eq. [I] above).

6 442 C.%i\'ADI.IN JOURNAL OF CHEMISTRY. VOL From these, and from values of the equilibrium constants at 0.1 ionic strength, the equilibrium constants at the first approximation to the ionic strength of the run were calculated. From these constants, the concentrations of all the species present were calculated, and hence a second approximation to the ionic strength was obtained. This cycle was repeated, giving new constants, hence new concentrations, and a new value for the ionic strength, until repetition gave no appreciable change in ionic strength. These values were then used in connection with the calculations on rate constants described below. Calculation of Rate Constants It was first assumed that some particular pair of ions were the main reacting species, and the appropriate rate constants were designated as follows. If the equilibrium constants are and then Reacting Species [KFe(CN) 3-] '- [Kf][Fe(CN):-] K - Constant where x is the free potassium ion concentration, which was obtained during the calculation of ionic strength. It varied little during a run, and \vas assumed constant. Hence kl can be calculated from this equation. Similarly, Each of these equations assumes that only one mechanism for the reaction is important. Rate constants kl, k2, k3, and k4 were calculated, and their variation with ionic strength ~vas investigated. Rronsted's equation is where k is the rate constant at some ionic strength p, k0 is the constant at zero ionic strength, A is the Debye-I-Iiiclcel constant, z, and z, are the charges on the reacting species, and F(p) is the function of the ionic strength in the Debye-Hiiclcel equation (eq. [I] above). The constants in the Debye-I-Iiickel equation are assumed to be the same both for the reacting species and for the activated complex, an assumption which can be avoided at the cost of lnalcing the equation somewhat more complicated. Accordingly log kl, log k2, etc. were plotted against F(p), taking a with an average value of 4.5 A. The results are shown in Figs. 1 and 2, for 25 and 40 "C respectively. Two

7 CHLEBEK AND LISTER: ION PAIR EFFECTS 443 FIG. 1. Logarithms of various rate constants at 35 O C lotted against the Debye-Huckel function of the ionic strength: X, log KI; 0, log Kz; A, log K3; +, log I<q. FIG. 3. Logarithlns of various rate constants at 40 "C plotted against the Debye-Huckel function of the ionic strength: X, log KI; 0, log I<?; A, log Ka; +, log R.1. things are apparent from these diagrams. (i) The runs with amounts of K4Fe(CN)G other than the usual amount of M fall off the general line (runs 1, 2, 4, 5, 7, 33, 34) but do so to a much smaller extent for log k4. 'This is evidence that the reacting species are KFe(CN)e3- and KS2O8-. (ii) Lines can be dra\vn for all types of k through the points for runs in which the initial ferrocyanide concentration was iv.the slopes of these lines can be compared with the predictions of the Bronsted equation. This is perhaps most easily seen by conlparing the values of z,z, calculated froin the slope with the actual values. This is done in Table IV, and it is seen that the values only agree for k4. also supports the view that the reacting species arc 1<Fe(CN)63- and KS208-. To some extent this agreement is fortuitous since it depends on the exact values of the parameters chosen for the Ilebye-Hiicltel equations. Fairly large alterations of these parameters could

8 444 CANADIAN JOURNAL OF CHEMISTRY. VOL. 44, 1966 change the slope by about 20%, but could not possibly give agreement for any other reacting species in Table IV. TABLE IV Con~parison of experimental values of z,zb with values calcuiated from the slope of the lines in Figs. 1-2 Rate t z,,zb calcd. Reacting species co~lstant ("C) zazb from slope These calculations assume only one mechanism is operative. At very low [Kf], others must doubtless become important, but there is no sign of this under the conditions used above. It may be noted that if Holluta and Herman's (I) data are compared with ours, the rate constants appear to be considerably larger. The chief difference in their conditions u7as that they added no potassium hydroxide. Presumably HFe(CN)63-, or even KHFe(CN)62-, is contributing to the reaction. The lines through the plots of log k4 against F(p), k4 in units of (g n~ole/l)-i inin-i, give for 25 "C and for 10 "C log k4 = F(p), log k4 = F(p). This malies the activation energy at zero ionic strength, AH*, equal to 9.0 kcal/g mole. If, as usual, n-e write the entropy of activations, AS*, is found to be cal/deg mole. This is rather strongly negative, but Laidler (16) deduces that for ionic reactions like the present one a value of -lozaz, might be expected. This n-ould lead one to expect a value of -30 cal/deg inole in the present reaction, so the observed value is quite plausible. Similar calculations for A F at zero ionic strength give: for K1, AS+ = 4.7 cal/deg mole with zazo = 8; for Kz, A F = 6.9 cal/deg mole 111ith zazo = 6; and for K3, AS* = -7.8 cal/deg mole with z,z, = 4. These results help to confirm the ~llechanisln for the reaction suggested above. The conciusion is not aitered if the calculations are made for F(p) = REFERENCES 1. J. HOLLUTA and W. HERMAN. Z. Physik. Che~n. Leipzig, A166, 453 (1933). 3. J. N. BRONSTED. Z. Physik. Chem. Leipzig, 102, 169 (1922); 115; 337 (1925). S. \.\I. BENSON. The foundations of chemical kinetics. McGraw-Hill Book Co.. Inc., Sew York o A. R. OLSON and T. R. SI~IONSON. J. Chem. Phys. 17, 1167 (1949). 4. C. W. DAVIES. Ion association. Butterworths, London p J. KIELLAND. J. Am. Chem. Soc. 59, 1675 (1937).

9 CHLEBEK AND LISTER: ION PAIR EFFECTS C. W. DAVIES. Trans. Faraday Soc. 23, 351 (1927). W. H. BANKS, E. C. RIGHELLATO, and C. W. DAVIES. Trans. Faraday Soc. 27, 621 (1931). T. SHEDLOVSKY. I. Am. Chem. Soc (1932).., I. L. TENKINS and-c. B. MONK. I. ~ m Chem. : Soc (1950).., C. B."MONK. 1. Chem. SOC ). J. C. JAMES and C. B. MONK. ~;anl~arada~ Soc. 46, 1041 (1950). J. C. JAMES. Trans. Faraday Soc. 45, 855 (1949). S. R. COHEN and R. A. PLANE. 1. Phys. Chem. 61, 1096 (1959). K. J. LAIDLER. Can. J. Chem. 34, 1107 (1956). E. HAKOILA. Ann. Univ. Turku. Ser. A, 66 (1963). I<. J. LAIDLI~R. Reaction kinetics. Vol. 11. Perganlon Press, London p. 12.