J. CHEM. SOC. DALTON TRANS. 1985 31The Peroxodisulphate-Iodide Reaction. Reactivity and IonicAssociation and Solvation in lsodielectric Water-SolventMixturesM. Carmen Carmona Guzmh,' Julian Rodriguez Velasco, Francisco SBnchez Burgos, andJose Hidalgo ToledoDepartamento de Fisicoquimica Aplicada de la Facultad de Farmacia y Departamento de QuimicaFisica de la Facultad de Quimica, Universidad de Sevilla, SpainThe association constants of the potassium peroxodisulphate ion pair ( KS208-) and the reaction ratebetween peroxodisulphate and iodide ions have been measured in several isodielectric water-solventmixtures. The sequence of the rate constants does not follow that of the association constants, butagrees qualitatively with the sequences of transition-state solvation energies calculated from excessfree energies of mixing.This fact suggests the influence of solvent structure on the reactivity.The reaction between peroxodisulphate ion and iodide ionhas been studied by several It is first order withrespect to both reactants. Generally, the kinetic salt effects of avariety of added salts of various valency types have been~tudied.~ The results of these studies have been interpreted bypostulating the formation of ion pair~.~*'O If the reactants werepresent as potassium salts, the rate-determining step wouldinvolve the participation of the KS20e- ion pair and I' asreactive species. However, the existence of the KS20s- ionpair in solution has never been proved by an independentprocedure.On the other hand, there is some kinetic information on thisreaction concerning binary aqueous solvent m i ~ t u r e s .~ - ~According to Amis and Potts,6 electrostatic influences pre-dominate for this reaction in ethanol-water mixtures.Meretoja,' working with methanol-water mixtures, reachedthe same conclusion. Nevertheless, how ell^,^ when usingdextrose solutions, observed that the reaction rate wasgreater than in water. This indicates ?hat there are instanceswhen some other solvent effects, aside from the electrostaticeffect, play an important role.In our opinion in order to understand the solvent effects inthis reaction, the solvent-water interactions should be takeninto account. An insight into such interactions can be gained,for a given mixture, from the thermodynamic properties.In fact, several authors 8 ~ 1 1 have tried to correlate kineticparameters (usually AG3 or k) with thermodynamic properties;their observations suggest that this correlation exists.For this reason we report in this paper a study of ionicassociation and reactivity in several isodielectric water-organic solvent mixtures.We have selected solvent mixtureswith different thermodynamic properties with the purpose ofascertaining whether ionic association or water-solvent inter-actions explain the experimental results.ExperimentalReagents.-The reagents used were all AnalaR gradechemicals from various sources, and were not purified further.The water used had a resistance > 5 MR and was obtained bydistilling from KMnO, and passing the distilled water througha mixed-bed ion-exchange column.Kinetic Dara.-Kinetic runs were carried out in l-cm silicacells in the thermostatted cell compartment of a Perkin-Elmer554 spectrophotometer.The temperature in the cell was fixedat 298.0 f 0.1 K. These kinetic runs were made in solutionscontaining an excess of iodide ions by following the changes inTable 1. Viscosity (q), molar absorption coefficient of 13- ( E ) in K1(0.1 mol dm-9, and observed rate constants for the reaction betweenS20sz- and 1 - in different isodielectric water-co-solvent mixturesCo-solvent % (w/w)Pure waterMethanolEthanolt-Butyl alcoholdmfAcetoni trileGlycerolSucroseDextrose-5.684.392.942.286.029.950.750.521 O-%/dm3rnol-' cm-'5.956.076.156.046.536.146.196.155.631 05k/s-'41.173 1.7533.2835.3013.0521.9037.3343.2550.70I OJQ/P-I .07861.09221.18381.17700.96271.15921.21201.1610absorbance at fixed time intervals at 400 nm (at this wave-length only tri-iodide ions absorb). Table 1 gives the valuesof the molar absorption coefficient ( E ) in water and in thewater-co-solvent mixtures.The concentrations of reactantswere [KI] = 0.1 and [K&08] = 2 x mol dm-3. Thesolutions also contained K2(H2edta) (edta = ethylenediamine-tetra-acetate) in order to prevent the catalysis of some metalions that could be present as impurities ([K2(H2edta)] = 5 xlo-' mol dm-3).418 In every case we found that the co-solventswere inert in relation to the reactants and products.The results of kinetic runs are collected in Table 1 aspseudo-first-order rate constants (k/s-').Table 1 also gives thecomposition of each mixture. This composition was selectedin order to have the same macroscopic dielectric constant forall the mixtures. Solvent mixtures were prepared by weight,and the dielectric constant data are from the literature.'2-'6Viscosity and Density Data.-We have measured the vis-cosities and densities of the water-co-solvent mixtures. Thedensities were determined picnometrically and the viscositiesfrom the flow time of solutions in an Ostwald-type viscosi-meter. These data are reported in Table 1.Conductance Measurements.-The conductance measure-ments were carried out using a Beckman RC18A bridge.Thecell, with a constant of 0.491 cm-', was a Beckman 6505conductance cell. The temperature was fixed at 298.15 f0.005 K using an oil-bath. The cell containing the solutionswas flushed with nitrogen before the measurements. Theresults are reported in Table 2, which gives the molar con-centrations, the equivalent conductances, and the associationconstants of the KS208- ion pair. Owing to the large number o32 J. CHEM. SOC. DALTON TRANS. 1985Table 2. Equivalent conductivity (A) and association constants (K) of the KS20s- ion pair at different molar concentrations (c)100% Water MeOH-water (5.68 : 94.32) EtOH-water (4.39 : 95.61)A/W' cm2 K/dm3 A / W cm2 K/dm3 A / W cmz K/dm31 04r./mol dm-' eq u i v.-' mol-' equiv.-' mol-' eq u i v.-' mol4.006.008.009.0010.00153.45 I I 141.30 150151.86 12 138.50 130150.48 12 135.70 123149.96 1 1 134.40 122149.65 9.0 133.30 119148.97 153145.00 149141.70 145145 140.20138.80 144Bu'OH-water (2.94 : 97.06) MeCN-water (6.02 : 93.98)A / W cmZ K/dm3 A / W cmz Kldm' A / W cmz K/dm3dmf-water (1 2.28 : 87.72)104r./n101 dm equiv.-' mol equiv: mot-' equiv.? mol4.006.008 .OO9.0010.00166.31 133 157.33 154162.45 122 153.85 141159.49 I I5 150.20 136157.85 1 I4 148.90 135156.35 110 147.40 134Glycerol-water (9.95 : 90.05)A / W cmz K/dm31O4c/rnol dm equiv.-' mol-'4.00 138.24 416.00 136.34 408.00 134.53 419.00 133.75 4110.00 133.03 41Sucrose-water (10.75 : 89.25)A / W cm2 K/dm3equiv.-' mot-'123.79 114121.76 100120.56 83.3119.95 76.9119.15 76.9114.93 191 13.58 19112.39 201 1 1.95 181 1 1.52 18Dextrose-water (10.52 : 89.48)A/W' cmZ K/dm3equiv.-' mol-'132.88 217128.30 217124.26 217122.68 21 7120.86 217individual measurements, only mean values of the equivalentconductances are recorded.The association constants havebeen calculated by the Davies' method as modified by Jenkinsand Monk,I7 using a program which computes the fraction ofthe KS20s- ion pair. The program has been checked usingdata for potassium sulphate. l 7DiscussionThe reasons for maintaining a constant value of the dielectricconstant are three-fold. (i) The long-range interactionsbetween the reactants are therefore approximately the same inthe different mixtures.(ii) Also, the association constants ofthe ion pair KS20s- would be similar in each case. (iii) Adrastic change in the first solvation shell of the reactants isnot probable in passing from water to the water-solvent,because the water is, by far, the most abundant component(see Table I). For these reasons, the same reactivity shouldbe found in the different media.However, results do not agree with the above hypothesis.They indicate that the rate constants in these mixtures followthe sequence for the co-solvent, NN-dimethylformamide(dmf) < acetonitrile < methanol < ethanol < t-butylalcohol < glycerol < pure water < sucrose < dextrose, andthe association constants K of the KSzO8- ion pair follow thesequence for the co-solvent, pure water < dmf < glycerol <sucrose < t-butyl alcohol < methanol < acetonitrile <ethanol < dextrose.Reactivity in water cannot be compared with the reactivityin the mixtures.In the former, the association constant is lowand therefore should give low reactivity, but the dielectricconstant is higher than in the other media, and the encounterbetween the reactants should be facilitated. If the associationfactor were the more important of the two, the rate constantin water would be the lowest, and if the coulombic effectswere the more important it would be the greatest. In any case,the rate constant sequence does not agree with the associationcons tan t sequence.Of course, the aforementioned reasoning is only valid ifi t is acknowledged that the first solvation shell of the reactantsis not very different in the different media.This is probablebecause water is the most abundant component and the molarabsorption coefficients of the tri-iodide ions, 13-, do not changenotably in the different media (see Table 1). We conclude thatthe assumption of ion association does not seem capable ofproviding a satisfactory interpretation of the experimentalresults.On the other hand, several authors ' * * 1 8 are currentlyexamining whether reactivities in binary aqueous mixtures canbe correlated with excess Gibb's free mixing energies of therespective mixtures. Binary aqueous mixtures can be classifiedinto three groups according to their excess molar thermo-dynamic functions of mixing.'8-20 These are the ' typicallyaqueous ' (t.a.) mixtures where GE is positive and is dominatedby its entropy component (ITASEI > lAHE\), ' typically non-aqueous positive ' (t.n.a.p.) mixtures with positive GE andlAHE( > (TASEI, and ' typically non-aqueous negative '(t.n.a.n.) mixtures with negative GE but again (AHE[ >I TASE(.It is useful in this analysis to bear in mind the properties ofbinary mixtures: methanol, ethanol, t-butyl alcohol, andglycerol with water are t.a.; 19*20 dmf and acetonitrile with waterare t.n.a.p. ;21+22 sucrose and dextrose with water are t.n.a.n.23It seems, therefore, that our kinetic data cover reactions in thethree types of systems, t.a., t.n.a.p., and t.n.a.n.There is a good relation between G,AGX and GE, where6,AGt = AG$(x2) - AGZ (x2 = 0) [x2 = mole fraction oforganic solvent, AG3 (x2) = free energy of activation a t thevalue of x2].Reactivity is greater in mixtures with GE < 0than in water, and the opposite is true for mixtures GE > 0.These results can be rationalised by taking the modelof Caldin and Beniietto 24 as a basis: in the process offorming a n ' encounter complex ' from the reactants, someof the solvent molecules in the second solvation zone ofthe reactants must pass to the bulk. Bearing in mind that thissecond zone is a very disordered one, then, according toCaldin and Bennetto, the solvent molecule arrangement(water + co-solvent) in such a zone must be similar to thaJ.CHEM. SOC. DALTON TRANS. 1985 33corresponding to an ideal mixture. This implies that the changein free energy accompanying the process (solvent in the secondzone) -+ (solvent in the bulk) can be approximated as in theequation below,ll where Gbulk is the free energy of the bulk,G,, is the free energy of the second solvation zone, Gldeal is thefree energy of an ideal mixture, and AGE is the excess freeenergy of the mixture.Therefore, the contribution of this step to the energy ofactivation will be positive for the mixtures in which GE > 0,and negative for those with GE < 0. According to this, the rateconstants in the t.n.a.n. type mixtures (dextrose-water andsucrose-water) are greater than in water, and lower in themixtures with GE > 0 (methanol-water, ethanol-water, t-butyl alcohol-water, glycerol-water, dmf-water, and aceto-nitrile-water). So the kinetic effects of non-electrolytes reflectthe non-electrolyte-water interactions.AcknowledgementsWe thank Dr.J. Burgess, University of Leicester, for helpfulsuggestions during the preparation of this paper.References1 M. Marshall, J. Chem. SOC., 1891, 771.2 T. S. Price, Z. Phys. Chem., 1898,27,474.3 J. N. Bronsted, Z. Phys. Chem., 1922,102, 169.4 A. Indelli apd J. E. Prue, J . Chem. SOC., 1959, 107.5 W. J. Howells, J. Chem. SOC., 1964, 5844.6 E. S. Amis and J. E. Potts, jun., J. Am. Chem. SOC., 1941, 63,7 A. Meretoja, Ann. Acad. Sci. Fenn. Ser. A2, 1947, 59, 24.8 J.Burgess, J. Chem. SOC. A, 1968, 2571.9 J. Burgess, J . Chem. SOC. A, 1970, 2351.2883.10 U. G. Krishnam Raju, J. Ananthaswamy, B. 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Bennetto, in ‘ The Physical Chemistry ofAqueous Systems,’ ed. R. L. Kay, Plenum Press, New York,Navaneeth Rao, Indian J. Chem., Sect. A, 1978, 16, 21 1.J . Chem. SOC., Dalton Trans., 1983, 2679.Sect. A, 1950, 45, 229.1973, pp. 129-131.Received 24th January 1984 ; Paper 4/ 12