J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1983-1986 Heterogeneous Catalysis in Solution Part 27.t-Reaction between Titanium(ll1) and Triiodide Ions Catalysed by Platinum Shaorong Xiaoz and Michael Spiro* Department of Chemistry, Imperial College of Science, Technology and Medicine, South Kensington, London, UK SW72AY The rate of the reaction between titaniumfiii) chloride and triiodide ions in an acid chloride medium has been studied in the absence and presence of a rotating platinum disk. At low concentrations of triiodide the catalytic rate at platinum was found to be first order in 13-, zero order with respect to Ti"' and H+, and proportional to the square root of the rotation speed of the disk. These results pointed to diffusion-controlled catalysis, as did the low activation energy of 19 kJ mol-' as compared with 40 kJ mol-' for the uncatalysed reaction.All these findings are consistent with an electrochemical interpretation of the catalytic mechanism, as was shown by the current-potential curves determined for the two reactants at the same reduced platinum surface. Provided that the voltammograms for Ti"' had been carried out in the presence of the same concentration of K! as in the reaction mixtures, the rates and mixture potentials determined electrochemically agreed well with the catalytic rates and potentials measured experimentally. The fact that quite different results were obtained when no KI was present in the TiCI, solution provides further confirmation for the modified form of the additivity principle.The redox reaction 2Ti"' + I, -+2Ti" + 31-(1) in aqueous hydrochloric acid is a slow process whose kinetics have been studied by several workers.'*2 An unusual feature of this reaction is that it can be homogeneously catalysed by certain quinones, phenazines and quin~xalines~,~ in concen- trations as low as lop7 to lop5 mol 1-'. The mechanism appears to depend on the catalyst4 and one case has been investigated in detail.5 Reaction (I) has also been found to be catalysed heterogeneously by metallic platinum.6 This was explained by an electrochemical mechanism whereby the elec- tron passed from Ti"' to the iodine via the noble metal. The present study aims to test this mechanism quantitatively. Theory As in the case of several other metal-catalysed redox reac- tion~,~,*the electrochemical mechanism can be tested by combining electrochemical and kinetic studies.The principle is illustrated in Fig. 1 where anodic currents are taken as positive and cathodic currents as negative. Curve (a) depicts the increase in current when a solution of Ti"' is oxidised electrochemically at a given platinum surface while curve (b) shows the variation of current with potential when a solution of iodine in KI solution is reduced electrochemically. When both Ti"' and iodine are present together in the solution, the two curves can be added algebraically provided they have been obtained in circumstances which correspond to those in the mixt~re.~,~ The platinum surface thus takes up a mixed or mixture potential Emixat which the anodic current Zmix on curve (a)exactly balances the cathodic current I Imixon curve I (b).By Faraday's law, the mixture current is directly pro- portional to the rate of the reaction between Ti"' and iodine on the platinum surface, as given by eqn. 1 umix = I,,JnFA (1) where n is the number of electrons cancelled out in the overall reaction equation [i.e. n = 2 for eqn. (I)], F is the t Part 26: Ref. 7. Department of Chemistry, Guangxi Teachers College, Nanning, Guangxi 530001,People's Republic of China. Faraday constant and A is the surface area of the platinum. If vmix, derived from purely electrochemical experiments with the separate reactants, agrees with the catalytic rate vCatfrom kinetic measurements of the reaction mixture, and if Emix obtained electrochemically also agrees with the potential E,,, taken up by the platinum catalyst during the reaction, then the catalysis has clearly proceeded by a purely electrochemi- cal mechanism.In order to control the hydrodynamic conditions, it is useful to present the platinum surface in the form of a large horizontal disk set in an inert trumpet-shaped former which rotates about a vertical axis." The thickness, 6, of the Nernst diffusion layer at the surface is then given by the Levich -2 -EjV vs. SCE -4 --8 t Fig. 1 Voltammograms at 10 mV s-' with the reduced platinum disk rotating at 9 Hz for the oxidation of (a') 23.7 mmol 1-' TiCl, and (a) 23.7 mmol I-' TiCI, in 0.1 mol 1-' KI, and (b) for the reduction of 0.630 mmol 1-' 1,-in 0.1 mol I-' KI. All solutions were at 25°C and also contained 0.1 mol 1-' HC1 and 0.8 mol I-' KCl.equation" 6 = 0.643D1/3v1/6f-1/2 (2) where D is the diffusion coeficient of the diffusing species, v is the kinematic viscosity of the solution and f is the rotation speed in Hz. Diffusion-controlled currents and diffusion- controlled catalytic rates vary inversely with S and are there- fore directly proportional to the square root of the rotation speed. Experimenta1 All solutions were made up with Milli-RO and Milli-Q de- ionised water (Millipore). The titanium(@ chloride was a BDH product, low in iron, which also contained ca. 0.049 g ZnC1, per ml.The Ti"' concentration was determined by standardizing with pure iron.', All other reagents were BDH AnalaR. The geometrical area of the platinum disk was 12.19 cm2. A saturated potassium chloride calomel electrode (SCE) was used as the reference electrode and a large platinum foil as the counter electrode. Before each experiment the platinum surface was polished with a suspension of 0.3 pm alumina in water, washed, and electrochemically cleaned by cycling it at 50 mV s-l between -0.2 and +1.7 V us. SCE in nitrogen- saturated 0.5 mol 1-' sulfuric acid while it was rotated at 9 Hz, until reproducible voltammograms were obtained. For the preparation of a reduced surface, the potential was dis- connected at 0.2 V and the electrode preconditioned at 0.2 V for 20 s, 1.7 V for 20 s and finally 0.2 V for 600 s.The disk was then thoroughly washed and stored in a desiccator. All the experiments were carried out in a thermostat bath, usually at 25.0 & 0.1 "C. Electrochemical experiments were carried out in a three-compartment cell' and the catalysed runs in a similar two-compartment cell.' The background electrolyte was normally a mixture of 0.1 mol 1-' HCl (to reduce the extent of Ti"' hydrolysis), 0.1 mol 1-' KI (to keep the iodine complexed as I,-) and 0.8 mol 1-' KCl (to main- tain a high and constant ionic strength). In the kinetic runs the background electrolyte and reactant solutions were ther- mally equilibrated before being mixed. In the catalysed runs the disk was allowed to attain the bath temperature by being spun for 15 min in the thermostatted background solution before the reactants were added.Nitrogen was passed through the solutions beforehand and the experiments were carried out under a nitrogen atmo-sphere. The reaction was followed by removing samples (0.5 or 1 ml) at regular intervals and diluting them with 10 ml of 0.1 mol 1-' KI solution. The absorbance A of the triiodide ions was then measured at the band maximum wavelength of 352 nm on a Perkin-Elmer Lambda 2 spectrophotometer. The applicability of Beer's law was confirmed. In the catalysed runs the potential adopted by the platinum disk was recorded each time us. the SCE reference. Results and Discussion Homogeneous Kinetics For both the homogeneous and the catalysed reactions, plots of In A us.time were normally linear for 30-60 min. The slopes, obtained by least-squares fitting, gave the first-order (with respect to 13-) rate constants, k. At a constant initial I,-concentration of 0.202 mmol 1-', k was found to be pro- portional to the initial concentration of TiCl, over the range 8 to 47 mmol 1-'. However, when the initial TiCl, concentra- tion was fixed at 23.7 mmol 1-', k declined gently as the initial concentration of triiodide increased from 0.1 to 0.6 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 mmol 1-'. All these results could be fitted, with an average deviation of less than 5%, by the equation -d[I,-]/dt = (9.6 x 10-3)[13-][TiC13] + (7.1 x lop7) x [TiCl,] (3) where the square brackets refer to concentrations in mol 1-' and the time t is in s.The first term on the right-hand side was always the larger one under our conditions. The rate of reaction fell almost inversely on raising the HCl concentra- tion, which suggests that TiOH2+ is the main reactant even though only ca. 5% of the Ti"' is present in this form in the medium empl~yed.'~ There was a lesser fall on increasing the concentration of KI. The activation energy between 9.8 and 25.0"C for the reaction between 0.202 mmol 1-' I,-and 23.7 mmol 1-' Ti"' was found to be 40 kJ mol-'. Johnson and Winstein2 obtained a similar rate law which they interpreted as indicating rate-determining reactions between TiOH2+ and both I,-and I,.For the same back- ground conditions of 0.1 moll-' HC1,O.l moll- ' KI and 0.8 mol 1-KCl and also at 25 "C, their kinetic equation was of the same form as eqn. 3 but with different rate constants, namely -d[I,-]/dt = 0.103[13-][Ti"'] + (1.92 x 10-5)[Ti"'] (4) This difference may be attributed to the presence of ZnC1, in the BDH TiCl, solution employed. Experiments with concen- trations of I,-and Ti"' similar to those used in ref. 2, but to which additional amounts of zinc chloride had been added, led to lower rates, as Fig. 2 shows. As the curve rises steeply at low ZnCl, concentrations, a much higher rate of reaction would be expected for the zinc chloride-free solutions employed by Johnson and Winstein. Catalysed Kinetics Reaction (I) was always faster in the presence of the spinning platinum disk, consistent with heterogeneous catalysis by platinum.In order to evaluate the catalytic component in these 'heterogeneous' experiments, their rates and those of the corresponding homogeneous runs were expressed in terms of the number of moles of triiodide reacting per second, (u'), by the equation 0' = kV[13-] (5) where V is the volume of the solution (normally 354 ml) and [I3-] is the initial concentration. The areal catalytic rate at 31 I 0 1 2 3 [Zr1Cl,]/l0-~ rnol dm-3 Fig. 2 Homogeneous first-order rate constant khom us. concentra-tion of zinc chloride, for a reaction mixture containing 8.3 mmol 1-' TiCl,, 2.52 mmol 1-' 13-, 0.11 moll-' KI, 0.1 moll-' HC1 and 0.82 moll-' KCl at 25 "C J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the surface of the platinum [in (mol I,-) m-2 s-'1 was then given by ucat = -Yhom)/A (6) Expressing the catalytic rate in this way involves no precon- ceptions about the kinetic form of the catalytic reaction. It should be borne in mind, however, that ucat depends on the difference between two rates of comparable magnitude and is therefore uncertain by ca. & 10%. When heterogeneous runs were carried out with the same initial concentrations of reactants as for the homogeneous runs, the catalytic kinetics were quite different. Thus, with [I3-] = 0.202 mmol 1-', u,,, was found to be completely independent of the Ti"' concentration over the range 8-47 mmol 1-'.However, when the initial concentration of TiC1, was kept constant at 23.7 mmol 1-', u,,, increased linearly with [I3-] according to the equation u,,Jmol m-2 s-' = (2.92 x lop6)+ (3.17 x 10-2)[13-] (7) The catalysed reaction was therefore first order in I,- and zero order in Ti"'. Unlike the homogeneous reaction rate, ucat was independent of the hydrogen ion concentration when it was varied from 0.05 to 0.2 mol 1-'. However, it decreased from 1.83 x lo-' to 1.02 x mol m-2 s-' when the KI concentration was raised from 0.1 to 0.2 mol 1-' and stayed at the lower value for KI concentrations of 0.3 and 0.5 mol 1-' (the ionic strength being kept constant by appropriately lowering the amount of KCl). As shown in Fig. 3, ucat increased proportionately with the square root of the rotation speed.This is a clear indication of diffusion control, a conclusion supported by the low activa- tion energy of 19., kJ mol-' obtained between 0.202 mmol 1-' I,-and 23.7 mmol dm-, Ti"' over the range 9.8-25 "C.It follows that the first-order (with respect to I,-) catalytic rate constant is given by the equation', where D is the tracer diffusion coefficient of I,-in the medium employed. Combination with eqn. 2 leads to u,,, = 1.555D213v-"6f'I2[I3 -3 (9) Taking the viscosity of the supporting electrolyte medium at 25°C as 0.8888 x lop3 kg m-l s-' '' and its density as 1.0493 g ml-' l6 gives v = 0.8470 x lop6 m2 s-'. The resulting value of D from the lower plot of Fig. 3 is 7 N €5-E4 u) 03 1 0 0 1 2 3 4 5 f 1 /2/H~1/2 Fig.3 Catalytic rate at 25 "C us. the square root of the disk rotation speed, for solutions containing 23.7 mmoll-' TiCI, ,0.1 mol 1-1 KI, 0.1 mol I-' HC1, 0.8 KC1 mol 1-' and (0)0.202 mmol 1-' triiodide or (m) 4.04 mmol 1-triiodide 1985 1.02 x m2 s-'. Allowance for the correction + 0.145(0/~)~/~][l + 0.298(D/~)'/~ gives D = 1.07 x lo-' m2 s-'. This is in reasonable agreement with the value of 1.13 x m2 s-l obtained by Newson and Riddiford," also in the presence of 0.1 mol 1-' KI. In most heterogeneous runs the catalyst potential E,,, rose in the early stages and then declined. In other cases, E,,, ini-tially stayed constant before decreasing while, with higher I, -concentrations, E,,, decreased throughout the experi- ments.The initial values of E,,, fell as the TiC1, concentra- tion increased and rose as the I,- concentration increased. These findings are explained in the next section. Electrochemical Experiments If the catalytic mechanism is an electrochemical one, the cata- lytic rates and potentials should be predictable from electro- chemical experiments with the two reactants. Voltammograms were therefore determined for appropriate solutions of TiCl, and I,-in the normal supporting electro- lyte medium. Two examples are depicted in Fig. 1. Here the mixture potential, Emj,obtained from curve (a) for 23.7 mmol 1-1 Ti111 and curve (b)for 0.630 mmol 1-' I,-was 274 mV us. SCE while the initial potential E,,, measured in the catalysed reaction mixture was 280 mV.Furthermore, the rate umix cal-culated from the mixture current of 4.26 mA in Fig. l by means of eqn. 1 was 1.81 x mol m-2 s-l while the mea- sured catalytic rate u,,, evaluated from eqn. 6 was 1.83 x mol m-2 s-'. This good agreement for both the potential and the rate would be diflicult to explain by any catalytic mechanism other than an electrochemical one in which the electrons are transferred from the Ti"' reductant to the I, -oxidant through the platinum catalyst. Fig. 4 shows that similar goad agreement between umix and u,,, was obtained in many other sets of experiments. The con- cordance found between Emix obtained from the voltam- mograms and E,,, measured in the reaction mixtures is demonstrated in Fig.5. It must be emphasized that all the above electrochemical data were based on voltammograms for TiC1, solutions con- taining 0.1 mol 1-' KI, the same KI concentration as in the reaction mixtures. Quite different voltammetric curves were obtained for solutions of TiC1, without KI, as curve (a') in Fig. 1 illustrates. This difference arose from the strong adsorption of iodide ions on the reduced platinum surface, a wcat/l 0-5 mol rn-2 s-I Fig. 4 uCaJvmix vs. uCat for experiments in which the following parameters were varied: 0,TiCl, concentration; 0,I,-concentra-tion; 0,KI concentration; .,HC1 concentration and A, tem-perature. The symbols, x, refer to values of umix obtained from voltammograms for TiCI, solutions containing no KI.The dashed lines represent the 10% uncertainty limits. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Xi IX -200 --300 0 ' 100 0 200 °300 140C E,,JrnV vs. SCE Fig. 5 Emixus. E,,, for experiments in which the following param- eters were varied: 0,TiCl, concentration; e,I,-concentration; 0, KI concentration. The symbols x refer to values of Emixobtained from voltammograms for TiCl, solutions containing no KI. The straight line has a slope of unity. well attested phenomenon.20*21 It was confirmed in the present work by a cyclic voltammogram taken after immers- ing the platinum disk in a typical reaction mixture, which showed a large anodic peak at ca. 1.3 V which disappeared in the second sweep.If curve (a') rather than curve (a) in Fig. 1 is combined with the I,-curve (b), Emixbecomes 152 mV, completely different from the E,,, value of 280 mV. More- over, the larger Imixvalue of 7.72 mA leads to a correspond- ingly larger umix of 3.28 x lo-' mol mM2 s-', some 79% greater than the experimental value of ucat.Similar disagree- ment in other cases is clearly indicated by the data points marked with crosses in Fig. 4 and Fig. 5. This is further con- firmation that the original principle of the additivity of current-potential curves22 should only be applied in the modified form given by Creeth and Spi1-0.~ This states that current-potential curves can be added only if they have been obtained in circumstances which correspond to those of the mixture.It remains to show how the observed catalytic kinetics follow directly from the electrochemical curves. This is demonstrated in Fig. 6 where all currents have been plotted as positive. The intersections of the I,- reduction curves (bl)-(b3) with the Ti"' oxidation curves (al) or (a2)therefore mark the respective mixture potentials and mixture currents. Inspection of the diagram makes it clear that, for the low I,- concentration curves (b,) and (b2),the intersections with both (al) and (a2)lie in the limiting-current plateau regions of the I,-curves. Thus Imixand umix, and hence ucat,are indepen- dent of the concentration of TiCl, . Since the limiting currents are proportional to [I3-], umix and hence uCatare first order in I,-.Moreover, limiting currents vary inversely with the thickness, 6, of the diffusion layer and therefore umix and ucat are proportional to the square root of the disk rotation speed. On the other hand, when [I3-] becomes sufficiently large [curve &)I, the intersection mixture point with curve (al)in Fig. 6 lies below the limiting-current plateau. It follows that umix and thus uCatwill rise less than proportionately with [I3-] at high concentration as can be seen, for example, by comparing the slopes of the two lines in Fig. 3. Inspection of Fig. 6 also makes it easy to understand why Emix,and hence E,,, , were found to rise with increasing I, -concentration and fall with increasing concentration of Ti"'. The electro- chemical interpretation of the catalytic mechanism therefore allows us to explain satisfactorily the various aspects of the catalysis by platinum of the reaction between Ti"' and I,-.-0.4 -0.2 0 0.2 0.4 E/V vs.SCE Fig. 6 Voltammograms at 10 mV s-' with the platinum disk rotat- ing at 9 Hz for the oxidation of TiCl, [(al)23.7 and (a2)47.3 mmol 1-'1 and the reduction of I,-[(b,) 0.135; (b2)0.202 and (b,) 0.630 mmol l-']. All solutions were at 25°C and also contained 0.1 mol I-' KI, 0.1 moll-' HC1 and 0.8 mol I-' KCI. We thank Guangxi Teachers College, Nanning, P. R. China for granting leave of absence to S.X. and the Chinese Govern- ment for an overseas scholarship. References 1 D. M. Yost and S. Zabaro, J. Am. Chem. SOC., 1926,48,1181.2 C. E. Johnson Jr. and S. Winstein, J. Am. Chem. SOC., 1951, 73, 2601. 3 P. A. Shaffer, J. Phys. Chem., 1936,40, 1021; Cold Spring Harbor Symposium on Quantitative Biology, Cold Spring Harbor Labor- atory, New York, 1939, vol. VII, p. 50. 4 C. E. Johnson Jr. and S. Winstein, J. Am. Chem. SOC., 1952, 74, 755. 5 C. E. Johnson Jr. and S. Winstein, J. Am. Chem. SOC., 1952, 74, 3 105. 6 M. Spiro and A. B. Ravno, J. Chem. SOC., 1965,78. 7 R. 0.Farchmin, U. Nickel and M. Spiro, J. Chem. SOC., Faraday Trans., 1993,89, 229, and references therein. 8 M. Spiro, Catal. Today, 1993, 17,517. 9 A. M. Creeth and M. Spiro, J. Electroanal. Chem., 1991, 312, 165. 10 M. Spiro, in Comprehensive Chemical Kinetics, Vol. 28: Reac-tions at the Liquid-Solid Interface, ed. R. G. Compton, Elsevier, Amsterdam, 1989, ch. 2. 11 V. G. Levich, Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ, 1962, p. 69. 12 A. I. Vogel, A Textbook of Quantitative Inorganic Analysis, Longmans, London, 1943, p. 391. 13 R.L. Pecsok and A. N. Fletcher, Inorg. Chem., 1962, 1, 155; Ya. I. Turyan and L. M. Maluka, J. Gen. Chem. USSR, 1983,53,222 (260).14 L. L. Bircumshaw and A. C. Riddiford, Quart. Rev. Chem. SOC., 1952, 6, 157. 15 R. H. Stokes and R. Mills, Viscosity of Electrolytes and Related Properties, Pergamon, Oxford, 1965, pp. 91, 105, 110. 16 International Critical Tables, ed. E. W. Washburn, McGraw- Hill, New York, vol. 111, 1928, pp. 54, 88, 89. 17 J. Newman, J. Phys. Chem., 1966,70,1327. 18 M. Spiro and A. M. Creeth, J. Chem. SOC., Faraday Trans., 1990, 86,3573. 19 J. D. Newson and A. C. Riddiford, J. Electrochem. SOC., 1961, 108, 695. 20 A. T. Hubbard, R. A. Osteryoung and F. C. Anson, Anal. Chem., 1966,38,692. 21 M. Spiro and P. L. Freund, J. Electroanal. Chem., 1983,144,293. 22 C. Wagner and W. Traud, 2.Elektrochem., 1938,44,391. Paper 4/00653D; Received 2nd February, 1994