See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/244145132 Diffusion coefficients of iodide in high temperature aqueous solutions Article in Electrochemistry Communications · May 2000 DOI: 10.1016/S1388-2481(00)00023-0 CITATIONS READS 13 58 3 authors: Liliana N. Trevani Ernesto J Calvo 29 PUBLICATIONS 342 CITATIONS 166 PUBLICATIONS 4,234 CITATIONS University of Ontario Institute of Technology SEE PROFILE University of Buenos Aires SEE PROFILE Horacio R Corti Comisión Nacional de Energía Atómica 128 PUBLICATIONS 1,674 CITATIONS SEE PROFILE All content following this page was uploaded by Horacio R Corti on 26 May 2015. The user has requested enhancement of the downloaded file. www.elsevier.nl/locate/elecom Electrochemistry Communications 2 (2000) 312–316 Diffusion coefficients of iodide in high temperature aqueous solutions Liliana N. Trevani a,1 , Ernesto Calvo a,2, Horacio R. Corti a,b,c, *,2 a ´ ´ ´ Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Instituto de Quımica Fısica de los Materiales, Medio Ambiente y Energıa. ´ II, 1428 Buenos Aires, Argentina Ciudad Universitaria, Pabellon b ´ ´ ´ Nacional de Energıa ´ Atomica, ´ ´ Unidad de Actividad Quımica, Centro Atomico Constituyentes, Comision Gral Paz 1499, 1625 San Martın, Buenos Aires, Argentina c ´ Universidad Nacional de Gral. San Martın, ´ Calle 78 No. 3901, 1653 Villa Ballester, Buenos Aires, Argentina Escuela de Ciencia y Tecnologıa, Received 10 January 2000; received in revised form 4 February 2000; accepted 4 February 2000 Abstract The diffusion coefficients of iodide in water solutions containing NaHSO4 as supporting electrolyte have been measured between 102 and 215 8C using a high-temperature wall-tube cell. The temperature behavior of the diffusion coefficients is well described by the Arrhenius law and the activation energy for the mass transport is 17 kJ moly1. The results are compared to those calculated from the iodide conductivity at infinite dilution and to recent results from other authors. The solvation and speciation of the iodide ion in aqueous solutions at high temperature are analyzed. q2000 Elsevier Science S.A. All rights reserved. Keywords: Iodide; Diffusion; High temperature; Wall-tube electrode; Solvation 1. Introduction. The chemistry of iodine in aqueous solutions at elevated temperatures has been studied extensively due to the fact that iodine is a fission product in the nuclear power industry and it is very important to know the fate of its volatile species (I2, HIO) which may be released into the environment [1]. Thus, the equilibrium constants and the rate constants of the reactions involving all the relevant iodine species have been reported [2]. The transport properties of the iodine species have also been studied at temperatures above 25 oC. Quist and Marshall [3] measured the conductivity of NaI and KI up to 800 8C and at pressures to 400 MPa. Bard and co-workers [4] reported diffusion coefficients of iodide up to temperatures close to the water critical point (375 8C) measured by chronoamperometry on a platinum macroelectrode in 0.2 M NaHSO4 at 24 MPa in the absence of convection. More recently, Bard and co-workers [5] employed a titanium cell to measure the diffusion of iodide by stationary voltammetry with a platinum microelectrode in the same media as in Ref. [4] at pressures between 15 and 27 MPa. Cantrel et al. [6] have recently measured the diffusion coefficients of iodide between 25 and 85 8C by hydrodynamic voltammetry using a rotating platinum disk electrode (2 mm in diameter) in 0.075 M H2SO4. The differences in the diffusion coefficient of the iodide ion reported in these studies have prompted us to investigate the diffusion of iodide in aqueous solutions by using a novel high-temperature wall-tube electrode previously described [7]. An additional motivation for the study of the iodide transport in aqueous solutions is that iodide does not obey the Stokes–Einstein law [8], which yields at 25 8C a hydrodynamic radius smaller than the crystallographic value (0.220 nm). The molecular dynamic simulation performed by Koneshan et al. [9] indicates that, at 25 8C, iodide mobility is unique among anions because its mobility decreases on charge neutralization due to solvent cage formation. This peculiar solvation effect could influence the temperature behavior of the iodide diffusion coefficient. 2. Experimental * Corresponding author. Tel.: q54-11-4754-7174; fax: q54-11-47547121; e-mail: hrcorti@cnea.gov.ar 1 Present address: Department of Chemistry, Memorial University Newfoundland, Saint’s John, Canada. 2 Permanent Research Staff of the Argentine Science Research Council (CONICET). 2.1. High-temperature electrochemical cell The electrochemical cell used in this work has been built in titanium and its design is similar to that of the stainless- 1388-2481/00/$ - see front matter q2000 Elsevier Science S.A. All rights reserved. PII S 1 3 8 8 - 2 4 8 1 ( 0 0 ) 0 0 0 2 3 - 0 Tuesday Apr 11 10:09 AM StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 200 L.N. Trevani et al. / Electrochemistry Communications 2 (2000) 312–316 steel cell reported in a previous work [7]. It can reach temperatures up to 240 8C and pressures up to 20 MPa. Fig. 1 illustrates the main parts of the cell: Part (A) shows the upper chamber (volume about 100 cm3): it houses a platinum resistor thermometer (1) located close to the nozzle inlet which measures the working temperature, a silver wire covered with AgI(s) as reference electrode (2), the solution inlet (3) connected to a platinum preheater line (1 m length, 0.5 mm inner diameter) wrapped around a 600 W electrical heater 10 mm in diameter, not shown in Fig. 1. The outlet (4) connected to an external highpressure valve is used during the cell fill-up. The titanium cylindrical diffuser (6) is used to increase the heat exchange and the residence time of the solution Part (B) is the middle part containing the titanium nozzle (7), 0.75 mm inner diameter and 40 mm length, and the platinum wire counter-electrode (8) wrapped around the nozzle, which acts as a Luggin, and is sealed to the body with PTFE ferrules. The bottom part (C) contains the working platinum microdisc electrode (9), encapsulated in soda glass (10) of 6 mm outer diameter. The pressure seal is performed by means of two chevron PTFE ferrules (11) and titanium followers on a bronze nut (13). The solution exits the cell through the outlet (12). Parts A, B and C are tightened by means of six stainlesssteel bolts which compress the silicone O’rings (5 and 59). The volume of the chamber housing the working electrode and the titanium nozzle (wall-tube electrode) is 10 cm3 and the distance from the nozzle to the microdisc is 2.0 mm. All titanium parts were previously heated in air at 600 8C for 6 h to form a blue, non-conducting, titanium oxide film. Only a well-centered microdisc electrode was used in the experiments. The scheme of the injection and pressure/temperaturecontrol system is similar to that used previously [7], except that the effluent solution was collected in a 5 L steel receiver with a glass liner kept at the pressure of the experiment with nitrogen. This modification avoids the use of a back-pressure regulator, which introduces oscillations in the measurements at high flow rates. The current–potential curves were carried out at a flow rate in the range of 2–10 cm3 miny1 using a potentiostat under computer control for data acquisition through an IEEE interface and Keithley multimeter. The cell was thermostat-controlled by immersion in a water bath (up to 90 8C) or a silicone bath (above 100 8C) to within 0.18C by means of a Haake thermostat. 313 Fig. 1. High-temperature wall-tube electrochemical cell. microelectrode under an optical microscope confirmed that the platinum wire does not extend beyond the glass surface at temperatures up to 250 8C. Moreover, the calculated area expansion of the platinum microdisc by heating from 25 to 215 8C is less than 0.3%. The resistivity of the Corning 0120 glass is higher than Pyrex glass, but lower than the Corning 8870 glass used by Bard and co-workers [5]. These authors reported very important current leakage in voltammetric experiments at temperatures above 230 8C. Nevertheless, within the range of temperature of this work the conductance of our glass is low enough to ensure a negligible current leakage. All analytical grade chemicals were used as received. Water was purified by a Millipore Milli-Q system yielding 10 MV cm and the solutions were deoxygenated by bubbling nitrogen for at least 4 h and keeping under nitrogen during the experiments. 3. Results and discussion 3.1. Voltammetric determination of diffusion coefficients 2.2. Working electrode The platinum microdisc electrode, 106.4 mm diameter, was encapsulated in soft glass (Corning 0120, o.d. 6 mm) having a coefficient of linear expansion 9.2=10y6 8Cy1, almost identical to that of platinum. Thus, we avoid the increase of the apparent area when the electrode is heated, as observed when Pyrex glass is used [5]. The direct observation of the Tuesday Apr 11 10:09 AM We have studied the oxidation of 10 mM iodide in 0.2 M NaHSO4 (initially at 25 8C) between 102 and 215 8C at 4 MPa. The electron transfer process can be represented by the direct reaction: 2Iy™I 2q2e (1) or through the tri-iodide ion: StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 200 314 L.N. Trevani et al. / Electrochemistry Communications 2 (2000) 312–316 2I 3 y™3I 2q2e (2) The convective-diffusion limiting current density for the impinging jet on a wall electrode was analyzed in a previous work [7]. We adopted the empirical equation proposed by Chin and Tsang [10], which introduces two dimensionless hydrodynamic parameters, a and b: i LsanFD 2/3 n y1/6 b ž/ H d c*v 1/2 (3) where n is the number of Faradays per mol, n is the kinematic viscosity of the solution, D and cU are the diffusion coefficient and the analytical concentration of the electroactive species, respectively. The geometrical parameters of the wall-tube electrode are the nozzle–wall distance, H, and the nozzle diameter, d. The mass transfer coefficient is proportional to v, defined by vs 4Q pd 3 (4) where Q is the volume flow rate of the solution through the nozzle (cm3 sy1). Written in this form, Eq. (3) resembles the Levich equation for the rotating disc electrode (RDE). The calibration of the wall-tube cell at 30 oC by oxidation of ferrocyanide ion gave for a and b the values 1.54 and –0.022, respectively [7]. Eq. (3) has been verified over a wide range of H/d for Reynolds number higher than 80; in this work for all the temperatures studied, it is satisfied at volume flow rates higher than 2 cm3 miny1 with H/ds2.67. Below this value of Q the limiting current is no longer linear with v1/2 and it converges to the diffusional value for a stationary microdisc of radius r [11] when vs0: i Ls4nFDcUr (5) Thus, we can determine diffusion coefficients with the microdisc electrode under the wall-tube regime or without convection. The typical polarization curves shown in Fig. 2 for 130 8C exhibit well-defined plateaus and shift to more negative potentials as the volume flow rate increases. The iodide diffusion coefficients were obtained from the slopes of the Levich plots shown in Fig. 3 by using Eq. (3). The kinematic viscosity of the solutions was approximated to the water values at the given temperature and 4 MPa, using the equation proposed by Watson et al. [12] for the dynamic viscosity, n, and the equation of state by Hill [13] for the density. The molar concentrations of iodide at each working temperature and 4 MPa were calculated from the molarity of the solution at 25 8C (10 mM) and the density of water [13]. Due to thermal expansion the iodide concentration decreases down to 8.5 mM at 215 8C. The results are summarized in Table 1, along with those obtained in voltammetric experiments without convection using Eq. (5). Tuesday Apr 11 10:09 AM Fig. 2. Current–potential curves on Pt at 130 8C and 4 MPa for a solution containing 0.01 M iodide in 0.2 M NaHSO4. Sweep rate 20 mV sy1; flow rates from bottom to top: 3, 4, 5, 6 and 8 cm3 miny1. Fig. 3. Levich plots for the oxidation of iodide on Pt in 0.2 M NaHSO4. Temperatures from bottom to top: 102, 130, 155, 182 and 215 8C. Table 1 Diffusion coefficients of iodide in 0.2 M NaHSO4 at 4 MPa T/8C D/105 cm2 sy1 18 102 105 130 151 155 180 182 215 1.66 a 7.62 8.12 a 11.3 13.2 a 14.3 17.4 a 23.9 28.8 a From limiting current without convection. 3.2. The temperature dependence of the iodide diffusion coefficient Fig. 4 shows the Arrhenius plots for the diffusion coefficient of iodide in aqueous solutions obtained in this work along with those reported by Bard and co-workers [4,5] and Cantrel et al. [6]. Our results can be described by the Arrhenius equation: StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 200 L.N. Trevani et al. / Electrochemistry Communications 2 (2000) 312–316 315 An additional point has been measured in this work at 18 8C in order to confirm this statement. The results reported by Spiro and Creeth [18] between 5 and 25 8C, also plotted in Fig. 4, lead to an effective hydrodynamic radius of 0.116 nm for the iodide radius, calculated from the Stokes–Einstein equation under stick conditions: Ds Fig. 4. Arrhenius diffusion coefficient plots of iodide in 0.2 M NaHSO4: (h) [4]; (j) [5]; (m) [6]; (,) [18]; (s) this work, with WTE; (d) this work, without convection; (∆) best fit of the experimental data; (—) calculated from electrical conductivity at infinite dilution. ž / DsD o exp y ED RT (6) where D8 is the pre-exponential factor and ED the activation energy for the diffusion process. The best-fit parameters in the temperature range studied in this work and in the previous ones are summarized in Table 2. The two sets of measurements by Bard and co-workers extend up to the supercritical region (375–385 8C). However, the fitting extends only up to 300 8C because deviations to the Arrhenius behavior are evident above this temperature. Cantrel et al. [6] used the Newman relation [14] to calculate the thickness of the diffusion layer as a function of the dimensionless Schmidt number, Scsn/D. In the limit of very high Sc (low temperature limit), the Newman relation becomes identical to the Levich relation [15] used in our hydrodynamic treatment of the wall-tube electrode [16]. In order to compare results we recalculated the diffusion coefficients of iodide reported by Cantrel et al., using the Levich relation. The diffusion coefficient of iodide at infinite dilution, D8, calculated from the electrical conductivity data by Robinson and Stokes [17] in the 25–85 8C region match quite well with these data as previously quoted by Cantrel et al. [6], as can be seen in Fig. 4. It is clear that the results obtained in this work for the diffusion coefficient of iodide above 100 8C match quite well with those reported by Cantrel et al. [6] at lower temperature. Table 2 Activation parameters for the diffusion of iodide in water DT/8C D8/103 cm2 sy1 ED/kJ moly1 Ref. 18–215 25–300 25–85 4.1"0.4 4.7"0.6 5.3"0.2 17.0" 1.2 14.6"1.6 15.3"0.5 this work [4,5] [6] Tuesday Apr 11 10:09 AM kT 6phr (7) This value is much smaller than its crystal radius (0.215 nm) and it is evidence of the structure-breaking nature of the iodide ion. Recently, Koneshan et al. [9] have performed molecular dynamic simulation of iodide in water and they ascribed the high mobility of iodide to the low residence time of the water molecules in the first hydration layer of the ion. As mentioned above, the diffusion coefficients of iodide reported by Bard and co-workers [4,5] are almost a factor of two lower than those reported in this work over the entire temperature range. Surprisingly, the effective hydrodynamic radius of iodide according to the data of these authors is close to the crystallographic value. 3.3. Speciation in iodide–iodine solutions at high temperature The oxidation of iodide in our experiments leads to the formation of triiodide over the electrode. It is interesting to analyze the formation of this and other iodine species at high temperature, which could account for the differences observed in the diffusion coefficient measured in this work and those previously reported [4,5]. The equilibrium constant for the reaction: IyqI 2 l I 3 y (8) has been studied by several authors [1,19] at high temperature and it could be expressed by logKs 555.0 q7.355y2.575logT T (9) Thus, at 25 8C Ks698, indicating that most of the I2 produced on the electrode surface is taking part in the triodide complex. Iodine can also suffer a disproportion reaction in water yielding HOI and HI. The complete set of equilibrium reactions taking place in this solution, including the dissociation of NaHSO4 and the autoprotolysis of water can be solved from the known values of the equilibrium constants [2] to obtain the speciation as a function of temperature. The results show that I3y is the only important species apart from Iy and I2. HOI concentration is negligible (less than 0.03%) below 150 8C, but it represents 3.4% of the total iodine concentration at 200 8C. The concentration gradient through the diffusion layer could be estimated by assuming that the iodine concentration reaches a maximum at the electrode surface and decays to zero through the convective-diffusion limiting layer, while StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 200 316 L.N. Trevani et al. / Electrochemistry Communications 2 (2000) 312–316 the iodide concentration goes from the bulk analytical concentration to zero at the electrode surface. At low temperatures the concentration of iodine can be limited by its solubility, while at higher temperature we assume that the sum of the I2, Iy and I3y concentrations is constant through the diffusion layer. It is observed that the concentration of I3y reaches a maximum at a given distance from the electrode. The concentration ratio I3y/Iy close to the electrode is higher than unity below 100 8C and decreases as the temperature is increased, due to the reduction of the equilibrium constant of the triodide formation reaction (Ks42 at 200 8C). Because the diffusion coefficient of I3y is almost half the value for iodide at 25 8C [18] and it is reasonable to assume that it remains lower at higher temperatures, one is tempted to conclude that the low diffusion coefficients reported by Bard and co-workers arise from the competition of reaction 1 with reaction 2. However, it should be noted that the diffusion coefficients of iodide obtained in our cell without convection agree quite well with those coming from WTE. It is not clear at the moment whether kinetics factors related to the formation of triiodide could be responsible for low diffusion coefficients measured with the Bard and co-workers cell. 4. Conclusions The high-temperature wall-tube electrode cell has been used to obtain diffusion coefficients of iodide in aqueous solutions up to 215 8C and 4 MPa. The temperature behavior of the diffusion coefficients follows the Arrhenius law and the activation parameters have been obtained. The diffusion coefficients reported in this work are in good agreement with those reported by other authors below 100 8C and with the values calculated from electrical conductivity data. The diffusion coefficients over the range of temperature studied here lead to effective hydrodynamic radius for this ion, confirming its structure-breaking nature. The enhanced mobility of the iodide in water has also been observed in molecular dynamic simulations. On the other hand, the values of diffusion coefficients obtained by Bard and co-workers using stationary voltammetry are too low and lead to an effective hydrodynamic radius close to its crystallographic Tuesday Apr 11 10:09 AM value. The formation of triiodide ions could account for the discrepancies, but a more detailed study devoted to measuring the diffusion coefficient of triiodide and the complex behavior of the iodide–triiodide flow interaction [20] should be performed to clarify this point. Acknowledgements The authors are grateful for partial financial support by ´ ´ Consejo Nacional de Investigaciones Cientıficas y Tecnicas (CONICET) and UBACyT. References [1] L. Ashton, H.R. Corti, D.J. Turner, in: A.M. Deane, P.E. Potter (Eds.), Proceedings of the Specialist’s Workshop on Iodine Chemistry in Reactor Safety, AERE, Harwell, UK, 1986. [2] D.A. Palmer, M.H. Lietzke, Radiochim. Acta 31 (1982) 37. [3] A.S. Quist, W.L. Marshall, J. Phys.Chem. 73 (1969) 978. [4] W.M. Flarsheim, Y. Tsou, I. Tratchtenberg, K.P. Johnston, A.J. Bard, J. Phys. Chem. 90 (1986) 3857. [5] C. Liu, S.R. Snyder, A.J. Bard, J. Phys. Chem. B 101 (1997) 1180. [6] L. Cantrel, J.-M. Fulconis, J. Chopin-Dumas, J. Solution Chem. 27 (1998) 373. [7] L.N. Trevani, E. Calvo, H.R. Corti, J. Chem. Soc., Faraday Trans. 93 (1997) 4319. [8] P.C.F. Pau, J.O. Berg, W.G. McMillan, J. Phys. Chem. 94 (1990) 2671. [9] S. Koneshan, J.C. Rasaiah, R.M. Lynden-Bell, S.H. Lee, J. Phys. Chem. B 102 (1998) 4193. [10] D.T. Chin, C.H. Tsang, J. Electrochem. Soc. 125 (1978) 1461. [11] R.M. Wightman, D.O. Wipf, in: A.J. Bard (Ed.), Electroanalytical Chemistry, vol. 15, Marcel Dekker, New York, 1989. [12] J.T.R. Watson, R.S. Basu, J.V. Levelt Sengers, J. Phys. Chem. Ref. Data 9 (1980) 1255. [13] P.G. Hill, J. Phys. Chem. Ref. Data 19 (1990) 1233. [14] J. Newman, J. Phys. Chem. 70 (1966) 1327. [15] B.G. Levich, Acta Physicochim. URSS 17 (1942) 257. [16] L.N. Trevani, Thesis, University of Buenos Aires, 1997. [17] R.A. Robinson, R.H. Stokes, in: Electrolyte Solutions, 2nd ed., Butterworth, London, 1959, Appendix 6.2. [18] M. Spiro, A.M. Creeth, J. Chem. Soc., Faraday Trans. 86 (1990) 3573. [19] D.A. Palmer, R.W. Ramette, R.E. Mesmer, J. Solution Chem. 13 (1984) 673. [20] D.G. Leaist, J. Solution Chem. 17 (1988) 359. StyleTag -- Journal: ELECOM (Electrochemistry Communications) Article: 200