Measurement of Hypoiodous Acid Concentration ... - ACS Publications

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Measurement of Hypoiodous Acid Concentration by a Novel Type Iodide Selective Electrode and a New Method To Prepare HOI. Monitoring HOI Levels in the Briggs−Rauscher Oscillatory Reaction Norbert Muntean,†,‡ Lawson Bich Thuy,‡ Kristóf Kály-Kullai,‡ Maria Wittmann,*,‡ Zoltán Noszticzius,‡ Lavinia Onel,§ and Stanley D. Furrow∥ †

Department of Physical Chemistry, Babes-Bolyai University, RO-400028 Cluj-Napoca, Romania Department of Physics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary § School of Chemistry, University of Leeds, Leeds LS2 9JT, U.K. ∥ Penn State Berks College, The Pennsylvania State University, Reading, Pennsylvania 19610, United States ‡

ABSTRACT: A new type of iodide selective electrode prepared by dipping a silver wire into molten silver iodide is reported. The electrode was calibrated for silver and iodide ions and the measured electromotive force for various Ag+ and I− concentrations was close to the theoretical within a few millivolts. Besides Ag+ and I− ions, however, the electrode also responds to hypoiodous acid. Thus, the electrode was calibrated for HOI as well, and for that purpose a new method of hypoiodous acid preparation was developed. To explain the close to Nernstian electrode response for HOI and also the effect of hydrogen ion and iodine concentration on that response, the corrosion potential theory suggested earlier by Noszticzius et al. was modified and developed further. Following oscillations in the Briggs−Rauscher reaction with the new electrode the potential crosses the “solubility limit potential” (SLP) of silver iodide. Potentials below SLP are controlled by the concentration of I−, but potentials above SLP are corrosion potentials determined by the concentration of HOI. Finally, the measured HOI oscillations are compared with calculated ones simulated by a model by Furrow et al.

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behavior, emerges from the “inorganic subset”, however. In that subset various molecular and radical oxyiodine species (like HOI, HIO2, IO2•) are assumed to play an important role. Unfortunately, we have no means presently to measure these key intermediates separately, mostly because their concentration is too low even to be detected, e.g., by spectrophotometry. A usual technique to follow the oscillations in the BR reaction is potentiometry: that is, to record the oscillatory potential of a platinum or an iodide selective electrode in the course of the reaction. Such a potentiometric trace can be transformed, at least in theory, to a concentration trace of the potential determining species, assuming a Nernstian response of the electrode. In that case the electrode potential is a logarithmic function of the potential determining chemical species. For certain chemical species the logarithmic response of the platinum and the iodide electrodes survives even below the micromolar region; thus, a rather sensitive concentration measurement would be possible, at least in theory. Presently it is a problem, however, that it is not quite clear what the potential determining species are for a platinum electrode in

INTRODUCTION In the field of chemical nonlinear dynamics1,2 a most studied subject is the classical Briggs−Rauscher (BR) reaction,3 the oscillatory oxidation and iodination of malonic acid by a mixture of hydrogen peroxide and acidic iodate, catalyzed by manganous ions. Since its discovery there is a continuous interest4−10 in the mechanism and the exotic dynamics of the BR reaction. Various skeleton models have been proposed but in general the simulations are still not in quantitative agreement with experiments. These models can simulate oscillations of about the correct frequency, but I2 and I¯ concentration curves and also dependence on initial concentrations as parameters are not well reproduced in these simulations. The Bray−Liebhafsky oscillator,11 based only on acidic H2O2 and KIO3, is an inorganic subset of the BR. Obviously a complete model for the BR must be able to handle both systems (adjusting for temperature and concentrations). However, a recent impressive BL model of Schmitz12 has steps that are not included in the BR skeleton model, indicating that it might be incomplete. Recently, the organic reactions of the BR were studied with various techniques like measuring the CO and CO 2 evolution13−16 and NMR;17,18 thus, the “organic subset” of the BR reaction is more clear now. The chemical instability, one or more autocatalytic reactions responsible for the oscillatory © 2012 American Chemical Society

Received: February 16, 2012 Revised: April 10, 2012 Published: May 3, 2012 6630

dx.doi.org/10.1021/jp3015673 | J. Phys. Chem. A 2012, 116, 6630−6642

The Journal of Physical Chemistry A

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Aldrich) were used as received. All solutions were prepared with doubly distilled water. New Method To Prepare Aqueous HOI Solutions. The new method is based on an earlier one suggested by Noszticzius et al.19 First they prepared an I(+1) solution in concentrated sulfuric acid by applying a method of Masson;22 then a small part of that was diluted with a large excess of water to obtain an aqueous HOI solution. It is a problem, however, that the HOI solution produced this way contains high amounts of sulfuric acid. To solve that problem, a new three step procedure (i)−(iii) was developed. i. Preparation of an I(+1) Solution in Concentrated Sulfuric Acid. KIO3 (128.4 mg, 0.6 mmol) was dissolved in 30 mL of concentrated H2SO4 in a 100 mL beaker with continuous stirring. In a 10 mL beaker 154.7 mg (0.6 mmol) of I2 was dissolved in 2−3 mL of CH2Cl2. Then the two solutions were mixed under continuous stirring, combined with a mild heating of the mixture to expedite the evaporation of CH2Cl2. (Thus, the iodate was applied in a 2-fold excess compared to the ideal stoichiometry of I5+ + 2I2 → 5I+.) A dark brown solution was obtained. Then it was left standing overnight, while the color became light brown. ii. Preparation of I2O Solution in Dichloromethane. Under continuous stirring 3 mL of water was added dropwise to the 30 mL light brown solution produced in the previous step. Then the solution was extracted with 30 mL of CH2Cl2. The light brown stock solution of I2O in CH2Cl2 produced this way was stored in the dark in a closed bottle at 5 °C. Adding 3 mL water to the sulfuric acid solution yielded more I2O in the organic phase and kept practically all I2O5 in the aqueous phase. iii. Preparation of Dilute Aqueous HOI Solutions. CH2Cl2 is a rather polar solvent; thus, 100 mL of water can dissolve about 1 mL of CH2Cl2. In our experiments we added (in most cases) 0.4 mL of CH2Cl2 containing I2O to 100 mL of 25 mM H2SO4 solution. Applying a rapid stirring the CH2 Cl2 phase disappeared (partly by dissolution, partly by evaporation) within 1 min, leaving a clean solution of HOI dissolved in 25 mM H2SO4. Preparation of Iodine Free Aqueous HOI Solutions. Aqueous HOI solutions prepared according to the previous paragraph (iii) are contaminated with trace amounts of iodine. That contamination does not disturb most of the experiments. If necessary, however, the contamination can be removed from the aqueous solution by extracting it with CH2Cl2. (For example 50 mL aqueous solution can be extracted with 1 mL CH2Cl2 two times.) In that case most of the iodine is removed by the CH2Cl2 whereas I(+1) stays mostly in the aqueous phase. The above conclusion is supported by parallel titrations of HOI solutions with and without the CH2Cl2 extraction procedure suggesting a less than 5% HOI loss due to the extraction. From the point of the electrode calibration, however, a HOI loss does not matter as the initial HOI concentration is always determined by a titration. The presence of an iodine contamination was indicated by a light pink color of the CH2Cl2 phase after the first extraction which color was nearly invisible after the second extraction. Preparation of Iodine Solutions. Iodine was dissolved first in dimethyl sulfoxide (DMSO) to obtain a 250 mM stock solution. Aqueous iodine solutions were prepared with the 250 mM stock or with a 10 times diluted (25 mM) iodine also in DMSO, mixing appropriately small (less than 1 mL) volumes of

the BR reaction, and there is a similar problem with the iodide selective electrode as well, when it indicates iodide concentrations below 10−8 M. In this paper we study how the above problematic signal of the iodide selective electrode can be explained. Our working hypothesis is that in the problematic region the iodide selective electrode responds to hypoiodous acid; thus, we measured its potential response as a function of the hypoiodous acid concentration. To prove that hypothesis and to obtain reliable and reproducible data, a new type of iodide selective electrode was fabricated and a new method to prepare HOI was developed. The new electrode was built to eliminate the disturbing memory effects of the traditional iodide selective electrodes due to their pressed pellet type sensors made of AgI/ Ag2S or pure AgI. The aim of the new HOI synthesis was to obtain a more pure product. The procedure is based on the discovery that stable I2O solutions can be prepared in dichloromethane. The electrode response for HOI can be understood regarding the corrosion reaction CR between HOI and AgI (the most common component in the membrane of an iodide selective electrode): AgI + HOI + H+ ↔ Ag + + I 2 + H 2O

(CR)

The potential will be determined by the Ag+ ions appearing in the above corrosion process at the surface of the electrode. The quasi-equilibrium theory of “corrosion potential” suggested earlier by Noszticzius et al.19 is developed here to a more realistic steady state description of the corrosion process that also includes the effect of hydrogen ion and iodine concentration on the corrosion potential. It is shown that the potential of an iodide selective electrode is determined either by the iodide ion or by the hypoiodous acid concentration. According to our measurements with the new electrode in an oscillatory BR reaction, whenever the electrode potential is above the SLP (solubility limit potential) of silver iodide, the potential determining species of the iodide selective electrode is no longer the I− ion but it is the HOI. SLP is defined as a potential indicated by the electrode when I− and Ag+ ion concentrations are equal, that is, [I−] = [Ag+] = KS1/2, where KS is the solubility product of AgI. An analogous behavior of the bromide selective electrode in the oscillatory Belousov−Zhabotinsky (BZ) reaction was observed by Noszticzius and co-workers19−21 who found that in a BZ system the potential of the electrode above the SLP is controlled not by the Br− ion but by the hypobromous acid concentration. Finally, model calculations were performed to compare the calculated and measured HOI maxima in a BR oscillator. The calculations also show that iodous acid concentrations are about 2 orders of magnitude smaller than that of the hypoiodous acid; thus, the corrosion potentials above the SLP in the course of BR oscillations are due to hypoiodous acid and any contribution due to the iodous acid can be neglected.

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EXPERIMENTAL SECTION Chemicals. NaIO3 (Fluka, puriss. pa; ≥ 99.5%), KI (RiedeldeHaën, puriss. pa), H2SO4 (97%, Merck, pa), AgNO3 (Reanal, pa), I2 (Reanal, pa), MnSO4·4H2O (Reanal, pa), H2O2 (Fluka, puriss. pa ACS; ≥ 30%), malonic acid (Fluka, puriss.), dimethyl sulfoxide (Sigma Aldrich), and dichloromethane (Sigma 6631



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these into 50 mL of 25 mM H2SO4 containing also HOI when needed. Stock solutions of I2 were prepared in DMSO as it is a good solvent of iodine, it does not react23 with I2 or HOI and can be mixed in any ratio with water. Inertness of DMSO toward I2 and HOI was also demonstrated in our experiments as in iodine stock solutions prepared with DMSO solvent no iodide production was observed which was not the case in stock solutions prepared with methanol. Motivations for Developing a New Iodide Selective Electrode. The sensor of commercial iodide selective electrodes (e.g., the Orion iodide/silver ion selective electrode24,25) are pellets pressed from AgI−Ag2S precipitate mixtures. Noszticzius et al.26 made pellets from pure AgI. Two common problems of such pellets are, however, (i) they are prone to develop microcracks27 and (ii) sooner or later a narrow gap appears between the pellet and the electrode body. Any electrolyte penetrating into the microcracks and/or the narrow gap causes a “memory” effect that is especially disturbing in the case of oscillatory reactions where fast concentration changes have to be followed and a short response time is an important requirement. With the new electrode construction suggested here, these problems can be eliminated. A silver wire is dip coated with a thin layer of AgI in a molten form; thus, no deep crack formation is possible. Moreover, in the new construction a hydrophobic PTFE sealing keeps away any electrolyte from penetrating into the interface between the AgI sensor and the electrode body. Preparation of the Iodide Selective Electrode. i. Preparation of AgI Precipitate. Under rapid magnetic stirring 200 mL of 0.1 M AgNO3 solution was poured slowly into a 800 mL beaker containing already 210 mL of 0.1 M HI solution. After the total amount was added, the slurry was stirred for 5 min. Then the precipitate was repeatedly washed with distilled water under continuous stirring and the washing water was separated by decantation. The pH of the used water was checked after each washing cycle with a pH indicator paper. In the beginning the pH was rather acidic but the acidity decreased after each washing. When the pH was close to that of the distilled water (between pH 5 and 6), the precipitate was filtered and dried at 50 °C overnight. The dried precipitate was ground in a porcelain mortar and was stored in a tightly closed brown glass bottle. In the above recipe HI was applied instead of other possible inorganic iodides because it is a volatile compound; thus, any HI traces adsorbed on the precipitate can evaporate in the course of drying. We remark that a higher excess of HI should be avoided because HI dissolves the precipitate in a complex form.28 ii. Fabricating a Silver Iodide Coated Silver Wire. The sensor of the novel iodide selective electrode is a AgI coated silver wire. As shown in Figure 1a, the coating is produced by dipping the wire into molten AgI. Because the melting point of AgI is relatively low (it is only 558 °C), that temperature can be reached even by a commercial 60 W (unregulated maximum) electric soldering iron. The electric power was controlled by a variable toroidal transformer around 40 W to avoid too high temperatures. The soldering iron was transformed to an electric furnace by removing its copper tip from the cavity and the tip was replaced with a piece of hollow stainless steel holder (Figure 1a). The latter served as a heat conductor (to distribute the heat evenly) and also as the holder of a small glass test tube.

Figure 1. Preparation and structure of the new iodide selective electrode. Cross-sectional views. (a) Dip coating of a 0.5 mm diameter silver wire with molten AgI. (b) Mounting of the AgI coated silver wire into the electrode body.

The upper part of the test tube was shaped to a funnel that helped to fill the test tube with ground AgI. It was enough to fill only a part of the test tube with AgI because molten AgI wets the silver wire very well and with the help of the surface tension a much larger part of the wire can be coated. Too thick coatings should be avoided because they might increase the impedance and the response time of the electrode. To obtain a relatively thin coating, the Ag wire should be kept about 20−30 s in the furnace. (Right after placing the cold Ag wire into the melt, a thick AgI layer froze on the surface, which later melted away, however.) Based on weight measurements of the Ag wire before and after its dip coating with AgI, the average thickness of the AgI coating produced this way was below 5 μm. iii. Stuffing Box for a Stringent Isolation of the Active Electrode Surface from the Inactive Ones. The purpose of the stuffing box shown in Figure 1b is to shield the inactive surfaces of the electrode with PTFE (Teflon) packing material as tightly as possible to keep out any electrolyte solution. This is important because it is a common electrode problem that, after a while, a crack is formed between the sensor and the electrode body and some electrolyte can penetrate into this crack. This 6632



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Voltmeter. The EMF of the galvanic cell was measured with a Keithley model 2000 multimeter connected to a computer which collected EMF values in every 0.4 s. Calibration of the Electrode for Ag+and I−. H2SO4 (50 mL, 25 mM) was filled into the reactor where the reference and the indicator electrodes were already present. Then a 1 mM AgNO3 or KI solution was added in increasing quantities, establishing first a concentration of 2 μM and increasing the concentration by a factor of 2 in each step. Titration of Iodine Free HOI with KI. Calibration of the Electrode for Hypoiodous Acid. Figure 2 shows that the

way a part of the originally inactive sensor surface becomes active, and after that the electrode has a mixed potential determined partly by the free electrolyte solution and partly by the electrolyte solution trapped in the crack. As the composition of the electrolyte in the crack may be very much different from that of the free electrolyte solution, the signal of such an electrode may be seriously flawed. To avoid crack formation and keep away any electrolyte from the inactive sensor surfaces, the hydrophobic and viscoelastic PTFE is an ideal packing material. Two millimeter wide strips were cut from a commercial 0.1 mm thick Teflon tape. The narrow strip was twisted, forming a thin spun cord that was wound around the Ag wire to fill the stuffing box in the form of a coil. Then under the pressure of the PVC compression screw, a tight hydrophobic seal is formed. Figure 1b shows the stuffing box made of poly(vinylidene chloride) (PVDF). PVDF is chemically inert like PTFE, but, unlike PTFE, it is not viscoelastic and thus keeps its form for a long time even under a strong mechanical stress. iv. Other Components of the Electrode Body. The function of all other components of the electrode body can be understood from Figure 1b. The glass shield is needed to prevent any damage or deformation of the soft silver wire while the electrode is in use. v. Aging of the Electrode. The surface of our electrode darkens when it is in use, and after 2−3 weeks it may become completely black. The darkening is mostly due to metallic silver produced by the light in the lab (AgI is a light sensitive material), but the formation of trace amounts of Ag2S cannot be excluded either (due to hydrogen sulfide traces in the atmosphere). According to our observations, however, the darkening of the sensor surface does not affect the electrode function in any measurable degree. Ag/AgCl Reference Electrode. The reference electrode was a silver−silver chloride electrode (prepared in a similar way to the silver−silver iodide electrode but applying a AgCl melt in this case) immersed in an electrolyte containing 0.1 M KCl and 25 mM H2SO4. The electrolyte was connected to the reactor of the BR experiments with two consecutive glass tube salt bridges both containing 25 mM H2SO4. Porous ceramic cylinders (1 mm diameter Al2O3 pellets melted into glass tubes of the salt bridges at their ends) provide the advection-free ionic conductance between the electrode, the salt bridges, and the reactor. (The pores of the pellets also contain 25 mM H2SO4.) This chain of salt bridges and the relatively low KCl concentration (instead of the more usual 1 M or saturated solution) was applied to avoid any measurable contamination of the reactor with chloride ions. The same 25 mM H2SO4 concentration was set in all compartments of the electrode and also in the reactor to keep the liquid junction potentials at a minimum, which also helped to eliminate most of the drift of the measured EMF values. The salt bridge adjoining the reactor could be easily removed to wash it with 25 mM H2SO4 thoroughly. That could be necessary in the case of sensitive measurements when contaminations in the salt bridge originating from a previous experiment with different concentrations might disturb. Reactor. The reactor was a double walled glass beaker of 80 mL thermostated to 25 °C. Besides the BR reaction, titrations and calibration measurements were also performed here at 25 °C.

Figure 2. Titration of 50 mL of iodine free hypoiodous acid dissolved in 25 mM H2SO4 with 2.5 mM KI in the presence of the novel iodide selective indicator electrode. The reference was a Ag/AgCl electrode filled with 0.1 M KCl and 25 mM H2SO4. Flow rate of the titrant: 44.2 μL/min.

iodide selective electrode can be applied as an indicator electrode when a dilute HOI solution is titrated with a KI solution. During the titration a constant flow rate of the titrant was maintained by a peristaltic pump (Ismatec ISM 832A). In the peristaltic pump a relatively thin tubing (inner diameter: 0.19 mm) was used, which ended in the reactor. The reactor contained the indicator and the triple junction reference electrode, and 50 mL of iodine free dilute hypoiodous acid solution (prepared with the method described here), which was stirred magnetically (600 rpm). In the acidic medium HOI reacts rapidly with iodide ion to form iodine HOI + I− + H+ → I 2 + H 2O

thus, the iodide inflow consumes the HOI in the vessel and the measured EMF falls accordingly. The equivalence point (tINF = 578 s) was determined as the inflection point of the measured potential vs time diagram. The actual titration time tTIT = tINF − t0 was only 458 s as the titration started at t0 = 120 s. (That 2 min waiting period before the titration was applied in all titrations to enhance the reproducibility of the measured potentials.) The initial HOI concentration [HOI]0 = 16.9 μM of the 50 mL HOI solution in the reactor was calculated from the concentration (2.5 mM) and the volume of the titrant pumped into the reactor until the inflection point (338 μL). Utilizing that the HOI consumption [HOI]0 − [HOI]t is proportional with the time elapsed since the start of the titration t − t0 (HOI consumption increases linearly because a constant iodide inflow is maintained; moreover, it can be assumed that in the inflection point [HOI]tINF ≈ 0), the hypoiodous acid concentration for any time t between t0 and tINF can be calculated with the following formula: 6633


The Journal of Physical Chemistry A [HOI]t = [HOI]0

Article

t INF − t t INF − t0

The equation for the theoretical line as it is shown in Appendix A when X = Ag+ and its concentration is measured in μM is

Thus, calibration points for HOI concentrations less than [HOI]0 can be obtained from a titration curve by calculating [HOI]t for a certain time “t” (t0 < t < tINF) and reading EMF(t) from the titration curve. Calibration of the Electrode for HOI in the Presence of Iodine. Two different methods were applied, method M1 and method M2. (i) In the case of M1 an approximately constant iodine concentration was maintained and the HOI concentration was changed by titration. To this end first a 15− 45 μM HOI solution was prepared in 25 mM H2SO4. Next 0.1−0.4 mL iodine stock solution in DMSO was added to establish the desired iodine concentration. Finally, the HOI content of the mixture was titrated with 2.5 mM KI solution. The EMF vs [HOI] calibration points were calculated from the titration curve like in the case of an iodine free HOI solution (see the previous paragraph). (ii) In the case of method M2 an approximately constant hypoiodous acid concentration was maintained and the iodine concentration was increased step by step. To this end two different HOI solutions were prepared: both containing the same HOI concentration (13.5 μM) but one was iodine free whereas in the other the iodine concentration was 500 μM. Calibration points were obtained by measuring equilibrium EMF values after adding aliquots of iodine containing HOI solution to the iodine free one.

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EMF = 162.9 mV + 59.2 mV × log([Ag +]/μM)

(1)

while the equation for the experimental line is EMF = 154.4 mV + 57.3 mV × log([Ag +]/μM)

(2)

(When calibrating the electrode with silver ions, there is no surface reaction and the electrolyte is homogeneous. Consequently, the surface and the bulk silver ion concentrations are equal: [Ag+]S = [Ag+]B = [Ag+].) As we can see, the 57.3 ± 0.5 mV/decade value for the measured slope is somewhat smaller than the theoretical 59.2 mV/decade. Moreover, the 154.4 ± 0.5 mV EMF value measured in a 1 μM Ag+ ion solution is also less than the theoretical 162.9 mV. Such small deviations between the theoretical and the experimental calibration curves occur, however, in the case of other AgI based iodide selective electrodes25,29 as well; thus, they are acceptable. Calibration of the Electrode for I−. The equation for the theoretical line (see Appendix A) when X = I− and its concentration is measured again in micromolar is EMF = − 78.5 mV − 59.2 mV × log([I−]/μM)

(3)

and the equation of the experimental line is EMF = − 79.7 mV − 56.1 mV × log([I−]/μM)

(4)

−

Here, at 1 μM I ion concentration, the theoretical and the experimental EMF values are much closer, but the experimental slope (56.1 ± 0.5 mV/decade) is even smaller than in the case of the silver ion. The relatively small deviation between the experimental and the theoretical calibration lines both in the case of Ag+ and I− ions not only proves the reliability of the new iodide selective electrode but also justifies the use of the atypical Ag/AgCl reference electrode that contains sulfuric acid beside the usual KCl. Determination of the Solubility Product of AgI and the Solubility Limit Potential from the Crossing Point of the Silver and Iodide Calibration Lines. As Figure 3 shows, both the experimental and the theoretical Ag+ and I− calibration lines cross each other in the extrapolated region. The coordinates of that crossing point give the logarithm of the square root of the solubility product of AgI and the solubility limit potential. The coordinates of the theoretical crossing point are log([X]/M) = −8.039 (KS = 8.36 × 10−17 M2), solubility limit potential = 42.2 mV. (We remark that the 8.36 × 10−17 M2 value calculated from the electrode potentials given the literature30 slightly differs from the solubility product reported in the same handbook:30 8.52 × 10−17 M2.) The coordinates of the experimental crossing point are log(([X]/M) = −8.06 (KS = 7.45 × 10−17 M2), solubility limit potential = 36.1 mV. As can be seen, the theoretical and the experimental values are rather close again. The measured solubility product is somewhat smaller than the theoretical one, however. The small deviation might be due to experimental errors or it is also possible that the solubility of AgI in the 25 mM sulfuric acid medium is slightly less than in pure water. Calibration curves are straight lines in all concentration regions if the x coordinate is the logarithm of the surface silver

RESULTS AND DISCUSSION

Calibration of the Electrode for Ag+. As a first step the new iodide selective electrode was calibrated for silver and iodide ions and the experimental response was compared with the theoretical one. According to the theory (see Appendix A) the calibration curves (EMF vs the logarithmic concentration diagrams) should be straight lines. These are depicted in Figure 3.

Figure 3. Calibration curves (EMF vs log(conc) lines) of the iodide selective electrode for Ag+, HOI, and I−. “max” and “min” are the maximum and the minimum values of the potential oscillations in the BR reaction shown in Figure 6b. Continuous lines indicated by X = Ag+ and X = I− are fitted to the experimental data, and dashed lines show the theoretical electromotive force of our galvanic cell at various Ag+ and I− concentrations. 6634



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because if we substitute expression 6 for [Ag+]S into eq 2 we obtain

or iodide concentration. The deviation between the surface and the bulk ion concentrations is negligible, however, if the bulk concentration is above 10−7 M. This is the basis of the extrapolations in Figure 3. Comparison of the Performance of the New Iodide Selective Electrode with That of a Commercial one. Kontoyannakos et al. calibrated an Orion iodide/silver ion selective electrode for silver and iodide ions.25 The sensor of that electrode is a silver iodide−silver sulfide pressed disk. The KS value measured with that electrode was 4 × 10−16 M2 (based on the crossing point of the extrapolated iodide and silver ion calibration lines) or (0.97−1.14) × 10−15 M2 (based on calibration points measured in the concentration range 10−8 to 10−6 M). Both values are much larger than either of ours (7.45 × 10−17 M2) or the accepted literature value30 (8.36 × 10−17 M2). Obviously, the membrane potential of a AgI−Ag2S pressed disk is different from that of a pure AgI membrane. Another problem of the commercial electrode is that its calibration curves for silver and iodide ions do not approach each other at low concentrations, but they keep a roughly 70 mV constant distance below 10−8 M iodide or silver ion concentrations.25 That distance is even higher if the points of the calibration curves are produced with a serial dilution. This observation suggests a memory effect: during the electrode calibration for silver ions or iodide ions, a part of these ions can stay adsorbed on the surface or in some microcracks of the electrode. These microcracks might appear either in the pressed sensor disk itself or between the disk and the plastic electrode body due to the different heat expansion coefficients of the various components. The new electrode exhibited no significant memory effect moreover its calibration curves were much closer to the theoretical ones than that of the commercial electrodes (see the next two paragraphs). Calibration of the Electrode for HOI. Points of the EMF vs log[HOI]B calibration diagram were calculated from titration curves like the one shown in Figure 2. (The method of calculation is given in the Experimental Section.) It was found that the experimental points are located along a straight line (Figure 3) with the following equation determined by the method of least-squares: EMF = 117.1 mV + 57.4mV × log([HOI]B /μM)

EMF = 154.4 mV + 57.3 mV × log([HOI]B /μM) − 57.3 mV × log(a)

Thus, the observed shift of 37.3 mV is equal to 57.3 mV × log(a). Consequently, the experimentally determined value of parameter a is 4.5. pH and Stirring Rate Dependence of Parameter a. According to formula 6 a is determined by six other parameters: two diffusion coefficients (DAg and DHOI), two unknown characteristic lengths (δD and δR), and k+ and [H+]. Two of these parameters can be controlled selectively in an experiment: one is the pH of the medium and the other is δD. The latter can be controlled by the rate of stirring. To check the pH dependence qualitatively, we calibrated the iodide selective electrode also in 250 mM H2SO4 for Ag+ and for HOI. At this 10 times higher hydrogen ion concentration (in this experiment the sulfuric acid concentration was increased in the salt bridges and in the reference electrode as well) the shift between these two parallel calibration lines was down by 20 mV to only 17 mV. From these “shift” values (37.4 and 17 mV at [H2SO4] = 25 and 250 mM, respectively) the following pH dependence of “a” can be calculated: a=

[HOI]B a

where a =

DAg DHOI

+

DAg DHOI

+

DAg δ D·δ R ·k+·[H+]

= 1.6 +

91 mM [H+]

(8)

+

(The actual hydrogen ion concentrations, [H ] = 31.8 mM and 261 mM, respectively, were calculated applying a formula31 that includes also the dissociation equilibrium HSO4− ↔ H+ + SO42−.) The ratio 1.6 (meaning that the diffusion of silver ions is about 60% faster than that of the hypoiodous acid) is acceptable as the size of the two particles are comparable, but the silver ion should be the smaller. Formula 6 predicts a higher [Ag+]S for lower stirring rates because δD increases when the stirring is slower. Although the tendency of the experimentally observed stirring effect agreed with the theory, its magnitude was small: about 5 mV when the rate of stirring was decreased from 1200 to 50 rpm, which is compatible with a mere 22% increase in δD. That result indicates that the diffusion boundary layer is somehow bound (or adsorbed) to the surface; thus, it is not too sensitive to stirring. Calibration of the Electrode for HOI in the Presence of Iodine. Points of the EMF vs log[HOI]B calibration diagram in the presence of iodine were measured with method M1 (see the Experimental Section). The result is shown in Figure 4. As can be seen in Figure 4, iodine has an effect on the electrode potential: all calibration lines are parallel with the calibration line measured in the absence of iodine but they are shifted down with the increasing iodine concentrations. A theoretical explanation of these parallel lines is based again on formula B13 of Appendix B according to which

(5)

As can be seen, this line has a slope of 57.4 ± 0.5 mV/decade, which agrees (within the experimental error) with the slope of the silver ion calibration line (57.3 mV/decade, see eq 2). The shift between the two parallel lines is 154.4 − 117.1 = 37.3 mV. Steady State Corrosion Potential Theory (CPT) Explains Why HOI and Ag+ Give Parallel Calibration Lines. When [HOI]B, the hypoiodous acid concentration in the bulk, drives the electrode potential above its SLP value, the electrode, in fact, measures [Ag+]S, the silver ion concentration at the surface of the electrode. Those silver ions are generated by the corrosion reaction CR. According to the CPT (see Appendix B, eq B13 in the case of [I2] = 0) in a steady state the following linear relationship holds between [Ag+]S and [HOI]B, [Ag +]S =

(7)

DAg

[HOI]B a + b·[I 2]B DAg DAg k− where a = + + , b = DHOI k+·[H+] δ D·δ R ·k+·[H ]

δ D·δ R ·k+·[H+]

[Ag +]S =

(6) +

According to eq 6 [Ag ]S is proportional with [HOI]B; thus, regarding eq 2 the electrode potential vs log(conc) lines for silver ions and hypoiodous acid should be parallel. This is

(9) 6635



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Figure 4. Effect of iodine on the HOI calibration curve (EMF vs log(conc) lines) of the iodide selective electrode. Observe the deviation of the theoretical and empirical lines at high (500 μM) iodine concentration. For lower iodine concentrations theoretical and empirical lines coincide within the experimental error. Ag+ calibration line is shown for comparison.

At a fixed iodine concentration, the denominator of eq 9 (a + b·[I2]) is constant; thus, according to the theory, the calibration line for HOI in the presence of iodine should be still parallel with the silver line but the higher the iodine concentration, the larger its shiftdown. This prediction of the theory is in a complete agreement with the experiments, and b values calculated for iodine concentrations between 0 and 200 μM also agree. On the other hand, when the iodine concentration is 500 μM the shift and consequently the b value are much higher. Most probably this is due to the adsorption of iodine onto silver iodide,32 which changes the conditions in the reaction layer. Determination of Coefficient b. Determination of the coefficient b was carried out by applying the calibration method M2 (see the Experimental Section). As Figure 5a shows, at constant hypoiodous acid concentration, the electrode potential decreased by the increasing iodine concentration. As in these experiments the electrode potential is determined by the silver ion concentration at the surface of the electrode [Ag+]S, that concentration can be calculated from the EMF regarding eq 2 that is from the calibration line for silver ions. As [HOI]B and [I2]B are known, the ratio [HOI]B/[Ag+]S can be depicted as a function of [I2]B to give a straight line with the slope equal to b and the intercept to a (see eq 9). The experimental value according to Figure 5b is b = 0.13 μM−1. Theoretical Estimate for Coefficient b. The corrosion reaction CR in the reaction zone can reach an equilibrium when the rate of the reaction r is zero. Regarding eq B1 in Appendix B r = 0 means that [H+]R ·[HOI]R k− = k+ [Ag +]R · [I 2]R

Figure 5. Effect of the increasing iodine concentration on the electrode potential at a fixed hypoiodous acid concentration. (a) Experiment: electrode potential drops caused by the addition of iodine to a hypoiodous acid solution. The HOI concentration is constant [HOI] = 13.5 μM in this experiment. The scale at the left shows the EMF value. The ordinate on the right is not scaled; the numbers there indicate only the actual iodine concentration in the solution after injecting the next iodine portion (injection times are marked with arrows). (b) Concentration ratio [HOI]B/[Ag+]S calculated from the measured electrode potential as a function of [I2]B.

[HOI]R ·[I−]R ·[H+] = KH [I 2]R

where KH is the equilibrium constant of the iodine hydrolysis reaction33,34,9 I 2 + H 2O ↔ HOI + I− + H+

Regarding eqs 10−12 [H+]R ·[HOI]R [H+]R ·[HOI]R ·[I−]R K k− = = = H k+ [Ag +]R ·[I2]R KS·[I 2]R KS (13)

consequently

(10)

k− k+·[H+] KH = KS·[H+]

b=

Indices R refer to the reaction zone. As an approximation we can assume that the reaction zone is an aqueous medium with the same equilibrium constants and hydrogen ion concentration as in the bulk. Thus, in equilibrium we can write [Ag +]R · [I−]R = KS

(12)

= (11)

5.4 × 10−13 M2 8.36 × 10−17 M2·26 × 103 μ M

= 0.25 μ M−1

and also in equilibrium 6636

(14)



Article

which is not too far from the experimental value of 0.13 μM−1. Potentiometric Oscillations of the New Electrode Recorded in a BR Reaction. Estimation of the Maximum HOI Concentrations. Figure 6a shows all the potential

(i) One is iodine, which diminishes the measured HOI signal as Figure 4 shows. This is because the same [HOI] in the bulk generates a smaller silver ion concentration at the surface of the electrode in the presence of iodine (see eq 9). Consequently, the 4 μM HOI concentration calculated assuming [I2] = 0 should be corrected according to the following formula: ⎛ ⎞ b [HOI]B (corr) = ⎜1 + · [I2]B ⎟[HOI]B (calc) ⎝ ⎠ (15) a where [HOI]B(calc) is the HOI concentration calculated from the HOI calibration line disregarding the interference due to iodine. Calculating with the experimentally measured a and b values (a = 4.5; b = 0.13 μM−1) and with [I2]B = 10 μM the corrected HOI concentration maximum is 5 μM. In the present BR reaction the spectrophotometrically measured iodine concentration was oscillating between 10 μM minimum and 50 μM maximum (Table 2). Unfortunately, spectrophotometric measurements for iodine and potentiometric measurements for HOI were made in separate laboratories and not simultaneously. According to the simulations (Figure 7), however, when the HOI concentration is at its maximum, the iodine concentration is close to its minimum. (ii) The other possible interfering component could be iodous acid (HOIO). However, the corrosion rate due to that component is considerably slower26 than that caused by HOI. Moreover, the maximum HOIO concentrations in our simulations were about 2 orders of magnitude smaller than the maximum HOI concentrations. Consequently, it is a realistic assumption to neglect any contribution by HOIO to the measured electrode potential above SLP.

Figure 6. Potential oscillations of the iodide selective electrode in a BR reaction. Initial conditions (after adding all components): [H2SO4] = 25 mM, [KIO3] = 40 mM, [H2O2] = 0.66 M, [MA] = 50 mM, [Mn2+] = 6.5 mM. (a) Addition of the components (indicated by arrows) and the subsequent oscillatory regime. At time zero the mixture contained sulfuric acid and iodate only. (b) First four potential oscillations.

Simulations. In the Bray−Liebhafsky reaction, reduction and oxidation processes alternate, giving rise to oscillations in [I2] and [IO3−]. In the BR reaction, alternating reduction and iodination processes were believed to dominate, with oxidation

oscillations of the new iodide selective electrode in the oscillatory regime of a BR reaction whereas in Figure 6b only the first four oscillations are displayed on an expanded time scale. Two of the first four oscillations are inserted into Figure 3 where both I− and HOI calibration lines are also shown together with the solubility limit potential (SLP). As can be seen, the potential oscillations cross the SLP value: its minima are below and the maxima are above that. Regarding the iodide calibration line and the recorded minimum EMF values, a maximum iodide concentration of 10−4.8 M = 16 μM can be calculated. That result can be trusted because in a BR system below the SLP there are no other potential determining components, only the iodide ion. Moreover, the potential response of ion selective electrodes to concentration changes is rather fast:35 the response time is below 0.1 s. Consequently, the calculated 16 μM iodide ion concentration maximum should be correct within an estimated experimental error of ±2 μM. Using the HOI calibration line in Figure 3 and the recorded maximum EMF values, a maximum HOI concentration of 10−5.4 M = 4 μM can be estimated. Above the SLP, however, two possible interfering components should be taken into account.

processes thought to be negligible. The simulation36 in Figure 7 adds oxidation of iodine species to previous overall processes of reduction and iodination.

Figure 7. Iodine, iodide, and hypoiodous acid oscillations in the BR reaction simulated with the same parameters as experiments depicted in Figure 6. 6637



Article

Table 1. Reactions and Rate Constants (M s−1, Activity of H2O = 1) at 25 °C Used for Simulation name*

equation*

I1 I2 I2A

a

9

I− + HIO2 → I 2O + OH−

5 × 109[I−][HIO2]

37

I 2O + H 2O ↔ 2HOI

0.10[I2O] − [HOI]2

37

−

2H + I +

I3A

a

reference

3.67 × 109[HOI][I−] − 0.00198[I2]/[H+]

+

I3

rate law

H+ + I− + HOI ↔ I 2 + H 2O

IO3−

+ 2

1200[H ] [I

→ I 2O2 + H 2O

I 2O2 + H 2O ↔ HIO2 + HOI

−

][IO3−]

38

20[I2O2] − [HIO2][HOI]

38

1 × 1010[IO2•]

4

I4a

2IO2 + H 2O → H +

Ma

HIO2 + H 2O2 + Mn → HOI + Mn III + HOO• + OH−

2 × 105[HIO2][H2O2][MnII]

9

MA

H 2O2 + Mn III → Mn II + HOO• + H+

3.2 × 10 [H2O2][Mn ]

39

D1

HOI + H 2O2 → H+ + I− + O2 + H 2O

5[HOI][H2O2]

H+ + IO3− + HOO• → IO2• + O2 + H 2O

3.5 × 10 [H ][IO3 ][HOO ]

D2

a

D3

a

U1

•

+

IO3−

+ HIO2

II

•

a

C1

4

•

9

200[IO2 ][H2O2]

9

I 2O + H 2O2 → HIO2 + HOI

0.9[I2O][H2O2]

37

CH 2(COOH)2 ↔ enol

0.0039[CH2(COOH)2] − 91[enol]

4

9.1 × 10 [enol][I2]

4

5

−

2HOO → H 2O2 + O2 +

−

H + OH ↔ H 2O

•

7.5 × 10 [2HOO ]

41

1 × 1010[H+][OH−] − 1 × 10−4

from Kw = 1 × 1014

4

•

W

40 −

+

IO2 + H 2O2 → HIO2 + HOO

enol + I 2 → CHI(COOH)2 + H + I

O1

III

•

•

+

C2

4

*

Reactions involving iodine species are designated as I1, I2, etc. The M designations are for metal (manganese) reactions. The D (“down”) reactions are used for reduction of iodine species (reduction in oxidation number), and U (“up”), for reactions (increase in oxidation number). C reactions involve carbon species (malonic acid), O is used for oxygen species, and W is for water equilibrium. aRate constants for the steps labeled with superscript “a” have been adjusted to get oscillations that match in frequency and are fairly close in maximum [I2] for the specific mixture compared.

A comparison of experimental and simulation results is shown in Table 2. The simulations were performed with the

5H 2O2 + 2H+ + 2IO3− → I 2 + 5O2 + 6H 2O (reduction process in BR and BL oscillators)

Table 2. Comparison, Experiment vs Simulation +

H +

IO3−

+ 2I 2 + 5RH → 5RI + 3H 2O

(iodination process in BR oscillator) 5H 2O2 + I 2 → 2H+ + 2IO3− + 4H 2O (oxidation process in BL oscillator)

measurement

experiment

simulation

time period [I2]max 1st four oscillations [I2]min1st four oscillations [I−]max 1st four oscillations [HOI]max 1st four oscillations

10.5 s 50 μM 10 μM 16 μM 5 μMa

10.0 s 49 μM 4 μM 26 μM 8 μM

Assuming a 10 μM iodine concentration when HOI concentration is maximum.

a

H 2O2 + HOI → HIO2 + H 2O (partial oxidation process in BR simulation)

COPASI36 program package. When the time period and [I2]max are approximately matched in the simulation, [I2]min is too low and [I−]max and [HOI]max are both too high, but the simulated values are approximately within a factor of 2 of the experimental values. When the time period was matched using simulations without oxidation steps, [I2]max was an order of magnitude too low, and [I2]min was 2 orders of magnitude too low.

We have tried without success to utilize the iodine oxidation steps in the Schmitz12 mechanism in the BR scheme. (We suspect the reduction mechanism in the BR is causing the problem. It is different (involving radicals) from the nonradical mechanism in BL.) Instead, having no good alternative to the reduction mechanism, we have added formation and oxidation of oxyiodine species, similar to those used by Schmitz, to the FCA mechanism9 of iodate reduction as shown in Table 1. The oxidation steps involve nonradical oxyiodine species. The FCA scheme uses processes “M” and “MA” to generate radicals for the reduction process. Rate constants for the steps labeled with superscript “a” have not been independently measured and have been adjusted to get oscillations that match in frequency and are fairly close in maximum [I2] for the specific mixture compared. With so many adjustable parameters, we claim not that the reactions and constants in the table are a preferred set, but rather that inclusion of oxidation processes improves the match between theory and experiment.

■

APPENDIX A: THEORETICAL RESPONSE OF A AGI ELECTRODE FOR AG+ AND I− IONS AND THE EMF CALCULATED FOR THE GIVEN EXPERIMENTAL CONDITIONS

Theoretical Response of a AgI electrode for Ag+ Ions

The potential determining species of a AgI membrane based iodide selective electrode is either the iodide or the silver ion. Potentials above the solubility limit potential are always due to silver ions. In that case the electrode potential is determined by [Ag+]S, that is, by the silver ion concentration at the surface of 6638



Article

the solid AgI. Thus, the electrode potential εAgI at 25 °C can be written as

Equation A8 can be solved to express [Ag+]S as a function of [Ag+]B

εAgI = εAg = ε0Ag + 59.2 mV × log([Ag +]S /M) = 799.6 mV + 59.2 mV × log([Ag +]S /M)

[Ag +]S = (A1)

2

+

EMFSL = 518.1 mV + 59.2 mV × log( KS /M) (A10)

= 42.2 mV −

Electrode Response for I Ions and the Calculated EMF

In our experiments a Ag/AgCl reference electrode containing 0.1 M KCl (and 25 mM H2SO4) was applied. The theoretical electrode potential of the reference electrode in a 0.1 M Cl− ion solution is

Potentials below the solubility limit potential are always due to iodide ions. In that case the electrode potential is determined by [I−]S that is by the iodide ion concentration at the surface of AgI. Thus, the electrode potential at 25 °C can be written as

εREF = ε0Ag/AgCl − 59.2 mV × log([Cl−]/M)

εAgI = ε0Ag/AgI − 59.2 mV × log([I−]S /M)

= 222.3 mV + 59.2 mV

= −152.2 mV − 59.2 mV × log([I−]S /M)

(A2)

(A11)

where ε0Ag/Agl = −152.2 mV is the standard electrode potential of a Ag/AgI electrode42 in a 1 M I− ion solution. Thus, the theoretical electromotive force EMF of our galvanic cell in the case of excess iodide is

where ε0Ag/AgCl = 222.3 mV is the standard electrode potential of a Ag/AgCl electrode43 in a 1 M Cl− ion solution. Thus, the theoretical electromotive force EMF of our galvanic cell is EMF = εAgI − εREF

EMF = εAgI − εREF

= 518.1 mV + 59.2 mV × log([Ag +]S /M)

(A3)

= −433.7 mV − 59.2 mV × log([I−]S /M)

EMF at Very Low Silver Ion Concentrations

[A+]S ≈ [Ag +]B

A formula for [I−]S analogous to eq A9 can be derived and with considerations similar to the ones applied for the derivation of eq A10 the calculated EMFSL: EMFSL = − 433.7 mV − 59.2 mV × log( KS /M) = 42.2 mV

(A4)

We remark that in Figure 3 only the extrapolated parts of the silver and iodide lines cross each other. At silver or iodide concentrations below 10−7 M, the calibration curves are not straight lines any more and the curves do not cross each other if the x coordinate is the logarithm of the bulk silver or iodide concentration. This is because the electrode measures the surface ion concentration (the concentration at the electrode surface) and that is always larger than that of the bulk due to the ions dissolved from the AgI electrode (see eqs A9 and A13).

(A5)

+

where [Ag ]D is the silver ion concentration coming from the dissolution of AgI. If there are no iodide ions in the bulk, we can assume that the amount of the iodide ions produced in the dissolution of the electrode is equal to the amount of the silver ions produced in the same process [I−]S = [Ag +]D

■

(A6)

The solubility equilibrium at the surface is +

[I ]S [Ag ]S = KS

APPENDIX B: STEADY STATE CORROSION POTENTIALS DUE TO HOI. A REACTION-DIFFUSION MODEL EXPLAINING THE RESPONSE OF THE ELECTRODE

Solid Phase−Reaction Zone−Diffusion Layer−Bulk Phase

The polycrystalline solid phase is not in direct contact with the bulk of the liquid phase: they are separated by a very thin reaction zone of thickness δR at the solid−liquid interface and by a diffusion boundary layer of thickness δD (Figure 8). The structure of these layers is not known. It seems that even a part of the liquid diffusion layer is bound to the solid crystalline

(A7)

From eqs A5−A7 we obtain eq A8 KS [Ag +]S

(A13)

Linearity of the Calibration Lines

is valid. Here [Ag+]B is the silver ion concentration in the bulk. When the bulk concentration is very small, however, the silver ion concentration at the surface of the electrode can be considerably higher than in the bulk, due to the dissolution of the solid AgI. Thus, instead of eq A4, we have to consider eq A5: [Ag +]S = [Ag +]B + [Ag +]D

(A12)

EMF at Very Low Iodide Ion Concentrations

As was mentioned, [Ag+]S is the silver ion concentration at the surface of the electrode, that is, at the surface of the solid AgI. When the silver ion concentration in the calibrating solution is above 10−7 M, there is no significant difference between the surface and the bulk silver ion concentrations; thus, the approximation

[Ag +]S = [Ag +]B +

(A9)

As can be seen from eq A9, when [Ag ]B ≫ 4KS, [Ag ]S ≈ [Ag+]B and, when [Ag+]B2 ≪ 4KS, [Ag+]S ≈ KS1/2. Thus, at higher silver ion concentrations the EMF vs [Ag+]B calibration curves are straight lines but at low [Ag+]B values the EMF approaches asymptotically to EMFSL, to the theoretical solubility limit potential

EMF Calculated for the Given Experimental Conditions

−

2

[Ag +]B + 4KS ) +

Here ε0Ag = 799.6 mV is the standard electrode potential42 of a silver electrode (its potential in a 1 M silver ion solution vs the standard hydrogen electrode at 25 °C) and [Ag+]S is the numerical value of the actual silver ion concentration calculated as mol/L at the surface. εAgI = εAg holds whenever the potential determining species are silver ions exclusively. In such an electrolyte, there is no potential difference between a silver and a silver/silver halogenide electrode.

= 281.5 mV

1 ([Ag +]B + 2

(A8) 6639



Article

Rate Equation for the Corrosion Reaction (Chemical Transport)

Regarding the corrosion reaction CR, it can be assumed that the rate of the forward reaction is proportional to [H+]R and [HOI] R , the hydrogen ion and the hypoiodous acid concentration in the reaction zone, whereas the backward rate is proportional to the product of the silver ion and iodine concentrations there. Thus, the net rate “r” is r = k+′ ·[H+]R [HOI]R − k −′ ·[Ag +]R ·[I 2]R

(B1)

Here k′+ and k′− are rate constants valid in the reaction zone. If eq B1 is multiplied by δR and we assume that the concentration of a component in the reaction zone is equal to or at least proportional to its surface concentration, then we obtain eq B2 σ = r ·δ R = δ R k+[H+]S ·[HOI]S − δ R k −·[Ag +]S ·[I 2]S (B2)

where the rate constants k+ and k− also include any factors of proportionality. i. Steady State Diffusion Transport Equations. The transport equations describe the diffusion transport of the various components (ions and molecules) participating in the corrosion process. For simplicity the following steady state, one-dimensional, and linear transport equations will be regarded:

Figure 8. Schematic view of the electrode−electrolyte interface with the assumed linear concentration profiles. [Ag+]S, [HOI]S, and [I2]S indicate the concentrations of silver ions, hypoiodous acid, and iodine at the surface of the electrode, and [Ag+]B, [HOI]B, and [I2]B are their concentrations in the bulk.

jAg = −DAg ·grad[Ag +]

phase like an adsorbed layer because stirring the liquid does not disturb it significantly. As a simplification, our model will assume that diffusion transport of ions and molecules takes place exclusively in the boundary layer and reactions are limited to the thin reaction zone.

([Ag +]S − [Ag +]B ) δD

= DAg ·

[Ag +]S δD

(B3)

because we assume that there are no silver ions in the bulk, that is, [Ag+]B ≈ 0.

Corrosion Reaction

When HOI is present in the aqueous phase, it diffuses through the boundary layer to the reaction layer, where it reacts with the solid AgI according to the following stoichiometry: AgI + HOI + H+ ↔ Ag + + I 2 + H 2O

≈ DAg ·

jHOI = −DHOI ·grad[HOI] ≈ −DHOI ·

(CR)

([HOI]B − [HOI]S ) δD

(B4)

jHOI is negative as the conventional positive direction points from the surface to the bulk (Figure 8).

The silver ions generated continuously by the above corrosion process diffuse away into the bulk and establish a steady state silver ion concentration on the surface (and a steady state concentration profile within the boundary layer). The electrode potential is determined by the steady state silver ion concentration [Ag+]S, which builds up at the surface of the solid AgI. The aim of the steady state theory is to give [Ag+]S as a function of [HOI]B and [I2]B the HOI and the I2 concentration in the bulk, respectively. To this end reaction rate and transport equations will be regarded.

jI = −DI2 ·grad[I 2] ≈ DI2 · 2

([I 2]S − [I 2]B ) δD

(B5)

ii. Steady State Balance Equations. In a steady state σ = jAg = −jHOI = jI (B6) 2 From eqs B3 and B6 the rate r of the surface reaction σ = DAg ·

Surface Reaction: A Thin Reaction Zone on the Surface

For simplicity it is often assumed that the corrosion reaction is a “quasi two-dimensional” one taking place on the surface of the solid AgI with a rate “σ” per unit surface. If we assume a very thin reaction zone instead, with a thickness of δR (δR ≪ δD) and with a more usual “three dimensional” reaction rate “r” per unit volume, then σ = r·δR. Actually, the thin reaction zone should be a separate condensed phase, however, which is different from both the liquid and the solid phases; thus, rate constants of certain reactions are not necessarily the same in the reaction zone and in the bulk.

[Ag +]S δD

(B7)

and from eqs B4 and B5 also the surface HOI and I2 concentrations can be expressed as a function of the surface silver ion concentration: [HOI]S = [HOI]B −

[I2]S = [I 2]B + 6640

DAg DI2

DAg DHOI

·[Ag +]S

·[Ag +]S

(B8)

(B9)



Article

Approximation for the Steady State Surface Silver Ion Concentration

(10) (a) Szabó, E.; Sevcik, P. J. Phys. Chem. A 2009, 113, 3127−3132. (b) Szabó, E.; Sevcik, P. J. Phys. Chem. A 2010, 114, 7898−7902. (11) Bray, W. C.; Liebhafsky, H. A. J. Am. Chem. Soc. 1931, 53, 38− 44. (12) Schmitz, G. Phys. Chem. Chem. Phys. 2011, 13, 7102−7111. (13) Szabó, G.; Csavdári, A.; Onel, L.; Bourceanu, G.; Noszticzius, Z.; Wittmann, M. J. Phys. Chem. A 2007, 111, 610−612. (14) Onel, L.; Bourceanu, G.; Wittmann, M.; Noszticzius, Z.; Szabó, G. J. Phys. Chem. A 2008, 112, 11649−11655. (15) Muntean, N.; Szabó, G.; Wittmann, M.; Lawson, T.; Noszticzius, Z.; Fülöp, J.; Onel, L. J. Phys. Chem. A 2009, 113, 9102−9108. (16) Lawson, T.; Fülöp, J.; Wittmann, M.; Noszticzius, Z.; Muntean, N.; Szabó, G.; Onel, L. J. Phys. Chem. A 2009, 113, 14095−14098. (17) Furrow, S. D; Aurentz, D. J. J. Phys. Chem. A 2010, 114, 2526− 2533. (18) Cervellati, R.; Greco, E.; Furrow, S. D. J. Phys. Chem. A 2010, 114, 12888−12892. (19) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J. Am. Chem. Soc. 1982, 104, 6194−6199. (20) Noszticzius, Z.; McCormick, W. D. J. Phys. Chem. 1987, 91, 4430−4431. (21) Foersterling, H. D.; Muranyi, Sz.; Noszticzius, Z. J. Phys. Chem. 1990, 2915−2921. (22) Masson, I.; Argument, C. J. Chem. Soc. 1938, 1702−1708. (23) Moorthy, J. N.; Senapati, K.; Kumar, S. J. Org. Chem. 2009, 74, 6287. (24) Bailey, O. L. Analysis with Ion-Selective Electrodes; Heyden: New York, 1976. (25) Kontoyannakos, J.; Moody, G. J.; Thomas, J. D. R. Anal. Chim. Acta 1976, 85, 47−53. (26) Noszticzius, Z.; Noszticzius, E.; Schelly, Z. A. J. Phys. Chem. 1983, 87, 510−524. (27) Noszticzius, Z.; Wittmann, M.; Stirling, P. 4th Symposium on IonSelective Electrodes; Akadémiai Kiadó: Budapest, 1984; pp 579−589. (28) King, E., L.; Krall, H., J.; Pandow, M.,L. J. Am. Chem. Soc. 1952, 74, 3492−3496. (29) (a) User Guide Iodide Selective Electrode. Thermo Scientific pp 12 and 32 http://www.fondriest.com/pdf/thermo_iodide_ise_ manual.pdf. (b) Technical Specifications for the Iodide Ion-Selective Electrode ELIT 8281 http://www.nico2000.net/ise_specs/iodide.pdf. (c) Operating Instructions &Technical Specifications directION Iodide Combination ISE http://www.edt.co.uk/files/ IodideInstructions.pdf. (30) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, Internet Version; CRC Press: Boca Raton, FL, 2005. (31) The following formula can be derived for the hydrogen ion concentration from the second ionization equilibrium and the component balance equations: [H+] = (c0 − K + (c0 − K)2 + 8Kc0)1/2/2, where K =12 mM from ref 30. (32) Germann, F. E. E.; Traxler, R. N. J. Am. Chem. Soc. 1922, 44, 460−464. (33) Allen, T. J.; Keefer, L. M. J. Am. Chem. Soc. 1955, 77, 2957− 2960. (34) (a) Lengyel, I.; Epstein, I.; Kustin, K. Inorg. Chem. 1993, 32, 5880−5882. (b) Lengyel, I.; Li, J.; Kustin, K.; Epstein, I. R. J. Am. Chem. Soc. 1996, 118, 3708−3719. (35) Lindner, E.; Tóth, K.; Pungor, E. Dynamic Characteristics of IonSelective Electrodes; CRC Press: Boca Raton, FL, 1988. (36) Hoops, S.; Sahle, S.; Gauges, R.; Lee, C.; Pahle, J.; Simus, N.; Singhal, M.; Xu, L.; Mendes, P.; Kummer, U. COPASI − a COmplex PAthway SImulator. Bioinformatics 2006, 22, 3067−3074. (37) Schmitz, G. Phys. Chem. Chem. Phys. 1999, 19, 4605−4608. (38) Bray, W. C. J. Am. Chem. Soc. 1930, 52, 3580−3586. (39) Davies, G.; Kirschenbaum, L. J.; Kustin, K. Inorg. Chem. 1968, 7, 146−154. (40) Furrow, S. D. J. Phys. Chem. 1987, 91, 2129−2135. (41) Behar, D.; Czapski, G.; Dorfman, L. M.; Schwarz, H. A. J. Phys. Chem. 1970, 74, 3209−3213.

Now eqs B7−B9 can be substituted into eq B2 which, after dividing with δR, [H+], and k+, gives the following second-order equation: A ·([Ag +]S )2 + B ·[Ag +]S − C = 0

(B10)

where A=

k −·DAg k+·[H+]·DI2

⎛ DAg ⎞ DAg k− B=⎜ + + + + · [I 2]B ⎟ δ D·δ R ·k+·[H ] k+·[H ] ⎝ DHOI ⎠ C = [HOI]B

(B11)

+

[Ag ]S is the positive root of the second-order equation (B10): [Ag +]S =

−B +

B2 + 4AC 2A

(B12)

That root can be approximated as [Ag +]S ≈

C = B

[HOI]B DAg DHOI

+

DAg δ D·δ R ·k+·[H+]

+

k− ·[I 2]B k+·[H+]

(B13)

The relative error γREL of the approximation B13 can be written as43 γREL

Measurement of Hypoiodous Acid Concentration ... - ACS Publications

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