The oxidation of sulfur(iv) by reaction with iron(iii): a critical review and data analysis.

The dependences on ionic strength of the hydrolysis constants of Fe3+ and of the first dissociation constant of sulfurous acid are briefly reviewed. The data are needed to derive from apparent stability constants reported in the literature the stability constants for the three iron-sulfito complexes defined by the equilibria (c1) FeOH2+ + HSO3- = FeSO3+ + H2O, (c2) FeSO3+ + HSO3- = Fe(SO3)2- + H+, (c3a) Fe(SO3)2- + HSO3- = Fe(SO3)3H2-, where Kc1 = 1982 ± 518 dm3 mol-1, Kc2 = 0.72 ± 0.08, Kc3a = 189 ± 9 dm3 mol-1 (ionic strength μ = 0.1 mol dm-3). The rapid formation of these complexes is followed by a slower decomposition leading to the formation of SO3- radicals; the associated rate coefficients are k1 = 0.19 s-1, k1a ≈ 0.04 s-1, and k1b ≈ 0.08 s-1, respectively. The subsequent reaction leads to dithionate and sulfate as products. Overall rates and product yields from a variety of studies of the slow reaction are found to be consistent with a mechanism, in which the production of dithionate occurs mainly by the reaction of SO3- with FeSO3+ and that of sulfate by the reaction of SO3- with FeOH2+ and/or Fe3+. The role of copper as a catalyst is also analyzed. Rate coefficients for individual reactions are estimated from the data at low pH (μ = 1.0 mol dm-3) under conditions where the 1 : 1-complex is prevalent. They are extrapolated to lower ionic strengths for an analysis of the data obtained at higher pH to explore conditions when reactions of the higher complexes become important. The overall rate and the product yields of the reaction depend critically on the pH, the initial ratio of S(iv) to Fe(iii) and the ionic strength of the solution.


Introduction
Iron belongs to a group of transition metals that are known to catalyze the oxidation of S(IV) in aqueous solution. 1 Such reactions are of interest especially in the atmospheric sciences because they are predicted to occur in the aqueous phase of clouds and fogs, where they would contribute to the removal of SO 2 from the atmosphere. [1][2][3] Thus, it is not surprising that the Fe(III)-catalyzed oxidation of S(IV) in aerated aqueous solutions has been studied in much detail. 1 A consistent chemical mechanism was developed, 4,5 which incorporates a chain reaction carried by sulfuroxy radicals, and rate coefficients are available for most of the individual reactions involved. [6][7][8] But Fe(III) is known to oxidize S(IV) also in the absence of oxygen. Far fewer studies have dealt with this process, [9][10][11][12][13][14][15][16] and no consensus has been reached regarding the relevant mechanism. This reaction in de-aerated solutions is the subject of the present critical analysis.
There is agreement that the reaction is initiated by the formation of one or more iron-sulfito complexes. The presence of such complexes is indicated by the appearance, and the subsequent fading, of a reddish brown color when a solution containing Fe(III) is mixed with another solution containing S(IV). Stopped flow spectrophotometry has been used to follow the formation and decay of the complexes. [14][15][16][17] Measurements at short reaction times suggest the existence of three complexes resulting from the successive addition to Fe(III) of S(IV) as ligand. 17,19,20 Absorbance changes due to the variation of S(IV) concentrations have been exploited to derive apparent stability constants for the complexes under various experimental conditions. 14,[17][18][19] Unfortunately, the results have never been subjected to a detailed analysis, so that the true stability constants are still not available. The slower subsequent reaction, which leads to Fe(II), S(V) and S(VI) as products, has been studied by product analysis under conditions when the reaction is sufficiently slow. [9][10][11][12][13][14] In reviewing these publications I have found that the modification of a simple reaction mechanism first proposed by Higginson and Marshall 9 can explain most if not all of the experimental results.
Fundamental to an analysis of all experimental data is a knowledge of the speciation of Fe(III) and S(IV) resulting from the hydrolysis of Fe 3+ and SO 2aq , respectively, and their dependence on pH and ionic strength. This makes it necessary to review briefly the hydrolysis constants of iron, and the first dissociation constant of sulfurous acid. Whereas the ionic strength dependences of the iron hydrolysis constants are quite well known, that of the dissociation constant of sulfurous acid appears to have not been well defined in the literature so that it The H 2 O molecule causing the hydrolysis is taken from the hydration sphere of Fe 3+ . In the following, the hydration sphere will be neglected, however. Fig. 1 shows K h1 as a function of ionic strength at 25 1C. Points are values obtained from spectrophotometric measurements -conducted mainly at 340 nm wavelength -and the solid line represents the best fit to the extended Debye-Hückel equation log K h1 = log 0 K h1 À 2.04m 1 2 /(1 + 2.4m 1 2 ) À 0.01m, (1) where log 0 K h1 = À2.174 is obtained by extrapolation. The numerical parameters in this equation were originally suggested by Milburn and Vosburgh, 21 whose measurements covered ionic strengths up to m = 3.0. While spectrophotometry has been the favored measurement technique, potentiometric titration has also been applied, based on measuring simultaneously the hydrogen ion concentration and the Fe 3+ /Fe 2+ redox potential. By means of computer-assisted analyses of the titration curves, Byrne et al. 30 and Stefanson 28 have obtained results in perfect agreement with those of Milburn and Vosburgh. 21 Whereas the dependence on ionic strength of the first hydrolysis constant is well documented, measurements of the second hydrolysis constant are still sparse. The equilibrium may be written in two ways: Both equilibrium constants are related in that K h2a = K h2 /K h1 . The first expression is prevalent in the literature, however. Early attempts to determine the equilibrium constant by means of potentiometric titration 25,31,32 gave results that scattered over a wide range. Then Byrne et al. 30 critically reviewed the data and concluded that potentiometric titration is not sufficiently sensitive and unsuitable for the determination of K h2 . On the other hand, more recent optical absorption studies over an extended range of pH have revealed a spectrum that was assigned, 28,33,34 to Fe(OH) 2 + . This made the determination of K h2 by means of spectrophotometry possible. Stefansson 28 has summarized the available data and suggested an ionic strength dependence log K h2 = log 0 K h2 À 3.06m where log 0 K h2 = À5.76 AE 0.06 was again obtained by extrapolation. This value, as well as that in the denominator of the second term, is still uncertain because of an insufficient number of data available at low ionic strengths. The equilibrium constant of the Fe 2 (OH) 2 4+ complex may also be defined in two ways:  The first of these is preferred because it is nearly independent of ionic strength, whereas the second varies strongly with it. According to Stefansson 28 log K h3 = log 0 K h3 + 0.022/m 1 2 (3) where log 0 K h3 = À2.92. Fig. 2 shows the distribution of Fe(III) species versus the pH for [Fe III ] tot = 0.5 mmol dm À3 . Under these conditions the dimer contributes mostly in the pH region 3.0-3.5, but when [Fe III ] tot r 0.1 mmol dm À3 the contribution of Fe 2 (OH) 2 4+ can be neglected, while the distribution of the other species remains essentially unaffected.

Sulfur(IV) in aqueous solution
When sulfur dioxide reacts with water, H 2 SO 3 , HSO 3 À and SO 3 2À are formed as products. The sum of these species and their total concentration are designated S(IV) and [ Here, SO 2aq denotes the sum of physically dissolved SO 2 in water and sulfurous acid proper. The former displays a typical feature in the near ultraviolet absorption spectrum, whereas the latter cannot be so identified. Values of the two equilibrium constants at 25 1C and zero ionic strength (very dilute solution) are: 35 0 K d1 = 1.39 Â 10 À2 , 0 K d2 = 6.72 Â 10 À8 (mol dm À3 ). In the acidic pH range considered here the second dissociation process is essentially negligible. Regarding the first dissociation constant a greater number of studies have sought to determine 0 K d1 , as reviewed by Goldberg and Parker, 35 whereas the dependence on ionic strength appears to have been of lesser interest. The few reliable data are summarized in Fig. 3, which shows a plot of pK d1 = Àlog K d1 as a function of m 1 2 at 25 1C. The only systematic studies are those of Huss and Eckert, 36 who used spectrophotometry and collected 33 data points at low ionic strength, and of Millero et al., 37 who employed potentiometric titration with a focus on high ionic strengths. The two data points of Sekine et al. 38 were obtained as a byproduct of studying the distribution of S(IV) between carbon tetrachloride and water by means of iodometry. They agree well with the other data. The single point due to Devèze and Rumpf 39 is included because these authors also used spectrophotometric measurements. This technique appears to be most reliable. The older data of Frydman et al. 40 obtained for m = 1.0 and m = 3.5 mol dm À3 by potentiometric titration fall outside the range of the other data by a wide margin and are not shown. The solid line in Fig. 3 represents the best fit to the experimental data by the extended Debye-Hückel equation: where log 0 K d1 = log 0.0139 = À1.85698 was kept fixed and the other two parameters were determined by a least square curve fitting program. The factor 1.3 in the denominator of the second term on the right is consistent with the value 1.64, which Huss and Eckert 36 had adopted by analogy with other 1-1 electrolytes of comparable size. By extrapolating the Debye-Hückel equation to m = 0 they had found 0 K d1 = 0.0138 AE 0.0004, in excellent agreement with 0 K d1 = 0.0139 AE 0.0002 obtained from conductivity measurements.

Iron(III)-sulfito complexes
The interaction of S(IV) with Fe(III) leads to the formation of addition complexes that feature absorption spectra in the wavelength region 300-600 nm, partly overlapping the absorption spectra of FeOH 2+ and Fe(OH) 2 + . The complexes are formed rapidly, whereas the subsequent reactions proceed more slowly, so that complex formation is best studied by means of stopped-flow techniques within a millisecond time frame. the formation of only one complex. The existence of three complexes was ultimately confirmed by Kraft and van Eldik 17 and by Prinsloo et al., 19 who employed rapid-scan spectrometry to follow the formation of the complexes as a function of time. The 1 : 1-complex was found to form very rapidly after mixing the reagents (in the mmol dm À3 concentration range), the formation of the 1 : 2-complex was completed within 10-50 ms, and the reaction to form the 1 : 3-complex took up to 200 ms to be completed. Conklin and Hoffmann 14 had used a fixed reaction time of 10 ms; Betterton 18 used a reaction time of 160 ms. The time frame in the latter study would have meant that at least the 1 : 1 and the 1 : 2-complexes were present. This led to uncertainties in the data interpretation. Kraft and van Eldik 17 had suggested that the 1 : 2-complex can exist in two isomeric forms, but the data of Prinsloo et al. 19 did not provide further support for the idea. The following analysis will focus on the results of the last authors because they reported the most comprehensive data set. Prinsloo et al. 19 Yet this reaction is equivalent to the equilibrium (c1) because of the simultaneous equilibrium between Fe 3+ and FeOH 2+ , so that K c1a = K c1 K h1 . The possibility that SO 3 2À is the reacting sulfur species rather than HSO 3 À is rather remote at pH o 3. It might become more important when the pH is raised to values exceeding pH 4. Prinsloo et al. 19 as well as other authors 14,18 have applied the technique of Newton and Arcand 41 to determine apparent equilibrium constants from the experimental data. The method is based on the equation  17 showed two intercepting linear portions (hockey-stick shape) that were interpreted as being due to the successive formation of 1 : 1 and 1 : 2-complexes. Betterton 18 had raised doubts about this interpretation because his data did not show a change in the slope. Prinsloo et al. 19 then restudied the absorption changes as a function of [S IV ] tot , again by means of rapid-scan spectrometry. They largely confirmed the earlier results of Kraft and van Eldik 17 and derived apparent stability constants for the complexes at pH 2.5 and pH 3, which they found to be essentially independent of wavelength in the region 390-470 nm (as required). The formation of the 1 : 1 and 1 : 2-complexes was studied at a reaction time of about 50 ms, that of the 1 : 3-complex at later times. The values reported at pH 2.5 and 3.0 (T = 25 1C, m = 0.1 mol dm À3 ) are: K c1app = 425 AE 18 and 861 AE 120, respectively, as well as K c2app = 231 AE 16  Prinsloo et al. 19 also presented (in their Fig. 2) measured absorbances A at l = 390 nm as a function of [S IV ] tot that can be used together with estimated values of A 0 to prepare new Newton-Arcand plots based on the calculated [S IV ] concentrations. The upper part of Fig. 4 shows the measured absorbance curves, 19 while the lower part presents the corresponding Newton-Arcand plots at pH 2 and pH 2.5. Both demonstrate the hockey-stick shape, which indicates the increasing influence of the 1 : 2-complex when [S IV ] tot is raised. The K c1app values obtained from the initial slopes are 320 AE 26 at pH 2 and 787 AE 216 at pH 2.5. Data for pH 3 are not shown, because the number of data points defining the initial rise of absorbance is insufficient to allow a reasonably reliable evaluation. An estimate obtained from the first two points is K c1app E 2230, which is much higher than, and clearly inconsistent with, the approximate value 1722 AE 240 obtained above. However, the value reported by Prinsloo et al. 19 at l = 390 nm, K c1app = 916 AE 113, is also higher than the average obtained from data at all wavelengths. The values for K c2app obtained at pH 2.5 and pH 3 were only slightly different from those given above, 19 the differences falling within the range of the experimental error.
In order to determine the true stability constants from the apparent ones, reference is made to the definitions of the equilibrium constants K c1 -K c3 and K c1app -K c3app . Thus, one finds for the 1 : ]) From the equilibria involving the reactants and the associated equilibrium constants K h1 = 2.87 Â 10 À3 ; K d1 = 2.24 Â 10 À2 ; K d2 = 1.5 Â 10 À7 (at m = 0.1 and 25 1C) it follows that The individual values of K c1 calculated from the apparent stability constants derived at pH 2 and pH 2.5 are 2075 AE 167 and 1889 AE 518 dm 3 mol À1 . The average is 1982 AE 518 dm 3 mol À1 , where the statistical uncertainty is that of the reported measurements. The value at pH 3 derived from the corrected overall average, 1722 AE 240, would be K c1 = 2426 AE 338, which is at the upper end of the error range. The value will not be used, because at pH 3 other iron-sulfito complexes may contribute to the observed absorbances (vide infra). The corrected value estimated from the overall average given by Prinsloo et al. 19 at pH 2.5 is K c1 = 1855 AE 80, which agrees well with that derived here from the data at 390 nm.
The equilibrium constant for the formation of the 1 : 2complex is, This value is the average of the individual results 0.834 AE 0.058 at pH 2.5 and 0.631 AE 0.054 at pH 3. Here, the statistical uncertainty is that of the averaging process. The experimental error range is larger.
Finally, the equilibrium between the 1 : 2-and 1 : 3-complexes is considered. In this case, the observed K c3app values show only a slight dependence on pH, indicating that the 1 : 3-complex remains nearly fully protonated in the (admittedly narrow) pH range covered. Accordingly, reaction (c3) should be written  The value on the right is the average of the two results 180 AE 21 and 198 AE 26 obtained at pH 2.5 and pH 3, respectively. Here, the experimental error range is again greater than the statistical uncertainty of the averaging process.
It must be kept in mind that these results refer to an ionic strength m = 0.1. The Debye-Hückel theory predicts log K c1 = log 0 K c1 À 2.04m 1 2 /(1 + am 1 2 ), log K c2 E log 0 K c2 (no significant ionic strength dependence), and log K c3a = log 0 K c3a + 1.02m 1 2 / (1 + bm 1 2 ). The factors a and b in the denominators of the second terms must be estimated. Regarding the equilibrium constant K c1 Lente and Fabian 16 have found K c1a = K c1 K h1 = 1.35 AE 0.15 at m = 1.0 mol dm À3 ; which is equivalent to K c1 = 825 AE 92 at this ionic strength. The corresponding value of a in the extended Debye-Hückel equation would be a E 1.5. The value of K c3a increases with increasing ionic strength, but the effect is not very pronounced, and it is neglected in calculating equilibrium distributions of the Fe(III) species.
In order to compare the above results with those obtained by Conklin and Hoffmann 14 and by Betterton 18 it is necessary to calculate the relative distribution among the three complexes at the reaction times used by these authors. Rate coefficients for the formation of the complexes that are required for the calculations will be discussed in the next section. Here, only the results of such calculations are used. 42 The experimental conditions applied by Conklin and Hoffmann 14 were: pH 2.1, [Fe III ] tot = 0.56 mmol dm À3 , [S IV ] tot = 0.5-45 mmol dm À3 , m = 0.4 mol dm À3 , Dt = 10 ms. The calculated distribution of the complexes under these conditions shows that the first complex dominates only at very low S(IV) concentrations where the scatter of the measured absorbances would have obscured the initial slope determined by K c1app . The bulk of the data refer to the second complex. In this region the contribution of the first complex remains nearly constant and the contribution of the third complex can be ignored. Measurements made at two wavelengths (350 and 450 nm) gave apparent K-values of 57.2 and 76.4, respectively, with an average of K c2app = 66.8 AE 10.4 dm 3 mol À1 . When the correction factor of eqn (8) is applied, one obtains the true equilibrium constant K c2 = 0.694 AE 0.11, which is in excellent agreement with the value calculated above from the data of Prinsloo et al. 19 Thus, the three values can be combined to derive an overall average K c2 = 0.72 AE 0.08. Betterton 18 has explored the change with pH of the apparent equilibrium constant under experimental conditions quite similar to those of Conklin and Hoffmann. 14 The major difference was the longer reaction time (Dt = 160 ms) spent between mixing the reagents and observing the products in the optical cuvette. The measured K app was found to increase as the pH was raised from 1 to 3 whence a plateau was reached. This observation is in accord with the notion that the formation of the complexes proceeds via FeOH 2+ and HSO 3 À as the active reactants, since the concentrations of both species increase with increasing pH. The calculated time dependence for the formation of the complexes indicates that at pH 1 where the concentrations of the reactants are small, the 1 : 1-complex is still dominant after 160 ms reaction time, even at high S(IV) concentrations. This condition applies also at pH 1.25  (8) is K c2 = 1.15 AE 0.16. This result is higher than that derived above from the data of the other authors, 14,19 but the calculated time dependence for complex formation shows that at the longer reaction time used by Betterton 18 the contribution of the 1 : 3-complex cannot be fully ignored. At concentrations [S IV ] tot Z 10 mmol dm À3 the 1 : 3-complex becomes the dominant species, requiring appropriate corrections. The overall conclusion is that the results obtained by Betterton 18 for this pH regime agree reasonably well with the other data discussed above. In the pH range 2-3, however, all three complexes are simultaneously present at similar concentrations, which makes it difficult to interpret the Newton-Arcand plots in a simple manner even if straight lines are observed. Note that nearly straight lines would be obtained if the 1 : 2-and 1 : 3-complexes featured absorption coefficients of similar magnitude. From the preceding discussion it will be clear that much of the difficulty experienced in disentangling the three equilibria from simple absorbance measurements is due to the complexity of the system and the necessity of finding suitable experimental conditions for the task.

Rates of formation of iron-sulfitocomplexes
Kraft and van Eldik 17 presented apparent rate coefficients for the formation of the second and third complexes. The formation of the first complex was too fast to be studied by stopped-flow spectrometry (k c1f 4 10 3 s À1 ). Betterton 18 used a pulseaccelerated flow technique to estimate the second order rate constant for the formation of the 1 : 1-complex. He reported k c1f = 4.0 Â 10 6 dm 3 mol À1 s À1 at pH 2. This result when combined with the equilibrium constant derived above suggests k c1f = 4.0 Â 10 6 , k c1r = 2.08 Â 10 3 for the rate coefficients of the forward and reverse reactions. Kraft and van Eldik 17 used a stopped-flow instrument with a short mixing time (B0.2 ms) to measure rate constants for the formation of the complex appearing within the 1-10 ms time frame (denoted step I). Experimental conditions were: [Fe III ] tot = 2 mmol dm À3 , pH 2.5, m = 0.1, and [S IV ] tot was varied between 10 and 60 mmol dm À3 . The high concentrations of S(IV) combined with the time frame used make it fairly certain that the 1 : 2-complex was observed. The rate constant was found to vary linearly with [S IV ] tot (their Fig. 6a). From the slope of the straight line one obtains k c2app = 5.2 Â 10 3 dm 3 mol À1 s À1 . A correction is needed to take into account that the reactive species is HSO 3 À . The appropriate correction factor (1 + [H + ]/K d1 + K d2 /[H + ]) leads to k c2f = 5.9 Â 10 3 dm 3 mol À1 s À1 . The rate coefficient for the reverse reaction step is calculated to be k c2r = k c2f /K c2 = 8.24 Â 10 3 dm 3 mol À1 s À1 . The formation of the 1 : 3-complex proceeds subsequent to that of the 1 : 2-complex. Kraft Fig. 8 and 9) one obtains k c3app = 3.3 Â 10 3 dm 3 mol À1 s À1 . The correction needed to take into account that HSO 3 À is the true reactant raises the value to k c3af = 3.8 Â 10 3 dm 3 mol À1 s À1 . The corresponding rate coefficient for the reverse reaction step then is k c3ar = k c3af /K c3a = 20.1 s À1 . These data were used to explore the successive formation of the three complexes and the overall development of the system as a function of time. Fig. 5 shows, as an example, the development calculated with [Fe III ] = 1 mmol dm À3 , [S IV ] tot = 10 mmol dm À3 , pH 2.5. The equilibrium between FeOH 2+ and the 1 : 1-complex is reached at times shorter than 1 ms. Full equilibrium between all three complexes is reached about 250 ms after mixing the reagents.

Absorption coefficients
As a consistency check the rate coefficients and equilibrium constants derived above may be used to calculate absorbance curves for comparison with the experimental results reported at l = 390 nm 19 as a function of [S IV ] tot at three different pH (2.0, 2.5 and 3.0). The reaction time was 50-100 ms, [Fe III ] tot = 1 mmol dm À3 (m = 0.1). Molar absorption coefficients required for the calculation can in principle be estimated from the Newton-Arcand plots by extrapolating the observed straight lines back to the ordinate, where A -A N . The method can also be applied when two complexes are successively formed, provided the straight lines observed are clearly separated. This implies that the absorption coefficients of the two complexes have distinctly different values. Prinsloo et al. 19 have estimated absorption coefficients (their Table 1), but these refer to Fe(III) and S(IV) as reactants and should be considered order of magnitude values. An alternative method is to calculate the relative distributions of the individual complexes under the experimental conditions applied and adjust the individual values of the absorption coefficients until the observed absorbance curve is reproduced. As absorption coefficients are constants, the values should not change when the pH is varied. Fig. 4 includes calculated absorbance curves for comparison with the measurements. The absorption coefficient of Fe 3+ at 390 nm is essentially zero, and that of the first hydrolysis product is e(FeOH 2+ ) E 60 dm 3 mol À1 cm À1 . 19,28,33 Absorption coefficients that were found to provide good agreement between calculated and observed absorbances at both pH 2.0 and 2.5 are e(FeSO 3 + ) = 270, e(Fe(SO 3 ) 2 À ) = 400, e(Fe(SO 3 ) 3 H 2À ) = 450 (dm 3 mol À1 cm À1 ). Fig. 4 indicates the extent of the agreement. These absorption coefficients, however, cannot reproduce the absorbance curve at pH 3.0. To obtain a good fit in this case would require e(FeSO 3 Fig. 4 shows the result by the broken line. The discrepancy suggests that at pH 3 the reaction mixture contains one or more additional absorbers. At pH 3 one enters into a pH regime where the Fe(III) hydrolysis product Fe(OH) 2 + increases in importance, and the dimer Fe 2 (OH) 2 4+ must also be taken into account (see Fig. 2).  16 and the rate of formation is rapid. The absorption coefficient of the complex at l = 450 nm is e(Fe 2 OHSO 3 3+ ) = 500 dm 3 mol À1 cm À1 ; at 390 nm it would be at least twice as large. When this complex is taken into account, the initial rise of the calculated absorbance curve, setting e(FeSO 3 + ) = 270 dm 3 mol À1 cm À1 , agrees much better with that observed experimentally, 19 but it does not entirely alleviate the discrepancy between calculated and observed absorbances at high concentrations of S(IV). The necessity of taking into account additional equilibria demonstrates the growing complexity of the system. Further studies are needed to identify the additional reactions active in the region pH Z 3. One of the consequences of the presence of other iron-sulfito complexes and their contribution to the total absorbance is their interference in the determination of K c1app by means of Newton-Arcand plots. These additional complexes presumably are responsible for the comparably high value of K c1 obtained at pH 3 from the measured absorbances at l = 390 nm.
Reactions following the formation of iron-sulfito complexes , thereby reducing the overall reaction rate, whereas the reaction with Fe 3+ scavenges SO 3 À radicals and promotes the decomposition of FeSO 3 + . The effect of Cu 2+ is to catalyze the last process. We note in passing that Cu(II) also interacts with S(IV) to form an addition complex, which is prone to decompose. 44 In acidic solutions, however, the reaction is slow (in contrast to alkaline solutions); hence its neglect is justified.
Pollard et al. 10 first demonstrated that the rate of the reaction between Fe(III) and S(IV) (without additives) decreases with time due to the rise of the concentration of Fe(II) formed as a product. They also found the rate of dithionate production to approach one half of that for the consumption of Fe(III) when [S(IV)] 0 /[Fe(III)] 0 4 0.5; but most importantly, they found that the reaction 2SO 3 À -S 2 O 6 2À , which Higginson and Marshall had assumed to be the source of dithionate, is incompatible with the observed dependence of the rate of dithionate formation on the initial reactant concentrations. Accordingly another reaction must serve as a source of dithionate. In the present study it was found that the reaction SO 3 À + FeSO 3 + -Fe 2+ + S 2 O 6 2À agrees with most of the experimental data. The reaction 2SO 3 À -S 2 O 6 2À will occur as well, but it is unimportant in this system. Table 1 shows the complete reaction mechanism that was used here to analyze the experimental data available in the literature. All the equilibria are established rapidly, and they are essentially maintained during the subsequent reaction. For the purpose of computer simulations the following forward or reverse rate coefficients were taken from the literature and combined with the established equilibrium constants (m = 1.0 mol dm À3 ): k h1f = 2.0 Â 10 7 , 50 k d1r = 2.0 Â 10 8 , 51 k d3r = 1.0 Â 10 11 , 51 k c4f = 6.3 Â 10 3 , 50 k c1f = 4.0 Â 10 6 . 18 Rate coefficients for some of the reactions following the formation of the complexes are known; appropriate references are indicated in Table 1. The analysis will begin with the results of Carlyle and Zeck, 12 as they have reported the most extensive data set. The conclusions reached will then provide a basis for discussing the results of the other authors.

Analysis of the data of Carlyle and Zeck
In their study the course of the overall reaction was followed by monitoring the optical absorption of the Fe(III) complex at wavelengths in the region 320-443 nm as a proxy for Fe(III).
In all experiments the temperature was 25 1C and the ionic Here, The principal parameters determining the reaction rate are k 1 A and the ratios k 3 /k 2 and k 4 /k 3 . The factor N in the denominator of eqn (10) is ]. The rate coefficient k 3 replaces the individual rate coefficients of reactions (3a) and (3b) in Table 1 as it is not possible to separate the two processes here: The above eqn (10) (10) is based on the assumption that only the 1 : 1-complex is present the results of those experiments that did not satisfy this condition were not used. This removes 8 data points from a total set of 25. The remaining data were subjected to a linear regression treatment that resulted in a slope of (6.7 AE 0.4) Â 10 À4 s À1 and an intercept with the ordinate of (1.6 AE 1.2) Â 10 À5 s À1 . According to eqn (10a) the slope and the intercept are equivalent to 2(k 1 k 3 /k 2 )(k 4 /k 3 ) and 2(k 1 k 3 /k 2 ), respectively. Their ratio is k 4 /k 3 = 42 with a large margin of error due to the uncertainty associated with the value of the intercept.
These data do not allow a determination of the value of k 3 /k 2 , because the second order rate coefficients k obs reported are not calibrated. The data can only describe the influence of important parameters on the reaction rate. In contrast to the exponential behavior of first order reactions, the decay of a reactant undergoing a second order reaction follows the rate law 1/x = 1/x 0 + k obs t. Due to experimental difficulties Carlyle and Zeck 12 could not determine x 0 , and for k obs t much larger than 1/x 0 the initial signature of x 0 is lost. However, the value of k 3 /k 2 can be estimated from other data discussed further below, in which the rise of Fe(II) was observed as a function of time.
Carlyle and Zeck 12 have also measured, in separate experiments, the yield of dithionate under various conditions (their Table 1). In this study the concentration of Fe(III) was raised to [Fe III ] 0 E 0.01 mol dm À3 compared to [Fe III ] 0 E (3-5) Â 10 À4 mol dm À3 in the reaction rate measurements; [S IV ] 0 /[Fe III ] 0 ranged from 0.4 to 11, approximately, and the hydrogen ion concentration was [H + ] = 0.1 in most cases. Only these data are considered here. The extent of dithionate production predicted by the reaction system shown in  ] N , that is, the reaction was assumed to have gone to completion, but the time periods between starting the reaction and the final product analysis were not given. The computer calculations showed that for reasonable values of k 3 /k 2 (vide infra) the reaction is essentially complete after 24 h, but even after 12 h the amount of dithionate formed is already close to the final value. The calculations confirmed the prediction that the rate of dithionate formation slows down as the reaction proceeds, because the consumption of S(IV) lowers the concentration of the FeSO 3 + complex as well. This effect diminishes with increasing excess of S(IV) over Fe(III). According to the stoichiometric equations associated with the reaction mechanism in Table 1 ÀD ] 0 ratio as expected. The results of computer calculations were largely found to agree with the measurements. The best fit to the measurements, resulting in an average deviation of 5%, was obtained with k 4 /k 3 = 45. The solid line in Fig. 6b, which represents the calculated values, indicates the extent of agreement reached. Thereby it is demonstrated that the data reported by Carlyle and Zeck for the Fe(III)-S(IV) reaction system are selfconsistent and agree with the adopted reaction mechanism in essentially all respects.

Comparison with other studies
A direct comparison of the results of Carlyle and Zeck 12 with those of other studies is not possible, not only because of the widely varying experimental conditions employed, but also because the data are not presented in a uniform manner. However, initial reaction rates and the production of dithionate were measured in most studies. Therefore, computer simulations were mostly used to determine how far the results are consistent with each other. Karraker 11 sought to suppress the formation of dithionate by working with iron in large excess over S(IV). In some experiments Fe(II) was added. The ionic strength was adjusted to m E 1.0 mol dm À3 , and the hydrogen ion concentration was set to   The ratio k 2 /k 3 E 22 can only be a coarse estimate, however, because dropping the term 2([S IV ] 0 -[S IV ]) in eqn (13a) is not really justified. Although this term may be taken into account when evaluating the equation, it was considered more appropriate to determine k 2 /k 3 by means of computer simulations. The procedure was to find the best fit between calculated and measured half-life times by varying k 2 /k 3 in a narrow range. The calculations made use of k 4 /k 3 = 42 determined from the data of Carlyle and Zeck. 12 10 have in one case explored the course of the reaction over a period of 24 h. They treated the reaction as bimolecular and plotted the logarithm of the ratio of the reactant loss rates versus time. Fig. 8 compares their measurements with computer simulations. The solid line was obtained with k 2 /k 3 = 61.4 and this value could also reproduce their other rate data, thus providing some support for the value of k 2 /k 3 derived above.
With regard to dithionate one should note that the mechanism in Table 1 Fig. 9 compares this ratio as a function of A[S IV ]. While the data of Higginson and Marshall 9 and of Carlyle and Zeck 12 are approximately in agreement, much higher relative dithionate production rates were obtained by Pollard et al. 10 and by Dasgupta et al. 13 The latter authors, in fact, found dithionate to be the exclusive S(IV) oxidation product. The incongruity of the data is perturbing, but may have its origin in analytical difficulties. The classical analytical procedure that most authors have used, involves the oxidation of dithionate to sulfate by dichromate. The oxidant is added in excess, and the surplus is then determined by back-titration. This procedure requires the prior removal of all   interfering substances (metal ions, sulfite, etc.). Carlyle and Zeck 12 have measured dichromate by spectrophotometry, which is more accurate than titration, whereas Dasgupta et al. 13 have used HNO 3 as oxidant and determined the amount of sulfate produced. This method is the least reliable, because it rests on the prior removal of sulfate produced during the reaction. In view of the good agreement of the results obtained by Carlyle and Zeck 12 with the proposed reaction mechanism, and the agreement of their rate data with dithionate production rates, their results are presently the most convincing. But the comparison shows that the extent of dithionate production in this reaction is not settled and should be reexamined with modern analytical techniques such as ion chromatography.

The role of copper as a catalyst
The addition of copper to the solution reduces the rate of dithionate formation. This effect is only weakly apparent in the results of Higginson and Marshall 9 due to the scatter of the data, but the results of Carlyle and Zeck 12 show it quite clearly. A concentration of Cu(II) similar to that of Fe(III) reduces the rate of dithionate production to about one third of that in the absence of copper. In the mechanism proposed by Higginson and Marshall 9 the effect arises from the role of copper as an efficient SO 3 À radical scavenger. Dithionate production rates measured by Carlyle and Zeck 12 included two experiments, in which copper was added. The measured decrease of dithionate production could be adequately reproduced by computer simulations when the rate coefficient for the reaction of SO 3 À with Cu(II) was assumed to be about ten times greater than that with Fe(III), that is k 6 /k 3  The results of these runs were subjected to a detailed analysis. As Table 1 indicates, the reaction with SO 3 À converts Cu(II) to Cu(I), which then reacts (more rapidly) with Fe(III) to restore Cu(II). The second reaction has been studied by means of pulse radiolysis 48,49 and was found to proceed primarily via the FeOH 2+ complex. If these two reactions are the only ones involving copper, the concentration of Cu(I) will be kept in a Here the factor N in the denominator of eqn (10) is replaced by ], the second term in N 1 becomes much smaller than unity. The further analysis showed that except for very low concentrations of copper, the third term is also smaller than the fourth, k 6 [Cu 2+ ]/k 2 [Fe 2+ ], so that eqn (10b) reduces to This equation agrees with the empirical rate law reported by Carlyle and Zeck 12 except for a term quadratic in [Cu 2+ ] in the denominator of their expression. It is interesting to note that in contrast to the second order rate behavior observed when copper is absent (eqn (10)), the rate law changes to one of first order in the presence of copper. The change is evident from the data of Carlyle and Zeck as well as from a comparison of eqn (10) and (10c). It may be taken to provide a further confirmation of the adopted mechanism. For the purpose of analysis it is convenient to rearrange the equation as follows In this form the equation predicts that a plot of Z versus the ratio [Fe 2+ ]/[Cu 2+ ] should yield a straight line with the slope being determined by (k 2 /k 6 ). Fig. 10 shows the corresponding plot. Here, the results of 22 experiments were used for which the above-mentioned conditions apply. While a linear relationship is clearly observed, it is also evident that a crowding of data points occurs in the region near the origin. This effect arises from the high concentration of copper used in 13 of the experiments. Despite the uneven distribution, a linear regression analysis shows the data to fall on a straight line with remarkably little variance. The line intersects the ordinate at 1.04 AE 0.17, and the slope is k 2 /k 6 = 3.7 AE 0.3.

Rate coefficients
The foregoing results suggest that apart from the chosen initial conditions, the rate of the reaction is defined by the rate coefficient k 1 for the decomposition of the FeSO 3 + complex, and by the ratios of rate coefficients k 2 /k 3 , k 4 /k 3 , and k 2 /k 6 .
To determine the individual rate coefficients requires separate measurements. Only one such study appears to exist. Buxton et al. 47 have studied reaction (2) by means of the pulse radiolysis technique and found the reaction to proceed via an intermediate complex, which is in fast equilibrium with the reactants SO 3 À and Fe 2+ . The pre-equilibrium constant was determined to be K 2 = 278, and the rate coefficient for the forward reaction k 2a = 3.05 Â 10 4 s À1 at 20 1C. The overall rate coefficient then is k 2 = 8.5 Â 10 6 dm 3 mol À1 s À1 . The value at 25 1C can be estimated by means of the activation energy, 46.6 kJ mol À1 , measured over the temperature range 20-30 1C: k 2 = 1.2 Â 10 7 dm 3 mol À1 s À1 . Unfortunately, the value refers to an ionic strength of m = 0.07 rather than m = 1.0 mol dm À3 as required here. All reactions between ions in aqueous solution are known to depend on the ionic strength. 52 It is customary to express this dependence by the modified Brønsted-Bjerrum relation log k = log 0 k + 1.02z A z B m 1 2 /(1 + m 1 2 ), where z A and z B are the electric charges of the reactants A and B. Several reactions in the sulfur-oxygen system have been found to obey this relation. 6,53 In the case of reaction (2) the product z A z B = À2, leading to an estimate of k 2 = 3.0 Â 10 6 dm 3 mol À1 s À1 at m = 1. This value, when used in conjunction with k 2 /k 3 = 61.4, provides k 3 = 4.9 Â 10 4 dm 3 mol À1 s À1 . In addition, the combination with the ratios k 3 /k 4 = 42 and k 6 /k 2 = 0.27 leads to k 4 = 2.1 Â 10 6 and k 6 = 8.1 Â 10 5 dm 3 mol À1 s À1 . These values must be considered estimates, and confirmation by direct measurements will be needed.
According to eqn (11) the overall rate coefficient k 3 is a pH-dependent average of k 3a and k 3b . If the reaction of SO 3 À with Fe 3+ were dominant, the value derived above for k 3 would refer to k 3a . Alternatively, if the reaction proceeded via FeOH 2+ , k 3 E k 3b K h1 /[H + ]. In this case k 3b E 7.6 Â 10 6 dm 3 mol À1 s À1 at m = 1.0. The experimental data, 10-12 especially those of Carlyle and Zeck in Fig. 6a, show little influence of the pH. This would suggest k 3 = k 3a . But the data points are rather scattered so that they do not allow a clear choice between the two alternatives. On the other hand, the results discussed further below, obtained at higher pH, indicate that reaction (3b) is important. In analyzing these data both possibilities will be considered, but the issue clearly is not resolved and will require further scrutiny.

Results from studies at higher pH
The preceding discussion referred to data obtained at low pH under conditions where the FeSO 3 + complex is dominant and higher complexes can be neglected. When the pH is raised, this condition no longer holds and the presence of the higher Fe(III)-S(IV) complexes must be taken into account. At higher pH the reaction also proceeds much more rapidly so that it cannot be studied by conventional techniques. Thus, Conklin and Hoffmann 14 and Kraft and van Eldik 15 have used spectrophotometry to follow the decay of the complexes with time, whereas Millero et al. 54 applied micro-molar concentrations of Fe(III) and S(IV) to extend the time scale of observation to 80 min. The latter authors unfortunately worked with seawater or concentrated NaCl solutions as solvents, which led to the formation of various other Fe(III) complexes in addition to those between iron and sulfite, This makes the system difficult to interpret. In fact, the observed rate coefficients were by orders of magnitude greater than those found in other studies. The presence of higher Fe(III)-S(IV) complexes requires an extension of the reaction mechanism in Table 1 because similar to FeSO 3 + these complexes may also decompose and react with SO 3 À radicals. For the purpose of discussion the additional reactions may be defined as follows: The reaction rate will be determined by an equation similar to eqn (10) 3 H 2À ] and k 1 and k 4 must be replaced by the weighted total rate coefficients k 1tot = k 1 f 1 + k 1a f 2 + k 1b f 3 and k 4tot = k 4 f 1 + k 4a f 2 + k 4b f 3 , respectively, where the f i denote the corresponding fractions of the three iron-sulfito complexes. Since the relative abundance of the three complexes is a function of the pH, the product distribution and the reaction rate are expected to vary accordingly. Although appropriate measurements should, in principle, provide information on the participation of each complex in the overall reaction, the available data are fragmentary, and measurements of the product distributions are almost totally lacking. Conklin and Hoffmann 14 have studied the reaction at pH 2 and m = 1.0 mol dm À3 in the presence of formic acid. They used spectrophotometry at l = 350 nm to monitor the decay of the absorbance resulting from the sum of Fe(III) species. Formic acid forms a complex with Fe(III), which ties up a considerable fraction of Fe(III) so that the concentration of free Fe(III) and the reaction rate are markedly reduced compared to values in the absence of formic acid. Hence, the time period of the decay extends for hours rather than seconds or minutes as in the absence of formic acid. According to Biruš et al. 50   Both equilibrium constants are related in that K cf = K cfa K d4 /K h1 . Here, K d4 = 2.95 Â 10 À4 mol dm À3 is the dissociation constant of formic acid at m = 1.0. 55 Accordingly, K cf = 2.2 Â 10 2 dm 3 mol À1 . Rate coefficients for the formation and decomposition of the complex as estimated by Moorhead and Sutin 56 are 2.5 Â 10 3 dm 3 mol À1 s À1 and 11 s À1 , respectively. The values are large enough to guarantee that the equilibrium between free Fe(III) and the FeOOCH 2+ complex is maintained during the Fe(III)-S(IV) reaction. Fig. 11 shows two of the absorbance decay curves observed by Conklin and Hoffmann. 14 Computer calculations were carried out with the aim to reproduce these decay curves. Absorption coefficients required in the calculations were estimated from the absorbance data given by the authors at l = 350 nm as a function of [S IV ] (their Fig. 3a).  26 The absorbances calculated with these data for the distributions of Fe(III) species at the start of the reaction under the experimental conditions used in Fig. 11 did not quite reproduce the observed initial values. However, the FeOOCH 2+ complex is known to be photochemically active, 57,58 and it is expected to contribute to the total absorbance at wavelengths near 350 nm. An absorption coefficient of e(FeOOCH 2+ ) E 170 was found to close the gap and to bring calculated and observed initial absorbances into agreement. This value is similar in magnitude to that estimated by Baxendale and Bridge 57 at l = 365 nm: e(FeOOCH 2+ ) E 100 dm 3 mol À1 cm À1 .
The experimental data shown in Fig. 11 refer to two initial concentrations: (a) [Fe III ] 0 = [S IV ] 0 = 5 mmol dm À3 , and (b) [Fe III ] 0 = 4 and [S IV ] 0 = 20 mmol dm À3 . The calculated equilibrium distributions indicate that in the first case about 95% of total iron is bound to the FeOOCH 2+ complex, in the second case it is about 84%. These fractions do not greatly vary during the reaction. The distributions of the remaining Fe(III) species and their changes as the reaction proceeds are indicated in the two lower frames of Fig. 11. In the first case the FeSO 3 + complex is dominant, in the second case (Fe(SO 3 ) 3 H 2À ) is more abundant. It was expected that the simple mechanism in Table 1 would suffice to reproduce the decay of absorbance in the first case, while in the second case the mechanism would have to be extended to include reactions of the 1 : 3-complex. The computer calculations first showed that the experimental data can be reproduced only by assuming that reaction (3b) is the main channel of reaction (3) with k 3b = 7.6 Â 10 6 dm 3 mol À1 s À1 (at m = 1.0 mol dm À3 ). But in contrast to expectation the calculations also showed that the basic mechanism of Table 1 is adequate to reproduce both sets of experimental data. The results are shown in Fig. 11 by the solid lines. The assumption of even a minimal contribution by the decomposition of the 1 : 3-complex only worsened the agreement between calculated and experimental data in that the initial decay rate became too rapid. The rate coefficient for the decomposition was estimated to be k 1b o 0.01 s À1 . These results suggest that under the experimental conditions chosen the 1 : 3-complex does not significantly participate in the reaction. The experimental data in Fig. 11 were also subjected to tests for first and/or second order reaction behavior. A first order decay was found to occur only in the very initial stage of the reaction. There follows a transition period, which is apparent in Fig. 11 by an adjustment of the distributions of Fe(III) species, until after about 20 min the decay of absorbance shows second order behavior. Conklin and Hoffmann 14 had tried to fit the observed decay curves by a rate expression with two consecutive exponential terms. This procedure provides only a coarse description of the experimental data, and it is in conflict with the present mechanism and its steady state description in eqn (10).
Kraft and van Eldik 15 have analyzed absorbance decay curves obtained at l = 390 nm, m = 0.1 mol dm À3 under various experimental conditions. They described decay curves only in general terms, 17 but did not present the original data. Following Conklin and Hoffmann, they interpreted the observed kinetic behavior as that of two consecutive reactions and reported apparent first order rate coefficients, one for the initial, and the second for a later stage of the reaction (stages III and IV in their notation). The preceding discussion has shown, however, that the true origin of the observed kinetic behavior is that of a shift from first to second order and not, for example, the decomposition of complexes occurring in parallel at different rates. Accordingly, only the first of the two apparent rate coefficients can be useful, whereas the second defies a meaningful analysis.
No details were given about how the rate coefficients were determined. The authors state that a standard least-square fitting program was used 17 in the data evaluation, but the time periods for the averaging process were not specified.
Computer calculations were performed with the aim to reproduce the apparent first order rate coefficients reported for the initial section of the decay curve. As the measured quantity is the absorbance A, the apparent rate coefficients are defined as k = ÀdA/Adt or, in integrated form, k = (1/Dt)ln(A 1 /A 2 ) with Dt = t 2 À t 1 . Both expressions were explored, with little difference in the results (Dt = 1 s). Fig. 5 had shown that the various Fe(III) species come to equilibrium at t E 0.2 s and this sets a lower limit to t 1 . The decomposition of iron-sulfito complexes begins before the equilibrium is fully achieved. All results show that the reaction can be truly of first order only at very short reaction times. Due to the rapidity of the reaction sufficient Fe 2+ develops early in the process to activate the back-reaction SO 3 À + Fe 2+ -FeSO 3 + whereupon the reaction rate decreases. This is evident also during the time period available to calculate apparent first order rate coefficients. Here, the time period was confined to the range 0.5-4 s. At longer times the values obtained are markedly lowered while the calculated standard deviation of the averages increases. Absorption coefficients at l = 390 nm for the three complexes and e(FeOH 2+ ) were derived earlier (see under Absorption coefficients), and e(FeSO 4 + ) E 100 dm 3 mol À1 cm À1 was obtained by extrapolation of published data; 26 the contribution by Fe 3+ to the absorbance can be neglected. The calculations made use of the reaction rate coefficients derived in the preceding section. They were adjusted to the difference in ionic strength (m = 0.1), which leads to k 1 = 0.19 s À1 , k 2 = 1.0 Â 10 7 , k 3a r 3.0 Â 10 5 , k 3b r 2.6 Â 10 7 , k 4 E 4.0 Â 10 6 (dm 3 mol À1 s À1 ). Additional rate coefficients for reactions involving the 1 : 2-and 1 : 3-complexes were then introduced on a trial basis as needed to bring observed and calculated data to agreement. Kraft  In this region the FeSO 3 + complex is dominant and contributions of the two higher complexes can be neglected. Calculations of the apparent first order rate coefficient were performed for two limiting cases of k 3 , setting either k 3a = 3.0 Â 10 5 and k 3b = 0 or k 3b = 2.6 Â 10 7 and k 3a = 0 (dm 3 mol À1 s À1 ). Average k app values obtained for [Fe III ] 0 = 2, 4, and 6 mmol dm À3 were 0.067 AE 0.013 s À1 in the first case, and 0.090 AE 0.012 s À1 in the second (9 data points each). The former result is closer to the value reported than the latter, suggesting that reaction (3b) is not the sole channel of reaction (3). The upper frame of Fig. 12 shows apparent initial first order rate coefficients obtained when [S IV ] 0 was varied and [Fe III ] 0 was kept constant. 15 The rate coefficient first rises with increasing [S IV ] 0 and then approaches a constant value of k app E 0.135 s À1 . The lower frame of the figure shows the corresponding change in the calculated distribution of Fe(III) species. As the S(IV) concentration is raised, the distribution shifts from FeSO 3 + to Fe(SO 3 ) 3 H 2À as the major species. The observation that the apparent rate coefficient still remains at a high value is a clear indication that the 1 : 3-complex is subject to decomposition and that it participates in the reaction. Computer calculations were performed in attempts to reproduce the observed variation in the k app values. The solid line shown in the upper part of Fig. 12 was obtained with the rate coefficients given above and the assumption that k 1a = 0.04 s À1 , k 1b = 0.08 s À1 for the decomposition of the 1 : 2-and 1 : 3-complexes, respectively, and k 4b = 1.2 Â 10 7 dm 3 mol À1 s À1 for the reaction of SO 3 À radicals with the 1 : 3-complex. The initial rise curve was better represented with k 3b = 2.6 Â 10 7 dm 3 mol À1 s À1 rather than with k 3a = 3.0 Â 10 5 dm 3 mol À1 s À1 and k 3b = 0 (shown by the broken line). The experimental data indicate a slight overshoot at [S IV ] 0 E 5 mmol dm À3 , which could be reproduced, if the value chosen for k 4 were raised by 50%. Fig. 13 shows the variation of the apparent initial first order rate coefficients with the pH and, in the lower part of the figure, the change in the equilibrium distribution of Fe(III) species. The distribution shifts from FeSO 3 + to Fe(SO 3 ) 3 H 2À as the pH is raised, indicating again that the higher complexes participate in the overall reaction. Computer calculations performed in attempts to reproduce the observed variation in the k app values showed that in this case the results differed little with the choice of k 3 (either k 3b = 2.6 Â 10 7 or k 3a = 3.0 Â 10 5 dm 3 mol À1 s À1 and k 3b = 0). The solid line shown in the upper part of Fig. 13 was calculated with the rate coefficients given above and the assumption that k 1a = 0.04 s À1 , k 1b = 0.06 s À1 for the decomposition of the 1 : 2-and 1 : 3-complexes, respectively, and k 4b = 1.2 Â 10 7 dm 3 mol À1 s À1 for the reaction of SO 3 À radicals with the 1 : 3-complex. These values are quite similar to those found applicable in the preceding case when the pH was kept constant and [S IV ] 0 was varied. Above pH 2.5 it was not possible to obtain a good fit between calculated and observed k app values. The overall result of the computer simulations is the recognition that all three complexes undergo decomposition, but the decomposition rates for the two higher complexes are markedly lower than that for the 1 : 1-complex (k 1a E 0.04 s À1 and k 1b E 0.08 s À1 compared to k 1 = 0.19 s À1 ). This conclusion obviously disagrees with that derived above in evaluating the data of Conklin and Hoffmann, 14 which had indicated that the 1 : 2 and 1 : 3 iron-sulfito complexes do not significantly participate in the reaction. The major difference in the applied experimental conditions, apart from the presence of formic acid in the latter case, is the difference in ionic strength (m = 0.1 versus m = 1.0). This may have a bearing on the reaction rate coefficients, but it should not affect the decomposition rates.
Kraft and van Eldik 15 have also used ion chromatography to determine the yields of sulfate and dithionate after a reaction time of 5 min and 40 min, respectively. The initial concentration of iron was [Fe III ] 0 = 0.5 mmol dm À3 , [S IV ] 0 was varied from 0.5 to 5.0 mmol dm À3 . The average pH was 3.47 (range 3.30-3.56). The ionic strength was not controlled but it is estimated to approximate to m E 0.006. These data are needed to calculate the equilibrium constants involved and to determine the equilibrium distribution of the Fe(III) species. At pH 3.5 the contribution of Fe 3 + to the sum of Fe(III) hydrolysis products is almost negligible, but that of Fe(OH) 2 + cannot be ignored as Fig. 2 showed. Fe(OH) 2 + is expected to react with HSO 3 À in a similar way as Fe(OH) 2+ to form an Fe(III)-S(IV) complex, but this reaction has not yet been explored and no definite knowledge exists about the nature of the complex. Both FeOHSO 3 and FeSO 3 + may be formed. In order to allow an analysis of the product yields it will be assumed that Fe(OH) 2 + reacts like Fe(OH) 2+ so that both species can be combined. The upper part of Fig. 14  In contrast to the experimentally observed rise in the yield of dithionate with increasing [S IV ] 0 Kraft and van Eldik found the yield of sulfate to stay nearly constant, 15 decreasing slightly from 0.33 to 0.26 mmol dm À3 . If the results for sulfate were correct, the sum of both product yields would significantly exceed the limit of 0.25 mmol dm À3 mandated by the reaction mechanism (cf. eqn (10a)). It appears, therefore, that the data for sulfate are spoiled by the presence of an impurity introduced with one of the solutions used to make up the reaction mixture. The occurrence of dithionate as an impurity is rather unlikely so that the measured concentrations of dithionate are taken to provide true yields.
In the foregoing, the reaction of SO 3 À radicals with the FeSO 3 + complex was shown to be the only source of dithionate,  but the extended reaction mechanism would allow this product to be formed also in reactions of SO 3 À radicals with one of the two higher complexes. This possibility was explored by means of computer simulations. The individual rate coefficients used in this case were obtained by an appropriate adjustment to the lower ionic strength m = 0.006 in these experiments. It was confirmed that at low [S IV ] concentrations, where FeSO 3 + contributes significantly to the mix of Fe(III) species, reaction (4) remains the most important source of dithionate. The rise of the dithionate yield with increasing [S IV ] 0 must then be due to a competing reaction (leading to sulfate). Reaction (3a) will be unimportant at pH 3.4 because the concentration [Fe 3+ ] is too small, but reaction (3b) fills the need if the rate coefficient is k 3b E 3.0 Â 10 7 dm 3 mol À1 s À1 . The value corresponds approximately to that obtained by extrapolation of the ionic strength to m = 0.006. The equivalent reaction (3c) of SO 3 À with Fe(OH) 2 + need not be invoked. A complete set of computer calculations then reveals that reactions (3b) and (4)  This result does not preclude the participation of higher complexes in the production of dithionate, provided sulfate or another product is formed in a parallel reaction. Trial calculations showed that the 1 : 2-complex is less likely a source of dithionate than the 1 : 3-complex, which gains prominence at the high end of the S(IV) concentration range. The addition of reaction (4b) with a rate coefficient of k 4b E 1.2 Â 10 7 dm 3 mol À1 s À1 would also provide good agreement with the measured dithionate yields, provided the reaction consisted of two channels, one leading to dithionate with a yield of 65%, the other one leading to sulfate with a yield of 35%. This partitioning determines the plateau of the dithionate concentration at high S(IV) concentrations. It will be clear that the limited data on dithionate formation reported by Kraft and van Eldik 15 cannot give definitive answers on all possible routes to dithionate production. However, the recognition that reaction (3b) is more likely in this mechanism than (3a) would be in accord with the conclusions reached in the preceding discussion of the apparent initial first order rate coefficients determined by the authors.

Conclusions
Three iron-sulfito complexes are formed by the successive addition of HSO 3 À to FeOH 2+ . These processes occur rapidly.
The subsequent slow reaction is due to the decomposition of the complexes and the formation of SO 3 À radicals. The decomposition of the 1 : 1-complex has been documented, the disintegration of the 1 : 2-and the 1 : 3-complexes are found to be slower. The mechanism in Table 1  Although it was possible to estimate rate coefficients of the reactions involved, the true values will have to be determined in future studies. One of the problems that will require closer attention is the ionic strength dependence of the stability constants of the complexes as well as that of the rate coefficients of the individual reactions.
Finally it important to note that the decomposition of the iron-sulfito complexes discussed in this study initiates the oxidation of S(IV) also in the presence of oxygen so that the same stability constants and decomposition rates of the complexes will be applicable. But in that case the SO 3 À radicals are converted to SO 5 À radicals and the subsequent mechanism takes a different course.

Conflicts of interest
There are no conflicts of interest to declare.