1. Introduction

The kinetics of oxidation of [Fe(CN)₆]⁴⁻ by IO₃⁻ in the pH 1.77 – 2.65 range, under conditions where [Fe(CN)₆]⁴⁻ is in vast excess has been reported previously[1]. It was observed that the reaction is autocatalytic whether IO₃^- or [Fe(CN)₆]⁴⁻ is in vast excess. This is in agreement with an earlier report[2]. Nonetheless, rate constants were measured from the linear parts of pseudo first order plots with the reductant in vast excess over that of the oxidant. The closely related reaction between BrO₃^- and [Fe(CN)₆]⁴⁻ has also been reported and has shown a similar complexity[3,4]. The kinetics of this reaction in the relatively high [H⁺] (0.05 – 0.5 M) was found to be partially autocatalytic. Autocatalysis is believed to be caused by Br₂ formed from the relatively fast reaction between Br⁻ and BrO₃⁻ in the employed [H⁺] range[3]. The Br₂ − [Fe(CN)₆]⁴⁻ reaction is shown to be very fast[3]. The kinetics of the BrO₃⁻ − [Fe(CN)₆]⁴⁻ reaction in the pH 3.6 – 5.8 range is also complex. The complexity of this reaction in this [H⁺] range, is claimed not to arise from the involvement of Br₂, which is not formed in the BrO₃^- - Br^- system at this pH range[4,5], but rather from the involvement of aquahexacaynoferrate(II) ([Fe(CN)₅(H₂O)]³⁻). Aquahexacaynoferrate(II) is formed very slowly in acidic solutions by replacing a CN^- by an H₂O and can be induced by light[6]. Deliberate addition of [Fe(CN)₅(H₂O)]³⁻ has shown a remarkable effect on the BrO₃^- − [Fe(CN)₆]⁴⁻ reaction[4].

Autocatalysis in IO₃^--[Fe (CN)₆]⁴⁻ reaction most likely arises from reaction between the product iodide and iodate in acidic solutions. The lower redox potential of I^- facilitates its oxidation to I₂ and/or I₃⁻ by IO₃⁻[7,8] at the pH values employed. The effect of deliberately added I^- on the IO₃⁻ -[Fe(CN)₆]⁴⁻ reaction has been reported[9]. It was found that added I⁻ accelerates this reaction considerably and the rate of reaction increases with increasing [I⁻] even at pH values where the reaction does not take place in absence of iodide. It has known that I₂ reacts very rapidly with [Fe(CN)₆]⁴⁻[10]. In recent years there has been a lot of interest and research activity in oscillating reactions. The system IO₃⁻ − SO₃²⁻ − [Fe(CN)₆]⁴⁻ is oscillatory. In these types of reactions it is important to know the rate constant of the likely processes. These are used to build models for oscillating reactions[11]. In this study we report the kinetics of both the uncatalized and the autocatalytic processes in the IO₃⁻ − [Fe(CN)₆]⁴⁻ reaction with iodate in large excess.

2. Experimental

All the chemicals were reagent grade and were used as received. Stock solutions, buffer (HSO₄⁻/SO₄²⁻) and solutions of K₄Fe(CN)₆.3H₂O were freshly prepared and used immediately as described earlier[1]. The absorption of the product [Fe(CN)₆]³⁻ was monitored at λ_max 420 nm using a Perkin Elmer Model Lambda 25 or a Shimadzu 1800 UV/VIS absorption spectrophotometer both equipped with a thermostatted cell-holder. The absorbance-time traces were recorded on XY recorder. The pH of the reaction solutions was measured using an ELICO LI 120 pH meter. The kinetics of the reaction was investigated under constant reaction conditions with [IO₃^-] in vast excess over that of [(Fe(CN)₆)^4-]. Both reactants concentrations as well as the pH were varied.

3. Results and Discussions

The stoichiometry of the IO₃^--[Fe(CN)₆]⁴⁻ is well established and is given by Eqn.(1).

(1)

It was previously reported that the IO₃⁻− [Fe(CN)₆]⁴⁻ reaction is autocatalytic[1,2]. The absorbance- time trace for the IO₃⁻ − [Fe(CN)₆]⁴⁻ reaction does not display the exponential growth of [Fe(CN)₆]³⁻ expected for a first order reaction. A similar behavior was observed in the [Fe(CN)₆]⁴⁻ − BrO₃⁻ reaction at relatively high [H⁺][3]. Plots of ln(A∞ -A_t) versus time, where A∞ and A_t are absorbance values at infinity and time t respectively, show marked deviation from linearity as shown in Fig. 1. The deviation from linearity of the plots depends on the initial concentrations of IO₃⁻, [Fe(CN)₆]⁴⁻ and [H⁺]. The higher the concentration of the reactants, the shorter is the linearity of the plots. The first order rate constants for the uncatalyzed path, k_u, were obtained from the linear parts of these plots. It was found that k_u is fairly constant and does not depend on the initial concentration of [Fe(CN)₆]]⁴⁻ at fixed reaction conditions as shown in Table 1. The data of Fig. 1 is analyzed using a treatment for an autocatalytic reaction[12-14]. Plots of ln[(A_t/A∞)/(1 - A_t/A∞)] versus time are linear as shown in Fig. 2. This treatment was applied only in the range where autocatalysis becomes dominant. In the low pH range autocatalysis starts early and a nearly S-shaped form of absorbance-time curve is observed. The values of the slopes (k_obs, s^-1) obtained from Fig. 2 and similar plots are dependent on the initial concentration of [Fe(CN)₆)⁴⁻]_i. The absorbance-time data were also treated using a nonlinear curve fitting using an Origin 7.0 sigmoidal growth curve fitting program. A typical nonlinear fit for the data in Fig. 1 is shown in Figure 3. Values of k_obs obtained using both methods are within 0- 8% variation. Most of k_obs values were obtained using the non-linear curve fitting program.

Figure 1. First order plot of the IO3-- [Fe(CN)6]4- reaction, [IO3-] = 5.0 X 10-3 M, [Fe(CN)64-] = 5.4 x 10-4 M, pH = 1.53, I = 1.0 M and T = 25.0 ℃

Figure 2. Data in Fig. 1 plotted using ln[At/A∞)/(1 - At/A∞)] versus time

Figure 3. Data in Fig. 1 plotted using Boltzmann sigmoidal growth for a non-linear curve fitting program

Table 1. Kinetic data for the for the uncatalyzed [Fe(CN)6 ]4- - IO3- reaction at 25.0 ℃, I = 1.0 M

Table 2. Kinetic data for the catalyzed [Fe(CN)5]4- − IO3- reaction at 25.0 ℃, I = 1.0 M

The value of k_obs varies with the [Fe(CN)₆)⁴⁻]_i, at fixed reaction conditions, according to Eqn. (2). The values of k_u obtained from plots o Eq. (2) are in fairly good agreement with values obtained directly from linear portions of the first order plots. The rate constants k_u and k_a are rate constants for the uncatalyzed and the autocatalytic reactions pathways respectively. Values of k_a were also calculated from Eqn. (2) using known values of k_obs, k_u and [Fe(CN)₆⁴⁻]_i.

(2)

Table 1 shows that k_u varies linearly with [IO₃^-] at fixed reaction conditions. The results in Table 1 also show that k_u is pH-dependent. The dependence of k_uc on [H⁺] seems to be complex as a plot of log k_u versus log [H⁺] has a slope ≈1.3. The rate law for the uncatalyzed oxidation of [Fe(CN)₆]⁴⁻ by IO₃⁻ is given by Eqn. (3) at fixed pH, ionic strength and temperature. The form of this rate law is the same as that reported before[1].

(3)

Hexacyanoferrate(II) is known to be extensively protonated in aqueous acidic solutions[15].

The thermodynamic dissociation constants for the mono- and diprotonated species ([HFe(CN)₆]³⁻ and [H₂Fe(CN)₆]²⁻ respectively) have been determined as 5.25 x 10^-5 and 4.3 x 10^-3 at 25 ℃ respectively. At 1.0 M ionic strength and 25 ℃ the values of the dissociation constants are 4.68 x 10^-3 and 0.32 for the mono and diprotonated species respectively[16]. The iodate ion is appreciably protonated in aqueous acidic solutions and has a thermodynamic dissociation constant of 0.16 at 25 ℃[17]. The value of the dissociation constant at I = 1.0 M, and T = 25 ℃ is reported as 0.514 M[18].

The major reaction steps for the uncatalyzed path are given by Eqns. 4 - 11.

(4)

(5)

(6)

(7)

(10)

From the above equilibria and reactions the rate law in Eq. (10) is derived.

(11)

Since the reaction is first order in both [Fe(CN)₆⁴⁻]_i and [IO₃⁻] , the second order rate constant k₂ (k2 = k_u/[IO₃⁻] varies with [H⁺] according to Eqn. (11).

(12)

Under conditions where (1 + K₁[H⁺]) >> (1 + K₁K₂[H⁺]²) (1 + K₃[H⁺]), Eqn. (12) takes the form of Eqn. (13).

(13)

(14)

Eqn. (13) may be rearranged to the form of Eqn. (14). A polynomial of the second degree fit of a plot of k₂(1 + K₁[H⁺]) vs [H⁺] is shown in Fig. 4. From the polynomial fit (Fig.4) the value (k₇K₁ + k₈K₃) = (81.4 ± 17.2) and (k₉K₁K₂ + k₁₀K₁K₃) = (2.01 ± 0.07) x 10⁴. These values are approximately twice as much as the previously determined values[1]. It was previously reported that the rate constant, contrary to expectation, decreases with increasing ionic strength. This may be rationalized by recalling that the protonation constants K₁ and of [Fe(CN)₆]^4- (for the formation of [HFe(CN)₆]^3-, [H₂Fe(CN)₆]^2- respectively) are lower at higher ionic strength values. Thus values of 1.49 x 10⁴ M^-1and 2.14 x 10² M^-1 are reported for K₁at infinite dilution and I = 1.0 M respectively[15,16].

Figure 4. A second degree polynomial plot of k2(1 + K1[H+]) vs [H+], [IO3-] = 5.0 x10-3, I = 1.0 M, T = 25.0 ℃

Figure 5. Dependence of ka on [H+], [IO3-] = 5.0 x10-3/ M, I = 1.0/ M, T = 25.0 ℃

The dependence of k_obs on [(Fe(CN)₆)⁴⁻]_i is indicative of the relationship between the concentration of the iodide product and the [(Fe(CN)₆)⁴⁻]_I; the higher the concentration of the latter, the higher would be the rate of formation of iodide. The iodide produced would react with IO₃⁻ according to Eqn.4 to generate iodine that would react rapidly with [(Fe(CN)₆)]^4- (Eqn. 5). Values of k_a at several pH values are shown in Table 2 at constant [IO₃⁻], ionic strength and temperature. The dependence of k_a on [H⁺] (Fig. 5) shows a linear plot of k_a versus [H⁺] with an almost zero intercept.

The autocatalytic pathway is caused by a product generated by the uncatalyzed reaction. The I^- produced in the direct reaction between [Fe(CN)₆]⁴⁻ and IO₃⁻ in acidic solutions (Eqn.1) reacts with IO₃^- to produce a more reactive species with [(Fe(CN)₆)]^4- than IO₃^- such as those in Eqn. (15).

(15)

The reaction may also proceed to produce I₂ which also reacts very rapidly with [Fe(CN)₆]⁴⁻ and this may cause autocatalysis in the [Fe(CN)₆]⁴⁻− IO₃⁻ reaction[10]. The IO₃⁻- I⁻ reaction is thus the rate determining step and the catalyzed reaction is simply an indirect method for the measurement of the kinetics of this reaction under condition of low [I⁻]. The kinetics of the IO₃⁻− I⁻ reaction has been studied extensively and different forms of the rate law has been reported[19]. The most accepted rate law is the one showing first order dependence on [IO₃⁻] and second order in both [I⁻] and [H⁺]. Results in Table 2 and Fig.5 show that k_a varies linearly with [H⁺] and is described by Eqn. (16).

In conclusion the iodate – hexacyanoferrate(II) reaction is partially autocatalytic whether the reductant or the oxidant is in excess. Autocatalysis becomes important at high reactant concentrations and low pH. Autocatalysis may be caused by I(III), I(I) and/or I₂ that are produced during IO₃⁻ - I⁻ reaction. At low reactants concentration and high pH autocatalysis only appears at late stages of the reaction. Qualitative experiments showed that the deliberate addition of I⁻ speeds up the reaction and it proceeds at a measureable at pH values it would not usually take place.

Acknowledgements

Y. S would like to thank Professor Ahmed A. Abdel-Khalek of the Department of Chemistry, Cairo University, Beni-Suef Branch, Egypt, for his help with some kinetic runs and Professor J. F. Perez-Benito of the Department of Chemistry, University of Barcelona, Portugal for useful information.