thermodynamics and kinetics of some inorganic

THERMODYNAMICS AND KINETICS OF SOME INORGANIC REACTIONS OF IODINE Guy Schmitz

Faculté des Sciences Appliquées, Université Libre de Bruxelles, CP165, Av.F.Roosevelt 50, 1050 Bruxelles, Belgium, E-mail: [email protected]

Abstract

We review and discuss thermodynamic and kinetic studies related to the components of the reaction IO3- + 5 I- + 6 H+

3 I2 + 3 H2O in acidic solutions. A special

attention is devoted to the reaction IO2H + I- + H+

2 IOH. It is not an elementary

reaction, I2O.H2O is an important intermediate in its mechanism and the rate in the forward direction is diffusion controlled. From the discussion of its kinetics it is concluded that the value of the standard Gibbs energy of formation of IO2H is equal to - 95 kJ/mol. The rate constants of the iodine species reactions in the conditions of the oscillating Bray-Liebhafsky and chlorite-iodide reactions are deduced from independent measurements.

Physical Chemistry 2002 - Belgrade, September 2002.

2

Introduction

The inorganic reactions of iodine are of considerable interest in two main fields, oscillating chemical systems and the safety of nuclear reactors. They are parts of the mechanisms of the Bray-Liebhafsky oscillating reaction1-7, the Briggs-Rauscher reaction8-10 and the chlorite-iodide oscillators2, 11, 12. In the case of a water-cooled nuclear reactor failure, radioactive iodine is one of the more toxic products released in the environment. The hydrolysis of iodine giving I(+1) and its disproportionation to non-volatile iodide and iodate are important reactions for the estimation of the quantity of iodine released under such circumstances13, 14.

The kinetics models of these systems include a large number of elementary steps, or supposed so, whose kinetics constants are unknown. They are adjusted to obtain a good fit between the calculated and experimental results. However, it is well known that with a large number of adjustable parameters such a good fit is neither a proof of the correctness of the rate constants nor of the validity of the model. Taking as an example the reaction IO2H + I- + H+ → 2 IOH in models of the chlorite-iodide reaction, we have found in the literature two different rate laws, r = k [IO2H][I-] and r = k' [IO2H][I-][H+], with k' values ranging from 1 106 to 2 1010 M-2s-1. It is necessary to obtain kinetic information about the components of these complex systems before studying a global model. Here we consider the components of reaction (1). IO3- + 5 I- + 6 H+

3 I2 + 3 H2O

(1)

Its general mechanism is not entirely elucidated but it is accepted that it can be split in the three reactions (2) to (4). The sum (2) + (3) - 3 (4) gives (1). These reactions are themselves not simple ones and we will discuss their mechanisms and apply the rules ensuring the thermodynamic consistency of reactions mechanisms15. IO3- + I- + 2 H+

IO2H + IOH

(2)

3

IO2H + I- + H+ I2 + H2O

2 IOH

(3)

IOH + I- + H+

(4)

Review and discussion of former works

1. The hydrolysis of iodine

Reaction (4) is the best known among the three components of reaction (1). From a detailed analysis of the large number of determinations of its equilibrium constant found in the literature16, we propose K4° = (5.2 ± 0.2) 10-13 at 25°C (The superscript ° means values extrapolated at zero ionic strength). Between 0 and 60 °C, the measurements are well represented by R ln K4° = - 63 700 / T - 21.5 J/mol.K with an estimated uncertainty less than 20%. This value of K4° at 25°C with the well known values of the Gibbs energy of formation ∆Gf,298.15(I2 aq) = 16.45 kJ/mol and ∆Gf,298.15(I-) = -51.57 kJ/mol17, 18 give ∆Gf,298.15(IOH) = - 99.0 kJ/mol in perfect agreement with the literature value. Eigen and Kustin19, studying the kinetics of reaction (4) by temperature-jump spectrophotometry, obtained r+4 = 3.0 [I2] M-1s-1 at 20°C and pH = 4 to 5. Miyake et al.20 deduced the rate of iodine hydrolysis from measurements of the rate of iodine vapors adsorption in borate buffers at pH = 4 to 6. They obtained r+4 = 3.4 109 [I2][OH-] M-1s-1. Palmer and van Eldik21, using the temperature-jump technique, proposed still another rate law but Lengyel et al.22 showed that their interpretation of the data contains several inconsistencies and have proposed a mechanism in six steps. Furrow23 proposed the rate law r4 = 0.0018 [I2]/[H+] - 3.6 109 [IOH][I-] from kinetic experiments in sulfuric acid solutions at 25°C. All these results can be understood considering the mechanism proposed by Eigen and Kustin19 and discussed by Lengyel et al.22. In summary, reaction (4) can follow two pathways, I2 + OH-

I2OH-

IOH + I- and I2 + H2O

I2OH- + H+

IOH + I- + H+, and the rate

determining step depends on the experimental conditions. However, some

4

discrepancies between the rate constants of the elementary steps deduced from the different works should still be resolved. This is not a serious problem because, at the time scale of most of the systems considered in this work, reaction (4) is quasi at equilibrium and the only important parameter is K4.

2. Thermodynamics of reaction (1) The two most careful determinations18, 24 of the equilibrium constant of reaction (1) agree giving K1° = (1.0 ± 0.2) 1047 M-9 at 25°C. Between 0 and 60 °C, the measurements are well represented by R ln K1° = 257 810 / T + 34.9 J/mol.K. The value of K1° at 25°C and the above values of the Gibbs energy of formation give ∆Gf,298.15(IO3-) = - 135.6 kJ/mol in accordance with the literature value, - 134.9 kJ/mol17. These values of K1° and K4° give the equilibrium constant of the reaction IO3- + 2 I- + 3 H+

3 IOH. K2°K3° = K1°(K4°)3 = 1.4 1010 M-3at 25°C, a value used

later in our discussion.

3. The kinetics of the iodate-iodide reaction (Dushman reaction) We have presented previously25 a detailed kinetic study of this reaction and compared it with the other halate-halide reactions26. In summary, in acidic non buffered solutions the first steps of its mechanism are IO3- + H+

IO3H

IO3H + I- + H+

(5)

I2O2.H2O

(6)

I2O2.H2O → IO2H + IOH

(7)

-

(8)

I2O2.H2O + I →

IO2-

+ I2 + H2O

If reactions (5) and (6) are equilibria we get the classical rate law r = K5K6 [IO3-][I-][H+]2 (k7 + k8[I-]) At low iodide concentrations (< 10-7 M) the rate determining step is (7) and the order with respect to iodide is one27. At medium iodide concentrations the rate determining step is (8) and the order is two. At high iodide concentrations (> 0.01 M) reaction (6)

5

is no longer equilibrium and the order becomes less than two28. In buffered solutions, there is a catalytic effect of the anion of the buffer B- explained by additional reactions of a complex I2O2B- (see ref.25 and references therein). Many works were devoted to the determination of the acidity constant of iodic acid29. At 25°C and zero ionic strength its value is 0.157 M. At ionic strengths µ ∼ 0.2, where the following kinetic values are known, we get the estimation K5 = γ2 /0.157 = 3.1 M-1 taking γ = 0.7 for the mean activity coefficient. The kinetic constant of the iodate-iodide reaction under conditions giving the order two in iodide is well known25, 30, 31, K5K6k8 = 3.2 108 M-4s-1 at 25°C and µ = 0.2. It increases if µ decreases. Under conditions where the order in iodide is one, Furuichi and Liebhafsky32 obtained K5K6k7 = 4 700 γ4 M-3s1

at 25°C. We obtained 1 200 M-3s-1 in perchloric solutions at 25°C and 0.2 M ionic

strenght27. Under these conditions, the model of Pitzer33 gives γHI = 0.75. The parameters for γHIO3 are unknown but, if we use the value γHBrO3 = 0.72, our measurements give K5K6k7 = 4 100 γ2HIγ2HIO3, in good agreement with Liebhafsky's value.

Measuring the deviations from the classical rate law at high iodide concentrations, Margerum et al.28 concluded that k8/k-6 = 2.3 ± 0.2 M-1 and k6 = (4.8 ± 0.2) 107 M-2s-1 if µ = 0.5. A test of consistency of the above values can be done. Calculating K5K6k8 = 3.1 * 2.3 * 4.8 107 we get 3.4 108 M-4s-1 in agreement with the value obtained in the classical works. At high acidities, one observe also deviations from the classical rate law because the concentration of I2O2,H2O becomes stoichiometrically signifiant34. These experiments, made at ionic strengths in the range 0.1 - 0.5 M, give K6 = 990 M-2. If we accept with the authors that γ is nearly constant in this range, we can estimate all the rate constants: k-6 = k6 / K6 = 4.8 104 s-1, k8 = 2.3 k-6 = 1.1 105 M-1s-1 and k7 = 1 200 / K5K6 = 0.4 s-1.

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4. The disproportionation of IOH in acidic solutions

From the value of K1, we see that the reverse reaction, the disproportionation of iodine, can only be observed at pH above 7. In acidic solutions, the hydrolysis of iodine gives a very small concentration of IOH and an extremely small rate of disproportionation. In order to measure it, we must lower the I- concentration and shift the equilibrium (4) to the right. This can be done using the reactions I- + Ag+ AgI↓ or I- + Hg(II)

HgI+. With Ag+ the main reaction is

I2 + Ag+ + H2O

AgI↓ + IOH + H+

followed by reaction (-3). Furrow23 obtained the rate law r-3 = k-3 (IOH)2 with k-3 = 25 M-1s-1 at 25°C independent on the acidity for perchloric acid concentrations between 0.025 and 0.1 M or sulfuric acid concentration equal to 0.58 M. Lengyel et al.35 obtained a similar value, k-3 = 22 M-1s-1, at pH = 1.8. On the other hand Bell and Gelles36 proposed an equilibrium constant K9 = 35 at 25°C for the reaction IOH + H+

IOH2+

(9)

a value generally accepted. However, with such a large value of K9, it is strange that the rate of disproportionation of IOH is independent on the pH at high acidities. Thus we have undertaken a new experimental work37, found a much lower value of K9 than Bell and Gelles, about 0.5 at 25°C and 2 at 40.2°C, and confirmed the results of Furrow. We will now discuss the mechanism of reaction (3) on the basis of the wellestablished rate law r-3 = k-3 (IOH)2.

Mechanism of reaction (3) and Gibbs energy of formation of IO2H

Reaction (3) is not an elementary reaction. The kinetics of IOH disproportionation in buffered solutions38 and the decreases of its rate constant when the temperature increases37 suggest that I2O is an intermediate in its mechanism. This was also an essential assumption in our mechanism of the Bray-Liebhafsky reaction3. Depending on the order of addition of H+ and I-, we can write down two mechanisms for reaction (3).

7

Mechanism A IO2H + H+

IO2H2+

IO2H2+ + I-

I2O.H2O

I2O.H2O

2 IOH

Mechanism B IO2H + I-

I2O.OH-

I2O.OH- + H+ I2O.H2O

I2O.H2O

2 IOH

Mechanism A gives the rate law rA =

k 1A k 2 A k 3A (IO 2 H )(I − )( H + ) − k −1A k −2 A k −3A (IOH ) 2 k −1A ( k −2 A + k 3A ) + k 2 A k 3A (I − )

or, introducing K3 = k1Ak2Ak3A/k-1Ak-2Ak-3A, rA =

k −1A k −2 A k −3A [ K 3 (IO 2 H )(I − )( H + ) − (IOH ) 2 ] k −1A ( k −2 A + k 3A ) + k 2A k 3A (I − )

As the rate in the reverse direction is given by 25 (IOH)2, we must have k-1A(k-2A + k3A) >> k2Ak3A(I-) and k-2Ak-3A = 25 (k-2A + k3A). The rate expression reduces to rA = 25 [K3(IO2H)(I-)(H+) - (IOH)2] The above values of the Gibbs energies of formation and the value ∆Gf,295.15(IO2H) = -75 kJ/mol proposed by Stanisavljev39 give RT ln K3 = 71.3 kJ/mol and K3 = 3 1012 M-1. The rate constant in the forward direction so calculated is much larger than allowed for a diffusion controlled process. As the work of Furrow23 suggests that this rate constant is actually very large, we have looked for the maximum value of K3 allowed by mechanism A. Introducing k-2Ak-3A = 25 (k-2A + k3A), its expression becomes K3 =

k 1A k 2 A k 3A k −1A 25 k −2 A + k 3A

8

The last factor is maximum if k3A >> k-2A. For diffusion controlled processes the value of k1A and k2A are about 1010. The value of k-1A cannot be small because we must satisfy the condition k-1A>> k2A (I-) and because if the k1A/k-1A ratio was too large IO2H would be entirely protonated in the considered range of acidities. This is in contradiction with the kinetic studies of its reactions23, 40. With mechanism A, the maximum allowed value of K3 is (k1A/k-1A)×1010 /25 ≤ 2 109 M-1 giving ∆Gf,295.15(IO2H) ≤ -93 kJ/mol.

Similarly, mechanism B gives the rate law rB =

k −1B k −2 B k −3B [ K 3 (IO 2 H )(I − )( H + ) − (IOH ) 2 ] + k −1B ( k −2 B + k 3B ) + k 2 B k 3BA ( H )

with the conditions k-1B(k-2B + k3B) >> k2Bk3B(H+) and k-2Bk-3B = 25 (k-2B + k3B). K3 is now given by K3 =

k 1B k 2 B k 3B k −1B 25 k −2 B + k 3B

The maximum allowed value of K3 with mechanism B is lower than with mechanism A because the maximum value of k1B is a little less (about 5 109) and the condition on k-1B is more stringent.

Kinetics and thermodynamics of reaction (2)

The kinetics of reaction (2) in the forward direction is the kinetics of the Dushman reaction at low iodide concentrations. We have seen that, under these conditions, reactions (5) and (6) are at equilibrium. Introducing the backward reaction we get the rate law r = K 5 K 6 k 7 (IO 3− )(I − )( H + ) 2 − k −7 (IO 2 H )(IOH ) with K5°K6°k7 = 4 400 ± 400 M-3s-1. We can now estimate the rate constant in the reverse direction using K2° = K5°K6°(k7/k-7) = 4 400/k-7.

9

Having K2°K3° = 1.4 1010 M-3 and K3° = γ2 K3 < 2 109 M-1, we get K2° > 7 M-2 and k7

< 630 M-1s-1. The experimental value of Furrow23 is 240 M-1s-1 independent on the

acidity in H2SO4 = 0.09 to 0.36 M. Notziczius et al.40 obtained 350 M-1s-1 in H2SO4 0.05 M and lower values at higher acidities. The agreement between our a priori estimation and these experimental values strengthens our discussion. A perfect agreement could been obtained taking K3° = 8 108 M-1 and ∆Gf,295.15(IO2H) = -95 kJ/mol.

A model of reaction (1) under the conditions of the Bray-Liebhafsky reaction

We now summarize the above discussions and present a model that can be used in acidic solutions with iodide concentrations lower than 10-7 M so that reaction (8) can be neglected. The values are given at 25°C with the second as time unit. They are estimated either from measurements at µ = 0.2 M or from thermodynamical values using γ = 0.7. In order to simplify the model, the fast equilibria are included in the other steps when there is no consequence on the results of the simulations. Reaction (10) is either the sum (1A)+(2A) or (1B)+(2B), both giving the same rate law r10 = k10(IO2H)(I-)(H+) - k-10(I2O). If reaction (4) cannot be considered as equilibrium, the best rate law seems to be r4 = 2 10-3 (I2)/(H+) - 2 109 (IOH)(I-)

10

Reactions IO3- + H+

k+ IO3H

IO3H + I- + H+ I2O2.H2O

I2O.H2O

(5) Equilibrium, K5 = 3.1

I2O2.H2O

IO2H + IOH

IO2H + I- + H+

k-

I2O.H2O

2 IOH

(6) 4.8 107

4.8 104

(7) 0.4

240

(10) 1010

25 K11

(11) Rate constants unknown with k11 larger than k-10.

I2 + H2O

IOH + I- + H+

(4) Usually at equilibrium, K4 = 5.2 10-13 / γ2 ~ 1 10-12

This model is now used successfully for the simulation of the kinetics of the oxidation of iodine by hydrogen peroxide7 at 25°C. The results will be published soon. The next step is to evaluate the rate constants at higher temperature to improve our set of rate constants for the Bray-Liebhafsky reaction. The effect of the temperature on the equilibrium constants K1 to K5 and on the Dushman reaction is rather well known. The rate constant controlled by diffusion cannot increase much. However, some values like K6 are known only at 25°C and remain adjustable parameters.

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