The cerium-catalyzed Belousov-Zhabotinsky oscillating reaction [1-3] and its variants (Fe [2,3], Ru [4,5], Mn [6-8]) are inherently connected to the chemistry of bromine oxoacids HBrO_x. The growing interest in nonlinear chemical systems [9-11] has provided strong incentives to study bromine chemistry, and especially the disproportionation of bromous acid has been studied in great detail [12-26]. The bromine chemistry of the Belousov-Zhabotinsky reaction (BZR) involves hypobromous acid HOBr (1), bromous acid HOBrO (2) and bromic acid HBrO₃ (3), and the disproportionation reaction of bromous acid (R4) is a key step.

H⁺ + Br^- + HOBrO ⇄ 2 HOBr (R2)

2 H⁺ + Br_- + BrO₃ ^- ⇄ HOBr + HOBrO (R3)

2 HOBrO ⇄ HOBr + H⁺ + BrO₃^-

It is generally agreed that hypobromous acid (pK_a(HOBr)=8.59 [27,28]) and bromous acid (pK_a (HOBrO)=3.43 [29]) are not dissociated at pH values typical for the BZR. In contrast, it has been assumed that bromic acid is dissociated under BZR conditions even though the acidity of bromic acid has not been well established. Experimental pK_a(3) values of 1.87 [30], 0.7 [31], and -0.29 [32] were reported and, most recently, Cortes and Faria concluded that pK_a(3) < -0.5 [33]. We wrote recently [34] that it will be important to firmly establish pK_a(3) because this value decides whether reactions R3 and R4 should be replaced by reactions R3’ and R4’, respectively, or whether reactions R3’ and R4’ need to be considered in addition to reactions R3 and R4.

HOBrO₂ ⇄ H⁺ + BrO₃^-

H⁺ + Br^- + HOBrO₂ ⇄ HOBr + HOBrO (R3’) = (R3) + (A(3))

2 HOBrO ⇄ HOBr + HOBrO₂

To explore the consequences of the acidity of bromic acid in Belousov-Zhabotinsky reactions, we considered four cases with greatly different concentrations and/or ratios of sulfuric acid and bromate. In Case 1, molar concentrations of H₂SO₄ and of KBrO₃ were used as a simple case of R₀ = [H₂SO₄]₀/[BrO₃ ^-]₀ = 1. In Case 2, we simulated the situation with 0.5 M H₂SO₄ and 0.1 M KBrO₃ (R₀=5). This case models the concentrations (0.567 M H₂SO₄, 0.089 M KBrO₃) we used in our studies of a variant of the ferroin-catalyzed BZR described by Keusch [6-8,35]. In Case 3, we studied the situation with 1.0 M H₂SO₄ and 0.1 M KBrO₃ (R₀ = 10), which closely mimics the Ce-catalyzed BZR [36] reported by Shakhashiri (0.9 M H₂SO₄, 0.075 M KBrO₃). Case 4 with 1.5 M H₂SO₄ and 0.05 M KBrO₃ (R₀ = 30) closely mimics the Mn-catalyzed BZR [37] reported by Shakhashiri (1.6 M H₂SO₄, 0.06 M KBrO₃).

H₂O ⇄ H⁺ + OH^-, K_w                (1)

H₂A ⇄ H⁺ + HA^-, K_a1,1             (2)

HA^- ⇄ H⁺+ A^2-, K_a1,2                (3)

HB ⇄ H⁺ + B^-, K_a2                    (4)

We evaluated the system of differential equations describing the equilibria of equations 1-4 with Mathematica [38,39]. K_w denotes the ion product of water (K_w=10^-14). H₂A denotes the diprotic sulfuric acid H₂SO₄ and we employed acidity constants pK_a1,1=-3 (a lower bound) and pK_a1,2=+2 for the first and second dissociations of sulfuric acid [39,40]. HB denotes the monoprotic acid HBrO₃ and we evaluated the four cases for integer values of pK_a2 between +3 and -3 to cover the entire range of reported experimental pK_a2 values (vide supra). The most pertinent results of the simulations are summarized in table 1 [39,40]. In supporting information we provide more extensive (Tables S1-S4) and these also include the results of the simulations without consideration of the second dissociation of sulfuric acid. In the present context it suffices to state that the protonation state of bromate is essentially the same irrespective as to whether the second dissociation of sulfuric acid is considered or neglected.

We begin our analysis of the data in table 1 by examination of the ratio R_P = [HBrO₃]/[BrO₃^-]. The measurements of the acidity of bromic acid gave values in the range pK_a(3)=0.5 ± 1.5, and we find that the RP values fall between 1.5 and 0.5 for pka(3)=0 and they fall between 2.9 and 14.6 for pK_a(3)=1. For all cases, neither bromic acid nor bromate is the dominant species (95%, R_P > 19, R_P < 0.05) over a range of at least three pK_a(3) units. This result leads to the important conclusion that reactions R3’ and R4’ must be considered in addition to reactions R3 and R4 in kinetic models of the BZ reaction with bromate.

It is qualitatively clear that the equilibrium pH value will be more sensitive to the value of pK_a(3) the lower one selects the ratio R₀ = [H₂SO₄]₀/[BrO₃ -]₀. The quantitative data in table 1 support this notion in that the values ΔpH = pH[pK_a(3)=+3] – pH[pK_a(3)=-3] decrease as R₀ increases. For Case 1 with R₀=1 the ΔpH value is as large as one full pH unit. As with Case 1, Case 5 is characterized by R₀=1 but in Case 5 this ratio is realized with much lower (one tenth) initial concentrations of sulfuric acid and bromate. Detailed results for Case 5 are listed in table S5 and the most pertinent data appear in table 1. While ΔpH ≈ 0.6 is significantly reduced in Case 5 as compared to Case 1, the ΔpH value remains large and of a magnitude that allows for experimental approaches to the determination of pK_a(3) via pH measurements as a function of R₀. We explored this notion for pK_a(3)=0 and two scenarios: In Scenario 1 the initial concentration of sulfuric acid is fixed to [H₂SO₄]₀ = 1.0 M while [BrO₃ ^-]₀ is allowed to vary between 0.0005 and 4 M. In Scenario 2 the initial bromate concentration is fixed to [BrO₃ ^-]₀ = 0.1 M and [H₂SO₄]₀ varies from 0.1 M to 5 M. The numerical results are summarized in tables S6 and S7, respectively, and they are illustrated in figure 1. The figure shows in a compelling fashion that variations of R₀ result in pH variations that are large. Especially Scenario 2 presents a promising approach to measure pK_a(3). We hope that this editorial will encourage such measurements by suitably equipped research groups, and we will be happy to perform the mathematical modeling necessary to extract the value of pK_a(3) from such experimental data sets.

Figure 1: Simulations of pH as a function of log(R0) for Scenario 1 (1.0 M H₂SO₄, variation of KBrO₃) and Scenario 2 (variation of H₂SO₄, 0.1 M KBrO₃) for pKa(3) = 0.