Table I: Reactions and rate constants of the MBM mechanism of the cerium catalysed BZ reaction

Table I:

Reactions and rate constants of the MBM mechanism of the cerium catalysed BZ reaction

No. Reaction Rate Constants

Forward Reverse

Inorganic reactions

R1 Br^- + HOBr + H⁺ ŕ Br₂ + H₂O 8×10⁺⁹ M^-2 s^-1 110 s^-1

R2 Br^- + HBrO₂ + H⁺ ŕ 2 HOBr 2.9×10⁺⁶ M^-2 s^-1 2.0×10^-5 M^-1 s^-1

R3 Br^- + BrO₃^- + 2 H⁺ ŕ HOBr + HBrO₂ f(conc.) a) M^-3 s^-1 3.2 M^-1 s^-1

R4 HBrO₂ + H⁺ ŕ H₂BrO₂⁺ 2×10⁺⁶ M^-1 s^-1 1.0×10⁺⁸ s^-1

R5 HBrO₂ + H₂BrO₂⁺ ŕ HOBr + BrO₃^- + 2 H⁺ 1.7×10⁺⁵ M^-1 s^-1 0

R6 HBrO₂ + BrO₃^- + H⁺ ŕ Br₂O₄+ H₂O 48 M^-2 s^-1 3.2×10⁺³ s^-1

R7 Br₂O₄ ŕ 2 lBrO₂ 7.5×10⁺⁴ s^-1 1.4×10⁺⁹ M^-1 s^-1

R8 Ce³⁺ + lBrO₂ + H⁺ ŕ Ce⁴⁺ + HBrO₂ 6.0×10⁺⁴ M^-2 s^-1 1.3×10⁺⁴ b) M^-1 s^-1

R9 2 BrO₃^- + 2 H⁺ ŕ 2 HBrO₂ + O₂ 6.0×10^-10 M^-3 s^-1 0

R10 lBrO₂ ŕ 1/2 Br₂+O₂ 0.06 s^-1 0

Reactions in the
BrMA subsystem

R11 BrMA + Ce⁴⁺ ŕ BrMAl + Ce³⁺+ H⁺ 0.1 M^-1 s^-1 400 M^-2 s^-1

R12 2 BrMAl ŕ BrEETRA + Br^- + CO₂ + H⁺ 1×10⁺⁹ M^-1 s^-1 0

R13 BrMA ŕ BrMA(enol) 1.2×10^-2 s^-1 800 s^-1

R14 BrMA(enol) + Br₂ ŕ Br₂MA + Br^- + H⁺ 3.5×10⁺⁶ M^-1 s^-1 0

R15 BrMA(enol) + HOBr ŕ Br₂MA + H₂O 1.1×10⁺⁶ M^-1 s^-1 0

R16 BrMAl + lBrO₂ ŕ BrMABrO₂ 2×10⁺⁹ M^-1 s^-1 0

R17 BrMABrO₂ ŕ OA + HOBr + Br^- + CO₂ + H⁺ 0.62 s^-1 0

R18 BrMABrO₂ ŕ BrTA + HBrO₂ 0.46 s^-1 0

R19 BrTA ŕ Br^- + MOA + H⁺ 1.5 s^-1 0

R20 MOA + Ce⁴⁺ + H₂O ŕ OA + Ce³⁺ + COOHl + H⁺ 7.0×10⁺³ M^-1 s^-1 0

R21 OA + Ce⁴⁺ ŕ COOHl + Ce³⁺ + CO₂ + H⁺ 28 M^-1 s^-1 0

R22 2 COOHl ŕ OA 5×10⁺⁹ M^-1 s^-1 0

R23 COOHl + Ce⁴⁺ ŕ Ce³⁺ + CO₂ + H⁺ 1×10⁺⁷ M^-1 s^-1 0

R24 COOHl + BrMA ŕ MAl + Br^- + CO₂ + H⁺ 1×10⁺⁷ M^-1 s^-1 0

R25 COOHl + BrMAl ŕ BrMA + CO₂ 3×10⁺⁹ M^-1 s^-1 0

R26 COOHl + lBrO₂ ŕ HBrO₂ + CO₂ 5×10⁺⁹ M^-1 s^-1 0

Reactions in the
MA subsystem

R27 MA + Ce⁴⁺ ŕ MAl + Ce³⁺ + H⁺ 0.23 M^-1 s^-1 2.2×10⁺⁴ M^-2 s^-1

R28 2 MAl ŕ ETA 3.2×10⁺⁹ M^-1 s^-1 0

R29 MA ŕ MA(enol) 2.6×10^-3 s^-1 180 s^-1

R30 MA(enol) + Br₂ ŕ BrMA + Br^- + H⁺ 2.0×10⁺⁶ M^-1 s^-1 0

R31 MA(enol) + HOBr ŕ BrMA + H₂O 6.7×10⁺⁵ M^-1 s^-1 0

R32 MAl + lBrO₂ ŕ MABrO₂ 5×10⁺⁹ M^-1 s^-1 0

R33 MABrO₂ ŕ MOA + HOBr 0.55 s^-1 0

R34 MABrO₂ ŕ TA + HBrO₂ 1.0 s^-1 0

R35 MAl + BrMAl ŕ Br^- + EETA + H⁺ 2×10⁺⁹ M^-1 s^-1 0

R36 MAl + COOHl ŕ MA + CO₂ 4×10⁺⁹ M^-1 s^-1 0

R37 TA + Ce⁴⁺ ŕ TAl + Ce³⁺ + H⁺ 0.66 M^-1 s^-1 1.7×10⁺⁴ M^-2 s^-1

R38 2 TAl ŕ CO₂ + EEHTRA + H₂O 1×10⁺⁹ M^-1 s^-1 0

R39 TA ŕ TA(enol) 2.3×10^-5 s^-1 1.5 s^-1

R40 TA(enol) + Br₂ ŕ BrTA + Br^- + H⁺ 3×10⁺⁵ M^-1 s^-1 0

R41 TA(enol) + HOBr ŕ BrTA + H₂O 2×10⁺⁵ M^-1 s^-1 0

R42 TAl + MAl ŕ EETA + H₂O 1×10⁺⁹ M^-1 s^-1 0

R43 TAl + BrMAl ŕ CO₂ + BrEETRA + H₂O 1×10⁺⁹ M^-1 s^-1 0

R44 TAl + COOHl ŕ TA + CO₂ 3×10⁺⁹ M^-1 s^-1 0

R45 TAl + lBrO₂ ŕ TABrO₂ 2×10⁺⁹ M^-1 s^-1 0

R46 TABrO₂ ŕ MOA + HBrO₂ 0.1 s^-1 0

R47 TA + BrO₃^- ŕ HBrO₂ + MOA 5×10^-5 M^-1 s^-1 0

R48 MAl + BrO₃^- + H⁺ ŕ lBrO₂ + TA 160 M^-1 s^-1 0

Abbreviations:

BrMA = bromomalonic acid, BrEETRA = bromoethenetricarboxylic acid, BrMAl = bromomalonyl radical, BrTA = bromotartronic acid, COOHl = carboxyl radical, EEHTRA = ethenehydroxytricarboxylic acid,
EETA = ethenetetracarboxylic acid, ETA = ethanetetracarboxylic acid, MA = malonic acid, MAl = malonyl radical, MOA = mesoxalic acid, OA = oxalic acid, TA = tartronic acid, TAl = tartronyl radical

a) k₃ can be described by a power series:

k₃ = c₀ + c₁×[Br^-/M] + c₂×[Br^-/M]² + c₃×[Br^-/M]³ for [Br^-]>2×10^-6 M; k₃ = 0.3 for [Br^-]<2×10^-6 M

c₀=0.48789 M^-1s^-1, c₁=0.143911×10⁺⁵ M^-1s^-1, c₂=-0.7076958×10⁺⁸ M^-1s^-1, c₃=0.116310×10⁺¹² M^-1s^-1

In the range of bromide concentrations typical for the BZ system (2×10^-6 M to 2×10^-5 M) k₃ can be approximated by the mean value k₃ = 0.6 M^-1s^-1

b) k_-8 depends on the ionic strength m of the solution:

k_-8 = c₀ + c₁×(m /M) + c₂×(m /M)]² + c₃×(m /M)³

c₀=-1.74743×10⁺⁴ M^-1s^-1, c₁=6.75949×10⁺⁴ M^-1s^-1, c₂=-4.30066×10⁺⁴ M^-1s^-1, c₃=0.797993×10⁺⁴ M^-1s^-1

For a typical BZ system with an initial concentration of 0.1 M bromate and 1 M sulfuric acid
the ionic strength is m =1.6 M^-1s^-1 and k_-8 = 1.3×10⁺⁴ M^-1s^-1.

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