Belousov-­‐Zhabo-nsky reac-on Marco Mazzo6 Modeling and mathema-cal methods FS 2014 Experimental evidence (Cerium) •  Malonic acid oxida-on by bromate in acidic solu-on, catalyzed by a metal ion (Ce4+) •  Long series of oscilla-ons in the concentra-on of the intermediate species (with a chroma-c effect) •  The main reactants are irreversibly consumed (but very slowly) •  Finally, the oscilla-ons vanish and chemical equilibrium is monotonically approached Chemistry Experimental evidence (ferroin) Detailed mechanism Detailed mechanism – Inorganic subset Detailed mechanism – Radicals and organic species Mechanism of the oscilla-ons Mechanism of the oscilla-ons Mechanism of the oscilla-ons + 2
r1 = k1 !"H #$ !"BrO−3 #$!"Br − #$
r2 = k2 !"H + #$[ HBrO 2 ] !"Br − #$
r3 = k3 !"H + #$[ HBrO 2 ] !"BrO−3 #$
r4 = k4 [ HBrO 2 ]
2
r5 = k5 !"Ce 4+ #$[ MA]
Mechanism of the oscilla-ons + 2
r1 = k1 !"H #$ !"BrO−3 #$!"Br − #$
r2 = k2 !"H + #$[ HBrO 2 ] !"Br − #$
r3 = k3 !"H + #$[ HBrO 2 ] !"BrO−3 #$
r4 = k4 [ HBrO 2 ]
2
r5 = k5 !"Ce 4+ #$[ MA]
Kine-c scheme: Oregonator Kine-c scheme: Oregonator Oregonator (dimensionless) dx
ε
= qay − xy + ax − x 2
dτ
dy
δ
= −qay − xy + fbz
dτ
dz
= ax − bz
dτ
ε = 0.12
δ = 0.0006
f = varying parameter ≈ 1
q = 0.0008
a,b = constant