Complexity of Growth & Decline
Delayed Consequences and Oscillations
Rainer Glaser, Chemistry
MLS Proseminar, November 16, 2009
(with updates)
Chemical Reaction Kinetics
Landolt Iodine Clock Reaction (Chem. Ber., 1885)
Belousov-Zhabotinsky Reaction (Nature, 1970)
Briggs-Rauscher Reaction (J. Chem. Educ., 1973)
Organization of Activities
1. Meeting, 11/16: Chemistry Background, Lecture, Dr. Glaser
2. Meeting, 11/30: Experiments by 4 Student Groups, Dr. Glaser & Ms. Miller
2 Student Groups perform Landolt and Briggs-Rauscher Reactions
2 Student Groups perform Landolt and Belousov-Zhabotinsky Reactions
3. Meeting, 12/7: Mathematical Simulation, Dr. Chicone
Focus on Lengyel Reaction, a Briggs-Rauscher-type Reaction
Simple Chemical Kinetics: Differential Form
Zero-Order Reaction (red)
The rate of reaction is a constant.
When the limiting reactant is
completely consumed, the
reaction abruptly stops.
First-Order Reaction (green)
The rate of reaction is directly
proportional to the concentration
of one of the reactants.
Second-Order Reaction (blue)
The rate of reaction is directly
proportional to the square of the
concentration of one of the
reactants.
Differential Rate Law: r = k
Unit of k: mole L-1 sec-1
Differential Rate Law: r = k [A]
Units of k: sec-1
Differential Rate Law: r = k [A]2
Units of k: L mole-1 sec-1
http://www.chm.davidson.edu/vce/Kinetics/index.html
Simple Chemical Kinetics
http://www.chemie.uni-regensburg.de/Organische_Chemie/Didaktik/Keusch/D-Video-e.htm
Organic Chemistry Demonstration Experiments on Video
Chemistry Visualized
Peter Keusch, University of Regensburg
Landolt Iodine Clock Reaction
How to recognize starch in your food…
And then my friendly local chemist reminded me of
the easy test for starch: simply drop iodine onto
the suspect food. If it contains starch, the color of
the iodine will darken from orange to shades
ranging from inky blue to black.
The Element Iodine
Iodine is a bluish-black, lustrous solid. It volatilizes
at ambient temperatures into a pretty blue-violet
gas with an irritating odor.
http://easyweb.easynet.co.uk/~design.machine-tanya/irritable.bowel/test.htm
http://www.webelements.com/iodine/
Landolt Iodine Clock Reaction
Starch
Amylose and Amylopectin
Glucose Polymers
http://www.elmhurst.edu/~chm/vchembook/548starchiodine.html
Landolt Iodine Clock Reaction
Bisulfite reduces Iodate to Iodine (Overall)
5 HSO3- + 2 IO3- + 2 H+
5 HSO4- + I2 + H2O
If this were a simple reaction, then one would expect
that iodine is formed as soon as the bisulfite and
iodate solutions are mixed.
Instead, the experiment shows that the iodine
concentration [I2] remains below detection limit until
[I2] builds up, quite suddenly, after a delay time t.
Now watch the video (requires Real Player).
Landolt Iodine Clock Reaction
Bisulfite reduces Iodate to Iodide (LR1)
3 HSO3- + IO33 HSO4- + I-
Iodate reacts with Iodide to Iodine (LR2)
5 I- + IO3- + 6 H+
3 I2 + 3 H2O
Bisulfite reduces Iodine to Iodide (LR3)
I2 + HSO3- + H2O
2 I- + HSO4- + 2 H+
Iodine-Iodide-Starch Complex Formation (LR4, fast!)
x I2 + y I- + amylose
blue complex
Landolt Iodine Clock Reaction
Iodate (+V)
IO3-
Iodine (0)
Iodide (-I)
I-
I2
LR1 - slow
LR2 - fast
LR3 - very fast
While LR1 and LR3 occur:
[1] Iodate concentration continuously decreases
[2] Iodide concentration increases, then collapses
[3] Iodine concentration cannot build up until bisulfite consumed
Landolt Iodine Clock Reaction
Stoichiometry: 5 bisulfite for every 2 iodate.
Solution A (1 L) contains 1.16 g NaHSO3. Solution B (1 L) contains 4.3 g KI.
MW(NaHSO3) = 104 g/mol; MW(KI) = 166 g/mol
50 mL of solution A contain 1.16/20 g NaHSO3, or 0.56 mmol.
50 mL of solution B contain 4.3/20 g KI, or 1.3 mmol.
25 mL of solution B contain 0.65 mmol.
Our conditions: Not stoichiometric. Excess of iodate.
We will run out of bisulfite for sure!
The slow reaction LR1 depends on the concentration of iodate.
Rate of reaction LR1 = kLR1 [HSO3-]m [IO3-]
The faster LR1, the faster we will run out of bisulfite!
Landolt Iodine Clock Reaction
0.0037sec mol 2 L2
P
[KIO 3 ] [NaHSO 3 ]

Church-Dreskin Induction Period
On the Kinetics of Color Development in the Landolt (“Iodine Clock”) Reaction.
Church, J. A.; Dreskin, S. A. J. Phys. Chem. 1968, 72, 1387-1390.
Belousov-Zhabotinsky Reaction
“unstirred”
http://www.youtube.com/watch?v=GEF_NtTNeMc&feature=related
http://www.youtube.com/watch?v=bH6bRt4XJcw
Click here for a great video
(requires Real Player).
Click here to see the video of
the “stirred” BZ Reaction
(requires Real Player).
http://www.youtube.com/watch?v=PI2Y7wzhjVA
Belousov-Zhabotinsky Reaction
[Fe(o-phen)3]2+
Ferroin
[Fe(o-phen)3
Ferriin
]3+
[(Ce3+)(NH4+)2(NO3-)5]
Bromate (+V), BrO3Bromite (+III), BrO2Hypobromite (+I), BrOBromide (-I), Br-
Oscillations in Chemical Systems. I. Detailed Mechanism in a System Showing Temporal Oscillations.
Noyes, R. N.; Field, R. J.; Koros, E. J. Am. Chem. Soc. 1972, 94, 1394-1395.
Belousov-Zhabotinsky Reaction
Noyes-Field-Koros Model
Bromination of Malonic Acid with Bromate and
in the presence of Bromide
BrO3- + Br- + 2 H+
HBrO2 + Br- + H+
HOBr + Br- + H+
Br2 + MA
HBrO2 + HOBr
2 HOBr
Br2 + H2O
BMA + HBr
BrO3- + 2 Br- + 3 MA + 3 H+
(R3) slow
(R2)
(R1)
(R8)
3 BMA + 3 H2O (A)
[HBrO2]A = k3/k2 [BrO3-][H+] = 510-10 [BrO3-][H+]
Lots of Br-, lots of Br2 production.
(1)
Belousov-Zhabotinsky Reaction
Noyes-Field-Koros Model
Bromination of Malonic Acid with Bromate and
in the absence of Bromide
BrO3- + HBrO2 + H+
BrO2 + Ce3+ + H+
2 HBrO2
HOBr + MA
BrO3- + 4 Ce3+ + MA + 5 H+
2 BrO2 + H2O
HBrO2 + Ce4+
BrO3- + HOBr + H+
BMA + H2O
(R5) slow
(R6)
(R4)
(R8a)
BMA + 4 Ce4+ + 3 H2O (B)
[HBrO2]B = k5/2k4 [BrO3-][H+] = 110-4 [BrO3-][H+]
(2)
[HBrO2] is 100,000 times higher compared to process A!
Independent of [Br-].
Belousov-Zhabotinsky Reaction
Noyes-Field-Koros Model
The Bromide Switch
BrO3- + 2 Br- + 3 MA + 3 H+
3 BMA + 3 H2O (A)
[HBrO2]A = k3/k2 [BrO3-][H+] = 510-10 [BrO3-][H+]
(1)
Lots of Br-, lots of Br2 production. Keeps [HBrO2] low.
BrO3- + 4 Ce3+ + MA + 5 H+
BMA + 4 Ce4+ + 3 H2O (B)
[HBrO2]B = k5/2k4 [BrO3-][H+] = 110-4 [BrO3-][H+]
(2)
Independent of [Br-].
[Br-]crit = k5/k2 [BrO3-] = 310-6 [BrO3-]
Now we know why solutions reacting by (A) will turn
themselves into solutions reacting by (B).
(3)
Belousov-Zhabotinsky Reaction
Noyes-Field-Koros Model
The Back-Switch
6Ce4+ + MA + 2H2O
4Ce4+ + BMA + 2H2O
6Ce3+ + HCOOH + 2CO2 + 6H+
(9)
4Ce3+ + Br- + HCO2H + 2CO2 + 5H+ (10)
Early: Mostly MA present, no bromide is formed.
Later: BMA is present, bromide is formed. Process (B) shuts
down when [HBrO2] drops below [HBrO2]crit.
Now we know why solutions reacting by (B) will turn
themselves into solutions reacting by (A).
Belousov-Zhabotinsky Reaction
NFK Model Modifications: COx
Lengyel Reaction
Iodination of Malonic Acid with Chlorite and
in the presence of Iodide
I2 + MA
IMA + HI
r3 = -d[I2]/dt = 410-3 [MA] [I2] / {110-4 + [l2]}
(L3) slow
(L3’)
Iodine consumption rate via reaction L3
Involves MA enolization and subsequent rxn with iodine
Batch Oscillation in the Reaction of Chlorine Dioxide with Iodine and Malonic Acid.
Lengyel, I.; Rabai, G.; Epstein, I. R. J. Am. Chem. Soc. 1990, 112, 4606-4607.
Lengyel Reaction
Iodination of Malonic Acid with Chlorite and
in the presence of Iodide
I2 + MA
ClO2 + IClO2- + 4 I- + 4 H+
IMA + HI
0.5 I2 + ClO22 I2 + Cl- + 2 H2O
(L3) slow
(L4)
(L5)
Iodine formation rates via reactions L4 & L5
r4 = 6.3103 [ClO2] [I-]
(4’)
r5 = 4.6102 [ClO2-] [I-][H+] + 2.6510-3 [ClO2-][l2]/[I-]
(5’)
r5 = 4.6102 [ClO2-] [I-][H+] + 2.6510-3 [ClO2-][l2][I-]/(u+[I-]2) (5”)
u = 10-13
This term reflects
self-inhibition by iodide
Avoid div.
by zero
Lengyel Reaction
Mathematical Evaluation: Numerically.
Start with initial conditions and evolve concentrations over small times.
Mathematical Evaluation: Analytically.
Keep constant: [MA], [I2], [ClO2]
Remaining variables: [I-] = X; [ClO2-] = Y; [ClO2] = Z.
Taube's Influence on the Design of Oscillating Reactions – CIO2 Radical-Driven CIO2-Anion Iodine Oscillator and Turing
Structures. Irving R. Epstein, Kenneth Kustin, and Istvan Lengyel, 1997.
Lengyel Reaction
Taube's Influence on the Design of Oscillating Reactions – CIO2 Radical-Driven CIO2-Anion Iodine Oscillator and Turing
Structures. Irving R. Epstein, Kenneth Kustin, and Istvan Lengyel, 1997.
Lengyel Reaction
Excel Simulation programmed by Dr. Montgomery-Smith
Series 1: X; Series 2: Y
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