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. Differential Rate Law: r = k Unit of k: mole L-1 sec-1 First-Order Reaction (green) The rate of reaction is directly proportional to the concentration of one of the reactants. Differential Rate Law: r = k [A] Units of k: sec-1 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 [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 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- + IO3- 3 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 Symproportionation

Landolt Iodine Clock Reaction Iodate (+V) Iodine (0) Iodide (-I) IO3- I2 I- 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 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.

Refs from Sobel, 2006.

Belousov-Zhabotinsky Reaction “unstirred” Rings or Spirals! 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). http://www.youtube.com/watch?v=PI2Y7wzhjVA Click here to see the video of the “stirred” BZ Reaction (requires Real Player).

Belousov-Zhabotinsky Reaction [Fe(o-phen)3]2+ Ferroin Bromate (+V), BrO3- Bromite (+III), BrO2- Hypobromite (+I), BrO- Bromide (-I), Br- [(Ce3+)(NH4+)2(NO3-)5] [Fe(o-phen)3]3+ Ferriin 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 + HOBr (R3) slow HBrO2 + Br- + H+ 2 HOBr (R2) HOBr + Br- + H+ Br2 + H2O (R1) Br2 + MA BMA + HBr (R8) 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.

Belousov-Zhabotinsky Reaction Noyes-Field-Koros Model Bromination of Malonic Acid with Bromate and in the absence of Bromide BrO3- + HBrO2 + H+ 2 BrO2 + H2O (R5) slow BrO2 + Ce3+ + H+ HBrO2 + Ce4+ (R6) 2 HBrO2 BrO3- + HOBr + H+ (R4) HOBr + MA BMA + H2O (R8a) BrO3- + 4 Ce3+ + MA + 5 H+ 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-] (3) Now we know why solutions reacting by (A) will turn themselves into solutions reacting by (B).

Belousov-Zhabotinsky Reaction Noyes-Field-Koros Model The Back-Switch 6Ce4+ + MA + 2H2O 6Ce3+ + HCOOH + 2CO2 + 6H+ (9) 4Ce4+ + BMA + 2H2O 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 (L3) slow r3 = -d[I2]/dt = 410-3 [MA] [I2] / {110-4 + [l2]} (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 IMA + HI (L3) slow ClO2 + I- 0.5 I2 + ClO2- (L4) ClO2- + 4 I- + 4 H+ 2 I2 + Cl- + 2 H2O (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 Iodine formation rates via reactions L4 & L5 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.

Excel Simulation programmed by Dr. Montgomery-Smith Lengyel Reaction Excel Simulation programmed by Dr. Montgomery-Smith Series 1: X; Series 2: Y