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Nonelementary Reaction Kinetics

Nonelementary Reaction Kinetics. ITK-329 Kinetika & Katalisis. Chapter 4. Dicky Dermawan www.dickydermawan.net78.net dickydermawan@gmail.com. Historical Perspective. Dobereiner (1829), Wilhelmy (1850) supposed that reaction rates would be simply related to the stoichiometry of the reaction

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Nonelementary Reaction Kinetics

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  1. Nonelementary Reaction Kinetics ITK-329 Kinetika & Katalisis Chapter 4 DickyDermawan www.dickydermawan.net78.net dickydermawan@gmail.com

  2. Historical Perspective Dobereiner (1829), Wilhelmy (1850) supposed that reaction rates would be simply related to the stoichiometry of the reaction 1878: Van’t Hoff showed that the rate equation had little correlation to stoichiometry.

  3. Historical Perspective Van’t Hoff: the kinetics of a reaction related to molecularity, i.e. the number of molecules participating in some critical step in the reaction Unimolecular reaction: Cyclopropane  Propylene Bimolecular reaction: *OH + C2H6  H2O + C2H5* Termolecular reaction: CH3* + CH3* + N2  C2H6 + N2 : all first-order reactions are unimolecular : all second-order reactions are bimolecular : all third-order reactions are termolecular Critical step: what about?

  4. Historical Findings When a reaction involves the formations and subsequent reactions of intermediate species, it is not uncommon to find a non-integer order or other type of kinetic expression: CH3CHO  CH4 + CO At +/- 500oC: -rCH3CHO = k.CCH3CHO3/2 H2 + I2 2 HI (CH3)2N2 C2H6 + N2 At low pressures below 50 mmHg: -rN2 ~ CAZO2 At high pressures greater than 1 atm: -rN2 ~ CAZO An elementary reaction is defined as a chemical reaction going from reactants to products without going through any stable intermediates. In this context, a species is said to be stable if it has lifetime longer than ~10-11 sec

  5. Reactive Intermediates Reactive Intermediates are by definition reactive. The undergo many reactions David Chapman (1913), Muriel Chapman & Max Bodenstein (1907): H2 + Cl2 2 HCl Cl • as reactive intermediates Every overall chemical reaction can be divided into a sequence of elementary reaction. Every reaction has a mechanism, defined as the sequence of elementary reactions that occur at appreciable rates when the reactants come together and react to form products CH3CH2HC=CH2 CH3HC=CHCH3 Mechanism:

  6. Kinetic of Elementary Reactions A + B —2 P +Q r2 = k2 [A] [B] -rA = k2 [A] [B] +rP = k2 [A] [B] -rB = k2 [A] [B] +rQ = k2 [A] [B]-rA = -rB = +rP = +rQ 2 A —4 P +Q r4 = k4 [A] [A] = k4 [A]2 +rP = k4 [A]2 +rQ = k4 [A]2 -rA = 2k4 [A]2 - rA/2 = +rP/1 = +rQ/1 = k4 [A]2 Collosion Partner Incorrect: A—1 P -rA = k1 [A] Correct: A + X—1 P + X -rA = k1 [A] [X]

  7. Rates of Overall Reaction A  P For each reaction: For each species: In a constant volume batch reactor:

  8. Pseudo-Steady-State Hypothesis A  P According to pseudo-steady-state approximation, one can compute accurate values of the concentrations of all of the intermediates in a reaction by assuming that the net rate of the intermediates is negligible. According to stoichiometry:

  9. Another Example:Rates of Overall Reaction (CH3)2N2 C2H6 + N2 AZO C2H6 + N2 At low pressures below 50 mmHg : -rN2 ~ CAZO2 At high pressures greater than 1 atm : -rN2 ~ CAZO Reaction mechanism [F.A. Lindemann,Trans. Faraday Soc., 17, 598 (1922)] (CH3)2N2+ (CH3)2N2 —k1 (CH3)2N2+ [(CH3)2N2]* rAZO*= k1.CAZO2 (CH3)2N2* + (CH3)2N2 —k2 (CH3)2N2+ (CH3)2N2 rAZO*= -k2.CAZOCAZO* (CH3)2N2* —k3C2H6+ N2rAZO*= -k3.CAZO* PSSH: rAZO*= k1.CAZO2 - k2.CAZOCAZO* -k3.CAZO* 0 Then,

  10. H4.1.3Find Rate Expression of Overall Reaction…. 2 N2O54 NO2+ O2 Mechanism: • What rate expression is consistent with this mechanism?

  11. Two Proposed Mechanismcan give rise to the same rate expression 2 NO+ 2 H2  N2 + 2 H2O • What rate expression is consistent with these mechanism?

  12. H4.2.1Example of Chain Reaction:Free Radical as Active Intermediate H2+ Br22 HBr Mechanism: Initiation X + Br2—12 Br• + X Propagation Br • + H2—2HBr + H • H • + Br2—3HBr + Br • Terminatiion X + 2 Br • —4Br2 + X H • + HBr —5H2 + Br • • What rate expression is consistent with this mechanism?

  13. Chain Reactions H-Il4.3 Mekanisme berantai di bawah ini diusulkan untuk reaksi dekomposisi ozon: Inisiasi : Propagasi : Terminasi : • Bagaimana persamaan laju reaksi dekomposisi ozon menurut mekanisme ini? • Hasil percobaan pada suhu rendah menunjukkan bahwa persamaan laju dekomposisi ozon mengikuti persamaan: Apakah mekanisme yang diusulkan konsisten dengan hasil percobaan ini?

  14. Chain Reactions H4.1 Houser & Lee [J. Phys. Chem., 71 (3422), 1967] have studied the pyrolysis of ethyl nitrate using a stirred flow reactor. They have proposed the following mechanism for the reaction. Initiation : Propagation : Termination : • What rate expression is consistent with this mechanism?

  15. Chain Reactions:Thermal Cracking of Ethane Ex.7-2 The thermal decomposition of ethane to ethylene, methane, butane, and hydrogen is believed to proceed in the following sequence: Use PSSH to derive a rate law for the formation of ethylene

  16. Chain Reactions: Flame Retardants P7-3B Hydrogen radicals are important to sustaining combustion reactions. Consequently, if chemical compounds that can scavenge the hidrogen radicals are introduced, the flame can be extinguished. While many reactions occur during the combustion process, we shall choose CO flames as a model system to ilustrate the process [S. Senkan et al., Combustion and Flame, 69, p. 113 (1987)] . In the absence of inhibitors: The last two reactions are rapid compared to the firs two. When HCl is introduced to the flame, the following additional reactions occur: Derive a rate law for consumption of CO for both when no retardant present and when HCl is introduced

  17. Chain Reactions:The Pyrolysis of Acetaldehyde P7-4A The pyrolysis of acetaldehyde is believed to take place according to the following sequence: Derive the rate expression for the rate of disappearance of acetaldehyde

  18. Chain Reactions in TribologyEngine Oil Degradation P7-7C One of the major reasons for engine oil degradation is the oxidation of the motor oil. To retard the degradation process, most oils contain an antioxidant [see Ind. Eng. Chem. 26, 902 (1987)]. Without an inhibitor to oxidation present, the suggested mechanism at low temperature is: Where I2 is an initiator and RH is the hydrocarbon in the oil. When the temperature is raised to 100oC, the following additional reaction occurs as a result of the decomposition of the unstable ROOH: • Derive the rate expression for the degradation of the uninhibited motor oil: • At low temperature (25oC) • At high temperature (100oC)

  19. Engine Oil Degradation:The Role of Antioxidant P7-7C (cont’) When an antioxidant is added to retard degradation at low temperatures, the following additional termination step occur: • Derive the rate expression for the degradation of the uninhibited motor oil: • At low temperature (25oC) • At high temperature (100oC)

  20. Free Radical Polymerization 1. The Reaction INITIATION This reaction produces the formation of the Primary Radical PROPAGATION TERMINATION Transfer Addition Disproportionation

  21. Rate-determining (-limiting) Step When one of the steps is much slower than all of the other steps in the mechanism, the rate of this step is fully control the overall rate, thus considerable simplification can be gained: Using PSSH: If it is known that reaction (3) is much slower than (1) & (2) reactions, it is easily derived that:

  22. Rate-determining (-limiting) Step When one of the steps is much slower than all of the other steps in the mechanism, the rate of this step is fully control the overall rate, one can often derive a suitable rate equation for the reaction using somewhat less algebra 2 N2O54 NO2+ O2 Mechanism: • Fast • Slow • Fast • What rate expression is consistent with this mechanism?

  23. Example : P7-8A Consider the application of the PSSH to epidemology. We shall treat each of the following steps as elementary in that the rate will be proportional to the number of people in a particular state of health. A healthy person, H, can become ill, I, spontaneously, (P7-11.1) H I Or he may become ill through contact with another ill person (P7-11.2) I + H 2I k1 k4 k3 k2 The ill person may become healty I H I D Or he may expire (P7-11.4) The reaction given in equation (P7-11.4) is normally considered completely ireversible, although the reverse reaction has been reported to occur :(a) Derive an equation for death rate.(b) At what concentration of healty people does the death rate become critical? (c) Comment the validity of the PSSH under the condition of part (b). (P7-11.3)

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