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CHBE 551 Lecture 22

CHBE 551 Lecture 22. Theory Of Activation Barriers. Last Time Found Barriers To Reaction Are Caused By. Uphill reactions Bond stretching and distortion Orbital distortion due to Pauli repulsions Quantum effects Special reactivity of excited states. Today Models. Polanyi

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CHBE 551 Lecture 22

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  1. CHBE 551 Lecture 22 Theory Of Activation Barriers

  2. Last Time Found Barriers To Reaction Are Caused By • Uphill reactions • Bond stretching and distortion • Orbital distortion due to Pauli repulsions • Quantum effects • Special reactivity of excited states

  3. Today Models • Polanyi • Bond stretching + Linearization • Marcus • Bond stretching + parabola • Blowers Masel • Bond streching + Pauli repulsions

  4. Polayni's Model Figure 10.3 A diagram illustrating how an upward displacement of the B-H curve affects the activation energy when the B-R distance is fixed. Figure 10.4 A diagram illustrating a case where the activation energy is zero.

  5. Derivation Of Polayni Equation (10.9) (10.10) Figure 10.6 A linear approximation to the Polanyi diagram used to derive equation (10.11).

  6. Case Where Polayni Works (Over A Limited Range Of ΔH) Figure 10.7 A plot of the activation barriers for the reaction R + H R RH + R with R, R = H, CH3, OH plotted as a function of the heat of reaction Hr.

  7. Equation Does Not Work Over Wide Range Of H Figure 10.11 A Polanyi plot for the enolization of NO2(C6H4)O(CH2)2COCH3. Data of Hupke and Wu[1977]. Note Ln (kac) is proportional to Ea.

  8. Seminov Approximation: Use Multiple Lines Figure 11.12 A comparison of the activation energies of 482 hydrogen transfer reactions to those predicted by the Seminov relationships, over a wider range of energies. Figure11.11 A comparison of the activation energies of a number of hydrogen transfer reactions to those predicted by the Seminov relationships, equations (11.33) and (11.34)

  9. Equation Does Not Work Over A Wide Data Set Figure 10.10 A Polanyi relationship for a series of reactions of the form RH + R R + HR. Data from Roberts and Steel[1994].

  10. Key Prediction Stronger Bonds Are Harder To Break Figure 10.8 A schematic of the curve crossing during the destruction of a weak bond and a strong one for the reaction AB + C  A + BC.

  11. Experiments Do Not Follow Predicted Trend Figure 10.9 The activation barrier for the reaction X- +CH3X  XCH3 + X-.The numbers are from the calculations of Glukhoustev, Pross and Radam[1995].

  12. Marcus: Why Curvature? Figure 10.11 A Polanyi plot for the enolization of NO2(C6H4)O(CH2)2COCH3. Data of Hupke and Wu[1977]. Note Ln (kac) is proportional to Ea.

  13. Derivation: Fit Potentials To Parabolas Not Lines Figure 10.13 An approximation to the change in the potential energy surface which occurs when Hr changes.

  14. Derivation Figure 10.13 An approximation to the change in the potential energy surface which occurs when Hr changes.

  15. Solving (10.23) (10.24) Result (10.33) (10.31)

  16. Qualitative Features Of The Marcus Equation Figure 10.11 A Polanyi plot for the enolization of NO2(C6H4)O(CH2)2COCH3. Data of Hupke and Wu[1977]. Note Ln (kac) is proportional to Ea.

  17. Marcus Is Great For Unimolecular Reactions

  18. Marcus Not As Good For Bimolecular Reactions Figure 10.18 The activation energy for florescence quenching of a series of molecules in acetonitrite plotted as a function of the heat of reaction. Data of Rehm et. al., Israel J. Chem. 8 (1970) 259.

  19. Comparison To Wider Bimolecular Data Set Figure 10.29 A comparison of the barriers computed from Blowers and Masel's model to barriers computed from the Marcus equation and to data for a series of reactions of the form R + HR1 RH + R1 with wO = 100 kcal/mole and = 10 kcal/mole.

  20. Why Inverted Behavior? At small distances bonds need to stretch to to TS.

  21. Limitations Of The Marcus Equation • Assumes that the bond distances in the molecule at the transition state does not change as the heat of reaction changes • Good assumption for unimolecular reactions • In bimolecular reactions bonds can stretch to lower barriers

  22. Explains Why Marcus Better For Unimolecular Than Bimolecular

  23. Blowers-Masel Derivation • Fit potential energy surface to empirical equation. • Solve for saddle point energy. • Only valid for bimolecular reaction.

  24. Derive Analytical Expression (10.63) Bond energies (10.64) Only parameter (10.65)

  25. Comparison To Experiments Figure 10.29 A comparison of the barriers computed from Blowers and Masel's model to barriers computed from the Marcus equation and to data for a series of reactions of the form R + HR1 RH + R1 with wO = 100 kcal/mole and Eao = 10 kcal/mole.

  26. Comparison Of Methods Figure 10.32 A comparison of the Marcus Equation, The Polanyi relationship and the Blowers Masel approximation for =9 kcal/mole and wO = 120 kcal/mole.

  27. Example: Activation Barriers Via The Blowers-Masel Approximation

  28. Solution: Step 1 Calculate VP VP is given by: (11.F.2)

  29. Step 1 Continued Substituting into equation (11.F.2) shows (11.F.3)

  30. Step 2: Plug Into Equation 11.F.1 (11.F.1) By comparison the experimental value from Westley is 9.6 kcal/mole.

  31. Solve Via The Marcus Equation: (11.F.4) which is the same as the Blowers-Masel approximation.

  32. Summary • Polayni: fair approximation – good over a limited range of H • Marcus: Great for unimolecular • Blowers-Masel Great for bimolecular • Only small differences between methods unless magnitude of heat of reaction is larger than 3-4 times Ea0

  33. Query • What did you learn new in this lecture?

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