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ChE 452 Lecture 23

ChE 452 Lecture 23. Transition State Theory, Continued. Last Time Transition State Theory. Also called conventional transition state theory (CTST). (7.43). Results From Last Time. F+H 2 HF+H. Comparison Of Transition State Theory And Collision Theory.

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ChE 452 Lecture 23

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  1. ChE 452 Lecture 23 Transition State Theory, Continued

  2. Last Time Transition State Theory Also called conventional transition state theory (CTST) (7.43)

  3. Results From Last Time F+H2HF+H

  4. Comparison Of Transition State Theory And Collision Theory • Transition state theory uses the transition state diameter rather than the collision diameter in the calculation. • Transition state theory multiplies by two extra terms: The ratio of the vibrational partition function, and the electronic partition function for the transition state, and the reactants.

  5. Key Prediction Of TST • Ea associated with barrier • Lots of parameters (i.e. qs) to fit to data. • Predicts Preexponentials

  6. Is The Saddle Point Energy A Good Approximation To The Activation Energy?

  7. Difference Between EA And Saddle Point Energy Due To: • Dynamic effects and quantum effects • Tunneling

  8. Accuracy of TST Only Fair Very hard to get better than 1 order of magnitude Figure 7.9 A comparison of the hp/kBT measured experimentally for the reactions in Table 9.4 to the transition state approximation of the same quantities.

  9. Why Was Transition State So Popular? • Gave a way of thinking about activation barriers. • Lots of parameters to fit data. • Eyring 500 papers. • People thought it was right (except for tunneling). • Only in 1998 did people realize that TST with tunneling is not accurate. • Still thought to be a useful way of thinking about reactions.

  10. One Application Of TST Is To Estimate Ko

  11. Solution Step 1: Count The Modes • Consider A+BCABC‡AB+C with a linear transition state. • In lecture 14 we found that molecules have 3 vibrational modes, 2 or 3 rotational modes and 5Na total modes

  12. Step 2: Find The Partition Functions A: BC: (7.B.1) (7.B.2) Transition state: (7.B.3)

  13. Transition State Approximation; Treat One Of The Vibration Modes As A Translational Mode (7.B.4) Where qAAC is the partition function for the motion of A toward BC. In transition state theory, we want q‡ not q*. By definition: (7.B.5)

  14. Combining Equations 7.B.1 Through 7.B.5 Yields (7.B.6)

  15. Approximation: For Today’s Example Take 2 translations Convert to vibrations (7.B.10)

  16. Solution Continued According to Table 6.6; qv1, qt 3/Å. Substituting into equation (7.B.10) (7.B.11)

  17. Solution For Nonlinear TST One can do the same analysis for a nonlinear transition state. The result is: (7.B.12)

  18. Estimate ko From Above • Showed 0.04<q‡/qAqBC<2 • kBT/h 5x1012/sec • Hence 1011 and 1013/sec

  19. Comparison To Experiments

  20. Not Accurate Compared To Experiments/Detailed • Transition state larger than reactants • Rotational partition function larger • Vibration larger too

  21. Strengths Of Transition State • Transition state theory allows you to calculate bcoll in equation (7.16) rather than guess it. In Chapter 9, we will show that for a simple collision bcoll is just the distance between the reactants at the transition state. • Transition state theory suggests that Preactions can be less than . For example, in the reaction: D+CHC+HD • The incoming deuterium has to hit the hydrogen atom for reaction to occur. Transition state theory accounts for that by saying that the transition state must be a linear CHD molecule. • Transition state theory also predicts that small changes in the shape of the potential energy surface produce large changes in , which in turn changes the rate.

  22. Accuracy Of TST Only Fair Very hard to get better than 1 order of magnitude Figure 7.9 A comparison of the khp/kBT measured experimentally for the reactions in Table 9.4 to the transition state approximation of the same quantities.

  23. Next: Relationship Between TST And Collision Theory • TST & collision theory very similar • Similar predictions • In fact, TST goes to collision theory if one ignores vibration and rotation of BC. • Book shows that TST goes to collision theory for structureless molecules.

  24. Transition State Theory Differs From Collision Theory In Two Key Ways: • One can actually make a calculation. • Collision theory bcoll unknown (7.16). • Transition state theory replaces bcoll with dcoll. The distance between reactants at the transition state geometry. dcoll can be calculated exactly. • Transition state theory allows you to consider reactions like reaction (7.27) where only special configurations lead to the desired products. • Partition function for TST gives many parameters

  25. Summary Transition state theory- • Extension of collision theory (used collision theory to derive) • Identifies bcoll as dcoll • Identifies S as S of saddle point • Slightly, more accurate that Collision theory • Still only accurate to order of magnitude

  26. Question • What did you learn new in this lecture?

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