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### CHBE 551 Lecture 20

Unimolecular Reactions

Last Time Transition State Theory

- Transition state theory generally gives preexponentials of the correct order of magnitude.
- Transition state theory is able to relate barriers to the saddle point energy in the potential energy surface;
- Transition state theory is able to consider isotope effects;
- Transition state theory is able to make useful prediction in parallel reactions like reactions (7.27) and (7.29).

Why Does Transition State Theory Fail?

- Ignores the effect of energy transfer on the rate
- Consider a stable molecule AB. How can AB A + B
- If you start with a stable molecule, it does not have enough energy to react.
- Need a collision partner so AB can accumulate enough energy to react.
- Energy accumulation ignored in TST

Lindeman Approximation

- Assume two step process
- First form a hot complex via collission
- Hot complex reacts

- Steady State Approximation Yields

Comparison To Data For CH3NC CH3CN

Why The Difference?

- Bimolecular collision lasts ~10-13 sec
- Molecule must be in the right configuration to react

- Hot unimolecular complex lasts
~10-8 sec

- Even if energy is put in the wrong mode, the reaction still happens

RRK Model

- Assume correction to TST by
- Qualitative, but not quantitative prediction

RRKM Model

- Improvement to RRK model proposed by Rudy Marcus (ex UIUC prof).

Derive Equation

- Consider
- Excite molecule to above the barrier then molecule falls apart
- Derive Equation for reverse reaction
- At Equilibrium

Derivation Continued

- From Tolman's equ
- Pages Of Algebra

Note

- Reactants have a fixed energy ~laser energy
- Products have a fixed energy too, but since they have translation, the products can have vibrational+ rotation energy between the top of the barrier and E*

Substituting, And Assuming Energy Transfer Fast

- N(E*) E* is the number of vibrational modes of the reactants with an vibrational energy between E* and E* + E*
- G+(E*) is the number of vibrational modes of the transition state with a vibrational energy between E‡ and E* independent of whether the mode directly couples to bond scission.

Next Separate Vibration and Rotation

where GVT is the number of vibrational states at the transition state, with an energy between E‡ and E*. NV(E*) is the number of vibrational states of the reactants with an energy between E* and E* +E ; qR‡ is the rotational partition function for the transition state and qR* is the rotational partition function for the excited products.

Does RRKM Always Work?

- Assumes fast dynamics compared to time molecule stays excited

A comparison of the experimental rate of isomerization of stilbene (C6H5)C=C(C6H5) to the predictions of the RRKM model

Summary

- Unimolecular reactions have higher rates because configurations that do not immediately lead to products still eventually get to products
- RRKM – rate enhanced by the number of extra states
- Close but not exact – still have dynamic effects

Query

- What did you learn new in this lecture?

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