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CHBE 551 Lecture 20

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CHBE 551 Lecture 20

Unimolecular Reactions

- 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).

- 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

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

- Steady State Approximation Yields

- 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

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

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

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

- From Tolman's equ
- Pages Of Algebra

- 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*

- 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.

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.

Tunneling

- 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

- 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

- What did you learn new in this lecture?