Chbe 551 lecture 20
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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;

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CHBE 551 Lecture 20

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Chbe 551 lecture 20

CHBE 551 Lecture 20

Unimolecular Reactions


Last time transition state theory

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).


Transition state theory fails for unimolecular reactions

Transition State Theory Fails For Unimolecular Reactions


Why does transition state theory fail

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

Lindeman Approximation

  • Assume two step process

    • First form a hot complex via collission

    • Hot complex reacts

  • Steady State Approximation Yields


Comparison to data for ch 3 nc ch 3 cn

Comparison To Data For CH3NC  CH3CN


But preexponentials for unimolecular reactions too big

But Preexponentials For Unimolecular Reactions Too Big


Why the difference

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

RRK Model

  • Assume correction to TST by

  • Qualitative, but not quantitative prediction


Rrkm model

RRKM Model

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


Derive equation

Derive Equation

  • Consider

  • Excite molecule to above the barrier then molecule falls apart

  • Derive Equation for reverse reaction

  • At Equilibrium


Derivation continued

Derivation Continued

  • From Tolman's equ

  • Pages Of Algebra


Chbe 551 lecture 20

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

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

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.


Chbe 551 lecture 20

Note


Qualitative results

Qualitative Results


Gives good predictions for long lived excited states

Gives Good Predictions for Long Lived Excited States

Tunneling


Ignores quantum effects

Ignores Quantum Effects


Details of calculation

Details Of Calculation


Does rrkm always work

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


Also fails for barrierless reactions

Also Fails for Barrierless Reactions


Summary

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

Query

  • What did you learn new in this lecture?


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