Lecture 22

Lecture 22 - Chem 338 Lecture 22 Absolute Rate Theory 1....

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Chem 338 0 / () ( /) Gk T rate kT k T h e −Δ = C h em 3 3 8 L e c t u r e 2 2 Absolute Rate Theory 1. The impact of Eyring’s Transition State theory 2. Interpretation: Collision Theory from TST Gibbs Free Energy of Activation: 3. Implementation: Absolute Rate Theory Ab initio Potential energy Surfaces 4. Variational Transition State theory Zero Curvature: ZC-VTST i. ZPE & q ( Rxn Path ): ii. Corner cutting and bobsledding iii. ZPE( Rxn Path ) 5. Comparison with Experiment
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Chem 338 1. The Impact of TST on Chemical Kinetics Eyring's transition state theory has provided the basic conceptual framework for the interpretation of the rates of nearly all chemical reactions on a bulk scale. He quickly applied his new theory to homogeneous gas phase thermochemical reactions, photochemical reactions, heterogeneous catalysis, and reactions in solution. He even considered such topics as viscosity and diffusion. The greatest immediate impact was a qualitative interpretive tool, rather than the achievement of the original goal of a quantitative theory of absolute rates. In spite of the difficulties in quantitative implementation, transition state theory provided a framework for understanding even the most complicated reactions. Transition state theory immediately provided a deeper understanding of collision theory.
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Chem 338 2. Interpretation: Collision Theory from TST Eyring’s transition state theory (TST): / () ( /) ( ) o q V E kT rate qq AB VV kT k T h E e κ ⎛⎞ ⎜⎟ −Δ ⎝⎠ = immediately provided a deeper understanding of collision theory. The collision theory rate can be recovered by evaluating TST for the reaction of two point particles, A and B (i.e. q rot = q vib = q elec = 1) to form a linear transition state (i.e. q rot // rp = q vib = q elec = 1): where q rot ( A+B ) is the partition function for rotations perpendicular to the reaction path. Evaluation of the partition functions gives: ‡‡ / ( ( ) o trans rot E kT rate trans trans qA B V q A B k T h E e V qB V ⎡⎤ ++ ⎣⎦ =
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Chem 338 () 12 2 8 / / E kT AB rate A B mm E kT rr k T e κ π σ −Δ ⎡⎤ + =+ ⎢⎥ ⎣⎦ ( ) 32 22 2 4 / // / / ( ) / o A B A B rate Ek T k T h r r k T h h mk T h Ee ππ μ ⎛⎞ ++ ⎜⎟ = ⎝⎠ × which simplifies to: The TST form of the steric factor is therefore: The rotational partition function for the transition state, q rot//rp , includes only the single rotation about the axis which is the direction of the reaction path! The much larger number of 3-dimensional rotations for both reactants gives a quantitative measure of steric effects on chemical reaction rates. ‡‡ // rot rp vib elec AB rot vib elec rot vib elec A B qq q E TST qqq =
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Chem 338 Collision Theory Rate Constant: k rate ( T ) Experimental rate constants vs. predictions by collision theory for gas phase reactions Reaction collision frequency Steric factor 2ClNO 2Cl + 2NO 5.9 10 10 0.16 2ClO Cl 2 + O 2 2.5 10 10 2.3 10 -3 H 2 + C 2 H 4 C 2 H 6 7.3 10 11 1.7 10 -6 Br 2 + K KBr + Br 2.1 10 11 4.3 () 12 2 8 / / : BA B B rat A B B e AB A Collision Freq kT m m E kT rr Arrhenius uency mm z e π ⎡⎤ ⎛⎞ + −Δ ≈+
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Lecture 22 - Chem 338 Lecture 22 Absolute Rate Theory 1....

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