Lecture 21

Lecture 21 - Chem 338 Lecture 21 Eyrings Transition State...

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Chem 338 / () E kT rate kT A e −Δ 12 2 8 / / E kT AB rate A B mm rr k T e π ⎡⎤ + =+ ⎢⎥ ⎣⎦ 0 / ( /) ( ) ( / ) q V Ek T rate qq VV k T h E e d E k T κ ⎛⎞ ⎜⎟ ⎝⎠ = C h em 3 3 8 L e c t u r e 2 1 Eyring’s Transition State Theory 1. Arrhenius activation energy: 2. Collision theory rate law: 3. Potential energy surface. 4. Eyring’s Transition State Theory: 5. Tunneling: ( E )
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Chem 338 / () E kT rate kT A e −Δ Eyring’s Transition State Theory 1. Arrhenius Deviation from straight line!
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Chem 338 () 12 2 8 / / AB BB A B mm dN N Vol r r kT dt π ⎡⎤ + =+ ⎢⎥ ⎣⎦ 8 / / AB AB kT υπ μ = 2 8 / / E kT rate A B T rr k e −Δ + [] 2 8 / #/ // A B dc o l V o l N Vol N Vol r r kT dt + 2. W. C. McC. Lewis: Collision Theory Collision cylinder of length υ AB dt and cross section π ( r A + r B ) 2 . The mean relative velocity A B had been calculated 50 years earlier by Maxwell and Boltzmann: so the number of collisions for each A molecule is: and the total rate of collisions per unit volume for all A molecules is: giving the collision theory rate constant:
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Chem 338 Collision Theory Wrong deviation from straight line! α ~ 2 () 12 2 8 / / E kT AB rate A B mm T kT rr k e π −Δ ⎡⎤ + =+ ⎢⎥ ⎣⎦
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Chem 338 3. Potential energy surface.
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Chem 338 4. Henry Eyring’s Transition State Theory: Eyring formulated absolute reaction rates " in terms of quantities which are available from potential energy surfaces ". He defined the " activated complex " (we now prefer transition state ) as " a saddle point with positive curvature in all degrees of freedom except the one which corresponds to crossing the barrier [i.e. the reaction path] for which it is of course negative ." He assumed that once the forces between atoms have been treated quantum mechanically, the reaction rate could then be calculated by the methods of statistical mechanics. The fundamental idea was to treat the molecular flux from reactants to products as a one-dimensional problem along the reaction path by taking an ensemble average over all other degrees of freedom.
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Chem 338
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This note was uploaded on 06/28/2010 for the course CHEM 338 taught by Professor Petersson during the Spring '10 term at Wesleyan.

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Lecture 21 - Chem 338 Lecture 21 Eyrings Transition State...

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