Transition State Theory. II. E‡ vs. Ea. Kinetic Isotope Effect.

5.62 Spring 2008

Lecture #34

Page 1

Transition State Theory. II. E‡ vs. Ea. Kinetic Isotope Effect. Want to get kTST into Arrhenius form

k TST = !

kT ‡" K h

K ‡" = e#G

but

‡

RT

$$ % #RTln K ‡ = &G‡

because

‡ kT #G‡ /RT kT ‡ e = ! eS /R e#H /RT h h ‡ ‡ ‡ G = H # TS

NOW :

H‡ = E ‡ + &nRT

k TST = !

so

where ∆n = (# molecules in TS) – (molecularity of reaction) (molecularity: e.g., unimolecular, bimolecular, etc.) e.g.

∆n =

1

–2

= –1

So: k TST = !

kT S‡ R 1 "E‡ RT e ee h

k TST # BTm e"E

‡

RT

where m = 1

Surprisingly, theory predicts a temperature dependence to the pre-exponential factor. This T-dependence is difficult to observe experimentally unless the rate constant is measured over a wide temperature range (at least a factor of 5) Now:

d ln k TST dT

) " k ‡ ‡, % d + ln $! eS /R e1 ' + lnT + e(E . * # h & = dT

=

1 E‡ + T RT 2

(TST)

Contrast this to Arrhenius model:

d ln k E = a2 dT RT

revised 4/24/08 11:34 AM