Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

11.3 Activation controlled reactions 234
11.3 Activation controlled reactions
The rate constant for an activation controlled reaction is
= {} (11.34)
I Estimation of K {} : We can estimate the equilibrium constant {} using simple
arguments based on the coordination number. Accordingly, the concentration of the
encounter complex is
[{}] =[] × (probability of finding next to ) (11.35)
=[] × []
[]
(11.36)
where [] is the solvent concentration and is the coordination number. y
{} = [{}]
[][] =
[]
(11.37)
For H 2 Oat =298K, [] =555moll −1 . Thus, taking for example =8,wefind
that
{} =014 l mol −1 (11.38)
I Application of thermodynamic TST: TSTcanbeappliedintwoways:
(1) Considering the overall reaction, we can write
=
exp ¡ −∆ ‡ ¢ (11.39)
where ∆ ‡ is the overall Gibbs free enthalphy for the reaction.
(2) We can also separate the effects from and {} by writing
´
{} =exp
³−∆ ª {}
(11.40)
and
=
exp ¡ −∆ + ¢ (11.41)
∆ ª {}
is the Gibbs free enthalpy change for the formation of the encounter
complex, and ∆ + is the Gibbs free enthalphy of activation from the encounter
complex. Thus,
= ³
exp −
³∆ ∆+´ ´
ª
{} + (11.42)
I Pressure dependence of the rate constant: ⇒ See section 7.3.5.