Activation Parameters |
In the Arrhenius theory, the only activation parameter that was introduced was the activation energy. In the transition state theory developed in this lecture, we have related the concentration of the activated complex to the reactant concentrations through an equilibrium constant K. Treating (p0 / RT)  of eq (33.27) and (33.28) as an equilibrium constant (although one vibrational mode is removed from C ), we can define the Gibbs free energy of activation
 G as |
| G = - RT ln ( p0 / RT) |
(33.35) |
| the rate constant k2 becomes |
k2 =  kBT /h (RT / p0) e
 |
(33.36) |
| |
| The free energy of activation can be divided into enthalpy and entropy terms ( analogous to G = H - TS) through |
| |
 G = H - T S |
(33.37) |
| For the time being let us either take = 1 or include it in the entropy term. The rate constant then becomes |
 with B = (k BT / h)( R T / p0) |
(33.38) |
| The activation energy of the Arrhenius equation, Ea is defined through Ea = R T 2 ( d ln k2 / dT). Substituting k2 into this, we get |
| Ea = H + 2 RT |
(33.39) |
| Substituting this in eq (33.38), we get |
k2 = e - 2 B
 e - E a / RT |
(33.40) |
| and the Arrhenius factor A becomes |
| A = e - 2 B |
(33.41) |
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