Page 191 - Instant notes

Energetics and mechanisms 177

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Since, ∆G =∆H −T∆S , the observed reaction rate constant can be written as:

This expression also has the form of the Arrhenius equation when the enthalpy of
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activation, ∆H , is identified with the activation energy E a, and the entropy of
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activation, ∆S , is identified with the pre-exponential factor (or more precisely with
RlnA). For a reaction which has strict orientation requirements (for example the approach
of a substrate molecule to an enzyme) the entropy of activation will be strongly negative
(because of the decrease in disorder when the activated complex forms) and the pre-
exponential factor will be small compared with a reaction that does not have such strict
orientation requirements. Thus activated complex theory incorporates information about
the intrinsic geometry of the transition state to account for the steric factor, P, arbitrarily
introduced into the pre-exponential factor derived from collision theory.

Catalysts

The rate constant for a reaction depends on the temperature, the height of the activation
barrier E A and the magnitude of the pre-exponential Arrhenius factor A. Whilst
increasing the temperature can be used to increase the rate constant the latter two
parameters cannot be altered since they are specific to the particular reaction path and
determined by the electronic structure and bonding arrangement of the reactants and
activated complex. Instead, a catalyst may be available that increases the rate of
reaction by providing an alternative reaction path with a lower activation energy (Fig. 5)
so that at a given temperature a greater proportion of collisions have energy greater than
the activation energy. (Note that the rate of back reaction must also increase when the
height of the activation barrier is lowered.)