Organic:entropy

The role of Entropy in a Reaction

The fundemantal equations for understanding rates of reactions are

1. ΔG^‡ = ΔH^‡ - TΔS^‡
2. ΔG^‡ = -RT Ln k

In equation 2, k is the rate constant for the reaction. From this, you can see that the rate of a reaction depends on the entropy of activation for that reaction, ΔS^‡.

For a unimolecular reaction of the type:

A ⇒ B + C

there are more degrees of freedom on the rhs than the lhs (the two molecules B and C can translate and rotate with respect to each other freely). ΔS^‡ for such a reaction is therefore +ve. Plugged into equation 1, this reduces ΔG^‡.

for an alternative bimolecular reaction invoking a base;

A + Base ⇒ C + D

there are more or less an equal number of degrees of freedom on both sides of this equation, and hence ΔS^‡ for such a reaction is therefore close to zero. ΔG^‡ in equation 1 is therefore not reduced. If ΔH^‡ is the same for both reactions, then the unimolecular form will always be much faster than the bimolecular form (by a factor of 10⁵ or so).