Entropy of activation

In chemical kinetics, the entropy of activation of a reaction is one of the two parameters (along with the enthalpy of activation) which are typically obtained from the temperature dependence of a reaction rate constant, when these data are analyzed using the Eyring equation. The standard entropy of activation is symbolized ΔS^‡ and equals the change in entropy when the reactants change from their initial state to the activated complex or transition state (Δ = change, S = entropy, ‡ = activation). It determines the preexponential factor A of the Arrhenius equation for temperature dependence of reaction rates. The relationship depends on the molecularity of the reaction: for reactions in solution and unimolecular gas reactions A = (ek_BT/h) exp(ΔS^‡/R), while for bimolecular gas reactions A = (e²k_BT/h) (R'T/p) exp(ΔS^‡/R). In these equations e is the base of natural logarithms, h is the Planck constant, k_B is the Boltzmann constant and T the absolute temperature. R' is the ideal gas constant in units of (bar*L)/(mol*K). The factor is needed because of the pressure dependence of the reaction rate. R' = 8.3145 * 10^-2 (bar*L)/(mol*K). ^[1]

The value of ΔS^‡ provides clues about the molecularity of the rate determining step in a reaction, i.e. whether the reactants are bonded to each other, or not. Positive values suggest that entropy increases upon achieving the transition state, which often indicates a dissociative mechanism in which the activated complex is loosely bound and about to dissociate. Negative values for ΔS^‡ indicate that entropy decreases on forming the transition state, which often indicates an associative mechanism in which two reaction partners form a single activated complex.^[2]

References

1. Laidler, K.J. and Meiser J.H. Physical Chemistry (Benjamin/Cummings 1982) p.381-2 ISBN 0-8053-5682-7
2. James H. Espenson Chemical Kinetics and Reaction Mechanisms (2nd ed., McGraw-Hill 2002), p.156-160 ISBN 0-07-288362-6