Entropy of activation

Importance

Entropy of activation 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) (RT/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. The factor is needed because of the pressure dependence of the reaction rate. R′ = 8.3145×10⁻² (bar·L)/(mol·K).

The value of ΔS^‡ provides clues about the molecularity of the rate determining step in a reaction, i.e. the number of molecules that enter this step. 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.