Entropy of activation

Importance

Entropy of activation determines the preexponential factor 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
• : ,
• while for bimolecular gas reactions
• : .

In these equations is the base of natural logarithms, is the Planck constant, is the Boltzmann constant and the absolute temperature. is the ideal gas constant. The factor is needed because of the pressure dependence of the reaction rate. = .

The value of 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 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.

Derivation

It is possible to obtain entropy of activation using Eyring equation. This equation is of the form k = \frac{\kappa k_\mathrm{B}T}{h} e^{\frac{\Delta S^\ddagger }{R}} e^{-\frac{\Delta H^\ddagger}{RT}} where:

• k = reaction rate constant
• T = absolute temperature
• \Delta H^\ddagger = enthalpy of activation
• R = gas constant
• \kappa = transmission coefficient
• k_\mathrm{B} = Boltzmann constant = R/NA, NA = Avogadro constant
• h = Planck constant
• \Delta S^\ddagger = entropy of activation

This equation can be turned into the form \ln \frac{k}{T} = \frac{-\Delta H^\ddagger}{R} \cdot \frac{1}{T} + \ln \frac{\kappa k_\mathrm{B}}{h} + \frac{\Delta S^\ddagger}{R} The plot of \ln(k/T) versus 1/T gives a straight line with slope -\Delta H^\ddagger/ R from which the enthalpy of activation can be derived and with intercept \ln(\kappa k_\mathrm{B} / h) + \Delta S^\ddagger/ R from which the entropy of activation is derived.

References

References

1. [[Keith J. Laidler. Laidler, K.J.]] and Meiser J.H. ''Physical Chemistry'' (Benjamin/Cummings 1982) p. 381–382 {{ISBN. 0-8053-5682-7
2. Laidler and Meiser p. 365
3. James H. Espenson ''Chemical Kinetics and Reaction Mechanisms'' (2nd ed., McGraw-Hill 2002), p. 156–160 {{ISBN. 0-07-288362-6