Entropy of activation explained

In chemical kinetics, the entropy of activation of a reaction is one of the two parameters (along with the enthalpy of activation) that are typically obtained from the temperature dependence of a reaction rate constant, when these data are analyzed using the Eyring equation of the transition state theory. The standard entropy of activation is symbolized and equals the change in entropy when the reactants change from their initial state to the activated complex or transition state (= change, = entropy, = 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. = .^[1]

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.^[2] 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.^[3]

Derivation

It is possible to obtain entropy of activation using Eyring equation. This equation is of the form$$k\; =\; \backslash frac\; e^\; e^$$where:

k = reaction rate constantT = absolute temperature\Delta H ^{\ddagger} = enthalpy of activationR = gas constant\kappa = transmission coefficientk _{B} = Boltzmann constant = R/N_A, N_A = Avogadro constanth = Planck constant\Delta S ^{\ddagger} = entropy of activation

This equation can be turned into the form$$\backslash ln\; \backslash frac\; =\; \backslash frac\; \backslash cdot\; \backslash frac\; +\; \backslash ln\; \backslash frac\; +\; \backslash frac$$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 _{B} / h) + \Delta S ^{\ddagger/} R from which the entropy of activation is derived.

Notes and References

1. [Keith J. Laidler|Laidler, K.J.]
2. Laidler and Meiser p. 365
3. James H. Espenson Chemical Kinetics and Reaction Mechanisms (2nd ed., McGraw-Hill 2002), p. 156–160