Entropy of activation

{{Short description|Concept in chemical kinetics}} 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 {{math|1=Δ''S''^‡}} and equals the change in entropy when the reactants change from their initial state to the activated complex or transition state ({{math|1=Δ}} = change, {{math|1=''S''}} = entropy, {{math|1=‡}} = activation).

== Importance == Entropy of activation determines the preexponential factor {{math|1=''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 *: {{math|1=''A'' = (e''k''_B''T''/''h'') exp(Δ''S''^‡/''R'')}}, * while for bimolecular gas reactions *: {{math|1=''A'' = (e²''k''_B''T''/''h'') (''RT''/''p'') exp(Δ''S''^‡/''R'')}}.

In these equations {{math|1=e}} is the base of natural logarithms, {{math|1=''h''}} is the Planck constant, {{math|1=''k''_B}} is the Boltzmann constant and {{math|1=''T''}} the absolute temperature. {{math|1=''R''′}} is the ideal gas constant. The factor is needed because of the pressure dependence of the reaction rate. {{math|1=''R''′}} = {{val|8.3145|e=−2|u=(bar·L)/(mol·K)}}.<ref>Laidler, K.J. and Meiser J.H. ''Physical Chemistry'' (Benjamin/Cummings 1982) p. 381–382 {{ISBN|0-8053-5682-7}}</ref>

The value of {{math|1=Δ''S''^‡}} provides clues about the molecularity of the rate determining step in a reaction, i.e. the number of molecules that enter this step.<ref>Laidler and Meiser p. 365</ref> 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 {{math|1=Δ''S''^‡}} 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.<ref>James H. Espenson ''Chemical Kinetics and Reaction Mechanisms'' (2nd ed., McGraw-Hill 2002), p. 156–160 {{ISBN|0-07-288362-6}}</ref>

== Derivation == It is possible to obtain entropy of activation using Eyring equation. This equation is of the form <math display="block"> k = \frac{\kappa k_\mathrm{B}T}{h} e^{\frac{\Delta S^\ddagger }{R}} e^{-\frac{\Delta H^\ddagger}{RT}}</math> where: * <math>k </math> = reaction rate constant * <math> T </math> = absolute temperature * <math>\Delta H^\ddagger </math> = enthalpy of activation * <math> R </math> = gas constant * <math> \kappa </math> = transmission coefficient * <math> k_\mathrm{B} </math> = Boltzmann constant = ''R''/''N''_A, ''N''_A = Avogadro constant * <math> h </math> = Planck constant * <math> \Delta S^\ddagger </math> = entropy of activation

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

== References == {{reflist}}

Category:Chemical kinetics