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 of the transition state theory. 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).
for reactions in solution and unimolecular gas reactions
A = (ekBT/h) exp(ΔS‡/R),
while for bimolecular gas reactions
A = (e2kBT/h) (RT/p) exp(ΔS‡/R).
In these equations e is the base of natural logarithms, h is the Planck constant, kB 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. 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 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.[3]
Derivationedit
It is possible to obtain entropy of activation using Eyring equation. This equation is of the form
The plot of versus gives a straight line with slope from which the enthalpy of activation can be derived and with intercept from which the entropy of activation is derived.
^James H. Espenson Chemical Kinetics and Reaction Mechanisms (2nd ed., McGraw-Hill 2002), p.156-160 ISBN0-07-288362-6
December 07, 2023
entropy, activation, chemical, kinetics, entropy, activation, reaction, parameters, along, with, enthalpy, activation, which, typically, obtained, from, temperature, dependence, reaction, rate, constant, when, these, data, analyzed, using, eyring, equation, tr. 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 of the transition state theory The standard entropy of activation is symbolized DS and equals the change in entropy when the reactants change from their initial state to the activated complex or transition state D change S entropy activation Importance editEntropy 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 reactionsA ekBT h exp DS R while for bimolecular gas reactionsA e2kBT h RT p exp DS R In these equations e is the base of natural logarithms h is the Planck constant kB 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 DS 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 DS 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 editIt is possible to obtain entropy of activation using Eyring equation This equation is of the formk k k B T h e D S R e D H R T displaystyle k frac kappa k mathrm B T h e frac Delta S ddagger R e frac Delta H ddagger RT nbsp where k displaystyle k nbsp reaction rate constant T displaystyle T nbsp absolute temperature D H displaystyle Delta H ddagger nbsp enthalpy of activation R displaystyle R nbsp gas constant k displaystyle kappa nbsp transmission coefficient k B displaystyle k mathrm B nbsp Boltzmann constant R NA NA Avogadro constant h displaystyle h nbsp Planck s constant D S displaystyle Delta S ddagger nbsp entropy of activationThis equation can be turned into the formln k T D H R 1 T ln k k B h D S R displaystyle 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 nbsp The plot of ln k T displaystyle ln k T nbsp versus 1 T displaystyle 1 T nbsp gives a straight line with slope D H R displaystyle Delta H ddagger R nbsp from which the enthalpy of activation can be derived and with intercept ln k k B h D S R displaystyle ln kappa k mathrm B h Delta S ddagger R nbsp from which the entropy of activation is derived References edit Laidler K J and Meiser J H Physical Chemistry Benjamin Cummings 1982 p 381 2 ISBN 0 8053 5682 7 Laidler and Meiser p 365 James H Espenson Chemical Kinetics and Reaction Mechanisms 2nd ed McGraw Hill 2002 p 156 160 ISBN 0 07 288362 6 Retrieved from https en wikipedia org w index php title Entropy of activation amp oldid 1158981079, wikipedia, wiki, book, books, library,
