Linking Kinetics and Thermodynamics: Microscopic Reversibility & Transition State Theory -, Study notes of Physical Chemistry

Download Linking Kinetics and Thermodynamics: Microscopic Reversibility & Transition State Theory - and more Study notes Physical Chemistry in PDF only on Docsity! 1 Kinetics Transition state rate constant K = k fk r ∆Hf * ∆Hr * ∆Hrxn o The relationship of kinetics and thermodynamics The principle of microscopic reversibility requires that: Using definitions from thermodynamics and from transition state theory: Note that at constant temperature the prefactor kBT/h is the same for each of the rate constants. K = k fk r e– ∆GoRT = e – ∆Gf */RT e– ∆Gr*/RT The math behind the comparison Using the definition of free energy: ∆G = ∆H – T∆S for each free energy gives: which can be separated into: and e– ∆Ho/RT = e – ∆Hf */RT e– ∆Hr*/RT e∆So/R = e ∆Sf */R e∆Sr*/R e∆So/Re– ∆Ho/RT = e ∆Sf */Re– ∆Hf*/RT e∆Sr*/Re– ∆Hr*/RT The connection of entropy and enthalpy These equations imply simply that: Note that the relationship between the enthalpies can be seen graphically in the energy diagram that we started with. Note: ‡ and * have the same meaning. ∆So = ∆Sf * – ∆Sr * ∆Ho = ∆Hf * – ∆Hr * Relationship to the Arrhenius parameters The transition state rate constant k = (kBT/h)e-∆G ‡/RT is k = (kBT/h)e∆S ‡/R e-∆H‡/RT and the Arrhenius rate constant is k = Ae-Ea/RT which leads to the identification A = (kBT/h)e∆S ‡/R The frequency factor depends on the exponential of the activation entropy. Ea = ∆H ‡ where Ea is the activation enthalpy.