Arrhenius Equation and Kinetics: Understanding Activation Energy and Transition State - Pr, Study notes of Physical Chemistry

Download Arrhenius Equation and Kinetics: Understanding Activation Energy and Transition State - Pr and more Study notes Physical Chemistry in PDF only on Docsity! Lecture 27 Ki tine cs The Arrhenius rate constant Transition state rate constant The Arrhenius equation The empirical observation is that: ln k = ln A – E aRT for many reactions. This means that a plot of ln(k) vs. 1/T gives a straight line. A is the pre-exponential or frequency factor. E i th ti ti Ala s e ac va on energy. so: k = Ae– E a/RT Th t iti t te rans on s a e The activated complex is a distorted structure that is intermediate between the structure the reactants and that of the products. At the peak of the potential energy surface between the reactants and products lies the transition state. The fundamental assumption of acti ated comple theo is that the t ansition v x ry r state Is in equilibium with the reactants and products . A + B C‡ The assumption of equilibrium between the reactants and the transition state Since the formation of the activated complex C‡ occurs in equilibrium with the reactants we can express the equilibrium constant as [C‡]K‡ [A][B] = and the rate constant is given by the product of a frequency factor kBT/h for the formation of the complex times the equilibrium constant. ΔHf * ΔHr * K = k fk r ΔHorxn The connection of entropy and th len a py These equations imply simply that: ΔSo = ΔSf * – ΔSr * ΔHo = ΔHf * – ΔHr * Note that the relationship between the enthalpies can be seen graphically in the energy diagram th t t t d itha we s ar e w . Note: ‡ and * have the same meaning . Relationship to the Arrhenius parameters The transition state rate constant k = (kBT/h)e-ΔG ‡/RT is k = (kBT/h)eΔS ‡/R e-ΔH‡/RT and the Arrhenius rate constant is k = Ae-Ea/RT which leads to the identification A = (kBT/h)eΔS ‡/R The frequency factor depends th ti l f th ti ti ton e exponen a o e ac va on en ropy. Ea = ΔH ‡ where Ea is the activation enthalpy.