Download Arrhenius Equation and Catalysis: Understanding Reaction Kinetics - Prof. Stefan Franzen and more Study notes Physical Chemistry in PDF only on Docsity! 1 Kinetics The Arrhenius rate constant Transition state rate constant Catalysis The Arrhenius equation The empirical observation is that: 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. Ea is the activation energy. Also: ln k = ln A – E a RT k = Ae – E a/RT Experimental determination of Arrhenius parameters We can plot ln(k) vs. 1/T to determine the activation energy. A plot of ln k vs. 1/T yields a slope of -Ea/R and an intercept of ln A. E a = – R d ln kd (1/T) Activated complex theory ∆H‡ The diagram depicts a reaction coordinate. The intermediate is the activated complex. The transition state 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 activated complex theory is that the transition 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‡] [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. K‡ = 2 Arrhenius parameters The reaction rate can also be written k = (kBT/h)e-∆G ‡/RT where ∆G‡ is the activation Gibbs energy. This provides an interpretation for the Arrhenius parameters: 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. Catalysis involves lowering of the energy barrier ∆H‡ A catalyst provides an alternative reaction pathway with a lower activation energy or activation enthalpy. ∆H‡ Types of catalysis Homogeneous catalysis - the catalyst is in the same phase as the reactants. Example: acid or base catalysis Heterogeneous catalysis - the catalyst is in a different phase from the reactants. Example: metal complexes, surfaces, zeolites Enzymatic catalysis - the catalyst is a protein that has a substrate binding site and controlled reaction path Zeolites: an important class of catalysts Database of zeolite structures: http://www.iza-structure.org/databases/ Example: search for ZSM-5 Unit cell parameters: a = 20.090Å b = 19.738Å c = 13.142 Å alpha = 90.0° beta = 90.0° gamma = 90.0° volume = 5211.28 Å3 Basis for heterogeneous catalysis in zeolites Zeolites are crystalline solids made up of SiO 4 building blocks. These tetrahedral units join together to form several different ring and cage structures. The characteristic that separates zeolites from all-silica minerals is the substitution of aluminum into the crystalline framework. The substitution of aluminum generates a charge imbalance, which is compensated by a proton. The acid site formed behaves as a classic Brønsted acid or proton donating acid site. The highly acidic sites combined with the high selectivity arising from shape selectivity and large internal surface area makes the zeolite an ideal industrial catalyst. Zeolites: shape selective catalysis The alkylation of benzene with propylene is an important petrochemical process because the product (cumene) is a chemical intermediate used to synthesize phenol and acetone. Classical industrial processes are based on "olid phosphoric acid" catalysts, with problems of handling, safety, corrosion and waste disposal. These can be avoided by using zeolite catalysts.
