CHEM 106 1nd Edition Lecture 14Outline of Last Lecture I. Rate expression and Rate lawII. Reaction Half-lifeIII. Rate law from experimental dataOutline of Current Lecture II. Arrhenius EquationIII. Collision TheoryIV. Potential Energy ProfileV. Origin of T Dependence of kVI. Reaction MechanismsCurrent LectureChapter 15: Chemical Kinetics (continued)15.4 Reaction rates, T, and the Arrhenius EquationRates vary as concentrations vary, but even for the same reaction at the same concentrations, the rate increases as T increases.This is because k increases with TArrhenius Equation: k = A e−EaRTA mathematical form that fits typical observationsk: rate constant A: Arrhenius frequency factor, s-1Ea: Arrhenius activation energy kJ/mol R: 8.314 J/mol*KT: in KelvinCollision TheoryA theory of kinetics Fig. 15.17O3(g) + NO(g) → O2(g) + NO2 (g)Many collisions will occur but only a small fraction of them have the correct orientation, and few of these have enough energy to react. - Most collisions are rather ineffective- A successful collision leads to a productPotential Energy ProfilePotential Energy: bond strengthKinetic Energy: energy of motionSuccessful reactions are those that convertKE to enough PE to overcome the requiredEa (minimum PE energy needed) Origin of T Dependence of kFig. 15.16a (review 6.8 kinetic-molecular theory of gases)At lower T, few molecules have enough KE to lead to high energy collisions. This fraction is much higher at higher T, as is the collision frequency. Ea for forward + reverse reactions:Fig. 15.18Forward Ea (fwd)Reverse Ea (fwd) + ΔHrxnFitting data to the Arrhenius Equationk = Ae−EaRT ln (k) = ln (A) – EaR(1T)(think y = b –mx)plot ln k vs. 1/T slope = −EaRintercept: ln (A)For only 2 points: algebraic methodln k1 = −EaR (1T 1) + ln (A)ln k2 = −EaR (1T 2) + ln (A)ln k1 – ln k2 = −EaR (1T 1−1T 2) ln k1 – ln k2 = EaR (1T 2−1T 1) (note switch in T’s)ln (k 1k 2¿=EaR(1T 2−1T 1)then solve for EaThen from any k, T pair + Ea, solve for Ak = A e−EaRT A = ke−Ea/ RTsee sample exercises 15.9 and 15.10 in book15.5 Reaction Mechanisms stepwise process by which a reaction occurs Elementary stepsIndividual steps in a mechanismIntermediateA species, neither a reactant nor a product, produced in one step andconsumed in the nextMolecularityNumber of molecules (or ions) in an elementary step Unimolecular: A → B rate = k [A]Bimolecular: A + A → C rate = k [ A ]2A + B → C rate = k [A]
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