Arrhenius Equation Revisited

Arrhenius Equation revisited kAe E/RTa A = pre-exponential factor Ea= activation energy Remember the NO2 + CO reaction pathway w/2 humps Just what IS a reaction coordinate? Reaction Potential Energy Surfaces: Born-Oppenheimer Approximation Generally a very accurate approximation, and one of the most important concepts in all of physical science. AB A+B Without it, there would be no chemistry as we know it. B-O approximation allows the construction of potential energy surfaces for molecules (e.g., AB) and for reactions. Still too many nuclear degrees of freedom! Reduce them somehow! That is, choose the configuration to be the minimum energy at every point in a reaction – this is the reaction coordinate. “Following the valley” in a complex universe Arrhenius Equation shortcomings transition state theory kAe E/RTa (Totally empirical!!) E Ea= activation energy a A = pre-exponential factor = PZAB A + B ZAB = collision density P = “steric factor” (0<P 1,empirical) Ethylene dimerization k 2C2H4 2 C4H8 (butene) -3 -1 -1 k2(obs’d.) = 5.6 x 10 atm hr -1 -1 k2(collision theory) = 4 atm hr The implication is that the Arrhenius “Steric factor” P is ~ 10-3 and we don’t know the origin. Transition state theory helps us refine the picture. Transition State Theory Theoretically predict E/RTa ‡ kAe2 k C‡ key concepts: (1) Pre-equilibrium between reactants ‡ Keq A + B and activated complex C‡. (2) C‡ forms the transition state, then product P is made with “microscopic” rate constant k‡. A + B ‡ ‡ ‡ ‡ (3) = k [C ] = k Keq [A][B], equate this with = k2[A][B]. P k = k‡ K ‡ (Need stat.mech. to 2 eq ‡ ‡ calculate k Keq ) Transition State Theory The Arrhenius Equation Insight from Transition State Theory TST - based on statistical mechanics (Eyring) ‡ o –23 kTB G/RT kB = 1.38 x 10 J/K ke h = 6.63 x 10–34 J s E h a Looks like e RT ‡ ‡ kT oo kee B S/R H/RT h The pre-exponential factor (and “steric factor”) relates to the entropy change for activation!! Back to ethylene dimerization k 2C2H4 2 C4H8 (butene) -3 -1 -1 k2(obs’d.) = 5.6 x 10 atm hr -1 -1 k2(collision theory) = 4 atm hr Arrhenius “Steric factor” P is ~ 10-3 and we don’t know the origin. TST: Assume (or calculate) a butene-like transition state structure ‡ 0 [CH2=CH2• • • CH2=CH2] and calculate S then k2. ‡S0 ≈ -30 cal K-1 (negative) Can be refined, but a k (TST) ≈ 4 x 10-4 atm-1 hr-1 2 reasonable agreement!! Transition State Theory explains origin of Ea H + H–H [H---H---H]‡ H–H + H Collinear A + BC AB + C (for simplicity) The only coordinates are R(A–B) and R(B-C) We can show the reaction progress on a (calculated) potential energy surface V(RAB, RBC). The surface might be calculated using quantum mechanics, and then we imagine allowing the system to propagate on the surface via classical mechanics. What does V(RAB, RBC) look like? Let A = B= C = H ‡ Hα + HβHε [Hα-- Hβ--Hε] HαHβ + Hε This simplification leaves only two nuclear co-ordinates, r and r. I can plot that! Contour plots are more common, and easier to interpret physically A + B – C [A---B---C]‡ A – B + C The picture gets much more complex when non collinear. The rate constant is obtained by averaging over collision energy, impact geometry, phase of BC vibration, BC rotation. Collinear H + H2 Reaction ‡ Hα + HβHε [Hα-- Hβ--Hε] HαHβ + Hε Reactants Hα + H βHε minimum energy path ) β Reaction co-ordinate? —H α H R ( Products HαHβ + Hε R (Hβ —Hε) Consider the SN2 reaction - - Cl + CH3Br ClCH3 + Br Transition State Reactant complex Product complex Reaction Coordinate Calculations by Bill Hase – Texas Tech http://monte.chem.ttu.edu/group/animations.html Happy Thanksgiving!.

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