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# Lec39post.pdf

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### Lec39post.pdf

1. 1. 3-d plot Contour Plot 2 of 3 coordinates Symmetric Stretch r Energy Simplest possible “reaction” D + H2 → → → → HD + H rHH Energy V(rHH) → → → → H2 as H - D distance increases. Potential Energy Surfaces Potential Energy Curves Energy Q Energy Q Reac. Prod. Endothermic Energy Q Reac. Prod. Exothermic Ea ∆ ∆ ∆ ∆E or ∆ ∆ ∆ ∆H ∆ ∆ ∆ ∆E or ∆ ∆ ∆ ∆H Ea Activation Energy, Ea Activation Energy, Ea Reaction Coordinate Reaction Coordinate Reac. Prod.
2. 2. Temperature Dependence of a Reaction Rate Constant: Temperature Dependence of a Reaction Rate Constant: Velocity distribution in gas phase at temperature T Nv |v| Critical velocity for reaction, vc |v| < vo No Reaction |v| > vo Reaction T = 300 K T = 500 K T = 1000 K T = 5000 K The minimum energy that must be supplied by a collision is the Activation Energy. KE = ½mv2 ≥ ≥ ≥ ≥ Ea k = A∞ ∞ ∞ ∞ e-Ea/kBT |v| Nv Rate constant Boltzmann Constant Pre-exponential factor Population with KE sufficient to drive the reaction.
3. 3. k = A∞ ∞ ∞ ∞ e-Ea/kBT Temperature k k = 0.9 A∞ ∞ ∞ ∞ k B T = 10 E a k B T = E a k = 0.36 A∞ ∞ ∞ ∞ Ea = Joules/molecule for Ea = Joules/mole k = A∞ ∞ ∞ ∞ e-Ea/RT RT = 10 E a RT = E a k = A∞ ∞ ∞ ∞ A∞ ∞ ∞ ∞ = maximum possible rate at infinite temperature ln k = -Ea 1 + ln A∞ ∞ ∞ ∞ R T A plot of ln k vs 1/T will be linear. ln k 1/T Intercept = ln A∞ ∞ ∞ ∞ Slope = -Ea/R Arrhenius Equation Arrhenius Equation Arrhenius Plot Arrhenius Plot Activation barriers are determined experimentally by measuring the rate over as large a range of T as possible.
4. 4. But What About Entropy? But What About Entropy? An exothermic reaction will occur rapidly if Ea < RT and only very slowly if Ea >> RT. Potential Energy ∆ ∆ ∆ ∆E Ea ∆ ∆ ∆ ∆H Reaction Coordinate An endothermic reaction will have a large activation energy, Ea. Reaction Coordinate ∆ ∆ ∆ ∆H Ea Potential Energy Entropy accounts for the number of different states that contribute all along the reaction path.
5. 5. We plot Gibbs energy along reaction coordinate to account for entropy. Gibbs Energy ∆ ∆ ∆ ∆Gŧ ∆ ∆ ∆ ∆rG Reaction Coordinate ∆ ∆ ∆ ∆Gŧ is the free energy or Gibbs energy of activation. = kBTe∆ ∆ ∆ ∆Sŧ/R e-∆ ∆ ∆ ∆Hŧ/RT h = kBT e-(∆ ∆ ∆ ∆Hŧ-T∆ ∆ ∆ ∆Sŧ)/RT h k = kBT e-∆ ∆ ∆ ∆Gŧ/RT h Pre-exponential factor A∞ ∞ ∞ ∞ k h = Planck’s Constant ∆ ∆ ∆ ∆Sŧ = Entropy of Activation ∆ ∆ ∆ ∆Hŧ = Enthalpy of Activation ⇒ ⇒ ⇒ ⇒ microscopic Ea
6. 6. Sample Problem: Sample Problem: Sample Problem: If a reaction doubles its rate when the temperature is increased from 305 K to 315 K, what is the activation energy? k = A∞ ∞ ∞ ∞ e-Ea/RT k(315 K) = A∞ ∞ ∞ ∞ e-Ea/R(315 K) = 2 k(305 K) A∞ ∞ ∞ ∞ e-Ea/R(305 K) 2 = e-Ea(1/305 – 1/315)/R A∞ ∞ ∞ ∞ is approximately T independent ln2 = -Ea(1/305 – 1/315)/R Ea = ln2 (8.3145 J mol-1 K-1) 10-3 kJ 0.0001041 K-1 J = 55.4 kJ/mol
7. 7. Catalysis: Catalysis: Catalysis: Consider: 2 H2O2(l) → → → → 2 H2O (l) + O2(g) ∆ ∆ ∆ ∆rG ∅ ∅ ∅ ∅ = 2(-237.13) + 0 - 2(-120.35) = -233.56 kJ ∆ ∆ ∆ ∆rH ∅ ∅ ∅ ∅ = 2(-285.83) + 0 - 2(-187.78) = -196.10 kJ In fact the equilibrium constant is huge. K = e-∆ ∆ ∆ ∆rG /RT ∅ ∅ ∅ ∅ K = exp = 1.15 × × × × 1041 233.56 × × × × 103 J 8.31451 J K-1 298 Energy Q Reac. Prod. H O – O H → → → → H O – H + O • • • • ∆ ∆ ∆ ∆rH ∅ ∅ ∅ ∅ Very high activation energy This reaction is exothermic and spontaneous!
8. 8. 2 H2O2(l) 2 H2O (l) + O2(g) MnO2 Add MnO2 MnO2 acts as a catalyst – that is, it provides a mechanism with a much smaller activation energy. Old Path Energy Along the Catalyzed Path Energy Q H2O + O2 H2O2 Initial and final states are unaffected by catalyst. The nature of the reaction coordinate is changed. “Q” Energy QCAT “Q” Energy QCAT
9. 9. Catalyst is in a different phase than reactants. Heterogeneous Catalysis: Heterogeneous Catalysis: Usually a solid surface catalyzing gas or liquid phase reactions. Homogeneous Catalysis: Homogeneous Catalysis: Catalyst is in the same phase as the reactants. Usually in liquid solution. Rhodium, Platinum, Zeolites, Metal Oxides, … Complexes of Rhodium and Platinum, Enzymes, Strong Acids, … Examples: Examples: 2 H2O2(l) 2 H2O (l) + O2(g) Catalase In the presence of Catalase Manganese Catalase in certain Lactobacillus type bacteria.