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Lec39post.pdf
- 1. 3-d plot Contour Plot 2 of3 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. Temperature Dependence ofa 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. 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. But What AboutEntropy? 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. We plot Gibbsenergy 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. Sample Problem: Sample Problem: SampleProblem: 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. 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. 2 H2O2(l) 2H2O (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. Catalyst is ina 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.