CEE 690K ENVIRONMENTAL REACTION KINETICS Lecture #13 Kinetic - PDF document

4/12/2008 Updated: 12 April 2008 CEE690K Lecture #13 1 Print version CEE 690K ENVIRONMENTAL REACTION KINETICS Lecture #13 Kinetic Theory: Transition State Model & Ionic Strength Effects Brezonik, pp.137-158 Introduction David A. Reckhow Transition State Theory I 2 � Consider the simple bimolecular reaction + ⎯ ⎯→ k k A A B B C C � Even though it is an elementary reaction, we can break it down into two steps ≠ ≠ + ⇔ ⎯ ⎯→ k A B AB C “Activated Complex” ≠ � Where the first “equilibrium” is: ≠ = [ AB ] K ≠ = [ A ][ B ] ≠ [ [ AB ] ] K [ [ A ][ ][ B ] ] Activated � So the forward rate is: Complex E a d [ C ] = ≠ ≠ = ≠ ≠ k [ AB ] k K [ A ][ B ] Energy reactants dt products CEE690K Lecture #13 David A. Reckhow Reaction Coordinate 1

4/12/2008 Transition State Theory II 3 � Now the transition state is just one bond vibration away from conversion to products conversion to products Frequency of vibration (s -1 ) E vib = ν � Planks Law: h vibrational Planck’s constant (6.62 x 10 -27 ergs·s) energy � Bond energy must be in the thermal region: Temperature (ºK) E bond ≈ Bond kT energy Boltzman constant (1.3807×10 − 16 ergs ºK -1 ) � So equating, we get: ν ν = kT ν ν = = h h kT kT h h � And since conversion occurs on the next vibration: kT = ≠ ≠ = ≠ k k K K h CEE690K Lecture #13 David A. Reckhow Transition State Theory III 4 � Now from basic thermodynamics: Δ Δ Δ G o = − − G o G o K = RT RT l ln K K or e RT � And also Δ Δ Δ = − G o H T S Δ S e Δ − � So: H = K e R RT Δ ≠ Δ ≠ kT − � And combining: S H = k e R e RT h Δ Δ Δ Δ � Recall: = − ≈ E H P V H ⎛ ⎞ − Δ ≠ kT E S a � And substituting back in: = ⎜ ⎟ k e R e RT ⎝ ⎠ h A CEE690K Lecture #13 David A. Reckhow 2

4/12/2008 Activation Energy 5 � Activation Energy must always be positive � Unlike ∆ H, which may be positive or negative U lik ∆ H hi h b i i i � Differing reaction rates Activated Complex Activated Complex E a E a E Energy Energy E reactants reactants Δ = Δ = Δ Δ E H E H f f products products Reaction Coordinate Reaction Coordinate CEE690K Lecture #13 David A. Reckhow Temperature Effects 6 � Arrhenius Equation ( ) − k T T E d ln k E = = 2 2 1 a a ln = − E a / RT 2 k Ae RT dT k RT T 1 1 2 Log A ( ) − Δ K T T H K = = 2 2 1 0 Log k L k ln ln E a /2.3R RT T 1 1 2 Analogous to Van’t Hoff Equation for Equilibria 1/T CEE690K Lecture #13 David A. Reckhow 3

4/12/2008 Ionic Strength Effects 7 � Ion-ion Reactions � Based on activated complex theory � Based on activated complex theory [ ] d C ≠ = ≠ ≠ = ≠ ≠ + ⇔ ≠ ⎯ ⎯→ k k [ AB ] k K [ A ][ B ] A B AB C dt � So let’s look at the equilibrium constant ≠ γ ⎛ ⎞ ≠ γ γ [ AB ] { AB } ⎜ ⎟ ≠ = ≠ ≠ = = ≠ or A B AB [ AB ] K [ A ][ B ] K ⎜ ⎟ γ γ γ ⎝ ⎠ { A }{ B } [ A ] [ B ] ≠ AB A B � Which means: � Which means: ⎛ ⎞ γ γ d [ C ] kT ⎜ ⎟ = ≠ A B K [ A ][ B ] ⎜ ⎟ γ dt h ⎝ ⎠ ≠ AB o (for I=0) K 2 CEE690K Lecture #13 David A. Reckhow Reactions with charged ions 8 � Using the Debye-Huckel Equation − γ i = 2 0 . 5 log 0 . 55 z i I � I<0 005 � I<0.005 { } ( ) = + − − + + o 2 2 2 0 . 5 log k log k 0 . 51 z 0 . 51 z 0 . 51 z z I 2 2 Z B A B = + 0 . 5 o log k 1 . 02 z z I + + 2 2 z 2 z z z 2 A B A A B B � Using the Guntelberg Approximation 2 0 . 5 0 . 55 z i I − γ = log + 0 . 5 i ( 1 I ) � I<0.01 0 . 5 o + I = = + log log k k log log k k 1 1 . 02 02 z z z z + 2 2 A B 0 . 5 ( 1 I ) CEE690K Lecture #13 David A. Reckhow 4

4/12/2008 9 CEE690K Lecture #13 David A. Reckhow I corrections (cont.) 10 � Neutral species − γ γ i = log g b i I i i { } I = + + − o log k log k b b b ≠ 2 2 A B AB � Some case studies: CEE690K Lecture #13 David A. Reckhow 5

4/12/2008 Case Study: TCP Note: both TCP and TCAC refer to the 1,1,1-trichloropropanone 11 � Observed loss of 1,1,1- trichloropropanone in trichloropropanone in distribution systems � Lab studies show that chloroform is the product � Logically presumed to be a simple hydrolysis Reckhow & Singer, 1985 “Mechanisms of Organic Halide Formation During Fulvic Acid Chlorination and Implications with Respect to Preozonation”, In Jolley et al., Water Chlorination; CEE690K Lecture #13 David A. Reckhow Chemistry, Environmental Impact and Health Effect, Volume 5, Lewis. TCP (cont.) 12 � Ionic strength effects = − − ln k H 4 . 81 1 . 4 I = − − log k H 2 . 08 0 . 6 I � Rate with chlorine � Increases greatly � High intercept [ ] = + k 0 . 024 32 HOCl T T CEE690K Lecture #13 David A. Reckhow 6

4/12/2008 Disagreement with prior study 13 � Gurol & Suffet showed 10x higher rate constants higher rate constants � Phosphate? CEE690K Lecture #13 David A. Reckhow Putting it together 14 CEE690K Lecture #13 David A. Reckhow 7

4/12/2008 Catalysis 15 � Homogeneous Catalysis � Definition D fi i i � Liquid-phase substances which react with the main reactants or intermediates thereby providing an alternative pathway to products with a lower activation energy or a higher frequency factor. Catalysts are often regenerated over the course of the reaction. + + + + + → + 2 3 termolecular reaction? – be skeptical 2 A B 2 A B + + + → + + + 2 2 A C A C What “C” serves as a sort of charge- + + + + really + → + 2 2 3 A C A C transfer facilitator, since “B” does happens: not exist in a divalent state + + + → + + + 3 3 C B C B + + + + + → + 2 3 2 A B 2 A B CEE690K Lecture #13 David A. Reckhow 16 � Summary CEE690K Lecture #13 David A. Reckhow 8

4/12/2008 17 � To next lecture CEE690K Lecture #13 David A. Reckhow 9