5.60 Spring 2008 Lecture #31 page 1 Complex Reactions and Mechanisms Mechanisms: A series of elementary steps that make up a reaction. e.g. for A + B + 2C → D + E Mechanism could be: A+B→F F+C→G+D G+C→E Elementary Single Step Reactions F and G are reaction intermediates Molecularity: The number of molecules that come together to react in one elementary step For single step elementary reactions, Molecularity = Order A → products 1st order rate = k[A] Unimolecular A → products 2nd order rate = k[A]2 Bimolecular A + B → prod. 2nd order rate = k[A][B] Bimolecular A + B + C → prod. 3rd order rate = k[A][B][C] Termolecular Etc… Molecularity is the number of molecules that need to collide, and in one step form the products. 5.60 Spring 2008 Lecture #31 page 2 Some Simple Mechanisms I) Parallel Reactions a) Parallel 1st order reactions A B k1 k2 − d[A] = k1 [A] + k2 [A] dt C [A] = [A]o e −(k1 +k2 )t [B] = [C] = k2 [A]o 1 − e −[k1 +k2 ]t k1 + k2 Branching Ratio: ( k1 [A]o 1 − e −[k1 +k2 ]t k1 + k2 ( ) [B] k1 = [C] k2 Conc. [A] [B] [C] Time ) 5.60 Spring 2008 Lecture #31 page 3 b) Parallel 1st and 2nd order reactions k1 A A k2 B d[B] = k1 [A] dt C d[C] = k2 [A] 2 dt − [A] = d[A] = k1 [A] + k2 [A] 2 dt k1 [A]o e k1t (k1 + k2 [A]o ) − k2 [A]o Limiting cases: i) k2[A]o << k1 ⇒ [A] = [A]o e −k1t ii) k2[A]o >> k1 ⇒ 1 1 = + k2 t [A] [A]o 5.60 Spring 2008 Lecture #31 page 4 c) Consecutive or Series Reactions (1st order) k1 A − B k2 C d[A] = k1 [A] dt − d[C] = k2 [B] dt d[B] = k1 [A] − k2 [B] dt [A] = [A]o e −k1t [B] = k1 [A]o −k1t e − e −k2t k1 − k2 ( ) with k1 ≠ k2 ⎧ ⎫ 1 [C] = [A]o ⎨1 + k2 e −k1t − k1 e −k2t ⎬ ⎩ k1 − k2 ⎭ ( Conc. ) [C] [A] [B]max [B] tmax B tmax = ln(k1 / k2 ) k1 − k2 with k1 ≠ k2 Time [B]max = B k1 [A]o e −k1tmax k2 5.60 Spring 2008 Lecture #31 page 5 Limiting cases: i) k1 = k2 ii) k1 >> k2 (homework) [A] = [A]o e −k1t [B] ≈ [A]o e −k2t [C] ≈ [A]o (1 − e −k2t ) Conc. [A] [C] [B] Time B k2 C is the rate determining step 5.60 Spring 2008 iii) Lecture #31 page 6 k1 << k2 [A] = [A]o e −k1t [B] ≈ k1 [A] k2 [C] ≈ [A]o − [A] Conc. [A] [C] [B] Time A k1 B is the rate limiting step