Seoul national university kinetics 33 another

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Unformatted text preview: 1 k 2 [C ] k1[ A] 1 1 dt k 1 k 2 k -1 kk k1 [ A] -1 2 [C ] -1 k -1 k 2 k -1 k 2 k1 [ A] k 2 [C ] Look slik ea f irst order reversiblereaction Solid State Ionics Research Lab. Seoul National University Kinetics 3.4 Concurrent Reaction k1 A B A C k2 k3 A D d[ A] (k 1 k 2 k 3 )[A] k[ A] dt - Integrating, [ A ] [ A ]0 e kt d[B] k 1A 0e kt dt k1 k1 kt [B] [ A ]0 e [B]0 [ A ]0 k k k [B]0 1 [ A ]0 (1 e kt ) k Solid State Ionics Research Lab. -Similarly k2 [ A]0 (1 e kt ) k k [D] [D]0 3 [ A]0 (1 e kt ) k [C] [C]0 Seoul National University Kinetics 3.5 The principle of detailed balance A L. Onsager, Phys. Rev., 37 (1931) 405; 38 (1931) 2265 k6 k2 k5 B k1 k3 C k4 k1 B at equilibrium, A k2 d[ A] d[B] d[ A] 0 or k 1[ A] k 2 [B] 0 dt dt dt The kinetic definition of equail. The condition for equilibrium should be distinguished by i) No change with time ii) The principle of detailed balance must be obeyed. d[ A] 0 k 1[ A ] k 2 [ B ] dt Solid State Ionics Research Lab. Seoul National University (optional) Kinetics d[ A] (k 1 k 6 )[A]e k 5 [B]e k 2 [C]e 0 dt d[B] k 6 [ A]e (k 4 k 5 )[B]e k 3 [C]e 0 dt d[C] k 1[ A]e k 4 [B]e (k 2 k 3 )[C]e 0 dt -For [A], [B], [C] has nonzero values : ( k1 k6 ) k5 k2 k6 ( k4 k5 ) k3 k1 k4 (k2 k3 ) 0 k k k 1k 5 k 4k 6 [B]e 14 [ A] k 2k 4 k 2k 5 k 3k 5 e [C]e k k k 2k 6 k 3k 6 13 [ A]e k 2k 4 k 2k 5 k 3k 5 Solid State Ionics Research Lab. Seoul National University Kinetics -Now the principle of detailed balance → Each individual step must also be in equilibrium or equilibrium must be obtained for each individual path [ B ]e k1 [C ]e k6 [ B ]e k4 ; ; [ A]e k2 [ A]e k5 [C ]e k3 k1k3k5 k2 k4 k6 Thus k 4k 6 k4 k5 [B]e k 1 k1 k1 k 3k 5 k 2 [ A ]e k 2 k4 k5 k2 Equilibrium condition of each individual path Overall equilibrium criteria Solid State Ionics Research Lab. Seoul National University (optional) Kinetics 4. Diffusion–controlled reactions 4.1 Overall rate constant - Consider a reaction A+B→AB in a condensed phase, say, liquid. A B A and B transported through the solvent by diffusion. Much time to react to form a product P ⇒ The overall reaction may be controlled by diffusion. cf) Reactions in gas phase ; Transport provides no problem. Solid State Ionics Research Lab. Seoul National University Kinetics - Example A B kd AB A & B approached to each other kd ' AB A B A & B in contact departed or AB k P ( product ) d AB dt A & B in contact reacted kd A B kd AB k AB Assuming a s teady s tate, kd dAB AB 0 Then AB k dt kd and t...
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