homework_Cao_section

homework_Cao_section - Homework for Yang Cao’s Section...

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Unformatted text preview: Homework for Yang Cao’s Section due on Oct 13th, 2011 1. Consider a set of chemical reactions given below /0 c → S 1 S 1 c 1 → /0 S 1 + S 1 c 2 ⇋ c 3 S 2 S 2 c 4 → /0 . (1) Write down the reaction rate equations. Describe what will happen when time goes to ∞ . Verify your description by showing a solution trajectory of this system in Matlab from t = 0 to t = 10 with the following parameters: c = 1000 , c 1 = 1 , c 2 = . 002 , c 3 = . 5 , c 4 = . 04 , and initial state x 1 ( ) = 10 , 000, x 2 ( ) = 0. 2. The Brusselator. The following hypothetical reaction mechanism was first pro- posed by Prigogine and Lefever, working in Brussels in 1968: A-→ X B + X-→ Y + D 2 X + Y-→ 3 X X-→ E (2) It is assumed that the concentrations of A, B, D and E are kept artificially con- stant, so that only X and Y vary with time. (a) Using the law of mass action, write the kinetic equations for d [ X ] / dt and d [ Y ] / dt ....
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homework_Cao_section - Homework for Yang Cao’s Section...

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