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ProblemSet7 - ChE 101 2012 Problem Set 7 Read Schmidt...

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ChE 101 2012 Problem Set 7 Read Schmidt Chapters 5 and 10 1. The steady-state approximation is not valid until the reactive intermediates approach their steady-state concentration. The time required for this to occur is called the relaxation time t r . Past the relaxation time, the steady-state approximation is normally satisfactory. Consider the reaction A k 1 -→ B k 2 -→ C Here B is the reactive intermediate. Let’s assume c B differs from its steady-state approxima- tion concentration c * B by an amount : c B = c * B (1 + ) (a) Assuming the feed is pure A , derive an expression for as a function of time. (b) What is lim t + ? (c) Plot the time dependence of for k 1 k 2 = 0 . 5 , 0 . 1 , 0 . 05 and k 2 = 0 . 1s - 1 . (d) The relaxation time is the time required for a quantity to decay to a fraction 1 e of its original value. If k 1 k 2 << 1, what is t r ? 2. The pyrolysis of acetaldehyde is believed to take place according to the following sequence CH 3 CHO k 1 -→ CH 3 · + CHO · CH 3 · + CH 3 CHO k 2 -→ CH 3 · + CO + CH 4 CHO · + CH 3 CHO k 3 -→ CH 3 · +2 CO + H 2 2 CH 3 · k 4 -→ C 2 H 6 (a) Identify the initiation, propagation, and termination steps.
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