ex1_rev_03212007 - 10.37 Chemical and Biological Reaction...

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10.37 Chemical and Biological Reaction Engineering, Spring 2007 Exam 1 Review In-Out+Production=Accumulation Accumulation=0 at steady state 0 0 AA A FF r V −+ = [ ] 00 0 A FA ν = [ ] A F A = For a liquid phase with constant density: 0 = For A B the reaction moles are the same, so 0 = For 2 A B , 0 [] ξ = moles (extent of reaction) (-) for a reactant and (+) for a product 0, 1 rxns N ii i n n NN n υξ = =+ Suppose A BC →+ 0 0 A A A A X N = () 0 1 A X =− Thermodynamics Suppose 1 1 2 k k A + ZZZX YZZZ GRT e Ke Δ = ,, f products f reactants GG G ΔΔ °° [ ][ ] c B C K A = has units. You need to use standard states, such as 1M, to make it dimensionless. Enzyme Catalysis Reaction Progress Energy S P with enzyme without enzyme Figure 1. Energy diagram for a reaction with and without enzyme. Cite as: William Green, Jr., and K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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ES + U E S E SE →+ P Pseudo steady state approximation: [ ] dE S = 0 dt [ ES ] = f () other species Cell Growth # cells N = volume NN = t 0 e μ Monod kinetics: [ ] [] max S = KS S + Δ A Y A = B B Rate Constants kT = Ae ER a T Given k 1 and k 2 , you can calculate k and a different temperature. CSTRs FX V = A 0 A r A If the reaction is 1 st order and it consists of liq ds with constant density: Incorporates changing volumetric flow rate ui X τ = A kX (1 A ) V volume == ν volumetric flow rate 0 k X A = 1 + k Da = k =Damköhler number: ratio of kinetic effect to volumetric effect or ratio of reaction rate to dilution rate 2 nd order reaction: 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Exam1 Review Page 2 of 10 Cite as: William Green, Jr., and K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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() X τ = A kC 1 2 AA 0 X Da = kC A 0 12 +− Da 14 + Da X A = 2 Da For constant density and 1 st order reaction: dN FF A 0 −+ r A V = dt dC CC A 0 r A ττ = dt Let: ˆ C A t Ct A == ˆ C A 0 Nondimesionalize: dC ˆ A ++ (1 Da ) C ˆ 1 dt ˆ A = Solve given ˆ 00 at A ˆ 1 Ce ˆ 1 (1 Dat ) ˆ A =− 1 + Da Tanks in series: 1 st order reaction C C A ,0 An , = 1 + Da n Reactor Design Equations CSTR: FX V = A 0 A r A Batch: dN rV A = A dt NV = [ A ]
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ex1_rev_03212007 - 10.37 Chemical and Biological Reaction...

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