quiz02_f06_soln

# quiz02_f06_soln - 10.34 - Quiz 2 Statistics Hi stogram 20...

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0 4 8 12 16 20 Frequency Average: 10.39 Std. Dev: 2.41 10.34 - Quiz 2 Statistics Histogram 0 to 3 3 to 5 5 to 7 7 to 9 9 to 11 11 to 13 13 to 15 Question Point Values: 1) 3 points 2) 6 points 3) 1 point 4) 2 points 5) 2 points 6) 1 point Total: 15 points Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

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10.34 Quiz 2 November 15, 2006 An isomerase (an enzyme that catalyzes an isomerization reaction) is used to convert a cheap unpalatable substrate S into its isomer, a delicious high-value product P called fructose (used to make soft drinks and candy). The enzyme reaction is expected to follow the Michaelis-Menton rate law: P S [] − [ ] Rn V = K eq = moles S P Eq.(1) Em [] K + S sec m where V m and K m depend on the enzyme, and K eq is for the equilibrium S=P, and n E is the moles of enzyme in the reactor. Note that throughout the isomerization process [S]+[P] = constant. We therefore suggest you use the dimensionless concentration C = [Substrate]/[Substrate] o rather than tracking S and P separately. 1) Simulate the batch conversion of S into P by writing a couple of short Matlab functions. Your Matlab functions should take [S] o , n E , V, Km, and Keq as inputs. Feel free to call any built-in Matlab functions. A microreactor for accomplishing this process continuously is constructed this way: a coating of the isomerase is chemically bonded to two flat plates. The coating density is 10 -11 moles enzyme/cm 2 . The two plates are then bonded to a thin spacer, to create a very thin channel (gap between the plates Y=0.01 cm (0.005 cm from the centerline to the wall), length X=5 cm, width of channel Z=2 cm), see figure. Inside the channel, flow can be accurately modeled as being laminar and two-dimensional, i.e. we only need to be concerned about gradients in x and y directions, not z, don’t worry about what happens close to z=0 or z=Z. The enzyme’s substrate, initial concentration [S] o is flowed at a rate of 0.1 ml/second through the channel from x=0, and the output stream (hopefully rich in product P) exits at x=X.
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## This note was uploaded on 11/27/2011 for the course CHEMICAL E 10.302 taught by Professor Clarkcolton during the Fall '04 term at MIT.

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quiz02_f06_soln - 10.34 - Quiz 2 Statistics Hi stogram 20...

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