Fall 2009 -- ChE 612 – Class Problems #1 PROBLEM #1barat/ChE612_Fall...
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Fall 2009 -- ChE 612 – Class Problems #1 PROBLEM #1 The gas phase, non-elementary reaction A B + C is being studied in an isothermal (T = T o ), variable volume (piston/cylinder) reactor. The piston is being driven by a motor reducing the volume at a constant rate V = V o (1- γt). The kinetics are actually pressure dependent such that –r A = kC A where k = k o P. The initial charge consists of pure A filled to initial pressure and volume of P o and V o , respectively. Data: P o = 30 torr γ = 0.05/sec T = 500 K V o = 1000 cm 3 k o = 10 -2 /sec-torr I) What time is required to reach a conversion X A of 90%? II) What are the corresponding P and V at that time? PROBLEM #2 The elementary, gas phase reaction A + B D is done in the fixed volume, semi-batch reactor shown below. A constant, B enters into the reactor starting at t = 0 at the slow flow rate of F B . The initial charge into the batch reactor is pure A to a pressure of P o . Questions I) Write all the ODEs needed to find C A vs. time. Include all relevant initial conditions. II) Because of the initial charge is pure A, and B is being fed slowly, one can assume for at least short times that C A ≈ C Ao ≈ constant. Using this assumption, derive C B vs. t. III) Now, with C B vs. t as an approximation, estimate C A vs. t. Using this two-step process, we've uncoupled the problem (as an approximation, of course). IV) Extra Credit : Derive the total pressure P vs. time. M V = V o (1- γ t) P V F B
Transcript of Fall 2009 -- ChE 612 – Class Problems #1 PROBLEM #1barat/ChE612_Fall...
Fall 2009 -- ChE 612 – Class Problems #1
PROBLEM #1 The gas phase, non-elementary reaction A B + C is being studied in an isothermal (T = To), variable volume (piston/cylinder) reactor. The piston is being driven by a motor reducing the volume at a constant rate V = Vo(1- γt). The kinetics are actually pressure dependent such that –rA = kCA where k = ko P. The initial charge consists of pure A filled to initial pressure and volume of Po and Vo, respectively. Data: Po = 30 torr γ = 0.05/sec T = 500 K Vo = 1000 cm3 ko = 10-2/sec-torr I) What time is required to reach a conversion XA of 90%? II) What are the corresponding P and V at that time? PROBLEM #2 The elementary, gas phase reaction A + B D is done in the fixed volume, semi-batch reactor shown below. A constant, B enters into the reactor starting at t = 0 at the slow flow rate of FB. The initial charge into the batch reactor is pure A to a pressure of Po.
Questions I) Write all the ODEs needed to find CA vs. time. Include all relevant initial conditions. II) Because of the initial charge is pure A, and B is being fed slowly, one can assume for
at least short times that CA ≈ CAo ≈ constant. Using this assumption, derive CB vs. t. III) Now, with CB vs. t as an approximation, estimate CA vs. t. Using this two-step
process, we've uncoupled the problem (as an approximation, of course). IV) Extra Credit: Derive the total pressure P vs. time.
M
V = V o(1- γt)
P
VFB
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Fall 2009 -- ChE 612 -- Homework #1
PROBLEMS FROM FOGLER TEXT (4TH ED.) # 3-17 # 4-12 #4-25 SUPPLEMENTARY PROBLEM The gas-phase dimerization reaction 2A B is to be tested in a constant-volume, isothermal (T = To) batch reactor.
P
FI
A drop in pressure with time is expected due to the reaction stoichiometry. However, we desire to run the reactor at constant pressure since this non-elementary reaction is expected to exhibit a pressure-dependent rate constant over the pressure range of this experiment. The rate expression is anticipated to be: rB = kPCA where k is a constant. The initial charge into the vessel is pure A to a pressure of Po. The pressure will be maintained at Po by flowing inert gas at a molar rate FI into the reactor. Questions:
I. Derive an expression for conversion XA vs. time t.
II. Derive an expression for FI vs. time t sufficient to maintain the pressure at Po. SHOW ALL YOUR WORK WITH DERIVATIONS – NO HANDWAVING! SOLUTIONS WILL BE POSTED AT: http://web.njit.edu/~barat
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