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

1

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

1

2

3

4

5

6