CHE 304 (Spring 2010)
__________________
LAST NAME, FIRST
Problem set #2
(1) 1
For a first-order reaction, the following rate coefficients were found:
Temperature, °C
38.5
53.1
77.9
k, h-1
0.044
0.301
1.665
Determine the activation energy of the reaction in kJ/mol.
(2)2 There are two reactors of equal volume available for your use: one a CSTR, the other a PFR.
The reaction is second order ( rA = kCA2 = kCA02(1  X)2), irreversible, and is carried out
isothermally
AB
There are three ways you can arrange your system:
(a) Reactors in series: CSTR followed by PFR
(b) Reactors in series: PFR followed by CSTR
(c) Reactors in parallel with half the feed rate going to each reactor after which the exit
streams are mixed.
(d) State which system will give the highest overall conversion and which system will
give the lowest overall conversion.
Note: Rearrange the mass balance equation to the form that contains the term
FA0
. Let
VkC A2 0
FA0
= 1 and solve for the fractional conversion.
VkC A2 0
1
2
G.F. Froment, K.B. Bischoff, J. De Wilde, Chemical Reactor Analysis and Design, Prentice Hall, 2010
Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall, 1999
(3)1 The exothermic reaction
AB+C
was carried out adiabatically and the following data recorded:
X
 rA mol/Lmin
0
10
0.2
16.67
0.4
50
0.5
50
0.6
50
0.8
12.5
0.9
9.09
The entering molar flow rate of A was 300 mol/min.
(a)
(b)
(c)
(d)
(e)
(f)
What are the PFR and CSTR volumes necessary to achieve 40% conversion?
Over what range of conversions would the CSTR and PFR reactor volumes be identical?
What conversion can be achieved in a 10.5 L CSTR?
What conversion can be achieved if a 7.2 L PFR is followed in series by a 2.4 L CSTR?
What conversion can be achieved if a 2.4 L CSTRR is followed in series by a 7.2 L PFR?
Plot the conversion and rate of reaction as a function of PFR reactor volume up to a
volume of 10 L.
(4)3 Consider an ideal batch reactor with the irreversible homogeneous reaction
A + 2B  3C + D
This liquid phase reaction has the rate equation
− rA = kCA2CB CD-1
The reaction rate constant is k = 1.5 L/mol∙hr at 350oK. The activation energy of the reaction is
100 kJ/mol. The initial concentrations are: CA0 = 2.0 mol/L, CB0 = 4.0 mol/L, CC0 = 0 mol/L, and
CD0 = 1.0 mol/L. We will neglect any reaction that takes place while the initial charge is being
added to the reactor, and while the reactor and contents are being heated to reaction temperature.
(a) How much time is required for the concentration of A to reach 0.10 mol/L if the reactor
run isothermally at 350oK? What is the concentration of C at this time?
(b) The reactor will be run isothermally at 350oK. The concentration of A in the final product
must be less than 0.20 mol/L, and the molecular weight of C is 125. An average of 10
hours is required between the batches in order to empty and clean the reactor, and prepare
for the next batch. How large must the reactor be in order to produce 200,000 kg of C
annually (with 8000 hours per year of operation)?
(c) We want to produce 200,000 kg of C annually, with a final concentration of A of 0.20
mol/L or less. The only reactor available has a working volume of 1400 L. At what
temperature does the reactor have to be operated, if it is operated isothermally? Once
again, an average of 10 hours is required between batches to empty and clean the reactor,
and to prepare for the next batch.
3
Roberts, G. W., Chemical Reactions and Chemical Reactors, Wiley, 2006
(5) The elementary gas-phase reaction3
(CH3)3COOH(CH3)3  C2H6 + 2CH3COCH3
is carried out isothermally in a flow reactor with no pressure drop. The specific reaction rate at
50oC is 10-4 min-1 and the activation energy is 85 kJ/mol. Pure di-tert-butyl peroxide enters the
reactor at 10 atm and 127oC and a molar flow rate of 4.0 mol/min. Calculate the reactor volume
to achieve 90% conversion in a CSTR and a PFR.
If this reaction is to be carried out at 10 atm and 127oC in a batch mode with 95% conversion,
what reactor size would be required to process (2.5 mol/min  60 min/h  24 h/day) 3600 mol of
di-tert-butyl peroxide per day? You can assume a downtime of 6 hr between batches for cleaning
and feed preparation.
Assume that the reaction is reversible with equilibrium constant KC = 0.025 mol2/L6 and
calculate the equilibrium conversion and then repeat the calculation for the CSTR and the PFR to
achieve 95% of the equilibrium conversion.
(6)4 Equilibrium with respect to the reaction
A(g) + B(g) = C(g)
will be studied by measuring the volume change accompany the reaction. The temperature and
pressure are held constant and the initial volume and the final volume of the reacting system are
recorded. Three tested were made and are summarized in the table. Has equilibrium been
established? If so what is the value of K?
P(mmHg)
500
600
600
yA
0.5
0.333
0
Initial composition
yB
yC
0.5
0
0.667
0
0
1.0
Volume (cm3)
Initial
Final
200
150
300
233
200
293
(7) Run Murder Mystery (http://www.engin.umich.edu/~cre/icm/cre.html)
Click on the CHE 304 distribution folder, then copy the Heat1 Murder folder to your flash
drive or H:\ drive. Open this folder and click on the appropriate program name (Murder
Mystery.exe). Turn in the last page of the program with performance number.
3
4
Fogler, H. S., Elements of Chemical Reaction Engineering, Prentice Hall
Kyle, B.G., Chemical and Process Thermodynamics, Prentice Hall, 1999